Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
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.bi (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Root | \(1.25639 - 1.19226i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1601 |
Dual form | 2100.2.bi.l.101.2 |
$q$-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 | ||||||||
\(3\) | −1.25639 | − | 1.19226i | −0.725377 | − | 0.688352i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.60761 | + | 2.10133i | 0.607620 | + | 0.794228i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.157032 | + | 2.99589i | 0.0523440 | + | 0.998629i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.05856 | − | 1.18851i | 0.620679 | − | 0.358349i | −0.156455 | − | 0.987685i | \(-0.550006\pi\) |
0.777133 | + | 0.629336i | \(0.216673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.748179i | 0.207508i | 0.994603 | + | 0.103754i | \(0.0330854\pi\) | ||||
−0.994603 | + | 0.103754i | \(0.966915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.77242 | + | 6.53402i | 0.914946 | + | 1.58473i | 0.806980 | + | 0.590578i | \(0.201100\pi\) |
0.107966 | + | 0.994155i | \(0.465566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.11872 | − | 3.53264i | −1.40373 | − | 0.810444i | −0.408957 | − | 0.912553i | \(-0.634108\pi\) |
−0.994773 | + | 0.102109i | \(0.967441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.485543 | − | 4.55678i | 0.105954 | − | 0.994371i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.83006 | + | 1.63394i | 0.590109 | + | 0.340699i | 0.765141 | − | 0.643863i | \(-0.222669\pi\) |
−0.175032 | + | 0.984563i | \(0.556003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.37458 | − | 3.95123i | 0.649439 | − | 0.760414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.48504i | − | 0.461460i | −0.973018 | − | 0.230730i | \(-0.925889\pi\) | ||
0.973018 | − | 0.230730i | \(-0.0741114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.84372 | + | 3.95123i | −1.22917 | + | 0.709661i | −0.966856 | − | 0.255322i | \(-0.917819\pi\) |
−0.262313 | + | 0.964983i | \(0.584485\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00336 | − | 0.961106i | −0.696896 | − | 0.167307i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.15905 | + | 3.73959i | −0.354946 | + | 0.614784i | −0.987109 | − | 0.160051i | \(-0.948834\pi\) |
0.632163 | + | 0.774835i | \(0.282167\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.892024 | − | 0.940005i | 0.142838 | − | 0.150521i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8663 | −1.69703 | −0.848514 | − | 0.529173i | \(-0.822502\pi\) | ||||
−0.848514 | + | 0.529173i | \(0.822502\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.03200 | −0.462375 | −0.231188 | − | 0.972909i | \(-0.574261\pi\) | ||||
−0.231188 | + | 0.972909i | \(0.574261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22790 | + | 5.59088i | −0.470837 | + | 0.815514i | −0.999444 | − | 0.0333530i | \(-0.989381\pi\) |
0.528606 | + | 0.848867i | \(0.322715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.83117 | + | 6.75624i | −0.261596 | + | 0.965178i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05062 | − | 12.7070i | 0.427173 | − | 1.77933i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0935472 | − | 0.0540095i | 0.0128497 | − | 0.00741878i | −0.493561 | − | 0.869711i | \(-0.664305\pi\) |
0.506411 | + | 0.862292i | \(0.330972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.47567 | + | 11.7335i | 0.460363 | + | 1.55414i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.60248 | + | 11.4358i | 0.859570 | + | 1.48882i | 0.872340 | + | 0.488900i | \(0.162602\pi\) |
−0.0127699 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90005 | + | 3.98375i | 0.883461 | + | 0.510067i | 0.871798 | − | 0.489865i | \(-0.162954\pi\) |
0.0116632 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.04290 | + | 5.14620i | −0.761334 | + | 0.648360i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.94367 | − | 5.09859i | −0.359627 | − | 0.622892i | 0.628272 | − | 0.777994i | \(-0.283763\pi\) |
−0.987898 | + | 0.155102i | \(0.950429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60758 | − | 5.42703i | −0.193530 | − | 0.653338i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.9589i | − | 1.65662i | −0.560273 | − | 0.828308i | \(-0.689304\pi\) | ||
0.560273 | − | 0.828308i | \(-0.310696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.35221 | + | 0.780701i | −0.158265 | + | 0.0913742i | −0.577041 | − | 0.816715i | \(-0.695793\pi\) |
0.418776 | + | 0.908090i | \(0.362459\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.80681 | + | 2.41505i | 0.661747 | + | 0.275220i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.27644 | + | 2.21086i | −0.143611 | + | 0.248742i | −0.928854 | − | 0.370446i | \(-0.879205\pi\) |
0.785243 | + | 0.619188i | \(0.212538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.95068 | + | 0.940900i | −0.994520 | + | 0.104544i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.901948 | 0.0990016 | 0.0495008 | − | 0.998774i | \(-0.484237\pi\) | ||||
0.0495008 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.96281 | + | 3.12218i | −0.317647 | + | 0.334732i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.43223 | − | 4.21274i | 0.257816 | − | 0.446550i | −0.707841 | − | 0.706372i | \(-0.750331\pi\) |
0.965656 | + | 0.259822i | \(0.0836640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.57217 | + | 1.20278i | −0.164808 | + | 0.126086i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.3093 | + | 3.19522i | 1.38011 | + | 0.331329i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9183i | 1.31166i | 0.754909 | + | 0.655829i | \(0.227681\pi\) | ||||
−0.754909 | + | 0.655829i | \(0.772319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.88390 | + | 5.98057i | 0.390346 | + | 0.601070i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.56718 | − | 2.71443i | −0.155940 | − | 0.270096i | 0.777461 | − | 0.628931i | \(-0.216507\pi\) |
−0.933401 | + | 0.358835i | \(0.883174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6667 | + | 7.89048i | 1.34662 | + | 0.777472i | 0.987769 | − | 0.155922i | \(-0.0498349\pi\) |
0.358852 | + | 0.933394i | \(0.383168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9952 | + | 6.92544i | 1.15962 | + | 0.669508i | 0.951213 | − | 0.308534i | \(-0.0998385\pi\) |
0.208408 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.863166 | + | 1.49505i | 0.0826763 | + | 0.143200i | 0.904399 | − | 0.426688i | \(-0.140320\pi\) |
−0.821722 | + | 0.569888i | \(0.806987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.17117 | − | 2.12423i | 0.680657 | − | 0.201623i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.93811i | 0.464539i | 0.972652 | + | 0.232269i | \(0.0746151\pi\) | ||||
−0.972652 | + | 0.232269i | \(0.925385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.24146 | + | 0.117488i | −0.207223 | + | 0.0108618i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.66554 | + | 18.4313i | −0.702699 | + | 1.68959i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.67489 | + | 4.63305i | −0.243172 | + | 0.421186i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.6523 | + | 12.9554i | 1.23099 | + | 1.16815i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.9416 | −1.41458 | −0.707292 | − | 0.706921i | \(-0.750083\pi\) | ||||
−0.707292 | + | 0.706921i | \(0.750083\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.80937 | + | 3.61493i | 0.335396 | + | 0.318277i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.17025 | − | 7.22309i | 0.364357 | − | 0.631084i | −0.624316 | − | 0.781172i | \(-0.714622\pi\) |
0.988673 | + | 0.150087i | \(0.0479555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41328 | − | 18.5366i | −0.209258 | − | 1.60732i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.94718 | + | 4.01096i | −0.593537 | + | 0.342679i | −0.766495 | − | 0.642250i | \(-0.778001\pi\) |
0.172958 | + | 0.984929i | \(0.444668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.61654i | 0.391570i | 0.980647 | + | 0.195785i | \(0.0627254\pi\) | ||||
−0.980647 | + | 0.195785i | \(0.937275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7213 | − | 3.17584i | 0.902895 | − | 0.267454i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.889218 | + | 1.54017i | 0.0743601 | + | 0.128796i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.3559 | − | 6.30525i | 0.854137 | − | 0.520048i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6215 | + | 9.01906i | 1.27976 | + | 0.738870i | 0.976804 | − | 0.214134i | \(-0.0686931\pi\) |
0.302956 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.12850 | + | 3.68667i | 0.173215 | + | 0.300017i | 0.939542 | − | 0.342434i | \(-0.111251\pi\) |
−0.766327 | + | 0.642451i | \(0.777918\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.9828 | + | 12.3278i | −1.53467 | + | 0.996643i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4250 | + | 8.32830i | −1.15124 | + | 0.664671i | −0.949190 | − | 0.314703i | \(-0.898095\pi\) |
−0.202054 | + | 0.979374i | \(0.564762\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.181925 | − | 0.0436756i | −0.0144276 | − | 0.00346370i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.11620 | + | 8.57363i | 0.0879690 | + | 0.675697i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.07999 | − | 13.9950i | 0.632874 | − | 1.09617i | −0.354087 | − | 0.935212i | \(-0.615208\pi\) |
0.986961 | − | 0.160957i | \(-0.0514582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4029 | 1.34668 | 0.673338 | − | 0.739335i | \(-0.264860\pi\) | ||||
0.673338 | + | 0.739335i | \(0.264860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4402 | 0.956941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.62257 | − | 18.8857i | 0.735856 | − | 1.44423i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.83038 | + | 17.0267i | −0.747390 | + | 1.29452i | 0.201680 | + | 0.979451i | \(0.435360\pi\) |
−0.949070 | + | 0.315066i | \(0.897973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.33920 | − | 22.2397i | 0.401318 | − | 1.67164i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.84722 | − | 3.37589i | 0.437042 | − | 0.252326i | −0.265300 | − | 0.964166i | \(-0.585471\pi\) |
0.702342 | + | 0.711840i | \(0.252138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.71256i | 0.573270i | 0.958040 | + | 0.286635i | \(0.0925367\pi\) | ||||
−0.958040 | + | 0.286635i | \(0.907463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.91950 | − | 13.2318i | −0.289737 | − | 0.978123i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5315 | + | 8.96711i | 1.13577 | + | 0.655740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7278 | + | 0.739073i | 0.998554 | + | 0.0537597i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7009 | + | 7.33284i | 0.919001 | + | 0.530586i | 0.883316 | − | 0.468777i | \(-0.155305\pi\) |
0.0356850 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.32299 | − | 9.21969i | −0.383157 | − | 0.663648i | 0.608354 | − | 0.793666i | \(-0.291830\pi\) |
−0.991512 | + | 0.130018i | \(0.958497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.53462i | 0.536820i | 0.963305 | + | 0.268410i | \(0.0864982\pi\) | ||||
−0.963305 | + | 0.268410i | \(0.913502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.993782 | − | 0.573760i | 0.0704473 | − | 0.0406728i | −0.464363 | − | 0.885645i | \(-0.653717\pi\) |
0.534810 | + | 0.844972i | \(0.320383\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.38044 | + | 9.91544i | −0.167904 | + | 0.699381i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.22188 | − | 3.99497i | 0.366504 | − | 0.280392i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.45068 | + | 8.73513i | −0.309344 | + | 0.607133i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7943 | −1.16169 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1248 | −0.765862 | −0.382931 | − | 0.923777i | \(-0.625085\pi\) | ||||
−0.382931 | + | 0.923777i | \(0.625085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.6426 | + | 17.5378i | −1.14033 | + | 1.20167i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.3049 | − | 8.02888i | −1.31050 | − | 0.545036i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.62971 | + | 0.631326i | 0.177699 | + | 0.0426610i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.88862 | + | 2.82245i | −0.328844 | + | 0.189858i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.6904i | − | 0.715883i | −0.933744 | − | 0.357942i | \(-0.883479\pi\) | ||
0.933744 | − | 0.357942i | \(-0.116521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.69603 | − | 11.5979i | −0.444431 | − | 0.769777i | 0.553581 | − | 0.832795i | \(-0.313261\pi\) |
−0.998012 | + | 0.0630180i | \(0.979927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.32905 | + | 4.80878i | 0.550399 | + | 0.317773i | 0.749283 | − | 0.662250i | \(-0.230398\pi\) |
−0.198884 | + | 0.980023i | \(0.563732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.41626 | − | 9.95747i | −0.290568 | − | 0.655153i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.5481 | + | 10.7087i | 1.21512 | + | 0.701552i | 0.963871 | − | 0.266369i | \(-0.0858240\pi\) |
0.251253 | + | 0.967921i | \(0.419157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.23964 | − | 1.25586i | 0.275394 | − | 0.0815766i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.2806i | − | 1.63527i | −0.575738 | − | 0.817634i | \(-0.695285\pi\) | ||
0.575738 | − | 0.817634i | \(-0.304715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7291 | + | 11.3906i | −1.27086 | + | 0.733733i | −0.975150 | − | 0.221543i | \(-0.928891\pi\) |
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3673 | + | 9.48940i | 0.793366 | + | 0.608746i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.64305 | − | 4.57790i | 0.168173 | − | 0.291285i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.13320 | − | 1.07536i | −0.0718135 | − | 0.0681479i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4201 | −1.03643 | −0.518215 | − | 0.855251i | \(-0.673403\pi\) | ||||
−0.518215 | + | 0.855251i | \(0.673403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.76780 | 0.488357 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.92452 | + | 10.2616i | −0.369562 | + | 0.640100i | −0.989497 | − | 0.144553i | \(-0.953825\pi\) |
0.619935 | + | 0.784653i | \(0.287159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3290 | + | 1.47493i | −0.703951 | + | 0.0916474i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.44489 | − | 0.390230i | 0.460827 | − | 0.0241546i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.79507 | − | 2.76844i | 0.295677 | − | 0.170709i | −0.344822 | − | 0.938668i | \(-0.612061\pi\) |
0.640499 | + | 0.767959i | \(0.278727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.07851 | + | 2.39300i | −0.494397 | + | 0.146449i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.504112 | − | 0.873148i | −0.0307363 | − | 0.0532368i | 0.850248 | − | 0.526382i | \(-0.176452\pi\) |
−0.880984 | + | 0.473145i | \(0.843119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.991979 | + | 0.572720i | 0.0602585 | + | 0.0347902i | 0.529827 | − | 0.848106i | \(-0.322257\pi\) |
−0.469568 | + | 0.882896i | \(0.655590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.40929 | + | 0.363274i | 0.206340 | + | 0.0219863i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.66672 | + | 8.08299i | 0.280396 | + | 0.485660i | 0.971482 | − | 0.237112i | \(-0.0762010\pi\) |
−0.691086 | + | 0.722772i | \(0.742868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9121 | − | 19.8826i | −0.773028 | − | 1.19034i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.922818i | − | 0.0550507i | −0.999621 | − | 0.0275253i | \(-0.991237\pi\) | ||
0.999621 | − | 0.0275253i | \(-0.00876270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.54162 | + | 3.77681i | −0.388859 | + | 0.224508i | −0.681666 | − | 0.731664i | \(-0.738744\pi\) |
0.292807 | + | 0.956172i | \(0.405411\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4688 | − | 22.8336i | −1.03115 | − | 1.34783i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.9623 | + | 34.5757i | −1.17425 | + | 2.03386i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4020 | − | 16.2305i | 0.902882 | − | 0.951447i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3909 | −1.24967 | −0.624834 | − | 0.780758i | \(-0.714833\pi\) | ||||
−0.624834 | + | 0.780758i | \(0.714833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.25071 | − | 12.1446i | 0.130599 | − | 0.704698i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.22248 | + | 2.11739i | −0.0706977 | + | 0.122452i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.87427 | − | 6.37122i | −0.280949 | − | 0.367231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.26732 | + | 5.27886i | −0.0728056 | + | 0.303263i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7500i | 0.955972i | 0.878368 | + | 0.477986i | \(0.158633\pi\) | ||||
−0.878368 | + | 0.477986i | \(0.841367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.76322 | − | 26.2078i | −0.441634 | − | 1.49091i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.52577 | − | 4.37477i | −0.143224 | − | 0.248070i | 0.785485 | − | 0.618880i | \(-0.212413\pi\) |
−0.928709 | + | 0.370810i | \(0.879080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9998 | + | 7.50546i | 0.734795 | + | 0.424234i | 0.820174 | − | 0.572115i | \(-0.193877\pi\) |
−0.0853790 | + | 0.996349i | \(0.527210\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.0531 | − | 12.7324i | −1.23863 | − | 0.715121i | −0.269812 | − | 0.962913i | \(-0.586962\pi\) |
−0.968813 | + | 0.247792i | \(0.920295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.95349 | − | 5.11559i | −0.165364 | − | 0.286418i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.81374 | − | 23.0025i | −0.380306 | − | 1.28387i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 53.3065i | − | 2.96605i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.698012 | − | 2.90748i | 0.0386002 | − | 0.160784i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9375 | + | 2.20509i | −0.933794 | + | 0.121571i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.45134 | + | 9.44199i | −0.299633 | + | 0.518979i | −0.976052 | − | 0.217538i | \(-0.930197\pi\) |
0.676419 | + | 0.736517i | \(0.263531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.5424 | − | 5.88104i | −0.632521 | − | 0.322279i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4210 | 1.00345 | 0.501727 | − | 0.865026i | \(-0.332698\pi\) | ||||
0.501727 | + | 0.865026i | \(0.332698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.88751 | − | 6.20420i | 0.319766 | − | 0.336966i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.39213 | + | 16.2677i | −0.508613 | + | 0.880943i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1409 | + | 7.01353i | −0.925522 | + | 0.378695i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.30010 | − | 4.79206i | 0.445573 | − | 0.257252i | −0.260386 | − | 0.965505i | \(-0.583850\pi\) |
0.705959 | + | 0.708253i | \(0.250516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.5601i | − | 0.886441i | −0.896413 | − | 0.443220i | \(-0.853836\pi\) | ||
0.896413 | − | 0.443220i | \(-0.146164\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.95623 | + | 2.52479i | 0.157792 | + | 0.134764i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00574 | − | 15.5984i | −0.479327 | − | 0.830219i | 0.520392 | − | 0.853928i | \(-0.325786\pi\) |
−0.999719 | + | 0.0237089i | \(0.992453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 31.6058 | − | 14.0175i | 1.67275 | − | 0.741887i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.47735 | − | 2.00765i | −0.183527 | − | 0.105960i | 0.405422 | − | 0.914130i | \(-0.367125\pi\) |
−0.588949 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4592 | + | 26.7760i | 0.813640 | + | 1.40927i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.88451 | − | 2.63175i | 0.466316 | − | 0.138131i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.4897 | − | 17.0259i | 1.53935 | − | 0.888744i | 0.540473 | − | 0.841361i | \(-0.318245\pi\) |
0.998877 | − | 0.0473832i | \(-0.0150882\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70635 | − | 32.5542i | −0.0888292 | − | 1.69470i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.263879 | + | 0.109747i | 0.0136999 | + | 0.00569779i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.70705 | − | 11.6169i | 0.347278 | − | 0.601503i | −0.638487 | − | 0.769632i | \(-0.720439\pi\) |
0.985765 | + | 0.168130i | \(0.0537728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.85925 | 0.0957564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3945 | −0.790764 | −0.395382 | − | 0.918517i | \(-0.629388\pi\) | ||||
−0.395382 | + | 0.918517i | \(0.629388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0288 | + | 19.0065i | 1.02611 | + | 0.973731i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2065 | − | 21.1422i | 0.623722 | − | 1.08032i | −0.365065 | − | 0.930982i | \(-0.618953\pi\) |
0.988787 | − | 0.149336i | \(-0.0477135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.476120 | − | 9.08352i | −0.0242026 | − | 0.461741i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.1938 | − | 17.4324i | 1.53089 | − | 0.883857i | 0.531564 | − | 0.847018i | \(-0.321604\pi\) |
0.999321 | − | 0.0368391i | \(-0.0117289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.6556i | 1.24689i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8513 | + | 4.10299i | −0.698704 | + | 0.206969i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5083 | − | 11.2631i | −0.979095 | − | 0.565281i | −0.0770980 | − | 0.997024i | \(-0.524565\pi\) |
−0.901997 | + | 0.431743i | \(0.857899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.0684 | + | 26.1664i | −0.954614 | + | 1.30996i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8774 | + | 9.16683i | 0.792881 | + | 0.457770i | 0.840976 | − | 0.541073i | \(-0.181982\pi\) |
−0.0480950 | + | 0.998843i | \(0.515315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.95623 | − | 5.12033i | −0.147260 | − | 0.255062i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2642i | 0.508778i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.37130 | − | 5.41052i | 0.463381 | − | 0.267533i | −0.250084 | − | 0.968224i | \(-0.580458\pi\) |
0.713465 | + | 0.700691i | \(0.247125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5105 | + | 3.24352i | 0.666422 | + | 0.159991i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4162 | + | 32.2584i | −0.660169 | + | 1.58733i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.50412 | − | 5.80018i | 0.269538 | − | 0.284036i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.1164 | −1.66670 | −0.833348 | − | 0.552749i | \(-0.813579\pi\) | ||||
−0.833348 | + | 0.552749i | \(0.813579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9892 | −1.46158 | −0.730792 | − | 0.682600i | \(-0.760849\pi\) | ||||
−0.730792 | + | 0.682600i | \(0.760849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.2565 | − | 8.79247i | −0.839042 | − | 0.427505i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.72144 | + | 20.9036i | 0.131700 | + | 1.01160i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.719079 | − | 2.99523i | 0.0347175 | − | 0.144611i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.6954 | − | 18.8767i | 1.57488 | − | 0.909258i | 0.579324 | − | 0.815097i | \(-0.303316\pi\) |
0.995557 | − | 0.0941612i | \(-0.0300169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.221375i | 0.0106386i | 0.999986 | + | 0.00531930i | \(0.00169319\pi\) | ||||
−0.999986 | + | 0.00531930i | \(0.998307\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.5442 | − | 19.9952i | −0.552236 | − | 0.956501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5292 | − | 7.23374i | −0.597987 | − | 0.345248i | 0.170262 | − | 0.985399i | \(-0.445538\pi\) |
−0.768249 | + | 0.640151i | \(0.778872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5285 | − | 4.42503i | −0.977547 | − | 0.210716i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.61783 | + | 5.55285i | 0.456957 | + | 0.263824i | 0.710764 | − | 0.703431i | \(-0.248349\pi\) |
−0.253807 | + | 0.967255i | \(0.581683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.87359 | − | 29.9563i | −0.419707 | − | 1.41688i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.1416i | − | 1.46966i | −0.678250 | − | 0.734831i | \(-0.737261\pi\) | ||
0.678250 | − | 0.734831i | \(-0.262739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.3689 | + | 12.9147i | −1.05331 | + | 0.608128i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.72124 | − | 7.16962i | 0.0808711 | − | 0.336858i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.47844 | + | 16.4171i | −0.443383 | + | 0.767962i | −0.997938 | − | 0.0641853i | \(-0.979555\pi\) |
0.554555 | + | 0.832147i | \(0.312888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 38.5477 | + | 7.14392i | 1.79925 | + | 0.333450i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1960 | 0.707746 | 0.353873 | − | 0.935293i | \(-0.384864\pi\) | ||||
0.353873 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.3400 | 1.36355 | 0.681773 | − | 0.731564i | \(-0.261209\pi\) | ||||
0.681773 | + | 0.731564i | \(0.261209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.39365 | − | 14.5382i | 0.388412 | − | 0.672749i | −0.603824 | − | 0.797117i | \(-0.706357\pi\) |
0.992236 | + | 0.124369i | \(0.0396905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.98153 | − | 14.3822i | 0.276201 | − | 0.664107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.0530 | + | 6.73481i | 1.29261 | + | 0.310324i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24154 | + | 3.60356i | −0.286986 | + | 0.165692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.176496 | + | 0.271776i | 0.00808121 | + | 0.0124438i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.07579 | − | 1.86333i | −0.0491542 | − | 0.0851376i | 0.840401 | − | 0.541964i | \(-0.182319\pi\) |
−0.889556 | + | 0.456827i | \(0.848986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.79788 | − | 1.61536i | −0.127572 | − | 0.0736540i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.81961 | − | 12.1026i | 0.401306 | − | 0.550689i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.74460 | − | 3.02174i | −0.0790555 | − | 0.136928i | 0.823787 | − | 0.566899i | \(-0.191857\pi\) |
−0.902843 | + | 0.429971i | \(0.858524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.8373 | + | 7.94967i | −1.21362 | + | 0.359497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1361i | 1.17950i | 0.807584 | + | 0.589752i | \(0.200775\pi\) | ||||
−0.807584 | + | 0.589752i | \(0.799225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.2373 | − | 9.37460i | 0.731290 | − | 0.422211i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.3322 | − | 22.4405i | 1.31573 | − | 1.00659i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15545 | + | 12.3936i | −0.320322 | + | 0.554814i | −0.980554 | − | 0.196247i | \(-0.937124\pi\) |
0.660232 | + | 0.751061i | \(0.270458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.8648 | − | 20.7488i | −0.976848 | − | 0.926987i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.3226 | −1.75331 | −0.876653 | − | 0.481123i | \(-0.840229\pi\) | ||||
−0.876653 | + | 0.481123i | \(0.840229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.6298 | − | 14.8320i | −0.694143 | − | 0.658712i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4284 | − | 30.1868i | 0.772498 | − | 1.33801i | −0.163692 | − | 0.986512i | \(-0.552340\pi\) |
0.936190 | − | 0.351495i | \(-0.114326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81435 | − | 1.58638i | −0.168737 | − | 0.0701774i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.6064 | + | 12.2552i | −1.52791 | + | 0.541082i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3455i | 0.674896i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.6511 | − | 9.67183i | 1.43322 | − | 0.424546i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.3030 | + | 21.3094i | 0.539005 | + | 0.933584i | 0.998958 | + | 0.0456406i | \(0.0145329\pi\) |
−0.459953 | + | 0.887943i | \(0.652134\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.9603 | − | 13.8335i | −1.04771 | − | 0.604897i | −0.125704 | − | 0.992068i | \(-0.540119\pi\) |
−0.922008 | + | 0.387171i | \(0.873452\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.6348 | − | 29.8114i | −2.24925 | − | 1.29860i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.16050 | − | 10.6703i | −0.267848 | − | 0.463926i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.2237 | + | 21.5761i | −1.44178 | + | 0.936322i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.12993i | − | 0.352146i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.3713 | − | 2.72997i | −0.490709 | − | 0.117807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.26029 | + | 16.0845i | 0.183504 | + | 0.692808i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.90334 | − | 13.6890i | 0.339791 | − | 0.588536i | −0.644602 | − | 0.764518i | \(-0.722977\pi\) |
0.984393 | + | 0.175983i | \(0.0563103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.19537 | − | 9.68998i | 0.394611 | − | 0.415837i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.9288 | −0.595553 | −0.297776 | − | 0.954636i | \(-0.596245\pi\) | ||||
−0.297776 | + | 0.954636i | \(0.596245\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8513 | + | 21.2974i | −0.463123 | + | 0.908949i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.77875 | + | 15.2052i | −0.373987 | + | 0.647765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.69778 | + | 0.871984i | −0.284818 | + | 0.0370805i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.9559 | + | 17.2950i | −1.26927 | + | 0.732814i | −0.974850 | − | 0.222862i | \(-0.928460\pi\) |
−0.294421 | + | 0.955676i | \(0.595127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.26848i | − | 0.0959464i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.82248 | − | 29.7838i | −0.372485 | − | 1.25747i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.4793 | + | 25.0789i | 0.610229 | + | 1.05695i | 0.991202 | + | 0.132361i | \(0.0422560\pi\) |
−0.380972 | + | 0.924586i | \(0.624411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.3664 | − | 17.2957i | −0.687323 | − | 0.726352i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.1544 | + | 5.86266i | 0.425696 | + | 0.245775i | 0.697511 | − | 0.716574i | \(-0.254291\pi\) |
−0.271816 | + | 0.962349i | \(0.587624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5541 | + | 30.4045i | 0.734614 | + | 1.27239i | 0.954892 | + | 0.296952i | \(0.0959703\pi\) |
−0.220278 | + | 0.975437i | \(0.570696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.21457 | − | 24.3556i | −0.301393 | − | 1.01747i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3937 | − | 10.0423i | 0.724110 | − | 0.418065i | −0.0921536 | − | 0.995745i | \(-0.529375\pi\) |
0.816263 | + | 0.577680i | \(0.196042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.30452 | + | 17.9299i | −0.178890 | + | 0.745142i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.44998 | + | 1.89529i | 0.0601554 | + | 0.0786298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.128382 | − | 0.222363i | 0.00531702 | − | 0.00920935i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.7111 | 1.35013 | 0.675066 | − | 0.737757i | \(-0.264115\pi\) | ||||
0.675066 | + | 0.737757i | \(0.264115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.8331 | 2.30056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.98323 | − | 9.46643i | 0.369521 | − | 0.389397i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.23240 | − | 3.86664i | 0.0916738 | − | 0.158784i | −0.816542 | − | 0.577286i | \(-0.804112\pi\) |
0.908216 | + | 0.418503i | \(0.137445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.93265 | − | 0.463980i | −0.0790981 | − | 0.0189894i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6126 | + | 18.2515i | −1.29165 | + | 0.745737i | −0.978947 | − | 0.204112i | \(-0.934569\pi\) |
−0.312707 | + | 0.949850i | \(0.601236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.4566i | − | 1.32393i | −0.749534 | − | 0.661966i | \(-0.769722\pi\) | ||
0.749534 | − | 0.661966i | \(-0.230278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8125 | − | 9.61955i | 0.603213 | − | 0.391738i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1187 | + | 10.4608i | 0.735416 | + | 0.424593i | 0.820400 | − | 0.571790i | \(-0.193751\pi\) |
−0.0849841 | + | 0.996382i | \(0.527084\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.3238 | − | 1.20659i | −0.458862 | − | 0.0488936i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.18298 | − | 2.41505i | −0.169225 | − | 0.0977023i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4442 | + | 33.6783i | 0.785343 | + | 1.36025i | 0.928794 | + | 0.370596i | \(0.120847\pi\) |
−0.143451 | + | 0.989657i | \(0.545820\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.8874i | 0.518828i | 0.965766 | + | 0.259414i | \(0.0835294\pi\) | ||||
−0.965766 | + | 0.259414i | \(0.916471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.89767 | − | 5.13707i | 0.357628 | − | 0.206476i | −0.310412 | − | 0.950602i | \(-0.600467\pi\) |
0.668040 | + | 0.744126i | \(0.267134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0063 | − | 5.66836i | 0.642312 | − | 0.227463i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7624 | − | 1.66154i | 0.511316 | − | 0.0665683i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.1002 | + | 20.0232i | 0.842661 | + | 0.799649i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.5794 | −1.29902 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.9308 | 1.78866 | 0.894332 | − | 0.447403i | \(-0.147651\pi\) | ||||
0.894332 | + | 0.447403i | \(0.147651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9771 | + | 13.2636i | 0.555538 | + | 0.527182i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.05488 | − | 1.37004i | −0.200282 | − | 0.0542831i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 41.8193 | − | 2.19199i | 1.65435 | − | 0.0867139i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7953 | + | 19.5118i | −1.33484 | + | 0.770668i | −0.986036 | − | 0.166529i | \(-0.946744\pi\) |
−0.348799 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2206i | 0.481932i | 0.970534 | + | 0.240966i | \(0.0774642\pi\) | ||||
−0.970534 | + | 0.240966i | \(0.922536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.43406 | − | 14.6082i | −0.331577 | − | 0.574308i | 0.651244 | − | 0.758868i | \(-0.274247\pi\) |
−0.982821 | + | 0.184560i | \(0.940914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1832 | + | 15.6942i | 1.06703 | + | 0.616052i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.6819 | + | 33.1038i | 0.575431 | + | 1.29744i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.7980 | + | 10.8531i | 0.735624 | + | 0.424713i | 0.820476 | − | 0.571681i | \(-0.193708\pi\) |
−0.0848520 | + | 0.996394i | \(0.527042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.55123 | − | 3.92849i | −0.0995331 | − | 0.153265i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.3752i | − | 1.41698i | −0.705722 | − | 0.708489i | \(-0.749377\pi\) | ||
0.705722 | − | 0.708489i | \(-0.250623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9940 | − | 7.50207i | 0.505407 | − | 0.291797i | −0.225537 | − | 0.974235i | \(-0.572414\pi\) |
0.730944 | + | 0.682438i | \(0.239080\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.50710 | + | 2.28241i | 0.369225 | + | 0.0886416i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.06039 | − | 7.03281i | 0.157219 | − | 0.272311i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.7458 | + | 13.4313i | −0.492779 | + | 0.519285i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.9389 | 0.731127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.119232 | 0.00459606 | 0.00229803 | − | 0.999997i | \(-0.499269\pi\) | ||||
0.00229803 | + | 0.999997i | \(0.499269\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.9293 | − | 20.6622i | 0.458482 | − | 0.794114i | −0.540399 | − | 0.841409i | \(-0.681727\pi\) |
0.998881 | + | 0.0472948i | \(0.0150600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.1457 | + | 20.7677i | −1.04176 | + | 0.796990i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.41484 | + | 22.5548i | −0.207497 | + | 0.864304i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.3022 | − | 14.6082i | 0.968161 | − | 0.558968i | 0.0694856 | − | 0.997583i | \(-0.477864\pi\) |
0.898675 | + | 0.438615i | \(0.144531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.73122 | − | 15.9721i | −0.180507 | − | 0.609374i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0404088 | + | 0.0699901i | 0.00153945 | + | 0.00266641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.0356 | − | 20.8052i | −1.37086 | − | 0.791465i | −0.379822 | − | 0.925059i | \(-0.624015\pi\) |
−0.991036 | + | 0.133594i | \(0.957348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.32335 | + | 17.7758i | −0.240204 | + | 0.675246i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.9922 | − | 71.0005i | −1.55269 | − | 2.68934i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5360 | − | 35.5685i | −0.398509 | − | 1.34532i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.6976i | − | 0.555122i | −0.960708 | − | 0.277561i | \(-0.910474\pi\) | ||
0.960708 | − | 0.277561i | \(-0.0895261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.4213 | − | 15.2543i | 0.996497 | − | 0.575328i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.18450 | − | 7.65690i | 0.119765 | − | 0.287967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.6403 | − | 32.2859i | 0.700050 | − | 1.21252i | −0.268398 | − | 0.963308i | \(-0.586494\pi\) |
0.968448 | − | 0.249214i | \(-0.0801723\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.82394 | − | 3.47690i | −0.255918 | − | 0.130394i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.8242 | −0.967125 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.1411 | + | 31.7624i | −1.12564 | + | 1.18619i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8612 | + | 27.4724i | −0.591522 | + | 1.02455i | 0.402505 | + | 0.915418i | \(0.368139\pi\) |
−0.994028 | + | 0.109129i | \(0.965194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.39027 | + | 41.4031i | 0.200744 | + | 1.54193i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 38.3680 | + | 9.21118i | 1.42692 | + | 0.342568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3126i | 1.12423i | 0.827058 | + | 0.562117i | \(0.190013\pi\) | ||||
−0.827058 | + | 0.562117i | \(0.809987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.22437 | − | 26.6675i | −0.156458 | − | 0.987685i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.4380 | − | 19.8111i | −0.423048 | − | 0.732741i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.06661 | + | 1.19316i | 0.0763321 | + | 0.0440703i | 0.537680 | − | 0.843149i | \(-0.319301\pi\) |
−0.461348 | + | 0.887219i | \(0.652634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.1194 | − | 6.99716i | −0.446425 | − | 0.257744i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.29721 | + | 3.97889i | 0.0845043 | + | 0.146366i | 0.905180 | − | 0.425029i | \(-0.139736\pi\) |
−0.820676 | + | 0.571394i | \(0.806403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.77875 | + | 2.60042i | −0.322496 | + | 0.0955289i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12.5047i | − | 0.458753i | −0.973338 | − | 0.229376i | \(-0.926331\pi\) | ||
0.973338 | − | 0.229376i | \(-0.0736687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.141635 | + | 2.70213i | 0.00518214 | + | 0.0988659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.73102 | + | 36.3393i | 0.172868 | + | 1.32781i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3708 | + | 30.0872i | −0.633871 | + | 1.09790i | 0.352883 | + | 0.935668i | \(0.385202\pi\) |
−0.986753 | + | 0.162229i | \(0.948132\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.6301 | + | 19.5771i | 0.751802 | + | 0.713428i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5066 | −0.527250 | −0.263625 | − | 0.964625i | \(-0.584918\pi\) | ||||
−0.263625 | + | 0.964625i | \(0.584918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.75938 | − | 9.26123i | −0.354243 | − | 0.336161i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.2457 | − | 35.0666i | 0.733906 | − | 1.27116i | −0.221296 | − | 0.975207i | \(-0.571029\pi\) |
0.955202 | − | 0.295955i | \(-0.0956379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.75395 | + | 4.21725i | −0.0634973 | + | 0.152675i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.55606 | + | 4.93984i | −0.308941 | + | 0.178367i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6907i | 1.43128i | 0.698468 | + | 0.715641i | \(0.253865\pi\) | ||||
−0.698468 | + | 0.715641i | \(0.746135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6780 | − | 5.82897i | 0.708685 | − | 0.209925i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.83006 | + | 4.90181i | 0.101790 | + | 0.176306i | 0.912422 | − | 0.409250i | \(-0.134210\pi\) |
−0.810632 | + | 0.585556i | \(0.800876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.9922 | + | 11.6541i | 0.573715 | + | 0.418087i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 66.4877 | + | 38.3867i | 2.38217 | + | 1.37535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5903 | − | 28.7352i | −0.593647 | − | 1.02823i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.81894 | − | 8.38596i | −0.350900 | − | 0.299690i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.76237 | − | 1.59485i | 0.0984677 | − | 0.0568504i | −0.449958 | − | 0.893050i | \(-0.648561\pi\) |
0.548425 | + | 0.836200i | \(0.315228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.32518 | − | 2.23874i | −0.331985 | − | 0.0797012i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3766 | + | 7.93857i | −0.368949 | + | 0.282263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.98056 | + | 5.16248i | −0.105843 | + | 0.183325i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.7853 | 0.665410 | 0.332705 | − | 0.943031i | \(-0.392039\pi\) | ||||
0.332705 | + | 0.943031i | \(0.392039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.7079 | −1.72316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.0028 | + | 6.62514i | 0.459433 | + | 0.234088i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.85574 | + | 3.21424i | −0.0654877 | + | 0.113428i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.407658 | + | 1.69805i | −0.0143502 | + | 0.0597741i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5995 | − | 14.2025i | 0.864873 | − | 0.499335i | −0.000767968 | − | 1.00000i | \(-0.500244\pi\) |
0.865641 | + | 0.500665i | \(0.166911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.9628i | − | 1.64909i | −0.565799 | − | 0.824543i | \(-0.691432\pi\) | ||
0.565799 | − | 0.824543i | \(-0.308568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.563482 | − | 1.90226i | −0.0197622 | − | 0.0667151i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5519 | + | 10.7110i | 0.649050 | + | 0.374729i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.85028 | − | 4.52117i | −0.134540 | − | 0.157983i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.9019 | − | 9.75831i | −0.589880 | − | 0.340567i | 0.175170 | − | 0.984538i | \(-0.443952\pi\) |
−0.765050 | + | 0.643971i | \(0.777286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5304 | − | 21.7033i | −0.436782 | − | 0.756529i | 0.560657 | − | 0.828048i | \(-0.310549\pi\) |
−0.997439 | + | 0.0715193i | \(0.977215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.2141i | 1.39838i | 0.714935 | + | 0.699191i | \(0.246456\pi\) | ||||
−0.714935 | + | 0.699191i | \(0.753544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.52711 | − | 3.19108i | 0.191964 | − | 0.110831i | −0.400937 | − | 0.916105i | \(-0.631316\pi\) |
0.592902 | + | 0.805275i | \(0.297982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.77381 | − | 15.7193i | 0.130912 | − | 0.545297i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −51.0534 | + | 13.5225i | −1.76889 | + | 0.468526i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.48253 | + | 40.3748i | −0.258634 | + | 1.39556i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.2513 | −0.526534 | −0.263267 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263267 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8246 | 0.787055 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.10024 | + | 1.15942i | −0.0378942 | + | 0.0399325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0358 | + | 1.82732i | −0.482274 | + | 0.0627873i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.7218 | + | 3.05417i | 0.436610 | + | 0.104819i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.2205 | + | 7.05551i | −0.418913 | + | 0.241860i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.7815i | − | 0.574586i | −0.957843 | − | 0.287293i | \(-0.907245\pi\) | ||
0.957843 | − | 0.287293i | \(-0.0927554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.68551 | + | 16.7758i | 0.330851 | + | 0.573050i | 0.982679 | − | 0.185317i | \(-0.0593311\pi\) |
−0.651828 | + | 0.758367i | \(0.725998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4714 | + | 24.5208i | 1.44910 | + | 0.836641i | 0.998428 | − | 0.0560471i | \(-0.0178497\pi\) |
0.450676 | + | 0.892688i | \(0.351183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.27605 | + | 49.5153i | −0.179807 | + | 1.68748i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.4609 | − | 11.2358i | −0.662458 | − | 0.382470i | 0.130755 | − | 0.991415i | \(-0.458260\pi\) |
−0.793213 | + | 0.608944i | \(0.791593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66.3036 | − | 19.6403i | 2.25179 | − | 0.667020i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.06826i | 0.205851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.81466 | − | 2.20239i | 0.129255 | − | 0.0746253i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.7019 | + | 2.02859i | −1.30986 | + | 0.0686574i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5087 | − | 26.8618i | 0.523691 | − | 0.907059i | −0.475929 | − | 0.879484i | \(-0.657888\pi\) |
0.999620 | − | 0.0275755i | \(-0.00877866\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.8753 | + | 25.5035i | 0.906480 | + | 0.860211i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.8713 | −0.736864 | −0.368432 | − | 0.929655i | \(-0.620105\pi\) | ||||
−0.368432 | + | 0.929655i | \(0.620105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.3430 | −1.15573 | −0.577867 | − | 0.816131i | \(-0.696115\pi\) | ||||
−0.577867 | + | 0.816131i | \(0.696115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9903 | + | 48.4807i | −0.939824 | + | 1.62782i | −0.174027 | + | 0.984741i | \(0.555678\pi\) |
−0.765797 | + | 0.643082i | \(0.777655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.6278 | − | 33.4985i | −0.859530 | − | 1.12350i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.3072 | + | 12.5749i | −0.579814 | + | 0.421274i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.5012 | − | 22.8060i | 1.32186 | − | 0.763175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.06039 | − | 1.20276i | 0.135573 | − | 0.0401590i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.81894 | + | 17.0069i | 0.327480 | + | 0.567212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.705799 | + | 0.407493i | 0.0235136 | + | 0.0135756i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.47217 | + | 13.8161i | −0.0489906 | + | 0.459773i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.494450 | − | 0.856413i | −0.0164180 | − | 0.0284367i | 0.857700 | − | 0.514151i | \(-0.171893\pi\) |
−0.874118 | + | 0.485714i | \(0.838560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.88602 | − | 5.12133i | 0.261563 | − | 0.169864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.5096i | − | 0.944567i | −0.881447 | − | 0.472283i | \(-0.843430\pi\) | ||
0.881447 | − | 0.472283i | \(-0.156570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.85671 | − | 1.07197i | 0.0614482 | − | 0.0354771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8822 | − | 2.84885i | 0.722615 | − | 0.0940774i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.40350 | − | 2.43093i | 0.0462971 | − | 0.0801889i | −0.841948 | − | 0.539558i | \(-0.818591\pi\) |
0.888245 | + | 0.459369i | \(0.151925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.9703 | − | 21.0445i | 0.658045 | − | 0.693440i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4438 | 0.343761 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.4929 | + | 42.1830i | −0.705919 | + | 1.38547i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.57702 | − | 11.3917i | 0.215785 | − | 0.373751i | −0.737730 | − | 0.675096i | \(-0.764102\pi\) |
0.953515 | + | 0.301345i | \(0.0974356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0718 | − | 34.8707i | 1.14943 | − | 1.14284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.04251 | + | 8.50780i | −0.0668686 | + | 0.278533i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2219i | 0.660622i | 0.943872 | + | 0.330311i | \(0.107154\pi\) | ||||
−0.943872 | + | 0.330311i | \(0.892846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.38441 | − | 24.9290i | −0.240981 | − | 0.813527i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.8119 | + | 39.5113i | 0.743646 | + | 1.28803i | 0.950825 | + | 0.309729i | \(0.100238\pi\) |
−0.207179 | + | 0.978303i | \(0.566428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.7523 | − | 17.7548i | −1.00143 | − | 0.578177i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.7421 | + | 29.2959i | 1.64890 | + | 0.951990i | 0.977512 | + | 0.210880i | \(0.0676329\pi\) |
0.671383 | + | 0.741110i | \(0.265700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.584105 | − | 1.01170i | −0.0189608 | − | 0.0328411i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5270 | + | 42.2898i | 0.406216 | + | 1.37134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.9224i | 0.872101i | 0.899922 | + | 0.436051i | \(0.143623\pi\) | ||||
−0.899922 | + | 0.436051i | \(0.856377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.38838 | + | 9.94851i | −0.0772054 | + | 0.321590i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5967 | − | 8.15025i | −0.632811 | − | 0.263185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7244 | − | 27.2354i | 0.507238 | − | 0.878562i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.8642 | + | 37.0238i | −0.607891 | + | 1.19308i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4008 | 0.559572 | 0.279786 | − | 0.960062i | \(-0.409737\pi\) | ||||
0.279786 | + | 0.960062i | \(0.409737\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −63.5552 | + | 66.9737i | −2.04169 | + | 2.15151i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6200 | − | 21.8585i | 0.404996 | − | 0.701474i | −0.589325 | − | 0.807896i | \(-0.700606\pi\) |
0.994321 | + | 0.106422i | \(0.0339395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.70087 | + | 7.42160i | −0.310996 | + | 0.237926i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.49450 | − | 3.74960i | 0.207778 | − | 0.119960i | −0.392501 | − | 0.919752i | \(-0.628390\pi\) |
0.600278 | + | 0.799791i | \(0.295057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.5629i | − | 0.369552i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.34345 | + | 2.82072i | −0.138676 | + | 0.0900586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9037 | + | 22.3498i | 0.411563 | + | 0.712848i | 0.995061 | − | 0.0992666i | \(-0.0316497\pi\) |
−0.583498 | + | 0.812115i | \(0.698316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.9091 | + | 17.4234i | 0.761036 | + | 0.554594i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.58074 | − | 4.95409i | −0.272852 | − | 0.157531i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4009 | − | 19.7469i | −0.362161 | − | 0.627280i | 0.626156 | − | 0.779698i | \(-0.284627\pi\) |
−0.988316 | + | 0.152418i | \(0.951294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1063 | − | 5.36341i | 0.574586 | − | 0.170203i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2479 | − | 5.91662i | 0.324554 | − | 0.187381i | −0.328867 | − | 0.944376i | \(-0.606667\pi\) |
0.653421 | + | 0.756995i | \(0.273333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.49005 | + | 21.1504i | 0.236975 | + | 0.669170i |
(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.bi.l.1601.2 | yes | 16 | |
3.2 | odd | 2 | inner | 2100.2.bi.l.1601.5 | yes | 16 | |
5.2 | odd | 4 | 2100.2.bo.i.1349.6 | 32 | |||
5.3 | odd | 4 | 2100.2.bo.i.1349.11 | 32 | |||
5.4 | even | 2 | 2100.2.bi.m.1601.7 | yes | 16 | ||
7.3 | odd | 6 | inner | 2100.2.bi.l.101.5 | yes | 16 | |
15.2 | even | 4 | 2100.2.bo.i.1349.16 | 32 | |||
15.8 | even | 4 | 2100.2.bo.i.1349.1 | 32 | |||
15.14 | odd | 2 | 2100.2.bi.m.1601.4 | yes | 16 | ||
21.17 | even | 6 | inner | 2100.2.bi.l.101.2 | ✓ | 16 | |
35.3 | even | 12 | 2100.2.bo.i.1949.16 | 32 | |||
35.17 | even | 12 | 2100.2.bo.i.1949.1 | 32 | |||
35.24 | odd | 6 | 2100.2.bi.m.101.4 | yes | 16 | ||
105.17 | odd | 12 | 2100.2.bo.i.1949.11 | 32 | |||
105.38 | odd | 12 | 2100.2.bo.i.1949.6 | 32 | |||
105.59 | even | 6 | 2100.2.bi.m.101.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.2 | ✓ | 16 | 21.17 | even | 6 | inner | |
2100.2.bi.l.101.5 | yes | 16 | 7.3 | odd | 6 | inner | |
2100.2.bi.l.1601.2 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.bi.l.1601.5 | yes | 16 | 3.2 | odd | 2 | inner | |
2100.2.bi.m.101.4 | yes | 16 | 35.24 | odd | 6 | ||
2100.2.bi.m.101.7 | yes | 16 | 105.59 | even | 6 | ||
2100.2.bi.m.1601.4 | yes | 16 | 15.14 | odd | 2 | ||
2100.2.bi.m.1601.7 | yes | 16 | 5.4 | even | 2 | ||
2100.2.bo.i.1349.1 | 32 | 15.8 | even | 4 | |||
2100.2.bo.i.1349.6 | 32 | 5.2 | odd | 4 | |||
2100.2.bo.i.1349.11 | 32 | 5.3 | odd | 4 | |||
2100.2.bo.i.1349.16 | 32 | 15.2 | even | 4 | |||
2100.2.bo.i.1949.1 | 32 | 35.17 | even | 12 | |||
2100.2.bo.i.1949.6 | 32 | 105.38 | odd | 12 | |||
2100.2.bo.i.1949.11 | 32 | 105.17 | odd | 12 | |||
2100.2.bo.i.1949.16 | 32 | 35.3 | even | 12 |