Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(289,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.s (of order \(3\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 802.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.802 |
Dual form | 819.2.s.a.289.1 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | 3.50000 | − | 6.06218i | 0.649934 | − | 1.12572i | −0.333205 | − | 0.942855i | \(-0.608130\pi\) |
0.983138 | − | 0.182864i | \(-0.0585367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 2.59808i | −0.269408 | + | 0.466628i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 7.50000 | + | 2.59808i | 1.26773 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −0.500000 | + | 0.866025i | −0.0811107 | + | 0.140488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.50000 | + | 7.79423i | 0.711512 | + | 1.23238i | ||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | + | 6.06218i | 0.533745 | + | 0.924473i | 0.999223 | + | 0.0394140i | \(0.0125491\pi\) |
−0.465478 | + | 0.885059i | \(0.654118\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 2.00000 | − | 3.46410i | 0.282843 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | + | 3.46410i | 0.138675 | + | 0.480384i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.50000 | − | 7.79423i | 0.606780 | − | 1.05097i | ||||
\(56\) | 6.00000 | − | 5.19615i | 0.801784 | − | 0.694365i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.50000 | + | 6.06218i | −0.459573 | + | 0.796003i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 1.50000 | − | 2.59808i | 0.190500 | − | 0.329956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 7.50000 | − | 7.79423i | 0.930261 | − | 0.966755i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.50000 | − | 2.59808i | −0.896421 | − | 0.310530i | ||||
\(71\) | 6.50000 | + | 11.2583i | 0.771408 | + | 1.33612i | 0.936791 | + | 0.349889i | \(0.113781\pi\) |
−0.165383 | + | 0.986229i | \(0.552886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50000 | − | 11.2583i | 0.760767 | − | 1.31769i | −0.181688 | − | 0.983356i | \(-0.558156\pi\) |
0.942455 | − | 0.334332i | \(-0.108511\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 0.866025i | −0.0573539 | + | 0.0993399i | ||||
\(77\) | −7.50000 | − | 2.59808i | −0.854704 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | −3.50000 | − | 6.06218i | −0.377415 | − | 0.653701i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.50000 | − | 7.79423i | −0.479702 | − | 0.830868i | ||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | − | 5.19615i | −0.838628 | − | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.500000 | − | 0.866025i | −0.0515711 | − | 0.0893237i | ||||
\(95\) | 3.00000 | 0.307794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | −1.00000 | + | 6.92820i | −0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −2.50000 | − | 4.33013i | −0.248759 | − | 0.430864i | 0.714423 | − | 0.699715i | \(-0.246689\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50000 | − | 4.33013i | −0.246332 | − | 0.426660i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.962505 | + | 0.271263i | \(0.912559\pi\) | |||||||
\(104\) | −3.00000 | − | 10.3923i | −0.294174 | − | 1.01905i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.50000 | + | 2.59808i | −0.145693 | + | 0.252347i | ||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | + | 6.06218i | −0.335239 | + | 0.580651i | −0.983531 | − | 0.180741i | \(-0.942150\pi\) |
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(110\) | −4.50000 | + | 7.79423i | −0.429058 | + | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | + | 1.73205i | −0.188982 | + | 0.163663i | ||||
\(113\) | 7.50000 | + | 12.9904i | 0.705541 | + | 1.22203i | 0.966496 | + | 0.256681i | \(0.0826291\pi\) |
−0.260955 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.50000 | + | 6.06218i | −0.324967 | + | 0.562859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 4.00000 | − | 3.46410i | 0.366679 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −6.50000 | + | 11.2583i | −0.588482 | + | 1.01928i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | − | 2.59808i | 0.134704 | − | 0.233314i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.50000 | + | 9.52628i | −0.488046 | + | 0.845321i | −0.999905 | − | 0.0137486i | \(-0.995624\pi\) |
0.511859 | + | 0.859069i | \(0.328957\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.50000 | + | 7.79423i | −0.657794 | + | 0.683599i | ||||
\(131\) | 2.50000 | + | 4.33013i | 0.218426 | + | 0.378325i | 0.954327 | − | 0.298764i | \(-0.0965744\pi\) |
−0.735901 | + | 0.677089i | \(0.763241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | − | 2.59808i | −0.0433555 | − | 0.225282i | ||||
\(134\) | −1.50000 | − | 2.59808i | −0.129580 | − | 0.224440i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.50000 | + | 12.9904i | 0.636142 | + | 1.10183i | 0.986272 | + | 0.165129i | \(0.0528040\pi\) |
−0.350130 | + | 0.936701i | \(0.613863\pi\) | |||||||
\(140\) | −7.50000 | − | 2.59808i | −0.633866 | − | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.50000 | − | 11.2583i | −0.545468 | − | 0.944778i | ||||
\(143\) | −7.50000 | + | 7.79423i | −0.627182 | + | 0.651786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0000 | 1.74396 | ||||||||
\(146\) | −6.50000 | + | 11.2583i | −0.537944 | + | 0.931746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 7.50000 | − | 12.9904i | 0.614424 | − | 1.06421i | −0.376061 | − | 0.926595i | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5000 | − | 18.1865i | 0.854478 | − | 1.48000i | −0.0226507 | − | 0.999743i | \(-0.507211\pi\) |
0.877129 | − | 0.480256i | \(-0.159456\pi\) | |||||||
\(152\) | 1.50000 | − | 2.59808i | 0.121666 | − | 0.210732i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.50000 | + | 2.59808i | 0.604367 | + | 0.209359i | ||||
\(155\) | −9.00000 | −0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.50000 | + | 16.4545i | −0.758183 | + | 1.31321i | 0.185594 | + | 0.982627i | \(0.440579\pi\) |
−0.943777 | + | 0.330584i | \(0.892754\pi\) | |||||||
\(158\) | −1.50000 | − | 2.59808i | −0.119334 | − | 0.206692i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.50000 | − | 12.9904i | −0.592927 | − | 1.02698i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.50000 | + | 11.2583i | −0.502985 | + | 0.871196i | 0.497009 | + | 0.867745i | \(0.334432\pi\) |
−0.999994 | + | 0.00345033i | \(0.998902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | −3.00000 | − | 5.19615i | −0.230089 | − | 0.398527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.50000 | − | 6.06218i | −0.266872 | − | 0.462237i | ||||
\(173\) | 9.50000 | − | 16.4545i | 0.722272 | − | 1.25101i | −0.237816 | − | 0.971310i | \(-0.576431\pi\) |
0.960087 | − | 0.279701i | \(-0.0902353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 10.3923i | 0.151186 | + | 0.785584i | ||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 8.50000 | + | 14.7224i | 0.635320 | + | 1.10041i | 0.986447 | + | 0.164079i | \(0.0524651\pi\) |
−0.351127 | + | 0.936328i | \(0.614202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 8.00000 | + | 5.19615i | 0.592999 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | −0.500000 | − | 0.866025i | −0.0364662 | − | 0.0631614i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | −8.50000 | + | 14.7224i | −0.615038 | + | 1.06528i | 0.375339 | + | 0.926887i | \(0.377526\pi\) |
−0.990378 | + | 0.138390i | \(0.955807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.50000 | − | 6.06218i | −0.251936 | − | 0.436365i | 0.712123 | − | 0.702055i | \(-0.247734\pi\) |
−0.964059 | + | 0.265689i | \(0.914400\pi\) | |||||||
\(194\) | −2.50000 | − | 4.33013i | −0.179490 | − | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | −0.500000 | + | 0.866025i | −0.0356235 | + | 0.0617018i | −0.883287 | − | 0.468832i | \(-0.844675\pi\) |
0.847664 | + | 0.530534i | \(0.178008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | −6.00000 | + | 10.3923i | −0.424264 | + | 0.734847i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.50000 | + | 4.33013i | 0.175899 | + | 0.304667i | ||||
\(203\) | −3.50000 | − | 18.1865i | −0.245652 | − | 1.27644i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | 0.628587 | ||||||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | + | 3.46410i | 0.0693375 | + | 0.240192i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50000 | + | 6.06218i | −0.240950 | + | 0.417338i | −0.960985 | − | 0.276600i | \(-0.910792\pi\) |
0.720035 | + | 0.693938i | \(0.244126\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | −10.5000 | + | 18.1865i | −0.716094 | + | 1.24031i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | + | 7.79423i | 0.101827 | + | 0.529107i | ||||
\(218\) | 3.50000 | − | 6.06218i | 0.237050 | − | 0.410582i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.50000 | + | 7.79423i | −0.303390 | + | 0.525487i | ||||
\(221\) | −2.00000 | − | 6.92820i | −0.134535 | − | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | − | 7.79423i | 0.301342 | − | 0.521940i | −0.675098 | − | 0.737728i | \(-0.735899\pi\) |
0.976440 | + | 0.215788i | \(0.0692320\pi\) | |||||||
\(224\) | −10.0000 | + | 8.66025i | −0.668153 | + | 0.578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.50000 | − | 12.9904i | −0.498893 | − | 0.864107i | ||||
\(227\) | 4.00000 | 0.265489 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.50000 | + | 11.2583i | 0.429532 | + | 0.743971i | 0.996832 | − | 0.0795401i | \(-0.0253452\pi\) |
−0.567300 | + | 0.823511i | \(0.692012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.5000 | − | 18.1865i | 0.689359 | − | 1.19400i | ||||
\(233\) | −10.5000 | − | 18.1865i | −0.687878 | − | 1.19144i | −0.972523 | − | 0.232806i | \(-0.925209\pi\) |
0.284645 | − | 0.958633i | \(-0.408124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.50000 | + | 2.59808i | −0.0978492 | + | 0.169480i | ||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.00000 | + | 3.46410i | −0.259281 | + | 0.224544i | ||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.50000 | + | 11.2583i | −0.416120 | + | 0.720741i | ||||
\(245\) | 19.5000 | − | 7.79423i | 1.24581 | − | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50000 | − | 0.866025i | −0.222700 | − | 0.0551039i | ||||
\(248\) | −4.50000 | + | 7.79423i | −0.285750 | + | 0.494934i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.00000 | −0.189737 | ||||||||
\(251\) | −11.5000 | − | 19.9186i | −0.725874 | − | 1.25725i | −0.958613 | − | 0.284711i | \(-0.908102\pi\) |
0.232740 | − | 0.972539i | \(-0.425231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.50000 | − | 9.52628i | 0.345101 | − | 0.597732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | − | 3.46410i | 0.248548 | − | 0.215249i | ||||
\(260\) | −7.50000 | + | 7.79423i | −0.465130 | + | 0.483378i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.50000 | − | 4.33013i | −0.154451 | − | 0.267516i | ||||
\(263\) | −13.5000 | − | 23.3827i | −0.832446 | − | 1.44184i | −0.896093 | − | 0.443866i | \(-0.853607\pi\) |
0.0636476 | − | 0.997972i | \(-0.479727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 0.500000 | + | 2.59808i | 0.0306570 | + | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 12.0000 | 0.723627 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | −7.50000 | − | 12.9904i | −0.449820 | − | 0.779111i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 22.5000 | + | 7.79423i | 1.34463 | + | 0.465794i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | − | 0.866025i | −0.0297219 | − | 0.0514799i | 0.850782 | − | 0.525519i | \(-0.176129\pi\) |
−0.880504 | + | 0.474039i | \(0.842796\pi\) | |||||||
\(284\) | −6.50000 | − | 11.2583i | −0.385704 | − | 0.668059i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.50000 | − | 7.79423i | 0.443484 | − | 0.460882i | ||||
\(287\) | −1.50000 | − | 7.79423i | −0.0885422 | − | 0.460079i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −21.0000 | −1.23316 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.50000 | + | 11.2583i | −0.380384 | + | 0.658844i | ||||
\(293\) | 5.50000 | + | 9.52628i | 0.321313 | + | 0.556531i | 0.980759 | − | 0.195221i | \(-0.0625424\pi\) |
−0.659446 | + | 0.751752i | \(0.729209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.50000 | + | 12.9904i | −0.434463 | + | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.5000 | + | 6.06218i | 1.00868 | + | 0.349418i | ||||
\(302\) | −10.5000 | + | 18.1865i | −0.604207 | + | 1.04652i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | ||||
\(305\) | 39.0000 | 2.23313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 7.50000 | + | 2.59808i | 0.427352 | + | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | 0.511166 | ||||||||
\(311\) | −4.50000 | + | 7.79423i | −0.255172 | + | 0.441970i | −0.964942 | − | 0.262463i | \(-0.915465\pi\) |
0.709771 | + | 0.704433i | \(0.248799\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | 9.50000 | − | 16.4545i | 0.536116 | − | 0.928580i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.50000 | − | 2.59808i | −0.0843816 | − | 0.146153i | ||||
\(317\) | −4.50000 | − | 7.79423i | −0.252745 | − | 0.437767i | 0.711535 | − | 0.702650i | \(-0.248000\pi\) |
−0.964281 | + | 0.264883i | \(0.914667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.0000 | −1.17577 | ||||||||
\(320\) | 10.5000 | + | 18.1865i | 0.586968 | + | 1.01666i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.00000 | − | 1.73205i | 0.0556415 | − | 0.0963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000 | + | 3.46410i | 0.776580 | + | 0.192154i | ||||
\(326\) | −0.500000 | + | 0.866025i | −0.0276924 | + | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 2.50000 | + | 0.866025i | 0.137829 | + | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5000 | − | 25.1147i | 0.796992 | − | 1.38043i | −0.124574 | − | 0.992210i | \(-0.539757\pi\) |
0.921567 | − | 0.388221i | \(-0.126910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.50000 | − | 11.2583i | 0.355664 | − | 0.616028i | ||||
\(335\) | −4.50000 | + | 7.79423i | −0.245861 | + | 0.425844i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 11.0000 | − | 6.92820i | 0.598321 | − | 0.376845i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | 9.00000 | 0.487377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 10.5000 | + | 18.1865i | 0.566122 | + | 0.980552i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.50000 | + | 16.4545i | −0.510723 | + | 0.884598i | ||||
\(347\) | 8.00000 | 0.429463 | 0.214731 | − | 0.976673i | \(-0.431112\pi\) | ||||
0.214731 | + | 0.976673i | \(0.431112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5000 | + | 19.9186i | −0.615581 | + | 1.06622i | 0.374701 | + | 0.927146i | \(0.377745\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | −2.00000 | − | 10.3923i | −0.106904 | − | 0.555492i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.50000 | + | 12.9904i | 0.399751 | + | 0.692390i | ||||
\(353\) | −12.5000 | − | 21.6506i | −0.665308 | − | 1.15235i | −0.979202 | − | 0.202889i | \(-0.934967\pi\) |
0.313894 | − | 0.949458i | \(-0.398366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5000 | + | 33.7750i | −1.03495 | + | 1.79259i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.50000 | − | 14.7224i | −0.449239 | − | 0.778105i | ||||
\(359\) | 8.50000 | + | 14.7224i | 0.448613 | + | 0.777020i | 0.998296 | − | 0.0583530i | \(-0.0185849\pi\) |
−0.549683 | + | 0.835373i | \(0.685252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 22.0000 | 1.15629 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | + | 5.19615i | 0.419314 | + | 0.272352i | ||||
\(365\) | 39.0000 | 2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5000 | + | 26.8468i | 0.809093 | + | 1.40139i | 0.913493 | + | 0.406855i | \(0.133375\pi\) |
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.00000 | − | 5.19615i | −0.155963 | − | 0.270135i | ||||
\(371\) | −1.50000 | − | 7.79423i | −0.0778761 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.50000 | − | 7.79423i | 0.233001 | − | 0.403570i | −0.725689 | − | 0.688023i | \(-0.758479\pi\) |
0.958690 | + | 0.284453i | \(0.0918121\pi\) | |||||||
\(374\) | 3.00000 | + | 5.19615i | 0.155126 | + | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | + | 2.59808i | 0.0773566 | + | 0.133986i | ||||
\(377\) | −24.5000 | − | 6.06218i | −1.26181 | − | 0.312218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.5000 | − | 28.5788i | 0.847548 | − | 1.46800i | −0.0358418 | − | 0.999357i | \(-0.511411\pi\) |
0.883390 | − | 0.468639i | \(-0.155255\pi\) | |||||||
\(380\) | −3.00000 | −0.153897 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.50000 | − | 14.7224i | 0.434898 | − | 0.753265i | ||||
\(383\) | −10.5000 | + | 18.1865i | −0.536525 | + | 0.929288i | 0.462563 | + | 0.886586i | \(0.346930\pi\) |
−0.999088 | + | 0.0427020i | \(0.986403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.50000 | − | 23.3827i | −0.229341 | − | 1.19169i | ||||
\(386\) | 3.50000 | + | 6.06218i | 0.178145 | + | 0.308557i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.50000 | − | 4.33013i | −0.126918 | − | 0.219829i | ||||
\(389\) | −16.5000 | + | 28.5788i | −0.836583 | + | 1.44900i | 0.0561516 | + | 0.998422i | \(0.482117\pi\) |
−0.892735 | + | 0.450582i | \(0.851216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000 | − | 20.7846i | 0.151523 | − | 1.04978i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.500000 | − | 0.866025i | 0.0251896 | − | 0.0436297i | ||||
\(395\) | −4.50000 | + | 7.79423i | −0.226420 | + | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.500000 | − | 0.866025i | 0.0250943 | − | 0.0434646i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 20.0000 | 1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5000 | + | 2.59808i | 0.523042 | + | 0.129419i | ||||
\(404\) | 2.50000 | + | 4.33013i | 0.124380 | + | 0.215432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.50000 | + | 18.1865i | 0.173702 | + | 0.902583i | ||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | −9.00000 | −0.444478 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.50000 | + | 4.33013i | 0.123166 | + | 0.213330i | ||||
\(413\) | 8.00000 | − | 6.92820i | 0.393654 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.00000 | + | 17.3205i | 0.245145 | + | 0.849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.00000 | 0.146735 | ||||||||
\(419\) | −12.5000 | + | 21.6506i | −0.610665 | + | 1.05770i | 0.380464 | + | 0.924796i | \(0.375764\pi\) |
−0.991129 | + | 0.132907i | \(0.957569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 3.50000 | − | 6.06218i | 0.170377 | − | 0.295102i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | −4.00000 | + | 6.92820i | −0.194029 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50000 | − | 33.7750i | −0.314557 | − | 1.63449i | ||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.5000 | − | 18.1865i | 0.506355 | − | 0.877033i | ||||
\(431\) | 4.50000 | + | 7.79423i | 0.216757 | + | 0.375435i | 0.953815 | − | 0.300395i | \(-0.0971186\pi\) |
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5000 | − | 23.3827i | −0.648769 | − | 1.12370i | −0.983417 | − | 0.181357i | \(-0.941951\pi\) |
0.334649 | − | 0.942343i | \(-0.391382\pi\) | |||||||
\(434\) | −1.50000 | − | 7.79423i | −0.0720023 | − | 0.374135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50000 | − | 6.06218i | 0.167620 | − | 0.290326i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 13.5000 | − | 23.3827i | 0.643587 | − | 1.11473i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | + | 6.92820i | 0.0951303 | + | 0.329541i | ||||
\(443\) | −5.50000 | − | 9.52628i | −0.261313 | − | 0.452607i | 0.705278 | − | 0.708931i | \(-0.250822\pi\) |
−0.966591 | + | 0.256323i | \(0.917489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | −4.50000 | + | 7.79423i | −0.213081 | + | 0.369067i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.0000 | − | 12.1244i | 0.661438 | − | 0.572822i | ||||
\(449\) | 7.50000 | + | 12.9904i | 0.353947 | + | 0.613054i | 0.986937 | − | 0.161106i | \(-0.0515060\pi\) |
−0.632990 | + | 0.774160i | \(0.718173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | −7.50000 | − | 12.9904i | −0.352770 | − | 0.611016i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | 1.50000 | − | 28.5788i | 0.0703211 | − | 1.33980i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | −6.50000 | − | 11.2583i | −0.303725 | − | 0.526067i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5000 | + | 30.3109i | 0.815056 | + | 1.41172i | 0.909288 | + | 0.416169i | \(0.136627\pi\) |
−0.0942312 | + | 0.995550i | \(0.530039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | −3.50000 | + | 6.06218i | −0.162483 | + | 0.281430i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | −3.50000 | − | 6.06218i | −0.161961 | − | 0.280524i | 0.773611 | − | 0.633661i | \(-0.218448\pi\) |
−0.935572 | + | 0.353137i | \(0.885115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | + | 2.59808i | 0.346318 | + | 0.119968i | ||||
\(470\) | 1.50000 | − | 2.59808i | 0.0691898 | − | 0.119840i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 10.5000 | − | 18.1865i | 0.482791 | − | 0.836218i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | + | 3.46410i | 0.0917663 | + | 0.158944i | ||||
\(476\) | −4.00000 | + | 3.46410i | −0.183340 | + | 0.158777i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.00000 | −0.182956 | ||||||||
\(479\) | −17.5000 | − | 30.3109i | −0.799595 | − | 1.38494i | −0.919880 | − | 0.392200i | \(-0.871714\pi\) |
0.120284 | − | 0.992739i | \(-0.461619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 6.92820i | −0.0911922 | − | 0.315899i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | −7.50000 | + | 12.9904i | −0.340557 | + | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 19.5000 | − | 33.7750i | 0.882724 | − | 1.52892i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19.5000 | + | 7.79423i | −0.880920 | + | 0.352107i | ||||
\(491\) | 7.50000 | − | 12.9904i | 0.338470 | − | 0.586248i | −0.645675 | − | 0.763612i | \(-0.723424\pi\) |
0.984145 | + | 0.177365i | \(0.0567572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.00000 | − | 12.1244i | 0.315264 | − | 0.546054i | ||||
\(494\) | 3.50000 | + | 0.866025i | 0.157472 | + | 0.0389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | − | 2.59808i | 0.0673520 | − | 0.116657i | ||||
\(497\) | 32.5000 | + | 11.2583i | 1.45782 | + | 0.505005i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | + | 26.8468i | 0.693875 | + | 1.20183i | 0.970558 | + | 0.240866i | \(0.0774314\pi\) |
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.5000 | + | 19.9186i | 0.513270 | + | 0.889010i | ||||
\(503\) | −15.5000 | − | 26.8468i | −0.691111 | − | 1.19704i | −0.971474 | − | 0.237145i | \(-0.923788\pi\) |
0.280363 | − | 0.959894i | \(-0.409545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.50000 | − | 12.9904i | 0.333746 | − | 0.578064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.50000 | − | 9.52628i | 0.244023 | − | 0.422660i | ||||
\(509\) | 34.0000 | 1.50702 | 0.753512 | − | 0.657434i | \(-0.228358\pi\) | ||||
0.753512 | + | 0.657434i | \(0.228358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.50000 | − | 33.7750i | −0.287543 | − | 1.49412i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.00000 | −0.0882162 | ||||||||
\(515\) | 7.50000 | − | 12.9904i | 0.330489 | − | 0.572425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50000 | − | 2.59808i | 0.0659699 | − | 0.114263i | ||||
\(518\) | −4.00000 | + | 3.46410i | −0.175750 | + | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.5000 | − | 23.3827i | 0.986690 | − | 1.02540i | ||||
\(521\) | −8.50000 | + | 14.7224i | −0.372392 | + | 0.645001i | −0.989933 | − | 0.141537i | \(-0.954796\pi\) |
0.617541 | + | 0.786539i | \(0.288129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | −2.50000 | − | 4.33013i | −0.109213 | − | 0.189162i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5000 | + | 23.3827i | 0.588628 | + | 1.01953i | ||||
\(527\) | −3.00000 | + | 5.19615i | −0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −9.00000 | −0.390935 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.500000 | + | 2.59808i | 0.0216777 | + | 0.112641i | ||||
\(533\) | −10.5000 | − | 2.59808i | −0.454805 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | − | 20.7846i | −0.518805 | − | 0.898597i | ||||
\(536\) | 4.50000 | + | 7.79423i | 0.194370 | + | 0.336659i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | −19.5000 | + | 7.79423i | −0.839924 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5000 | + | 32.0429i | 0.795377 | + | 1.37763i | 0.922599 | + | 0.385759i | \(0.126061\pi\) |
−0.127222 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(542\) | 16.0000 | 0.687259 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.0000 | −0.428746 | ||||||||
\(545\) | −21.0000 | −0.899541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 10.0000 | 0.427179 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.0000 | −0.511682 | ||||||||
\(551\) | −3.50000 | − | 6.06218i | −0.149105 | − | 0.258257i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | + | 2.59808i | 0.318932 | + | 0.110481i | ||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.50000 | − | 12.9904i | −0.318071 | − | 0.550915i | ||||
\(557\) | 1.50000 | + | 2.59808i | 0.0635570 | + | 0.110084i | 0.896053 | − | 0.443947i | \(-0.146422\pi\) |
−0.832496 | + | 0.554031i | \(0.813089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5000 | − | 18.1865i | 0.740171 | − | 0.769208i | ||||
\(560\) | −7.50000 | − | 2.59808i | −0.316933 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5000 | + | 38.9711i | −0.946582 | + | 1.63953i | ||||
\(566\) | 0.500000 | + | 0.866025i | 0.0210166 | + | 0.0364018i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.5000 | + | 33.7750i | 0.818202 | + | 1.41717i | ||||
\(569\) | −10.0000 | −0.419222 | −0.209611 | − | 0.977785i | \(-0.567220\pi\) | ||||
−0.209611 | + | 0.977785i | \(0.567220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5000 | + | 37.2391i | −0.899747 | + | 1.55841i | −0.0719297 | + | 0.997410i | \(0.522916\pi\) |
−0.827817 | + | 0.560998i | \(0.810418\pi\) | |||||||
\(572\) | 7.50000 | − | 7.79423i | 0.313591 | − | 0.325893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.50000 | + | 7.79423i | 0.0626088 | + | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.500000 | − | 0.866025i | 0.0208153 | − | 0.0360531i | −0.855430 | − | 0.517918i | \(-0.826707\pi\) |
0.876245 | + | 0.481865i | \(0.160040\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.0000 | −0.871978 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | −0.372742 | ||||||||
\(584\) | 19.5000 | − | 33.7750i | 0.806916 | − | 1.39762i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.50000 | − | 9.52628i | −0.227203 | − | 0.393527i | ||||
\(587\) | −16.5000 | + | 28.5788i | −0.681028 | + | 1.17957i | 0.293640 | + | 0.955916i | \(0.405133\pi\) |
−0.974668 | + | 0.223659i | \(0.928200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | + | 2.59808i | 0.0618064 | + | 0.107052i | ||||
\(590\) | −6.00000 | − | 10.3923i | −0.247016 | − | 0.427844i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 13.5000 | + | 23.3827i | 0.554379 | + | 0.960212i | 0.997952 | + | 0.0639736i | \(0.0203773\pi\) |
−0.443573 | + | 0.896238i | \(0.646289\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0000 | + | 5.19615i | 0.614940 | + | 0.213021i | ||||
\(596\) | −7.50000 | + | 12.9904i | −0.307212 | + | 0.532107i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5000 | + | 21.6506i | −0.510736 | + | 0.884621i | 0.489186 | + | 0.872179i | \(0.337294\pi\) |
−0.999923 | + | 0.0124417i | \(0.996040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | −17.5000 | − | 6.06218i | −0.713247 | − | 0.247076i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.5000 | + | 18.1865i | −0.427239 | + | 0.740000i | ||||
\(605\) | 6.00000 | 0.243935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.50000 | + | 9.52628i | −0.223238 | + | 0.386660i | −0.955789 | − | 0.294052i | \(-0.904996\pi\) |
0.732551 | + | 0.680712i | \(0.238329\pi\) | |||||||
\(608\) | −2.50000 | + | 4.33013i | −0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.0000 | −1.57906 | ||||||||
\(611\) | 2.50000 | − | 2.59808i | 0.101139 | − | 0.105107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5000 | + | 21.6506i | 0.504870 | + | 0.874461i | 0.999984 | + | 0.00563283i | \(0.00179300\pi\) |
−0.495114 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(614\) | −12.0000 | −0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5000 | − | 7.79423i | −0.906551 | − | 0.314038i | ||||
\(617\) | −16.5000 | − | 28.5788i | −0.664265 | − | 1.15054i | −0.979484 | − | 0.201522i | \(-0.935411\pi\) |
0.315219 | − | 0.949019i | \(-0.397922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.50000 | + | 9.52628i | −0.221064 | + | 0.382893i | −0.955131 | − | 0.296183i | \(-0.904286\pi\) |
0.734068 | + | 0.679076i | \(0.237620\pi\) | |||||||
\(620\) | 9.00000 | 0.361449 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.50000 | − | 7.79423i | 0.180434 | − | 0.312520i | ||||
\(623\) | −12.0000 | + | 10.3923i | −0.480770 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 9.50000 | + | 16.4545i | 0.379696 | + | 0.657653i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.50000 | − | 16.4545i | 0.379091 | − | 0.656605i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5000 | − | 21.6506i | −0.497617 | − | 0.861898i | 0.502379 | − | 0.864647i | \(-0.332458\pi\) |
−0.999996 | + | 0.00274930i | \(0.999125\pi\) | |||||||
\(632\) | 4.50000 | + | 7.79423i | 0.179000 | + | 0.310038i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.50000 | + | 7.79423i | 0.178718 | + | 0.309548i | ||||
\(635\) | −33.0000 | −1.30957 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.0000 | + | 3.46410i | −0.990536 | + | 0.137253i | ||||
\(638\) | 21.0000 | 0.831398 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.50000 | + | 7.79423i | 0.177878 | + | 0.308094i | ||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.50000 | + | 16.4545i | 0.374643 | + | 0.648901i | 0.990274 | − | 0.139134i | \(-0.0444318\pi\) |
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00000 | + | 1.73205i | −0.0393445 | + | 0.0681466i | ||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | − | 10.3923i | −0.235521 | − | 0.407934i | ||||
\(650\) | −14.0000 | − | 3.46410i | −0.549125 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.500000 | + | 0.866025i | −0.0195815 | + | 0.0339162i | ||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.50000 | + | 12.9904i | −0.293049 | + | 0.507576i | ||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.50000 | − | 0.866025i | −0.0974601 | − | 0.0337612i | ||||
\(659\) | 14.5000 | + | 25.1147i | 0.564840 | + | 0.978331i | 0.997065 | + | 0.0765653i | \(0.0243954\pi\) |
−0.432225 | + | 0.901766i | \(0.642271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50000 | + | 7.79423i | 0.175030 | + | 0.303160i | 0.940172 | − | 0.340701i | \(-0.110665\pi\) |
−0.765142 | + | 0.643862i | \(0.777331\pi\) | |||||||
\(662\) | −14.5000 | + | 25.1147i | −0.563559 | + | 0.976112i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | − | 5.19615i | 0.232670 | − | 0.201498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.50000 | − | 11.2583i | 0.251493 | − | 0.435598i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.50000 | − | 7.79423i | 0.173850 | − | 0.301117i | ||||
\(671\) | −39.0000 | −1.50558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5000 | − | 35.5070i | 0.790217 | − | 1.36870i | −0.135615 | − | 0.990762i | \(-0.543301\pi\) |
0.925832 | − | 0.377934i | \(-0.123365\pi\) | |||||||
\(674\) | −14.0000 | −0.539260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | − | 6.92820i | 0.423077 | − | 0.266469i | ||||
\(677\) | 3.50000 | + | 6.06218i | 0.134516 | + | 0.232988i | 0.925412 | − | 0.378962i | \(-0.123719\pi\) |
−0.790897 | + | 0.611950i | \(0.790385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5000 | + | 4.33013i | 0.479706 | + | 0.166175i | ||||
\(680\) | 9.00000 | + | 15.5885i | 0.345134 | + | 0.597790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.00000 | −0.344628 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0000 | − | 25.9808i | −0.573121 | − | 0.992674i | ||||
\(686\) | 10.0000 | + | 15.5885i | 0.381802 | + | 0.595170i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | −10.5000 | − | 2.59808i | −0.400018 | − | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | −0.152167 | −0.0760836 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760836 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(692\) | −9.50000 | + | 16.4545i | −0.361136 | + | 0.625506i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | −0.303676 | ||||||||
\(695\) | −22.5000 | + | 38.9711i | −0.853474 | + | 1.47826i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | − | 5.19615i | 0.113633 | − | 0.196818i | ||||
\(698\) | 11.5000 | − | 19.9186i | 0.435281 | − | 0.753930i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 10.3923i | −0.0755929 | − | 0.392792i | ||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00000 | − | 1.73205i | 0.0377157 | − | 0.0653255i | ||||
\(704\) | −10.5000 | − | 18.1865i | −0.395734 | − | 0.685431i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5000 | + | 21.6506i | 0.470444 | + | 0.814832i | ||||
\(707\) | −12.5000 | − | 4.33013i | −0.470111 | − | 0.162851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.50000 | + | 9.52628i | −0.206557 | + | 0.357767i | −0.950628 | − | 0.310334i | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | 19.5000 | − | 33.7750i | 0.731822 | − | 1.26755i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.0000 | −0.674579 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.5000 | − | 7.79423i | −1.17803 | − | 0.291488i | ||||
\(716\) | −8.50000 | − | 14.7224i | −0.317660 | − | 0.550203i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.50000 | − | 14.7224i | −0.317217 | − | 0.549436i | ||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5000 | − | 4.33013i | −0.465524 | − | 0.161262i | ||||
\(722\) | −9.00000 | − | 15.5885i | −0.334945 | − | 0.580142i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.0000 | 0.817624 | ||||||||
\(725\) | 14.0000 | + | 24.2487i | 0.519947 | + | 0.900575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | −24.0000 | − | 15.5885i | −0.889499 | − | 0.577747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −39.0000 | −1.44345 | ||||||||
\(731\) | 7.00000 | + | 12.1244i | 0.258904 | + | 0.448435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.50000 | + | 7.79423i | 0.166211 | + | 0.287886i | 0.937085 | − | 0.349102i | \(-0.113513\pi\) |
−0.770873 | + | 0.636988i | \(0.780180\pi\) | |||||||
\(734\) | −15.5000 | − | 26.8468i | −0.572115 | − | 0.990933i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.50000 | − | 7.79423i | 0.165760 | − | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.500000 | − | 0.866025i | −0.0183928 | − | 0.0318573i | 0.856683 | − | 0.515844i | \(-0.172522\pi\) |
−0.875075 | + | 0.483987i | \(0.839188\pi\) | |||||||
\(740\) | −3.00000 | − | 5.19615i | −0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.50000 | + | 7.79423i | 0.0550667 | + | 0.286135i | ||||
\(743\) | 25.5000 | − | 44.1673i | 0.935504 | − | 1.62034i | 0.161772 | − | 0.986828i | \(-0.448279\pi\) |
0.773732 | − | 0.633513i | \(-0.218388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.0000 | 1.64867 | ||||||||
\(746\) | −4.50000 | + | 7.79423i | −0.164757 | + | 0.285367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.00000 | + | 5.19615i | 0.109691 | + | 0.189990i | ||||
\(749\) | −16.0000 | + | 13.8564i | −0.584627 | + | 0.506302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.0000 | 1.02173 | 0.510867 | − | 0.859660i | \(-0.329324\pi\) | ||||
0.510867 | + | 0.859660i | \(0.329324\pi\) | |||||||
\(752\) | −0.500000 | − | 0.866025i | −0.0182331 | − | 0.0315807i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.5000 | + | 6.06218i | 0.892237 | + | 0.220771i | ||||
\(755\) | 63.0000 | 2.29280 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.50000 | + | 2.59808i | −0.0545184 | + | 0.0944287i | −0.891997 | − | 0.452042i | \(-0.850696\pi\) |
0.837478 | + | 0.546471i | \(0.184029\pi\) | |||||||
\(758\) | −16.5000 | + | 28.5788i | −0.599307 | + | 1.03803i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.00000 | 0.326464 | ||||||||
\(761\) | −4.50000 | + | 7.79423i | −0.163125 | + | 0.282541i | −0.935988 | − | 0.352032i | \(-0.885491\pi\) |
0.772863 | + | 0.634573i | \(0.218824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50000 | + | 18.1865i | 0.126709 | + | 0.658397i | ||||
\(764\) | 8.50000 | − | 14.7224i | 0.307519 | − | 0.532639i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5000 | − | 18.1865i | 0.379380 | − | 0.657106i | ||||
\(767\) | −4.00000 | − | 13.8564i | −0.144432 | − | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.50000 | + | 16.4545i | −0.342579 | + | 0.593364i | −0.984911 | − | 0.173063i | \(-0.944634\pi\) |
0.642332 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(770\) | 4.50000 | + | 23.3827i | 0.162169 | + | 0.842654i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | + | 6.06218i | 0.125968 | + | 0.218183i | ||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | − | 10.3923i | −0.215526 | − | 0.373303i | ||||
\(776\) | 7.50000 | + | 12.9904i | 0.269234 | + | 0.466328i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.5000 | − | 28.5788i | 0.591554 | − | 1.02460i | ||||
\(779\) | −1.50000 | − | 2.59808i | −0.0537431 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5000 | − | 33.7750i | 0.697765 | − | 1.20856i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | + | 6.92820i | −0.0357143 | + | 0.247436i | ||||
\(785\) | −57.0000 | −2.03442 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | −0.712923 | −0.356462 | − | 0.934310i | \(-0.616017\pi\) | ||||
−0.356462 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(788\) | 0.500000 | − | 0.866025i | 0.0178118 | − | 0.0308509i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.50000 | − | 7.79423i | 0.160103 | − | 0.277306i | ||||
\(791\) | 37.5000 | + | 12.9904i | 1.33335 | + | 0.461885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.5000 | − | 11.2583i | −1.61575 | − | 0.399795i | ||||
\(794\) | −0.500000 | + | 0.866025i | −0.0177443 | + | 0.0307341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | 1.50000 | + | 2.59808i | 0.0531327 | + | 0.0920286i | 0.891368 | − | 0.453279i | \(-0.149746\pi\) |
−0.838236 | + | 0.545308i | \(0.816413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.00000 | + | 1.73205i | 0.0353775 | + | 0.0612756i | ||||
\(800\) | 10.0000 | − | 17.3205i | 0.353553 | − | 0.612372i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.00000 | −0.0706225 | ||||||||
\(803\) | −39.0000 | −1.37628 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.5000 | − | 2.59808i | −0.369847 | − | 0.0915133i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.50000 | − | 12.9904i | −0.263849 | − | 0.457000i | ||||
\(809\) | 5.50000 | + | 9.52628i | 0.193370 | + | 0.334926i | 0.946365 | − | 0.323100i | \(-0.104725\pi\) |
−0.752995 | + | 0.658026i | \(0.771392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 3.50000 | + | 18.1865i | 0.122826 | + | 0.638222i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.00000 | + | 5.19615i | 0.105150 | + | 0.182125i | ||||
\(815\) | 3.00000 | 0.105085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | 0.244899 | ||||||||
\(818\) | −14.0000 | −0.489499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 54.0000 | 1.88461 | 0.942306 | − | 0.334751i | \(-0.108652\pi\) | ||||
0.942306 | + | 0.334751i | \(0.108652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0000 | 1.39431 | 0.697156 | − | 0.716919i | \(-0.254448\pi\) | ||||
0.697156 | + | 0.716919i | \(0.254448\pi\) | |||||||
\(824\) | −7.50000 | − | 12.9904i | −0.261275 | − | 0.452541i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | + | 6.92820i | −0.278356 | + | 0.241063i | ||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.00000 | − | 24.2487i | −0.242681 | − | 0.840673i | ||||
\(833\) | 2.00000 | − | 13.8564i | 0.0692959 | − | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.0000 | −1.34965 | ||||||||
\(836\) | 3.00000 | 0.103757 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.5000 | − | 21.6506i | 0.431805 | − | 0.747909i | ||||
\(839\) | 18.5000 | + | 32.0429i | 0.638691 | + | 1.10625i | 0.985720 | + | 0.168391i | \(0.0538571\pi\) |
−0.347029 | + | 0.937854i | \(0.612810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | −18.0000 | −0.620321 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.50000 | − | 6.06218i | 0.120475 | − | 0.208669i | ||||
\(845\) | −34.5000 | − | 18.1865i | −1.18684 | − | 0.625636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | − | 5.19615i | −0.0343604 | − | 0.178542i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00000 | − | 6.92820i | 0.137199 | − | 0.237635i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.00000 | −0.205436 | −0.102718 | − | 0.994711i | \(-0.532754\pi\) | ||||
−0.102718 | + | 0.994711i | \(0.532754\pi\) | |||||||
\(854\) | 6.50000 | + | 33.7750i | 0.222425 | + | 1.15576i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.0000 | −0.820303 | ||||||||
\(857\) | −16.5000 | + | 28.5788i | −0.563629 | + | 0.976235i | 0.433546 | + | 0.901131i | \(0.357262\pi\) |
−0.997176 | + | 0.0751033i | \(0.976071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5000 | − | 21.6506i | −0.426494 | − | 0.738710i | 0.570064 | − | 0.821600i | \(-0.306918\pi\) |
−0.996559 | + | 0.0828900i | \(0.973585\pi\) | |||||||
\(860\) | 10.5000 | − | 18.1865i | 0.358047 | − | 0.620156i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.50000 | − | 7.79423i | −0.153271 | − | 0.265472i | ||||
\(863\) | 18.5000 | + | 32.0429i | 0.629747 | + | 1.09075i | 0.987602 | + | 0.156977i | \(0.0501749\pi\) |
−0.357855 | + | 0.933777i | \(0.616492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.0000 | 1.93806 | ||||||||
\(866\) | 13.5000 | + | 23.3827i | 0.458749 | + | 0.794576i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.50000 | − | 7.79423i | −0.0509133 | − | 0.264553i | ||||
\(869\) | 4.50000 | − | 7.79423i | 0.152652 | − | 0.264401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.50000 | − | 7.79423i | 0.254128 | − | 0.264097i | ||||
\(872\) | −10.5000 | + | 18.1865i | −0.355575 | + | 0.615874i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | − | 5.19615i | 0.202837 | − | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.5000 | − | 38.9711i | 0.759771 | − | 1.31596i | −0.183196 | − | 0.983076i | \(-0.558644\pi\) |
0.942967 | − | 0.332886i | \(-0.108022\pi\) | |||||||
\(878\) | 16.0000 | 0.539974 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.50000 | + | 7.79423i | −0.151695 | + | 0.262743i | ||||
\(881\) | 7.50000 | − | 12.9904i | 0.252681 | − | 0.437657i | −0.711582 | − | 0.702603i | \(-0.752021\pi\) |
0.964263 | + | 0.264946i | \(0.0853542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 2.00000 | + | 6.92820i | 0.0672673 | + | 0.233021i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.50000 | + | 9.52628i | 0.184776 | + | 0.320042i | ||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.50000 | + | 28.5788i | 0.184464 | + | 0.958503i | ||||
\(890\) | 9.00000 | + | 15.5885i | 0.301681 | + | 0.522526i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.50000 | + | 7.79423i | −0.150671 | + | 0.260970i | ||||
\(893\) | 1.00000 | 0.0334637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.5000 | + | 44.1673i | −0.852371 | + | 1.47635i | ||||
\(896\) | 6.00000 | − | 5.19615i | 0.200446 | − | 0.173591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.50000 | − | 12.9904i | −0.250278 | − | 0.433495i | ||||
\(899\) | 10.5000 | + | 18.1865i | 0.350195 | + | 0.606555i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.00000 | − | 5.19615i | 0.0999445 | − | 0.173109i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.5000 | + | 38.9711i | 0.748339 | + | 1.29616i | ||||
\(905\) | −33.0000 | − | 57.1577i | −1.09696 | − | 1.89999i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.5000 | + | 40.7032i | 0.780305 | + | 1.35153i | 0.931764 | + | 0.363064i | \(0.118269\pi\) |
−0.151460 | + | 0.988463i | \(0.548397\pi\) | |||||||
\(908\) | −4.00000 | −0.132745 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.50000 | + | 28.5788i | −0.0497245 | + | 0.947379i | ||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.0000 | 0.595387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.50000 | − | 11.2583i | −0.214766 | − | 0.371986i | ||||
\(917\) | 12.5000 | + | 4.33013i | 0.412786 | + | 0.142993i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5000 | − | 21.6506i | 0.412337 | − | 0.714189i | −0.582808 | − | 0.812610i | \(-0.698046\pi\) |
0.995145 | + | 0.0984214i | \(0.0313793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.5000 | − | 30.3109i | −0.576332 | − | 0.998236i | ||||
\(923\) | 32.5000 | − | 33.7750i | 1.06975 | − | 1.11172i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.5000 | + | 30.3109i | −0.574466 | + | 0.995004i | ||||
\(929\) | −6.50000 | + | 11.2583i | −0.213258 | + | 0.369374i | −0.952732 | − | 0.303811i | \(-0.901741\pi\) |
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.50000 | − | 4.33013i | −0.180255 | − | 0.141914i | ||||
\(932\) | 10.5000 | + | 18.1865i | 0.343939 | + | 0.595720i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.50000 | + | 6.06218i | 0.114523 | + | 0.198361i | ||||
\(935\) | 9.00000 | − | 15.5885i | 0.294331 | − | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | −7.50000 | − | 2.59808i | −0.244884 | − | 0.0848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.50000 | − | 2.59808i | 0.0489246 | − | 0.0847399i | ||||
\(941\) | −8.50000 | + | 14.7224i | −0.277092 | + | 0.479938i | −0.970661 | − | 0.240453i | \(-0.922704\pi\) |
0.693569 | + | 0.720390i | \(0.256037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.5000 | + | 18.1865i | −0.341384 | + | 0.591295i | ||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.5000 | − | 11.2583i | −1.47699 | − | 0.365461i | ||||
\(950\) | −2.00000 | − | 3.46410i | −0.0648886 | − | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.0000 | − | 10.3923i | 0.388922 | − | 0.336817i | ||||
\(953\) | −16.5000 | − | 28.5788i | −0.534487 | − | 0.925759i | −0.999188 | − | 0.0402915i | \(-0.987171\pi\) |
0.464701 | − | 0.885468i | \(-0.346162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51.0000 | −1.65032 | ||||||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.5000 | + | 30.3109i | 0.565399 | + | 0.979300i | ||||
\(959\) | −20.0000 | + | 17.3205i | −0.645834 | + | 0.559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 2.00000 | + | 6.92820i | 0.0644826 | + | 0.223374i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.0000 | 0.837404 | ||||||||
\(965\) | 10.5000 | − | 18.1865i | 0.338007 | − | 0.585445i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 3.00000 | − | 5.19615i | 0.0964237 | − | 0.167011i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.50000 | − | 12.9904i | 0.240810 | − | 0.417096i | ||||
\(971\) | −0.500000 | + | 0.866025i | −0.0160458 | + | 0.0277921i | −0.873937 | − | 0.486040i | \(-0.838441\pi\) |
0.857891 | + | 0.513832i | \(0.171774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.5000 | + | 12.9904i | 1.20219 | + | 0.416452i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.50000 | + | 11.2583i | −0.208060 | + | 0.360370i | ||||
\(977\) | −2.50000 | − | 4.33013i | −0.0799821 | − | 0.138533i | 0.823260 | − | 0.567665i | \(-0.192153\pi\) |
−0.903242 | + | 0.429132i | \(0.858820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | −19.5000 | + | 7.79423i | −0.622905 | + | 0.248978i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.50000 | + | 12.9904i | −0.239335 | + | 0.414540i | ||||
\(983\) | 23.5000 | − | 40.7032i | 0.749534 | − | 1.29823i | −0.198513 | − | 0.980098i | \(-0.563611\pi\) |
0.948046 | − | 0.318132i | \(-0.103056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.00000 | −0.0955879 | ||||||||
\(986\) | −7.00000 | + | 12.1244i | −0.222925 | + | 0.386118i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.50000 | + | 0.866025i | 0.111350 | + | 0.0275519i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.50000 | − | 11.2583i | −0.206479 | − | 0.357633i | 0.744124 | − | 0.668042i | \(-0.232867\pi\) |
−0.950603 | + | 0.310409i | \(0.899534\pi\) | |||||||
\(992\) | 7.50000 | − | 12.9904i | 0.238125 | − | 0.412445i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.5000 | − | 11.2583i | −1.03084 | − | 0.357093i | ||||
\(995\) | −30.0000 | − | 51.9615i | −0.951064 | − | 1.64729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.00000 | 0.0633406 | 0.0316703 | − | 0.999498i | \(-0.489917\pi\) | ||||
0.0316703 | + | 0.999498i | \(0.489917\pi\) | |||||||
\(998\) | −15.5000 | − | 26.8468i | −0.490644 | − | 0.849820i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.s.a.802.1 | 2 | ||
3.2 | odd | 2 | 91.2.h.a.74.1 | yes | 2 | ||
7.2 | even | 3 | 819.2.n.c.100.1 | 2 | |||
13.3 | even | 3 | 819.2.n.c.172.1 | 2 | |||
21.2 | odd | 6 | 91.2.g.a.9.1 | ✓ | 2 | ||
21.5 | even | 6 | 637.2.g.a.373.1 | 2 | |||
21.11 | odd | 6 | 637.2.f.b.295.1 | 2 | |||
21.17 | even | 6 | 637.2.f.a.295.1 | 2 | |||
21.20 | even | 2 | 637.2.h.a.165.1 | 2 | |||
39.17 | odd | 6 | 1183.2.e.c.508.1 | 2 | |||
39.29 | odd | 6 | 91.2.g.a.81.1 | yes | 2 | ||
39.35 | odd | 6 | 1183.2.e.a.508.1 | 2 | |||
91.16 | even | 3 | inner | 819.2.s.a.289.1 | 2 | ||
273.17 | even | 6 | 8281.2.a.g.1.1 | 1 | |||
273.68 | even | 6 | 637.2.h.a.471.1 | 2 | |||
273.74 | odd | 6 | 8281.2.a.i.1.1 | 1 | |||
273.95 | odd | 6 | 8281.2.a.c.1.1 | 1 | |||
273.107 | odd | 6 | 91.2.h.a.16.1 | yes | 2 | ||
273.146 | even | 6 | 637.2.g.a.263.1 | 2 | |||
273.185 | even | 6 | 637.2.f.a.393.1 | 2 | |||
273.191 | odd | 6 | 1183.2.e.a.170.1 | 2 | |||
273.212 | odd | 6 | 1183.2.e.c.170.1 | 2 | |||
273.263 | odd | 6 | 637.2.f.b.393.1 | 2 | |||
273.269 | even | 6 | 8281.2.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.a.9.1 | ✓ | 2 | 21.2 | odd | 6 | ||
91.2.g.a.81.1 | yes | 2 | 39.29 | odd | 6 | ||
91.2.h.a.16.1 | yes | 2 | 273.107 | odd | 6 | ||
91.2.h.a.74.1 | yes | 2 | 3.2 | odd | 2 | ||
637.2.f.a.295.1 | 2 | 21.17 | even | 6 | |||
637.2.f.a.393.1 | 2 | 273.185 | even | 6 | |||
637.2.f.b.295.1 | 2 | 21.11 | odd | 6 | |||
637.2.f.b.393.1 | 2 | 273.263 | odd | 6 | |||
637.2.g.a.263.1 | 2 | 273.146 | even | 6 | |||
637.2.g.a.373.1 | 2 | 21.5 | even | 6 | |||
637.2.h.a.165.1 | 2 | 21.20 | even | 2 | |||
637.2.h.a.471.1 | 2 | 273.68 | even | 6 | |||
819.2.n.c.100.1 | 2 | 7.2 | even | 3 | |||
819.2.n.c.172.1 | 2 | 13.3 | even | 3 | |||
819.2.s.a.289.1 | 2 | 91.16 | even | 3 | inner | ||
819.2.s.a.802.1 | 2 | 1.1 | even | 1 | trivial | ||
1183.2.e.a.170.1 | 2 | 273.191 | odd | 6 | |||
1183.2.e.a.508.1 | 2 | 39.35 | odd | 6 | |||
1183.2.e.c.170.1 | 2 | 273.212 | odd | 6 | |||
1183.2.e.c.508.1 | 2 | 39.17 | odd | 6 | |||
8281.2.a.c.1.1 | 1 | 273.95 | odd | 6 | |||
8281.2.a.g.1.1 | 1 | 273.17 | even | 6 | |||
8281.2.a.i.1.1 | 1 | 273.74 | odd | 6 | |||
8281.2.a.j.1.1 | 1 | 273.269 | even | 6 |