Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(365,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.365");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 365.10 | ||
Character | \(\chi\) | \(=\) | 804.365 |
Dual form | 804.2.o.d.641.10 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.355178 | − | 1.69524i | 0.205062 | − | 0.978749i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.60368 | 1.61161 | 0.805806 | − | 0.592179i | \(-0.201732\pi\) | ||||
0.805806 | + | 0.592179i | \(0.201732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20029 | + | 1.84769i | 1.20959 | + | 0.698359i | 0.962671 | − | 0.270676i | \(-0.0872470\pi\) |
0.246923 | + | 0.969035i | \(0.420580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.74770 | − | 1.20423i | −0.915899 | − | 0.401409i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.48078 | − | 2.56478i | 0.446471 | − | 0.773311i | −0.551682 | − | 0.834055i | \(-0.686014\pi\) |
0.998153 | + | 0.0607433i | \(0.0193471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95258 | − | 1.12732i | 0.541547 | − | 0.312663i | −0.204158 | − | 0.978938i | \(-0.565446\pi\) |
0.745706 | + | 0.666275i | \(0.232112\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27995 | − | 6.10911i | 0.330481 | − | 1.57736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00058 | + | 2.30974i | −0.970283 | + | 0.560193i | −0.899323 | − | 0.437286i | \(-0.855940\pi\) |
−0.0709605 | + | 0.997479i | \(0.522606\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.85606 | + | 4.94684i | 0.655225 | + | 1.13488i | 0.981837 | + | 0.189725i | \(0.0607596\pi\) |
−0.326612 | + | 0.945158i | \(0.605907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.26895 | − | 4.76900i | 0.931561 | − | 1.04068i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.12280 | + | 4.11235i | −1.48521 | + | 0.857484i | −0.999858 | − | 0.0168370i | \(-0.994640\pi\) |
−0.485348 | + | 0.874321i | \(0.661307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.98648 | 1.59730 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.01738 | + | 4.23030i | −0.580695 | + | 0.814121i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.16985 | + | 2.40746i | 0.774321 | + | 0.447054i | 0.834414 | − | 0.551138i | \(-0.185806\pi\) |
−0.0600929 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.73963 | − | 3.89113i | −1.21047 | − | 0.698867i | −0.247611 | − | 0.968860i | \(-0.579645\pi\) |
−0.962862 | + | 0.269993i | \(0.912979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.82199 | − | 3.42123i | −0.665323 | − | 0.595560i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.5328 | + | 6.65846i | 1.94940 | + | 1.12549i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.09202 | + | 7.08759i | 0.672724 | + | 1.16519i | 0.977129 | + | 0.212650i | \(0.0682093\pi\) |
−0.304404 | + | 0.952543i | \(0.598457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.21757 | − | 3.71049i | −0.194967 | − | 0.594154i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.243870 | + | 0.422396i | −0.0380862 | + | 0.0659672i | −0.884440 | − | 0.466654i | \(-0.845459\pi\) |
0.846354 | + | 0.532621i | \(0.178793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.0216i | − | 1.68077i | −0.541986 | − | 0.840387i | \(-0.682328\pi\) | ||
0.541986 | − | 0.840387i | \(-0.317672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.90181 | − | 4.33964i | −1.47607 | − | 0.646916i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.37585 | − | 4.25845i | −1.07588 | − | 0.621159i | −0.146097 | − | 0.989270i | \(-0.546671\pi\) |
−0.929782 | + | 0.368111i | \(0.880005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.32788 | + | 5.76406i | 0.475412 | + | 0.823438i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.49464 | + | 7.60232i | 0.349320 | + | 1.06454i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5924 | −1.45498 | −0.727492 | − | 0.686116i | \(-0.759314\pi\) | ||||
−0.727492 | + | 0.686116i | \(0.759314\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.33624 | − | 9.24265i | 0.719539 | − | 1.24628i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.40051 | − | 3.08470i | 1.24513 | − | 0.408579i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.3999i | − | 1.48414i | −0.670324 | − | 0.742068i | \(-0.733845\pi\) | ||
0.670324 | − | 0.742068i | \(-0.266155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.97066 | + | 2.29246i | −0.508391 | + | 0.293520i | −0.732172 | − | 0.681120i | \(-0.761493\pi\) |
0.223781 | + | 0.974640i | \(0.428160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.56838 | − | 8.93075i | −0.827538 | − | 1.12517i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.03646 | − | 4.06250i | 0.872765 | − | 0.503891i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.48761 | − | 7.79819i | 0.303910 | − | 0.952701i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.44157 | + | 13.5355i | 0.534702 | + | 1.62948i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3588 | − | 7.13533i | −1.46672 | − | 0.846808i | −0.467408 | − | 0.884041i | \(-0.654812\pi\) |
−0.999307 | + | 0.0372332i | \(0.988146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.629763 | + | 1.09078i | 0.0737082 | + | 0.127666i | 0.900524 | − | 0.434807i | \(-0.143183\pi\) |
−0.826816 | + | 0.562473i | \(0.809850\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.83662 | − | 13.5390i | 0.327545 | − | 1.56335i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.47783 | − | 5.47203i | 1.08010 | − | 0.623595i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.80258 | + | 2.19542i | 0.427824 | + | 0.247004i | 0.698419 | − | 0.715689i | \(-0.253887\pi\) |
−0.270595 | + | 0.962693i | \(0.587220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.09967 | + | 6.61770i | 0.677742 | + | 0.735300i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.80997 | + | 1.62234i | −0.308434 | + | 0.178075i | −0.646226 | − | 0.763146i | \(-0.723654\pi\) |
0.337791 | + | 0.941221i | \(0.390320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4168 | + | 8.32354i | −1.56372 | + | 0.902815i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.56227 | − | 6.21382i | 0.596338 | − | 0.666192i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.12774i | − | 0.225540i | −0.993621 | − | 0.112770i | \(-0.964028\pi\) | ||
0.993621 | − | 0.112770i | \(-0.0359723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.33174 | 0.873404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.99017 | + | 10.0433i | −0.932238 | + | 1.04144i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2923 | + | 17.8268i | 1.05597 | + | 1.82899i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.97837 | − | 5.18366i | 0.911615 | − | 0.526321i | 0.0306648 | − | 0.999530i | \(-0.490238\pi\) |
0.880951 | + | 0.473208i | \(0.156904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.15731 | + | 5.26405i | −0.719337 | + | 0.529057i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.04180 | − | 12.1968i | 0.700685 | − | 1.21362i | −0.267541 | − | 0.963546i | \(-0.586211\pi\) |
0.968226 | − | 0.250076i | \(-0.0804556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.26301 | + | 5.65170i | −0.321514 | + | 0.556878i | −0.980801 | − | 0.195013i | \(-0.937525\pi\) |
0.659287 | + | 0.751892i | \(0.270858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.3839 | − | 17.1859i | 1.50132 | − | 1.67718i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.23281i | 0.119180i | 0.998223 | + | 0.0595899i | \(0.0189793\pi\) | ||||
−0.998223 | + | 0.0595899i | \(0.981021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.87642i | 0.850207i | 0.905145 | + | 0.425103i | \(0.139762\pi\) | ||||
−0.905145 | + | 0.425103i | \(0.860238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.4686 | − | 4.41961i | 1.27838 | − | 0.419491i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.367153 | + | 0.635928i | −0.0345388 | + | 0.0598230i | −0.882778 | − | 0.469790i | \(-0.844330\pi\) |
0.848239 | + | 0.529613i | \(0.177663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.6683 | + | 14.8196i | −2.39358 | + | 1.38193i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.72264 | + | 0.746190i | −0.621508 | + | 0.0689853i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.0707 | −1.56486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.11459 | + | 1.93053i | 0.101326 | + | 0.175503i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.629446 | + | 0.563446i | 0.0567553 | + | 0.0508042i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7623 | 0.962610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.78672 | + | 10.0229i | −0.513488 | + | 0.889388i | 0.486389 | + | 0.873742i | \(0.338314\pi\) |
−0.999878 | + | 0.0156455i | \(0.995020\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.6842 | − | 3.91463i | −1.64506 | − | 0.344664i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0364i | 1.57585i | 0.615770 | + | 0.787926i | \(0.288845\pi\) | ||||
−0.615770 | + | 0.787926i | \(0.711155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.1084i | 1.83033i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.8737 | + | 15.2446i | −0.935856 | + | 1.31205i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.18254 | −0.186467 | −0.0932334 | − | 0.995644i | \(-0.529720\pi\) | ||||
−0.0932334 | + | 0.995644i | \(0.529720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.48230i | 0.125727i | 0.998022 | + | 0.0628637i | \(0.0200233\pi\) | ||||
−0.998022 | + | 0.0628637i | \(0.979977\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.83885 | + | 10.9914i | −0.828581 | + | 0.925639i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.67725i | − | 0.558380i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0268 | + | 8.67571i | 1.24791 | + | 0.720479i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9535 | − | 3.59430i | 0.903428 | − | 0.296453i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.54319i | 0.208346i | 0.994559 | + | 0.104173i | \(0.0332196\pi\) | ||||
−0.994559 | + | 0.104173i | \(0.966780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.61380 | − | 7.99133i | −0.375466 | − | 0.650326i | 0.614931 | − | 0.788581i | \(-0.289184\pi\) |
−0.990397 | + | 0.138255i | \(0.955851\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.7738 | − | 1.52885i | 1.11355 | − | 0.123600i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.2874 | − | 14.0224i | −1.95081 | − | 1.12630i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.35503 | + | 2.34698i | 0.108143 | + | 0.187309i | 0.915018 | − | 0.403413i | \(-0.132176\pi\) |
−0.806875 | + | 0.590722i | \(0.798843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.76221 | + | 17.9568i | −0.298363 | + | 1.42406i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.3933 | −2.39533 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.61168 | − | 11.4518i | 0.517867 | − | 0.896972i | −0.481918 | − | 0.876217i | \(-0.660060\pi\) |
0.999785 | − | 0.0207554i | \(-0.00660713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.7732 | − | 12.3290i | −1.07224 | − | 0.959813i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.97167 | + | 4.60245i | 0.616867 | + | 0.356148i | 0.775648 | − | 0.631166i | \(-0.217423\pi\) |
−0.158781 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.95829 | + | 6.85597i | −0.304484 | + | 0.527382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.89047 | − | 17.0318i | −0.144568 | − | 1.30245i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5022 | − | 6.64078i | 0.874493 | − | 0.504889i | 0.00565462 | − | 0.999984i | \(-0.498200\pi\) |
0.868839 | + | 0.495095i | \(0.164867\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25.5590 | + | 14.7565i | 1.93208 | + | 1.11549i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3255 | − | 4.04899i | −1.45260 | − | 0.304340i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.1945 | 1.21043 | 0.605217 | − | 0.796060i | \(-0.293086\pi\) | ||||
0.605217 | + | 0.796060i | \(0.293086\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.831318 | + | 1.43989i | −0.0617914 | + | 0.107026i | −0.895266 | − | 0.445532i | \(-0.853015\pi\) |
0.833475 | + | 0.552557i | \(0.186348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.47599 | + | 7.54547i | 0.183030 | + | 0.557777i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7463 | + | 25.5414i | 1.08417 | + | 1.87784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6808i | 1.00044i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.4727 | + | 7.96299i | −1.27095 | + | 0.579222i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.65708 | − | 13.2625i | −0.554047 | − | 0.959638i | −0.997977 | − | 0.0635761i | \(-0.979749\pi\) |
0.443930 | − | 0.896061i | \(-0.353584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.65307 | 0.550880 | 0.275440 | − | 0.961318i | \(-0.411176\pi\) | ||||
0.275440 | + | 0.961318i | \(0.411176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.38773 | − | 13.3714i | −0.314212 | − | 0.957547i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.55409 | − | 2.69175i | 0.110724 | − | 0.191780i | −0.805338 | − | 0.592815i | \(-0.798016\pi\) |
0.916062 | + | 0.401036i | \(0.131350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.134799 | + | 0.233479i | 0.00955567 | + | 0.0165509i | 0.870764 | − | 0.491702i | \(-0.163625\pi\) |
−0.861208 | + | 0.508253i | \(0.830292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.3363 | − | 6.98685i | −0.870134 | − | 0.492815i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.89646 | + | 15.4091i | 0.624409 | + | 1.08151i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.878830 | + | 1.52218i | −0.0613802 | + | 0.106314i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.5235 | − | 2.72202i | 1.70450 | − | 0.189194i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9168 | 1.17016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5489 | − | 23.4673i | −0.932743 | − | 1.61556i | −0.778610 | − | 0.627508i | \(-0.784075\pi\) |
−0.154133 | − | 0.988050i | \(-0.549258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.4857 | + | 18.4168i | −1.12958 | + | 1.26190i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 39.7182i | − | 2.70876i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.3792 | − | 24.9054i | −0.976121 | − | 1.69069i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.07282 | − | 0.680179i | 0.140068 | − | 0.0459623i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.20763 | + | 9.01987i | −0.350303 | + | 0.606742i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.51661 | −0.570314 | −0.285157 | − | 0.958481i | \(-0.592046\pi\) | ||||
−0.285157 | + | 0.958481i | \(0.592046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.9444 | − | 9.61754i | −1.46296 | − | 0.641169i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.5472 | + | 8.39882i | 0.965530 | + | 0.557449i | 0.897871 | − | 0.440259i | \(-0.145114\pi\) |
0.0676595 | + | 0.997708i | \(0.478447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.13981 | + | 2.39012i | −0.273566 | + | 0.157944i | −0.630507 | − | 0.776183i | \(-0.717153\pi\) |
0.356941 | + | 0.934127i | \(0.383820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.91009 | − | 18.0108i | −0.388856 | − | 1.18502i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.05550 | + | 1.82818i | −0.0691480 | + | 0.119768i | −0.898527 | − | 0.438919i | \(-0.855361\pi\) |
0.829378 | + | 0.558687i | \(0.188695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.5802 | − | 15.3461i | −1.73390 | − | 1.00107i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.07237 | − | 5.66654i | 0.329486 | − | 0.368081i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.41223 | + | 11.1063i | −0.414773 | + | 0.718407i | −0.995405 | − | 0.0957589i | \(-0.969472\pi\) |
0.580632 | + | 0.814166i | \(0.302806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.62450 | 0.362306 | 0.181153 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181153 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.3851 | − | 7.98996i | 0.858654 | − | 0.512556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.9926 | + | 20.7718i | 0.766180 | + | 1.32706i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1534 | + | 6.43939i | 0.709671 | + | 0.409729i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.75221 | + | 5.33980i | 0.111042 | + | 0.338396i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2371 | + | 17.7313i | 0.646163 | + | 1.11919i | 0.984032 | + | 0.177994i | \(0.0569607\pi\) |
−0.337869 | + | 0.941193i | \(0.609706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.3579i | 1.53137i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.98989 | + | 27.3963i | 0.562969 | + | 1.71562i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.3494 | − | 9.43933i | −1.01985 | − | 0.588809i | −0.105788 | − | 0.994389i | \(-0.533736\pi\) |
−0.914060 | + | 0.405580i | \(0.867070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.2431i | 1.87921i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.55834 | − | 11.6364i | −0.529748 | − | 0.720276i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.8353i | 1.16144i | 0.814105 | + | 0.580718i | \(0.197228\pi\) | ||||
−0.814105 | + | 0.580718i | \(0.802772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.1717 | −2.34487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.60704 | − | 0.755727i | −0.220747 | − | 0.0462498i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 22.2511i | − | 1.35667i | −0.734752 | − | 0.678336i | \(-0.762701\pi\) | ||
0.734752 | − | 0.678336i | \(-0.237299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8294i | 0.657838i | 0.944358 | + | 0.328919i | \(0.106684\pi\) | ||||
−0.944358 | + | 0.328919i | \(0.893316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.95925 | − | 14.1243i | 0.179102 | − | 0.854843i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8262 | − | 20.4836i | 0.713147 | − | 1.23521i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.46809 | −0.328546 | −0.164273 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164273 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.8327 | + | 18.8077i | 0.828139 | + | 1.12599i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.71219 | + | 13.3579i | 0.460071 | + | 0.796866i | 0.998964 | − | 0.0455083i | \(-0.0144907\pi\) |
−0.538893 | + | 0.842374i | \(0.681157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7372 | −0.876038 | −0.438019 | − | 0.898966i | \(-0.644320\pi\) | ||||
−0.438019 | + | 0.898966i | \(0.644320\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.8764 | − | 11.1163i | 2.00666 | − | 0.658471i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.56091 | + | 0.901192i | −0.0921376 | + | 0.0531957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.16976 | − | 3.75813i | 0.127633 | − | 0.221067i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.59865 | − | 17.0616i | −0.328199 | − | 1.00017i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.13657i | 0.416923i | 0.978031 | + | 0.208461i | \(0.0668456\pi\) | ||||
−0.978031 | + | 0.208461i | \(0.933154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 41.0814i | − | 2.39185i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.38173 | + | 14.0031i | 0.370305 | + | 0.812540i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.27188 | + | 16.0594i | −0.536206 | + | 0.928737i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3644 | − | 35.2722i | 1.17378 | − | 2.03306i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.1754 | − | 16.2696i | −1.04415 | − | 0.934663i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.3090 | + | 8.26130i | −0.819330 | + | 0.473040i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0773160 | + | 0.133915i | 0.00441266 | + | 0.00764295i | 0.868223 | − | 0.496174i | \(-0.165262\pi\) |
−0.863811 | + | 0.503817i | \(0.831929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.42205 | + | 7.53895i | 0.479113 | + | 0.428876i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4333 | 1.27208 | 0.636039 | − | 0.771657i | \(-0.280572\pi\) | ||||
0.636039 | + | 0.771657i | \(0.280572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.54773i | 0.370100i | 0.982729 | + | 0.185050i | \(0.0592447\pi\) | ||||
−0.982729 | + | 0.185050i | \(0.940755\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.6703 | − | 32.1835i | −1.33367 | − | 1.81334i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9285 | + | 8.04165i | −0.782305 | + | 0.451664i | −0.837247 | − | 0.546826i | \(-0.815836\pi\) |
0.0549415 | + | 0.998490i | \(0.482503\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.3492 | − | 7.12983i | 0.691424 | − | 0.399194i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.08991 | + | 0.437866i | 0.116647 | + | 0.0244393i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8518 | − | 13.1935i | −1.27151 | − | 0.734105i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.5942 | − | 9.00333i | 0.865012 | − | 0.499415i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.0477 | + | 3.15271i | 0.832139 | + | 0.174345i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.7366 | − | 27.2565i | −0.867585 | − | 1.50270i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7622 | + | 12.5644i | 1.19616 | + | 0.690602i | 0.959696 | − | 0.281039i | \(-0.0906790\pi\) |
0.236461 | + | 0.971641i | \(0.424012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.70857 | − | 24.4023i | −0.148429 | − | 1.33724i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.96454 | − | 28.1022i | 0.489785 | − | 1.53538i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.8300 | − | 11.4488i | 1.08021 | − | 0.623659i | 0.149256 | − | 0.988799i | \(-0.452312\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.947647 | + | 0.848281i | 0.0514691 | + | 0.0460723i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.9598 | + | 11.5238i | −1.08088 | + | 0.624048i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.27207i | − | 0.0686853i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0060 | + | 48.7775i | 0.861732 | + | 2.62609i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.4805 | + | 21.6168i | −0.669986 | + | 1.16045i | 0.307922 | + | 0.951412i | \(0.400367\pi\) |
−0.977908 | + | 0.209038i | \(0.932967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2064 | 1.08162 | 0.540812 | − | 0.841144i | \(-0.318117\pi\) | ||||
0.540812 | + | 0.841144i | \(0.318117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.12276 | + | 11.6615i | −0.0599287 | + | 0.622447i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5145 | + | 30.3359i | 0.932200 | + | 1.61462i | 0.779552 | + | 0.626338i | \(0.215447\pi\) |
0.152648 | + | 0.988281i | \(0.451220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.5370 | − | 25.7134i | −2.36378 | − | 1.36473i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.06313 | + | 28.9389i | −0.320895 | + | 1.53161i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.5980i | − | 0.717674i | −0.933400 | − | 0.358837i | \(-0.883173\pi\) | ||
0.933400 | − | 0.358837i | \(-0.116827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.81416 | + | 11.8025i | −0.358640 | + | 0.621183i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.66859 | − | 1.20382i | 0.192551 | − | 0.0631842i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.26946 | + | 3.93082i | 0.118789 | + | 0.205749i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.52728 | + | 2.61383i | 0.236322 | + | 0.136441i | 0.613485 | − | 0.789706i | \(-0.289767\pi\) |
−0.377163 | + | 0.926147i | \(0.623100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.17874 | − | 0.866941i | 0.0613629 | − | 0.0451311i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.8989 | − | 19.5715i | −1.75994 | − | 1.01610i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.06973 | − | 0.617607i | −0.0553884 | − | 0.0319785i | 0.472050 | − | 0.881572i | \(-0.343514\pi\) |
−0.527438 | + | 0.849593i | \(0.676847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.82254 | − | 18.2447i | 0.197395 | − | 0.942153i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8559 | 0.559109 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.461731 | + | 0.266580i | −0.0237175 | + | 0.0136933i | −0.511812 | − | 0.859098i | \(-0.671026\pi\) |
0.488094 | + | 0.872791i | \(0.337692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.9359 | + | 13.3698i | 0.765190 | + | 0.684956i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.76314 | − | 3.05384i | −0.0900920 | − | 0.156044i | 0.817458 | − | 0.575989i | \(-0.195383\pi\) |
−0.907550 | + | 0.419945i | \(0.862049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.1550 | − | 19.7194i | 1.74070 | − | 1.00499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2725 | + | 30.2840i | −0.674678 | + | 1.53942i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.31060 | + | 3.64343i | −0.319960 | + | 0.184729i | −0.651375 | − | 0.758756i | \(-0.725807\pi\) |
0.331415 | + | 0.943485i | \(0.392474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9969 | − | 32.9036i | 0.960714 | − | 1.66400i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.5761 | + | 6.40615i | 1.54236 | + | 0.323148i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7033 | + | 7.91159i | 0.689487 | + | 0.398075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.1142 | 0.708371 | 0.354185 | − | 0.935175i | \(-0.384758\pi\) | ||||
0.354185 | + | 0.935175i | \(0.384758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 35.7839 | + | 7.49725i | 1.79143 | + | 0.375332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.05940 | 0.102842 | 0.0514208 | − | 0.998677i | \(-0.483625\pi\) | ||||
0.0514208 | + | 0.998677i | \(0.483625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5462 | −0.874038 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.9812 | + | 23.8481i | 1.09226 | + | 1.18502i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2375 | 1.20141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.0958 | − | 12.7570i | −1.09257 | − | 0.630794i | −0.158309 | − | 0.987390i | \(-0.550604\pi\) |
−0.934259 | + | 0.356595i | \(0.883938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.775190 | + | 3.69993i | −0.0382373 | + | 0.182504i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.0634 | − | 36.4828i | 1.03646 | − | 1.79520i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.1262 | + | 5.84638i | −0.497077 | + | 0.286987i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.51287 | + | 0.526482i | 0.123056 | + | 0.0257820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2976 | − | 7.67735i | 0.649628 | − | 0.375063i | −0.138686 | − | 0.990336i | \(-0.544288\pi\) |
0.788314 | + | 0.615273i | \(0.210954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1923 | + | 26.3139i | 0.740428 | + | 1.28246i | 0.952300 | + | 0.305162i | \(0.0987106\pi\) |
−0.211872 | + | 0.977297i | \(0.567956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.1385 | + | 20.5831i | 0.736057 | + | 1.00079i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.9505 | + | 18.4467i | −1.54983 | + | 0.894794i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9430 | −0.819930 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.3196 | − | 2.37161i | −0.546514 | − | 0.114503i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8202 | + | 11.4432i | 0.954707 | + | 0.551201i | 0.894540 | − | 0.446988i | \(-0.147503\pi\) |
0.0601674 | + | 0.998188i | \(0.480837\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.6525 | + | 13.0784i | 1.08861 | + | 0.628508i | 0.933206 | − | 0.359343i | \(-0.116999\pi\) |
0.155403 | + | 0.987851i | \(0.450332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.0446 | − | 22.3926i | 0.961066 | − | 1.07364i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.6863 | − | 23.4902i | −1.94629 | − | 1.12369i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.95944 | − | 13.7861i | −0.379883 | − | 0.657977i | 0.611162 | − | 0.791506i | \(-0.290702\pi\) |
−0.991045 | + | 0.133529i | \(0.957369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.20277 | − | 19.8454i | −0.104894 | − | 0.945020i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.66008 | − | 13.2677i | 0.363942 | − | 0.630365i | −0.624664 | − | 0.780894i | \(-0.714764\pi\) |
0.988606 | + | 0.150528i | \(0.0480974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7.66769i | − | 0.363483i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.31132 | + | 0.903285i | 0.203918 | + | 0.0427239i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.40241 | + | 3.69643i | 0.302149 | + | 0.174446i | 0.643408 | − | 0.765524i | \(-0.277520\pi\) |
−0.341259 | + | 0.939969i | \(0.610853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.722236 | + | 1.25095i | 0.0340088 | + | 0.0589049i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.1860 | + | 4.98316i | −0.713499 | + | 0.234129i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.0249 | 1.40759 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.60191 | + | 4.50665i | −0.121712 | + | 0.210812i | −0.920443 | − | 0.390877i | \(-0.872172\pi\) |
0.798731 | + | 0.601689i | \(0.205505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.30040 | − | 23.8930i | 0.107373 | − | 1.11523i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.6857i | − | 1.56890i | −0.620192 | − | 0.784450i | \(-0.712945\pi\) | ||
0.620192 | − | 0.784450i | \(-0.287055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4453 | + | 7.76263i | −0.624854 | + | 0.360760i | −0.778757 | − | 0.627326i | \(-0.784149\pi\) |
0.153902 | + | 0.988086i | \(0.450816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32.3977 | + | 36.1927i | −1.50241 | + | 1.67839i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3144 | + | 6.53235i | −0.523567 | + | 0.302281i | −0.738393 | − | 0.674371i | \(-0.764415\pi\) |
0.214826 | + | 0.976652i | \(0.431082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.3697 | − | 20.3601i | 1.03294 | − | 0.940143i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.45997 | − | 1.46350i | 0.205505 | − | 0.0674347i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.2680 | − | 16.3205i | −1.29976 | − | 0.750418i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.8099 | + | 39.5078i | 1.04659 | + | 1.81274i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.1048 | + | 12.7557i | 1.33262 | + | 0.584044i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.387072 | − | 0.223476i | 0.0176858 | − | 0.0102109i | −0.491131 | − | 0.871086i | \(-0.663416\pi\) |
0.508817 | + | 0.860875i | \(0.330083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9800 | + | 9.22604i | 0.728624 | + | 0.420671i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.7950 | + | 51.5240i | −0.491192 | + | 2.34443i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.3551 | − | 18.6802i | 1.46917 | − | 0.848226i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0165 | + | 6.36037i | −0.499204 | + | 0.288216i | −0.728385 | − | 0.685168i | \(-0.759729\pi\) |
0.229181 | + | 0.973384i | \(0.426395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.0652 | − | 15.2758i | −0.771715 | − | 0.690797i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 44.0337i | − | 1.98721i | −0.112892 | − | 0.993607i | \(-0.536011\pi\) | ||
0.112892 | − | 0.993607i | \(-0.463989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2424 | −1.00175 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.7926 | + | 18.9699i | −1.15929 | + | 0.852635i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.3677 | − | 45.6702i | −1.18275 | − | 2.04859i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.43529 | − | 1.98336i | 0.153785 | − | 0.0887876i | −0.421133 | − | 0.906999i | \(-0.638367\pi\) |
0.574918 | + | 0.818211i | \(0.305034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.6336 | − | 11.8792i | 0.475076 | − | 0.530725i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.23418 | + | 14.2620i | −0.367144 | + | 0.635912i | −0.989118 | − | 0.147126i | \(-0.952998\pi\) |
0.621974 | + | 0.783038i | \(0.286331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.3764 | − | 43.9531i | 1.12923 | − | 1.95589i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.2166 | + | 9.14536i | 0.453736 | + | 0.406160i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.04756i | 0.401026i | 0.979691 | + | 0.200513i | \(0.0642609\pi\) | ||||
−0.979691 | + | 0.200513i | \(0.935739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.65442i | 0.205899i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.5444 | − | 2.84451i | −1.30442 | − | 0.125588i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7588 | + | 20.3669i | −0.518156 | + | 0.897472i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8440 | + | 12.6116i | −0.960698 | + | 0.554660i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.17241 | − | 21.8576i | −0.314834 | − | 0.959443i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.9377 | 0.829678 | 0.414839 | − | 0.909895i | \(-0.363838\pi\) | ||||
0.414839 | + | 0.909895i | \(0.363838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.4271 | − | 19.7922i | −0.499670 | − | 0.865454i | 0.500330 | − | 0.865835i | \(-0.333212\pi\) |
−1.00000 | 0.000380701i | \(0.999879\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 34.0939 | − | 38.0875i | 1.48798 | − | 1.66228i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.9499 | 1.56600 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3228 | − | 38.6643i | 0.970558 | − | 1.68106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.7280 | + | 31.3234i | −0.595746 | + | 1.35932i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.09968i | 0.0476325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.44263i | 0.192072i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.75194 | − | 27.4536i | 0.248214 | − | 1.18471i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.7114 | 0.849031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 42.8342i | − | 1.84159i | −0.390051 | − | 0.920793i | \(-0.627543\pi\) | ||
0.390051 | − | 0.920793i | \(-0.372457\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.14569 | + | 1.92070i | 0.0920803 | + | 0.0824252i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.9877i | 1.37020i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.8728 | + | 16.0924i | 1.19175 | + | 0.688060i | 0.958704 | − | 0.284405i | \(-0.0917959\pi\) |
0.233051 | + | 0.972465i | \(0.425129\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.6708 | − | 1.51741i | 0.583457 | − | 0.0647617i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.5034i | 1.17169i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.11290 | + | 14.0520i | 0.344996 | + | 0.597550i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 48.5364 | − | 15.9268i | 2.06026 | − | 0.676057i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7497 | + | 7.93838i | 0.582593 | + | 0.336360i | 0.762163 | − | 0.647385i | \(-0.224137\pi\) |
−0.179570 | + | 0.983745i | \(0.557471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4249 | − | 21.5205i | −0.525515 | − | 0.910219i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.1923 | + | 4.85913i | 0.979181 | + | 0.205153i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.9295 | −0.924217 | −0.462108 | − | 0.886823i | \(-0.652907\pi\) | ||||
−0.462108 | + | 0.886823i | \(0.652907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.32310 | + | 2.29168i | −0.0556633 | + | 0.0964116i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.29326 | + | 32.4488i | 0.306288 | + | 1.36272i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0417 | + | 5.79755i | 0.420968 | + | 0.243046i | 0.695491 | − | 0.718534i | \(-0.255187\pi\) |
−0.274523 | + | 0.961580i | \(0.588520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0411 | − | 31.2481i | 0.754998 | − | 1.30769i | −0.190378 | − | 0.981711i | \(-0.560971\pi\) |
0.945376 | − | 0.325983i | \(-0.105695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.2027 | + | 8.27008i | −1.05286 | + | 0.345487i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −56.8861 | + | 32.8432i | −2.37231 | + | 1.36966i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.7861 | − | 18.3517i | −1.32327 | − | 0.763993i | −0.339025 | − | 0.940778i | \(-0.610097\pi\) |
−0.984250 | + | 0.176785i | \(0.943430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.71821 | − | 12.9738i | 0.112965 | − | 0.539173i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.9903 | −0.497440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.6851 | + | 27.1673i | −0.649609 | + | 1.12516i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.2262 | + | 2.68903i | −1.00163 | + | 0.111178i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.02789 | − | 5.24447i | −0.124975 | − | 0.216462i | 0.796748 | − | 0.604311i | \(-0.206552\pi\) |
−0.921723 | + | 0.387849i | \(0.873218\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 44.4532i | − | 1.83166i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.01120 | − | 3.59061i | −0.164999 | − | 0.147698i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.587963 | + | 1.01838i | 0.0241447 | + | 0.0418199i | 0.877845 | − | 0.478944i | \(-0.158980\pi\) |
−0.853701 | + | 0.520764i | \(0.825647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −61.5171 | −2.52196 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.443682 | − | 0.145591i | 0.0181587 | − | 0.00595864i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.14540 | + | 10.6441i | −0.251094 | + | 0.434908i | −0.963827 | − | 0.266527i | \(-0.914124\pi\) |
0.712733 | + | 0.701435i | \(0.247457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.36040 | − | 7.55243i | −0.177864 | − | 0.308070i | 0.763284 | − | 0.646063i | \(-0.223586\pi\) |
−0.941149 | + | 0.337992i | \(0.890252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.2260 | + | 18.4314i | −0.660773 | + | 0.750585i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.01663 | + | 6.95700i | 0.163299 | + | 0.282842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.97906 | + | 3.42782i | −0.0803274 | + | 0.139131i | −0.903391 | − | 0.428819i | \(-0.858930\pi\) |
0.823063 | + | 0.567950i | \(0.192263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.2820 | − | 9.60868i | 1.18657 | − | 0.389363i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.2026 | −0.776853 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.85267 | + | 6.67301i | 0.155608 | + | 0.269520i | 0.933280 | − | 0.359149i | \(-0.116933\pi\) |
−0.777672 | + | 0.628670i | \(0.783600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.26832 | + | 2.03048i | 0.0914675 | + | 0.0818767i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.9608i | − | 1.16592i | −0.812502 | − | 0.582958i | \(-0.801895\pi\) | ||
0.812502 | − | 0.582958i | \(-0.198105\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.14678 | − | 10.6465i | −0.247060 | − | 0.427920i | 0.715649 | − | 0.698460i | \(-0.246131\pi\) |
−0.962709 | + | 0.270540i | \(0.912798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.09573 | − | 42.5401i | 0.164356 | − | 1.70707i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.93140 | − | 6.80938i | 0.157508 | − | 0.272812i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14854 | −0.0459418 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.00847 | − | 28.6780i | 0.239955 | − | 1.14529i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.7409 | − | 18.9030i | −1.30547 | − | 0.753711i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.05504 | + | 1.18648i | −0.0818097 | + | 0.0472328i | −0.540347 | − | 0.841442i | \(-0.681707\pi\) |
0.458537 | + | 0.888675i | \(0.348374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.5951 | + | 14.6335i | −1.77250 | + | 0.581631i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.8535 | + | 36.1192i | −0.827544 | + | 1.43335i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.9959 | + | 7.50319i | 0.514916 | + | 0.297287i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.3656 | + | 34.4885i | 1.00345 | + | 1.36434i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2442 | − | 24.6717i | 0.562613 | − | 0.974473i | −0.434655 | − | 0.900597i | \(-0.643130\pi\) |
0.997267 | − | 0.0738763i | \(-0.0235370\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.32535 | −0.0917029 | −0.0458514 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458514 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −67.3320 | − | 14.1070i | −2.65119 | − | 0.555464i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9762 | + | 34.5999i | 0.785347 | + | 1.36026i | 0.928791 | + | 0.370603i | \(0.120849\pi\) |
−0.143444 | + | 0.989658i | \(0.545818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.2382 | − | 16.8807i | −1.14770 | − | 0.662624i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −47.3279 | + | 15.5303i | −1.85493 | + | 0.608680i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.75318 | + | 8.23275i | 0.186006 | + | 0.322172i | 0.943915 | − | 0.330188i | \(-0.107112\pi\) |
−0.757909 | + | 0.652360i | \(0.773779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.9975i | 2.53966i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.416849 | − | 3.75551i | −0.0162628 | − | 0.146517i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.1336 | − | 23.1711i | −1.56338 | − | 0.902620i | −0.996911 | − | 0.0785391i | \(-0.974974\pi\) |
−0.566472 | − | 0.824081i | \(-0.691692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0198i | 1.12874i | 0.825523 | + | 0.564369i | \(0.190881\pi\) | ||||
−0.825523 | + | 0.564369i | \(0.809119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.4412 | + | 12.0319i | 0.522015 | + | 0.467279i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 76.0678i | 2.94978i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.6013 | −1.53337 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.02492 | + | 14.4377i | −0.116950 | + | 0.558195i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5785i | 0.524193i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6836i | 0.720199i | 0.932914 | + | 0.360100i | \(0.117257\pi\) | ||||
−0.932914 | + | 0.360100i | \(0.882743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.0982 | + | 33.7852i | −0.927542 | + | 1.30039i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.74938 | + | 16.8864i | −0.374699 | + | 0.648998i | −0.990282 | − | 0.139074i | \(-0.955587\pi\) |
0.615583 | + | 0.788072i | \(0.288921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.3111 | 1.47025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4049 | − | 21.6779i | 0.743596 | − | 0.830700i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.63754 | + | 13.2286i | 0.292242 | + | 0.506179i | 0.974340 | − | 0.225083i | \(-0.0722652\pi\) |
−0.682097 | + | 0.731262i | \(0.738932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.86516 | −0.300512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.58146 | + | 7.86690i | 0.0984890 | + | 0.300141i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.6826 | + | 11.9411i | −0.787943 | + | 0.454919i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1115 | − | 20.9777i | 0.460743 | − | 0.798030i | −0.538255 | − | 0.842782i | \(-0.680916\pi\) |
0.998998 | + | 0.0447519i | \(0.0142497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.6318 | + | 3.62201i | −1.23958 | + | 0.137589i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.34174i | 0.202624i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.25311i | − | 0.0853424i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.72431 | + | 2.43866i | 0.103043 | + | 0.0922384i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.11912 | − | 7.13453i | 0.155577 | − | 0.269467i | −0.777692 | − | 0.628646i | \(-0.783610\pi\) |
0.933269 | + | 0.359178i | \(0.116943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.3741 | + | 40.4852i | −0.881572 | + | 1.52693i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35.4560 | + | 39.6093i | −1.33535 | + | 1.49177i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.0715 | − | 26.0221i | 1.69509 | − | 0.978660i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5151 | + | 23.4089i | 0.507571 | + | 0.879139i | 0.999962 | + | 0.00876447i | \(0.00278985\pi\) |
−0.492391 | + | 0.870374i | \(0.663877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.80456 | − | 10.6115i | −0.292694 | − | 0.397963i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 64.0067 | 2.39707 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.0626i | − | 0.899892i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.5504 | + | 14.8150i | 0.618086 | + | 0.553277i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.1549 | − | 21.4514i | 1.38564 | − | 0.800002i | 0.392823 | − | 0.919614i | \(-0.371498\pi\) |
0.992821 | + | 0.119612i | \(0.0381650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.8851 | + | 12.0580i | −0.777802 | + | 0.449064i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.99770 | − | 9.53490i | 0.0742953 | − | 0.354607i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.3024 | + | 19.2271i | 1.23682 | + | 0.714078i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.5056 | − | 12.4163i | 0.797599 | − | 0.460494i | −0.0450320 | − | 0.998986i | \(-0.514339\pi\) |
0.842631 | + | 0.538492i | \(0.181006\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.79084 | − | 25.5288i | −0.325587 | − | 0.945512i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4569 | + | 44.0927i | 0.941559 | + | 1.63083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.1568 | − | 23.7619i | −1.52016 | − | 0.877665i | −0.999718 | − | 0.0237679i | \(-0.992434\pi\) |
−0.520442 | − | 0.853897i | \(-0.674233\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 39.4728 | − | 12.9527i | 1.45598 | − | 0.477767i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.3171 | − | 17.9276i | −0.601047 | − | 0.660371i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.28091 | + | 3.62629i | −0.231047 | + | 0.133395i | −0.611055 | − | 0.791588i | \(-0.709255\pi\) |
0.380008 | + | 0.924983i | \(0.375921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.8778 | − | 16.6205i | 0.546548 | − | 0.610570i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.7112 | − | 11.9576i | 0.759819 | − | 0.438681i | −0.0694121 | − | 0.997588i | \(-0.522112\pi\) |
0.829231 | + | 0.558907i | \(0.188779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.16482i | 0.335773i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.67461 | − | 1.07385i | 0.353975 | − | 0.0392900i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.27784 | + | 3.94533i | −0.0832304 | + | 0.144159i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.7088 | 0.974618 | 0.487309 | − | 0.873230i | \(-0.337979\pi\) | ||||
0.487309 | + | 0.873230i | \(0.337979\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.6948 | − | 11.0567i | 1.22791 | − | 0.402928i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6266 | − | 28.7982i | −0.605105 | − | 1.04807i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1680 | − | 22.0363i | −1.38724 | − | 0.800924i | −0.394237 | − | 0.919009i | \(-0.628991\pi\) |
−0.993003 | + | 0.118085i | \(0.962324\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41.2926 | + | 8.65140i | 1.49883 | + | 0.314026i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.93893i | − | 0.142786i | −0.997448 | − | 0.0713931i | \(-0.977256\pi\) | ||
0.997448 | − | 0.0713931i | \(-0.0227445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4008 | + | 28.4071i | −0.593750 | + | 1.02841i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 49.6364 | − | 5.50947i | 1.79461 | − | 0.199195i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.8513 | − | 22.2591i | −0.464034 | − | 0.803730i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6091 | − | 7.85722i | −0.490757 | − | 0.283339i | 0.234131 | − | 0.972205i | \(-0.424775\pi\) |
−0.724888 | + | 0.688866i | \(0.758109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.8089 | + | 24.3636i | −0.785429 | + | 0.877432i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.69280 | − | 3.28674i | −0.204756 | − | 0.118216i | 0.394116 | − | 0.919061i | \(-0.371051\pi\) |
−0.598872 | + | 0.800845i | \(0.704384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −53.8259 | − | 31.0764i | −1.93348 | − | 1.11630i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.2694 | + | 10.7417i | 1.83928 | + | 0.385356i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.78603 | −0.0998200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.6012 | + | 21.1317i | −1.30969 | + | 0.756151i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.7663 | + | 10.3755i | −0.813601 | + | 0.370789i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.88308 | + | 8.45774i | 0.174285 | + | 0.301870i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.0667 | + | 9.27613i | −0.572717 | + | 0.330658i | −0.758234 | − | 0.651983i | \(-0.773937\pi\) |
0.185517 | + | 0.982641i | \(0.440604\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.9304 | + | 6.68990i | 1.13675 | + | 0.238167i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.34999 | + | 1.35677i | −0.0835560 | + | 0.0482411i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.16869 | + | 8.95243i | −0.183545 | + | 0.317910i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5578 | + | 64.7104i | −0.480845 | + | 2.29504i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.71007 | + | 5.60611i | 0.343948 | + | 0.198579i | 0.662017 | − | 0.749489i | \(-0.269701\pi\) |
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.3436 | 1.39188 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56228 | + | 5.84639i | −0.0905338 | + | 0.206572i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.73016 | 0.131634 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −109.528 | −3.86034 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.7210 | − | 7.90310i | −1.32784 | − | 0.278202i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.69575 | 0.200252 | 0.100126 | − | 0.994975i | \(-0.468075\pi\) | ||||
0.100126 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.58570 | − | 2.07020i | −0.125911 | − | 0.0726947i | 0.435722 | − | 0.900081i | \(-0.356493\pi\) |
−0.561633 | + | 0.827387i | \(0.689827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.3584 | + | 3.84636i | 0.643858 | + | 0.134898i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.8264 | − | 41.2685i | 0.834601 | − | 1.44557i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.5220 | − | 31.4783i | 1.90748 | − | 1.10129i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.8931 | − | 10.0333i | −0.799949 | − | 0.350592i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.9010 | + | 12.0672i | −0.729450 | + | 0.421148i | −0.818221 | − | 0.574904i | \(-0.805039\pi\) |
0.0887707 | + | 0.996052i | \(0.471706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4375 | + | 35.3987i | 0.712406 | + | 1.23392i | 0.963952 | + | 0.266077i | \(0.0857277\pi\) |
−0.251546 | + | 0.967845i | \(0.580939\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.5242 | − | 27.3236i | −1.06272 | − | 0.951286i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.1522 | − | 21.4499i | 1.29191 | − | 0.745884i | 0.312917 | − | 0.949780i | \(-0.398694\pi\) |
0.978993 | + | 0.203896i | \(0.0653604\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5255 | 0.643419 | 0.321709 | − | 0.946838i | \(-0.395743\pi\) | ||||
0.321709 | + | 0.946838i | \(0.395743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.94215 | + | 9.26974i | −0.0673723 | + | 0.321564i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.6269 | − | 15.3731i | −0.922568 | − | 0.532645i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.7273 | + | 16.5857i | 0.994150 | + | 0.573973i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.7966 | − | 16.7696i | 1.27188 | − | 0.579643i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.7508 | + | 16.5993i | 0.992586 | + | 0.573070i | 0.906046 | − | 0.423178i | \(-0.139086\pi\) |
0.0865399 | + | 0.996248i | \(0.472419\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.90826 | − | 5.03725i | −0.100285 | − | 0.173698i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.3841 | − | 8.32960i | 0.874275 | − | 0.286887i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.2644 | + | 24.7067i | −0.490711 | + | 0.849936i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.23766i | 0.283049i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.23435 | + | 24.9832i | −0.179642 | + | 0.857422i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.2933 | − | 33.6556i | −1.99827 | − | 1.15370i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.2252 | + | 28.1029i | 0.555541 | + | 0.962225i | 0.997861 | + | 0.0653678i | \(0.0208221\pi\) |
−0.442320 | + | 0.896857i | \(0.645845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.81263 | − | 61.3770i | −0.232987 | − | 2.09905i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.9928 | 1.63940 | 0.819701 | − | 0.572791i | \(-0.194139\pi\) | ||||
0.819701 | + | 0.572791i | \(0.194139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.44272 | + | 5.96297i | −0.117464 | + | 0.203454i | −0.918762 | − | 0.394812i | \(-0.870810\pi\) |
0.801298 | + | 0.598265i | \(0.204143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.973337 | + | 2.96621i | 0.0331713 | + | 0.101088i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.688741i | − | 0.0234450i | −0.999931 | − | 0.0117225i | \(-0.996269\pi\) | ||
0.999931 | − | 0.0117225i | \(-0.00373148\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.4501 | − | 23.9312i | 1.40934 | − | 0.813686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.60029 | − | 5.01307i | −0.190196 | − | 0.170253i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.2616 | − | 6.50187i | 0.382023 | − | 0.220561i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.93381 | − | 18.0309i | −0.133292 | − | 0.610954i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.9121 | + | 3.43114i | −1.04622 | + | 0.116127i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.4424 | + | 19.8854i | 1.16437 | + | 0.672248i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02107 | + | 3.50059i | 0.0682466 | + | 0.118207i | 0.898130 | − | 0.439731i | \(-0.144926\pi\) |
−0.829883 | + | 0.557938i | \(0.811593\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0982 | + | 2.53475i | 0.408063 | + | 0.0854951i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1225 | − | 14.5045i | 0.846399 | − | 0.488668i | −0.0130355 | − | 0.999915i | \(-0.504149\pi\) |
0.859434 | + | 0.511247i | \(0.170816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3892 | − | 10.6170i | −0.618847 | − | 0.357292i | 0.157573 | − | 0.987507i | \(-0.449633\pi\) |
−0.776420 | + | 0.630216i | \(0.782966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −69.6430 | − | 14.5912i | −2.34102 | − | 0.490479i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.7696 | + | 17.1875i | −0.999566 | + | 0.577099i | −0.908120 | − | 0.418711i | \(-0.862482\pi\) |
−0.0914458 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.0383 | + | 21.3841i | −1.24222 | + | 0.717199i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.0052 | − | 5.84499i | 0.871208 | − | 0.195815i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 48.6496i | − | 1.62800i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.3598 | 1.95075 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.9313 | + | 21.4220i | 0.799044 | + | 0.715260i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.7355 | − | 32.4508i | −0.624863 | − | 1.08229i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.3759 | − | 24.4658i | 1.41175 | − | 0.815073i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −52.5619 | − | 47.0505i | −1.74915 | − | 1.56574i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.99580 | + | 5.18888i | −0.0995838 | + | 0.172484i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.4099 | − | 19.7625i | 0.378858 | − | 0.656202i | −0.612038 | − | 0.790828i | \(-0.709650\pi\) |
0.990896 | + | 0.134627i | \(0.0429835\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.0364 | + | 25.0331i | −1.12892 | + | 0.830294i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8372i | 1.12108i | 0.828129 | + | 0.560538i | \(0.189406\pi\) | ||||
−0.828129 | + | 0.560538i | \(0.810594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.60929i | 0.318021i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.92266 | + | 27.1914i | 0.294974 | + | 0.898921i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.3257 | + | 57.7218i | −1.10051 | + | 1.90614i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.39111 | − | 0.803156i | 0.0458884 | − | 0.0264937i | −0.476880 | − | 0.878968i | \(-0.658232\pi\) |
0.522769 | + | 0.852475i | \(0.324899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.254480 | − | 0.0835056i | 0.00838540 | − | 0.00275160i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.1752 | −1.05906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.6808 | + | 56.6049i | 1.07454 | + | 1.86116i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.7717 | − | 11.5997i | 0.518010 | − | 0.380986i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5542 | −1.10088 | −0.550439 | − | 0.834875i | \(-0.685540\pi\) | ||||
−0.550439 | + | 0.834875i | \(0.685540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0093 | + | 32.9250i | −0.623004 | + | 1.07907i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.96783 | − | 38.0299i | 0.260855 | − | 1.24504i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 49.3013i | 1.61232i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.6902i | − | 1.00261i | −0.865272 | − | 0.501303i | \(-0.832854\pi\) | ||
0.865272 | − | 0.501303i | \(-0.167146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1000 | + | 2.32561i | 0.362235 | + | 0.0758935i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0344 | −0.881296 | −0.440648 | − | 0.897680i | \(-0.645251\pi\) | ||||
−0.440648 | + | 0.897680i | \(0.645251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.01152i | − | 0.130633i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −62.9661 | + | 28.6960i | −2.04829 | + | 0.933482i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.3183i | 0.627760i | 0.949463 | + | 0.313880i | \(0.101629\pi\) | ||||
−0.949463 | + | 0.313880i | \(0.898371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.45932 | + | 1.41989i | 0.0798330 | + | 0.0460916i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.68543 | + | 26.4685i | 0.281644 | + | 0.858299i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.5725i | − | 0.795983i | −0.917389 | − | 0.397991i | \(-0.869707\pi\) | ||
0.917389 | − | 0.397991i | \(-0.130293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.5936 | − | 47.7936i | −0.892909 | − | 1.54656i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.70062 | − | 23.4673i | −0.248926 | − | 0.758591i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.98474 | − | 4.03264i | −0.225549 | − | 0.130221i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7817 | + | 25.6027i | 0.476830 | + | 0.825894i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.48458 | − | 3.38738i | 0.0478399 | − | 0.109157i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.5792 | 0.887806 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5787 | + | 39.1075i | −0.726083 | + | 1.25761i | 0.232444 | + | 0.972610i | \(0.425328\pi\) |
−0.958527 | + | 0.285003i | \(0.908006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.4826 | + | 34.0533i | −0.979243 | + | 1.09395i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.2612 | + | 18.0487i | 1.00322 | + | 0.579209i | 0.909199 | − | 0.416361i | \(-0.136695\pi\) |
0.0940204 | + | 0.995570i | \(0.470028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.73883 | + | 4.74380i | −0.0878029 | + | 0.152079i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.72410 | − | 29.6338i | −0.311420 | − | 0.949040i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.5345 | + | 9.54621i | −0.528986 | + | 0.305410i | −0.740604 | − | 0.671942i | \(-0.765460\pi\) |
0.211617 | + | 0.977353i | \(0.432127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.45719 | − | 3.15071i | −0.174413 | − | 0.100697i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6892 | − | 24.3897i | 0.341281 | − | 0.778703i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.2412 | −1.18781 | −0.593906 | − | 0.804535i | \(-0.702415\pi\) | ||||
−0.593906 | + | 0.804535i | \(0.702415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.60042 | − | 9.70021i | 0.178444 | − | 0.309074i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −51.7957 | + | 16.9964i | −1.64868 | + | 0.541000i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.3246 | + | 78.5045i | 1.44124 | + | 2.49630i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4788i | 0.809360i | 0.914458 | + | 0.404680i | \(0.132617\pi\) | ||||
−0.914458 | + | 0.404680i | \(0.867383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.0292 | − | 32.4296i | 0.921213 | − | 1.02912i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.485773 | + | 0.841384i | 0.0154000 | + | 0.0266737i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.6275 | −1.22335 | −0.611673 | − | 0.791111i | \(-0.709503\pi\) | ||||
−0.611673 | + | 0.791111i | \(0.709503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −42.3298 | − | 4.07548i | −1.33926 | − | 0.128942i |
(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 | 804.2.o.d.365.10 | yes | 36 | |
3.2 | odd | 2 | inner | 804.2.o.d.365.9 | ✓ | 36 | |
67.38 | odd | 6 | inner | 804.2.o.d.641.9 | yes | 36 | |
201.38 | even | 6 | inner | 804.2.o.d.641.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.o.d.365.9 | ✓ | 36 | 3.2 | odd | 2 | inner | |
804.2.o.d.365.10 | yes | 36 | 1.1 | even | 1 | trivial | |
804.2.o.d.641.9 | yes | 36 | 67.38 | odd | 6 | inner | |
804.2.o.d.641.10 | yes | 36 | 201.38 | even | 6 | inner |