Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [650,2,Mod(451,650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(650, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("650.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 650 = 2 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 650.e (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: | \(5.19027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.591408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 601.1 | ||
Root | \(0.155554 - 0.269427i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 650.601 |
Dual form | 650.2.e.j.451.1 |
$q$-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 \(\left(\mathbb{Z}/650\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.10716 | − | 1.91766i | −0.639219 | − | 1.10716i | −0.985604 | − | 0.169068i | \(-0.945924\pi\) |
0.346385 | − | 0.938092i | \(-0.387409\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.10716 | + | 1.91766i | −0.451996 | + | 0.782880i | ||||
\(7\) | 1.95161 | − | 3.38028i | 0.737638 | − | 1.27763i | −0.215919 | − | 0.976411i | \(-0.569275\pi\) |
0.953556 | − | 0.301215i | \(-0.0973921\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.951606 | + | 1.64823i | −0.317202 | + | 0.549410i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.533338 | − | 0.923769i | −0.160808 | − | 0.278527i | 0.774351 | − | 0.632756i | \(-0.218077\pi\) |
−0.935159 | + | 0.354229i | \(0.884743\pi\) | |||||||
\(12\) | 2.21432 | 0.639219 | ||||||||
\(13\) | 2.82148 | − | 2.24483i | 0.782538 | − | 0.622603i | ||||
\(14\) | −3.90321 | −1.04318 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.655554 | + | 1.13545i | −0.158995 | + | 0.275388i | −0.934507 | − | 0.355946i | \(-0.884159\pi\) |
0.775511 | + | 0.631334i | \(0.217492\pi\) | |||||||
\(18\) | 1.90321 | 0.448591 | ||||||||
\(19\) | 3.29605 | − | 5.70893i | 0.756166 | − | 1.30972i | −0.188626 | − | 0.982049i | \(-0.560403\pi\) |
0.944792 | − | 0.327669i | \(-0.106263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.64296 | −1.88605 | ||||||||
\(22\) | −0.533338 | + | 0.923769i | −0.113708 | + | 0.196948i | ||||
\(23\) | −1.07382 | − | 1.85991i | −0.223907 | − | 0.387819i | 0.732084 | − | 0.681215i | \(-0.238548\pi\) |
−0.955991 | + | 0.293396i | \(0.905215\pi\) | |||||||
\(24\) | −1.10716 | − | 1.91766i | −0.225998 | − | 0.391440i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.35482 | − | 1.32106i | −0.657934 | − | 0.259081i | ||||
\(27\) | −2.42864 | −0.467392 | ||||||||
\(28\) | 1.95161 | + | 3.38028i | 0.368819 | + | 0.638813i | ||||
\(29\) | 4.52543 | + | 7.83827i | 0.840351 | + | 1.45553i | 0.889598 | + | 0.456744i | \(0.150984\pi\) |
−0.0492475 | + | 0.998787i | \(0.515682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.92396 | −1.24358 | −0.621790 | − | 0.783184i | \(-0.713594\pi\) | ||||
−0.621790 | + | 0.783184i | \(0.713594\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.18098 | + | 2.04552i | −0.205582 | + | 0.356079i | ||||
\(34\) | 1.31111 | 0.224853 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.951606 | − | 1.64823i | −0.158601 | − | 0.274705i | ||||
\(37\) | −2.51037 | − | 4.34809i | −0.412703 | − | 0.714822i | 0.582482 | − | 0.812844i | \(-0.302082\pi\) |
−0.995184 | + | 0.0980220i | \(0.968748\pi\) | |||||||
\(38\) | −6.59210 | −1.06938 | ||||||||
\(39\) | −7.42864 | − | 2.92525i | −1.18953 | − | 0.468414i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.97703 | + | 5.15637i | 0.464935 | + | 0.805290i | 0.999199 | − | 0.0400274i | \(-0.0127445\pi\) |
−0.534264 | + | 0.845318i | \(0.679411\pi\) | |||||||
\(42\) | 4.32148 | + | 7.48502i | 0.666819 | + | 1.15496i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 1.06668 | 0.160808 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.07382 | + | 1.85991i | −0.158326 | + | 0.274229i | ||||
\(47\) | −0.0967881 | −0.0141180 | −0.00705900 | − | 0.999975i | \(-0.502247\pi\) | ||||
−0.00705900 | + | 0.999975i | \(0.502247\pi\) | |||||||
\(48\) | −1.10716 | + | 1.91766i | −0.159805 | + | 0.276790i | ||||
\(49\) | −4.11753 | − | 7.13177i | −0.588219 | − | 1.01882i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.90321 | 0.406531 | ||||||||
\(52\) | 0.533338 | + | 3.56589i | 0.0739607 | + | 0.494500i | ||||
\(53\) | −1.49532 | −0.205397 | −0.102699 | − | 0.994713i | \(-0.532748\pi\) | ||||
−0.102699 | + | 0.994713i | \(0.532748\pi\) | |||||||
\(54\) | 1.21432 | + | 2.10326i | 0.165248 | + | 0.286218i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.95161 | − | 3.38028i | 0.260794 | − | 0.451709i | ||||
\(57\) | −14.5970 | −1.93342 | ||||||||
\(58\) | 4.52543 | − | 7.83827i | 0.594218 | − | 1.02922i | ||||
\(59\) | −3.59210 | + | 6.22171i | −0.467652 | + | 0.809997i | −0.999317 | − | 0.0369577i | \(-0.988233\pi\) |
0.531665 | + | 0.846955i | \(0.321567\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.94370 | + | 6.83068i | −0.504938 | + | 0.874579i | 0.495045 | + | 0.868867i | \(0.335151\pi\) |
−0.999984 | + | 0.00571183i | \(0.998182\pi\) | |||||||
\(62\) | 3.46198 | + | 5.99632i | 0.439672 | + | 0.761534i | ||||
\(63\) | 3.71432 | + | 6.43339i | 0.467960 | + | 0.810531i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.36196 | 0.290738 | ||||||||
\(67\) | 4.21432 | + | 7.29942i | 0.514861 | + | 0.891766i | 0.999851 | + | 0.0172460i | \(0.00548984\pi\) |
−0.484990 | + | 0.874520i | \(0.661177\pi\) | |||||||
\(68\) | −0.655554 | − | 1.13545i | −0.0794976 | − | 0.137694i | ||||
\(69\) | −2.37778 | + | 4.11844i | −0.286252 | + | 0.495802i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.73975 | − | 13.4056i | 0.918539 | − | 1.59096i | 0.116903 | − | 0.993143i | \(-0.462703\pi\) |
0.801636 | − | 0.597813i | \(-0.203963\pi\) | |||||||
\(72\) | −0.951606 | + | 1.64823i | −0.112148 | + | 0.194246i | ||||
\(73\) | −15.3526 | −1.79689 | −0.898443 | − | 0.439091i | \(-0.855301\pi\) | ||||
−0.898443 | + | 0.439091i | \(0.855301\pi\) | |||||||
\(74\) | −2.51037 | + | 4.34809i | −0.291825 | + | 0.505455i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.29605 | + | 5.70893i | 0.378083 | + | 0.654859i | ||||
\(77\) | −4.16346 | −0.474471 | ||||||||
\(78\) | 1.18098 | + | 7.89601i | 0.133720 | + | 0.894048i | ||||
\(79\) | 4.30174 | 0.483984 | 0.241992 | − | 0.970278i | \(-0.422199\pi\) | ||||
0.241992 | + | 0.970278i | \(0.422199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.54371 | + | 9.60199i | 0.615968 | + | 1.06689i | ||||
\(82\) | 2.97703 | − | 5.15637i | 0.328758 | − | 0.569426i | ||||
\(83\) | 9.69381 | 1.06403 | 0.532017 | − | 0.846734i | \(-0.321434\pi\) | ||||
0.532017 | + | 0.846734i | \(0.321434\pi\) | |||||||
\(84\) | 4.32148 | − | 7.48502i | 0.471512 | − | 0.816683i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 10.0207 | − | 17.3564i | 1.07434 | − | 1.86081i | ||||
\(88\) | −0.533338 | − | 0.923769i | −0.0568541 | − | 0.0984741i | ||||
\(89\) | −2.26271 | − | 3.91914i | −0.239847 | − | 0.415428i | 0.720823 | − | 0.693119i | \(-0.243764\pi\) |
−0.960670 | + | 0.277692i | \(0.910431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.08173 | − | 13.9184i | −0.218225 | − | 1.45905i | ||||
\(92\) | 2.14764 | 0.223907 | ||||||||
\(93\) | 7.66593 | + | 13.2778i | 0.794919 | + | 1.37684i | ||||
\(94\) | 0.0483940 | + | 0.0838209i | 0.00499146 | + | 0.00864547i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.21432 | 0.225998 | ||||||||
\(97\) | 2.13013 | − | 3.68949i | 0.216282 | − | 0.374611i | −0.737387 | − | 0.675471i | \(-0.763940\pi\) |
0.953668 | + | 0.300860i | \(0.0972738\pi\) | |||||||
\(98\) | −4.11753 | + | 7.13177i | −0.415934 | + | 0.720418i | ||||
\(99\) | 2.03011 | 0.204034 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.729376 | − | 1.26332i | −0.0725756 | − | 0.125705i | 0.827454 | − | 0.561534i | \(-0.189789\pi\) |
−0.900029 | + | 0.435829i | \(0.856455\pi\) | |||||||
\(102\) | −1.45161 | − | 2.51426i | −0.143730 | − | 0.248948i | ||||
\(103\) | −10.2444 | −1.00941 | −0.504707 | − | 0.863291i | \(-0.668399\pi\) | ||||
−0.504707 | + | 0.863291i | \(0.668399\pi\) | |||||||
\(104\) | 2.82148 | − | 2.24483i | 0.276669 | − | 0.220123i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.747658 | + | 1.29498i | 0.0726190 | + | 0.125780i | ||||
\(107\) | 1.10716 | + | 1.91766i | 0.107033 | + | 0.185387i | 0.914567 | − | 0.404434i | \(-0.132532\pi\) |
−0.807534 | + | 0.589821i | \(0.799198\pi\) | |||||||
\(108\) | 1.21432 | − | 2.10326i | 0.116848 | − | 0.202387i | ||||
\(109\) | 0.133353 | 0.0127729 | 0.00638645 | − | 0.999980i | \(-0.497967\pi\) | ||||
0.00638645 | + | 0.999980i | \(0.497967\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.55877 | + | 9.62806i | −0.527615 | + | 0.913855i | ||||
\(112\) | −3.90321 | −0.368819 | ||||||||
\(113\) | 7.00000 | − | 12.1244i | 0.658505 | − | 1.14056i | −0.322498 | − | 0.946570i | \(-0.604523\pi\) |
0.981003 | − | 0.193993i | \(-0.0621440\pi\) | |||||||
\(114\) | 7.29851 | + | 12.6414i | 0.683568 | + | 1.18398i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.05086 | −0.840351 | ||||||||
\(117\) | 1.01506 | + | 6.78664i | 0.0938419 | + | 0.627425i | ||||
\(118\) | 7.18421 | 0.661360 | ||||||||
\(119\) | 2.55877 | + | 4.43191i | 0.234562 | + | 0.406273i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.93110 | − | 8.54092i | 0.448282 | − | 0.776447i | ||||
\(122\) | 7.88739 | 0.714091 | ||||||||
\(123\) | 6.59210 | − | 11.4179i | 0.594390 | − | 1.02951i | ||||
\(124\) | 3.46198 | − | 5.99632i | 0.310895 | − | 0.538486i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.71432 | − | 6.43339i | 0.330898 | − | 0.573132i | ||||
\(127\) | −4.99532 | − | 8.65214i | −0.443263 | − | 0.767753i | 0.554667 | − | 0.832073i | \(-0.312846\pi\) |
−0.997929 | + | 0.0643192i | \(0.979512\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.42864 | 0.389920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.25581 | 0.808684 | 0.404342 | − | 0.914608i | \(-0.367501\pi\) | ||||
0.404342 | + | 0.914608i | \(0.367501\pi\) | |||||||
\(132\) | −1.18098 | − | 2.04552i | −0.102791 | − | 0.178040i | ||||
\(133\) | −12.8652 | − | 22.2832i | −1.11555 | − | 1.93220i | ||||
\(134\) | 4.21432 | − | 7.29942i | 0.364062 | − | 0.630573i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.655554 | + | 1.13545i | −0.0562133 | + | 0.0973643i | ||||
\(137\) | 7.39530 | − | 12.8090i | 0.631823 | − | 1.09435i | −0.355356 | − | 0.934731i | \(-0.615640\pi\) |
0.987179 | − | 0.159619i | \(-0.0510265\pi\) | |||||||
\(138\) | 4.75557 | 0.404821 | ||||||||
\(139\) | 6.34691 | − | 10.9932i | 0.538338 | − | 0.932428i | −0.460656 | − | 0.887579i | \(-0.652386\pi\) |
0.998994 | − | 0.0448494i | \(-0.0142808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.107160 | + | 0.185606i | 0.00902449 | + | 0.0156309i | ||||
\(142\) | −15.4795 | −1.29901 | ||||||||
\(143\) | −3.57851 | − | 1.40914i | −0.299250 | − | 0.117838i | ||||
\(144\) | 1.90321 | 0.158601 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.67630 | + | 13.2957i | 0.635295 | + | 1.10036i | ||||
\(147\) | −9.11753 | + | 15.7920i | −0.752001 | + | 1.30250i | ||||
\(148\) | 5.02074 | 0.412703 | ||||||||
\(149\) | −3.64296 | + | 6.30979i | −0.298443 | + | 0.516918i | −0.975780 | − | 0.218755i | \(-0.929801\pi\) |
0.677337 | + | 0.735673i | \(0.263134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1082 | 1.63638 | 0.818190 | − | 0.574949i | \(-0.194978\pi\) | ||||
0.818190 | + | 0.574949i | \(0.194978\pi\) | |||||||
\(152\) | 3.29605 | − | 5.70893i | 0.267345 | − | 0.463055i | ||||
\(153\) | −1.24766 | − | 2.16101i | −0.100867 | − | 0.174707i | ||||
\(154\) | 2.08173 | + | 3.60567i | 0.167751 | + | 0.290553i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.24766 | − | 4.97077i | 0.500213 | − | 0.397980i | ||||
\(157\) | −1.98418 | −0.158355 | −0.0791773 | − | 0.996861i | \(-0.525229\pi\) | ||||
−0.0791773 | + | 0.996861i | \(0.525229\pi\) | |||||||
\(158\) | −2.15087 | − | 3.72542i | −0.171114 | − | 0.296378i | ||||
\(159\) | 1.65555 | + | 2.86750i | 0.131294 | + | 0.227408i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.38271 | −0.660650 | ||||||||
\(162\) | 5.54371 | − | 9.60199i | 0.435555 | − | 0.754403i | ||||
\(163\) | 2.35159 | − | 4.07308i | 0.184191 | − | 0.319028i | −0.759113 | − | 0.650959i | \(-0.774367\pi\) |
0.943304 | + | 0.331931i | \(0.107700\pi\) | |||||||
\(164\) | −5.95407 | −0.464935 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.84691 | − | 8.39509i | −0.376193 | − | 0.651585i | ||||
\(167\) | 4.84767 | + | 8.39642i | 0.375124 | + | 0.649734i | 0.990346 | − | 0.138620i | \(-0.0442667\pi\) |
−0.615221 | + | 0.788354i | \(0.710933\pi\) | |||||||
\(168\) | −8.64296 | −0.666819 | ||||||||
\(169\) | 2.92149 | − | 12.6675i | 0.224730 | − | 0.974421i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.27309 | + | 10.8653i | 0.479715 | + | 0.830890i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −12.0358 | + | 20.8466i | −0.915065 | + | 1.58494i | −0.108259 | + | 0.994123i | \(0.534527\pi\) |
−0.806806 | + | 0.590816i | \(0.798806\pi\) | |||||||
\(174\) | −20.0415 | −1.51934 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.533338 | + | 0.923769i | −0.0402019 | + | 0.0696317i | ||||
\(177\) | 15.9081 | 1.19573 | ||||||||
\(178\) | −2.26271 | + | 3.91914i | −0.169598 | + | 0.293752i | ||||
\(179\) | −1.52543 | − | 2.64212i | −0.114016 | − | 0.197481i | 0.803370 | − | 0.595480i | \(-0.203038\pi\) |
−0.917386 | + | 0.397999i | \(0.869705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6430 | 0.791085 | 0.395542 | − | 0.918448i | \(-0.370557\pi\) | ||||
0.395542 | + | 0.918448i | \(0.370557\pi\) | |||||||
\(182\) | −11.0128 | + | 8.76204i | −0.816325 | + | 0.649486i | ||||
\(183\) | 17.4652 | 1.29107 | ||||||||
\(184\) | −1.07382 | − | 1.85991i | −0.0791632 | − | 0.137115i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.66593 | − | 13.2778i | 0.562093 | − | 0.973574i | ||||
\(187\) | 1.39853 | 0.102270 | ||||||||
\(188\) | 0.0483940 | − | 0.0838209i | 0.00352950 | − | 0.00611327i | ||||
\(189\) | −4.73975 | + | 8.20948i | −0.344766 | + | 0.597152i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.36519 | + | 12.7569i | −0.532926 | + | 0.923056i | 0.466334 | + | 0.884609i | \(0.345574\pi\) |
−0.999261 | + | 0.0384470i | \(0.987759\pi\) | |||||||
\(192\) | −1.10716 | − | 1.91766i | −0.0799024 | − | 0.138395i | ||||
\(193\) | 7.00000 | + | 12.1244i | 0.503871 | + | 0.872730i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | −4.26025 | −0.305868 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.23506 | 0.588219 | ||||||||
\(197\) | 5.20641 | + | 9.01776i | 0.370941 | + | 0.642489i | 0.989711 | − | 0.143084i | \(-0.0457018\pi\) |
−0.618769 | + | 0.785573i | \(0.712368\pi\) | |||||||
\(198\) | −1.01506 | − | 1.75813i | −0.0721369 | − | 0.124945i | ||||
\(199\) | 2.18421 | − | 3.78316i | 0.154834 | − | 0.268181i | −0.778164 | − | 0.628061i | \(-0.783849\pi\) |
0.932999 | + | 0.359880i | \(0.117182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.33185 | − | 16.1632i | 0.658218 | − | 1.14007i | ||||
\(202\) | −0.729376 | + | 1.26332i | −0.0513187 | + | 0.0888866i | ||||
\(203\) | 35.3274 | 2.47950 | ||||||||
\(204\) | −1.45161 | + | 2.51426i | −0.101633 | + | 0.176033i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.12222 | + | 8.87194i | 0.356882 | + | 0.618137i | ||||
\(207\) | 4.08742 | 0.284095 | ||||||||
\(208\) | −3.35482 | − | 1.32106i | −0.232615 | − | 0.0915990i | ||||
\(209\) | −7.03164 | −0.486389 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74766 | − | 4.75908i | −0.189157 | − | 0.327629i | 0.755813 | − | 0.654788i | \(-0.227242\pi\) |
−0.944969 | + | 0.327159i | \(0.893909\pi\) | |||||||
\(212\) | 0.747658 | − | 1.29498i | 0.0513494 | − | 0.0889397i | ||||
\(213\) | −34.2766 | −2.34859 | ||||||||
\(214\) | 1.10716 | − | 1.91766i | 0.0756839 | − | 0.131088i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.42864 | −0.165248 | ||||||||
\(217\) | −13.5128 | + | 23.4049i | −0.917311 | + | 1.58883i | ||||
\(218\) | −0.0666765 | − | 0.115487i | −0.00451591 | − | 0.00782178i | ||||
\(219\) | 16.9978 | + | 29.4410i | 1.14860 | + | 1.98944i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.699264 | + | 4.67526i | 0.0470376 | + | 0.314492i | ||||
\(222\) | 11.1175 | 0.746160 | ||||||||
\(223\) | 10.0484 | + | 17.4043i | 0.672890 | + | 1.16548i | 0.977081 | + | 0.212869i | \(0.0682807\pi\) |
−0.304191 | + | 0.952611i | \(0.598386\pi\) | |||||||
\(224\) | 1.95161 | + | 3.38028i | 0.130397 | + | 0.225855i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −9.67952 | + | 16.7654i | −0.642453 | + | 1.11276i | 0.342431 | + | 0.939543i | \(0.388750\pi\) |
−0.984884 | + | 0.173218i | \(0.944584\pi\) | |||||||
\(228\) | 7.29851 | − | 12.6414i | 0.483356 | − | 0.837197i | ||||
\(229\) | 15.7255 | 1.03917 | 0.519584 | − | 0.854420i | \(-0.326087\pi\) | ||||
0.519584 | + | 0.854420i | \(0.326087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.60962 | + | 7.98410i | 0.303291 | + | 0.525315i | ||||
\(232\) | 4.52543 | + | 7.83827i | 0.297109 | + | 0.514608i | ||||
\(233\) | −14.8825 | −0.974983 | −0.487491 | − | 0.873128i | \(-0.662088\pi\) | ||||
−0.487491 | + | 0.873128i | \(0.662088\pi\) | |||||||
\(234\) | 5.36987 | − | 4.27238i | 0.351040 | − | 0.279294i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.59210 | − | 6.22171i | −0.233826 | − | 0.404999i | ||||
\(237\) | −4.76271 | − | 8.24926i | −0.309372 | − | 0.535847i | ||||
\(238\) | 2.55877 | − | 4.43191i | 0.165860 | − | 0.287278i | ||||
\(239\) | 4.42219 | 0.286047 | 0.143024 | − | 0.989719i | \(-0.454317\pi\) | ||||
0.143024 | + | 0.989719i | \(0.454317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.64050 | − | 9.76963i | 0.363336 | − | 0.629317i | −0.625171 | − | 0.780488i | \(-0.714971\pi\) |
0.988508 | + | 0.151170i | \(0.0483042\pi\) | |||||||
\(242\) | −9.86220 | −0.633966 | ||||||||
\(243\) | 8.63259 | − | 14.9521i | 0.553781 | − | 0.959176i | ||||
\(244\) | −3.94370 | − | 6.83068i | −0.252469 | − | 0.437290i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.1842 | −0.840594 | ||||||||
\(247\) | −3.51582 | − | 23.5067i | −0.223706 | − | 1.49570i | ||||
\(248\) | −6.92396 | −0.439672 | ||||||||
\(249\) | −10.7326 | − | 18.5894i | −0.680151 | − | 1.17806i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.32616 | + | 2.29698i | −0.0837067 | + | 0.144984i | −0.904839 | − | 0.425753i | \(-0.860009\pi\) |
0.821133 | + | 0.570737i | \(0.193343\pi\) | |||||||
\(252\) | −7.42864 | −0.467960 | ||||||||
\(253\) | −1.14542 | + | 1.98393i | −0.0720120 | + | 0.124728i | ||||
\(254\) | −4.99532 | + | 8.65214i | −0.313434 | + | 0.542884i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.05086 | − | 3.55219i | −0.127929 | − | 0.221579i | 0.794945 | − | 0.606681i | \(-0.207500\pi\) |
−0.922874 | + | 0.385102i | \(0.874166\pi\) | |||||||
\(258\) | −2.21432 | − | 3.83531i | −0.137858 | − | 0.238776i | ||||
\(259\) | −19.5970 | −1.21770 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.2257 | −1.06624 | ||||||||
\(262\) | −4.62790 | − | 8.01576i | −0.285913 | − | 0.495216i | ||||
\(263\) | 5.40099 | + | 9.35479i | 0.333039 | + | 0.576841i | 0.983106 | − | 0.183036i | \(-0.0585925\pi\) |
−0.650067 | + | 0.759877i | \(0.725259\pi\) | |||||||
\(264\) | −1.18098 | + | 2.04552i | −0.0726844 | + | 0.125893i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.8652 | + | 22.2832i | −0.788815 | + | 1.36627i | ||||
\(267\) | −5.01037 | + | 8.67822i | −0.306630 | + | 0.531098i | ||||
\(268\) | −8.42864 | −0.514861 | ||||||||
\(269\) | 9.29137 | − | 16.0931i | 0.566505 | − | 0.981215i | −0.430403 | − | 0.902637i | \(-0.641629\pi\) |
0.996908 | − | 0.0785782i | \(-0.0250380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.88739 | − | 17.1255i | −0.600616 | − | 1.04030i | −0.992728 | − | 0.120380i | \(-0.961589\pi\) |
0.392112 | − | 0.919918i | \(-0.371745\pi\) | |||||||
\(272\) | 1.31111 | 0.0794976 | ||||||||
\(273\) | −24.3859 | + | 19.4020i | −1.47590 | + | 1.17426i | ||||
\(274\) | −14.7906 | −0.893533 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.37778 | − | 4.11844i | −0.143126 | − | 0.247901i | ||||
\(277\) | −0.102476 | + | 0.177493i | −0.00615718 | + | 0.0106645i | −0.869088 | − | 0.494658i | \(-0.835293\pi\) |
0.862930 | + | 0.505323i | \(0.168627\pi\) | |||||||
\(278\) | −12.6938 | −0.761324 | ||||||||
\(279\) | 6.58888 | − | 11.4123i | 0.394466 | − | 0.683235i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4558 | −1.22029 | −0.610146 | − | 0.792289i | \(-0.708889\pi\) | ||||
−0.610146 | + | 0.792289i | \(0.708889\pi\) | |||||||
\(282\) | 0.107160 | − | 0.185606i | 0.00638128 | − | 0.0110527i | ||||
\(283\) | −0.719004 | − | 1.24535i | −0.0427403 | − | 0.0740284i | 0.843864 | − | 0.536557i | \(-0.180275\pi\) |
−0.886604 | + | 0.462529i | \(0.846942\pi\) | |||||||
\(284\) | 7.73975 | + | 13.4056i | 0.459270 | + | 0.795478i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.568899 | + | 3.80365i | 0.0336397 | + | 0.224914i | ||||
\(287\) | 23.2400 | 1.37181 | ||||||||
\(288\) | −0.951606 | − | 1.64823i | −0.0560739 | − | 0.0971229i | ||||
\(289\) | 7.64050 | + | 13.2337i | 0.449441 | + | 0.778455i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.43356 | −0.553005 | ||||||||
\(292\) | 7.67630 | − | 13.2957i | 0.449221 | − | 0.778074i | ||||
\(293\) | 10.4573 | − | 18.1126i | 0.610922 | − | 1.05815i | −0.380164 | − | 0.924919i | \(-0.624132\pi\) |
0.991085 | − | 0.133228i | \(-0.0425343\pi\) | |||||||
\(294\) | 18.2351 | 1.06349 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.51037 | − | 4.34809i | −0.145912 | − | 0.252728i | ||||
\(297\) | 1.29529 | + | 2.24350i | 0.0751601 | + | 0.130181i | ||||
\(298\) | 7.28592 | 0.422062 | ||||||||
\(299\) | −7.20495 | − | 2.83716i | −0.416673 | − | 0.164077i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.90321 | + | 6.76056i | 0.224977 | + | 0.389672i | ||||
\(302\) | −10.0541 | − | 17.4142i | −0.578547 | − | 1.00207i | ||||
\(303\) | −1.61507 | + | 2.79738i | −0.0927834 | + | 0.160706i | ||||
\(304\) | −6.59210 | −0.378083 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.24766 | + | 2.16101i | −0.0713239 | + | 0.123537i | ||||
\(307\) | 12.5303 | 0.715145 | 0.357572 | − | 0.933885i | \(-0.383605\pi\) | ||||
0.357572 | + | 0.933885i | \(0.383605\pi\) | |||||||
\(308\) | 2.08173 | − | 3.60567i | 0.118618 | − | 0.205452i | ||||
\(309\) | 11.3422 | + | 19.6453i | 0.645237 | + | 1.11758i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.78123 | −0.554643 | −0.277321 | − | 0.960777i | \(-0.589447\pi\) | ||||
−0.277321 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(312\) | −7.42864 | − | 2.92525i | −0.420564 | − | 0.165610i | ||||
\(313\) | 17.2128 | 0.972924 | 0.486462 | − | 0.873702i | \(-0.338287\pi\) | ||||
0.486462 | + | 0.873702i | \(0.338287\pi\) | |||||||
\(314\) | 0.992089 | + | 1.71835i | 0.0559868 | + | 0.0969720i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.15087 | + | 3.72542i | −0.120996 | + | 0.209571i | ||||
\(317\) | 13.7447 | 0.771978 | 0.385989 | − | 0.922503i | \(-0.373860\pi\) | ||||
0.385989 | + | 0.922503i | \(0.373860\pi\) | |||||||
\(318\) | 1.65555 | − | 2.86750i | 0.0928389 | − | 0.160802i | ||||
\(319\) | 4.82717 | − | 8.36090i | 0.270269 | − | 0.468120i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.45161 | − | 4.24631i | 0.136835 | − | 0.237006i | ||||
\(322\) | 4.19135 | + | 7.25964i | 0.233575 | + | 0.404564i | ||||
\(323\) | 4.32148 | + | 7.48502i | 0.240454 | + | 0.416478i | ||||
\(324\) | −11.0874 | −0.615968 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.70318 | −0.260485 | ||||||||
\(327\) | −0.147643 | − | 0.255726i | −0.00816469 | − | 0.0141417i | ||||
\(328\) | 2.97703 | + | 5.15637i | 0.164379 | + | 0.284713i | ||||
\(329\) | −0.188892 | + | 0.327171i | −0.0104140 | + | 0.0180375i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.69381 | + | 16.7902i | −0.532820 | + | 0.922872i | 0.466445 | + | 0.884550i | \(0.345534\pi\) |
−0.999265 | + | 0.0383216i | \(0.987799\pi\) | |||||||
\(332\) | −4.84691 | + | 8.39509i | −0.266009 | + | 0.460740i | ||||
\(333\) | 9.55554 | 0.523640 | ||||||||
\(334\) | 4.84767 | − | 8.39642i | 0.265253 | − | 0.459431i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.32148 | + | 7.48502i | 0.235756 | + | 0.408341i | ||||
\(337\) | 0.555539 | 0.0302621 | 0.0151311 | − | 0.999886i | \(-0.495183\pi\) | ||||
0.0151311 | + | 0.999886i | \(0.495183\pi\) | |||||||
\(338\) | −12.4311 | + | 3.80365i | −0.676163 | + | 0.206891i | ||||
\(339\) | −31.0005 | −1.68371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.69281 | + | 6.39614i | 0.199977 | + | 0.346370i | ||||
\(342\) | 6.27309 | − | 10.8653i | 0.339210 | − | 0.587528i | ||||
\(343\) | −4.82071 | −0.260294 | ||||||||
\(344\) | −1.00000 | + | 1.73205i | −0.0539164 | + | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0716 | 1.29410 | ||||||||
\(347\) | −3.34222 | + | 5.78890i | −0.179420 | + | 0.310764i | −0.941682 | − | 0.336504i | \(-0.890755\pi\) |
0.762262 | + | 0.647269i | \(0.224089\pi\) | |||||||
\(348\) | 10.0207 | + | 17.3564i | 0.537168 | + | 0.930403i | ||||
\(349\) | −5.29137 | − | 9.16492i | −0.283240 | − | 0.490587i | 0.688941 | − | 0.724818i | \(-0.258076\pi\) |
−0.972181 | + | 0.234231i | \(0.924743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.85236 | + | 5.45188i | −0.365752 | + | 0.291000i | ||||
\(352\) | 1.06668 | 0.0568541 | ||||||||
\(353\) | 4.60470 | + | 7.97557i | 0.245083 | + | 0.424497i | 0.962155 | − | 0.272503i | \(-0.0878513\pi\) |
−0.717072 | + | 0.696999i | \(0.754518\pi\) | |||||||
\(354\) | −7.95407 | − | 13.7768i | −0.422754 | − | 0.732231i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.52543 | 0.239847 | ||||||||
\(357\) | 5.66593 | − | 9.81367i | 0.299873 | − | 0.519395i | ||||
\(358\) | −1.52543 | + | 2.64212i | −0.0806214 | + | 0.139640i | ||||
\(359\) | −4.19358 | −0.221328 | −0.110664 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110664 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2279 | − | 21.1794i | −0.643575 | − | 1.11470i | ||||
\(362\) | −5.32148 | − | 9.21707i | −0.279691 | − | 0.484439i | ||||
\(363\) | −21.8381 | −1.14620 | ||||||||
\(364\) | 13.0946 | + | 5.15637i | 0.686342 | + | 0.270267i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.73260 | − | 15.1253i | −0.456460 | − | 0.790613i | ||||
\(367\) | −6.98418 | − | 12.0970i | −0.364571 | − | 0.631456i | 0.624136 | − | 0.781316i | \(-0.285451\pi\) |
−0.988707 | + | 0.149860i | \(0.952118\pi\) | |||||||
\(368\) | −1.07382 | + | 1.85991i | −0.0559768 | + | 0.0969547i | ||||
\(369\) | −11.3319 | −0.589913 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.91827 | + | 5.05459i | −0.151509 | + | 0.262421i | ||||
\(372\) | −15.3319 | −0.794919 | ||||||||
\(373\) | −5.92396 | + | 10.2606i | −0.306731 | + | 0.531273i | −0.977645 | − | 0.210262i | \(-0.932568\pi\) |
0.670914 | + | 0.741535i | \(0.265902\pi\) | |||||||
\(374\) | −0.699264 | − | 1.21116i | −0.0361581 | − | 0.0626276i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0967881 | −0.00499146 | ||||||||
\(377\) | 30.3640 | + | 11.9567i | 1.56382 | + | 0.615802i | ||||
\(378\) | 9.47949 | 0.487573 | ||||||||
\(379\) | −0.303197 | − | 0.525153i | −0.0155742 | − | 0.0269753i | 0.858133 | − | 0.513427i | \(-0.171624\pi\) |
−0.873707 | + | 0.486452i | \(0.838291\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0612 | + | 19.1586i | −0.566684 | + | 0.981525i | ||||
\(382\) | 14.7304 | 0.753672 | ||||||||
\(383\) | 17.3899 | − | 30.1201i | 0.888580 | − | 1.53907i | 0.0470252 | − | 0.998894i | \(-0.485026\pi\) |
0.841555 | − | 0.540172i | \(-0.181641\pi\) | |||||||
\(384\) | −1.10716 | + | 1.91766i | −0.0564995 | + | 0.0978600i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.00000 | − | 12.1244i | 0.356291 | − | 0.617113i | ||||
\(387\) | −1.90321 | − | 3.29646i | −0.0967457 | − | 0.167568i | ||||
\(388\) | 2.13013 | + | 3.68949i | 0.108141 | + | 0.187305i | ||||
\(389\) | −18.6844 | −0.947339 | −0.473670 | − | 0.880703i | \(-0.657071\pi\) | ||||
−0.473670 | + | 0.880703i | \(0.657071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.81579 | 0.142401 | ||||||||
\(392\) | −4.11753 | − | 7.13177i | −0.207967 | − | 0.360209i | ||||
\(393\) | −10.2477 | − | 17.7495i | −0.516926 | − | 0.895342i | ||||
\(394\) | 5.20641 | − | 9.01776i | 0.262295 | − | 0.454308i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.01506 | + | 1.75813i | −0.0510085 | + | 0.0883493i | ||||
\(397\) | −11.4874 | + | 19.8968i | −0.576536 | + | 0.998590i | 0.419337 | + | 0.907831i | \(0.362263\pi\) |
−0.995873 | + | 0.0907594i | \(0.971071\pi\) | |||||||
\(398\) | −4.36842 | −0.218969 | ||||||||
\(399\) | −28.4876 | + | 49.3420i | −1.42617 | + | 2.47019i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.18667 | + | 3.78742i | 0.109197 | + | 0.189135i | 0.915445 | − | 0.402443i | \(-0.131839\pi\) |
−0.806248 | + | 0.591577i | \(0.798505\pi\) | |||||||
\(402\) | −18.6637 | −0.930861 | ||||||||
\(403\) | −19.5358 | + | 15.5431i | −0.973147 | + | 0.774256i | ||||
\(404\) | 1.45875 | 0.0725756 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.6637 | − | 30.5944i | −0.876635 | − | 1.51838i | ||||
\(407\) | −2.67775 | + | 4.63801i | −0.132731 | + | 0.229897i | ||||
\(408\) | 2.90321 | 0.143730 | ||||||||
\(409\) | 1.88493 | − | 3.26479i | 0.0932038 | − | 0.161434i | −0.815654 | − | 0.578540i | \(-0.803623\pi\) |
0.908858 | + | 0.417107i | \(0.136956\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.7511 | −1.61549 | ||||||||
\(412\) | 5.12222 | − | 8.87194i | 0.252353 | − | 0.437089i | ||||
\(413\) | 14.0207 | + | 24.2846i | 0.689916 | + | 1.19497i | ||||
\(414\) | −2.04371 | − | 3.53981i | −0.100443 | − | 0.173972i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.533338 | + | 3.56589i | 0.0261491 | + | 0.174832i | ||||
\(417\) | −28.1082 | −1.37646 | ||||||||
\(418\) | 3.51582 | + | 6.08958i | 0.171964 | + | 0.297851i | ||||
\(419\) | −3.72615 | − | 6.45388i | −0.182034 | − | 0.315293i | 0.760539 | − | 0.649292i | \(-0.224935\pi\) |
−0.942573 | + | 0.334000i | \(0.891602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6751 | 1.34880 | 0.674400 | − | 0.738366i | \(-0.264402\pi\) | ||||
0.674400 | + | 0.738366i | \(0.264402\pi\) | |||||||
\(422\) | −2.74766 | + | 4.75908i | −0.133754 | + | 0.231669i | ||||
\(423\) | 0.0921041 | − | 0.159529i | 0.00447825 | − | 0.00775657i | ||||
\(424\) | −1.49532 | −0.0726190 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.1383 | + | 29.6844i | 0.830352 | + | 1.43821i | ||||
\(427\) | 15.3931 | + | 26.6616i | 0.744923 | + | 1.29024i | ||||
\(428\) | −2.21432 | −0.107033 | ||||||||
\(429\) | 1.25973 | + | 8.42249i | 0.0608201 | + | 0.406642i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.84468 | − | 17.0515i | −0.474202 | − | 0.821342i | 0.525362 | − | 0.850879i | \(-0.323930\pi\) |
−0.999564 | + | 0.0295373i | \(0.990597\pi\) | |||||||
\(432\) | 1.21432 | + | 2.10326i | 0.0584240 | + | 0.101193i | ||||
\(433\) | 6.87310 | − | 11.9046i | 0.330300 | − | 0.572097i | −0.652270 | − | 0.757986i | \(-0.726183\pi\) |
0.982571 | + | 0.185890i | \(0.0595167\pi\) | |||||||
\(434\) | 27.0257 | 1.29727 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0666765 | + | 0.115487i | −0.00319323 | + | 0.00553083i | ||||
\(437\) | −14.1575 | −0.677244 | ||||||||
\(438\) | 16.9978 | − | 29.4410i | 0.812185 | − | 1.40675i | ||||
\(439\) | −20.9114 | − | 36.2195i | −0.998045 | − | 1.72866i | −0.553151 | − | 0.833081i | \(-0.686575\pi\) |
−0.444894 | − | 0.895583i | \(-0.646758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.6731 | 0.746337 | ||||||||
\(442\) | 3.69926 | − | 2.94321i | 0.175956 | − | 0.139994i | ||||
\(443\) | −23.6829 | −1.12521 | −0.562605 | − | 0.826726i | \(-0.690201\pi\) | ||||
−0.562605 | + | 0.826726i | \(0.690201\pi\) | |||||||
\(444\) | −5.55877 | − | 9.62806i | −0.263807 | − | 0.456928i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.0484 | − | 17.4043i | 0.475805 | − | 0.824119i | ||||
\(447\) | 16.1334 | 0.763081 | ||||||||
\(448\) | 1.95161 | − | 3.38028i | 0.0922047 | − | 0.159703i | ||||
\(449\) | −3.52789 | + | 6.11048i | −0.166491 | + | 0.288371i | −0.937184 | − | 0.348836i | \(-0.886577\pi\) |
0.770693 | + | 0.637207i | \(0.219910\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17553 | − | 5.50018i | 0.149530 | − | 0.258993i | ||||
\(452\) | 7.00000 | + | 12.1244i | 0.329252 | + | 0.570282i | ||||
\(453\) | −22.2630 | − | 38.5606i | −1.04600 | − | 1.81173i | ||||
\(454\) | 19.3590 | 0.908565 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.5970 | −0.683568 | ||||||||
\(457\) | 17.8398 | + | 30.8994i | 0.834509 | + | 1.44541i | 0.894430 | + | 0.447209i | \(0.147582\pi\) |
−0.0599208 | + | 0.998203i | \(0.519085\pi\) | |||||||
\(458\) | −7.86273 | − | 13.6186i | −0.367401 | − | 0.636358i | ||||
\(459\) | 1.59210 | − | 2.75761i | 0.0743131 | − | 0.128714i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.30074 | − | 12.6452i | 0.340029 | − | 0.588948i | −0.644409 | − | 0.764681i | \(-0.722896\pi\) |
0.984438 | + | 0.175734i | \(0.0562297\pi\) | |||||||
\(462\) | 4.60962 | − | 7.98410i | 0.214459 | − | 0.371454i | ||||
\(463\) | 30.7511 | 1.42913 | 0.714563 | − | 0.699571i | \(-0.246626\pi\) | ||||
0.714563 | + | 0.699571i | \(0.246626\pi\) | |||||||
\(464\) | 4.52543 | − | 7.83827i | 0.210088 | − | 0.363883i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.44123 | + | 12.8886i | 0.344709 | + | 0.597053i | ||||
\(467\) | −20.5620 | −0.951496 | −0.475748 | − | 0.879582i | \(-0.657822\pi\) | ||||
−0.475748 | + | 0.879582i | \(0.657822\pi\) | |||||||
\(468\) | −6.38493 | − | 2.51426i | −0.295143 | − | 0.116221i | ||||
\(469\) | 32.8988 | 1.51912 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.19680 | + | 3.80497i | 0.101223 | + | 0.175324i | ||||
\(472\) | −3.59210 | + | 6.22171i | −0.165340 | + | 0.286377i | ||||
\(473\) | 2.13335 | 0.0980917 | ||||||||
\(474\) | −4.76271 | + | 8.24926i | −0.218759 | + | 0.378901i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.11753 | −0.234562 | ||||||||
\(477\) | 1.42295 | − | 2.46462i | 0.0651525 | − | 0.112847i | ||||
\(478\) | −2.21109 | − | 3.82973i | −0.101133 | − | 0.175168i | ||||
\(479\) | −5.96666 | − | 10.3346i | −0.272624 | − | 0.472198i | 0.696909 | − | 0.717159i | \(-0.254558\pi\) |
−0.969533 | + | 0.244961i | \(0.921225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8437 | − | 6.63270i | −0.768006 | − | 0.302425i | ||||
\(482\) | −11.2810 | −0.513835 | ||||||||
\(483\) | 9.28100 | + | 16.0752i | 0.422300 | + | 0.731445i | ||||
\(484\) | 4.93110 | + | 8.54092i | 0.224141 | + | 0.388223i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17.2652 | −0.783164 | ||||||||
\(487\) | 13.9859 | − | 24.2244i | 0.633764 | − | 1.09771i | −0.353012 | − | 0.935619i | \(-0.614842\pi\) |
0.986776 | − | 0.162092i | \(-0.0518242\pi\) | |||||||
\(488\) | −3.94370 | + | 6.83068i | −0.178523 | + | 0.309210i | ||||
\(489\) | −10.4143 | −0.470953 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3906 | + | 17.9971i | 0.468922 | + | 0.812197i | 0.999369 | − | 0.0355214i | \(-0.0113092\pi\) |
−0.530447 | + | 0.847718i | \(0.677976\pi\) | |||||||
\(492\) | 6.59210 | + | 11.4179i | 0.297195 | + | 0.514757i | ||||
\(493\) | −11.8666 | −0.534447 | ||||||||
\(494\) | −18.5995 | + | 14.7981i | −0.836830 | + | 0.665800i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.46198 | + | 5.99632i | 0.155447 | + | 0.269243i | ||||
\(497\) | −30.2099 | − | 52.3250i | −1.35510 | − | 2.34710i | ||||
\(498\) | −10.7326 | + | 18.5894i | −0.480939 | + | 0.833011i | ||||
\(499\) | 34.2908 | 1.53507 | 0.767534 | − | 0.641008i | \(-0.221483\pi\) | ||||
0.767534 | + | 0.641008i | \(0.221483\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7343 | − | 18.5923i | 0.479573 | − | 0.830645i | ||||
\(502\) | 2.65233 | 0.118379 | ||||||||
\(503\) | 10.1128 | − | 17.5160i | 0.450910 | − | 0.780998i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.998443 | + | 0.0557857i | \(0.0177663\pi\) | |||||||
\(504\) | 3.71432 | + | 6.43339i | 0.165449 | + | 0.286566i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.29084 | 0.101840 | ||||||||
\(507\) | −27.5264 | + | 8.42249i | −1.22249 | + | 0.374056i | ||||
\(508\) | 9.99063 | 0.443263 | ||||||||
\(509\) | 13.6889 | + | 23.7099i | 0.606749 | + | 1.05092i | 0.991772 | + | 0.128014i | \(0.0408602\pi\) |
−0.385023 | + | 0.922907i | \(0.625806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.9622 | + | 51.8961i | −1.32545 | + | 2.29575i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −8.00492 | + | 13.8649i | −0.353426 | + | 0.612152i | ||||
\(514\) | −2.05086 | + | 3.55219i | −0.0904593 | + | 0.156680i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.21432 | + | 3.83531i | −0.0974800 | + | 0.168840i | ||||
\(517\) | 0.0516208 | + | 0.0894098i | 0.00227028 | + | 0.00393224i | ||||
\(518\) | 9.79851 | + | 16.9715i | 0.430522 | + | 0.745686i | ||||
\(519\) | 53.3022 | 2.33971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.2034 | −1.36705 | −0.683523 | − | 0.729929i | \(-0.739553\pi\) | ||||
−0.683523 | + | 0.729929i | \(0.739553\pi\) | |||||||
\(522\) | 8.61285 | + | 14.9179i | 0.376974 | + | 0.652938i | ||||
\(523\) | 4.92396 | + | 8.52854i | 0.215310 | + | 0.372927i | 0.953368 | − | 0.301809i | \(-0.0975906\pi\) |
−0.738059 | + | 0.674736i | \(0.764257\pi\) | |||||||
\(524\) | −4.62790 | + | 8.01576i | −0.202171 | + | 0.350170i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.40099 | − | 9.35479i | 0.235494 | − | 0.407888i | ||||
\(527\) | 4.53903 | − | 7.86182i | 0.197723 | − | 0.342466i | ||||
\(528\) | 2.36196 | 0.102791 | ||||||||
\(529\) | 9.19381 | − | 15.9242i | 0.399731 | − | 0.692355i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83654 | − | 11.8412i | −0.296680 | − | 0.513865i | ||||
\(532\) | 25.7304 | 1.11555 | ||||||||
\(533\) | 19.9748 | + | 7.86567i | 0.865205 | + | 0.340700i | ||||
\(534\) | 10.0207 | 0.433640 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.21432 | + | 7.29942i | 0.182031 | + | 0.315287i | ||||
\(537\) | −3.37778 | + | 5.85049i | −0.145762 | + | 0.252467i | ||||
\(538\) | −18.5827 | −0.801159 | ||||||||
\(539\) | −4.39207 | + | 7.60730i | −0.189180 | + | 0.327669i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.6149 | 1.78916 | 0.894581 | − | 0.446905i | \(-0.147474\pi\) | ||||
0.894581 | + | 0.446905i | \(0.147474\pi\) | |||||||
\(542\) | −9.88739 | + | 17.1255i | −0.424700 | + | 0.735602i | ||||
\(543\) | −11.7835 | − | 20.4095i | −0.505677 | − | 0.875857i | ||||
\(544\) | −0.655554 | − | 1.13545i | −0.0281066 | − | 0.0486821i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 28.9956 | + | 11.4179i | 1.24090 | + | 0.488639i | ||||
\(547\) | 6.77430 | 0.289648 | 0.144824 | − | 0.989457i | \(-0.453738\pi\) | ||||
0.144824 | + | 0.989457i | \(0.453738\pi\) | |||||||
\(548\) | 7.39530 | + | 12.8090i | 0.315912 | + | 0.547175i | ||||
\(549\) | −7.50569 | − | 13.0002i | −0.320335 | − | 0.554836i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 59.6642 | 2.54178 | ||||||||
\(552\) | −2.37778 | + | 4.11844i | −0.101205 | + | 0.175293i | ||||
\(553\) | 8.39530 | − | 14.5411i | 0.357005 | − | 0.618350i | ||||
\(554\) | 0.204952 | 0.00870757 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.34691 | + | 10.9932i | 0.269169 | + | 0.466214i | ||||
\(557\) | −12.7225 | − | 22.0360i | −0.539068 | − | 0.933694i | −0.998954 | − | 0.0457158i | \(-0.985443\pi\) |
0.459886 | − | 0.887978i | \(-0.347890\pi\) | |||||||
\(558\) | −13.1778 | −0.557859 | ||||||||
\(559\) | 1.06668 | + | 7.13177i | 0.0451156 | + | 0.301642i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.54839 | − | 2.68190i | −0.0653732 | − | 0.113230i | ||||
\(562\) | 10.2279 | + | 17.7153i | 0.431439 | + | 0.747274i | ||||
\(563\) | −6.59210 | + | 11.4179i | −0.277824 | + | 0.481205i | −0.970844 | − | 0.239713i | \(-0.922947\pi\) |
0.693020 | + | 0.720919i | \(0.256280\pi\) | |||||||
\(564\) | −0.214320 | −0.00902449 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.719004 | + | 1.24535i | −0.0302220 | + | 0.0523460i | ||||
\(567\) | 43.2766 | 1.81744 | ||||||||
\(568\) | 7.73975 | − | 13.4056i | 0.324753 | − | 0.562488i | ||||
\(569\) | 12.2304 | + | 21.1836i | 0.512724 | + | 0.888064i | 0.999891 | + | 0.0147555i | \(0.00469698\pi\) |
−0.487167 | + | 0.873309i | \(0.661970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3526 | 1.01912 | 0.509562 | − | 0.860434i | \(-0.329807\pi\) | ||||
0.509562 | + | 0.860434i | \(0.329807\pi\) | |||||||
\(572\) | 3.00961 | − | 2.39451i | 0.125838 | − | 0.100119i | ||||
\(573\) | 32.6178 | 1.36263 | ||||||||
\(574\) | −11.6200 | − | 20.1264i | −0.485009 | − | 0.840060i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.951606 | + | 1.64823i | −0.0396502 | + | 0.0686762i | ||||
\(577\) | −42.0479 | −1.75048 | −0.875239 | − | 0.483690i | \(-0.839296\pi\) | ||||
−0.875239 | + | 0.483690i | \(0.839296\pi\) | |||||||
\(578\) | 7.64050 | − | 13.2337i | 0.317803 | − | 0.550451i | ||||
\(579\) | 15.5002 | − | 26.8472i | 0.644168 | − | 1.11573i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.9185 | − | 32.7678i | 0.784872 | − | 1.35944i | ||||
\(582\) | 4.71678 | + | 8.16970i | 0.195517 | + | 0.338645i | ||||
\(583\) | 0.797509 | + | 1.38133i | 0.0330295 | + | 0.0572087i | ||||
\(584\) | −15.3526 | −0.635295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.9146 | −0.863974 | ||||||||
\(587\) | 3.67307 | + | 6.36195i | 0.151604 | + | 0.262586i | 0.931817 | − | 0.362928i | \(-0.118223\pi\) |
−0.780213 | + | 0.625513i | \(0.784890\pi\) | |||||||
\(588\) | −9.11753 | − | 15.7920i | −0.376001 | − | 0.651252i | ||||
\(589\) | −22.8217 | + | 39.5284i | −0.940353 | + | 1.62874i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5287 | − | 19.9682i | 0.474225 | − | 0.821383i | ||||
\(592\) | −2.51037 | + | 4.34809i | −0.103176 | + | 0.178705i | ||||
\(593\) | 4.19358 | 0.172210 | 0.0861048 | − | 0.996286i | \(-0.472558\pi\) | ||||
0.0861048 | + | 0.996286i | \(0.472558\pi\) | |||||||
\(594\) | 1.29529 | − | 2.24350i | 0.0531462 | − | 0.0920520i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.64296 | − | 6.30979i | −0.149221 | − | 0.258459i | ||||
\(597\) | −9.67307 | −0.395892 | ||||||||
\(598\) | 1.14542 | + | 7.65825i | 0.0468397 | + | 0.313169i | ||||
\(599\) | 9.33630 | 0.381471 | 0.190735 | − | 0.981641i | \(-0.438913\pi\) | ||||
0.190735 | + | 0.981641i | \(0.438913\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.48571 | + | 2.57333i | 0.0606034 | + | 0.104968i | 0.894735 | − | 0.446597i | \(-0.147364\pi\) |
−0.834132 | + | 0.551565i | \(0.814031\pi\) | |||||||
\(602\) | 3.90321 | − | 6.76056i | 0.159083 | − | 0.275540i | ||||
\(603\) | −16.0415 | −0.653260 | ||||||||
\(604\) | −10.0541 | + | 17.4142i | −0.409095 | + | 0.708573i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.23014 | 0.131216 | ||||||||
\(607\) | 8.57160 | − | 14.8464i | 0.347910 | − | 0.602599i | −0.637968 | − | 0.770063i | \(-0.720225\pi\) |
0.985878 | + | 0.167465i | \(0.0535580\pi\) | |||||||
\(608\) | 3.29605 | + | 5.70893i | 0.133673 | + | 0.231528i | ||||
\(609\) | −39.1131 | − | 67.7459i | −1.58494 | − | 2.74520i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.273086 | + | 0.217273i | −0.0110479 | + | 0.00878991i | ||||
\(612\) | 2.49532 | 0.100867 | ||||||||
\(613\) | 14.6422 | + | 25.3610i | 0.591393 | + | 1.02432i | 0.994045 | + | 0.108969i | \(0.0347550\pi\) |
−0.402653 | + | 0.915353i | \(0.631912\pi\) | |||||||
\(614\) | −6.26517 | − | 10.8516i | −0.252842 | − | 0.437935i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.16346 | −0.167751 | ||||||||
\(617\) | 6.60793 | − | 11.4453i | 0.266025 | − | 0.460769i | −0.701807 | − | 0.712368i | \(-0.747623\pi\) |
0.967832 | + | 0.251599i | \(0.0809563\pi\) | |||||||
\(618\) | 11.3422 | − | 19.6453i | 0.456251 | − | 0.790250i | ||||
\(619\) | −18.9333 | −0.760995 | −0.380497 | − | 0.924782i | \(-0.624247\pi\) | ||||
−0.380497 | + | 0.924782i | \(0.624247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.60793 | + | 4.51706i | 0.104652 | + | 0.181263i | ||||
\(622\) | 4.89062 | + | 8.47080i | 0.196096 | + | 0.339648i | ||||
\(623\) | −17.6637 | −0.707681 | ||||||||
\(624\) | 1.18098 | + | 7.89601i | 0.0472771 | + | 0.316094i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.60639 | − | 14.9067i | −0.343981 | − | 0.595792i | ||||
\(627\) | 7.78515 | + | 13.4843i | 0.310909 | + | 0.538510i | ||||
\(628\) | 0.992089 | − | 1.71835i | 0.0395887 | − | 0.0685696i | ||||
\(629\) | 6.58274 | 0.262471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.21432 | + | 2.10326i | −0.0483413 | + | 0.0837296i | −0.889184 | − | 0.457551i | \(-0.848727\pi\) |
0.840842 | + | 0.541280i | \(0.182060\pi\) | |||||||
\(632\) | 4.30174 | 0.171114 | ||||||||
\(633\) | −6.08419 | + | 10.5381i | −0.241825 | + | 0.418853i | ||||
\(634\) | −6.87233 | − | 11.9032i | −0.272935 | − | 0.472738i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.31111 | −0.131294 | ||||||||
\(637\) | −27.6271 | − | 10.8790i | −1.09463 | − | 0.431042i | ||||
\(638\) | −9.65433 | −0.382219 | ||||||||
\(639\) | 14.7304 | + | 25.5138i | 0.582725 | + | 1.00931i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.54371 | + | 13.0661i | −0.297959 | + | 0.516079i | −0.975669 | − | 0.219250i | \(-0.929639\pi\) |
0.677710 | + | 0.735329i | \(0.262972\pi\) | |||||||
\(642\) | −4.90321 | −0.193514 | ||||||||
\(643\) | 3.35159 | − | 5.80513i | 0.132174 | − | 0.228932i | −0.792340 | − | 0.610079i | \(-0.791138\pi\) |
0.924514 | + | 0.381147i | \(0.124471\pi\) | |||||||
\(644\) | 4.19135 | − | 7.25964i | 0.165162 | − | 0.286070i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.32148 | − | 7.48502i | 0.170026 | − | 0.294494i | ||||
\(647\) | −11.1867 | − | 19.3759i | −0.439793 | − | 0.761744i | 0.557880 | − | 0.829922i | \(-0.311615\pi\) |
−0.997673 | + | 0.0681773i | \(0.978282\pi\) | |||||||
\(648\) | 5.54371 | + | 9.60199i | 0.217777 | + | 0.377202i | ||||
\(649\) | 7.66323 | 0.300808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.8435 | 2.34545 | ||||||||
\(652\) | 2.35159 | + | 4.07308i | 0.0920954 | + | 0.159514i | ||||
\(653\) | −8.20641 | − | 14.2139i | −0.321142 | − | 0.556234i | 0.659582 | − | 0.751632i | \(-0.270733\pi\) |
−0.980724 | + | 0.195399i | \(0.937400\pi\) | |||||||
\(654\) | −0.147643 | + | 0.255726i | −0.00577331 | + | 0.00999966i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.97703 | − | 5.15637i | 0.116234 | − | 0.201323i | ||||
\(657\) | 14.6096 | − | 25.3046i | 0.569976 | − | 0.987227i | ||||
\(658\) | 0.377784 | 0.0147276 | ||||||||
\(659\) | −4.33407 | + | 7.50684i | −0.168832 | + | 0.292425i | −0.938009 | − | 0.346610i | \(-0.887333\pi\) |
0.769178 | + | 0.639035i | \(0.220666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.71509 | − | 15.0950i | −0.338978 | − | 0.587126i | 0.645263 | − | 0.763960i | \(-0.276748\pi\) |
−0.984241 | + | 0.176834i | \(0.943414\pi\) | |||||||
\(662\) | 19.3876 | 0.753522 | ||||||||
\(663\) | 8.19135 | − | 6.51721i | 0.318126 | − | 0.253108i | ||||
\(664\) | 9.69381 | 0.376193 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.77777 | − | 8.27534i | −0.185135 | − | 0.320663i | ||||
\(667\) | 9.71900 | − | 16.8338i | 0.376321 | − | 0.651808i | ||||
\(668\) | −9.69535 | −0.375124 | ||||||||
\(669\) | 22.2504 | − | 38.5387i | 0.860249 | − | 1.48999i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.41329 | 0.324792 | ||||||||
\(672\) | 4.32148 | − | 7.48502i | 0.166705 | − | 0.288741i | ||||
\(673\) | −20.2415 | − | 35.0593i | −0.780253 | − | 1.35144i | −0.931794 | − | 0.362987i | \(-0.881757\pi\) |
0.151541 | − | 0.988451i | \(-0.451576\pi\) | |||||||
\(674\) | −0.277770 | − | 0.481111i | −0.0106993 | − | 0.0185317i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.50961 | + | 8.86382i | 0.365754 | + | 0.340916i | ||||
\(677\) | 40.0228 | 1.53820 | 0.769100 | − | 0.639129i | \(-0.220705\pi\) | ||||
0.769100 | + | 0.639129i | \(0.220705\pi\) | |||||||
\(678\) | 15.5002 | + | 26.8472i | 0.595283 | + | 1.03106i | ||||
\(679\) | −8.31433 | − | 14.4008i | −0.319075 | − | 0.552654i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.8671 | 1.64267 | ||||||||
\(682\) | 3.69281 | − | 6.39614i | 0.141405 | − | 0.244921i | ||||
\(683\) | −21.6543 | + | 37.5064i | −0.828580 | + | 1.43514i | 0.0705721 | + | 0.997507i | \(0.477518\pi\) |
−0.899152 | + | 0.437636i | \(0.855816\pi\) | |||||||
\(684\) | −12.5462 | −0.479715 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.41036 | + | 4.17486i | 0.0920279 | + | 0.159397i | ||||
\(687\) | −17.4106 | − | 30.1560i | −0.664256 | − | 1.15052i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | −4.21900 | + | 3.35673i | −0.160731 | + | 0.127881i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1741 | − | 24.5502i | −0.539207 | − | 0.933934i | −0.998947 | − | 0.0458806i | \(-0.985391\pi\) |
0.459740 | − | 0.888054i | \(-0.347943\pi\) | |||||||
\(692\) | −12.0358 | − | 20.8466i | −0.457532 | − | 0.792469i | ||||
\(693\) | 3.96198 | − | 6.86235i | 0.150503 | − | 0.260679i | ||||
\(694\) | 6.68445 | 0.253738 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.0207 | − | 17.3564i | 0.379835 | − | 0.657894i | ||||
\(697\) | −7.80642 | −0.295689 | ||||||||
\(698\) | −5.29137 | + | 9.16492i | −0.200281 | + | 0.346897i | ||||
\(699\) | 16.4773 | + | 28.5395i | 0.623228 | + | 1.07946i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.8080 | 0.483750 | 0.241875 | − | 0.970307i | \(-0.422238\pi\) | ||||
0.241875 | + | 0.970307i | \(0.422238\pi\) | |||||||
\(702\) | 8.14764 | + | 3.20838i | 0.307513 | + | 0.121092i | ||||
\(703\) | −33.0973 | −1.24829 | ||||||||
\(704\) | −0.533338 | − | 0.923769i | −0.0201009 | − | 0.0348159i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.60470 | − | 7.97557i | 0.173300 | − | 0.300165i | ||||
\(707\) | −5.69381 | −0.214138 | ||||||||
\(708\) | −7.95407 | + | 13.7768i | −0.298932 | + | 0.517766i | ||||
\(709\) | −1.26126 | + | 2.18456i | −0.0473675 | + | 0.0820429i | −0.888737 | − | 0.458417i | \(-0.848417\pi\) |
0.841370 | + | 0.540460i | \(0.181750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.09356 | + | 7.09026i | −0.153521 | + | 0.265905i | ||||
\(712\) | −2.26271 | − | 3.91914i | −0.0847988 | − | 0.146876i | ||||
\(713\) | 7.43509 | + | 12.8780i | 0.278446 | + | 0.482283i | ||||
\(714\) | −11.3319 | −0.424084 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.05086 | 0.114016 | ||||||||
\(717\) | −4.89607 | − | 8.48024i | −0.182847 | − | 0.316700i | ||||
\(718\) | 2.09679 | + | 3.63174i | 0.0782514 | + | 0.135535i | ||||
\(719\) | −8.51114 | + | 14.7417i | −0.317412 | + | 0.549773i | −0.979947 | − | 0.199257i | \(-0.936147\pi\) |
0.662535 | + | 0.749031i | \(0.269480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.9931 | + | 34.6291i | −0.744582 | + | 1.28965i | ||||
\(722\) | −12.2279 | + | 21.1794i | −0.455076 | + | 0.788215i | ||||
\(723\) | −24.9797 | −0.929006 | ||||||||
\(724\) | −5.32148 | + | 9.21707i | −0.197771 | + | 0.342550i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.9190 | + | 18.9123i | 0.405243 | + | 0.701902i | ||||
\(727\) | −30.5353 | −1.13249 | −0.566245 | − | 0.824237i | \(-0.691605\pi\) | ||||
−0.566245 | + | 0.824237i | \(0.691605\pi\) | |||||||
\(728\) | −2.08173 | − | 13.9184i | −0.0771541 | − | 0.515851i | ||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.31111 | − | 2.27091i | −0.0484931 | − | 0.0839925i | ||||
\(732\) | −8.73260 | + | 15.1253i | −0.322766 | + | 0.559048i | ||||
\(733\) | 24.4499 | 0.903076 | 0.451538 | − | 0.892252i | \(-0.350876\pi\) | ||||
0.451538 | + | 0.892252i | \(0.350876\pi\) | |||||||
\(734\) | −6.98418 | + | 12.0970i | −0.257791 | + | 0.446507i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.14764 | 0.0791632 | ||||||||
\(737\) | 4.49532 | − | 7.78612i | 0.165587 | − | 0.286805i | ||||
\(738\) | 5.66593 | + | 9.81367i | 0.208566 | + | 0.361246i | ||||
\(739\) | 5.39776 | + | 9.34920i | 0.198560 | + | 0.343916i | 0.948062 | − | 0.318086i | \(-0.103040\pi\) |
−0.749502 | + | 0.662002i | \(0.769707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.1852 | + | 32.7678i | −1.51298 | + | 1.20376i | ||||
\(742\) | 5.83654 | 0.214266 | ||||||||
\(743\) | −14.9677 | − | 25.9248i | −0.549110 | − | 0.951087i | −0.998336 | − | 0.0576686i | \(-0.981633\pi\) |
0.449225 | − | 0.893418i | \(-0.351700\pi\) | |||||||
\(744\) | 7.66593 | + | 13.2778i | 0.281046 | + | 0.486787i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.8479 | 0.433783 | ||||||||
\(747\) | −9.22469 | + | 15.9776i | −0.337514 | + | 0.584591i | ||||
\(748\) | −0.699264 | + | 1.21116i | −0.0255676 | + | 0.0442844i | ||||
\(749\) | 8.64296 | 0.315807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.4588 | − | 23.3112i | −0.491117 | − | 0.850639i | 0.508831 | − | 0.860866i | \(-0.330078\pi\) |
−0.999948 | + | 0.0102272i | \(0.996745\pi\) | |||||||
\(752\) | 0.0483940 | + | 0.0838209i | 0.00176475 | + | 0.00305663i | ||||
\(753\) | 5.87310 | 0.214028 | ||||||||
\(754\) | −4.82717 | − | 32.2743i | −0.175795 | − | 1.17536i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.73975 | − | 8.20948i | −0.172383 | − | 0.298576i | ||||
\(757\) | 17.9533 | + | 31.0960i | 0.652524 | + | 1.13020i | 0.982508 | + | 0.186218i | \(0.0596231\pi\) |
−0.329985 | + | 0.943986i | \(0.607044\pi\) | |||||||
\(758\) | −0.303197 | + | 0.525153i | −0.0110126 | + | 0.0190744i | ||||
\(759\) | 5.07265 | 0.184126 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.2699 | + | 19.5200i | −0.408532 | + | 0.707598i | −0.994725 | − | 0.102573i | \(-0.967293\pi\) |
0.586193 | + | 0.810171i | \(0.300626\pi\) | |||||||
\(762\) | 22.1225 | 0.801412 | ||||||||
\(763\) | 0.260253 | − | 0.450771i | 0.00942178 | − | 0.0163190i | ||||
\(764\) | −7.36519 | − | 12.7569i | −0.266463 | − | 0.461528i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.7797 | −1.25664 | ||||||||
\(767\) | 3.83161 | + | 25.6181i | 0.138352 | + | 0.925015i | ||||
\(768\) | 2.21432 | 0.0799024 | ||||||||
\(769\) | −1.23729 | − | 2.14304i | −0.0446177 | − | 0.0772801i | 0.842854 | − | 0.538142i | \(-0.180874\pi\) |
−0.887472 | + | 0.460862i | \(0.847540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.54125 | + | 7.86567i | −0.163549 | + | 0.283275i | ||||
\(772\) | −14.0000 | −0.503871 | ||||||||
\(773\) | 22.1003 | − | 38.2788i | 0.794891 | − | 1.37679i | −0.128018 | − | 0.991772i | \(-0.540861\pi\) |
0.922908 | − | 0.385019i | \(-0.125805\pi\) | |||||||
\(774\) | −1.90321 | + | 3.29646i | −0.0684095 | + | 0.118489i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.13013 | − | 3.68949i | 0.0764671 | − | 0.132445i | ||||
\(777\) | 21.6970 | + | 37.5804i | 0.778377 | + | 1.34819i | ||||
\(778\) | 9.34222 | + | 16.1812i | 0.334935 | + | 0.580124i | ||||
\(779\) | 39.2498 | 1.40627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5116 | −0.590832 | ||||||||
\(782\) | −1.40790 | − | 2.43855i | −0.0503463 | − | 0.0872023i | ||||
\(783\) | −10.9906 | − | 19.0363i | −0.392773 | − | 0.680303i | ||||
\(784\) | −4.11753 | + | 7.13177i | −0.147055 | + | 0.254706i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.2477 | + | 17.7495i | −0.365522 | + | 0.633102i | ||||
\(787\) | −17.0153 | + | 29.4714i | −0.606530 | + | 1.05054i | 0.385278 | + | 0.922801i | \(0.374106\pi\) |
−0.991808 | + | 0.127740i | \(0.959228\pi\) | |||||||
\(788\) | −10.4128 | −0.370941 | ||||||||
\(789\) | 11.9595 | − | 20.7145i | 0.425770 | − | 0.737455i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.3225 | − | 47.3239i | −0.971476 | − | 1.68265i | ||||
\(792\) | 2.03011 | 0.0721369 | ||||||||
\(793\) | 4.20665 | + | 28.1255i | 0.149382 | + | 0.998767i | ||||
\(794\) | 22.9748 | 0.815346 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.18421 | + | 3.78316i | 0.0774172 | + | 0.134091i | ||||
\(797\) | −4.06890 | + | 7.04754i | −0.144128 | + | 0.249637i | −0.929047 | − | 0.369961i | \(-0.879371\pi\) |
0.784919 | + | 0.619598i | \(0.212704\pi\) | |||||||
\(798\) | 56.9753 | 2.01690 | ||||||||
\(799\) | 0.0634498 | − | 0.109898i | 0.00224469 | − | 0.00388792i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.61285 | 0.304320 | ||||||||
\(802\) | 2.18667 | − | 3.78742i | 0.0772140 | − | 0.133739i | ||||
\(803\) | 8.18813 | + | 14.1823i | 0.288953 | + | 0.500481i | ||||
\(804\) | 9.33185 | + | 16.1632i | 0.329109 | + | 0.570034i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.2286 | + | 9.14695i | 0.818193 | + | 0.322188i | ||||
\(807\) | −41.1481 | −1.44848 | ||||||||
\(808\) | −0.729376 | − | 1.26332i | −0.0256593 | − | 0.0444433i | ||||
\(809\) | 3.92618 | + | 6.80034i | 0.138037 | + | 0.239087i | 0.926754 | − | 0.375670i | \(-0.122587\pi\) |
−0.788716 | + | 0.614757i | \(0.789254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.33477 | 0.327788 | 0.163894 | − | 0.986478i | \(-0.447595\pi\) | ||||
0.163894 | + | 0.986478i | \(0.447595\pi\) | |||||||
\(812\) | −17.6637 | + | 30.5944i | −0.619874 | + | 1.07365i | ||||
\(813\) | −21.8938 | + | 37.9213i | −0.767851 | + | 1.32996i | ||||
\(814\) | 5.35551 | 0.187711 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.45161 | − | 2.51426i | −0.0508164 | − | 0.0880165i | ||||
\(817\) | 6.59210 | + | 11.4179i | 0.230629 | + | 0.399460i | ||||
\(818\) | −3.76986 | −0.131810 | ||||||||
\(819\) | 24.9217 | + | 9.81367i | 0.870836 | + | 0.342917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.7659 | + | 41.1638i | 0.829437 | + | 1.43663i | 0.898480 | + | 0.439013i | \(0.144672\pi\) |
−0.0690434 | + | 0.997614i | \(0.521995\pi\) | |||||||
\(822\) | 16.3756 | + | 28.3633i | 0.571163 | + | 0.989284i | ||||
\(823\) | 0.693576 | − | 1.20131i | 0.0241765 | − | 0.0418750i | −0.853684 | − | 0.520791i | \(-0.825637\pi\) |
0.877861 | + | 0.478916i | \(0.158970\pi\) | |||||||
\(824\) | −10.2444 | −0.356882 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.0207 | − | 24.2846i | 0.487844 | − | 0.844971i | ||||
\(827\) | −31.5131 | −1.09582 | −0.547910 | − | 0.836537i | \(-0.684576\pi\) | ||||
−0.547910 | + | 0.836537i | \(0.684576\pi\) | |||||||
\(828\) | −2.04371 | + | 3.53981i | −0.0710238 | + | 0.123017i | ||||
\(829\) | 14.4128 | + | 24.9637i | 0.500578 | + | 0.867026i | 1.00000 | 0.000667386i | \(0.000212436\pi\) | |
−0.499422 | + | 0.866359i | \(0.666454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.453829 | 0.0157431 | ||||||||
\(832\) | 2.82148 | − | 2.24483i | 0.0978172 | − | 0.0778254i | ||||
\(833\) | 10.7971 | 0.374096 | ||||||||
\(834\) | 14.0541 | + | 24.3424i | 0.486653 | + | 0.842908i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.51582 | − | 6.08958i | 0.121597 | − | 0.210613i | ||||
\(837\) | 16.8158 | 0.581239 | ||||||||
\(838\) | −3.72615 | + | 6.45388i | −0.128718 | + | 0.222946i | ||||
\(839\) | −4.21755 | + | 7.30500i | −0.145606 | + | 0.252197i | −0.929599 | − | 0.368573i | \(-0.879846\pi\) |
0.783993 | + | 0.620770i | \(0.213180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4590 | + | 45.8283i | −0.912379 | + | 1.58029i | ||||
\(842\) | −13.8375 | − | 23.9673i | −0.476873 | − | 0.825968i | ||||
\(843\) | 22.6479 | + | 39.2273i | 0.780034 | + | 1.35106i | ||||
\(844\) | 5.49532 | 0.189157 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.184208 | −0.00633321 | ||||||||
\(847\) | −19.2471 | − | 33.3370i | −0.661339 | − | 1.14547i | ||||
\(848\) | 0.747658 | + | 1.29498i | 0.0256747 | + | 0.0444699i | ||||
\(849\) | −1.59210 | + | 2.75761i | −0.0546409 | + | 0.0946408i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.39138 | + | 9.33815i | −0.184814 | + | 0.320108i | ||||
\(852\) | 17.1383 | − | 29.6844i | 0.587148 | − | 1.01697i | ||||
\(853\) | −40.0656 | −1.37182 | −0.685910 | − | 0.727686i | \(-0.740596\pi\) | ||||
−0.685910 | + | 0.727686i | \(0.740596\pi\) | |||||||
\(854\) | 15.3931 | − | 26.6616i | 0.526740 | − | 0.912341i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.10716 | + | 1.91766i | 0.0378419 | + | 0.0655442i | ||||
\(857\) | 32.0479 | 1.09474 | 0.547368 | − | 0.836892i | \(-0.315630\pi\) | ||||
0.547368 | + | 0.836892i | \(0.315630\pi\) | |||||||
\(858\) | 6.66423 | − | 5.30220i | 0.227513 | − | 0.181014i | ||||
\(859\) | −26.6894 | −0.910630 | −0.455315 | − | 0.890331i | \(-0.650473\pi\) | ||||
−0.455315 | + | 0.890331i | \(0.650473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.7304 | − | 44.5663i | −0.876889 | − | 1.51882i | ||||
\(862\) | −9.84468 | + | 17.0515i | −0.335311 | + | 0.580776i | ||||
\(863\) | 30.6593 | 1.04365 | 0.521827 | − | 0.853052i | \(-0.325251\pi\) | ||||
0.521827 | + | 0.853052i | \(0.325251\pi\) | |||||||
\(864\) | 1.21432 | − | 2.10326i | 0.0413120 | − | 0.0715545i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.7462 | −0.467115 | ||||||||
\(867\) | 16.9185 | − | 29.3037i | 0.574583 | − | 0.995206i | ||||
\(868\) | −13.5128 | − | 23.4049i | −0.458655 | − | 0.794415i | ||||
\(869\) | −2.29428 | − | 3.97381i | −0.0778282 | − | 0.134802i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2766 | + | 11.1347i | 0.958114 | + | 0.377286i | ||||
\(872\) | 0.133353 | 0.00451591 | ||||||||
\(873\) | 4.05408 | + | 7.02188i | 0.137210 | + | 0.237654i | ||||
\(874\) | 7.07874 | + | 12.2607i | 0.239442 | + | 0.414726i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.9956 | −1.14860 | ||||||||
\(877\) | −10.4652 | + | 18.1263i | −0.353385 | + | 0.612081i | −0.986840 | − | 0.161699i | \(-0.948303\pi\) |
0.633455 | + | 0.773779i | \(0.281636\pi\) | |||||||
\(878\) | −20.9114 | + | 36.2195i | −0.705724 | + | 1.22235i | ||||
\(879\) | −46.3116 | −1.56205 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.7351 | − | 18.5937i | −0.361673 | − | 0.626437i | 0.626563 | − | 0.779371i | \(-0.284461\pi\) |
−0.988236 | + | 0.152934i | \(0.951128\pi\) | |||||||
\(882\) | −7.83654 | − | 13.5733i | −0.263870 | − | 0.457036i | ||||
\(883\) | −7.73530 | −0.260314 | −0.130157 | − | 0.991493i | \(-0.541548\pi\) | ||||
−0.130157 | + | 0.991493i | \(0.541548\pi\) | |||||||
\(884\) | −4.39853 | − | 1.73205i | −0.147939 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.8415 | + | 20.5100i | 0.397822 | + | 0.689047i | ||||
\(887\) | 24.2232 | + | 41.9559i | 0.813337 | + | 1.40874i | 0.910516 | + | 0.413473i | \(0.135685\pi\) |
−0.0971796 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(888\) | −5.55877 | + | 9.62806i | −0.186540 | + | 0.323097i | ||||
\(889\) | −38.9956 | −1.30787 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.91335 | − | 10.2422i | 0.198105 | − | 0.343127i | ||||
\(892\) | −20.0968 | −0.672890 | ||||||||
\(893\) | −0.319019 | + | 0.552556i | −0.0106755 | + | 0.0184906i | ||||
\(894\) | −8.06668 | − | 13.9719i | −0.269790 | − | 0.467290i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.90321 | −0.130397 | ||||||||
\(897\) | 2.53633 | + | 16.9578i | 0.0846855 | + | 0.566205i | ||||
\(898\) | 7.05578 | 0.235454 | ||||||||
\(899\) | −31.3339 | − | 54.2718i | −1.04504 | − | 1.81007i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.980260 | − | 1.69786i | 0.0326572 | − | 0.0565639i | ||||
\(902\) | −6.35106 | −0.211467 | ||||||||
\(903\) | 8.64296 | − | 14.9700i | 0.287620 | − | 0.498172i | ||||
\(904\) | 7.00000 | − | 12.1244i | 0.232817 | − | 0.403250i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22.2630 | + | 38.5606i | −0.739637 | + | 1.28109i | ||||
\(907\) | −6.00545 | − | 10.4017i | −0.199408 | − | 0.345384i | 0.748929 | − | 0.662650i | \(-0.230568\pi\) |
−0.948337 | + | 0.317266i | \(0.897235\pi\) | |||||||
\(908\) | −9.67952 | − | 16.7654i | −0.321226 | − | 0.556380i | ||||
\(909\) | 2.77631 | 0.0920845 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.10171 | −0.268422 | −0.134211 | − | 0.990953i | \(-0.542850\pi\) | ||||
−0.134211 | + | 0.990953i | \(0.542850\pi\) | |||||||
\(912\) | 7.29851 | + | 12.6414i | 0.241678 | + | 0.418598i | ||||
\(913\) | −5.17008 | − | 8.95485i | −0.171105 | − | 0.296362i | ||||
\(914\) | 17.8398 | − | 30.8994i | 0.590087 | − | 1.02206i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.86273 | + | 13.6186i | −0.259792 | + | 0.449973i | ||||
\(917\) | 18.0637 | − | 31.2872i | 0.596516 | − | 1.03320i | ||||
\(918\) | −3.18421 | −0.105095 | ||||||||
\(919\) | −8.29682 | + | 14.3705i | −0.273687 | + | 0.474039i | −0.969803 | − | 0.243890i | \(-0.921576\pi\) |
0.696116 | + | 0.717929i | \(0.254910\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.8731 | − | 24.0289i | −0.457134 | − | 0.791780i | ||||
\(922\) | −14.6015 | −0.480874 | ||||||||
\(923\) | −8.25581 | − | 55.1981i | −0.271743 | − | 1.81687i | ||||
\(924\) | −9.21924 | −0.303291 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.3756 | − | 26.6313i | −0.505272 | − | 0.875157i | ||||
\(927\) | 9.74866 | − | 16.8852i | 0.320188 | − | 0.554582i | ||||
\(928\) | −9.05086 | −0.297109 | ||||||||
\(929\) | −28.5605 | + | 49.4682i | −0.937038 | + | 1.62300i | −0.166080 | + | 0.986112i | \(0.553111\pi\) |
−0.770958 | + | 0.636886i | \(0.780222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.2864 | −1.77916 | ||||||||
\(932\) | 7.44123 | − | 12.8886i | 0.243746 | − | 0.422180i | ||||
\(933\) | 10.8294 | + | 18.7571i | 0.354538 | + | 0.614078i | ||||
\(934\) | 10.2810 | + | 17.8072i | 0.336404 | + | 0.582670i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.01506 | + | 6.78664i | 0.0331781 | + | 0.221828i | ||||
\(937\) | −11.1842 | −0.365372 | −0.182686 | − | 0.983171i | \(-0.558479\pi\) | ||||
−0.182686 | + | 0.983171i | \(0.558479\pi\) | |||||||
\(938\) | −16.4494 | − | 28.4912i | −0.537091 | − | 0.930270i | ||||
\(939\) | −19.0573 | − | 33.0082i | −0.621912 | − | 1.07718i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.68598 | −0.250556 | −0.125278 | − | 0.992122i | \(-0.539982\pi\) | ||||
−0.125278 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(942\) | 2.19680 | − | 3.80497i | 0.0715757 | − | 0.123973i | ||||
\(943\) | 6.39361 | − | 11.0741i | 0.208204 | − | 0.360621i | ||||
\(944\) | 7.18421 | 0.233826 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.06668 | − | 1.84754i | −0.0346806 | − | 0.0600686i | ||||
\(947\) | −10.3373 | − | 17.9047i | −0.335917 | − | 0.581826i | 0.647743 | − | 0.761859i | \(-0.275713\pi\) |
−0.983661 | + | 0.180033i | \(0.942380\pi\) | |||||||
\(948\) | 9.52543 | 0.309372 | ||||||||
\(949\) | −43.3170 | + | 34.4639i | −1.40613 | + | 1.11875i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.2175 | − | 26.3576i | −0.493463 | − | 0.854703i | ||||
\(952\) | 2.55877 | + | 4.43191i | 0.0829301 | + | 0.143639i | ||||
\(953\) | 15.4876 | − | 26.8254i | 0.501694 | − | 0.868959i | −0.498304 | − | 0.867002i | \(-0.666044\pi\) |
0.999998 | − | 0.00195715i | \(-0.000622981\pi\) | |||||||
\(954\) | −2.84590 | −0.0921395 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.21109 | + | 3.82973i | −0.0715119 | + | 0.123862i | ||||
\(957\) | −21.3778 | −0.691046 | ||||||||
\(958\) | −5.96666 | + | 10.3346i | −0.192774 | + | 0.333895i | ||||
\(959\) | −28.8654 | − | 49.9964i | −0.932113 | − | 1.61447i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.9412 | 0.546489 | ||||||||
\(962\) | 2.67775 | + | 17.9034i | 0.0863343 | + | 0.577229i | ||||
\(963\) | −4.21432 | −0.135805 | ||||||||
\(964\) | 5.64050 | + | 9.76963i | 0.181668 | + | 0.314659i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.28100 | − | 16.0752i | 0.298611 | − | 0.517210i | ||||
\(967\) | −0.529873 | −0.0170396 | −0.00851979 | − | 0.999964i | \(-0.502712\pi\) | ||||
−0.00851979 | + | 0.999964i | \(0.502712\pi\) | |||||||
\(968\) | 4.93110 | − | 8.54092i | 0.158492 | − | 0.274515i | ||||
\(969\) | 9.56914 | − | 16.5742i | 0.307405 | − | 0.532441i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.1620 | − | 29.7255i | 0.550755 | − | 0.953936i | −0.447465 | − | 0.894301i | \(-0.647673\pi\) |
0.998220 | − | 0.0596344i | \(-0.0189935\pi\) | |||||||
\(972\) | 8.63259 | + | 14.9521i | 0.276890 | + | 0.479588i | ||||
\(973\) | −24.7733 | − | 42.9087i | −0.794196 | − | 1.37559i | ||||
\(974\) | −27.9719 | −0.896277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.88739 | 0.252469 | ||||||||
\(977\) | −9.98418 | − | 17.2931i | −0.319422 | − | 0.553255i | 0.660945 | − | 0.750434i | \(-0.270155\pi\) |
−0.980368 | + | 0.197179i | \(0.936822\pi\) | |||||||
\(978\) | 5.20717 | + | 9.01909i | 0.166507 | + | 0.288399i | ||||
\(979\) | −2.41358 | + | 4.18045i | −0.0771385 | + | 0.133608i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.126900 | + | 0.219797i | −0.00405159 | + | 0.00701756i | ||||
\(982\) | 10.3906 | − | 17.9971i | 0.331578 | − | 0.574310i | ||||
\(983\) | −20.8524 | −0.665087 | −0.332543 | − | 0.943088i | \(-0.607907\pi\) | ||||
−0.332543 | + | 0.943088i | \(0.607907\pi\) | |||||||
\(984\) | 6.59210 | − | 11.4179i | 0.210149 | − | 0.363988i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.93332 | + | 10.2768i | 0.188956 | + | 0.327281i | ||||
\(987\) | 0.836535 | 0.0266272 | ||||||||
\(988\) | 22.1153 | + | 8.70856i | 0.703582 | + | 0.277056i | ||||
\(989\) | 4.29529 | 0.136582 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.47949 | + | 2.56256i | 0.0469977 | + | 0.0814024i | 0.888567 | − | 0.458746i | \(-0.151701\pi\) |
−0.841570 | + | 0.540149i | \(0.818368\pi\) | |||||||
\(992\) | 3.46198 | − | 5.99632i | 0.109918 | − | 0.190383i | ||||
\(993\) | 42.9304 | 1.36236 | ||||||||
\(994\) | −30.2099 | + | 52.3250i | −0.958199 | + | 1.65965i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.4652 | 0.680151 | ||||||||
\(997\) | 10.5240 | − | 18.2281i | 0.333297 | − | 0.577288i | −0.649859 | − | 0.760055i | \(-0.725172\pi\) |
0.983156 | + | 0.182767i | \(0.0585053\pi\) | |||||||
\(998\) | −17.1454 | − | 29.6967i | −0.542729 | − | 0.940034i | ||||
\(999\) | 6.09679 | + | 10.5599i | 0.192894 | + | 0.334102i |
(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 | 650.2.e.j.601.1 | 6 | ||
5.2 | odd | 4 | 130.2.n.a.29.4 | yes | 12 | ||
5.3 | odd | 4 | 130.2.n.a.29.3 | yes | 12 | ||
5.4 | even | 2 | 650.2.e.k.601.3 | 6 | |||
13.3 | even | 3 | 8450.2.a.cb.1.3 | 3 | |||
13.9 | even | 3 | inner | 650.2.e.j.451.1 | 6 | ||
13.10 | even | 6 | 8450.2.a.bt.1.3 | 3 | |||
15.2 | even | 4 | 1170.2.bp.h.289.1 | 12 | |||
15.8 | even | 4 | 1170.2.bp.h.289.4 | 12 | |||
20.3 | even | 4 | 1040.2.dh.b.289.1 | 12 | |||
20.7 | even | 4 | 1040.2.dh.b.289.6 | 12 | |||
65.2 | even | 12 | 1690.2.c.c.1689.1 | 6 | |||
65.3 | odd | 12 | 1690.2.b.c.339.3 | 6 | |||
65.9 | even | 6 | 650.2.e.k.451.3 | 6 | |||
65.22 | odd | 12 | 130.2.n.a.9.3 | ✓ | 12 | ||
65.23 | odd | 12 | 1690.2.b.b.339.6 | 6 | |||
65.28 | even | 12 | 1690.2.c.b.1689.6 | 6 | |||
65.29 | even | 6 | 8450.2.a.bu.1.1 | 3 | |||
65.37 | even | 12 | 1690.2.c.b.1689.1 | 6 | |||
65.42 | odd | 12 | 1690.2.b.c.339.4 | 6 | |||
65.48 | odd | 12 | 130.2.n.a.9.4 | yes | 12 | ||
65.49 | even | 6 | 8450.2.a.ca.1.1 | 3 | |||
65.62 | odd | 12 | 1690.2.b.b.339.1 | 6 | |||
65.63 | even | 12 | 1690.2.c.c.1689.6 | 6 | |||
195.113 | even | 12 | 1170.2.bp.h.919.1 | 12 | |||
195.152 | even | 12 | 1170.2.bp.h.919.4 | 12 | |||
260.87 | even | 12 | 1040.2.dh.b.529.1 | 12 | |||
260.243 | even | 12 | 1040.2.dh.b.529.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.n.a.9.3 | ✓ | 12 | 65.22 | odd | 12 | ||
130.2.n.a.9.4 | yes | 12 | 65.48 | odd | 12 | ||
130.2.n.a.29.3 | yes | 12 | 5.3 | odd | 4 | ||
130.2.n.a.29.4 | yes | 12 | 5.2 | odd | 4 | ||
650.2.e.j.451.1 | 6 | 13.9 | even | 3 | inner | ||
650.2.e.j.601.1 | 6 | 1.1 | even | 1 | trivial | ||
650.2.e.k.451.3 | 6 | 65.9 | even | 6 | |||
650.2.e.k.601.3 | 6 | 5.4 | even | 2 | |||
1040.2.dh.b.289.1 | 12 | 20.3 | even | 4 | |||
1040.2.dh.b.289.6 | 12 | 20.7 | even | 4 | |||
1040.2.dh.b.529.1 | 12 | 260.87 | even | 12 | |||
1040.2.dh.b.529.6 | 12 | 260.243 | even | 12 | |||
1170.2.bp.h.289.1 | 12 | 15.2 | even | 4 | |||
1170.2.bp.h.289.4 | 12 | 15.8 | even | 4 | |||
1170.2.bp.h.919.1 | 12 | 195.113 | even | 12 | |||
1170.2.bp.h.919.4 | 12 | 195.152 | even | 12 | |||
1690.2.b.b.339.1 | 6 | 65.62 | odd | 12 | |||
1690.2.b.b.339.6 | 6 | 65.23 | odd | 12 | |||
1690.2.b.c.339.3 | 6 | 65.3 | odd | 12 | |||
1690.2.b.c.339.4 | 6 | 65.42 | odd | 12 | |||
1690.2.c.b.1689.1 | 6 | 65.37 | even | 12 | |||
1690.2.c.b.1689.6 | 6 | 65.28 | even | 12 | |||
1690.2.c.c.1689.1 | 6 | 65.2 | even | 12 | |||
1690.2.c.c.1689.6 | 6 | 65.63 | even | 12 | |||
8450.2.a.bt.1.3 | 3 | 13.10 | even | 6 | |||
8450.2.a.bu.1.1 | 3 | 65.29 | even | 6 | |||
8450.2.a.ca.1.1 | 3 | 65.49 | even | 6 | |||
8450.2.a.cb.1.3 | 3 | 13.3 | even | 3 |