Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.a (trivial) |
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: | yes |
Analytic conductor: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17009 | 1.53448 | 0.767241 | − | 0.641358i | \(-0.221629\pi\) | ||||
0.767241 | + | 0.641358i | \(0.221629\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.70928 | 1.35464 | ||||||||
\(5\) | −0.630898 | −0.282146 | −0.141073 | − | 0.989999i | \(-0.545055\pi\) | ||||
−0.141073 | + | 0.989999i | \(0.545055\pi\) | |||||||
\(6\) | 2.17009 | 0.885934 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.53919 | 0.544185 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.36910 | −0.432948 | ||||||||
\(11\) | −5.70928 | −1.72141 | −0.860706 | − | 0.509103i | \(-0.829977\pi\) | ||||
−0.860706 | + | 0.509103i | \(0.829977\pi\) | |||||||
\(12\) | 2.70928 | 0.782100 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.17009 | −0.579980 | ||||||||
\(15\) | −0.630898 | −0.162897 | ||||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | −1.07838 | −0.261545 | −0.130773 | − | 0.991412i | \(-0.541746\pi\) | ||||
−0.130773 | + | 0.991412i | \(0.541746\pi\) | |||||||
\(18\) | 2.17009 | 0.511494 | ||||||||
\(19\) | −7.41855 | −1.70193 | −0.850966 | − | 0.525221i | \(-0.823983\pi\) | ||||
−0.850966 | + | 0.525221i | \(0.823983\pi\) | |||||||
\(20\) | −1.70928 | −0.382206 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −12.3896 | −2.64148 | ||||||||
\(23\) | −5.41855 | −1.12985 | −0.564923 | − | 0.825144i | \(-0.691094\pi\) | ||||
−0.564923 | + | 0.825144i | \(0.691094\pi\) | |||||||
\(24\) | 1.53919 | 0.314186 | ||||||||
\(25\) | −4.60197 | −0.920394 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.70928 | −0.512005 | ||||||||
\(29\) | 6.68035 | 1.24051 | 0.620255 | − | 0.784401i | \(-0.287029\pi\) | ||||
0.620255 | + | 0.784401i | \(0.287029\pi\) | |||||||
\(30\) | −1.36910 | −0.249963 | ||||||||
\(31\) | −6.15676 | −1.10579 | −0.552893 | − | 0.833252i | \(-0.686476\pi\) | ||||
−0.552893 | + | 0.833252i | \(0.686476\pi\) | |||||||
\(32\) | −7.58864 | −1.34149 | ||||||||
\(33\) | −5.70928 | −0.993857 | ||||||||
\(34\) | −2.34017 | −0.401336 | ||||||||
\(35\) | 0.630898 | 0.106641 | ||||||||
\(36\) | 2.70928 | 0.451546 | ||||||||
\(37\) | 3.41855 | 0.562006 | 0.281003 | − | 0.959707i | \(-0.409333\pi\) | ||||
0.281003 | + | 0.959707i | \(0.409333\pi\) | |||||||
\(38\) | −16.0989 | −2.61159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.971071 | −0.153540 | ||||||||
\(41\) | −1.21235 | −0.189337 | −0.0946684 | − | 0.995509i | \(-0.530179\pi\) | ||||
−0.0946684 | + | 0.995509i | \(0.530179\pi\) | |||||||
\(42\) | −2.17009 | −0.334852 | ||||||||
\(43\) | 12.6803 | 1.93373 | 0.966867 | − | 0.255279i | \(-0.0821675\pi\) | ||||
0.966867 | + | 0.255279i | \(0.0821675\pi\) | |||||||
\(44\) | −15.4680 | −2.33189 | ||||||||
\(45\) | −0.630898 | −0.0940487 | ||||||||
\(46\) | −11.7587 | −1.73373 | ||||||||
\(47\) | 6.04945 | 0.882403 | 0.441201 | − | 0.897408i | \(-0.354552\pi\) | ||||
0.441201 | + | 0.897408i | \(0.354552\pi\) | |||||||
\(48\) | −2.07838 | −0.299988 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.98667 | −1.41233 | ||||||||
\(51\) | −1.07838 | −0.151003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 2.17009 | 0.295311 | ||||||||
\(55\) | 3.60197 | 0.485689 | ||||||||
\(56\) | −1.53919 | −0.205683 | ||||||||
\(57\) | −7.41855 | −0.982611 | ||||||||
\(58\) | 14.4969 | 1.90354 | ||||||||
\(59\) | −1.36910 | −0.178242 | −0.0891210 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891210 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(60\) | −1.70928 | −0.220667 | ||||||||
\(61\) | 12.6537 | 1.62014 | 0.810069 | − | 0.586334i | \(-0.199430\pi\) | ||||
0.810069 | + | 0.586334i | \(0.199430\pi\) | |||||||
\(62\) | −13.3607 | −1.69681 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −12.3112 | −1.53891 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.3896 | −1.52506 | ||||||||
\(67\) | −0.581449 | −0.0710353 | −0.0355177 | − | 0.999369i | \(-0.511308\pi\) | ||||
−0.0355177 | + | 0.999369i | \(0.511308\pi\) | |||||||
\(68\) | −2.92162 | −0.354299 | ||||||||
\(69\) | −5.41855 | −0.652317 | ||||||||
\(70\) | 1.36910 | 0.163639 | ||||||||
\(71\) | 4.81432 | 0.571354 | 0.285677 | − | 0.958326i | \(-0.407782\pi\) | ||||
0.285677 | + | 0.958326i | \(0.407782\pi\) | |||||||
\(72\) | 1.53919 | 0.181395 | ||||||||
\(73\) | −3.81658 | −0.446697 | −0.223349 | − | 0.974739i | \(-0.571699\pi\) | ||||
−0.223349 | + | 0.974739i | \(0.571699\pi\) | |||||||
\(74\) | 7.41855 | 0.862389 | ||||||||
\(75\) | −4.60197 | −0.531390 | ||||||||
\(76\) | −20.0989 | −2.30550 | ||||||||
\(77\) | 5.70928 | 0.650632 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.65983 | −0.186745 | −0.0933726 | − | 0.995631i | \(-0.529765\pi\) | ||||
−0.0933726 | + | 0.995631i | \(0.529765\pi\) | |||||||
\(80\) | 1.31124 | 0.146601 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.63090 | −0.290534 | ||||||||
\(83\) | 12.8865 | 1.41448 | 0.707241 | − | 0.706972i | \(-0.249939\pi\) | ||||
0.707241 | + | 0.706972i | \(0.249939\pi\) | |||||||
\(84\) | −2.70928 | −0.295606 | ||||||||
\(85\) | 0.680346 | 0.0737939 | ||||||||
\(86\) | 27.5174 | 2.96728 | ||||||||
\(87\) | 6.68035 | 0.716208 | ||||||||
\(88\) | −8.78765 | −0.936767 | ||||||||
\(89\) | 6.20620 | 0.657856 | 0.328928 | − | 0.944355i | \(-0.393313\pi\) | ||||
0.328928 | + | 0.944355i | \(0.393313\pi\) | |||||||
\(90\) | −1.36910 | −0.144316 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.6803 | −1.53053 | ||||||||
\(93\) | −6.15676 | −0.638426 | ||||||||
\(94\) | 13.1278 | 1.35403 | ||||||||
\(95\) | 4.68035 | 0.480193 | ||||||||
\(96\) | −7.58864 | −0.774512 | ||||||||
\(97\) | 1.07838 | 0.109493 | 0.0547463 | − | 0.998500i | \(-0.482565\pi\) | ||||
0.0547463 | + | 0.998500i | \(0.482565\pi\) | |||||||
\(98\) | 2.17009 | 0.219212 | ||||||||
\(99\) | −5.70928 | −0.573804 | ||||||||
\(100\) | −12.4680 | −1.24680 | ||||||||
\(101\) | 7.23513 | 0.719923 | 0.359961 | − | 0.932967i | \(-0.382790\pi\) | ||||
0.359961 | + | 0.932967i | \(0.382790\pi\) | |||||||
\(102\) | −2.34017 | −0.231712 | ||||||||
\(103\) | −13.7587 | −1.35569 | −0.677844 | − | 0.735206i | \(-0.737085\pi\) | ||||
−0.677844 | + | 0.735206i | \(0.737085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.630898 | 0.0615693 | ||||||||
\(106\) | −13.0205 | −1.26466 | ||||||||
\(107\) | −10.0989 | −0.976297 | −0.488149 | − | 0.872761i | \(-0.662328\pi\) | ||||
−0.488149 | + | 0.872761i | \(0.662328\pi\) | |||||||
\(108\) | 2.70928 | 0.260700 | ||||||||
\(109\) | −17.9421 | −1.71855 | −0.859273 | − | 0.511518i | \(-0.829083\pi\) | ||||
−0.859273 | + | 0.511518i | \(0.829083\pi\) | |||||||
\(110\) | 7.81658 | 0.745282 | ||||||||
\(111\) | 3.41855 | 0.324474 | ||||||||
\(112\) | 2.07838 | 0.196388 | ||||||||
\(113\) | 10.6803 | 1.00472 | 0.502361 | − | 0.864658i | \(-0.332465\pi\) | ||||
0.502361 | + | 0.864658i | \(0.332465\pi\) | |||||||
\(114\) | −16.0989 | −1.50780 | ||||||||
\(115\) | 3.41855 | 0.318781 | ||||||||
\(116\) | 18.0989 | 1.68044 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.97107 | −0.273509 | ||||||||
\(119\) | 1.07838 | 0.0988547 | ||||||||
\(120\) | −0.971071 | −0.0886462 | ||||||||
\(121\) | 21.5958 | 1.96326 | ||||||||
\(122\) | 27.4596 | 2.48607 | ||||||||
\(123\) | −1.21235 | −0.109314 | ||||||||
\(124\) | −16.6803 | −1.49794 | ||||||||
\(125\) | 6.05786 | 0.541831 | ||||||||
\(126\) | −2.17009 | −0.193327 | ||||||||
\(127\) | −6.34017 | −0.562599 | −0.281300 | − | 0.959620i | \(-0.590765\pi\) | ||||
−0.281300 | + | 0.959620i | \(0.590765\pi\) | |||||||
\(128\) | −11.5392 | −1.01993 | ||||||||
\(129\) | 12.6803 | 1.11644 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.51745 | −0.656802 | −0.328401 | − | 0.944538i | \(-0.606510\pi\) | ||||
−0.328401 | + | 0.944538i | \(0.606510\pi\) | |||||||
\(132\) | −15.4680 | −1.34632 | ||||||||
\(133\) | 7.41855 | 0.643270 | ||||||||
\(134\) | −1.26180 | −0.109003 | ||||||||
\(135\) | −0.630898 | −0.0542990 | ||||||||
\(136\) | −1.65983 | −0.142329 | ||||||||
\(137\) | −4.47414 | −0.382252 | −0.191126 | − | 0.981566i | \(-0.561214\pi\) | ||||
−0.191126 | + | 0.981566i | \(0.561214\pi\) | |||||||
\(138\) | −11.7587 | −1.00097 | ||||||||
\(139\) | −9.75872 | −0.827724 | −0.413862 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413862 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(140\) | 1.70928 | 0.144460 | ||||||||
\(141\) | 6.04945 | 0.509455 | ||||||||
\(142\) | 10.4475 | 0.876733 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.07838 | −0.173198 | ||||||||
\(145\) | −4.21461 | −0.350005 | ||||||||
\(146\) | −8.28231 | −0.685449 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 9.26180 | 0.761315 | ||||||||
\(149\) | −1.46800 | −0.120263 | −0.0601316 | − | 0.998190i | \(-0.519152\pi\) | ||||
−0.0601316 | + | 0.998190i | \(0.519152\pi\) | |||||||
\(150\) | −9.98667 | −0.815408 | ||||||||
\(151\) | −13.3607 | −1.08728 | −0.543639 | − | 0.839319i | \(-0.682954\pi\) | ||||
−0.543639 | + | 0.839319i | \(0.682954\pi\) | |||||||
\(152\) | −11.4186 | −0.926167 | ||||||||
\(153\) | −1.07838 | −0.0871817 | ||||||||
\(154\) | 12.3896 | 0.998384 | ||||||||
\(155\) | 3.88428 | 0.311993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.15676 | −0.650980 | −0.325490 | − | 0.945545i | \(-0.605529\pi\) | ||||
−0.325490 | + | 0.945545i | \(0.605529\pi\) | |||||||
\(158\) | −3.60197 | −0.286557 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 4.78765 | 0.378497 | ||||||||
\(161\) | 5.41855 | 0.427042 | ||||||||
\(162\) | 2.17009 | 0.170498 | ||||||||
\(163\) | −4.58145 | −0.358847 | −0.179423 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179423 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(164\) | −3.28458 | −0.256483 | ||||||||
\(165\) | 3.60197 | 0.280413 | ||||||||
\(166\) | 27.9649 | 2.17050 | ||||||||
\(167\) | −7.31124 | −0.565761 | −0.282881 | − | 0.959155i | \(-0.591290\pi\) | ||||
−0.282881 | + | 0.959155i | \(0.591290\pi\) | |||||||
\(168\) | −1.53919 | −0.118751 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.47641 | 0.113235 | ||||||||
\(171\) | −7.41855 | −0.567311 | ||||||||
\(172\) | 34.3545 | 2.61951 | ||||||||
\(173\) | −7.60197 | −0.577967 | −0.288983 | − | 0.957334i | \(-0.593317\pi\) | ||||
−0.288983 | + | 0.957334i | \(0.593317\pi\) | |||||||
\(174\) | 14.4969 | 1.09901 | ||||||||
\(175\) | 4.60197 | 0.347876 | ||||||||
\(176\) | 11.8660 | 0.894436 | ||||||||
\(177\) | −1.36910 | −0.102908 | ||||||||
\(178\) | 13.4680 | 1.00947 | ||||||||
\(179\) | −9.10504 | −0.680543 | −0.340271 | − | 0.940327i | \(-0.610519\pi\) | ||||
−0.340271 | + | 0.940327i | \(0.610519\pi\) | |||||||
\(180\) | −1.70928 | −0.127402 | ||||||||
\(181\) | −15.3607 | −1.14175 | −0.570876 | − | 0.821037i | \(-0.693396\pi\) | ||||
−0.570876 | + | 0.821037i | \(0.693396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.6537 | 0.935387 | ||||||||
\(184\) | −8.34017 | −0.614846 | ||||||||
\(185\) | −2.15676 | −0.158568 | ||||||||
\(186\) | −13.3607 | −0.979653 | ||||||||
\(187\) | 6.15676 | 0.450227 | ||||||||
\(188\) | 16.3896 | 1.19534 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 10.1568 | 0.736848 | ||||||||
\(191\) | −24.5692 | −1.77776 | −0.888881 | − | 0.458138i | \(-0.848517\pi\) | ||||
−0.888881 | + | 0.458138i | \(0.848517\pi\) | |||||||
\(192\) | −12.3112 | −0.888487 | ||||||||
\(193\) | −13.5753 | −0.977172 | −0.488586 | − | 0.872516i | \(-0.662487\pi\) | ||||
−0.488586 | + | 0.872516i | \(0.662487\pi\) | |||||||
\(194\) | 2.34017 | 0.168015 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.70928 | 0.193520 | ||||||||
\(197\) | 2.94441 | 0.209780 | 0.104890 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104890 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(198\) | −12.3896 | −0.880492 | ||||||||
\(199\) | 10.5236 | 0.745998 | 0.372999 | − | 0.927832i | \(-0.378330\pi\) | ||||
0.372999 | + | 0.927832i | \(0.378330\pi\) | |||||||
\(200\) | −7.08330 | −0.500865 | ||||||||
\(201\) | −0.581449 | −0.0410123 | ||||||||
\(202\) | 15.7009 | 1.10471 | ||||||||
\(203\) | −6.68035 | −0.468868 | ||||||||
\(204\) | −2.92162 | −0.204554 | ||||||||
\(205\) | 0.764867 | 0.0534206 | ||||||||
\(206\) | −29.8576 | −2.08028 | ||||||||
\(207\) | −5.41855 | −0.376615 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42.3545 | 2.92973 | ||||||||
\(210\) | 1.36910 | 0.0944770 | ||||||||
\(211\) | −3.02052 | −0.207941 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(212\) | −16.2557 | −1.11644 | ||||||||
\(213\) | 4.81432 | 0.329871 | ||||||||
\(214\) | −21.9155 | −1.49811 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 1.53919 | 0.104729 | ||||||||
\(217\) | 6.15676 | 0.417948 | ||||||||
\(218\) | −38.9360 | −2.63708 | ||||||||
\(219\) | −3.81658 | −0.257901 | ||||||||
\(220\) | 9.75872 | 0.657933 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.41855 | 0.497901 | ||||||||
\(223\) | −22.6225 | −1.51491 | −0.757457 | − | 0.652885i | \(-0.773558\pi\) | ||||
−0.757457 | + | 0.652885i | \(0.773558\pi\) | |||||||
\(224\) | 7.58864 | 0.507037 | ||||||||
\(225\) | −4.60197 | −0.306798 | ||||||||
\(226\) | 23.1773 | 1.54173 | ||||||||
\(227\) | 22.9444 | 1.52287 | 0.761437 | − | 0.648239i | \(-0.224494\pi\) | ||||
0.761437 | + | 0.648239i | \(0.224494\pi\) | |||||||
\(228\) | −20.0989 | −1.33108 | ||||||||
\(229\) | 21.5441 | 1.42367 | 0.711837 | − | 0.702344i | \(-0.247863\pi\) | ||||
0.711837 | + | 0.702344i | \(0.247863\pi\) | |||||||
\(230\) | 7.41855 | 0.489165 | ||||||||
\(231\) | 5.70928 | 0.375643 | ||||||||
\(232\) | 10.2823 | 0.675067 | ||||||||
\(233\) | −7.36069 | −0.482215 | −0.241107 | − | 0.970498i | \(-0.577511\pi\) | ||||
−0.241107 | + | 0.970498i | \(0.577511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.81658 | −0.248966 | ||||||||
\(236\) | −3.70928 | −0.241453 | ||||||||
\(237\) | −1.65983 | −0.107817 | ||||||||
\(238\) | 2.34017 | 0.151691 | ||||||||
\(239\) | −15.5525 | −1.00601 | −0.503004 | − | 0.864284i | \(-0.667772\pi\) | ||||
−0.503004 | + | 0.864284i | \(0.667772\pi\) | |||||||
\(240\) | 1.31124 | 0.0846404 | ||||||||
\(241\) | 7.33403 | 0.472426 | 0.236213 | − | 0.971701i | \(-0.424094\pi\) | ||||
0.236213 | + | 0.971701i | \(0.424094\pi\) | |||||||
\(242\) | 46.8648 | 3.01258 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 34.2823 | 2.19470 | ||||||||
\(245\) | −0.630898 | −0.0403066 | ||||||||
\(246\) | −2.63090 | −0.167740 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.47641 | −0.601753 | ||||||||
\(249\) | 12.8865 | 0.816652 | ||||||||
\(250\) | 13.1461 | 0.831431 | ||||||||
\(251\) | 13.6742 | 0.863108 | 0.431554 | − | 0.902087i | \(-0.357965\pi\) | ||||
0.431554 | + | 0.902087i | \(0.357965\pi\) | |||||||
\(252\) | −2.70928 | −0.170668 | ||||||||
\(253\) | 30.9360 | 1.94493 | ||||||||
\(254\) | −13.7587 | −0.863299 | ||||||||
\(255\) | 0.680346 | 0.0426049 | ||||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | 26.1256 | 1.62967 | 0.814834 | − | 0.579695i | \(-0.196828\pi\) | ||||
0.814834 | + | 0.579695i | \(0.196828\pi\) | |||||||
\(258\) | 27.5174 | 1.71316 | ||||||||
\(259\) | −3.41855 | −0.212418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.68035 | 0.413503 | ||||||||
\(262\) | −16.3135 | −1.00785 | ||||||||
\(263\) | −30.7792 | −1.89793 | −0.948965 | − | 0.315382i | \(-0.897867\pi\) | ||||
−0.948965 | + | 0.315382i | \(0.897867\pi\) | |||||||
\(264\) | −8.78765 | −0.540843 | ||||||||
\(265\) | 3.78539 | 0.232534 | ||||||||
\(266\) | 16.0989 | 0.987087 | ||||||||
\(267\) | 6.20620 | 0.379814 | ||||||||
\(268\) | −1.57531 | −0.0962271 | ||||||||
\(269\) | 5.39189 | 0.328749 | 0.164375 | − | 0.986398i | \(-0.447439\pi\) | ||||
0.164375 | + | 0.986398i | \(0.447439\pi\) | |||||||
\(270\) | −1.36910 | −0.0833209 | ||||||||
\(271\) | 11.4186 | 0.693628 | 0.346814 | − | 0.937934i | \(-0.387264\pi\) | ||||
0.346814 | + | 0.937934i | \(0.387264\pi\) | |||||||
\(272\) | 2.24128 | 0.135897 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.70928 | −0.586559 | ||||||||
\(275\) | 26.2739 | 1.58438 | ||||||||
\(276\) | −14.6803 | −0.883653 | ||||||||
\(277\) | −13.1506 | −0.790144 | −0.395072 | − | 0.918650i | \(-0.629280\pi\) | ||||
−0.395072 | + | 0.918650i | \(0.629280\pi\) | |||||||
\(278\) | −21.1773 | −1.27013 | ||||||||
\(279\) | −6.15676 | −0.368595 | ||||||||
\(280\) | 0.971071 | 0.0580326 | ||||||||
\(281\) | −2.14834 | −0.128160 | −0.0640798 | − | 0.997945i | \(-0.520411\pi\) | ||||
−0.0640798 | + | 0.997945i | \(0.520411\pi\) | |||||||
\(282\) | 13.1278 | 0.781751 | ||||||||
\(283\) | 12.1978 | 0.725084 | 0.362542 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362542 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(284\) | 13.0433 | 0.773978 | ||||||||
\(285\) | 4.68035 | 0.277240 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21235 | 0.0715626 | ||||||||
\(288\) | −7.58864 | −0.447165 | ||||||||
\(289\) | −15.8371 | −0.931594 | ||||||||
\(290\) | −9.14608 | −0.537076 | ||||||||
\(291\) | 1.07838 | 0.0632156 | ||||||||
\(292\) | −10.3402 | −0.605113 | ||||||||
\(293\) | 7.15449 | 0.417970 | 0.208985 | − | 0.977919i | \(-0.432984\pi\) | ||||
0.208985 | + | 0.977919i | \(0.432984\pi\) | |||||||
\(294\) | 2.17009 | 0.126562 | ||||||||
\(295\) | 0.863763 | 0.0502903 | ||||||||
\(296\) | 5.26180 | 0.305836 | ||||||||
\(297\) | −5.70928 | −0.331286 | ||||||||
\(298\) | −3.18568 | −0.184542 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.4680 | −0.719840 | ||||||||
\(301\) | −12.6803 | −0.730883 | ||||||||
\(302\) | −28.9939 | −1.66841 | ||||||||
\(303\) | 7.23513 | 0.415648 | ||||||||
\(304\) | 15.4186 | 0.884315 | ||||||||
\(305\) | −7.98318 | −0.457116 | ||||||||
\(306\) | −2.34017 | −0.133779 | ||||||||
\(307\) | −21.8432 | −1.24666 | −0.623330 | − | 0.781959i | \(-0.714221\pi\) | ||||
−0.623330 | + | 0.781959i | \(0.714221\pi\) | |||||||
\(308\) | 15.4680 | 0.881371 | ||||||||
\(309\) | −13.7587 | −0.782706 | ||||||||
\(310\) | 8.42923 | 0.478748 | ||||||||
\(311\) | 7.51745 | 0.426275 | 0.213138 | − | 0.977022i | \(-0.431632\pi\) | ||||
0.213138 | + | 0.977022i | \(0.431632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.7009 | 1.45270 | 0.726349 | − | 0.687326i | \(-0.241215\pi\) | ||||
0.726349 | + | 0.687326i | \(0.241215\pi\) | |||||||
\(314\) | −17.7009 | −0.998918 | ||||||||
\(315\) | 0.630898 | 0.0355471 | ||||||||
\(316\) | −4.49693 | −0.252972 | ||||||||
\(317\) | −9.36910 | −0.526221 | −0.263111 | − | 0.964766i | \(-0.584748\pi\) | ||||
−0.263111 | + | 0.964766i | \(0.584748\pi\) | |||||||
\(318\) | −13.0205 | −0.730154 | ||||||||
\(319\) | −38.1399 | −2.13543 | ||||||||
\(320\) | 7.76713 | 0.434196 | ||||||||
\(321\) | −10.0989 | −0.563665 | ||||||||
\(322\) | 11.7587 | 0.655288 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 2.70928 | 0.150515 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.94214 | −0.550644 | ||||||||
\(327\) | −17.9421 | −0.992203 | ||||||||
\(328\) | −1.86603 | −0.103034 | ||||||||
\(329\) | −6.04945 | −0.333517 | ||||||||
\(330\) | 7.81658 | 0.430289 | ||||||||
\(331\) | −21.0472 | −1.15686 | −0.578429 | − | 0.815733i | \(-0.696334\pi\) | ||||
−0.578429 | + | 0.815733i | \(0.696334\pi\) | |||||||
\(332\) | 34.9132 | 1.91611 | ||||||||
\(333\) | 3.41855 | 0.187335 | ||||||||
\(334\) | −15.8660 | −0.868151 | ||||||||
\(335\) | 0.366835 | 0.0200423 | ||||||||
\(336\) | 2.07838 | 0.113385 | ||||||||
\(337\) | −15.4452 | −0.841354 | −0.420677 | − | 0.907210i | \(-0.638207\pi\) | ||||
−0.420677 | + | 0.907210i | \(0.638207\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6803 | 0.580077 | ||||||||
\(340\) | 1.84324 | 0.0999640 | ||||||||
\(341\) | 35.1506 | 1.90351 | ||||||||
\(342\) | −16.0989 | −0.870529 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 19.5174 | 1.05231 | ||||||||
\(345\) | 3.41855 | 0.184049 | ||||||||
\(346\) | −16.4969 | −0.886880 | ||||||||
\(347\) | 21.7321 | 1.16664 | 0.583319 | − | 0.812243i | \(-0.301754\pi\) | ||||
0.583319 | + | 0.812243i | \(0.301754\pi\) | |||||||
\(348\) | 18.0989 | 0.970203 | ||||||||
\(349\) | −5.65983 | −0.302964 | −0.151482 | − | 0.988460i | \(-0.548404\pi\) | ||||
−0.151482 | + | 0.988460i | \(0.548404\pi\) | |||||||
\(350\) | 9.98667 | 0.533810 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 43.3256 | 2.30926 | ||||||||
\(353\) | −33.7237 | −1.79493 | −0.897464 | − | 0.441087i | \(-0.854593\pi\) | ||||
−0.897464 | + | 0.441087i | \(0.854593\pi\) | |||||||
\(354\) | −2.97107 | −0.157911 | ||||||||
\(355\) | −3.03734 | −0.161205 | ||||||||
\(356\) | 16.8143 | 0.891157 | ||||||||
\(357\) | 1.07838 | 0.0570738 | ||||||||
\(358\) | −19.7587 | −1.04428 | ||||||||
\(359\) | −18.7031 | −0.987114 | −0.493557 | − | 0.869714i | \(-0.664303\pi\) | ||||
−0.493557 | + | 0.869714i | \(0.664303\pi\) | |||||||
\(360\) | −0.971071 | −0.0511799 | ||||||||
\(361\) | 36.0349 | 1.89657 | ||||||||
\(362\) | −33.3340 | −1.75200 | ||||||||
\(363\) | 21.5958 | 1.13349 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40787 | 0.126034 | ||||||||
\(366\) | 27.4596 | 1.43534 | ||||||||
\(367\) | 10.0722 | 0.525766 | 0.262883 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262883 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(368\) | 11.2618 | 0.587062 | ||||||||
\(369\) | −1.21235 | −0.0631123 | ||||||||
\(370\) | −4.68035 | −0.243320 | ||||||||
\(371\) | 6.00000 | 0.311504 | ||||||||
\(372\) | −16.6803 | −0.864836 | ||||||||
\(373\) | 4.24128 | 0.219605 | 0.109802 | − | 0.993953i | \(-0.464978\pi\) | ||||
0.109802 | + | 0.993953i | \(0.464978\pi\) | |||||||
\(374\) | 13.3607 | 0.690865 | ||||||||
\(375\) | 6.05786 | 0.312826 | ||||||||
\(376\) | 9.31124 | 0.480191 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.17009 | −0.111617 | ||||||||
\(379\) | 20.1978 | 1.03749 | 0.518745 | − | 0.854929i | \(-0.326399\pi\) | ||||
0.518745 | + | 0.854929i | \(0.326399\pi\) | |||||||
\(380\) | 12.6803 | 0.650488 | ||||||||
\(381\) | −6.34017 | −0.324817 | ||||||||
\(382\) | −53.3172 | −2.72795 | ||||||||
\(383\) | −7.04331 | −0.359896 | −0.179948 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179948 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(384\) | −11.5392 | −0.588857 | ||||||||
\(385\) | −3.60197 | −0.183573 | ||||||||
\(386\) | −29.4596 | −1.49945 | ||||||||
\(387\) | 12.6803 | 0.644578 | ||||||||
\(388\) | 2.92162 | 0.148323 | ||||||||
\(389\) | 3.84324 | 0.194860 | 0.0974301 | − | 0.995242i | \(-0.468938\pi\) | ||||
0.0974301 | + | 0.995242i | \(0.468938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.84324 | 0.295506 | ||||||||
\(392\) | 1.53919 | 0.0777408 | ||||||||
\(393\) | −7.51745 | −0.379205 | ||||||||
\(394\) | 6.38962 | 0.321904 | ||||||||
\(395\) | 1.04718 | 0.0526894 | ||||||||
\(396\) | −15.4680 | −0.777296 | ||||||||
\(397\) | −14.4391 | −0.724676 | −0.362338 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362338 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(398\) | 22.8371 | 1.14472 | ||||||||
\(399\) | 7.41855 | 0.371392 | ||||||||
\(400\) | 9.56463 | 0.478231 | ||||||||
\(401\) | 9.83483 | 0.491128 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(402\) | −1.26180 | −0.0629326 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 19.6020 | 0.975234 | ||||||||
\(405\) | −0.630898 | −0.0313496 | ||||||||
\(406\) | −14.4969 | −0.719470 | ||||||||
\(407\) | −19.5174 | −0.967444 | ||||||||
\(408\) | −1.65983 | −0.0821737 | ||||||||
\(409\) | −7.54864 | −0.373256 | −0.186628 | − | 0.982431i | \(-0.559756\pi\) | ||||
−0.186628 | + | 0.982431i | \(0.559756\pi\) | |||||||
\(410\) | 1.65983 | 0.0819730 | ||||||||
\(411\) | −4.47414 | −0.220693 | ||||||||
\(412\) | −37.2762 | −1.83647 | ||||||||
\(413\) | 1.36910 | 0.0673691 | ||||||||
\(414\) | −11.7587 | −0.577910 | ||||||||
\(415\) | −8.13009 | −0.399091 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.75872 | −0.477887 | ||||||||
\(418\) | 91.9130 | 4.49561 | ||||||||
\(419\) | −35.1506 | −1.71722 | −0.858610 | − | 0.512630i | \(-0.828671\pi\) | ||||
−0.858610 | + | 0.512630i | \(0.828671\pi\) | |||||||
\(420\) | 1.70928 | 0.0834041 | ||||||||
\(421\) | 25.6742 | 1.25128 | 0.625642 | − | 0.780110i | \(-0.284837\pi\) | ||||
0.625642 | + | 0.780110i | \(0.284837\pi\) | |||||||
\(422\) | −6.55479 | −0.319082 | ||||||||
\(423\) | 6.04945 | 0.294134 | ||||||||
\(424\) | −9.23513 | −0.448498 | ||||||||
\(425\) | 4.96266 | 0.240724 | ||||||||
\(426\) | 10.4475 | 0.506182 | ||||||||
\(427\) | −12.6537 | −0.612355 | ||||||||
\(428\) | −27.3607 | −1.32253 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.3607 | −0.837207 | ||||||||
\(431\) | 16.2329 | 0.781910 | 0.390955 | − | 0.920410i | \(-0.372145\pi\) | ||||
0.390955 | + | 0.920410i | \(0.372145\pi\) | |||||||
\(432\) | −2.07838 | −0.0999960 | ||||||||
\(433\) | 5.38735 | 0.258900 | 0.129450 | − | 0.991586i | \(-0.458679\pi\) | ||||
0.129450 | + | 0.991586i | \(0.458679\pi\) | |||||||
\(434\) | 13.3607 | 0.641334 | ||||||||
\(435\) | −4.21461 | −0.202075 | ||||||||
\(436\) | −48.6102 | −2.32801 | ||||||||
\(437\) | 40.1978 | 1.92292 | ||||||||
\(438\) | −8.28231 | −0.395744 | ||||||||
\(439\) | 10.2413 | 0.488789 | 0.244395 | − | 0.969676i | \(-0.421411\pi\) | ||||
0.244395 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(440\) | 5.54411 | 0.264305 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.9421 | 0.757434 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(444\) | 9.26180 | 0.439545 | ||||||||
\(445\) | −3.91548 | −0.185612 | ||||||||
\(446\) | −49.0928 | −2.32461 | ||||||||
\(447\) | −1.46800 | −0.0694340 | ||||||||
\(448\) | 12.3112 | 0.581652 | ||||||||
\(449\) | −13.2001 | −0.622949 | −0.311475 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311475 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(450\) | −9.98667 | −0.470776 | ||||||||
\(451\) | 6.92162 | 0.325926 | ||||||||
\(452\) | 28.9360 | 1.36103 | ||||||||
\(453\) | −13.3607 | −0.627740 | ||||||||
\(454\) | 49.7914 | 2.33682 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.4186 | −0.534723 | ||||||||
\(457\) | −18.3090 | −0.856458 | −0.428229 | − | 0.903670i | \(-0.640862\pi\) | ||||
−0.428229 | + | 0.903670i | \(0.640862\pi\) | |||||||
\(458\) | 46.7526 | 2.18460 | ||||||||
\(459\) | −1.07838 | −0.0503344 | ||||||||
\(460\) | 9.26180 | 0.431833 | ||||||||
\(461\) | 18.9399 | 0.882118 | 0.441059 | − | 0.897478i | \(-0.354603\pi\) | ||||
0.441059 | + | 0.897478i | \(0.354603\pi\) | |||||||
\(462\) | 12.3896 | 0.576417 | ||||||||
\(463\) | −1.74435 | −0.0810667 | −0.0405334 | − | 0.999178i | \(-0.512906\pi\) | ||||
−0.0405334 | + | 0.999178i | \(0.512906\pi\) | |||||||
\(464\) | −13.8843 | −0.644562 | ||||||||
\(465\) | 3.88428 | 0.180129 | ||||||||
\(466\) | −15.9733 | −0.739951 | ||||||||
\(467\) | 18.1568 | 0.840194 | 0.420097 | − | 0.907479i | \(-0.361996\pi\) | ||||
0.420097 | + | 0.907479i | \(0.361996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.581449 | 0.0268488 | ||||||||
\(470\) | −8.28231 | −0.382035 | ||||||||
\(471\) | −8.15676 | −0.375843 | ||||||||
\(472\) | −2.10731 | −0.0969967 | ||||||||
\(473\) | −72.3956 | −3.32875 | ||||||||
\(474\) | −3.60197 | −0.165444 | ||||||||
\(475\) | 34.1399 | 1.56645 | ||||||||
\(476\) | 2.92162 | 0.133912 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | −33.7503 | −1.54370 | ||||||||
\(479\) | 30.4619 | 1.39184 | 0.695919 | − | 0.718120i | \(-0.254997\pi\) | ||||
0.695919 | + | 0.718120i | \(0.254997\pi\) | |||||||
\(480\) | 4.78765 | 0.218525 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.9155 | 0.724930 | ||||||||
\(483\) | 5.41855 | 0.246553 | ||||||||
\(484\) | 58.5090 | 2.65950 | ||||||||
\(485\) | −0.680346 | −0.0308929 | ||||||||
\(486\) | 2.17009 | 0.0984371 | ||||||||
\(487\) | 0.313511 | 0.0142065 | 0.00710327 | − | 0.999975i | \(-0.497739\pi\) | ||||
0.00710327 | + | 0.999975i | \(0.497739\pi\) | |||||||
\(488\) | 19.4764 | 0.881656 | ||||||||
\(489\) | −4.58145 | −0.207180 | ||||||||
\(490\) | −1.36910 | −0.0618497 | ||||||||
\(491\) | 8.93600 | 0.403276 | 0.201638 | − | 0.979460i | \(-0.435374\pi\) | ||||
0.201638 | + | 0.979460i | \(0.435374\pi\) | |||||||
\(492\) | −3.28458 | −0.148080 | ||||||||
\(493\) | −7.20394 | −0.324449 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.60197 | 0.161896 | ||||||||
\(496\) | 12.7961 | 0.574560 | ||||||||
\(497\) | −4.81432 | −0.215952 | ||||||||
\(498\) | 27.9649 | 1.25314 | ||||||||
\(499\) | −33.9877 | −1.52150 | −0.760750 | − | 0.649046i | \(-0.775168\pi\) | ||||
−0.760750 | + | 0.649046i | \(0.775168\pi\) | |||||||
\(500\) | 16.4124 | 0.733985 | ||||||||
\(501\) | −7.31124 | −0.326642 | ||||||||
\(502\) | 29.6742 | 1.32442 | ||||||||
\(503\) | 33.5585 | 1.49630 | 0.748149 | − | 0.663530i | \(-0.230943\pi\) | ||||
0.748149 | + | 0.663530i | \(0.230943\pi\) | |||||||
\(504\) | −1.53919 | −0.0685609 | ||||||||
\(505\) | −4.56463 | −0.203123 | ||||||||
\(506\) | 67.1338 | 2.98446 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.1773 | −0.762118 | ||||||||
\(509\) | −24.8287 | −1.10051 | −0.550256 | − | 0.834996i | \(-0.685470\pi\) | ||||
−0.550256 | + | 0.834996i | \(0.685470\pi\) | |||||||
\(510\) | 1.47641 | 0.0653765 | ||||||||
\(511\) | 3.81658 | 0.168836 | ||||||||
\(512\) | 22.1701 | 0.979789 | ||||||||
\(513\) | −7.41855 | −0.327537 | ||||||||
\(514\) | 56.6947 | 2.50070 | ||||||||
\(515\) | 8.68035 | 0.382502 | ||||||||
\(516\) | 34.3545 | 1.51237 | ||||||||
\(517\) | −34.5380 | −1.51898 | ||||||||
\(518\) | −7.41855 | −0.325952 | ||||||||
\(519\) | −7.60197 | −0.333689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2290 | 0.886248 | 0.443124 | − | 0.896460i | \(-0.353870\pi\) | ||||
0.443124 | + | 0.896460i | \(0.353870\pi\) | |||||||
\(522\) | 14.4969 | 0.634513 | ||||||||
\(523\) | −40.1666 | −1.75636 | −0.878181 | − | 0.478328i | \(-0.841243\pi\) | ||||
−0.878181 | + | 0.478328i | \(0.841243\pi\) | |||||||
\(524\) | −20.3668 | −0.889729 | ||||||||
\(525\) | 4.60197 | 0.200846 | ||||||||
\(526\) | −66.7936 | −2.91234 | ||||||||
\(527\) | 6.63931 | 0.289213 | ||||||||
\(528\) | 11.8660 | 0.516403 | ||||||||
\(529\) | 6.36069 | 0.276552 | ||||||||
\(530\) | 8.21461 | 0.356820 | ||||||||
\(531\) | −1.36910 | −0.0594140 | ||||||||
\(532\) | 20.0989 | 0.871398 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.4680 | 0.582817 | ||||||||
\(535\) | 6.37137 | 0.275458 | ||||||||
\(536\) | −0.894960 | −0.0386564 | ||||||||
\(537\) | −9.10504 | −0.392911 | ||||||||
\(538\) | 11.7009 | 0.504460 | ||||||||
\(539\) | −5.70928 | −0.245916 | ||||||||
\(540\) | −1.70928 | −0.0735555 | ||||||||
\(541\) | −18.2101 | −0.782912 | −0.391456 | − | 0.920197i | \(-0.628029\pi\) | ||||
−0.391456 | + | 0.920197i | \(0.628029\pi\) | |||||||
\(542\) | 24.7792 | 1.06436 | ||||||||
\(543\) | −15.3607 | −0.659190 | ||||||||
\(544\) | 8.18342 | 0.350861 | ||||||||
\(545\) | 11.3197 | 0.484881 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.32580 | −0.270472 | −0.135236 | − | 0.990813i | \(-0.543179\pi\) | ||||
−0.135236 | + | 0.990813i | \(0.543179\pi\) | |||||||
\(548\) | −12.1217 | −0.517813 | ||||||||
\(549\) | 12.6537 | 0.540046 | ||||||||
\(550\) | 57.0166 | 2.43120 | ||||||||
\(551\) | −49.5585 | −2.11126 | ||||||||
\(552\) | −8.34017 | −0.354981 | ||||||||
\(553\) | 1.65983 | 0.0705830 | ||||||||
\(554\) | −28.5380 | −1.21246 | ||||||||
\(555\) | −2.15676 | −0.0915492 | ||||||||
\(556\) | −26.4391 | −1.12127 | ||||||||
\(557\) | −10.6309 | −0.450446 | −0.225223 | − | 0.974307i | \(-0.572311\pi\) | ||||
−0.225223 | + | 0.974307i | \(0.572311\pi\) | |||||||
\(558\) | −13.3607 | −0.565603 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.31124 | −0.0554102 | ||||||||
\(561\) | 6.15676 | 0.259938 | ||||||||
\(562\) | −4.66209 | −0.196659 | ||||||||
\(563\) | 37.0472 | 1.56135 | 0.780676 | − | 0.624936i | \(-0.214875\pi\) | ||||
0.780676 | + | 0.624936i | \(0.214875\pi\) | |||||||
\(564\) | 16.3896 | 0.690128 | ||||||||
\(565\) | −6.73820 | −0.283478 | ||||||||
\(566\) | 26.4703 | 1.11263 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 7.41014 | 0.310923 | ||||||||
\(569\) | −25.7152 | −1.07804 | −0.539019 | − | 0.842293i | \(-0.681205\pi\) | ||||
−0.539019 | + | 0.842293i | \(0.681205\pi\) | |||||||
\(570\) | 10.1568 | 0.425420 | ||||||||
\(571\) | 12.4969 | 0.522980 | 0.261490 | − | 0.965206i | \(-0.415786\pi\) | ||||
0.261490 | + | 0.965206i | \(0.415786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.5692 | −1.02639 | ||||||||
\(574\) | 2.63090 | 0.109812 | ||||||||
\(575\) | 24.9360 | 1.03990 | ||||||||
\(576\) | −12.3112 | −0.512968 | ||||||||
\(577\) | 3.91548 | 0.163004 | 0.0815018 | − | 0.996673i | \(-0.474028\pi\) | ||||
0.0815018 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(578\) | −34.3679 | −1.42952 | ||||||||
\(579\) | −13.5753 | −0.564170 | ||||||||
\(580\) | −11.4186 | −0.474130 | ||||||||
\(581\) | −12.8865 | −0.534624 | ||||||||
\(582\) | 2.34017 | 0.0970033 | ||||||||
\(583\) | 34.2557 | 1.41872 | ||||||||
\(584\) | −5.87444 | −0.243086 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.5259 | 0.641367 | ||||||||
\(587\) | −6.94441 | −0.286626 | −0.143313 | − | 0.989677i | \(-0.545776\pi\) | ||||
−0.143313 | + | 0.989677i | \(0.545776\pi\) | |||||||
\(588\) | 2.70928 | 0.111729 | ||||||||
\(589\) | 45.6742 | 1.88197 | ||||||||
\(590\) | 1.87444 | 0.0771695 | ||||||||
\(591\) | 2.94441 | 0.121117 | ||||||||
\(592\) | −7.10504 | −0.292015 | ||||||||
\(593\) | −29.9383 | −1.22942 | −0.614709 | − | 0.788754i | \(-0.710726\pi\) | ||||
−0.614709 | + | 0.788754i | \(0.710726\pi\) | |||||||
\(594\) | −12.3896 | −0.508352 | ||||||||
\(595\) | −0.680346 | −0.0278915 | ||||||||
\(596\) | −3.97721 | −0.162913 | ||||||||
\(597\) | 10.5236 | 0.430702 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.2905 | 1.76880 | 0.884402 | − | 0.466726i | \(-0.154567\pi\) | ||||
0.884402 | + | 0.466726i | \(0.154567\pi\) | |||||||
\(600\) | −7.08330 | −0.289174 | ||||||||
\(601\) | −31.2306 | −1.27392 | −0.636961 | − | 0.770896i | \(-0.719809\pi\) | ||||
−0.636961 | + | 0.770896i | \(0.719809\pi\) | |||||||
\(602\) | −27.5174 | −1.12153 | ||||||||
\(603\) | −0.581449 | −0.0236784 | ||||||||
\(604\) | −36.1978 | −1.47287 | ||||||||
\(605\) | −13.6248 | −0.553925 | ||||||||
\(606\) | 15.7009 | 0.637804 | ||||||||
\(607\) | 4.96266 | 0.201428 | 0.100714 | − | 0.994915i | \(-0.467887\pi\) | ||||
0.100714 | + | 0.994915i | \(0.467887\pi\) | |||||||
\(608\) | 56.2967 | 2.28313 | ||||||||
\(609\) | −6.68035 | −0.270701 | ||||||||
\(610\) | −17.3242 | −0.701436 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.92162 | −0.118100 | ||||||||
\(613\) | 0.366835 | 0.0148163 | 0.00740816 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740816 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(614\) | −47.4017 | −1.91298 | ||||||||
\(615\) | 0.764867 | 0.0308424 | ||||||||
\(616\) | 8.78765 | 0.354065 | ||||||||
\(617\) | 47.7237 | 1.92128 | 0.960641 | − | 0.277793i | \(-0.0896030\pi\) | ||||
0.960641 | + | 0.277793i | \(0.0896030\pi\) | |||||||
\(618\) | −29.8576 | −1.20105 | ||||||||
\(619\) | −19.7854 | −0.795242 | −0.397621 | − | 0.917550i | \(-0.630164\pi\) | ||||
−0.397621 | + | 0.917550i | \(0.630164\pi\) | |||||||
\(620\) | 10.5236 | 0.422638 | ||||||||
\(621\) | −5.41855 | −0.217439 | ||||||||
\(622\) | 16.3135 | 0.654112 | ||||||||
\(623\) | −6.20620 | −0.248646 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1880 | 0.767518 | ||||||||
\(626\) | 55.7731 | 2.22914 | ||||||||
\(627\) | 42.3545 | 1.69148 | ||||||||
\(628\) | −22.0989 | −0.881842 | ||||||||
\(629\) | −3.68649 | −0.146990 | ||||||||
\(630\) | 1.36910 | 0.0545463 | ||||||||
\(631\) | 20.1522 | 0.802247 | 0.401124 | − | 0.916024i | \(-0.368620\pi\) | ||||
0.401124 | + | 0.916024i | \(0.368620\pi\) | |||||||
\(632\) | −2.55479 | −0.101624 | ||||||||
\(633\) | −3.02052 | −0.120055 | ||||||||
\(634\) | −20.3318 | −0.807477 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | −16.2557 | −0.644579 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −82.7670 | −3.27678 | ||||||||
\(639\) | 4.81432 | 0.190451 | ||||||||
\(640\) | 7.28005 | 0.287769 | ||||||||
\(641\) | 12.1034 | 0.478057 | 0.239028 | − | 0.971013i | \(-0.423171\pi\) | ||||
0.239028 | + | 0.971013i | \(0.423171\pi\) | |||||||
\(642\) | −21.9155 | −0.864935 | ||||||||
\(643\) | −20.6803 | −0.815553 | −0.407777 | − | 0.913082i | \(-0.633696\pi\) | ||||
−0.407777 | + | 0.913082i | \(0.633696\pi\) | |||||||
\(644\) | 14.6803 | 0.578487 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 17.3607 | 0.683047 | ||||||||
\(647\) | −40.8781 | −1.60709 | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||||
−0.803543 | + | 0.595247i | \(0.797054\pi\) | |||||||
\(648\) | 1.53919 | 0.0604650 | ||||||||
\(649\) | 7.81658 | 0.306828 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.15676 | 0.241302 | ||||||||
\(652\) | −12.4124 | −0.486107 | ||||||||
\(653\) | 6.31351 | 0.247067 | 0.123533 | − | 0.992340i | \(-0.460577\pi\) | ||||
0.123533 | + | 0.992340i | \(0.460577\pi\) | |||||||
\(654\) | −38.9360 | −1.52252 | ||||||||
\(655\) | 4.74274 | 0.185314 | ||||||||
\(656\) | 2.51971 | 0.0983783 | ||||||||
\(657\) | −3.81658 | −0.148899 | ||||||||
\(658\) | −13.1278 | −0.511776 | ||||||||
\(659\) | −20.9360 | −0.815551 | −0.407775 | − | 0.913082i | \(-0.633695\pi\) | ||||
−0.407775 | + | 0.913082i | \(0.633695\pi\) | |||||||
\(660\) | 9.75872 | 0.379858 | ||||||||
\(661\) | 22.2245 | 0.864431 | 0.432216 | − | 0.901770i | \(-0.357732\pi\) | ||||
0.432216 | + | 0.901770i | \(0.357732\pi\) | |||||||
\(662\) | −45.6742 | −1.77518 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.8348 | 0.769741 | ||||||||
\(665\) | −4.68035 | −0.181496 | ||||||||
\(666\) | 7.41855 | 0.287463 | ||||||||
\(667\) | −36.1978 | −1.40158 | ||||||||
\(668\) | −19.8082 | −0.766401 | ||||||||
\(669\) | −22.6225 | −0.874636 | ||||||||
\(670\) | 0.796064 | 0.0307546 | ||||||||
\(671\) | −72.2434 | −2.78892 | ||||||||
\(672\) | 7.58864 | 0.292738 | ||||||||
\(673\) | 1.15061 | 0.0443528 | 0.0221764 | − | 0.999754i | \(-0.492940\pi\) | ||||
0.0221764 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(674\) | −33.5174 | −1.29104 | ||||||||
\(675\) | −4.60197 | −0.177130 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5897 | −1.29096 | −0.645478 | − | 0.763779i | \(-0.723342\pi\) | ||||
−0.645478 | + | 0.763779i | \(0.723342\pi\) | |||||||
\(678\) | 23.1773 | 0.890118 | ||||||||
\(679\) | −1.07838 | −0.0413843 | ||||||||
\(680\) | 1.04718 | 0.0401576 | ||||||||
\(681\) | 22.9444 | 0.879232 | ||||||||
\(682\) | 76.2799 | 2.92091 | ||||||||
\(683\) | −25.1110 | −0.960846 | −0.480423 | − | 0.877037i | \(-0.659517\pi\) | ||||
−0.480423 | + | 0.877037i | \(0.659517\pi\) | |||||||
\(684\) | −20.0989 | −0.768501 | ||||||||
\(685\) | 2.82273 | 0.107851 | ||||||||
\(686\) | −2.17009 | −0.0828543 | ||||||||
\(687\) | 21.5441 | 0.821959 | ||||||||
\(688\) | −26.3545 | −1.00476 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.41855 | 0.282419 | ||||||||
\(691\) | 6.30898 | 0.240005 | 0.120002 | − | 0.992774i | \(-0.461710\pi\) | ||||
0.120002 | + | 0.992774i | \(0.461710\pi\) | |||||||
\(692\) | −20.5958 | −0.782936 | ||||||||
\(693\) | 5.70928 | 0.216877 | ||||||||
\(694\) | 47.1605 | 1.79019 | ||||||||
\(695\) | 6.15676 | 0.233539 | ||||||||
\(696\) | 10.2823 | 0.389750 | ||||||||
\(697\) | 1.30737 | 0.0495201 | ||||||||
\(698\) | −12.2823 | −0.464892 | ||||||||
\(699\) | −7.36069 | −0.278407 | ||||||||
\(700\) | 12.4680 | 0.471246 | ||||||||
\(701\) | −45.8843 | −1.73303 | −0.866513 | − | 0.499155i | \(-0.833644\pi\) | ||||
−0.866513 | + | 0.499155i | \(0.833644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.3607 | −0.956497 | ||||||||
\(704\) | 70.2883 | 2.64909 | ||||||||
\(705\) | −3.81658 | −0.143741 | ||||||||
\(706\) | −73.1832 | −2.75429 | ||||||||
\(707\) | −7.23513 | −0.272105 | ||||||||
\(708\) | −3.70928 | −0.139403 | ||||||||
\(709\) | 46.4534 | 1.74460 | 0.872298 | − | 0.488975i | \(-0.162629\pi\) | ||||
0.872298 | + | 0.488975i | \(0.162629\pi\) | |||||||
\(710\) | −6.59129 | −0.247367 | ||||||||
\(711\) | −1.65983 | −0.0622484 | ||||||||
\(712\) | 9.55252 | 0.357996 | ||||||||
\(713\) | 33.3607 | 1.24937 | ||||||||
\(714\) | 2.34017 | 0.0875788 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.6681 | −0.921889 | ||||||||
\(717\) | −15.5525 | −0.580819 | ||||||||
\(718\) | −40.5874 | −1.51471 | ||||||||
\(719\) | 7.20394 | 0.268661 | 0.134331 | − | 0.990937i | \(-0.457112\pi\) | ||||
0.134331 | + | 0.990937i | \(0.457112\pi\) | |||||||
\(720\) | 1.31124 | 0.0488672 | ||||||||
\(721\) | 13.7587 | 0.512402 | ||||||||
\(722\) | 78.1988 | 2.91026 | ||||||||
\(723\) | 7.33403 | 0.272756 | ||||||||
\(724\) | −41.6163 | −1.54666 | ||||||||
\(725\) | −30.7427 | −1.14176 | ||||||||
\(726\) | 46.8648 | 1.73932 | ||||||||
\(727\) | −13.6742 | −0.507148 | −0.253574 | − | 0.967316i | \(-0.581606\pi\) | ||||
−0.253574 | + | 0.967316i | \(0.581606\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.22529 | 0.193397 | ||||||||
\(731\) | −13.6742 | −0.505759 | ||||||||
\(732\) | 34.2823 | 1.26711 | ||||||||
\(733\) | 7.70086 | 0.284438 | 0.142219 | − | 0.989835i | \(-0.454576\pi\) | ||||
0.142219 | + | 0.989835i | \(0.454576\pi\) | |||||||
\(734\) | 21.8576 | 0.806779 | ||||||||
\(735\) | −0.630898 | −0.0232710 | ||||||||
\(736\) | 41.1194 | 1.51568 | ||||||||
\(737\) | 3.31965 | 0.122281 | ||||||||
\(738\) | −2.63090 | −0.0968447 | ||||||||
\(739\) | 24.5814 | 0.904243 | 0.452122 | − | 0.891956i | \(-0.350667\pi\) | ||||
0.452122 | + | 0.891956i | \(0.350667\pi\) | |||||||
\(740\) | −5.84324 | −0.214802 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.0205 | 0.477998 | ||||||||
\(743\) | −24.3773 | −0.894318 | −0.447159 | − | 0.894455i | \(-0.647564\pi\) | ||||
−0.447159 | + | 0.894455i | \(0.647564\pi\) | |||||||
\(744\) | −9.47641 | −0.347422 | ||||||||
\(745\) | 0.926157 | 0.0339318 | ||||||||
\(746\) | 9.20394 | 0.336980 | ||||||||
\(747\) | 12.8865 | 0.471494 | ||||||||
\(748\) | 16.6803 | 0.609894 | ||||||||
\(749\) | 10.0989 | 0.369006 | ||||||||
\(750\) | 13.1461 | 0.480027 | ||||||||
\(751\) | 24.6803 | 0.900599 | 0.450299 | − | 0.892878i | \(-0.351317\pi\) | ||||
0.450299 | + | 0.892878i | \(0.351317\pi\) | |||||||
\(752\) | −12.5730 | −0.458492 | ||||||||
\(753\) | 13.6742 | 0.498316 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.42923 | 0.306771 | ||||||||
\(756\) | −2.70928 | −0.0985354 | ||||||||
\(757\) | −41.3172 | −1.50170 | −0.750850 | − | 0.660473i | \(-0.770356\pi\) | ||||
−0.750850 | + | 0.660473i | \(0.770356\pi\) | |||||||
\(758\) | 43.8310 | 1.59201 | ||||||||
\(759\) | 30.9360 | 1.12291 | ||||||||
\(760\) | 7.20394 | 0.261314 | ||||||||
\(761\) | 15.9506 | 0.578207 | 0.289104 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289104 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(762\) | −13.7587 | −0.498426 | ||||||||
\(763\) | 17.9421 | 0.649549 | ||||||||
\(764\) | −66.5646 | −2.40822 | ||||||||
\(765\) | 0.680346 | 0.0245980 | ||||||||
\(766\) | −15.2846 | −0.552254 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.418551 | −0.0151031 | ||||||||
\(769\) | 6.22446 | 0.224460 | 0.112230 | − | 0.993682i | \(-0.464201\pi\) | ||||
0.112230 | + | 0.993682i | \(0.464201\pi\) | |||||||
\(770\) | −7.81658 | −0.281690 | ||||||||
\(771\) | 26.1256 | 0.940889 | ||||||||
\(772\) | −36.7792 | −1.32371 | ||||||||
\(773\) | 39.1545 | 1.40829 | 0.704145 | − | 0.710057i | \(-0.251331\pi\) | ||||
0.704145 | + | 0.710057i | \(0.251331\pi\) | |||||||
\(774\) | 27.5174 | 0.989094 | ||||||||
\(775\) | 28.3332 | 1.01776 | ||||||||
\(776\) | 1.65983 | 0.0595843 | ||||||||
\(777\) | −3.41855 | −0.122640 | ||||||||
\(778\) | 8.34017 | 0.299010 | ||||||||
\(779\) | 8.99386 | 0.322238 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.4863 | −0.983535 | ||||||||
\(782\) | 12.6803 | 0.453448 | ||||||||
\(783\) | 6.68035 | 0.238736 | ||||||||
\(784\) | −2.07838 | −0.0742278 | ||||||||
\(785\) | 5.14608 | 0.183671 | ||||||||
\(786\) | −16.3135 | −0.581884 | ||||||||
\(787\) | −32.2967 | −1.15125 | −0.575626 | − | 0.817713i | \(-0.695242\pi\) | ||||
−0.575626 | + | 0.817713i | \(0.695242\pi\) | |||||||
\(788\) | 7.97721 | 0.284176 | ||||||||
\(789\) | −30.7792 | −1.09577 | ||||||||
\(790\) | 2.27247 | 0.0808510 | ||||||||
\(791\) | −10.6803 | −0.379749 | ||||||||
\(792\) | −8.78765 | −0.312256 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −31.3340 | −1.11200 | ||||||||
\(795\) | 3.78539 | 0.134254 | ||||||||
\(796\) | 28.5113 | 1.01056 | ||||||||
\(797\) | 30.2700 | 1.07222 | 0.536110 | − | 0.844148i | \(-0.319893\pi\) | ||||
0.536110 | + | 0.844148i | \(0.319893\pi\) | |||||||
\(798\) | 16.0989 | 0.569895 | ||||||||
\(799\) | −6.52359 | −0.230788 | ||||||||
\(800\) | 34.9227 | 1.23470 | ||||||||
\(801\) | 6.20620 | 0.219285 | ||||||||
\(802\) | 21.3424 | 0.753628 | ||||||||
\(803\) | 21.7899 | 0.768950 | ||||||||
\(804\) | −1.57531 | −0.0555568 | ||||||||
\(805\) | −3.41855 | −0.120488 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.39189 | 0.189803 | ||||||||
\(808\) | 11.1362 | 0.391771 | ||||||||
\(809\) | 39.5585 | 1.39080 | 0.695401 | − | 0.718622i | \(-0.255227\pi\) | ||||
0.695401 | + | 0.718622i | \(0.255227\pi\) | |||||||
\(810\) | −1.36910 | −0.0481054 | ||||||||
\(811\) | 34.4079 | 1.20822 | 0.604112 | − | 0.796899i | \(-0.293528\pi\) | ||||
0.604112 | + | 0.796899i | \(0.293528\pi\) | |||||||
\(812\) | −18.0989 | −0.635147 | ||||||||
\(813\) | 11.4186 | 0.400466 | ||||||||
\(814\) | −42.3545 | −1.48453 | ||||||||
\(815\) | 2.89043 | 0.101247 | ||||||||
\(816\) | 2.24128 | 0.0784604 | ||||||||
\(817\) | −94.0698 | −3.29109 | ||||||||
\(818\) | −16.3812 | −0.572756 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.07223 | 0.0723656 | ||||||||
\(821\) | 7.89269 | 0.275457 | 0.137728 | − | 0.990470i | \(-0.456020\pi\) | ||||
0.137728 | + | 0.990470i | \(0.456020\pi\) | |||||||
\(822\) | −9.70928 | −0.338650 | ||||||||
\(823\) | −29.6742 | −1.03438 | −0.517189 | − | 0.855871i | \(-0.673022\pi\) | ||||
−0.517189 | + | 0.855871i | \(0.673022\pi\) | |||||||
\(824\) | −21.1773 | −0.737745 | ||||||||
\(825\) | 26.2739 | 0.914740 | ||||||||
\(826\) | 2.97107 | 0.103377 | ||||||||
\(827\) | −14.1918 | −0.493498 | −0.246749 | − | 0.969079i | \(-0.579362\pi\) | ||||
−0.246749 | + | 0.969079i | \(0.579362\pi\) | |||||||
\(828\) | −14.6803 | −0.510177 | ||||||||
\(829\) | −3.71315 | −0.128963 | −0.0644815 | − | 0.997919i | \(-0.520539\pi\) | ||||
−0.0644815 | + | 0.997919i | \(0.520539\pi\) | |||||||
\(830\) | −17.6430 | −0.612398 | ||||||||
\(831\) | −13.1506 | −0.456190 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.07838 | −0.0373636 | ||||||||
\(834\) | −21.1773 | −0.733309 | ||||||||
\(835\) | 4.61265 | 0.159627 | ||||||||
\(836\) | 114.750 | 3.96872 | ||||||||
\(837\) | −6.15676 | −0.212809 | ||||||||
\(838\) | −76.2799 | −2.63504 | ||||||||
\(839\) | 48.6719 | 1.68034 | 0.840171 | − | 0.542322i | \(-0.182455\pi\) | ||||
0.840171 | + | 0.542322i | \(0.182455\pi\) | |||||||
\(840\) | 0.971071 | 0.0335051 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | 55.7152 | 1.92007 | ||||||||
\(843\) | −2.14834 | −0.0739929 | ||||||||
\(844\) | −8.18342 | −0.281685 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.1278 | 0.451344 | ||||||||
\(847\) | −21.5958 | −0.742041 | ||||||||
\(848\) | 12.4703 | 0.428231 | ||||||||
\(849\) | 12.1978 | 0.418627 | ||||||||
\(850\) | 10.7694 | 0.369387 | ||||||||
\(851\) | −18.5236 | −0.634981 | ||||||||
\(852\) | 13.0433 | 0.446856 | ||||||||
\(853\) | 1.92777 | 0.0660054 | 0.0330027 | − | 0.999455i | \(-0.489493\pi\) | ||||
0.0330027 | + | 0.999455i | \(0.489493\pi\) | |||||||
\(854\) | −27.4596 | −0.939648 | ||||||||
\(855\) | 4.68035 | 0.160064 | ||||||||
\(856\) | −15.5441 | −0.531287 | ||||||||
\(857\) | −24.3980 | −0.833421 | −0.416710 | − | 0.909039i | \(-0.636817\pi\) | ||||
−0.416710 | + | 0.909039i | \(0.636817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.1506 | −0.516932 | −0.258466 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258466 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(860\) | −21.6742 | −0.739084 | ||||||||
\(861\) | 1.21235 | 0.0413167 | ||||||||
\(862\) | 35.2267 | 1.19983 | ||||||||
\(863\) | 49.7380 | 1.69310 | 0.846551 | − | 0.532308i | \(-0.178675\pi\) | ||||
0.846551 | + | 0.532308i | \(0.178675\pi\) | |||||||
\(864\) | −7.58864 | −0.258171 | ||||||||
\(865\) | 4.79606 | 0.163071 | ||||||||
\(866\) | 11.6910 | 0.397277 | ||||||||
\(867\) | −15.8371 | −0.537856 | ||||||||
\(868\) | 16.6803 | 0.566168 | ||||||||
\(869\) | 9.47641 | 0.321465 | ||||||||
\(870\) | −9.14608 | −0.310081 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −27.6163 | −0.935207 | ||||||||
\(873\) | 1.07838 | 0.0364976 | ||||||||
\(874\) | 87.2327 | 2.95069 | ||||||||
\(875\) | −6.05786 | −0.204793 | ||||||||
\(876\) | −10.3402 | −0.349362 | ||||||||
\(877\) | −9.72753 | −0.328475 | −0.164238 | − | 0.986421i | \(-0.552516\pi\) | ||||
−0.164238 | + | 0.986421i | \(0.552516\pi\) | |||||||
\(878\) | 22.2245 | 0.750039 | ||||||||
\(879\) | 7.15449 | 0.241315 | ||||||||
\(880\) | −7.48625 | −0.252361 | ||||||||
\(881\) | −6.12556 | −0.206375 | −0.103188 | − | 0.994662i | \(-0.532904\pi\) | ||||
−0.103188 | + | 0.994662i | \(0.532904\pi\) | |||||||
\(882\) | 2.17009 | 0.0730706 | ||||||||
\(883\) | −1.03281 | −0.0347567 | −0.0173783 | − | 0.999849i | \(-0.505532\pi\) | ||||
−0.0173783 | + | 0.999849i | \(0.505532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.863763 | 0.0290351 | ||||||||
\(886\) | 34.5958 | 1.16227 | ||||||||
\(887\) | 39.0882 | 1.31245 | 0.656227 | − | 0.754564i | \(-0.272151\pi\) | ||||
0.656227 | + | 0.754564i | \(0.272151\pi\) | |||||||
\(888\) | 5.26180 | 0.176574 | ||||||||
\(889\) | 6.34017 | 0.212643 | ||||||||
\(890\) | −8.49693 | −0.284818 | ||||||||
\(891\) | −5.70928 | −0.191268 | ||||||||
\(892\) | −61.2905 | −2.05216 | ||||||||
\(893\) | −44.8781 | −1.50179 | ||||||||
\(894\) | −3.18568 | −0.106545 | ||||||||
\(895\) | 5.74435 | 0.192012 | ||||||||
\(896\) | 11.5392 | 0.385497 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.6453 | −0.955905 | ||||||||
\(899\) | −41.1293 | −1.37174 | ||||||||
\(900\) | −12.4680 | −0.415600 | ||||||||
\(901\) | 6.47027 | 0.215556 | ||||||||
\(902\) | 15.0205 | 0.500129 | ||||||||
\(903\) | −12.6803 | −0.421975 | ||||||||
\(904\) | 16.4391 | 0.546755 | ||||||||
\(905\) | 9.69102 | 0.322141 | ||||||||
\(906\) | −28.9939 | −0.963256 | ||||||||
\(907\) | −45.3751 | −1.50665 | −0.753327 | − | 0.657646i | \(-0.771552\pi\) | ||||
−0.753327 | + | 0.657646i | \(0.771552\pi\) | |||||||
\(908\) | 62.1627 | 2.06294 | ||||||||
\(909\) | 7.23513 | 0.239974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.3090 | −0.805392 | −0.402696 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402696 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(912\) | 15.4186 | 0.510559 | ||||||||
\(913\) | −73.5729 | −2.43491 | ||||||||
\(914\) | −39.7321 | −1.31422 | ||||||||
\(915\) | −7.98318 | −0.263916 | ||||||||
\(916\) | 58.3689 | 1.92856 | ||||||||
\(917\) | 7.51745 | 0.248248 | ||||||||
\(918\) | −2.34017 | −0.0772372 | ||||||||
\(919\) | 55.8453 | 1.84217 | 0.921084 | − | 0.389364i | \(-0.127305\pi\) | ||||
0.921084 | + | 0.389364i | \(0.127305\pi\) | |||||||
\(920\) | 5.26180 | 0.173476 | ||||||||
\(921\) | −21.8432 | −0.719759 | ||||||||
\(922\) | 41.1012 | 1.35359 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 15.4680 | 0.508860 | ||||||||
\(925\) | −15.7321 | −0.517267 | ||||||||
\(926\) | −3.78539 | −0.124395 | ||||||||
\(927\) | −13.7587 | −0.451896 | ||||||||
\(928\) | −50.6947 | −1.66414 | ||||||||
\(929\) | 39.4680 | 1.29490 | 0.647452 | − | 0.762107i | \(-0.275835\pi\) | ||||
0.647452 | + | 0.762107i | \(0.275835\pi\) | |||||||
\(930\) | 8.42923 | 0.276405 | ||||||||
\(931\) | −7.41855 | −0.243133 | ||||||||
\(932\) | −19.9421 | −0.653227 | ||||||||
\(933\) | 7.51745 | 0.246110 | ||||||||
\(934\) | 39.4017 | 1.28926 | ||||||||
\(935\) | −3.88428 | −0.127030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.2122 | −0.725640 | −0.362820 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362820 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(938\) | 1.26180 | 0.0411991 | ||||||||
\(939\) | 25.7009 | 0.838716 | ||||||||
\(940\) | −10.3402 | −0.337259 | ||||||||
\(941\) | 32.1483 | 1.04801 | 0.524003 | − | 0.851716i | \(-0.324438\pi\) | ||||
0.524003 | + | 0.851716i | \(0.324438\pi\) | |||||||
\(942\) | −17.7009 | −0.576725 | ||||||||
\(943\) | 6.56916 | 0.213921 | ||||||||
\(944\) | 2.84551 | 0.0926135 | ||||||||
\(945\) | 0.630898 | 0.0205231 | ||||||||
\(946\) | −157.105 | −5.10791 | ||||||||
\(947\) | 19.2390 | 0.625184 | 0.312592 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312592 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(948\) | −4.49693 | −0.146053 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 74.0866 | 2.40369 | ||||||||
\(951\) | −9.36910 | −0.303814 | ||||||||
\(952\) | 1.65983 | 0.0537953 | ||||||||
\(953\) | −54.3423 | −1.76032 | −0.880159 | − | 0.474678i | \(-0.842564\pi\) | ||||
−0.880159 | + | 0.474678i | \(0.842564\pi\) | |||||||
\(954\) | −13.0205 | −0.421555 | ||||||||
\(955\) | 15.5006 | 0.501588 | ||||||||
\(956\) | −42.1361 | −1.36278 | ||||||||
\(957\) | −38.1399 | −1.23289 | ||||||||
\(958\) | 66.1049 | 2.13575 | ||||||||
\(959\) | 4.47414 | 0.144478 | ||||||||
\(960\) | 7.76713 | 0.250683 | ||||||||
\(961\) | 6.90564 | 0.222763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.0989 | −0.325432 | ||||||||
\(964\) | 19.8699 | 0.639967 | ||||||||
\(965\) | 8.56463 | 0.275705 | ||||||||
\(966\) | 11.7587 | 0.378331 | ||||||||
\(967\) | 1.43084 | 0.0460126 | 0.0230063 | − | 0.999735i | \(-0.492676\pi\) | ||||
0.0230063 | + | 0.999735i | \(0.492676\pi\) | |||||||
\(968\) | 33.2401 | 1.06838 | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | −1.47641 | −0.0474047 | ||||||||
\(971\) | −25.2450 | −0.810150 | −0.405075 | − | 0.914284i | \(-0.632755\pi\) | ||||
−0.405075 | + | 0.914284i | \(0.632755\pi\) | |||||||
\(972\) | 2.70928 | 0.0869000 | ||||||||
\(973\) | 9.75872 | 0.312850 | ||||||||
\(974\) | 0.680346 | 0.0217997 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.2991 | −0.841815 | ||||||||
\(977\) | 7.31124 | 0.233907 | 0.116954 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116954 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(978\) | −9.94214 | −0.317915 | ||||||||
\(979\) | −35.4329 | −1.13244 | ||||||||
\(980\) | −1.70928 | −0.0546008 | ||||||||
\(981\) | −17.9421 | −0.572848 | ||||||||
\(982\) | 19.3919 | 0.618820 | ||||||||
\(983\) | −21.0556 | −0.671569 | −0.335785 | − | 0.941939i | \(-0.609001\pi\) | ||||
−0.335785 | + | 0.941939i | \(0.609001\pi\) | |||||||
\(984\) | −1.86603 | −0.0594869 | ||||||||
\(985\) | −1.85762 | −0.0591887 | ||||||||
\(986\) | −15.6332 | −0.497861 | ||||||||
\(987\) | −6.04945 | −0.192556 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.7091 | −2.18482 | ||||||||
\(990\) | 7.81658 | 0.248427 | ||||||||
\(991\) | 42.0410 | 1.33548 | 0.667739 | − | 0.744396i | \(-0.267262\pi\) | ||||
0.667739 | + | 0.744396i | \(0.267262\pi\) | |||||||
\(992\) | 46.7214 | 1.48341 | ||||||||
\(993\) | −21.0472 | −0.667912 | ||||||||
\(994\) | −10.4475 | −0.331374 | ||||||||
\(995\) | −6.63931 | −0.210480 | ||||||||
\(996\) | 34.9132 | 1.10627 | ||||||||
\(997\) | −9.20394 | −0.291492 | −0.145746 | − | 0.989322i | \(-0.546558\pi\) | ||||
−0.145746 | + | 0.989322i | \(0.546558\pi\) | |||||||
\(998\) | −73.7563 | −2.33471 | ||||||||
\(999\) | 3.41855 | 0.108158 |
(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 | 3549.2.a.q.1.3 | 3 | ||
13.5 | odd | 4 | 273.2.c.b.64.1 | ✓ | 6 | ||
13.8 | odd | 4 | 273.2.c.b.64.6 | yes | 6 | ||
13.12 | even | 2 | 3549.2.a.k.1.1 | 3 | |||
39.5 | even | 4 | 819.2.c.c.64.6 | 6 | |||
39.8 | even | 4 | 819.2.c.c.64.1 | 6 | |||
52.31 | even | 4 | 4368.2.h.o.337.4 | 6 | |||
52.47 | even | 4 | 4368.2.h.o.337.3 | 6 | |||
91.34 | even | 4 | 1911.2.c.h.883.6 | 6 | |||
91.83 | even | 4 | 1911.2.c.h.883.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.b.64.1 | ✓ | 6 | 13.5 | odd | 4 | ||
273.2.c.b.64.6 | yes | 6 | 13.8 | odd | 4 | ||
819.2.c.c.64.1 | 6 | 39.8 | even | 4 | |||
819.2.c.c.64.6 | 6 | 39.5 | even | 4 | |||
1911.2.c.h.883.1 | 6 | 91.83 | even | 4 | |||
1911.2.c.h.883.6 | 6 | 91.34 | even | 4 | |||
3549.2.a.k.1.1 | 3 | 13.12 | even | 2 | |||
3549.2.a.q.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4368.2.h.o.337.3 | 6 | 52.47 | even | 4 | |||
4368.2.h.o.337.4 | 6 | 52.31 | even | 4 |