Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 24 x^{14} - 48 x^{13} + 160 x^{12} - 292 x^{11} + 436 x^{10} - 176 x^{9} - 914 x^{8} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.8 | ||
Root | \(-1.03797 + 0.429941i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.h.737.8 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.46791 | − | 1.68678i | 0.656470 | − | 0.754352i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.23071 | − | 0.154765i | 0.705411 | − | 0.0489410i | ||||
\(11\) | 1.23907i | 0.373594i | 0.982399 | + | 0.186797i | \(0.0598106\pi\) | ||||
−0.982399 | + | 0.186797i | \(0.940189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.46141 | + | 4.46141i | 1.23737 | + | 1.23737i | 0.961071 | + | 0.276302i | \(0.0891090\pi\) |
0.276302 | + | 0.961071i | \(0.410891\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.78778 | + | 4.78778i | 1.16121 | + | 1.16121i | 0.984212 | + | 0.176995i | \(0.0566377\pi\) |
0.176995 | + | 0.984212i | \(0.443362\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.84235i | − | 1.34033i | −0.742213 | − | 0.670164i | \(-0.766224\pi\) | ||
0.742213 | − | 0.670164i | \(-0.233776\pi\) | |||||||
\(20\) | 1.68678 | + | 1.46791i | 0.377176 | + | 0.328235i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.876155 | + | 0.876155i | −0.186797 | + | 0.186797i | ||||
\(23\) | −0.707107 | + | 0.707107i | −0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.690470 | − | 4.95210i | −0.138094 | − | 0.990419i | ||||
\(26\) | 6.30939i | 1.23737i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.52518 | −0.840305 | −0.420152 | − | 0.907454i | \(-0.638023\pi\) | ||||
−0.420152 | + | 0.907454i | \(0.638023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.77094i | 1.16121i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.76641 | − | 3.76641i | 0.619194 | − | 0.619194i | −0.326131 | − | 0.945325i | \(-0.605745\pi\) |
0.945325 | + | 0.326131i | \(0.105745\pi\) | |||||||
\(38\) | 4.13117 | − | 4.13117i | 0.670164 | − | 0.670164i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.154765 | + | 2.23071i | 0.0244705 | + | 0.352706i | ||||
\(41\) | − | 8.85528i | − | 1.38296i | −0.722395 | − | 0.691481i | \(-0.756959\pi\) | ||
0.722395 | − | 0.691481i | \(-0.243041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.64710 | + | 7.64710i | 1.16617 | + | 1.16617i | 0.983100 | + | 0.183072i | \(0.0586040\pi\) |
0.183072 | + | 0.983100i | \(0.441396\pi\) | |||||||
\(44\) | −1.23907 | −0.186797 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 1.69675 | + | 1.69675i | 0.247497 | + | 0.247497i | 0.819943 | − | 0.572446i | \(-0.194005\pi\) |
−0.572446 | + | 0.819943i | \(0.694005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 3.01342 | − | 3.98990i | 0.426163 | − | 0.564257i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.46141 | + | 4.46141i | −0.618686 | + | 0.618686i | ||||
\(53\) | −3.04730 | + | 3.04730i | −0.418579 | + | 0.418579i | −0.884714 | − | 0.466135i | \(-0.845646\pi\) |
0.466135 | + | 0.884714i | \(0.345646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09004 | + | 1.81885i | 0.281821 | + | 0.245253i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.19979 | − | 3.19979i | −0.420152 | − | 0.420152i | ||||
\(59\) | 0.693932 | 0.0903423 | 0.0451711 | − | 0.998979i | \(-0.485617\pi\) | ||||
0.0451711 | + | 0.998979i | \(0.485617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.3656 | 1.83933 | 0.919663 | − | 0.392707i | \(-0.128461\pi\) | ||||
0.919663 | + | 0.392707i | \(0.128461\pi\) | |||||||
\(62\) | −4.24264 | − | 4.24264i | −0.538816 | − | 0.538816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 14.0744 | − | 0.976472i | 1.74571 | − | 0.121116i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96620 | − | 2.96620i | 0.362379 | − | 0.362379i | −0.502309 | − | 0.864688i | \(-0.667516\pi\) |
0.864688 | + | 0.502309i | \(0.167516\pi\) | |||||||
\(68\) | −4.78778 | + | 4.78778i | −0.580603 | + | 0.580603i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2089i | 1.92364i | 0.273682 | + | 0.961820i | \(0.411758\pi\) | ||||
−0.273682 | + | 0.961820i | \(0.588242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.66120 | + | 4.66120i | 0.545552 | + | 0.545552i | 0.925151 | − | 0.379599i | \(-0.123938\pi\) |
−0.379599 | + | 0.925151i | \(0.623938\pi\) | |||||||
\(74\) | 5.32651 | 0.619194 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.84235 | 0.670164 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.15188i | 0.917158i | 0.888654 | + | 0.458579i | \(0.151641\pi\) | ||||
−0.888654 | + | 0.458579i | \(0.848359\pi\) | |||||||
\(80\) | −1.46791 | + | 1.68678i | −0.164118 | + | 0.188588i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.26163 | − | 6.26163i | 0.691481 | − | 0.691481i | ||||
\(83\) | 0.939152 | − | 0.939152i | 0.103085 | − | 0.103085i | −0.653683 | − | 0.756768i | \(-0.726777\pi\) |
0.756768 | + | 0.653683i | \(0.226777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.1040 | − | 1.04790i | 1.63826 | − | 0.113661i | ||||
\(86\) | 10.8146i | 1.16617i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.876155 | − | 0.876155i | −0.0933984 | − | 0.0933984i | ||||
\(89\) | 4.52518 | 0.479668 | 0.239834 | − | 0.970814i | \(-0.422907\pi\) | ||||
0.239834 | + | 0.970814i | \(0.422907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.707107 | − | 0.707107i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.39957i | 0.247497i | ||||||||
\(95\) | −9.85478 | − | 8.57606i | −1.01108 | − | 0.879885i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.57116 | − | 9.57116i | 0.971804 | − | 0.971804i | −0.0278096 | − | 0.999613i | \(-0.508853\pi\) |
0.999613 | + | 0.0278096i | \(0.00885323\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.95210 | − | 0.690470i | 0.495210 | − | 0.0690470i | ||||
\(101\) | − | 9.83175i | − | 0.978295i | −0.872201 | − | 0.489148i | \(-0.837308\pi\) | ||
0.872201 | − | 0.489148i | \(-0.162692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 6.00000i | −0.591198 | − | 0.591198i | 0.346757 | − | 0.937955i | \(-0.387283\pi\) |
−0.937955 | + | 0.346757i | \(0.887283\pi\) | |||||||
\(104\) | −6.30939 | −0.618686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.30953 | −0.418579 | ||||||||
\(107\) | −7.83508 | − | 7.83508i | −0.757445 | − | 0.757445i | 0.218411 | − | 0.975857i | \(-0.429913\pi\) |
−0.975857 | + | 0.218411i | \(0.929913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7091i | 1.02575i | 0.858465 | + | 0.512873i | \(0.171419\pi\) | ||||
−0.858465 | + | 0.512873i | \(0.828581\pi\) | |||||||
\(110\) | 0.191765 | + | 2.76400i | 0.0182840 | + | 0.263537i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3534 | + | 11.3534i | −1.06803 | + | 1.06803i | −0.0705240 | + | 0.997510i | \(0.522467\pi\) |
−0.997510 | + | 0.0705240i | \(0.977533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.154765 | + | 2.23071i | 0.0144319 | + | 0.208014i | ||||
\(116\) | − | 4.52518i | − | 0.420152i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.490684 | + | 0.490684i | 0.0451711 | + | 0.0451711i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.46471 | 0.860428 | ||||||||
\(122\) | 10.1580 | + | 10.1580i | 0.919663 | + | 0.919663i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.00000i | − | 0.538816i | ||||||
\(125\) | −9.36666 | − | 6.10457i | −0.837779 | − | 0.546009i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.61329 | − | 9.61329i | 0.853042 | − | 0.853042i | −0.137465 | − | 0.990507i | \(-0.543895\pi\) |
0.990507 | + | 0.137465i | \(0.0438954\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.6426 | + | 9.26163i | 0.933415 | + | 0.812298i | ||||
\(131\) | − | 16.1411i | − | 1.41026i | −0.709079 | − | 0.705129i | \(-0.750889\pi\) | ||
0.709079 | − | 0.705129i | \(-0.249111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.19484 | 0.362379 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.77094 | −0.580603 | ||||||||
\(137\) | −3.65610 | − | 3.65610i | −0.312362 | − | 0.312362i | 0.533462 | − | 0.845824i | \(-0.320891\pi\) |
−0.845824 | + | 0.533462i | \(0.820891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.83855i | 0.240762i | 0.992728 | + | 0.120381i | \(0.0384117\pi\) | ||||
−0.992728 | + | 0.120381i | \(0.961588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.4614 | + | 11.4614i | −0.961820 | + | 0.961820i | ||||
\(143\) | −5.52800 | + | 5.52800i | −0.462275 | + | 0.462275i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.64257 | + | 7.63300i | −0.551635 | + | 0.633886i | ||||
\(146\) | 6.59193i | 0.545552i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.76641 | + | 3.76641i | 0.309597 | + | 0.309597i | ||||
\(149\) | −4.76143 | −0.390072 | −0.195036 | − | 0.980796i | \(-0.562482\pi\) | ||||
−0.195036 | + | 0.980796i | \(0.562482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.90419 | −0.480476 | −0.240238 | − | 0.970714i | \(-0.577226\pi\) | ||||
−0.240238 | + | 0.970714i | \(0.577226\pi\) | |||||||
\(152\) | 4.13117 | + | 4.13117i | 0.335082 | + | 0.335082i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.80747 | + | 10.1207i | −0.707433 | + | 0.812914i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.99547 | − | 2.99547i | 0.239064 | − | 0.239064i | −0.577398 | − | 0.816463i | \(-0.695932\pi\) |
0.816463 | + | 0.577398i | \(0.195932\pi\) | |||||||
\(158\) | −5.76425 | + | 5.76425i | −0.458579 | + | 0.458579i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.23071 | + | 0.154765i | −0.176353 | + | 0.0122352i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2851 | − | 11.2851i | −0.883920 | − | 0.883920i | 0.110011 | − | 0.993930i | \(-0.464911\pi\) |
−0.993930 | + | 0.110011i | \(0.964911\pi\) | |||||||
\(164\) | 8.85528 | 0.691481 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.32816 | 0.103085 | ||||||||
\(167\) | −3.19842 | − | 3.19842i | −0.247501 | − | 0.247501i | 0.572443 | − | 0.819944i | \(-0.305996\pi\) |
−0.819944 | + | 0.572443i | \(0.805996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.8084i | 2.06218i | ||||||||
\(170\) | 11.4211 | + | 9.93914i | 0.875959 | + | 0.762298i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.64710 | + | 7.64710i | −0.583086 | + | 0.583086i | ||||
\(173\) | −14.5121 | + | 14.5121i | −1.10334 | + | 1.10334i | −0.109331 | + | 0.994005i | \(0.534871\pi\) |
−0.994005 | + | 0.109331i | \(0.965129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.23907i | − | 0.0933984i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.19979 | + | 3.19979i | 0.239834 | + | 0.239834i | ||||
\(179\) | 8.51852 | 0.636704 | 0.318352 | − | 0.947973i | \(-0.396871\pi\) | ||||
0.318352 | + | 0.947973i | \(0.396871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.36560 | 0.175834 | 0.0879169 | − | 0.996128i | \(-0.471979\pi\) | ||||
0.0879169 | + | 0.996128i | \(0.471979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | −0.824357 | − | 11.8819i | −0.0606079 | − | 0.873573i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.93239 | + | 5.93239i | −0.433820 | + | 0.433820i | ||||
\(188\) | −1.69675 | + | 1.69675i | −0.123748 | + | 0.123748i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.904191 | − | 13.0326i | −0.0655969 | − | 0.945482i | ||||
\(191\) | − | 6.39684i | − | 0.462859i | −0.972852 | − | 0.231430i | \(-0.925660\pi\) | ||
0.972852 | − | 0.231430i | \(-0.0743403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.68470 | − | 8.68470i | −0.625139 | − | 0.625139i | 0.321702 | − | 0.946841i | \(-0.395745\pi\) |
−0.946841 | + | 0.321702i | \(0.895745\pi\) | |||||||
\(194\) | 13.5357 | 0.971804 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −5.50165 | − | 5.50165i | −0.391977 | − | 0.391977i | 0.483415 | − | 0.875391i | \(-0.339396\pi\) |
−0.875391 | + | 0.483415i | \(0.839396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 26.8552i | − | 1.90372i | −0.306540 | − | 0.951858i | \(-0.599171\pi\) | ||
0.306540 | − | 0.951858i | \(-0.400829\pi\) | |||||||
\(200\) | 3.98990 | + | 3.01342i | 0.282128 | + | 0.213081i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.95210 | − | 6.95210i | 0.489148 | − | 0.489148i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9369 | − | 12.9988i | −1.04324 | − | 0.907873i | ||||
\(206\) | − | 8.48528i | − | 0.591198i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.46141 | − | 4.46141i | −0.309343 | − | 0.309343i | ||||
\(209\) | 7.23908 | 0.500738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1609 | 0.974879 | 0.487440 | − | 0.873157i | \(-0.337931\pi\) | ||||
0.487440 | + | 0.873157i | \(0.337931\pi\) | |||||||
\(212\) | −3.04730 | − | 3.04730i | −0.209289 | − | 0.209289i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 11.0805i | − | 0.757445i | ||||||
\(215\) | 24.1243 | − | 1.67373i | 1.64526 | − | 0.114147i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.57248 | + | 7.57248i | −0.512873 | + | 0.512873i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.81885 | + | 2.09004i | −0.122627 | + | 0.140911i | ||||
\(221\) | 42.7205i | 2.87369i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4849 | + | 17.4849i | 1.17088 | + | 1.17088i | 0.982001 | + | 0.188876i | \(0.0604843\pi\) |
0.188876 | + | 0.982001i | \(0.439516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0561 | −1.06803 | ||||||||
\(227\) | −17.4106 | − | 17.4106i | −1.15558 | − | 1.15558i | −0.985415 | − | 0.170170i | \(-0.945568\pi\) |
−0.170170 | − | 0.985415i | \(-0.554432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.93816i | 0.392405i | 0.980563 | + | 0.196202i | \(0.0628609\pi\) | ||||
−0.980563 | + | 0.196202i | \(0.937139\pi\) | |||||||
\(230\) | −1.46791 | + | 1.68678i | −0.0967912 | + | 0.111223i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.19979 | − | 3.19979i | 0.210076 | − | 0.210076i | ||||
\(233\) | −0.437741 | + | 0.437741i | −0.0286774 | + | 0.0286774i | −0.721300 | − | 0.692623i | \(-0.756455\pi\) |
0.692623 | + | 0.721300i | \(0.256455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.35274 | − | 0.371370i | 0.349174 | − | 0.0242255i | ||||
\(236\) | 0.693932i | 0.0451711i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.1808 | −1.69349 | −0.846747 | − | 0.531996i | \(-0.821442\pi\) | ||||
−0.846747 | + | 0.531996i | \(0.821442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3618 | −0.989540 | −0.494770 | − | 0.869024i | \(-0.664748\pi\) | ||||
−0.494770 | + | 0.869024i | \(0.664748\pi\) | |||||||
\(242\) | 6.69256 | + | 6.69256i | 0.430214 | + | 0.430214i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.3656i | 0.919663i | ||||||||
\(245\) | 11.8075 | + | 10.2754i | 0.754352 | + | 0.656470i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0651 | − | 26.0651i | 1.65848 | − | 1.65848i | ||||
\(248\) | 4.24264 | − | 4.24264i | 0.269408 | − | 0.269408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.30665 | − | 10.9398i | −0.145885 | − | 0.691894i | ||||
\(251\) | 21.1174i | 1.33292i | 0.745543 | + | 0.666458i | \(0.232190\pi\) | ||||
−0.745543 | + | 0.666458i | \(0.767810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.876155 | − | 0.876155i | −0.0550834 | − | 0.0550834i | ||||
\(254\) | 13.5952 | 0.853042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.8346 | − | 10.8346i | −0.675842 | − | 0.675842i | 0.283215 | − | 0.959057i | \(-0.408599\pi\) |
−0.959057 | + | 0.283215i | \(0.908599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.976472 | + | 14.0744i | 0.0605582 | + | 0.872857i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.4135 | − | 11.4135i | 0.705129 | − | 0.705129i | ||||
\(263\) | −12.6602 | + | 12.6602i | −0.780660 | + | 0.780660i | −0.979942 | − | 0.199282i | \(-0.936139\pi\) |
0.199282 | + | 0.979942i | \(0.436139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.666964 | + | 9.61329i | 0.0409713 | + | 0.590540i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.96620 | + | 2.96620i | 0.181189 | + | 0.181189i | ||||
\(269\) | 11.6226 | 0.708642 | 0.354321 | − | 0.935124i | \(-0.384712\pi\) | ||||
0.354321 | + | 0.935124i | \(0.384712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.1121 | −1.70769 | −0.853846 | − | 0.520526i | \(-0.825736\pi\) | ||||
−0.853846 | + | 0.520526i | \(0.825736\pi\) | |||||||
\(272\) | −4.78778 | − | 4.78778i | −0.290302 | − | 0.290302i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.17051i | − | 0.312362i | ||||||
\(275\) | 6.13599 | − | 0.855541i | 0.370014 | − | 0.0515911i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.09004 | − | 8.09004i | 0.486083 | − | 0.486083i | −0.420984 | − | 0.907068i | \(-0.638315\pi\) |
0.907068 | + | 0.420984i | \(0.138315\pi\) | |||||||
\(278\) | −2.00716 | + | 2.00716i | −0.120381 | + | 0.120381i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.60981i | 0.215343i | 0.994187 | + | 0.107672i | \(0.0343395\pi\) | ||||
−0.994187 | + | 0.107672i | \(0.965660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6413 | − | 21.6413i | −1.28644 | − | 1.28644i | −0.936932 | − | 0.349511i | \(-0.886348\pi\) |
−0.349511 | − | 0.936932i | \(-0.613652\pi\) | |||||||
\(284\) | −16.2089 | −0.961820 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.81777 | −0.462275 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.8456i | 1.69680i | ||||||||
\(290\) | −10.0943 | + | 0.700339i | −0.592760 | + | 0.0411253i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.66120 | + | 4.66120i | −0.272776 | + | 0.272776i | ||||
\(293\) | 6.63566 | − | 6.63566i | 0.387659 | − | 0.387659i | −0.486193 | − | 0.873852i | \(-0.661615\pi\) |
0.873852 | + | 0.486193i | \(0.161615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01863 | − | 1.17051i | 0.0593070 | − | 0.0681499i | ||||
\(296\) | 5.32651i | 0.309597i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.36684 | − | 3.36684i | −0.195036 | − | 0.195036i | ||||
\(299\) | −6.30939 | −0.364881 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.17489 | − | 4.17489i | −0.240238 | − | 0.240238i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.84235i | 0.335082i | ||||||||
\(305\) | 21.0874 | − | 24.2316i | 1.20746 | − | 1.38750i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5419 | − | 17.5419i | 1.00117 | − | 1.00117i | 0.00116880 | − | 0.999999i | \(-0.499628\pi\) |
0.999999 | − | 0.00116880i | \(-0.000372040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.3842 | + | 0.928590i | −0.760173 | + | 0.0527404i | ||||
\(311\) | − | 25.3053i | − | 1.43493i | −0.696594 | − | 0.717466i | \(-0.745302\pi\) | ||
0.696594 | − | 0.717466i | \(-0.254698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6086 | + | 10.6086i | 0.599633 | + | 0.599633i | 0.940215 | − | 0.340582i | \(-0.110624\pi\) |
−0.340582 | + | 0.940215i | \(0.610624\pi\) | |||||||
\(314\) | 4.23623 | 0.239064 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.15188 | −0.458579 | ||||||||
\(317\) | 6.67938 | + | 6.67938i | 0.375152 | + | 0.375152i | 0.869349 | − | 0.494198i | \(-0.164538\pi\) |
−0.494198 | + | 0.869349i | \(0.664538\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.60702i | − | 0.313933i | ||||||
\(320\) | −1.68678 | − | 1.46791i | −0.0942940 | − | 0.0820588i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.9719 | − | 27.9719i | 1.55640 | − | 1.55640i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.0129 | − | 25.1738i | 1.05464 | − | 1.39639i | ||||
\(326\) | − | 15.9596i | − | 0.883920i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.26163 | + | 6.26163i | 0.345740 | + | 0.345740i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.7498 | −1.96499 | −0.982494 | − | 0.186292i | \(-0.940353\pi\) | ||||
−0.982494 | + | 0.186292i | \(0.940353\pi\) | |||||||
\(332\) | 0.939152 | + | 0.939152i | 0.0515427 | + | 0.0515427i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 4.52325i | − | 0.247501i | ||||||
\(335\) | −0.649214 | − | 9.35744i | −0.0354703 | − | 0.511252i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1600 | + | 23.1600i | −1.26161 | + | 1.26161i | −0.311295 | + | 0.950313i | \(0.600763\pi\) |
−0.950313 | + | 0.311295i | \(0.899237\pi\) | |||||||
\(338\) | −18.9564 | + | 18.9564i | −1.03109 | + | 1.03109i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.04790 | + | 15.1040i | 0.0568306 | + | 0.819128i | ||||
\(341\) | − | 7.43442i | − | 0.402596i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.8146 | −0.583086 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.5233 | −1.10334 | ||||||||
\(347\) | −6.47812 | − | 6.47812i | −0.347764 | − | 0.347764i | 0.511512 | − | 0.859276i | \(-0.329086\pi\) |
−0.859276 | + | 0.511512i | \(0.829086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.3316i | − | 1.51656i | −0.651930 | − | 0.758279i | \(-0.726041\pi\) | ||
0.651930 | − | 0.758279i | \(-0.273959\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.876155 | − | 0.876155i | 0.0466992 | − | 0.0466992i | ||||
\(353\) | 5.10997 | − | 5.10997i | 0.271976 | − | 0.271976i | −0.557919 | − | 0.829895i | \(-0.688400\pi\) |
0.829895 | + | 0.557919i | \(0.188400\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.3409 | + | 23.7932i | 1.45110 | + | 1.26281i | ||||
\(356\) | 4.52518i | 0.239834i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.02351 | + | 6.02351i | 0.318352 | + | 0.318352i | ||||
\(359\) | −29.4937 | −1.55662 | −0.778310 | − | 0.627881i | \(-0.783923\pi\) | ||||
−0.778310 | + | 0.627881i | \(0.783923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1331 | −0.796477 | ||||||||
\(362\) | 1.67273 | + | 1.67273i | 0.0879169 | + | 0.0879169i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7047 | − | 1.02020i | 0.769677 | − | 0.0533997i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.07470 | + | 5.07470i | −0.264897 | + | 0.264897i | −0.827040 | − | 0.562143i | \(-0.809977\pi\) |
0.562143 | + | 0.827040i | \(0.309977\pi\) | |||||||
\(368\) | 0.707107 | − | 0.707107i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.81885 | − | 8.98466i | 0.406482 | − | 0.467090i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.77547 | − | 5.77547i | −0.299043 | − | 0.299043i | 0.541596 | − | 0.840639i | \(-0.317820\pi\) |
−0.840639 | + | 0.541596i | \(0.817820\pi\) | |||||||
\(374\) | −8.38967 | −0.433820 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.39957 | −0.123748 | ||||||||
\(377\) | −20.1887 | − | 20.1887i | −1.03977 | − | 1.03977i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3166i | 1.30043i | 0.759751 | + | 0.650214i | \(0.225321\pi\) | ||||
−0.759751 | + | 0.650214i | \(0.774679\pi\) | |||||||
\(380\) | 8.57606 | − | 9.85478i | 0.439942 | − | 0.505539i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.52325 | − | 4.52325i | 0.231430 | − | 0.231430i | ||||
\(383\) | 2.35744 | − | 2.35744i | 0.120460 | − | 0.120460i | −0.644307 | − | 0.764767i | \(-0.722854\pi\) |
0.764767 | + | 0.644307i | \(0.222854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.2820i | − | 0.625139i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.57116 | + | 9.57116i | 0.485902 | + | 0.485902i | ||||
\(389\) | 0.457683 | 0.0232055 | 0.0116027 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116027 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.77094 | −0.342421 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 7.78051i | − | 0.391977i | ||||||
\(395\) | 13.7505 | + | 11.9662i | 0.691860 | + | 0.602087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.09910 | + | 4.09910i | −0.205728 | + | 0.205728i | −0.802449 | − | 0.596721i | \(-0.796470\pi\) |
0.596721 | + | 0.802449i | \(0.296470\pi\) | |||||||
\(398\) | 18.9895 | − | 18.9895i | 0.951858 | − | 0.951858i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.690470 | + | 4.95210i | 0.0345235 | + | 0.247605i | ||||
\(401\) | − | 28.8474i | − | 1.44057i | −0.693679 | − | 0.720284i | \(-0.744011\pi\) | ||
0.693679 | − | 0.720284i | \(-0.255989\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7685 | − | 26.7685i | −1.33343 | − | 1.33343i | ||||
\(404\) | 9.83175 | 0.489148 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.66685 | + | 4.66685i | 0.231327 | + | 0.231327i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.3694i | − | 1.05665i | −0.849042 | − | 0.528325i | \(-0.822820\pi\) | ||
0.849042 | − | 0.528325i | \(-0.177180\pi\) | |||||||
\(410\) | −1.37049 | − | 19.7535i | −0.0676835 | − | 0.975557i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.00000 | − | 6.00000i | 0.295599 | − | 0.295599i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.205553 | − | 2.96274i | −0.0100902 | − | 0.145435i | ||||
\(416\) | − | 6.30939i | − | 0.309343i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.11880 | + | 5.11880i | 0.250369 | + | 0.250369i | ||||
\(419\) | −17.3388 | −0.847056 | −0.423528 | − | 0.905883i | \(-0.639209\pi\) | ||||
−0.423528 | + | 0.905883i | \(0.639209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8700 | −0.822196 | −0.411098 | − | 0.911591i | \(-0.634855\pi\) | ||||
−0.411098 | + | 0.911591i | \(0.634855\pi\) | |||||||
\(422\) | 10.0133 | + | 10.0133i | 0.487440 | + | 0.487440i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 4.30953i | − | 0.209289i | ||||||
\(425\) | 20.4037 | − | 27.0154i | 0.989726 | − | 1.31044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.83508 | − | 7.83508i | 0.378723 | − | 0.378723i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.2419 | + | 15.8749i | 0.879704 | + | 0.765557i | ||||
\(431\) | 5.88446i | 0.283445i | 0.989906 | + | 0.141722i | \(0.0452640\pi\) | ||||
−0.989906 | + | 0.141722i | \(0.954736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.97073 | + | 3.97073i | 0.190821 | + | 0.190821i | 0.796051 | − | 0.605230i | \(-0.206919\pi\) |
−0.605230 | + | 0.796051i | \(0.706919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.7091 | −0.512873 | ||||||||
\(437\) | 4.13117 | + | 4.13117i | 0.197620 | + | 0.197620i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.64744i | 0.364992i | 0.983207 | + | 0.182496i | \(0.0584177\pi\) | ||||
−0.983207 | + | 0.182496i | \(0.941582\pi\) | |||||||
\(440\) | −2.76400 | + | 0.191765i | −0.131769 | + | 0.00914202i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.2080 | + | 30.2080i | −1.43685 | + | 1.43685i | ||||
\(443\) | −15.0095 | + | 15.0095i | −0.713121 | + | 0.713121i | −0.967187 | − | 0.254066i | \(-0.918232\pi\) |
0.254066 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.64257 | − | 7.63300i | 0.314888 | − | 0.361839i | ||||
\(446\) | 24.7274i | 1.17088i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8282 | 0.794171 | 0.397085 | − | 0.917782i | \(-0.370022\pi\) | ||||
0.397085 | + | 0.917782i | \(0.370022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9723 | 0.516666 | ||||||||
\(452\) | −11.3534 | − | 11.3534i | −0.534017 | − | 0.534017i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 24.6224i | − | 1.15558i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.2184 | − | 22.2184i | 1.03933 | − | 1.03933i | 0.0401396 | − | 0.999194i | \(-0.487220\pi\) |
0.999194 | − | 0.0401396i | \(-0.0127803\pi\) | |||||||
\(458\) | −4.19891 | + | 4.19891i | −0.196202 | + | 0.196202i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.23071 | + | 0.154765i | −0.104007 | + | 0.00721595i | ||||
\(461\) | − | 7.47279i | − | 0.348043i | −0.984742 | − | 0.174021i | \(-0.944324\pi\) | ||
0.984742 | − | 0.174021i | \(-0.0556762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8514 | − | 16.8514i | −0.783152 | − | 0.783152i | 0.197210 | − | 0.980361i | \(-0.436812\pi\) |
−0.980361 | + | 0.197210i | \(0.936812\pi\) | |||||||
\(464\) | 4.52518 | 0.210076 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.619060 | −0.0286774 | ||||||||
\(467\) | 6.58785 | + | 6.58785i | 0.304849 | + | 0.304849i | 0.842908 | − | 0.538058i | \(-0.180842\pi\) |
−0.538058 | + | 0.842908i | \(0.680842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.04756 | + | 3.52236i | 0.186700 | + | 0.162474i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.490684 | + | 0.490684i | −0.0225856 | + | 0.0225856i | ||||
\(473\) | −9.47529 | + | 9.47529i | −0.435674 | + | 0.435674i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.9319 | + | 4.03397i | −1.32749 | + | 0.185091i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.5126 | − | 18.5126i | −0.846747 | − | 0.846747i | ||||
\(479\) | 13.7091 | 0.626383 | 0.313191 | − | 0.949690i | \(-0.398602\pi\) | ||||
0.313191 | + | 0.949690i | \(0.398602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6070 | 1.53235 | ||||||||
\(482\) | −10.8624 | − | 10.8624i | −0.494770 | − | 0.494770i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.46471i | 0.430214i | ||||||||
\(485\) | −2.09485 | − | 30.1941i | −0.0951220 | − | 1.37104i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7091 | − | 17.7091i | 0.802476 | − | 0.802476i | −0.181006 | − | 0.983482i | \(-0.557935\pi\) |
0.983482 | + | 0.181006i | \(0.0579353\pi\) | |||||||
\(488\) | −10.1580 | + | 10.1580i | −0.459832 | + | 0.459832i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.08335 | + | 15.6149i | 0.0489410 | + | 0.705411i | ||||
\(491\) | 14.4858i | 0.653734i | 0.945070 | + | 0.326867i | \(0.105993\pi\) | ||||
−0.945070 | + | 0.326867i | \(0.894007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.6656 | − | 21.6656i | −0.975768 | − | 0.975768i | ||||
\(494\) | 36.8617 | 1.65848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.495380i | 0.0221763i | 0.999939 | + | 0.0110881i | \(0.00352954\pi\) | ||||
−0.999939 | + | 0.0110881i | \(0.996470\pi\) | |||||||
\(500\) | 6.10457 | − | 9.36666i | 0.273005 | − | 0.418890i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.9322 | + | 14.9322i | −0.666458 | + | 0.666458i | ||||
\(503\) | −6.82177 | + | 6.82177i | −0.304168 | + | 0.304168i | −0.842642 | − | 0.538474i | \(-0.819001\pi\) |
0.538474 | + | 0.842642i | \(0.319001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.5840 | − | 14.4321i | −0.737979 | − | 0.642222i | ||||
\(506\) | − | 1.23907i | − | 0.0550834i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.61329 | + | 9.61329i | 0.426521 | + | 0.426521i | ||||
\(509\) | −2.70773 | −0.120018 | −0.0600090 | − | 0.998198i | \(-0.519113\pi\) | ||||
−0.0600090 | + | 0.998198i | \(0.519113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 15.3224i | − | 0.675842i | ||||||
\(515\) | −18.9282 | + | 1.31322i | −0.834075 | + | 0.0578676i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.10240 | + | 2.10240i | −0.0924633 | + | 0.0924633i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.26163 | + | 10.6426i | −0.406149 | + | 0.466707i | ||||
\(521\) | 19.5029i | 0.854438i | 0.904148 | + | 0.427219i | \(0.140507\pi\) | ||||
−0.904148 | + | 0.427219i | \(0.859493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.4555 | + | 19.4555i | 0.850729 | + | 0.850729i | 0.990223 | − | 0.139494i | \(-0.0445477\pi\) |
−0.139494 | + | 0.990223i | \(0.544548\pi\) | |||||||
\(524\) | 16.1411 | 0.705129 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.9042 | −0.780660 | ||||||||
\(527\) | −28.7267 | − | 28.7267i | −1.25135 | − | 1.25135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −6.32601 | + | 7.26924i | −0.274784 | + | 0.315756i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.5070 | − | 39.5070i | 1.71124 | − | 1.71124i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.7173 | + | 1.71487i | −1.06862 | + | 0.0741402i | ||||
\(536\) | 4.19484i | 0.181189i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.21842 | + | 8.21842i | 0.354321 | + | 0.354321i | ||||
\(539\) | −8.67349 | −0.373594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.2754 | 0.742727 | 0.371363 | − | 0.928488i | \(-0.378890\pi\) | ||||
0.371363 | + | 0.928488i | \(0.378890\pi\) | |||||||
\(542\) | −19.8783 | − | 19.8783i | −0.853846 | − | 0.853846i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.77094i | − | 0.290302i | ||||||
\(545\) | 18.0639 | + | 15.7200i | 0.773774 | + | 0.673372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0561 | + | 12.0561i | −0.515480 | + | 0.515480i | −0.916201 | − | 0.400720i | \(-0.868760\pi\) |
0.400720 | + | 0.916201i | \(0.368760\pi\) | |||||||
\(548\) | 3.65610 | − | 3.65610i | 0.156181 | − | 0.156181i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.94376 | + | 3.73384i | 0.210803 | + | 0.159212i | ||||
\(551\) | 26.4377i | 1.12628i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.4410 | 0.486083 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.83855 | −0.120381 | ||||||||
\(557\) | 7.86143 | + | 7.86143i | 0.333099 | + | 0.333099i | 0.853762 | − | 0.520663i | \(-0.174315\pi\) |
−0.520663 | + | 0.853762i | \(0.674315\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 68.2337i | 2.88598i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.55252 | + | 2.55252i | −0.107672 | + | 0.107672i | ||||
\(563\) | 18.8517 | − | 18.8517i | 0.794504 | − | 0.794504i | −0.187719 | − | 0.982223i | \(-0.560109\pi\) |
0.982223 | + | 0.187719i | \(0.0601095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.48492 | + | 35.8164i | 0.104541 | + | 1.50681i | ||||
\(566\) | − | 30.6055i | − | 1.28644i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.4614 | − | 11.4614i | −0.480910 | − | 0.480910i | ||||
\(569\) | 7.64770 | 0.320608 | 0.160304 | − | 0.987068i | \(-0.448753\pi\) | ||||
0.160304 | + | 0.987068i | \(0.448753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5854 | −0.526684 | −0.263342 | − | 0.964703i | \(-0.584825\pi\) | ||||
−0.263342 | + | 0.964703i | \(0.584825\pi\) | |||||||
\(572\) | −5.52800 | − | 5.52800i | −0.231137 | − | 0.231137i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.98990 | + | 3.01342i | 0.166390 | + | 0.125668i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2803 | + | 13.2803i | −0.552864 | + | 0.552864i | −0.927266 | − | 0.374402i | \(-0.877848\pi\) |
0.374402 | + | 0.927266i | \(0.377848\pi\) | |||||||
\(578\) | −20.3970 | + | 20.3970i | −0.848401 | + | 0.848401i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.63300 | − | 6.64257i | −0.316943 | − | 0.275818i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.77582 | − | 3.77582i | −0.156378 | − | 0.156378i | ||||
\(584\) | −6.59193 | −0.272776 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.38423 | 0.387659 | ||||||||
\(587\) | 22.8883 | + | 22.8883i | 0.944700 | + | 0.944700i | 0.998549 | − | 0.0538492i | \(-0.0171490\pi\) |
−0.0538492 | + | 0.998549i | \(0.517149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0541i | 1.44438i | ||||||||
\(590\) | 1.54796 | − | 0.107396i | 0.0637285 | − | 0.00442144i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.76641 | + | 3.76641i | −0.154799 | + | 0.154799i | ||||
\(593\) | −15.2785 | + | 15.2785i | −0.627411 | + | 0.627411i | −0.947416 | − | 0.320005i | \(-0.896316\pi\) |
0.320005 | + | 0.947416i | \(0.396316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 4.76143i | − | 0.195036i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.46141 | − | 4.46141i | −0.182441 | − | 0.182441i | ||||
\(599\) | 21.3467 | 0.872203 | 0.436102 | − | 0.899897i | \(-0.356359\pi\) | ||||
0.436102 | + | 0.899897i | \(0.356359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2736 | −1.19409 | −0.597047 | − | 0.802206i | \(-0.703660\pi\) | ||||
−0.597047 | + | 0.802206i | \(0.703660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 5.90419i | − | 0.240238i | ||||||
\(605\) | 13.8934 | − | 15.9649i | 0.564845 | − | 0.649065i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.162523 | + | 0.162523i | −0.00659660 | + | 0.00659660i | −0.710397 | − | 0.703801i | \(-0.751485\pi\) |
0.703801 | + | 0.710397i | \(0.251485\pi\) | |||||||
\(608\) | −4.13117 | + | 4.13117i | −0.167541 | + | 0.167541i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.0454 | − | 2.22329i | 1.29748 | − | 0.0900185i | ||||
\(611\) | 15.1398i | 0.612492i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3116 | + | 23.3116i | 0.941546 | + | 0.941546i | 0.998383 | − | 0.0568373i | \(-0.0181016\pi\) |
−0.0568373 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(614\) | 24.8080 | 1.00117 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.2825 | − | 28.2825i | −1.13861 | − | 1.13861i | −0.988699 | − | 0.149912i | \(-0.952101\pi\) |
−0.149912 | − | 0.988699i | \(-0.547899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.2414i | − | 0.692991i | −0.938052 | − | 0.346495i | \(-0.887372\pi\) | ||
0.938052 | − | 0.346495i | \(-0.112628\pi\) | |||||||
\(620\) | −10.1207 | − | 8.80747i | −0.406457 | − | 0.353717i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.8935 | − | 17.8935i | 0.717466 | − | 0.717466i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0465 | + | 6.83855i | −0.961860 | + | 0.273542i | ||||
\(626\) | 15.0028i | 0.599633i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.99547 | + | 2.99547i | 0.119532 | + | 0.119532i | ||||
\(629\) | 36.0655 | 1.43802 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7337 | 0.586538 | 0.293269 | − | 0.956030i | \(-0.405257\pi\) | ||||
0.293269 | + | 0.956030i | \(0.405257\pi\) | |||||||
\(632\) | −5.76425 | − | 5.76425i | −0.229290 | − | 0.229290i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.44607i | 0.375152i | ||||||||
\(635\) | −2.10407 | − | 30.3270i | −0.0834974 | − | 1.20349i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.2299 | + | 31.2299i | −1.23737 | + | 1.23737i | ||||
\(638\) | 3.96476 | − | 3.96476i | 0.156966 | − | 0.156966i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.154765 | − | 2.23071i | −0.00611762 | − | 0.0881764i | ||||
\(641\) | 15.8517i | 0.626105i | 0.949736 | + | 0.313052i | \(0.101352\pi\) | ||||
−0.949736 | + | 0.313052i | \(0.898648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.3748 | − | 19.3748i | −0.764069 | − | 0.764069i | 0.212986 | − | 0.977055i | \(-0.431681\pi\) |
−0.977055 | + | 0.212986i | \(0.931681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.5582 | 1.55640 | ||||||||
\(647\) | 4.71362 | + | 4.71362i | 0.185312 | + | 0.185312i | 0.793666 | − | 0.608354i | \(-0.208170\pi\) |
−0.608354 | + | 0.793666i | \(0.708170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.859831i | 0.0337513i | ||||||||
\(650\) | 31.2447 | − | 4.35644i | 1.22552 | − | 0.170874i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.2851 | − | 11.2851i | 0.441960 | − | 0.441960i | ||||
\(653\) | 35.2327 | − | 35.2327i | 1.37876 | − | 1.37876i | 0.532043 | − | 0.846717i | \(-0.321424\pi\) |
0.846717 | − | 0.532043i | \(-0.178576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.2266 | − | 23.6938i | −1.06383 | − | 0.925792i | ||||
\(656\) | 8.85528i | 0.345740i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0613400 | −0.00238947 | −0.00119473 | − | 0.999999i | \(-0.500380\pi\) | ||||
−0.00119473 | + | 0.999999i | \(0.500380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.94722 | −0.309111 | −0.154556 | − | 0.987984i | \(-0.549395\pi\) | ||||
−0.154556 | + | 0.987984i | \(0.549395\pi\) | |||||||
\(662\) | −25.2790 | − | 25.2790i | −0.982494 | − | 0.982494i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.32816i | 0.0515427i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.19979 | − | 3.19979i | 0.123896 | − | 0.123896i | ||||
\(668\) | 3.19842 | − | 3.19842i | 0.123751 | − | 0.123751i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.15765 | − | 7.07577i | 0.237891 | − | 0.273361i | ||||
\(671\) | 17.8000i | 0.687161i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5654 | + | 14.5654i | 0.561454 | + | 0.561454i | 0.929720 | − | 0.368266i | \(-0.120048\pi\) |
−0.368266 | + | 0.929720i | \(0.620048\pi\) | |||||||
\(674\) | −32.7533 | −1.26161 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.8084 | −1.03109 | ||||||||
\(677\) | 34.4341 | + | 34.4341i | 1.32341 | + | 1.32341i | 0.910996 | + | 0.412416i | \(0.135315\pi\) |
0.412416 | + | 0.910996i | \(0.364685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.93914 | + | 11.4211i | −0.381149 | + | 0.437979i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.25693 | − | 5.25693i | 0.201298 | − | 0.201298i | ||||
\(683\) | −35.5898 | + | 35.5898i | −1.36181 | + | 1.36181i | −0.490194 | + | 0.871613i | \(0.663074\pi\) |
−0.871613 | + | 0.490194i | \(0.836926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.5339 | + | 0.800214i | −0.440687 | + | 0.0305746i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.64710 | − | 7.64710i | −0.291543 | − | 0.291543i | ||||
\(689\) | −27.1905 | −1.03588 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.3130 | −0.886868 | −0.443434 | − | 0.896307i | \(-0.646240\pi\) | ||||
−0.443434 | + | 0.896307i | \(0.646240\pi\) | |||||||
\(692\) | −14.5121 | − | 14.5121i | −0.551668 | − | 0.551668i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 9.16145i | − | 0.347764i | ||||||
\(695\) | 4.78801 | + | 4.16674i | 0.181620 | + | 0.158053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.3971 | − | 42.3971i | 1.60590 | − | 1.60590i | ||||
\(698\) | 20.0335 | − | 20.0335i | 0.758279 | − | 0.758279i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.54280i | − | 0.360427i | −0.983628 | − | 0.180213i | \(-0.942321\pi\) | ||
0.983628 | − | 0.180213i | \(-0.0576788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.0047 | − | 22.0047i | −0.829923 | − | 0.829923i | ||||
\(704\) | 1.23907 | 0.0466992 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.22659 | 0.271976 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 11.0902i | − | 0.416502i | −0.978075 | − | 0.208251i | \(-0.933223\pi\) | ||
0.978075 | − | 0.208251i | \(-0.0667771\pi\) | |||||||
\(710\) | 2.50857 | + | 36.1572i | 0.0941448 | + | 1.35696i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.19979 | + | 3.19979i | −0.119917 | + | 0.119917i | ||||
\(713\) | 4.24264 | − | 4.24264i | 0.158888 | − | 0.158888i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.20992 | + | 17.4392i | 0.0452483 | + | 0.652187i | ||||
\(716\) | 8.51852i | 0.318352i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.8552 | − | 20.8552i | −0.778310 | − | 0.778310i | ||||
\(719\) | 23.8647 | 0.890005 | 0.445002 | − | 0.895529i | \(-0.353203\pi\) | ||||
0.445002 | + | 0.895529i | \(0.353203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.7007 | − | 10.7007i | −0.398239 | − | 0.398239i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.36560i | 0.0879169i | ||||||||
\(725\) | 3.12450 | + | 22.4091i | 0.116041 | + | 0.832254i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8084 | − | 13.8084i | 0.512125 | − | 0.512125i | −0.403052 | − | 0.915177i | \(-0.632051\pi\) |
0.915177 | + | 0.403052i | \(0.132051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.1191 | + | 9.67637i | 0.411538 | + | 0.358138i | ||||
\(731\) | 73.2252i | 2.70833i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.9801 | − | 13.9801i | −0.516368 | − | 0.516368i | 0.400102 | − | 0.916470i | \(-0.368975\pi\) |
−0.916470 | + | 0.400102i | \(0.868975\pi\) | |||||||
\(734\) | −7.17672 | −0.264897 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 3.67533 | + | 3.67533i | 0.135382 | + | 0.135382i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.0722i | − | 1.43730i | −0.695374 | − | 0.718648i | \(-0.744761\pi\) | ||
0.695374 | − | 0.718648i | \(-0.255239\pi\) | |||||||
\(740\) | 11.8819 | − | 0.824357i | 0.436786 | − | 0.0303040i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.7937 | + | 16.7937i | −0.616100 | + | 0.616100i | −0.944529 | − | 0.328429i | \(-0.893481\pi\) |
0.328429 | + | 0.944529i | \(0.393481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.98936 | + | 8.03150i | −0.256070 | + | 0.294251i | ||||
\(746\) | − | 8.16775i | − | 0.299043i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.93239 | − | 5.93239i | −0.216910 | − | 0.216910i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.10487 | 0.295751 | 0.147875 | − | 0.989006i | \(-0.452757\pi\) | ||||
0.147875 | + | 0.989006i | \(0.452757\pi\) | |||||||
\(752\) | −1.69675 | − | 1.69675i | −0.0618742 | − | 0.0618742i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 28.5511i | − | 1.03977i | ||||||
\(755\) | −8.66683 | + | 9.95909i | −0.315418 | + | 0.362448i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.98970 | + | 6.98970i | −0.254045 | + | 0.254045i | −0.822627 | − | 0.568582i | \(-0.807492\pi\) |
0.568582 | + | 0.822627i | \(0.307492\pi\) | |||||||
\(758\) | −17.9016 | + | 17.9016i | −0.650214 | + | 0.650214i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.0326 | − | 0.904191i | 0.472741 | − | 0.0327985i | ||||
\(761\) | − | 30.6134i | − | 1.10973i | −0.831939 | − | 0.554867i | \(-0.812769\pi\) | ||
0.831939 | − | 0.554867i | \(-0.187231\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.39684 | 0.231430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.33393 | 0.120460 | ||||||||
\(767\) | 3.09592 | + | 3.09592i | 0.111787 | + | 0.111787i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6070i | 1.13978i | 0.821722 | + | 0.569889i | \(0.193014\pi\) | ||||
−0.821722 | + | 0.569889i | \(0.806986\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.68470 | − | 8.68470i | 0.312569 | − | 0.312569i | ||||
\(773\) | 20.6622 | − | 20.6622i | 0.743169 | − | 0.743169i | −0.230017 | − | 0.973187i | \(-0.573878\pi\) |
0.973187 | + | 0.230017i | \(0.0738783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.14282 | + | 29.7126i | 0.148815 | + | 1.06731i | ||||
\(776\) | 13.5357i | 0.485902i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.323631 | + | 0.323631i | 0.0116027 | + | 0.0116027i | ||||
\(779\) | −51.7356 | −1.85362 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0839 | −0.718660 | ||||||||
\(782\) | −4.78778 | − | 4.78778i | −0.171211 | − | 0.171211i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | −0.655620 | − | 9.44979i | −0.0234001 | − | 0.337277i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.64380 | − | 7.64380i | 0.272472 | − | 0.272472i | −0.557623 | − | 0.830095i | \(-0.688286\pi\) |
0.830095 | + | 0.557623i | \(0.188286\pi\) | |||||||
\(788\) | 5.50165 | − | 5.50165i | 0.195988 | − | 0.195988i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.26163 | + | 18.1844i | 0.0448866 | + | 0.646974i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.0909 | + | 64.0909i | 2.27593 | + | 2.27593i | ||||
\(794\) | −5.79701 | −0.205728 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.8552 | 0.951858 | ||||||||
\(797\) | 6.53641 | + | 6.53641i | 0.231532 | + | 0.231532i | 0.813332 | − | 0.581800i | \(-0.197651\pi\) |
−0.581800 | + | 0.813332i | \(0.697651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.2474i | 0.574790i | ||||||||
\(800\) | −3.01342 | + | 3.98990i | −0.106541 | + | 0.141064i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.3982 | − | 20.3982i | 0.720284 | − | 0.720284i | ||||
\(803\) | −5.77555 | + | 5.77555i | −0.203815 | + | 0.203815i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 37.8563i | − | 1.33343i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.95210 | + | 6.95210i | 0.244574 | + | 0.244574i | ||||
\(809\) | 33.6137 | 1.18179 | 0.590897 | − | 0.806747i | \(-0.298774\pi\) | ||||
0.590897 | + | 0.806747i | \(0.298774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7291 | 1.43019 | 0.715095 | − | 0.699027i | \(-0.246383\pi\) | ||||
0.715095 | + | 0.699027i | \(0.246383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.59992i | 0.231327i | ||||||||
\(815\) | −35.6011 | + | 2.46998i | −1.24705 | + | 0.0865198i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.6770 | − | 44.6770i | 1.56305 | − | 1.56305i | ||||
\(818\) | 15.1105 | − | 15.1105i | 0.528325 | − | 0.528325i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.9988 | − | 14.9369i | 0.453937 | − | 0.521620i | ||||
\(821\) | − | 16.6582i | − | 0.581374i | −0.956818 | − | 0.290687i | \(-0.906116\pi\) | ||
0.956818 | − | 0.290687i | \(-0.0938839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.4663 | − | 14.4663i | −0.504263 | − | 0.504263i | 0.408497 | − | 0.912760i | \(-0.366053\pi\) |
−0.912760 | + | 0.408497i | \(0.866053\pi\) | |||||||
\(824\) | 8.48528 | 0.295599 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.5175 | − | 39.5175i | −1.37416 | − | 1.37416i | −0.854178 | − | 0.519980i | \(-0.825939\pi\) |
−0.519980 | − | 0.854178i | \(-0.674061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.3875i | 1.15960i | 0.814760 | + | 0.579798i | \(0.196869\pi\) | ||||
−0.814760 | + | 0.579798i | \(0.803131\pi\) | |||||||
\(830\) | 1.94962 | − | 2.24032i | 0.0676724 | − | 0.0777626i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.46141 | − | 4.46141i | 0.154672 | − | 0.154672i | ||||
\(833\) | −33.5144 | + | 33.5144i | −1.16121 | + | 1.16121i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0900 | + | 0.700041i | −0.349180 | + | 0.0242259i | ||||
\(836\) | 7.23908i | 0.250369i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.2604 | − | 12.2604i | −0.423528 | − | 0.423528i | ||||
\(839\) | 0.591681 | 0.0204271 | 0.0102135 | − | 0.999948i | \(-0.496749\pi\) | ||||
0.0102135 | + | 0.999948i | \(0.496749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.52274 | −0.293888 | ||||||||
\(842\) | −11.9289 | − | 11.9289i | −0.411098 | − | 0.411098i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.1609i | 0.487440i | ||||||||
\(845\) | 45.2199 | + | 39.3523i | 1.55561 | + | 1.35376i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.04730 | − | 3.04730i | 0.104645 | − | 0.104645i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33.5303 | − | 4.67513i | 1.15008 | − | 0.160356i | ||||
\(851\) | 5.32651i | 0.182590i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.3071 | − | 34.3071i | −1.17465 | − | 1.17465i | −0.981088 | − | 0.193564i | \(-0.937995\pi\) |
−0.193564 | − | 0.981088i | \(-0.562005\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0805 | 0.378723 | ||||||||
\(857\) | −14.2559 | − | 14.2559i | −0.486974 | − | 0.486974i | 0.420376 | − | 0.907350i | \(-0.361898\pi\) |
−0.907350 | + | 0.420376i | \(0.861898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39.2545i | − | 1.33934i | −0.742657 | − | 0.669672i | \(-0.766435\pi\) | ||
0.742657 | − | 0.669672i | \(-0.233565\pi\) | |||||||
\(860\) | 1.67373 | + | 24.1243i | 0.0570736 | + | 0.822630i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.16094 | + | 4.16094i | −0.141722 | + | 0.141722i | ||||
\(863\) | 17.6300 | − | 17.6300i | 0.600132 | − | 0.600132i | −0.340216 | − | 0.940347i | \(-0.610500\pi\) |
0.940347 | + | 0.340216i | \(0.110500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.17628 | + | 45.7813i | 0.107997 | + | 1.55661i | ||||
\(866\) | 5.61546i | 0.190821i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1008 | −0.342645 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4668 | 0.896795 | ||||||||
\(872\) | −7.57248 | − | 7.57248i | −0.256436 | − | 0.256436i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.84235i | 0.197620i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.45184 | − | 9.45184i | 0.319166 | − | 0.319166i | −0.529281 | − | 0.848447i | \(-0.677538\pi\) |
0.848447 | + | 0.529281i | \(0.177538\pi\) | |||||||
\(878\) | −5.40756 | + | 5.40756i | −0.182496 | + | 0.182496i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.09004 | − | 1.81885i | −0.0704553 | − | 0.0613133i | ||||
\(881\) | − | 23.9576i | − | 0.807151i | −0.914946 | − | 0.403576i | \(-0.867767\pi\) | ||
0.914946 | − | 0.403576i | \(-0.132233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.9319 | − | 10.9319i | −0.367887 | − | 0.367887i | 0.498819 | − | 0.866706i | \(-0.333767\pi\) |
−0.866706 | + | 0.498819i | \(0.833767\pi\) | |||||||
\(884\) | −42.7205 | −1.43685 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.2266 | −0.713121 | ||||||||
\(887\) | 24.0931 | + | 24.0931i | 0.808966 | + | 0.808966i | 0.984477 | − | 0.175511i | \(-0.0561579\pi\) |
−0.175511 | + | 0.984477i | \(0.556158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0943 | − | 0.700339i | 0.338363 | − | 0.0234754i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.4849 | + | 17.4849i | −0.585438 | + | 0.585438i | ||||
\(893\) | 9.91303 | − | 9.91303i | 0.331727 | − | 0.331727i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5044 | − | 14.3689i | 0.417977 | − | 0.480299i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.8993 | + | 11.8993i | 0.397085 | + | 0.397085i | ||||
\(899\) | 27.1511 | 0.905539 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.1796 | −0.972113 | ||||||||
\(902\) | 7.75859 | + | 7.75859i | 0.258333 | + | 0.258333i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.0561i | − | 0.534017i | ||||||
\(905\) | 3.47250 | − | 3.99026i | 0.115430 | − | 0.132641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.2546 | − | 20.2546i | 0.672544 | − | 0.672544i | −0.285758 | − | 0.958302i | \(-0.592245\pi\) |
0.958302 | + | 0.285758i | \(0.0922454\pi\) | |||||||
\(908\) | 17.4106 | − | 17.4106i | 0.577792 | − | 0.577792i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.8841i | − | 0.360607i | −0.983611 | − | 0.180304i | \(-0.942292\pi\) | ||
0.983611 | − | 0.180304i | \(-0.0577080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16368 | + | 1.16368i | 0.0385120 | + | 0.0385120i | ||||
\(914\) | 31.4216 | 1.03933 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.93816 | −0.196202 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3598i | 0.341739i | 0.985294 | + | 0.170870i | \(0.0546577\pi\) | ||||
−0.985294 | + | 0.170870i | \(0.945342\pi\) | |||||||
\(920\) | −1.68678 | − | 1.46791i | −0.0556116 | − | 0.0483956i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.28406 | − | 5.28406i | 0.174021 | − | 0.174021i | ||||
\(923\) | −72.3145 | + | 72.3145i | −2.38026 | + | 2.38026i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.2522 | − | 16.0510i | −0.698769 | − | 0.527755i | ||||
\(926\) | − | 23.8315i | − | 0.783152i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.19979 | + | 3.19979i | 0.105038 | + | 0.105038i | ||||
\(929\) | −11.4817 | −0.376703 | −0.188352 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188352 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.8965 | 1.34033 | ||||||||
\(932\) | −0.437741 | − | 0.437741i | −0.0143387 | − | 0.0143387i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.31663i | 0.304849i | ||||||||
\(935\) | 1.29843 | + | 18.7149i | 0.0424631 | + | 0.612042i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.72551 | + | 5.72551i | −0.187044 | + | 0.187044i | −0.794417 | − | 0.607373i | \(-0.792223\pi\) |
0.607373 | + | 0.794417i | \(0.292223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.371370 | + | 5.35274i | 0.0121127 | + | 0.174587i | ||||
\(941\) | 42.4347i | 1.38333i | 0.722218 | + | 0.691666i | \(0.243123\pi\) | ||||
−0.722218 | + | 0.691666i | \(0.756877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.26163 | + | 6.26163i | 0.203907 | + | 0.203907i | ||||
\(944\) | −0.693932 | −0.0225856 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.4001 | −0.435674 | ||||||||
\(947\) | −13.8251 | − | 13.8251i | −0.449255 | − | 0.449255i | 0.445852 | − | 0.895107i | \(-0.352901\pi\) |
−0.895107 | + | 0.445852i | \(0.852901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.5910i | 1.35010i | ||||||||
\(950\) | −23.3104 | − | 17.6055i | −0.756289 | − | 0.571197i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.83815 | + | 9.83815i | −0.318689 | + | 0.318689i | −0.848263 | − | 0.529574i | \(-0.822352\pi\) |
0.529574 | + | 0.848263i | \(0.322352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7901 | − | 9.39000i | −0.349159 | − | 0.303853i | ||||
\(956\) | − | 26.1808i | − | 0.846747i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.69376 | + | 9.69376i | 0.313191 | + | 0.313191i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 23.7637 | + | 23.7637i | 0.766174 | + | 0.766174i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 15.3618i | − | 0.494770i | ||||||
\(965\) | −27.3976 | + | 1.90083i | −0.881959 | + | 0.0611898i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.20902 | − | 1.20902i | 0.0388796 | − | 0.0388796i | −0.687400 | − | 0.726279i | \(-0.741248\pi\) |
0.726279 | + | 0.687400i | \(0.241248\pi\) | |||||||
\(968\) | −6.69256 | + | 6.69256i | −0.215107 | + | 0.215107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.8692 | − | 22.8317i | 0.637960 | − | 0.733082i | ||||
\(971\) | 12.4490i | 0.399508i | 0.979846 | + | 0.199754i | \(0.0640143\pi\) | ||||
−0.979846 | + | 0.199754i | \(0.935986\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 25.0445 | 0.802476 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.3656 | −0.459832 | ||||||||
\(977\) | −33.3661 | − | 33.3661i | −1.06748 | − | 1.06748i | −0.997552 | − | 0.0699252i | \(-0.977724\pi\) |
−0.0699252 | − | 0.997552i | \(-0.522276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.60702i | 0.179201i | ||||||||
\(980\) | −10.2754 | + | 11.8075i | −0.328235 | + | 0.377176i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2430 | + | 10.2430i | −0.326867 | + | 0.326867i | ||||
\(983\) | 0.948609 | − | 0.948609i | 0.0302559 | − | 0.0302559i | −0.691817 | − | 0.722073i | \(-0.743190\pi\) |
0.722073 | + | 0.691817i | \(0.243190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3560 | + | 1.20415i | −0.553009 | + | 0.0383674i | ||||
\(986\) | − | 30.6397i | − | 0.975768i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.0651 | + | 26.0651i | 0.829242 | + | 0.829242i | ||||
\(989\) | −10.8146 | −0.343885 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.4461 | 1.76130 | 0.880651 | − | 0.473765i | \(-0.157105\pi\) | ||||
0.880651 | + | 0.473765i | \(0.157105\pi\) | |||||||
\(992\) | 4.24264 | + | 4.24264i | 0.134704 | + | 0.134704i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.2989 | − | 39.4211i | −1.43607 | − | 1.24973i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.11791 | + | 6.11791i | −0.193756 | + | 0.193756i | −0.797317 | − | 0.603561i | \(-0.793748\pi\) |
0.603561 | + | 0.797317i | \(0.293748\pi\) | |||||||
\(998\) | −0.350287 | + | 0.350287i | −0.0110881 | + | 0.0110881i | ||||
\(999\) | 0 | 0 |
(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 | 2070.2.j.h.323.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.h.323.1 | ✓ | 16 | |
5.2 | odd | 4 | inner | 2070.2.j.h.737.1 | yes | 16 | |
15.2 | even | 4 | inner | 2070.2.j.h.737.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.h.323.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
2070.2.j.h.323.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.h.737.1 | yes | 16 | 5.2 | odd | 4 | inner | |
2070.2.j.h.737.8 | yes | 16 | 15.2 | even | 4 | inner |