Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
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: | \( x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(0.914718i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.43 |
Dual form | 770.2.m.e.197.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||
\(3\) | −2.14984 | − | 2.14984i | −1.24121 | − | 1.24121i | −0.959498 | − | 0.281714i | \(-0.909097\pi\) |
−0.281714 | − | 0.959498i | \(-0.590903\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.71500 | − | 1.43484i | −0.766972 | − | 0.641681i | ||||
\(6\) | 3.04034i | 1.24121i | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 6.24365i | 2.08122i | ||||||||
\(10\) | 0.198102 | + | 2.22728i | 0.0626455 | + | 0.704326i | ||||
\(11\) | 0.280159 | + | 3.30477i | 0.0844711 | + | 0.996426i | ||||
\(12\) | 2.14984 | − | 2.14984i | 0.620606 | − | 0.620606i | ||||
\(13\) | 3.30477 | − | 3.30477i | 0.916579 | − | 0.916579i | −0.0802002 | − | 0.996779i | \(-0.525556\pi\) |
0.996779 | + | 0.0802002i | \(0.0255560\pi\) | |||||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 0.602298 | + | 6.77167i | 0.155513 | + | 1.74844i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.29361 | + | 2.29361i | 0.556281 | + | 0.556281i | 0.928247 | − | 0.371965i | \(-0.121316\pi\) |
−0.371965 | + | 0.928247i | \(0.621316\pi\) | |||||||
\(18\) | 4.41493 | − | 4.41493i | 1.04061 | − | 1.04061i | ||||
\(19\) | −0.396205 | −0.0908956 | −0.0454478 | − | 0.998967i | \(-0.514471\pi\) | ||||
−0.0454478 | + | 0.998967i | \(0.514471\pi\) | |||||||
\(20\) | 1.43484 | − | 1.71500i | 0.320840 | − | 0.383486i | ||||
\(21\) | − | 3.04034i | − | 0.663456i | ||||||
\(22\) | 2.13872 | − | 2.53493i | 0.455977 | − | 0.540449i | ||||
\(23\) | 5.93428 | + | 5.93428i | 1.23738 | + | 1.23738i | 0.961066 | + | 0.276317i | \(0.0891141\pi\) |
0.276317 | + | 0.961066i | \(0.410886\pi\) | |||||||
\(24\) | −3.04034 | −0.620606 | ||||||||
\(25\) | 0.882457 | + | 4.92151i | 0.176491 | + | 0.984302i | ||||
\(26\) | −4.67365 | −0.916579 | ||||||||
\(27\) | 6.97334 | − | 6.97334i | 1.34202 | − | 1.34202i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −4.95580 | −0.920270 | −0.460135 | − | 0.887849i | \(-0.652199\pi\) | ||||
−0.460135 | + | 0.887849i | \(0.652199\pi\) | |||||||
\(30\) | 4.36240 | − | 5.21418i | 0.796462 | − | 0.951975i | ||||
\(31\) | 3.24365 | 0.582577 | 0.291288 | − | 0.956635i | \(-0.405916\pi\) | ||||
0.291288 | + | 0.956635i | \(0.405916\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 6.50244 | − | 7.70704i | 1.13193 | − | 1.34162i | ||||
\(34\) | − | 3.24365i | − | 0.556281i | ||||||
\(35\) | −0.198102 | − | 2.22728i | −0.0334854 | − | 0.376478i | ||||
\(36\) | −6.24365 | −1.04061 | ||||||||
\(37\) | −5.43000 | + | 5.43000i | −0.892687 | + | 0.892687i | −0.994775 | − | 0.102088i | \(-0.967448\pi\) |
0.102088 | + | 0.994775i | \(0.467448\pi\) | |||||||
\(38\) | 0.280159 | + | 0.280159i | 0.0454478 | + | 0.0454478i | ||||
\(39\) | −14.2095 | −2.27534 | ||||||||
\(40\) | −2.22728 | + | 0.198102i | −0.352163 | + | 0.0313227i | ||||
\(41\) | − | 6.00143i | − | 0.937265i | −0.883393 | − | 0.468633i | \(-0.844747\pi\) | ||
0.883393 | − | 0.468633i | \(-0.155253\pi\) | |||||||
\(42\) | −2.14984 | + | 2.14984i | −0.331728 | + | 0.331728i | ||||
\(43\) | 7.83946 | − | 7.83946i | 1.19551 | − | 1.19551i | 0.220009 | − | 0.975498i | \(-0.429391\pi\) |
0.975498 | − | 0.220009i | \(-0.0706086\pi\) | |||||||
\(44\) | −3.30477 | + | 0.280159i | −0.498213 | + | 0.0422356i | ||||
\(45\) | 8.95865 | − | 10.7079i | 1.33548 | − | 1.59623i | ||||
\(46\) | − | 8.39234i | − | 1.23738i | ||||||
\(47\) | −3.29969 | + | 3.29969i | −0.481309 | + | 0.481309i | −0.905549 | − | 0.424241i | \(-0.860541\pi\) |
0.424241 | + | 0.905549i | \(0.360541\pi\) | |||||||
\(48\) | 2.14984 | + | 2.14984i | 0.310303 | + | 0.310303i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 2.85604 | − | 4.10403i | 0.403905 | − | 0.580397i | ||||
\(51\) | − | 9.86179i | − | 1.38093i | ||||||
\(52\) | 3.30477 | + | 3.30477i | 0.458289 | + | 0.458289i | ||||
\(53\) | −9.91730 | − | 9.91730i | −1.36225 | − | 1.36225i | −0.871048 | − | 0.491198i | \(-0.836559\pi\) |
−0.491198 | − | 0.871048i | \(-0.663441\pi\) | |||||||
\(54\) | −9.86179 | −1.34202 | ||||||||
\(55\) | 4.26135 | − | 6.06967i | 0.574600 | − | 0.818434i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.851778 | + | 0.851778i | 0.112821 | + | 0.112821i | ||||
\(58\) | 3.50428 | + | 3.50428i | 0.460135 | + | 0.460135i | ||||
\(59\) | 12.4521i | 1.62112i | 0.585654 | + | 0.810561i | \(0.300838\pi\) | ||||
−0.585654 | + | 0.810561i | \(0.699162\pi\) | |||||||
\(60\) | −6.77167 | + | 0.602298i | −0.874219 | + | 0.0777563i | ||||
\(61\) | 7.90478i | 1.01210i | 0.862503 | + | 0.506052i | \(0.168896\pi\) | ||||
−0.862503 | + | 0.506052i | \(0.831104\pi\) | |||||||
\(62\) | −2.29361 | − | 2.29361i | −0.291288 | − | 0.291288i | ||||
\(63\) | −4.41493 | + | 4.41493i | −0.556229 | + | 0.556229i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −10.4095 | + | 0.925861i | −1.29114 | + | 0.114839i | ||||
\(66\) | −10.0476 | + | 0.851778i | −1.23678 | + | 0.104847i | ||||
\(67\) | 8.03905 | − | 8.03905i | 0.982127 | − | 0.982127i | −0.0177163 | − | 0.999843i | \(-0.505640\pi\) |
0.999843 | + | 0.0177163i | \(0.00563957\pi\) | |||||||
\(68\) | −2.29361 | + | 2.29361i | −0.278141 | + | 0.278141i | ||||
\(69\) | − | 25.5156i | − | 3.07171i | ||||||
\(70\) | −1.43484 | + | 1.71500i | −0.171496 | + | 0.204982i | ||||
\(71\) | 6.66397 | 0.790868 | 0.395434 | − | 0.918494i | \(-0.370594\pi\) | ||||
0.395434 | + | 0.918494i | \(0.370594\pi\) | |||||||
\(72\) | 4.41493 | + | 4.41493i | 0.520304 | + | 0.520304i | ||||
\(73\) | 3.89212 | − | 3.89212i | 0.455538 | − | 0.455538i | −0.441650 | − | 0.897187i | \(-0.645607\pi\) |
0.897187 | + | 0.441650i | \(0.145607\pi\) | |||||||
\(74\) | 7.67918 | 0.892687 | ||||||||
\(75\) | 8.68333 | − | 12.4776i | 1.00266 | − | 1.44079i | ||||
\(76\) | − | 0.396205i | − | 0.0454478i | ||||||
\(77\) | −2.13872 | + | 2.53493i | −0.243730 | + | 0.288882i | ||||
\(78\) | 10.0476 | + | 10.0476i | 1.13767 | + | 1.13767i | ||||
\(79\) | 14.1181 | 1.58841 | 0.794206 | − | 0.607648i | \(-0.207887\pi\) | ||||
0.794206 | + | 0.607648i | \(0.207887\pi\) | |||||||
\(80\) | 1.71500 | + | 1.43484i | 0.191743 | + | 0.160420i | ||||
\(81\) | −11.2522 | −1.25025 | ||||||||
\(82\) | −4.24365 | + | 4.24365i | −0.468633 | + | 0.468633i | ||||
\(83\) | −1.89651 | + | 1.89651i | −0.208169 | + | 0.208169i | −0.803489 | − | 0.595320i | \(-0.797025\pi\) |
0.595320 | + | 0.803489i | \(0.297025\pi\) | |||||||
\(84\) | 3.04034 | 0.331728 | ||||||||
\(85\) | −0.642575 | − | 7.22450i | −0.0696970 | − | 0.783607i | ||||
\(86\) | −11.0867 | −1.19551 | ||||||||
\(87\) | 10.6542 | + | 10.6542i | 1.14225 | + | 1.14225i | ||||
\(88\) | 2.53493 | + | 2.13872i | 0.270224 | + | 0.227989i | ||||
\(89\) | 5.86857i | 0.622067i | 0.950399 | + | 0.311033i | \(0.100675\pi\) | ||||
−0.950399 | + | 0.311033i | \(0.899325\pi\) | |||||||
\(90\) | −13.9063 | + | 1.23688i | −1.46586 | + | 0.130379i | ||||
\(91\) | 4.67365 | 0.489932 | ||||||||
\(92\) | −5.93428 | + | 5.93428i | −0.618692 | + | 0.618692i | ||||
\(93\) | −6.97334 | − | 6.97334i | −0.723101 | − | 0.723101i | ||||
\(94\) | 4.66646 | 0.481309 | ||||||||
\(95\) | 0.679492 | + | 0.568491i | 0.0697144 | + | 0.0583260i | ||||
\(96\) | − | 3.04034i | − | 0.310303i | ||||||
\(97\) | 3.24365 | − | 3.24365i | 0.329343 | − | 0.329343i | −0.522994 | − | 0.852337i | \(-0.675185\pi\) |
0.852337 | + | 0.522994i | \(0.175185\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | −20.6338 | + | 1.74921i | −2.07378 | + | 0.175803i | ||||
\(100\) | −4.92151 | + | 0.882457i | −0.492151 | + | 0.0882457i | ||||
\(101\) | 2.98511i | 0.297029i | 0.988910 | + | 0.148515i | \(0.0474492\pi\) | ||||
−0.988910 | + | 0.148515i | \(0.952551\pi\) | |||||||
\(102\) | −6.97334 | + | 6.97334i | −0.690463 | + | 0.690463i | ||||
\(103\) | −2.43968 | − | 2.43968i | −0.240389 | − | 0.240389i | 0.576622 | − | 0.817011i | \(-0.304371\pi\) |
−0.817011 | + | 0.576622i | \(0.804371\pi\) | |||||||
\(104\) | − | 4.67365i | − | 0.458289i | ||||||
\(105\) | −4.36240 | + | 5.21418i | −0.425727 | + | 0.508852i | ||||
\(106\) | 14.0252i | 1.36225i | ||||||||
\(107\) | 2.33929 | + | 2.33929i | 0.226147 | + | 0.226147i | 0.811081 | − | 0.584934i | \(-0.198880\pi\) |
−0.584934 | + | 0.811081i | \(0.698880\pi\) | |||||||
\(108\) | 6.97334 | + | 6.97334i | 0.671010 | + | 0.671010i | ||||
\(109\) | 9.86179 | 0.944588 | 0.472294 | − | 0.881441i | \(-0.343426\pi\) | ||||
0.472294 | + | 0.881441i | \(0.343426\pi\) | |||||||
\(110\) | −7.30513 | + | 1.27867i | −0.696517 | + | 0.121917i | ||||
\(111\) | 23.3473 | 2.21603 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | 2.68333 | + | 2.68333i | 0.252427 | + | 0.252427i | 0.821965 | − | 0.569538i | \(-0.192878\pi\) |
−0.569538 | + | 0.821965i | \(0.692878\pi\) | |||||||
\(114\) | − | 1.20460i | − | 0.112821i | ||||||
\(115\) | −1.66254 | − | 18.6921i | −0.155033 | − | 1.74304i | ||||
\(116\) | − | 4.95580i | − | 0.460135i | ||||||
\(117\) | 20.6338 | + | 20.6338i | 1.90760 | + | 1.90760i | ||||
\(118\) | 8.80495 | − | 8.80495i | 0.810561 | − | 0.810561i | ||||
\(119\) | 3.24365i | 0.297345i | ||||||||
\(120\) | 5.21418 | + | 4.36240i | 0.475987 | + | 0.398231i | ||||
\(121\) | −10.8430 | + | 1.85172i | −0.985729 | + | 0.168338i | ||||
\(122\) | 5.58952 | − | 5.58952i | 0.506052 | − | 0.506052i | ||||
\(123\) | −12.9021 | + | 12.9021i | −1.16335 | + | 1.16335i | ||||
\(124\) | 3.24365i | 0.291288i | ||||||||
\(125\) | 5.54818 | − | 9.70658i | 0.496244 | − | 0.868183i | ||||
\(126\) | 6.24365 | 0.556229 | ||||||||
\(127\) | −1.52521 | − | 1.52521i | −0.135341 | − | 0.135341i | 0.636191 | − | 0.771532i | \(-0.280509\pi\) |
−0.771532 | + | 0.636191i | \(0.780509\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −33.7072 | −2.96776 | ||||||||
\(130\) | 8.01532 | + | 6.70595i | 0.702990 | + | 0.588151i | ||||
\(131\) | − | 11.7099i | − | 1.02310i | −0.859254 | − | 0.511550i | \(-0.829072\pi\) | ||
0.859254 | − | 0.511550i | \(-0.170928\pi\) | |||||||
\(132\) | 7.70704 | + | 6.50244i | 0.670811 | + | 0.565965i | ||||
\(133\) | −0.280159 | − | 0.280159i | −0.0242929 | − | 0.0242929i | ||||
\(134\) | −11.3689 | −0.982127 | ||||||||
\(135\) | −21.9649 | + | 1.95364i | −1.89044 | + | 0.168143i | ||||
\(136\) | 3.24365 | 0.278141 | ||||||||
\(137\) | −9.10365 | + | 9.10365i | −0.777778 | + | 0.777778i | −0.979453 | − | 0.201675i | \(-0.935362\pi\) |
0.201675 | + | 0.979453i | \(0.435362\pi\) | |||||||
\(138\) | −18.0422 | + | 18.0422i | −1.53586 | + | 1.53586i | ||||
\(139\) | 12.3301 | 1.04583 | 0.522914 | − | 0.852385i | \(-0.324845\pi\) | ||||
0.522914 | + | 0.852385i | \(0.324845\pi\) | |||||||
\(140\) | 2.22728 | − | 0.198102i | 0.188239 | − | 0.0167427i | ||||
\(141\) | 14.1876 | 1.19481 | ||||||||
\(142\) | −4.71214 | − | 4.71214i | −0.395434 | − | 0.395434i | ||||
\(143\) | 11.8474 | + | 9.99565i | 0.990727 | + | 0.835878i | ||||
\(144\) | − | 6.24365i | − | 0.520304i | ||||||
\(145\) | 8.49921 | + | 7.11079i | 0.705821 | + | 0.590519i | ||||
\(146\) | −5.50428 | −0.455538 | ||||||||
\(147\) | 2.14984 | − | 2.14984i | 0.177316 | − | 0.177316i | ||||
\(148\) | −5.43000 | − | 5.43000i | −0.446343 | − | 0.446343i | ||||
\(149\) | 5.76190 | 0.472033 | 0.236017 | − | 0.971749i | \(-0.424158\pi\) | ||||
0.236017 | + | 0.971749i | \(0.424158\pi\) | |||||||
\(150\) | −14.9631 | + | 2.68297i | −1.22173 | + | 0.219063i | ||||
\(151\) | 14.0115i | 1.14024i | 0.821562 | + | 0.570120i | \(0.193103\pi\) | ||||
−0.821562 | + | 0.570120i | \(0.806897\pi\) | |||||||
\(152\) | −0.280159 | + | 0.280159i | −0.0227239 | + | 0.0227239i | ||||
\(153\) | −14.3205 | + | 14.3205i | −1.15774 | + | 1.15774i | ||||
\(154\) | 3.30477 | − | 0.280159i | 0.266306 | − | 0.0225759i | ||||
\(155\) | −5.56286 | − | 4.65412i | −0.446820 | − | 0.373828i | ||||
\(156\) | − | 14.2095i | − | 1.13767i | ||||||
\(157\) | 5.18890 | − | 5.18890i | 0.414119 | − | 0.414119i | −0.469052 | − | 0.883171i | \(-0.655404\pi\) |
0.883171 | + | 0.469052i | \(0.155404\pi\) | |||||||
\(158\) | −9.98302 | − | 9.98302i | −0.794206 | − | 0.794206i | ||||
\(159\) | 42.6413i | 3.38167i | ||||||||
\(160\) | −0.198102 | − | 2.22728i | −0.0156614 | − | 0.176082i | ||||
\(161\) | 8.39234i | 0.661409i | ||||||||
\(162\) | 7.95652 | + | 7.95652i | 0.625123 | + | 0.625123i | ||||
\(163\) | 8.77731 | + | 8.77731i | 0.687492 | + | 0.687492i | 0.961677 | − | 0.274185i | \(-0.0884081\pi\) |
−0.274185 | + | 0.961677i | \(0.588408\pi\) | |||||||
\(164\) | 6.00143 | 0.468633 | ||||||||
\(165\) | −22.2101 | + | 3.88760i | −1.72905 | + | 0.302649i | ||||
\(166\) | 2.68207 | 0.208169 | ||||||||
\(167\) | 7.12630 | + | 7.12630i | 0.551450 | + | 0.551450i | 0.926859 | − | 0.375410i | \(-0.122498\pi\) |
−0.375410 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(168\) | −2.14984 | − | 2.14984i | −0.165864 | − | 0.165864i | ||||
\(169\) | − | 8.84302i | − | 0.680232i | ||||||
\(170\) | −4.65412 | + | 5.56286i | −0.356955 | + | 0.426652i | ||||
\(171\) | − | 2.47376i | − | 0.189173i | ||||||
\(172\) | 7.83946 | + | 7.83946i | 0.597753 | + | 0.597753i | ||||
\(173\) | 11.6695 | − | 11.6695i | 0.887216 | − | 0.887216i | −0.107039 | − | 0.994255i | \(-0.534137\pi\) |
0.994255 | + | 0.107039i | \(0.0341370\pi\) | |||||||
\(174\) | − | 15.0673i | − | 1.14225i | ||||||
\(175\) | −2.85604 | + | 4.10403i | −0.215897 | + | 0.310235i | ||||
\(176\) | −0.280159 | − | 3.30477i | −0.0211178 | − | 0.249106i | ||||
\(177\) | 26.7700 | − | 26.7700i | 2.01216 | − | 2.01216i | ||||
\(178\) | 4.14970 | − | 4.14970i | 0.311033 | − | 0.311033i | ||||
\(179\) | 7.23523i | 0.540787i | 0.962750 | + | 0.270393i | \(0.0871537\pi\) | ||||
−0.962750 | + | 0.270393i | \(0.912846\pi\) | |||||||
\(180\) | 10.7079 | + | 8.95865i | 0.798117 | + | 0.667738i | ||||
\(181\) | −13.9173 | −1.03446 | −0.517232 | − | 0.855845i | \(-0.673038\pi\) | ||||
−0.517232 | + | 0.855845i | \(0.673038\pi\) | |||||||
\(182\) | −3.30477 | − | 3.30477i | −0.244966 | − | 0.244966i | ||||
\(183\) | 16.9940 | − | 16.9940i | 1.25624 | − | 1.25624i | ||||
\(184\) | 8.39234 | 0.618692 | ||||||||
\(185\) | 17.1037 | − | 1.52126i | 1.25749 | − | 0.111846i | ||||
\(186\) | 9.86179i | 0.723101i | ||||||||
\(187\) | −6.93727 | + | 8.22242i | −0.507303 | + | 0.601283i | ||||
\(188\) | −3.29969 | − | 3.29969i | −0.240654 | − | 0.240654i | ||||
\(189\) | 9.86179 | 0.717340 | ||||||||
\(190\) | −0.0784891 | − | 0.882457i | −0.00569420 | − | 0.0640202i | ||||
\(191\) | −1.33603 | −0.0966716 | −0.0483358 | − | 0.998831i | \(-0.515392\pi\) | ||||
−0.0483358 | + | 0.998831i | \(0.515392\pi\) | |||||||
\(192\) | −2.14984 | + | 2.14984i | −0.155152 | + | 0.155152i | ||||
\(193\) | 9.99085 | − | 9.99085i | 0.719157 | − | 0.719157i | −0.249275 | − | 0.968433i | \(-0.580192\pi\) |
0.968433 | + | 0.249275i | \(0.0801924\pi\) | |||||||
\(194\) | −4.58721 | −0.329343 | ||||||||
\(195\) | 24.3693 | + | 20.3884i | 1.74512 | + | 1.46004i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 9.91342 | + | 9.91342i | 0.706302 | + | 0.706302i | 0.965756 | − | 0.259454i | \(-0.0835425\pi\) |
−0.259454 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(198\) | 15.8272 | + | 13.3534i | 1.12479 | + | 0.948988i | ||||
\(199\) | 8.36429i | 0.592929i | 0.955044 | + | 0.296464i | \(0.0958076\pi\) | ||||
−0.955044 | + | 0.296464i | \(0.904192\pi\) | |||||||
\(200\) | 4.10403 | + | 2.85604i | 0.290198 | + | 0.201953i | ||||
\(201\) | −34.5654 | −2.43806 | ||||||||
\(202\) | 2.11079 | − | 2.11079i | 0.148515 | − | 0.148515i | ||||
\(203\) | −3.50428 | − | 3.50428i | −0.245952 | − | 0.245952i | ||||
\(204\) | 9.86179 | 0.690463 | ||||||||
\(205\) | −8.61110 | + | 10.2925i | −0.601425 | + | 0.718856i | ||||
\(206\) | 3.45023i | 0.240389i | ||||||||
\(207\) | −37.0516 | + | 37.0516i | −2.57526 | + | 2.57526i | ||||
\(208\) | −3.30477 | + | 3.30477i | −0.229145 | + | 0.229145i | ||||
\(209\) | −0.111000 | − | 1.30937i | −0.00767805 | − | 0.0905707i | ||||
\(210\) | 6.77167 | − | 0.602298i | 0.467289 | − | 0.0415625i | ||||
\(211\) | 21.1203i | 1.45398i | 0.686649 | + | 0.726990i | \(0.259081\pi\) | ||||
−0.686649 | + | 0.726990i | \(0.740919\pi\) | |||||||
\(212\) | 9.91730 | − | 9.91730i | 0.681123 | − | 0.681123i | ||||
\(213\) | −14.3265 | − | 14.3265i | −0.981635 | − | 0.981635i | ||||
\(214\) | − | 3.30825i | − | 0.226147i | ||||||
\(215\) | −24.6931 | + | 2.19630i | −1.68405 | + | 0.149786i | ||||
\(216\) | − | 9.86179i | − | 0.671010i | ||||||
\(217\) | 2.29361 | + | 2.29361i | 0.155700 | + | 0.155700i | ||||
\(218\) | −6.97334 | − | 6.97334i | −0.472294 | − | 0.472294i | ||||
\(219\) | −16.7349 | −1.13084 | ||||||||
\(220\) | 6.06967 | + | 4.26135i | 0.409217 | + | 0.287300i | ||||
\(221\) | 15.1597 | 1.01975 | ||||||||
\(222\) | −16.5090 | − | 16.5090i | −1.10801 | − | 1.10801i | ||||
\(223\) | 7.59095 | + | 7.59095i | 0.508328 | + | 0.508328i | 0.914013 | − | 0.405685i | \(-0.132967\pi\) |
−0.405685 | + | 0.914013i | \(0.632967\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | −30.7282 | + | 5.50975i | −2.04855 | + | 0.367317i | ||||
\(226\) | − | 3.79480i | − | 0.252427i | ||||||
\(227\) | −18.3263 | − | 18.3263i | −1.21636 | − | 1.21636i | −0.968898 | − | 0.247462i | \(-0.920404\pi\) |
−0.247462 | − | 0.968898i | \(-0.579596\pi\) | |||||||
\(228\) | −0.851778 | + | 0.851778i | −0.0564104 | + | 0.0564104i | ||||
\(229\) | 2.02681i | 0.133935i | 0.997755 | + | 0.0669676i | \(0.0213324\pi\) | ||||
−0.997755 | + | 0.0669676i | \(0.978668\pi\) | |||||||
\(230\) | −12.0417 | + | 14.3929i | −0.794005 | + | 0.949038i | ||||
\(231\) | 10.0476 | − | 0.851778i | 0.661085 | − | 0.0560429i | ||||
\(232\) | −3.50428 | + | 3.50428i | −0.230067 | + | 0.230067i | ||||
\(233\) | 5.66641 | − | 5.66641i | 0.371219 | − | 0.371219i | −0.496702 | − | 0.867921i | \(-0.665456\pi\) |
0.867921 | + | 0.496702i | \(0.165456\pi\) | |||||||
\(234\) | − | 29.1806i | − | 1.90760i | ||||||
\(235\) | 10.3935 | − | 0.924437i | 0.677997 | − | 0.0603036i | ||||
\(236\) | −12.4521 | −0.810561 | ||||||||
\(237\) | −30.3517 | − | 30.3517i | −1.97156 | − | 1.97156i | ||||
\(238\) | 2.29361 | − | 2.29361i | 0.148672 | − | 0.148672i | ||||
\(239\) | −0.0913582 | −0.00590947 | −0.00295474 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295474 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(240\) | −0.602298 | − | 6.77167i | −0.0388782 | − | 0.437109i | ||||
\(241\) | − | 24.6673i | − | 1.58896i | −0.607291 | − | 0.794479i | \(-0.707744\pi\) | ||
0.607291 | − | 0.794479i | \(-0.292256\pi\) | |||||||
\(242\) | 8.97654 | + | 6.35781i | 0.577034 | + | 0.408695i | ||||
\(243\) | 3.27048 | + | 3.27048i | 0.209801 | + | 0.209801i | ||||
\(244\) | −7.90478 | −0.506052 | ||||||||
\(245\) | 1.43484 | − | 1.71500i | 0.0916687 | − | 0.109567i | ||||
\(246\) | 18.2464 | 1.16335 | ||||||||
\(247\) | −1.30937 | + | 1.30937i | −0.0833130 | + | 0.0833130i | ||||
\(248\) | 2.29361 | − | 2.29361i | 0.145644 | − | 0.145644i | ||||
\(249\) | 8.15440 | 0.516764 | ||||||||
\(250\) | −10.7867 | + | 2.94044i | −0.682214 | + | 0.185970i | ||||
\(251\) | 4.52253 | 0.285459 | 0.142730 | − | 0.989762i | \(-0.454412\pi\) | ||||
0.142730 | + | 0.989762i | \(0.454412\pi\) | |||||||
\(252\) | −4.41493 | − | 4.41493i | −0.278114 | − | 0.278114i | ||||
\(253\) | −17.9489 | + | 21.2740i | −1.12844 | + | 1.33748i | ||||
\(254\) | 2.15698i | 0.135341i | ||||||||
\(255\) | −14.1501 | + | 16.9130i | −0.886114 | + | 1.05913i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.19603 | − | 4.19603i | 0.261741 | − | 0.261741i | −0.564020 | − | 0.825761i | \(-0.690746\pi\) |
0.825761 | + | 0.564020i | \(0.190746\pi\) | |||||||
\(258\) | 23.8346 | + | 23.8346i | 1.48388 | + | 1.48388i | ||||
\(259\) | −7.67918 | −0.477161 | ||||||||
\(260\) | −0.925861 | − | 10.4095i | −0.0574195 | − | 0.645570i | ||||
\(261\) | − | 30.9423i | − | 1.91528i | ||||||
\(262\) | −8.28016 | + | 8.28016i | −0.511550 | + | 0.511550i | ||||
\(263\) | −0.0552305 | + | 0.0552305i | −0.00340566 | + | 0.00340566i | −0.708808 | − | 0.705402i | \(-0.750767\pi\) |
0.705402 | + | 0.708808i | \(0.250767\pi\) | |||||||
\(264\) | −0.851778 | − | 10.0476i | −0.0524233 | − | 0.618388i | ||||
\(265\) | 2.77842 | + | 31.2379i | 0.170677 | + | 1.91893i | ||||
\(266\) | 0.396205i | 0.0242929i | ||||||||
\(267\) | 12.6165 | − | 12.6165i | 0.772117 | − | 0.772117i | ||||
\(268\) | 8.03905 | + | 8.03905i | 0.491063 | + | 0.491063i | ||||
\(269\) | 12.1268i | 0.739387i | 0.929154 | + | 0.369693i | \(0.120537\pi\) | ||||
−0.929154 | + | 0.369693i | \(0.879463\pi\) | |||||||
\(270\) | 16.9130 | + | 14.1501i | 1.02929 | + | 0.861148i | ||||
\(271\) | − | 29.5438i | − | 1.79466i | −0.441361 | − | 0.897330i | \(-0.645504\pi\) | ||
0.441361 | − | 0.897330i | \(-0.354496\pi\) | |||||||
\(272\) | −2.29361 | − | 2.29361i | −0.139070 | − | 0.139070i | ||||
\(273\) | −10.0476 | − | 10.0476i | −0.608109 | − | 0.608109i | ||||
\(274\) | 12.8745 | 0.777778 | ||||||||
\(275\) | −16.0172 | + | 4.29512i | −0.965876 | + | 0.259006i | ||||
\(276\) | 25.5156 | 1.53586 | ||||||||
\(277\) | −13.8272 | − | 13.8272i | −0.830796 | − | 0.830796i | 0.156830 | − | 0.987626i | \(-0.449873\pi\) |
−0.987626 | + | 0.156830i | \(0.949873\pi\) | |||||||
\(278\) | −8.71872 | − | 8.71872i | −0.522914 | − | 0.522914i | ||||
\(279\) | 20.2522i | 1.21247i | ||||||||
\(280\) | −1.71500 | − | 1.43484i | −0.102491 | − | 0.0857482i | ||||
\(281\) | − | 9.82025i | − | 0.585827i | −0.956139 | − | 0.292913i | \(-0.905375\pi\) | ||
0.956139 | − | 0.292913i | \(-0.0946248\pi\) | |||||||
\(282\) | −10.0322 | − | 10.0322i | −0.597406 | − | 0.597406i | ||||
\(283\) | −16.4625 | + | 16.4625i | −0.978592 | + | 0.978592i | −0.999776 | − | 0.0211836i | \(-0.993257\pi\) |
0.0211836 | + | 0.999776i | \(0.493257\pi\) | |||||||
\(284\) | 6.66397i | 0.395434i | ||||||||
\(285\) | −0.238633 | − | 2.68297i | −0.0141354 | − | 0.158925i | ||||
\(286\) | −1.30937 | − | 15.4453i | −0.0774244 | − | 0.913303i | ||||
\(287\) | 4.24365 | − | 4.24365i | 0.250495 | − | 0.250495i | ||||
\(288\) | −4.41493 | + | 4.41493i | −0.260152 | + | 0.260152i | ||||
\(289\) | − | 6.47874i | − | 0.381102i | ||||||
\(290\) | −0.981756 | − | 11.0379i | −0.0576507 | − | 0.648170i | ||||
\(291\) | −13.9467 | −0.817569 | ||||||||
\(292\) | 3.89212 | + | 3.89212i | 0.227769 | + | 0.227769i | ||||
\(293\) | 0.805207 | − | 0.805207i | 0.0470407 | − | 0.0470407i | −0.683195 | − | 0.730236i | \(-0.739410\pi\) |
0.730236 | + | 0.683195i | \(0.239410\pi\) | |||||||
\(294\) | −3.04034 | −0.177316 | ||||||||
\(295\) | 17.8668 | − | 21.3553i | 1.04024 | − | 1.24335i | ||||
\(296\) | 7.67918i | 0.446343i | ||||||||
\(297\) | 24.9989 | + | 21.0916i | 1.45058 | + | 1.22386i | ||||
\(298\) | −4.07428 | − | 4.07428i | −0.236017 | − | 0.236017i | ||||
\(299\) | 39.2229 | 2.26832 | ||||||||
\(300\) | 12.4776 | + | 8.68333i | 0.720396 | + | 0.501332i | ||||
\(301\) | 11.0867 | 0.639025 | ||||||||
\(302\) | 9.90762 | − | 9.90762i | 0.570120 | − | 0.570120i | ||||
\(303\) | 6.41751 | − | 6.41751i | 0.368676 | − | 0.368676i | ||||
\(304\) | 0.396205 | 0.0227239 | ||||||||
\(305\) | 11.3421 | − | 13.5567i | 0.649447 | − | 0.776255i | ||||
\(306\) | 20.2522 | 1.15774 | ||||||||
\(307\) | 20.5089 | + | 20.5089i | 1.17051 | + | 1.17051i | 0.982089 | + | 0.188416i | \(0.0603352\pi\) |
0.188416 | + | 0.982089i | \(0.439665\pi\) | |||||||
\(308\) | −2.53493 | − | 2.13872i | −0.144441 | − | 0.121865i | ||||
\(309\) | 10.4899i | 0.596748i | ||||||||
\(310\) | 0.642575 | + | 7.22450i | 0.0364958 | + | 0.410324i | ||||
\(311\) | 3.03411 | 0.172049 | 0.0860243 | − | 0.996293i | \(-0.472584\pi\) | ||||
0.0860243 | + | 0.996293i | \(0.472584\pi\) | |||||||
\(312\) | −10.0476 | + | 10.0476i | −0.568834 | + | 0.568834i | ||||
\(313\) | −10.7870 | − | 10.7870i | −0.609716 | − | 0.609716i | 0.333155 | − | 0.942872i | \(-0.391887\pi\) |
−0.942872 | + | 0.333155i | \(0.891887\pi\) | |||||||
\(314\) | −7.33821 | −0.414119 | ||||||||
\(315\) | 13.9063 | − | 1.23688i | 0.783533 | − | 0.0696904i | ||||
\(316\) | 14.1181i | 0.794206i | ||||||||
\(317\) | 1.99158 | − | 1.99158i | 0.111858 | − | 0.111858i | −0.648962 | − | 0.760821i | \(-0.724797\pi\) |
0.760821 | + | 0.648962i | \(0.224797\pi\) | |||||||
\(318\) | 30.1519 | − | 30.1519i | 1.69084 | − | 1.69084i | ||||
\(319\) | −1.38841 | − | 16.3778i | −0.0777362 | − | 0.916980i | ||||
\(320\) | −1.43484 | + | 1.71500i | −0.0802101 | + | 0.0958715i | ||||
\(321\) | − | 10.0582i | − | 0.561394i | ||||||
\(322\) | 5.93428 | − | 5.93428i | 0.330705 | − | 0.330705i | ||||
\(323\) | −0.908738 | − | 0.908738i | −0.0505635 | − | 0.0505635i | ||||
\(324\) | − | 11.2522i | − | 0.625123i | ||||||
\(325\) | 19.1808 | + | 13.3481i | 1.06396 | + | 0.740422i | ||||
\(326\) | − | 12.4130i | − | 0.687492i | ||||||
\(327\) | −21.2013 | − | 21.2013i | −1.17243 | − | 1.17243i | ||||
\(328\) | −4.24365 | − | 4.24365i | −0.234316 | − | 0.234316i | ||||
\(329\) | −4.66646 | −0.257270 | ||||||||
\(330\) | 18.4538 | + | 12.9559i | 1.01585 | + | 0.713201i | ||||
\(331\) | 18.2292 | 1.00197 | 0.500985 | − | 0.865456i | \(-0.332971\pi\) | ||||
0.500985 | + | 0.865456i | \(0.332971\pi\) | |||||||
\(332\) | −1.89651 | − | 1.89651i | −0.104085 | − | 0.104085i | ||||
\(333\) | −33.9030 | − | 33.9030i | −1.85787 | − | 1.85787i | ||||
\(334\) | − | 10.0781i | − | 0.551450i | ||||||
\(335\) | −25.3218 | + | 2.25221i | −1.38348 | + | 0.123052i | ||||
\(336\) | 3.04034i | 0.165864i | ||||||||
\(337\) | 12.3955 | + | 12.3955i | 0.675224 | + | 0.675224i | 0.958916 | − | 0.283692i | \(-0.0915593\pi\) |
−0.283692 | + | 0.958916i | \(0.591559\pi\) | |||||||
\(338\) | −6.25296 | + | 6.25296i | −0.340116 | + | 0.340116i | ||||
\(339\) | − | 11.5375i | − | 0.626630i | ||||||
\(340\) | 7.22450 | − | 0.642575i | 0.391804 | − | 0.0348485i | ||||
\(341\) | 0.908738 | + | 10.7195i | 0.0492109 | + | 0.580495i | ||||
\(342\) | −1.74921 | + | 1.74921i | −0.0945867 | + | 0.0945867i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 11.0867i | − | 0.597753i | ||||||
\(345\) | −36.6108 | + | 43.7592i | −1.97106 | + | 2.35592i | ||||
\(346\) | −16.5032 | −0.887216 | ||||||||
\(347\) | −12.2112 | − | 12.2112i | −0.655530 | − | 0.655530i | 0.298789 | − | 0.954319i | \(-0.403417\pi\) |
−0.954319 | + | 0.298789i | \(0.903417\pi\) | |||||||
\(348\) | −10.6542 | + | 10.6542i | −0.571125 | + | 0.571125i | ||||
\(349\) | 28.1572 | 1.50722 | 0.753611 | − | 0.657321i | \(-0.228310\pi\) | ||||
0.753611 | + | 0.657321i | \(0.228310\pi\) | |||||||
\(350\) | 4.92151 | − | 0.882457i | 0.263066 | − | 0.0471693i | ||||
\(351\) | − | 46.0906i | − | 2.46013i | ||||||
\(352\) | −2.13872 | + | 2.53493i | −0.113994 | + | 0.135112i | ||||
\(353\) | −7.08667 | − | 7.08667i | −0.377185 | − | 0.377185i | 0.492900 | − | 0.870086i | \(-0.335937\pi\) |
−0.870086 | + | 0.492900i | \(0.835937\pi\) | |||||||
\(354\) | −37.8585 | −2.01216 | ||||||||
\(355\) | −11.4287 | − | 9.56175i | −0.606573 | − | 0.507485i | ||||
\(356\) | −5.86857 | −0.311033 | ||||||||
\(357\) | 6.97334 | − | 6.97334i | 0.369068 | − | 0.369068i | ||||
\(358\) | 5.11608 | − | 5.11608i | 0.270393 | − | 0.270393i | ||||
\(359\) | −2.73707 | −0.144457 | −0.0722285 | − | 0.997388i | \(-0.523011\pi\) | ||||
−0.0722285 | + | 0.997388i | \(0.523011\pi\) | |||||||
\(360\) | −1.23688 | − | 13.9063i | −0.0651894 | − | 0.732928i | ||||
\(361\) | −18.8430 | −0.991738 | ||||||||
\(362\) | 9.84102 | + | 9.84102i | 0.517232 | + | 0.517232i | ||||
\(363\) | 27.2917 | + | 19.3299i | 1.43244 | + | 1.01456i | ||||
\(364\) | 4.67365i | 0.244966i | ||||||||
\(365\) | −12.2596 | + | 1.09041i | −0.641694 | + | 0.0570747i | ||||
\(366\) | −24.0332 | −1.25624 | ||||||||
\(367\) | −0.607936 | + | 0.607936i | −0.0317340 | + | 0.0317340i | −0.722796 | − | 0.691062i | \(-0.757143\pi\) |
0.691062 | + | 0.722796i | \(0.257143\pi\) | |||||||
\(368\) | −5.93428 | − | 5.93428i | −0.309346 | − | 0.309346i | ||||
\(369\) | 37.4708 | 1.95065 | ||||||||
\(370\) | −13.1698 | − | 11.0184i | −0.684666 | − | 0.572820i | ||||
\(371\) | − | 14.0252i | − | 0.728151i | ||||||
\(372\) | 6.97334 | − | 6.97334i | 0.361551 | − | 0.361551i | ||||
\(373\) | −0.912961 | + | 0.912961i | −0.0472713 | + | 0.0472713i | −0.730347 | − | 0.683076i | \(-0.760642\pi\) |
0.683076 | + | 0.730347i | \(0.260642\pi\) | |||||||
\(374\) | 10.7195 | − | 0.908738i | 0.554293 | − | 0.0469897i | ||||
\(375\) | −32.7953 | + | 8.93992i | −1.69354 | + | 0.461656i | ||||
\(376\) | 4.66646i | 0.240654i | ||||||||
\(377\) | −16.3778 | + | 16.3778i | −0.843499 | + | 0.843499i | ||||
\(378\) | −6.97334 | − | 6.97334i | −0.358670 | − | 0.358670i | ||||
\(379\) | 4.09747i | 0.210473i | 0.994447 | + | 0.105236i | \(0.0335599\pi\) | ||||
−0.994447 | + | 0.105236i | \(0.966440\pi\) | |||||||
\(380\) | −0.568491 | + | 0.679492i | −0.0291630 | + | 0.0348572i | ||||
\(381\) | 6.55794i | 0.335973i | ||||||||
\(382\) | 0.944714 | + | 0.944714i | 0.0483358 | + | 0.0483358i | ||||
\(383\) | −16.3864 | − | 16.3864i | −0.837304 | − | 0.837304i | 0.151200 | − | 0.988503i | \(-0.451686\pi\) |
−0.988503 | + | 0.151200i | \(0.951686\pi\) | |||||||
\(384\) | 3.04034 | 0.155152 | ||||||||
\(385\) | 7.30513 | − | 1.27867i | 0.372304 | − | 0.0651673i | ||||
\(386\) | −14.1292 | −0.719157 | ||||||||
\(387\) | 48.9468 | + | 48.9468i | 2.48811 | + | 2.48811i | ||||
\(388\) | 3.24365 | + | 3.24365i | 0.164671 | + | 0.164671i | ||||
\(389\) | 25.7371i | 1.30492i | 0.757821 | + | 0.652462i | \(0.226264\pi\) | ||||
−0.757821 | + | 0.652462i | \(0.773736\pi\) | |||||||
\(390\) | −2.81493 | − | 31.6484i | −0.142540 | − | 1.60258i | ||||
\(391\) | 27.2218i | 1.37667i | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | −25.1745 | + | 25.1745i | −1.26988 | + | 1.26988i | ||||
\(394\) | − | 14.0197i | − | 0.706302i | ||||||
\(395\) | −24.2126 | − | 20.2573i | −1.21827 | − | 1.01925i | ||||
\(396\) | −1.74921 | − | 20.6338i | −0.0879014 | − | 1.03689i | ||||
\(397\) | −7.97079 | + | 7.97079i | −0.400043 | + | 0.400043i | −0.878248 | − | 0.478205i | \(-0.841287\pi\) |
0.478205 | + | 0.878248i | \(0.341287\pi\) | |||||||
\(398\) | 5.91444 | − | 5.91444i | 0.296464 | − | 0.296464i | ||||
\(399\) | 1.20460i | 0.0603052i | ||||||||
\(400\) | −0.882457 | − | 4.92151i | −0.0441229 | − | 0.246076i | ||||
\(401\) | 26.0503 | 1.30089 | 0.650446 | − | 0.759553i | \(-0.274582\pi\) | ||||
0.650446 | + | 0.759553i | \(0.274582\pi\) | |||||||
\(402\) | 24.4414 | + | 24.4414i | 1.21903 | + | 1.21903i | ||||
\(403\) | 10.7195 | − | 10.7195i | 0.533977 | − | 0.533977i | ||||
\(404\) | −2.98511 | −0.148515 | ||||||||
\(405\) | 19.2976 | + | 16.1451i | 0.958903 | + | 0.802259i | ||||
\(406\) | 4.95580i | 0.245952i | ||||||||
\(407\) | −19.4662 | − | 16.4236i | −0.964903 | − | 0.814090i | ||||
\(408\) | −6.97334 | − | 6.97334i | −0.345232 | − | 0.345232i | ||||
\(409\) | 8.50930 | 0.420758 | 0.210379 | − | 0.977620i | \(-0.432530\pi\) | ||||
0.210379 | + | 0.977620i | \(0.432530\pi\) | |||||||
\(410\) | 13.3668 | − | 1.18890i | 0.660141 | − | 0.0587154i | ||||
\(411\) | 39.1429 | 1.93077 | ||||||||
\(412\) | 2.43968 | − | 2.43968i | 0.120195 | − | 0.120195i | ||||
\(413\) | −8.80495 | + | 8.80495i | −0.433263 | + | 0.433263i | ||||
\(414\) | 52.3989 | 2.57526 | ||||||||
\(415\) | 5.97371 | − | 0.531324i | 0.293238 | − | 0.0260817i | ||||
\(416\) | 4.67365 | 0.229145 | ||||||||
\(417\) | −26.5079 | − | 26.5079i | −1.29810 | − | 1.29810i | ||||
\(418\) | −0.847372 | + | 1.00435i | −0.0414463 | + | 0.0491244i | ||||
\(419\) | 3.69905i | 0.180711i | 0.995910 | + | 0.0903553i | \(0.0288003\pi\) | ||||
−0.995910 | + | 0.0903553i | \(0.971200\pi\) | |||||||
\(420\) | −5.21418 | − | 4.36240i | −0.254426 | − | 0.212863i | ||||
\(421\) | −13.8295 | −0.674009 | −0.337005 | − | 0.941503i | \(-0.609414\pi\) | ||||
−0.337005 | + | 0.941503i | \(0.609414\pi\) | |||||||
\(422\) | 14.9343 | − | 14.9343i | 0.726990 | − | 0.726990i | ||||
\(423\) | −20.6021 | − | 20.6021i | −1.00171 | − | 1.00171i | ||||
\(424\) | −14.0252 | −0.681123 | ||||||||
\(425\) | −9.26400 | + | 13.3120i | −0.449370 | + | 0.645728i | ||||
\(426\) | 20.2607i | 0.981635i | ||||||||
\(427\) | −5.58952 | + | 5.58952i | −0.270496 | + | 0.270496i | ||||
\(428\) | −2.33929 | + | 2.33929i | −0.113074 | + | 0.113074i | ||||
\(429\) | −3.98091 | − | 46.9591i | −0.192200 | − | 2.26721i | ||||
\(430\) | 19.0137 | + | 15.9076i | 0.916920 | + | 0.767134i | ||||
\(431\) | 34.4635i | 1.66005i | 0.557727 | + | 0.830024i | \(0.311673\pi\) | ||||
−0.557727 | + | 0.830024i | \(0.688327\pi\) | |||||||
\(432\) | −6.97334 | + | 6.97334i | −0.335505 | + | 0.335505i | ||||
\(433\) | 6.51285 | + | 6.51285i | 0.312987 | + | 0.312987i | 0.846066 | − | 0.533078i | \(-0.178965\pi\) |
−0.533078 | + | 0.846066i | \(0.678965\pi\) | |||||||
\(434\) | − | 3.24365i | − | 0.155700i | ||||||
\(435\) | −2.98487 | − | 33.5591i | −0.143114 | − | 1.60903i | ||||
\(436\) | 9.86179i | 0.472294i | ||||||||
\(437\) | −2.35119 | − | 2.35119i | −0.112473 | − | 0.112473i | ||||
\(438\) | 11.8333 | + | 11.8333i | 0.565419 | + | 0.565419i | ||||
\(439\) | −25.6850 | −1.22588 | −0.612940 | − | 0.790129i | \(-0.710013\pi\) | ||||
−0.612940 | + | 0.790129i | \(0.710013\pi\) | |||||||
\(440\) | −1.27867 | − | 7.30513i | −0.0609584 | − | 0.348259i | ||||
\(441\) | −6.24365 | −0.297317 | ||||||||
\(442\) | −10.7195 | − | 10.7195i | −0.509876 | − | 0.509876i | ||||
\(443\) | 22.1440 | + | 22.1440i | 1.05209 | + | 1.05209i | 0.998566 | + | 0.0535252i | \(0.0170458\pi\) |
0.0535252 | + | 0.998566i | \(0.482954\pi\) | |||||||
\(444\) | 23.3473i | 1.10801i | ||||||||
\(445\) | 8.42047 | − | 10.0646i | 0.399168 | − | 0.477108i | ||||
\(446\) | − | 10.7352i | − | 0.508328i | ||||||
\(447\) | −12.3872 | − | 12.3872i | −0.585894 | − | 0.585894i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | − | 8.11207i | − | 0.382832i | −0.981509 | − | 0.191416i | \(-0.938692\pi\) | ||
0.981509 | − | 0.191416i | \(-0.0613080\pi\) | |||||||
\(450\) | 25.6241 | + | 17.8321i | 1.20793 | + | 0.840615i | ||||
\(451\) | 19.8333 | − | 1.68135i | 0.933916 | − | 0.0791719i | ||||
\(452\) | −2.68333 | + | 2.68333i | −0.126213 | + | 0.126213i | ||||
\(453\) | 30.1225 | − | 30.1225i | 1.41528 | − | 1.41528i | ||||
\(454\) | 25.9173i | 1.21636i | ||||||||
\(455\) | −8.01532 | − | 6.70595i | −0.375764 | − | 0.314380i | ||||
\(456\) | 1.20460 | 0.0564104 | ||||||||
\(457\) | −3.42443 | − | 3.42443i | −0.160188 | − | 0.160188i | 0.622462 | − | 0.782650i | \(-0.286133\pi\) |
−0.782650 | + | 0.622462i | \(0.786133\pi\) | |||||||
\(458\) | 1.43317 | − | 1.43317i | 0.0669676 | − | 0.0669676i | ||||
\(459\) | 31.9882 | 1.49308 | ||||||||
\(460\) | 18.6921 | − | 1.66254i | 0.871522 | − | 0.0775165i | ||||
\(461\) | − | 12.1649i | − | 0.566578i | −0.959035 | − | 0.283289i | \(-0.908574\pi\) | ||
0.959035 | − | 0.283289i | \(-0.0914256\pi\) | |||||||
\(462\) | −7.70704 | − | 6.50244i | −0.358564 | − | 0.302521i | ||||
\(463\) | −10.6249 | − | 10.6249i | −0.493782 | − | 0.493782i | 0.415714 | − | 0.909496i | \(-0.363532\pi\) |
−0.909496 | + | 0.415714i | \(0.863532\pi\) | |||||||
\(464\) | 4.95580 | 0.230067 | ||||||||
\(465\) | 1.95364 | + | 21.9649i | 0.0905981 | + | 1.01860i | ||||
\(466\) | −8.01351 | −0.371219 | ||||||||
\(467\) | 3.74065 | − | 3.74065i | 0.173097 | − | 0.173097i | −0.615242 | − | 0.788338i | \(-0.710942\pi\) |
0.788338 | + | 0.615242i | \(0.210942\pi\) | |||||||
\(468\) | −20.6338 | + | 20.6338i | −0.953799 | + | 0.953799i | ||||
\(469\) | 11.3689 | 0.524969 | ||||||||
\(470\) | −8.00298 | − | 6.69563i | −0.369150 | − | 0.308847i | ||||
\(471\) | −22.3106 | −1.02802 | ||||||||
\(472\) | 8.80495 | + | 8.80495i | 0.405280 | + | 0.405280i | ||||
\(473\) | 28.1039 | + | 23.7113i | 1.29222 | + | 1.09025i | ||||
\(474\) | 42.9238i | 1.97156i | ||||||||
\(475\) | −0.349634 | − | 1.94993i | −0.0160423 | − | 0.0894687i | ||||
\(476\) | −3.24365 | −0.148672 | ||||||||
\(477\) | 61.9202 | − | 61.9202i | 2.83513 | − | 2.83513i | ||||
\(478\) | 0.0646000 | + | 0.0646000i | 0.00295474 | + | 0.00295474i | ||||
\(479\) | 24.1281 | 1.10244 | 0.551220 | − | 0.834360i | \(-0.314163\pi\) | ||||
0.551220 | + | 0.834360i | \(0.314163\pi\) | |||||||
\(480\) | −4.36240 | + | 5.21418i | −0.199116 | + | 0.237994i | ||||
\(481\) | 35.8898i | 1.63644i | ||||||||
\(482\) | −17.4424 | + | 17.4424i | −0.794479 | + | 0.794479i | ||||
\(483\) | 18.0422 | − | 18.0422i | 0.820950 | − | 0.820950i | ||||
\(484\) | −1.85172 | − | 10.8430i | −0.0841692 | − | 0.492865i | ||||
\(485\) | −10.2170 | + | 0.908738i | −0.463930 | + | 0.0412637i | ||||
\(486\) | − | 4.62516i | − | 0.209801i | ||||||
\(487\) | −12.1610 | + | 12.1610i | −0.551065 | + | 0.551065i | −0.926748 | − | 0.375683i | \(-0.877408\pi\) |
0.375683 | + | 0.926748i | \(0.377408\pi\) | |||||||
\(488\) | 5.58952 | + | 5.58952i | 0.253026 | + | 0.253026i | ||||
\(489\) | − | 37.7397i | − | 1.70665i | ||||||
\(490\) | −2.22728 | + | 0.198102i | −0.100618 | + | 0.00894935i | ||||
\(491\) | 5.15042i | 0.232435i | 0.993224 | + | 0.116218i | \(0.0370770\pi\) | ||||
−0.993224 | + | 0.116218i | \(0.962923\pi\) | |||||||
\(492\) | −12.9021 | − | 12.9021i | −0.581673 | − | 0.581673i | ||||
\(493\) | −11.3667 | − | 11.3667i | −0.511929 | − | 0.511929i | ||||
\(494\) | 1.85172 | 0.0833130 | ||||||||
\(495\) | 37.8969 | + | 26.6064i | 1.70334 | + | 1.19587i | ||||
\(496\) | −3.24365 | −0.145644 | ||||||||
\(497\) | 4.71214 | + | 4.71214i | 0.211368 | + | 0.211368i | ||||
\(498\) | −5.76603 | − | 5.76603i | −0.258382 | − | 0.258382i | ||||
\(499\) | − | 28.5435i | − | 1.27778i | −0.769297 | − | 0.638891i | \(-0.779394\pi\) | ||
0.769297 | − | 0.638891i | \(-0.220606\pi\) | |||||||
\(500\) | 9.70658 | + | 5.54818i | 0.434092 | + | 0.248122i | ||||
\(501\) | − | 30.6408i | − | 1.36893i | ||||||
\(502\) | −3.19791 | − | 3.19791i | −0.142730 | − | 0.142730i | ||||
\(503\) | 0.756282 | − | 0.756282i | 0.0337209 | − | 0.0337209i | −0.690045 | − | 0.723766i | \(-0.742409\pi\) |
0.723766 | + | 0.690045i | \(0.242409\pi\) | |||||||
\(504\) | 6.24365i | 0.278114i | ||||||||
\(505\) | 4.28316 | − | 5.11946i | 0.190598 | − | 0.227813i | ||||
\(506\) | 27.7348 | − | 2.35119i | 1.23296 | − | 0.104523i | ||||
\(507\) | −19.0111 | + | 19.0111i | −0.844313 | + | 0.844313i | ||||
\(508\) | 1.52521 | − | 1.52521i | 0.0676704 | − | 0.0676704i | ||||
\(509\) | 15.1157i | 0.669992i | 0.942220 | + | 0.334996i | \(0.108735\pi\) | ||||
−0.942220 | + | 0.334996i | \(0.891265\pi\) | |||||||
\(510\) | 21.9649 | − | 1.95364i | 0.972623 | − | 0.0865088i | ||||
\(511\) | 5.50428 | 0.243495 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.76287 | + | 2.76287i | −0.121984 | + | 0.121984i | ||||
\(514\) | −5.93409 | −0.261741 | ||||||||
\(515\) | 0.683499 | + | 7.68461i | 0.0301186 | + | 0.338625i | ||||
\(516\) | − | 33.7072i | − | 1.48388i | ||||||
\(517\) | −11.8291 | − | 9.98027i | −0.520245 | − | 0.438932i | ||||
\(518\) | 5.43000 | + | 5.43000i | 0.238581 | + | 0.238581i | ||||
\(519\) | −50.1752 | −2.20245 | ||||||||
\(520\) | −6.70595 | + | 8.01532i | −0.294075 | + | 0.351495i | ||||
\(521\) | 31.0844 | 1.36183 | 0.680917 | − | 0.732361i | \(-0.261581\pi\) | ||||
0.680917 | + | 0.732361i | \(0.261581\pi\) | |||||||
\(522\) | −21.8795 | + | 21.8795i | −0.957640 | + | 0.957640i | ||||
\(523\) | 11.5361 | − | 11.5361i | 0.504437 | − | 0.504437i | −0.408377 | − | 0.912813i | \(-0.633905\pi\) |
0.912813 | + | 0.408377i | \(0.133905\pi\) | |||||||
\(524\) | 11.7099 | 0.511550 | ||||||||
\(525\) | 14.9631 | − | 2.68297i | 0.653041 | − | 0.117094i | ||||
\(526\) | 0.0781078 | 0.00340566 | ||||||||
\(527\) | 7.43966 | + | 7.43966i | 0.324077 | + | 0.324077i | ||||
\(528\) | −6.50244 | + | 7.70704i | −0.282982 | + | 0.335406i | ||||
\(529\) | 47.4315i | 2.06224i | ||||||||
\(530\) | 20.1239 | − | 24.0532i | 0.874127 | − | 1.04480i | ||||
\(531\) | −77.7464 | −3.37391 | ||||||||
\(532\) | 0.280159 | − | 0.280159i | 0.0121464 | − | 0.0121464i | ||||
\(533\) | −19.8333 | − | 19.8333i | −0.859077 | − | 0.859077i | ||||
\(534\) | −17.8424 | −0.772117 | ||||||||
\(535\) | −0.655372 | − | 7.36838i | −0.0283342 | − | 0.318563i | ||||
\(536\) | − | 11.3689i | − | 0.491063i | ||||||
\(537\) | 15.5546 | − | 15.5546i | 0.671231 | − | 0.671231i | ||||
\(538\) | 8.57497 | − | 8.57497i | 0.369693 | − | 0.369693i | ||||
\(539\) | −3.30477 | + | 0.280159i | −0.142347 | + | 0.0120673i | ||||
\(540\) | −1.95364 | − | 21.9649i | −0.0840714 | − | 0.945220i | ||||
\(541\) | 35.3282i | 1.51888i | 0.650579 | + | 0.759438i | \(0.274526\pi\) | ||||
−0.650579 | + | 0.759438i | \(0.725474\pi\) | |||||||
\(542\) | −20.8906 | + | 20.8906i | −0.897330 | + | 0.897330i | ||||
\(543\) | 29.9200 | + | 29.9200i | 1.28399 | + | 1.28399i | ||||
\(544\) | 3.24365i | 0.139070i | ||||||||
\(545\) | −16.9130 | − | 14.1501i | −0.724472 | − | 0.606124i | ||||
\(546\) | 14.2095i | 0.608109i | ||||||||
\(547\) | −15.7186 | − | 15.7186i | −0.672081 | − | 0.672081i | 0.286115 | − | 0.958195i | \(-0.407636\pi\) |
−0.958195 | + | 0.286115i | \(0.907636\pi\) | |||||||
\(548\) | −9.10365 | − | 9.10365i | −0.388889 | − | 0.388889i | ||||
\(549\) | −49.3547 | −2.10641 | ||||||||
\(550\) | 14.3630 | + | 8.28879i | 0.612441 | + | 0.353435i | ||||
\(551\) | 1.96351 | 0.0836484 | ||||||||
\(552\) | −18.0422 | − | 18.0422i | −0.767928 | − | 0.767928i | ||||
\(553\) | 9.98302 | + | 9.98302i | 0.424521 | + | 0.424521i | ||||
\(554\) | 19.5546i | 0.830796i | ||||||||
\(555\) | −40.0406 | − | 33.4997i | −1.69963 | − | 1.42198i | ||||
\(556\) | 12.3301i | 0.522914i | ||||||||
\(557\) | 9.98234 | + | 9.98234i | 0.422965 | + | 0.422965i | 0.886223 | − | 0.463258i | \(-0.153320\pi\) |
−0.463258 | + | 0.886223i | \(0.653320\pi\) | |||||||
\(558\) | 14.3205 | − | 14.3205i | 0.606234 | − | 0.606234i | ||||
\(559\) | − | 51.8152i | − | 2.19155i | ||||||
\(560\) | 0.198102 | + | 2.22728i | 0.00837135 | + | 0.0941196i | ||||
\(561\) | 32.5910 | − | 2.76287i | 1.37599 | − | 0.116648i | ||||
\(562\) | −6.94396 | + | 6.94396i | −0.292913 | + | 0.292913i | ||||
\(563\) | −14.4920 | + | 14.4920i | −0.610764 | + | 0.610764i | −0.943145 | − | 0.332381i | \(-0.892148\pi\) |
0.332381 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(564\) | 14.1876i | 0.597406i | ||||||||
\(565\) | −0.751760 | − | 8.45207i | −0.0316268 | − | 0.355581i | ||||
\(566\) | 23.2814 | 0.978592 | ||||||||
\(567\) | −7.95652 | − | 7.95652i | −0.334142 | − | 0.334142i | ||||
\(568\) | 4.71214 | − | 4.71214i | 0.197717 | − | 0.197717i | ||||
\(569\) | −22.6568 | −0.949824 | −0.474912 | − | 0.880033i | \(-0.657520\pi\) | ||||
−0.474912 | + | 0.880033i | \(0.657520\pi\) | |||||||
\(570\) | −1.72840 | + | 2.06588i | −0.0723949 | + | 0.0865303i | ||||
\(571\) | 18.4539i | 0.772272i | 0.922442 | + | 0.386136i | \(0.126190\pi\) | ||||
−0.922442 | + | 0.386136i | \(0.873810\pi\) | |||||||
\(572\) | −9.99565 | + | 11.8474i | −0.417939 | + | 0.495364i | ||||
\(573\) | 2.87225 | + | 2.87225i | 0.119990 | + | 0.119990i | ||||
\(574\) | −6.00143 | −0.250495 | ||||||||
\(575\) | −23.9689 | + | 34.4424i | −0.999572 | + | 1.43635i | ||||
\(576\) | 6.24365 | 0.260152 | ||||||||
\(577\) | −12.6833 | + | 12.6833i | −0.528014 | + | 0.528014i | −0.919980 | − | 0.391966i | \(-0.871795\pi\) |
0.391966 | + | 0.919980i | \(0.371795\pi\) | |||||||
\(578\) | −4.58116 | + | 4.58116i | −0.190551 | + | 0.190551i | ||||
\(579\) | −42.9575 | −1.78525 | ||||||||
\(580\) | −7.11079 | + | 8.49921i | −0.295260 | + | 0.352910i | ||||
\(581\) | −2.68207 | −0.111271 | ||||||||
\(582\) | 9.86179 | + | 9.86179i | 0.408784 | + | 0.408784i | ||||
\(583\) | 29.9960 | − | 35.5528i | 1.24231 | − | 1.47245i | ||||
\(584\) | − | 5.50428i | − | 0.227769i | ||||||
\(585\) | −5.78075 | − | 64.9933i | −0.239005 | − | 2.68714i | ||||
\(586\) | −1.13873 | −0.0470407 | ||||||||
\(587\) | 18.6007 | − | 18.6007i | 0.767731 | − | 0.767731i | −0.209975 | − | 0.977707i | \(-0.567338\pi\) |
0.977707 | + | 0.209975i | \(0.0673384\pi\) | |||||||
\(588\) | 2.14984 | + | 2.14984i | 0.0886580 | + | 0.0886580i | ||||
\(589\) | −1.28515 | −0.0529537 | ||||||||
\(590\) | −27.7342 | + | 2.46679i | −1.14180 | + | 0.101556i | ||||
\(591\) | − | 42.6246i | − | 1.75334i | ||||||
\(592\) | 5.43000 | − | 5.43000i | 0.223172 | − | 0.223172i | ||||
\(593\) | −33.5426 | + | 33.5426i | −1.37743 | + | 1.37743i | −0.528486 | + | 0.848942i | \(0.677240\pi\) |
−0.848942 | + | 0.528486i | \(0.822760\pi\) | |||||||
\(594\) | −2.76287 | − | 32.5910i | −0.113362 | − | 1.33722i | ||||
\(595\) | 4.65412 | − | 5.56286i | 0.190801 | − | 0.228055i | ||||
\(596\) | 5.76190i | 0.236017i | ||||||||
\(597\) | 17.9819 | − | 17.9819i | 0.735950 | − | 0.735950i | ||||
\(598\) | −27.7348 | − | 27.7348i | −1.13416 | − | 1.13416i | ||||
\(599\) | − | 17.9354i | − | 0.732821i | −0.930453 | − | 0.366410i | \(-0.880587\pi\) | ||
0.930453 | − | 0.366410i | \(-0.119413\pi\) | |||||||
\(600\) | −2.68297 | − | 14.9631i | −0.109532 | − | 0.610864i | ||||
\(601\) | 9.42764i | 0.384562i | 0.981340 | + | 0.192281i | \(0.0615884\pi\) | ||||
−0.981340 | + | 0.192281i | \(0.938412\pi\) | |||||||
\(602\) | −7.83946 | − | 7.83946i | −0.319513 | − | 0.319513i | ||||
\(603\) | 50.1930 | + | 50.1930i | 2.04402 | + | 2.04402i | ||||
\(604\) | −14.0115 | −0.570120 | ||||||||
\(605\) | 21.2527 | + | 12.3823i | 0.864046 | + | 0.503413i | ||||
\(606\) | −9.07573 | −0.368676 | ||||||||
\(607\) | −0.368589 | − | 0.368589i | −0.0149606 | − | 0.0149606i | 0.699587 | − | 0.714548i | \(-0.253367\pi\) |
−0.714548 | + | 0.699587i | \(0.753367\pi\) | |||||||
\(608\) | −0.280159 | − | 0.280159i | −0.0113619 | − | 0.0113619i | ||||
\(609\) | 15.0673i | 0.610558i | ||||||||
\(610\) | −17.6061 | + | 1.56596i | −0.712851 | + | 0.0634037i | ||||
\(611\) | 21.8094i | 0.882314i | ||||||||
\(612\) | −14.3205 | − | 14.3205i | −0.578871 | − | 0.578871i | ||||
\(613\) | −6.75253 | + | 6.75253i | −0.272732 | + | 0.272732i | −0.830199 | − | 0.557467i | \(-0.811773\pi\) |
0.557467 | + | 0.830199i | \(0.311773\pi\) | |||||||
\(614\) | − | 29.0040i | − | 1.17051i | ||||||
\(615\) | 40.6397 | − | 3.61465i | 1.63875 | − | 0.145757i | ||||
\(616\) | 0.280159 | + | 3.30477i | 0.0112879 | + | 0.133153i | ||||
\(617\) | 6.80159 | − | 6.80159i | 0.273822 | − | 0.273822i | −0.556815 | − | 0.830637i | \(-0.687977\pi\) |
0.830637 | + | 0.556815i | \(0.187977\pi\) | |||||||
\(618\) | 7.41746 | − | 7.41746i | 0.298374 | − | 0.298374i | ||||
\(619\) | − | 13.1025i | − | 0.526635i | −0.964709 | − | 0.263318i | \(-0.915183\pi\) | ||
0.964709 | − | 0.263318i | \(-0.0848168\pi\) | |||||||
\(620\) | 4.65412 | − | 5.56286i | 0.186914 | − | 0.223410i | ||||
\(621\) | 82.7635 | 3.32119 | ||||||||
\(622\) | −2.14544 | − | 2.14544i | −0.0860243 | − | 0.0860243i | ||||
\(623\) | −4.14970 | + | 4.14970i | −0.166254 | + | 0.166254i | ||||
\(624\) | 14.2095 | 0.568834 | ||||||||
\(625\) | −23.4425 | + | 8.68604i | −0.937702 | + | 0.347442i | ||||
\(626\) | 15.2551i | 0.609716i | ||||||||
\(627\) | −2.57630 | + | 3.05356i | −0.102887 | + | 0.121948i | ||||
\(628\) | 5.18890 | + | 5.18890i | 0.207060 | + | 0.207060i | ||||
\(629\) | −24.9086 | −0.993170 | ||||||||
\(630\) | −10.7079 | − | 8.95865i | −0.426612 | − | 0.356921i | ||||
\(631\) | −48.4453 | −1.92857 | −0.964287 | − | 0.264858i | \(-0.914675\pi\) | ||||
−0.964287 | + | 0.264858i | \(0.914675\pi\) | |||||||
\(632\) | 9.98302 | − | 9.98302i | 0.397103 | − | 0.397103i | ||||
\(633\) | 45.4053 | − | 45.4053i | 1.80470 | − | 1.80470i | ||||
\(634\) | −2.81652 | −0.111858 | ||||||||
\(635\) | 0.427302 | + | 4.80418i | 0.0169570 | + | 0.190648i | ||||
\(636\) | −42.6413 | −1.69084 | ||||||||
\(637\) | 3.30477 | + | 3.30477i | 0.130940 | + | 0.130940i | ||||
\(638\) | −10.5991 | + | 12.5626i | −0.419622 | + | 0.497358i | ||||
\(639\) | 41.6075i | 1.64597i | ||||||||
\(640\) | 2.22728 | − | 0.198102i | 0.0880408 | − | 0.00783068i | ||||
\(641\) | 18.5376 | 0.732192 | 0.366096 | − | 0.930577i | \(-0.380694\pi\) | ||||
0.366096 | + | 0.930577i | \(0.380694\pi\) | |||||||
\(642\) | −7.11222 | + | 7.11222i | −0.280697 | + | 0.280697i | ||||
\(643\) | 24.1330 | + | 24.1330i | 0.951713 | + | 0.951713i | 0.998887 | − | 0.0471738i | \(-0.0150215\pi\) |
−0.0471738 | + | 0.998887i | \(0.515021\pi\) | |||||||
\(644\) | −8.39234 | −0.330705 | ||||||||
\(645\) | 57.8079 | + | 48.3645i | 2.27618 | + | 1.90435i | ||||
\(646\) | 1.28515i | 0.0505635i | ||||||||
\(647\) | −26.8627 | + | 26.8627i | −1.05608 | + | 1.05608i | −0.0577513 | + | 0.998331i | \(0.518393\pi\) |
−0.998331 | + | 0.0577513i | \(0.981607\pi\) | |||||||
\(648\) | −7.95652 | + | 7.95652i | −0.312561 | + | 0.312561i | ||||
\(649\) | −41.1513 | + | 3.48856i | −1.61533 | + | 0.136938i | ||||
\(650\) | −4.12430 | − | 23.0014i | −0.161768 | − | 0.902190i | ||||
\(651\) | − | 9.86179i | − | 0.386514i | ||||||
\(652\) | −8.77731 | + | 8.77731i | −0.343746 | + | 0.343746i | ||||
\(653\) | −9.03668 | − | 9.03668i | −0.353632 | − | 0.353632i | 0.507827 | − | 0.861459i | \(-0.330449\pi\) |
−0.861459 | + | 0.507827i | \(0.830449\pi\) | |||||||
\(654\) | 29.9832i | 1.17243i | ||||||||
\(655\) | −16.8019 | + | 20.0825i | −0.656504 | + | 0.784689i | ||||
\(656\) | 6.00143i | 0.234316i | ||||||||
\(657\) | 24.3010 | + | 24.3010i | 0.948072 | + | 0.948072i | ||||
\(658\) | 3.29969 | + | 3.29969i | 0.128635 | + | 0.128635i | ||||
\(659\) | 13.8288 | 0.538693 | 0.269346 | − | 0.963043i | \(-0.413192\pi\) | ||||
0.269346 | + | 0.963043i | \(0.413192\pi\) | |||||||
\(660\) | −3.88760 | − | 22.2101i | −0.151325 | − | 0.864526i | ||||
\(661\) | 15.8833 | 0.617790 | 0.308895 | − | 0.951096i | \(-0.400041\pi\) | ||||
0.308895 | + | 0.951096i | \(0.400041\pi\) | |||||||
\(662\) | −12.8900 | − | 12.8900i | −0.500985 | − | 0.500985i | ||||
\(663\) | −32.5910 | − | 32.5910i | −1.26573 | − | 1.26573i | ||||
\(664\) | 2.68207i | 0.104085i | ||||||||
\(665\) | 0.0784891 | + | 0.882457i | 0.00304368 | + | 0.0342202i | ||||
\(666\) | 47.9461i | 1.85787i | ||||||||
\(667\) | −29.4091 | − | 29.4091i | −1.13873 | − | 1.13873i | ||||
\(668\) | −7.12630 | + | 7.12630i | −0.275725 | + | 0.275725i | ||||
\(669\) | − | 32.6387i | − | 1.26189i | ||||||
\(670\) | 19.4977 | + | 16.3126i | 0.753263 | + | 0.630212i | ||||
\(671\) | −26.1235 | + | 2.21460i | −1.00849 | + | 0.0854935i | ||||
\(672\) | 2.14984 | − | 2.14984i | 0.0829320 | − | 0.0829320i | ||||
\(673\) | 28.4404 | − | 28.4404i | 1.09630 | − | 1.09630i | 0.101457 | − | 0.994840i | \(-0.467649\pi\) |
0.994840 | − | 0.101457i | \(-0.0323506\pi\) | |||||||
\(674\) | − | 17.5298i | − | 0.675224i | ||||||
\(675\) | 40.4730 | + | 28.1657i | 1.55781 | + | 1.08410i | ||||
\(676\) | 8.84302 | 0.340116 | ||||||||
\(677\) | −7.22013 | − | 7.22013i | −0.277492 | − | 0.277492i | 0.554615 | − | 0.832107i | \(-0.312866\pi\) |
−0.832107 | + | 0.554615i | \(0.812866\pi\) | |||||||
\(678\) | −8.15823 | + | 8.15823i | −0.313315 | + | 0.313315i | ||||
\(679\) | 4.58721 | 0.176041 | ||||||||
\(680\) | −5.56286 | − | 4.65412i | −0.213326 | − | 0.178478i | ||||
\(681\) | 78.7973i | 3.01952i | ||||||||
\(682\) | 6.93727 | − | 8.22242i | 0.265642 | − | 0.314853i | ||||
\(683\) | 0.553161 | + | 0.553161i | 0.0211661 | + | 0.0211661i | 0.717611 | − | 0.696445i | \(-0.245236\pi\) |
−0.696445 | + | 0.717611i | \(0.745236\pi\) | |||||||
\(684\) | 2.47376 | 0.0945867 | ||||||||
\(685\) | 28.6751 | − | 2.55047i | 1.09562 | − | 0.0974485i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 4.35732 | − | 4.35732i | 0.166242 | − | 0.166242i | ||||
\(688\) | −7.83946 | + | 7.83946i | −0.298877 | + | 0.298877i | ||||
\(689\) | −65.5488 | −2.49721 | ||||||||
\(690\) | 56.8302 | − | 5.05469i | 2.16349 | − | 0.192429i | ||||
\(691\) | −37.0102 | −1.40793 | −0.703966 | − | 0.710233i | \(-0.748589\pi\) | ||||
−0.703966 | + | 0.710233i | \(0.748589\pi\) | |||||||
\(692\) | 11.6695 | + | 11.6695i | 0.443608 | + | 0.443608i | ||||
\(693\) | −15.8272 | − | 13.3534i | −0.601226 | − | 0.507255i | ||||
\(694\) | 17.2692i | 0.655530i | ||||||||
\(695\) | −21.1462 | − | 17.6918i | −0.802121 | − | 0.671088i | ||||
\(696\) | 15.0673 | 0.571125 | ||||||||
\(697\) | 13.7649 | − | 13.7649i | 0.521383 | − | 0.521383i | ||||
\(698\) | −19.9102 | − | 19.9102i | −0.753611 | − | 0.753611i | ||||
\(699\) | −24.3638 | −0.921522 | ||||||||
\(700\) | −4.10403 | − | 2.85604i | −0.155118 | − | 0.107948i | ||||
\(701\) | 17.0518i | 0.644038i | 0.946733 | + | 0.322019i | \(0.104361\pi\) | ||||
−0.946733 | + | 0.322019i | \(0.895639\pi\) | |||||||
\(702\) | −32.5910 | + | 32.5910i | −1.23007 | + | 1.23007i | ||||
\(703\) | 2.15139 | − | 2.15139i | 0.0811413 | − | 0.0811413i | ||||
\(704\) | 3.30477 | − | 0.280159i | 0.124553 | − | 0.0105589i | ||||
\(705\) | −24.3318 | − | 20.3570i | −0.916388 | − | 0.766688i | ||||
\(706\) | 10.0221i | 0.377185i | ||||||||
\(707\) | −2.11079 | + | 2.11079i | −0.0793844 | + | 0.0793844i | ||||
\(708\) | 26.7700 | + | 26.7700i | 1.00608 | + | 1.00608i | ||||
\(709\) | 49.0505i | 1.84213i | 0.389410 | + | 0.921065i | \(0.372679\pi\) | ||||
−0.389410 | + | 0.921065i | \(0.627321\pi\) | |||||||
\(710\) | 1.32015 | + | 14.8425i | 0.0495443 | + | 0.557029i | ||||
\(711\) | 88.1486i | 3.30583i | ||||||||
\(712\) | 4.14970 | + | 4.14970i | 0.155517 | + | 0.155517i | ||||
\(713\) | 19.2487 | + | 19.2487i | 0.720871 | + | 0.720871i | ||||
\(714\) | −9.86179 | −0.369068 | ||||||||
\(715\) | −5.97608 | − | 34.1417i | −0.223493 | − | 1.27683i | ||||
\(716\) | −7.23523 | −0.270393 | ||||||||
\(717\) | 0.196406 | + | 0.196406i | 0.00733491 | + | 0.00733491i | ||||
\(718\) | 1.93540 | + | 1.93540i | 0.0722285 | + | 0.0722285i | ||||
\(719\) | − | 30.3303i | − | 1.13113i | −0.824704 | − | 0.565565i | \(-0.808658\pi\) | ||
0.824704 | − | 0.565565i | \(-0.191342\pi\) | |||||||
\(720\) | −8.95865 | + | 10.7079i | −0.333869 | + | 0.399059i | ||||
\(721\) | − | 3.45023i | − | 0.128493i | ||||||
\(722\) | 13.3240 | + | 13.3240i | 0.495869 | + | 0.495869i | ||||
\(723\) | −53.0308 | + | 53.0308i | −1.97224 | + | 1.97224i | ||||
\(724\) | − | 13.9173i | − | 0.517232i | ||||||
\(725\) | −4.37328 | − | 24.3900i | −0.162420 | − | 0.905823i | ||||
\(726\) | −5.62986 | − | 32.9664i | −0.208944 | − | 1.22350i | ||||
\(727\) | −17.5774 | + | 17.5774i | −0.651911 | + | 0.651911i | −0.953453 | − | 0.301542i | \(-0.902499\pi\) |
0.301542 | + | 0.953453i | \(0.402499\pi\) | |||||||
\(728\) | 3.30477 | − | 3.30477i | 0.122483 | − | 0.122483i | ||||
\(729\) | 19.6946i | 0.729430i | ||||||||
\(730\) | 9.43985 | + | 7.89777i | 0.349384 | + | 0.292310i | ||||
\(731\) | 35.9613 | 1.33008 | ||||||||
\(732\) | 16.9940 | + | 16.9940i | 0.628118 | + | 0.628118i | ||||
\(733\) | 13.4698 | − | 13.4698i | 0.497519 | − | 0.497519i | −0.413146 | − | 0.910665i | \(-0.635570\pi\) |
0.910665 | + | 0.413146i | \(0.135570\pi\) | |||||||
\(734\) | 0.859751 | 0.0317340 | ||||||||
\(735\) | −6.77167 | + | 0.602298i | −0.249777 | + | 0.0222161i | ||||
\(736\) | 8.39234i | 0.309346i | ||||||||
\(737\) | 28.8194 | + | 24.3150i | 1.06158 | + | 0.895655i | ||||
\(738\) | −26.4959 | − | 26.4959i | −0.975326 | − | 0.975326i | ||||
\(739\) | 40.8681 | 1.50336 | 0.751678 | − | 0.659530i | \(-0.229245\pi\) | ||||
0.751678 | + | 0.659530i | \(0.229245\pi\) | |||||||
\(740\) | 1.52126 | + | 17.1037i | 0.0559228 | + | 0.628743i | ||||
\(741\) | 5.62986 | 0.206818 | ||||||||
\(742\) | −9.91730 | + | 9.91730i | −0.364076 | + | 0.364076i | ||||
\(743\) | −25.1350 | + | 25.1350i | −0.922112 | + | 0.922112i | −0.997179 | − | 0.0750665i | \(-0.976083\pi\) |
0.0750665 | + | 0.997179i | \(0.476083\pi\) | |||||||
\(744\) | −9.86179 | −0.361551 | ||||||||
\(745\) | −9.88167 | − | 8.26742i | −0.362036 | − | 0.302895i | ||||
\(746\) | 1.29112 | 0.0472713 | ||||||||
\(747\) | −11.8411 | − | 11.8411i | −0.433245 | − | 0.433245i | ||||
\(748\) | −8.22242 | − | 6.93727i | −0.300641 | − | 0.253652i | ||||
\(749\) | 3.30825i | 0.120881i | ||||||||
\(750\) | 29.5113 | + | 16.8683i | 1.07760 | + | 0.615944i | ||||
\(751\) | 14.9041 | 0.543860 | 0.271930 | − | 0.962317i | \(-0.412338\pi\) | ||||
0.271930 | + | 0.962317i | \(0.412338\pi\) | |||||||
\(752\) | 3.29969 | − | 3.29969i | 0.120327 | − | 0.120327i | ||||
\(753\) | −9.72272 | − | 9.72272i | −0.354316 | − | 0.354316i | ||||
\(754\) | 23.1617 | 0.843499 | ||||||||
\(755\) | 20.1043 | − | 24.0297i | 0.731670 | − | 0.874531i | ||||
\(756\) | 9.86179i | 0.358670i | ||||||||
\(757\) | −33.1370 | + | 33.1370i | −1.20438 | + | 1.20438i | −0.231565 | + | 0.972819i | \(0.574385\pi\) |
−0.972819 | + | 0.231565i | \(0.925615\pi\) | |||||||
\(758\) | 2.89735 | − | 2.89735i | 0.105236 | − | 0.105236i | ||||
\(759\) | 84.3231 | − | 7.14841i | 3.06073 | − | 0.259471i | ||||
\(760\) | 0.882457 | − | 0.0784891i | 0.0320101 | − | 0.00284710i | ||||
\(761\) | 35.8947i | 1.30118i | 0.759428 | + | 0.650592i | \(0.225479\pi\) | ||||
−0.759428 | + | 0.650592i | \(0.774521\pi\) | |||||||
\(762\) | 4.63716 | − | 4.63716i | 0.167987 | − | 0.167987i | ||||
\(763\) | 6.97334 | + | 6.97334i | 0.252452 | + | 0.252452i | ||||
\(764\) | − | 1.33603i | − | 0.0483358i | ||||||
\(765\) | 45.1073 | − | 4.01201i | 1.63086 | − | 0.145055i | ||||
\(766\) | 23.1738i | 0.837304i | ||||||||
\(767\) | 41.1513 | + | 41.1513i | 1.48589 | + | 1.48589i | ||||
\(768\) | −2.14984 | − | 2.14984i | −0.0775758 | − | 0.0775758i | ||||
\(769\) | 23.3132 | 0.840696 | 0.420348 | − | 0.907363i | \(-0.361908\pi\) | ||||
0.420348 | + | 0.907363i | \(0.361908\pi\) | |||||||
\(770\) | −6.06967 | − | 4.26135i | −0.218736 | − | 0.153568i | ||||
\(771\) | −18.0416 | −0.649753 | ||||||||
\(772\) | 9.99085 | + | 9.99085i | 0.359579 | + | 0.359579i | ||||
\(773\) | −9.24967 | − | 9.24967i | −0.332687 | − | 0.332687i | 0.520919 | − | 0.853606i | \(-0.325589\pi\) |
−0.853606 | + | 0.520919i | \(0.825589\pi\) | |||||||
\(774\) | − | 69.2213i | − | 2.48811i | ||||||
\(775\) | 2.86238 | + | 15.9637i | 0.102820 | + | 0.573432i | ||||
\(776\) | − | 4.58721i | − | 0.164671i | ||||||
\(777\) | 16.5090 | + | 16.5090i | 0.592258 | + | 0.592258i | ||||
\(778\) | 18.1989 | − | 18.1989i | 0.652462 | − | 0.652462i | ||||
\(779\) | 2.37779i | 0.0851933i | ||||||||
\(780\) | −20.3884 | + | 24.3693i | −0.730020 | + | 0.872560i | ||||
\(781\) | 1.86697 | + | 22.0229i | 0.0668055 | + | 0.788041i | ||||
\(782\) | 19.2487 | − | 19.2487i | 0.688334 | − | 0.688334i | ||||
\(783\) | −34.5585 | + | 34.5585i | −1.23502 | + | 1.23502i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −16.3442 | + | 1.45372i | −0.583350 | + | 0.0518854i | ||||
\(786\) | 35.6021 | 1.26988 | ||||||||
\(787\) | 38.5215 | + | 38.5215i | 1.37314 | + | 1.37314i | 0.855745 | + | 0.517398i | \(0.173099\pi\) |
0.517398 | + | 0.855745i | \(0.326901\pi\) | |||||||
\(788\) | −9.91342 | + | 9.91342i | −0.353151 | + | 0.353151i | ||||
\(789\) | 0.237474 | 0.00845430 | ||||||||
\(790\) | 2.79683 | + | 31.4449i | 0.0995068 | + | 1.11876i | ||||
\(791\) | 3.79480i | 0.134928i | ||||||||
\(792\) | −13.3534 | + | 15.8272i | −0.474494 | + | 0.562395i | ||||
\(793\) | 26.1235 | + | 26.1235i | 0.927672 | + | 0.927672i | ||||
\(794\) | 11.2724 | 0.400043 | ||||||||
\(795\) | 61.1835 | − | 73.1298i | 2.16996 | − | 2.59365i | ||||
\(796\) | −8.36429 | −0.296464 | ||||||||
\(797\) | 20.0195 | − | 20.0195i | 0.709128 | − | 0.709128i | −0.257224 | − | 0.966352i | \(-0.582808\pi\) |
0.966352 | + | 0.257224i | \(0.0828078\pi\) | |||||||
\(798\) | 0.851778 | − | 0.851778i | 0.0301526 | − | 0.0301526i | ||||
\(799\) | −15.1364 | −0.535486 | ||||||||
\(800\) | −2.85604 | + | 4.10403i | −0.100976 | + | 0.145099i | ||||
\(801\) | −36.6413 | −1.29466 | ||||||||
\(802\) | −18.4204 | − | 18.4204i | −0.650446 | − | 0.650446i | ||||
\(803\) | 13.9530 | + | 11.7721i | 0.492389 | + | 0.415430i | ||||
\(804\) | − | 34.5654i | − | 1.21903i | ||||||
\(805\) | 12.0417 | − | 14.3929i | 0.424414 | − | 0.507282i | ||||
\(806\) | −15.1597 | −0.533977 | ||||||||
\(807\) | 26.0708 | − | 26.0708i | 0.917736 | − | 0.917736i | ||||
\(808\) | 2.11079 | + | 2.11079i | 0.0742573 | + | 0.0742573i | ||||
\(809\) | 19.2982 | 0.678488 | 0.339244 | − | 0.940698i | \(-0.389829\pi\) | ||||
0.339244 | + | 0.940698i | \(0.389829\pi\) | |||||||
\(810\) | −2.22909 | − | 25.0618i | −0.0783222 | − | 0.880581i | ||||
\(811\) | 37.9101i | 1.33120i | 0.746307 | + | 0.665602i | \(0.231825\pi\) | ||||
−0.746307 | + | 0.665602i | \(0.768175\pi\) | |||||||
\(812\) | 3.50428 | − | 3.50428i | 0.122976 | − | 0.122976i | ||||
\(813\) | −63.5146 | + | 63.5146i | −2.22755 | + | 2.22755i | ||||
\(814\) | 2.15139 | + | 25.3779i | 0.0754063 | + | 0.889496i | ||||
\(815\) | −2.45904 | − | 27.6471i | −0.0861365 | − | 0.968437i | ||||
\(816\) | 9.86179i | 0.345232i | ||||||||
\(817\) | −3.10603 | + | 3.10603i | −0.108666 | + | 0.108666i | ||||
\(818\) | −6.01698 | − | 6.01698i | −0.210379 | − | 0.210379i | ||||
\(819\) | 29.1806i | 1.01965i | ||||||||
\(820\) | −10.2925 | − | 8.61110i | −0.359428 | − | 0.300713i | ||||
\(821\) | − | 46.0769i | − | 1.60809i | −0.594566 | − | 0.804047i | \(-0.702676\pi\) | ||
0.594566 | − | 0.804047i | \(-0.297324\pi\) | |||||||
\(822\) | −27.6782 | − | 27.6782i | −0.965387 | − | 0.965387i | ||||
\(823\) | −4.86619 | − | 4.86619i | −0.169625 | − | 0.169625i | 0.617190 | − | 0.786814i | \(-0.288271\pi\) |
−0.786814 | + | 0.617190i | \(0.788271\pi\) | |||||||
\(824\) | −3.45023 | −0.120195 | ||||||||
\(825\) | 43.6684 | + | 25.2007i | 1.52034 | + | 0.877376i | ||||
\(826\) | 12.4521 | 0.433263 | ||||||||
\(827\) | −14.7761 | − | 14.7761i | −0.513814 | − | 0.513814i | 0.401879 | − | 0.915693i | \(-0.368357\pi\) |
−0.915693 | + | 0.401879i | \(0.868357\pi\) | |||||||
\(828\) | −37.0516 | − | 37.0516i | −1.28763 | − | 1.28763i | ||||
\(829\) | − | 18.8528i | − | 0.654786i | −0.944888 | − | 0.327393i | \(-0.893830\pi\) | ||
0.944888 | − | 0.327393i | \(-0.106170\pi\) | |||||||
\(830\) | −4.59975 | − | 3.84835i | −0.159660 | − | 0.133578i | ||||
\(831\) | 59.4526i | 2.06239i | ||||||||
\(832\) | −3.30477 | − | 3.30477i | −0.114572 | − | 0.114572i | ||||
\(833\) | −2.29361 | + | 2.29361i | −0.0794688 | + | 0.0794688i | ||||
\(834\) | 37.4878i | 1.29810i | ||||||||
\(835\) | −1.99650 | − | 22.4467i | −0.0690916 | − | 0.776801i | ||||
\(836\) | 1.30937 | − | 0.111000i | 0.0452854 | − | 0.00383903i | ||||
\(837\) | 22.6191 | − | 22.6191i | 0.781829 | − | 0.781829i | ||||
\(838\) | 2.61563 | − | 2.61563i | 0.0903553 | − | 0.0903553i | ||||
\(839\) | − | 47.8316i | − | 1.65133i | −0.564160 | − | 0.825665i | \(-0.690800\pi\) | ||
0.564160 | − | 0.825665i | \(-0.309200\pi\) | |||||||
\(840\) | 0.602298 | + | 6.77167i | 0.0207813 | + | 0.233645i | ||||
\(841\) | −4.44002 | −0.153104 | ||||||||
\(842\) | 9.77894 | + | 9.77894i | 0.337005 | + | 0.337005i | ||||
\(843\) | −21.1120 | + | 21.1120i | −0.727136 | + | 0.727136i | ||||
\(844\) | −21.1203 | −0.726990 | ||||||||
\(845\) | −12.6883 | + | 15.1658i | −0.436492 | + | 0.521719i | ||||
\(846\) | 29.1357i | 1.00171i | ||||||||
\(847\) | −8.97654 | − | 6.35781i | −0.308438 | − | 0.218457i | ||||
\(848\) | 9.91730 | + | 9.91730i | 0.340562 | + | 0.340562i | ||||
\(849\) | 70.7834 | 2.42928 | ||||||||
\(850\) | 15.9637 | − | 2.86238i | 0.547549 | − | 0.0981789i | ||||
\(851\) | −64.4463 | −2.20919 | ||||||||
\(852\) | 14.3265 | − | 14.3265i | 0.490818 | − | 0.490818i | ||||
\(853\) | −29.2794 | + | 29.2794i | −1.00251 | + | 1.00251i | −0.00251044 | + | 0.999997i | \(0.500799\pi\) |
−0.999997 | + | 0.00251044i | \(0.999201\pi\) | |||||||
\(854\) | 7.90478 | 0.270496 | ||||||||
\(855\) | −3.54946 | + | 4.24251i | −0.121389 | + | 0.145091i | ||||
\(856\) | 3.30825 | 0.113074 | ||||||||
\(857\) | −6.57238 | − | 6.57238i | −0.224508 | − | 0.224508i | 0.585886 | − | 0.810394i | \(-0.300747\pi\) |
−0.810394 | + | 0.585886i | \(0.800747\pi\) | |||||||
\(858\) | −30.3901 | + | 36.0200i | −1.03750 | + | 1.22970i | ||||
\(859\) | 16.3959i | 0.559421i | 0.960084 | + | 0.279710i | \(0.0902384\pi\) | ||||
−0.960084 | + | 0.279710i | \(0.909762\pi\) | |||||||
\(860\) | −2.19630 | − | 24.6931i | −0.0748931 | − | 0.842027i | ||||
\(861\) | −18.2464 | −0.621834 | ||||||||
\(862\) | 24.3694 | − | 24.3694i | 0.830024 | − | 0.830024i | ||||
\(863\) | 14.5603 | + | 14.5603i | 0.495639 | + | 0.495639i | 0.910077 | − | 0.414438i | \(-0.136022\pi\) |
−0.414438 | + | 0.910077i | \(0.636022\pi\) | |||||||
\(864\) | 9.86179 | 0.335505 | ||||||||
\(865\) | −36.7571 | + | 3.26932i | −1.24978 | + | 0.111160i | ||||
\(866\) | − | 9.21055i | − | 0.312987i | ||||||
\(867\) | −13.9283 | + | 13.9283i | −0.473029 | + | 0.473029i | ||||
\(868\) | −2.29361 | + | 2.29361i | −0.0778501 | + | 0.0778501i | ||||
\(869\) | 3.95532 | + | 46.6571i | 0.134175 | + | 1.58274i | ||||
\(870\) | −21.6192 | + | 25.8405i | −0.732960 | + | 0.876073i | ||||
\(871\) | − | 53.1345i | − | 1.80039i | ||||||
\(872\) | 6.97334 | − | 6.97334i | 0.236147 | − | 0.236147i | ||||
\(873\) | 20.2522 | + | 20.2522i | 0.685434 | + | 0.685434i | ||||
\(874\) | 3.32509i | 0.112473i | ||||||||
\(875\) | 10.7867 | − | 2.94044i | 0.364658 | − | 0.0994049i | ||||
\(876\) | − | 16.7349i | − | 0.565419i | ||||||
\(877\) | −19.8407 | − | 19.8407i | −0.669974 | − | 0.669974i | 0.287736 | − | 0.957710i | \(-0.407098\pi\) |
−0.957710 | + | 0.287736i | \(0.907098\pi\) | |||||||
\(878\) | 18.1621 | + | 18.1621i | 0.612940 | + | 0.612940i | ||||
\(879\) | −3.46214 | −0.116775 | ||||||||
\(880\) | −4.26135 | + | 6.06967i | −0.143650 | + | 0.204609i | ||||
\(881\) | −6.16569 | −0.207727 | −0.103864 | − | 0.994592i | \(-0.533121\pi\) | ||||
−0.103864 | + | 0.994592i | \(0.533121\pi\) | |||||||
\(882\) | 4.41493 | + | 4.41493i | 0.148658 | + | 0.148658i | ||||
\(883\) | 13.6906 | + | 13.6906i | 0.460727 | + | 0.460727i | 0.898894 | − | 0.438167i | \(-0.144372\pi\) |
−0.438167 | + | 0.898894i | \(0.644372\pi\) | |||||||
\(884\) | 15.1597i | 0.509876i | ||||||||
\(885\) | −84.3213 | + | 7.49986i | −2.83443 | + | 0.252105i | ||||
\(886\) | − | 31.3163i | − | 1.05209i | ||||||
\(887\) | 17.5547 | + | 17.5547i | 0.589428 | + | 0.589428i | 0.937476 | − | 0.348049i | \(-0.113156\pi\) |
−0.348049 | + | 0.937476i | \(0.613156\pi\) | |||||||
\(888\) | 16.5090 | − | 16.5090i | 0.554007 | − | 0.554007i | ||||
\(889\) | − | 2.15698i | − | 0.0723427i | ||||||
\(890\) | −13.0709 | + | 1.16258i | −0.438138 | + | 0.0389697i | ||||
\(891\) | −3.15241 | − | 37.1860i | −0.105610 | − | 1.24578i | ||||
\(892\) | −7.59095 | + | 7.59095i | −0.254164 | + | 0.254164i | ||||
\(893\) | 1.30735 | − | 1.30735i | 0.0437488 | − | 0.0437488i | ||||
\(894\) | 17.5181i | 0.585894i | ||||||||
\(895\) | 10.3814 | − | 12.4084i | 0.347012 | − | 0.414768i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −84.3231 | − | 84.3231i | −2.81547 | − | 2.81547i | ||||
\(898\) | −5.73610 | + | 5.73610i | −0.191416 | + | 0.191416i | ||||
\(899\) | −16.0749 | −0.536128 | ||||||||
\(900\) | −5.50975 | − | 30.7282i | −0.183658 | − | 1.02427i | ||||
\(901\) | − | 45.4928i | − | 1.51558i | ||||||
\(902\) | −15.2132 | − | 12.8354i | −0.506544 | − | 0.427372i | ||||
\(903\) | −23.8346 | − | 23.8346i | −0.793166 | − | 0.793166i | ||||
\(904\) | 3.79480 | 0.126213 | ||||||||
\(905\) | 23.8682 | + | 19.9691i | 0.793405 | + | 0.663796i | ||||
\(906\) | −42.5997 | −1.41528 | ||||||||
\(907\) | 28.1124 | − | 28.1124i | 0.933456 | − | 0.933456i | −0.0644643 | − | 0.997920i | \(-0.520534\pi\) |
0.997920 | + | 0.0644643i | \(0.0205339\pi\) | |||||||
\(908\) | 18.3263 | − | 18.3263i | 0.608180 | − | 0.608180i | ||||
\(909\) | −18.6380 | −0.618182 | ||||||||
\(910\) | 0.925861 | + | 10.4095i | 0.0306920 | + | 0.345072i | ||||
\(911\) | 37.3644 | 1.23794 | 0.618969 | − | 0.785415i | \(-0.287550\pi\) | ||||
0.618969 | + | 0.785415i | \(0.287550\pi\) | |||||||
\(912\) | −0.851778 | − | 0.851778i | −0.0282052 | − | 0.0282052i | ||||
\(913\) | −6.79886 | − | 5.73621i | −0.225009 | − | 0.189841i | ||||
\(914\) | 4.84288i | 0.160188i | ||||||||
\(915\) | −53.5286 | + | 4.76103i | −1.76960 | + | 0.157395i | ||||
\(916\) | −2.02681 | −0.0669676 | ||||||||
\(917\) | 8.28016 | − | 8.28016i | 0.273435 | − | 0.273435i | ||||
\(918\) | −22.6191 | − | 22.6191i | −0.746540 | − | 0.746540i | ||||
\(919\) | −24.3864 | −0.804433 | −0.402217 | − | 0.915544i | \(-0.631760\pi\) | ||||
−0.402217 | + | 0.915544i | \(0.631760\pi\) | |||||||
\(920\) | −14.3929 | − | 12.0417i | −0.474519 | − | 0.397003i | ||||
\(921\) | − | 88.1819i | − | 2.90569i | ||||||
\(922\) | −8.60192 | + | 8.60192i | −0.283289 | + | 0.283289i | ||||
\(923\) | 22.0229 | − | 22.0229i | 0.724893 | − | 0.724893i | ||||
\(924\) | 0.851778 | + | 10.0476i | 0.0280214 | + | 0.330542i | ||||
\(925\) | −31.5156 | − | 21.9321i | −1.03623 | − | 0.721122i | ||||
\(926\) | 15.0259i | 0.493782i | ||||||||
\(927\) | 15.2325 | − | 15.2325i | 0.500302 | − | 0.500302i | ||||
\(928\) | −3.50428 | − | 3.50428i | −0.115034 | − | 0.115034i | ||||
\(929\) | − | 27.2794i | − | 0.895007i | −0.894282 | − | 0.447504i | \(-0.852313\pi\) | ||
0.894282 | − | 0.447504i | \(-0.147687\pi\) | |||||||
\(930\) | 14.1501 | − | 16.9130i | 0.464000 | − | 0.554598i | ||||
\(931\) | − | 0.396205i | − | 0.0129851i | ||||||
\(932\) | 5.66641 | + | 5.66641i | 0.185609 | + | 0.185609i | ||||
\(933\) | −6.52286 | − | 6.52286i | −0.213549 | − | 0.213549i | ||||
\(934\) | −5.29008 | −0.173097 | ||||||||
\(935\) | 23.6953 | − | 4.14757i | 0.774919 | − | 0.135640i | ||||
\(936\) | 29.1806 | 0.953799 | ||||||||
\(937\) | 16.1087 | + | 16.1087i | 0.526248 | + | 0.526248i | 0.919452 | − | 0.393203i | \(-0.128633\pi\) |
−0.393203 | + | 0.919452i | \(0.628633\pi\) | |||||||
\(938\) | −8.03905 | − | 8.03905i | −0.262484 | − | 0.262484i | ||||
\(939\) | 46.3807i | 1.51358i | ||||||||
\(940\) | 0.924437 | + | 10.3935i | 0.0301518 | + | 0.338998i | ||||
\(941\) | 3.51397i | 0.114552i | 0.998358 | + | 0.0572761i | \(0.0182415\pi\) | ||||
−0.998358 | + | 0.0572761i | \(0.981758\pi\) | |||||||
\(942\) | 15.7760 | + | 15.7760i | 0.514010 | + | 0.514010i | ||||
\(943\) | 35.6142 | − | 35.6142i | 1.15976 | − | 1.15976i | ||||
\(944\) | − | 12.4521i | − | 0.405280i | ||||||
\(945\) | −16.9130 | − | 14.1501i | −0.550179 | − | 0.460303i | ||||
\(946\) | −3.10603 | − | 36.6389i | −0.100986 | − | 1.19123i | ||||
\(947\) | 20.6556 | − | 20.6556i | 0.671215 | − | 0.671215i | −0.286781 | − | 0.957996i | \(-0.592585\pi\) |
0.957996 | + | 0.286781i | \(0.0925852\pi\) | |||||||
\(948\) | 30.3517 | − | 30.3517i | 0.985779 | − | 0.985779i | ||||
\(949\) | − | 25.7251i | − | 0.835072i | ||||||
\(950\) | −1.13158 | + | 1.62603i | −0.0367132 | + | 0.0527555i | ||||
\(951\) | −8.56318 | −0.277680 | ||||||||
\(952\) | 2.29361 | + | 2.29361i | 0.0743362 | + | 0.0743362i | ||||
\(953\) | 1.88351 | − | 1.88351i | 0.0610128 | − | 0.0610128i | −0.675942 | − | 0.736955i | \(-0.736263\pi\) |
0.736955 | + | 0.675942i | \(0.236263\pi\) | |||||||
\(954\) | −87.5683 | −2.83513 | ||||||||
\(955\) | 2.29129 | + | 1.91699i | 0.0741444 | + | 0.0620323i | ||||
\(956\) | − | 0.0913582i | − | 0.00295474i | ||||||
\(957\) | −32.2248 | + | 38.1946i | −1.04168 | + | 1.23465i | ||||
\(958\) | −17.0611 | − | 17.0611i | −0.551220 | − | 0.551220i | ||||
\(959\) | −12.8745 | −0.415740 | ||||||||
\(960\) | 6.77167 | − | 0.602298i | 0.218555 | − | 0.0194391i | ||||
\(961\) | −20.4787 | −0.660604 | ||||||||
\(962\) | 25.3779 | − | 25.3779i | 0.818218 | − | 0.818218i | ||||
\(963\) | −14.6057 | + | 14.6057i | −0.470662 | + | 0.470662i | ||||
\(964\) | 24.6673 | 0.794479 | ||||||||
\(965\) | −31.4696 | + | 2.79903i | −1.01304 | + | 0.0901039i | ||||
\(966\) | −25.5156 | −0.820950 | ||||||||
\(967\) | −6.65882 | − | 6.65882i | −0.214133 | − | 0.214133i | 0.591887 | − | 0.806021i | \(-0.298383\pi\) |
−0.806021 | + | 0.591887i | \(0.798383\pi\) | |||||||
\(968\) | −6.35781 | + | 8.97654i | −0.204348 | + | 0.288517i | ||||
\(969\) | 3.90729i | 0.125520i | ||||||||
\(970\) | 7.86708 | + | 6.58193i | 0.252597 | + | 0.211333i | ||||
\(971\) | −3.41873 | −0.109712 | −0.0548561 | − | 0.998494i | \(-0.517470\pi\) | ||||
−0.0548561 | + | 0.998494i | \(0.517470\pi\) | |||||||
\(972\) | −3.27048 | + | 3.27048i | −0.104901 | + | 0.104901i | ||||
\(973\) | 8.71872 | + | 8.71872i | 0.279509 | + | 0.279509i | ||||
\(974\) | 17.1982 | 0.551065 | ||||||||
\(975\) | −12.5393 | − | 69.9321i | −0.401577 | − | 2.23962i | ||||
\(976\) | − | 7.90478i | − | 0.253026i | ||||||
\(977\) | 15.4705 | − | 15.4705i | 0.494944 | − | 0.494944i | −0.414916 | − | 0.909860i | \(-0.636189\pi\) |
0.909860 | + | 0.414916i | \(0.136189\pi\) | |||||||
\(978\) | −26.6860 | + | 26.6860i | −0.853323 | + | 0.853323i | ||||
\(979\) | −19.3943 | + | 1.64413i | −0.619844 | + | 0.0525467i | ||||
\(980\) | 1.71500 | + | 1.43484i | 0.0547837 | + | 0.0458343i | ||||
\(981\) | 61.5736i | 1.96589i | ||||||||
\(982\) | 3.64190 | − | 3.64190i | 0.116218 | − | 0.116218i | ||||
\(983\) | 5.78699 | + | 5.78699i | 0.184576 | + | 0.184576i | 0.793347 | − | 0.608770i | \(-0.208337\pi\) |
−0.608770 | + | 0.793347i | \(0.708337\pi\) | |||||||
\(984\) | 18.2464i | 0.581673i | ||||||||
\(985\) | −2.77733 | − | 31.2257i | −0.0884932 | − | 0.994934i | ||||
\(986\) | 16.0749i | 0.511929i | ||||||||
\(987\) | 10.0322 | + | 10.0322i | 0.319327 | + | 0.319327i | ||||
\(988\) | −1.30937 | − | 1.30937i | −0.0416565 | − | 0.0416565i | ||||
\(989\) | 93.0432 | 2.95860 | ||||||||
\(990\) | −7.98359 | − | 45.6107i | −0.253735 | − | 1.44960i | ||||
\(991\) | 30.8370 | 0.979570 | 0.489785 | − | 0.871843i | \(-0.337075\pi\) | ||||
0.489785 | + | 0.871843i | \(0.337075\pi\) | |||||||
\(992\) | 2.29361 | + | 2.29361i | 0.0728221 | + | 0.0728221i | ||||
\(993\) | −39.1900 | − | 39.1900i | −1.24366 | − | 1.24366i | ||||
\(994\) | − | 6.66397i | − | 0.211368i | ||||||
\(995\) | 12.0014 | − | 14.3448i | 0.380471 | − | 0.454759i | ||||
\(996\) | 8.15440i | 0.258382i | ||||||||
\(997\) | −30.0148 | − | 30.0148i | −0.950577 | − | 0.950577i | 0.0482580 | − | 0.998835i | \(-0.484633\pi\) |
−0.998835 | + | 0.0482580i | \(0.984633\pi\) | |||||||
\(998\) | −20.1833 | + | 20.1833i | −0.638891 | + | 0.638891i | ||||
\(999\) | 75.7305i | 2.39601i |
(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 | 770.2.m.e.43.1 | ✓ | 16 | |
5.2 | odd | 4 | inner | 770.2.m.e.197.5 | yes | 16 | |
11.10 | odd | 2 | inner | 770.2.m.e.43.5 | yes | 16 | |
55.32 | even | 4 | inner | 770.2.m.e.197.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.e.43.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
770.2.m.e.43.5 | yes | 16 | 11.10 | odd | 2 | inner | |
770.2.m.e.197.1 | yes | 16 | 55.32 | even | 4 | inner | |
770.2.m.e.197.5 | yes | 16 | 5.2 | odd | 4 | inner |