Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 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("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.13 | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.i.1949.13 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56253 | + | 0.747325i | 0.902128 | + | 0.431468i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52603 | + | 0.786875i | 0.954750 | + | 0.297411i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.88301 | + | 2.33544i | 0.627670 | + | 0.778479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34474 | + | 1.35373i | −0.706965 | + | 0.408166i | −0.809936 | − | 0.586518i | \(-0.800498\pi\) |
0.102971 | + | 0.994684i | \(0.467165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.12489 | −0.311987 | −0.155994 | − | 0.987758i | \(-0.549858\pi\) | ||||
−0.155994 | + | 0.987758i | \(0.549858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.39336 | + | 3.69121i | −1.55062 | + | 0.895250i | −0.552527 | + | 0.833495i | \(0.686336\pi\) |
−0.998091 | + | 0.0617544i | \(0.980330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.412264 | + | 0.238021i | 0.0945799 | + | 0.0546057i | 0.546544 | − | 0.837430i | \(-0.315943\pi\) |
−0.451964 | + | 0.892036i | \(0.649276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.35895 | + | 3.11728i | 0.732983 | + | 0.680247i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.79845 | + | 4.84706i | −0.583518 | + | 1.01068i | 0.411540 | + | 0.911392i | \(0.364991\pi\) |
−0.995058 | + | 0.0992913i | \(0.968342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.19693 | + | 5.05642i | 0.230350 | + | 0.973108i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.20372i | 0.409220i | 0.978844 | + | 0.204610i | \(0.0655926\pi\) | ||||
−0.978844 | + | 0.204610i | \(0.934407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.07315 | + | 1.19693i | −0.372348 | + | 0.214975i | −0.674484 | − | 0.738290i | \(-0.735634\pi\) |
0.302136 | + | 0.953265i | \(0.402300\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.67541 | + | 0.362972i | −0.813884 | + | 0.0631854i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.53233 | + | 4.34879i | 1.23831 | + | 0.714937i | 0.968748 | − | 0.248047i | \(-0.0797888\pi\) |
0.269559 | + | 0.962984i | \(0.413122\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.75767 | − | 0.840655i | −0.281452 | − | 0.134613i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.42336 | −0.846986 | −0.423493 | − | 0.905899i | \(-0.639196\pi\) | ||||
−0.423493 | + | 0.905899i | \(0.639196\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.16209i | − | 0.634712i | −0.948306 | − | 0.317356i | \(-0.897205\pi\) | ||
0.948306 | − | 0.317356i | \(-0.102795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.7600 | + | 6.21227i | 1.56950 | + | 0.906153i | 0.996227 | + | 0.0867912i | \(0.0276613\pi\) |
0.573277 | + | 0.819362i | \(0.305672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.76166 | + | 3.97534i | 0.823094 | + | 0.567905i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.7484 | + | 0.989712i | −1.78513 | + | 0.138587i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.45559 | − | 4.25321i | −0.337302 | − | 0.584224i | 0.646622 | − | 0.762810i | \(-0.276181\pi\) |
−0.983924 | + | 0.178586i | \(0.942848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.466297 | + | 0.680011i | 0.0617626 | + | 0.0900696i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.15586 | + | 2.00200i | 0.150480 | + | 0.260638i | 0.931404 | − | 0.363987i | \(-0.118585\pi\) |
−0.780924 | + | 0.624626i | \(0.785252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.26895 | − | 1.30998i | −0.290509 | − | 0.167726i | 0.347662 | − | 0.937620i | \(-0.386976\pi\) |
−0.638172 | + | 0.769894i | \(0.720309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.91884 | + | 7.38108i | 0.367740 | + | 0.929929i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7169 | − | 7.34210i | 1.55361 | − | 0.896980i | 0.555772 | − | 0.831335i | \(-0.312423\pi\) |
0.997843 | − | 0.0656452i | \(-0.0209106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.99501 | + | 5.48234i | −0.962486 | + | 0.659996i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.89729i | − | 1.17459i | −0.809372 | − | 0.587296i | \(-0.800193\pi\) | ||
0.809372 | − | 0.587296i | \(-0.199807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.63180 | − | 6.29046i | −0.425070 | − | 0.736242i | 0.571357 | − | 0.820701i | \(-0.306417\pi\) |
−0.996427 | + | 0.0844591i | \(0.973084\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.98810 | + | 1.57456i | −0.796368 | + | 0.179438i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.47478 | + | 6.01850i | −0.390944 | + | 0.677134i | −0.992574 | − | 0.121640i | \(-0.961185\pi\) |
0.601631 | + | 0.798774i | \(0.294518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.90854 | + | 8.79531i | −0.212060 | + | 0.977257i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.3005i | − | 1.24040i | −0.784446 | − | 0.620198i | \(-0.787052\pi\) | ||
0.784446 | − | 0.620198i | \(-0.212948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.64689 | + | 3.44338i | −0.176566 | + | 0.369169i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.48186 | − | 6.03075i | 0.369076 | − | 0.639258i | −0.620345 | − | 0.784329i | \(-0.713008\pi\) |
0.989421 | + | 0.145070i | \(0.0463409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.84150 | − | 0.885144i | −0.297870 | − | 0.0927883i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.13385 | + | 0.320929i | −0.428661 | + | 0.0332788i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.79691 | 0.893190 | 0.446595 | − | 0.894736i | \(-0.352636\pi\) | ||||
0.446595 | + | 0.894736i | \(0.352636\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.57673 | − | 2.92689i | −0.761490 | − | 0.294164i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23274 | + | 9.06338i | 0.520677 | + | 0.901840i | 0.999711 | + | 0.0240431i | \(0.00765389\pi\) |
−0.479034 | + | 0.877797i | \(0.659013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.63440 | + | 2.83087i | −0.161042 | + | 0.278934i | −0.935243 | − | 0.354007i | \(-0.884819\pi\) |
0.774200 | + | 0.632941i | \(0.218152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.49305 | + | 4.31809i | −0.241012 | + | 0.417445i | −0.961003 | − | 0.276538i | \(-0.910813\pi\) |
0.719991 | + | 0.693984i | \(0.244146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.40043 | + | 4.15767i | 0.229920 | + | 0.398232i | 0.957784 | − | 0.287489i | \(-0.0928204\pi\) |
−0.727864 | + | 0.685721i | \(0.759487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.51954 | + | 12.4242i | 0.808639 | + | 1.17925i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.8874 | 1.77678 | 0.888388 | − | 0.459094i | \(-0.151826\pi\) | ||||
0.888388 | + | 0.459094i | \(0.151826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.11817 | − | 2.62710i | −0.195825 | − | 0.242876i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.0543 | + | 4.29333i | −1.74671 | + | 0.393569i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83480 | + | 3.17797i | −0.166800 | + | 0.288907i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.47417 | − | 4.05301i | −0.764090 | − | 0.365448i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.77289i | − | 0.689732i | −0.938652 | − | 0.344866i | \(-0.887924\pi\) | ||
0.938652 | − | 0.344866i | \(-0.112076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.11043 | − | 6.50339i | 0.273858 | − | 0.572592i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.32600 | − | 4.02875i | 0.203224 | − | 0.351994i | −0.746342 | − | 0.665563i | \(-0.768191\pi\) |
0.949565 | + | 0.313569i | \(0.101525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.854100 | + | 0.925648i | 0.0740598 | + | 0.0802639i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.50592 | + | 9.53654i | 0.470403 | + | 0.814762i | 0.999427 | − | 0.0338451i | \(-0.0107753\pi\) |
−0.529024 | + | 0.848607i | \(0.677442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.5928i | 1.74665i | 0.487134 | + | 0.873327i | \(0.338042\pi\) | ||||
−0.487134 | + | 0.873327i | \(0.661958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1702 | + | 17.7481i | 1.02492 | + | 1.49466i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63756 | − | 1.52280i | 0.220564 | − | 0.127343i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.03190 | + | 10.5174i | 0.497503 | + | 0.867462i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.8906 | − | 8.59708i | −1.21988 | − | 0.704300i | −0.254991 | − | 0.966943i | \(-0.582072\pi\) |
−0.964893 | + | 0.262643i | \(0.915406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00060 | − | 1.73309i | −0.0814279 | − | 0.141037i | 0.822436 | − | 0.568858i | \(-0.192615\pi\) |
−0.903863 | + | 0.427821i | \(0.859281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.6594 | − | 7.98072i | −1.67021 | − | 0.645203i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.11856 | + | 15.7938i | 0.727741 | + | 1.26048i | 0.957836 | + | 0.287316i | \(0.0927628\pi\) |
−0.230095 | + | 0.973168i | \(0.573904\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.658410 | − | 8.48091i | −0.0522153 | − | 0.672580i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8830 | + | 10.0418i | −0.857701 | + | 0.791405i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1563 | + | 9.90522i | 1.34379 | + | 0.775837i | 0.987361 | − | 0.158487i | \(-0.0506615\pi\) |
0.356427 | + | 0.934323i | \(0.383995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.5257i | − | 0.969269i | −0.874717 | − | 0.484634i | \(-0.838953\pi\) | ||
0.874717 | − | 0.484634i | \(-0.161047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7346 | −0.902664 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.220415 | + | 1.41101i | 0.0168555 | + | 0.107903i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7620 | − | 7.36813i | −0.970275 | − | 0.560188i | −0.0709548 | − | 0.997480i | \(-0.522605\pi\) |
−0.899320 | + | 0.437291i | \(0.855938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.309916 | + | 3.99199i | 0.0232947 | + | 0.300056i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.18770 | − | 0.685720i | 0.0887730 | − | 0.0512531i | −0.454956 | − | 0.890514i | \(-0.650345\pi\) |
0.543729 | + | 0.839261i | \(0.317012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.3843i | − | 1.58949i | −0.606947 | − | 0.794743i | \(-0.707606\pi\) | ||
0.606947 | − | 0.794743i | \(-0.292394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.56633 | − | 3.74253i | −0.189708 | − | 0.276656i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.99384 | − | 17.3098i | 0.730822 | − | 1.26582i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.955280 | + | 13.7145i | −0.0694864 | + | 0.997583i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9775 | − | 8.64724i | −1.08373 | − | 0.625692i | −0.151830 | − | 0.988407i | \(-0.548517\pi\) |
−0.931900 | + | 0.362714i | \(0.881850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0921 | − | 6.40401i | 0.798425 | − | 0.460971i | −0.0444950 | − | 0.999010i | \(-0.514168\pi\) |
0.842920 | + | 0.538039i | \(0.180835\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.17207 | 0.653483 | 0.326741 | − | 0.945114i | \(-0.394049\pi\) | ||||
0.326741 | + | 0.945114i | \(0.394049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.16818 | + | 4.13855i | −0.508139 | + | 0.293374i | −0.732068 | − | 0.681231i | \(-0.761445\pi\) |
0.223930 | + | 0.974605i | \(0.428111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.3575 | − | 1.96861i | 1.78858 | − | 0.138855i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.73405 | + | 5.56666i | −0.121706 | + | 0.390703i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.5895 | + | 2.59146i | −1.15305 | + | 0.180119i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.28887 | −0.0891529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.50872 | −0.585765 | −0.292882 | − | 0.956148i | \(-0.594614\pi\) | ||||
−0.292882 | + | 0.956148i | \(0.594614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.39649 | − | 15.4648i | 0.506799 | − | 1.05963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.17867 | + | 1.39218i | −0.419435 | + | 0.0945073i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.973782 | − | 12.5432i | −0.0658021 | − | 0.847589i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.19180 | − | 4.15219i | 0.483773 | − | 0.279306i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.54451 | −0.371288 | −0.185644 | − | 0.982617i | \(-0.559437\pi\) | ||||
−0.185644 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.36478 | − | 3.09736i | 0.356073 | − | 0.205579i | −0.311284 | − | 0.950317i | \(-0.600759\pi\) |
0.667357 | + | 0.744738i | \(0.267426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.307553 | + | 0.177566i | 0.0203237 | + | 0.0117339i | 0.510127 | − | 0.860099i | \(-0.329598\pi\) |
−0.489804 | + | 0.871833i | \(0.662932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0958 | − | 2.76208i | −0.795847 | − | 0.181732i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.33296 | + | 16.1652i | −0.611422 | + | 1.05901i | 0.379578 | + | 0.925160i | \(0.376069\pi\) |
−0.991001 | + | 0.133855i | \(0.957264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.92723 | + | 6.80730i | −0.644843 | + | 0.442182i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.1914i | − | 1.37076i | −0.728186 | − | 0.685379i | \(-0.759636\pi\) | ||
0.728186 | − | 0.685379i | \(-0.240364\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92350 | + | 1.11053i | −0.123903 | + | 0.0715356i | −0.560671 | − | 0.828039i | \(-0.689457\pi\) |
0.436767 | + | 0.899574i | \(0.356123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.55511 | + | 12.3166i | −0.612961 | + | 0.790113i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.463750 | − | 0.267746i | −0.0295077 | − | 0.0170363i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.44517 | − | 17.6574i | 0.535191 | − | 1.11900i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.3017 | 1.15519 | 0.577597 | − | 0.816322i | \(-0.303990\pi\) | ||||
0.577597 | + | 0.816322i | \(0.303990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.1535i | − | 0.952690i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.69894 | − | 5.59968i | −0.605003 | − | 0.349299i | 0.166004 | − | 0.986125i | \(-0.446913\pi\) |
−0.771007 | + | 0.636826i | \(0.780247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.6049 | + | 16.9122i | 0.969643 | + | 1.05087i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.14665 | + | 4.14962i | −0.318569 | + | 0.256855i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.60778 | + | 11.4450i | 0.407453 | + | 0.705730i | 0.994604 | − | 0.103748i | \(-0.0330836\pi\) |
−0.587150 | + | 0.809478i | \(0.699750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.94744 | − | 6.82116i | 0.608774 | − | 0.417448i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6657 | + | 21.9377i | 0.772244 | + | 1.33757i | 0.936330 | + | 0.351120i | \(0.114199\pi\) |
−0.164086 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.9303 | − | 13.8162i | −1.45366 | − | 0.839273i | −0.454976 | − | 0.890504i | \(-0.650352\pi\) |
−0.998687 | + | 0.0512313i | \(0.983685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.77844 | − | 3.50659i | −0.228681 | − | 0.212228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.4917 | − | 11.8309i | 1.23122 | − | 0.710848i | 0.263939 | − | 0.964539i | \(-0.414978\pi\) |
0.967285 | + | 0.253691i | \(0.0816448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.69912 | − | 2.58787i | −0.401066 | − | 0.154932i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3694i | 1.03617i | 0.855329 | + | 0.518085i | \(0.173355\pi\) | ||||
−0.855329 | + | 0.518085i | \(0.826645\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.46037 | + | 11.1897i | 0.384029 | + | 0.665158i | 0.991634 | − | 0.129082i | \(-0.0412030\pi\) |
−0.607605 | + | 0.794239i | \(0.707870\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.6996 | − | 4.26750i | −0.808660 | − | 0.251903i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.7500 | − | 32.4760i | 1.10294 | − | 1.91036i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7454 | + | 6.57415i | 0.805772 | + | 0.385383i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.2345i | − | 0.656326i | −0.944621 | − | 0.328163i | \(-0.893571\pi\) | ||
0.944621 | − | 0.328163i | \(-0.106429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.65154 | − | 10.2356i | −0.560039 | − | 0.593932i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.14794 | − | 5.45239i | 0.182050 | − | 0.315320i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.27504 | − | 10.5136i | 0.188770 | − | 0.605991i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.40304 | + | 18.0724i | 0.0806024 | + | 1.03823i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.0165 | −1.77021 | −0.885103 | − | 0.465395i | \(-0.845912\pi\) | ||||
−0.885103 | + | 0.465395i | \(0.845912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.66938 | + | 3.20189i | −0.265632 | + | 0.182149i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.771357 | − | 1.33603i | −0.0437396 | − | 0.0757593i | 0.843327 | − | 0.537401i | \(-0.180594\pi\) |
−0.887066 | + | 0.461642i | \(0.847261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8545 | − | 22.2646i | 0.726579 | − | 1.25847i | −0.231742 | − | 0.972777i | \(-0.574442\pi\) |
0.958321 | − | 0.285694i | \(-0.0922242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.55545 | − | 2.69412i | 0.0873629 | − | 0.151317i | −0.819033 | − | 0.573747i | \(-0.805489\pi\) |
0.906396 | + | 0.422430i | \(0.138823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.98325 | − | 5.16714i | −0.167030 | − | 0.289304i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.12248 | + | 4.88403i | −0.397538 | + | 0.272600i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.51434 | −0.195543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.643619 | + | 8.29039i | 0.0355922 | + | 0.458460i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.2917 | + | 24.1591i | 1.22898 | + | 1.33194i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.139978 | − | 0.242450i | 0.00769391 | − | 0.0133262i | −0.862153 | − | 0.506648i | \(-0.830884\pi\) |
0.869847 | + | 0.493322i | \(0.164218\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.02712 | + | 25.7801i | 0.220685 | + | 1.41274i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.96891i | − | 0.325147i | −0.986696 | − | 0.162574i | \(-0.948021\pi\) | ||
0.986696 | − | 0.162574i | \(-0.0519795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.5121 | + | 14.1150i | 1.60288 | + | 0.766622i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24066 | − | 5.61298i | 0.175491 | − | 0.303960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4260 | + | 14.5755i | 0.616947 | + | 0.787004i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.28063 | + | 7.41426i | 0.229796 | + | 0.398019i | 0.957748 | − | 0.287610i | \(-0.0928607\pi\) |
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.23833i | 0.387459i | 0.981055 | + | 0.193729i | \(0.0620584\pi\) | ||||
−0.981055 | + | 0.193729i | \(0.937942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.34641 | − | 5.68789i | −0.0718661 | − | 0.303597i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5790 | − | 11.8813i | 1.09531 | − | 0.632377i | 0.160324 | − | 0.987065i | \(-0.448746\pi\) |
0.934985 | + | 0.354688i | \(0.115413\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −32.9815 | − | 7.53132i | −1.74557 | − | 0.398600i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.3993 | + | 18.1284i | 1.65719 | + | 0.956780i | 0.974003 | + | 0.226537i | \(0.0727405\pi\) |
0.683188 | + | 0.730242i | \(0.260593\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.38669 | − | 16.2582i | −0.494036 | − | 0.855696i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.24192 | + | 3.59449i | −0.275129 | + | 0.188662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.730418 | + | 1.26512i | 0.0381275 | + | 0.0660387i | 0.884459 | − | 0.466617i | \(-0.154527\pi\) |
−0.846332 | + | 0.532656i | \(0.821194\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.2122 | − | 12.6659i | −0.531628 | − | 0.659361i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.85616 | − | 12.6760i | −0.148284 | − | 0.658105i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3457 | + | 10.5919i | 0.949907 | + | 0.548429i | 0.893052 | − | 0.449954i | \(-0.148559\pi\) |
0.0568547 | + | 0.998382i | \(0.481893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.47893i | − | 0.127671i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3581 | −1.25119 | −0.625596 | − | 0.780147i | \(-0.715144\pi\) | ||||
−0.625596 | + | 0.780147i | \(0.715144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.80887 | − | 12.1454i | 0.297598 | − | 0.622227i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.8176 | − | 12.5964i | −1.11483 | − | 0.643647i | −0.174754 | − | 0.984612i | \(-0.555913\pi\) |
−0.940076 | + | 0.340965i | \(0.889246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.72030 | − | 7.83725i | 0.494110 | − | 0.398390i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.9380 | − | 6.31508i | 0.554581 | − | 0.320187i | −0.196387 | − | 0.980527i | \(-0.562921\pi\) |
0.750967 | + | 0.660339i | \(0.229587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 41.3187i | − | 2.08958i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.64524 | − | 4.55677i | 0.335208 | − | 0.229859i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.27166 | + | 14.3269i | −0.415143 | + | 0.719048i | −0.995443 | − | 0.0953542i | \(-0.969602\pi\) |
0.580301 | + | 0.814402i | \(0.302935\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.642797 | + | 2.08465i | 0.0321801 | + | 0.104363i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.72834 | + | 5.61666i | 0.485810 | + | 0.280482i | 0.722835 | − | 0.691021i | \(-0.242839\pi\) |
−0.237025 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.33205 | − | 1.34641i | 0.116168 | − | 0.0670695i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.5484 | −1.16725 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.6764 | − | 18.2884i | 1.56630 | − | 0.904303i | 0.569703 | − | 0.821851i | \(-0.307058\pi\) |
0.996595 | − | 0.0824520i | \(-0.0262751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.47628 | + | 19.0159i | 0.0728198 | + | 0.937983i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.34440 | + | 5.96663i | 0.0661537 | + | 0.293599i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.3895 | + | 32.1768i | −0.753626 | + | 1.57571i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.29006 | −0.404996 | −0.202498 | − | 0.979283i | \(-0.564906\pi\) | ||||
−0.202498 | + | 0.979283i | \(0.564906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8826 | 1.16397 | 0.581984 | − | 0.813200i | \(-0.302277\pi\) | ||||
0.581984 | + | 0.813200i | \(0.302277\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.75276 | + | 36.8270i | 0.279709 | + | 1.79059i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.70065 | − | 5.09443i | −0.227480 | − | 0.246537i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.25930 | − | 0.408303i | 0.253921 | − | 0.0197130i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.93859 | + | 5.73805i | −0.478725 | + | 0.276392i | −0.719885 | − | 0.694093i | \(-0.755806\pi\) |
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.31657 | 0.159384 | 0.0796920 | − | 0.996820i | \(-0.474606\pi\) | ||||
0.0796920 | + | 0.996820i | \(0.474606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.30741 | + | 1.33218i | −0.110378 | + | 0.0637269i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.6144 | − | 13.6338i | −1.12705 | − | 0.650705i | −0.183862 | − | 0.982952i | \(-0.558860\pi\) |
−0.943192 | + | 0.332247i | \(0.892193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.56510 | + | 20.9416i | 0.0745287 | + | 0.997219i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.4555 | + | 35.4300i | −0.971872 | + | 1.68333i | −0.281979 | + | 0.959421i | \(0.590991\pi\) |
−0.689893 | + | 0.723911i | \(0.742343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.8422 | − | 24.5613i | −0.796608 | − | 1.16171i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.6734i | − | 0.928446i | −0.885718 | − | 0.464223i | \(-0.846334\pi\) | ||
0.885718 | − | 0.464223i | \(-0.153666\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.7164 | − | 7.34179i | 0.598790 | − | 0.345711i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.268288 | − | 3.45579i | −0.0126053 | − | 0.162367i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.95987 | + | 4.59563i | 0.372347 | + | 0.214975i | 0.674483 | − | 0.738290i | \(-0.264366\pi\) |
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.3167 | − | 27.9094i | −1.22836 | − | 1.30270i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.7958 | 1.34115 | 0.670577 | − | 0.741840i | \(-0.266047\pi\) | ||||
0.670577 | + | 0.741840i | \(0.266047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.0825i | − | 1.16568i | −0.812586 | − | 0.582841i | \(-0.801941\pi\) | ||
0.812586 | − | 0.582841i | \(-0.198059\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.2087 | + | 11.6675i | 0.935145 | + | 0.539907i | 0.888435 | − | 0.459002i | \(-0.151793\pi\) |
0.0467103 | + | 0.998908i | \(0.485126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.9005 | − | 8.53977i | 1.75008 | − | 0.394330i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.44493 | + | 31.4929i | 0.112656 | + | 1.45111i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.63436 | + | 9.75900i | 0.259068 | + | 0.448719i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.30921 | − | 13.7437i | 0.243092 | − | 0.629282i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.12075 | − | 14.0655i | −0.371046 | − | 0.642671i | 0.618680 | − | 0.785643i | \(-0.287668\pi\) |
−0.989727 | + | 0.142971i | \(0.954334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.47301 | − | 4.89189i | −0.386336 | − | 0.223051i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.5095 | + | 7.55748i | −1.11522 | + | 0.343877i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.79420 | + | 5.07733i | −0.398503 | + | 0.230076i | −0.685838 | − | 0.727754i | \(-0.740564\pi\) |
0.287335 | + | 0.957830i | \(0.407231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.4049 | + | 28.2986i | 0.877520 | + | 1.27971i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5734i | 1.15411i | 0.816704 | + | 0.577057i | \(0.195799\pi\) | ||||
−0.816704 | + | 0.577057i | \(0.804201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.13438 | − | 14.0892i | −0.366354 | − | 0.634544i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.78792 | − | 25.0008i | 0.349336 | − | 1.12144i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.80838 | − | 8.32836i | 0.215253 | − | 0.372829i | −0.738098 | − | 0.674693i | \(-0.764276\pi\) |
0.953351 | + | 0.301865i | \(0.0976092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.36078 | − | 19.5718i | 0.418209 | − | 0.874405i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.82743i | 0.304420i | 0.988348 | + | 0.152210i | \(0.0486390\pi\) | ||||
−0.988348 | + | 0.152210i | \(0.951361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.3357 | − | 8.76958i | −0.814319 | − | 0.389471i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.02977 | + | 12.1759i | −0.311589 | + | 0.539688i | −0.978707 | − | 0.205265i | \(-0.934195\pi\) |
0.667118 | + | 0.744952i | \(0.267528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.22423 | − | 18.7477i | −0.186869 | − | 0.829347i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.710081 | + | 2.36948i | −0.0313508 | + | 0.104615i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.6391 | −1.47945 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.4346 | − | 21.0503i | −0.633609 | − | 0.924005i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.6122 | − | 23.5771i | −0.596363 | − | 1.03293i | −0.993353 | − | 0.115109i | \(-0.963278\pi\) |
0.396990 | − | 0.917823i | \(-0.370055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.528969 | + | 0.916202i | −0.0231302 | + | 0.0400627i | −0.877359 | − | 0.479835i | \(-0.840697\pi\) |
0.854229 | + | 0.519898i | \(0.174030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.83625 | − | 15.3048i | 0.384913 | − | 0.666689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.16269 | − | 7.20999i | −0.180987 | − | 0.313478i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.49906 | + | 6.46922i | −0.108450 | + | 0.280740i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.10066 | 0.264249 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.36828 | − | 0.183860i | 0.102199 | − | 0.00793414i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.8911 | − | 1.52137i | −0.813698 | − | 0.0655300i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1032 | − | 22.6953i | 0.563349 | − | 0.975748i | −0.433853 | − | 0.900984i | \(-0.642846\pi\) |
0.997201 | − | 0.0747644i | \(-0.0238205\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.9810 | − | 33.4137i | 0.685812 | − | 1.43392i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 36.6385i | − | 1.56655i | −0.621675 | − | 0.783275i | \(-0.713548\pi\) | ||
0.621675 | − | 0.783275i | \(-0.286452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.21308 | − | 7.76570i | −0.0517731 | − | 0.331432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.524531 | + | 0.908514i | −0.0223458 | + | 0.0387040i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.5132 | + | 12.4687i | −0.574640 | + | 0.530223i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.1032 | − | 29.6236i | −0.724685 | − | 1.25519i | −0.959104 | − | 0.283055i | \(-0.908652\pi\) |
0.234419 | − | 0.972136i | \(-0.424681\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68187i | 0.198022i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.5518 | − | 19.5785i | 1.20546 | − | 0.826606i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.6666 | + | 11.9319i | −0.870993 | + | 0.502868i | −0.867678 | − | 0.497127i | \(-0.834388\pi\) |
−0.00331483 | + | 0.999995i | \(0.501055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.7418 | + | 20.7154i | −0.493111 | + | 0.869966i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8326 | + | 16.0692i | 1.16680 | + | 0.673655i | 0.952925 | − | 0.303205i | \(-0.0980567\pi\) |
0.213879 | + | 0.976860i | \(0.431390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.85333 | + | 17.0665i | 0.412349 | + | 0.714209i | 0.995146 | − | 0.0984083i | \(-0.0313751\pi\) |
−0.582797 | + | 0.812618i | \(0.698042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9405 | − | 24.7046i | −0.707697 | − | 1.03205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.20731 | + | 10.7514i | 0.258414 | + | 0.447586i | 0.965817 | − | 0.259224i | \(-0.0834669\pi\) |
−0.707403 | + | 0.706810i | \(0.750134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.1176 | − | 1.71709i | 0.919176 | − | 0.0713597i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.89211 | − | 28.5455i | 0.368907 | − | 1.18427i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5154 | + | 6.64845i | 0.476921 | + | 0.275351i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 30.6227i | − | 1.26394i | −0.774995 | − | 0.631968i | \(-0.782247\pi\) | ||
0.774995 | − | 0.631968i | \(-0.217753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.13958 | −0.0469556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.3316 | + | 6.85452i | 0.589525 | + | 0.281957i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.6999 | + | 21.7660i | 1.54815 | + | 0.893823i | 0.998283 | + | 0.0585693i | \(0.0186539\pi\) |
0.549864 | + | 0.835254i | \(0.314679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.2933 | + | 1.10966i | −0.584988 | + | 0.0454152i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8060 | − | 13.1670i | 0.931827 | − | 0.537991i | 0.0444381 | − | 0.999012i | \(-0.485850\pi\) |
0.887389 | + | 0.461022i | \(0.152517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18.8846i | − | 0.770317i | −0.922850 | − | 0.385159i | \(-0.874147\pi\) | ||
0.922850 | − | 0.385159i | \(-0.125853\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.0930 | + | 15.8743i | 1.67344 | + | 0.646450i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.16622 | + | 12.4123i | −0.290868 | + | 0.503798i | −0.974015 | − | 0.226482i | \(-0.927277\pi\) |
0.683147 | + | 0.730281i | \(0.260611\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.86961 | + | 7.40218i | −0.278371 | + | 0.299951i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1037 | − | 6.98810i | −0.489665 | − | 0.282708i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0421 | − | 9.26188i | 0.647932 | − | 0.374084i | −0.139731 | − | 0.990189i | \(-0.544624\pi\) |
0.787664 | + | 0.616106i | \(0.211291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.6900 | 1.87967 | 0.939833 | − | 0.341633i | \(-0.110980\pi\) | ||||
0.939833 | + | 0.341633i | \(0.110980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.0066 | + | 19.0564i | −1.32665 | + | 0.765940i | −0.984780 | − | 0.173808i | \(-0.944393\pi\) |
−0.341868 | + | 0.939748i | \(0.611059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.8583 | − | 8.34854i | −1.11792 | − | 0.335016i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5407 | − | 12.4941i | 0.542498 | − | 0.500565i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.01390 | − | 0.963204i | −0.0804274 | − | 0.0384667i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −64.2092 | −2.56019 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.1097 | −0.681128 | −0.340564 | − | 0.940221i | \(-0.610618\pi\) | ||||
−0.340564 | + | 0.940221i | \(0.610618\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.2952 | − | 6.35878i | −0.528435 | − | 0.252739i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.48121 | − | 4.47180i | −0.256795 | − | 0.177179i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.1145 | − | 18.6367i | 0.914395 | − | 0.737256i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.2874 | − | 10.5583i | 0.722310 | − | 0.417026i | −0.0932922 | − | 0.995639i | \(-0.529739\pi\) |
0.815602 | + | 0.578613i | \(0.196406\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.86538 | −0.270744 | −0.135372 | − | 0.990795i | \(-0.543223\pi\) | ||||
−0.135372 | + | 0.990795i | \(0.543223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4243 | − | 8.90522i | 0.606391 | − | 0.350100i | −0.165161 | − | 0.986267i | \(-0.552814\pi\) |
0.771552 | + | 0.636167i | \(0.219481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.42036 | − | 3.12944i | −0.212768 | − | 0.122841i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6948 | − | 2.44215i | −0.419161 | − | 0.0957153i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.8610 | − | 39.5964i | 0.894619 | − | 1.54953i | 0.0603437 | − | 0.998178i | \(-0.480780\pi\) |
0.834275 | − | 0.551348i | \(-0.185886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.85226 | − | 20.3268i | 0.306346 | − | 0.793025i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.74688i | − | 0.262821i | −0.991328 | − | 0.131411i | \(-0.958049\pi\) | ||
0.991328 | − | 0.131411i | \(-0.0419506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.2369 | + | 24.9628i | −1.68172 | + | 0.970942i | −0.721203 | + | 0.692724i | \(0.756410\pi\) |
−0.960518 | + | 0.278218i | \(0.910256\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.3405 | − | 1.11331i | 0.556937 | − | 0.0432375i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.6816 | − | 6.16700i | −0.413592 | − | 0.238787i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.66348 | − | 4.14355i | −0.334949 | − | 0.160199i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.09346 | 0.273840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.0600i | − | 0.773257i | −0.922236 | − | 0.386628i | \(-0.873640\pi\) | ||
0.922236 | − | 0.386628i | \(-0.126360\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6076 | − | 12.4751i | −0.830446 | − | 0.479458i | 0.0235594 | − | 0.999722i | \(-0.492500\pi\) |
−0.854005 | + | 0.520264i | \(0.825833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.2212 | + | 6.92206i | 0.852773 | + | 0.265644i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.6974 | − | 0.830484i | 0.409924 | − | 0.0318242i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.4243 | − | 26.7156i | −0.590194 | − | 1.02225i | −0.994206 | − | 0.107492i | \(-0.965718\pi\) |
0.404012 | − | 0.914754i | \(-0.367615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.347862 | + | 0.507294i | 0.0132718 | + | 0.0193545i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.76226 | + | 4.78438i | 0.105234 | + | 0.182270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5472 | + | 8.97619i | 0.591444 | + | 0.341470i | 0.765668 | − | 0.643236i | \(-0.222408\pi\) |
−0.174224 | + | 0.984706i | \(0.555742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8360 | − | 13.3554i | −0.639545 | − | 0.507328i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6735 | − | 20.0188i | 1.31335 | − | 0.758264i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.6637 | + | 18.2838i | −1.00851 | + | 0.691557i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7744i | 1.20010i | 0.799961 | + | 0.600052i | \(0.204853\pi\) | ||||
−0.799961 | + | 0.600052i | \(0.795147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.07021 | + | 3.58570i | 0.0780793 | + | 0.135237i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.08633 | + | 27.0119i | 0.228900 | + | 1.01589i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.2201 | − | 22.8978i | 0.496490 | − | 0.859946i | −0.503502 | − | 0.863994i | \(-0.667955\pi\) |
0.999992 | + | 0.00404829i | \(0.00128862\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5989 | + | 3.21776i | −0.772518 | + | 0.120675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 13.3982i | − | 0.501768i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.8369 | − | 33.1123i | 0.591439 | − | 1.23660i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.2625 | − | 21.2393i | 0.457314 | − | 0.792092i | −0.541504 | − | 0.840698i | \(-0.682145\pi\) |
0.998818 | + | 0.0486066i | \(0.0154781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.35608 | + | 5.86478i | −0.236713 | + | 0.218416i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.83545 | + | 0.297763i | −0.142642 | + | 0.0110739i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.4804 | −1.83513 | −0.917564 | − | 0.397589i | \(-0.869847\pi\) | ||||
−0.917564 | + | 0.397589i | \(0.869847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1347 | + | 12.1044i | −0.893878 | + | 0.448310i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.3631 | + | 26.6097i | 0.568226 | + | 0.984196i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.27642 | + | 14.3352i | −0.305697 | + | 0.529482i | −0.977416 | − | 0.211324i | \(-0.932223\pi\) |
0.671720 | + | 0.740805i | \(0.265556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.8785 | + | 34.4306i | −0.732234 | + | 1.26827i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.41010 | + | 14.5667i | 0.309371 | + | 0.535846i | 0.978225 | − | 0.207548i | \(-0.0665483\pi\) |
−0.668854 | + | 0.743394i | \(0.733215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.524531 | − | 0.764935i | −0.0192691 | − | 0.0281006i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.76463 | 0.174797 | 0.0873987 | − | 0.996173i | \(-0.472145\pi\) | ||||
0.0873987 | + | 0.996173i | \(0.472145\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.3917 | − | 21.2790i | 0.965622 | − | 0.778559i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.69531 | + | 8.94590i | −0.354259 | + | 0.326876i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.11749 | + | 7.13171i | −0.150249 | + | 0.260240i | −0.931319 | − | 0.364204i | \(-0.881341\pi\) |
0.781070 | + | 0.624444i | \(0.214674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.5970 | + | 13.6773i | 1.04213 | + | 0.498430i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.01624i | − | 0.109627i | −0.998497 | − | 0.0548136i | \(-0.982544\pi\) | ||
0.998497 | − | 0.0548136i | \(-0.0174565\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3246 | − | 23.6778i | 0.411055 | − | 0.859448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.59504 | + | 13.1550i | −0.275320 | + | 0.476868i | −0.970216 | − | 0.242242i | \(-0.922117\pi\) |
0.694896 | + | 0.719110i | \(0.255450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.79200 | + | 12.3912i | 0.101077 | + | 0.448593i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30021 | − | 2.25202i | −0.0469477 | − | 0.0813158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1611i | 1.19582i | 0.801563 | + | 0.597910i | \(0.204002\pi\) | ||||
−0.801563 | + | 0.597910i | \(0.795998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.9701 | − | 15.9979i | −0.395079 | − | 0.576152i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.39536 | + | 4.84706i | −0.301960 | + | 0.174337i | −0.643323 | − | 0.765595i | \(-0.722445\pi\) |
0.341363 | + | 0.939932i | \(0.389111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.7443 | + | 38.0878i | 0.421325 | + | 1.36639i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.23586 | − | 1.29087i | −0.0801079 | − | 0.0462503i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3983 | + | 23.2065i | 0.479429 | + | 0.830395i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.1429 | + | 2.63770i | −0.398215 | + | 0.0942637i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9882 | + | 36.3526i | 0.748148 | + | 1.29583i | 0.948710 | + | 0.316149i | \(0.102390\pi\) |
−0.200562 | + | 0.979681i | \(0.564277\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.77172 | + | 22.8214i | 0.0630750 | + | 0.812462i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.7101 | + | 14.8620i | 1.69638 | + | 0.528432i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55231 | + | 1.47358i | 0.0906352 | + | 0.0523283i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.8186i | 1.05623i | 0.849173 | + | 0.528115i | \(0.177101\pi\) | ||||
−0.849173 | + | 0.528115i | \(0.822899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −91.7232 | −3.24493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.6408 | − | 3.22431i | 0.729308 | − | 0.113925i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.0312 | + | 9.83298i | 0.601019 | + | 0.346998i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.39602 | + | 43.7438i | 0.119546 | + | 1.53985i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.5493 | + | 8.97739i | −0.546684 | + | 0.315628i | −0.747784 | − | 0.663942i | \(-0.768882\pi\) |
0.201099 | + | 0.979571i | \(0.435549\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.42584i | 0.155412i | 0.996976 | + | 0.0777061i | \(0.0247596\pi\) | ||||
−0.996976 | + | 0.0777061i | \(0.975240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.0667 | − | 39.4719i | −0.949270 | − | 1.38434i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.990664 | − | 1.71588i | 0.0346589 | − | 0.0600311i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.28337 | − | 8.30287i | −0.114730 | − | 0.290126i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.5257 | − | 18.7787i | −1.13515 | − | 0.655381i | −0.189927 | − | 0.981798i | \(-0.560825\pi\) |
−0.945226 | + | 0.326417i | \(0.894159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.8982 | + | 18.4164i | −1.11190 | + | 0.641957i | −0.939321 | − | 0.343038i | \(-0.888544\pi\) |
−0.172581 | + | 0.984995i | \(0.555211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.9737 | 0.520686 | 0.260343 | − | 0.965516i | \(-0.416164\pi\) | ||||
0.260343 | + | 0.965516i | \(0.416164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.95565 | − | 1.70645i | 0.102654 | − | 0.0592674i | −0.447794 | − | 0.894137i | \(-0.647790\pi\) |
0.550448 | + | 0.834869i | \(0.314457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 40.8604 | − | 3.17217i | 1.41743 | − | 0.110041i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −51.5102 | − | 4.14829i | −1.78472 | − | 0.143730i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.53360 | − | 9.05005i | −0.294964 | − | 0.312815i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.71578 | 0.128283 | 0.0641416 | − | 0.997941i | \(-0.479569\pi\) | ||||
0.0641416 | + | 0.997941i | \(0.479569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1436 | 0.832539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.9806 | + | 27.1402i | −0.447075 | + | 0.934759i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.13544 | + | 6.58390i | −0.245176 | + | 0.226225i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.73220 | + | 22.3122i | 0.0594488 | + | 0.765754i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.1577 | + | 24.3398i | −1.44515 | + | 0.834357i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5549 | −0.361393 | −0.180696 | − | 0.983539i | \(-0.557835\pi\) | ||||
−0.180696 | + | 0.983539i | \(0.557835\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.4229 | + | 19.2967i | −1.14170 | + | 0.659163i | −0.946852 | − | 0.321669i | \(-0.895756\pi\) |
−0.194852 | + | 0.980833i | \(0.562423\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9876 | + | 15.0039i | 0.886685 | + | 0.511928i | 0.872857 | − | 0.487977i | \(-0.162265\pi\) |
0.0138282 | + | 0.999904i | \(0.495598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2168 | − | 16.9061i | −0.620827 | − | 0.576160i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.0643 | − | 33.0204i | 0.648958 | − | 1.12403i | −0.334414 | − | 0.942426i | \(-0.608538\pi\) |
0.983372 | − | 0.181602i | \(-0.0581283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 53.5677 | − | 36.7325i | 1.81925 | − | 1.24750i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.8157i | − | 0.638280i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3050 | + | 8.25902i | −0.484708 | + | 0.279846i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.5647 | + | 20.5446i | 0.560629 | + | 0.695330i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7268 | + | 16.5855i | 0.970037 | + | 0.560051i | 0.899247 | − | 0.437440i | \(-0.144115\pi\) |
0.0707893 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.39581 | − | 17.5542i | 0.283184 | − | 0.592090i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8093 | −0.667393 | −0.333697 | − | 0.942681i | \(-0.608296\pi\) | ||||
−0.333697 | + | 0.942681i | \(0.608296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.37029i | − | 0.113419i | −0.998391 | − | 0.0567096i | \(-0.981939\pi\) | ||
0.998391 | − | 0.0567096i | \(-0.0180609\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.3008 | − | 18.0715i | −1.05098 | − | 0.606783i | −0.128056 | − | 0.991767i | \(-0.540874\pi\) |
−0.922923 | + | 0.384984i | \(0.874207\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.11629 | − | 19.6346i | 0.205134 | − | 0.658522i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.43148 | − | 23.2064i | −0.248964 | − | 0.777442i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.95730 | + | 5.12220i | 0.0989623 | + | 0.171408i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.99347 | − | 6.16700i | 0.300283 | − | 0.205910i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.63770 | − | 4.56863i | −0.0879722 | − | 0.152372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.3990 | + | 18.1282i | 1.04605 | + | 0.603939i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.9744 | − | 13.9802i | 0.431761 | − | 0.465233i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.9260 | − | 23.0513i | 1.32572 | − | 0.765405i | 0.341086 | − | 0.940032i | \(-0.389205\pi\) |
0.984635 | + | 0.174627i | \(0.0558718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.3136 | + | 29.2872i | −0.375250 | + | 0.971394i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 58.0403i | − | 1.92296i | −0.274871 | − | 0.961481i | \(-0.588635\pi\) | ||
0.274871 | − | 0.961481i | \(-0.411365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.2979 | + | 26.4968i | 0.506288 | + | 0.876916i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.04567 | − | 8.34648i | 0.298714 | − | 0.275625i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.66148 | − | 4.60983i | 0.0877943 | − | 0.152064i | −0.818784 | − | 0.574101i | \(-0.805352\pi\) |
0.906578 | + | 0.422037i | \(0.138685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.4643 | − | 23.1794i | −1.59695 | − | 0.763788i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.1333i | 0.366458i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.68891 | + | 1.51351i | −0.318226 | + | 0.0497101i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7113 | − | 35.8731i | 0.679517 | − | 1.17696i | −0.295610 | − | 0.955309i | \(-0.595523\pi\) |
0.975127 | − | 0.221649i | \(-0.0711439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.42911 | + | 3.01029i | 0.0468373 | + | 0.0986581i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.206821 | − | 2.66404i | −0.00677103 | − | 0.0872168i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.523249 | 0.0170938 | 0.00854690 | − | 0.999963i | \(-0.497279\pi\) | ||||
0.00854690 | + | 0.999963i | \(0.497279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.7245 | − | 25.1827i | 1.19846 | − | 0.821807i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.58594 | − | 16.6033i | −0.312493 | − | 0.541253i | 0.666409 | − | 0.745587i | \(-0.267831\pi\) |
−0.978901 | + | 0.204333i | \(0.934497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1770 | − | 26.2874i | 0.494232 | − | 0.856035i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.0654 | + | 26.0940i | −0.489558 | + | 0.847940i | −0.999928 | − | 0.0120156i | \(-0.996175\pi\) |
0.510370 | + | 0.859955i | \(0.329509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.08536 | + | 7.07605i | 0.132616 | + | 0.229698i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.44383 | − | 3.04722i | 0.144101 | − | 0.0988130i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.4015 | −0.563691 | −0.281846 | − | 0.959460i | \(-0.590947\pi\) | ||||
−0.281846 | + | 0.959460i | \(0.590947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.799889 | − | 10.3033i | −0.0258567 | − | 0.333058i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.40407 | + | 28.4221i | 0.206798 | + | 0.917796i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6347 | + | 21.8840i | −0.407571 | + | 0.705934i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7791 | + | 2.30864i | −0.476249 | + | 0.0743949i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.9154i | 0.801224i | 0.916248 | + | 0.400612i | \(0.131203\pi\) | ||||
−0.916248 | + | 0.400612i | \(0.868797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.49127 | − | 2.62635i | −0.176405 | − | 0.0843707i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.45293 | + | 16.3730i | −0.303359 | + | 0.525433i | −0.976895 | − | 0.213722i | \(-0.931441\pi\) |
0.673536 | + | 0.739155i | \(0.264775\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.2039 | + | 52.0179i | −0.519474 | + | 1.66762i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.2411 | + | 35.0586i | 0.647571 | + | 1.12163i | 0.983701 | + | 0.179810i | \(0.0575483\pi\) |
−0.336131 | + | 0.941815i | \(0.609118\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8540i | 0.602578i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.18994 | + | 13.4350i | −0.165702 | + | 0.428946i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.0341 | + | 27.1552i | −1.50016 | + | 0.866116i | −0.500156 | + | 0.865935i | \(0.666724\pi\) |
−1.00000 | 0.000180339i | \(0.999943\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.7768 | + | 54.4086i | 0.534012 | + | 1.73184i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.1739 | + | 11.6474i | 0.641493 | + | 0.370366i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8784 | + | 53.4830i | 0.980886 | + | 1.69894i | 0.658957 | + | 0.752181i | \(0.270998\pi\) |
0.321929 | + | 0.946764i | \(0.395669\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.399910 | − | 0.274226i | 0.0126907 | − | 0.00870230i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2738 | + | 17.7948i | 0.325375 | + | 0.563566i | 0.981588 | − | 0.191009i | \(-0.0611761\pi\) |
−0.656213 | + | 0.754576i | \(0.727843\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.9736 | + | 43.2918i | −0.410467 | + | 1.36969i |
(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 | 2100.2.bo.i.1349.13 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bo.i.1349.8 | 32 | ||
5.2 | odd | 4 | 2100.2.bi.m.1601.5 | yes | 16 | ||
5.3 | odd | 4 | 2100.2.bi.l.1601.4 | yes | 16 | ||
5.4 | even | 2 | inner | 2100.2.bo.i.1349.4 | 32 | ||
7.3 | odd | 6 | inner | 2100.2.bo.i.1949.9 | 32 | ||
15.2 | even | 4 | 2100.2.bi.m.1601.8 | yes | 16 | ||
15.8 | even | 4 | 2100.2.bi.l.1601.1 | yes | 16 | ||
15.14 | odd | 2 | inner | 2100.2.bo.i.1349.9 | 32 | ||
21.17 | even | 6 | inner | 2100.2.bo.i.1949.4 | 32 | ||
35.3 | even | 12 | 2100.2.bi.l.101.1 | ✓ | 16 | ||
35.17 | even | 12 | 2100.2.bi.m.101.8 | yes | 16 | ||
35.24 | odd | 6 | inner | 2100.2.bo.i.1949.8 | 32 | ||
105.17 | odd | 12 | 2100.2.bi.m.101.5 | yes | 16 | ||
105.38 | odd | 12 | 2100.2.bi.l.101.4 | yes | 16 | ||
105.59 | even | 6 | inner | 2100.2.bo.i.1949.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.1 | ✓ | 16 | 35.3 | even | 12 | ||
2100.2.bi.l.101.4 | yes | 16 | 105.38 | odd | 12 | ||
2100.2.bi.l.1601.1 | yes | 16 | 15.8 | even | 4 | ||
2100.2.bi.l.1601.4 | yes | 16 | 5.3 | odd | 4 | ||
2100.2.bi.m.101.5 | yes | 16 | 105.17 | odd | 12 | ||
2100.2.bi.m.101.8 | yes | 16 | 35.17 | even | 12 | ||
2100.2.bi.m.1601.5 | yes | 16 | 5.2 | odd | 4 | ||
2100.2.bi.m.1601.8 | yes | 16 | 15.2 | even | 4 | ||
2100.2.bo.i.1349.4 | 32 | 5.4 | even | 2 | inner | ||
2100.2.bo.i.1349.8 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bo.i.1349.9 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bo.i.1349.13 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bo.i.1949.4 | 32 | 21.17 | even | 6 | inner | ||
2100.2.bo.i.1949.8 | 32 | 35.24 | odd | 6 | inner | ||
2100.2.bo.i.1949.9 | 32 | 7.3 | odd | 6 | inner | ||
2100.2.bo.i.1949.13 | 32 | 105.59 | even | 6 | inner |