Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(4013,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.d (of order \(2\), degree \(1\), 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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.3 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.4 |
$q$-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 \(\left(\mathbb{Z}/4014\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.969046 | −0.433370 | −0.216685 | − | 0.976242i | \(-0.569525\pi\) | ||||
−0.216685 | + | 0.976242i | \(0.569525\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46872 | −1.31105 | −0.655526 | − | 0.755172i | \(-0.727553\pi\) | ||||
−0.655526 | + | 0.755172i | \(0.727553\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.969046i | 0.306439i | ||||||||
\(11\) | −2.55954 | −0.771731 | −0.385865 | − | 0.922555i | \(-0.626097\pi\) | ||||
−0.385865 | + | 0.922555i | \(0.626097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.72007i | 1.86381i | 0.362698 | + | 0.931907i | \(0.381856\pi\) | ||||
−0.362698 | + | 0.931907i | \(0.618144\pi\) | |||||||
\(14\) | 3.46872i | 0.927054i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.07269i | 0.260166i | 0.991503 | + | 0.130083i | \(0.0415245\pi\) | ||||
−0.991503 | + | 0.130083i | \(0.958476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.07962 | 0.477096 | 0.238548 | − | 0.971131i | \(-0.423328\pi\) | ||||
0.238548 | + | 0.971131i | \(0.423328\pi\) | |||||||
\(20\) | 0.969046 | 0.216685 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.55954i | 0.545696i | ||||||||
\(23\) | −3.34775 | −0.698054 | −0.349027 | − | 0.937113i | \(-0.613488\pi\) | ||||
−0.349027 | + | 0.937113i | \(0.613488\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.06095 | −0.812190 | ||||||||
\(26\) | 6.72007 | 1.31791 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.46872 | 0.655526 | ||||||||
\(29\) | 1.25255i | 0.232593i | 0.993215 | + | 0.116296i | \(0.0371022\pi\) | ||||
−0.993215 | + | 0.116296i | \(0.962898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.16125 | 0.567777 | 0.283888 | − | 0.958857i | \(-0.408376\pi\) | ||||
0.283888 | + | 0.958857i | \(0.408376\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.07269 | 0.183965 | ||||||||
\(35\) | 3.36135 | 0.568171 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.73443 | 0.285139 | 0.142569 | − | 0.989785i | \(-0.454464\pi\) | ||||
0.142569 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(38\) | − | 2.07962i | − | 0.337358i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.969046i | − | 0.153220i | ||||||
\(41\) | 2.41214i | 0.376714i | 0.982101 | + | 0.188357i | \(0.0603161\pi\) | ||||
−0.982101 | + | 0.188357i | \(0.939684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61201 | −0.245829 | −0.122915 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122915 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(44\) | 2.55954 | 0.385865 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.34775i | 0.493599i | ||||||||
\(47\) | − | 10.7575i | − | 1.56914i | −0.620039 | − | 0.784571i | \(-0.712883\pi\) | ||
0.620039 | − | 0.784571i | \(-0.287117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.03201 | 0.718858 | ||||||||
\(50\) | 4.06095i | 0.574305i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 6.72007i | − | 0.931907i | ||||||
\(53\) | 1.87835i | 0.258011i | 0.991644 | + | 0.129006i | \(0.0411786\pi\) | ||||
−0.991644 | + | 0.129006i | \(0.958821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.48031 | 0.334445 | ||||||||
\(56\) | − | 3.46872i | − | 0.463527i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.25255 | 0.164468 | ||||||||
\(59\) | 6.77146 | 0.881569 | 0.440785 | − | 0.897613i | \(-0.354700\pi\) | ||||
0.440785 | + | 0.897613i | \(0.354700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.49500i | − | 0.959636i | −0.877368 | − | 0.479818i | \(-0.840703\pi\) | ||
0.877368 | − | 0.479818i | \(-0.159297\pi\) | |||||||
\(62\) | − | 3.16125i | − | 0.401479i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 6.51206i | − | 0.807721i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.86045i | 0.349460i | 0.984616 | + | 0.174730i | \(0.0559053\pi\) | ||||
−0.984616 | + | 0.174730i | \(0.944095\pi\) | |||||||
\(68\) | − | 1.07269i | − | 0.130083i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 3.36135i | − | 0.401758i | ||||||
\(71\) | −2.10243 | −0.249512 | −0.124756 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124756 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.281139 | 0.0329049 | 0.0164524 | − | 0.999865i | \(-0.494763\pi\) | ||||
0.0164524 | + | 0.999865i | \(0.494763\pi\) | |||||||
\(74\) | − | 1.73443i | − | 0.201623i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.07962 | −0.238548 | ||||||||
\(77\) | 8.87833 | 1.01178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.49716i | − | 0.168443i | −0.996447 | − | 0.0842216i | \(-0.973160\pi\) | ||
0.996447 | − | 0.0842216i | \(-0.0268403\pi\) | |||||||
\(80\) | −0.969046 | −0.108343 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.41214 | 0.266377 | ||||||||
\(83\) | − | 9.35419i | − | 1.02676i | −0.858163 | − | 0.513378i | \(-0.828394\pi\) | ||
0.858163 | − | 0.513378i | \(-0.171606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.03949i | − | 0.112748i | ||||||
\(86\) | 1.61201i | 0.173828i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.55954i | − | 0.272848i | ||||||
\(89\) | − | 3.81081i | − | 0.403945i | −0.979391 | − | 0.201973i | \(-0.935265\pi\) | ||
0.979391 | − | 0.201973i | \(-0.0647352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 23.3100i | − | 2.44356i | ||||||
\(92\) | 3.34775 | 0.349027 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.7575 | −1.10955 | ||||||||
\(95\) | −2.01524 | −0.206759 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0886i | 1.32895i | 0.747310 | + | 0.664475i | \(0.231345\pi\) | ||||
−0.747310 | + | 0.664475i | \(0.768655\pi\) | |||||||
\(98\) | − | 5.03201i | − | 0.508310i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.06095 | 0.406095 | ||||||||
\(101\) | − | 10.3809i | − | 1.03294i | −0.856306 | − | 0.516469i | \(-0.827246\pi\) | ||
0.856306 | − | 0.516469i | \(-0.172754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.40046i | 0.335057i | 0.985867 | + | 0.167528i | \(0.0535786\pi\) | ||||
−0.985867 | + | 0.167528i | \(0.946421\pi\) | |||||||
\(104\) | −6.72007 | −0.658957 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.87835 | 0.182442 | ||||||||
\(107\) | 13.0004 | 1.25680 | 0.628399 | − | 0.777891i | \(-0.283711\pi\) | ||||
0.628399 | + | 0.777891i | \(0.283711\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.8716 | −1.52022 | −0.760110 | − | 0.649794i | \(-0.774855\pi\) | ||||
−0.760110 | + | 0.649794i | \(0.774855\pi\) | |||||||
\(110\) | − | 2.48031i | − | 0.236489i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46872 | −0.327763 | ||||||||
\(113\) | −0.213882 | −0.0201203 | −0.0100602 | − | 0.999949i | \(-0.503202\pi\) | ||||
−0.0100602 | + | 0.999949i | \(0.503202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.24412 | 0.302516 | ||||||||
\(116\) | − | 1.25255i | − | 0.116296i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.77146i | − | 0.623363i | ||||||
\(119\) | − | 3.72087i | − | 0.341092i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.44875 | −0.404431 | ||||||||
\(122\) | −7.49500 | −0.678565 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.16125 | −0.283888 | ||||||||
\(125\) | 8.78047 | 0.785350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.76173 | −0.245064 | −0.122532 | − | 0.992465i | \(-0.539101\pi\) | ||||
−0.122532 | + | 0.992465i | \(0.539101\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.51206 | −0.571145 | ||||||||
\(131\) | − | 11.6965i | − | 1.02193i | −0.859602 | − | 0.510964i | \(-0.829289\pi\) | ||
0.859602 | − | 0.510964i | \(-0.170711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.21360 | −0.625498 | ||||||||
\(134\) | 2.86045 | 0.247106 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.07269 | −0.0919827 | ||||||||
\(137\) | 12.9587 | 1.10714 | 0.553569 | − | 0.832804i | \(-0.313266\pi\) | ||||
0.553569 | + | 0.832804i | \(0.313266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9531 | −1.01385 | −0.506924 | − | 0.861991i | \(-0.669218\pi\) | ||||
−0.506924 | + | 0.861991i | \(0.669218\pi\) | |||||||
\(140\) | −3.36135 | −0.284086 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.10243i | 0.176432i | ||||||||
\(143\) | − | 17.2003i | − | 1.43836i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.21378i | − | 0.100799i | ||||||
\(146\) | − | 0.281139i | − | 0.0232673i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.73443 | −0.142569 | ||||||||
\(149\) | −13.5939 | −1.11366 | −0.556829 | − | 0.830627i | \(-0.687982\pi\) | ||||
−0.556829 | + | 0.830627i | \(0.687982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.07562i | 0.0875326i | 0.999042 | + | 0.0437663i | \(0.0139357\pi\) | ||||
−0.999042 | + | 0.0437663i | \(0.986064\pi\) | |||||||
\(152\) | 2.07962i | 0.168679i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 8.87833i | − | 0.715436i | ||||||
\(155\) | −3.06339 | −0.246058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.39354i | 0.270834i | 0.990789 | + | 0.135417i | \(0.0432374\pi\) | ||||
−0.990789 | + | 0.135417i | \(0.956763\pi\) | |||||||
\(158\) | −1.49716 | −0.119107 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.969046i | 0.0766098i | ||||||||
\(161\) | 11.6124 | 0.915185 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.09521i | 0.477414i | 0.971092 | + | 0.238707i | \(0.0767235\pi\) | ||||
−0.971092 | + | 0.238707i | \(0.923276\pi\) | |||||||
\(164\) | − | 2.41214i | − | 0.188357i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.35419 | −0.726026 | ||||||||
\(167\) | −7.12890 | −0.551651 | −0.275825 | − | 0.961208i | \(-0.588951\pi\) | ||||
−0.275825 | + | 0.961208i | \(0.588951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −32.1594 | −2.47380 | ||||||||
\(170\) | −1.03949 | −0.0797252 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.61201 | 0.122915 | ||||||||
\(173\) | 12.3333 | 0.937685 | 0.468843 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468843 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0863 | 1.06482 | ||||||||
\(176\) | −2.55954 | −0.192933 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.81081 | −0.285633 | ||||||||
\(179\) | − | 20.1718i | − | 1.50771i | −0.657041 | − | 0.753855i | \(-0.728192\pi\) | ||
0.657041 | − | 0.753855i | \(-0.271808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.88222 | −0.214233 | −0.107117 | − | 0.994246i | \(-0.534162\pi\) | ||||
−0.107117 | + | 0.994246i | \(0.534162\pi\) | |||||||
\(182\) | −23.3100 | −1.72786 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 3.34775i | − | 0.246799i | ||||||
\(185\) | −1.68074 | −0.123571 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.74560i | − | 0.200778i | ||||||
\(188\) | 10.7575i | 0.784571i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.01524i | 0.146201i | ||||||||
\(191\) | 11.6916 | 0.845978 | 0.422989 | − | 0.906135i | \(-0.360981\pi\) | ||||
0.422989 | + | 0.906135i | \(0.360981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 0.0831582i | − | 0.00598586i | −0.999996 | − | 0.00299293i | \(-0.999047\pi\) | ||
0.999996 | − | 0.00299293i | \(-0.000952680\pi\) | |||||||
\(194\) | 13.0886 | 0.939710 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.03201 | −0.359429 | ||||||||
\(197\) | − | 9.84566i | − | 0.701474i | −0.936474 | − | 0.350737i | \(-0.885931\pi\) | ||
0.936474 | − | 0.350737i | \(-0.114069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.3477 | −0.875305 | −0.437652 | − | 0.899144i | \(-0.644190\pi\) | ||||
−0.437652 | + | 0.899144i | \(0.644190\pi\) | |||||||
\(200\) | − | 4.06095i | − | 0.287153i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.3809 | −0.730398 | ||||||||
\(203\) | − | 4.34474i | − | 0.304941i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.33748i | − | 0.163257i | ||||||
\(206\) | 3.40046 | 0.236921 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.72007i | 0.465953i | ||||||||
\(209\) | −5.32286 | −0.368190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7720 | 1.56769 | 0.783845 | − | 0.620957i | \(-0.213256\pi\) | ||||
0.783845 | + | 0.620957i | \(0.213256\pi\) | |||||||
\(212\) | − | 1.87835i | − | 0.129006i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 13.0004i | − | 0.888690i | ||||||
\(215\) | 1.56211 | 0.106535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.9655 | −0.744385 | ||||||||
\(218\) | 15.8716i | 1.07496i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.48031 | −0.167223 | ||||||||
\(221\) | −7.20858 | −0.484902 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3682 | − | 6.65524i | 0.895199 | − | 0.445667i | ||||
\(224\) | 3.46872i | 0.231764i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.213882i | 0.0142272i | ||||||||
\(227\) | − | 16.1068i | − | 1.06905i | −0.845154 | − | 0.534523i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534523i | \(-0.179509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 23.1904i | − | 1.53246i | −0.642565 | − | 0.766231i | \(-0.722130\pi\) | ||
0.642565 | − | 0.766231i | \(-0.277870\pi\) | |||||||
\(230\) | − | 3.24412i | − | 0.213911i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.25255 | −0.0822339 | ||||||||
\(233\) | 19.4967 | 1.27727 | 0.638637 | − | 0.769508i | \(-0.279499\pi\) | ||||
0.638637 | + | 0.769508i | \(0.279499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4245i | 0.680020i | ||||||||
\(236\) | −6.77146 | −0.440785 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.72087 | −0.241188 | ||||||||
\(239\) | 7.31789i | 0.473355i | 0.971588 | + | 0.236677i | \(0.0760585\pi\) | ||||
−0.971588 | + | 0.236677i | \(0.923942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.68387 | 0.301715 | 0.150857 | − | 0.988556i | \(-0.451797\pi\) | ||||
0.150857 | + | 0.988556i | \(0.451797\pi\) | |||||||
\(242\) | 4.44875i | 0.285976i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.49500i | 0.479818i | ||||||||
\(245\) | −4.87625 | −0.311532 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9752i | 0.889219i | ||||||||
\(248\) | 3.16125i | 0.200739i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 8.78047i | − | 0.555326i | ||||||
\(251\) | − | 12.7990i | − | 0.807865i | −0.914789 | − | 0.403932i | \(-0.867643\pi\) | ||
0.914789 | − | 0.403932i | \(-0.132357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.56870 | 0.538710 | ||||||||
\(254\) | 2.76173i | 0.173286i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.15971i | 0.134719i | 0.997729 | + | 0.0673596i | \(0.0214575\pi\) | ||||
−0.997729 | + | 0.0673596i | \(0.978543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.01625 | −0.373832 | ||||||||
\(260\) | 6.51206i | 0.403861i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.6965 | −0.722612 | ||||||||
\(263\) | 11.3470 | 0.699688 | 0.349844 | − | 0.936808i | \(-0.386235\pi\) | ||||
0.349844 | + | 0.936808i | \(0.386235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.82021i | − | 0.111815i | ||||||
\(266\) | 7.21360i | 0.442294i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.86045i | − | 0.174730i | ||||||
\(269\) | −18.2555 | −1.11306 | −0.556529 | − | 0.830828i | \(-0.687867\pi\) | ||||
−0.556529 | + | 0.830828i | \(0.687867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.22822i | − | 0.499829i | −0.968268 | − | 0.249914i | \(-0.919598\pi\) | ||
0.968268 | − | 0.249914i | \(-0.0804025\pi\) | |||||||
\(272\) | 1.07269i | 0.0650416i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.9587i | − | 0.782864i | ||||||
\(275\) | 10.3942 | 0.626792 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4646i | 0.869095i | 0.900649 | + | 0.434548i | \(0.143092\pi\) | ||||
−0.900649 | + | 0.434548i | \(0.856908\pi\) | |||||||
\(278\) | 11.9531i | 0.716899i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.36135i | 0.200879i | ||||||||
\(281\) | 5.90766i | 0.352421i | 0.984352 | + | 0.176211i | \(0.0563840\pi\) | ||||
−0.984352 | + | 0.176211i | \(0.943616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.7225 | 1.58849 | 0.794243 | − | 0.607601i | \(-0.207868\pi\) | ||||
0.794243 | + | 0.607601i | \(0.207868\pi\) | |||||||
\(284\) | 2.10243 | 0.124756 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.2003 | −1.01708 | ||||||||
\(287\) | − | 8.36705i | − | 0.493891i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8493 | 0.932313 | ||||||||
\(290\) | −1.21378 | −0.0712755 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.281139 | −0.0164524 | ||||||||
\(293\) | −15.3541 | −0.896996 | −0.448498 | − | 0.893784i | \(-0.648041\pi\) | ||||
−0.448498 | + | 0.893784i | \(0.648041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.56185 | −0.382046 | ||||||||
\(296\) | 1.73443i | 0.100812i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.5939i | 0.787475i | ||||||||
\(299\) | − | 22.4971i | − | 1.30104i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.59161 | 0.322295 | ||||||||
\(302\) | 1.07562 | 0.0618949 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.07962 | 0.119274 | ||||||||
\(305\) | 7.26299i | 0.415878i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7608i | 1.58439i | 0.610265 | + | 0.792197i | \(0.291063\pi\) | ||||
−0.610265 | + | 0.792197i | \(0.708937\pi\) | |||||||
\(308\) | −8.87833 | −0.505890 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.06339i | 0.173989i | ||||||||
\(311\) | 29.7913 | 1.68931 | 0.844656 | − | 0.535310i | \(-0.179805\pi\) | ||||
0.844656 | + | 0.535310i | \(0.179805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.8166i | − | 1.06358i | −0.846877 | − | 0.531788i | \(-0.821520\pi\) | ||
0.846877 | − | 0.531788i | \(-0.178480\pi\) | |||||||
\(314\) | 3.39354 | 0.191509 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.49716i | 0.0842216i | ||||||||
\(317\) | − | 9.96393i | − | 0.559630i | −0.960054 | − | 0.279815i | \(-0.909727\pi\) | ||
0.960054 | − | 0.279815i | \(-0.0902731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.20595i | − | 0.179499i | ||||||
\(320\) | 0.969046 | 0.0541713 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 11.6124i | − | 0.647134i | ||||||
\(323\) | 2.23079i | 0.124124i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 27.2899i | − | 1.51377i | ||||||
\(326\) | 6.09521 | 0.337582 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.41214 | −0.133188 | ||||||||
\(329\) | 37.3147i | 2.05723i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.0451i | − | 1.10178i | −0.834578 | − | 0.550890i | \(-0.814288\pi\) | ||
0.834578 | − | 0.550890i | \(-0.185712\pi\) | |||||||
\(332\) | 9.35419i | 0.513378i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.12890i | 0.390076i | ||||||||
\(335\) | − | 2.77191i | − | 0.151446i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.6452i | − | 1.50593i | −0.658062 | − | 0.752964i | \(-0.728624\pi\) | ||
0.658062 | − | 0.752964i | \(-0.271376\pi\) | |||||||
\(338\) | 32.1594i | 1.74924i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.03949i | 0.0563742i | ||||||||
\(341\) | −8.09134 | −0.438171 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.82641 | 0.368591 | ||||||||
\(344\) | − | 1.61201i | − | 0.0869138i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 12.3333i | − | 0.663044i | ||||||
\(347\) | − | 3.58620i | − | 0.192517i | −0.995356 | − | 0.0962586i | \(-0.969312\pi\) | ||
0.995356 | − | 0.0962586i | \(-0.0306876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.16650 | 0.383614 | 0.191807 | − | 0.981433i | \(-0.438565\pi\) | ||||
0.191807 | + | 0.981433i | \(0.438565\pi\) | |||||||
\(350\) | − | 14.0863i | − | 0.752944i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.55954i | 0.136424i | ||||||||
\(353\) | − | 2.94264i | − | 0.156621i | −0.996929 | − | 0.0783105i | \(-0.975047\pi\) | ||
0.996929 | − | 0.0783105i | \(-0.0249525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.03735 | 0.108131 | ||||||||
\(356\) | 3.81081i | 0.201973i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.1718 | −1.06611 | ||||||||
\(359\) | − | 14.9608i | − | 0.789601i | −0.918767 | − | 0.394801i | \(-0.870814\pi\) | ||
0.918767 | − | 0.394801i | \(-0.129186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6752 | −0.772379 | ||||||||
\(362\) | 2.88222i | 0.151486i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.3100i | 1.22178i | ||||||||
\(365\) | −0.272437 | −0.0142600 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.2011 | −1.05449 | −0.527243 | − | 0.849714i | \(-0.676774\pi\) | ||||
−0.527243 | + | 0.849714i | \(0.676774\pi\) | |||||||
\(368\) | −3.34775 | −0.174513 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.68074i | 0.0873776i | ||||||||
\(371\) | − | 6.51547i | − | 0.338267i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.38424i | 0.278785i | 0.990237 | + | 0.139393i | \(0.0445150\pi\) | ||||
−0.990237 | + | 0.139393i | \(0.955485\pi\) | |||||||
\(374\) | −2.74560 | −0.141972 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.7575 | 0.554776 | ||||||||
\(377\) | −8.41722 | −0.433509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.94431 | −0.459438 | −0.229719 | − | 0.973257i | \(-0.573781\pi\) | ||||
−0.229719 | + | 0.973257i | \(0.573781\pi\) | |||||||
\(380\) | 2.01524 | 0.103380 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 11.6916i | − | 0.598197i | ||||||
\(383\) | 7.05417 | 0.360451 | 0.180226 | − | 0.983625i | \(-0.442317\pi\) | ||||
0.180226 | + | 0.983625i | \(0.442317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.60351 | −0.438475 | ||||||||
\(386\) | −0.0831582 | −0.00423264 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 13.0886i | − | 0.664475i | ||||||
\(389\) | − | 2.40158i | − | 0.121765i | −0.998145 | − | 0.0608824i | \(-0.980609\pi\) | ||
0.998145 | − | 0.0608824i | \(-0.0193915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.59111i | − | 0.181610i | ||||||
\(392\) | 5.03201i | 0.254155i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.84566 | −0.496017 | ||||||||
\(395\) | 1.45081i | 0.0729983i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 37.6516i | − | 1.88968i | −0.327531 | − | 0.944841i | \(-0.606216\pi\) | ||
0.327531 | − | 0.944841i | \(-0.393784\pi\) | |||||||
\(398\) | 12.3477i | 0.618934i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.06095 | −0.203048 | ||||||||
\(401\) | 23.1534i | 1.15622i | 0.815958 | + | 0.578112i | \(0.196210\pi\) | ||||
−0.815958 | + | 0.578112i | \(0.803790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2438i | 1.05823i | ||||||||
\(404\) | 10.3809i | 0.516469i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.34474 | −0.215626 | ||||||||
\(407\) | −4.43935 | −0.220050 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6033i | 0.623193i | 0.950215 | + | 0.311596i | \(0.100864\pi\) | ||||
−0.950215 | + | 0.311596i | \(0.899136\pi\) | |||||||
\(410\) | −2.33748 | −0.115440 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 3.40046i | − | 0.167528i | ||||||
\(413\) | −23.4883 | −1.15578 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.06464i | 0.444966i | ||||||||
\(416\) | 6.72007 | 0.329479 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.32286i | 0.260350i | ||||||||
\(419\) | − | 21.0493i | − | 1.02833i | −0.857692 | − | 0.514164i | \(-0.828102\pi\) | ||
0.857692 | − | 0.514164i | \(-0.171898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6340i | 1.10311i | 0.834137 | + | 0.551557i | \(0.185966\pi\) | ||||
−0.834137 | + | 0.551557i | \(0.814034\pi\) | |||||||
\(422\) | − | 22.7720i | − | 1.10852i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.87835 | −0.0912208 | ||||||||
\(425\) | − | 4.35616i | − | 0.211305i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.9980i | 1.25813i | ||||||||
\(428\) | −13.0004 | −0.628399 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 1.56211i | − | 0.0753317i | ||||||
\(431\) | −15.1291 | −0.728745 | −0.364373 | − | 0.931253i | \(-0.618717\pi\) | ||||
−0.364373 | + | 0.931253i | \(0.618717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.37944 | 0.306576 | 0.153288 | − | 0.988182i | \(-0.451014\pi\) | ||||
0.153288 | + | 0.988182i | \(0.451014\pi\) | |||||||
\(434\) | 10.9655i | 0.526360i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.8716 | 0.760110 | ||||||||
\(437\) | −6.96203 | −0.333039 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1574i | 0.866606i | 0.901248 | + | 0.433303i | \(0.142652\pi\) | ||||
−0.901248 | + | 0.433303i | \(0.857348\pi\) | |||||||
\(440\) | 2.48031i | 0.118244i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.20858i | 0.342877i | ||||||||
\(443\) | 15.7071i | 0.746269i | 0.927777 | + | 0.373135i | \(0.121717\pi\) | ||||
−0.927777 | + | 0.373135i | \(0.878283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.69285i | 0.175058i | ||||||||
\(446\) | −6.65524 | − | 13.3682i | −0.315135 | − | 0.633001i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.46872 | 0.163882 | ||||||||
\(449\) | 24.7835 | 1.16961 | 0.584803 | − | 0.811175i | \(-0.301172\pi\) | ||||
0.584803 | + | 0.811175i | \(0.301172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.17398i | − | 0.290722i | ||||||
\(452\) | 0.213882 | 0.0100602 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.1068 | −0.755930 | ||||||||
\(455\) | 22.5885i | 1.05897i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.04644i | − | 0.189284i | −0.995511 | − | 0.0946422i | \(-0.969829\pi\) | ||
0.995511 | − | 0.0946422i | \(-0.0301707\pi\) | |||||||
\(458\) | −23.1904 | −1.08361 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.24412 | −0.151258 | ||||||||
\(461\) | 28.4921i | 1.32701i | 0.748171 | + | 0.663506i | \(0.230932\pi\) | ||||
−0.748171 | + | 0.663506i | \(0.769068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.30080 | −0.246349 | −0.123174 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123174 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(464\) | 1.25255i | 0.0581481i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 19.4967i | − | 0.903169i | ||||||
\(467\) | 3.24020 | 0.149939 | 0.0749693 | − | 0.997186i | \(-0.476114\pi\) | ||||
0.0749693 | + | 0.997186i | \(0.476114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.92211i | − | 0.458160i | ||||||
\(470\) | 10.4245 | 0.480847 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.77146i | 0.311682i | ||||||||
\(473\) | 4.12601 | 0.189714 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.44521 | −0.387493 | ||||||||
\(476\) | 3.72087i | 0.170546i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.31789 | 0.334712 | ||||||||
\(479\) | 12.7509i | 0.582605i | 0.956631 | + | 0.291303i | \(0.0940886\pi\) | ||||
−0.956631 | + | 0.291303i | \(0.905911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6555i | 0.531445i | ||||||||
\(482\) | − | 4.68387i | − | 0.213345i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.44875 | 0.202216 | ||||||||
\(485\) | − | 12.6835i | − | 0.575928i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.2673 | 0.646512 | 0.323256 | − | 0.946312i | \(-0.395223\pi\) | ||||
0.323256 | + | 0.946312i | \(0.395223\pi\) | |||||||
\(488\) | 7.49500 | 0.339283 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.87625i | 0.220286i | ||||||||
\(491\) | 0.174465 | 0.00787348 | 0.00393674 | − | 0.999992i | \(-0.498747\pi\) | ||||
0.00393674 | + | 0.999992i | \(0.498747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.34360 | −0.0605128 | ||||||||
\(494\) | 13.9752 | 0.628773 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.16125 | 0.141944 | ||||||||
\(497\) | 7.29272 | 0.327123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8629 | 0.575824 | 0.287912 | − | 0.957657i | \(-0.407039\pi\) | ||||
0.287912 | + | 0.957657i | \(0.407039\pi\) | |||||||
\(500\) | −8.78047 | −0.392675 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.7990 | −0.571247 | ||||||||
\(503\) | −20.2862 | −0.904517 | −0.452258 | − | 0.891887i | \(-0.649382\pi\) | ||||
−0.452258 | + | 0.891887i | \(0.649382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0596i | 0.447645i | ||||||||
\(506\) | − | 8.56870i | − | 0.380925i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.76173 | 0.122532 | ||||||||
\(509\) | 4.44407i | 0.196980i | 0.995138 | + | 0.0984900i | \(0.0314013\pi\) | ||||
−0.995138 | + | 0.0984900i | \(0.968599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.975193 | −0.0431400 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.15971 | 0.0952609 | ||||||||
\(515\) | − | 3.29520i | − | 0.145204i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.5343i | 1.21096i | ||||||||
\(518\) | 6.01625i | 0.264339i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.51206 | 0.285573 | ||||||||
\(521\) | −5.99851 | −0.262800 | −0.131400 | − | 0.991329i | \(-0.541947\pi\) | ||||
−0.131400 | + | 0.991329i | \(0.541947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9703i | 1.39796i | 0.715140 | + | 0.698981i | \(0.246363\pi\) | ||||
−0.715140 | + | 0.698981i | \(0.753637\pi\) | |||||||
\(524\) | 11.6965i | 0.510964i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 11.3470i | − | 0.494754i | ||||||
\(527\) | 3.39105i | 0.147716i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7926 | −0.512721 | ||||||||
\(530\) | −1.82021 | −0.0790648 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.21360 | 0.312749 | ||||||||
\(533\) | −16.2098 | −0.702124 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5980 | −0.544659 | ||||||||
\(536\) | −2.86045 | −0.123553 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.2555i | 0.787051i | ||||||||
\(539\) | −12.8796 | −0.554765 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 18.2573i | − | 0.784944i | −0.919764 | − | 0.392472i | \(-0.871620\pi\) | ||
0.919764 | − | 0.392472i | \(-0.128380\pi\) | |||||||
\(542\) | −8.22822 | −0.353432 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.07269 | 0.0459914 | ||||||||
\(545\) | 15.3803 | 0.658818 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.64075 | −0.198424 | −0.0992120 | − | 0.995066i | \(-0.531632\pi\) | ||||
−0.0992120 | + | 0.995066i | \(0.531632\pi\) | |||||||
\(548\) | −12.9587 | −0.553569 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 10.3942i | − | 0.443209i | ||||||
\(551\) | 2.60482i | 0.110969i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.19321i | 0.220838i | ||||||||
\(554\) | 14.4646 | 0.614543 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.9531 | 0.506924 | ||||||||
\(557\) | −2.08638 | −0.0884026 | −0.0442013 | − | 0.999023i | \(-0.514074\pi\) | ||||
−0.0442013 | + | 0.999023i | \(0.514074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.8328i | − | 0.458180i | ||||||
\(560\) | 3.36135 | 0.142043 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.90766 | 0.249200 | ||||||||
\(563\) | −31.9607 | −1.34698 | −0.673492 | − | 0.739195i | \(-0.735206\pi\) | ||||
−0.673492 | + | 0.739195i | \(0.735206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.207261 | 0.00871955 | ||||||||
\(566\) | − | 26.7225i | − | 1.12323i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.10243i | − | 0.0882158i | ||||||
\(569\) | 36.4343 | 1.52741 | 0.763703 | − | 0.645568i | \(-0.223379\pi\) | ||||
0.763703 | + | 0.645568i | \(0.223379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6602i | 0.822752i | 0.911466 | + | 0.411376i | \(0.134952\pi\) | ||||
−0.911466 | + | 0.411376i | \(0.865048\pi\) | |||||||
\(572\) | 17.2003i | 0.719181i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.36705 | −0.349234 | ||||||||
\(575\) | 13.5950 | 0.566952 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5502 | −0.564104 | −0.282052 | − | 0.959399i | \(-0.591015\pi\) | ||||
−0.282052 | + | 0.959399i | \(0.591015\pi\) | |||||||
\(578\) | − | 15.8493i | − | 0.659245i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.21378i | 0.0503994i | ||||||||
\(581\) | 32.4471i | 1.34613i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.80772i | − | 0.199115i | ||||||
\(584\) | 0.281139i | 0.0116336i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.3541i | 0.634272i | ||||||||
\(587\) | 25.8057 | 1.06511 | 0.532557 | − | 0.846394i | \(-0.321231\pi\) | ||||
0.532557 | + | 0.846394i | \(0.321231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.57418 | 0.270884 | ||||||||
\(590\) | 6.56185i | 0.270147i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.73443 | 0.0712847 | ||||||||
\(593\) | −28.3711 | −1.16506 | −0.582531 | − | 0.812809i | \(-0.697937\pi\) | ||||
−0.582531 | + | 0.812809i | \(0.697937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.60570i | 0.147819i | ||||||||
\(596\) | 13.5939 | 0.556829 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.4971 | −0.919975 | ||||||||
\(599\) | 16.6569i | 0.680585i | 0.940320 | + | 0.340292i | \(0.110526\pi\) | ||||
−0.940320 | + | 0.340292i | \(0.889474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.39838i | − | 0.0570413i | −0.999593 | − | 0.0285206i | \(-0.990920\pi\) | ||
0.999593 | − | 0.0285206i | \(-0.00907963\pi\) | |||||||
\(602\) | − | 5.59161i | − | 0.227897i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.07562i | − | 0.0437663i | ||||||
\(605\) | 4.31104 | 0.175269 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.1391i | − | 0.736242i | −0.929778 | − | 0.368121i | \(-0.880001\pi\) | ||
0.929778 | − | 0.368121i | \(-0.119999\pi\) | |||||||
\(608\) | − | 2.07962i | − | 0.0843395i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.26299 | 0.294070 | ||||||||
\(611\) | 72.2912 | 2.92459 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 19.4232i | − | 0.784496i | −0.919860 | − | 0.392248i | \(-0.871698\pi\) | ||
0.919860 | − | 0.392248i | \(-0.128302\pi\) | |||||||
\(614\) | 27.7608 | 1.12034 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.87833i | 0.357718i | ||||||||
\(617\) | − | 30.8809i | − | 1.24322i | −0.783328 | − | 0.621609i | \(-0.786479\pi\) | ||
0.783328 | − | 0.621609i | \(-0.213521\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.61552i | − | 0.265900i | −0.991123 | − | 0.132950i | \(-0.957555\pi\) | ||
0.991123 | − | 0.132950i | \(-0.0424450\pi\) | |||||||
\(620\) | 3.06339 | 0.123029 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 29.7913i | − | 1.19452i | ||||||
\(623\) | 13.2186i | 0.529594i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.7961 | 0.471843 | ||||||||
\(626\) | −18.8166 | −0.752062 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 3.39354i | − | 0.135417i | ||||||
\(629\) | 1.86051i | 0.0741835i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5797i | 0.421173i | 0.977575 | + | 0.210587i | \(0.0675374\pi\) | ||||
−0.977575 | + | 0.210587i | \(0.932463\pi\) | |||||||
\(632\) | 1.49716 | 0.0595536 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.96393 | −0.395718 | ||||||||
\(635\) | 2.67624 | 0.106203 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.8155i | 1.33982i | ||||||||
\(638\) | −3.20595 | −0.126925 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.969046i | − | 0.0383049i | ||||||
\(641\) | 26.2818 | 1.03807 | 0.519034 | − | 0.854754i | \(-0.326292\pi\) | ||||
0.519034 | + | 0.854754i | \(0.326292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.0453 | 1.81585 | 0.907925 | − | 0.419133i | \(-0.137666\pi\) | ||||
0.907925 | + | 0.419133i | \(0.137666\pi\) | |||||||
\(644\) | −11.6124 | −0.457592 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.23079 | 0.0877693 | ||||||||
\(647\) | − | 9.16705i | − | 0.360394i | −0.983631 | − | 0.180197i | \(-0.942326\pi\) | ||
0.983631 | − | 0.180197i | \(-0.0576735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.3318 | −0.680334 | ||||||||
\(650\) | −27.2899 | −1.07040 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.09521i | − | 0.238707i | ||||||
\(653\) | −39.2613 | −1.53641 | −0.768207 | − | 0.640202i | \(-0.778851\pi\) | ||||
−0.768207 | + | 0.640202i | \(0.778851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3344i | 0.442873i | ||||||||
\(656\) | 2.41214i | 0.0941784i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 37.3147 | 1.45468 | ||||||||
\(659\) | − | 5.39054i | − | 0.209986i | −0.994473 | − | 0.104993i | \(-0.966518\pi\) | ||
0.994473 | − | 0.104993i | \(-0.0334820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14.9885i | − | 0.582984i | −0.956573 | − | 0.291492i | \(-0.905848\pi\) | ||
0.956573 | − | 0.291492i | \(-0.0941517\pi\) | |||||||
\(662\) | −20.0451 | −0.779076 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.35419 | 0.363013 | ||||||||
\(665\) | 6.99031 | 0.271073 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.19322i | − | 0.162362i | ||||||
\(668\) | 7.12890 | 0.275825 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.77191 | −0.107088 | ||||||||
\(671\) | 19.1838i | 0.740581i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.6649 | 1.76025 | 0.880126 | − | 0.474740i | \(-0.157458\pi\) | ||||
0.880126 | + | 0.474740i | \(0.157458\pi\) | |||||||
\(674\) | −27.6452 | −1.06485 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.1594 | 1.23690 | ||||||||
\(677\) | − | 9.85412i | − | 0.378725i | −0.981907 | − | 0.189362i | \(-0.939358\pi\) | ||
0.981907 | − | 0.189362i | \(-0.0606421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 45.4008i | − | 1.74232i | ||||||
\(680\) | 1.03949 | 0.0398626 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.09134i | 0.309834i | ||||||||
\(683\) | − | 17.8209i | − | 0.681896i | −0.940082 | − | 0.340948i | \(-0.889252\pi\) | ||
0.940082 | − | 0.340948i | \(-0.110748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.5576 | −0.479801 | ||||||||
\(686\) | − | 6.82641i | − | 0.260633i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.61201 | −0.0614573 | ||||||||
\(689\) | −12.6227 | −0.480885 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.19590i | − | 0.121578i | −0.998151 | − | 0.0607890i | \(-0.980638\pi\) | ||
0.998151 | − | 0.0607890i | \(-0.0193617\pi\) | |||||||
\(692\) | −12.3333 | −0.468843 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.58620 | −0.136130 | ||||||||
\(695\) | 11.5831 | 0.439372 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.58749 | −0.0980083 | ||||||||
\(698\) | − | 7.16650i | − | 0.271256i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.0863 | −0.532412 | ||||||||
\(701\) | − | 0.307901i | − | 0.0116293i | −0.999983 | − | 0.00581463i | \(-0.998149\pi\) | ||
0.999983 | − | 0.00581463i | \(-0.00185086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.60695 | 0.136039 | ||||||||
\(704\) | 2.55954 | 0.0964664 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.94264 | −0.110748 | ||||||||
\(707\) | 36.0084i | 1.35424i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 22.9088i | − | 0.860358i | −0.902744 | − | 0.430179i | \(-0.858450\pi\) | ||
0.902744 | − | 0.430179i | \(-0.141550\pi\) | |||||||
\(710\) | − | 2.03735i | − | 0.0764602i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.81081 | 0.142816 | ||||||||
\(713\) | −10.5831 | −0.396339 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.6679i | 0.623344i | ||||||||
\(716\) | 20.1718i | 0.753855i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.9608 | −0.558332 | ||||||||
\(719\) | − | 16.3360i | − | 0.609229i | −0.952476 | − | 0.304614i | \(-0.901472\pi\) | ||
0.952476 | − | 0.304614i | \(-0.0985276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11.7952i | − | 0.439277i | ||||||
\(722\) | 14.6752i | 0.546154i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.88222 | 0.107117 | ||||||||
\(725\) | − | 5.08654i | − | 0.188909i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.4292 | −0.535148 | −0.267574 | − | 0.963537i | \(-0.586222\pi\) | ||||
−0.267574 | + | 0.963537i | \(0.586222\pi\) | |||||||
\(728\) | 23.3100 | 0.863928 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.272437i | 0.0100833i | ||||||||
\(731\) | − | 1.72919i | − | 0.0639565i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9730 | 0.774656 | 0.387328 | − | 0.921942i | \(-0.373398\pi\) | ||||
0.387328 | + | 0.921942i | \(0.373398\pi\) | |||||||
\(734\) | 20.2011i | 0.745634i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.34775i | 0.123400i | ||||||||
\(737\) | − | 7.32145i | − | 0.269689i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.4015i | 0.897625i | 0.893626 | + | 0.448812i | \(0.148153\pi\) | ||||
−0.893626 | + | 0.448812i | \(0.851847\pi\) | |||||||
\(740\) | 1.68074 | 0.0617853 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.51547 | −0.239191 | ||||||||
\(743\) | 19.0115i | 0.697465i | 0.937222 | + | 0.348732i | \(0.113388\pi\) | ||||
−0.937222 | + | 0.348732i | \(0.886612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1731 | 0.482627 | ||||||||
\(746\) | 5.38424 | 0.197131 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.74560i | 0.100389i | ||||||||
\(749\) | −45.0948 | −1.64773 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.71157 | 0.244909 | 0.122454 | − | 0.992474i | \(-0.460923\pi\) | ||||
0.122454 | + | 0.992474i | \(0.460923\pi\) | |||||||
\(752\) | − | 10.7575i | − | 0.392286i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.41722i | 0.306537i | ||||||||
\(755\) | − | 1.04232i | − | 0.0379340i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 50.8520i | − | 1.84825i | −0.382093 | − | 0.924124i | \(-0.624797\pi\) | ||
0.382093 | − | 0.924124i | \(-0.375203\pi\) | |||||||
\(758\) | 8.94431i | 0.324872i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 2.01524i | − | 0.0731005i | ||||||
\(761\) | −11.4685 | −0.415732 | −0.207866 | − | 0.978157i | \(-0.566652\pi\) | ||||
−0.207866 | + | 0.978157i | \(0.566652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.0540 | 1.99309 | ||||||||
\(764\) | −11.6916 | −0.422989 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 7.05417i | − | 0.254877i | ||||||
\(767\) | 45.5047i | 1.64308i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.5809 | 0.958531 | 0.479265 | − | 0.877670i | \(-0.340903\pi\) | ||||
0.479265 | + | 0.877670i | \(0.340903\pi\) | |||||||
\(770\) | 8.60351i | 0.310049i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.0831582i | 0.00299293i | ||||||||
\(773\) | 1.89399 | 0.0681223 | 0.0340611 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340611 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.8377 | −0.461143 | ||||||||
\(776\) | −13.0886 | −0.469855 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.40158 | −0.0861007 | ||||||||
\(779\) | 5.01633i | 0.179729i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.38125 | 0.192556 | ||||||||
\(782\) | −3.59111 | −0.128418 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.03201 | 0.179715 | ||||||||
\(785\) | − | 3.28850i | − | 0.117371i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.3861i | 0.726685i | 0.931656 | + | 0.363342i | \(0.118364\pi\) | ||||
−0.931656 | + | 0.363342i | \(0.881636\pi\) | |||||||
\(788\) | 9.84566i | 0.350737i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.45081 | 0.0516176 | ||||||||
\(791\) | 0.741896 | 0.0263788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.3669 | 1.78858 | ||||||||
\(794\) | −37.6516 | −1.33621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.3477 | 0.437652 | ||||||||
\(797\) | 26.3038i | 0.931729i | 0.884856 | + | 0.465864i | \(0.154256\pi\) | ||||
−0.884856 | + | 0.465864i | \(0.845744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.5395 | 0.408238 | ||||||||
\(800\) | 4.06095i | 0.143576i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.1534 | 0.817573 | ||||||||
\(803\) | −0.719588 | −0.0253937 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2529 | −0.396614 | ||||||||
\(806\) | 21.2438 | 0.748281 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3809 | 0.365199 | ||||||||
\(809\) | −36.4983 | −1.28321 | −0.641607 | − | 0.767034i | \(-0.721732\pi\) | ||||
−0.641607 | + | 0.767034i | \(0.721732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.974702i | − | 0.0342264i | −0.999854 | − | 0.0171132i | \(-0.994552\pi\) | ||
0.999854 | − | 0.0171132i | \(-0.00544757\pi\) | |||||||
\(812\) | 4.34474i | 0.152471i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.43935i | 0.155599i | ||||||||
\(815\) | − | 5.90654i | − | 0.206897i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.35236 | −0.117284 | ||||||||
\(818\) | 12.6033 | 0.440664 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.33748i | 0.0816283i | ||||||||
\(821\) | 21.5793i | 0.753122i | 0.926392 | + | 0.376561i | \(0.122894\pi\) | ||||
−0.926392 | + | 0.376561i | \(0.877106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 20.7826i | − | 0.724435i | −0.932094 | − | 0.362217i | \(-0.882020\pi\) | ||
0.932094 | − | 0.362217i | \(-0.117980\pi\) | |||||||
\(824\) | −3.40046 | −0.118460 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.4883i | 0.817262i | ||||||||
\(827\) | −21.6578 | −0.753116 | −0.376558 | − | 0.926393i | \(-0.622893\pi\) | ||||
−0.376558 | + | 0.926393i | \(0.622893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.23302i | 0.251213i | 0.992080 | + | 0.125607i | \(0.0400877\pi\) | ||||
−0.992080 | + | 0.125607i | \(0.959912\pi\) | |||||||
\(830\) | 9.06464 | 0.314638 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 6.72007i | − | 0.232977i | ||||||
\(833\) | 5.39780i | 0.187023i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.90823 | 0.239069 | ||||||||
\(836\) | 5.32286 | 0.184095 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.0493 | −0.727137 | ||||||||
\(839\) | −47.1529 | −1.62790 | −0.813949 | − | 0.580937i | \(-0.802686\pi\) | ||||
−0.813949 | + | 0.580937i | \(0.802686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4311 | 0.945901 | ||||||||
\(842\) | 22.6340 | 0.780019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.7720 | −0.783845 | ||||||||
\(845\) | 31.1639 | 1.07207 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4314 | 0.530231 | ||||||||
\(848\) | 1.87835i | 0.0645029i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.35616 | −0.149415 | ||||||||
\(851\) | −5.80644 | −0.199042 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.9928i | 0.924215i | 0.886824 | + | 0.462107i | \(0.152907\pi\) | ||||
−0.886824 | + | 0.462107i | \(0.847093\pi\) | |||||||
\(854\) | 25.9980 | 0.889634 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.0004i | 0.444345i | ||||||||
\(857\) | − | 7.48806i | − | 0.255787i | −0.991788 | − | 0.127894i | \(-0.959178\pi\) | ||
0.991788 | − | 0.127894i | \(-0.0408216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.7038i | 0.706405i | 0.935547 | + | 0.353202i | \(0.114907\pi\) | ||||
−0.935547 | + | 0.353202i | \(0.885093\pi\) | |||||||
\(860\) | −1.56211 | −0.0532676 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.1291i | 0.515301i | ||||||||
\(863\) | −21.1713 | −0.720680 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.9516 | −0.406365 | ||||||||
\(866\) | − | 6.37944i | − | 0.216782i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.9655 | 0.372192 | ||||||||
\(869\) | 3.83203i | 0.129993i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.2225 | −0.651328 | ||||||||
\(872\) | − | 15.8716i | − | 0.537479i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.96203i | 0.235494i | ||||||||
\(875\) | −30.4570 | −1.02963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.7673i | 1.47792i | 0.673750 | + | 0.738959i | \(0.264682\pi\) | ||||
−0.673750 | + | 0.738959i | \(0.735318\pi\) | |||||||
\(878\) | 18.1574 | 0.612783 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.48031 | 0.0836113 | ||||||||
\(881\) | − | 51.3943i | − | 1.73152i | −0.500460 | − | 0.865759i | \(-0.666836\pi\) | ||
0.500460 | − | 0.865759i | \(-0.333164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0427i | 0.910059i | 0.890476 | + | 0.455029i | \(0.150371\pi\) | ||||
−0.890476 | + | 0.455029i | \(0.849629\pi\) | |||||||
\(884\) | 7.20858 | 0.242451 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.7071 | 0.527692 | ||||||||
\(887\) | − | 9.49108i | − | 0.318679i | −0.987224 | − | 0.159340i | \(-0.949063\pi\) | ||
0.987224 | − | 0.159340i | \(-0.0509365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.57966 | 0.321291 | ||||||||
\(890\) | 3.69285 | 0.123785 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.3682 | + | 6.65524i | −0.447599 | + | 0.222834i | ||||
\(893\) | − | 22.3715i | − | 0.748632i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.5474i | 0.653397i | ||||||||
\(896\) | − | 3.46872i | − | 0.115882i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 24.7835i | − | 0.827036i | ||||||
\(899\) | 3.95962i | 0.132061i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.01490 | −0.0671259 | ||||||||
\(902\) | −6.17398 | −0.205571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.213882i | − | 0.00711361i | ||||||
\(905\) | 2.79300 | 0.0928425 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9365 | 1.29286 | 0.646432 | − | 0.762972i | \(-0.276260\pi\) | ||||
0.646432 | + | 0.762972i | \(0.276260\pi\) | |||||||
\(908\) | 16.1068i | 0.534523i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.5885 | 0.748801 | ||||||||
\(911\) | − | 30.5496i | − | 1.01215i | −0.862488 | − | 0.506077i | \(-0.831095\pi\) | ||
0.862488 | − | 0.506077i | \(-0.168905\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9424i | 0.792379i | ||||||||
\(914\) | −4.04644 | −0.133844 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.1904i | 0.766231i | ||||||||
\(917\) | 40.5718i | 1.33980i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.6393i | 1.07667i | 0.842731 | + | 0.538335i | \(0.180946\pi\) | ||||
−0.842731 | + | 0.538335i | \(0.819054\pi\) | |||||||
\(920\) | 3.24412i | 0.106955i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.4921 | 0.938339 | ||||||||
\(923\) | − | 14.1285i | − | 0.465044i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.04344 | −0.231587 | ||||||||
\(926\) | 5.30080i | 0.174195i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.25255 | 0.0411169 | ||||||||
\(929\) | 13.5638i | 0.445014i | 0.974931 | + | 0.222507i | \(0.0714241\pi\) | ||||
−0.974931 | + | 0.222507i | \(0.928576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4646 | 0.342965 | ||||||||
\(932\) | −19.4967 | −0.638637 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 3.24020i | − | 0.106023i | ||||||
\(935\) | 2.66062i | 0.0870115i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.2124i | 1.15034i | 0.818034 | + | 0.575170i | \(0.195064\pi\) | ||||
−0.818034 | + | 0.575170i | \(0.804936\pi\) | |||||||
\(938\) | −9.92211 | −0.323968 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 10.4245i | − | 0.340010i | ||||||
\(941\) | − | 10.8191i | − | 0.352691i | −0.984328 | − | 0.176346i | \(-0.943572\pi\) | ||
0.984328 | − | 0.176346i | \(-0.0564277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.07525i | − | 0.262966i | ||||||
\(944\) | 6.77146 | 0.220392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 4.12601i | − | 0.134148i | ||||||
\(947\) | 10.6045i | 0.344599i | 0.985045 | + | 0.172300i | \(0.0551198\pi\) | ||||
−0.985045 | + | 0.172300i | \(0.944880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.88928i | 0.0613285i | ||||||||
\(950\) | 8.44521i | 0.273999i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.72087 | 0.120594 | ||||||||
\(953\) | −12.3593 | −0.400356 | −0.200178 | − | 0.979760i | \(-0.564152\pi\) | ||||
−0.200178 | + | 0.979760i | \(0.564152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3297 | −0.366622 | ||||||||
\(956\) | − | 7.31789i | − | 0.236677i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.7509 | 0.411964 | ||||||||
\(959\) | −44.9501 | −1.45151 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0065 | −0.677630 | ||||||||
\(962\) | 11.6555 | 0.375788 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.68387 | −0.150857 | ||||||||
\(965\) | 0.0805841i | 0.00259409i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.2823i | − | 1.10244i | −0.834359 | − | 0.551222i | \(-0.814162\pi\) | ||
0.834359 | − | 0.551222i | \(-0.185838\pi\) | |||||||
\(968\) | − | 4.44875i | − | 0.142988i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.6835 | −0.407243 | ||||||||
\(971\) | −23.9188 | −0.767590 | −0.383795 | − | 0.923418i | \(-0.625383\pi\) | ||||
−0.383795 | + | 0.923418i | \(0.625383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.4619 | 1.32921 | ||||||||
\(974\) | − | 14.2673i | − | 0.457153i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 7.49500i | − | 0.239909i | ||||||
\(977\) | 12.6179 | 0.403683 | 0.201842 | − | 0.979418i | \(-0.435307\pi\) | ||||
0.201842 | + | 0.979418i | \(0.435307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.75394i | 0.311737i | ||||||||
\(980\) | 4.87625 | 0.155766 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 0.174465i | − | 0.00556739i | ||||||
\(983\) | 52.6913 | 1.68059 | 0.840295 | − | 0.542129i | \(-0.182382\pi\) | ||||
0.840295 | + | 0.542129i | \(0.182382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.54090i | 0.303998i | ||||||||
\(986\) | 1.34360i | 0.0427890i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 13.9752i | − | 0.444609i | ||||||
\(989\) | 5.39661 | 0.171602 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.80050i | 0.152493i | 0.997089 | + | 0.0762465i | \(0.0242936\pi\) | ||||
−0.997089 | + | 0.0762465i | \(0.975706\pi\) | |||||||
\(992\) | − | 3.16125i | − | 0.100370i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 7.29272i | − | 0.231311i | ||||||
\(995\) | 11.9655 | 0.379331 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.0125 | −1.26721 | −0.633604 | − | 0.773657i | \(-0.718425\pi\) | ||||
−0.633604 | + | 0.773657i | \(0.718425\pi\) | |||||||
\(998\) | − | 12.8629i | − | 0.407169i | ||||||
\(999\) | 0 | 0 |
(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 | 4014.2.d.a.4013.3 | ✓ | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.68 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.67 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.4 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.3 | ✓ | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.4 | yes | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.67 | yes | 72 | 223.222 | odd | 2 | inner | |
4014.2.d.a.4013.68 | yes | 72 | 3.2 | odd | 2 | inner |