Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(739,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.e (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: | \(8.86339462436\) |
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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 739.2 | ||
Root | \(-1.32920 + 1.32920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.739 |
Dual form | 1110.2.e.d.739.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.32920 | + | 1.79812i | −0.594434 | + | 0.804144i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | − | 1.87266i | − | 0.707799i | −0.935283 | − | 0.353900i | \(-0.884855\pi\) | ||
0.935283 | − | 0.353900i | \(-0.115145\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.32920 | + | 1.79812i | −0.420328 | + | 0.568616i | ||||
\(11\) | −1.51044 | −0.455413 | −0.227707 | − | 0.973730i | \(-0.573123\pi\) | ||||
−0.227707 | + | 0.973730i | \(0.573123\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 4.78011 | 1.32576 | 0.662882 | − | 0.748724i | \(-0.269333\pi\) | ||||
0.662882 | + | 0.748724i | \(0.269333\pi\) | |||||||
\(14\) | − | 1.87266i | − | 0.500490i | ||||||
\(15\) | 1.79812 | + | 1.32920i | 0.464273 | + | 0.343197i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.99190 | 0.968179 | 0.484089 | − | 0.875018i | \(-0.339151\pi\) | ||||
0.484089 | + | 0.875018i | \(0.339151\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | − | 4.68621i | − | 1.07509i | −0.843235 | − | 0.537545i | \(-0.819352\pi\) | ||
0.843235 | − | 0.537545i | \(-0.180648\pi\) | |||||||
\(20\) | −1.32920 | + | 1.79812i | −0.297217 | + | 0.402072i | ||||
\(21\) | −1.87266 | −0.408648 | ||||||||
\(22\) | −1.51044 | −0.322026 | ||||||||
\(23\) | 6.51179 | 1.35780 | 0.678901 | − | 0.734230i | \(-0.262457\pi\) | ||||
0.678901 | + | 0.734230i | \(0.262457\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −1.46648 | − | 4.78011i | −0.293296 | − | 0.956022i | ||||
\(26\) | 4.78011 | 0.937456 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 1.87266i | − | 0.353900i | ||||||
\(29\) | − | 0.200007i | − | 0.0371403i | −0.999828 | − | 0.0185702i | \(-0.994089\pi\) | ||
0.999828 | − | 0.0185702i | \(-0.00591141\pi\) | |||||||
\(30\) | 1.79812 | + | 1.32920i | 0.328291 | + | 0.242677i | ||||
\(31\) | − | 5.79625i | − | 1.04104i | −0.853850 | − | 0.520519i | \(-0.825739\pi\) | ||
0.853850 | − | 0.520519i | \(-0.174261\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.51044i | 0.262933i | ||||||||
\(34\) | 3.99190 | 0.684606 | ||||||||
\(35\) | 3.36727 | + | 2.48913i | 0.569173 | + | 0.420740i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 6.03820 | + | 0.734967i | 0.992673 | + | 0.120828i | ||||
\(38\) | − | 4.68621i | − | 0.760203i | ||||||
\(39\) | − | 4.78011i | − | 0.765430i | ||||||
\(40\) | −1.32920 | + | 1.79812i | −0.210164 | + | 0.284308i | ||||
\(41\) | 4.10248 | 0.640700 | 0.320350 | − | 0.947299i | \(-0.396199\pi\) | ||||
0.320350 | + | 0.947299i | \(0.396199\pi\) | |||||||
\(42\) | −1.87266 | −0.288958 | ||||||||
\(43\) | −10.9236 | −1.66583 | −0.832916 | − | 0.553399i | \(-0.813330\pi\) | ||||
−0.832916 | + | 0.553399i | \(0.813330\pi\) | |||||||
\(44\) | −1.51044 | −0.227707 | ||||||||
\(45\) | 1.32920 | − | 1.79812i | 0.198145 | − | 0.268048i | ||||
\(46\) | 6.51179 | 0.960110 | ||||||||
\(47\) | − | 5.15269i | − | 0.751596i | −0.926702 | − | 0.375798i | \(-0.877369\pi\) | ||
0.926702 | − | 0.375798i | \(-0.122631\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 3.49314 | 0.499020 | ||||||||
\(50\) | −1.46648 | − | 4.78011i | −0.207392 | − | 0.676009i | ||||
\(51\) | − | 3.99190i | − | 0.558978i | ||||||
\(52\) | 4.78011 | 0.662882 | ||||||||
\(53\) | 2.22232i | 0.305259i | 0.988284 | + | 0.152629i | \(0.0487740\pi\) | ||||
−0.988284 | + | 0.152629i | \(0.951226\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 2.00766 | − | 2.71595i | 0.270713 | − | 0.366218i | ||||
\(56\) | − | 1.87266i | − | 0.250245i | ||||||
\(57\) | −4.68621 | −0.620703 | ||||||||
\(58\) | − | 0.200007i | − | 0.0262622i | ||||||
\(59\) | 13.2646i | 1.72690i | 0.504435 | + | 0.863450i | \(0.331701\pi\) | ||||
−0.504435 | + | 0.863450i | \(0.668299\pi\) | |||||||
\(60\) | 1.79812 | + | 1.32920i | 0.232136 | + | 0.171598i | ||||
\(61\) | − | 4.09616i | − | 0.524459i | −0.965005 | − | 0.262230i | \(-0.915542\pi\) | ||
0.965005 | − | 0.262230i | \(-0.0844578\pi\) | |||||||
\(62\) | − | 5.79625i | − | 0.736124i | ||||||
\(63\) | 1.87266i | 0.235933i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.35370 | + | 8.59521i | −0.788079 | + | 1.06611i | ||||
\(66\) | 1.51044i | 0.185922i | ||||||||
\(67\) | − | 5.76584i | − | 0.704410i | −0.935923 | − | 0.352205i | \(-0.885432\pi\) | ||
0.935923 | − | 0.352205i | \(-0.114568\pi\) | |||||||
\(68\) | 3.99190 | 0.484089 | ||||||||
\(69\) | − | 6.51179i | − | 0.783927i | ||||||
\(70\) | 3.36727 | + | 2.48913i | 0.402466 | + | 0.297508i | ||||
\(71\) | −9.17428 | −1.08879 | −0.544393 | − | 0.838830i | \(-0.683240\pi\) | ||||
−0.544393 | + | 0.838830i | \(0.683240\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.2905i | 1.67257i | 0.548294 | + | 0.836286i | \(0.315278\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684722\pi\) | |||||||
\(74\) | 6.03820 | + | 0.734967i | 0.701926 | + | 0.0854382i | ||||
\(75\) | −4.78011 | + | 1.46648i | −0.551959 | + | 0.169334i | ||||
\(76\) | − | 4.68621i | − | 0.537545i | ||||||
\(77\) | 2.82853i | 0.322341i | ||||||||
\(78\) | − | 4.78011i | − | 0.541241i | ||||||
\(79\) | 5.95465i | 0.669950i | 0.942227 | + | 0.334975i | \(0.108728\pi\) | ||||
−0.942227 | + | 0.334975i | \(0.891272\pi\) | |||||||
\(80\) | −1.32920 | + | 1.79812i | −0.148609 | + | 0.201036i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.10248 | 0.453044 | ||||||||
\(83\) | − | 9.42048i | − | 1.03403i | −0.855976 | − | 0.517016i | \(-0.827043\pi\) | ||
0.855976 | − | 0.517016i | \(-0.172957\pi\) | |||||||
\(84\) | −1.87266 | −0.204324 | ||||||||
\(85\) | −5.30602 | + | 7.17793i | −0.575519 | + | 0.778556i | ||||
\(86\) | −10.9236 | −1.17792 | ||||||||
\(87\) | −0.200007 | −0.0214430 | ||||||||
\(88\) | −1.51044 | −0.161013 | ||||||||
\(89\) | 5.47289i | 0.580126i | 0.957008 | + | 0.290063i | \(0.0936762\pi\) | ||||
−0.957008 | + | 0.290063i | \(0.906324\pi\) | |||||||
\(90\) | 1.32920 | − | 1.79812i | 0.140109 | − | 0.189539i | ||||
\(91\) | − | 8.95152i | − | 0.938375i | ||||||
\(92\) | 6.51179 | 0.678901 | ||||||||
\(93\) | −5.79625 | −0.601043 | ||||||||
\(94\) | − | 5.15269i | − | 0.531459i | ||||||
\(95\) | 8.42637 | + | 6.22888i | 0.864527 | + | 0.639070i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 2.03303 | 0.206423 | 0.103211 | − | 0.994659i | \(-0.467088\pi\) | ||||
0.103211 | + | 0.994659i | \(0.467088\pi\) | |||||||
\(98\) | 3.49314 | 0.352860 | ||||||||
\(99\) | 1.51044 | 0.151804 | ||||||||
\(100\) | −1.46648 | − | 4.78011i | −0.146648 | − | 0.478011i | ||||
\(101\) | −9.70730 | −0.965913 | −0.482956 | − | 0.875644i | \(-0.660437\pi\) | ||||
−0.482956 | + | 0.875644i | \(0.660437\pi\) | |||||||
\(102\) | − | 3.99190i | − | 0.395257i | ||||||
\(103\) | −2.66390 | −0.262482 | −0.131241 | − | 0.991351i | \(-0.541896\pi\) | ||||
−0.131241 | + | 0.991351i | \(0.541896\pi\) | |||||||
\(104\) | 4.78011 | 0.468728 | ||||||||
\(105\) | 2.48913 | − | 3.36727i | 0.242914 | − | 0.328612i | ||||
\(106\) | 2.22232i | 0.215850i | ||||||||
\(107\) | − | 0.823199i | − | 0.0795816i | −0.999208 | − | 0.0397908i | \(-0.987331\pi\) | ||
0.999208 | − | 0.0397908i | \(-0.0126692\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 0.478427i | 0.0458250i | 0.999737 | + | 0.0229125i | \(0.00729391\pi\) | ||||
−0.999737 | + | 0.0229125i | \(0.992706\pi\) | |||||||
\(110\) | 2.00766 | − | 2.71595i | 0.191423 | − | 0.258955i | ||||
\(111\) | 0.734967 | − | 6.03820i | 0.0697600 | − | 0.573120i | ||||
\(112\) | − | 1.87266i | − | 0.176950i | ||||||
\(113\) | 19.8469 | 1.86704 | 0.933522 | − | 0.358521i | \(-0.116719\pi\) | ||||
0.933522 | + | 0.358521i | \(0.116719\pi\) | |||||||
\(114\) | −4.68621 | −0.438903 | ||||||||
\(115\) | −8.65543 | + | 11.7090i | −0.807123 | + | 1.09187i | ||||
\(116\) | − | 0.200007i | − | 0.0185702i | ||||||
\(117\) | −4.78011 | −0.441921 | ||||||||
\(118\) | 13.2646i | 1.22110i | ||||||||
\(119\) | − | 7.47548i | − | 0.685277i | ||||||
\(120\) | 1.79812 | + | 1.32920i | 0.164145 | + | 0.121338i | ||||
\(121\) | −8.71858 | −0.792599 | ||||||||
\(122\) | − | 4.09616i | − | 0.370849i | ||||||
\(123\) | − | 4.10248i | − | 0.369909i | ||||||
\(124\) | − | 5.79625i | − | 0.520519i | ||||||
\(125\) | 10.5445 | + | 3.71679i | 0.943124 | + | 0.332440i | ||||
\(126\) | 1.87266i | 0.166830i | ||||||||
\(127\) | − | 6.85655i | − | 0.608420i | −0.952605 | − | 0.304210i | \(-0.901608\pi\) | ||
0.952605 | − | 0.304210i | \(-0.0983925\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.9236i | 0.961769i | ||||||||
\(130\) | −6.35370 | + | 8.59521i | −0.557256 | + | 0.753850i | ||||
\(131\) | 3.26950i | 0.285658i | 0.989747 | + | 0.142829i | \(0.0456198\pi\) | ||||
−0.989747 | + | 0.142829i | \(0.954380\pi\) | |||||||
\(132\) | 1.51044i | 0.131467i | ||||||||
\(133\) | −8.77568 | −0.760948 | ||||||||
\(134\) | − | 5.76584i | − | 0.498093i | ||||||
\(135\) | −1.79812 | − | 1.32920i | −0.154758 | − | 0.114399i | ||||
\(136\) | 3.99190 | 0.342303 | ||||||||
\(137\) | − | 2.11793i | − | 0.180947i | −0.995899 | − | 0.0904733i | \(-0.971162\pi\) | ||
0.995899 | − | 0.0904733i | \(-0.0288380\pi\) | |||||||
\(138\) | − | 6.51179i | − | 0.554320i | ||||||
\(139\) | −15.7132 | −1.33277 | −0.666387 | − | 0.745606i | \(-0.732160\pi\) | ||||
−0.666387 | + | 0.745606i | \(0.732160\pi\) | |||||||
\(140\) | 3.36727 | + | 2.48913i | 0.284586 | + | 0.210370i | ||||
\(141\) | −5.15269 | −0.433934 | ||||||||
\(142\) | −9.17428 | −0.769889 | ||||||||
\(143\) | −7.22005 | −0.603771 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0.359637 | + | 0.265848i | 0.0298662 | + | 0.0220775i | ||||
\(146\) | 14.2905i | 1.18269i | ||||||||
\(147\) | − | 3.49314i | − | 0.288109i | ||||||
\(148\) | 6.03820 | + | 0.734967i | 0.496337 | + | 0.0604139i | ||||
\(149\) | −4.47152 | −0.366321 | −0.183161 | − | 0.983083i | \(-0.558633\pi\) | ||||
−0.183161 | + | 0.983083i | \(0.558633\pi\) | |||||||
\(150\) | −4.78011 | + | 1.46648i | −0.390294 | + | 0.119738i | ||||
\(151\) | 3.25118 | 0.264577 | 0.132289 | − | 0.991211i | \(-0.457767\pi\) | ||||
0.132289 | + | 0.991211i | \(0.457767\pi\) | |||||||
\(152\) | − | 4.68621i | − | 0.380101i | ||||||
\(153\) | −3.99190 | −0.322726 | ||||||||
\(154\) | 2.82853i | 0.227930i | ||||||||
\(155\) | 10.4224 | + | 7.70435i | 0.837144 | + | 0.618828i | ||||
\(156\) | − | 4.78011i | − | 0.382715i | ||||||
\(157\) | 0.0713960i | 0.00569802i | 0.999996 | + | 0.00284901i | \(0.000906870\pi\) | ||||
−0.999996 | + | 0.00284901i | \(0.999093\pi\) | |||||||
\(158\) | 5.95465i | 0.473726i | ||||||||
\(159\) | 2.22232 | 0.176241 | ||||||||
\(160\) | −1.32920 | + | 1.79812i | −0.105082 | + | 0.142154i | ||||
\(161\) | − | 12.1944i | − | 0.961051i | ||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.06145 | 0.0831389 | 0.0415695 | − | 0.999136i | \(-0.486764\pi\) | ||||
0.0415695 | + | 0.999136i | \(0.486764\pi\) | |||||||
\(164\) | 4.10248 | 0.320350 | ||||||||
\(165\) | −2.71595 | − | 2.00766i | −0.211436 | − | 0.156296i | ||||
\(166\) | − | 9.42048i | − | 0.731171i | ||||||
\(167\) | −20.4097 | −1.57935 | −0.789673 | − | 0.613528i | \(-0.789750\pi\) | ||||
−0.789673 | + | 0.613528i | \(0.789750\pi\) | |||||||
\(168\) | −1.87266 | −0.144479 | ||||||||
\(169\) | 9.84944 | 0.757649 | ||||||||
\(170\) | −5.30602 | + | 7.17793i | −0.406953 | + | 0.550522i | ||||
\(171\) | 4.68621i | 0.358363i | ||||||||
\(172\) | −10.9236 | −0.832916 | ||||||||
\(173\) | 16.9195i | 1.28636i | 0.765713 | + | 0.643182i | \(0.222386\pi\) | ||||
−0.765713 | + | 0.643182i | \(0.777614\pi\) | |||||||
\(174\) | −0.200007 | −0.0151625 | ||||||||
\(175\) | −8.95152 | + | 2.74622i | −0.676672 | + | 0.207595i | ||||
\(176\) | −1.51044 | −0.113853 | ||||||||
\(177\) | 13.2646 | 0.997026 | ||||||||
\(178\) | 5.47289i | 0.410211i | ||||||||
\(179\) | 26.6575i | 1.99247i | 0.0866723 | + | 0.996237i | \(0.472377\pi\) | ||||
−0.0866723 | + | 0.996237i | \(0.527623\pi\) | |||||||
\(180\) | 1.32920 | − | 1.79812i | 0.0990724 | − | 0.134024i | ||||
\(181\) | −13.4428 | −0.999196 | −0.499598 | − | 0.866257i | \(-0.666519\pi\) | ||||
−0.499598 | + | 0.866257i | \(0.666519\pi\) | |||||||
\(182\) | − | 8.95152i | − | 0.663531i | ||||||
\(183\) | −4.09616 | −0.302797 | ||||||||
\(184\) | 6.51179 | 0.480055 | ||||||||
\(185\) | −9.34750 | + | 9.88049i | −0.687242 | + | 0.726428i | ||||
\(186\) | −5.79625 | −0.425002 | ||||||||
\(187\) | −6.02951 | −0.440922 | ||||||||
\(188\) | − | 5.15269i | − | 0.375798i | ||||||
\(189\) | 1.87266 | 0.136216 | ||||||||
\(190\) | 8.42637 | + | 6.22888i | 0.611313 | + | 0.451891i | ||||
\(191\) | − | 6.76465i | − | 0.489473i | −0.969590 | − | 0.244736i | \(-0.921299\pi\) | ||
0.969590 | − | 0.244736i | \(-0.0787014\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 15.4592 | 1.11278 | 0.556389 | − | 0.830922i | \(-0.312186\pi\) | ||||
0.556389 | + | 0.830922i | \(0.312186\pi\) | |||||||
\(194\) | 2.03303 | 0.145963 | ||||||||
\(195\) | 8.59521 | + | 6.35370i | 0.615516 | + | 0.454998i | ||||
\(196\) | 3.49314 | 0.249510 | ||||||||
\(197\) | − | 12.5068i | − | 0.891072i | −0.895264 | − | 0.445536i | \(-0.853013\pi\) | ||
0.895264 | − | 0.445536i | \(-0.146987\pi\) | |||||||
\(198\) | 1.51044 | 0.107342 | ||||||||
\(199\) | 13.4172i | 0.951119i | 0.879684 | + | 0.475559i | \(0.157754\pi\) | ||||
−0.879684 | + | 0.475559i | \(0.842246\pi\) | |||||||
\(200\) | −1.46648 | − | 4.78011i | −0.103696 | − | 0.338005i | ||||
\(201\) | −5.76584 | −0.406691 | ||||||||
\(202\) | −9.70730 | −0.683003 | ||||||||
\(203\) | −0.374545 | −0.0262879 | ||||||||
\(204\) | − | 3.99190i | − | 0.279489i | ||||||
\(205\) | −5.45300 | + | 7.37676i | −0.380854 | + | 0.515216i | ||||
\(206\) | −2.66390 | −0.185603 | ||||||||
\(207\) | −6.51179 | −0.452600 | ||||||||
\(208\) | 4.78011 | 0.331441 | ||||||||
\(209\) | 7.07821i | 0.489610i | ||||||||
\(210\) | 2.48913 | − | 3.36727i | 0.171766 | − | 0.232364i | ||||
\(211\) | 6.46040 | 0.444752 | 0.222376 | − | 0.974961i | \(-0.428619\pi\) | ||||
0.222376 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(212\) | 2.22232i | 0.152629i | ||||||||
\(213\) | 9.17428i | 0.628611i | ||||||||
\(214\) | − | 0.823199i | − | 0.0562727i | ||||||
\(215\) | 14.5196 | − | 19.6419i | 0.990228 | − | 1.33957i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −10.8544 | −0.736845 | ||||||||
\(218\) | 0.478427i | 0.0324031i | ||||||||
\(219\) | 14.2905 | 0.965660 | ||||||||
\(220\) | 2.00766 | − | 2.71595i | 0.135357 | − | 0.183109i | ||||
\(221\) | 19.0817 | 1.28358 | ||||||||
\(222\) | 0.734967 | − | 6.03820i | 0.0493278 | − | 0.405257i | ||||
\(223\) | 8.15634i | 0.546189i | 0.961987 | + | 0.273095i | \(0.0880472\pi\) | ||||
−0.961987 | + | 0.273095i | \(0.911953\pi\) | |||||||
\(224\) | − | 1.87266i | − | 0.125122i | ||||||
\(225\) | 1.46648 | + | 4.78011i | 0.0977653 | + | 0.318674i | ||||
\(226\) | 19.8469 | 1.32020 | ||||||||
\(227\) | 13.0456 | 0.865866 | 0.432933 | − | 0.901426i | \(-0.357479\pi\) | ||||
0.432933 | + | 0.901426i | \(0.357479\pi\) | |||||||
\(228\) | −4.68621 | −0.310352 | ||||||||
\(229\) | 13.3621 | 0.882995 | 0.441498 | − | 0.897262i | \(-0.354447\pi\) | ||||
0.441498 | + | 0.897262i | \(0.354447\pi\) | |||||||
\(230\) | −8.65543 | + | 11.7090i | −0.570722 | + | 0.772067i | ||||
\(231\) | 2.82853 | 0.186104 | ||||||||
\(232\) | − | 0.200007i | − | 0.0131311i | ||||||
\(233\) | − | 27.2277i | − | 1.78375i | −0.452283 | − | 0.891875i | \(-0.649390\pi\) | ||
0.452283 | − | 0.891875i | \(-0.350610\pi\) | |||||||
\(234\) | −4.78011 | −0.312485 | ||||||||
\(235\) | 9.26515 | + | 6.84893i | 0.604392 | + | 0.446775i | ||||
\(236\) | 13.2646i | 0.863450i | ||||||||
\(237\) | 5.95465 | 0.386796 | ||||||||
\(238\) | − | 7.47548i | − | 0.484564i | ||||||
\(239\) | 10.5417i | 0.681888i | 0.940084 | + | 0.340944i | \(0.110747\pi\) | ||||
−0.940084 | + | 0.340944i | \(0.889253\pi\) | |||||||
\(240\) | 1.79812 | + | 1.32920i | 0.116068 | + | 0.0857992i | ||||
\(241\) | 13.3732i | 0.861446i | 0.902484 | + | 0.430723i | \(0.141741\pi\) | ||||
−0.902484 | + | 0.430723i | \(0.858259\pi\) | |||||||
\(242\) | −8.71858 | −0.560452 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | − | 4.09616i | − | 0.262230i | ||||||
\(245\) | −4.64307 | + | 6.28109i | −0.296635 | + | 0.401284i | ||||
\(246\) | − | 4.10248i | − | 0.261565i | ||||||
\(247\) | − | 22.4006i | − | 1.42531i | ||||||
\(248\) | − | 5.79625i | − | 0.368062i | ||||||
\(249\) | −9.42048 | −0.596999 | ||||||||
\(250\) | 10.5445 | + | 3.71679i | 0.666890 | + | 0.235070i | ||||
\(251\) | 6.68149i | 0.421732i | 0.977515 | + | 0.210866i | \(0.0676283\pi\) | ||||
−0.977515 | + | 0.210866i | \(0.932372\pi\) | |||||||
\(252\) | 1.87266i | 0.117967i | ||||||||
\(253\) | −9.83563 | −0.618361 | ||||||||
\(254\) | − | 6.85655i | − | 0.430218i | ||||||
\(255\) | 7.17793 | + | 5.30602i | 0.449499 | + | 0.332276i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.63516 | −0.289133 | −0.144567 | − | 0.989495i | \(-0.546179\pi\) | ||||
−0.144567 | + | 0.989495i | \(0.546179\pi\) | |||||||
\(258\) | 10.9236i | 0.680073i | ||||||||
\(259\) | 1.37634 | − | 11.3075i | 0.0855219 | − | 0.702614i | ||||
\(260\) | −6.35370 | + | 8.59521i | −0.394040 | + | 0.533053i | ||||
\(261\) | 0.200007i | 0.0123801i | ||||||||
\(262\) | 3.26950i | 0.201990i | ||||||||
\(263\) | 29.5118i | 1.81977i | 0.414857 | + | 0.909887i | \(0.363832\pi\) | ||||
−0.414857 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(264\) | 1.51044i | 0.0929609i | ||||||||
\(265\) | −3.99599 | − | 2.95389i | −0.245472 | − | 0.181456i | ||||
\(266\) | −8.77568 | −0.538071 | ||||||||
\(267\) | 5.47289 | 0.334936 | ||||||||
\(268\) | − | 5.76584i | − | 0.352205i | ||||||
\(269\) | −21.3385 | −1.30103 | −0.650516 | − | 0.759493i | \(-0.725447\pi\) | ||||
−0.650516 | + | 0.759493i | \(0.725447\pi\) | |||||||
\(270\) | −1.79812 | − | 1.32920i | −0.109430 | − | 0.0808923i | ||||
\(271\) | 16.5121 | 1.00304 | 0.501521 | − | 0.865146i | \(-0.332774\pi\) | ||||
0.501521 | + | 0.865146i | \(0.332774\pi\) | |||||||
\(272\) | 3.99190 | 0.242045 | ||||||||
\(273\) | −8.95152 | −0.541771 | ||||||||
\(274\) | − | 2.11793i | − | 0.127949i | ||||||
\(275\) | 2.21502 | + | 7.22005i | 0.133571 | + | 0.435385i | ||||
\(276\) | − | 6.51179i | − | 0.391963i | ||||||
\(277\) | −11.0446 | −0.663605 | −0.331802 | − | 0.943349i | \(-0.607657\pi\) | ||||
−0.331802 | + | 0.943349i | \(0.607657\pi\) | |||||||
\(278\) | −15.7132 | −0.942414 | ||||||||
\(279\) | 5.79625i | 0.347012i | ||||||||
\(280\) | 3.36727 | + | 2.48913i | 0.201233 | + | 0.148754i | ||||
\(281\) | 17.9190i | 1.06896i | 0.845182 | + | 0.534478i | \(0.179492\pi\) | ||||
−0.845182 | + | 0.534478i | \(0.820508\pi\) | |||||||
\(282\) | −5.15269 | −0.306838 | ||||||||
\(283\) | −14.0543 | −0.835440 | −0.417720 | − | 0.908576i | \(-0.637171\pi\) | ||||
−0.417720 | + | 0.908576i | \(0.637171\pi\) | |||||||
\(284\) | −9.17428 | −0.544393 | ||||||||
\(285\) | 6.22888 | − | 8.42637i | 0.368967 | − | 0.499135i | ||||
\(286\) | −7.22005 | −0.426930 | ||||||||
\(287\) | − | 7.68256i | − | 0.453487i | ||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.06470 | −0.0626295 | ||||||||
\(290\) | 0.359637 | + | 0.265848i | 0.0211186 | + | 0.0156111i | ||||
\(291\) | − | 2.03303i | − | 0.119178i | ||||||
\(292\) | 14.2905i | 0.836286i | ||||||||
\(293\) | 32.2561i | 1.88442i | 0.335018 | + | 0.942212i | \(0.391258\pi\) | ||||
−0.335018 | + | 0.942212i | \(0.608742\pi\) | |||||||
\(294\) | − | 3.49314i | − | 0.203724i | ||||||
\(295\) | −23.8513 | − | 17.6312i | −1.38868 | − | 1.02653i | ||||
\(296\) | 6.03820 | + | 0.734967i | 0.350963 | + | 0.0427191i | ||||
\(297\) | − | 1.51044i | − | 0.0876444i | ||||||
\(298\) | −4.47152 | −0.259028 | ||||||||
\(299\) | 31.1270 | 1.80012 | ||||||||
\(300\) | −4.78011 | + | 1.46648i | −0.275980 | + | 0.0846672i | ||||
\(301\) | 20.4562i | 1.17908i | ||||||||
\(302\) | 3.25118 | 0.187084 | ||||||||
\(303\) | 9.70730i | 0.557670i | ||||||||
\(304\) | − | 4.68621i | − | 0.268772i | ||||||
\(305\) | 7.36539 | + | 5.44459i | 0.421741 | + | 0.311757i | ||||
\(306\) | −3.99190 | −0.228202 | ||||||||
\(307\) | − | 27.5771i | − | 1.57391i | −0.617012 | − | 0.786953i | \(-0.711657\pi\) | ||
0.617012 | − | 0.786953i | \(-0.288343\pi\) | |||||||
\(308\) | 2.82853i | 0.161171i | ||||||||
\(309\) | 2.66390i | 0.151544i | ||||||||
\(310\) | 10.4224 | + | 7.70435i | 0.591950 | + | 0.437578i | ||||
\(311\) | − | 13.8537i | − | 0.785570i | −0.919630 | − | 0.392785i | \(-0.871512\pi\) | ||
0.919630 | − | 0.392785i | \(-0.128488\pi\) | |||||||
\(312\) | − | 4.78011i | − | 0.270620i | ||||||
\(313\) | −24.3768 | −1.37786 | −0.688930 | − | 0.724828i | \(-0.741919\pi\) | ||||
−0.688930 | + | 0.724828i | \(0.741919\pi\) | |||||||
\(314\) | 0.0713960i | 0.00402911i | ||||||||
\(315\) | −3.36727 | − | 2.48913i | −0.189724 | − | 0.140247i | ||||
\(316\) | 5.95465i | 0.334975i | ||||||||
\(317\) | 8.91522i | 0.500729i | 0.968152 | + | 0.250364i | \(0.0805504\pi\) | ||||
−0.968152 | + | 0.250364i | \(0.919450\pi\) | |||||||
\(318\) | 2.22232 | 0.124621 | ||||||||
\(319\) | 0.302097i | 0.0169142i | ||||||||
\(320\) | −1.32920 | + | 1.79812i | −0.0743043 | + | 0.100518i | ||||
\(321\) | −0.823199 | −0.0459465 | ||||||||
\(322\) | − | 12.1944i | − | 0.679566i | ||||||
\(323\) | − | 18.7069i | − | 1.04088i | ||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.00993 | − | 22.8494i | −0.388841 | − | 1.26746i | ||||
\(326\) | 1.06145 | 0.0587881 | ||||||||
\(327\) | 0.478427 | 0.0264570 | ||||||||
\(328\) | 4.10248 | 0.226522 | ||||||||
\(329\) | −9.64923 | −0.531979 | ||||||||
\(330\) | −2.71595 | − | 2.00766i | −0.149508 | − | 0.110518i | ||||
\(331\) | − | 25.6563i | − | 1.41020i | −0.709109 | − | 0.705099i | \(-0.750903\pi\) | ||
0.709109 | − | 0.705099i | \(-0.249097\pi\) | |||||||
\(332\) | − | 9.42048i | − | 0.517016i | ||||||
\(333\) | −6.03820 | − | 0.734967i | −0.330891 | − | 0.0402760i | ||||
\(334\) | −20.4097 | −1.11677 | ||||||||
\(335\) | 10.3677 | + | 7.66393i | 0.566447 | + | 0.418725i | ||||
\(336\) | −1.87266 | −0.102162 | ||||||||
\(337\) | − | 18.5473i | − | 1.01033i | −0.863021 | − | 0.505167i | \(-0.831431\pi\) | ||
0.863021 | − | 0.505167i | \(-0.168569\pi\) | |||||||
\(338\) | 9.84944 | 0.535739 | ||||||||
\(339\) | − | 19.8469i | − | 1.07794i | ||||||
\(340\) | −5.30602 | + | 7.17793i | −0.287759 | + | 0.389278i | ||||
\(341\) | 8.75486i | 0.474102i | ||||||||
\(342\) | 4.68621i | 0.253401i | ||||||||
\(343\) | − | 19.6501i | − | 1.06101i | ||||||
\(344\) | −10.9236 | −0.588961 | ||||||||
\(345\) | 11.7090 | + | 8.65543i | 0.630390 | + | 0.465993i | ||||
\(346\) | 16.9195i | 0.909597i | ||||||||
\(347\) | −9.07304 | −0.487066 | −0.243533 | − | 0.969893i | \(-0.578306\pi\) | ||||
−0.243533 | + | 0.969893i | \(0.578306\pi\) | |||||||
\(348\) | −0.200007 | −0.0107215 | ||||||||
\(349\) | −31.1022 | −1.66486 | −0.832431 | − | 0.554129i | \(-0.813052\pi\) | ||||
−0.832431 | + | 0.554129i | \(0.813052\pi\) | |||||||
\(350\) | −8.95152 | + | 2.74622i | −0.478479 | + | 0.146792i | ||||
\(351\) | 4.78011i | 0.255143i | ||||||||
\(352\) | −1.51044 | −0.0805065 | ||||||||
\(353\) | −16.3289 | −0.869098 | −0.434549 | − | 0.900648i | \(-0.643092\pi\) | ||||
−0.434549 | + | 0.900648i | \(0.643092\pi\) | |||||||
\(354\) | 13.2646 | 0.705004 | ||||||||
\(355\) | 12.1944 | − | 16.4965i | 0.647212 | − | 0.875542i | ||||
\(356\) | 5.47289i | 0.290063i | ||||||||
\(357\) | −7.47548 | −0.395645 | ||||||||
\(358\) | 26.6575i | 1.40889i | ||||||||
\(359\) | 17.1135 | 0.903216 | 0.451608 | − | 0.892217i | \(-0.350851\pi\) | ||||
0.451608 | + | 0.892217i | \(0.350851\pi\) | |||||||
\(360\) | 1.32920 | − | 1.79812i | 0.0700547 | − | 0.0947693i | ||||
\(361\) | −2.96053 | −0.155817 | ||||||||
\(362\) | −13.4428 | −0.706538 | ||||||||
\(363\) | 8.71858i | 0.457607i | ||||||||
\(364\) | − | 8.95152i | − | 0.469187i | ||||||
\(365\) | −25.6960 | − | 18.9948i | −1.34499 | − | 0.994234i | ||||
\(366\) | −4.09616 | −0.214110 | ||||||||
\(367\) | − | 23.2045i | − | 1.21126i | −0.795745 | − | 0.605632i | \(-0.792920\pi\) | ||
0.795745 | − | 0.605632i | \(-0.207080\pi\) | |||||||
\(368\) | 6.51179 | 0.339450 | ||||||||
\(369\) | −4.10248 | −0.213567 | ||||||||
\(370\) | −9.34750 | + | 9.88049i | −0.485954 | + | 0.513662i | ||||
\(371\) | 4.16164 | 0.216062 | ||||||||
\(372\) | −5.79625 | −0.300522 | ||||||||
\(373\) | 9.69704i | 0.502094i | 0.967975 | + | 0.251047i | \(0.0807748\pi\) | ||||
−0.967975 | + | 0.251047i | \(0.919225\pi\) | |||||||
\(374\) | −6.02951 | −0.311779 | ||||||||
\(375\) | 3.71679 | − | 10.5445i | 0.191934 | − | 0.544513i | ||||
\(376\) | − | 5.15269i | − | 0.265729i | ||||||
\(377\) | − | 0.956055i | − | 0.0492393i | ||||||
\(378\) | 1.87266 | 0.0963193 | ||||||||
\(379\) | −9.40066 | −0.482880 | −0.241440 | − | 0.970416i | \(-0.577620\pi\) | ||||
−0.241440 | + | 0.970416i | \(0.577620\pi\) | |||||||
\(380\) | 8.42637 | + | 6.22888i | 0.432263 | + | 0.319535i | ||||
\(381\) | −6.85655 | −0.351272 | ||||||||
\(382\) | − | 6.76465i | − | 0.346109i | ||||||
\(383\) | 32.3874 | 1.65492 | 0.827459 | − | 0.561526i | \(-0.189785\pi\) | ||||
0.827459 | + | 0.561526i | \(0.189785\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −5.08605 | − | 3.75967i | −0.259209 | − | 0.191611i | ||||
\(386\) | 15.4592 | 0.786853 | ||||||||
\(387\) | 10.9236 | 0.555278 | ||||||||
\(388\) | 2.03303 | 0.103211 | ||||||||
\(389\) | − | 20.8774i | − | 1.05853i | −0.848457 | − | 0.529264i | \(-0.822468\pi\) | ||
0.848457 | − | 0.529264i | \(-0.177532\pi\) | |||||||
\(390\) | 8.59521 | + | 6.35370i | 0.435236 | + | 0.321732i | ||||
\(391\) | 25.9944 | 1.31459 | ||||||||
\(392\) | 3.49314 | 0.176430 | ||||||||
\(393\) | 3.26950 | 0.164925 | ||||||||
\(394\) | − | 12.5068i | − | 0.630083i | ||||||
\(395\) | −10.7072 | − | 7.91489i | −0.538737 | − | 0.398241i | ||||
\(396\) | 1.51044 | 0.0759022 | ||||||||
\(397\) | 12.2447i | 0.614546i | 0.951621 | + | 0.307273i | \(0.0994164\pi\) | ||||
−0.951621 | + | 0.307273i | \(0.900584\pi\) | |||||||
\(398\) | 13.4172i | 0.672543i | ||||||||
\(399\) | 8.77568i | 0.439333i | ||||||||
\(400\) | −1.46648 | − | 4.78011i | −0.0733240 | − | 0.239005i | ||||
\(401\) | − | 13.7736i | − | 0.687820i | −0.939003 | − | 0.343910i | \(-0.888248\pi\) | ||
0.939003 | − | 0.343910i | \(-0.111752\pi\) | |||||||
\(402\) | −5.76584 | −0.287574 | ||||||||
\(403\) | − | 27.7067i | − | 1.38017i | ||||||
\(404\) | −9.70730 | −0.482956 | ||||||||
\(405\) | −1.32920 | + | 1.79812i | −0.0660482 | + | 0.0893494i | ||||
\(406\) | −0.374545 | −0.0185884 | ||||||||
\(407\) | −9.12031 | − | 1.11012i | −0.452077 | − | 0.0550266i | ||||
\(408\) | − | 3.99190i | − | 0.197629i | ||||||
\(409\) | 34.5667i | 1.70921i | 0.519276 | + | 0.854606i | \(0.326202\pi\) | ||||
−0.519276 | + | 0.854606i | \(0.673798\pi\) | |||||||
\(410\) | −5.45300 | + | 7.37676i | −0.269305 | + | 0.364312i | ||||
\(411\) | −2.11793 | −0.104470 | ||||||||
\(412\) | −2.66390 | −0.131241 | ||||||||
\(413\) | 24.8400 | 1.22230 | ||||||||
\(414\) | −6.51179 | −0.320037 | ||||||||
\(415\) | 16.9392 | + | 12.5217i | 0.831511 | + | 0.614664i | ||||
\(416\) | 4.78011 | 0.234364 | ||||||||
\(417\) | 15.7132i | 0.769478i | ||||||||
\(418\) | 7.07821i | 0.346207i | ||||||||
\(419\) | 22.9413 | 1.12076 | 0.560378 | − | 0.828237i | \(-0.310656\pi\) | ||||
0.560378 | + | 0.828237i | \(0.310656\pi\) | |||||||
\(420\) | 2.48913 | − | 3.36727i | 0.121457 | − | 0.164306i | ||||
\(421\) | − | 12.1679i | − | 0.593026i | −0.955029 | − | 0.296513i | \(-0.904176\pi\) | ||
0.955029 | − | 0.296513i | \(-0.0958239\pi\) | |||||||
\(422\) | 6.46040 | 0.314487 | ||||||||
\(423\) | 5.15269i | 0.250532i | ||||||||
\(424\) | 2.22232i | 0.107925i | ||||||||
\(425\) | −5.85405 | − | 19.0817i | −0.283963 | − | 0.925600i | ||||
\(426\) | 9.17428i | 0.444495i | ||||||||
\(427\) | −7.67072 | −0.371212 | ||||||||
\(428\) | − | 0.823199i | − | 0.0397908i | ||||||
\(429\) | 7.22005i | 0.348587i | ||||||||
\(430\) | 14.5196 | − | 19.6419i | 0.700197 | − | 0.947219i | ||||
\(431\) | − | 11.2076i | − | 0.539853i | −0.962881 | − | 0.269927i | \(-0.913001\pi\) | ||
0.962881 | − | 0.269927i | \(-0.0869995\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 31.6559i | − | 1.52128i | −0.649172 | − | 0.760642i | \(-0.724884\pi\) | ||
0.649172 | − | 0.760642i | \(-0.275116\pi\) | |||||||
\(434\) | −10.8544 | −0.521028 | ||||||||
\(435\) | 0.265848 | − | 0.359637i | 0.0127464 | − | 0.0172433i | ||||
\(436\) | 0.478427i | 0.0229125i | ||||||||
\(437\) | − | 30.5156i | − | 1.45976i | ||||||
\(438\) | 14.2905 | 0.682824 | ||||||||
\(439\) | 33.9912i | 1.62231i | 0.584831 | + | 0.811155i | \(0.301161\pi\) | ||||
−0.584831 | + | 0.811155i | \(0.698839\pi\) | |||||||
\(440\) | 2.00766 | − | 2.71595i | 0.0957116 | − | 0.129478i | ||||
\(441\) | −3.49314 | −0.166340 | ||||||||
\(442\) | 19.0817 | 0.907626 | ||||||||
\(443\) | 34.9477i | 1.66042i | 0.557454 | + | 0.830208i | \(0.311778\pi\) | ||||
−0.557454 | + | 0.830208i | \(0.688222\pi\) | |||||||
\(444\) | 0.734967 | − | 6.03820i | 0.0348800 | − | 0.286560i | ||||
\(445\) | −9.84093 | − | 7.27454i | −0.466505 | − | 0.344846i | ||||
\(446\) | 8.15634i | 0.386214i | ||||||||
\(447\) | 4.47152i | 0.211496i | ||||||||
\(448\) | − | 1.87266i | − | 0.0884749i | ||||||
\(449\) | − | 17.2274i | − | 0.813012i | −0.913648 | − | 0.406506i | \(-0.866747\pi\) | ||
0.913648 | − | 0.406506i | \(-0.133253\pi\) | |||||||
\(450\) | 1.46648 | + | 4.78011i | 0.0691305 | + | 0.225336i | ||||
\(451\) | −6.19654 | −0.291784 | ||||||||
\(452\) | 19.8469 | 0.933522 | ||||||||
\(453\) | − | 3.25118i | − | 0.152754i | ||||||
\(454\) | 13.0456 | 0.612260 | ||||||||
\(455\) | 16.0959 | + | 11.8983i | 0.754589 | + | 0.557802i | ||||
\(456\) | −4.68621 | −0.219452 | ||||||||
\(457\) | 24.5044 | 1.14627 | 0.573133 | − | 0.819463i | \(-0.305728\pi\) | ||||
0.573133 | + | 0.819463i | \(0.305728\pi\) | |||||||
\(458\) | 13.3621 | 0.624372 | ||||||||
\(459\) | 3.99190i | 0.186326i | ||||||||
\(460\) | −8.65543 | + | 11.7090i | −0.403562 | + | 0.545934i | ||||
\(461\) | 9.05274i | 0.421628i | 0.977526 | + | 0.210814i | \(0.0676115\pi\) | ||||
−0.977526 | + | 0.210814i | \(0.932389\pi\) | |||||||
\(462\) | 2.82853 | 0.131595 | ||||||||
\(463\) | −2.10640 | −0.0978927 | −0.0489463 | − | 0.998801i | \(-0.515586\pi\) | ||||
−0.0489463 | + | 0.998801i | \(0.515586\pi\) | |||||||
\(464\) | − | 0.200007i | − | 0.00928509i | ||||||
\(465\) | 7.70435 | − | 10.4224i | 0.357281 | − | 0.483325i | ||||
\(466\) | − | 27.2277i | − | 1.26130i | ||||||
\(467\) | 24.0814 | 1.11435 | 0.557177 | − | 0.830394i | \(-0.311884\pi\) | ||||
0.557177 | + | 0.830394i | \(0.311884\pi\) | |||||||
\(468\) | −4.78011 | −0.220961 | ||||||||
\(469\) | −10.7975 | −0.498581 | ||||||||
\(470\) | 9.26515 | + | 6.84893i | 0.427370 | + | 0.315917i | ||||
\(471\) | 0.0713960 | 0.00328976 | ||||||||
\(472\) | 13.2646i | 0.610551i | ||||||||
\(473\) | 16.4994 | 0.758642 | ||||||||
\(474\) | 5.95465 | 0.273506 | ||||||||
\(475\) | −22.4006 | + | 6.87223i | −1.02781 | + | 0.315319i | ||||
\(476\) | − | 7.47548i | − | 0.342638i | ||||||
\(477\) | − | 2.22232i | − | 0.101753i | ||||||
\(478\) | 10.5417i | 0.482168i | ||||||||
\(479\) | 5.46224i | 0.249576i | 0.992183 | + | 0.124788i | \(0.0398251\pi\) | ||||
−0.992183 | + | 0.124788i | \(0.960175\pi\) | |||||||
\(480\) | 1.79812 | + | 1.32920i | 0.0820726 | + | 0.0606692i | ||||
\(481\) | 28.8632 | + | 3.51322i | 1.31605 | + | 0.160189i | ||||
\(482\) | 13.3732i | 0.609134i | ||||||||
\(483\) | −12.1944 | −0.554863 | ||||||||
\(484\) | −8.71858 | −0.396299 | ||||||||
\(485\) | −2.70229 | + | 3.65563i | −0.122705 | + | 0.165994i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 11.8494 | 0.536949 | 0.268475 | − | 0.963287i | \(-0.413480\pi\) | ||||
0.268475 | + | 0.963287i | \(0.413480\pi\) | |||||||
\(488\) | − | 4.09616i | − | 0.185424i | ||||||
\(489\) | − | 1.06145i | − | 0.0480003i | ||||||
\(490\) | −4.64307 | + | 6.28109i | −0.209752 | + | 0.283751i | ||||
\(491\) | −7.19955 | −0.324911 | −0.162456 | − | 0.986716i | \(-0.551941\pi\) | ||||
−0.162456 | + | 0.986716i | \(0.551941\pi\) | |||||||
\(492\) | − | 4.10248i | − | 0.184954i | ||||||
\(493\) | − | 0.798408i | − | 0.0359585i | ||||||
\(494\) | − | 22.4006i | − | 1.00785i | ||||||
\(495\) | −2.00766 | + | 2.71595i | −0.0902378 | + | 0.122073i | ||||
\(496\) | − | 5.79625i | − | 0.260259i | ||||||
\(497\) | 17.1803i | 0.770643i | ||||||||
\(498\) | −9.42048 | −0.422142 | ||||||||
\(499\) | − | 3.32481i | − | 0.148839i | −0.997227 | − | 0.0744194i | \(-0.976290\pi\) | ||
0.997227 | − | 0.0744194i | \(-0.0237104\pi\) | |||||||
\(500\) | 10.5445 | + | 3.71679i | 0.471562 | + | 0.166220i | ||||
\(501\) | 20.4097i | 0.911836i | ||||||||
\(502\) | 6.68149i | 0.298209i | ||||||||
\(503\) | −9.09539 | −0.405544 | −0.202772 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202772 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(504\) | 1.87266i | 0.0834150i | ||||||||
\(505\) | 12.9029 | − | 17.4549i | 0.574172 | − | 0.776733i | ||||
\(506\) | −9.83563 | −0.437247 | ||||||||
\(507\) | − | 9.84944i | − | 0.437429i | ||||||
\(508\) | − | 6.85655i | − | 0.304210i | ||||||
\(509\) | −12.7781 | −0.566380 | −0.283190 | − | 0.959064i | \(-0.591393\pi\) | ||||
−0.283190 | + | 0.959064i | \(0.591393\pi\) | |||||||
\(510\) | 7.17793 | + | 5.30602i | 0.317844 | + | 0.234955i | ||||
\(511\) | 26.7612 | 1.18385 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.68621 | 0.206901 | ||||||||
\(514\) | −4.63516 | −0.204448 | ||||||||
\(515\) | 3.54084 | − | 4.79001i | 0.156028 | − | 0.211073i | ||||
\(516\) | 10.9236i | 0.480884i | ||||||||
\(517\) | 7.78280i | 0.342287i | ||||||||
\(518\) | 1.37634 | − | 11.3075i | 0.0604731 | − | 0.496823i | ||||
\(519\) | 16.9195 | 0.742683 | ||||||||
\(520\) | −6.35370 | + | 8.59521i | −0.278628 | + | 0.376925i | ||||
\(521\) | −37.3185 | −1.63495 | −0.817476 | − | 0.575963i | \(-0.804627\pi\) | ||||
−0.817476 | + | 0.575963i | \(0.804627\pi\) | |||||||
\(522\) | 0.200007i | 0.00875406i | ||||||||
\(523\) | 1.83536 | 0.0802549 | 0.0401274 | − | 0.999195i | \(-0.487224\pi\) | ||||
0.0401274 | + | 0.999195i | \(0.487224\pi\) | |||||||
\(524\) | 3.26950i | 0.142829i | ||||||||
\(525\) | 2.74622 | + | 8.95152i | 0.119855 | + | 0.390677i | ||||
\(526\) | 29.5118i | 1.28677i | ||||||||
\(527\) | − | 23.1381i | − | 1.00791i | ||||||
\(528\) | 1.51044i | 0.0657333i | ||||||||
\(529\) | 19.4034 | 0.843624 | ||||||||
\(530\) | −3.99599 | − | 2.95389i | −0.173575 | − | 0.128309i | ||||
\(531\) | − | 13.2646i | − | 0.575633i | ||||||
\(532\) | −8.77568 | −0.380474 | ||||||||
\(533\) | 19.6103 | 0.849417 | ||||||||
\(534\) | 5.47289 | 0.236835 | ||||||||
\(535\) | 1.48021 | + | 1.09419i | 0.0639951 | + | 0.0473060i | ||||
\(536\) | − | 5.76584i | − | 0.249047i | ||||||
\(537\) | 26.6575 | 1.15036 | ||||||||
\(538\) | −21.3385 | −0.919968 | ||||||||
\(539\) | −5.27616 | −0.227260 | ||||||||
\(540\) | −1.79812 | − | 1.32920i | −0.0773788 | − | 0.0571995i | ||||
\(541\) | − | 37.3336i | − | 1.60510i | −0.596587 | − | 0.802548i | \(-0.703477\pi\) | ||
0.596587 | − | 0.802548i | \(-0.296523\pi\) | |||||||
\(542\) | 16.5121 | 0.709257 | ||||||||
\(543\) | 13.4428i | 0.576886i | ||||||||
\(544\) | 3.99190 | 0.171151 | ||||||||
\(545\) | −0.860269 | − | 0.635922i | −0.0368499 | − | 0.0272399i | ||||
\(546\) | −8.95152 | −0.383090 | ||||||||
\(547\) | 17.5386 | 0.749897 | 0.374949 | − | 0.927046i | \(-0.377660\pi\) | ||||
0.374949 | + | 0.927046i | \(0.377660\pi\) | |||||||
\(548\) | − | 2.11793i | − | 0.0904733i | ||||||
\(549\) | 4.09616i | 0.174820i | ||||||||
\(550\) | 2.21502 | + | 7.22005i | 0.0944489 | + | 0.307864i | ||||
\(551\) | −0.937273 | −0.0399292 | ||||||||
\(552\) | − | 6.51179i | − | 0.277160i | ||||||
\(553\) | 11.1510 | 0.474191 | ||||||||
\(554\) | −11.0446 | −0.469239 | ||||||||
\(555\) | 9.88049 | + | 9.34750i | 0.419404 | + | 0.396779i | ||||
\(556\) | −15.7132 | −0.666387 | ||||||||
\(557\) | −40.7617 | −1.72713 | −0.863565 | − | 0.504237i | \(-0.831774\pi\) | ||||
−0.863565 | + | 0.504237i | \(0.831774\pi\) | |||||||
\(558\) | 5.79625i | 0.245375i | ||||||||
\(559\) | −52.2160 | −2.20850 | ||||||||
\(560\) | 3.36727 | + | 2.48913i | 0.142293 | + | 0.105185i | ||||
\(561\) | 6.02951i | 0.254566i | ||||||||
\(562\) | 17.9190i | 0.755867i | ||||||||
\(563\) | 4.47929 | 0.188779 | 0.0943897 | − | 0.995535i | \(-0.469910\pi\) | ||||
0.0943897 | + | 0.995535i | \(0.469910\pi\) | |||||||
\(564\) | −5.15269 | −0.216967 | ||||||||
\(565\) | −26.3805 | + | 35.6872i | −1.10983 | + | 1.50137i | ||||
\(566\) | −14.0543 | −0.590746 | ||||||||
\(567\) | − | 1.87266i | − | 0.0786444i | ||||||
\(568\) | −9.17428 | −0.384944 | ||||||||
\(569\) | − | 0.243177i | − | 0.0101945i | −0.999987 | − | 0.00509725i | \(-0.998377\pi\) | ||
0.999987 | − | 0.00509725i | \(-0.00162251\pi\) | |||||||
\(570\) | 6.22888 | − | 8.42637i | 0.260899 | − | 0.352942i | ||||
\(571\) | 34.2552 | 1.43353 | 0.716767 | − | 0.697313i | \(-0.245621\pi\) | ||||
0.716767 | + | 0.697313i | \(0.245621\pi\) | |||||||
\(572\) | −7.22005 | −0.301885 | ||||||||
\(573\) | −6.76465 | −0.282597 | ||||||||
\(574\) | − | 7.68256i | − | 0.320664i | ||||||
\(575\) | −9.54940 | − | 31.1270i | −0.398238 | − | 1.29809i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 10.5028 | 0.437239 | 0.218620 | − | 0.975810i | \(-0.429845\pi\) | ||||
0.218620 | + | 0.975810i | \(0.429845\pi\) | |||||||
\(578\) | −1.06470 | −0.0442857 | ||||||||
\(579\) | − | 15.4592i | − | 0.642463i | ||||||
\(580\) | 0.359637 | + | 0.265848i | 0.0149331 | + | 0.0110387i | ||||
\(581\) | −17.6414 | −0.731887 | ||||||||
\(582\) | − | 2.03303i | − | 0.0842718i | ||||||
\(583\) | − | 3.35666i | − | 0.139019i | ||||||
\(584\) | 14.2905i | 0.591343i | ||||||||
\(585\) | 6.35370 | − | 8.59521i | 0.262693 | − | 0.355368i | ||||
\(586\) | 32.2561i | 1.33249i | ||||||||
\(587\) | −27.0890 | −1.11808 | −0.559042 | − | 0.829139i | \(-0.688831\pi\) | ||||
−0.559042 | + | 0.829139i | \(0.688831\pi\) | |||||||
\(588\) | − | 3.49314i | − | 0.144055i | ||||||
\(589\) | −27.1624 | −1.11921 | ||||||||
\(590\) | −23.8513 | − | 17.6312i | −0.981942 | − | 0.725865i | ||||
\(591\) | −12.5068 | −0.514461 | ||||||||
\(592\) | 6.03820 | + | 0.734967i | 0.248168 | + | 0.0302070i | ||||
\(593\) | − | 24.2823i | − | 0.997156i | −0.866845 | − | 0.498578i | \(-0.833856\pi\) | ||
0.866845 | − | 0.498578i | \(-0.166144\pi\) | |||||||
\(594\) | − | 1.51044i | − | 0.0619739i | ||||||
\(595\) | 13.4418 | + | 9.93638i | 0.551061 | + | 0.407352i | ||||
\(596\) | −4.47152 | −0.183161 | ||||||||
\(597\) | 13.4172 | 0.549129 | ||||||||
\(598\) | 31.1270 | 1.27288 | ||||||||
\(599\) | −16.0532 | −0.655916 | −0.327958 | − | 0.944692i | \(-0.606360\pi\) | ||||
−0.327958 | + | 0.944692i | \(0.606360\pi\) | |||||||
\(600\) | −4.78011 | + | 1.46648i | −0.195147 | + | 0.0598688i | ||||
\(601\) | 42.5213 | 1.73448 | 0.867240 | − | 0.497891i | \(-0.165892\pi\) | ||||
0.867240 | + | 0.497891i | \(0.165892\pi\) | |||||||
\(602\) | 20.4562i | 0.833732i | ||||||||
\(603\) | 5.76584i | 0.234803i | ||||||||
\(604\) | 3.25118 | 0.132289 | ||||||||
\(605\) | 11.5887 | − | 15.6771i | 0.471148 | − | 0.637364i | ||||
\(606\) | 9.70730i | 0.394332i | ||||||||
\(607\) | 28.4432 | 1.15447 | 0.577237 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577237 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(608\) | − | 4.68621i | − | 0.190051i | ||||||
\(609\) | 0.374545i | 0.0151773i | ||||||||
\(610\) | 7.36539 | + | 5.44459i | 0.298216 | + | 0.220445i | ||||
\(611\) | − | 24.6304i | − | 0.996439i | ||||||
\(612\) | −3.99190 | −0.161363 | ||||||||
\(613\) | 20.9056i | 0.844370i | 0.906510 | + | 0.422185i | \(0.138737\pi\) | ||||
−0.906510 | + | 0.422185i | \(0.861263\pi\) | |||||||
\(614\) | − | 27.5771i | − | 1.11292i | ||||||
\(615\) | 7.37676 | + | 5.45300i | 0.297460 | + | 0.219886i | ||||
\(616\) | 2.82853i | 0.113965i | ||||||||
\(617\) | 4.08940i | 0.164633i | 0.996606 | + | 0.0823165i | \(0.0262318\pi\) | ||||
−0.996606 | + | 0.0823165i | \(0.973768\pi\) | |||||||
\(618\) | 2.66390i | 0.107158i | ||||||||
\(619\) | 11.4039 | 0.458361 | 0.229181 | − | 0.973384i | \(-0.426395\pi\) | ||||
0.229181 | + | 0.973384i | \(0.426395\pi\) | |||||||
\(620\) | 10.4224 | + | 7.70435i | 0.418572 | + | 0.309414i | ||||
\(621\) | 6.51179i | 0.261309i | ||||||||
\(622\) | − | 13.8537i | − | 0.555482i | ||||||
\(623\) | 10.2489 | 0.410613 | ||||||||
\(624\) | − | 4.78011i | − | 0.191357i | ||||||
\(625\) | −20.6989 | + | 14.0199i | −0.827955 | + | 0.560795i | ||||
\(626\) | −24.3768 | −0.974294 | ||||||||
\(627\) | 7.07821 | 0.282677 | ||||||||
\(628\) | 0.0713960i | 0.00284901i | ||||||||
\(629\) | 24.1039 | + | 2.93392i | 0.961086 | + | 0.116983i | ||||
\(630\) | −3.36727 | − | 2.48913i | −0.134155 | − | 0.0991694i | ||||
\(631\) | 28.1305i | 1.11986i | 0.828541 | + | 0.559929i | \(0.189171\pi\) | ||||
−0.828541 | + | 0.559929i | \(0.810829\pi\) | |||||||
\(632\) | 5.95465i | 0.236863i | ||||||||
\(633\) | − | 6.46040i | − | 0.256778i | ||||||
\(634\) | 8.91522i | 0.354069i | ||||||||
\(635\) | 12.3289 | + | 9.11369i | 0.489258 | + | 0.361666i | ||||
\(636\) | 2.22232 | 0.0881205 | ||||||||
\(637\) | 16.6976 | 0.661583 | ||||||||
\(638\) | 0.302097i | 0.0119602i | ||||||||
\(639\) | 9.17428 | 0.362929 | ||||||||
\(640\) | −1.32920 | + | 1.79812i | −0.0525411 | + | 0.0710770i | ||||
\(641\) | 26.3364 | 1.04023 | 0.520113 | − | 0.854098i | \(-0.325890\pi\) | ||||
0.520113 | + | 0.854098i | \(0.325890\pi\) | |||||||
\(642\) | −0.823199 | −0.0324891 | ||||||||
\(643\) | 32.4390 | 1.27927 | 0.639636 | − | 0.768678i | \(-0.279085\pi\) | ||||
0.639636 | + | 0.768678i | \(0.279085\pi\) | |||||||
\(644\) | − | 12.1944i | − | 0.480525i | ||||||
\(645\) | −19.6419 | − | 14.5196i | −0.773401 | − | 0.571708i | ||||
\(646\) | − | 18.7069i | − | 0.736013i | ||||||
\(647\) | −40.5401 | −1.59380 | −0.796898 | − | 0.604114i | \(-0.793527\pi\) | ||||
−0.796898 | + | 0.604114i | \(0.793527\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | − | 20.0353i | − | 0.786453i | ||||||
\(650\) | −7.00993 | − | 22.8494i | −0.274952 | − | 0.896229i | ||||
\(651\) | 10.8544i | 0.425418i | ||||||||
\(652\) | 1.06145 | 0.0415695 | ||||||||
\(653\) | 1.15329 | 0.0451319 | 0.0225659 | − | 0.999745i | \(-0.492816\pi\) | ||||
0.0225659 | + | 0.999745i | \(0.492816\pi\) | |||||||
\(654\) | 0.478427 | 0.0187080 | ||||||||
\(655\) | −5.87896 | − | 4.34581i | −0.229710 | − | 0.169805i | ||||
\(656\) | 4.10248 | 0.160175 | ||||||||
\(657\) | − | 14.2905i | − | 0.557524i | ||||||
\(658\) | −9.64923 | −0.376166 | ||||||||
\(659\) | 46.3614 | 1.80598 | 0.902992 | − | 0.429657i | \(-0.141366\pi\) | ||||
0.902992 | + | 0.429657i | \(0.141366\pi\) | |||||||
\(660\) | −2.71595 | − | 2.00766i | −0.105718 | − | 0.0781482i | ||||
\(661\) | 40.8589i | 1.58923i | 0.607117 | + | 0.794613i | \(0.292326\pi\) | ||||
−0.607117 | + | 0.794613i | \(0.707674\pi\) | |||||||
\(662\) | − | 25.6563i | − | 0.997160i | ||||||
\(663\) | − | 19.0817i | − | 0.741073i | ||||||
\(664\) | − | 9.42048i | − | 0.365585i | ||||||
\(665\) | 11.6646 | − | 15.7797i | 0.452333 | − | 0.611912i | ||||
\(666\) | −6.03820 | − | 0.734967i | −0.233975 | − | 0.0284794i | ||||
\(667\) | − | 1.30240i | − | 0.0504292i | ||||||
\(668\) | −20.4097 | −0.789673 | ||||||||
\(669\) | 8.15634 | 0.315342 | ||||||||
\(670\) | 10.3677 | + | 7.66393i | 0.400539 | + | 0.296084i | ||||
\(671\) | 6.18698i | 0.238846i | ||||||||
\(672\) | −1.87266 | −0.0722395 | ||||||||
\(673\) | 31.1524i | 1.20084i | 0.799686 | + | 0.600419i | \(0.204999\pi\) | ||||
−0.799686 | + | 0.600419i | \(0.795001\pi\) | |||||||
\(674\) | − | 18.5473i | − | 0.714415i | ||||||
\(675\) | 4.78011 | − | 1.46648i | 0.183986 | − | 0.0564448i | ||||
\(676\) | 9.84944 | 0.378825 | ||||||||
\(677\) | − | 19.8870i | − | 0.764321i | −0.924096 | − | 0.382160i | \(-0.875180\pi\) | ||
0.924096 | − | 0.382160i | \(-0.124820\pi\) | |||||||
\(678\) | − | 19.8469i | − | 0.762217i | ||||||
\(679\) | − | 3.80718i | − | 0.146106i | ||||||
\(680\) | −5.30602 | + | 7.17793i | −0.203477 | + | 0.275261i | ||||
\(681\) | − | 13.0456i | − | 0.499908i | ||||||
\(682\) | 8.75486i | 0.335241i | ||||||||
\(683\) | −11.3646 | −0.434855 | −0.217428 | − | 0.976076i | \(-0.569767\pi\) | ||||
−0.217428 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(684\) | 4.68621i | 0.179182i | ||||||||
\(685\) | 3.80829 | + | 2.81514i | 0.145507 | + | 0.107561i | ||||
\(686\) | − | 19.6501i | − | 0.750244i | ||||||
\(687\) | − | 13.3621i | − | 0.509798i | ||||||
\(688\) | −10.9236 | −0.416458 | ||||||||
\(689\) | 10.6229i | 0.404701i | ||||||||
\(690\) | 11.7090 | + | 8.65543i | 0.445753 | + | 0.329507i | ||||
\(691\) | −27.8449 | −1.05927 | −0.529635 | − | 0.848226i | \(-0.677671\pi\) | ||||
−0.529635 | + | 0.848226i | \(0.677671\pi\) | |||||||
\(692\) | 16.9195i | 0.643182i | ||||||||
\(693\) | − | 2.82853i | − | 0.107447i | ||||||
\(694\) | −9.07304 | −0.344408 | ||||||||
\(695\) | 20.8859 | − | 28.2542i | 0.792247 | − | 1.07174i | ||||
\(696\) | −0.200007 | −0.00758124 | ||||||||
\(697\) | 16.3767 | 0.620313 | ||||||||
\(698\) | −31.1022 | −1.17724 | ||||||||
\(699\) | −27.2277 | −1.02985 | ||||||||
\(700\) | −8.95152 | + | 2.74622i | −0.338336 | + | 0.103797i | ||||
\(701\) | 30.8041i | 1.16346i | 0.813384 | + | 0.581728i | \(0.197623\pi\) | ||||
−0.813384 | + | 0.581728i | \(0.802377\pi\) | |||||||
\(702\) | 4.78011i | 0.180414i | ||||||||
\(703\) | 3.44421 | − | 28.2962i | 0.129901 | − | 1.06721i | ||||
\(704\) | −1.51044 | −0.0569267 | ||||||||
\(705\) | 6.84893 | − | 9.26515i | 0.257945 | − | 0.348946i | ||||
\(706\) | −16.3289 | −0.614545 | ||||||||
\(707\) | 18.1785i | 0.683672i | ||||||||
\(708\) | 13.2646 | 0.498513 | ||||||||
\(709\) | − | 48.0105i | − | 1.80307i | −0.432704 | − | 0.901536i | \(-0.642441\pi\) | ||
0.432704 | − | 0.901536i | \(-0.357559\pi\) | |||||||
\(710\) | 12.1944 | − | 16.4965i | 0.457648 | − | 0.619102i | ||||
\(711\) | − | 5.95465i | − | 0.223317i | ||||||
\(712\) | 5.47289i | 0.205105i | ||||||||
\(713\) | − | 37.7439i | − | 1.41352i | ||||||
\(714\) | −7.47548 | −0.279763 | ||||||||
\(715\) | 9.59685 | − | 12.9825i | 0.358902 | − | 0.485519i | ||||
\(716\) | 26.6575i | 0.996237i | ||||||||
\(717\) | 10.5417 | 0.393688 | ||||||||
\(718\) | 17.1135 | 0.638670 | ||||||||
\(719\) | 10.5990 | 0.395275 | 0.197638 | − | 0.980275i | \(-0.436673\pi\) | ||||
0.197638 | + | 0.980275i | \(0.436673\pi\) | |||||||
\(720\) | 1.32920 | − | 1.79812i | 0.0495362 | − | 0.0670120i | ||||
\(721\) | 4.98858i | 0.185784i | ||||||||
\(722\) | −2.96053 | −0.110179 | ||||||||
\(723\) | 13.3732 | 0.497356 | ||||||||
\(724\) | −13.4428 | −0.499598 | ||||||||
\(725\) | −0.956055 | + | 0.293306i | −0.0355070 | + | 0.0108931i | ||||
\(726\) | 8.71858i | 0.323577i | ||||||||
\(727\) | −38.9977 | −1.44634 | −0.723172 | − | 0.690668i | \(-0.757317\pi\) | ||||
−0.723172 | + | 0.690668i | \(0.757317\pi\) | |||||||
\(728\) | − | 8.95152i | − | 0.331766i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −25.6960 | − | 18.9948i | −0.951051 | − | 0.703029i | ||||
\(731\) | −43.6059 | −1.61282 | ||||||||
\(732\) | −4.09616 | −0.151398 | ||||||||
\(733\) | 16.0616i | 0.593250i | 0.954994 | + | 0.296625i | \(0.0958611\pi\) | ||||
−0.954994 | + | 0.296625i | \(0.904139\pi\) | |||||||
\(734\) | − | 23.2045i | − | 0.856493i | ||||||
\(735\) | 6.28109 | + | 4.64307i | 0.231681 | + | 0.171262i | ||||
\(736\) | 6.51179 | 0.240028 | ||||||||
\(737\) | 8.70894i | 0.320798i | ||||||||
\(738\) | −4.10248 | −0.151015 | ||||||||
\(739\) | 28.6759 | 1.05486 | 0.527430 | − | 0.849599i | \(-0.323156\pi\) | ||||
0.527430 | + | 0.849599i | \(0.323156\pi\) | |||||||
\(740\) | −9.34750 | + | 9.88049i | −0.343621 | + | 0.363214i | ||||
\(741\) | −22.4006 | −0.822906 | ||||||||
\(742\) | 4.16164 | 0.152779 | ||||||||
\(743\) | − | 23.4444i | − | 0.860090i | −0.902807 | − | 0.430045i | \(-0.858498\pi\) | ||
0.902807 | − | 0.430045i | \(-0.141502\pi\) | |||||||
\(744\) | −5.79625 | −0.212501 | ||||||||
\(745\) | 5.94353 | − | 8.04034i | 0.217754 | − | 0.294575i | ||||
\(746\) | 9.69704i | 0.355034i | ||||||||
\(747\) | 9.42048i | 0.344677i | ||||||||
\(748\) | −6.02951 | −0.220461 | ||||||||
\(749\) | −1.54157 | −0.0563278 | ||||||||
\(750\) | 3.71679 | − | 10.5445i | 0.135718 | − | 0.385029i | ||||
\(751\) | −20.3229 | −0.741592 | −0.370796 | − | 0.928714i | \(-0.620915\pi\) | ||||
−0.370796 | + | 0.928714i | \(0.620915\pi\) | |||||||
\(752\) | − | 5.15269i | − | 0.187899i | ||||||
\(753\) | 6.68149 | 0.243487 | ||||||||
\(754\) | − | 0.956055i | − | 0.0348175i | ||||||
\(755\) | −4.32145 | + | 5.84601i | −0.157274 | + | 0.212758i | ||||
\(756\) | 1.87266 | 0.0681080 | ||||||||
\(757\) | 37.8496 | 1.37567 | 0.687834 | − | 0.725868i | \(-0.258562\pi\) | ||||
0.687834 | + | 0.725868i | \(0.258562\pi\) | |||||||
\(758\) | −9.40066 | −0.341448 | ||||||||
\(759\) | 9.83563i | 0.357011i | ||||||||
\(760\) | 8.42637 | + | 6.22888i | 0.305656 | + | 0.225945i | ||||
\(761\) | −13.4618 | −0.487990 | −0.243995 | − | 0.969777i | \(-0.578458\pi\) | ||||
−0.243995 | + | 0.969777i | \(0.578458\pi\) | |||||||
\(762\) | −6.85655 | −0.248386 | ||||||||
\(763\) | 0.895931 | 0.0324349 | ||||||||
\(764\) | − | 6.76465i | − | 0.244736i | ||||||
\(765\) | 5.30602 | − | 7.17793i | 0.191840 | − | 0.259519i | ||||
\(766\) | 32.3874 | 1.17020 | ||||||||
\(767\) | 63.4061i | 2.28946i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 19.7800i | 0.713285i | 0.934241 | + | 0.356642i | \(0.116079\pi\) | ||||
−0.934241 | + | 0.356642i | \(0.883921\pi\) | |||||||
\(770\) | −5.08605 | − | 3.75967i | −0.183288 | − | 0.135489i | ||||
\(771\) | 4.63516i | 0.166931i | ||||||||
\(772\) | 15.4592 | 0.556389 | ||||||||
\(773\) | 25.4792i | 0.916423i | 0.888843 | + | 0.458212i | \(0.151510\pi\) | ||||
−0.888843 | + | 0.458212i | \(0.848490\pi\) | |||||||
\(774\) | 10.9236 | 0.392640 | ||||||||
\(775\) | −27.7067 | + | 8.50008i | −0.995254 | + | 0.305332i | ||||
\(776\) | 2.03303 | 0.0729815 | ||||||||
\(777\) | −11.3075 | − | 1.37634i | −0.405654 | − | 0.0493761i | ||||
\(778\) | − | 20.8774i | − | 0.748492i | ||||||
\(779\) | − | 19.2251i | − | 0.688810i | ||||||
\(780\) | 8.59521 | + | 6.35370i | 0.307758 | + | 0.227499i | ||||
\(781\) | 13.8572 | 0.495848 | ||||||||
\(782\) | 25.9944 | 0.929559 | ||||||||
\(783\) | 0.200007 | 0.00714766 | ||||||||
\(784\) | 3.49314 | 0.124755 | ||||||||
\(785\) | −0.128379 | − | 0.0948993i | −0.00458203 | − | 0.00338710i | ||||
\(786\) | 3.26950 | 0.116619 | ||||||||
\(787\) | 50.1801i | 1.78873i | 0.447339 | + | 0.894364i | \(0.352372\pi\) | ||||
−0.447339 | + | 0.894364i | \(0.647628\pi\) | |||||||
\(788\) | − | 12.5068i | − | 0.445536i | ||||||
\(789\) | 29.5118 | 1.05065 | ||||||||
\(790\) | −10.7072 | − | 7.91489i | −0.380944 | − | 0.281599i | ||||
\(791\) | − | 37.1666i | − | 1.32149i | ||||||
\(792\) | 1.51044 | 0.0536710 | ||||||||
\(793\) | − | 19.5801i | − | 0.695309i | ||||||
\(794\) | 12.2447i | 0.434549i | ||||||||
\(795\) | −2.95389 | + | 3.99599i | −0.104764 | + | 0.141723i | ||||
\(796\) | 13.4172i | 0.475559i | ||||||||
\(797\) | −26.4099 | −0.935485 | −0.467743 | − | 0.883865i | \(-0.654933\pi\) | ||||
−0.467743 | + | 0.883865i | \(0.654933\pi\) | |||||||
\(798\) | 8.77568i | 0.310656i | ||||||||
\(799\) | − | 20.5690i | − | 0.727680i | ||||||
\(800\) | −1.46648 | − | 4.78011i | −0.0518479 | − | 0.169002i | ||||
\(801\) | − | 5.47289i | − | 0.193375i | ||||||
\(802\) | − | 13.7736i | − | 0.486362i | ||||||
\(803\) | − | 21.5848i | − | 0.761711i | ||||||
\(804\) | −5.76584 | −0.203346 | ||||||||
\(805\) | 21.9270 | + | 16.2087i | 0.772823 | + | 0.571282i | ||||
\(806\) | − | 27.7067i | − | 0.975927i | ||||||
\(807\) | 21.3385i | 0.751151i | ||||||||
\(808\) | −9.70730 | −0.341502 | ||||||||
\(809\) | − | 8.11189i | − | 0.285199i | −0.989780 | − | 0.142599i | \(-0.954454\pi\) | ||
0.989780 | − | 0.142599i | \(-0.0455461\pi\) | |||||||
\(810\) | −1.32920 | + | 1.79812i | −0.0467032 | + | 0.0631795i | ||||
\(811\) | 27.0320 | 0.949223 | 0.474611 | − | 0.880195i | \(-0.342589\pi\) | ||||
0.474611 | + | 0.880195i | \(0.342589\pi\) | |||||||
\(812\) | −0.374545 | −0.0131440 | ||||||||
\(813\) | − | 16.5121i | − | 0.579106i | ||||||
\(814\) | −9.12031 | − | 1.11012i | −0.319667 | − | 0.0389097i | ||||
\(815\) | −1.41087 | + | 1.90861i | −0.0494206 | + | 0.0668557i | ||||
\(816\) | − | 3.99190i | − | 0.139745i | ||||||
\(817\) | 51.1902i | 1.79092i | ||||||||
\(818\) | 34.5667i | 1.20860i | ||||||||
\(819\) | 8.95152i | 0.312792i | ||||||||
\(820\) | −5.45300 | + | 7.37676i | −0.190427 | + | 0.257608i | ||||
\(821\) | −19.7666 | −0.689859 | −0.344930 | − | 0.938629i | \(-0.612097\pi\) | ||||
−0.344930 | + | 0.938629i | \(0.612097\pi\) | |||||||
\(822\) | −2.11793 | −0.0738711 | ||||||||
\(823\) | − | 41.4991i | − | 1.44657i | −0.690550 | − | 0.723285i | \(-0.742632\pi\) | ||
0.690550 | − | 0.723285i | \(-0.257368\pi\) | |||||||
\(824\) | −2.66390 | −0.0928013 | ||||||||
\(825\) | 7.22005 | − | 2.21502i | 0.251370 | − | 0.0771172i | ||||
\(826\) | 24.8400 | 0.864295 | ||||||||
\(827\) | −39.6665 | −1.37934 | −0.689671 | − | 0.724123i | \(-0.742245\pi\) | ||||
−0.689671 | + | 0.724123i | \(0.742245\pi\) | |||||||
\(828\) | −6.51179 | −0.226300 | ||||||||
\(829\) | 27.0227i | 0.938538i | 0.883055 | + | 0.469269i | \(0.155483\pi\) | ||||
−0.883055 | + | 0.469269i | \(0.844517\pi\) | |||||||
\(830\) | 16.9392 | + | 12.5217i | 0.587967 | + | 0.434633i | ||||
\(831\) | 11.0446i | 0.383132i | ||||||||
\(832\) | 4.78011 | 0.165720 | ||||||||
\(833\) | 13.9443 | 0.483141 | ||||||||
\(834\) | 15.7132i | 0.544103i | ||||||||
\(835\) | 27.1284 | − | 36.6990i | 0.938818 | − | 1.27002i | ||||
\(836\) | 7.07821i | 0.244805i | ||||||||
\(837\) | 5.79625 | 0.200348 | ||||||||
\(838\) | 22.9413 | 0.792495 | ||||||||
\(839\) | 6.29148 | 0.217206 | 0.108603 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108603 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(840\) | 2.48913 | − | 3.36727i | 0.0858832 | − | 0.116182i | ||||
\(841\) | 28.9600 | 0.998621 | ||||||||
\(842\) | − | 12.1679i | − | 0.419333i | ||||||
\(843\) | 17.9190 | 0.617162 | ||||||||
\(844\) | 6.46040 | 0.222376 | ||||||||
\(845\) | −13.0918 | + | 17.7105i | −0.450373 | + | 0.609259i | ||||
\(846\) | 5.15269i | 0.177153i | ||||||||
\(847\) | 16.3270i | 0.561001i | ||||||||
\(848\) | 2.22232i | 0.0763146i | ||||||||
\(849\) | 14.0543i | 0.482342i | ||||||||
\(850\) | −5.85405 | − | 19.0817i | −0.200792 | − | 0.654498i | ||||
\(851\) | 39.3194 | + | 4.78595i | 1.34785 | + | 0.164060i | ||||
\(852\) | 9.17428i | 0.314306i | ||||||||
\(853\) | 1.33464 | 0.0456971 | 0.0228486 | − | 0.999739i | \(-0.492726\pi\) | ||||
0.0228486 | + | 0.999739i | \(0.492726\pi\) | |||||||
\(854\) | −7.67072 | −0.262487 | ||||||||
\(855\) | −8.42637 | − | 6.22888i | −0.288176 | − | 0.213023i | ||||
\(856\) | − | 0.823199i | − | 0.0281364i | ||||||
\(857\) | −22.7053 | −0.775597 | −0.387799 | − | 0.921744i | \(-0.626764\pi\) | ||||
−0.387799 | + | 0.921744i | \(0.626764\pi\) | |||||||
\(858\) | 7.22005i | 0.246488i | ||||||||
\(859\) | 8.92509i | 0.304520i | 0.988340 | + | 0.152260i | \(0.0486551\pi\) | ||||
−0.988340 | + | 0.152260i | \(0.951345\pi\) | |||||||
\(860\) | 14.5196 | − | 19.6419i | 0.495114 | − | 0.669785i | ||||
\(861\) | −7.68256 | −0.261821 | ||||||||
\(862\) | − | 11.2076i | − | 0.381734i | ||||||
\(863\) | − | 8.98998i | − | 0.306022i | −0.988224 | − | 0.153011i | \(-0.951103\pi\) | ||
0.988224 | − | 0.153011i | \(-0.0488971\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | −30.4233 | − | 22.4893i | −1.03442 | − | 0.764659i | ||||
\(866\) | − | 31.6559i | − | 1.07571i | ||||||
\(867\) | 1.06470i | 0.0361591i | ||||||||
\(868\) | −10.8544 | −0.368423 | ||||||||
\(869\) | − | 8.99411i | − | 0.305104i | ||||||
\(870\) | 0.265848 | − | 0.359637i | 0.00901310 | − | 0.0121928i | ||||
\(871\) | − | 27.5614i | − | 0.933881i | ||||||
\(872\) | 0.478427i | 0.0162016i | ||||||||
\(873\) | −2.03303 | −0.0688076 | ||||||||
\(874\) | − | 30.5156i | − | 1.03220i | ||||||
\(875\) | 6.96029 | − | 19.7462i | 0.235301 | − | 0.667543i | ||||
\(876\) | 14.2905 | 0.482830 | ||||||||
\(877\) | − | 9.40084i | − | 0.317444i | −0.987323 | − | 0.158722i | \(-0.949263\pi\) | ||
0.987323 | − | 0.158722i | \(-0.0507373\pi\) | |||||||
\(878\) | 33.9912i | 1.14715i | ||||||||
\(879\) | 32.2561 | 1.08797 | ||||||||
\(880\) | 2.00766 | − | 2.71595i | 0.0676783 | − | 0.0915545i | ||||
\(881\) | −19.9044 | −0.670596 | −0.335298 | − | 0.942112i | \(-0.608837\pi\) | ||||
−0.335298 | + | 0.942112i | \(0.608837\pi\) | |||||||
\(882\) | −3.49314 | −0.117620 | ||||||||
\(883\) | −48.8646 | −1.64442 | −0.822212 | − | 0.569181i | \(-0.807260\pi\) | ||||
−0.822212 | + | 0.569181i | \(0.807260\pi\) | |||||||
\(884\) | 19.0817 | 0.641788 | ||||||||
\(885\) | −17.6312 | + | 23.8513i | −0.592666 | + | 0.801752i | ||||
\(886\) | 34.9477i | 1.17409i | ||||||||
\(887\) | 32.4651i | 1.09007i | 0.838413 | + | 0.545036i | \(0.183484\pi\) | ||||
−0.838413 | + | 0.545036i | \(0.816516\pi\) | |||||||
\(888\) | 0.734967 | − | 6.03820i | 0.0246639 | − | 0.202629i | ||||
\(889\) | −12.8400 | −0.430639 | ||||||||
\(890\) | −9.84093 | − | 7.27454i | −0.329869 | − | 0.243843i | ||||
\(891\) | −1.51044 | −0.0506015 | ||||||||
\(892\) | 8.15634i | 0.273095i | ||||||||
\(893\) | −24.1465 | −0.808033 | ||||||||
\(894\) | 4.47152i | 0.149550i | ||||||||
\(895\) | −47.9334 | − | 35.4330i | −1.60224 | − | 1.18439i | ||||
\(896\) | − | 1.87266i | − | 0.0625612i | ||||||
\(897\) | − | 31.1270i | − | 1.03930i | ||||||
\(898\) | − | 17.2274i | − | 0.574886i | ||||||
\(899\) | −1.15929 | −0.0386645 | ||||||||
\(900\) | 1.46648 | + | 4.78011i | 0.0488827 | + | 0.159337i | ||||
\(901\) | 8.87127i | 0.295545i | ||||||||
\(902\) | −6.19654 | −0.206322 | ||||||||
\(903\) | 20.4562 | 0.680739 | ||||||||
\(904\) | 19.8469 | 0.660099 | ||||||||
\(905\) | 17.8681 | − | 24.1718i | 0.593956 | − | 0.803497i | ||||
\(906\) | − | 3.25118i | − | 0.108013i | ||||||
\(907\) | 6.47916 | 0.215137 | 0.107568 | − | 0.994198i | \(-0.465694\pi\) | ||||
0.107568 | + | 0.994198i | \(0.465694\pi\) | |||||||
\(908\) | 13.0456 | 0.432933 | ||||||||
\(909\) | 9.70730 | 0.321971 | ||||||||
\(910\) | 16.0959 | + | 11.8983i | 0.533575 | + | 0.394426i | ||||
\(911\) | − | 17.1972i | − | 0.569767i | −0.958562 | − | 0.284884i | \(-0.908045\pi\) | ||
0.958562 | − | 0.284884i | \(-0.0919550\pi\) | |||||||
\(912\) | −4.68621 | −0.155176 | ||||||||
\(913\) | 14.2290i | 0.470912i | ||||||||
\(914\) | 24.5044 | 0.810532 | ||||||||
\(915\) | 5.44459 | − | 7.36539i | 0.179993 | − | 0.243492i | ||||
\(916\) | 13.3621 | 0.441498 | ||||||||
\(917\) | 6.12267 | 0.202188 | ||||||||
\(918\) | 3.99190i | 0.131752i | ||||||||
\(919\) | 39.5341i | 1.30411i | 0.758172 | + | 0.652054i | \(0.226093\pi\) | ||||
−0.758172 | + | 0.652054i | \(0.773907\pi\) | |||||||
\(920\) | −8.65543 | + | 11.7090i | −0.285361 | + | 0.386034i | ||||
\(921\) | −27.5771 | −0.908695 | ||||||||
\(922\) | 9.05274i | 0.298136i | ||||||||
\(923\) | −43.8541 | −1.44347 | ||||||||
\(924\) | 2.82853 | 0.0930519 | ||||||||
\(925\) | −5.34167 | − | 29.9411i | −0.175633 | − | 0.984456i | ||||
\(926\) | −2.10640 | −0.0692206 | ||||||||
\(927\) | 2.66390 | 0.0874939 | ||||||||
\(928\) | − | 0.200007i | − | 0.00656555i | ||||||
\(929\) | 53.4172 | 1.75256 | 0.876281 | − | 0.481800i | \(-0.160017\pi\) | ||||
0.876281 | + | 0.481800i | \(0.160017\pi\) | |||||||
\(930\) | 7.70435 | − | 10.4224i | 0.252636 | − | 0.341763i | ||||
\(931\) | − | 16.3696i | − | 0.536491i | ||||||
\(932\) | − | 27.2277i | − | 0.891875i | ||||||
\(933\) | −13.8537 | −0.453549 | ||||||||
\(934\) | 24.0814 | 0.787967 | ||||||||
\(935\) | 8.01440 | − | 10.8418i | 0.262099 | − | 0.354565i | ||||
\(936\) | −4.78011 | −0.156243 | ||||||||
\(937\) | − | 15.1507i | − | 0.494953i | −0.968894 | − | 0.247477i | \(-0.920399\pi\) | ||
0.968894 | − | 0.247477i | \(-0.0796013\pi\) | |||||||
\(938\) | −10.7975 | −0.352550 | ||||||||
\(939\) | 24.3768i | 0.795508i | ||||||||
\(940\) | 9.26515 | + | 6.84893i | 0.302196 | + | 0.223387i | ||||
\(941\) | 24.9479 | 0.813279 | 0.406639 | − | 0.913589i | \(-0.366701\pi\) | ||||
0.406639 | + | 0.913589i | \(0.366701\pi\) | |||||||
\(942\) | 0.0713960 | 0.00232621 | ||||||||
\(943\) | 26.7145 | 0.869944 | ||||||||
\(944\) | 13.2646i | 0.431725i | ||||||||
\(945\) | −2.48913 | + | 3.36727i | −0.0809715 | + | 0.109537i | ||||
\(946\) | 16.4994 | 0.536441 | ||||||||
\(947\) | 3.44085 | 0.111813 | 0.0559063 | − | 0.998436i | \(-0.482195\pi\) | ||||
0.0559063 | + | 0.998436i | \(0.482195\pi\) | |||||||
\(948\) | 5.95465 | 0.193398 | ||||||||
\(949\) | 68.3099i | 2.21743i | ||||||||
\(950\) | −22.4006 | + | 6.87223i | −0.726771 | + | 0.222964i | ||||
\(951\) | 8.91522 | 0.289096 | ||||||||
\(952\) | − | 7.47548i | − | 0.242282i | ||||||
\(953\) | − | 16.3551i | − | 0.529794i | −0.964277 | − | 0.264897i | \(-0.914662\pi\) | ||
0.964277 | − | 0.264897i | \(-0.0853380\pi\) | |||||||
\(954\) | − | 2.22232i | − | 0.0719501i | ||||||
\(955\) | 12.1637 | + | 8.99153i | 0.393607 | + | 0.290959i | ||||
\(956\) | 10.5417i | 0.340944i | ||||||||
\(957\) | 0.302097 | 0.00976542 | ||||||||
\(958\) | 5.46224i | 0.176477i | ||||||||
\(959\) | −3.96616 | −0.128074 | ||||||||
\(960\) | 1.79812 | + | 1.32920i | 0.0580341 | + | 0.0428996i | ||||
\(961\) | −2.59651 | −0.0837582 | ||||||||
\(962\) | 28.8632 | + | 3.51322i | 0.930588 | + | 0.113271i | ||||
\(963\) | 0.823199i | 0.0265272i | ||||||||
\(964\) | 13.3732i | 0.430723i | ||||||||
\(965\) | −20.5483 | + | 27.7975i | −0.661473 | + | 0.894834i | ||||
\(966\) | −12.1944 | −0.392347 | ||||||||
\(967\) | −40.2993 | −1.29594 | −0.647968 | − | 0.761667i | \(-0.724381\pi\) | ||||
−0.647968 | + | 0.761667i | \(0.724381\pi\) | |||||||
\(968\) | −8.71858 | −0.280226 | ||||||||
\(969\) | −18.7069 | −0.600952 | ||||||||
\(970\) | −2.70229 | + | 3.65563i | −0.0867654 | + | 0.117375i | ||||
\(971\) | −45.6611 | −1.46533 | −0.732667 | − | 0.680587i | \(-0.761725\pi\) | ||||
−0.732667 | + | 0.680587i | \(0.761725\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 29.4255i | 0.943337i | ||||||||
\(974\) | 11.8494 | 0.379681 | ||||||||
\(975\) | −22.8494 | + | 7.00993i | −0.731768 | + | 0.224497i | ||||
\(976\) | − | 4.09616i | − | 0.131115i | ||||||
\(977\) | 4.88784 | 0.156376 | 0.0781879 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781879 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(978\) | − | 1.06145i | − | 0.0339413i | ||||||
\(979\) | − | 8.26645i | − | 0.264197i | ||||||
\(980\) | −4.64307 | + | 6.28109i | −0.148317 | + | 0.200642i | ||||
\(981\) | − | 0.478427i | − | 0.0152750i | ||||||
\(982\) | −7.19955 | −0.229747 | ||||||||
\(983\) | − | 0.259395i | − | 0.00827341i | −0.999991 | − | 0.00413670i | \(-0.998683\pi\) | ||
0.999991 | − | 0.00413670i | \(-0.00131676\pi\) | |||||||
\(984\) | − | 4.10248i | − | 0.130782i | ||||||
\(985\) | 22.4887 | + | 16.6240i | 0.716550 | + | 0.529684i | ||||
\(986\) | − | 0.798408i | − | 0.0254265i | ||||||
\(987\) | 9.64923i | 0.307139i | ||||||||
\(988\) | − | 22.4006i | − | 0.712657i | ||||||
\(989\) | −71.1321 | −2.26187 | ||||||||
\(990\) | −2.00766 | + | 2.71595i | −0.0638077 | + | 0.0863184i | ||||
\(991\) | − | 29.6464i | − | 0.941750i | −0.882200 | − | 0.470875i | \(-0.843938\pi\) | ||
0.882200 | − | 0.470875i | \(-0.156062\pi\) | |||||||
\(992\) | − | 5.79625i | − | 0.184031i | ||||||
\(993\) | −25.6563 | −0.814178 | ||||||||
\(994\) | 17.1803i | 0.544927i | ||||||||
\(995\) | −24.1257 | − | 17.8341i | −0.764837 | − | 0.565378i | ||||
\(996\) | −9.42048 | −0.298499 | ||||||||
\(997\) | −33.3064 | −1.05482 | −0.527411 | − | 0.849610i | \(-0.676837\pi\) | ||||
−0.527411 | + | 0.849610i | \(0.676837\pi\) | |||||||
\(998\) | − | 3.32481i | − | 0.105245i | ||||||
\(999\) | −0.734967 | + | 6.03820i | −0.0232533 | + | 0.191040i |
(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 | 1110.2.e.d.739.2 | yes | 16 | |
3.2 | odd | 2 | 3330.2.e.e.739.13 | 16 | |||
5.4 | even | 2 | 1110.2.e.c.739.15 | yes | 16 | ||
15.14 | odd | 2 | 3330.2.e.f.739.3 | 16 | |||
37.36 | even | 2 | 1110.2.e.c.739.7 | ✓ | 16 | ||
111.110 | odd | 2 | 3330.2.e.f.739.4 | 16 | |||
185.184 | even | 2 | inner | 1110.2.e.d.739.10 | yes | 16 | |
555.554 | odd | 2 | 3330.2.e.e.739.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.c.739.7 | ✓ | 16 | 37.36 | even | 2 | ||
1110.2.e.c.739.15 | yes | 16 | 5.4 | even | 2 | ||
1110.2.e.d.739.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1110.2.e.d.739.10 | yes | 16 | 185.184 | even | 2 | inner | |
3330.2.e.e.739.13 | 16 | 3.2 | odd | 2 | |||
3330.2.e.e.739.14 | 16 | 555.554 | odd | 2 | |||
3330.2.e.f.739.3 | 16 | 15.14 | odd | 2 | |||
3330.2.e.f.739.4 | 16 | 111.110 | odd | 2 |