Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(57,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.31678304256.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 8x^{5} + 32x^{4} - 20x^{3} + 8x^{2} + 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(-0.285451 + 0.285451i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.73 |
Dual form | 260.2.m.c.57.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.285451 | − | 0.285451i | −0.164805 | − | 0.164805i | 0.619886 | − | 0.784692i | \(-0.287179\pi\) |
−0.784692 | + | 0.619886i | \(0.787179\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21777 | + | 0.285451i | −0.991818 | + | 0.127658i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.26613i | − | 0.478553i | −0.970951 | − | 0.239277i | \(-0.923090\pi\) | ||
0.970951 | − | 0.239277i | \(-0.0769103\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.83704i | − | 0.945678i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.21777 | − | 4.21777i | 1.27171 | − | 1.27171i | 0.326514 | − | 0.945192i | \(-0.394126\pi\) |
0.945192 | − | 0.326514i | \(-0.105874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28545 | − | 2.78868i | 0.633870 | − | 0.773439i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.714549 | + | 0.551584i | 0.184496 | + | 0.142418i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.93232 | − | 1.93232i | −0.468657 | − | 0.468657i | 0.432822 | − | 0.901479i | \(-0.357518\pi\) |
−0.901479 | + | 0.432822i | \(0.857518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55158 | + | 2.55158i | −0.585373 | + | 0.585373i | −0.936375 | − | 0.351001i | \(-0.885841\pi\) |
0.351001 | + | 0.936375i | \(0.385841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.361419 | + | 0.361419i | −0.0788681 | + | 0.0788681i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.21777 | + | 5.21777i | −1.08798 | + | 1.08798i | −0.0922445 | + | 0.995736i | \(0.529404\pi\) |
−0.995736 | + | 0.0922445i | \(0.970596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.83704 | − | 1.26613i | 0.967407 | − | 0.253226i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.66619 | + | 1.66619i | −0.320658 | + | 0.320658i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.16941i | − | 1.33133i | −0.746252 | − | 0.665663i | \(-0.768149\pi\) | ||
0.746252 | − | 0.665663i | \(-0.231851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.78868 | + | 2.78868i | 0.500861 | + | 0.500861i | 0.911705 | − | 0.410844i | \(-0.134766\pi\) |
−0.410844 | + | 0.911705i | \(0.634766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.40794 | −0.419168 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.361419 | + | 2.80799i | 0.0610910 | + | 0.474638i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.83704i | 0.959603i | 0.877377 | + | 0.479801i | \(0.159291\pi\) | ||||
−0.877377 | + | 0.479801i | \(0.840709\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.44842 | + | 0.143646i | −0.231932 | + | 0.0230018i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.33381 | − | 1.33381i | −0.208306 | − | 0.208306i | 0.595241 | − | 0.803547i | \(-0.297057\pi\) |
−0.803547 | + | 0.595241i | \(0.797057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65332 | − | 5.65332i | 0.862123 | − | 0.862123i | −0.129461 | − | 0.991584i | \(-0.541325\pi\) |
0.991584 | + | 0.129461i | \(0.0413248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.809835 | + | 6.29190i | 0.120723 | + | 0.937941i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8048i | 1.57605i | 0.615644 | + | 0.788024i | \(0.288896\pi\) | ||||
−0.615644 | + | 0.788024i | \(0.711104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39691 | 0.770987 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.10317i | 0.154474i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.27258 | − | 9.27258i | −1.27369 | − | 1.27369i | −0.944139 | − | 0.329548i | \(-0.893104\pi\) |
−0.329548 | − | 0.944139i | \(-0.606896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.15009 | + | 10.5580i | −1.09896 | + | 1.42364i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.45671 | 0.192945 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.55158 | − | 2.55158i | −0.332188 | − | 0.332188i | 0.521229 | − | 0.853417i | \(-0.325474\pi\) |
−0.853417 | + | 0.521229i | \(0.825474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8499 | 1.77330 | 0.886651 | − | 0.462439i | \(-0.153026\pi\) | ||||
0.886651 | + | 0.462439i | \(0.153026\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.59206 | −0.452557 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.27258 | + | 6.83704i | −0.529948 | + | 0.848030i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.30477 | 0.159403 | 0.0797015 | − | 0.996819i | \(-0.474603\pi\) | ||||
0.0797015 | + | 0.996819i | \(0.474603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.97884 | 0.358610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.72745 | + | 8.72745i | 1.03576 | + | 1.03576i | 0.999337 | + | 0.0364208i | \(0.0115957\pi\) |
0.0364208 | + | 0.999337i | \(0.488404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.64360 | −0.894615 | −0.447308 | − | 0.894380i | \(-0.647617\pi\) | ||||
−0.447308 | + | 0.894380i | \(0.647617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.74216 | − | 1.01932i | −0.201167 | − | 0.117701i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.34026 | − | 5.34026i | −0.608579 | − | 0.608579i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.954914i | 0.107436i | 0.998556 | + | 0.0537181i | \(0.0171072\pi\) | ||||
−0.998556 | + | 0.0537181i | \(0.982893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.55987 | −0.839986 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.13078i | 0.563176i | 0.959535 | + | 0.281588i | \(0.0908611\pi\) | ||||
−0.959535 | + | 0.281588i | \(0.909139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.83704 | + | 3.73387i | 0.524650 | + | 0.404995i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.04652 | + | 2.04652i | −0.219410 | + | 0.219410i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.31122 | + | 5.31122i | 0.562988 | + | 0.562988i | 0.930155 | − | 0.367167i | \(-0.119672\pi\) |
−0.367167 | + | 0.930155i | \(0.619672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.53083 | − | 2.89368i | −0.370132 | − | 0.303341i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.59206i | − | 0.165089i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.93048 | − | 6.38719i | 0.505857 | − | 0.655312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.81956 | 0.286283 | 0.143141 | − | 0.989702i | \(-0.454280\pi\) | ||||
0.143141 | + | 0.989702i | \(0.454280\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.9660 | − | 11.9660i | −1.20263 | − | 1.20263i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.27716i | − | 0.127082i | −0.997979 | − | 0.0635412i | \(-0.979761\pi\) | ||
0.997979 | − | 0.0635412i | \(-0.0202394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.313060 | − | 0.313060i | 0.0308467 | − | 0.0308467i | −0.691515 | − | 0.722362i | \(-0.743057\pi\) |
0.722362 | + | 0.691515i | \(0.243057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.698378 | − | 0.904713i | 0.0681547 | − | 0.0882910i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.19016 | − | 7.19016i | 0.695099 | − | 0.695099i | −0.268250 | − | 0.963349i | \(-0.586445\pi\) |
0.963349 | + | 0.268250i | \(0.0864453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.07413 | − | 3.07413i | 0.294448 | − | 0.294448i | −0.544387 | − | 0.838834i | \(-0.683238\pi\) |
0.838834 | + | 0.544387i | \(0.183238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.66619 | − | 1.66619i | 0.158148 | − | 0.158148i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.06310 | + | 9.06310i | 0.852585 | + | 0.852585i | 0.990451 | − | 0.137866i | \(-0.0440244\pi\) |
−0.137866 | + | 0.990451i | \(0.544024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0824 | − | 13.0613i | 0.940190 | − | 1.21797i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.91157 | − | 6.48391i | −0.731425 | − | 0.599437i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.44658 | + | 2.44658i | −0.224277 | + | 0.224277i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 24.5792i | − | 2.23447i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.761476i | 0.0686600i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3660 | + | 4.18873i | −0.927166 | + | 0.374652i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.88396 | + | 6.88396i | 0.610853 | + | 0.610853i | 0.943168 | − | 0.332315i | \(-0.107830\pi\) |
−0.332315 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.22749 | −0.284165 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.193437 | 0.0169007 | 0.00845036 | − | 0.999964i | \(-0.497310\pi\) | ||||
0.00845036 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23064 | + | 3.23064i | 0.280132 | + | 0.280132i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.21961 | − | 4.17085i | 0.277100 | − | 0.358969i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.03864i | − | 0.345044i | −0.985006 | − | 0.172522i | \(-0.944808\pi\) | ||
0.985006 | − | 0.172522i | \(-0.0551916\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.57090i | 0.218061i | 0.994038 | + | 0.109031i | \(0.0347746\pi\) | ||||
−0.994038 | + | 0.109031i | \(0.965225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.08426 | − | 3.08426i | 0.259741 | − | 0.259741i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.12249 | − | 21.4015i | −0.177491 | − | 1.78968i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.04652 | + | 15.9001i | 0.169954 | + | 1.32043i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.54055 | − | 1.54055i | −0.127063 | − | 0.127063i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.898264 | − | 0.898264i | 0.0735887 | − | 0.0735887i | −0.669354 | − | 0.742943i | \(-0.733429\pi\) |
0.742943 | + | 0.669354i | \(0.233429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.58564 | + | 7.58564i | −0.617311 | + | 0.617311i | −0.944841 | − | 0.327530i | \(-0.893784\pi\) |
0.327530 | + | 0.944841i | \(0.393784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.48206 | + | 5.48206i | −0.443199 | + | 0.443199i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.98068 | − | 5.38862i | −0.560702 | − | 0.432824i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.36142 | + | 5.36142i | −0.427888 | + | 0.427888i | −0.887908 | − | 0.460020i | \(-0.847842\pi\) |
0.460020 | + | 0.887908i | \(0.347842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.29374i | 0.419821i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.60639 | + | 6.60639i | 0.520657 | + | 0.520657i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7883 | 1.31496 | 0.657479 | − | 0.753473i | \(-0.271623\pi\) | ||||
0.657479 | + | 0.753473i | \(0.271623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.34026 | − | 0.687349i | 0.415739 | − | 0.0535100i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.2790i | − | 1.33709i | −0.743671 | − | 0.668546i | \(-0.766917\pi\) | ||
0.743671 | − | 0.668546i | \(-0.233083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.55342 | − | 12.7468i | −0.196417 | − | 0.980520i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.23893 | + | 7.23893i | 0.553575 | + | 0.553575i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.52582 | + | 4.52582i | −0.344091 | + | 0.344091i | −0.857903 | − | 0.513812i | \(-0.828233\pi\) |
0.513812 | + | 0.857903i | \(0.328233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.60309 | − | 6.12433i | −0.121182 | − | 0.462956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.45671i | 0.109493i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.01935 | −0.524651 | −0.262325 | − | 0.964980i | \(-0.584489\pi\) | ||||
−0.262325 | + | 0.964980i | \(0.584489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.02116i | 0.224561i | 0.993677 | + | 0.112281i | \(0.0358155\pi\) | ||||
−0.993677 | + | 0.112281i | \(0.964184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.95348 | − | 3.95348i | −0.292250 | − | 0.292250i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.66619 | − | 12.9452i | −0.122501 | − | 0.951751i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.3002 | −1.19199 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.10962 | + | 2.10962i | 0.153452 | + | 0.153452i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.916276 | −0.0662994 | −0.0331497 | − | 0.999450i | \(-0.510554\pi\) | ||||
−0.0331497 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0580 | 1.08390 | 0.541949 | − | 0.840412i | \(-0.317687\pi\) | ||||
0.541949 | + | 0.840412i | \(0.317687\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.17125 | − | 0.732027i | 0.227098 | − | 0.0524215i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.56445 | −0.396451 | −0.198225 | − | 0.980156i | \(-0.563518\pi\) | ||||
−0.198225 | + | 0.980156i | \(0.563518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2616 | 1.15275 | 0.576375 | − | 0.817185i | \(-0.304467\pi\) | ||||
0.576375 | + | 0.817185i | \(0.304467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.372448 | − | 0.372448i | −0.0262705 | − | 0.0262705i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.07743 | −0.637111 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.33883 | + | 2.57735i | 0.233194 | + | 0.180010i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.8030 | + | 14.8030i | 1.02888 | + | 1.02888i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.5240i | 1.48885i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.4383 | −1.33819 | −0.669094 | − | 0.743177i | \(-0.733318\pi\) | ||||
−0.669094 | + | 0.743177i | \(0.733318\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 4.98252i | − | 0.341397i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.9240 | + | 14.1515i | −0.745013 | + | 0.965126i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.53083 | − | 3.53083i | 0.239689 | − | 0.239689i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.18187 | + | 2.18187i | 0.147437 | + | 0.147437i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.80485 | + | 0.972392i | −0.659545 | + | 0.0654101i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.60496i | 0.241406i | 0.992689 | + | 0.120703i | \(0.0385149\pi\) | ||||
−0.992689 | + | 0.120703i | \(0.961485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.59206 | − | 13.7228i | −0.239471 | − | 0.914856i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.4374 | 1.62197 | 0.810984 | − | 0.585068i | \(-0.198932\pi\) | ||||
0.810984 | + | 0.585068i | \(0.198932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.46315 | + | 9.46315i | 0.625343 | + | 0.625343i | 0.946893 | − | 0.321550i | \(-0.104204\pi\) |
−0.321550 | + | 0.946893i | \(0.604204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.04877i | 0.200594i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.80011 | + | 1.80011i | −0.117929 | + | 0.117929i | −0.763609 | − | 0.645679i | \(-0.776574\pi\) |
0.645679 | + | 0.763609i | \(0.276574\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.08426 | − | 23.9627i | −0.201195 | − | 1.56315i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.272581 | − | 0.272581i | 0.0177061 | − | 0.0177061i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0999 | + | 13.0999i | −0.847362 | + | 0.847362i | −0.989803 | − | 0.142441i | \(-0.954505\pi\) |
0.142441 | + | 0.989803i | \(0.454505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2371 | + | 13.2371i | −0.852676 | + | 0.852676i | −0.990462 | − | 0.137786i | \(-0.956001\pi\) |
0.137786 | + | 0.990462i | \(0.456001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.15654 | + | 7.15654i | 0.459092 | + | 0.459092i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.9691 | + | 1.54055i | −0.764679 | + | 0.0984224i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.28402 | + | 12.9471i | 0.0817002 | + | 0.823802i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.46459 | − | 1.46459i | 0.0928144 | − | 0.0928144i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.62612i | − | 0.291998i | −0.989285 | − | 0.145999i | \(-0.953360\pi\) | ||
0.989285 | − | 0.145999i | \(-0.0466396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.0148i | 2.76718i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.314901 | − | 2.44658i | −0.0197198 | − | 0.153210i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.55342 | − | 4.55342i | −0.284035 | − | 0.284035i | 0.550681 | − | 0.834716i | \(-0.314368\pi\) |
−0.834716 | + | 0.550681i | \(0.814368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.39046 | 0.459221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.3399 | −1.25901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.72100 | − | 2.72100i | −0.167784 | − | 0.167784i | 0.618221 | − | 0.786005i | \(-0.287854\pi\) |
−0.786005 | + | 0.618221i | \(0.787854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.2114 | + | 17.9176i | 1.42586 | + | 1.10067i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.03219i | − | 0.185567i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6870i | 0.712567i | 0.934378 | + | 0.356284i | \(0.115956\pi\) | ||||
−0.934378 | + | 0.356284i | \(0.884044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9660 | + | 13.9660i | −0.848372 | + | 0.848372i | −0.989930 | − | 0.141558i | \(-0.954789\pi\) |
0.141558 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.181875 | + | 1.83389i | 0.0110076 | + | 0.110992i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.0613 | − | 25.7418i | 0.908228 | − | 1.55229i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.09672 | + | 1.09672i | 0.0658954 | + | 0.0658954i | 0.739286 | − | 0.673391i | \(-0.235163\pi\) |
−0.673391 | + | 0.739286i | \(0.735163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.91157 | − | 7.91157i | 0.473653 | − | 0.473653i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.62755 | + | 8.62755i | −0.514677 | + | 0.514677i | −0.915956 | − | 0.401279i | \(-0.868566\pi\) |
0.401279 | + | 0.915956i | \(0.368566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.50507 | − | 7.50507i | 0.446130 | − | 0.446130i | −0.447936 | − | 0.894066i | \(-0.647841\pi\) |
0.894066 | + | 0.447936i | \(0.147841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.23064 | + | 0.415819i | −0.191367 | + | 0.0246310i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.68878 | + | 1.68878i | −0.0996856 | + | 0.0996856i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 9.53226i | − | 0.560721i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.804846 | − | 0.804846i | −0.0471809 | − | 0.0471809i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0341 | 1.22882 | 0.614411 | − | 0.788986i | \(-0.289394\pi\) | ||||
0.614411 | + | 0.788986i | \(0.289394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.38719 | + | 4.93048i | 0.371876 | + | 0.287064i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.0552i | 0.815566i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.62571 | + | 26.4756i | 0.151849 | + | 1.53113i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.15785 | − | 7.15785i | −0.412572 | − | 0.412572i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.364567 | + | 0.364567i | −0.0209439 | + | 0.0209439i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.7160 | + | 3.95348i | −1.75879 | + | 0.226376i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.7984i | − | 0.787516i | −0.919214 | − | 0.393758i | \(-0.871175\pi\) | ||
0.919214 | − | 0.393758i | \(-0.128825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.178727 | −0.0101674 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.9743i | − | 1.13264i | −0.824187 | − | 0.566318i | \(-0.808367\pi\) | ||
0.824187 | − | 0.566318i | \(-0.191633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.92587 | − | 4.92587i | −0.278427 | − | 0.278427i | 0.554054 | − | 0.832481i | \(-0.313080\pi\) |
−0.832481 | + | 0.554054i | \(0.813080\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.96638 | − | 1.02536i | 0.448855 | − | 0.0577724i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7146 | 0.657956 | 0.328978 | − | 0.944338i | \(-0.393296\pi\) | ||||
0.328978 | + | 0.944338i | \(0.393296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.2390 | − | 30.2390i | −1.69306 | − | 1.69306i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.10488 | −0.229112 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.86096 | 0.548679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.52398 | − | 16.3826i | 0.417355 | − | 0.908744i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.75503 | −0.0970532 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6804 | 0.754223 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.94061 | − | 4.94061i | −0.271561 | − | 0.271561i | 0.558168 | − | 0.829728i | \(-0.311505\pi\) |
−0.829728 | + | 0.558168i | \(0.811505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.5599 | 0.907475 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.89368 | + | 0.372448i | −0.158099 | + | 0.0203490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.67909 | − | 8.67909i | −0.472780 | − | 0.472780i | 0.430033 | − | 0.902813i | \(-0.358502\pi\) |
−0.902813 | + | 0.430033i | \(0.858502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 5.17415i | − | 0.281021i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.5240 | 1.27390 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.6961i | − | 0.847511i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.60639 | + | 0.850314i | −0.355676 | + | 0.0457794i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0627 | − | 19.0627i | 1.02334 | − | 1.02334i | 0.0236177 | − | 0.999721i | \(-0.492482\pi\) |
0.999721 | − | 0.0236177i | \(-0.00751845\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00645 | + | 2.00645i | 0.107403 | + | 0.107403i | 0.758766 | − | 0.651363i | \(-0.225803\pi\) |
−0.651363 | + | 0.758766i | \(0.725803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.838467 | + | 8.45446i | 0.0447541 | + | 0.451265i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.41162i | − | 0.128358i | −0.997938 | − | 0.0641788i | \(-0.979557\pi\) | ||
0.997938 | − | 0.0641788i | \(-0.0204428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8468 | − | 16.8642i | −1.15951 | − | 0.895061i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.39676 | 0.0739242 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.92546 | + | 1.92546i | 0.101622 | + | 0.101622i | 0.756090 | − | 0.654468i | \(-0.227107\pi\) |
−0.654468 | + | 0.756090i | \(0.727107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.97884i | 0.314676i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.01617 | + | 7.01617i | −0.368253 | + | 0.368253i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9518 | − | 2.18187i | 0.887296 | − | 0.114205i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.8435 | + | 16.8435i | −0.879224 | + | 0.879224i | −0.993454 | − | 0.114230i | \(-0.963560\pi\) |
0.114230 | + | 0.993454i | \(0.463560\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.78407 | + | 3.78407i | −0.196991 | + | 0.196991i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.7403 | + | 11.7403i | −0.609527 | + | 0.609527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.4388 | − | 20.4388i | −1.05828 | − | 1.05828i | −0.998193 | − | 0.0600904i | \(-0.980861\pi\) |
−0.0600904 | − | 0.998193i | \(-0.519139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.15468 | + | 1.76332i | 0.214547 | + | 0.0910573i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.9932 | − | 16.3853i | −1.02970 | − | 0.843888i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7841 | + | 15.7841i | −0.810775 | + | 0.810775i | −0.984750 | − | 0.173975i | \(-0.944339\pi\) |
0.173975 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3.93007i | − | 0.201344i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7432i | 1.11102i | 0.831508 | + | 0.555512i | \(0.187478\pi\) | ||||
−0.831508 | + | 0.555512i | \(0.812522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.3679 | + | 10.3191i | 0.681290 | + | 0.525910i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.0387 | − | 16.0387i | −0.815291 | − | 0.815291i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.9227 | 0.908718 | 0.454359 | − | 0.890819i | \(-0.349868\pi\) | ||||
0.454359 | + | 0.890819i | \(0.349868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.1648 | 1.01978 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0552170 | − | 0.0552170i | −0.00278533 | − | 0.00278533i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.272581 | − | 2.11778i | −0.0137151 | − | 0.106557i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 33.9632i | − | 1.70457i | −0.523081 | − | 0.852283i | \(-0.675218\pi\) | ||
0.523081 | − | 0.852283i | \(-0.324782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.84438i | − | 0.0923346i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0857 | − | 15.0857i | 0.753343 | − | 0.753343i | −0.221758 | − | 0.975102i | \(-0.571180\pi\) |
0.975102 | + | 0.221758i | \(0.0711796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.1501 | − | 1.40333i | 0.704866 | − | 0.0699048i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.7661 | − | 2.15798i | 0.833113 | − | 0.107231i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.6193 | + | 24.6193i | 1.22033 | + | 1.22033i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7141 | − | 11.7141i | 0.579227 | − | 0.579227i | −0.355463 | − | 0.934690i | \(-0.615677\pi\) |
0.934690 | + | 0.355463i | \(0.115677\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.15283 | + | 1.15283i | −0.0568651 | + | 0.0568651i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.23064 | + | 3.23064i | −0.158970 | + | 0.158970i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.46459 | − | 11.3789i | −0.0718937 | − | 0.558568i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.733868 | − | 0.733868i | 0.0359376 | − | 0.0359376i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2486i | 0.647234i | 0.946188 | + | 0.323617i | \(0.104899\pi\) | ||||
−0.946188 | + | 0.323617i | \(0.895101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.17729 | − | 6.17729i | −0.301063 | − | 0.301063i | 0.540367 | − | 0.841430i | \(-0.318286\pi\) |
−0.841430 | + | 0.540367i | \(0.818286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.6537 | 1.49044 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.7933 | − | 6.90013i | −0.572058 | − | 0.334706i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17.5358i | − | 0.848619i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.50322 | + | 6.71496i | −0.265698 | + | 0.324201i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.25641 | + | 4.25641i | 0.205024 | + | 0.205024i | 0.802149 | − | 0.597124i | \(-0.203690\pi\) |
−0.597124 | + | 0.802149i | \(0.703690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.2579 | + | 27.2579i | −1.30993 | + | 1.30993i | −0.388467 | + | 0.921463i | \(0.626995\pi\) |
−0.921463 | + | 0.388467i | \(0.873005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.95453 | − | 5.12290i | 0.189605 | − | 0.245624i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 26.6272i | − | 1.27375i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2063 | −1.15531 | −0.577653 | − | 0.816283i | \(-0.696031\pi\) | ||||
−0.577653 | + | 0.816283i | \(0.696031\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 15.3112i | − | 0.729106i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.84991 | − | 9.84991i | −0.467983 | − | 0.467983i | 0.433277 | − | 0.901261i | \(-0.357357\pi\) |
−0.901261 | + | 0.433277i | \(0.857357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2952 | − | 10.2630i | −0.630252 | − | 0.486512i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.512822 | −0.0242556 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7067 | + | 12.7067i | 0.599666 | + | 0.599666i | 0.940224 | − | 0.340558i | \(-0.110616\pi\) |
−0.340558 | + | 0.940224i | \(0.610616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2514 | −0.529809 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.33066 | 0.203472 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.65659 | + | 5.40965i | 0.405827 | + | 0.253608i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4226 | 0.487551 | 0.243775 | − | 0.969832i | \(-0.421614\pi\) | ||||
0.243775 | + | 0.969832i | \(0.421614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.43923 | 0.300557 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2616 | − | 23.2616i | −1.08340 | − | 1.08340i | −0.996190 | − | 0.0872084i | \(-0.972205\pi\) |
−0.0872084 | − | 0.996190i | \(-0.527795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36644 | 0.109978 | 0.0549888 | − | 0.998487i | \(-0.482488\pi\) | ||||
0.0549888 | + | 0.998487i | \(0.482488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.454456 | + | 3.53083i | 0.0210749 | + | 0.163738i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6648 | + | 22.6648i | 1.04880 | + | 1.04880i | 0.998746 | + | 0.0500547i | \(0.0159396\pi\) |
0.0500547 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.65201i | − | 0.0762828i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.06085 | 0.141036 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 47.6888i | − | 2.19274i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.11146 | + | 15.5727i | −0.418062 | + | 0.714526i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.3066 | + | 26.3066i | −1.20450 | + | 1.20450i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.74861 | − | 1.74861i | −0.0798958 | − | 0.0798958i | 0.666030 | − | 0.745925i | \(-0.267992\pi\) |
−0.745925 | + | 0.666030i | \(0.767992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2776 | + | 13.3403i | 0.742195 | + | 0.608263i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.77161i | − | 0.171614i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.25314 | + | 0.804846i | −0.283940 | + | 0.0365462i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3822 | −0.651720 | −0.325860 | − | 0.945418i | \(-0.605654\pi\) | ||||
−0.325860 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.79223 | − | 4.79223i | −0.216712 | − | 0.216712i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.4770i | − | 0.608206i | −0.952639 | − | 0.304103i | \(-0.901643\pi\) | ||
0.952639 | − | 0.304103i | \(-0.0983568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.8536 | + | 13.8536i | −0.623935 | + | 0.623935i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.9535 | + | 23.1221i | 1.34631 | + | 1.03926i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.0501 | − | 11.0501i | 0.495665 | − | 0.495665i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7644 | + | 19.7644i | −0.884775 | + | 0.884775i | −0.994015 | − | 0.109241i | \(-0.965158\pi\) |
0.109241 | + | 0.994015i | \(0.465158\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.93232 | + | 4.93232i | −0.220360 | + | 0.220360i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.04181 | − | 6.04181i | −0.269391 | − | 0.269391i | 0.559464 | − | 0.828855i | \(-0.311007\pi\) |
−0.828855 | + | 0.559464i | \(0.811007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.364567 | + | 2.83245i | 0.0162230 | + | 0.126043i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.90970 | + | 4.36746i | −0.129224 | + | 0.193966i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1677 | + | 13.1677i | −0.583648 | + | 0.583648i | −0.935904 | − | 0.352256i | \(-0.885415\pi\) |
0.352256 | + | 0.935904i | \(0.385415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.67781i | 0.428121i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 8.50284i | − | 0.375410i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.604932 | + | 0.783659i | −0.0266565 | + | 0.0345321i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.5724 | + | 45.5724i | 2.00427 | + | 2.00427i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58380 | 0.113416 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8720 | 0.520121 | 0.260061 | − | 0.965592i | \(-0.416257\pi\) | ||||
0.260061 | + | 0.965592i | \(0.416257\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.9954 | + | 28.9954i | 1.26788 | + | 1.26788i | 0.947180 | + | 0.320702i | \(0.103919\pi\) |
0.320702 | + | 0.947180i | \(0.396081\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.29059 | + | 2.20580i | −0.0563261 | + | 0.0962691i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.7772i | − | 0.469464i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 31.4503i | − | 1.36740i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.23893 | + | 7.23893i | −0.314143 | + | 0.314143i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.76792 | + | 0.671206i | −0.293151 | + | 0.0290732i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.8937 | + | 17.9986i | −0.600678 | + | 0.778147i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.00368 | + | 2.00368i | 0.0864652 | + | 0.0864652i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.7629 | − | 22.7629i | 0.980469 | − | 0.980469i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.93375 | + | 4.93375i | −0.212119 | + | 0.212119i | −0.805167 | − | 0.593048i | \(-0.797924\pi\) |
0.593048 | + | 0.805167i | \(0.297924\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.862394 | − | 0.862394i | 0.0370089 | − | 0.0370089i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.94020 | + | 7.69523i | −0.254450 | + | 0.329627i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6257 | + | 19.6257i | −0.839135 | + | 0.839135i | −0.988745 | − | 0.149610i | \(-0.952198\pi\) |
0.149610 | + | 0.988745i | \(0.452198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 39.2927i | − | 1.67697i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.2934 | + | 18.2934i | 0.779323 | + | 0.779323i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20905 | 0.0514139 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.21961 | + | 4.17085i | −0.136665 | + | 0.177043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.5792i | 1.33805i | 0.743238 | + | 0.669027i | \(0.233289\pi\) | ||||
−0.743238 | + | 0.669027i | \(0.766711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.84489 | − | 28.6857i | −0.120326 | − | 1.21327i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.65291 | + | 4.65291i | 0.196446 | + | 0.196446i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.3660 | + | 21.3660i | −0.900471 | + | 0.900471i | −0.995477 | − | 0.0950060i | \(-0.969713\pi\) |
0.0950060 | + | 0.995477i | \(0.469713\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.6870 | − | 17.5128i | −0.954448 | − | 0.736770i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.57180i | 0.401978i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.8436 | 1.75418 | 0.877088 | − | 0.480329i | \(-0.159483\pi\) | ||||
0.877088 | + | 0.480329i | \(0.159483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5809i | 0.944983i | 0.881335 | + | 0.472491i | \(0.156645\pi\) | ||||
−0.881335 | + | 0.472491i | \(0.843355\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.261552 | + | 0.261552i | 0.0109265 | + | 0.0109265i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.6322 | + | 31.8449i | −0.777015 | + | 1.32803i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6436 | −0.984296 | −0.492148 | − | 0.870512i | \(-0.663788\pi\) | ||||
−0.492148 | + | 0.870512i | \(0.663788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.29832 | − | 4.29832i | −0.178632 | − | 0.178632i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.49624 | 0.269510 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −78.2193 | −3.23951 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.3969 | + | 12.1215i | 0.801963 | + | 0.501161i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.8370 | −1.56170 | −0.780851 | − | 0.624718i | \(-0.785214\pi\) | ||||
−0.780851 | + | 0.624718i | \(0.785214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.2311 | −0.586381 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.58838 | + | 1.58838i | 0.0653372 | + | 0.0653372i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.64547 | 0.149701 | 0.0748507 | − | 0.997195i | \(-0.476152\pi\) | ||||
0.0748507 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.72757 | − | 6.12433i | 0.193812 | − | 0.251073i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.64188 | − | 4.64188i | −0.189980 | − | 0.189980i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.0451i | 1.02331i | 0.859190 | + | 0.511657i | \(0.170968\pi\) | ||||
−0.859190 | + | 0.511657i | \(0.829032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.47132 | 0.182389 | 0.0911945 | − | 0.995833i | \(-0.470932\pi\) | ||||
0.0911945 | + | 0.995833i | \(0.470932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.70168i | − | 0.150744i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.01617 | + | 54.5111i | 0.285248 | + | 2.21619i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.24538 | + | 3.24538i | −0.131726 | + | 0.131726i | −0.769896 | − | 0.638170i | \(-0.779692\pi\) |
0.638170 | + | 0.769896i | \(0.279692\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.59116 | + | 2.59116i | 0.104999 | + | 0.104999i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.1312 | + | 24.6940i | 1.21898 | + | 0.999010i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.3997i | − | 1.91445i | −0.289337 | − | 0.957227i | \(-0.593435\pi\) | ||
0.289337 | − | 0.957227i | \(-0.406565\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.217364 | − | 1.68878i | −0.00876498 | − | 0.0680982i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.45402 | 0.0585366 | 0.0292683 | − | 0.999572i | \(-0.490682\pi\) | ||||
0.0292683 | + | 0.999572i | \(0.490682\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7229 | + | 11.7229i | 0.471182 | + | 0.471182i | 0.902297 | − | 0.431115i | \(-0.141880\pi\) |
−0.431115 | + | 0.902297i | \(0.641880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 17.3876i | − | 0.697740i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.72471 | − | 6.72471i | 0.269420 | − | 0.269420i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7938 | − | 12.2487i | 0.871753 | − | 0.489946i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.14405 | − | 6.14405i | 0.245370 | − | 0.245370i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.2790 | − | 11.2790i | 0.449724 | − | 0.449724i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2758 | − | 21.2758i | 0.846975 | − | 0.846975i | −0.142780 | − | 0.989754i | \(-0.545604\pi\) |
0.989754 | + | 0.142780i | \(0.0456041\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.54869 | + | 5.54869i | 0.220541 | + | 0.220541i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.2321 | − | 13.3020i | −0.683835 | − | 0.527875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3344 | − | 15.0502i | 0.488706 | − | 0.596312i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.7601 | − | 24.7601i | 0.979493 | − | 0.979493i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.2716i | 0.721684i | 0.932627 | + | 0.360842i | \(0.117511\pi\) | ||||
−0.932627 | + | 0.360842i | \(0.882489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.6308i | − | 1.08965i | −0.838550 | − | 0.544825i | \(-0.816596\pi\) | ||
0.838550 | − | 0.544825i | \(-0.183404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.15785 | − | 0.921293i | 0.281840 | − | 0.0362759i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6648 | − | 22.6648i | −0.891045 | − | 0.891045i | 0.103577 | − | 0.994621i | \(-0.466971\pi\) |
−0.994621 | + | 0.103577i | \(0.966971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.5240 | −0.844891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.01576 | −0.0790039 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.3338 | + | 17.3338i | 0.678324 | + | 0.678324i | 0.959621 | − | 0.281296i | \(-0.0907644\pi\) |
−0.281296 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.429000 | + | 0.0552170i | −0.0167624 | + | 0.00215751i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.6852i | 0.846018i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5065i | 0.876730i | 0.898797 | + | 0.438365i | \(0.144442\pi\) | ||||
−0.898797 | + | 0.438365i | \(0.855558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.66806 | + | 8.66806i | −0.337148 | + | 0.337148i | −0.855293 | − | 0.518145i | \(-0.826623\pi\) |
0.518145 | + | 0.855293i | \(0.326623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.07638 | + | 2.52124i | 0.119477 | + | 0.0979167i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.08702 | − | 6.24264i | −0.313601 | − | 0.242079i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.4084 | + | 37.4084i | 1.44846 | + | 1.44846i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.02904 | − | 1.02904i | 0.0397850 | − | 0.0397850i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 58.4159 | − | 58.4159i | 2.25512 | − | 2.25512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.10360 | − | 9.10360i | 0.350918 | − | 0.350918i | −0.509533 | − | 0.860451i | \(-0.670182\pi\) |
0.860451 | + | 0.509533i | \(0.170182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.94980 | + | 10.1690i | −0.229008 | + | 0.391406i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.29832 | + | 9.29832i | −0.357364 | + | 0.357364i | −0.862840 | − | 0.505477i | \(-0.831317\pi\) |
0.505477 | + | 0.862840i | \(0.331317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.56993i | − | 0.137001i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.97569 | − | 6.97569i | −0.267309 | − | 0.267309i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.8177 | 0.413927 | 0.206964 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206964 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.15283 | + | 8.95678i | 0.0440475 | + | 0.342221i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.40254i | − | 0.206120i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.0503 | + | 4.66619i | −1.79247 | + | 0.177768i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.121054 | − | 0.121054i | −0.00460512 | − | 0.00460512i | 0.704800 | − | 0.709406i | \(-0.251037\pi\) |
−0.709406 | + | 0.704800i | \(0.751037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.1505 | + | 15.1505i | −0.575520 | + | 0.575520i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.733868 | − | 5.70168i | −0.0278372 | − | 0.216277i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.15470i | 0.195248i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.02769 | 0.0388708 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.15470i | 0.0436125i | 0.999762 | + | 0.0218063i | \(0.00694170\pi\) | ||||
−0.999762 | + | 0.0218063i | \(0.993058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.8937 | − | 14.8937i | −0.561726 | − | 0.561726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.95978 | + | 7.72059i | −0.224458 | + | 0.290774i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.61706 | −0.0608156 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.1464 | − | 37.1464i | −1.39506 | − | 1.39506i | −0.813503 | − | 0.581561i | \(-0.802442\pi\) |
−0.581561 | − | 0.813503i | \(-0.697558\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.70912 | 0.101600 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.1014 | −1.08985 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.8163 | + | 46.8578i | 0.404506 | + | 1.75238i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.47876 | 0.279300 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.4383 | −0.501165 | −0.250582 | − | 0.968095i | \(-0.580622\pi\) | ||||
−0.250582 | + | 0.968095i | \(0.580622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.396375 | − | 0.396375i | −0.0147618 | − | 0.0147618i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.55709 | 0.281051 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.07743 | − | 34.6787i | −0.337127 | − | 1.28793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.7860 | − | 28.7860i | −1.06761 | − | 1.06761i | −0.997542 | − | 0.0700702i | \(-0.977678\pi\) |
−0.0700702 | − | 0.997542i | \(-0.522322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.5939i | 0.688664i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.8481 | −0.808080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.5996i | 1.05635i | 0.849136 | + | 0.528174i | \(0.177123\pi\) | ||||
−0.849136 | + | 0.528174i | \(0.822877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.85635 | + | 2.97685i | 0.142244 | + | 0.109803i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.50322 | − | 5.50322i | 0.202714 | − | 0.202714i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0484 | + | 11.0484i | 0.406420 | + | 0.406420i | 0.880488 | − | 0.474068i | \(-0.157215\pi\) |
−0.474068 | + | 0.880488i | \(0.657215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.32923 | − | 4.06228i | 0.122302 | − | 0.149232i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.7882i | − | 0.432466i | −0.976342 | − | 0.216233i | \(-0.930623\pi\) | ||
0.976342 | − | 0.216233i | \(-0.0693771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.73574 | + | 2.24856i | −0.0635924 | + | 0.0823808i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.5562 | 0.532583 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.10370 | − | 9.10370i | −0.332642 | − | 0.332642i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 30.3583i | − | 1.10779i | −0.832587 | − | 0.553895i | \(-0.813141\pi\) | ||
0.832587 | − | 0.553895i | \(-0.186859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.32053 | + | 1.32053i | −0.0481229 | + | 0.0481229i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.6579 | − | 18.9886i | 0.533456 | − | 0.691065i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1677 | − | 19.1677i | 0.696662 | − | 0.696662i | −0.267027 | − | 0.963689i | \(-0.586041\pi\) |
0.963689 | + | 0.267027i | \(0.0860414\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.5641 | − | 12.5641i | 0.456047 | − | 0.456047i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2165 | − | 12.2165i | 0.442847 | − | 0.442847i | −0.450121 | − | 0.892968i | \(-0.648619\pi\) |
0.892968 | + | 0.450121i | \(0.148619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.89225 | − | 3.89225i | −0.140909 | − | 0.140909i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.5931 | − | 13.7228i | 0.382995 | − | 0.496150i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.9471 | + | 1.28402i | −0.467491 | + | 0.0463632i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5875 | + | 23.5875i | −0.850586 | + | 0.850586i | −0.990205 | − | 0.139619i | \(-0.955412\pi\) |
0.139619 | + | 0.990205i | \(0.455412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.59956i | 0.0936209i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.8600i | − | 1.14592i | −0.819582 | − | 0.572962i | \(-0.805794\pi\) | ||
0.819582 | − | 0.572962i | \(-0.194206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0198 | + | 9.95809i | 0.611368 | + | 0.357705i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.10962 | − | 2.10962i | −0.0756821 | − | 0.0756821i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.80666 | 0.243874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.6208 | 2.63436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.9456 | + | 11.9456i | 0.426901 | + | 0.426901i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.3600 | − | 13.4208i | 0.369764 | − | 0.479010i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.3333i | − | 1.00997i | −0.863127 | − | 0.504987i | \(-0.831497\pi\) | ||
0.863127 | − | 0.504987i | \(-0.168503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.55342i | 0.0553034i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4751 | − | 11.4751i | 0.408007 | − | 0.408007i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6533 | − | 38.6230i | 1.12404 | − | 1.37154i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.51111 | − | 11.7403i | −0.0535934 | − | 0.416386i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2610 | − | 21.2610i | −0.753104 | − | 0.753104i | 0.221953 | − | 0.975057i | \(-0.428757\pi\) |
−0.975057 | + | 0.221953i | \(0.928757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.8784 | − | 20.8784i | 0.738626 | − | 0.738626i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0681 | − | 15.0681i | 0.532406 | − | 0.532406i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.2390 | + | 32.2390i | −1.13769 | + | 1.13769i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.5373 | − | 12.7657i | −0.582863 | − | 0.449931i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.33606 | − | 3.33606i | 0.117435 | − | 0.117435i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.8766i | − | 0.804300i | −0.915574 | − | 0.402150i | \(-0.868263\pi\) | ||
0.915574 | − | 0.402150i | \(-0.131737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7214 | − | 20.7214i | −0.727628 | − | 0.727628i | 0.242519 | − | 0.970147i | \(-0.422026\pi\) |
−0.970147 | + | 0.242519i | \(0.922026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.97321 | 0.279633 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.2326 | + | 4.79223i | −1.30420 | + | 0.167865i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.8498i | 1.00933i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.20948 | + | 10.0171i | −0.286863 | + | 0.350026i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2951 | + | 28.2951i | 0.987505 | + | 0.987505i | 0.999923 | − | 0.0124179i | \(-0.00395285\pi\) |
−0.0124179 | + | 0.999923i | \(0.503953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.8518 | + | 13.8518i | −0.482842 | + | 0.482842i | −0.906038 | − | 0.423196i | \(-0.860908\pi\) |
0.423196 | + | 0.906038i | \(0.360908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.6473 | + | 3.04877i | −0.405506 | + | 0.106144i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.5533i | − | 0.366975i | −0.983022 | − | 0.183488i | \(-0.941261\pi\) | ||
0.983022 | − | 0.183488i | \(-0.0587387\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3056 | 1.22622 | 0.613108 | − | 0.789999i | \(-0.289919\pi\) | ||||
0.613108 | + | 0.789999i | \(0.289919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 0.626120i | − | 0.0217198i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.4286 | − | 10.4286i | −0.361328 | − | 0.361328i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.93232 | + | 38.3210i | 0.170690 | + | 1.32615i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.29292 | −0.321210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.46456 | − | 2.46456i | −0.0850860 | − | 0.0850860i | 0.663283 | − | 0.748369i | \(-0.269163\pi\) |
−0.748369 | + | 0.663283i | \(0.769163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4005 | −0.772431 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.92549 | 0.169643 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.30150 | + | 27.5406i | 0.319981 | + | 0.947424i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.1205 | −1.06931 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.28466 | −0.147049 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.4563 | − | 30.4563i | −1.04403 | − | 1.04403i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.8214 | 0.918348 | 0.459174 | − | 0.888346i | \(-0.348145\pi\) | ||||
0.459174 | + | 0.888346i | \(0.348145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.1207 | − | 13.9879i | −0.619714 | − | 0.478378i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.6207 | + | 20.6207i | 0.704390 | + | 0.704390i | 0.965350 | − | 0.260959i | \(-0.0840389\pi\) |
−0.260959 | + | 0.965350i | \(0.584039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.3195i | − | 0.522696i | −0.965245 | − | 0.261348i | \(-0.915833\pi\) | ||
0.965245 | − | 0.261348i | \(-0.0841670\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.964130 | 0.0328574 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19.7984i | − | 0.673945i | −0.941514 | − | 0.336973i | \(-0.890597\pi\) | ||
0.941514 | − | 0.336973i | \(-0.109403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.74533 | − | 11.3291i | 0.297350 | − | 0.385202i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.72100 | + | 2.72100i | −0.0924099 | + | 0.0924099i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.02761 | + | 4.02761i | 0.136627 | + | 0.136627i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.98199 | − | 3.63858i | 0.101041 | − | 0.123289i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.99918i | − | 0.270731i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.30349 | + | 13.1248i | 0.179291 | + | 0.443698i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.4393 | −1.23047 | −0.615234 | − | 0.788345i | \(-0.710938\pi\) | ||||
−0.615234 | + | 0.788345i | \(0.710938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00420 | − | 6.00420i | −0.202517 | − | 0.202517i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.4236i | 1.32821i | 0.747637 | + | 0.664107i | \(0.231188\pi\) | ||||
−0.747637 | + | 0.664107i | \(0.768812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.9341 | + | 23.9341i | −0.805445 | + | 0.805445i | −0.983941 | − | 0.178495i | \(-0.942877\pi\) |
0.178495 | + | 0.983941i | \(0.442877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.415819 | − | 3.23064i | −0.0139776 | − | 0.108597i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.8887 | − | 28.8887i | 0.969987 | − | 0.969987i | −0.0295751 | − | 0.999563i | \(-0.509415\pi\) |
0.999563 | + | 0.0295751i | \(0.00941542\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.71601 | − | 8.71601i | 0.292326 | − | 0.292326i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.8858 | + | 31.8858i | −1.06822 | + | 1.06822i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.5695 | − | 27.5695i | −0.922577 | − | 0.922577i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.5673 | − | 2.00368i | 0.520358 | − | 0.0669757i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.80799 | − | 8.30702i | 0.227312 | − | 0.277363i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.9932 | − | 19.9932i | 0.666810 | − | 0.666810i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.8352i | 1.19384i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.08644i | 0.135988i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.862394 | − | 6.70025i | −0.0286669 | − | 0.222724i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.9907 | + | 22.9907i | 0.763394 | + | 0.763394i | 0.976934 | − | 0.213540i | \(-0.0684994\pi\) |
−0.213540 | + | 0.976934i | \(0.568499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.62335 | −0.120179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1427 | 1.23059 | 0.615296 | − | 0.788296i | \(-0.289037\pi\) | ||||
0.615296 | + | 0.788296i | \(0.289037\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.6404 | + | 21.6404i | 0.716194 | + | 0.716194i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.89645 | + | 7.63940i | 0.327167 | + | 0.252551i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.244917i | − | 0.00808789i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46.7810i | − | 1.54316i | −0.636131 | − | 0.771581i | \(-0.719466\pi\) | ||
0.636131 | − | 0.771581i | \(-0.280534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.93877 | + | 3.93877i | −0.129787 | + | 0.129787i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.2842 | − | 4.39186i | 1.45763 | − | 0.144560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.39046 | + | 28.2339i | 0.242997 | + | 0.928326i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.888162 | − | 0.888162i | −0.0291711 | − | 0.0291711i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.4287 | + | 29.4287i | −0.965525 | + | 0.965525i | −0.999425 | − | 0.0339004i | \(-0.989207\pi\) |
0.0339004 | + | 0.999425i | \(0.489207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.7707 | + | 13.7707i | −0.451315 | + | 0.451315i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.70168 | + | 5.70168i | −0.186665 | + | 0.186665i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.1501 | − | 4.65291i | 1.18224 | − | 0.152166i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2450 | + | 29.2450i | −0.955392 | + | 0.955392i | −0.999047 | − | 0.0436550i | \(-0.986100\pi\) |
0.0436550 | + | 0.999047i | \(0.486100\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.81219i | 0.0917725i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1015 | + | 15.1015i | 0.492293 | + | 0.492293i | 0.909028 | − | 0.416735i | \(-0.136826\pi\) |
−0.416735 | + | 0.909028i | \(0.636826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9190 | 0.453266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.28084 | − | 4.07646i | −0.171786 | − | 0.132607i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.1180i | 1.23867i | 0.785127 | + | 0.619335i | \(0.212598\pi\) | ||||
−0.785127 | + | 0.619335i | \(0.787402\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4691 | + | 21.3155i | −0.567070 | + | 0.691931i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.34394 | − | 3.34394i | −0.108435 | − | 0.108435i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.8177 | + | 35.8177i | −1.16025 | + | 1.16025i | −0.175830 | + | 0.984421i | \(0.556261\pi\) |
−0.984421 | + | 0.175830i | \(0.943739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.03209 | − | 0.261552i | 0.0657570 | − | 0.00846363i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.2635i | 0.558050i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.11345 | −0.165122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 15.4466i | − | 0.498277i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.3987 | − | 20.3987i | −0.657341 | − | 0.657341i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.3952 | + | 4.29832i | −1.07503 | + | 0.138368i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.1852 | −0.488322 | −0.244161 | − | 0.969735i | \(-0.578513\pi\) | ||||
−0.244161 | + | 0.969735i | \(0.578513\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.81482 | − | 2.81482i | −0.0904252 | − | 0.0904252i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.5959 | −1.68788 | −0.843941 | − | 0.536436i | \(-0.819770\pi\) | ||||
−0.843941 | + | 0.536436i | \(0.819770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.25510 | 0.104354 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.82417 | + | 2.52871i | −0.218548 | + | 0.0809835i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.6014 | 1.29895 | 0.649477 | − | 0.760381i | \(-0.274988\pi\) | ||||
0.649477 | + | 0.760381i | \(0.274988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.8030 | 1.43191 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.72141 | − | 8.72141i | −0.278453 | − | 0.278453i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.2368 | 0.390294 | 0.195147 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195147 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3407 | − | 1.58838i | 0.393207 | − | 0.0506100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.90508 | − | 3.90508i | −0.124300 | − | 0.124300i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.9955i | 1.87595i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.9218 | −0.664603 | −0.332302 | − | 0.943173i | \(-0.607825\pi\) | ||||
−0.332302 | + | 0.943173i | \(0.607825\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.82061i | 0.0895093i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.0644 | + | 4.64188i | −1.14332 | + | 0.147158i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.72732 | − | 9.72732i | 0.308067 | − | 0.308067i | −0.536092 | − | 0.844159i | \(-0.680100\pi\) |
0.844159 | + | 0.536092i | \(0.180100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.72561 | − | 9.72561i | −0.307705 | − | 0.307705i |
(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 | 260.2.m.c.73.2 | yes | 8 | |
3.2 | odd | 2 | 2340.2.u.g.73.4 | 8 | |||
4.3 | odd | 2 | 1040.2.bg.m.593.3 | 8 | |||
5.2 | odd | 4 | 260.2.r.c.177.2 | yes | 8 | ||
5.3 | odd | 4 | 1300.2.r.c.957.3 | 8 | |||
5.4 | even | 2 | 1300.2.m.c.593.3 | 8 | |||
13.5 | odd | 4 | 260.2.r.c.213.2 | yes | 8 | ||
15.2 | even | 4 | 2340.2.bp.g.1477.2 | 8 | |||
20.7 | even | 4 | 1040.2.cd.m.177.3 | 8 | |||
39.5 | even | 4 | 2340.2.bp.g.1513.2 | 8 | |||
52.31 | even | 4 | 1040.2.cd.m.993.3 | 8 | |||
65.18 | even | 4 | 1300.2.m.c.57.3 | 8 | |||
65.44 | odd | 4 | 1300.2.r.c.993.3 | 8 | |||
65.57 | even | 4 | inner | 260.2.m.c.57.2 | ✓ | 8 | |
195.122 | odd | 4 | 2340.2.u.g.577.4 | 8 | |||
260.187 | odd | 4 | 1040.2.bg.m.577.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.m.c.57.2 | ✓ | 8 | 65.57 | even | 4 | inner | |
260.2.m.c.73.2 | yes | 8 | 1.1 | even | 1 | trivial | |
260.2.r.c.177.2 | yes | 8 | 5.2 | odd | 4 | ||
260.2.r.c.213.2 | yes | 8 | 13.5 | odd | 4 | ||
1040.2.bg.m.577.3 | 8 | 260.187 | odd | 4 | |||
1040.2.bg.m.593.3 | 8 | 4.3 | odd | 2 | |||
1040.2.cd.m.177.3 | 8 | 20.7 | even | 4 | |||
1040.2.cd.m.993.3 | 8 | 52.31 | even | 4 | |||
1300.2.m.c.57.3 | 8 | 65.18 | even | 4 | |||
1300.2.m.c.593.3 | 8 | 5.4 | even | 2 | |||
1300.2.r.c.957.3 | 8 | 5.3 | odd | 4 | |||
1300.2.r.c.993.3 | 8 | 65.44 | odd | 4 | |||
2340.2.u.g.73.4 | 8 | 3.2 | odd | 2 | |||
2340.2.u.g.577.4 | 8 | 195.122 | odd | 4 | |||
2340.2.bp.g.1477.2 | 8 | 15.2 | even | 4 | |||
2340.2.bp.g.1513.2 | 8 | 39.5 | even | 4 |