Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + 4799806 x^{4} + 51487320 x^{3} - 123648876 x^{2} + \cdots + 6882692292 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.5 | ||
Root | \(-4.82374 + 1.03135i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.451 |
Dual form | 1050.3.p.f.901.5 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 0.866025i | 0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −1.72580 | − | 6.78392i | −0.246543 | − | 0.969132i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.79066 | + | 16.9579i | −0.890060 | + | 1.54163i | −0.0502590 | + | 0.998736i | \(0.516005\pi\) |
−0.839801 | + | 0.542894i | \(0.817329\pi\) | |||||||
\(12\) | −3.00000 | + | 1.73205i | −0.250000 | + | 0.144338i | ||||
\(13\) | 2.16261i | 0.166355i | 0.996535 | + | 0.0831775i | \(0.0265068\pi\) | ||||
−0.996535 | + | 0.0831775i | \(0.973493\pi\) | |||||||
\(14\) | 7.08825 | − | 6.91062i | 0.506303 | − | 0.493616i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 16.9975 | + | 9.81350i | 0.999852 | + | 0.577265i | 0.908205 | − | 0.418527i | \(-0.137453\pi\) |
0.0916476 | + | 0.995792i | \(0.470787\pi\) | |||||||
\(18\) | −2.12132 | + | 3.67423i | −0.117851 | + | 0.204124i | ||||
\(19\) | −19.8410 | + | 11.4552i | −1.04426 | + | 0.602905i | −0.921037 | − | 0.389474i | \(-0.872657\pi\) |
−0.123224 | + | 0.992379i | \(0.539323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.28635 | − | 11.6705i | 0.156493 | − | 0.555737i | ||||
\(22\) | −27.6922 | −1.25874 | ||||||||
\(23\) | −16.2734 | − | 28.1864i | −0.707539 | − | 1.22549i | −0.965767 | − | 0.259410i | \(-0.916472\pi\) |
0.258228 | − | 0.966084i | \(-0.416861\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.64865 | + | 1.52920i | −0.101871 | + | 0.0588153i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 13.4759 | + | 3.79475i | 0.481282 | + | 0.135527i | ||||
\(29\) | 27.6922 | 0.954903 | 0.477451 | − | 0.878658i | \(-0.341561\pi\) | ||||
0.477451 | + | 0.878658i | \(0.341561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.3761 | − | 21.0018i | −1.17342 | − | 0.677477i | −0.218940 | − | 0.975738i | \(-0.570260\pi\) |
−0.954484 | + | 0.298262i | \(0.903593\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −29.3720 | + | 16.9579i | −0.890060 | + | 0.513877i | ||||
\(34\) | 27.7568i | 0.816376i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 30.2280 | + | 52.3564i | 0.816973 | + | 1.41504i | 0.907902 | + | 0.419181i | \(0.137683\pi\) |
−0.0909295 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(38\) | −28.0594 | − | 16.2001i | −0.738405 | − | 0.426318i | ||||
\(39\) | −1.87288 | + | 3.24392i | −0.0480225 | + | 0.0831775i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 66.3893i | − | 1.61925i | −0.586947 | − | 0.809625i | \(-0.699670\pi\) | ||
0.586947 | − | 0.809625i | \(-0.300330\pi\) | |||||||
\(42\) | 16.6171 | − | 4.22733i | 0.395646 | − | 0.100651i | ||||
\(43\) | −73.9553 | −1.71989 | −0.859945 | − | 0.510386i | \(-0.829502\pi\) | ||||
−0.859945 | + | 0.510386i | \(0.829502\pi\) | |||||||
\(44\) | −19.5813 | − | 33.9159i | −0.445030 | − | 0.770815i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 23.0141 | − | 39.8615i | 0.500306 | − | 0.866555i | ||||
\(47\) | −52.7322 | + | 30.4450i | −1.12196 | + | 0.647765i | −0.941901 | − | 0.335890i | \(-0.890963\pi\) |
−0.180061 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | −43.0432 | + | 23.4154i | −0.878433 | + | 0.477866i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.9975 | + | 29.4405i | 0.333284 | + | 0.577265i | ||||
\(52\) | −3.74576 | − | 2.16261i | −0.0720338 | − | 0.0415887i | ||||
\(53\) | −46.3119 | + | 80.2145i | −0.873809 | + | 1.51348i | −0.0157830 | + | 0.999875i | \(0.505024\pi\) |
−0.858026 | + | 0.513606i | \(0.828309\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.88130 | + | 19.1878i | 0.0871662 | + | 0.342640i | ||||
\(57\) | −39.6819 | −0.696174 | ||||||||
\(58\) | 19.5813 | + | 33.9159i | 0.337609 | + | 0.584756i | ||||
\(59\) | −24.9434 | − | 14.4011i | −0.422770 | − | 0.244086i | 0.273492 | − | 0.961874i | \(-0.411821\pi\) |
−0.696262 | + | 0.717788i | \(0.745155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.7954 | + | 42.0285i | −1.19337 | + | 0.688991i | −0.959069 | − | 0.283173i | \(-0.908613\pi\) |
−0.234299 | + | 0.972165i | \(0.575280\pi\) | |||||||
\(62\) | − | 59.4020i | − | 0.958097i | ||||||
\(63\) | 15.0364 | − | 14.6596i | 0.238674 | − | 0.232693i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −41.5383 | − | 23.9821i | −0.629368 | − | 0.363366i | ||||
\(67\) | −1.62591 | + | 2.81616i | −0.0242673 | + | 0.0420322i | −0.877904 | − | 0.478837i | \(-0.841059\pi\) |
0.853637 | + | 0.520869i | \(0.174392\pi\) | |||||||
\(68\) | −33.9950 | + | 19.6270i | −0.499926 | + | 0.288632i | ||||
\(69\) | − | 56.3727i | − | 0.816996i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38.9302 | −0.548313 | −0.274156 | − | 0.961685i | \(-0.588399\pi\) | ||||
−0.274156 | + | 0.961685i | \(0.588399\pi\) | |||||||
\(72\) | −4.24264 | − | 7.34847i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 30.5285 | + | 17.6257i | 0.418199 | + | 0.241447i | 0.694307 | − | 0.719679i | \(-0.255711\pi\) |
−0.276107 | + | 0.961127i | \(0.589045\pi\) | |||||||
\(74\) | −42.7488 | + | 74.0432i | −0.577687 | + | 1.00058i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 45.8208i | − | 0.602905i | ||||||
\(77\) | 131.938 | + | 37.1531i | 1.71348 | + | 0.482508i | ||||
\(78\) | −5.29730 | −0.0679141 | ||||||||
\(79\) | −10.7857 | − | 18.6813i | −0.136527 | − | 0.236472i | 0.789653 | − | 0.613554i | \(-0.210261\pi\) |
−0.926180 | + | 0.377082i | \(0.876927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 81.3099 | − | 46.9443i | 0.991585 | − | 0.572492i | ||||
\(83\) | − | 40.3650i | − | 0.486325i | −0.969986 | − | 0.243162i | \(-0.921815\pi\) | ||
0.969986 | − | 0.243162i | \(-0.0781848\pi\) | |||||||
\(84\) | 16.9275 | + | 17.3626i | 0.201518 | + | 0.206698i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −52.2943 | − | 90.5764i | −0.608073 | − | 1.05321i | ||||
\(87\) | 41.5383 | + | 23.9821i | 0.477451 | + | 0.275657i | ||||
\(88\) | 27.6922 | − | 47.9643i | 0.314684 | − | 0.545048i | ||||
\(89\) | 42.1123 | − | 24.3136i | 0.473172 | − | 0.273186i | −0.244395 | − | 0.969676i | \(-0.578589\pi\) |
0.717567 | + | 0.696490i | \(0.245256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.6710 | − | 3.73224i | 0.161220 | − | 0.0410137i | ||||
\(92\) | 65.0936 | 0.707539 | ||||||||
\(93\) | −36.3761 | − | 63.0053i | −0.391141 | − | 0.677477i | ||||
\(94\) | −74.5746 | − | 43.0557i | −0.793347 | − | 0.458039i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | − | 25.2493i | − | 0.260302i | −0.991494 | − | 0.130151i | \(-0.958454\pi\) | ||
0.991494 | − | 0.130151i | \(-0.0415462\pi\) | |||||||
\(98\) | −59.1141 | − | 36.1598i | −0.603205 | − | 0.368977i | ||||
\(99\) | −58.7440 | −0.593374 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.6467 | + | 30.3956i | 0.521255 | + | 0.300947i | 0.737448 | − | 0.675404i | \(-0.236031\pi\) |
−0.216193 | + | 0.976351i | \(0.569364\pi\) | |||||||
\(102\) | −24.0381 | + | 41.6352i | −0.235667 | + | 0.408188i | ||||
\(103\) | 37.0217 | − | 21.3745i | 0.359434 | − | 0.207519i | −0.309399 | − | 0.950932i | \(-0.600128\pi\) |
0.668832 | + | 0.743413i | \(0.266794\pi\) | |||||||
\(104\) | − | 6.11680i | − | 0.0588153i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −130.990 | −1.23575 | ||||||||
\(107\) | 76.6488 | + | 132.760i | 0.716343 | + | 1.24074i | 0.962439 | + | 0.271498i | \(0.0875189\pi\) |
−0.246096 | + | 0.969246i | \(0.579148\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −28.8885 | + | 50.0364i | −0.265032 | + | 0.459050i | −0.967572 | − | 0.252595i | \(-0.918716\pi\) |
0.702540 | + | 0.711645i | \(0.252049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 104.713i | 0.943359i | ||||||||
\(112\) | −20.0486 | + | 19.5462i | −0.179005 | + | 0.174520i | ||||
\(113\) | −149.523 | −1.32322 | −0.661608 | − | 0.749850i | \(-0.730126\pi\) | ||||
−0.661608 | + | 0.749850i | \(0.730126\pi\) | |||||||
\(114\) | −28.0594 | − | 48.6003i | −0.246135 | − | 0.426318i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −27.6922 | + | 47.9643i | −0.238726 | + | 0.413485i | ||||
\(117\) | −5.61864 | + | 3.24392i | −0.0480225 | + | 0.0277258i | ||||
\(118\) | − | 40.7325i | − | 0.345190i | ||||||
\(119\) | 37.2398 | − | 132.246i | 0.312939 | − | 1.11131i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −131.214 | − | 227.270i | −1.08442 | − | 1.87826i | ||||
\(122\) | −102.948 | − | 59.4372i | −0.843839 | − | 0.487190i | ||||
\(123\) | 57.4948 | − | 99.5839i | 0.467437 | − | 0.809625i | ||||
\(124\) | 72.7523 | − | 42.0035i | 0.586712 | − | 0.338738i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.5867 | + | 8.04987i | 0.226879 | + | 0.0638879i | ||||
\(127\) | 176.212 | 1.38750 | 0.693749 | − | 0.720217i | \(-0.255958\pi\) | ||||
0.693749 | + | 0.720217i | \(0.255958\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −110.933 | − | 64.0472i | −0.859945 | − | 0.496490i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 63.0502 | − | 36.4021i | 0.481300 | − | 0.277878i | −0.239658 | − | 0.970857i | \(-0.577035\pi\) |
0.720958 | + | 0.692979i | \(0.243702\pi\) | |||||||
\(132\) | − | 67.8317i | − | 0.513877i | ||||||
\(133\) | 111.953 | + | 114.830i | 0.841750 | + | 0.863385i | ||||
\(134\) | −4.59876 | −0.0343191 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −48.0762 | − | 27.7568i | −0.353501 | − | 0.204094i | ||||
\(137\) | 74.7510 | − | 129.472i | 0.545628 | − | 0.945055i | −0.452940 | − | 0.891541i | \(-0.649625\pi\) |
0.998567 | − | 0.0535134i | \(-0.0170420\pi\) | |||||||
\(138\) | 69.0422 | − | 39.8615i | 0.500306 | − | 0.288852i | ||||
\(139\) | − | 57.4753i | − | 0.413491i | −0.978395 | − | 0.206746i | \(-0.933713\pi\) | ||
0.978395 | − | 0.206746i | \(-0.0662873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −105.464 | −0.747975 | ||||||||
\(142\) | −27.5278 | − | 47.6796i | −0.193858 | − | 0.335772i | ||||
\(143\) | −36.6735 | − | 21.1734i | −0.256458 | − | 0.148066i | ||||
\(144\) | 6.00000 | − | 10.3923i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 49.8529i | 0.341458i | ||||||||
\(147\) | −84.8432 | − | 2.15340i | −0.577164 | − | 0.0146490i | ||||
\(148\) | −120.912 | −0.816973 | ||||||||
\(149\) | 12.5813 | + | 21.7915i | 0.0844385 | + | 0.146252i | 0.905152 | − | 0.425088i | \(-0.139757\pi\) |
−0.820713 | + | 0.571340i | \(0.806424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1332 | + | 19.2832i | −0.0737296 | + | 0.127703i | −0.900533 | − | 0.434787i | \(-0.856824\pi\) |
0.826804 | + | 0.562491i | \(0.190157\pi\) | |||||||
\(152\) | 56.1187 | − | 32.4002i | 0.369202 | − | 0.213159i | ||||
\(153\) | 58.8810i | 0.384843i | ||||||||
\(154\) | 47.7912 | + | 187.862i | 0.310333 | + | 1.21988i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.74576 | − | 6.48784i | −0.0240113 | − | 0.0415887i | ||||
\(157\) | 242.578 | + | 140.053i | 1.54508 | + | 0.892054i | 0.998506 | + | 0.0546460i | \(0.0174030\pi\) |
0.546578 | + | 0.837408i | \(0.315930\pi\) | |||||||
\(158\) | 15.2532 | − | 26.4193i | 0.0965393 | − | 0.167211i | ||||
\(159\) | −138.936 | + | 80.2145i | −0.873809 | + | 0.504494i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −163.129 | + | 159.042i | −1.01323 | + | 0.987836i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 66.3200 | + | 114.870i | 0.406871 | + | 0.704722i | 0.994537 | − | 0.104382i | \(-0.0332864\pi\) |
−0.587666 | + | 0.809104i | \(0.699953\pi\) | |||||||
\(164\) | 114.990 | + | 66.3893i | 0.701156 | + | 0.404813i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 49.4368 | − | 28.5423i | 0.297812 | − | 0.171942i | ||||
\(167\) | 119.492i | 0.715520i | 0.933814 | + | 0.357760i | \(0.116459\pi\) | ||||
−0.933814 | + | 0.357760i | \(0.883541\pi\) | |||||||
\(168\) | −9.29519 | + | 33.0091i | −0.0553285 | + | 0.196483i | ||||
\(169\) | 164.323 | 0.972326 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −59.5229 | − | 34.3656i | −0.348087 | − | 0.200968i | ||||
\(172\) | 73.9553 | − | 128.094i | 0.429973 | − | 0.744734i | ||||
\(173\) | 218.340 | − | 126.059i | 1.26208 | − | 0.728664i | 0.288606 | − | 0.957448i | \(-0.406808\pi\) |
0.973477 | + | 0.228784i | \(0.0734750\pi\) | |||||||
\(174\) | 67.8317i | 0.389837i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 78.3253 | 0.445030 | ||||||||
\(177\) | −24.9434 | − | 43.2033i | −0.140923 | − | 0.244086i | ||||
\(178\) | 59.5558 | + | 34.3846i | 0.334583 | + | 0.193172i | ||||
\(179\) | −20.7738 | + | 35.9814i | −0.116055 | + | 0.201013i | −0.918201 | − | 0.396115i | \(-0.870358\pi\) |
0.802146 | + | 0.597128i | \(0.203692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 258.208i | 1.42656i | 0.700878 | + | 0.713281i | \(0.252792\pi\) | ||||
−0.700878 | + | 0.713281i | \(0.747208\pi\) | |||||||
\(182\) | 14.9450 | + | 15.3291i | 0.0821155 | + | 0.0842261i | ||||
\(183\) | −145.591 | −0.795579 | ||||||||
\(184\) | 46.0281 | + | 79.7230i | 0.250153 | + | 0.433277i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 51.4436 | − | 89.1030i | 0.276579 | − | 0.479048i | ||||
\(187\) | −332.833 | + | 192.161i | −1.77986 | + | 1.02760i | ||||
\(188\) | − | 121.780i | − | 0.647765i | ||||||
\(189\) | 35.2503 | − | 8.96753i | 0.186510 | − | 0.0474472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 45.1850 | + | 78.2627i | 0.236571 | + | 0.409752i | 0.959728 | − | 0.280931i | \(-0.0906432\pi\) |
−0.723157 | + | 0.690683i | \(0.757310\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −30.4605 | + | 52.7591i | −0.157826 | + | 0.273363i | −0.934085 | − | 0.357052i | \(-0.883782\pi\) |
0.776258 | + | 0.630415i | \(0.217115\pi\) | |||||||
\(194\) | 30.9240 | − | 17.8540i | 0.159402 | − | 0.0920307i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.48653 | − | 97.9684i | 0.0126864 | − | 0.499839i | ||||
\(197\) | −74.1310 | −0.376299 | −0.188150 | − | 0.982140i | \(-0.560249\pi\) | ||||
−0.188150 | + | 0.982140i | \(0.560249\pi\) | |||||||
\(198\) | −41.5383 | − | 71.9464i | −0.209789 | − | 0.363366i | ||||
\(199\) | 77.5575 | + | 44.7778i | 0.389736 | + | 0.225014i | 0.682046 | − | 0.731309i | \(-0.261090\pi\) |
−0.292310 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.87773 | + | 2.81616i | −0.0242673 | + | 0.0140107i | ||||
\(202\) | 85.9717i | 0.425603i | ||||||||
\(203\) | −47.7912 | − | 187.862i | −0.235425 | − | 0.925427i | ||||
\(204\) | −67.9899 | −0.333284 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 52.3565 | + | 30.2281i | 0.254158 | + | 0.146738i | ||||
\(207\) | 48.8202 | − | 84.5591i | 0.235846 | − | 0.408498i | ||||
\(208\) | 7.49151 | − | 4.32523i | 0.0360169 | − | 0.0207944i | ||||
\(209\) | − | 448.616i | − | 2.14649i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 69.8647 | 0.331112 | 0.165556 | − | 0.986200i | \(-0.447058\pi\) | ||||
0.165556 | + | 0.986200i | \(0.447058\pi\) | |||||||
\(212\) | −92.6238 | − | 160.429i | −0.436905 | − | 0.756741i | ||||
\(213\) | −58.3953 | − | 33.7145i | −0.274156 | − | 0.158284i | ||||
\(214\) | −108.398 | + | 187.750i | −0.506531 | + | 0.877338i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −79.6964 | + | 283.018i | −0.367265 | + | 1.30423i | ||||
\(218\) | −81.7091 | −0.374812 | ||||||||
\(219\) | 30.5285 | + | 52.8770i | 0.139400 | + | 0.241447i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.2228 | + | 36.7590i | −0.0960309 | + | 0.166330i | ||||
\(222\) | −128.247 | + | 74.0432i | −0.577687 | + | 0.333528i | ||||
\(223\) | 389.679i | 1.74744i | 0.486430 | + | 0.873719i | \(0.338299\pi\) | ||||
−0.486430 | + | 0.873719i | \(0.661701\pi\) | |||||||
\(224\) | −38.1156 | − | 10.7332i | −0.170159 | − | 0.0479159i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −105.729 | − | 183.128i | −0.467828 | − | 0.810301i | ||||
\(227\) | 6.47172 | + | 3.73645i | 0.0285098 | + | 0.0164601i | 0.514187 | − | 0.857678i | \(-0.328094\pi\) |
−0.485677 | + | 0.874138i | \(0.661427\pi\) | |||||||
\(228\) | 39.6819 | − | 68.7311i | 0.174044 | − | 0.301452i | ||||
\(229\) | −86.8317 | + | 50.1323i | −0.379178 | + | 0.218918i | −0.677460 | − | 0.735559i | \(-0.736920\pi\) |
0.298283 | + | 0.954478i | \(0.403586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 165.732 | + | 169.991i | 0.717452 | + | 0.735893i | ||||
\(232\) | −78.3253 | −0.337609 | ||||||||
\(233\) | −169.986 | − | 294.424i | −0.729552 | − | 1.26362i | −0.957073 | − | 0.289848i | \(-0.906395\pi\) |
0.227520 | − | 0.973773i | \(-0.426938\pi\) | |||||||
\(234\) | −7.94595 | − | 4.58760i | −0.0339571 | − | 0.0196051i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 49.8869 | − | 28.8022i | 0.211385 | − | 0.122043i | ||||
\(237\) | − | 37.3626i | − | 0.157648i | ||||||
\(238\) | 188.300 | − | 47.9027i | 0.791176 | − | 0.201272i | ||||
\(239\) | 37.7094 | 0.157780 | 0.0788899 | − | 0.996883i | \(-0.474862\pi\) | ||||
0.0788899 | + | 0.996883i | \(0.474862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −258.515 | − | 149.254i | −1.07268 | − | 0.619310i | −0.143765 | − | 0.989612i | \(-0.545921\pi\) |
−0.928912 | + | 0.370301i | \(0.879254\pi\) | |||||||
\(242\) | 185.565 | − | 321.408i | 0.766797 | − | 1.32813i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | − | 168.114i | − | 0.688991i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 162.620 | 0.661056 | ||||||||
\(247\) | −24.7732 | − | 42.9084i | −0.100296 | − | 0.173718i | ||||
\(248\) | 102.887 | + | 59.4020i | 0.414868 | + | 0.239524i | ||||
\(249\) | 34.9571 | − | 60.5474i | 0.140390 | − | 0.243162i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 251.129i | − | 1.00051i | −0.865877 | − | 0.500257i | \(-0.833239\pi\) | ||
0.865877 | − | 0.500257i | \(-0.166761\pi\) | |||||||
\(252\) | 10.3548 | + | 40.7035i | 0.0410905 | + | 0.161522i | ||||
\(253\) | 637.310 | 2.51901 | ||||||||
\(254\) | 124.601 | + | 215.815i | 0.490554 | + | 0.849665i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −51.6733 | + | 29.8336i | −0.201063 | + | 0.116084i | −0.597151 | − | 0.802129i | \(-0.703701\pi\) |
0.396088 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(258\) | − | 181.153i | − | 0.702142i | ||||||
\(259\) | 303.014 | − | 295.421i | 1.16994 | − | 1.14062i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.5383 | + | 71.9464i | 0.159150 | + | 0.275657i | ||||
\(262\) | 89.1665 | + | 51.4803i | 0.340330 | + | 0.196490i | ||||
\(263\) | −62.4039 | + | 108.087i | −0.237277 | + | 0.410976i | −0.959932 | − | 0.280233i | \(-0.909588\pi\) |
0.722655 | + | 0.691209i | \(0.242922\pi\) | |||||||
\(264\) | 83.0765 | − | 47.9643i | 0.314684 | − | 0.181683i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −61.4752 | + | 218.311i | −0.231110 | + | 0.820717i | ||||
\(267\) | 84.2246 | 0.315448 | ||||||||
\(268\) | −3.25182 | − | 5.63231i | −0.0121336 | − | 0.0210161i | ||||
\(269\) | −180.299 | − | 104.096i | −0.670257 | − | 0.386973i | 0.125917 | − | 0.992041i | \(-0.459813\pi\) |
−0.796174 | + | 0.605068i | \(0.793146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1857 | − | 9.92217i | 0.0634159 | − | 0.0366132i | −0.467957 | − | 0.883751i | \(-0.655010\pi\) |
0.531373 | + | 0.847138i | \(0.321676\pi\) | |||||||
\(272\) | − | 78.5080i | − | 0.288632i | ||||||
\(273\) | 25.2387 | + | 7.10710i | 0.0924496 | + | 0.0260333i | ||||
\(274\) | 211.428 | 0.771634 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 97.6404 | + | 56.3727i | 0.353770 | + | 0.204249i | ||||
\(277\) | −43.5077 | + | 75.3576i | −0.157068 | + | 0.272049i | −0.933810 | − | 0.357769i | \(-0.883537\pi\) |
0.776742 | + | 0.629818i | \(0.216871\pi\) | |||||||
\(278\) | 70.3926 | − | 40.6412i | 0.253211 | − | 0.146191i | ||||
\(279\) | − | 126.011i | − | 0.451651i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 145.993 | 0.519549 | 0.259774 | − | 0.965669i | \(-0.416352\pi\) | ||||
0.259774 | + | 0.965669i | \(0.416352\pi\) | |||||||
\(282\) | −74.5746 | − | 129.167i | −0.264449 | − | 0.458039i | ||||
\(283\) | 306.352 | + | 176.873i | 1.08252 | + | 0.624991i | 0.931574 | − | 0.363551i | \(-0.118436\pi\) |
0.150943 | + | 0.988543i | \(0.451769\pi\) | |||||||
\(284\) | 38.9302 | − | 67.4291i | 0.137078 | − | 0.237426i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 59.8875i | − | 0.209397i | ||||||
\(287\) | −450.380 | + | 114.575i | −1.56927 | + | 0.399215i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 48.1097 | + | 83.3284i | 0.166470 | + | 0.288334i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.8665 | − | 37.8740i | 0.0751428 | − | 0.130151i | ||||
\(292\) | −61.0571 | + | 35.2513i | −0.209100 | + | 0.120724i | ||||
\(293\) | 118.997i | 0.406135i | 0.979165 | + | 0.203067i | \(0.0650910\pi\) | ||||
−0.979165 | + | 0.203067i | \(0.934909\pi\) | |||||||
\(294\) | −57.3558 | − | 105.434i | −0.195088 | − | 0.358619i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −85.4977 | − | 148.086i | −0.288844 | − | 0.500292i | ||||
\(297\) | −88.1160 | − | 50.8738i | −0.296687 | − | 0.171292i | ||||
\(298\) | −17.7927 | + | 30.8179i | −0.0597071 | + | 0.103416i | ||||
\(299\) | 60.9562 | − | 35.1931i | 0.203867 | − | 0.117703i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 127.632 | + | 501.707i | 0.424027 | + | 1.66680i | ||||
\(302\) | −31.4894 | −0.104269 | ||||||||
\(303\) | 52.6467 | + | 91.1868i | 0.173752 | + | 0.300947i | ||||
\(304\) | 79.3639 | + | 45.8208i | 0.261065 | + | 0.150726i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −72.1142 | + | 41.6352i | −0.235667 | + | 0.136063i | ||||
\(307\) | − | 481.700i | − | 1.56905i | −0.620095 | − | 0.784527i | \(-0.712906\pi\) | ||
0.620095 | − | 0.784527i | \(-0.287094\pi\) | |||||||
\(308\) | −196.289 | + | 191.370i | −0.637302 | + | 0.621332i | ||||
\(309\) | 74.0433 | 0.239622 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 498.665 | + | 287.904i | 1.60343 | + | 0.925738i | 0.990795 | + | 0.135368i | \(0.0432216\pi\) |
0.612630 | + | 0.790370i | \(0.290112\pi\) | |||||||
\(312\) | 5.29730 | − | 9.17519i | 0.0169785 | − | 0.0294077i | ||||
\(313\) | −369.168 | + | 213.139i | −1.17945 | + | 0.680957i | −0.955888 | − | 0.293733i | \(-0.905102\pi\) |
−0.223564 | + | 0.974689i | \(0.571769\pi\) | |||||||
\(314\) | 396.128i | 1.26156i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43.1426 | 0.136527 | ||||||||
\(317\) | 12.6099 | + | 21.8410i | 0.0397789 | + | 0.0688990i | 0.885229 | − | 0.465155i | \(-0.154001\pi\) |
−0.845451 | + | 0.534054i | \(0.820668\pi\) | |||||||
\(318\) | −196.485 | − | 113.440i | −0.617876 | − | 0.356731i | ||||
\(319\) | −271.125 | + | 469.602i | −0.849921 | + | 1.47211i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 265.519i | 0.827162i | ||||||||
\(322\) | −310.135 | − | 87.3325i | −0.963153 | − | 0.271219i | ||||
\(323\) | −449.662 | −1.39214 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −93.7907 | + | 162.450i | −0.287701 | + | 0.498313i | ||||
\(327\) | −86.6656 | + | 50.0364i | −0.265032 | + | 0.153017i | ||||
\(328\) | 187.777i | 0.572492i | ||||||||
\(329\) | 297.542 | + | 305.189i | 0.904382 | + | 0.927627i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.955424 | + | 1.65484i | 0.00288648 | + | 0.00499953i | 0.867465 | − | 0.497498i | \(-0.165748\pi\) |
−0.864579 | + | 0.502498i | \(0.832415\pi\) | |||||||
\(332\) | 69.9142 | + | 40.3650i | 0.210585 | + | 0.121581i | ||||
\(333\) | −90.6840 | + | 157.069i | −0.272324 | + | 0.471680i | ||||
\(334\) | −146.347 | + | 84.4935i | −0.438165 | + | 0.252975i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −47.0004 | + | 11.9567i | −0.139882 | + | 0.0355854i | ||||
\(337\) | −337.622 | −1.00184 | −0.500922 | − | 0.865492i | \(-0.667006\pi\) | ||||
−0.500922 | + | 0.865492i | \(0.667006\pi\) | |||||||
\(338\) | 116.194 | + | 201.254i | 0.343769 | + | 0.595426i | ||||
\(339\) | −224.285 | − | 129.491i | −0.661608 | − | 0.381980i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 712.293 | − | 411.243i | 2.08884 | − | 1.20599i | ||||
\(342\) | − | 97.2005i | − | 0.284212i | ||||||
\(343\) | 233.132 | + | 251.591i | 0.679686 | + | 0.733503i | ||||
\(344\) | 209.177 | 0.608073 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 308.780 | + | 178.274i | 0.892427 | + | 0.515243i | ||||
\(347\) | 148.250 | − | 256.776i | 0.427232 | − | 0.739988i | −0.569394 | − | 0.822065i | \(-0.692822\pi\) |
0.996626 | + | 0.0820768i | \(0.0261553\pi\) | |||||||
\(348\) | −83.0765 | + | 47.9643i | −0.238726 | + | 0.137828i | ||||
\(349\) | 367.499i | 1.05300i | 0.850174 | + | 0.526502i | \(0.176497\pi\) | ||||
−0.850174 | + | 0.526502i | \(0.823503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.2373 | −0.0320150 | ||||||||
\(352\) | 55.3844 | + | 95.9285i | 0.157342 | + | 0.272524i | ||||
\(353\) | 456.656 | + | 263.651i | 1.29364 | + | 0.746886i | 0.979298 | − | 0.202423i | \(-0.0648816\pi\) |
0.314346 | + | 0.949309i | \(0.398215\pi\) | |||||||
\(354\) | 35.2753 | − | 61.0987i | 0.0996479 | − | 0.172595i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 97.2542i | 0.273186i | ||||||||
\(357\) | 170.388 | − | 166.118i | 0.477277 | − | 0.465317i | ||||
\(358\) | −58.7573 | −0.164127 | ||||||||
\(359\) | −294.338 | − | 509.809i | −0.819884 | − | 1.42008i | −0.905767 | − | 0.423775i | \(-0.860705\pi\) |
0.0858836 | − | 0.996305i | \(-0.472629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 81.9428 | − | 141.929i | 0.226988 | − | 0.393155i | ||||
\(362\) | −316.239 | + | 182.580i | −0.873587 | + | 0.504366i | ||||
\(363\) | − | 454.539i | − | 1.25217i | ||||||
\(364\) | −8.20657 | + | 29.1432i | −0.0225455 | + | 0.0800637i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −102.948 | − | 178.312i | −0.281280 | − | 0.487190i | ||||
\(367\) | 295.319 | + | 170.503i | 0.804685 | + | 0.464585i | 0.845107 | − | 0.534598i | \(-0.179537\pi\) |
−0.0404219 | + | 0.999183i | \(0.512870\pi\) | |||||||
\(368\) | −65.0936 | + | 112.745i | −0.176885 | + | 0.306373i | ||||
\(369\) | 172.484 | − | 99.5839i | 0.467437 | − | 0.269875i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 624.094 | + | 175.742i | 1.68219 | + | 0.473698i | ||||
\(372\) | 145.505 | 0.391141 | ||||||||
\(373\) | 58.6711 | + | 101.621i | 0.157295 | + | 0.272443i | 0.933892 | − | 0.357554i | \(-0.116389\pi\) |
−0.776597 | + | 0.629998i | \(0.783056\pi\) | |||||||
\(374\) | −470.697 | − | 271.757i | −1.25855 | − | 0.726624i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 149.149 | − | 86.1114i | 0.396674 | − | 0.229020i | ||||
\(377\) | 59.8875i | 0.158853i | ||||||||
\(378\) | 35.9087 | + | 36.8316i | 0.0949965 | + | 0.0974381i | ||||
\(379\) | −188.135 | −0.496398 | −0.248199 | − | 0.968709i | \(-0.579839\pi\) | ||||
−0.248199 | + | 0.968709i | \(0.579839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 264.318 | + | 152.604i | 0.693749 | + | 0.400536i | ||||
\(382\) | −63.9012 | + | 110.680i | −0.167281 | + | 0.289739i | ||||
\(383\) | 232.895 | − | 134.462i | 0.608081 | − | 0.351076i | −0.164133 | − | 0.986438i | \(-0.552483\pi\) |
0.772214 | + | 0.635363i | \(0.219149\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −86.1552 | −0.223200 | ||||||||
\(387\) | −110.933 | − | 192.141i | −0.286648 | − | 0.496490i | ||||
\(388\) | 43.7331 | + | 25.2493i | 0.112714 | + | 0.0650755i | ||||
\(389\) | −148.182 | + | 256.658i | −0.380930 | + | 0.659790i | −0.991195 | − | 0.132407i | \(-0.957729\pi\) |
0.610265 | + | 0.792197i | \(0.291063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 638.796i | − | 1.63375i | ||||||
\(392\) | 121.745 | − | 66.2288i | 0.310573 | − | 0.168951i | ||||
\(393\) | 126.100 | 0.320866 | ||||||||
\(394\) | −52.4185 | − | 90.7915i | −0.133042 | − | 0.230435i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 58.7440 | − | 101.748i | 0.148343 | − | 0.256938i | ||||
\(397\) | −16.3455 | + | 9.43705i | −0.0411724 | + | 0.0237709i | −0.520445 | − | 0.853895i | \(-0.674234\pi\) |
0.479273 | + | 0.877666i | \(0.340901\pi\) | |||||||
\(398\) | 126.651i | 0.318218i | ||||||||
\(399\) | 68.4832 | + | 269.199i | 0.171637 | + | 0.674685i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −171.967 | − | 297.856i | −0.428845 | − | 0.742782i | 0.567925 | − | 0.823080i | \(-0.307746\pi\) |
−0.996771 | + | 0.0802979i | \(0.974413\pi\) | |||||||
\(402\) | −6.89815 | − | 3.98265i | −0.0171596 | − | 0.00990708i | ||||
\(403\) | 45.4187 | − | 78.6675i | 0.112702 | − | 0.195205i | ||||
\(404\) | −105.293 | + | 60.7912i | −0.260627 | + | 0.150473i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 196.289 | − | 191.370i | 0.483471 | − | 0.471355i | ||||
\(407\) | −1183.81 | −2.90862 | ||||||||
\(408\) | −48.0762 | − | 83.2703i | −0.117834 | − | 0.204094i | ||||
\(409\) | 376.358 | + | 217.291i | 0.920192 | + | 0.531273i | 0.883696 | − | 0.468061i | \(-0.155047\pi\) |
0.0364954 | + | 0.999334i | \(0.488381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 224.253 | − | 129.472i | 0.545628 | − | 0.315018i | ||||
\(412\) | 85.4978i | 0.207519i | ||||||||
\(413\) | −54.6485 | + | 194.068i | −0.132321 | + | 0.469898i | ||||
\(414\) | 138.084 | 0.333537 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.5946 | + | 6.11680i | 0.0254678 | + | 0.0147038i | ||||
\(417\) | 49.7751 | − | 86.2129i | 0.119365 | − | 0.206746i | ||||
\(418\) | 549.440 | − | 317.219i | 1.31445 | − | 0.758898i | ||||
\(419\) | 319.236i | 0.761899i | 0.924596 | + | 0.380949i | \(0.124403\pi\) | ||||
−0.924596 | + | 0.380949i | \(0.875597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −663.506 | −1.57602 | −0.788012 | − | 0.615660i | \(-0.788889\pi\) | ||||
−0.788012 | + | 0.615660i | \(0.788889\pi\) | |||||||
\(422\) | 49.4018 | + | 85.5664i | 0.117066 | + | 0.202764i | ||||
\(423\) | −158.197 | − | 91.3349i | −0.373987 | − | 0.215922i | ||||
\(424\) | 130.990 | − | 226.881i | 0.308938 | − | 0.535097i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 95.3591i | − | 0.223848i | ||||||
\(427\) | 410.748 | + | 421.306i | 0.961940 | + | 0.986665i | ||||
\(428\) | −306.595 | −0.716343 | ||||||||
\(429\) | −36.6735 | − | 63.5203i | −0.0854859 | − | 0.148066i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 50.5285 | − | 87.5179i | 0.117235 | − | 0.203058i | −0.801436 | − | 0.598081i | \(-0.795930\pi\) |
0.918671 | + | 0.395023i | \(0.129263\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 490.183i | 1.13206i | 0.824384 | + | 0.566031i | \(0.191522\pi\) | ||||
−0.824384 | + | 0.566031i | \(0.808478\pi\) | |||||||
\(434\) | −402.978 | + | 102.516i | −0.928522 | + | 0.236212i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −57.7771 | − | 100.073i | −0.132516 | − | 0.229525i | ||||
\(437\) | 645.760 | + | 372.830i | 1.47771 | + | 0.853157i | ||||
\(438\) | −43.1739 | + | 74.7793i | −0.0985705 | + | 0.170729i | ||||
\(439\) | 399.753 | − | 230.797i | 0.910599 | − | 0.525735i | 0.0299751 | − | 0.999551i | \(-0.490457\pi\) |
0.880624 | + | 0.473816i | \(0.157124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −125.400 | − | 76.7064i | −0.284353 | − | 0.173937i | ||||
\(442\) | −60.0272 | −0.135808 | ||||||||
\(443\) | −100.023 | − | 173.245i | −0.225786 | − | 0.391073i | 0.730769 | − | 0.682625i | \(-0.239162\pi\) |
−0.956555 | + | 0.291552i | \(0.905828\pi\) | |||||||
\(444\) | −181.368 | − | 104.713i | −0.408487 | − | 0.235840i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −477.257 | + | 275.545i | −1.07008 | + | 0.617813i | ||||
\(447\) | 43.5830i | 0.0975012i | ||||||||
\(448\) | −13.8064 | − | 54.2714i | −0.0308179 | − | 0.121141i | ||||
\(449\) | −75.8015 | −0.168823 | −0.0844115 | − | 0.996431i | \(-0.526901\pi\) | ||||
−0.0844115 | + | 0.996431i | \(0.526901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1125.82 | + | 649.995i | 2.49629 | + | 1.44123i | ||||
\(452\) | 149.523 | − | 258.982i | 0.330804 | − | 0.572970i | ||||
\(453\) | −33.3995 | + | 19.2832i | −0.0737296 | + | 0.0425678i | ||||
\(454\) | 10.5683i | 0.0232781i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 112.237 | 0.246135 | ||||||||
\(457\) | 205.573 | + | 356.062i | 0.449831 | + | 0.779129i | 0.998375 | − | 0.0569922i | \(-0.0181510\pi\) |
−0.548544 | + | 0.836122i | \(0.684818\pi\) | |||||||
\(458\) | −122.799 | − | 70.8978i | −0.268119 | − | 0.154799i | ||||
\(459\) | −50.9925 | + | 88.3215i | −0.111095 | + | 0.192422i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 278.002i | 0.603041i | 0.953460 | + | 0.301521i | \(0.0974942\pi\) | ||||
−0.953460 | + | 0.301521i | \(0.902506\pi\) | |||||||
\(462\) | −91.0061 | + | 323.181i | −0.196983 | + | 0.699526i | ||||
\(463\) | −492.573 | −1.06387 | −0.531936 | − | 0.846784i | \(-0.678535\pi\) | ||||
−0.531936 | + | 0.846784i | \(0.678535\pi\) | |||||||
\(464\) | −55.3844 | − | 95.9285i | −0.119363 | − | 0.206743i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 240.396 | − | 416.378i | 0.515871 | − | 0.893515i | ||||
\(467\) | −279.726 | + | 161.500i | −0.598985 | + | 0.345824i | −0.768642 | − | 0.639679i | \(-0.779067\pi\) |
0.169657 | + | 0.985503i | \(0.445734\pi\) | |||||||
\(468\) | − | 12.9757i | − | 0.0277258i | ||||||
\(469\) | 21.9106 | + | 6.16991i | 0.0467177 | + | 0.0131555i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 242.578 | + | 420.158i | 0.515028 | + | 0.892054i | ||||
\(472\) | 70.5507 | + | 40.7325i | 0.149472 | + | 0.0862976i | ||||
\(473\) | 724.072 | − | 1254.13i | 1.53081 | − | 2.65143i | ||||
\(474\) | 45.7597 | − | 26.4193i | 0.0965393 | − | 0.0557370i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 191.817 | + | 196.747i | 0.402976 | + | 0.413334i | ||||
\(477\) | −277.871 | −0.582539 | ||||||||
\(478\) | 26.6646 | + | 46.1844i | 0.0557836 | + | 0.0966200i | ||||
\(479\) | −267.845 | − | 154.641i | −0.559176 | − | 0.322841i | 0.193639 | − | 0.981073i | \(-0.437971\pi\) |
−0.752815 | + | 0.658232i | \(0.771304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −113.227 | + | 65.3715i | −0.235399 | + | 0.135907i | ||||
\(482\) | − | 422.154i | − | 0.875837i | ||||||
\(483\) | −382.428 | + | 97.2881i | −0.791777 | + | 0.201425i | ||||
\(484\) | 524.857 | 1.08442 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | 282.854 | − | 489.918i | 0.580809 | − | 1.00599i | −0.414574 | − | 0.910015i | \(-0.636070\pi\) |
0.995384 | − | 0.0959758i | \(-0.0305971\pi\) | |||||||
\(488\) | 205.897 | − | 118.874i | 0.421919 | − | 0.243595i | ||||
\(489\) | 229.739i | 0.469814i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −379.335 | −0.772577 | −0.386288 | − | 0.922378i | \(-0.626243\pi\) | ||||
−0.386288 | + | 0.922378i | \(0.626243\pi\) | |||||||
\(492\) | 114.990 | + | 199.168i | 0.233719 | + | 0.404813i | ||||
\(493\) | 470.697 | + | 271.757i | 0.954762 | + | 0.551232i | ||||
\(494\) | 35.0345 | − | 60.6816i | 0.0709201 | − | 0.122837i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 168.014i | 0.338738i | ||||||||
\(497\) | 67.1858 | + | 264.099i | 0.135183 | + | 0.531387i | ||||
\(498\) | 98.8736 | 0.198541 | ||||||||
\(499\) | 271.332 | + | 469.961i | 0.543751 | + | 0.941805i | 0.998684 | + | 0.0512794i | \(0.0163299\pi\) |
−0.454933 | + | 0.890526i | \(0.650337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −103.483 | + | 179.238i | −0.206553 | + | 0.357760i | ||||
\(502\) | 307.569 | − | 177.575i | 0.612687 | − | 0.353735i | ||||
\(503\) | − | 281.628i | − | 0.559896i | −0.960015 | − | 0.279948i | \(-0.909683\pi\) | ||
0.960015 | − | 0.279948i | \(-0.0903173\pi\) | |||||||
\(504\) | −42.5295 | + | 41.4637i | −0.0843839 | + | 0.0822693i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 450.646 | + | 780.542i | 0.890605 | + | 1.54257i | ||||
\(507\) | 246.485 | + | 142.308i | 0.486163 | + | 0.280686i | ||||
\(508\) | −176.212 | + | 305.208i | −0.346874 | + | 0.600804i | ||||
\(509\) | −8.88432 | + | 5.12937i | −0.0174545 | + | 0.0100773i | −0.508702 | − | 0.860943i | \(-0.669874\pi\) |
0.491247 | + | 0.871020i | \(0.336541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 66.8849 | − | 237.522i | 0.130890 | − | 0.464817i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −59.5229 | − | 103.097i | −0.116029 | − | 0.200968i | ||||
\(514\) | −73.0771 | − | 42.1911i | −0.142173 | − | 0.0820838i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 221.866 | − | 128.094i | 0.429973 | − | 0.248245i | ||||
\(517\) | − | 1192.31i | − | 2.30620i | ||||||
\(518\) | 576.079 | + | 162.221i | 1.11212 | + | 0.313168i | ||||
\(519\) | 436.681 | 0.841389 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −666.970 | − | 385.075i | −1.28017 | − | 0.739108i | −0.303292 | − | 0.952898i | \(-0.598086\pi\) |
−0.976880 | + | 0.213790i | \(0.931419\pi\) | |||||||
\(522\) | −58.7440 | + | 101.748i | −0.112536 | + | 0.194919i | ||||
\(523\) | −260.981 | + | 150.678i | −0.499008 | + | 0.288102i | −0.728304 | − | 0.685254i | \(-0.759691\pi\) |
0.229296 | + | 0.973357i | \(0.426358\pi\) | |||||||
\(524\) | 145.608i | 0.277878i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −176.505 | −0.335561 | ||||||||
\(527\) | −412.202 | − | 713.955i | −0.782167 | − | 1.35475i | ||||
\(528\) | 117.488 | + | 67.8317i | 0.222515 | + | 0.128469i | ||||
\(529\) | −265.147 | + | 459.248i | −0.501223 | + | 0.868144i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 86.4066i | − | 0.162724i | ||||||
\(532\) | −310.845 | + | 79.0776i | −0.584294 | + | 0.148642i | ||||
\(533\) | 143.574 | 0.269370 | ||||||||
\(534\) | 59.5558 | + | 103.154i | 0.111528 | + | 0.193172i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.59876 | − | 7.96529i | 0.00857978 | − | 0.0148606i | ||||
\(537\) | −62.3215 | + | 35.9814i | −0.116055 | + | 0.0670044i | ||||
\(538\) | − | 294.427i | − | 0.547263i | ||||||
\(539\) | 24.3448 | − | 959.176i | 0.0451666 | − | 1.77955i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −488.481 | − | 846.074i | −0.902922 | − | 1.56391i | −0.823682 | − | 0.567052i | \(-0.808084\pi\) |
−0.0792400 | − | 0.996856i | \(-0.525249\pi\) | |||||||
\(542\) | 24.3042 | + | 14.0321i | 0.0448418 | + | 0.0258894i | ||||
\(543\) | −223.614 | + | 387.311i | −0.411813 | + | 0.713281i | ||||
\(544\) | 96.1523 | − | 55.5136i | 0.176751 | − | 0.102047i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.14209 | + | 35.9365i | 0.0167438 | + | 0.0658177i | ||||
\(547\) | 231.665 | 0.423520 | 0.211760 | − | 0.977322i | \(-0.432080\pi\) | ||||
0.211760 | + | 0.977322i | \(0.432080\pi\) | |||||||
\(548\) | 149.502 | + | 258.945i | 0.272814 | + | 0.472527i | ||||
\(549\) | −218.386 | − | 126.085i | −0.397789 | − | 0.229664i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −549.440 | + | 317.219i | −0.997168 | + | 0.575715i | ||||
\(552\) | 159.446i | 0.288852i | ||||||||
\(553\) | −108.119 | + | 105.409i | −0.195513 | + | 0.190613i | ||||
\(554\) | −123.058 | −0.222127 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 99.5501 | + | 57.4753i | 0.179047 | + | 0.103373i | ||||
\(557\) | −92.4015 | + | 160.044i | −0.165891 | + | 0.287332i | −0.936971 | − | 0.349406i | \(-0.886383\pi\) |
0.771080 | + | 0.636738i | \(0.219717\pi\) | |||||||
\(558\) | 154.331 | − | 89.1030i | 0.276579 | − | 0.159683i | ||||
\(559\) | − | 159.937i | − | 0.286112i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −665.667 | −1.18657 | ||||||||
\(562\) | 103.233 | + | 178.804i | 0.183688 | + | 0.318157i | ||||
\(563\) | −35.3570 | − | 20.4134i | −0.0628011 | − | 0.0362582i | 0.468271 | − | 0.883585i | \(-0.344877\pi\) |
−0.531072 | + | 0.847327i | \(0.678211\pi\) | |||||||
\(564\) | 105.464 | − | 182.670i | 0.186994 | − | 0.323883i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 500.271i | 0.883871i | ||||||||
\(567\) | 60.6416 | + | 17.0764i | 0.106952 | + | 0.0301170i | ||||
\(568\) | 110.111 | 0.193858 | ||||||||
\(569\) | 300.722 | + | 520.866i | 0.528509 | + | 0.915405i | 0.999447 | + | 0.0332389i | \(0.0105822\pi\) |
−0.470938 | + | 0.882166i | \(0.656084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −434.599 | + | 752.747i | −0.761119 | + | 1.31830i | 0.181156 | + | 0.983454i | \(0.442016\pi\) |
−0.942274 | + | 0.334842i | \(0.891317\pi\) | |||||||
\(572\) | 73.3469 | − | 42.3469i | 0.128229 | − | 0.0740330i | ||||
\(573\) | 156.525i | 0.273168i | ||||||||
\(574\) | −458.791 | − | 470.584i | −0.799288 | − | 0.819832i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 54.2326 | + | 31.3112i | 0.0939906 | + | 0.0542655i | 0.546259 | − | 0.837617i | \(-0.316052\pi\) |
−0.452268 | + | 0.891882i | \(0.649385\pi\) | |||||||
\(578\) | −68.0374 | + | 117.844i | −0.117712 | + | 0.203883i | ||||
\(579\) | −91.3814 | + | 52.7591i | −0.157826 | + | 0.0911210i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −273.833 | + | 69.6619i | −0.471313 | + | 0.119900i | ||||
\(582\) | 61.8479 | 0.106268 | ||||||||
\(583\) | −906.848 | − | 1570.71i | −1.55549 | − | 2.69418i | ||||
\(584\) | −86.3477 | − | 49.8529i | −0.147856 | − | 0.0853645i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −145.741 | + | 84.1439i | −0.248706 | + | 0.143590i | ||||
\(587\) | − | 112.217i | − | 0.191170i | −0.995421 | − | 0.0955852i | \(-0.969528\pi\) | ||
0.995421 | − | 0.0955852i | \(-0.0304722\pi\) | |||||||
\(588\) | 88.5730 | − | 144.799i | 0.150634 | − | 0.246257i | ||||
\(589\) | 962.317 | 1.63382 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −111.196 | − | 64.1993i | −0.188150 | − | 0.108628i | ||||
\(592\) | 120.912 | − | 209.426i | 0.204243 | − | 0.353760i | ||||
\(593\) | 449.992 | − | 259.803i | 0.758841 | − | 0.438117i | −0.0700388 | − | 0.997544i | \(-0.522312\pi\) |
0.828879 | + | 0.559427i | \(0.188979\pi\) | |||||||
\(594\) | − | 143.893i | − | 0.242244i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −50.3254 | −0.0844385 | ||||||||
\(597\) | 77.5575 | + | 134.334i | 0.129912 | + | 0.225014i | ||||
\(598\) | 86.2051 | + | 49.7705i | 0.144156 | + | 0.0832283i | ||||
\(599\) | 123.317 | − | 213.591i | 0.205871 | − | 0.356579i | −0.744539 | − | 0.667579i | \(-0.767331\pi\) |
0.950410 | + | 0.311000i | \(0.100664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 244.671i | − | 0.407106i | −0.979064 | − | 0.203553i | \(-0.934751\pi\) | ||
0.979064 | − | 0.203553i | \(-0.0652489\pi\) | |||||||
\(602\) | −524.214 | + | 511.077i | −0.870787 | + | 0.848966i | ||||
\(603\) | −9.75545 | −0.0161782 | ||||||||
\(604\) | −22.2663 | − | 38.5664i | −0.0368648 | − | 0.0638517i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −74.4537 | + | 128.958i | −0.122861 | + | 0.212801i | ||||
\(607\) | −35.1564 | + | 20.2975i | −0.0579183 | + | 0.0334391i | −0.528680 | − | 0.848822i | \(-0.677313\pi\) |
0.470761 | + | 0.882261i | \(0.343979\pi\) | |||||||
\(608\) | 129.601i | 0.213159i | ||||||||
\(609\) | 91.0061 | − | 323.181i | 0.149435 | − | 0.530675i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −65.8407 | − | 114.039i | −0.107759 | − | 0.186644i | ||||
\(612\) | −101.985 | − | 58.8810i | −0.166642 | − | 0.0962108i | ||||
\(613\) | −54.9828 | + | 95.2330i | −0.0896946 | + | 0.155356i | −0.907382 | − | 0.420307i | \(-0.861922\pi\) |
0.817687 | + | 0.575662i | \(0.195256\pi\) | |||||||
\(614\) | 589.959 | − | 340.613i | 0.960845 | − | 0.554744i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −373.177 | − | 105.085i | −0.605807 | − | 0.170592i | ||||
\(617\) | 168.842 | 0.273650 | 0.136825 | − | 0.990595i | \(-0.456310\pi\) | ||||
0.136825 | + | 0.990595i | \(0.456310\pi\) | |||||||
\(618\) | 52.3565 | + | 90.6842i | 0.0847193 | + | 0.146738i | ||||
\(619\) | −607.202 | − | 350.568i | −0.980940 | − | 0.566346i | −0.0783859 | − | 0.996923i | \(-0.524977\pi\) |
−0.902554 | + | 0.430577i | \(0.858310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 146.461 | − | 84.5591i | 0.235846 | − | 0.136166i | ||||
\(622\) | 814.317i | 1.30919i | ||||||||
\(623\) | −237.619 | − | 243.726i | −0.381411 | − | 0.391214i | ||||
\(624\) | 14.9830 | 0.0240113 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −522.083 | − | 301.425i | −0.833998 | − | 0.481509i | ||||
\(627\) | 388.513 | − | 672.924i | 0.619637 | − | 1.07324i | ||||
\(628\) | −485.156 | + | 280.105i | −0.772542 | + | 0.446027i | ||||
\(629\) | 1186.57i | 1.88644i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −465.556 | −0.737807 | −0.368903 | − | 0.929468i | \(-0.620267\pi\) | ||||
−0.368903 | + | 0.929468i | \(0.620267\pi\) | |||||||
\(632\) | 30.5064 | + | 52.8387i | 0.0482697 | + | 0.0836055i | ||||
\(633\) | 104.797 | + | 60.5046i | 0.165556 | + | 0.0955838i | ||||
\(634\) | −17.8331 | + | 30.8878i | −0.0281279 | + | 0.0487189i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 320.858i | − | 0.504494i | ||||||
\(637\) | −50.6385 | − | 93.0859i | −0.0794953 | − | 0.146132i | ||||
\(638\) | −766.857 | −1.20197 | ||||||||
\(639\) | −58.3953 | − | 101.144i | −0.0913854 | − | 0.158284i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 615.260 | − | 1065.66i | 0.959844 | − | 1.66250i | 0.236973 | − | 0.971516i | \(-0.423845\pi\) |
0.722871 | − | 0.690983i | \(-0.242822\pi\) | |||||||
\(642\) | −325.193 | + | 187.750i | −0.506531 | + | 0.292446i | ||||
\(643\) | − | 322.975i | − | 0.502293i | −0.967949 | − | 0.251147i | \(-0.919192\pi\) | ||
0.967949 | − | 0.251147i | \(-0.0808076\pi\) | |||||||
\(644\) | −112.339 | − | 441.590i | −0.174439 | − | 0.685699i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −317.959 | − | 550.721i | −0.492197 | − | 0.852510i | ||||
\(647\) | 1025.79 | + | 592.243i | 1.58546 | + | 0.915368i | 0.994041 | + | 0.109006i | \(0.0347667\pi\) |
0.591422 | + | 0.806362i | \(0.298567\pi\) | |||||||
\(648\) | 12.7279 | − | 22.0454i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 488.426 | − | 281.993i | 0.752582 | − | 0.434503i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −364.645 | + | 355.508i | −0.560131 | + | 0.546095i | ||||
\(652\) | −265.280 | −0.406871 | ||||||||
\(653\) | −131.660 | − | 228.041i | −0.201623 | − | 0.349221i | 0.747429 | − | 0.664342i | \(-0.231288\pi\) |
−0.949052 | + | 0.315121i | \(0.897955\pi\) | |||||||
\(654\) | −122.564 | − | 70.7622i | −0.187406 | − | 0.108199i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −229.979 | + | 132.779i | −0.350578 | + | 0.202406i | ||||
\(657\) | 105.754i | 0.160965i | ||||||||
\(658\) | −163.385 | + | 580.214i | −0.248306 | + | 0.881784i | ||||
\(659\) | −1199.70 | −1.82049 | −0.910246 | − | 0.414069i | \(-0.864107\pi\) | ||||
−0.910246 | + | 0.414069i | \(0.864107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 497.702 | + | 287.349i | 0.752954 | + | 0.434718i | 0.826760 | − | 0.562555i | \(-0.190181\pi\) |
−0.0738065 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(662\) | −1.35117 | + | 2.34030i | −0.00204105 | + | 0.00353520i | ||||
\(663\) | −63.6685 | + | 36.7590i | −0.0960309 | + | 0.0554434i | ||||
\(664\) | 114.169i | 0.171942i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −256.493 | −0.385125 | ||||||||
\(667\) | −450.646 | − | 780.542i | −0.675631 | − | 1.17023i | ||||
\(668\) | −206.966 | − | 119.492i | −0.309829 | − | 0.178880i | ||||
\(669\) | −337.472 | + | 584.518i | −0.504442 | + | 0.873719i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1645.95i | − | 2.45298i | ||||||
\(672\) | −47.8782 | − | 49.1088i | −0.0712473 | − | 0.0730786i | ||||
\(673\) | 958.817 | 1.42469 | 0.712346 | − | 0.701829i | \(-0.247633\pi\) | ||||
0.712346 | + | 0.701829i | \(0.247633\pi\) | |||||||
\(674\) | −238.735 | − | 413.500i | −0.354206 | − | 0.613502i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −164.323 | + | 284.616i | −0.243082 | + | 0.421030i | ||||
\(677\) | −394.839 | + | 227.961i | −0.583219 | + | 0.336722i | −0.762412 | − | 0.647092i | \(-0.775985\pi\) |
0.179192 | + | 0.983814i | \(0.442652\pi\) | |||||||
\(678\) | − | 366.256i | − | 0.540201i | ||||||
\(679\) | −171.289 | + | 43.5753i | −0.252267 | + | 0.0641757i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.47172 | + | 11.2093i | 0.00950325 | + | 0.0164601i | ||||
\(682\) | 1007.33 | + | 581.585i | 1.47703 | + | 0.852764i | ||||
\(683\) | −115.479 | + | 200.015i | −0.169076 | + | 0.292848i | −0.938095 | − | 0.346378i | \(-0.887412\pi\) |
0.769019 | + | 0.639225i | \(0.220745\pi\) | |||||||
\(684\) | 119.046 | − | 68.7311i | 0.174044 | − | 0.100484i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −143.286 | + | 463.430i | −0.208872 | + | 0.675554i | ||||
\(687\) | −173.663 | −0.252785 | ||||||||
\(688\) | 147.911 | + | 256.189i | 0.214986 | + | 0.372367i | ||||
\(689\) | −173.473 | − | 100.155i | −0.251775 | − | 0.145362i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −92.1832 | + | 53.2220i | −0.133405 | + | 0.0770217i | −0.565217 | − | 0.824942i | \(-0.691208\pi\) |
0.431812 | + | 0.901964i | \(0.357874\pi\) | |||||||
\(692\) | 504.235i | 0.728664i | ||||||||
\(693\) | 101.380 | + | 398.515i | 0.146292 | + | 0.575057i | ||||
\(694\) | 419.313 | 0.604198 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −117.488 | − | 67.8317i | −0.168805 | − | 0.0974594i | ||||
\(697\) | 651.511 | − | 1128.45i | 0.934737 | − | 1.61901i | ||||
\(698\) | −450.092 | + | 259.861i | −0.644831 | + | 0.372293i | ||||
\(699\) | − | 588.848i | − | 0.842414i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −623.489 | −0.889429 | −0.444714 | − | 0.895672i | \(-0.646695\pi\) | ||||
−0.444714 | + | 0.895672i | \(0.646695\pi\) | |||||||
\(702\) | −7.94595 | − | 13.7628i | −0.0113190 | − | 0.0196051i | ||||
\(703\) | −1199.51 | − | 692.535i | −1.70627 | − | 0.985114i | ||||
\(704\) | −78.3253 | + | 135.663i | −0.111258 | + | 0.192704i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 745.717i | 1.05626i | ||||||||
\(707\) | 115.344 | − | 409.608i | 0.163145 | − | 0.579361i | ||||
\(708\) | 99.7737 | 0.140923 | ||||||||
\(709\) | −397.184 | − | 687.943i | −0.560203 | − | 0.970300i | −0.997478 | − | 0.0709721i | \(-0.977390\pi\) |
0.437275 | − | 0.899328i | \(-0.355943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.3570 | − | 56.0439i | 0.0455091 | − | 0.0788240i | ||||
\(712\) | −119.112 | + | 68.7691i | −0.167292 | + | 0.0965858i | ||||
\(713\) | 1367.08i | 1.91736i | ||||||||
\(714\) | 323.935 | + | 91.2184i | 0.453690 | + | 0.127757i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −41.5477 | − | 71.9627i | −0.0580275 | − | 0.100507i | ||||
\(717\) | 56.5641 | + | 32.6573i | 0.0788899 | + | 0.0455471i | ||||
\(718\) | 416.257 | − | 720.979i | 0.579745 | − | 1.00415i | ||||
\(719\) | −33.4178 | + | 19.2938i | −0.0464782 | + | 0.0268342i | −0.523059 | − | 0.852296i | \(-0.675209\pi\) |
0.476581 | + | 0.879131i | \(0.341876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −208.895 | − | 214.264i | −0.289729 | − | 0.297176i | ||||
\(722\) | 231.769 | 0.321010 | ||||||||
\(723\) | −258.515 | − | 447.761i | −0.357559 | − | 0.619310i | ||||
\(724\) | −447.229 | − | 258.208i | −0.617719 | − | 0.356640i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 556.695 | − | 321.408i | 0.766797 | − | 0.442711i | ||||
\(727\) | 867.980i | 1.19392i | 0.802271 | + | 0.596960i | \(0.203625\pi\) | ||||
−0.802271 | + | 0.596960i | \(0.796375\pi\) | |||||||
\(728\) | −41.4959 | + | 10.5564i | −0.0569998 | + | 0.0145005i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1257.05 | − | 725.761i | −1.71964 | − | 0.992832i | ||||
\(732\) | 145.591 | − | 252.171i | 0.198895 | − | 0.344496i | ||||
\(733\) | −283.830 | + | 163.869i | −0.387217 | + | 0.223560i | −0.680954 | − | 0.732327i | \(-0.738434\pi\) |
0.293737 | + | 0.955886i | \(0.405101\pi\) | |||||||
\(734\) | 482.254i | 0.657022i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −184.112 | −0.250153 | ||||||||
\(737\) | −31.8375 | − | 55.1441i | −0.0431987 | − | 0.0748224i | ||||
\(738\) | 243.930 | + | 140.833i | 0.330528 | + | 0.190831i | ||||
\(739\) | −598.500 | + | 1036.63i | −0.809878 | + | 1.40275i | 0.103070 | + | 0.994674i | \(0.467134\pi\) |
−0.912948 | + | 0.408076i | \(0.866200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 85.8167i | − | 0.115812i | ||||||
\(742\) | 226.062 | + | 888.625i | 0.304666 | + | 1.19761i | ||||
\(743\) | 685.246 | 0.922269 | 0.461135 | − | 0.887330i | \(-0.347443\pi\) | ||||
0.461135 | + | 0.887330i | \(0.347443\pi\) | |||||||
\(744\) | 102.887 | + | 178.206i | 0.138289 | + | 0.239524i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −82.9735 | + | 143.714i | −0.111225 | + | 0.192647i | ||||
\(747\) | 104.871 | − | 60.5474i | 0.140390 | − | 0.0810541i | ||||
\(748\) | − | 768.646i | − | 1.02760i | ||||||
\(749\) | 768.350 | − | 749.096i | 1.02583 | − | 1.00013i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.2714 | − | 69.7521i | −0.0536237 | − | 0.0928789i | 0.837968 | − | 0.545720i | \(-0.183744\pi\) |
−0.891591 | + | 0.452841i | \(0.850410\pi\) | |||||||
\(752\) | 210.929 | + | 121.780i | 0.280491 | + | 0.161941i | ||||
\(753\) | 217.484 | − | 376.694i | 0.288824 | − | 0.500257i | ||||
\(754\) | −73.3469 | + | 42.3469i | −0.0972771 | + | 0.0561629i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −19.7181 | + | 70.0228i | −0.0260821 | + | 0.0926228i | ||||
\(757\) | −978.106 | −1.29208 | −0.646041 | − | 0.763303i | \(-0.723576\pi\) | ||||
−0.646041 | + | 0.763303i | \(0.723576\pi\) | |||||||
\(758\) | −133.031 | − | 230.417i | −0.175503 | − | 0.303981i | ||||
\(759\) | 955.964 | + | 551.926i | 1.25951 | + | 0.727176i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −514.781 | + | 297.209i | −0.676453 | + | 0.390550i | −0.798517 | − | 0.601972i | \(-0.794382\pi\) |
0.122064 | + | 0.992522i | \(0.461049\pi\) | |||||||
\(762\) | 431.630i | 0.566443i | ||||||||
\(763\) | 389.299 | + | 109.625i | 0.510221 | + | 0.143676i | ||||
\(764\) | −180.740 | −0.236571 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 329.363 | + | 190.158i | 0.429978 | + | 0.248248i | ||||
\(767\) | 31.1440 | − | 53.9430i | 0.0406050 | − | 0.0703299i | ||||
\(768\) | −24.0000 | + | 13.8564i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 1475.89i | − | 1.91923i | −0.281321 | − | 0.959614i | \(-0.590772\pi\) | ||
0.281321 | − | 0.959614i | \(-0.409228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −103.347 | −0.134042 | ||||||||
\(772\) | −60.9209 | − | 105.518i | −0.0789131 | − | 0.136682i | ||||
\(773\) | −34.0155 | − | 19.6389i | −0.0440045 | − | 0.0254060i | 0.477836 | − | 0.878449i | \(-0.341421\pi\) |
−0.521841 | + | 0.853043i | \(0.674755\pi\) | |||||||
\(774\) | 156.883 | − | 271.729i | 0.202691 | − | 0.351071i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 71.4158i | 0.0920307i | ||||||||
\(777\) | 710.364 | − | 180.714i | 0.914239 | − | 0.232579i | ||||
\(778\) | −419.121 | −0.538716 | ||||||||
\(779\) | 760.502 | + | 1317.23i | 0.976254 | + | 1.69092i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 381.153 | − | 660.176i | 0.488031 | − | 0.845295i | ||||
\(782\) | 782.362 | − | 451.697i | 1.00046 | − | 0.577618i | ||||
\(783\) | 143.893i | 0.183771i | ||||||||
\(784\) | 167.200 | + | 102.275i | 0.213265 | + | 0.130453i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 89.1665 | + | 154.441i | 0.113443 | + | 0.196490i | ||||
\(787\) | −769.456 | − | 444.246i | −0.977708 | − | 0.564480i | −0.0761308 | − | 0.997098i | \(-0.524257\pi\) |
−0.901577 | + | 0.432618i | \(0.857590\pi\) | |||||||
\(788\) | 74.1310 | − | 128.399i | 0.0940749 | − | 0.162942i | ||||
\(789\) | −187.212 | + | 108.087i | −0.237277 | + | 0.136992i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 258.048 | + | 1014.36i | 0.326230 | + | 1.28237i | ||||
\(792\) | 166.153 | 0.209789 | ||||||||
\(793\) | −90.8914 | − | 157.428i | −0.114617 | − | 0.198523i | ||||
\(794\) | −23.1160 | − | 13.3460i | −0.0291133 | − | 0.0168086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −155.115 | + | 89.5557i | −0.194868 | + | 0.112507i | ||||
\(797\) | 340.067i | 0.426684i | 0.976978 | + | 0.213342i | \(0.0684349\pi\) | ||||
−0.976978 | + | 0.213342i | \(0.931565\pi\) | |||||||
\(798\) | −281.275 | + | 274.227i | −0.352476 | + | 0.343643i | ||||
\(799\) | −1195.09 | −1.49573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 126.337 | + | 72.9407i | 0.157724 | + | 0.0910620i | ||||
\(802\) | 243.198 | − | 421.231i | 0.303240 | − | 0.525226i | ||||
\(803\) | −597.789 | + | 345.134i | −0.744445 | + | 0.429806i | ||||
\(804\) | − | 11.2646i | − | 0.0140107i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 128.464 | 0.159384 | ||||||||
\(807\) | −180.299 | − | 312.287i | −0.223419 | − | 0.386973i | ||||
\(808\) | −148.907 | − | 85.9717i | −0.184291 | − | 0.106401i | ||||
\(809\) | 17.5840 | − | 30.4564i | 0.0217355 | − | 0.0376470i | −0.854953 | − | 0.518705i | \(-0.826414\pi\) |
0.876689 | + | 0.481058i | \(0.159747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1408.87i | 1.73720i | 0.495511 | + | 0.868602i | \(0.334981\pi\) | ||||
−0.495511 | + | 0.868602i | \(0.665019\pi\) | |||||||
\(812\) | 373.177 | + | 105.085i | 0.459578 | + | 0.129415i | ||||
\(813\) | 34.3714 | 0.0422772 | ||||||||
\(814\) | −837.079 | − | 1449.86i | −1.02835 | − | 1.78116i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 67.9899 | − | 117.762i | 0.0833210 | − | 0.144316i | ||||
\(817\) | 1467.35 | − | 847.172i | 1.79602 | − | 1.03693i | ||||
\(818\) | 614.591i | 0.751333i | ||||||||
\(819\) | 31.7032 | + | 32.5180i | 0.0387096 | + | 0.0397046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −218.908 | − | 379.160i | −0.266636 | − | 0.461827i | 0.701355 | − | 0.712812i | \(-0.252579\pi\) |
−0.967991 | + | 0.250985i | \(0.919245\pi\) | |||||||
\(822\) | 317.141 | + | 183.102i | 0.385817 | + | 0.222751i | ||||
\(823\) | 394.124 | − | 682.642i | 0.478887 | − | 0.829456i | −0.520820 | − | 0.853666i | \(-0.674374\pi\) |
0.999707 | + | 0.0242104i | \(0.00770715\pi\) | |||||||
\(824\) | −104.713 | + | 60.4561i | −0.127079 | + | 0.0733691i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −276.326 | + | 70.2962i | −0.334535 | + | 0.0851043i | ||||
\(827\) | −45.9270 | −0.0555345 | −0.0277673 | − | 0.999614i | \(-0.508840\pi\) | ||||
−0.0277673 | + | 0.999614i | \(0.508840\pi\) | |||||||
\(828\) | 97.6404 | + | 169.118i | 0.117923 | + | 0.204249i | ||||
\(829\) | 519.195 | + | 299.757i | 0.626290 | + | 0.361589i | 0.779314 | − | 0.626634i | \(-0.215568\pi\) |
−0.153024 | + | 0.988223i | \(0.548901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −130.523 | + | 75.3576i | −0.157068 | + | 0.0906830i | ||||
\(832\) | 17.3009i | 0.0207944i | ||||||||
\(833\) | −961.414 | − | 24.4016i | −1.15416 | − | 0.0292936i | ||||
\(834\) | 140.785 | 0.168807 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 777.025 | + | 448.616i | 0.929456 | + | 0.536622i | ||||
\(837\) | 109.128 | − | 189.016i | 0.130380 | − | 0.225826i | ||||
\(838\) | −390.982 | + | 225.734i | −0.466566 | + | 0.269372i | ||||
\(839\) | − | 933.368i | − | 1.11248i | −0.831023 | − | 0.556238i | \(-0.812244\pi\) | ||
0.831023 | − | 0.556238i | \(-0.187756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −74.1431 | −0.0881606 | ||||||||
\(842\) | −469.170 | − | 812.626i | −0.557209 | − | 0.965114i | ||||
\(843\) | 218.990 | + | 126.434i | 0.259774 | + | 0.149981i | ||||
\(844\) | −69.8647 | + | 121.009i | −0.0827780 | + | 0.143376i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 258.334i | − | 0.305359i | ||||||
\(847\) | −1315.33 | + | 1282.37i | −1.55293 | + | 1.51401i | ||||
\(848\) | 370.495 | 0.436905 | ||||||||
\(849\) | 306.352 | + | 530.618i | 0.360839 | + | 0.624991i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 983.825 | − | 1704.03i | 1.15608 | − | 2.00239i | ||||
\(852\) | 116.791 | − | 67.4291i | 0.137078 | − | 0.0791421i | ||||
\(853\) | − | 1336.84i | − | 1.56722i | −0.621255 | − | 0.783608i | \(-0.713377\pi\) | ||
0.621255 | − | 0.783608i | \(-0.286623\pi\) | |||||||
\(854\) | −225.549 | + | 800.970i | −0.264109 | + | 0.937904i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −216.795 | − | 375.501i | −0.253266 | − | 0.438669i | ||||
\(857\) | 1045.96 | + | 603.883i | 1.22049 | + | 0.704647i | 0.965021 | − | 0.262171i | \(-0.0844385\pi\) |
0.255464 | + | 0.966819i | \(0.417772\pi\) | |||||||
\(858\) | 51.8641 | − | 89.8313i | 0.0604477 | − | 0.104698i | ||||
\(859\) | −1377.37 | + | 795.223i | −1.60345 | + | 0.925755i | −0.612665 | + | 0.790343i | \(0.709902\pi\) |
−0.990789 | + | 0.135412i | \(0.956764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −774.794 | − | 218.178i | −0.899877 | − | 0.253401i | ||||
\(862\) | 142.916 | 0.165796 | ||||||||
\(863\) | −28.9950 | − | 50.2209i | −0.0335980 | − | 0.0581934i | 0.848737 | − | 0.528814i | \(-0.177363\pi\) |
−0.882335 | + | 0.470621i | \(0.844030\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −600.349 | + | 346.612i | −0.693243 | + | 0.400244i | ||||
\(867\) | 166.657i | 0.192222i | ||||||||
\(868\) | −410.505 | − | 421.056i | −0.472932 | − | 0.485088i | ||||
\(869\) | 422.395 | 0.486070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.09026 | − | 3.51621i | −0.00699226 | − | 0.00403698i | ||||
\(872\) | 81.7091 | − | 141.524i | 0.0937031 | − | 0.162299i | ||||
\(873\) | 65.5996 | − | 37.8740i | 0.0751428 | − | 0.0433837i | ||||
\(874\) | 1054.52i | 1.20655i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −122.114 | −0.139400 | ||||||||
\(877\) | 255.414 | + | 442.389i | 0.291236 | + | 0.504435i | 0.974102 | − | 0.226108i | \(-0.0726003\pi\) |
−0.682867 | + | 0.730543i | \(0.739267\pi\) | |||||||
\(878\) | 565.336 | + | 326.397i | 0.643891 | + | 0.371750i | ||||
\(879\) | −103.055 | + | 178.496i | −0.117241 | + | 0.203067i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 631.045i | − | 0.716282i | −0.933667 | − | 0.358141i | \(-0.883411\pi\) | ||
0.933667 | − | 0.358141i | \(-0.116589\pi\) | |||||||
\(882\) | 5.27473 | − | 207.822i | 0.00598042 | − | 0.235626i | ||||
\(883\) | −918.874 | −1.04063 | −0.520314 | − | 0.853975i | \(-0.674185\pi\) | ||||
−0.520314 | + | 0.853975i | \(0.674185\pi\) | |||||||
\(884\) | −42.4456 | − | 73.5180i | −0.0480154 | − | 0.0831652i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 141.454 | − | 245.006i | 0.159655 | − | 0.276530i | ||||
\(887\) | 84.1745 | − | 48.5981i | 0.0948979 | − | 0.0547893i | −0.451800 | − | 0.892119i | \(-0.649218\pi\) |
0.546698 | + | 0.837330i | \(0.315885\pi\) | |||||||
\(888\) | − | 296.173i | − | 0.333528i | ||||||
\(889\) | −304.107 | − | 1195.41i | −0.342078 | − | 1.34467i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −88.1160 | − | 152.621i | −0.0988956 | − | 0.171292i | ||||
\(892\) | −674.944 | − | 389.679i | −0.756663 | − | 0.436860i | ||||
\(893\) | 697.506 | − | 1208.12i | 0.781082 | − | 1.35287i | ||||
\(894\) | −53.3781 | + | 30.8179i | −0.0597071 | + | 0.0344719i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 56.7060 | − | 55.2850i | 0.0632879 | − | 0.0617020i | ||||
\(897\) | 121.912 | 0.135911 | ||||||||
\(898\) | −53.5998 | − | 92.8375i | −0.0596880 | − | 0.103383i | ||||
\(899\) | −1007.33 | − | 581.585i | −1.12051 | − | 0.646924i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1574.37 | + | 908.964i | −1.74736 | + | 1.00884i | ||||
\(902\) | 1838.46i | 2.03821i | ||||||||
\(903\) | −243.043 | + | 863.093i | −0.269150 | + | 0.955806i | ||||
\(904\) | 422.916 | 0.467828 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −47.2340 | − | 27.2706i | −0.0521347 | − | 0.0301000i | ||||
\(907\) | 293.890 | − | 509.032i | 0.324024 | − | 0.561226i | −0.657291 | − | 0.753637i | \(-0.728298\pi\) |
0.981314 | + | 0.192412i | \(0.0616309\pi\) | |||||||
\(908\) | −12.9434 | + | 7.47289i | −0.0142549 | + | 0.00823006i | ||||
\(909\) | 182.374i | 0.200631i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −406.902 | −0.446654 | −0.223327 | − | 0.974744i | \(-0.571692\pi\) | ||||
−0.223327 | + | 0.974744i | \(0.571692\pi\) | |||||||
\(912\) | 79.3639 | + | 137.462i | 0.0870218 | + | 0.150726i | ||||
\(913\) | 684.506 | + | 395.200i | 0.749733 | + | 0.432858i | ||||
\(914\) | −290.724 | + | 503.548i | −0.318078 | + | 0.550928i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 200.529i | − | 0.218918i | ||||||
\(917\) | −355.761 | − | 364.905i | −0.387962 | − | 0.397934i | ||||
\(918\) | −144.228 | −0.157112 | ||||||||
\(919\) | 480.514 | + | 832.275i | 0.522866 | + | 0.905631i | 0.999646 | + | 0.0266079i | \(0.00847057\pi\) |
−0.476780 | + | 0.879023i | \(0.658196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 417.164 | − | 722.549i | 0.452947 | − | 0.784527i | ||||
\(922\) | −340.481 | + | 196.577i | −0.369286 | + | 0.213207i | ||||
\(923\) | − | 84.1910i | − | 0.0912145i | ||||||
\(924\) | −460.165 | + | 117.064i | −0.498014 | + | 0.126693i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −348.302 | − | 603.276i | −0.376136 | − | 0.651486i | ||||
\(927\) | 111.065 | + | 64.1234i | 0.119811 | + | 0.0691730i | ||||
\(928\) | 78.3253 | − | 135.663i | 0.0844023 | − | 0.146189i | ||||
\(929\) | 1072.91 | − | 619.447i | 1.15491 | − | 0.666789i | 0.204832 | − | 0.978797i | \(-0.434335\pi\) |
0.950079 | + | 0.312009i | \(0.101002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 585.791 | − | 957.653i | 0.629206 | − | 1.02863i | ||||
\(932\) | 679.943 | 0.729552 | ||||||||
\(933\) | 498.665 | + | 863.713i | 0.534475 | + | 0.925738i | ||||
\(934\) | −395.593 | − | 228.395i | −0.423547 | − | 0.244535i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15.8919 | − | 9.17519i | 0.0169785 | − | 0.00980256i | ||||
\(937\) | 219.917i | 0.234703i | 0.993090 | + | 0.117351i | \(0.0374404\pi\) | ||||
−0.993090 | + | 0.117351i | \(0.962560\pi\) | |||||||
\(938\) | 7.93656 | + | 31.1977i | 0.00846115 | + | 0.0332598i | ||||
\(939\) | −738.337 | −0.786301 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1070.33 | + | 617.954i | 1.13744 | + | 0.656700i | 0.945795 | − | 0.324765i | \(-0.105285\pi\) |
0.191642 | + | 0.981465i | \(0.438619\pi\) | |||||||
\(942\) | −343.057 | + | 594.193i | −0.364180 | + | 0.630778i | ||||
\(943\) | −1871.27 | + | 1080.38i | −1.98438 | + | 1.14568i | ||||
\(944\) | 115.209i | 0.122043i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2047.98 | 2.16489 | ||||||||
\(947\) | 288.231 | + | 499.231i | 0.304363 | + | 0.527172i | 0.977119 | − | 0.212692i | \(-0.0682232\pi\) |
−0.672757 | + | 0.739864i | \(0.734890\pi\) | |||||||
\(948\) | 64.7139 | + | 37.3626i | 0.0682636 | + | 0.0394120i | ||||
\(949\) | −38.1175 | + | 66.0214i | −0.0401660 | + | 0.0695695i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.6820i | 0.0459327i | ||||||||
\(952\) | −105.330 | + | 374.048i | −0.110641 | + | 0.392907i | ||||
\(953\) | −976.945 | −1.02513 | −0.512563 | − | 0.858650i | \(-0.671304\pi\) | ||||
−0.512563 | + | 0.858650i | \(0.671304\pi\) | |||||||
\(954\) | −196.485 | − | 340.321i | −0.205959 | − | 0.356731i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −37.7094 | + | 65.3145i | −0.0394449 | + | 0.0683207i | ||||
\(957\) | −813.375 | + | 469.602i | −0.849921 | + | 0.490702i | ||||
\(958\) | − | 437.390i | − | 0.456566i | ||||||
\(959\) | −1007.34 | − | 283.661i | −1.05040 | − | 0.295788i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 401.649 | + | 695.676i | 0.417949 | + | 0.723909i | ||||
\(962\) | −160.127 | − | 92.4493i | −0.166452 | − | 0.0961011i | ||||
\(963\) | −229.946 | + | 398.279i | −0.238781 | + | 0.413581i | ||||
\(964\) | 517.030 | − | 298.508i | 0.536339 | − | 0.309655i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −389.571 | − | 399.584i | −0.403282 | − | 0.413648i | ||||
\(967\) | −805.489 | −0.832978 | −0.416489 | − | 0.909141i | \(-0.636740\pi\) | ||||
−0.416489 | + | 0.909141i | \(0.636740\pi\) | |||||||
\(968\) | 371.130 | + | 642.816i | 0.383399 | + | 0.664066i | ||||
\(969\) | −674.493 | − | 389.419i | −0.696072 | − | 0.401877i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1332.28 | − | 769.192i | 1.37207 | − | 0.792165i | 0.380881 | − | 0.924624i | \(-0.375621\pi\) |
0.991188 | + | 0.132459i | \(0.0422873\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −389.908 | + | 99.1910i | −0.400728 | + | 0.101943i | ||||
\(974\) | 800.032 | 0.821388 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 291.182 | + | 168.114i | 0.298342 | + | 0.172248i | ||||
\(977\) | 585.004 | − | 1013.26i | 0.598775 | − | 1.03711i | −0.394227 | − | 0.919013i | \(-0.628988\pi\) |
0.993002 | − | 0.118096i | \(-0.0376791\pi\) | |||||||
\(978\) | −281.372 | + | 162.450i | −0.287701 | + | 0.166104i | ||||
\(979\) | 952.183i | 0.972608i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −173.331 | −0.176688 | ||||||||
\(982\) | −268.230 | − | 464.589i | −0.273147 | − | 0.473105i | ||||
\(983\) | −383.708 | − | 221.534i | −0.390344 | − | 0.225365i | 0.291965 | − | 0.956429i | \(-0.405691\pi\) |
−0.682309 | + | 0.731064i | \(0.739024\pi\) | |||||||
\(984\) | −162.620 | + | 281.666i | −0.165264 | + | 0.286246i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 768.646i | 0.779560i | ||||||||
\(987\) | 182.011 | + | 715.463i | 0.184408 | + | 0.724886i | ||||
\(988\) | 99.0926 | 0.100296 | ||||||||
\(989\) | 1203.50 | + | 2084.53i | 1.21689 | + | 2.10771i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −72.4829 | + | 125.544i | −0.0731411 | + | 0.126684i | −0.900276 | − | 0.435319i | \(-0.856636\pi\) |
0.827135 | + | 0.562003i | \(0.189969\pi\) | |||||||
\(992\) | −205.775 | + | 118.804i | −0.207434 | + | 0.119762i | ||||
\(993\) | 3.30969i | 0.00333302i | ||||||||
\(994\) | −275.947 | + | 269.032i | −0.277613 | + | 0.270656i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 69.9142 | + | 121.095i | 0.0701949 | + | 0.121581i | ||||
\(997\) | 781.912 | + | 451.437i | 0.784265 | + | 0.452796i | 0.837940 | − | 0.545763i | \(-0.183760\pi\) |
−0.0536748 | + | 0.998558i | \(0.517093\pi\) | |||||||
\(998\) | −383.721 | + | 664.625i | −0.384490 | + | 0.665957i | ||||
\(999\) | −272.052 | + | 157.069i | −0.272324 | + | 0.157227i |
(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 | 1050.3.p.f.451.5 | yes | 12 | |
5.2 | odd | 4 | 1050.3.q.d.199.5 | 24 | |||
5.3 | odd | 4 | 1050.3.q.d.199.12 | 24 | |||
5.4 | even | 2 | 1050.3.p.e.451.2 | ✓ | 12 | ||
7.5 | odd | 6 | inner | 1050.3.p.f.901.5 | yes | 12 | |
35.12 | even | 12 | 1050.3.q.d.649.12 | 24 | |||
35.19 | odd | 6 | 1050.3.p.e.901.2 | yes | 12 | ||
35.33 | even | 12 | 1050.3.q.d.649.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.e.451.2 | ✓ | 12 | 5.4 | even | 2 | ||
1050.3.p.e.901.2 | yes | 12 | 35.19 | odd | 6 | ||
1050.3.p.f.451.5 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.p.f.901.5 | yes | 12 | 7.5 | odd | 6 | inner | |
1050.3.q.d.199.5 | 24 | 5.2 | odd | 4 | |||
1050.3.q.d.199.12 | 24 | 5.3 | odd | 4 | |||
1050.3.q.d.649.5 | 24 | 35.33 | even | 12 | |||
1050.3.q.d.649.12 | 24 | 35.12 | even | 12 |