Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), degree \(2\), not 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.8 | ||
Root | \(1.87108 - 1.08027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.949 |
Dual form | 1470.2.n.k.79.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.89827 | − | 1.18176i | 0.848933 | − | 0.528501i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.05307 | − | 1.97257i | 0.333010 | − | 0.623782i | ||||
\(11\) | 1.52773 | − | 2.64610i | 0.460627 | − | 0.797829i | −0.538365 | − | 0.842711i | \(-0.680958\pi\) |
0.998992 | + | 0.0448824i | \(0.0142913\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | − | 1.64124i | − | 0.455198i | −0.973755 | − | 0.227599i | \(-0.926912\pi\) | ||
0.973755 | − | 0.227599i | \(-0.0730875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23483 | − | 0.0743018i | 0.577031 | − | 0.0191846i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.51741 | + | 1.45342i | 0.610560 | + | 0.352507i | 0.773185 | − | 0.634181i | \(-0.218663\pi\) |
−0.162624 | + | 0.986688i | \(0.551996\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | 1.10508 | + | 1.91405i | 0.253522 | + | 0.439114i | 0.964493 | − | 0.264108i | \(-0.0850775\pi\) |
−0.710971 | + | 0.703222i | \(0.751744\pi\) | |||||||
\(20\) | −0.0743018 | − | 2.23483i | −0.0166144 | − | 0.499724i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.05545i | − | 0.651425i | ||||||
\(23\) | −1.55005 | + | 0.894921i | −0.323208 | + | 0.186604i | −0.652821 | − | 0.757512i | \(-0.726415\pi\) |
0.329614 | + | 0.944116i | \(0.393081\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 2.20687 | − | 4.48662i | 0.441374 | − | 0.897323i | ||||
\(26\) | −0.820620 | − | 1.42135i | −0.160937 | − | 0.278751i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.58667 | −1.03742 | −0.518710 | − | 0.854951i | \(-0.673587\pi\) | ||||
−0.518710 | + | 0.854951i | \(0.673587\pi\) | |||||||
\(30\) | 1.89827 | − | 1.18176i | 0.346575 | − | 0.215760i | ||||
\(31\) | −0.472274 | + | 0.818002i | −0.0848228 | + | 0.146917i | −0.905316 | − | 0.424739i | \(-0.860366\pi\) |
0.820493 | + | 0.571657i | \(0.193699\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 2.64610 | − | 1.52773i | 0.460627 | − | 0.265943i | ||||
\(34\) | 2.90685 | 0.498521 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.27713 | + | 5.35615i | −1.52515 | + | 0.880546i | −0.525595 | + | 0.850735i | \(0.676157\pi\) |
−0.999556 | + | 0.0298114i | \(0.990509\pi\) | |||||||
\(38\) | 1.91405 | + | 1.10508i | 0.310500 | + | 0.179267i | ||||
\(39\) | 0.820620 | − | 1.42135i | 0.131404 | − | 0.227599i | ||||
\(40\) | −1.18176 | − | 1.89827i | −0.186853 | − | 0.300143i | ||||
\(41\) | 6.67982 | 1.04321 | 0.521607 | − | 0.853186i | \(-0.325333\pi\) | ||||
0.521607 | + | 0.853186i | \(0.325333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.5021i | − | 1.60156i | −0.598957 | − | 0.800781i | \(-0.704418\pi\) | ||
0.598957 | − | 0.800781i | \(-0.295582\pi\) | |||||||
\(44\) | −1.52773 | − | 2.64610i | −0.230313 | − | 0.398915i | ||||
\(45\) | 1.97257 | + | 1.05307i | 0.294054 | + | 0.156982i | ||||
\(46\) | −0.894921 | + | 1.55005i | −0.131949 | + | 0.228542i | ||||
\(47\) | 9.85235 | − | 5.68826i | 1.43711 | − | 0.829718i | 0.439465 | − | 0.898260i | \(-0.355168\pi\) |
0.997648 | + | 0.0685421i | \(0.0218347\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.332104 | − | 4.98896i | −0.0469666 | − | 0.705545i | ||||
\(51\) | 1.45342 | + | 2.51741i | 0.203520 | + | 0.352507i | ||||
\(52\) | −1.42135 | − | 0.820620i | −0.197106 | − | 0.113799i | ||||
\(53\) | 5.01415 | + | 2.89492i | 0.688747 | + | 0.397648i | 0.803142 | − | 0.595787i | \(-0.203160\pi\) |
−0.114396 | + | 0.993435i | \(0.536493\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −0.227026 | − | 6.82843i | −0.0306121 | − | 0.920745i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.21016i | 0.292742i | ||||||||
\(58\) | −4.83820 | + | 2.79334i | −0.635287 | + | 0.366783i | ||||
\(59\) | −2.98896 | + | 5.17703i | −0.389129 | + | 0.673992i | −0.992333 | − | 0.123596i | \(-0.960557\pi\) |
0.603203 | + | 0.797587i | \(0.293891\pi\) | |||||||
\(60\) | 1.05307 | − | 1.97257i | 0.135951 | − | 0.254658i | ||||
\(61\) | −0.222905 | − | 0.386083i | −0.0285401 | − | 0.0494329i | 0.851403 | − | 0.524513i | \(-0.175752\pi\) |
−0.879943 | + | 0.475080i | \(0.842419\pi\) | |||||||
\(62\) | 0.944547i | 0.119958i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.93956 | − | 3.11552i | −0.240572 | − | 0.386432i | ||||
\(66\) | 1.52773 | − | 2.64610i | 0.188050 | − | 0.325712i | ||||
\(67\) | −1.09605 | − | 0.632805i | −0.133904 | − | 0.0773094i | 0.431552 | − | 0.902088i | \(-0.357966\pi\) |
−0.565456 | + | 0.824779i | \(0.691300\pi\) | |||||||
\(68\) | 2.51741 | − | 1.45342i | 0.305280 | − | 0.176254i | ||||
\(69\) | −1.78984 | −0.215472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8523 | −1.76264 | −0.881321 | − | 0.472518i | \(-0.843345\pi\) | ||||
−0.881321 | + | 0.472518i | \(0.843345\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 6.85577 | + | 3.95818i | 0.802407 | + | 0.463270i | 0.844312 | − | 0.535851i | \(-0.180009\pi\) |
−0.0419049 | + | 0.999122i | \(0.513343\pi\) | |||||||
\(74\) | −5.35615 | + | 9.27713i | −0.622640 | + | 1.07844i | ||||
\(75\) | 4.15451 | − | 2.78209i | 0.479722 | − | 0.321248i | ||||
\(76\) | 2.21016 | 0.253522 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 1.64124i | − | 0.185834i | ||||||
\(79\) | 7.14949 | + | 12.3833i | 0.804380 | + | 1.39323i | 0.916709 | + | 0.399557i | \(0.130836\pi\) |
−0.112328 | + | 0.993671i | \(0.535831\pi\) | |||||||
\(80\) | −1.97257 | − | 1.05307i | −0.220540 | − | 0.117737i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.78490 | − | 3.33991i | 0.638835 | − | 0.368832i | ||||
\(83\) | − | 0.874366i | − | 0.0959741i | −0.998848 | − | 0.0479871i | \(-0.984719\pi\) | ||
0.998848 | − | 0.0479871i | \(-0.0152806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.49632 | − | 0.215984i | 0.704625 | − | 0.0234268i | ||||
\(86\) | −5.25107 | − | 9.09513i | −0.566238 | − | 0.980753i | ||||
\(87\) | −4.83820 | − | 2.79334i | −0.518710 | − | 0.299477i | ||||
\(88\) | −2.64610 | − | 1.52773i | −0.282075 | − | 0.162856i | ||||
\(89\) | 8.75413 | + | 15.1626i | 0.927935 | + | 1.60723i | 0.786771 | + | 0.617245i | \(0.211751\pi\) |
0.141165 | + | 0.989986i | \(0.454915\pi\) | |||||||
\(90\) | 2.23483 | − | 0.0743018i | 0.235572 | − | 0.00783210i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.78984i | 0.186604i | ||||||||
\(93\) | −0.818002 | + | 0.472274i | −0.0848228 | + | 0.0489725i | ||||
\(94\) | 5.68826 | − | 9.85235i | 0.586699 | − | 1.01619i | ||||
\(95\) | 4.35970 | + | 2.32745i | 0.447295 | + | 0.238791i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 10.4476i | − | 1.06079i | −0.847750 | − | 0.530396i | \(-0.822043\pi\) | ||
0.847750 | − | 0.530396i | \(-0.177957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.05545 | 0.307085 | ||||||||
\(100\) | −2.78209 | − | 4.15451i | −0.278209 | − | 0.415451i | ||||
\(101\) | −7.72747 | + | 13.3844i | −0.768912 | + | 1.33179i | 0.169242 | + | 0.985575i | \(0.445868\pi\) |
−0.938153 | + | 0.346220i | \(0.887465\pi\) | |||||||
\(102\) | 2.51741 | + | 1.45342i | 0.249260 | + | 0.143910i | ||||
\(103\) | −2.70688 | + | 1.56282i | −0.266717 | + | 0.153989i | −0.627395 | − | 0.778701i | \(-0.715879\pi\) |
0.360678 | + | 0.932690i | \(0.382545\pi\) | |||||||
\(104\) | −1.64124 | −0.160937 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.78984 | 0.562359 | ||||||||
\(107\) | −4.14176 | + | 2.39124i | −0.400399 | + | 0.231170i | −0.686656 | − | 0.726982i | \(-0.740922\pi\) |
0.286257 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −4.55178 | + | 7.88391i | −0.435981 | + | 0.755141i | −0.997375 | − | 0.0724073i | \(-0.976932\pi\) |
0.561394 | + | 0.827549i | \(0.310265\pi\) | |||||||
\(110\) | −3.61082 | − | 5.80008i | −0.344279 | − | 0.553016i | ||||
\(111\) | −10.7123 | −1.01677 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.3982i | − | 1.35447i | −0.735766 | − | 0.677236i | \(-0.763178\pi\) | ||
0.735766 | − | 0.677236i | \(-0.236822\pi\) | |||||||
\(114\) | 1.10508 | + | 1.91405i | 0.103500 | + | 0.179267i | ||||
\(115\) | −1.88483 | + | 3.53060i | −0.175761 | + | 0.329230i | ||||
\(116\) | −2.79334 | + | 4.83820i | −0.259355 | + | 0.449216i | ||||
\(117\) | 1.42135 | − | 0.820620i | 0.131404 | − | 0.0758663i | ||||
\(118\) | 5.97792i | 0.550312i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.0743018 | − | 2.23483i | −0.00678279 | − | 0.204011i | ||||
\(121\) | 0.832104 | + | 1.44125i | 0.0756458 | + | 0.131022i | ||||
\(122\) | −0.386083 | − | 0.222905i | −0.0349544 | − | 0.0201809i | ||||
\(123\) | 5.78490 | + | 3.33991i | 0.521607 | + | 0.301150i | ||||
\(124\) | 0.472274 | + | 0.818002i | 0.0424114 | + | 0.0734587i | ||||
\(125\) | −1.11289 | − | 11.1248i | −0.0995396 | − | 0.995034i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.45405i | − | 0.750176i | −0.926989 | − | 0.375088i | \(-0.877613\pi\) | ||
0.926989 | − | 0.375088i | \(-0.122387\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 5.25107 | − | 9.09513i | 0.462331 | − | 0.800781i | ||||
\(130\) | −3.23746 | − | 1.72834i | −0.283944 | − | 0.151585i | ||||
\(131\) | −4.16053 | − | 7.20625i | −0.363507 | − | 0.629613i | 0.625028 | − | 0.780602i | \(-0.285087\pi\) |
−0.988535 | + | 0.150989i | \(0.951754\pi\) | |||||||
\(132\) | − | 3.05545i | − | 0.265943i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.26561 | −0.109332 | ||||||||
\(135\) | 1.18176 | + | 1.89827i | 0.101710 | + | 0.163377i | ||||
\(136\) | 1.45342 | − | 2.51741i | 0.124630 | − | 0.215866i | ||||
\(137\) | −8.54508 | − | 4.93351i | −0.730056 | − | 0.421498i | 0.0883869 | − | 0.996086i | \(-0.471829\pi\) |
−0.818443 | + | 0.574588i | \(0.805162\pi\) | |||||||
\(138\) | −1.55005 | + | 0.894921i | −0.131949 | + | 0.0761808i | ||||
\(139\) | −16.9632 | −1.43880 | −0.719399 | − | 0.694597i | \(-0.755583\pi\) | ||||
−0.719399 | + | 0.694597i | \(0.755583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3765 | 0.958075 | ||||||||
\(142\) | −12.8625 | + | 7.42614i | −1.07939 | + | 0.623188i | ||||
\(143\) | −4.34288 | − | 2.50736i | −0.363170 | − | 0.209676i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −10.6050 | + | 6.60213i | −0.880699 | + | 0.548277i | ||||
\(146\) | 7.91636 | 0.655163 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.7123i | 0.880546i | ||||||||
\(149\) | 4.02405 | + | 6.96986i | 0.329663 | + | 0.570993i | 0.982445 | − | 0.186553i | \(-0.0597316\pi\) |
−0.652782 | + | 0.757546i | \(0.726398\pi\) | |||||||
\(150\) | 2.20687 | − | 4.48662i | 0.180190 | − | 0.366331i | ||||
\(151\) | 4.98896 | − | 8.64113i | 0.405996 | − | 0.703205i | −0.588441 | − | 0.808540i | \(-0.700258\pi\) |
0.994437 | + | 0.105335i | \(0.0335915\pi\) | |||||||
\(152\) | 1.91405 | − | 1.10508i | 0.155250 | − | 0.0896337i | ||||
\(153\) | 2.90685i | 0.235005i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0701816 | + | 2.11091i | 0.00563712 | + | 0.169552i | ||||
\(156\) | −0.820620 | − | 1.42135i | −0.0657022 | − | 0.113799i | ||||
\(157\) | 10.9705 | + | 6.33381i | 0.875540 | + | 0.505493i | 0.869185 | − | 0.494487i | \(-0.164644\pi\) |
0.00635459 | + | 0.999980i | \(0.497977\pi\) | |||||||
\(158\) | 12.3833 | + | 7.14949i | 0.985161 | + | 0.568783i | ||||
\(159\) | 2.89492 | + | 5.01415i | 0.229582 | + | 0.397648i | ||||
\(160\) | −2.23483 | + | 0.0743018i | −0.176679 | + | 0.00587407i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 20.4075 | − | 11.7823i | 1.59844 | − | 0.922861i | 0.606654 | − | 0.794966i | \(-0.292512\pi\) |
0.991788 | − | 0.127894i | \(-0.0408218\pi\) | |||||||
\(164\) | 3.33991 | − | 5.78490i | 0.260803 | − | 0.451725i | ||||
\(165\) | 3.21760 | − | 6.02710i | 0.250490 | − | 0.469209i | ||||
\(166\) | −0.437183 | − | 0.757223i | −0.0339320 | − | 0.0587719i | ||||
\(167\) | 18.0818i | 1.39921i | 0.714528 | + | 0.699607i | \(0.246642\pi\) | ||||
−0.714528 | + | 0.699607i | \(0.753358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3063 | 0.792795 | ||||||||
\(170\) | 5.51799 | − | 3.43521i | 0.423210 | − | 0.263469i | ||||
\(171\) | −1.10508 | + | 1.91405i | −0.0845075 | + | 0.146371i | ||||
\(172\) | −9.09513 | − | 5.25107i | −0.693497 | − | 0.400391i | ||||
\(173\) | 1.67874 | − | 0.969223i | 0.127633 | − | 0.0736887i | −0.434824 | − | 0.900515i | \(-0.643190\pi\) |
0.562457 | + | 0.826827i | \(0.309856\pi\) | |||||||
\(174\) | −5.58667 | −0.423525 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.05545 | −0.230313 | ||||||||
\(177\) | −5.17703 | + | 2.98896i | −0.389129 | + | 0.224664i | ||||
\(178\) | 15.1626 | + | 8.75413i | 1.13648 | + | 0.656149i | ||||
\(179\) | −12.2232 | + | 21.1711i | −0.913602 | + | 1.58241i | −0.104667 | + | 0.994507i | \(0.533378\pi\) |
−0.808935 | + | 0.587898i | \(0.799956\pi\) | |||||||
\(180\) | 1.89827 | − | 1.18176i | 0.141489 | − | 0.0880835i | ||||
\(181\) | −16.9788 | −1.26202 | −0.631012 | − | 0.775773i | \(-0.717360\pi\) | ||||
−0.631012 | + | 0.775773i | \(0.717360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.445811i | − | 0.0329553i | ||||||
\(184\) | 0.894921 | + | 1.55005i | 0.0659745 | + | 0.114271i | ||||
\(185\) | −11.2808 | + | 21.1308i | −0.829381 | + | 1.55357i | ||||
\(186\) | −0.472274 | + | 0.818002i | −0.0346288 | + | 0.0599788i | ||||
\(187\) | 7.69181 | − | 4.44087i | 0.562481 | − | 0.324749i | ||||
\(188\) | − | 11.3765i | − | 0.829718i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.93933 | − | 0.164219i | 0.358337 | − | 0.0119137i | ||||
\(191\) | −0.370689 | − | 0.642051i | −0.0268221 | − | 0.0464572i | 0.852303 | − | 0.523049i | \(-0.175205\pi\) |
−0.879125 | + | 0.476592i | \(0.841872\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −5.29220 | − | 3.05545i | −0.380941 | − | 0.219936i | 0.297287 | − | 0.954788i | \(-0.403918\pi\) |
−0.678228 | + | 0.734852i | \(0.737252\pi\) | |||||||
\(194\) | −5.22379 | − | 9.04787i | −0.375046 | − | 0.649599i | ||||
\(195\) | −0.121947 | − | 3.66790i | −0.00873281 | − | 0.262663i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.6832i | 1.47362i | 0.676100 | + | 0.736810i | \(0.263669\pi\) | ||||
−0.676100 | + | 0.736810i | \(0.736331\pi\) | |||||||
\(198\) | 2.64610 | − | 1.52773i | 0.188050 | − | 0.108571i | ||||
\(199\) | 6.03509 | − | 10.4531i | 0.427816 | − | 0.740999i | −0.568863 | − | 0.822433i | \(-0.692616\pi\) |
0.996679 | + | 0.0814331i | \(0.0259497\pi\) | |||||||
\(200\) | −4.48662 | − | 2.20687i | −0.317252 | − | 0.156049i | ||||
\(201\) | −0.632805 | − | 1.09605i | −0.0446346 | − | 0.0773094i | ||||
\(202\) | 15.4549i | 1.08741i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.90685 | 0.203520 | ||||||||
\(205\) | 12.6801 | − | 7.89397i | 0.885618 | − | 0.551339i | ||||
\(206\) | −1.56282 | + | 2.70688i | −0.108887 | + | 0.188597i | ||||
\(207\) | −1.55005 | − | 0.894921i | −0.107736 | − | 0.0622013i | ||||
\(208\) | −1.42135 | + | 0.820620i | −0.0985532 | + | 0.0568997i | ||||
\(209\) | 6.75303 | 0.467117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.95153 | 0.203192 | 0.101596 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101596 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(212\) | 5.01415 | − | 2.89492i | 0.344373 | − | 0.198824i | ||||
\(213\) | −12.8625 | − | 7.42614i | −0.881321 | − | 0.508831i | ||||
\(214\) | −2.39124 | + | 4.14176i | −0.163462 | + | 0.283125i | ||||
\(215\) | −12.4111 | − | 19.9359i | −0.846427 | − | 1.35962i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.10355i | 0.616570i | ||||||||
\(219\) | 3.95818 | + | 6.85577i | 0.267469 | + | 0.463270i | ||||
\(220\) | −6.02710 | − | 3.21760i | −0.406347 | − | 0.216931i | ||||
\(221\) | 2.38542 | − | 4.13166i | 0.160461 | − | 0.277926i | ||||
\(222\) | −9.27713 | + | 5.35615i | −0.622640 | + | 0.359481i | ||||
\(223\) | 11.7678i | 0.788027i | 0.919105 | + | 0.394014i | \(0.128914\pi\) | ||||
−0.919105 | + | 0.394014i | \(0.871086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.98896 | − | 0.332104i | 0.332597 | − | 0.0221403i | ||||
\(226\) | −7.19912 | − | 12.4692i | −0.478878 | − | 0.829441i | ||||
\(227\) | −11.4632 | − | 6.61827i | −0.760838 | − | 0.439270i | 0.0687586 | − | 0.997633i | \(-0.478096\pi\) |
−0.829597 | + | 0.558363i | \(0.811430\pi\) | |||||||
\(228\) | 1.91405 | + | 1.10508i | 0.126761 | + | 0.0731856i | ||||
\(229\) | 12.6224 | + | 21.8626i | 0.834111 | + | 1.44472i | 0.894752 | + | 0.446563i | \(0.147352\pi\) |
−0.0606412 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(230\) | 0.132989 | + | 4.00000i | 0.00876900 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.58667i | 0.366783i | ||||||||
\(233\) | −2.88249 | + | 1.66421i | −0.188838 | + | 0.109026i | −0.591439 | − | 0.806350i | \(-0.701440\pi\) |
0.402600 | + | 0.915376i | \(0.368106\pi\) | |||||||
\(234\) | 0.820620 | − | 1.42135i | 0.0536456 | − | 0.0929169i | ||||
\(235\) | 11.9803 | − | 22.4410i | 0.781506 | − | 1.46389i | ||||
\(236\) | 2.98896 | + | 5.17703i | 0.194565 | + | 0.336996i | ||||
\(237\) | 14.2990i | 0.928819i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.8713 | −1.60879 | −0.804396 | − | 0.594094i | \(-0.797511\pi\) | ||||
−0.804396 | + | 0.594094i | \(0.797511\pi\) | |||||||
\(240\) | −1.18176 | − | 1.89827i | −0.0762825 | − | 0.122533i | ||||
\(241\) | −5.17677 | + | 8.96643i | −0.333465 | + | 0.577579i | −0.983189 | − | 0.182592i | \(-0.941551\pi\) |
0.649724 | + | 0.760171i | \(0.274885\pi\) | |||||||
\(242\) | 1.44125 | + | 0.832104i | 0.0926469 | + | 0.0534897i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −0.445811 | −0.0285401 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.67982 | 0.425890 | ||||||||
\(247\) | 3.14142 | − | 1.81370i | 0.199884 | − | 0.115403i | ||||
\(248\) | 0.818002 | + | 0.472274i | 0.0519432 | + | 0.0299894i | ||||
\(249\) | 0.437183 | − | 0.757223i | 0.0277053 | − | 0.0479871i | ||||
\(250\) | −6.52619 | − | 9.07793i | −0.412753 | − | 0.574139i | ||||
\(251\) | 16.5502 | 1.04464 | 0.522321 | − | 0.852749i | \(-0.325066\pi\) | ||||
0.522321 | + | 0.852749i | \(0.325066\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.46878i | 0.343819i | ||||||||
\(254\) | −4.22703 | − | 7.32142i | −0.265227 | − | 0.459387i | ||||
\(255\) | 5.73397 | + | 3.06111i | 0.359075 | + | 0.191694i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −21.1783 | + | 12.2273i | −1.32106 | + | 0.762717i | −0.983899 | − | 0.178728i | \(-0.942802\pi\) |
−0.337166 | + | 0.941445i | \(0.609468\pi\) | |||||||
\(258\) | − | 10.5021i | − | 0.653835i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.66790 | + | 0.121947i | −0.227473 | + | 0.00756283i | ||||
\(261\) | −2.79334 | − | 4.83820i | −0.172903 | − | 0.299477i | ||||
\(262\) | −7.20625 | − | 4.16053i | −0.445204 | − | 0.257038i | ||||
\(263\) | −10.8332 | − | 6.25457i | −0.668006 | − | 0.385673i | 0.127315 | − | 0.991862i | \(-0.459364\pi\) |
−0.795321 | + | 0.606189i | \(0.792697\pi\) | |||||||
\(264\) | −1.52773 | − | 2.64610i | −0.0940251 | − | 0.162856i | ||||
\(265\) | 12.9393 | − | 0.430196i | 0.794857 | − | 0.0264267i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.5083i | 1.07149i | ||||||||
\(268\) | −1.09605 | + | 0.632805i | −0.0669519 | + | 0.0386547i | ||||
\(269\) | −9.48330 | + | 16.4256i | −0.578207 | + | 1.00148i | 0.417478 | + | 0.908687i | \(0.362914\pi\) |
−0.995685 | + | 0.0927970i | \(0.970419\pi\) | |||||||
\(270\) | 1.97257 | + | 1.05307i | 0.120047 | + | 0.0640878i | ||||
\(271\) | −9.83192 | − | 17.0294i | −0.597247 | − | 1.03446i | −0.993226 | − | 0.116202i | \(-0.962928\pi\) |
0.395979 | − | 0.918260i | \(-0.370405\pi\) | |||||||
\(272\) | − | 2.90685i | − | 0.176254i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.86701 | −0.596088 | ||||||||
\(275\) | −8.50054 | − | 12.6939i | −0.512602 | − | 0.765472i | ||||
\(276\) | −0.894921 | + | 1.55005i | −0.0538679 | + | 0.0933020i | ||||
\(277\) | 5.31737 | + | 3.06999i | 0.319490 | + | 0.184458i | 0.651165 | − | 0.758936i | \(-0.274280\pi\) |
−0.331675 | + | 0.943394i | \(0.607614\pi\) | |||||||
\(278\) | −14.6906 | + | 8.48159i | −0.881081 | + | 0.508692i | ||||
\(279\) | −0.944547 | −0.0565486 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1330 | −0.723793 | −0.361897 | − | 0.932218i | \(-0.617871\pi\) | ||||
−0.361897 | + | 0.932218i | \(0.617871\pi\) | |||||||
\(282\) | 9.85235 | − | 5.68826i | 0.586699 | − | 0.338731i | ||||
\(283\) | −15.0838 | − | 8.70862i | −0.896637 | − | 0.517674i | −0.0205295 | − | 0.999789i | \(-0.506535\pi\) |
−0.876108 | + | 0.482116i | \(0.839869\pi\) | |||||||
\(284\) | −7.42614 | + | 12.8625i | −0.440660 | + | 0.763246i | ||||
\(285\) | 2.61188 | + | 4.19548i | 0.154715 | + | 0.248519i | ||||
\(286\) | −5.01473 | −0.296527 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −4.27511 | − | 7.40471i | −0.251477 | − | 0.435571i | ||||
\(290\) | −5.88315 | + | 11.0201i | −0.345471 | + | 0.647124i | ||||
\(291\) | 5.22379 | − | 9.04787i | 0.306224 | − | 0.530396i | ||||
\(292\) | 6.85577 | − | 3.95818i | 0.401204 | − | 0.231635i | ||||
\(293\) | 23.7521i | 1.38762i | 0.720160 | + | 0.693808i | \(0.244068\pi\) | ||||
−0.720160 | + | 0.693808i | \(0.755932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.444170 | + | 13.3596i | 0.0258606 | + | 0.777829i | ||||
\(296\) | 5.35615 | + | 9.27713i | 0.311320 | + | 0.539222i | ||||
\(297\) | 2.64610 | + | 1.52773i | 0.153542 | + | 0.0886477i | ||||
\(298\) | 6.96986 | + | 4.02405i | 0.403753 | + | 0.233107i | ||||
\(299\) | 1.46878 | + | 2.54400i | 0.0849417 | + | 0.147123i | ||||
\(300\) | −0.332104 | − | 4.98896i | −0.0191740 | − | 0.288038i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 9.97792i | − | 0.574165i | ||||||
\(303\) | −13.3844 | + | 7.72747i | −0.768912 | + | 0.443931i | ||||
\(304\) | 1.10508 | − | 1.91405i | 0.0633806 | − | 0.109778i | ||||
\(305\) | −0.879394 | − | 0.469470i | −0.0503540 | − | 0.0268818i | ||||
\(306\) | 1.45342 | + | 2.51741i | 0.0830868 | + | 0.143910i | ||||
\(307\) | − | 7.90812i | − | 0.451340i | −0.974204 | − | 0.225670i | \(-0.927543\pi\) | ||
0.974204 | − | 0.225670i | \(-0.0724572\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.12563 | −0.177811 | ||||||||
\(310\) | 1.11623 | + | 1.79301i | 0.0633977 | + | 0.101836i | ||||
\(311\) | 5.03858 | − | 8.72708i | 0.285712 | − | 0.494868i | −0.687070 | − | 0.726592i | \(-0.741103\pi\) |
0.972782 | + | 0.231724i | \(0.0744366\pi\) | |||||||
\(312\) | −1.42135 | − | 0.820620i | −0.0804684 | − | 0.0464584i | ||||
\(313\) | −17.6534 | + | 10.1922i | −0.997829 | + | 0.576097i | −0.907605 | − | 0.419825i | \(-0.862092\pi\) |
−0.0902238 | + | 0.995922i | \(0.528758\pi\) | |||||||
\(314\) | 12.6676 | 0.714875 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.2990 | 0.804380 | ||||||||
\(317\) | −0.278048 | + | 0.160531i | −0.0156168 | + | 0.00901634i | −0.507788 | − | 0.861482i | \(-0.669537\pi\) |
0.492171 | + | 0.870498i | \(0.336203\pi\) | |||||||
\(318\) | 5.01415 | + | 2.89492i | 0.281180 | + | 0.162339i | ||||
\(319\) | −8.53491 | + | 14.7829i | −0.477863 | + | 0.827683i | ||||
\(320\) | −1.89827 | + | 1.18176i | −0.106117 | + | 0.0660626i | ||||
\(321\) | −4.78249 | −0.266932 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42459i | 0.357474i | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −7.36361 | − | 3.62200i | −0.408460 | − | 0.200912i | ||||
\(326\) | 11.7823 | − | 20.4075i | 0.652561 | − | 1.13027i | ||||
\(327\) | −7.88391 | + | 4.55178i | −0.435981 | + | 0.251714i | ||||
\(328\) | − | 6.67982i | − | 0.368832i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.227026 | − | 6.82843i | −0.0124973 | − | 0.375893i | ||||
\(331\) | 8.30419 | + | 14.3833i | 0.456440 | + | 0.790577i | 0.998770 | − | 0.0495887i | \(-0.0157910\pi\) |
−0.542330 | + | 0.840166i | \(0.682458\pi\) | |||||||
\(332\) | −0.757223 | − | 0.437183i | −0.0415580 | − | 0.0239935i | ||||
\(333\) | −9.27713 | − | 5.35615i | −0.508384 | − | 0.293515i | ||||
\(334\) | 9.04092 | + | 15.6593i | 0.494697 | + | 0.856840i | ||||
\(335\) | −2.82843 | + | 0.0940371i | −0.154533 | + | 0.00513780i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.91118i | − | 0.104108i | −0.998644 | − | 0.0520542i | \(-0.983423\pi\) | ||
0.998644 | − | 0.0520542i | \(-0.0165769\pi\) | |||||||
\(338\) | 8.92555 | − | 5.15317i | 0.485486 | − | 0.280295i | ||||
\(339\) | 7.19912 | − | 12.4692i | 0.391002 | − | 0.677236i | ||||
\(340\) | 3.06111 | − | 5.73397i | 0.166012 | − | 0.310968i | ||||
\(341\) | 1.44301 | + | 2.49937i | 0.0781434 | + | 0.135348i | ||||
\(342\) | 2.21016i | 0.119512i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.5021 | −0.566238 | ||||||||
\(345\) | −3.39761 | + | 2.11517i | −0.182921 | + | 0.113877i | ||||
\(346\) | 0.969223 | − | 1.67874i | 0.0521058 | − | 0.0902498i | ||||
\(347\) | 6.84864 | + | 3.95406i | 0.367654 | + | 0.212265i | 0.672433 | − | 0.740158i | \(-0.265249\pi\) |
−0.304779 | + | 0.952423i | \(0.598583\pi\) | |||||||
\(348\) | −4.83820 | + | 2.79334i | −0.259355 | + | 0.149739i | ||||
\(349\) | 23.5273 | 1.25939 | 0.629693 | − | 0.776844i | \(-0.283181\pi\) | ||||
0.629693 | + | 0.776844i | \(0.283181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.64124 | 0.0876029 | ||||||||
\(352\) | −2.64610 | + | 1.52773i | −0.141038 | + | 0.0814281i | ||||
\(353\) | −19.8942 | − | 11.4859i | −1.05886 | − | 0.611333i | −0.133743 | − | 0.991016i | \(-0.542700\pi\) |
−0.925117 | + | 0.379683i | \(0.876033\pi\) | |||||||
\(354\) | −2.98896 | + | 5.17703i | −0.158861 | + | 0.275156i | ||||
\(355\) | −28.1937 | + | 17.5519i | −1.49636 | + | 0.931558i | ||||
\(356\) | 17.5083 | 0.927935 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.4463i | 1.29203i | ||||||||
\(359\) | 5.51319 | + | 9.54913i | 0.290975 | + | 0.503984i | 0.974041 | − | 0.226373i | \(-0.0726870\pi\) |
−0.683065 | + | 0.730357i | \(0.739354\pi\) | |||||||
\(360\) | 1.05307 | − | 1.97257i | 0.0555016 | − | 0.103964i | ||||
\(361\) | 7.05760 | − | 12.2241i | 0.371453 | − | 0.643375i | ||||
\(362\) | −14.7041 | + | 8.48940i | −0.772829 | + | 0.446193i | ||||
\(363\) | 1.66421i | 0.0873483i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.6918 | − | 0.588200i | 0.926029 | − | 0.0307878i | ||||
\(366\) | −0.222905 | − | 0.386083i | −0.0116515 | − | 0.0201809i | ||||
\(367\) | −8.78552 | − | 5.07232i | −0.458600 | − | 0.264773i | 0.252855 | − | 0.967504i | \(-0.418630\pi\) |
−0.711456 | + | 0.702731i | \(0.751964\pi\) | |||||||
\(368\) | 1.55005 | + | 0.894921i | 0.0808019 | + | 0.0466510i | ||||
\(369\) | 3.33991 | + | 5.78490i | 0.173869 | + | 0.301150i | ||||
\(370\) | 0.795944 | + | 23.9402i | 0.0413791 | + | 1.24459i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.944547i | 0.0489725i | ||||||||
\(373\) | 22.9515 | − | 13.2511i | 1.18839 | − | 0.686115i | 0.230446 | − | 0.973085i | \(-0.425981\pi\) |
0.957939 | + | 0.286970i | \(0.0926482\pi\) | |||||||
\(374\) | 4.44087 | − | 7.69181i | 0.229632 | − | 0.397734i | ||||
\(375\) | 4.59862 | − | 10.1908i | 0.237472 | − | 0.526251i | ||||
\(376\) | −5.68826 | − | 9.85235i | −0.293349 | − | 0.508096i | ||||
\(377\) | 9.16907i | 0.472231i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.4142 | −1.51091 | −0.755453 | − | 0.655203i | \(-0.772583\pi\) | ||||
−0.755453 | + | 0.655203i | \(0.772583\pi\) | |||||||
\(380\) | 4.19548 | − | 2.61188i | 0.215223 | − | 0.133987i | ||||
\(381\) | 4.22703 | − | 7.32142i | 0.216557 | − | 0.375088i | ||||
\(382\) | −0.642051 | − | 0.370689i | −0.0328502 | − | 0.0189661i | ||||
\(383\) | −3.15449 | + | 1.82125i | −0.161187 | + | 0.0930613i | −0.578424 | − | 0.815737i | \(-0.696332\pi\) |
0.417237 | + | 0.908798i | \(0.362999\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.11091 | −0.311037 | ||||||||
\(387\) | 9.09513 | − | 5.25107i | 0.462331 | − | 0.266927i | ||||
\(388\) | −9.04787 | − | 5.22379i | −0.459336 | − | 0.265198i | ||||
\(389\) | −11.8969 | + | 20.6060i | −0.603196 | + | 1.04477i | 0.389138 | + | 0.921180i | \(0.372773\pi\) |
−0.992334 | + | 0.123587i | \(0.960560\pi\) | |||||||
\(390\) | −1.93956 | − | 3.11552i | −0.0982133 | − | 0.157760i | ||||
\(391\) | −5.20280 | −0.263117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.32106i | − | 0.419742i | ||||||
\(394\) | 10.3416 | + | 17.9122i | 0.521003 | + | 0.902404i | ||||
\(395\) | 28.2058 | + | 15.0578i | 1.41919 | + | 0.757641i | ||||
\(396\) | 1.52773 | − | 2.64610i | 0.0767711 | − | 0.132972i | ||||
\(397\) | 8.45353 | − | 4.88065i | 0.424270 | − | 0.244953i | −0.272632 | − | 0.962118i | \(-0.587894\pi\) |
0.696903 | + | 0.717166i | \(0.254561\pi\) | |||||||
\(398\) | − | 12.0702i | − | 0.605024i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98896 | + | 0.332104i | −0.249448 | + | 0.0166052i | ||||
\(401\) | −4.98896 | − | 8.64113i | −0.249137 | − | 0.431517i | 0.714150 | − | 0.699993i | \(-0.246814\pi\) |
−0.963287 | + | 0.268475i | \(0.913480\pi\) | |||||||
\(402\) | −1.09605 | − | 0.632805i | −0.0546660 | − | 0.0315614i | ||||
\(403\) | 1.34254 | + | 0.775114i | 0.0668765 | + | 0.0386112i | ||||
\(404\) | 7.72747 | + | 13.3844i | 0.384456 | + | 0.665897i | ||||
\(405\) | 0.0743018 | + | 2.23483i | 0.00369209 | + | 0.111050i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.7309i | 1.62241i | ||||||||
\(408\) | 2.51741 | − | 1.45342i | 0.124630 | − | 0.0719552i | ||||
\(409\) | 17.5919 | − | 30.4700i | 0.869862 | − | 1.50665i | 0.00772514 | − | 0.999970i | \(-0.497541\pi\) |
0.862137 | − | 0.506675i | \(-0.169126\pi\) | |||||||
\(410\) | 7.03432 | − | 13.1764i | 0.347400 | − | 0.650738i | ||||
\(411\) | −4.93351 | − | 8.54508i | −0.243352 | − | 0.421498i | ||||
\(412\) | 3.12563i | 0.153989i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.78984 | −0.0879660 | ||||||||
\(415\) | −1.03329 | − | 1.65978i | −0.0507224 | − | 0.0814756i | ||||
\(416\) | −0.820620 | + | 1.42135i | −0.0402342 | + | 0.0696877i | ||||
\(417\) | −14.6906 | − | 8.48159i | −0.719399 | − | 0.415345i | ||||
\(418\) | 5.84830 | − | 3.37652i | 0.286050 | − | 0.165151i | ||||
\(419\) | −18.6274 | −0.910009 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.6464 | 1.54235 | 0.771176 | − | 0.636622i | \(-0.219669\pi\) | ||||
0.771176 | + | 0.636622i | \(0.219669\pi\) | |||||||
\(422\) | 2.55610 | − | 1.47577i | 0.124429 | − | 0.0718392i | ||||
\(423\) | 9.85235 | + | 5.68826i | 0.479038 | + | 0.276573i | ||||
\(424\) | 2.89492 | − | 5.01415i | 0.140590 | − | 0.243509i | ||||
\(425\) | 12.0765 | − | 8.08712i | 0.585798 | − | 0.392283i | ||||
\(426\) | −14.8523 | −0.719595 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.78249i | 0.231170i | ||||||||
\(429\) | −2.50736 | − | 4.34288i | −0.121057 | − | 0.209676i | ||||
\(430\) | −20.7163 | − | 11.0595i | −0.999027 | − | 0.533336i | ||||
\(431\) | 7.40229 | − | 12.8211i | 0.356556 | − | 0.617572i | −0.630827 | − | 0.775923i | \(-0.717284\pi\) |
0.987383 | + | 0.158351i | \(0.0506177\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 4.24731i | − | 0.204113i | −0.994779 | − | 0.102056i | \(-0.967458\pi\) | ||
0.994779 | − | 0.102056i | \(-0.0325422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.4853 | + | 0.415100i | −0.598623 | + | 0.0199025i | ||||
\(436\) | 4.55178 | + | 7.88391i | 0.217991 | + | 0.377571i | ||||
\(437\) | −3.42585 | − | 1.97792i | −0.163881 | − | 0.0946166i | ||||
\(438\) | 6.85577 | + | 3.95818i | 0.327581 | + | 0.189129i | ||||
\(439\) | −1.11440 | − | 1.93020i | −0.0531874 | − | 0.0921232i | 0.838206 | − | 0.545354i | \(-0.183605\pi\) |
−0.891393 | + | 0.453231i | \(0.850271\pi\) | |||||||
\(440\) | −6.82843 | + | 0.227026i | −0.325532 | + | 0.0108230i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4.77083i | − | 0.226925i | ||||||
\(443\) | 4.02020 | − | 2.32106i | 0.191005 | − | 0.110277i | −0.401448 | − | 0.915882i | \(-0.631493\pi\) |
0.592453 | + | 0.805605i | \(0.298160\pi\) | |||||||
\(444\) | −5.35615 | + | 9.27713i | −0.254192 | + | 0.440273i | ||||
\(445\) | 34.5363 | + | 18.4374i | 1.63718 | + | 0.874017i | ||||
\(446\) | 5.88388 | + | 10.1912i | 0.278610 | + | 0.482566i | ||||
\(447\) | 8.04810i | 0.380662i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.69059 | 0.174170 | 0.0870849 | − | 0.996201i | \(-0.472245\pi\) | ||||
0.0870849 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(450\) | 4.15451 | − | 2.78209i | 0.195846 | − | 0.131149i | ||||
\(451\) | 10.2049 | − | 17.6755i | 0.480532 | − | 0.832306i | ||||
\(452\) | −12.4692 | − | 7.19912i | −0.586503 | − | 0.338618i | ||||
\(453\) | 8.64113 | − | 4.98896i | 0.405996 | − | 0.234402i | ||||
\(454\) | −13.2365 | −0.621222 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.21016 | 0.103500 | ||||||||
\(457\) | −2.36401 | + | 1.36486i | −0.110584 | + | 0.0638455i | −0.554272 | − | 0.832336i | \(-0.687003\pi\) |
0.443688 | + | 0.896181i | \(0.353670\pi\) | |||||||
\(458\) | 21.8626 | + | 12.6224i | 1.02157 | + | 0.589806i | ||||
\(459\) | −1.45342 | + | 2.51741i | −0.0678400 | + | 0.117502i | ||||
\(460\) | 2.11517 | + | 3.39761i | 0.0986204 | + | 0.158414i | ||||
\(461\) | 11.8072 | 0.549918 | 0.274959 | − | 0.961456i | \(-0.411336\pi\) | ||||
0.274959 | + | 0.961456i | \(0.411336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.40561i | − | 0.111798i | −0.998436 | − | 0.0558990i | \(-0.982198\pi\) | ||
0.998436 | − | 0.0558990i | \(-0.0178025\pi\) | |||||||
\(464\) | 2.79334 | + | 4.83820i | 0.129677 | + | 0.224608i | ||||
\(465\) | −0.994674 | + | 1.86319i | −0.0461269 | + | 0.0864033i | ||||
\(466\) | −1.66421 | + | 2.88249i | −0.0770930 | + | 0.133529i | ||||
\(467\) | −12.6969 | + | 7.33058i | −0.587544 | + | 0.339219i | −0.764126 | − | 0.645067i | \(-0.776829\pi\) |
0.176582 | + | 0.984286i | \(0.443496\pi\) | |||||||
\(468\) | − | 1.64124i | − | 0.0758663i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.845296 | − | 25.4246i | −0.0389906 | − | 1.17275i | ||||
\(471\) | 6.33381 | + | 10.9705i | 0.291847 | + | 0.505493i | ||||
\(472\) | 5.17703 | + | 2.98896i | 0.238292 | + | 0.137578i | ||||
\(473\) | −27.7897 | − | 16.0444i | −1.27777 | − | 0.737723i | ||||
\(474\) | 7.14949 | + | 12.3833i | 0.328387 | + | 0.568783i | ||||
\(475\) | 11.0264 | − | 0.734003i | 0.505925 | − | 0.0336783i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.78984i | 0.265099i | ||||||||
\(478\) | −21.5392 | + | 12.4357i | −0.985179 | + | 0.568794i | ||||
\(479\) | 5.94669 | − | 10.3000i | 0.271711 | − | 0.470617i | −0.697589 | − | 0.716498i | \(-0.745744\pi\) |
0.969300 | + | 0.245881i | \(0.0790772\pi\) | |||||||
\(480\) | −1.97257 | − | 1.05307i | −0.0900352 | − | 0.0480658i | ||||
\(481\) | 8.79073 | + | 15.2260i | 0.400823 | + | 0.694245i | ||||
\(482\) | 10.3535i | 0.471591i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.66421 | 0.0756458 | ||||||||
\(485\) | −12.3466 | − | 19.8323i | −0.560629 | − | 0.900541i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 30.7454 | + | 17.7509i | 1.39321 | + | 0.804370i | 0.993669 | − | 0.112346i | \(-0.0358365\pi\) |
0.399540 | + | 0.916716i | \(0.369170\pi\) | |||||||
\(488\) | −0.386083 | + | 0.222905i | −0.0174772 | + | 0.0100905i | ||||
\(489\) | 23.5646 | 1.06563 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.978284 | −0.0441493 | −0.0220747 | − | 0.999756i | \(-0.507027\pi\) | ||||
−0.0220747 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(492\) | 5.78490 | − | 3.33991i | 0.260803 | − | 0.150575i | ||||
\(493\) | −14.0639 | − | 8.11981i | −0.633407 | − | 0.365698i | ||||
\(494\) | 1.81370 | − | 3.14142i | 0.0816021 | − | 0.141339i | ||||
\(495\) | 5.80008 | − | 3.61082i | 0.260694 | − | 0.162294i | ||||
\(496\) | 0.944547 | 0.0424114 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 0.874366i | − | 0.0391813i | ||||||
\(499\) | 5.86701 | + | 10.1620i | 0.262644 | + | 0.454912i | 0.966944 | − | 0.254991i | \(-0.0820724\pi\) |
−0.704300 | + | 0.709902i | \(0.748739\pi\) | |||||||
\(500\) | −10.1908 | − | 4.59862i | −0.455747 | − | 0.205657i | ||||
\(501\) | −9.04092 | + | 15.6593i | −0.403918 | + | 0.699607i | ||||
\(502\) | 14.3329 | − | 8.27512i | 0.639710 | − | 0.369337i | ||||
\(503\) | − | 17.3618i | − | 0.774125i | −0.922054 | − | 0.387062i | \(-0.873490\pi\) | ||
0.922054 | − | 0.387062i | \(-0.126510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14833 | + | 34.5392i | 0.0511000 | + | 1.53697i | ||||
\(506\) | 2.73439 | + | 4.73610i | 0.121558 | + | 0.210545i | ||||
\(507\) | 8.92555 | + | 5.15317i | 0.396397 | + | 0.228860i | ||||
\(508\) | −7.32142 | − | 4.22703i | −0.324836 | − | 0.187544i | ||||
\(509\) | 12.9147 | + | 22.3688i | 0.572432 | + | 0.991481i | 0.996315 | + | 0.0857647i | \(0.0273333\pi\) |
−0.423883 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(510\) | 6.49632 | − | 0.215984i | 0.287662 | − | 0.00956394i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.91405 | + | 1.10508i | −0.0845075 | + | 0.0487904i | ||||
\(514\) | −12.2273 | + | 21.1783i | −0.539322 | + | 0.934134i | ||||
\(515\) | −3.29151 | + | 6.16554i | −0.145041 | + | 0.271686i | ||||
\(516\) | −5.25107 | − | 9.09513i | −0.231166 | − | 0.400391i | ||||
\(517\) | − | 34.7604i | − | 1.52876i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.93845 | 0.0850884 | ||||||||
\(520\) | −3.11552 | + | 1.93956i | −0.136624 | + | 0.0850552i | ||||
\(521\) | 12.3733 | − | 21.4312i | 0.542083 | − | 0.938916i | −0.456701 | − | 0.889620i | \(-0.650969\pi\) |
0.998784 | − | 0.0492955i | \(-0.0156976\pi\) | |||||||
\(522\) | −4.83820 | − | 2.79334i | −0.211762 | − | 0.122261i | ||||
\(523\) | 1.39927 | − | 0.807871i | 0.0611860 | − | 0.0353258i | −0.469095 | − | 0.883148i | \(-0.655420\pi\) |
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(524\) | −8.32106 | −0.363507 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.5091 | −0.545424 | ||||||||
\(527\) | −2.37781 | + | 1.37283i | −0.103579 | + | 0.0598013i | ||||
\(528\) | −2.64610 | − | 1.52773i | −0.115157 | − | 0.0664858i | ||||
\(529\) | −9.89823 | + | 17.1442i | −0.430358 | + | 0.745402i | ||||
\(530\) | 10.9907 | − | 6.84223i | 0.477405 | − | 0.297207i | ||||
\(531\) | −5.97792 | −0.259420 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.9632i | − | 0.474868i | ||||||
\(534\) | 8.75413 | + | 15.1626i | 0.378828 | + | 0.656149i | ||||
\(535\) | −5.03629 | + | 9.43381i | −0.217738 | + | 0.407859i | ||||
\(536\) | −0.632805 | + | 1.09605i | −0.0273330 | + | 0.0473422i | ||||
\(537\) | −21.1711 | + | 12.2232i | −0.913602 | + | 0.527469i | ||||
\(538\) | 18.9666i | 0.817708i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.23483 | − | 0.0743018i | 0.0961719 | − | 0.00319744i | ||||
\(541\) | −12.3765 | − | 21.4368i | −0.532108 | − | 0.921638i | −0.999297 | − | 0.0374808i | \(-0.988067\pi\) |
0.467189 | − | 0.884157i | \(-0.345267\pi\) | |||||||
\(542\) | −17.0294 | − | 9.83192i | −0.731475 | − | 0.422317i | ||||
\(543\) | −14.7041 | − | 8.48940i | −0.631012 | − | 0.364315i | ||||
\(544\) | −1.45342 | − | 2.51741i | −0.0623151 | − | 0.107933i | ||||
\(545\) | 0.676410 | + | 20.3449i | 0.0289742 | + | 0.871481i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 44.0524i | − | 1.88354i | −0.336253 | − | 0.941772i | \(-0.609160\pi\) | ||
0.336253 | − | 0.941772i | \(-0.390840\pi\) | |||||||
\(548\) | −8.54508 | + | 4.93351i | −0.365028 | + | 0.210749i | ||||
\(549\) | 0.222905 | − | 0.386083i | 0.00951337 | − | 0.0164776i | ||||
\(550\) | −13.7086 | − | 6.74298i | −0.584539 | − | 0.287522i | ||||
\(551\) | −6.17371 | − | 10.6932i | −0.263009 | − | 0.455545i | ||||
\(552\) | 1.78984i | 0.0761808i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.13998 | 0.260863 | ||||||||
\(555\) | −20.3349 | + | 12.6594i | −0.863167 | + | 0.537362i | ||||
\(556\) | −8.48159 | + | 14.6906i | −0.359700 | + | 0.623018i | ||||
\(557\) | 1.79249 | + | 1.03490i | 0.0759504 | + | 0.0438500i | 0.537494 | − | 0.843267i | \(-0.319371\pi\) |
−0.461544 | + | 0.887117i | \(0.652704\pi\) | |||||||
\(558\) | −0.818002 | + | 0.472274i | −0.0346288 | + | 0.0199929i | ||||
\(559\) | −17.2365 | −0.729028 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.88174 | 0.374987 | ||||||||
\(562\) | −10.5075 | + | 6.06649i | −0.443231 | + | 0.255900i | ||||
\(563\) | 8.52596 | + | 4.92246i | 0.359326 | + | 0.207457i | 0.668785 | − | 0.743456i | \(-0.266815\pi\) |
−0.309459 | + | 0.950913i | \(0.600148\pi\) | |||||||
\(564\) | 5.68826 | − | 9.85235i | 0.239519 | − | 0.414859i | ||||
\(565\) | −17.0153 | − | 27.3318i | −0.715839 | − | 1.14986i | ||||
\(566\) | −17.4172 | −0.732101 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.8523i | 0.623188i | ||||||||
\(569\) | 6.87805 | + | 11.9131i | 0.288343 | + | 0.499425i | 0.973414 | − | 0.229051i | \(-0.0735623\pi\) |
−0.685071 | + | 0.728476i | \(0.740229\pi\) | |||||||
\(570\) | 4.35970 | + | 2.32745i | 0.182608 | + | 0.0974861i | ||||
\(571\) | −9.60354 | + | 16.6338i | −0.401896 | + | 0.696104i | −0.993955 | − | 0.109791i | \(-0.964982\pi\) |
0.592059 | + | 0.805895i | \(0.298315\pi\) | |||||||
\(572\) | −4.34288 | + | 2.50736i | −0.181585 | + | 0.104838i | ||||
\(573\) | − | 0.741377i | − | 0.0309715i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.594414 | + | 8.92945i | 0.0247888 | + | 0.372384i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 32.3090 | + | 18.6536i | 1.34504 | + | 0.776560i | 0.987542 | − | 0.157353i | \(-0.0502960\pi\) |
0.357500 | + | 0.933913i | \(0.383629\pi\) | |||||||
\(578\) | −7.40471 | − | 4.27511i | −0.307996 | − | 0.177821i | ||||
\(579\) | −3.05545 | − | 5.29220i | −0.126980 | − | 0.219936i | ||||
\(580\) | 0.415100 | + | 12.4853i | 0.0172361 | + | 0.518423i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 10.4476i | − | 0.433066i | ||||||
\(583\) | 15.3205 | − | 8.84530i | 0.634510 | − | 0.366335i | ||||
\(584\) | 3.95818 | − | 6.85577i | 0.163791 | − | 0.283694i | ||||
\(585\) | 1.72834 | − | 3.23746i | 0.0714580 | − | 0.133853i | ||||
\(586\) | 11.8761 | + | 20.5700i | 0.490596 | + | 0.849737i | ||||
\(587\) | − | 19.5459i | − | 0.806748i | −0.915035 | − | 0.403374i | \(-0.867837\pi\) | ||
0.915035 | − | 0.403374i | \(-0.132163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.08760 | −0.0860180 | ||||||||
\(590\) | 7.06449 | + | 11.3477i | 0.290840 | + | 0.467178i | ||||
\(591\) | −10.3416 | + | 17.9122i | −0.425397 | + | 0.736810i | ||||
\(592\) | 9.27713 | + | 5.35615i | 0.381288 | + | 0.220137i | ||||
\(593\) | 25.0648 | − | 14.4712i | 1.02929 | − | 0.594260i | 0.112508 | − | 0.993651i | \(-0.464112\pi\) |
0.916781 | + | 0.399391i | \(0.130778\pi\) | |||||||
\(594\) | 3.05545 | 0.125367 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.04810 | 0.329663 | ||||||||
\(597\) | 10.4531 | − | 6.03509i | 0.427816 | − | 0.247000i | ||||
\(598\) | 2.54400 | + | 1.46878i | 0.104032 | + | 0.0600629i | ||||
\(599\) | −4.86585 | + | 8.42790i | −0.198813 | + | 0.344355i | −0.948144 | − | 0.317841i | \(-0.897042\pi\) |
0.749331 | + | 0.662196i | \(0.230375\pi\) | |||||||
\(600\) | −2.78209 | − | 4.15451i | −0.113578 | − | 0.169607i | ||||
\(601\) | 33.4038 | 1.36257 | 0.681284 | − | 0.732019i | \(-0.261422\pi\) | ||||
0.681284 | + | 0.732019i | \(0.261422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.26561i | − | 0.0515396i | ||||||
\(604\) | −4.98896 | − | 8.64113i | −0.202998 | − | 0.351603i | ||||
\(605\) | 3.28277 | + | 1.75253i | 0.133464 | + | 0.0712504i | ||||
\(606\) | −7.72747 | + | 13.3844i | −0.313907 | + | 0.543703i | ||||
\(607\) | 37.4433 | − | 21.6179i | 1.51978 | − | 0.877444i | 0.520049 | − | 0.854137i | \(-0.325914\pi\) |
0.999728 | − | 0.0233069i | \(-0.00741949\pi\) | |||||||
\(608\) | − | 2.21016i | − | 0.0896337i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.996313 | + | 0.0331245i | −0.0403395 | + | 0.00134117i | ||||
\(611\) | −9.33579 | − | 16.1701i | −0.377686 | − | 0.654171i | ||||
\(612\) | 2.51741 | + | 1.45342i | 0.101760 | + | 0.0587512i | ||||
\(613\) | −1.55038 | − | 0.895115i | −0.0626195 | − | 0.0361534i | 0.468363 | − | 0.883536i | \(-0.344844\pi\) |
−0.530983 | + | 0.847383i | \(0.678177\pi\) | |||||||
\(614\) | −3.95406 | − | 6.84864i | −0.159573 | − | 0.276388i | ||||
\(615\) | 14.9283 | − | 0.496323i | 0.601967 | − | 0.0200137i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 38.2665i | − | 1.54055i | −0.637712 | − | 0.770275i | \(-0.720119\pi\) | ||
0.637712 | − | 0.770275i | \(-0.279881\pi\) | |||||||
\(618\) | −2.70688 | + | 1.56282i | −0.108887 | + | 0.0628657i | ||||
\(619\) | 0.0664943 | − | 0.115171i | 0.00267263 | − | 0.00462913i | −0.864686 | − | 0.502313i | \(-0.832483\pi\) |
0.867359 | + | 0.497684i | \(0.165816\pi\) | |||||||
\(620\) | 1.86319 | + | 0.994674i | 0.0748275 | + | 0.0399471i | ||||
\(621\) | −0.894921 | − | 1.55005i | −0.0359120 | − | 0.0622013i | ||||
\(622\) | − | 10.0772i | − | 0.404058i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.64124 | −0.0657022 | ||||||||
\(625\) | −15.2595 | − | 19.8027i | −0.610379 | − | 0.792110i | ||||
\(626\) | −10.1922 | + | 17.6534i | −0.407362 | + | 0.705572i | ||||
\(627\) | 5.84830 | + | 3.37652i | 0.233558 | + | 0.134845i | ||||
\(628\) | 10.9705 | − | 6.33381i | 0.437770 | − | 0.252747i | ||||
\(629\) | −31.1391 | −1.24160 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1850 | −1.00260 | −0.501299 | − | 0.865274i | \(-0.667145\pi\) | ||||
−0.501299 | + | 0.865274i | \(0.667145\pi\) | |||||||
\(632\) | 12.3833 | − | 7.14949i | 0.492580 | − | 0.284391i | ||||
\(633\) | 2.55610 | + | 1.47577i | 0.101596 | + | 0.0586565i | ||||
\(634\) | −0.160531 | + | 0.278048i | −0.00637551 | + | 0.0110427i | ||||
\(635\) | −9.99069 | − | 16.0481i | −0.396469 | − | 0.636849i | ||||
\(636\) | 5.78984 | 0.229582 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17.0698i | 0.675800i | ||||||||
\(639\) | −7.42614 | − | 12.8625i | −0.293774 | − | 0.508831i | ||||
\(640\) | −1.05307 | + | 1.97257i | −0.0416262 | + | 0.0779728i | ||||
\(641\) | 12.2953 | − | 21.2961i | 0.485635 | − | 0.841144i | −0.514229 | − | 0.857653i | \(-0.671922\pi\) |
0.999864 | + | 0.0165088i | \(0.00525514\pi\) | |||||||
\(642\) | −4.14176 | + | 2.39124i | −0.163462 | + | 0.0943749i | ||||
\(643\) | − | 9.15126i | − | 0.360891i | −0.983585 | − | 0.180445i | \(-0.942246\pi\) | ||
0.983585 | − | 0.180445i | \(-0.0577539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.780329 | − | 23.4706i | −0.0307254 | − | 0.924152i | ||||
\(646\) | 3.21230 | + | 5.56386i | 0.126386 | + | 0.218907i | ||||
\(647\) | 27.6494 | + | 15.9634i | 1.08701 | + | 0.627585i | 0.932779 | − | 0.360450i | \(-0.117377\pi\) |
0.154231 | + | 0.988035i | \(0.450710\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 9.13262 | + | 15.8182i | 0.358487 | + | 0.620917i | ||||
\(650\) | −8.18807 | + | 0.545062i | −0.321163 | + | 0.0213791i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 23.5646i | − | 0.922861i | ||||||
\(653\) | −2.65215 | + | 1.53122i | −0.103787 | + | 0.0599213i | −0.550995 | − | 0.834509i | \(-0.685752\pi\) |
0.447208 | + | 0.894430i | \(0.352418\pi\) | |||||||
\(654\) | −4.55178 | + | 7.88391i | −0.177989 | + | 0.308285i | ||||
\(655\) | −16.4139 | − | 8.76266i | −0.641344 | − | 0.342385i | ||||
\(656\) | −3.33991 | − | 5.78490i | −0.130402 | − | 0.225862i | ||||
\(657\) | 7.91636i | 0.308847i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.16636 | 0.357071 | 0.178535 | − | 0.983934i | \(-0.442864\pi\) | ||||
0.178535 | + | 0.983934i | \(0.442864\pi\) | |||||||
\(660\) | −3.61082 | − | 5.80008i | −0.140551 | − | 0.225768i | ||||
\(661\) | −15.7091 | + | 27.2089i | −0.611012 | + | 1.05830i | 0.380058 | + | 0.924963i | \(0.375904\pi\) |
−0.991070 | + | 0.133341i | \(0.957429\pi\) | |||||||
\(662\) | 14.3833 | + | 8.30419i | 0.559022 | + | 0.322752i | ||||
\(663\) | 4.13166 | − | 2.38542i | 0.160461 | − | 0.0926419i | ||||
\(664\) | −0.874366 | −0.0339320 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.7123 | −0.415093 | ||||||||
\(667\) | 8.65962 | − | 4.99963i | 0.335302 | − | 0.193587i | ||||
\(668\) | 15.6593 | + | 9.04092i | 0.605878 | + | 0.349804i | ||||
\(669\) | −5.88388 | + | 10.1912i | −0.227484 | + | 0.394014i | ||||
\(670\) | −2.40247 | + | 1.49565i | −0.0928156 | + | 0.0577821i | ||||
\(671\) | −1.36215 | −0.0525854 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.45100i | − | 0.248668i | −0.992240 | − | 0.124334i | \(-0.960321\pi\) | ||
0.992240 | − | 0.124334i | \(-0.0396794\pi\) | |||||||
\(674\) | −0.955589 | − | 1.65513i | −0.0368079 | − | 0.0637532i | ||||
\(675\) | 4.48662 | + | 2.20687i | 0.172690 | + | 0.0849424i | ||||
\(676\) | 5.15317 | − | 8.92555i | 0.198199 | − | 0.343290i | ||||
\(677\) | −5.20814 | + | 3.00692i | −0.200165 | + | 0.115565i | −0.596732 | − | 0.802440i | \(-0.703535\pi\) |
0.396567 | + | 0.918006i | \(0.370201\pi\) | |||||||
\(678\) | − | 14.3982i | − | 0.552961i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.215984 | − | 6.49632i | −0.00828261 | − | 0.249123i | ||||
\(681\) | −6.61827 | − | 11.4632i | −0.253613 | − | 0.439270i | ||||
\(682\) | 2.49937 | + | 1.44301i | 0.0957057 | + | 0.0552557i | ||||
\(683\) | 7.72675 | + | 4.46104i | 0.295656 | + | 0.170697i | 0.640490 | − | 0.767967i | \(-0.278731\pi\) |
−0.344834 | + | 0.938664i | \(0.612065\pi\) | |||||||
\(684\) | 1.10508 | + | 1.91405i | 0.0422537 | + | 0.0731856i | ||||
\(685\) | −22.0511 | + | 0.733137i | −0.842530 | + | 0.0280117i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.2448i | 0.963148i | ||||||||
\(688\) | −9.09513 | + | 5.25107i | −0.346749 | + | 0.200195i | ||||
\(689\) | 4.75126 | − | 8.22942i | 0.181009 | − | 0.313516i | ||||
\(690\) | −1.88483 | + | 3.53060i | −0.0717542 | + | 0.134407i | ||||
\(691\) | −23.8290 | − | 41.2731i | −0.906499 | − | 1.57010i | −0.818892 | − | 0.573948i | \(-0.805411\pi\) |
−0.0876076 | − | 0.996155i | \(-0.527922\pi\) | |||||||
\(692\) | − | 1.93845i | − | 0.0736887i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.90812 | 0.300188 | ||||||||
\(695\) | −32.2007 | + | 20.0465i | −1.22144 | + | 0.760406i | ||||
\(696\) | −2.79334 | + | 4.83820i | −0.105881 | + | 0.183392i | ||||
\(697\) | 16.8158 | + | 9.70862i | 0.636945 | + | 0.367740i | ||||
\(698\) | 20.3752 | − | 11.7636i | 0.771214 | − | 0.445260i | ||||
\(699\) | −3.32842 | −0.125892 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0788 | 1.17383 | 0.586914 | − | 0.809649i | \(-0.300343\pi\) | ||||
0.586914 | + | 0.809649i | \(0.300343\pi\) | |||||||
\(702\) | 1.42135 | − | 0.820620i | 0.0536456 | − | 0.0309723i | ||||
\(703\) | −20.5039 | − | 11.8379i | −0.773320 | − | 0.446476i | ||||
\(704\) | −1.52773 | + | 2.64610i | −0.0575784 | + | 0.0997286i | ||||
\(705\) | 21.5957 | − | 13.4444i | 0.813342 | − | 0.506344i | ||||
\(706\) | −22.9718 | −0.864556 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.97792i | 0.224664i | ||||||||
\(709\) | −6.09074 | − | 10.5495i | −0.228742 | − | 0.396194i | 0.728693 | − | 0.684840i | \(-0.240128\pi\) |
−0.957436 | + | 0.288647i | \(0.906795\pi\) | |||||||
\(710\) | −15.6405 | + | 29.2972i | −0.586977 | + | 1.09950i | ||||
\(711\) | −7.14949 | + | 12.3833i | −0.268127 | + | 0.464409i | ||||
\(712\) | 15.1626 | − | 8.75413i | 0.568242 | − | 0.328075i | ||||
\(713\) | − | 1.69059i | − | 0.0633131i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2071 | + | 0.372603i | −0.419121 | + | 0.0139346i | ||||
\(716\) | 12.2232 | + | 21.1711i | 0.456801 | + | 0.791203i | ||||
\(717\) | −21.5392 | − | 12.4357i | −0.804396 | − | 0.464418i | ||||
\(718\) | 9.54913 | + | 5.51319i | 0.356370 | + | 0.205750i | ||||
\(719\) | −15.9948 | − | 27.7038i | −0.596505 | − | 1.03318i | −0.993333 | − | 0.115284i | \(-0.963222\pi\) |
0.396828 | − | 0.917893i | \(-0.370111\pi\) | |||||||
\(720\) | −0.0743018 | − | 2.23483i | −0.00276906 | − | 0.0832873i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 14.1152i | − | 0.525314i | ||||||
\(723\) | −8.96643 | + | 5.17677i | −0.333465 | + | 0.192526i | ||||
\(724\) | −8.48940 | + | 14.7041i | −0.315506 | + | 0.546473i | ||||
\(725\) | −12.3291 | + | 25.0653i | −0.457890 | + | 0.930900i | ||||
\(726\) | 0.832104 | + | 1.44125i | 0.0308823 | + | 0.0534897i | ||||
\(727\) | − | 22.9992i | − | 0.852995i | −0.904489 | − | 0.426497i | \(-0.859747\pi\) | ||
0.904489 | − | 0.426497i | \(-0.140253\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 15.0274 | − | 9.35527i | 0.556189 | − | 0.346254i | ||||
\(731\) | 15.2641 | − | 26.4382i | 0.564562 | − | 0.977851i | ||||
\(732\) | −0.386083 | − | 0.222905i | −0.0142701 | − | 0.00823882i | ||||
\(733\) | 15.2422 | − | 8.80006i | 0.562982 | − | 0.325038i | −0.191360 | − | 0.981520i | \(-0.561290\pi\) |
0.754341 | + | 0.656482i | \(0.227956\pi\) | |||||||
\(734\) | −10.1446 | −0.374446 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.78984 | 0.0659745 | ||||||||
\(737\) | −3.34893 | + | 1.93351i | −0.123359 | + | 0.0712216i | ||||
\(738\) | 5.78490 | + | 3.33991i | 0.212945 | + | 0.122944i | ||||
\(739\) | −0.0870500 | + | 0.150775i | −0.00320218 | + | 0.00554635i | −0.867622 | − | 0.497224i | \(-0.834353\pi\) |
0.864420 | + | 0.502771i | \(0.167686\pi\) | |||||||
\(740\) | 12.6594 | + | 20.3349i | 0.465369 | + | 0.747525i | ||||
\(741\) | 3.62740 | 0.133256 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 53.6360i | − | 1.96771i | −0.178957 | − | 0.983857i | \(-0.557272\pi\) | ||
0.178957 | − | 0.983857i | \(-0.442728\pi\) | |||||||
\(744\) | 0.472274 | + | 0.818002i | 0.0173144 | + | 0.0299894i | ||||
\(745\) | 15.8755 | + | 8.47521i | 0.581632 | + | 0.310508i | ||||
\(746\) | 13.2511 | − | 22.9515i | 0.485156 | − | 0.840315i | ||||
\(747\) | 0.757223 | − | 0.437183i | 0.0277053 | − | 0.0159957i | ||||
\(748\) | − | 8.88174i | − | 0.324749i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.11289 | − | 11.1248i | −0.0406369 | − | 0.406221i | ||||
\(751\) | −14.5466 | − | 25.1954i | −0.530812 | − | 0.919393i | −0.999354 | − | 0.0359513i | \(-0.988554\pi\) |
0.468542 | − | 0.883441i | \(-0.344779\pi\) | |||||||
\(752\) | −9.85235 | − | 5.68826i | −0.359278 | − | 0.207429i | ||||
\(753\) | 14.3329 | + | 8.27512i | 0.522321 | + | 0.301562i | ||||
\(754\) | 4.58453 | + | 7.94064i | 0.166959 | + | 0.289181i | ||||
\(755\) | −0.741377 | − | 22.2990i | −0.0269815 | − | 0.811543i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.0842i | − | 1.23881i | −0.785072 | − | 0.619405i | \(-0.787374\pi\) | ||
0.785072 | − | 0.619405i | \(-0.212626\pi\) | |||||||
\(758\) | −25.4734 | + | 14.7071i | −0.925237 | + | 0.534186i | ||||
\(759\) | −2.73439 | + | 4.73610i | −0.0992521 | + | 0.171910i | ||||
\(760\) | 2.32745 | − | 4.35970i | 0.0844254 | − | 0.158143i | ||||
\(761\) | 3.81479 | + | 6.60741i | 0.138286 | + | 0.239519i | 0.926848 | − | 0.375437i | \(-0.122507\pi\) |
−0.788562 | + | 0.614955i | \(0.789174\pi\) | |||||||
\(762\) | − | 8.45405i | − | 0.306258i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.741377 | −0.0268221 | ||||||||
\(765\) | 3.43521 | + | 5.51799i | 0.124200 | + | 0.199503i | ||||
\(766\) | −1.82125 | + | 3.15449i | −0.0658043 | + | 0.113976i | ||||
\(767\) | 8.49674 | + | 4.90560i | 0.306800 | + | 0.177131i | ||||
\(768\) | −0.866025 | + | 0.500000i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 37.8241 | 1.36397 | 0.681986 | − | 0.731365i | \(-0.261117\pi\) | ||||
0.681986 | + | 0.731365i | \(0.261117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.4546 | −0.880710 | ||||||||
\(772\) | −5.29220 | + | 3.05545i | −0.190470 | + | 0.109968i | ||||
\(773\) | −21.8541 | − | 12.6174i | −0.786036 | − | 0.453818i | 0.0525292 | − | 0.998619i | \(-0.483272\pi\) |
−0.838565 | + | 0.544801i | \(0.816605\pi\) | |||||||
\(774\) | 5.25107 | − | 9.09513i | 0.188746 | − | 0.326918i | ||||
\(775\) | 2.62782 | + | 3.92413i | 0.0943939 | + | 0.140959i | ||||
\(776\) | −10.4476 | −0.375046 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.7938i | 0.853048i | ||||||||
\(779\) | 7.38173 | + | 12.7855i | 0.264478 | + | 0.458089i | ||||
\(780\) | −3.23746 | − | 1.72834i | −0.115920 | − | 0.0618845i | ||||
\(781\) | −22.6902 | + | 39.3006i | −0.811920 | + | 1.40629i | ||||
\(782\) | −4.50576 | + | 2.60140i | −0.161126 | + | 0.0930259i | ||||
\(783\) | − | 5.58667i | − | 0.199651i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.3100 | − | 0.941227i | 1.01043 | − | 0.0335938i | ||||
\(786\) | −4.16053 | − | 7.20625i | −0.148401 | − | 0.257038i | ||||
\(787\) | 19.6755 | + | 11.3596i | 0.701355 | + | 0.404928i | 0.807852 | − | 0.589385i | \(-0.200630\pi\) |
−0.106497 | + | 0.994313i | \(0.533963\pi\) | |||||||
\(788\) | 17.9122 | + | 10.3416i | 0.638096 | + | 0.368405i | ||||
\(789\) | −6.25457 | − | 10.8332i | −0.222669 | − | 0.385673i | ||||
\(790\) | 31.9558 | − | 1.06244i | 1.13694 | − | 0.0377999i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 3.05545i | − | 0.108571i | ||||||
\(793\) | −0.633655 | + | 0.365841i | −0.0225018 | + | 0.0129914i | ||||
\(794\) | 4.88065 | − | 8.45353i | 0.173208 | − | 0.300004i | ||||
\(795\) | 11.4209 | + | 6.09711i | 0.405057 | + | 0.216242i | ||||
\(796\) | −6.03509 | − | 10.4531i | −0.213908 | − | 0.370500i | ||||
\(797\) | − | 10.1057i | − | 0.357963i | −0.983852 | − | 0.178981i | \(-0.942720\pi\) | ||
0.983852 | − | 0.178981i | \(-0.0572802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.0698 | 1.16993 | ||||||||
\(800\) | −4.15451 | + | 2.78209i | −0.146884 | + | 0.0983617i | ||||
\(801\) | −8.75413 | + | 15.1626i | −0.309312 | + | 0.535744i | ||||
\(802\) | −8.64113 | − | 4.98896i | −0.305129 | − | 0.176166i | ||||
\(803\) | 20.9475 | − | 12.0940i | 0.739221 | − | 0.426789i | ||||
\(804\) | −1.26561 | −0.0446346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.55023 | 0.0546045 | ||||||||
\(807\) | −16.4256 | + | 9.48330i | −0.578207 | + | 0.333828i | ||||
\(808\) | 13.3844 | + | 7.72747i | 0.470860 | + | 0.271851i | ||||
\(809\) | 23.1590 | − | 40.1126i | 0.814227 | − | 1.41028i | −0.0956543 | − | 0.995415i | \(-0.530494\pi\) |
0.909881 | − | 0.414868i | \(-0.136172\pi\) | |||||||
\(810\) | 1.18176 | + | 1.89827i | 0.0415229 | + | 0.0666985i | ||||
\(811\) | −42.0012 | −1.47486 | −0.737431 | − | 0.675422i | \(-0.763961\pi\) | ||||
−0.737431 | + | 0.675422i | \(0.763961\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 19.6638i | − | 0.689641i | ||||||
\(814\) | 16.3655 | + | 28.3458i | 0.573610 | + | 0.993521i | ||||
\(815\) | 24.8151 | − | 46.4829i | 0.869237 | − | 1.62822i | ||||
\(816\) | 1.45342 | − | 2.51741i | 0.0508800 | − | 0.0881268i | ||||
\(817\) | 20.1017 | − | 11.6057i | 0.703268 | − | 0.406032i | ||||
\(818\) | − | 35.1837i | − | 1.23017i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.496323 | − | 14.9283i | −0.0173323 | − | 0.521319i | ||||
\(821\) | −8.44903 | − | 14.6341i | −0.294873 | − | 0.510735i | 0.680082 | − | 0.733136i | \(-0.261944\pi\) |
−0.974955 | + | 0.222401i | \(0.928611\pi\) | |||||||
\(822\) | −8.54508 | − | 4.93351i | −0.298044 | − | 0.172076i | ||||
\(823\) | −39.1791 | − | 22.6200i | −1.36570 | − | 0.788485i | −0.375321 | − | 0.926895i | \(-0.622468\pi\) |
−0.990375 | + | 0.138410i | \(0.955801\pi\) | |||||||
\(824\) | 1.56282 | + | 2.70688i | 0.0544433 | + | 0.0942986i | ||||
\(825\) | −1.01473 | − | 15.2435i | −0.0353283 | − | 0.530711i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5452i | 1.20125i | 0.799529 | + | 0.600627i | \(0.205082\pi\) | ||||
−0.799529 | + | 0.600627i | \(0.794918\pi\) | |||||||
\(828\) | −1.55005 | + | 0.894921i | −0.0538679 | + | 0.0311007i | ||||
\(829\) | −4.99802 | + | 8.65682i | −0.173588 | + | 0.300664i | −0.939672 | − | 0.342077i | \(-0.888870\pi\) |
0.766083 | + | 0.642741i | \(0.222203\pi\) | |||||||
\(830\) | −1.72475 | − | 0.920768i | −0.0598670 | − | 0.0319603i | ||||
\(831\) | 3.06999 | + | 5.31737i | 0.106497 | + | 0.184458i | ||||
\(832\) | 1.64124i | 0.0568997i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.9632 | −0.587387 | ||||||||
\(835\) | 21.3685 | + | 34.3242i | 0.739486 | + | 1.18784i | ||||
\(836\) | 3.37652 | − | 5.84830i | 0.116779 | − | 0.202268i | ||||
\(837\) | −0.818002 | − | 0.472274i | −0.0282743 | − | 0.0163242i | ||||
\(838\) | −16.1318 | + | 9.31371i | −0.557264 | + | 0.321737i | ||||
\(839\) | −32.3180 | −1.11574 | −0.557871 | − | 0.829928i | \(-0.688382\pi\) | ||||
−0.557871 | + | 0.829928i | \(0.688382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.21091 | 0.0762383 | ||||||||
\(842\) | 27.4066 | − | 15.8232i | 0.944494 | − | 0.545304i | ||||
\(843\) | −10.5075 | − | 6.06649i | −0.361897 | − | 0.208941i | ||||
\(844\) | 1.47577 | − | 2.55610i | 0.0507980 | − | 0.0879847i | ||||
\(845\) | 19.5642 | − | 12.1797i | 0.673030 | − | 0.418993i | ||||
\(846\) | 11.3765 | 0.391133 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 5.78984i | − | 0.198824i | ||||||
\(849\) | −8.70862 | − | 15.0838i | −0.298879 | − | 0.517674i | ||||
\(850\) | 6.41503 | − | 13.0419i | 0.220034 | − | 0.447334i | ||||
\(851\) | 9.58667 | − | 16.6046i | 0.328627 | − | 0.569199i | ||||
\(852\) | −12.8625 | + | 7.42614i | −0.440660 | + | 0.254415i | ||||
\(853\) | 13.7577i | 0.471056i | 0.971868 | + | 0.235528i | \(0.0756820\pi\) | ||||
−0.971868 | + | 0.235528i | \(0.924318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.164219 | + | 4.93933i | 0.00561616 | + | 0.168922i | ||||
\(856\) | 2.39124 | + | 4.14176i | 0.0817310 | + | 0.141562i | ||||
\(857\) | −6.45804 | − | 3.72855i | −0.220602 | − | 0.127365i | 0.385627 | − | 0.922655i | \(-0.373985\pi\) |
−0.606229 | + | 0.795290i | \(0.707319\pi\) | |||||||
\(858\) | −4.34288 | − | 2.50736i | −0.148264 | − | 0.0856000i | ||||
\(859\) | −16.9430 | − | 29.3462i | −0.578088 | − | 1.00128i | −0.995699 | − | 0.0926521i | \(-0.970466\pi\) |
0.417610 | − | 0.908626i | \(-0.362868\pi\) | |||||||
\(860\) | −23.4706 | + | 0.780329i | −0.800339 | + | 0.0266090i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 14.8046i | − | 0.504246i | ||||||
\(863\) | −35.7532 | + | 20.6421i | −1.21705 | + | 0.702666i | −0.964287 | − | 0.264861i | \(-0.914674\pi\) |
−0.252767 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 2.04132 | − | 3.82373i | 0.0694069 | − | 0.130011i | ||||
\(866\) | −2.12365 | − | 3.67828i | −0.0721647 | − | 0.124993i | ||||
\(867\) | − | 8.55023i | − | 0.290381i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.6899 | 1.48208 | ||||||||
\(870\) | −10.6050 | + | 6.60213i | −0.359544 | + | 0.223833i | ||||
\(871\) | −1.03858 | + | 1.79888i | −0.0351911 | + | 0.0609528i | ||||
\(872\) | 7.88391 | + | 4.55178i | 0.266983 | + | 0.154143i | ||||
\(873\) | 9.04787 | − | 5.22379i | 0.306224 | − | 0.176799i | ||||
\(874\) | −3.95583 | −0.133808 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.91636 | 0.267469 | ||||||||
\(877\) | −23.2041 | + | 13.3969i | −0.783546 | + | 0.452380i | −0.837685 | − | 0.546153i | \(-0.816092\pi\) |
0.0541396 | + | 0.998533i | \(0.482758\pi\) | |||||||
\(878\) | −1.93020 | − | 1.11440i | −0.0651410 | − | 0.0376091i | ||||
\(879\) | −11.8761 | + | 20.5700i | −0.400570 | + | 0.693808i | ||||
\(880\) | −5.80008 | + | 3.61082i | −0.195521 | + | 0.121721i | ||||
\(881\) | 31.0247 | 1.04525 | 0.522625 | − | 0.852563i | \(-0.324953\pi\) | ||||
0.522625 | + | 0.852563i | \(0.324953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.6123i | − | 1.33306i | −0.745478 | − | 0.666530i | \(-0.767779\pi\) | ||
0.745478 | − | 0.666530i | \(-0.232221\pi\) | |||||||
\(884\) | −2.38542 | − | 4.13166i | −0.0802303 | − | 0.138963i | ||||
\(885\) | −6.29516 | + | 11.7919i | −0.211610 | + | 0.396380i | ||||
\(886\) | 2.32106 | − | 4.02020i | 0.0779776 | − | 0.135061i | ||||
\(887\) | −10.2583 | + | 5.92266i | −0.344441 | + | 0.198863i | −0.662234 | − | 0.749297i | \(-0.730392\pi\) |
0.317793 | + | 0.948160i | \(0.397058\pi\) | |||||||
\(888\) | 10.7123i | 0.359481i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 39.1280 | − | 1.30089i | 1.31157 | − | 0.0436061i | ||||
\(891\) | 1.52773 | + | 2.64610i | 0.0511808 | + | 0.0886477i | ||||
\(892\) | 10.1912 | + | 5.88388i | 0.341226 | + | 0.197007i | ||||
\(893\) | 21.7752 | + | 12.5719i | 0.728681 | + | 0.420704i | ||||
\(894\) | 4.02405 | + | 6.96986i | 0.134584 | + | 0.233107i | ||||
\(895\) | 1.81641 | + | 54.6335i | 0.0607158 | + | 1.82620i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.93756i | 0.0980823i | ||||||||
\(898\) | 3.19615 | − | 1.84530i | 0.106657 | − | 0.0615783i | ||||
\(899\) | 2.63844 | − | 4.56991i | 0.0879968 | − | 0.152415i | ||||
\(900\) | 2.20687 | − | 4.48662i | 0.0735623 | − | 0.149554i | ||||
\(901\) | 8.41510 | + | 14.5754i | 0.280348 | + | 0.485576i | ||||
\(902\) | − | 20.4099i | − | 0.679575i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.3982 | −0.478878 | ||||||||
\(905\) | −32.2304 | + | 20.0649i | −1.07137 | + | 0.666981i | ||||
\(906\) | 4.98896 | − | 8.64113i | 0.165747 | − | 0.287082i | ||||
\(907\) | −14.7093 | − | 8.49244i | −0.488416 | − | 0.281987i | 0.235501 | − | 0.971874i | \(-0.424327\pi\) |
−0.723917 | + | 0.689887i | \(0.757660\pi\) | |||||||
\(908\) | −11.4632 | + | 6.61827i | −0.380419 | + | 0.219635i | ||||
\(909\) | −15.4549 | −0.512608 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5723 | 0.515934 | 0.257967 | − | 0.966154i | \(-0.416947\pi\) | ||||
0.257967 | + | 0.966154i | \(0.416947\pi\) | |||||||
\(912\) | 1.91405 | − | 1.10508i | 0.0633806 | − | 0.0365928i | ||||
\(913\) | −2.31366 | − | 1.33579i | −0.0765709 | − | 0.0442082i | ||||
\(914\) | −1.36486 | + | 2.36401i | −0.0451456 | + | 0.0781945i | ||||
\(915\) | −0.526843 | − | 0.846270i | −0.0174169 | − | 0.0279768i | ||||
\(916\) | 25.2448 | 0.834111 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.90685i | 0.0959403i | ||||||||
\(919\) | −18.4816 | − | 32.0111i | −0.609652 | − | 1.05595i | −0.991298 | − | 0.131639i | \(-0.957976\pi\) |
0.381646 | − | 0.924308i | \(-0.375357\pi\) | |||||||
\(920\) | 3.53060 | + | 1.88483i | 0.116400 | + | 0.0621410i | ||||
\(921\) | 3.95406 | − | 6.84864i | 0.130291 | − | 0.225670i | ||||
\(922\) | 10.2254 | − | 5.90362i | 0.336754 | − | 0.194425i | ||||
\(923\) | 24.3761i | 0.802351i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.55760 | + | 53.4433i | 0.116973 | + | 1.75720i | ||||
\(926\) | −1.20280 | − | 2.08332i | −0.0395266 | − | 0.0684620i | ||||
\(927\) | −2.70688 | − | 1.56282i | −0.0889056 | − | 0.0513296i | ||||
\(928\) | 4.83820 | + | 2.79334i | 0.158822 | + | 0.0916958i | ||||
\(929\) | 16.9916 | + | 29.4302i | 0.557475 | + | 0.965575i | 0.997706 | + | 0.0676903i | \(0.0215630\pi\) |
−0.440232 | + | 0.897884i | \(0.645104\pi\) | |||||||
\(930\) | 0.0701816 | + | 2.11091i | 0.00230134 | + | 0.0692193i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.32842i | 0.109026i | ||||||||
\(933\) | 8.72708 | − | 5.03858i | 0.285712 | − | 0.164956i | ||||
\(934\) | −7.33058 | + | 12.6969i | −0.239864 | + | 0.415456i | ||||
\(935\) | 9.35309 | − | 17.5199i | 0.305879 | − | 0.572961i | ||||
\(936\) | −0.820620 | − | 1.42135i | −0.0268228 | − | 0.0464584i | ||||
\(937\) | − | 43.1719i | − | 1.41037i | −0.709026 | − | 0.705183i | \(-0.750865\pi\) | ||
0.709026 | − | 0.705183i | \(-0.249135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.3844 | −0.665219 | ||||||||
\(940\) | −13.4444 | − | 21.5957i | −0.438506 | − | 0.704375i | ||||
\(941\) | 16.5593 | − | 28.6816i | 0.539818 | − | 0.934992i | −0.459095 | − | 0.888387i | \(-0.651826\pi\) |
0.998913 | − | 0.0466053i | \(-0.0148403\pi\) | |||||||
\(942\) | 10.9705 | + | 6.33381i | 0.357438 | + | 0.206367i | ||||
\(943\) | −10.3541 | + | 5.97792i | −0.337174 | + | 0.194668i | ||||
\(944\) | 5.97792 | 0.194565 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.0888 | −1.04330 | ||||||||
\(947\) | 36.5816 | − | 21.1204i | 1.18874 | − | 0.686321i | 0.230723 | − | 0.973020i | \(-0.425891\pi\) |
0.958021 | + | 0.286698i | \(0.0925577\pi\) | |||||||
\(948\) | 12.3833 | + | 7.14949i | 0.402190 | + | 0.232205i | ||||
\(949\) | 6.49632 | − | 11.2520i | 0.210880 | − | 0.365254i | ||||
\(950\) | 9.18213 | − | 6.14886i | 0.297908 | − | 0.199495i | ||||
\(951\) | −0.321063 | −0.0104112 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.2358i | 0.525929i | 0.964806 | + | 0.262964i | \(0.0847002\pi\) | ||||
−0.964806 | + | 0.262964i | \(0.915300\pi\) | |||||||
\(954\) | 2.89492 | + | 5.01415i | 0.0937265 | + | 0.162339i | ||||
\(955\) | −1.46242 | − | 0.780722i | −0.0473228 | − | 0.0252636i | ||||
\(956\) | −12.4357 | + | 21.5392i | −0.402198 | + | 0.696627i | ||||
\(957\) | −14.7829 | + | 8.53491i | −0.477863 | + | 0.275894i | ||||
\(958\) | − | 11.8934i | − | 0.384257i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.23483 | + | 0.0743018i | −0.0721289 | + | 0.00239808i | ||||
\(961\) | 15.0539 | + | 26.0741i | 0.485610 | + | 0.841101i | ||||
\(962\) | 15.2260 | + | 8.79073i | 0.490906 | + | 0.283424i | ||||
\(963\) | −4.14176 | − | 2.39124i | −0.133466 | − | 0.0770568i | ||||
\(964\) | 5.17677 | + | 8.96643i | 0.166733 | + | 0.288789i | ||||
\(965\) | −13.6569 | + | 0.454051i | −0.439630 | + | 0.0146164i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 56.9706i | − | 1.83205i | −0.401121 | − | 0.916025i | \(-0.631379\pi\) | ||
0.401121 | − | 0.916025i | \(-0.368621\pi\) | |||||||
\(968\) | 1.44125 | − | 0.832104i | 0.0463234 | − | 0.0267448i | ||||
\(969\) | −3.21230 | + | 5.56386i | −0.103194 | + | 0.178737i | ||||
\(970\) | −20.6086 | − | 11.0020i | −0.661703 | − | 0.353254i | ||||
\(971\) | 24.1997 | + | 41.9152i | 0.776606 | + | 1.34512i | 0.933887 | + | 0.357568i | \(0.116394\pi\) |
−0.157281 | + | 0.987554i | \(0.550273\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35.5018 | 1.13755 | ||||||||
\(975\) | −4.56608 | − | 6.81855i | −0.146231 | − | 0.218368i | ||||
\(976\) | −0.222905 | + | 0.386083i | −0.00713503 | + | 0.0123582i | ||||
\(977\) | −33.9829 | − | 19.6200i | −1.08721 | − | 0.627701i | −0.154377 | − | 0.988012i | \(-0.549337\pi\) |
−0.932832 | + | 0.360311i | \(0.882671\pi\) | |||||||
\(978\) | 20.4075 | − | 11.7823i | 0.652561 | − | 0.376756i | ||||
\(979\) | 53.4956 | 1.70973 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.10355 | −0.290654 | ||||||||
\(982\) | −0.847219 | + | 0.489142i | −0.0270358 | + | 0.0156091i | ||||
\(983\) | 10.2583 | + | 5.92266i | 0.327190 | + | 0.188903i | 0.654593 | − | 0.755981i | \(-0.272840\pi\) |
−0.327403 | + | 0.944885i | \(0.606173\pi\) | |||||||
\(984\) | 3.33991 | − | 5.78490i | 0.106472 | − | 0.184416i | ||||
\(985\) | 24.4427 | + | 39.2624i | 0.778809 | + | 1.25100i | ||||
\(986\) | −16.2396 | −0.517175 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 3.62740i | − | 0.115403i | ||||||
\(989\) | 9.39860 | + | 16.2789i | 0.298858 | + | 0.517637i | ||||
\(990\) | 3.21760 | − | 6.02710i | 0.102262 | − | 0.191554i | ||||
\(991\) | −3.07601 | + | 5.32780i | −0.0977126 | + | 0.169243i | −0.910738 | − | 0.412986i | \(-0.864486\pi\) |
0.813025 | + | 0.582229i | \(0.197819\pi\) | |||||||
\(992\) | 0.818002 | − | 0.472274i | 0.0259716 | − | 0.0149947i | ||||
\(993\) | 16.6084i | 0.527051i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.896836 | − | 26.9748i | −0.0284316 | − | 0.855160i | ||||
\(996\) | −0.437183 | − | 0.757223i | −0.0138527 | − | 0.0239935i | ||||
\(997\) | 43.0945 | + | 24.8806i | 1.36482 | + | 0.787978i | 0.990261 | − | 0.139226i | \(-0.0444614\pi\) |
0.374557 | + | 0.927204i | \(0.377795\pi\) | |||||||
\(998\) | 10.1620 | + | 5.86701i | 0.321671 | + | 0.185717i | ||||
\(999\) | −5.35615 | − | 9.27713i | −0.169461 | − | 0.293515i |
(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 | 1470.2.n.k.949.8 | 16 | ||
5.4 | even | 2 | inner | 1470.2.n.k.949.1 | 16 | ||
7.2 | even | 3 | inner | 1470.2.n.k.79.1 | 16 | ||
7.3 | odd | 6 | 1470.2.g.j.589.7 | yes | 8 | ||
7.4 | even | 3 | 1470.2.g.k.589.6 | yes | 8 | ||
7.5 | odd | 6 | 1470.2.n.l.79.4 | 16 | |||
7.6 | odd | 2 | 1470.2.n.l.949.5 | 16 | |||
35.3 | even | 12 | 7350.2.a.dt.1.1 | 4 | |||
35.4 | even | 6 | 1470.2.g.k.589.2 | yes | 8 | ||
35.9 | even | 6 | inner | 1470.2.n.k.79.8 | 16 | ||
35.17 | even | 12 | 7350.2.a.ds.1.1 | 4 | |||
35.18 | odd | 12 | 7350.2.a.du.1.1 | 4 | |||
35.19 | odd | 6 | 1470.2.n.l.79.5 | 16 | |||
35.24 | odd | 6 | 1470.2.g.j.589.3 | ✓ | 8 | ||
35.32 | odd | 12 | 7350.2.a.dr.1.1 | 4 | |||
35.34 | odd | 2 | 1470.2.n.l.949.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.3 | ✓ | 8 | 35.24 | odd | 6 | ||
1470.2.g.j.589.7 | yes | 8 | 7.3 | odd | 6 | ||
1470.2.g.k.589.2 | yes | 8 | 35.4 | even | 6 | ||
1470.2.g.k.589.6 | yes | 8 | 7.4 | even | 3 | ||
1470.2.n.k.79.1 | 16 | 7.2 | even | 3 | inner | ||
1470.2.n.k.79.8 | 16 | 35.9 | even | 6 | inner | ||
1470.2.n.k.949.1 | 16 | 5.4 | even | 2 | inner | ||
1470.2.n.k.949.8 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.n.l.79.4 | 16 | 7.5 | odd | 6 | |||
1470.2.n.l.79.5 | 16 | 35.19 | odd | 6 | |||
1470.2.n.l.949.4 | 16 | 35.34 | odd | 2 | |||
1470.2.n.l.949.5 | 16 | 7.6 | odd | 2 | |||
7350.2.a.dr.1.1 | 4 | 35.32 | odd | 12 | |||
7350.2.a.ds.1.1 | 4 | 35.17 | even | 12 | |||
7350.2.a.dt.1.1 | 4 | 35.3 | even | 12 | |||
7350.2.a.du.1.1 | 4 | 35.18 | odd | 12 |