Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(305,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1064.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.q (of order \(3\), 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: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 457.4 | ||
Root | \(-0.342094 - 0.592525i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.457 |
Dual form | 1064.2.q.n.305.4 |
$q$-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 \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(799\) | \(913\) | \(1009\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.342094 | − | 0.592525i | −0.197508 | − | 0.342094i | 0.750212 | − | 0.661198i | \(-0.229952\pi\) |
−0.947720 | + | 0.319103i | \(0.896618\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.82548 | − | 3.16183i | 0.816380 | − | 1.41401i | −0.0919522 | − | 0.995763i | \(-0.529311\pi\) |
0.908333 | − | 0.418249i | \(-0.137356\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.95459 | − | 1.78314i | −0.738766 | − | 0.673962i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.26594 | − | 2.19268i | 0.421981 | − | 0.730892i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.18865 | − | 2.05880i | −0.358391 | − | 0.620751i | 0.629301 | − | 0.777161i | \(-0.283341\pi\) |
−0.987692 | + | 0.156410i | \(0.950008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.46860 | 1.51672 | 0.758358 | − | 0.651838i | \(-0.226002\pi\) | ||||
0.758358 | + | 0.651838i | \(0.226002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.49795 | −0.644968 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.43032 | + | 4.20943i | 0.589438 | + | 1.02094i | 0.994306 | + | 0.106562i | \(0.0339842\pi\) |
−0.404868 | + | 0.914375i | \(0.632682\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.387898 | + | 1.76814i | −0.0846462 | + | 0.385841i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.887746 | − | 1.53762i | 0.185108 | − | 0.320616i | −0.758505 | − | 0.651667i | \(-0.774070\pi\) |
0.943613 | + | 0.331051i | \(0.107403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.16477 | − | 7.21359i | −0.832954 | − | 1.44272i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.78485 | −0.728396 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.04283 | −1.12213 | −0.561063 | − | 0.827773i | \(-0.689607\pi\) | ||||
−0.561063 | + | 0.827773i | \(0.689607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.849279 | − | 1.47099i | −0.152535 | − | 0.264198i | 0.779624 | − | 0.626248i | \(-0.215410\pi\) |
−0.932159 | + | 0.362050i | \(0.882077\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.813260 | + | 1.40861i | −0.141570 | + | 0.245207i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.20604 | + | 2.92500i | −1.55610 | + | 0.494415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.81318 | + | 4.87257i | −0.462483 | + | 0.801045i | −0.999084 | − | 0.0427915i | \(-0.986375\pi\) |
0.536601 | + | 0.843836i | \(0.319708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.87078 | − | 3.24028i | −0.299564 | − | 0.518860i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.10972 | 0.474227 | 0.237114 | − | 0.971482i | \(-0.423799\pi\) | ||||
0.237114 | + | 0.971482i | \(0.423799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.62191 | − | 8.00539i | −0.688994 | − | 1.19337i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.61508 | − | 4.52946i | 0.381449 | − | 0.660689i | −0.609820 | − | 0.792540i | \(-0.708758\pi\) |
0.991270 | + | 0.131850i | \(0.0420918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.640854 | + | 6.97060i | 0.0915506 | + | 0.995800i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.66280 | − | 2.88005i | 0.232838 | − | 0.403287i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.23257 | + | 5.59897i | 0.444027 | + | 0.769077i | 0.997984 | − | 0.0634680i | \(-0.0202161\pi\) |
−0.553957 | + | 0.832545i | \(0.686883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.67942 | −1.17033 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.684189 | 0.0906230 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.76133 | + | 6.51482i | 0.489684 | + | 0.848157i | 0.999930 | − | 0.0118716i | \(-0.00377892\pi\) |
−0.510246 | + | 0.860029i | \(0.670446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.87796 | − | 6.71683i | 0.496522 | − | 0.860002i | −0.503470 | − | 0.864013i | \(-0.667943\pi\) |
0.999992 | + | 0.00401117i | \(0.00127680\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.38424 | + | 2.02844i | −0.804339 | + | 0.255559i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.98283 | − | 17.2908i | 1.23822 | − | 2.14466i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.31045 | + | 2.26977i | 0.160097 | + | 0.277296i | 0.934903 | − | 0.354902i | \(-0.115486\pi\) |
−0.774806 | + | 0.632199i | \(0.782153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.21477 | −0.146241 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1529 | 1.32361 | 0.661805 | − | 0.749676i | \(-0.269791\pi\) | ||||
0.661805 | + | 0.749676i | \(0.269791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.26525 | − | 12.5838i | −0.850333 | − | 1.47282i | −0.880908 | − | 0.473288i | \(-0.843067\pi\) |
0.0305744 | − | 0.999532i | \(-0.490266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.84949 | + | 4.93546i | −0.329030 | + | 0.569898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.34780 | + | 6.14363i | −0.153596 | + | 0.700132i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.480902 | + | 0.832946i | −0.0541057 | + | 0.0937138i | −0.891810 | − | 0.452411i | \(-0.850564\pi\) |
0.837704 | + | 0.546124i | \(0.183897\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.50305 | − | 4.33541i | −0.278117 | − | 0.481712i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0476 | −1.65169 | −0.825844 | − | 0.563898i | \(-0.809301\pi\) | ||||
−0.825844 | + | 0.563898i | \(0.809301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.7460 | 1.92482 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.06722 | + | 3.58053i | 0.221629 | + | 0.383873i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.01606 | + | 10.4201i | −0.637701 | + | 1.10453i | 0.348235 | + | 0.937407i | \(0.386781\pi\) |
−0.985936 | + | 0.167123i | \(0.946552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6889 | − | 9.75126i | −1.12050 | − | 1.02221i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.581067 | + | 1.00644i | −0.0602539 | + | 0.104363i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.82548 | + | 3.16183i | 0.187290 | + | 0.324397i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.26438 | −0.636052 | −0.318026 | − | 0.948082i | \(-0.603020\pi\) | ||||
−0.318026 | + | 0.948082i | \(0.603020\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.01904 | −0.604937 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.85798 | + | 4.95016i | 0.284379 | + | 0.492559i | 0.972458 | − | 0.233076i | \(-0.0748792\pi\) |
−0.688079 | + | 0.725636i | \(0.741546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.849397 | − | 1.47120i | 0.0836935 | − | 0.144961i | −0.821140 | − | 0.570726i | \(-0.806662\pi\) |
0.904834 | + | 0.425765i | \(0.139995\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.88247 | + | 4.45418i | 0.476480 | + | 0.434684i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.62921 | + | 6.28598i | −0.350849 | + | 0.607688i | −0.986398 | − | 0.164372i | \(-0.947440\pi\) |
0.635550 | + | 0.772060i | \(0.280774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.22246 | − | 15.9738i | −0.883351 | − | 1.53001i | −0.847592 | − | 0.530648i | \(-0.821948\pi\) |
−0.0357590 | − | 0.999360i | \(-0.511385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.84949 | 0.365377 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9243 | 1.68618 | 0.843090 | − | 0.537772i | \(-0.180734\pi\) | ||||
0.843090 | + | 0.537772i | \(0.180734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.24113 | − | 5.61380i | −0.302237 | − | 0.523490i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.92294 | − | 11.9909i | 0.640026 | − | 1.10856i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.75571 | − | 12.5613i | 0.252616 | − | 1.15149i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.67423 | − | 4.63190i | 0.243112 | − | 0.421082i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.684189 | + | 1.18505i | 0.0616912 | + | 0.106852i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1560 | −1.08727 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.8044 | 1.49115 | 0.745575 | − | 0.666421i | \(-0.232175\pi\) | ||||
0.745575 | + | 0.666421i | \(0.232175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.06382 | − | 1.84258i | −0.0936638 | − | 0.162230i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.05319 | − | 8.75239i | 0.441500 | − | 0.764700i | −0.556301 | − | 0.830981i | \(-0.687780\pi\) |
0.997801 | + | 0.0662810i | \(0.0211134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52154 | − | 0.801158i | 0.218645 | − | 0.0694692i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.90918 | + | 11.9671i | −0.594648 | + | 1.02996i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.77605 | + | 4.80826i | 0.237174 | + | 0.410797i | 0.959902 | − | 0.280335i | \(-0.0904456\pi\) |
−0.722728 | + | 0.691132i | \(0.757112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.35122 | 0.369066 | 0.184533 | − | 0.982826i | \(-0.440923\pi\) | ||||
0.184533 | + | 0.982826i | \(0.440923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.57842 | −0.301357 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.50024 | − | 11.2588i | −0.543578 | − | 0.941504i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0311 | + | 19.1064i | −0.916081 | + | 1.58670i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.91102 | − | 2.76433i | 0.322576 | − | 0.227998i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.07213 | + | 10.5172i | −0.497448 | + | 0.861605i | −0.999996 | − | 0.00294443i | \(-0.999063\pi\) |
0.502548 | + | 0.864549i | \(0.332396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.89604 | + | 13.6763i | 0.642571 | + | 1.11297i | 0.984857 | + | 0.173370i | \(0.0554655\pi\) |
−0.342286 | + | 0.939596i | \(0.611201\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.3066 | 0.994927 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.20138 | −0.498106 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.91918 | − | 6.78822i | −0.312785 | − | 0.541759i | 0.666180 | − | 0.745791i | \(-0.267928\pi\) |
−0.978964 | + | 0.204033i | \(0.934595\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.21169 | − | 3.83075i | 0.175398 | − | 0.303798i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47697 | + | 1.42245i | −0.352835 | + | 0.112105i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.43233 | − | 4.21292i | 0.190515 | − | 0.329982i | −0.754906 | − | 0.655833i | \(-0.772318\pi\) |
0.945421 | + | 0.325851i | \(0.105651\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.96918 | + | 5.14277i | 0.231151 | + | 0.400364i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6708 | −1.05788 | −0.528939 | − | 0.848660i | \(-0.677410\pi\) | ||||
−0.528939 | + | 0.848660i | \(0.677410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9056 | 1.30043 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.26594 | + | 2.19268i | 0.0968091 | + | 0.167678i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.67454 | − | 4.63243i | 0.203341 | − | 0.352197i | −0.746262 | − | 0.665653i | \(-0.768153\pi\) |
0.949603 | + | 0.313455i | \(0.101487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72239 | + | 21.5260i | −0.356979 | + | 1.62721i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.57346 | − | 4.45737i | 0.193433 | − | 0.335036i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.343912 | + | 0.595673i | 0.0257052 | + | 0.0445227i | 0.878592 | − | 0.477573i | \(-0.158484\pi\) |
−0.852887 | + | 0.522096i | \(0.825150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.91388 | 0.588234 | 0.294117 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294117 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.30652 | −0.392269 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.2708 | + | 17.7896i | 0.755125 | + | 1.30791i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.77758 | − | 10.0071i | 0.422499 | − | 0.731789i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.39784 | + | 6.74891i | 0.538114 | + | 0.490911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0448 | + | 20.8622i | −0.871530 | + | 1.50954i | −0.0111172 | + | 0.999938i | \(0.503539\pi\) |
−0.860413 | + | 0.509597i | \(0.829795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23886 | + | 3.87783i | 0.161157 | + | 0.279132i | 0.935284 | − | 0.353898i | \(-0.115144\pi\) |
−0.774127 | + | 0.633030i | \(0.781811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.6603 | −0.978233 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0277 | 1.07068 | 0.535339 | − | 0.844637i | \(-0.320184\pi\) | ||||
0.535339 | + | 0.844637i | \(0.320184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6957 | + | 23.7217i | 0.970866 | + | 1.68159i | 0.692953 | + | 0.720983i | \(0.256309\pi\) |
0.277913 | + | 0.960606i | \(0.410357\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.896596 | − | 1.55295i | 0.0632410 | − | 0.109537i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8113 | + | 10.7752i | 0.828988 | + | 0.756270i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.65096 | + | 6.32365i | −0.254994 | + | 0.441663i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.24767 | − | 3.89308i | −0.156224 | − | 0.270588i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.37730 | 0.164441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.37592 | −0.0947219 | −0.0473610 | − | 0.998878i | \(-0.515081\pi\) | ||||
−0.0473610 | + | 0.998878i | \(0.515081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.81535 | − | 6.60839i | −0.261424 | − | 0.452799i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.67673 | − | 9.83239i | 0.387150 | − | 0.670563i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.962990 | + | 4.38957i | −0.0653720 | + | 0.297984i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.97080 | + | 8.60968i | −0.335896 | + | 0.581789i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2904 | + | 23.0197i | 0.894011 | + | 1.54847i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.7782 | 1.86016 | 0.930082 | − | 0.367352i | \(-0.119735\pi\) | ||||
0.930082 | + | 0.367352i | \(0.119735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.0894 | −1.40596 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2953 | − | 17.8319i | −0.683320 | − | 1.18355i | −0.973962 | − | 0.226713i | \(-0.927202\pi\) |
0.290641 | − | 0.956832i | \(-0.406131\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0793 | + | 22.6541i | −0.864307 | + | 1.49702i | 0.00342574 | + | 0.999994i | \(0.498910\pi\) |
−0.867733 | + | 0.497030i | \(0.834424\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.10133 | − | 1.30310i | 0.269848 | − | 0.0857376i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.29226 | − | 10.8985i | 0.412219 | − | 0.713985i | −0.582913 | − | 0.812535i | \(-0.698087\pi\) |
0.995132 | + | 0.0985498i | \(0.0314204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.54758 | − | 16.5369i | −0.622815 | − | 1.07875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.658055 | 0.0427453 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.5846 | 1.84898 | 0.924492 | − | 0.381202i | \(-0.124490\pi\) | ||||
0.924492 | + | 0.381202i | \(0.124490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.32273 | − | 4.02309i | −0.149620 | − | 0.259150i | 0.781467 | − | 0.623947i | \(-0.214472\pi\) |
−0.931087 | + | 0.364797i | \(0.881138\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.38984 | + | 12.7996i | −0.474059 | + | 0.821093i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.2097 | + | 10.6984i | 1.48281 | + | 0.683498i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.73430 | + | 4.73595i | −0.173979 | + | 0.301341i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.14770 | + | 8.91608i | 0.326222 | + | 0.565033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0953 | −0.763446 | −0.381723 | − | 0.924277i | \(-0.624669\pi\) | ||||
−0.381723 | + | 0.924277i | \(0.624669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.22087 | −0.265364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.07081 | − | 10.5149i | −0.380169 | − | 0.658471i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.946193 | + | 1.63885i | −0.0590219 | + | 0.102229i | −0.894027 | − | 0.448014i | \(-0.852132\pi\) |
0.835005 | + | 0.550243i | \(0.185465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.1871 | − | 4.50760i | 0.881541 | − | 0.280088i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.64988 | + | 13.2500i | −0.473516 | + | 0.820153i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.5901 | − | 20.0746i | −0.714674 | − | 1.23785i | −0.963085 | − | 0.269197i | \(-0.913242\pi\) |
0.248411 | − | 0.968655i | \(-0.420092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.6040 | 1.44998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.23224 | 0.503805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.1491 | − | 21.0429i | −0.740744 | − | 1.28301i | −0.952157 | − | 0.305610i | \(-0.901140\pi\) |
0.211412 | − | 0.977397i | \(-0.432194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.20481 | + | 10.7470i | −0.376915 | + | 0.652836i | −0.990612 | − | 0.136706i | \(-0.956349\pi\) |
0.613696 | + | 0.789542i | \(0.289682\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.12126 | + | 9.66928i | −0.128384 | + | 0.585211i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.90089 | + | 17.1488i | −0.597046 | + | 1.03411i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16899 | + | 2.02475i | 0.0702377 | + | 0.121655i | 0.899005 | − | 0.437938i | \(-0.144291\pi\) |
−0.828768 | + | 0.559593i | \(0.810958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.30056 | −0.257468 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.65566 | 0.218078 | 0.109039 | − | 0.994037i | \(-0.465223\pi\) | ||||
0.109039 | + | 0.994037i | \(0.465223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.79237 | − | 8.30064i | −0.284877 | − | 0.493422i | 0.687702 | − | 0.725993i | \(-0.258619\pi\) |
−0.972579 | + | 0.232571i | \(0.925286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.24897 | − | 2.16329i | 0.0739828 | − | 0.128142i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.90918 | + | 3.56627i | 0.230752 | + | 0.210510i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.31288 | + | 5.73807i | −0.194875 | + | 0.337534i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.14301 | + | 3.71180i | 0.125625 | + | 0.217590i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0249 | −0.585662 | −0.292831 | − | 0.956164i | \(-0.594597\pi\) | ||||
−0.292831 | + | 0.956164i | \(0.594597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.4650 | 1.59907 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.49886 | + | 7.79226i | 0.261050 | + | 0.452153i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.85473 | − | 8.40864i | 0.280756 | − | 0.486284i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.07822 | − | 5.54505i | −0.350343 | − | 0.319611i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.95540 | − | 3.38684i | 0.112335 | − | 0.194569i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.1583 | − | 24.5229i | −0.810702 | − | 1.40418i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.0911 | 1.77446 | 0.887230 | − | 0.461327i | \(-0.152627\pi\) | ||||
0.887230 | + | 0.461327i | \(0.152627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.16230 | −0.0661207 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.29995 | + | 2.25158i | 0.0737134 | + | 0.127675i | 0.900526 | − | 0.434802i | \(-0.143182\pi\) |
−0.826813 | + | 0.562477i | \(0.809848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.28660 | − | 12.6208i | 0.411863 | − | 0.713368i | −0.583230 | − | 0.812307i | \(-0.698211\pi\) |
0.995094 | + | 0.0989388i | \(0.0315448\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.24074 | + | 23.8888i | −0.295282 | + | 1.34598i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.65025 | + | 9.78653i | −0.317350 | + | 0.549666i | −0.979934 | − | 0.199321i | \(-0.936126\pi\) |
0.662584 | + | 0.748987i | \(0.269460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.18280 | + | 12.4410i | 0.402160 | + | 0.696561i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.96613 | 0.277182 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.86063 | −0.270453 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.7755 | − | 39.4482i | −1.26335 | − | 2.18819i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.30990 | + | 10.9291i | −0.348938 | + | 0.604379i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1881 | + | 4.19019i | −0.727081 | + | 0.231013i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.66890 | − | 13.2829i | 0.421521 | − | 0.730096i | −0.574568 | − | 0.818457i | \(-0.694830\pi\) |
0.996088 | + | 0.0883616i | \(0.0281631\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.12264 | + | 12.3368i | 0.390318 | + | 0.676051i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.56882 | 0.522801 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.62537 | 0.415380 | 0.207690 | − | 0.978195i | \(-0.433405\pi\) | ||||
0.207690 | + | 0.978195i | \(0.433405\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.13182 | − | 10.6206i | −0.333035 | − | 0.576833i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.01899 | + | 3.49699i | −0.109334 | + | 0.189373i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1769 | − | 14.7674i | 0.603497 | − | 0.797365i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.21754 | + | 3.84090i | −0.119389 | + | 0.206787i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.4379 | − | 21.5430i | −0.667700 | − | 1.15649i | −0.978546 | − | 0.206029i | \(-0.933946\pi\) |
0.310846 | − | 0.950460i | \(-0.399388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.0832 | 1.66384 | 0.831922 | − | 0.554893i | \(-0.187241\pi\) | ||||
0.831922 | + | 0.554893i | \(0.187241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6979 | −1.10477 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.35250 | − | 12.7349i | −0.391334 | − | 0.677810i | 0.601292 | − | 0.799029i | \(-0.294653\pi\) |
−0.992626 | + | 0.121219i | \(0.961320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3595 | − | 35.2636i | 1.08057 | − | 1.87160i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.38560 | + | 2.66432i | −0.443813 | + | 0.141011i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0452 | + | 17.3988i | −0.530165 | + | 0.918272i | 0.469216 | + | 0.883083i | \(0.344537\pi\) |
−0.999381 | + | 0.0351887i | \(0.988797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.65936 | −0.192066 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −53.0503 | −2.77678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2569 | + | 29.8898i | 0.900802 | + | 1.56023i | 0.826455 | + | 0.563002i | \(0.190354\pi\) |
0.0743465 | + | 0.997232i | \(0.476313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.53189 | + | 4.38535i | −0.131805 | + | 0.228292i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.66538 | − | 16.7078i | 0.190297 | − | 0.867426i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.7955 | − | 23.8944i | 0.714301 | − | 1.23721i | −0.248927 | − | 0.968522i | \(-0.580078\pi\) |
0.963228 | − | 0.268684i | \(-0.0865888\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.15850 | + | 7.20274i | 0.214744 | + | 0.371948i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.0458 | −1.70195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.40171 | 0.482933 | 0.241467 | − | 0.970409i | \(-0.422372\pi\) | ||||
0.241467 | + | 0.970409i | \(0.422372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.74869 | − | 9.95703i | −0.294515 | − | 0.510114i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.16005 | + | 12.4016i | −0.365861 | + | 0.633691i | −0.988914 | − | 0.148489i | \(-0.952559\pi\) |
0.623053 | + | 0.782180i | \(0.285892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.9647 | + | 15.4766i | 0.864603 | + | 0.788760i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.93672 | − | 6.81860i | 0.200115 | − | 0.346609i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.817066 | + | 1.41520i | 0.0414269 | + | 0.0717535i | 0.885995 | − | 0.463694i | \(-0.153476\pi\) |
−0.844569 | + | 0.535448i | \(0.820143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.63002 | 0.436439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.91468 | −0.348799 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.75575 | + | 3.04106i | 0.0883416 | + | 0.153012i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.65489 | + | 6.33046i | −0.183434 | + | 0.317717i | −0.943048 | − | 0.332658i | \(-0.892055\pi\) |
0.759614 | + | 0.650374i | \(0.225388\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.33731 | − | 1.22000i | −0.0669492 | − | 0.0610765i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4986 | + | 23.3803i | −0.674088 | + | 1.16756i | 0.302646 | + | 0.953103i | \(0.402130\pi\) |
−0.976734 | + | 0.214452i | \(0.931203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.64437 | − | 8.04428i | −0.231352 | − | 0.400714i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.2771 | −0.908196 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.3755 | 0.663000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6820 | − | 21.9658i | −0.627082 | − | 1.08614i | −0.988134 | − | 0.153593i | \(-0.950916\pi\) |
0.361052 | − | 0.932546i | \(-0.382418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.89934 | − | 3.28976i | 0.0936876 | − | 0.162272i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26494 | − | 19.4408i | 0.209864 | − | 0.956618i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.4691 | + | 47.5779i | −1.34841 | + | 2.33551i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.48853 | − | 2.57821i | −0.0728935 | − | 0.126255i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.43567 | 0.412109 | 0.206055 | − | 0.978540i | \(-0.433938\pi\) | ||||
0.206055 | + | 0.978540i | \(0.433938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5892 | 0.516087 | 0.258044 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258044 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.62109 | − | 11.4681i | −0.321929 | − | 0.557597i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.2434 | − | 35.0626i | 0.981950 | − | 1.70079i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.5568 | + | 6.21372i | −0.946422 | + | 0.300703i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.44739 | + | 7.70311i | −0.214722 | + | 0.371910i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5234 | + | 25.1553i | 0.699567 | + | 1.21169i | 0.968617 | + | 0.248560i | \(0.0799573\pi\) |
−0.269049 | + | 0.963126i | \(0.586709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.4759 | −0.743725 | −0.371862 | − | 0.928288i | \(-0.621281\pi\) | ||||
−0.371862 | + | 0.928288i | \(0.621281\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.0947 | 0.723734 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.887746 | + | 1.53762i | 0.0424667 | + | 0.0735544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3095 | − | 21.3206i | 0.587499 | − | 1.01758i | −0.407060 | − | 0.913401i | \(-0.633446\pi\) |
0.994559 | − | 0.104176i | \(-0.0332206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.0956 | + | 7.41920i | 0.766456 | + | 0.353295i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.22398 | + | 7.31614i | −0.200687 | + | 0.347600i | −0.948750 | − | 0.316027i | \(-0.897651\pi\) |
0.748063 | + | 0.663628i | \(0.230984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.9644 | + | 38.0435i | 1.04121 | + | 1.80343i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.30896 | 0.393000 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.8063 | −0.604368 | −0.302184 | − | 0.953250i | \(-0.597716\pi\) | ||||
−0.302184 | + | 0.953250i | \(0.597716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.37730 | + | 4.11760i | 0.111943 | + | 0.193890i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.40238 | − | 9.35720i | 0.253826 | − | 0.439640i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50.3441 | + | 15.9956i | −2.36017 | + | 0.749887i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.2579 | − | 24.6953i | 0.666954 | − | 1.15520i | −0.311797 | − | 0.950149i | \(-0.600931\pi\) |
0.978751 | − | 0.205050i | \(-0.0657358\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.19839 | − | 15.9321i | −0.429344 | − | 0.743646i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.8648 | −1.76354 | −0.881771 | − | 0.471679i | \(-0.843648\pi\) | ||||
−0.881771 | + | 0.471679i | \(0.843648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6922 | 1.14754 | 0.573772 | − | 0.819015i | \(-0.305480\pi\) | ||||
0.573772 | + | 0.819015i | \(0.305480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.12146 | + | 3.67447i | 0.0983802 | + | 0.170399i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.17249 | − | 2.03081i | 0.0542563 | − | 0.0939747i | −0.837622 | − | 0.546251i | \(-0.816055\pi\) |
0.891878 | + | 0.452276i | \(0.149388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.48591 | − | 6.77318i | 0.0686129 | − | 0.312757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.68146 | + | 4.64442i | −0.123555 | + | 0.214004i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.69636 | − | 6.40228i | −0.169959 | − | 0.294377i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.32954 | 0.382185 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.3690 | 0.749484 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.6564 | − | 25.3857i | −0.669670 | − | 1.15990i | −0.977996 | − | 0.208621i | \(-0.933102\pi\) |
0.308327 | − | 0.951281i | \(-0.400231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.3841 | + | 26.6461i | −0.701456 | + | 1.21496i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.37438 | + | 2.16610i | 0.108038 | + | 0.0985611i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4355 | + | 19.8069i | −0.519260 | + | 0.899385i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.03223 | − | 12.1802i | −0.318661 | − | 0.551937i | 0.661548 | − | 0.749903i | \(-0.269900\pi\) |
−0.980209 | + | 0.197966i | \(0.936566\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.32835 | −0.150513 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8667 | 1.52838 | 0.764191 | − | 0.644991i | \(-0.223139\pi\) | ||||
0.764191 | + | 0.644991i | \(0.223139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6860 | − | 25.4369i | −0.661424 | − | 1.14562i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.9877 | + | 19.0312i | −0.493858 | + | 0.855388i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.7994 | − | 19.8872i | −0.977838 | − | 0.892062i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1457 | + | 22.7690i | −0.588482 | + | 1.01928i | 0.405950 | + | 0.913895i | \(0.366941\pi\) |
−0.994432 | + | 0.105385i | \(0.966393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.67670 | + | 8.10028i | 0.208940 | + | 0.361894i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.7282 | 1.63763 | 0.818815 | − | 0.574058i | \(-0.194632\pi\) | ||||
0.818815 | + | 0.574058i | \(0.194632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.8687 | 0.928646 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.78331 | − | 10.0170i | −0.256846 | − | 0.444870i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.38848 | + | 5.86901i | −0.150192 | + | 0.260139i | −0.931298 | − | 0.364259i | \(-0.881322\pi\) |
0.781106 | + | 0.624398i | \(0.214656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.23800 | + | 37.5511i | −0.364428 | + | 1.66116i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.89243 | − | 3.27778i | 0.0835527 | − | 0.144718i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.10112 | − | 5.37129i | −0.136651 | − | 0.236687i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4337 | −0.546832 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.65977 | −0.160646 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6681 | + | 27.1379i | 0.686431 | + | 1.18893i | 0.972985 | + | 0.230869i | \(0.0741569\pi\) |
−0.286554 | + | 0.958064i | \(0.592510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9196 | − | 27.5735i | 0.696114 | − | 1.20570i | −0.273690 | − | 0.961818i | \(-0.588244\pi\) |
0.969804 | − | 0.243887i | \(-0.0784225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.3702 | − | 4.56578i | 0.627166 | − | 0.199267i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.12803 | − | 7.14997i | 0.179820 | − | 0.311457i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.92381 | + | 17.1885i | 0.431470 | + | 0.747328i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.0465 | 0.826549 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9372 | −0.473743 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2501 | + | 22.9499i | 0.572852 | + | 0.992209i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.235301 | − | 0.407553i | 0.0101540 | − | 0.0175872i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.5893 | − | 9.60499i | 0.585334 | − | 0.413716i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.48383 | + | 7.76621i | −0.192775 | + | 0.333896i | −0.946169 | − | 0.323674i | \(-0.895082\pi\) |
0.753394 | + | 0.657569i | \(0.228415\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.70729 | − | 4.68917i | −0.116181 | − | 0.201232i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −67.3417 | −2.88460 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0700 | −1.11467 | −0.557337 | − | 0.830287i | \(-0.688177\pi\) | ||||
−0.557337 | + | 0.830287i | \(0.688177\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.81856 | − | 17.0062i | −0.419046 | − | 0.725809i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.02142 | − | 5.23324i | 0.128717 | − | 0.222944i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.42522 | − | 0.770556i | 0.103131 | − | 0.0327674i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.02717 | − | 12.1714i | 0.298287 | − | 0.516648i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.1375 | − | 21.0228i | −0.514284 | − | 0.890766i | −0.999863 | − | 0.0165730i | \(-0.994724\pi\) |
0.485579 | − | 0.874193i | \(-0.338609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.0058 | 0.719268 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.90592 | −0.333788 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6075 | − | 27.0330i | −0.657779 | − | 1.13931i | −0.981189 | − | 0.193048i | \(-0.938163\pi\) |
0.323410 | − | 0.946259i | \(-0.395171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.7206 | − | 56.6737i | 1.37656 | − | 2.38428i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.83819 | + | 12.9372i | −0.119193 | + | 0.543313i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.48242 | − | 14.6920i | 0.355602 | − | 0.615920i | −0.631619 | − | 0.775279i | \(-0.717609\pi\) |
0.987221 | + | 0.159359i | \(0.0509426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.14069 | − | 5.43984i | −0.131434 | − | 0.227650i | 0.792796 | − | 0.609488i | \(-0.208625\pi\) |
−0.924230 | + | 0.381837i | \(0.875291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4818 | 0.688538 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7890 | −0.616745 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.12592 | + | 14.0745i | 0.338287 | + | 0.585930i | 0.984111 | − | 0.177557i | \(-0.0568193\pi\) |
−0.645824 | + | 0.763486i | \(0.723486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.53181 | − | 2.65316i | 0.0636597 | − | 0.110262i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.4119 | + | 26.8319i | 1.22021 | + | 1.11318i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.68477 | − | 13.3104i | 0.318271 | − | 0.551261i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.2754 | − | 43.7783i | −1.04501 | − | 1.81001i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.7490 | −1.88826 | −0.944131 | − | 0.329571i | \(-0.893096\pi\) | ||||
−0.944131 | + | 0.329571i | \(0.893096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.69856 | 0.0699879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.14089 | − | 8.90428i | −0.211468 | − | 0.366273i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.47092 | + | 6.01180i | −0.142533 | + | 0.246875i | −0.928450 | − | 0.371457i | \(-0.878858\pi\) |
0.785917 | + | 0.618333i | \(0.212192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.6862 | − | 31.6435i | −1.42199 | − | 1.29726i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.37048 | − | 16.2301i | 0.383508 | − | 0.664256i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.29513 | − | 12.6355i | −0.298071 | − | 0.516274i | 0.677624 | − | 0.735409i | \(-0.263010\pi\) |
−0.975695 | + | 0.219135i | \(0.929677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.5586 | −1.77679 | −0.888396 | − | 0.459077i | \(-0.848180\pi\) | ||||
−0.888396 | + | 0.459077i | \(0.848180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.63583 | 0.270232 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.76352 | − | 16.9109i | −0.396943 | − | 0.687526i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7216 | − | 20.3023i | 0.475763 | − | 0.824046i | −0.523851 | − | 0.851810i | \(-0.675505\pi\) |
0.999615 | + | 0.0277638i | \(0.00883863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.34400 | − | 10.6846i | 0.0949836 | − | 0.432962i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3008 | − | 24.7698i | 0.578550 | − | 1.00208i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.79313 | + | 3.10580i | 0.0724240 | + | 0.125442i | 0.899963 | − | 0.435966i | \(-0.143593\pi\) |
−0.827539 | + | 0.561408i | \(0.810260\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.99590 | 0.201454 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.93981 | 0.239128 | 0.119564 | − | 0.992827i | \(-0.461850\pi\) | ||||
0.119564 | + | 0.992827i | \(0.461850\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7618 | − | 23.8361i | −0.553134 | − | 0.958055i | −0.998046 | − | 0.0624814i | \(-0.980099\pi\) |
0.444913 | − | 0.895574i | \(-0.353235\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.35999 | + | 5.81967i | −0.134832 | + | 0.233535i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.3394 | − | 9.63962i | 1.21552 | − | 0.386203i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.36675 | + | 2.36727i | −0.0546698 | + | 0.0946909i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.813260 | − | 1.40861i | −0.0324785 | − | 0.0562544i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.3476 | −1.09042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.2443 | −1.80115 | −0.900573 | − | 0.434705i | \(-0.856853\pi\) | ||||
−0.900573 | + | 0.434705i | \(0.856853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.470693 | + | 0.815264i | 0.0187084 | + | 0.0324038i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.6761 | − | 53.1326i | 1.21735 | − | 2.10850i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.50457 | + | 38.1194i | 0.138856 | + | 1.51035i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1190 | − | 24.4548i | 0.558538 | − | 0.967416i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2499 | + | 24.6816i | 0.562838 | + | 0.974863i | 0.997247 | + | 0.0741480i | \(0.0236237\pi\) |
−0.434410 | + | 0.900715i | \(0.643043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.8611 | −0.901553 | −0.450776 | − | 0.892637i | \(-0.648853\pi\) | ||||
−0.450776 | + | 0.892637i | \(0.648853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.76791 | −0.305861 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0417 | + | 20.8568i | 0.473408 | + | 0.819967i | 0.999537 | − | 0.0304384i | \(-0.00969034\pi\) |
−0.526129 | + | 0.850405i | \(0.676357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.94180 | − | 15.4877i | 0.350996 | − | 0.607944i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.93037 | − | 0.931053i | 0.114850 | − | 0.0364909i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.02629 | + | 3.50964i | −0.0792950 | + | 0.137343i | −0.902946 | − | 0.429754i | \(-0.858600\pi\) |
0.823651 | + | 0.567097i | \(0.191934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.4490 | − | 31.9546i | −0.720863 | − | 1.24857i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.7896 | −1.43530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.7165 | 0.923864 | 0.461932 | − | 0.886915i | \(-0.347156\pi\) | ||||
0.461932 | + | 0.886915i | \(0.347156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.60872 | + | 14.9107i | 0.334840 | + | 0.579961i | 0.983454 | − | 0.181157i | \(-0.0579842\pi\) |
−0.648614 | + | 0.761118i | \(0.724651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.09316 | − | 15.7498i | 0.353149 | − | 0.611672i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.06990 | − | 9.43516i | 0.0802671 | − | 0.365880i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.36450 | + | 9.29159i | −0.207714 | + | 0.359772i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50276 | − | 16.4593i | −0.367398 | − | 0.636352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.4381 | −0.711796 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1890 | −0.778229 | −0.389115 | − | 0.921189i | \(-0.627219\pi\) | ||||
−0.389115 | + | 0.921189i | \(0.627219\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.7630 | + | 27.3024i | 0.606720 | + | 1.05087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.7264 | + | 20.3107i | −0.450681 | + | 0.780602i | −0.998428 | − | 0.0560413i | \(-0.982152\pi\) |
0.547747 | + | 0.836644i | \(0.315485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2443 | + | 11.1702i | 0.469893 | + | 0.428675i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.04390 | + | 12.2004i | −0.269923 | + | 0.467520i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8619 | − | 22.2775i | −0.492148 | − | 0.852425i | 0.507811 | − | 0.861468i | \(-0.330455\pi\) |
−0.999959 | + | 0.00904340i | \(0.997121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.2705 | 0.774496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.8975 | 0.682832 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.6776 | + | 30.6185i | 0.673463 | + | 1.16647i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4045 | + | 44.0019i | −0.966434 | + | 1.67391i | −0.260722 | + | 0.965414i | \(0.583961\pi\) |
−0.705712 | + | 0.708499i | \(0.749373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.7648 | + | 10.7328i | 0.446907 | + | 0.407704i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.94307 | − | 13.7578i | 0.301298 | − | 0.521863i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.86063 | − | 8.41886i | −0.184110 | − | 0.318887i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.61018 | −0.325667 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4663 | 1.75501 | 0.877504 | − | 0.479570i | \(-0.159207\pi\) | ||||
0.877504 | + | 0.479570i | \(0.159207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.81318 | − | 4.87257i | −0.106101 | − | 0.183772i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.53234 | + | 11.3144i | −0.246022 | + | 0.426123i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.24063 | − | 14.7717i | 0.121876 | − | 0.555547i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.46179 | + | 2.53189i | −0.0548986 | + | 0.0950872i | −0.892169 | − | 0.451702i | \(-0.850817\pi\) |
0.837270 | + | 0.546790i | \(0.184150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21759 | + | 2.10892i | 0.0456631 | + | 0.0790909i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.01578 | −0.112942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −47.4643 | −1.77506 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.77863 | − | 16.9371i | −0.365190 | − | 0.632527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.8003 | + | 25.6349i | −0.551959 | + | 0.956020i | 0.446175 | + | 0.894946i | \(0.352786\pi\) |
−0.998133 | + | 0.0610745i | \(0.980547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28357 | + | 1.36100i | −0.159528 | + | 0.0506863i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.58919 | + | 2.75255i | −0.0591025 | + | 0.102369i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.1670 | + | 43.5905i | 0.934678 | + | 1.61891i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.1285 | 1.45119 | 0.725597 | − | 0.688120i | \(-0.241564\pi\) | ||||
0.725597 | + | 0.688120i | \(0.241564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.90622 | −0.181712 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.55759 | + | 13.0901i | 0.279528 | + | 0.484156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.34720 | + | 12.7257i | −0.271375 | + | 0.470035i | −0.969214 | − | 0.246219i | \(-0.920812\pi\) |
0.697839 | + | 0.716254i | \(0.254145\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.60082 | − | 17.4122i | −0.0590471 | − | 0.642259i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.11533 | − | 5.39591i | 0.114755 | − | 0.198761i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.08118 | − | 13.9970i | −0.297271 | − | 0.514888i | 0.678240 | − | 0.734841i | \(-0.262743\pi\) |
−0.975511 | + | 0.219952i | \(0.929410\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.74155 | 0.137449 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2412 | 0.779265 | 0.389632 | − | 0.920971i | \(-0.372602\pi\) | ||||
0.389632 | + | 0.920971i | \(0.372602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.1691 | + | 38.3980i | 0.812213 | + | 1.40679i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.0494 | + | 32.9945i | −0.696981 | + | 1.20721i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3024 | − | 5.81514i | 0.668754 | − | 0.212481i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0177 | − | 45.0639i | 0.949398 | − | 1.64441i | 0.202702 | − | 0.979240i | \(-0.435028\pi\) |
0.746696 | − | 0.665165i | \(-0.231639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.13772 | + | 7.16675i | 0.150787 | + | 0.261171i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.6563 | 2.09833 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.6379 | 1.11355 | 0.556777 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556777 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.44394 | + | 2.50097i | 0.0524116 | + | 0.0907795i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.79628 | − | 16.9677i | 0.355115 | − | 0.615077i | −0.632023 | − | 0.774950i | \(-0.717775\pi\) |
0.987138 | + | 0.159873i | \(0.0511084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4573 | + | 47.6671i | −0.378578 | + | 1.72566i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.4654 | − | 38.9112i | 0.812239 | − | 1.40684i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.5692 | + | 35.6269i | 0.742711 | + | 1.28641i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.70349 | −0.241734 | −0.120867 | − | 0.992669i | \(-0.538567\pi\) | ||||
−0.120867 | + | 0.992669i | \(0.538567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29475 | 0.0466293 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.77547 | + | 11.7355i | 0.243697 | + | 0.422095i | 0.961764 | − | 0.273878i | \(-0.0883065\pi\) |
−0.718068 | + | 0.695973i | \(0.754973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.07410 | + | 12.2527i | −0.254109 | + | 0.440130i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.52418 | − | 6.86416i | −0.269928 | − | 0.246250i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | − | 1.73205i | 0.0358287 | − | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2569 | − | 22.9616i | −0.474370 | − | 0.821632i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.8712 | 0.817351 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.6176 | −1.02140 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1660 | + | 31.4644i | 0.647547 | + | 1.12158i | 0.983707 | + | 0.179779i | \(0.0575383\pi\) |
−0.336160 | + | 0.941805i | \(0.609128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.92980 | + | 13.7348i | −0.282308 | + | 0.488972i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.0348 | − | 31.9615i | −1.24569 | − | 1.13642i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.2070 | − | 36.7316i | 0.753084 | − | 1.30438i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.07478 | − | 13.9859i | −0.286383 | − | 0.496030i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −55.0232 | −1.94902 | −0.974511 | − | 0.224338i | \(-0.927978\pi\) | ||||
−0.974511 | + | 0.224338i | \(0.927978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4219 | 0.899363 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.2320 | + | 26.3825i | 0.538195 | + | 0.932181i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.2717 | + | 29.9154i | −0.609504 | + | 1.05569i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.67508 | + | 16.7521i | −0.129530 | + | 0.590432i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.31229 | + | 14.3973i | −0.292606 | + | 0.506809i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5581 | + | 23.4833i | 0.476677 | + | 0.825629i | 0.999643 | − | 0.0267249i | \(-0.00850782\pi\) |
−0.522966 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7862 | −0.729903 | −0.364952 | − | 0.931027i | \(-0.618914\pi\) | ||||
−0.364952 | + | 0.931027i | \(0.618914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.49052 | 0.297776 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.88035 | − | 15.3812i | −0.311065 | − | 0.538781i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.55486 | + | 2.69309i | −0.0543976 | + | 0.0942194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −34.9129 | + | 11.0927i | −1.21995 | + | 0.387611i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0837 | + | 36.5181i | −0.735826 | + | 1.27449i | 0.218533 | + | 0.975829i | \(0.429873\pi\) |
−0.954360 | + | 0.298659i | \(0.903461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9765 | − | 24.2079i | −0.487189 | − | 0.843836i | 0.512703 | − | 0.858566i | \(-0.328644\pi\) |
−0.999891 | + | 0.0147305i | \(0.995311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5482 | 0.471686 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.6553 | −1.62236 | −0.811182 | − | 0.584794i | \(-0.801175\pi\) | ||||
−0.811182 | + | 0.584794i | \(0.801175\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.7908 | + | 25.6184i | 0.513706 | + | 0.889764i | 0.999874 | + | 0.0158990i | \(0.00506101\pi\) |
−0.486168 | + | 0.873865i | \(0.661606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.799808 | − | 1.38531i | 0.0277450 | − | 0.0480558i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7848 | + | 19.6384i | −0.962686 | + | 0.680430i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.9558 | + | 43.2247i | −0.863630 | + | 1.49585i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.21440 | + | 5.56750i | 0.111106 | + | 0.192441i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0614 | −0.934263 | −0.467132 | − | 0.884188i | \(-0.654713\pi\) | ||||
−0.467132 | + | 0.884188i | \(0.654713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.51580 | 0.259166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.25058 | − | 2.16607i | −0.0430723 | − | 0.0746034i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.8608 | − | 53.4526i | 1.06165 | − | 1.83882i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.4863 | + | 4.28496i | −0.463396 | + | 0.147233i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.27889 | + | 5.67920i | −0.112531 | + | 0.194910i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.99477 | + | 8.65120i | 0.171219 | + | 0.296559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.19742 | −0.0409989 | −0.0204995 | − | 0.999790i | \(-0.506526\pi\) | ||||
−0.0204995 | + | 0.999790i | \(0.506526\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.24382 | 0.316132 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.2208 | − | 29.8274i | −0.588253 | − | 1.01888i | −0.994461 | − | 0.105103i | \(-0.966483\pi\) |
0.406208 | − | 0.913780i | \(-0.366851\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.87274 | − | 3.24369i | 0.0638972 | − | 0.110673i | −0.832307 | − | 0.554315i | \(-0.812980\pi\) |
0.896204 | + | 0.443642i | \(0.146314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.775795 | − | 3.53629i | 0.0264390 | − | 0.120516i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.9335 | − | 25.8656i | 0.508343 | − | 0.880477i | −0.491610 | − | 0.870816i | \(-0.663591\pi\) |
0.999953 | − | 0.00966107i | \(-0.00307526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.76463 | − | 16.9128i | −0.332007 | − | 0.575054i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.53327 | 0.153958 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.28649 | 0.0775639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.16634 | + | 12.4125i | 0.242822 | + | 0.420580i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.93035 | + | 13.7358i | −0.268402 | + | 0.464885i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.7600 | + | 21.6758i | 0.803236 | + | 0.732777i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.74105 | − | 8.21174i | 0.160094 | − | 0.277291i | −0.774808 | − | 0.632196i | \(-0.782154\pi\) |
0.934902 | + | 0.354906i | \(0.115487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.42947 | + | 5.94002i | 0.115673 | + | 0.200352i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.1936 | 1.11832 | 0.559160 | − | 0.829060i | \(-0.311124\pi\) | ||||
0.559160 | + | 0.829060i | \(0.311124\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.9645 | −0.941079 | −0.470540 | − | 0.882379i | \(-0.655941\pi\) | ||||
−0.470540 | + | 0.882379i | \(0.655941\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.39561 | − | 16.2737i | −0.315830 | − | 0.547034i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.6812 | + | 27.1606i | −0.526523 | + | 0.911965i | 0.472999 | + | 0.881063i | \(0.343171\pi\) |
−0.999522 | + | 0.0309023i | \(0.990162\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8458 | − | 29.9645i | −1.10161 | − | 1.00498i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.95050 | + | 10.3066i | −0.199349 | + | 0.345283i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.61508 | + | 4.52946i | 0.0875104 | + | 0.151573i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.51122 | 0.0839409 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.64310 | −0.221807 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.13205 | + | 8.88897i | 0.171163 | + | 0.296464i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.7123 | + | 27.2145i | −0.523453 | + | 0.906647i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.20625 | + | 5.49843i | −0.0401415 | + | 0.182976i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.4466 | − | 25.0223i | 0.480223 | − | 0.831770i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.36780 | − | 7.56526i | −0.145031 | − | 0.251200i | 0.784354 | − | 0.620314i | \(-0.212995\pi\) |
−0.929384 | + | 0.369113i | \(0.879661\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4721 | 0.480011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.50534 | 0.215532 | 0.107766 | − | 0.994176i | \(-0.465630\pi\) | ||||
0.107766 | + | 0.994176i | \(0.465630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.8863 | + | 30.9800i | 0.591950 | + | 1.02529i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.68695 | + | 16.7783i | −0.320241 | + | 0.554673i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.4836 | + | 8.09681i | −0.841543 | + | 0.267380i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.2251 | + | 28.1027i | −0.535216 | + | 0.927022i | 0.463937 | + | 0.885868i | \(0.346437\pi\) |
−0.999153 | + | 0.0411532i | \(0.986897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.6361 | − | 18.4222i | −0.350471 | − | 0.607033i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.9909 | 2.00754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.8649 | 1.54091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.15057 | − | 3.72491i | −0.0706341 | − | 0.122342i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.9756 | − | 19.0103i | 0.360098 | − | 0.623708i | −0.627879 | − | 0.778311i | \(-0.716077\pi\) |
0.987977 | + | 0.154603i | \(0.0494099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.35715 | − | 2.93031i | −0.208347 | − | 0.0960369i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.889411 | − | 1.54050i | 0.0291180 | − | 0.0504339i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.0937 | − | 36.5354i | −0.689839 | − | 1.19484i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.0361 | −0.654552 | −0.327276 | − | 0.944929i | \(-0.606131\pi\) | ||||
−0.327276 | + | 0.944929i | \(0.606131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.97083 | −0.325386 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.25615 | + | 5.63981i | 0.106147 | + | 0.183853i | 0.914206 | − | 0.405249i | \(-0.132815\pi\) |
−0.808059 | + | 0.589102i | \(0.799482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.77549 | + | 3.07524i | −0.0578180 | + | 0.100144i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34.8435 | − | 11.0707i | 1.13346 | − | 0.360130i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0531 | + | 48.5893i | −0.911602 | + | 1.57894i | −0.0998014 | + | 0.995007i | \(0.531821\pi\) |
−0.811801 | + | 0.583934i | \(0.801513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.7308 | − | 68.8157i | −1.28971 | − | 2.23385i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.73168 | 0.250717 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.9841 | 0.776920 | 0.388460 | − | 0.921466i | \(-0.373007\pi\) | ||||
0.388460 | + | 0.921466i | \(0.373007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.9751 | + | 76.1671i | 1.42300 | + | 2.46471i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.91439 | − | 8.51198i | 0.158860 | − | 0.275153i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.14774 | − | 14.3483i | 0.101646 | − | 0.463329i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0574 | − | 24.3482i | 0.453466 | − | 0.785426i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.18874 | + | 15.9154i | 0.296103 | + | 0.512866i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.3480 | 0.526261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6539 | 0.824974 | 0.412487 | − | 0.910963i | \(-0.364660\pi\) | ||||
0.412487 | + | 0.910963i | \(0.364660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.66280 | + | 2.88005i | 0.0534167 | + | 0.0925204i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.75173 | + | 6.49819i | −0.120399 | + | 0.208537i | −0.919925 | − | 0.392094i | \(-0.871751\pi\) |
0.799526 | + | 0.600631i | \(0.205084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.50486 | − | 7.75881i | −0.272653 | − | 0.248736i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.5827 | + | 26.9900i | −0.499046 | + | 0.864373i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3271 | + | 50.7959i | 0.938255 | + | 1.62511i | 0.768723 | + | 0.639581i | \(0.220892\pi\) |
0.169532 | + | 0.985525i | \(0.445774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.6039 | 0.914185 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.7004 | −1.49103 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.19313 | + | 14.1909i | 0.261320 | + | 0.452620i | 0.966593 | − | 0.256316i | \(-0.0825088\pi\) |
−0.705273 | + | 0.708936i | \(0.749176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.4328 | − | 47.5150i | 0.874081 | − | 1.51395i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.99435 | + | 6.38081i | 0.222633 | + | 0.203103i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76064 | − | 4.78157i | 0.0877832 | − | 0.152045i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.5210 | + | 39.0075i | 0.715402 | + | 1.23911i | 0.962804 | + | 0.270200i | \(0.0870899\pi\) |
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.4940 | −0.333015 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 100.005 | 3.17038 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.70418 | + | 2.95172i | 0.0539719 | + | 0.0934821i | 0.891749 | − | 0.452530i | \(-0.149479\pi\) |
−0.837777 | + | 0.546012i | \(0.816145\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.6475 | − | 18.4419i | 0.336871 | − | 0.583477i |
(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 | 1064.2.q.n.457.4 | yes | 16 | |
7.2 | even | 3 | 7448.2.a.bq.1.5 | 8 | |||
7.4 | even | 3 | inner | 1064.2.q.n.305.4 | ✓ | 16 | |
7.5 | odd | 6 | 7448.2.a.br.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.4 | ✓ | 16 | 7.4 | even | 3 | inner | |
1064.2.q.n.457.4 | yes | 16 | 1.1 | even | 1 | trivial | |
7448.2.a.bq.1.5 | 8 | 7.2 | even | 3 | |||
7448.2.a.br.1.4 | 8 | 7.5 | odd | 6 |