Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(489,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.489");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 489.12 | ||
Character | \(\chi\) | \(=\) | 637.489 |
Dual form | 637.2.i.a.538.11 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.15715 | + | 1.15715i | 0.818231 | + | 0.818231i | 0.985852 | − | 0.167620i | \(-0.0536083\pi\) |
−0.167620 | + | 0.985852i | \(0.553608\pi\) | |||||||
\(3\) | 1.98136i | 1.14394i | 0.820276 | + | 0.571968i | \(0.193820\pi\) | ||||
−0.820276 | + | 0.571968i | \(0.806180\pi\) | |||||||
\(4\) | 0.678010i | 0.339005i | ||||||||
\(5\) | 2.02979 | − | 2.02979i | 0.907749 | − | 0.907749i | −0.0883414 | − | 0.996090i | \(-0.528157\pi\) |
0.996090 | + | 0.0883414i | \(0.0281566\pi\) | |||||||
\(6\) | −2.29273 | + | 2.29273i | −0.936005 | + | 0.936005i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.52975 | − | 1.52975i | 0.540847 | − | 0.540847i | ||||
\(9\) | −0.925772 | −0.308591 | ||||||||
\(10\) | 4.69755 | 1.48550 | ||||||||
\(11\) | 2.44444 | − | 2.44444i | 0.737025 | − | 0.737025i | −0.234976 | − | 0.972001i | \(-0.575501\pi\) |
0.972001 | + | 0.234976i | \(0.0755012\pi\) | |||||||
\(12\) | −1.34338 | −0.387800 | ||||||||
\(13\) | 2.29273 | + | 2.78269i | 0.635890 | + | 0.771780i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.02173 | + | 4.02173i | 1.03841 | + | 1.03841i | ||||
\(16\) | 4.89632 | 1.22408 | ||||||||
\(17\) | −6.44887 | −1.56408 | −0.782040 | − | 0.623228i | \(-0.785821\pi\) | ||||
−0.782040 | + | 0.623228i | \(0.785821\pi\) | |||||||
\(18\) | −1.07126 | − | 1.07126i | −0.252499 | − | 0.252499i | ||||
\(19\) | −2.14924 | + | 2.14924i | −0.493070 | + | 0.493070i | −0.909272 | − | 0.416202i | \(-0.863361\pi\) |
0.416202 | + | 0.909272i | \(0.363361\pi\) | |||||||
\(20\) | 1.37622 | + | 1.37622i | 0.307731 | + | 0.307731i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.65717 | 1.20611 | ||||||||
\(23\) | − | 3.43181i | − | 0.715582i | −0.933802 | − | 0.357791i | \(-0.883530\pi\) | ||
0.933802 | − | 0.357791i | \(-0.116470\pi\) | |||||||
\(24\) | 3.03097 | + | 3.03097i | 0.618695 | + | 0.618695i | ||||
\(25\) | − | 3.24008i | − | 0.648016i | ||||||
\(26\) | −0.566956 | + | 5.87305i | −0.111189 | + | 1.15180i | ||||
\(27\) | 4.10978i | 0.790928i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.40371 | −0.817748 | −0.408874 | − | 0.912591i | \(-0.634079\pi\) | ||||
−0.408874 | + | 0.912591i | \(0.634079\pi\) | |||||||
\(30\) | 9.30753i | 1.69931i | ||||||||
\(31\) | 2.37198 | − | 2.37198i | 0.426021 | − | 0.426021i | −0.461250 | − | 0.887270i | \(-0.652599\pi\) |
0.887270 | + | 0.461250i | \(0.152599\pi\) | |||||||
\(32\) | 2.60631 | + | 2.60631i | 0.460734 | + | 0.460734i | ||||
\(33\) | 4.84330 | + | 4.84330i | 0.843110 | + | 0.843110i | ||||
\(34\) | −7.46233 | − | 7.46233i | −1.27978 | − | 1.27978i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 0.627683i | − | 0.104614i | ||||||
\(37\) | −2.75238 | + | 2.75238i | −0.452488 | + | 0.452488i | −0.896179 | − | 0.443692i | \(-0.853669\pi\) |
0.443692 | + | 0.896179i | \(0.353669\pi\) | |||||||
\(38\) | −4.97401 | −0.806890 | ||||||||
\(39\) | −5.51350 | + | 4.54272i | −0.882867 | + | 0.727418i | ||||
\(40\) | − | 6.21012i | − | 0.981906i | ||||||
\(41\) | −3.03989 | + | 3.03989i | −0.474751 | + | 0.474751i | −0.903448 | − | 0.428697i | \(-0.858973\pi\) |
0.428697 | + | 0.903448i | \(0.358973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48958i | 0.684654i | 0.939581 | + | 0.342327i | \(0.111215\pi\) | ||||
−0.939581 | + | 0.342327i | \(0.888785\pi\) | |||||||
\(44\) | 1.65735 | + | 1.65735i | 0.249855 | + | 0.249855i | ||||
\(45\) | −1.87912 | + | 1.87912i | −0.280123 | + | 0.280123i | ||||
\(46\) | 3.97113 | − | 3.97113i | 0.585511 | − | 0.585511i | ||||
\(47\) | −4.03771 | − | 4.03771i | −0.588960 | − | 0.588960i | 0.348390 | − | 0.937350i | \(-0.386729\pi\) |
−0.937350 | + | 0.348390i | \(0.886729\pi\) | |||||||
\(48\) | 9.70136i | 1.40027i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.74927 | − | 3.74927i | 0.530227 | − | 0.530227i | ||||
\(51\) | − | 12.7775i | − | 1.78921i | ||||||
\(52\) | −1.88669 | + | 1.55450i | −0.261637 | + | 0.215570i | ||||
\(53\) | −11.4505 | −1.57285 | −0.786425 | − | 0.617686i | \(-0.788070\pi\) | ||||
−0.786425 | + | 0.617686i | \(0.788070\pi\) | |||||||
\(54\) | −4.75565 | + | 4.75565i | −0.647162 | + | 0.647162i | ||||
\(55\) | − | 9.92337i | − | 1.33807i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.25841 | − | 4.25841i | −0.564041 | − | 0.564041i | ||||
\(58\) | −5.09577 | − | 5.09577i | −0.669107 | − | 0.669107i | ||||
\(59\) | −2.09403 | − | 2.09403i | −0.272620 | − | 0.272620i | 0.557534 | − | 0.830154i | \(-0.311748\pi\) |
−0.830154 | + | 0.557534i | \(0.811748\pi\) | |||||||
\(60\) | −2.72677 | + | 2.72677i | −0.352025 | + | 0.352025i | ||||
\(61\) | − | 3.50457i | − | 0.448714i | −0.974507 | − | 0.224357i | \(-0.927972\pi\) | ||
0.974507 | − | 0.224357i | \(-0.0720281\pi\) | |||||||
\(62\) | 5.48950 | 0.697167 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 3.76085i | − | 0.470107i | ||||||
\(65\) | 10.3020 | + | 0.994510i | 1.27781 | + | 0.123354i | ||||
\(66\) | 11.2089i | 1.37972i | ||||||||
\(67\) | 5.15836 | + | 5.15836i | 0.630194 | + | 0.630194i | 0.948117 | − | 0.317923i | \(-0.102985\pi\) |
−0.317923 | + | 0.948117i | \(0.602985\pi\) | |||||||
\(68\) | − | 4.37240i | − | 0.530231i | ||||||
\(69\) | 6.79964 | 0.818580 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.31408 | + | 8.31408i | 0.986700 | + | 0.986700i | 0.999913 | − | 0.0132127i | \(-0.00420586\pi\) |
−0.0132127 | + | 0.999913i | \(0.504206\pi\) | |||||||
\(72\) | −1.41620 | + | 1.41620i | −0.166900 | + | 0.166900i | ||||
\(73\) | −3.30282 | − | 3.30282i | −0.386566 | − | 0.386566i | 0.486895 | − | 0.873461i | \(-0.338130\pi\) |
−0.873461 | + | 0.486895i | \(0.838130\pi\) | |||||||
\(74\) | −6.36984 | −0.740479 | ||||||||
\(75\) | 6.41975 | 0.741289 | ||||||||
\(76\) | −1.45721 | − | 1.45721i | −0.167153 | − | 0.167153i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6366 | − | 1.12334i | −1.31759 | − | 0.127193i | ||||
\(79\) | 1.08784 | 0.122391 | 0.0611957 | − | 0.998126i | \(-0.480509\pi\) | ||||
0.0611957 | + | 0.998126i | \(0.480509\pi\) | |||||||
\(80\) | 9.93850 | − | 9.93850i | 1.11116 | − | 1.11116i | ||||
\(81\) | −10.9203 | −1.21336 | ||||||||
\(82\) | −7.03523 | −0.776912 | ||||||||
\(83\) | 2.01261 | − | 2.01261i | 0.220913 | − | 0.220913i | −0.587970 | − | 0.808883i | \(-0.700073\pi\) |
0.808883 | + | 0.587970i | \(0.200073\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0898 | + | 13.0898i | −1.41979 | + | 1.41979i | ||||
\(86\) | −5.19513 | + | 5.19513i | −0.560205 | + | 0.560205i | ||||
\(87\) | − | 8.72532i | − | 0.935452i | ||||||
\(88\) | − | 7.47873i | − | 0.797235i | ||||||
\(89\) | 3.50857 | + | 3.50857i | 0.371908 | + | 0.371908i | 0.868172 | − | 0.496264i | \(-0.165295\pi\) |
−0.496264 | + | 0.868172i | \(0.665295\pi\) | |||||||
\(90\) | −4.34887 | −0.458411 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.32680 | 0.242586 | ||||||||
\(93\) | 4.69974 | + | 4.69974i | 0.487341 | + | 0.487341i | ||||
\(94\) | − | 9.34450i | − | 0.963811i | ||||||
\(95\) | 8.72501i | 0.895167i | ||||||||
\(96\) | −5.16402 | + | 5.16402i | −0.527051 | + | 0.527051i | ||||
\(97\) | −3.20816 | + | 3.20816i | −0.325739 | + | 0.325739i | −0.850964 | − | 0.525225i | \(-0.823981\pi\) |
0.525225 | + | 0.850964i | \(0.323981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.26299 | + | 2.26299i | −0.227439 | + | 0.227439i | ||||
\(100\) | 2.19681 | 0.219681 | ||||||||
\(101\) | 9.14073 | 0.909537 | 0.454769 | − | 0.890610i | \(-0.349722\pi\) | ||||
0.454769 | + | 0.890610i | \(0.349722\pi\) | |||||||
\(102\) | 14.7855 | − | 14.7855i | 1.46399 | − | 1.46399i | ||||
\(103\) | 5.12360 | 0.504843 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(104\) | 7.76411 | + | 0.749511i | 0.761334 | + | 0.0734956i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.2500 | − | 13.2500i | −1.28696 | − | 1.28696i | ||||
\(107\) | −12.5537 | −1.21361 | −0.606804 | − | 0.794851i | \(-0.707549\pi\) | ||||
−0.606804 | + | 0.794851i | \(0.707549\pi\) | |||||||
\(108\) | −2.78647 | −0.268128 | ||||||||
\(109\) | 13.8075 | + | 13.8075i | 1.32252 | + | 1.32252i | 0.911732 | + | 0.410786i | \(0.134746\pi\) |
0.410786 | + | 0.911732i | \(0.365254\pi\) | |||||||
\(110\) | 11.4829 | − | 11.4829i | 1.09485 | − | 1.09485i | ||||
\(111\) | −5.45344 | − | 5.45344i | −0.517617 | − | 0.517617i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.000230976 | 0 | 2.17284e−5 | 0 | 1.08642e−5 | − | 1.00000i | \(-0.499997\pi\) | ||
1.08642e−5 | 1.00000i | \(0.499997\pi\) | ||||||||
\(114\) | − | 9.85528i | − | 0.923031i | ||||||
\(115\) | −6.96585 | − | 6.96585i | −0.649569 | − | 0.649569i | ||||
\(116\) | − | 2.98576i | − | 0.277221i | ||||||
\(117\) | −2.12255 | − | 2.57614i | −0.196230 | − | 0.238164i | ||||
\(118\) | − | 4.84623i | − | 0.446132i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.3045 | 1.12324 | ||||||||
\(121\) | − | 0.950526i | − | 0.0864115i | ||||||
\(122\) | 4.05532 | − | 4.05532i | 0.367152 | − | 0.367152i | ||||
\(123\) | −6.02310 | − | 6.02310i | −0.543085 | − | 0.543085i | ||||
\(124\) | 1.60823 | + | 1.60823i | 0.144423 | + | 0.144423i | ||||
\(125\) | 3.57226 | + | 3.57226i | 0.319513 | + | 0.319513i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.4887i | − | 1.10820i | −0.832452 | − | 0.554098i | \(-0.813063\pi\) | ||
0.832452 | − | 0.554098i | \(-0.186937\pi\) | |||||||
\(128\) | 9.56450 | − | 9.56450i | 0.845390 | − | 0.845390i | ||||
\(129\) | −8.89545 | −0.783201 | ||||||||
\(130\) | 10.7702 | + | 13.0718i | 0.944613 | + | 1.14648i | ||||
\(131\) | − | 13.5868i | − | 1.18708i | −0.804803 | − | 0.593542i | \(-0.797729\pi\) | ||
0.804803 | − | 0.593542i | \(-0.202271\pi\) | |||||||
\(132\) | −3.28380 | + | 3.28380i | −0.285818 | + | 0.285818i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.9380i | 1.03129i | ||||||||
\(135\) | 8.34199 | + | 8.34199i | 0.717964 | + | 0.717964i | ||||
\(136\) | −9.86513 | + | 9.86513i | −0.845928 | + | 0.845928i | ||||
\(137\) | 0.955848 | − | 0.955848i | 0.0816636 | − | 0.0816636i | −0.665095 | − | 0.746759i | \(-0.731609\pi\) |
0.746759 | + | 0.665095i | \(0.231609\pi\) | |||||||
\(138\) | 7.86823 | + | 7.86823i | 0.669788 | + | 0.669788i | ||||
\(139\) | − | 18.8190i | − | 1.59621i | −0.602521 | − | 0.798103i | \(-0.705837\pi\) | ||
0.602521 | − | 0.798103i | \(-0.294163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00014 | − | 8.00014i | 0.673733 | − | 0.673733i | ||||
\(142\) | 19.2413i | 1.61470i | ||||||||
\(143\) | 12.4065 | + | 1.19767i | 1.03749 | + | 0.100154i | ||||
\(144\) | −4.53288 | −0.377740 | ||||||||
\(145\) | −8.93860 | + | 8.93860i | −0.742310 | + | 0.742310i | ||||
\(146\) | − | 7.64375i | − | 0.632601i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.86614 | − | 1.86614i | −0.153396 | − | 0.153396i | ||||
\(149\) | −15.0822 | − | 15.0822i | −1.23558 | − | 1.23558i | −0.961790 | − | 0.273789i | \(-0.911723\pi\) |
−0.273789 | − | 0.961790i | \(-0.588277\pi\) | |||||||
\(150\) | 7.42864 | + | 7.42864i | 0.606546 | + | 0.606546i | ||||
\(151\) | 11.9297 | − | 11.9297i | 0.970828 | − | 0.970828i | −0.0287588 | − | 0.999586i | \(-0.509155\pi\) |
0.999586 | + | 0.0287588i | \(0.00915547\pi\) | |||||||
\(152\) | 6.57559i | 0.533351i | ||||||||
\(153\) | 5.97019 | 0.482661 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9.62925i | − | 0.773440i | ||||||
\(156\) | −3.08001 | − | 3.73821i | −0.246598 | − | 0.299296i | ||||
\(157\) | 10.9269i | 0.872061i | 0.899932 | + | 0.436031i | \(0.143616\pi\) | ||||
−0.899932 | + | 0.436031i | \(0.856384\pi\) | |||||||
\(158\) | 1.25880 | + | 1.25880i | 0.100145 | + | 0.100145i | ||||
\(159\) | − | 22.6876i | − | 1.79924i | ||||||
\(160\) | 10.5805 | 0.836462 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.6364 | − | 12.6364i | −0.992811 | − | 0.992811i | ||||
\(163\) | −6.13353 | + | 6.13353i | −0.480415 | + | 0.480415i | −0.905264 | − | 0.424849i | \(-0.860327\pi\) |
0.424849 | + | 0.905264i | \(0.360327\pi\) | |||||||
\(164\) | −2.06107 | − | 2.06107i | −0.160943 | − | 0.160943i | ||||
\(165\) | 19.6617 | 1.53066 | ||||||||
\(166\) | 4.65780 | 0.361515 | ||||||||
\(167\) | −8.00174 | − | 8.00174i | −0.619193 | − | 0.619193i | 0.326131 | − | 0.945324i | \(-0.394255\pi\) |
−0.945324 | + | 0.326131i | \(0.894255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48674 | + | 12.7599i | −0.191288 | + | 0.981534i | ||||
\(170\) | −30.2939 | −2.32344 | ||||||||
\(171\) | 1.98971 | − | 1.98971i | 0.152157 | − | 0.152157i | ||||
\(172\) | −3.04398 | −0.232101 | ||||||||
\(173\) | −3.27667 | −0.249121 | −0.124560 | − | 0.992212i | \(-0.539752\pi\) | ||||
−0.124560 | + | 0.992212i | \(0.539752\pi\) | |||||||
\(174\) | 10.0965 | − | 10.0965i | 0.765416 | − | 0.765416i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.9687 | − | 11.9687i | 0.902178 | − | 0.902178i | ||||
\(177\) | 4.14902 | − | 4.14902i | 0.311860 | − | 0.311860i | ||||
\(178\) | 8.11991i | 0.608613i | ||||||||
\(179\) | 2.25009i | 0.168179i | 0.996458 | + | 0.0840897i | \(0.0267982\pi\) | ||||
−0.996458 | + | 0.0840897i | \(0.973202\pi\) | |||||||
\(180\) | −1.27406 | − | 1.27406i | −0.0949630 | − | 0.0949630i | ||||
\(181\) | −15.5420 | −1.15523 | −0.577615 | − | 0.816310i | \(-0.696016\pi\) | ||||
−0.577615 | + | 0.816310i | \(0.696016\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.94380 | 0.513300 | ||||||||
\(184\) | −5.24980 | − | 5.24980i | −0.387020 | − | 0.387020i | ||||
\(185\) | 11.1735i | 0.821491i | ||||||||
\(186\) | 10.8767i | 0.797515i | ||||||||
\(187\) | −15.7638 | + | 15.7638i | −1.15277 | + | 1.15277i | ||||
\(188\) | 2.73761 | − | 2.73761i | 0.199660 | − | 0.199660i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0962 | + | 10.0962i | −0.732454 | + | 0.732454i | ||||
\(191\) | −2.37794 | −0.172062 | −0.0860308 | − | 0.996292i | \(-0.527418\pi\) | ||||
−0.0860308 | + | 0.996292i | \(0.527418\pi\) | |||||||
\(192\) | 7.45159 | 0.537772 | ||||||||
\(193\) | −5.51979 | + | 5.51979i | −0.397323 | + | 0.397323i | −0.877288 | − | 0.479965i | \(-0.840649\pi\) |
0.479965 | + | 0.877288i | \(0.340649\pi\) | |||||||
\(194\) | −7.42466 | −0.533060 | ||||||||
\(195\) | −1.97048 | + | 20.4120i | −0.141109 | + | 1.46173i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9402 | − | 10.9402i | −0.779454 | − | 0.779454i | 0.200284 | − | 0.979738i | \(-0.435813\pi\) |
−0.979738 | + | 0.200284i | \(0.935813\pi\) | |||||||
\(198\) | −5.23726 | −0.372196 | ||||||||
\(199\) | 20.1735 | 1.43006 | 0.715031 | − | 0.699092i | \(-0.246412\pi\) | ||||
0.715031 | + | 0.699092i | \(0.246412\pi\) | |||||||
\(200\) | −4.95650 | − | 4.95650i | −0.350477 | − | 0.350477i | ||||
\(201\) | −10.2206 | + | 10.2206i | −0.720902 | + | 0.720902i | ||||
\(202\) | 10.5772 | + | 10.5772i | 0.744212 | + | 0.744212i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.66327 | 0.606551 | ||||||||
\(205\) | 12.3407i | 0.861909i | ||||||||
\(206\) | 5.92879 | + | 5.92879i | 0.413078 | + | 0.413078i | ||||
\(207\) | 3.17707i | 0.220822i | ||||||||
\(208\) | 11.2260 | + | 13.6250i | 0.778381 | + | 0.944721i | ||||
\(209\) | 10.5074i | 0.726809i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.36943 | 0.163118 | 0.0815591 | − | 0.996669i | \(-0.474010\pi\) | ||||
0.0815591 | + | 0.996669i | \(0.474010\pi\) | |||||||
\(212\) | − | 7.76356i | − | 0.533204i | ||||||
\(213\) | −16.4732 | + | 16.4732i | −1.12872 | + | 1.12872i | ||||
\(214\) | −14.5265 | − | 14.5265i | −0.993012 | − | 0.993012i | ||||
\(215\) | 9.11289 | + | 9.11289i | 0.621494 | + | 0.621494i | ||||
\(216\) | 6.28693 | + | 6.28693i | 0.427771 | + | 0.427771i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 31.9548i | 2.16425i | ||||||||
\(219\) | 6.54407 | − | 6.54407i | 0.442207 | − | 0.442207i | ||||
\(220\) | 6.72814 | 0.453611 | ||||||||
\(221\) | −14.7855 | − | 17.9452i | −0.994583 | − | 1.20713i | ||||
\(222\) | − | 12.6209i | − | 0.847061i | ||||||
\(223\) | 9.67825 | − | 9.67825i | 0.648103 | − | 0.648103i | −0.304431 | − | 0.952534i | \(-0.598466\pi\) |
0.952534 | + | 0.304431i | \(0.0984663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.99958i | 0.199972i | ||||||||
\(226\) | 0.000267274 | 0 | 0.000267274i | 1.77788e−5 | 0 | 1.77788e-5i | ||||
\(227\) | −9.21946 | + | 9.21946i | −0.611917 | + | 0.611917i | −0.943445 | − | 0.331528i | \(-0.892436\pi\) |
0.331528 | + | 0.943445i | \(0.392436\pi\) | |||||||
\(228\) | 2.88724 | − | 2.88724i | 0.191212 | − | 0.191212i | ||||
\(229\) | 10.7471 | + | 10.7471i | 0.710191 | + | 0.710191i | 0.966575 | − | 0.256384i | \(-0.0825311\pi\) |
−0.256384 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(230\) | − | 16.1211i | − | 1.06299i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.73656 | + | 6.73656i | −0.442277 | + | 0.442277i | ||||
\(233\) | − | 7.73487i | − | 0.506728i | −0.967371 | − | 0.253364i | \(-0.918463\pi\) | ||
0.967371 | − | 0.253364i | \(-0.0815370\pi\) | |||||||
\(234\) | 0.524873 | − | 5.43711i | 0.0343120 | − | 0.355435i | ||||
\(235\) | −16.3914 | −1.06926 | ||||||||
\(236\) | 1.41977 | − | 1.41977i | 0.0924194 | − | 0.0924194i | ||||
\(237\) | 2.15540i | 0.140008i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.10971 | + | 2.10971i | 0.136466 | + | 0.136466i | 0.772040 | − | 0.635574i | \(-0.219237\pi\) |
−0.635574 | + | 0.772040i | \(0.719237\pi\) | |||||||
\(240\) | 19.6917 | + | 19.6917i | 1.27109 | + | 1.27109i | ||||
\(241\) | −18.6721 | − | 18.6721i | −1.20278 | − | 1.20278i | −0.973318 | − | 0.229460i | \(-0.926304\pi\) |
−0.229460 | − | 0.973318i | \(-0.573696\pi\) | |||||||
\(242\) | 1.09991 | − | 1.09991i | 0.0707046 | − | 0.0707046i | ||||
\(243\) | − | 9.30758i | − | 0.597082i | ||||||
\(244\) | 2.37613 | 0.152116 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 13.9393i | − | 0.888738i | ||||||
\(247\) | −10.9083 | − | 1.05304i | −0.694079 | − | 0.0670032i | ||||
\(248\) | − | 7.25706i | − | 0.460824i | ||||||
\(249\) | 3.98770 | + | 3.98770i | 0.252710 | + | 0.252710i | ||||
\(250\) | 8.26732i | 0.522871i | ||||||||
\(251\) | 7.06132 | 0.445707 | 0.222853 | − | 0.974852i | \(-0.428463\pi\) | ||||
0.222853 | + | 0.974852i | \(0.428463\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.38884 | − | 8.38884i | −0.527402 | − | 0.527402i | ||||
\(254\) | 14.4514 | − | 14.4514i | 0.906760 | − | 0.906760i | ||||
\(255\) | −25.9356 | − | 25.9356i | −1.62415 | − | 1.62415i | ||||
\(256\) | 14.6135 | 0.913342 | ||||||||
\(257\) | −13.0534 | −0.814250 | −0.407125 | − | 0.913373i | \(-0.633469\pi\) | ||||
−0.407125 | + | 0.913373i | \(0.633469\pi\) | |||||||
\(258\) | −10.2934 | − | 10.2934i | −0.640839 | − | 0.640839i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.674288 | + | 6.98488i | −0.0418175 | + | 0.433184i | ||||
\(261\) | 4.07683 | 0.252350 | ||||||||
\(262\) | 15.7220 | − | 15.7220i | 0.971309 | − | 0.971309i | ||||
\(263\) | 22.3346 | 1.37721 | 0.688606 | − | 0.725136i | \(-0.258223\pi\) | ||||
0.688606 | + | 0.725136i | \(0.258223\pi\) | |||||||
\(264\) | 14.8180 | 0.911987 | ||||||||
\(265\) | −23.2421 | + | 23.2421i | −1.42775 | + | 1.42775i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.95173 | + | 6.95173i | −0.425439 | + | 0.425439i | ||||
\(268\) | −3.49742 | + | 3.49742i | −0.213639 | + | 0.213639i | ||||
\(269\) | − | 3.13431i | − | 0.191102i | −0.995425 | − | 0.0955511i | \(-0.969539\pi\) | ||
0.995425 | − | 0.0955511i | \(-0.0304613\pi\) | |||||||
\(270\) | 19.3059i | 1.17492i | ||||||||
\(271\) | −11.1792 | − | 11.1792i | −0.679088 | − | 0.679088i | 0.280706 | − | 0.959794i | \(-0.409431\pi\) |
−0.959794 | + | 0.280706i | \(0.909431\pi\) | |||||||
\(272\) | −31.5757 | −1.91456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.21213 | 0.133639 | ||||||||
\(275\) | −7.92017 | − | 7.92017i | −0.477604 | − | 0.477604i | ||||
\(276\) | 4.61022i | 0.277503i | ||||||||
\(277\) | 29.4841i | 1.77153i | 0.464134 | + | 0.885765i | \(0.346366\pi\) | ||||
−0.464134 | + | 0.885765i | \(0.653634\pi\) | |||||||
\(278\) | 21.7765 | − | 21.7765i | 1.30607 | − | 1.30607i | ||||
\(279\) | −2.19592 | + | 2.19592i | −0.131466 | + | 0.131466i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8969 | − | 16.8969i | 1.00798 | − | 1.00798i | 0.00801615 | − | 0.999968i | \(-0.497448\pi\) |
0.999968 | − | 0.00801615i | \(-0.00255165\pi\) | |||||||
\(282\) | 18.5148 | 1.10254 | ||||||||
\(283\) | −9.33438 | −0.554871 | −0.277436 | − | 0.960744i | \(-0.589485\pi\) | ||||
−0.277436 | + | 0.960744i | \(0.589485\pi\) | |||||||
\(284\) | −5.63703 | + | 5.63703i | −0.334496 | + | 0.334496i | ||||
\(285\) | −17.2874 | −1.02401 | ||||||||
\(286\) | 12.9704 | + | 15.7422i | 0.766956 | + | 0.930854i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.41285 | − | 2.41285i | −0.142178 | − | 0.142178i | ||||
\(289\) | 24.5879 | 1.44635 | ||||||||
\(290\) | −20.6867 | −1.21476 | ||||||||
\(291\) | −6.35650 | − | 6.35650i | −0.372625 | − | 0.372625i | ||||
\(292\) | 2.23935 | − | 2.23935i | 0.131048 | − | 0.131048i | ||||
\(293\) | 2.08232 | + | 2.08232i | 0.121650 | + | 0.121650i | 0.765311 | − | 0.643661i | \(-0.222585\pi\) |
−0.643661 | + | 0.765311i | \(0.722585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.50088 | −0.494940 | ||||||||
\(296\) | 8.42087i | 0.489453i | ||||||||
\(297\) | 10.0461 | + | 10.0461i | 0.582934 | + | 0.582934i | ||||
\(298\) | − | 34.9048i | − | 2.02198i | ||||||
\(299\) | 9.54967 | − | 7.86823i | 0.552272 | − | 0.455031i | ||||
\(300\) | 4.35265i | 0.251301i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.6091 | 1.58872 | ||||||||
\(303\) | 18.1111i | 1.04045i | ||||||||
\(304\) | −10.5234 | + | 10.5234i | −0.603557 | + | 0.603557i | ||||
\(305\) | −7.11353 | − | 7.11353i | −0.407319 | − | 0.407319i | ||||
\(306\) | 6.90842 | + | 6.90842i | 0.394928 | + | 0.394928i | ||||
\(307\) | −3.85597 | − | 3.85597i | −0.220072 | − | 0.220072i | 0.588457 | − | 0.808529i | \(-0.299736\pi\) |
−0.808529 | + | 0.588457i | \(0.799736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1517i | 0.577508i | ||||||||
\(310\) | 11.1425 | − | 11.1425i | 0.632852 | − | 0.632852i | ||||
\(311\) | 14.0750 | 0.798120 | 0.399060 | − | 0.916925i | \(-0.369337\pi\) | ||||
0.399060 | + | 0.916925i | \(0.369337\pi\) | |||||||
\(312\) | −1.48505 | + | 15.3835i | −0.0840743 | + | 0.870918i | ||||
\(313\) | 4.70655i | 0.266030i | 0.991114 | + | 0.133015i | \(0.0424658\pi\) | ||||
−0.991114 | + | 0.133015i | \(0.957534\pi\) | |||||||
\(314\) | −12.6441 | + | 12.6441i | −0.713548 | + | 0.713548i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.737566i | 0.0414913i | ||||||||
\(317\) | 20.7068 | + | 20.7068i | 1.16301 | + | 1.16301i | 0.983814 | + | 0.179195i | \(0.0573492\pi\) |
0.179195 | + | 0.983814i | \(0.442651\pi\) | |||||||
\(318\) | 26.2530 | − | 26.2530i | 1.47220 | − | 1.47220i | ||||
\(319\) | −10.7646 | + | 10.7646i | −0.602701 | + | 0.602701i | ||||
\(320\) | −7.63373 | − | 7.63373i | −0.426739 | − | 0.426739i | ||||
\(321\) | − | 24.8733i | − | 1.38829i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.8602 | − | 13.8602i | 0.771201 | − | 0.771201i | ||||
\(324\) | − | 7.40404i | − | 0.411336i | ||||||
\(325\) | 9.01614 | − | 7.42864i | 0.500126 | − | 0.412067i | ||||
\(326\) | −14.1949 | −0.786181 | ||||||||
\(327\) | −27.3576 | + | 27.3576i | −1.51288 | + | 1.51288i | ||||
\(328\) | 9.30051i | 0.513535i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 22.7516 | + | 22.7516i | 1.25244 | + | 1.25244i | ||||
\(331\) | 10.4784 | + | 10.4784i | 0.575946 | + | 0.575946i | 0.933784 | − | 0.357838i | \(-0.116486\pi\) |
−0.357838 | + | 0.933784i | \(0.616486\pi\) | |||||||
\(332\) | 1.36457 | + | 1.36457i | 0.0748905 | + | 0.0748905i | ||||
\(333\) | 2.54807 | − | 2.54807i | 0.139634 | − | 0.139634i | ||||
\(334\) | − | 18.5185i | − | 1.01329i | ||||||
\(335\) | 20.9408 | 1.14412 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.51919i | 0.518543i | 0.965804 | + | 0.259272i | \(0.0834825\pi\) | ||||
−0.965804 | + | 0.259272i | \(0.916518\pi\) | |||||||
\(338\) | −17.6428 | + | 11.8877i | −0.959640 | + | 0.646604i | ||||
\(339\) | 0 | 0.000457645i | 0 | 2.48559e-5i | ||||||
\(340\) | −8.87504 | − | 8.87504i | −0.481317 | − | 0.481317i | ||||
\(341\) | − | 11.5963i | − | 0.627976i | ||||||
\(342\) | 4.60480 | 0.248999 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.86791 | + | 6.86791i | 0.370293 | + | 0.370293i | ||||
\(345\) | 13.8018 | − | 13.8018i | 0.743065 | − | 0.743065i | ||||
\(346\) | −3.79161 | − | 3.79161i | −0.203838 | − | 0.203838i | ||||
\(347\) | −35.1298 | −1.88587 | −0.942933 | − | 0.332983i | \(-0.891945\pi\) | ||||
−0.942933 | + | 0.332983i | \(0.891945\pi\) | |||||||
\(348\) | 5.91585 | 0.317123 | ||||||||
\(349\) | −6.64759 | − | 6.64759i | −0.355837 | − | 0.355837i | 0.506439 | − | 0.862276i | \(-0.330962\pi\) |
−0.862276 | + | 0.506439i | \(0.830962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4363 | + | 9.42264i | −0.610422 | + | 0.502943i | ||||
\(352\) | 12.7419 | 0.679145 | ||||||||
\(353\) | 8.74920 | − | 8.74920i | 0.465673 | − | 0.465673i | −0.434837 | − | 0.900509i | \(-0.643194\pi\) |
0.900509 | + | 0.434837i | \(0.143194\pi\) | |||||||
\(354\) | 9.60211 | 0.510347 | ||||||||
\(355\) | 33.7517 | 1.79135 | ||||||||
\(356\) | −2.37885 | + | 2.37885i | −0.126079 | + | 0.126079i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.60370 | + | 2.60370i | −0.137610 | + | 0.137610i | ||||
\(359\) | −3.03173 | + | 3.03173i | −0.160009 | + | 0.160009i | −0.782571 | − | 0.622562i | \(-0.786092\pi\) |
0.622562 | + | 0.782571i | \(0.286092\pi\) | |||||||
\(360\) | 5.74916i | 0.303007i | ||||||||
\(361\) | 9.76152i | 0.513764i | ||||||||
\(362\) | −17.9845 | − | 17.9845i | −0.945245 | − | 0.945245i | ||||
\(363\) | 1.88333 | 0.0988493 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4081 | −0.701810 | ||||||||
\(366\) | 8.03504 | + | 8.03504i | 0.419998 | + | 0.419998i | ||||
\(367\) | 24.7345i | 1.29113i | 0.763705 | + | 0.645565i | \(0.223378\pi\) | ||||
−0.763705 | + | 0.645565i | \(0.776622\pi\) | |||||||
\(368\) | − | 16.8032i | − | 0.875930i | ||||||
\(369\) | 2.81424 | − | 2.81424i | 0.146504 | − | 0.146504i | ||||
\(370\) | −12.9294 | + | 12.9294i | −0.672169 | + | 0.672169i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.18647 | + | 3.18647i | −0.165211 | + | 0.165211i | ||||
\(373\) | −7.91354 | −0.409747 | −0.204874 | − | 0.978788i | \(-0.565678\pi\) | ||||
−0.204874 | + | 0.978788i | \(0.565678\pi\) | |||||||
\(374\) | −36.4824 | −1.88646 | ||||||||
\(375\) | −7.07793 | + | 7.07793i | −0.365503 | + | 0.365503i | ||||
\(376\) | −12.3533 | −0.637075 | ||||||||
\(377\) | −10.0965 | − | 12.2542i | −0.519998 | − | 0.631122i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.32389 | + | 3.32389i | 0.170737 | + | 0.170737i | 0.787303 | − | 0.616566i | \(-0.211477\pi\) |
−0.616566 | + | 0.787303i | \(0.711477\pi\) | |||||||
\(380\) | −5.91564 | −0.303466 | ||||||||
\(381\) | 24.7446 | 1.26771 | ||||||||
\(382\) | −2.75164 | − | 2.75164i | −0.140786 | − | 0.140786i | ||||
\(383\) | 6.40422 | − | 6.40422i | 0.327241 | − | 0.327241i | −0.524296 | − | 0.851536i | \(-0.675671\pi\) |
0.851536 | + | 0.524296i | \(0.175671\pi\) | |||||||
\(384\) | 18.9507 | + | 18.9507i | 0.967072 | + | 0.967072i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.7745 | −0.650204 | ||||||||
\(387\) | − | 4.15633i | − | 0.211278i | ||||||
\(388\) | −2.17516 | − | 2.17516i | −0.110427 | − | 0.110427i | ||||
\(389\) | − | 21.4608i | − | 1.08811i | −0.839051 | − | 0.544053i | \(-0.816889\pi\) | ||
0.839051 | − | 0.544053i | \(-0.183111\pi\) | |||||||
\(390\) | −25.9000 | + | 21.3397i | −1.31150 | + | 1.08058i | ||||
\(391\) | 22.1313i | 1.11923i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.9203 | 1.35795 | ||||||||
\(394\) | − | 25.3189i | − | 1.27555i | ||||||
\(395\) | 2.20808 | − | 2.20808i | 0.111101 | − | 0.111101i | ||||
\(396\) | −1.53433 | − | 1.53433i | −0.0771030 | − | 0.0771030i | ||||
\(397\) | −9.24490 | − | 9.24490i | −0.463988 | − | 0.463988i | 0.435972 | − | 0.899960i | \(-0.356405\pi\) |
−0.899960 | + | 0.435972i | \(0.856405\pi\) | |||||||
\(398\) | 23.3439 | + | 23.3439i | 1.17012 | + | 1.17012i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 15.8645i | − | 0.793224i | ||||||
\(401\) | −15.0072 | + | 15.0072i | −0.749423 | + | 0.749423i | −0.974371 | − | 0.224948i | \(-0.927779\pi\) |
0.224948 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(402\) | −23.6535 | −1.17973 | ||||||||
\(403\) | 12.0388 | + | 1.16217i | 0.599696 | + | 0.0578919i | ||||
\(404\) | 6.19751i | 0.308337i | ||||||||
\(405\) | −22.1658 | + | 22.1658i | −1.10143 | + | 1.10143i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.4560i | 0.666990i | ||||||||
\(408\) | −19.5463 | − | 19.5463i | −0.967688 | − | 0.967688i | ||||
\(409\) | −6.02317 | + | 6.02317i | −0.297827 | + | 0.297827i | −0.840162 | − | 0.542335i | \(-0.817540\pi\) |
0.542335 | + | 0.840162i | \(0.317540\pi\) | |||||||
\(410\) | −14.2800 | + | 14.2800i | −0.705241 | + | 0.705241i | ||||
\(411\) | 1.89388 | + | 1.89388i | 0.0934180 | + | 0.0934180i | ||||
\(412\) | 3.47385i | 0.171144i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.67636 | + | 3.67636i | −0.180683 | + | 0.180683i | ||||
\(415\) | − | 8.17035i | − | 0.401067i | ||||||
\(416\) | −1.27698 | + | 13.2281i | −0.0626091 | + | 0.648561i | ||||
\(417\) | 37.2871 | 1.82596 | ||||||||
\(418\) | −12.1586 | + | 12.1586i | −0.594698 | + | 0.594698i | ||||
\(419\) | 8.39090i | 0.409922i | 0.978770 | + | 0.204961i | \(0.0657068\pi\) | ||||
−0.978770 | + | 0.204961i | \(0.934293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5414 | + | 20.5414i | 1.00113 | + | 1.00113i | 0.999999 | + | 0.00112764i | \(0.000358939\pi\) |
0.00112764 | + | 0.999999i | \(0.499641\pi\) | |||||||
\(422\) | 2.74179 | + | 2.74179i | 0.133468 | + | 0.133468i | ||||
\(423\) | 3.73800 | + | 3.73800i | 0.181748 | + | 0.181748i | ||||
\(424\) | −17.5164 | + | 17.5164i | −0.850671 | + | 0.850671i | ||||
\(425\) | 20.8949i | 1.01355i | ||||||||
\(426\) | −38.1240 | −1.84711 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8.51150i | − | 0.411419i | ||||||
\(429\) | −2.37301 | + | 24.5818i | −0.114570 | + | 1.18682i | ||||
\(430\) | 21.0900i | 1.01705i | ||||||||
\(431\) | 7.07391 | + | 7.07391i | 0.340738 | + | 0.340738i | 0.856645 | − | 0.515907i | \(-0.172545\pi\) |
−0.515907 | + | 0.856645i | \(0.672545\pi\) | |||||||
\(432\) | 20.1228i | 0.968160i | ||||||||
\(433\) | 41.3846 | 1.98882 | 0.994409 | − | 0.105595i | \(-0.0336746\pi\) | ||||
0.994409 | + | 0.105595i | \(0.0336746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.7105 | − | 17.7105i | −0.849156 | − | 0.849156i | ||||
\(436\) | −9.36161 | + | 9.36161i | −0.448340 | + | 0.448340i | ||||
\(437\) | 7.37579 | + | 7.37579i | 0.352832 | + | 0.352832i | ||||
\(438\) | 15.1450 | 0.723655 | ||||||||
\(439\) | 0.142577 | 0.00680482 | 0.00340241 | − | 0.999994i | \(-0.498917\pi\) | ||||
0.00340241 | + | 0.999994i | \(0.498917\pi\) | |||||||
\(440\) | −15.1802 | − | 15.1802i | −0.723689 | − | 0.723689i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.65623 | − | 37.8745i | 0.173909 | − | 1.80151i | ||||
\(443\) | 25.8736 | 1.22929 | 0.614647 | − | 0.788803i | \(-0.289299\pi\) | ||||
0.614647 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(444\) | 3.69748 | − | 3.69748i | 0.175475 | − | 0.175475i | ||||
\(445\) | 14.2433 | 0.675198 | ||||||||
\(446\) | 22.3984 | 1.06060 | ||||||||
\(447\) | 29.8831 | − | 29.8831i | 1.41342 | − | 1.41342i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.26645 | − | 1.26645i | 0.0597675 | − | 0.0597675i | −0.676591 | − | 0.736359i | \(-0.736544\pi\) |
0.736359 | + | 0.676591i | \(0.236544\pi\) | |||||||
\(450\) | −3.47097 | + | 3.47097i | −0.163623 | + | 0.163623i | ||||
\(451\) | 14.8616i | 0.699806i | ||||||||
\(452\) | 0 | 0.000156604i | 0 | 7.36602e-6i | ||||||
\(453\) | 23.6370 | + | 23.6370i | 1.11057 | + | 1.11057i | ||||
\(454\) | −21.3367 | −1.00138 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.0286 | −0.610119 | ||||||||
\(457\) | −3.29682 | − | 3.29682i | −0.154219 | − | 0.154219i | 0.625781 | − | 0.779999i | \(-0.284781\pi\) |
−0.779999 | + | 0.625781i | \(0.784781\pi\) | |||||||
\(458\) | 24.8722i | 1.16220i | ||||||||
\(459\) | − | 26.5035i | − | 1.23708i | ||||||
\(460\) | 4.72291 | − | 4.72291i | 0.220207 | − | 0.220207i | ||||
\(461\) | 3.60896 | − | 3.60896i | 0.168086 | − | 0.168086i | −0.618052 | − | 0.786137i | \(-0.712078\pi\) |
0.786137 | + | 0.618052i | \(0.212078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00230 | + | 4.00230i | −0.186003 | + | 0.186003i | −0.793965 | − | 0.607963i | \(-0.791987\pi\) |
0.607963 | + | 0.793965i | \(0.291987\pi\) | |||||||
\(464\) | −21.5620 | −1.00099 | ||||||||
\(465\) | 19.0790 | 0.884766 | ||||||||
\(466\) | 8.95043 | − | 8.95043i | 0.414621 | − | 0.414621i | ||||
\(467\) | 40.0619 | 1.85384 | 0.926921 | − | 0.375257i | \(-0.122445\pi\) | ||||
0.926921 | + | 0.375257i | \(0.122445\pi\) | |||||||
\(468\) | 1.74665 | − | 1.43911i | 0.0807388 | − | 0.0665228i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18.9674 | − | 18.9674i | −0.874899 | − | 0.874899i | ||||
\(471\) | −21.6501 | −0.997583 | ||||||||
\(472\) | −6.40667 | −0.294891 | ||||||||
\(473\) | 10.9745 | + | 10.9745i | 0.504607 | + | 0.504607i | ||||
\(474\) | −2.49413 | + | 2.49413i | −0.114559 | + | 0.114559i | ||||
\(475\) | 6.96371 | + | 6.96371i | 0.319517 | + | 0.319517i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6006 | 0.485367 | ||||||||
\(478\) | 4.88252i | 0.223321i | ||||||||
\(479\) | −8.33722 | − | 8.33722i | −0.380937 | − | 0.380937i | 0.490503 | − | 0.871440i | \(-0.336813\pi\) |
−0.871440 | + | 0.490503i | \(0.836813\pi\) | |||||||
\(480\) | 20.9637i | 0.956859i | ||||||||
\(481\) | −13.9695 | − | 1.34855i | −0.636953 | − | 0.0614885i | ||||
\(482\) | − | 43.2131i | − | 1.96830i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.644466 | 0.0292939 | ||||||||
\(485\) | 13.0238i | 0.591379i | ||||||||
\(486\) | 10.7703 | − | 10.7703i | 0.488551 | − | 0.488551i | ||||
\(487\) | 0.389122 | + | 0.389122i | 0.0176328 | + | 0.0176328i | 0.715868 | − | 0.698235i | \(-0.246031\pi\) |
−0.698235 | + | 0.715868i | \(0.746031\pi\) | |||||||
\(488\) | −5.36110 | − | 5.36110i | −0.242686 | − | 0.242686i | ||||
\(489\) | −12.1527 | − | 12.1527i | −0.549564 | − | 0.549564i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.02403i | − | 0.136472i | −0.997669 | − | 0.0682362i | \(-0.978263\pi\) | ||
0.997669 | − | 0.0682362i | \(-0.0217372\pi\) | |||||||
\(492\) | 4.08372 | − | 4.08372i | 0.184108 | − | 0.184108i | ||||
\(493\) | 28.3990 | 1.27902 | ||||||||
\(494\) | −11.4041 | − | 13.8411i | −0.513093 | − | 0.622742i | ||||
\(495\) | 9.18678i | 0.412915i | ||||||||
\(496\) | 11.6140 | − | 11.6140i | 0.521484 | − | 0.521484i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.22876i | 0.413551i | ||||||||
\(499\) | −27.1172 | − | 27.1172i | −1.21393 | − | 1.21393i | −0.969723 | − | 0.244208i | \(-0.921472\pi\) |
−0.244208 | − | 0.969723i | \(-0.578528\pi\) | |||||||
\(500\) | −2.42203 | + | 2.42203i | −0.108316 | + | 0.108316i | ||||
\(501\) | 15.8543 | − | 15.8543i | 0.708317 | − | 0.708317i | ||||
\(502\) | 8.17104 | + | 8.17104i | 0.364691 | + | 0.364691i | ||||
\(503\) | 27.2615i | 1.21553i | 0.794117 | + | 0.607765i | \(0.207934\pi\) | ||||
−0.794117 | + | 0.607765i | \(0.792066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.5538 | − | 18.5538i | 0.825631 | − | 0.825631i | ||||
\(506\) | − | 19.4143i | − | 0.863073i | ||||||
\(507\) | −25.2820 | − | 4.92712i | −1.12281 | − | 0.218821i | ||||
\(508\) | 8.46748 | 0.375684 | ||||||||
\(509\) | 12.7798 | − | 12.7798i | 0.566454 | − | 0.566454i | −0.364679 | − | 0.931133i | \(-0.618821\pi\) |
0.931133 | + | 0.364679i | \(0.118821\pi\) | |||||||
\(510\) | − | 60.0230i | − | 2.65786i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.21895 | − | 2.21895i | −0.0980646 | − | 0.0980646i | ||||
\(513\) | −8.83292 | − | 8.83292i | −0.389983 | − | 0.389983i | ||||
\(514\) | −15.1048 | − | 15.1048i | −0.666245 | − | 0.666245i | ||||
\(515\) | 10.3998 | − | 10.3998i | 0.458271 | − | 0.458271i | ||||
\(516\) | − | 6.03120i | − | 0.265509i | ||||||
\(517\) | −19.7398 | −0.868157 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.49225i | − | 0.284978i | ||||||
\(520\) | 17.2809 | − | 14.2382i | 0.757815 | − | 0.624384i | ||||
\(521\) | − | 11.5778i | − | 0.507231i | −0.967305 | − | 0.253616i | \(-0.918380\pi\) | ||
0.967305 | − | 0.253616i | \(-0.0816198\pi\) | |||||||
\(522\) | 4.71752 | + | 4.71752i | 0.206480 | + | 0.206480i | ||||
\(523\) | − | 9.65911i | − | 0.422363i | −0.977447 | − | 0.211182i | \(-0.932269\pi\) | ||
0.977447 | − | 0.211182i | \(-0.0677312\pi\) | |||||||
\(524\) | 9.21198 | 0.402427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8446 | + | 25.8446i | 1.12688 | + | 1.12688i | ||||
\(527\) | −15.2966 | + | 15.2966i | −0.666331 | + | 0.666331i | ||||
\(528\) | 23.7143 | + | 23.7143i | 1.03203 | + | 1.03203i | ||||
\(529\) | 11.2227 | 0.487943 | ||||||||
\(530\) | −53.7894 | −2.33646 | ||||||||
\(531\) | 1.93860 | + | 1.93860i | 0.0841279 | + | 0.0841279i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.4287 | − | 1.48942i | −0.668292 | − | 0.0645138i | ||||
\(534\) | −16.0884 | −0.696215 | ||||||||
\(535\) | −25.4813 | + | 25.4813i | −1.10165 | + | 1.10165i | ||||
\(536\) | 15.7820 | 0.681677 | ||||||||
\(537\) | −4.45823 | −0.192387 | ||||||||
\(538\) | 3.62688 | − | 3.62688i | 0.156366 | − | 0.156366i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.65595 | + | 5.65595i | −0.243393 | + | 0.243393i | ||||
\(541\) | 21.5333 | − | 21.5333i | 0.925791 | − | 0.925791i | −0.0716399 | − | 0.997431i | \(-0.522823\pi\) |
0.997431 | + | 0.0716399i | \(0.0228232\pi\) | |||||||
\(542\) | − | 25.8721i | − | 1.11130i | ||||||
\(543\) | − | 30.7943i | − | 1.32151i | ||||||
\(544\) | −16.8077 | − | 16.8077i | −0.720625 | − | 0.720625i | ||||
\(545\) | 56.0526 | 2.40103 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0288 | 1.75427 | 0.877133 | − | 0.480247i | \(-0.159453\pi\) | ||||
0.877133 | + | 0.480247i | \(0.159453\pi\) | |||||||
\(548\) | 0.648074 | + | 0.648074i | 0.0276844 | + | 0.0276844i | ||||
\(549\) | 3.24443i | 0.138469i | ||||||||
\(550\) | − | 18.3297i | − | 0.781581i | ||||||
\(551\) | 9.46464 | − | 9.46464i | 0.403207 | − | 0.403207i | ||||
\(552\) | 10.4017 | − | 10.4017i | 0.442727 | − | 0.442727i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −34.1177 | + | 34.1177i | −1.44952 | + | 1.44952i | ||||
\(555\) | −22.1386 | −0.939733 | ||||||||
\(556\) | 12.7595 | 0.541122 | ||||||||
\(557\) | 2.79438 | − | 2.79438i | 0.118402 | − | 0.118402i | −0.645423 | − | 0.763825i | \(-0.723319\pi\) |
0.763825 | + | 0.645423i | \(0.223319\pi\) | |||||||
\(558\) | −5.08203 | −0.215139 | ||||||||
\(559\) | −12.4931 | + | 10.2934i | −0.528402 | + | 0.435365i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.2338 | − | 31.2338i | −1.31869 | − | 1.31869i | ||||
\(562\) | 39.1046 | 1.64953 | ||||||||
\(563\) | 29.7553 | 1.25404 | 0.627018 | − | 0.779004i | \(-0.284275\pi\) | ||||
0.627018 | + | 0.779004i | \(0.284275\pi\) | |||||||
\(564\) | 5.42417 | + | 5.42417i | 0.228399 | + | 0.228399i | ||||
\(565\) | 0.000468832 | 0 | 0.000468832i | 1.97239e−5 | 0 | 1.97239e-5i | ||||
\(566\) | −10.8013 | − | 10.8013i | −0.454013 | − | 0.454013i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.4369 | 1.06731 | ||||||||
\(569\) | − | 11.9282i | − | 0.500057i | −0.968239 | − | 0.250028i | \(-0.919560\pi\) | ||
0.968239 | − | 0.250028i | \(-0.0804400\pi\) | |||||||
\(570\) | −20.0041 | − | 20.0041i | −0.837881 | − | 0.837881i | ||||
\(571\) | 11.4760i | 0.480256i | 0.970741 | + | 0.240128i | \(0.0771894\pi\) | ||||
−0.970741 | + | 0.240128i | \(0.922811\pi\) | |||||||
\(572\) | −0.812032 | + | 8.41176i | −0.0339527 | + | 0.351713i | ||||
\(573\) | − | 4.71154i | − | 0.196828i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.1193 | −0.463708 | ||||||||
\(576\) | 3.48169i | 0.145071i | ||||||||
\(577\) | 2.72055 | − | 2.72055i | 0.113258 | − | 0.113258i | −0.648207 | − | 0.761465i | \(-0.724481\pi\) |
0.761465 | + | 0.648207i | \(0.224481\pi\) | |||||||
\(578\) | 28.4520 | + | 28.4520i | 1.18345 | + | 1.18345i | ||||
\(579\) | −10.9367 | − | 10.9367i | −0.454512 | − | 0.454512i | ||||
\(580\) | −6.06046 | − | 6.06046i | −0.251647 | − | 0.251647i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 14.7109i | − | 0.609787i | ||||||
\(583\) | −27.9901 | + | 27.9901i | −1.15923 | + | 1.15923i | ||||
\(584\) | −10.1050 | −0.418146 | ||||||||
\(585\) | −9.53734 | − | 0.920690i | −0.394321 | − | 0.0380659i | ||||
\(586\) | 4.81912i | 0.199076i | ||||||||
\(587\) | −26.9080 | + | 26.9080i | −1.11061 | + | 1.11061i | −0.117543 | + | 0.993068i | \(0.537502\pi\) |
−0.993068 | + | 0.117543i | \(0.962498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1959i | 0.420116i | ||||||||
\(590\) | −9.83683 | − | 9.83683i | −0.404976 | − | 0.404976i | ||||
\(591\) | 21.6763 | − | 21.6763i | 0.891645 | − | 0.891645i | ||||
\(592\) | −13.4765 | + | 13.4765i | −0.553881 | + | 0.553881i | ||||
\(593\) | 7.21930 | + | 7.21930i | 0.296461 | + | 0.296461i | 0.839626 | − | 0.543165i | \(-0.182774\pi\) |
−0.543165 | + | 0.839626i | \(0.682774\pi\) | |||||||
\(594\) | 23.2498i | 0.953949i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.2258 | − | 10.2258i | 0.418867 | − | 0.418867i | ||||
\(597\) | 39.9709i | 1.63590i | ||||||||
\(598\) | 20.1552 | + | 1.94569i | 0.824207 | + | 0.0795650i | ||||
\(599\) | −22.6509 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(600\) | 9.82059 | − | 9.82059i | 0.400924 | − | 0.400924i | ||||
\(601\) | − | 8.02946i | − | 0.327529i | −0.986499 | − | 0.163764i | \(-0.947636\pi\) | ||
0.986499 | − | 0.163764i | \(-0.0523637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.77547 | − | 4.77547i | −0.194472 | − | 0.194472i | ||||
\(604\) | 8.08847 | + | 8.08847i | 0.329115 | + | 0.329115i | ||||
\(605\) | −1.92937 | − | 1.92937i | −0.0784399 | − | 0.0784399i | ||||
\(606\) | −20.9573 | + | 20.9573i | −0.851331 | + | 0.851331i | ||||
\(607\) | 3.36912i | 0.136748i | 0.997660 | + | 0.0683741i | \(0.0217812\pi\) | ||||
−0.997660 | + | 0.0683741i | \(0.978219\pi\) | |||||||
\(608\) | −11.2032 | −0.454348 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 16.4629i | − | 0.666563i | ||||||
\(611\) | 1.97831 | − | 20.4931i | 0.0800337 | − | 0.829062i | ||||
\(612\) | 4.04784i | 0.163624i | ||||||||
\(613\) | −23.0156 | − | 23.0156i | −0.929591 | − | 0.929591i | 0.0680884 | − | 0.997679i | \(-0.478310\pi\) |
−0.997679 | + | 0.0680884i | \(0.978310\pi\) | |||||||
\(614\) | − | 8.92389i | − | 0.360139i | ||||||
\(615\) | −24.4512 | −0.985969 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.9178 | − | 24.9178i | −1.00315 | − | 1.00315i | −0.999995 | − | 0.00315687i | \(-0.998995\pi\) |
−0.00315687 | − | 0.999995i | \(-0.501005\pi\) | |||||||
\(618\) | −11.7470 | + | 11.7470i | −0.472535 | + | 0.472535i | ||||
\(619\) | −11.2549 | − | 11.2549i | −0.452372 | − | 0.452372i | 0.443769 | − | 0.896141i | \(-0.353641\pi\) |
−0.896141 | + | 0.443769i | \(0.853641\pi\) | |||||||
\(620\) | 6.52872 | 0.262200 | ||||||||
\(621\) | 14.1040 | 0.565974 | ||||||||
\(622\) | 16.2869 | + | 16.2869i | 0.653047 | + | 0.653047i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −26.9959 | + | 22.2426i | −1.08070 | + | 0.890418i | ||||
\(625\) | 30.7023 | 1.22809 | ||||||||
\(626\) | −5.44620 | + | 5.44620i | −0.217674 | + | 0.217674i | ||||
\(627\) | −20.8188 | −0.831424 | ||||||||
\(628\) | −7.40854 | −0.295633 | ||||||||
\(629\) | 17.7497 | − | 17.7497i | 0.707727 | − | 0.707727i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7103 | + | 31.7103i | −1.26237 | + | 1.26237i | −0.312427 | + | 0.949942i | \(0.601142\pi\) |
−0.949942 | + | 0.312427i | \(0.898858\pi\) | |||||||
\(632\) | 1.66412 | − | 1.66412i | 0.0661951 | − | 0.0661951i | ||||
\(633\) | 4.69468i | 0.186597i | ||||||||
\(634\) | 47.9218i | 1.90322i | ||||||||
\(635\) | −25.3495 | − | 25.3495i | −1.00596 | − | 1.00596i | ||||
\(636\) | 15.3824 | 0.609951 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.9126 | −0.986298 | ||||||||
\(639\) | −7.69695 | − | 7.69695i | −0.304487 | − | 0.304487i | ||||
\(640\) | − | 38.8278i | − | 1.53480i | ||||||
\(641\) | 4.11882i | 0.162684i | 0.996686 | + | 0.0813418i | \(0.0259205\pi\) | ||||
−0.996686 | + | 0.0813418i | \(0.974079\pi\) | |||||||
\(642\) | 28.7822 | − | 28.7822i | 1.13594 | − | 1.13594i | ||||
\(643\) | 6.89221 | − | 6.89221i | 0.271802 | − | 0.271802i | −0.558023 | − | 0.829825i | \(-0.688440\pi\) |
0.829825 | + | 0.558023i | \(0.188440\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.0559 | + | 18.0559i | −0.710950 | + | 0.710950i | ||||
\(646\) | 32.0767 | 1.26204 | ||||||||
\(647\) | 12.7884 | 0.502762 | 0.251381 | − | 0.967888i | \(-0.419115\pi\) | ||||
0.251381 | + | 0.967888i | \(0.419115\pi\) | |||||||
\(648\) | −16.7052 | + | 16.7052i | −0.656243 | + | 0.656243i | ||||
\(649\) | −10.2374 | −0.401855 | ||||||||
\(650\) | 19.0291 | + | 1.83698i | 0.746384 | + | 0.0720524i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.15859 | − | 4.15859i | −0.162863 | − | 0.162863i | ||||
\(653\) | 14.2581 | 0.557961 | 0.278981 | − | 0.960297i | \(-0.410003\pi\) | ||||
0.278981 | + | 0.960297i | \(0.410003\pi\) | |||||||
\(654\) | −63.3138 | −2.47577 | ||||||||
\(655\) | −27.5783 | − | 27.5783i | −1.07757 | − | 1.07757i | ||||
\(656\) | −14.8843 | + | 14.8843i | −0.581133 | + | 0.581133i | ||||
\(657\) | 3.05766 | + | 3.05766i | 0.119291 | + | 0.119291i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4714 | 0.719542 | 0.359771 | − | 0.933041i | \(-0.382855\pi\) | ||||
0.359771 | + | 0.933041i | \(0.382855\pi\) | |||||||
\(660\) | 13.3308i | 0.518902i | ||||||||
\(661\) | 23.1384 | + | 23.1384i | 0.899978 | + | 0.899978i | 0.995434 | − | 0.0954556i | \(-0.0304308\pi\) |
−0.0954556 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(662\) | 24.2503i | 0.942515i | ||||||||
\(663\) | 35.5559 | − | 29.2954i | 1.38088 | − | 1.13774i | ||||
\(664\) | − | 6.15757i | − | 0.238960i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.89703 | 0.228505 | ||||||||
\(667\) | 15.1127i | 0.585166i | ||||||||
\(668\) | 5.42525 | − | 5.42525i | 0.209909 | − | 0.209909i | ||||
\(669\) | 19.1761 | + | 19.1761i | 0.741389 | + | 0.741389i | ||||
\(670\) | 24.2317 | + | 24.2317i | 0.936151 | + | 0.936151i | ||||
\(671\) | −8.56669 | − | 8.56669i | −0.330713 | − | 0.330713i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.6367i | − | 1.37370i | −0.726801 | − | 0.686848i | \(-0.758994\pi\) | ||
0.726801 | − | 0.686848i | \(-0.241006\pi\) | |||||||
\(674\) | −11.0152 | + | 11.0152i | −0.424288 | + | 0.424288i | ||||
\(675\) | 13.3160 | 0.512534 | ||||||||
\(676\) | −8.65136 | − | 1.68604i | −0.332745 | − | 0.0648475i | ||||
\(677\) | 27.6606i | 1.06308i | 0.847032 | + | 0.531542i | \(0.178387\pi\) | ||||
−0.847032 | + | 0.531542i | \(0.821613\pi\) | |||||||
\(678\) | −0.000529566 | 0 | 0.000529566i | −2.03379e−5 | 0 | 2.03379e-5i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 40.0483i | 1.53578i | ||||||||
\(681\) | −18.2670 | − | 18.2670i | −0.699994 | − | 0.699994i | ||||
\(682\) | 13.4187 | − | 13.4187i | 0.513829 | − | 0.513829i | ||||
\(683\) | −1.14228 | + | 1.14228i | −0.0437082 | + | 0.0437082i | −0.728623 | − | 0.684915i | \(-0.759839\pi\) |
0.684915 | + | 0.728623i | \(0.259839\pi\) | |||||||
\(684\) | 1.34904 | + | 1.34904i | 0.0515819 | + | 0.0515819i | ||||
\(685\) | − | 3.88034i | − | 0.148260i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.2939 | + | 21.2939i | −0.812414 | + | 0.812414i | ||||
\(688\) | 21.9824i | 0.838072i | ||||||||
\(689\) | −26.2530 | − | 31.8633i | −1.00016 | − | 1.21389i | ||||
\(690\) | 31.9417 | 1.21600 | ||||||||
\(691\) | 18.8431 | − | 18.8431i | 0.716827 | − | 0.716827i | −0.251127 | − | 0.967954i | \(-0.580801\pi\) |
0.967954 | + | 0.251127i | \(0.0808013\pi\) | |||||||
\(692\) | − | 2.22161i | − | 0.0844531i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.6506 | − | 40.6506i | −1.54307 | − | 1.54307i | ||||
\(695\) | −38.1986 | − | 38.1986i | −1.44895 | − | 1.44895i | ||||
\(696\) | −13.3475 | − | 13.3475i | −0.505936 | − | 0.505936i | ||||
\(697\) | 19.6038 | − | 19.6038i | 0.742548 | − | 0.742548i | ||||
\(698\) | − | 15.3846i | − | 0.582314i | ||||||
\(699\) | 15.3255 | 0.579665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.72322i | − | 0.216163i | −0.994142 | − | 0.108081i | \(-0.965529\pi\) | ||
0.994142 | − | 0.108081i | \(-0.0344707\pi\) | |||||||
\(702\) | −24.1370 | − | 2.33007i | −0.910991 | − | 0.0879427i | ||||
\(703\) | − | 11.8310i | − | 0.446216i | ||||||
\(704\) | −9.19316 | − | 9.19316i | −0.346480 | − | 0.346480i | ||||
\(705\) | − | 32.4772i | − | 1.22316i | ||||||
\(706\) | 20.2483 | 0.762056 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.81308 | + | 2.81308i | 0.105722 | + | 0.105722i | ||||
\(709\) | −8.47775 | + | 8.47775i | −0.318388 | + | 0.318388i | −0.848148 | − | 0.529759i | \(-0.822282\pi\) |
0.529759 | + | 0.848148i | \(0.322282\pi\) | |||||||
\(710\) | 39.0558 | + | 39.0558i | 1.46574 | + | 1.46574i | ||||
\(711\) | −1.00709 | −0.0377689 | ||||||||
\(712\) | 10.7344 | 0.402290 | ||||||||
\(713\) | −8.14019 | − | 8.14019i | −0.304853 | − | 0.304853i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.6137 | − | 22.7516i | 1.03269 | − | 0.850863i | ||||
\(716\) | −1.52558 | −0.0570136 | ||||||||
\(717\) | −4.18009 | + | 4.18009i | −0.156108 | + | 0.156108i | ||||
\(718\) | −7.01636 | −0.261848 | ||||||||
\(719\) | 15.2388 | 0.568311 | 0.284155 | − | 0.958778i | \(-0.408287\pi\) | ||||
0.284155 | + | 0.958778i | \(0.408287\pi\) | |||||||
\(720\) | −9.20079 | + | 9.20079i | −0.342893 | + | 0.342893i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.2956 | + | 11.2956i | −0.420378 | + | 0.420378i | ||||
\(723\) | 36.9962 | − | 36.9962i | 1.37590 | − | 1.37590i | ||||
\(724\) | − | 10.5376i | − | 0.391628i | ||||||
\(725\) | 14.2684i | 0.529914i | ||||||||
\(726\) | 2.17930 | + | 2.17930i | 0.0808816 | + | 0.0808816i | ||||
\(727\) | −19.4937 | −0.722981 | −0.361491 | − | 0.932376i | \(-0.617732\pi\) | ||||
−0.361491 | + | 0.932376i | \(0.617732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.3192 | −0.530339 | ||||||||
\(730\) | −15.5152 | − | 15.5152i | −0.574243 | − | 0.574243i | ||||
\(731\) | − | 28.9527i | − | 1.07085i | ||||||
\(732\) | 4.70796i | 0.174011i | ||||||||
\(733\) | −20.9891 | + | 20.9891i | −0.775250 | + | 0.775250i | −0.979019 | − | 0.203769i | \(-0.934681\pi\) |
0.203769 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(734\) | −28.6216 | + | 28.6216i | −1.05644 | + | 1.05644i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.94434 | − | 8.94434i | 0.329693 | − | 0.329693i | ||||
\(737\) | 25.2186 | 0.928938 | ||||||||
\(738\) | 6.51303 | 0.239748 | ||||||||
\(739\) | −0.594151 | + | 0.594151i | −0.0218562 | + | 0.0218562i | −0.717950 | − | 0.696094i | \(-0.754920\pi\) |
0.696094 | + | 0.717950i | \(0.254920\pi\) | |||||||
\(740\) | −7.57573 | −0.278489 | ||||||||
\(741\) | 2.08644 | − | 21.6133i | 0.0766474 | − | 0.793983i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5891 | + | 22.5891i | 0.828715 | + | 0.828715i | 0.987339 | − | 0.158624i | \(-0.0507056\pi\) |
−0.158624 | + | 0.987339i | \(0.550706\pi\) | |||||||
\(744\) | 14.3788 | 0.527153 | ||||||||
\(745\) | −61.2272 | −2.24319 | ||||||||
\(746\) | −9.15718 | − | 9.15718i | −0.335268 | − | 0.335268i | ||||
\(747\) | −1.86322 | + | 1.86322i | −0.0681717 | + | 0.0681717i | ||||
\(748\) | −10.6880 | − | 10.6880i | −0.390793 | − | 0.390793i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.3805 | −0.598131 | ||||||||
\(751\) | − | 14.9867i | − | 0.546872i | −0.961890 | − | 0.273436i | \(-0.911840\pi\) | ||
0.961890 | − | 0.273436i | \(-0.0881602\pi\) | |||||||
\(752\) | −19.7699 | − | 19.7699i | −0.720935 | − | 0.720935i | ||||
\(753\) | 13.9910i | 0.509860i | ||||||||
\(754\) | 2.49671 | − | 25.8632i | 0.0909249 | − | 0.941882i | ||||
\(755\) | − | 48.4296i | − | 1.76254i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.27355 | −0.155325 | −0.0776624 | − | 0.996980i | \(-0.524746\pi\) | ||||
−0.0776624 | + | 0.996980i | \(0.524746\pi\) | |||||||
\(758\) | 7.69251i | 0.279405i | ||||||||
\(759\) | 16.6213 | − | 16.6213i | 0.603314 | − | 0.603314i | ||||
\(760\) | 13.3470 | + | 13.3470i | 0.484148 | + | 0.484148i | ||||
\(761\) | −5.54810 | − | 5.54810i | −0.201118 | − | 0.201118i | 0.599361 | − | 0.800479i | \(-0.295422\pi\) |
−0.800479 | + | 0.599361i | \(0.795422\pi\) | |||||||
\(762\) | 28.6333 | + | 28.6333i | 1.03728 | + | 1.03728i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.61227i | − | 0.0583297i | ||||||
\(765\) | 12.1182 | − | 12.1182i | 0.438135 | − | 0.438135i | ||||
\(766\) | 14.8213 | 0.535517 | ||||||||
\(767\) | 1.02599 | − | 10.6281i | 0.0370462 | − | 0.383758i | ||||
\(768\) | 28.9545i | 1.04481i | ||||||||
\(769\) | −5.34450 | + | 5.34450i | −0.192727 | + | 0.192727i | −0.796874 | − | 0.604146i | \(-0.793514\pi\) |
0.604146 | + | 0.796874i | \(0.293514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.8635i | − | 0.931450i | ||||||
\(772\) | −3.74247 | − | 3.74247i | −0.134694 | − | 0.134694i | ||||
\(773\) | −21.5544 | + | 21.5544i | −0.775257 | + | 0.775257i | −0.979020 | − | 0.203763i | \(-0.934683\pi\) |
0.203763 | + | 0.979020i | \(0.434683\pi\) | |||||||
\(774\) | 4.80951 | − | 4.80951i | 0.172874 | − | 0.172874i | ||||
\(775\) | −7.68541 | − | 7.68541i | −0.276068 | − | 0.276068i | ||||
\(776\) | 9.81534i | 0.352350i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.8335 | − | 24.8335i | 0.890323 | − | 0.890323i | ||||
\(779\) | − | 13.0669i | − | 0.468170i | ||||||
\(780\) | −13.8395 | − | 1.33600i | −0.495535 | − | 0.0478366i | ||||
\(781\) | 40.6465 | 1.45444 | ||||||||
\(782\) | −25.6093 | + | 25.6093i | −0.915787 | + | 0.915787i | ||||
\(783\) | − | 18.0983i | − | 0.646780i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.1793 | + | 22.1793i | 0.791613 | + | 0.791613i | ||||
\(786\) | 31.1509 | + | 31.1509i | 1.11112 | + | 1.11112i | ||||
\(787\) | 38.3225 | + | 38.3225i | 1.36605 | + | 1.36605i | 0.865994 | + | 0.500054i | \(0.166687\pi\) |
0.500054 | + | 0.865994i | \(0.333313\pi\) | |||||||
\(788\) | 7.41753 | − | 7.41753i | 0.264239 | − | 0.264239i | ||||
\(789\) | 44.2528i | 1.57544i | ||||||||
\(790\) | 5.11018 | 0.181812 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.92360i | 0.246020i | ||||||||
\(793\) | 9.75213 | − | 8.03504i | 0.346308 | − | 0.285333i | ||||
\(794\) | − | 21.3955i | − | 0.759299i | ||||||
\(795\) | −46.0509 | − | 46.0509i | −1.63326 | − | 1.63326i | ||||
\(796\) | 13.6778i | 0.484798i | ||||||||
\(797\) | −28.0843 | −0.994797 | −0.497399 | − | 0.867522i | \(-0.665711\pi\) | ||||
−0.497399 | + | 0.867522i | \(0.665711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0387 | + | 26.0387i | 0.921181 | + | 0.921181i | ||||
\(800\) | 8.44464 | − | 8.44464i | 0.298563 | − | 0.298563i | ||||
\(801\) | −3.24814 | − | 3.24814i | −0.114767 | − | 0.114767i | ||||
\(802\) | −34.7312 | −1.22640 | ||||||||
\(803\) | −16.1471 | −0.569818 | ||||||||
\(804\) | −6.92963 | − | 6.92963i | −0.244389 | − | 0.244389i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.5860 | + | 15.2756i | 0.443321 | + | 0.538059i | ||||
\(807\) | 6.21018 | 0.218609 | ||||||||
\(808\) | 13.9830 | − | 13.9830i | 0.491920 | − | 0.491920i | ||||
\(809\) | −12.7749 | −0.449143 | −0.224572 | − | 0.974458i | \(-0.572098\pi\) | ||||
−0.224572 | + | 0.974458i | \(0.572098\pi\) | |||||||
\(810\) | −51.2985 | −1.80245 | ||||||||
\(811\) | 20.6613 | − | 20.6613i | 0.725515 | − | 0.725515i | −0.244208 | − | 0.969723i | \(-0.578528\pi\) |
0.969723 | + | 0.244208i | \(0.0785279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.1500 | − | 22.1500i | 0.776833 | − | 0.776833i | ||||
\(814\) | −15.5707 | + | 15.5707i | −0.545752 | + | 0.545752i | ||||
\(815\) | 24.8995i | 0.872192i | ||||||||
\(816\) | − | 62.5628i | − | 2.19014i | ||||||
\(817\) | −9.64918 | − | 9.64918i | −0.337582 | − | 0.337582i | ||||
\(818\) | −13.9395 | −0.487382 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.36708 | −0.292191 | ||||||||
\(821\) | 0.901780 | + | 0.901780i | 0.0314723 | + | 0.0314723i | 0.722668 | − | 0.691195i | \(-0.242916\pi\) |
−0.691195 | + | 0.722668i | \(0.742916\pi\) | |||||||
\(822\) | 4.38301i | 0.152875i | ||||||||
\(823\) | − | 22.0804i | − | 0.769676i | −0.922984 | − | 0.384838i | \(-0.874257\pi\) | ||
0.922984 | − | 0.384838i | \(-0.125743\pi\) | |||||||
\(824\) | 7.83780 | − | 7.83780i | 0.273043 | − | 0.273043i | ||||
\(825\) | 15.6927 | − | 15.6927i | 0.546349 | − | 0.546349i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.30639 | − | 9.30639i | 0.323615 | − | 0.323615i | −0.526537 | − | 0.850152i | \(-0.676510\pi\) |
0.850152 | + | 0.526537i | \(0.176510\pi\) | |||||||
\(828\) | −2.15409 | −0.0748597 | ||||||||
\(829\) | −30.9681 | −1.07557 | −0.537784 | − | 0.843083i | \(-0.680738\pi\) | ||||
−0.537784 | + | 0.843083i | \(0.680738\pi\) | |||||||
\(830\) | 9.45435 | − | 9.45435i | 0.328165 | − | 0.328165i | ||||
\(831\) | −58.4186 | −2.02652 | ||||||||
\(832\) | 10.4653 | − | 8.62263i | 0.362819 | − | 0.298936i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 43.1470 | + | 43.1470i | 1.49406 | + | 1.49406i | ||||
\(835\) | −32.4837 | −1.12414 | ||||||||
\(836\) | −7.12409 | −0.246392 | ||||||||
\(837\) | 9.74834 | + | 9.74834i | 0.336952 | + | 0.336952i | ||||
\(838\) | −9.70956 | + | 9.70956i | −0.335411 | + | 0.335411i | ||||
\(839\) | −22.1620 | − | 22.1620i | −0.765116 | − | 0.765116i | 0.212126 | − | 0.977242i | \(-0.431961\pi\) |
−0.977242 | + | 0.212126i | \(0.931961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.60734 | −0.331288 | ||||||||
\(842\) | 47.5391i | 1.63831i | ||||||||
\(843\) | 33.4788 | + | 33.4788i | 1.15307 | + | 1.15307i | ||||
\(844\) | 1.60650i | 0.0552979i | ||||||||
\(845\) | 20.8524 | + | 30.9475i | 0.717345 | + | 1.06463i | ||||
\(846\) | 8.65088i | 0.297423i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −56.0654 | −1.92530 | ||||||||
\(849\) | − | 18.4947i | − | 0.634737i | ||||||
\(850\) | −24.1786 | + | 24.1786i | −0.829318 | + | 0.829318i | ||||
\(851\) | 9.44563 | + | 9.44563i | 0.323792 | + | 0.323792i | ||||
\(852\) | −11.1690 | − | 11.1690i | −0.382642 | − | 0.382642i | ||||
\(853\) | 15.0740 | + | 15.0740i | 0.516125 | + | 0.516125i | 0.916397 | − | 0.400271i | \(-0.131084\pi\) |
−0.400271 | + | 0.916397i | \(0.631084\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.07737i | − | 0.276240i | ||||||
\(856\) | −19.2039 | + | 19.2039i | −0.656376 | + | 0.656376i | ||||
\(857\) | 37.6852 | 1.28730 | 0.643650 | − | 0.765320i | \(-0.277419\pi\) | ||||
0.643650 | + | 0.765320i | \(0.277419\pi\) | |||||||
\(858\) | −31.1908 | + | 25.6990i | −1.06484 | + | 0.877348i | ||||
\(859\) | 9.30207i | 0.317383i | 0.987328 | + | 0.158691i | \(0.0507275\pi\) | ||||
−0.987328 | + | 0.158691i | \(0.949273\pi\) | |||||||
\(860\) | −6.17863 | + | 6.17863i | −0.210689 | + | 0.210689i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.3712i | 0.557605i | ||||||||
\(863\) | 16.2595 | + | 16.2595i | 0.553481 | + | 0.553481i | 0.927444 | − | 0.373962i | \(-0.122001\pi\) |
−0.373962 | + | 0.927444i | \(0.622001\pi\) | |||||||
\(864\) | −10.7114 | + | 10.7114i | −0.364408 | + | 0.364408i | ||||
\(865\) | −6.65094 | + | 6.65094i | −0.226139 | + | 0.226139i | ||||
\(866\) | 47.8884 | + | 47.8884i | 1.62731 | + | 1.62731i | ||||
\(867\) | 48.7174i | 1.65453i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.65915 | − | 2.65915i | 0.0902056 | − | 0.0902056i | ||||
\(870\) | − | 40.9877i | − | 1.38961i | ||||||
\(871\) | −2.52738 | + | 26.1809i | −0.0856370 | + | 0.887105i | ||||
\(872\) | 42.2439 | 1.43056 | ||||||||
\(873\) | 2.97002 | − | 2.97002i | 0.100520 | − | 0.100520i | ||||
\(874\) | 17.0698i | 0.577396i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.43694 | + | 4.43694i | 0.149910 | + | 0.149910i | ||||
\(877\) | −7.47672 | − | 7.47672i | −0.252471 | − | 0.252471i | 0.569512 | − | 0.821983i | \(-0.307132\pi\) |
−0.821983 | + | 0.569512i | \(0.807132\pi\) | |||||||
\(878\) | 0.164983 | + | 0.164983i | 0.00556791 | + | 0.00556791i | ||||
\(879\) | −4.12581 | + | 4.12581i | −0.139160 | + | 0.139160i | ||||
\(880\) | − | 48.5880i | − | 1.63790i | ||||||
\(881\) | 19.0687 | 0.642440 | 0.321220 | − | 0.947005i | \(-0.395907\pi\) | ||||
0.321220 | + | 0.947005i | \(0.395907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.27586i | − | 0.143894i | −0.997408 | − | 0.0719471i | \(-0.977079\pi\) | ||
0.997408 | − | 0.0719471i | \(-0.0229213\pi\) | |||||||
\(884\) | 12.1670 | − | 10.0247i | 0.409221 | − | 0.337169i | ||||
\(885\) | − | 16.8433i | − | 0.566180i | ||||||
\(886\) | 29.9398 | + | 29.9398i | 1.00585 | + | 1.00585i | ||||
\(887\) | 6.64767i | 0.223207i | 0.993753 | + | 0.111603i | \(0.0355986\pi\) | ||||
−0.993753 | + | 0.111603i | \(0.964401\pi\) | |||||||
\(888\) | −16.6847 | −0.559903 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.4817 | + | 16.4817i | 0.552468 | + | 0.552468i | ||||
\(891\) | −26.6939 | + | 26.6939i | −0.894278 | + | 0.894278i | ||||
\(892\) | 6.56194 | + | 6.56194i | 0.219710 | + | 0.219710i | ||||
\(893\) | 17.3560 | 0.580797 | ||||||||
\(894\) | 69.1587 | 2.31301 | ||||||||
\(895\) | 4.56720 | + | 4.56720i | 0.152665 | + | 0.152665i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.5898 | + | 18.9213i | 0.520527 | + | 0.631764i | ||||
\(898\) | 2.93096 | 0.0978073 | ||||||||
\(899\) | −10.4455 | + | 10.4455i | −0.348378 | + | 0.348378i | ||||
\(900\) | −2.03374 | −0.0677914 | ||||||||
\(901\) | 73.8429 | 2.46006 | ||||||||
\(902\) | −17.1972 | + | 17.1972i | −0.572603 | + | 0.572603i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.000353334 | 0 | 0.000353334i | 1.17517e−5 | 0 | 1.17517e-5i | ||||
\(905\) | −31.5470 | + | 31.5470i | −1.04866 | + | 1.04866i | ||||
\(906\) | 54.7034i | 1.81740i | ||||||||
\(907\) | 14.6887i | 0.487729i | 0.969809 | + | 0.243865i | \(0.0784152\pi\) | ||||
−0.969809 | + | 0.243865i | \(0.921585\pi\) | |||||||
\(908\) | −6.25088 | − | 6.25088i | −0.207443 | − | 0.207443i | ||||
\(909\) | −8.46224 | −0.280675 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7868 | 0.589301 | 0.294651 | − | 0.955605i | \(-0.404797\pi\) | ||||
0.294651 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(912\) | −20.8506 | − | 20.8506i | −0.690431 | − | 0.690431i | ||||
\(913\) | − | 9.83940i | − | 0.325636i | ||||||
\(914\) | − | 7.62985i | − | 0.252373i | ||||||
\(915\) | 14.0944 | − | 14.0944i | 0.465948 | − | 0.465948i | ||||
\(916\) | −7.28667 | + | 7.28667i | −0.240758 | + | 0.240758i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 30.6686 | − | 30.6686i | 1.01221 | − | 1.01221i | ||||
\(919\) | 22.2865 | 0.735163 | 0.367581 | − | 0.929991i | \(-0.380186\pi\) | ||||
0.367581 | + | 0.929991i | \(0.380186\pi\) | |||||||
\(920\) | −21.3120 | −0.702634 | ||||||||
\(921\) | 7.64004 | − | 7.64004i | 0.251748 | − | 0.251748i | ||||
\(922\) | 8.35223 | 0.275066 | ||||||||
\(923\) | −4.07355 | + | 42.1975i | −0.134082 | + | 1.38895i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.91792 | + | 8.91792i | 0.293219 | + | 0.293219i | ||||
\(926\) | −9.26255 | −0.304386 | ||||||||
\(927\) | −4.74328 | −0.155790 | ||||||||
\(928\) | −11.4774 | − | 11.4774i | −0.376765 | − | 0.376765i | ||||
\(929\) | −30.3717 | + | 30.3717i | −0.996464 | + | 0.996464i | −0.999994 | − | 0.00352958i | \(-0.998876\pi\) |
0.00352958 | + | 0.999994i | \(0.498876\pi\) | |||||||
\(930\) | 22.0773 | + | 22.0773i | 0.723943 | + | 0.723943i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.24431 | 0.171783 | ||||||||
\(933\) | 27.8876i | 0.912998i | ||||||||
\(934\) | 46.3577 | + | 46.3577i | 1.51687 | + | 1.51687i | ||||
\(935\) | 63.9945i | 2.09285i | ||||||||
\(936\) | −7.18780 | − | 0.693877i | −0.234941 | − | 0.0226801i | ||||
\(937\) | 52.3733i | 1.71096i | 0.517835 | + | 0.855481i | \(0.326738\pi\) | ||||
−0.517835 | + | 0.855481i | \(0.673262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.32534 | −0.304321 | ||||||||
\(940\) | − | 11.1135i | − | 0.362483i | ||||||
\(941\) | 11.0169 | − | 11.0169i | 0.359141 | − | 0.359141i | −0.504355 | − | 0.863496i | \(-0.668270\pi\) |
0.863496 | + | 0.504355i | \(0.168270\pi\) | |||||||
\(942\) | −25.0525 | − | 25.0525i | −0.816254 | − | 0.816254i | ||||
\(943\) | 10.4323 | + | 10.4323i | 0.339723 | + | 0.339723i | ||||
\(944\) | −10.2531 | − | 10.2531i | −0.333708 | − | 0.333708i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.3983i | 0.825771i | ||||||||
\(947\) | 30.1246 | − | 30.1246i | 0.978918 | − | 0.978918i | −0.0208644 | − | 0.999782i | \(-0.506642\pi\) |
0.999782 | + | 0.0208644i | \(0.00664182\pi\) | |||||||
\(948\) | −1.46138 | −0.0474634 | ||||||||
\(949\) | 1.61824 | − | 16.7632i | 0.0525304 | − | 0.544157i | ||||
\(950\) | 16.1162i | 0.522878i | ||||||||
\(951\) | −41.0275 | + | 41.0275i | −1.33041 | + | 1.33041i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.9437i | − | 1.16433i | −0.813070 | − | 0.582165i | \(-0.802206\pi\) | ||
0.813070 | − | 0.582165i | \(-0.197794\pi\) | |||||||
\(954\) | 12.2665 | + | 12.2665i | 0.397143 | + | 0.397143i | ||||
\(955\) | −4.82671 | + | 4.82671i | −0.156189 | + | 0.156189i | ||||
\(956\) | −1.43040 | + | 1.43040i | −0.0462626 | + | 0.0462626i | ||||
\(957\) | −21.3285 | − | 21.3285i | −0.689452 | − | 0.689452i | ||||
\(958\) | − | 19.2949i | − | 0.623390i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 15.1251 | − | 15.1251i | 0.488162 | − | 0.488162i | ||||
\(961\) | 19.7474i | 0.637013i | ||||||||
\(962\) | −14.6044 | − | 17.7253i | −0.470863 | − | 0.571487i | ||||
\(963\) | 11.6218 | 0.374508 | ||||||||
\(964\) | 12.6599 | − | 12.6599i | 0.407748 | − | 0.407748i | ||||
\(965\) | 22.4080i | 0.721339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.7209 | − | 31.7209i | −1.02008 | − | 1.02008i | −0.999794 | − | 0.0202813i | \(-0.993544\pi\) |
−0.0202813 | − | 0.999794i | \(-0.506456\pi\) | |||||||
\(968\) | −1.45406 | − | 1.45406i | −0.0467354 | − | 0.0467354i | ||||
\(969\) | 27.4620 | + | 27.4620i | 0.882205 | + | 0.882205i | ||||
\(970\) | −15.0705 | + | 15.0705i | −0.483884 | + | 0.483884i | ||||
\(971\) | 23.9259i | 0.767818i | 0.923371 | + | 0.383909i | \(0.125422\pi\) | ||||
−0.923371 | + | 0.383909i | \(0.874578\pi\) | |||||||
\(972\) | 6.31063 | 0.202414 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.900548i | 0.0288554i | ||||||||
\(975\) | 14.7188 | + | 17.8642i | 0.471378 | + | 0.572112i | ||||
\(976\) | − | 17.1595i | − | 0.549262i | ||||||
\(977\) | −31.2419 | − | 31.2419i | −0.999517 | − | 0.999517i | 0.000483091 | − | 1.00000i | \(-0.499846\pi\) |
−1.00000 | 0.000483091i | \(0.999846\pi\) | ||||||||
\(978\) | − | 28.1251i | − | 0.899341i | ||||||
\(979\) | 17.1530 | 0.548211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.7826 | − | 12.7826i | −0.408117 | − | 0.408117i | ||||
\(982\) | 3.49927 | − | 3.49927i | 0.111666 | − | 0.111666i | ||||
\(983\) | 2.85615 | + | 2.85615i | 0.0910971 | + | 0.0910971i | 0.751187 | − | 0.660090i | \(-0.229482\pi\) |
−0.660090 | + | 0.751187i | \(0.729482\pi\) | |||||||
\(984\) | −18.4276 | −0.587451 | ||||||||
\(985\) | −44.4124 | −1.41510 | ||||||||
\(986\) | 32.8620 | + | 32.8620i | 1.04654 | + | 1.04654i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.713969 | − | 7.39594i | 0.0227144 | − | 0.235296i | ||||
\(989\) | 15.4074 | 0.489926 | ||||||||
\(990\) | −10.6305 | + | 10.6305i | −0.337860 | + | 0.337860i | ||||
\(991\) | −30.8167 | −0.978925 | −0.489463 | − | 0.872024i | \(-0.662807\pi\) | ||||
−0.489463 | + | 0.872024i | \(0.662807\pi\) | |||||||
\(992\) | 12.3642 | 0.392564 | ||||||||
\(993\) | −20.7615 | + | 20.7615i | −0.658846 | + | 0.658846i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.9480 | − | 40.9480i | 1.29814 | − | 1.29814i | ||||
\(996\) | −2.70370 | + | 2.70370i | −0.0856700 | + | 0.0856700i | ||||
\(997\) | − | 40.3578i | − | 1.27814i | −0.769147 | − | 0.639072i | \(-0.779319\pi\) | ||
0.769147 | − | 0.639072i | \(-0.220681\pi\) | |||||||
\(998\) | − | 62.7575i | − | 1.98655i | ||||||
\(999\) | −11.3117 | − | 11.3117i | −0.357885 | − | 0.357885i |
(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 | 637.2.i.a.489.12 | 32 | ||
7.2 | even | 3 | 91.2.bb.a.73.6 | yes | 32 | ||
7.3 | odd | 6 | 91.2.bb.a.47.3 | yes | 32 | ||
7.4 | even | 3 | 637.2.bc.b.411.3 | 32 | |||
7.5 | odd | 6 | 637.2.bc.b.619.6 | 32 | |||
7.6 | odd | 2 | inner | 637.2.i.a.489.11 | 32 | ||
13.5 | odd | 4 | inner | 637.2.i.a.538.12 | 32 | ||
21.2 | odd | 6 | 819.2.fn.e.73.3 | 32 | |||
21.17 | even | 6 | 819.2.fn.e.775.6 | 32 | |||
91.5 | even | 12 | 637.2.bc.b.31.3 | 32 | |||
91.18 | odd | 12 | 637.2.bc.b.460.6 | 32 | |||
91.31 | even | 12 | 91.2.bb.a.5.6 | ✓ | 32 | ||
91.44 | odd | 12 | 91.2.bb.a.31.3 | yes | 32 | ||
91.83 | even | 4 | inner | 637.2.i.a.538.11 | 32 | ||
273.44 | even | 12 | 819.2.fn.e.577.6 | 32 | |||
273.122 | odd | 12 | 819.2.fn.e.460.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bb.a.5.6 | ✓ | 32 | 91.31 | even | 12 | ||
91.2.bb.a.31.3 | yes | 32 | 91.44 | odd | 12 | ||
91.2.bb.a.47.3 | yes | 32 | 7.3 | odd | 6 | ||
91.2.bb.a.73.6 | yes | 32 | 7.2 | even | 3 | ||
637.2.i.a.489.11 | 32 | 7.6 | odd | 2 | inner | ||
637.2.i.a.489.12 | 32 | 1.1 | even | 1 | trivial | ||
637.2.i.a.538.11 | 32 | 91.83 | even | 4 | inner | ||
637.2.i.a.538.12 | 32 | 13.5 | odd | 4 | inner | ||
637.2.bc.b.31.3 | 32 | 91.5 | even | 12 | |||
637.2.bc.b.411.3 | 32 | 7.4 | even | 3 | |||
637.2.bc.b.460.6 | 32 | 91.18 | odd | 12 | |||
637.2.bc.b.619.6 | 32 | 7.5 | odd | 6 | |||
819.2.fn.e.73.3 | 32 | 21.2 | odd | 6 | |||
819.2.fn.e.460.3 | 32 | 273.122 | odd | 12 | |||
819.2.fn.e.577.6 | 32 | 273.44 | even | 12 | |||
819.2.fn.e.775.6 | 32 | 21.17 | even | 6 |