Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.580017.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 4x^{2} + 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.941569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.941569 | −0.665790 | −0.332895 | − | 0.942964i | \(-0.608025\pi\) | ||||
−0.332895 | + | 0.942964i | \(0.608025\pi\) | |||||||
\(3\) | 1.53997 | 0.889102 | 0.444551 | − | 0.895754i | \(-0.353363\pi\) | ||||
0.444551 | + | 0.895754i | \(0.353363\pi\) | |||||||
\(4\) | −1.11345 | −0.556724 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.44999 | −0.591955 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.93153 | 1.03645 | ||||||||
\(9\) | −0.628495 | −0.209498 | ||||||||
\(10\) | 0.941569 | 0.297750 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.71467 | −0.494984 | ||||||||
\(13\) | 1.39156 | 0.385948 | 0.192974 | − | 0.981204i | \(-0.438187\pi\) | ||||
0.192974 | + | 0.981204i | \(0.438187\pi\) | |||||||
\(14\) | −0.941569 | −0.251645 | ||||||||
\(15\) | −1.53997 | −0.397618 | ||||||||
\(16\) | −0.533340 | −0.133335 | ||||||||
\(17\) | −2.87651 | −0.697656 | −0.348828 | − | 0.937187i | \(-0.613420\pi\) | ||||
−0.348828 | + | 0.937187i | \(0.613420\pi\) | |||||||
\(18\) | 0.591771 | 0.139482 | ||||||||
\(19\) | −1.39301 | −0.319579 | −0.159790 | − | 0.987151i | \(-0.551082\pi\) | ||||
−0.159790 | + | 0.987151i | \(0.551082\pi\) | |||||||
\(20\) | 1.11345 | 0.248974 | ||||||||
\(21\) | 1.53997 | 0.336049 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.46428 | 1.34790 | 0.673948 | − | 0.738779i | \(-0.264597\pi\) | ||||
0.673948 | + | 0.738779i | \(0.264597\pi\) | |||||||
\(24\) | 4.51446 | 0.921510 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.31025 | −0.256961 | ||||||||
\(27\) | −5.58777 | −1.07537 | ||||||||
\(28\) | −1.11345 | −0.210422 | ||||||||
\(29\) | −2.72955 | −0.506865 | −0.253433 | − | 0.967353i | \(-0.581560\pi\) | ||||
−0.253433 | + | 0.967353i | \(0.581560\pi\) | |||||||
\(30\) | 1.44999 | 0.264730 | ||||||||
\(31\) | −2.10106 | −0.377361 | −0.188681 | − | 0.982038i | \(-0.560421\pi\) | ||||
−0.188681 | + | 0.982038i | \(0.560421\pi\) | |||||||
\(32\) | −5.36088 | −0.947678 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.70843 | 0.464492 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0.699796 | 0.116633 | ||||||||
\(37\) | −6.54173 | −1.07545 | −0.537727 | − | 0.843119i | \(-0.680717\pi\) | ||||
−0.537727 | + | 0.843119i | \(0.680717\pi\) | |||||||
\(38\) | 1.31162 | 0.212773 | ||||||||
\(39\) | 2.14296 | 0.343147 | ||||||||
\(40\) | −2.93153 | −0.463515 | ||||||||
\(41\) | −7.54422 | −1.17821 | −0.589104 | − | 0.808057i | \(-0.700519\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(42\) | −1.44999 | −0.223738 | ||||||||
\(43\) | 5.24119 | 0.799273 | 0.399637 | − | 0.916674i | \(-0.369136\pi\) | ||||
0.399637 | + | 0.916674i | \(0.369136\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.628495 | 0.0936904 | ||||||||
\(46\) | −6.08657 | −0.897415 | ||||||||
\(47\) | 8.87972 | 1.29524 | 0.647620 | − | 0.761963i | \(-0.275764\pi\) | ||||
0.647620 | + | 0.761963i | \(0.275764\pi\) | |||||||
\(48\) | −0.821328 | −0.118548 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.941569 | −0.133158 | ||||||||
\(51\) | −4.42974 | −0.620287 | ||||||||
\(52\) | −1.54943 | −0.214867 | ||||||||
\(53\) | 7.31070 | 1.00420 | 0.502101 | − | 0.864809i | \(-0.332561\pi\) | ||||
0.502101 | + | 0.864809i | \(0.332561\pi\) | |||||||
\(54\) | 5.26127 | 0.715969 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.93153 | 0.391742 | ||||||||
\(57\) | −2.14520 | −0.284138 | ||||||||
\(58\) | 2.57006 | 0.337466 | ||||||||
\(59\) | −8.87651 | −1.15562 | −0.577812 | − | 0.816170i | \(-0.696093\pi\) | ||||
−0.577812 | + | 0.816170i | \(0.696093\pi\) | |||||||
\(60\) | 1.71467 | 0.221364 | ||||||||
\(61\) | −1.70038 | −0.217712 | −0.108856 | − | 0.994058i | \(-0.534719\pi\) | ||||
−0.108856 | + | 0.994058i | \(0.534719\pi\) | |||||||
\(62\) | 1.97829 | 0.251243 | ||||||||
\(63\) | −0.628495 | −0.0791829 | ||||||||
\(64\) | 6.11432 | 0.764290 | ||||||||
\(65\) | −1.39156 | −0.172601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.00145621 | 0.000177904 0 | 8.89522e−5 | − | 1.00000i | \(-0.499972\pi\) | ||||
8.89522e−5 | 1.00000i | \(0.499972\pi\) | ||||||||
\(68\) | 3.20284 | 0.388402 | ||||||||
\(69\) | 9.95479 | 1.19842 | ||||||||
\(70\) | 0.941569 | 0.112539 | ||||||||
\(71\) | 6.94923 | 0.824722 | 0.412361 | − | 0.911020i | \(-0.364704\pi\) | ||||
0.412361 | + | 0.911020i | \(0.364704\pi\) | |||||||
\(72\) | −1.84245 | −0.217135 | ||||||||
\(73\) | 0.0957409 | 0.0112056 | 0.00560281 | − | 0.999984i | \(-0.498217\pi\) | ||||
0.00560281 | + | 0.999984i | \(0.498217\pi\) | |||||||
\(74\) | 6.15949 | 0.716026 | ||||||||
\(75\) | 1.53997 | 0.177820 | ||||||||
\(76\) | 1.55105 | 0.177917 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.01774 | −0.228464 | ||||||||
\(79\) | −9.24782 | −1.04046 | −0.520230 | − | 0.854026i | \(-0.674154\pi\) | ||||
−0.520230 | + | 0.854026i | \(0.674154\pi\) | |||||||
\(80\) | 0.533340 | 0.0596293 | ||||||||
\(81\) | −6.71951 | −0.746612 | ||||||||
\(82\) | 7.10340 | 0.784440 | ||||||||
\(83\) | −13.2464 | −1.45398 | −0.726988 | − | 0.686650i | \(-0.759081\pi\) | ||||
−0.726988 | + | 0.686650i | \(0.759081\pi\) | |||||||
\(84\) | −1.71467 | −0.187086 | ||||||||
\(85\) | 2.87651 | 0.312001 | ||||||||
\(86\) | −4.93494 | −0.532148 | ||||||||
\(87\) | −4.20343 | −0.450655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.516504 | 0.0547493 | 0.0273746 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273746 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(90\) | −0.591771 | −0.0623782 | ||||||||
\(91\) | 1.39156 | 0.145875 | ||||||||
\(92\) | −7.19764 | −0.750405 | ||||||||
\(93\) | −3.23557 | −0.335513 | ||||||||
\(94\) | −8.36088 | −0.862358 | ||||||||
\(95\) | 1.39301 | 0.142920 | ||||||||
\(96\) | −8.25558 | −0.842582 | ||||||||
\(97\) | 0.474323 | 0.0481602 | 0.0240801 | − | 0.999710i | \(-0.492334\pi\) | ||||
0.0240801 | + | 0.999710i | \(0.492334\pi\) | |||||||
\(98\) | −0.941569 | −0.0951129 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.11345 | −0.111345 | ||||||||
\(101\) | −9.70989 | −0.966170 | −0.483085 | − | 0.875573i | \(-0.660484\pi\) | ||||
−0.483085 | + | 0.875573i | \(0.660484\pi\) | |||||||
\(102\) | 4.17090 | 0.412981 | ||||||||
\(103\) | 0.722725 | 0.0712122 | 0.0356061 | − | 0.999366i | \(-0.488664\pi\) | ||||
0.0356061 | + | 0.999366i | \(0.488664\pi\) | |||||||
\(104\) | 4.07939 | 0.400017 | ||||||||
\(105\) | −1.53997 | −0.150286 | ||||||||
\(106\) | −6.88353 | −0.668587 | ||||||||
\(107\) | −12.0970 | −1.16946 | −0.584732 | − | 0.811227i | \(-0.698800\pi\) | ||||
−0.584732 | + | 0.811227i | \(0.698800\pi\) | |||||||
\(108\) | 6.22169 | 0.598682 | ||||||||
\(109\) | −2.06951 | −0.198223 | −0.0991115 | − | 0.995076i | \(-0.531600\pi\) | ||||
−0.0991115 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0741 | −0.956187 | ||||||||
\(112\) | −0.533340 | −0.0503959 | ||||||||
\(113\) | 18.3350 | 1.72481 | 0.862404 | − | 0.506220i | \(-0.168958\pi\) | ||||
0.862404 | + | 0.506220i | \(0.168958\pi\) | |||||||
\(114\) | 2.01985 | 0.189176 | ||||||||
\(115\) | −6.46428 | −0.602797 | ||||||||
\(116\) | 3.03921 | 0.282184 | ||||||||
\(117\) | −0.874586 | −0.0808555 | ||||||||
\(118\) | 8.35785 | 0.769402 | ||||||||
\(119\) | −2.87651 | −0.263689 | ||||||||
\(120\) | −4.51446 | −0.412112 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.60103 | 0.144950 | ||||||||
\(123\) | −11.6179 | −1.04755 | ||||||||
\(124\) | 2.33942 | 0.210086 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.591771 | 0.0527192 | ||||||||
\(127\) | 15.6786 | 1.39125 | 0.695625 | − | 0.718405i | \(-0.255128\pi\) | ||||
0.695625 | + | 0.718405i | \(0.255128\pi\) | |||||||
\(128\) | 4.96470 | 0.438821 | ||||||||
\(129\) | 8.07127 | 0.710635 | ||||||||
\(130\) | 1.31025 | 0.114916 | ||||||||
\(131\) | −14.8387 | −1.29646 | −0.648230 | − | 0.761445i | \(-0.724490\pi\) | ||||
−0.648230 | + | 0.761445i | \(0.724490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.39301 | −0.120790 | ||||||||
\(134\) | −0.00137112 | −0.000118447 0 | ||||||||
\(135\) | 5.58777 | 0.480919 | ||||||||
\(136\) | −8.43256 | −0.723086 | ||||||||
\(137\) | 13.0351 | 1.11366 | 0.556830 | − | 0.830626i | \(-0.312017\pi\) | ||||
0.556830 | + | 0.830626i | \(0.312017\pi\) | |||||||
\(138\) | −9.37313 | −0.797894 | ||||||||
\(139\) | −18.9218 | −1.60492 | −0.802462 | − | 0.596703i | \(-0.796477\pi\) | ||||
−0.802462 | + | 0.596703i | \(0.796477\pi\) | |||||||
\(140\) | 1.11345 | 0.0941035 | ||||||||
\(141\) | 13.6745 | 1.15160 | ||||||||
\(142\) | −6.54318 | −0.549092 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.335202 | 0.0279335 | ||||||||
\(145\) | 2.72955 | 0.226677 | ||||||||
\(146\) | −0.0901467 | −0.00746060 | ||||||||
\(147\) | 1.53997 | 0.127015 | ||||||||
\(148\) | 7.28387 | 0.598730 | ||||||||
\(149\) | 5.13736 | 0.420869 | 0.210435 | − | 0.977608i | \(-0.432512\pi\) | ||||
0.210435 | + | 0.977608i | \(0.432512\pi\) | |||||||
\(150\) | −1.44999 | −0.118391 | ||||||||
\(151\) | −9.51339 | −0.774189 | −0.387094 | − | 0.922040i | \(-0.626521\pi\) | ||||
−0.387094 | + | 0.922040i | \(0.626521\pi\) | |||||||
\(152\) | −4.08365 | −0.331228 | ||||||||
\(153\) | 1.80787 | 0.146158 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.10106 | 0.168761 | ||||||||
\(156\) | −2.38607 | −0.191038 | ||||||||
\(157\) | −4.94602 | −0.394735 | −0.197368 | − | 0.980330i | \(-0.563239\pi\) | ||||
−0.197368 | + | 0.980330i | \(0.563239\pi\) | |||||||
\(158\) | 8.70746 | 0.692728 | ||||||||
\(159\) | 11.2582 | 0.892837 | ||||||||
\(160\) | 5.36088 | 0.423814 | ||||||||
\(161\) | 6.46428 | 0.509457 | ||||||||
\(162\) | 6.32688 | 0.497087 | ||||||||
\(163\) | −19.1488 | −1.49985 | −0.749926 | − | 0.661522i | \(-0.769911\pi\) | ||||
−0.749926 | + | 0.661522i | \(0.769911\pi\) | |||||||
\(164\) | 8.40009 | 0.655937 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4724 | 0.968043 | ||||||||
\(167\) | 11.7906 | 0.912382 | 0.456191 | − | 0.889882i | \(-0.349213\pi\) | ||||
0.456191 | + | 0.889882i | \(0.349213\pi\) | |||||||
\(168\) | 4.51446 | 0.348298 | ||||||||
\(169\) | −11.0636 | −0.851044 | ||||||||
\(170\) | −2.70843 | −0.207727 | ||||||||
\(171\) | 0.875501 | 0.0669513 | ||||||||
\(172\) | −5.83579 | −0.444974 | ||||||||
\(173\) | −22.0859 | −1.67916 | −0.839582 | − | 0.543233i | \(-0.817200\pi\) | ||||
−0.839582 | + | 0.543233i | \(0.817200\pi\) | |||||||
\(174\) | 3.95782 | 0.300042 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.6696 | −1.02747 | ||||||||
\(178\) | −0.486324 | −0.0364515 | ||||||||
\(179\) | −14.5651 | −1.08865 | −0.544325 | − | 0.838875i | \(-0.683214\pi\) | ||||
−0.544325 | + | 0.838875i | \(0.683214\pi\) | |||||||
\(180\) | −0.699796 | −0.0521597 | ||||||||
\(181\) | 4.14710 | 0.308252 | 0.154126 | − | 0.988051i | \(-0.450744\pi\) | ||||
0.154126 | + | 0.988051i | \(0.450744\pi\) | |||||||
\(182\) | −1.31025 | −0.0971220 | ||||||||
\(183\) | −2.61854 | −0.193568 | ||||||||
\(184\) | 18.9502 | 1.39703 | ||||||||
\(185\) | 6.54173 | 0.480957 | ||||||||
\(186\) | 3.04651 | 0.223381 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.88711 | −0.721091 | ||||||||
\(189\) | −5.58777 | −0.406450 | ||||||||
\(190\) | −1.31162 | −0.0951548 | ||||||||
\(191\) | −13.3933 | −0.969106 | −0.484553 | − | 0.874762i | \(-0.661018\pi\) | ||||
−0.484553 | + | 0.874762i | \(0.661018\pi\) | |||||||
\(192\) | 9.41586 | 0.679531 | ||||||||
\(193\) | −14.7344 | −1.06060 | −0.530302 | − | 0.847809i | \(-0.677922\pi\) | ||||
−0.530302 | + | 0.847809i | \(0.677922\pi\) | |||||||
\(194\) | −0.446608 | −0.0320646 | ||||||||
\(195\) | −2.14296 | −0.153460 | ||||||||
\(196\) | −1.11345 | −0.0795320 | ||||||||
\(197\) | −3.94112 | −0.280793 | −0.140397 | − | 0.990095i | \(-0.544838\pi\) | ||||
−0.140397 | + | 0.990095i | \(0.544838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.2444 | −0.726206 | −0.363103 | − | 0.931749i | \(-0.618283\pi\) | ||||
−0.363103 | + | 0.931749i | \(0.618283\pi\) | |||||||
\(200\) | 2.93153 | 0.207290 | ||||||||
\(201\) | 0.00224252 | 0.000158175 0 | ||||||||
\(202\) | 9.14253 | 0.643266 | ||||||||
\(203\) | −2.72955 | −0.191577 | ||||||||
\(204\) | 4.93228 | 0.345329 | ||||||||
\(205\) | 7.54422 | 0.526911 | ||||||||
\(206\) | −0.680496 | −0.0474124 | ||||||||
\(207\) | −4.06277 | −0.282382 | ||||||||
\(208\) | −0.742174 | −0.0514605 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.44999 | 0.100059 | ||||||||
\(211\) | −8.32284 | −0.572968 | −0.286484 | − | 0.958085i | \(-0.592486\pi\) | ||||
−0.286484 | + | 0.958085i | \(0.592486\pi\) | |||||||
\(212\) | −8.14007 | −0.559063 | ||||||||
\(213\) | 10.7016 | 0.733262 | ||||||||
\(214\) | 11.3902 | 0.778617 | ||||||||
\(215\) | −5.24119 | −0.357446 | ||||||||
\(216\) | −16.3807 | −1.11457 | ||||||||
\(217\) | −2.10106 | −0.142629 | ||||||||
\(218\) | 1.94859 | 0.131975 | ||||||||
\(219\) | 0.147438 | 0.00996294 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00283 | −0.269259 | ||||||||
\(222\) | 9.48543 | 0.636620 | ||||||||
\(223\) | 20.0014 | 1.33939 | 0.669695 | − | 0.742636i | \(-0.266425\pi\) | ||||
0.669695 | + | 0.742636i | \(0.266425\pi\) | |||||||
\(224\) | −5.36088 | −0.358189 | ||||||||
\(225\) | −0.628495 | −0.0418996 | ||||||||
\(226\) | −17.2636 | −1.14836 | ||||||||
\(227\) | 13.2057 | 0.876494 | 0.438247 | − | 0.898854i | \(-0.355599\pi\) | ||||
0.438247 | + | 0.898854i | \(0.355599\pi\) | |||||||
\(228\) | 2.38856 | 0.158187 | ||||||||
\(229\) | −25.7475 | −1.70144 | −0.850720 | − | 0.525618i | \(-0.823834\pi\) | ||||
−0.850720 | + | 0.525618i | \(0.823834\pi\) | |||||||
\(230\) | 6.08657 | 0.401336 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00176 | −0.525341 | ||||||||
\(233\) | 11.9028 | 0.779776 | 0.389888 | − | 0.920862i | \(-0.372514\pi\) | ||||
0.389888 | + | 0.920862i | \(0.372514\pi\) | |||||||
\(234\) | 0.823483 | 0.0538328 | ||||||||
\(235\) | −8.87972 | −0.579249 | ||||||||
\(236\) | 9.88353 | 0.643363 | ||||||||
\(237\) | −14.2414 | −0.925075 | ||||||||
\(238\) | 2.70843 | 0.175562 | ||||||||
\(239\) | 17.4196 | 1.12678 | 0.563390 | − | 0.826191i | \(-0.309497\pi\) | ||||
0.563390 | + | 0.826191i | \(0.309497\pi\) | |||||||
\(240\) | 0.821328 | 0.0530165 | ||||||||
\(241\) | −2.30561 | −0.148517 | −0.0742587 | − | 0.997239i | \(-0.523659\pi\) | ||||
−0.0742587 | + | 0.997239i | \(0.523659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.41547 | 0.411553 | ||||||||
\(244\) | 1.89329 | 0.121205 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 10.9390 | 0.697447 | ||||||||
\(247\) | −1.93846 | −0.123341 | ||||||||
\(248\) | −6.15931 | −0.391117 | ||||||||
\(249\) | −20.3990 | −1.29273 | ||||||||
\(250\) | 0.941569 | 0.0595501 | ||||||||
\(251\) | −9.53947 | −0.602126 | −0.301063 | − | 0.953604i | \(-0.597341\pi\) | ||||
−0.301063 | + | 0.953604i | \(0.597341\pi\) | |||||||
\(252\) | 0.699796 | 0.0440830 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.7625 | −0.926280 | ||||||||
\(255\) | 4.42974 | 0.277401 | ||||||||
\(256\) | −16.9032 | −1.05645 | ||||||||
\(257\) | −29.4161 | −1.83493 | −0.917463 | − | 0.397821i | \(-0.869767\pi\) | ||||
−0.917463 | + | 0.397821i | \(0.869767\pi\) | |||||||
\(258\) | −7.59966 | −0.473134 | ||||||||
\(259\) | −6.54173 | −0.406483 | ||||||||
\(260\) | 1.54943 | 0.0960913 | ||||||||
\(261\) | 1.71551 | 0.106187 | ||||||||
\(262\) | 13.9716 | 0.863170 | ||||||||
\(263\) | 3.05267 | 0.188236 | 0.0941179 | − | 0.995561i | \(-0.469997\pi\) | ||||
0.0941179 | + | 0.995561i | \(0.469997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.31070 | −0.449092 | ||||||||
\(266\) | 1.31162 | 0.0804205 | ||||||||
\(267\) | 0.795400 | 0.0486777 | ||||||||
\(268\) | −0.00162141 | −9.90436e−5 0 | ||||||||
\(269\) | −2.00386 | −0.122178 | −0.0610888 | − | 0.998132i | \(-0.519457\pi\) | ||||
−0.0610888 | + | 0.998132i | \(0.519457\pi\) | |||||||
\(270\) | −5.26127 | −0.320191 | ||||||||
\(271\) | −23.7039 | −1.43991 | −0.719955 | − | 0.694021i | \(-0.755837\pi\) | ||||
−0.719955 | + | 0.694021i | \(0.755837\pi\) | |||||||
\(272\) | 1.53416 | 0.0930221 | ||||||||
\(273\) | 2.14296 | 0.129698 | ||||||||
\(274\) | −12.2734 | −0.741464 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.0841 | −0.667187 | ||||||||
\(277\) | −18.9545 | −1.13886 | −0.569432 | − | 0.822038i | \(-0.692837\pi\) | ||||
−0.569432 | + | 0.822038i | \(0.692837\pi\) | |||||||
\(278\) | 17.8162 | 1.06854 | ||||||||
\(279\) | 1.32050 | 0.0790565 | ||||||||
\(280\) | −2.93153 | −0.175192 | ||||||||
\(281\) | 1.50221 | 0.0896144 | 0.0448072 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448072 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(282\) | −12.8755 | −0.766724 | ||||||||
\(283\) | 1.69585 | 0.100808 | 0.0504038 | − | 0.998729i | \(-0.483949\pi\) | ||||
0.0504038 | + | 0.998729i | \(0.483949\pi\) | |||||||
\(284\) | −7.73760 | −0.459142 | ||||||||
\(285\) | 2.14520 | 0.127071 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.54422 | −0.445321 | ||||||||
\(288\) | 3.36928 | 0.198537 | ||||||||
\(289\) | −8.72569 | −0.513276 | ||||||||
\(290\) | −2.57006 | −0.150919 | ||||||||
\(291\) | 0.730443 | 0.0428193 | ||||||||
\(292\) | −0.106602 | −0.00623844 | ||||||||
\(293\) | 8.76253 | 0.511912 | 0.255956 | − | 0.966688i | \(-0.417610\pi\) | ||||
0.255956 | + | 0.966688i | \(0.417610\pi\) | |||||||
\(294\) | −1.44999 | −0.0845650 | ||||||||
\(295\) | 8.87651 | 0.516810 | ||||||||
\(296\) | −19.1772 | −1.11465 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.83718 | −0.280210 | ||||||||
\(299\) | 8.99541 | 0.520218 | ||||||||
\(300\) | −1.71467 | −0.0989968 | ||||||||
\(301\) | 5.24119 | 0.302097 | ||||||||
\(302\) | 8.95752 | 0.515447 | ||||||||
\(303\) | −14.9529 | −0.859023 | ||||||||
\(304\) | 0.742950 | 0.0426111 | ||||||||
\(305\) | 1.70038 | 0.0973636 | ||||||||
\(306\) | −1.70224 | −0.0973103 | ||||||||
\(307\) | −15.6989 | −0.895985 | −0.447992 | − | 0.894037i | \(-0.647861\pi\) | ||||
−0.447992 | + | 0.894037i | \(0.647861\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.11297 | 0.0633149 | ||||||||
\(310\) | −1.97829 | −0.112359 | ||||||||
\(311\) | 4.53471 | 0.257140 | 0.128570 | − | 0.991700i | \(-0.458961\pi\) | ||||
0.128570 | + | 0.991700i | \(0.458961\pi\) | |||||||
\(312\) | 6.28213 | 0.355656 | ||||||||
\(313\) | −2.68654 | −0.151852 | −0.0759261 | − | 0.997113i | \(-0.524191\pi\) | ||||
−0.0759261 | + | 0.997113i | \(0.524191\pi\) | |||||||
\(314\) | 4.65702 | 0.262811 | ||||||||
\(315\) | 0.628495 | 0.0354117 | ||||||||
\(316\) | 10.2970 | 0.579249 | ||||||||
\(317\) | −14.0343 | −0.788244 | −0.394122 | − | 0.919058i | \(-0.628951\pi\) | ||||
−0.394122 | + | 0.919058i | \(0.628951\pi\) | |||||||
\(318\) | −10.6004 | −0.594442 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −6.11432 | −0.341801 | ||||||||
\(321\) | −18.6290 | −1.03977 | ||||||||
\(322\) | −6.08657 | −0.339191 | ||||||||
\(323\) | 4.00702 | 0.222956 | ||||||||
\(324\) | 7.48182 | 0.415657 | ||||||||
\(325\) | 1.39156 | 0.0771897 | ||||||||
\(326\) | 18.0299 | 0.998586 | ||||||||
\(327\) | −3.18698 | −0.176240 | ||||||||
\(328\) | −22.1161 | −1.22116 | ||||||||
\(329\) | 8.87972 | 0.489555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5349 | 1.18367 | 0.591833 | − | 0.806060i | \(-0.298404\pi\) | ||||
0.591833 | + | 0.806060i | \(0.298404\pi\) | |||||||
\(332\) | 14.7491 | 0.809463 | ||||||||
\(333\) | 4.11144 | 0.225306 | ||||||||
\(334\) | −11.1016 | −0.607455 | ||||||||
\(335\) | −0.00145621 | −7.95613e−5 0 | ||||||||
\(336\) | −0.821328 | −0.0448071 | ||||||||
\(337\) | 26.0578 | 1.41946 | 0.709730 | − | 0.704474i | \(-0.248817\pi\) | ||||
0.709730 | + | 0.704474i | \(0.248817\pi\) | |||||||
\(338\) | 10.4171 | 0.566616 | ||||||||
\(339\) | 28.2353 | 1.53353 | ||||||||
\(340\) | −3.20284 | −0.173698 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.824345 | −0.0445755 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 15.3647 | 0.828408 | ||||||||
\(345\) | −9.95479 | −0.535948 | ||||||||
\(346\) | 20.7954 | 1.11797 | ||||||||
\(347\) | −29.2251 | −1.56888 | −0.784442 | − | 0.620202i | \(-0.787050\pi\) | ||||
−0.784442 | + | 0.620202i | \(0.787050\pi\) | |||||||
\(348\) | 4.68030 | 0.250890 | ||||||||
\(349\) | 7.70633 | 0.412510 | 0.206255 | − | 0.978498i | \(-0.433872\pi\) | ||||
0.206255 | + | 0.978498i | \(0.433872\pi\) | |||||||
\(350\) | −0.941569 | −0.0503290 | ||||||||
\(351\) | −7.77570 | −0.415036 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2765 | −1.18566 | −0.592829 | − | 0.805328i | \(-0.701989\pi\) | ||||
−0.592829 | + | 0.805328i | \(0.701989\pi\) | |||||||
\(354\) | 12.8708 | 0.684077 | ||||||||
\(355\) | −6.94923 | −0.368827 | ||||||||
\(356\) | −0.575099 | −0.0304802 | ||||||||
\(357\) | −4.42974 | −0.234447 | ||||||||
\(358\) | 13.7141 | 0.724812 | ||||||||
\(359\) | −1.69238 | −0.0893205 | −0.0446603 | − | 0.999002i | \(-0.514221\pi\) | ||||
−0.0446603 | + | 0.999002i | \(0.514221\pi\) | |||||||
\(360\) | 1.84245 | 0.0971056 | ||||||||
\(361\) | −17.0595 | −0.897869 | ||||||||
\(362\) | −3.90478 | −0.205231 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.54943 | −0.0812120 | ||||||||
\(365\) | −0.0957409 | −0.00501131 | ||||||||
\(366\) | 2.46553 | 0.128876 | ||||||||
\(367\) | −13.2925 | −0.693862 | −0.346931 | − | 0.937891i | \(-0.612776\pi\) | ||||
−0.346931 | + | 0.937891i | \(0.612776\pi\) | |||||||
\(368\) | −3.44766 | −0.179722 | ||||||||
\(369\) | 4.74150 | 0.246833 | ||||||||
\(370\) | −6.15949 | −0.320217 | ||||||||
\(371\) | 7.31070 | 0.379552 | ||||||||
\(372\) | 3.60263 | 0.186788 | ||||||||
\(373\) | 5.17666 | 0.268037 | 0.134019 | − | 0.990979i | \(-0.457212\pi\) | ||||
0.134019 | + | 0.990979i | \(0.457212\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.53997 | −0.0795237 | ||||||||
\(376\) | 26.0311 | 1.34245 | ||||||||
\(377\) | −3.79833 | −0.195624 | ||||||||
\(378\) | 5.26127 | 0.270611 | ||||||||
\(379\) | 20.8034 | 1.06860 | 0.534299 | − | 0.845295i | \(-0.320576\pi\) | ||||
0.534299 | + | 0.845295i | \(0.320576\pi\) | |||||||
\(380\) | −1.55105 | −0.0795670 | ||||||||
\(381\) | 24.1445 | 1.23696 | ||||||||
\(382\) | 12.6107 | 0.645221 | ||||||||
\(383\) | −5.55781 | −0.283991 | −0.141996 | − | 0.989867i | \(-0.545352\pi\) | ||||
−0.141996 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(384\) | 7.64548 | 0.390157 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8734 | 0.706140 | ||||||||
\(387\) | −3.29406 | −0.167446 | ||||||||
\(388\) | −0.528134 | −0.0268119 | ||||||||
\(389\) | 30.9206 | 1.56774 | 0.783869 | − | 0.620927i | \(-0.213244\pi\) | ||||
0.783869 | + | 0.620927i | \(0.213244\pi\) | |||||||
\(390\) | 2.01774 | 0.102172 | ||||||||
\(391\) | −18.5946 | −0.940368 | ||||||||
\(392\) | 2.93153 | 0.148064 | ||||||||
\(393\) | −22.8511 | −1.15268 | ||||||||
\(394\) | 3.71084 | 0.186949 | ||||||||
\(395\) | 9.24782 | 0.465308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.4744 | 1.52946 | 0.764732 | − | 0.644348i | \(-0.222871\pi\) | ||||
0.764732 | + | 0.644348i | \(0.222871\pi\) | |||||||
\(398\) | 9.64581 | 0.483501 | ||||||||
\(399\) | −2.14520 | −0.107394 | ||||||||
\(400\) | −0.533340 | −0.0266670 | ||||||||
\(401\) | −27.1836 | −1.35749 | −0.678743 | − | 0.734376i | \(-0.737475\pi\) | ||||
−0.678743 | + | 0.734376i | \(0.737475\pi\) | |||||||
\(402\) | −0.00211149 | −0.000105311 0 | ||||||||
\(403\) | −2.92374 | −0.145642 | ||||||||
\(404\) | 10.8115 | 0.537890 | ||||||||
\(405\) | 6.71951 | 0.333895 | ||||||||
\(406\) | 2.57006 | 0.127550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −12.9859 | −0.642897 | ||||||||
\(409\) | −12.4138 | −0.613822 | −0.306911 | − | 0.951738i | \(-0.599295\pi\) | ||||
−0.306911 | + | 0.951738i | \(0.599295\pi\) | |||||||
\(410\) | −7.10340 | −0.350812 | ||||||||
\(411\) | 20.0736 | 0.990158 | ||||||||
\(412\) | −0.804717 | −0.0396455 | ||||||||
\(413\) | −8.87651 | −0.436784 | ||||||||
\(414\) | 3.82537 | 0.188007 | ||||||||
\(415\) | 13.2464 | 0.650238 | ||||||||
\(416\) | −7.45996 | −0.365755 | ||||||||
\(417\) | −29.1390 | −1.42694 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5333 | 0.514585 | 0.257292 | − | 0.966334i | \(-0.417170\pi\) | ||||
0.257292 | + | 0.966334i | \(0.417170\pi\) | |||||||
\(420\) | 1.71467 | 0.0836676 | ||||||||
\(421\) | 19.6680 | 0.958560 | 0.479280 | − | 0.877662i | \(-0.340898\pi\) | ||||
0.479280 | + | 0.877662i | \(0.340898\pi\) | |||||||
\(422\) | 7.83653 | 0.381476 | ||||||||
\(423\) | −5.58086 | −0.271351 | ||||||||
\(424\) | 21.4315 | 1.04081 | ||||||||
\(425\) | −2.87651 | −0.139531 | ||||||||
\(426\) | −10.0763 | −0.488198 | ||||||||
\(427\) | −1.70038 | −0.0822873 | ||||||||
\(428\) | 13.4694 | 0.651068 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.93494 | 0.237984 | ||||||||
\(431\) | −15.7944 | −0.760788 | −0.380394 | − | 0.924824i | \(-0.624212\pi\) | ||||
−0.380394 | + | 0.924824i | \(0.624212\pi\) | |||||||
\(432\) | 2.98018 | 0.143384 | ||||||||
\(433\) | 7.09301 | 0.340868 | 0.170434 | − | 0.985369i | \(-0.445483\pi\) | ||||
0.170434 | + | 0.985369i | \(0.445483\pi\) | |||||||
\(434\) | 1.97829 | 0.0949611 | ||||||||
\(435\) | 4.20343 | 0.201539 | ||||||||
\(436\) | 2.30429 | 0.110355 | ||||||||
\(437\) | −9.00483 | −0.430759 | ||||||||
\(438\) | −0.138823 | −0.00663323 | ||||||||
\(439\) | 24.5227 | 1.17040 | 0.585202 | − | 0.810888i | \(-0.301015\pi\) | ||||
0.585202 | + | 0.810888i | \(0.301015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.628495 | −0.0299283 | ||||||||
\(442\) | 3.76894 | 0.179270 | ||||||||
\(443\) | −10.0332 | −0.476693 | −0.238346 | − | 0.971180i | \(-0.576605\pi\) | ||||
−0.238346 | + | 0.971180i | \(0.576605\pi\) | |||||||
\(444\) | 11.2169 | 0.532332 | ||||||||
\(445\) | −0.516504 | −0.0244846 | ||||||||
\(446\) | −18.8327 | −0.891753 | ||||||||
\(447\) | 7.91138 | 0.374195 | ||||||||
\(448\) | 6.11432 | 0.288874 | ||||||||
\(449\) | 28.3911 | 1.33986 | 0.669929 | − | 0.742425i | \(-0.266325\pi\) | ||||
0.669929 | + | 0.742425i | \(0.266325\pi\) | |||||||
\(450\) | 0.591771 | 0.0278964 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −20.4150 | −0.960242 | ||||||||
\(453\) | −14.6503 | −0.688333 | ||||||||
\(454\) | −12.4341 | −0.583561 | ||||||||
\(455\) | −1.39156 | −0.0652372 | ||||||||
\(456\) | −6.28870 | −0.294496 | ||||||||
\(457\) | 17.9107 | 0.837825 | 0.418913 | − | 0.908027i | \(-0.362411\pi\) | ||||
0.418913 | + | 0.908027i | \(0.362411\pi\) | |||||||
\(458\) | 24.2430 | 1.13280 | ||||||||
\(459\) | 16.0733 | 0.750236 | ||||||||
\(460\) | 7.19764 | 0.335591 | ||||||||
\(461\) | 22.3455 | 1.04073 | 0.520366 | − | 0.853943i | \(-0.325796\pi\) | ||||
0.520366 | + | 0.853943i | \(0.325796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.7804 | −1.47696 | −0.738480 | − | 0.674275i | \(-0.764456\pi\) | ||||
−0.738480 | + | 0.674275i | \(0.764456\pi\) | |||||||
\(464\) | 1.45578 | 0.0675830 | ||||||||
\(465\) | 3.23557 | 0.150046 | ||||||||
\(466\) | −11.2073 | −0.519167 | ||||||||
\(467\) | 13.4270 | 0.621328 | 0.310664 | − | 0.950520i | \(-0.399449\pi\) | ||||
0.310664 | + | 0.950520i | \(0.399449\pi\) | |||||||
\(468\) | 0.973806 | 0.0450142 | ||||||||
\(469\) | 0.00145621 | 6.72415e−5 0 | ||||||||
\(470\) | 8.36088 | 0.385658 | ||||||||
\(471\) | −7.61672 | −0.350960 | ||||||||
\(472\) | −26.0217 | −1.19775 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 13.4092 | 0.615906 | ||||||||
\(475\) | −1.39301 | −0.0639158 | ||||||||
\(476\) | 3.20284 | 0.146802 | ||||||||
\(477\) | −4.59473 | −0.210378 | ||||||||
\(478\) | −16.4018 | −0.750199 | ||||||||
\(479\) | −9.65688 | −0.441234 | −0.220617 | − | 0.975361i | \(-0.570807\pi\) | ||||
−0.220617 | + | 0.975361i | \(0.570807\pi\) | |||||||
\(480\) | 8.25558 | 0.376814 | ||||||||
\(481\) | −9.10319 | −0.415070 | ||||||||
\(482\) | 2.17089 | 0.0988814 | ||||||||
\(483\) | 9.95479 | 0.452959 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.474323 | −0.0215379 | ||||||||
\(486\) | −6.04061 | −0.274008 | ||||||||
\(487\) | −34.1522 | −1.54759 | −0.773793 | − | 0.633439i | \(-0.781643\pi\) | ||||
−0.773793 | + | 0.633439i | \(0.781643\pi\) | |||||||
\(488\) | −4.98472 | −0.225647 | ||||||||
\(489\) | −29.4886 | −1.33352 | ||||||||
\(490\) | 0.941569 | 0.0425358 | ||||||||
\(491\) | −1.54632 | −0.0697845 | −0.0348923 | − | 0.999391i | \(-0.511109\pi\) | ||||
−0.0348923 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(492\) | 12.9359 | 0.583195 | ||||||||
\(493\) | 7.85159 | 0.353618 | ||||||||
\(494\) | 1.82519 | 0.0821193 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.12058 | 0.0503155 | ||||||||
\(497\) | 6.94923 | 0.311716 | ||||||||
\(498\) | 19.2071 | 0.860689 | ||||||||
\(499\) | −14.9721 | −0.670241 | −0.335121 | − | 0.942175i | \(-0.608777\pi\) | ||||
−0.335121 | + | 0.942175i | \(0.608777\pi\) | |||||||
\(500\) | 1.11345 | 0.0497949 | ||||||||
\(501\) | 18.1571 | 0.811201 | ||||||||
\(502\) | 8.98207 | 0.400889 | ||||||||
\(503\) | −3.62122 | −0.161462 | −0.0807311 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807311 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(504\) | −1.84245 | −0.0820692 | ||||||||
\(505\) | 9.70989 | 0.432084 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.0376 | −0.756664 | ||||||||
\(508\) | −17.4573 | −0.774542 | ||||||||
\(509\) | −2.39707 | −0.106248 | −0.0531240 | − | 0.998588i | \(-0.516918\pi\) | ||||
−0.0531240 | + | 0.998588i | \(0.516918\pi\) | |||||||
\(510\) | −4.17090 | −0.184691 | ||||||||
\(511\) | 0.0957409 | 0.00423533 | ||||||||
\(512\) | 5.98618 | 0.264554 | ||||||||
\(513\) | 7.78384 | 0.343665 | ||||||||
\(514\) | 27.6973 | 1.22168 | ||||||||
\(515\) | −0.722725 | −0.0318471 | ||||||||
\(516\) | −8.98693 | −0.395628 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.15949 | 0.270632 | ||||||||
\(519\) | −34.0117 | −1.49295 | ||||||||
\(520\) | −4.07939 | −0.178893 | ||||||||
\(521\) | 41.8248 | 1.83238 | 0.916189 | − | 0.400747i | \(-0.131250\pi\) | ||||
0.916189 | + | 0.400747i | \(0.131250\pi\) | |||||||
\(522\) | −1.61527 | −0.0706985 | ||||||||
\(523\) | 28.7142 | 1.25559 | 0.627793 | − | 0.778380i | \(-0.283958\pi\) | ||||
0.627793 | + | 0.778380i | \(0.283958\pi\) | |||||||
\(524\) | 16.5221 | 0.721770 | ||||||||
\(525\) | 1.53997 | 0.0672098 | ||||||||
\(526\) | −2.87430 | −0.125326 | ||||||||
\(527\) | 6.04372 | 0.263268 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.7869 | 0.816822 | ||||||||
\(530\) | 6.88353 | 0.299001 | ||||||||
\(531\) | 5.57884 | 0.242101 | ||||||||
\(532\) | 1.55105 | 0.0672464 | ||||||||
\(533\) | −10.4982 | −0.454728 | ||||||||
\(534\) | −0.748924 | −0.0324091 | ||||||||
\(535\) | 12.0970 | 0.523000 | ||||||||
\(536\) | 0.00426892 | 0.000184389 0 | ||||||||
\(537\) | −22.4299 | −0.967920 | ||||||||
\(538\) | 1.88677 | 0.0813446 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.22169 | −0.267739 | ||||||||
\(541\) | −41.4908 | −1.78383 | −0.891914 | − | 0.452205i | \(-0.850638\pi\) | ||||
−0.891914 | + | 0.452205i | \(0.850638\pi\) | |||||||
\(542\) | 22.3189 | 0.958677 | ||||||||
\(543\) | 6.38641 | 0.274067 | ||||||||
\(544\) | 15.4206 | 0.661153 | ||||||||
\(545\) | 2.06951 | 0.0886480 | ||||||||
\(546\) | −2.01774 | −0.0863513 | ||||||||
\(547\) | −12.1246 | −0.518412 | −0.259206 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259206 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(548\) | −14.5139 | −0.620001 | ||||||||
\(549\) | 1.06868 | 0.0456102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.80230 | 0.161984 | ||||||||
\(552\) | 29.1827 | 1.24210 | ||||||||
\(553\) | −9.24782 | −0.393257 | ||||||||
\(554\) | 17.8470 | 0.758245 | ||||||||
\(555\) | 10.0741 | 0.427620 | ||||||||
\(556\) | 21.0684 | 0.893500 | ||||||||
\(557\) | −2.35811 | −0.0999163 | −0.0499581 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499581 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(558\) | −1.24335 | −0.0526350 | ||||||||
\(559\) | 7.29341 | 0.308478 | ||||||||
\(560\) | 0.533340 | 0.0225377 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.41444 | −0.0596644 | ||||||||
\(563\) | −42.3956 | −1.78676 | −0.893380 | − | 0.449302i | \(-0.851673\pi\) | ||||
−0.893380 | + | 0.449302i | \(0.851673\pi\) | |||||||
\(564\) | −15.2258 | −0.641123 | ||||||||
\(565\) | −18.3350 | −0.771358 | ||||||||
\(566\) | −1.59676 | −0.0671167 | ||||||||
\(567\) | −6.71951 | −0.282193 | ||||||||
\(568\) | 20.3719 | 0.854784 | ||||||||
\(569\) | 2.97701 | 0.124803 | 0.0624013 | − | 0.998051i | \(-0.480124\pi\) | ||||
0.0624013 | + | 0.998051i | \(0.480124\pi\) | |||||||
\(570\) | −2.01985 | −0.0846023 | ||||||||
\(571\) | −46.8050 | −1.95873 | −0.979364 | − | 0.202107i | \(-0.935221\pi\) | ||||
−0.979364 | + | 0.202107i | \(0.935221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.6253 | −0.861634 | ||||||||
\(574\) | 7.10340 | 0.296490 | ||||||||
\(575\) | 6.46428 | 0.269579 | ||||||||
\(576\) | −3.84282 | −0.160117 | ||||||||
\(577\) | −26.4035 | −1.09919 | −0.549596 | − | 0.835431i | \(-0.685218\pi\) | ||||
−0.549596 | + | 0.835431i | \(0.685218\pi\) | |||||||
\(578\) | 8.21584 | 0.341734 | ||||||||
\(579\) | −22.6905 | −0.942985 | ||||||||
\(580\) | −3.03921 | −0.126197 | ||||||||
\(581\) | −13.2464 | −0.549552 | ||||||||
\(582\) | −0.687762 | −0.0285087 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.280667 | 0.0116141 | ||||||||
\(585\) | 0.874586 | 0.0361597 | ||||||||
\(586\) | −8.25053 | −0.340826 | ||||||||
\(587\) | −33.7101 | −1.39136 | −0.695682 | − | 0.718349i | \(-0.744898\pi\) | ||||
−0.695682 | + | 0.718349i | \(0.744898\pi\) | |||||||
\(588\) | −1.71467 | −0.0707120 | ||||||||
\(589\) | 2.92680 | 0.120597 | ||||||||
\(590\) | −8.35785 | −0.344087 | ||||||||
\(591\) | −6.06921 | −0.249654 | ||||||||
\(592\) | 3.48897 | 0.143396 | ||||||||
\(593\) | 34.4146 | 1.41324 | 0.706620 | − | 0.707594i | \(-0.250219\pi\) | ||||
0.706620 | + | 0.707594i | \(0.250219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.87651 | 0.117925 | ||||||||
\(596\) | −5.72018 | −0.234308 | ||||||||
\(597\) | −15.7761 | −0.645671 | ||||||||
\(598\) | −8.46981 | −0.346356 | ||||||||
\(599\) | 40.4876 | 1.65428 | 0.827140 | − | 0.561996i | \(-0.189967\pi\) | ||||
0.827140 | + | 0.561996i | \(0.189967\pi\) | |||||||
\(600\) | 4.51446 | 0.184302 | ||||||||
\(601\) | −22.7587 | −0.928346 | −0.464173 | − | 0.885744i | \(-0.653648\pi\) | ||||
−0.464173 | + | 0.885744i | \(0.653648\pi\) | |||||||
\(602\) | −4.93494 | −0.201133 | ||||||||
\(603\) | −0.000915220 0 | −3.72706e−5 0 | ||||||||
\(604\) | 10.5927 | 0.431009 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.0792 | 0.571929 | ||||||||
\(607\) | 3.61857 | 0.146873 | 0.0734365 | − | 0.997300i | \(-0.476603\pi\) | ||||
0.0734365 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(608\) | 7.46777 | 0.302858 | ||||||||
\(609\) | −4.20343 | −0.170332 | ||||||||
\(610\) | −1.60103 | −0.0648237 | ||||||||
\(611\) | 12.3566 | 0.499896 | ||||||||
\(612\) | −2.01297 | −0.0813694 | ||||||||
\(613\) | −33.2875 | −1.34447 | −0.672235 | − | 0.740337i | \(-0.734666\pi\) | ||||
−0.672235 | + | 0.740337i | \(0.734666\pi\) | |||||||
\(614\) | 14.7816 | 0.596538 | ||||||||
\(615\) | 11.6179 | 0.468478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2743 | 0.574662 | 0.287331 | − | 0.957831i | \(-0.407232\pi\) | ||||
0.287331 | + | 0.957831i | \(0.407232\pi\) | |||||||
\(618\) | −1.04794 | −0.0421544 | ||||||||
\(619\) | −40.8425 | −1.64160 | −0.820800 | − | 0.571216i | \(-0.806472\pi\) | ||||
−0.820800 | + | 0.571216i | \(0.806472\pi\) | |||||||
\(620\) | −2.33942 | −0.0939533 | ||||||||
\(621\) | −36.1209 | −1.44948 | ||||||||
\(622\) | −4.26975 | −0.171201 | ||||||||
\(623\) | 0.516504 | 0.0206933 | ||||||||
\(624\) | −1.14292 | −0.0457536 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.52956 | 0.101102 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.50713 | 0.219758 | ||||||||
\(629\) | 18.8173 | 0.750297 | ||||||||
\(630\) | −0.591771 | −0.0235767 | ||||||||
\(631\) | 19.6251 | 0.781264 | 0.390632 | − | 0.920547i | \(-0.372256\pi\) | ||||
0.390632 | + | 0.920547i | \(0.372256\pi\) | |||||||
\(632\) | −27.1102 | −1.07839 | ||||||||
\(633\) | −12.8169 | −0.509426 | ||||||||
\(634\) | 13.2142 | 0.524805 | ||||||||
\(635\) | −15.6786 | −0.622186 | ||||||||
\(636\) | −12.5355 | −0.497063 | ||||||||
\(637\) | 1.39156 | 0.0551355 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.36756 | −0.172778 | ||||||||
\(640\) | −4.96470 | −0.196247 | ||||||||
\(641\) | −1.26648 | −0.0500228 | −0.0250114 | − | 0.999687i | \(-0.507962\pi\) | ||||
−0.0250114 | + | 0.999687i | \(0.507962\pi\) | |||||||
\(642\) | 17.5405 | 0.692270 | ||||||||
\(643\) | −1.93346 | −0.0762481 | −0.0381241 | − | 0.999273i | \(-0.512138\pi\) | ||||
−0.0381241 | + | 0.999273i | \(0.512138\pi\) | |||||||
\(644\) | −7.19764 | −0.283627 | ||||||||
\(645\) | −8.07127 | −0.317806 | ||||||||
\(646\) | −3.77288 | −0.148442 | ||||||||
\(647\) | 7.99759 | 0.314418 | 0.157209 | − | 0.987565i | \(-0.449750\pi\) | ||||
0.157209 | + | 0.987565i | \(0.449750\pi\) | |||||||
\(648\) | −19.6984 | −0.773827 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.31025 | −0.0513921 | ||||||||
\(651\) | −3.23557 | −0.126812 | ||||||||
\(652\) | 21.3212 | 0.835003 | ||||||||
\(653\) | 46.2529 | 1.81002 | 0.905009 | − | 0.425393i | \(-0.139864\pi\) | ||||
0.905009 | + | 0.425393i | \(0.139864\pi\) | |||||||
\(654\) | 3.00076 | 0.117339 | ||||||||
\(655\) | 14.8387 | 0.579795 | ||||||||
\(656\) | 4.02364 | 0.157097 | ||||||||
\(657\) | −0.0601727 | −0.00234756 | ||||||||
\(658\) | −8.36088 | −0.325941 | ||||||||
\(659\) | 15.8183 | 0.616193 | 0.308097 | − | 0.951355i | \(-0.400308\pi\) | ||||
0.308097 | + | 0.951355i | \(0.400308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2510 | 0.593195 | 0.296597 | − | 0.955003i | \(-0.404148\pi\) | ||||
0.296597 | + | 0.955003i | \(0.404148\pi\) | |||||||
\(662\) | −20.2766 | −0.788073 | ||||||||
\(663\) | −6.16423 | −0.239399 | ||||||||
\(664\) | −38.8321 | −1.50698 | ||||||||
\(665\) | 1.39301 | 0.0540187 | ||||||||
\(666\) | −3.87121 | −0.150006 | ||||||||
\(667\) | −17.6446 | −0.683202 | ||||||||
\(668\) | −13.1282 | −0.507945 | ||||||||
\(669\) | 30.8015 | 1.19085 | ||||||||
\(670\) | 0.00137112 | 5.29711e−5 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.25558 | −0.318466 | ||||||||
\(673\) | −13.4813 | −0.519666 | −0.259833 | − | 0.965654i | \(-0.583667\pi\) | ||||
−0.259833 | + | 0.965654i | \(0.583667\pi\) | |||||||
\(674\) | −24.5352 | −0.945062 | ||||||||
\(675\) | −5.58777 | −0.215073 | ||||||||
\(676\) | 12.3187 | 0.473796 | ||||||||
\(677\) | 2.21002 | 0.0849381 | 0.0424690 | − | 0.999098i | \(-0.486478\pi\) | ||||
0.0424690 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(678\) | −26.5855 | −1.02101 | ||||||||
\(679\) | 0.474323 | 0.0182028 | ||||||||
\(680\) | 8.43256 | 0.323374 | ||||||||
\(681\) | 20.3364 | 0.779293 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.4249 | 1.69987 | 0.849935 | − | 0.526888i | \(-0.176641\pi\) | ||||
0.849935 | + | 0.526888i | \(0.176641\pi\) | |||||||
\(684\) | −0.974825 | −0.0372733 | ||||||||
\(685\) | −13.0351 | −0.498044 | ||||||||
\(686\) | −0.941569 | −0.0359493 | ||||||||
\(687\) | −39.6503 | −1.51275 | ||||||||
\(688\) | −2.79534 | −0.106571 | ||||||||
\(689\) | 10.1732 | 0.387570 | ||||||||
\(690\) | 9.37313 | 0.356829 | ||||||||
\(691\) | 29.0538 | 1.10526 | 0.552629 | − | 0.833427i | \(-0.313625\pi\) | ||||
0.552629 | + | 0.833427i | \(0.313625\pi\) | |||||||
\(692\) | 24.5915 | 0.934830 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.5174 | 1.04455 | ||||||||
\(695\) | 18.9218 | 0.717744 | ||||||||
\(696\) | −12.3225 | −0.467082 | ||||||||
\(697\) | 21.7010 | 0.821985 | ||||||||
\(698\) | −7.25604 | −0.274645 | ||||||||
\(699\) | 18.3299 | 0.693300 | ||||||||
\(700\) | −1.11345 | −0.0420844 | ||||||||
\(701\) | −26.7632 | −1.01083 | −0.505416 | − | 0.862876i | \(-0.668661\pi\) | ||||
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(702\) | 7.32136 | 0.276327 | ||||||||
\(703\) | 9.11271 | 0.343692 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6745 | −0.515012 | ||||||||
\(706\) | 20.9749 | 0.789399 | ||||||||
\(707\) | −9.70989 | −0.365178 | ||||||||
\(708\) | 15.2203 | 0.572015 | ||||||||
\(709\) | 9.52139 | 0.357583 | 0.178792 | − | 0.983887i | \(-0.442781\pi\) | ||||
0.178792 | + | 0.983887i | \(0.442781\pi\) | |||||||
\(710\) | 6.54318 | 0.245561 | ||||||||
\(711\) | 5.81220 | 0.217975 | ||||||||
\(712\) | 1.51414 | 0.0567449 | ||||||||
\(713\) | −13.5818 | −0.508644 | ||||||||
\(714\) | 4.17090 | 0.156092 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2175 | 0.606077 | ||||||||
\(717\) | 26.8257 | 1.00182 | ||||||||
\(718\) | 1.59350 | 0.0594687 | ||||||||
\(719\) | −28.4864 | −1.06236 | −0.531182 | − | 0.847258i | \(-0.678252\pi\) | ||||
−0.531182 | + | 0.847258i | \(0.678252\pi\) | |||||||
\(720\) | −0.335202 | −0.0124922 | ||||||||
\(721\) | 0.722725 | 0.0269157 | ||||||||
\(722\) | 16.0627 | 0.597792 | ||||||||
\(723\) | −3.55057 | −0.132047 | ||||||||
\(724\) | −4.61758 | −0.171611 | ||||||||
\(725\) | −2.72955 | −0.101373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.7611 | 1.80845 | 0.904225 | − | 0.427057i | \(-0.140449\pi\) | ||||
0.904225 | + | 0.427057i | \(0.140449\pi\) | |||||||
\(728\) | 4.07939 | 0.151192 | ||||||||
\(729\) | 30.0382 | 1.11252 | ||||||||
\(730\) | 0.0901467 | 0.00333648 | ||||||||
\(731\) | −15.0763 | −0.557618 | ||||||||
\(732\) | 2.91560 | 0.107764 | ||||||||
\(733\) | −29.8881 | −1.10394 | −0.551972 | − | 0.833863i | \(-0.686124\pi\) | ||||
−0.551972 | + | 0.833863i | \(0.686124\pi\) | |||||||
\(734\) | 12.5158 | 0.461967 | ||||||||
\(735\) | −1.53997 | −0.0568026 | ||||||||
\(736\) | −34.6542 | −1.27737 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.46445 | −0.164339 | ||||||||
\(739\) | −15.1162 | −0.556058 | −0.278029 | − | 0.960573i | \(-0.589681\pi\) | ||||
−0.278029 | + | 0.960573i | \(0.589681\pi\) | |||||||
\(740\) | −7.28387 | −0.267760 | ||||||||
\(741\) | −2.98516 | −0.109663 | ||||||||
\(742\) | −6.88353 | −0.252702 | ||||||||
\(743\) | 42.9453 | 1.57551 | 0.787756 | − | 0.615988i | \(-0.211243\pi\) | ||||
0.787756 | + | 0.615988i | \(0.211243\pi\) | |||||||
\(744\) | −9.48515 | −0.347742 | ||||||||
\(745\) | −5.13736 | −0.188218 | ||||||||
\(746\) | −4.87418 | −0.178457 | ||||||||
\(747\) | 8.32527 | 0.304606 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0970 | −0.442016 | ||||||||
\(750\) | 1.44999 | 0.0529461 | ||||||||
\(751\) | −17.3139 | −0.631793 | −0.315896 | − | 0.948794i | \(-0.602305\pi\) | ||||
−0.315896 | + | 0.948794i | \(0.602305\pi\) | |||||||
\(752\) | −4.73592 | −0.172701 | ||||||||
\(753\) | −14.6905 | −0.535351 | ||||||||
\(754\) | 3.57639 | 0.130244 | ||||||||
\(755\) | 9.51339 | 0.346228 | ||||||||
\(756\) | 6.22169 | 0.226281 | ||||||||
\(757\) | 10.0094 | 0.363798 | 0.181899 | − | 0.983317i | \(-0.441776\pi\) | ||||
0.181899 | + | 0.983317i | \(0.441776\pi\) | |||||||
\(758\) | −19.5878 | −0.711462 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.08365 | 0.148130 | ||||||||
\(761\) | 47.8699 | 1.73528 | 0.867642 | − | 0.497190i | \(-0.165635\pi\) | ||||
0.867642 | + | 0.497190i | \(0.165635\pi\) | |||||||
\(762\) | −22.7338 | −0.823557 | ||||||||
\(763\) | −2.06951 | −0.0749212 | ||||||||
\(764\) | 14.9128 | 0.539524 | ||||||||
\(765\) | −1.80787 | −0.0653637 | ||||||||
\(766\) | 5.23307 | 0.189078 | ||||||||
\(767\) | −12.3522 | −0.446011 | ||||||||
\(768\) | −26.0305 | −0.939294 | ||||||||
\(769\) | 54.1437 | 1.95247 | 0.976236 | − | 0.216708i | \(-0.0695321\pi\) | ||||
0.976236 | + | 0.216708i | \(0.0695321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.2999 | −1.63144 | ||||||||
\(772\) | 16.4060 | 0.590464 | ||||||||
\(773\) | 44.3052 | 1.59355 | 0.796774 | − | 0.604278i | \(-0.206538\pi\) | ||||
0.796774 | + | 0.604278i | \(0.206538\pi\) | |||||||
\(774\) | 3.10158 | 0.111484 | ||||||||
\(775\) | −2.10106 | −0.0754723 | ||||||||
\(776\) | 1.39049 | 0.0499157 | ||||||||
\(777\) | −10.0741 | −0.361405 | ||||||||
\(778\) | −29.1139 | −1.04378 | ||||||||
\(779\) | 10.5092 | 0.376531 | ||||||||
\(780\) | 2.38607 | 0.0854349 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 17.5081 | 0.626087 | ||||||||
\(783\) | 15.2521 | 0.545066 | ||||||||
\(784\) | −0.533340 | −0.0190479 | ||||||||
\(785\) | 4.94602 | 0.176531 | ||||||||
\(786\) | 21.5159 | 0.767446 | ||||||||
\(787\) | 30.0712 | 1.07192 | 0.535961 | − | 0.844243i | \(-0.319949\pi\) | ||||
0.535961 | + | 0.844243i | \(0.319949\pi\) | |||||||
\(788\) | 4.38823 | 0.156324 | ||||||||
\(789\) | 4.70102 | 0.167361 | ||||||||
\(790\) | −8.70746 | −0.309797 | ||||||||
\(791\) | 18.3350 | 0.651916 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.36618 | −0.0840255 | ||||||||
\(794\) | −28.6937 | −1.01830 | ||||||||
\(795\) | −11.2582 | −0.399289 | ||||||||
\(796\) | 11.4066 | 0.404296 | ||||||||
\(797\) | −38.1915 | −1.35281 | −0.676406 | − | 0.736529i | \(-0.736463\pi\) | ||||
−0.676406 | + | 0.736529i | \(0.736463\pi\) | |||||||
\(798\) | 2.01985 | 0.0715020 | ||||||||
\(799\) | −25.5426 | −0.903633 | ||||||||
\(800\) | −5.36088 | −0.189536 | ||||||||
\(801\) | −0.324620 | −0.0114699 | ||||||||
\(802\) | 25.5953 | 0.903801 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.00249693 | −8.80598e−5 0 | ||||||||
\(805\) | −6.46428 | −0.227836 | ||||||||
\(806\) | 2.75291 | 0.0969670 | ||||||||
\(807\) | −3.08589 | −0.108628 | ||||||||
\(808\) | −28.4648 | −1.00139 | ||||||||
\(809\) | −1.13775 | −0.0400011 | −0.0200005 | − | 0.999800i | \(-0.506367\pi\) | ||||
−0.0200005 | + | 0.999800i | \(0.506367\pi\) | |||||||
\(810\) | −6.32688 | −0.222304 | ||||||||
\(811\) | 48.3009 | 1.69607 | 0.848037 | − | 0.529937i | \(-0.177784\pi\) | ||||
0.848037 | + | 0.529937i | \(0.177784\pi\) | |||||||
\(812\) | 3.03921 | 0.106656 | ||||||||
\(813\) | −36.5033 | −1.28023 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.1488 | 0.670754 | ||||||||
\(816\) | 2.36256 | 0.0827061 | ||||||||
\(817\) | −7.30104 | −0.255431 | ||||||||
\(818\) | 11.6884 | 0.408677 | ||||||||
\(819\) | −0.874586 | −0.0305605 | ||||||||
\(820\) | −8.40009 | −0.293344 | ||||||||
\(821\) | 42.5334 | 1.48443 | 0.742213 | − | 0.670164i | \(-0.233776\pi\) | ||||
0.742213 | + | 0.670164i | \(0.233776\pi\) | |||||||
\(822\) | −18.9007 | −0.659237 | ||||||||
\(823\) | −16.3459 | −0.569781 | −0.284891 | − | 0.958560i | \(-0.591957\pi\) | ||||
−0.284891 | + | 0.958560i | \(0.591957\pi\) | |||||||
\(824\) | 2.11869 | 0.0738080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.35785 | 0.290807 | ||||||||
\(827\) | −39.8338 | −1.38516 | −0.692578 | − | 0.721343i | \(-0.743525\pi\) | ||||
−0.692578 | + | 0.721343i | \(0.743525\pi\) | |||||||
\(828\) | 4.52367 | 0.157209 | ||||||||
\(829\) | 17.9400 | 0.623081 | 0.311540 | − | 0.950233i | \(-0.399155\pi\) | ||||
0.311540 | + | 0.950233i | \(0.399155\pi\) | |||||||
\(830\) | −12.4724 | −0.432922 | ||||||||
\(831\) | −29.1893 | −1.01257 | ||||||||
\(832\) | 8.50842 | 0.294976 | ||||||||
\(833\) | −2.87651 | −0.0996652 | ||||||||
\(834\) | 27.4364 | 0.950043 | ||||||||
\(835\) | −11.7906 | −0.408030 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.7402 | 0.405802 | ||||||||
\(838\) | −9.91782 | −0.342605 | ||||||||
\(839\) | −51.5966 | −1.78131 | −0.890656 | − | 0.454677i | \(-0.849755\pi\) | ||||
−0.890656 | + | 0.454677i | \(0.849755\pi\) | |||||||
\(840\) | −4.51446 | −0.155764 | ||||||||
\(841\) | −21.5495 | −0.743087 | ||||||||
\(842\) | −18.5188 | −0.638200 | ||||||||
\(843\) | 2.31336 | 0.0796763 | ||||||||
\(844\) | 9.26704 | 0.318985 | ||||||||
\(845\) | 11.0636 | 0.380598 | ||||||||
\(846\) | 5.25477 | 0.180663 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.89909 | −0.133895 | ||||||||
\(849\) | 2.61155 | 0.0896282 | ||||||||
\(850\) | 2.70843 | 0.0928985 | ||||||||
\(851\) | −42.2876 | −1.44960 | ||||||||
\(852\) | −11.9157 | −0.408224 | ||||||||
\(853\) | −28.2200 | −0.966235 | −0.483117 | − | 0.875556i | \(-0.660496\pi\) | ||||
−0.483117 | + | 0.875556i | \(0.660496\pi\) | |||||||
\(854\) | 1.60103 | 0.0547860 | ||||||||
\(855\) | −0.875501 | −0.0299415 | ||||||||
\(856\) | −35.4627 | −1.21209 | ||||||||
\(857\) | 6.27743 | 0.214433 | 0.107216 | − | 0.994236i | \(-0.465806\pi\) | ||||
0.107216 | + | 0.994236i | \(0.465806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9580 | 0.885675 | 0.442837 | − | 0.896602i | \(-0.353972\pi\) | ||||
0.442837 | + | 0.896602i | \(0.353972\pi\) | |||||||
\(860\) | 5.83579 | 0.198999 | ||||||||
\(861\) | −11.6179 | −0.395936 | ||||||||
\(862\) | 14.8715 | 0.506525 | ||||||||
\(863\) | 7.62600 | 0.259592 | 0.129796 | − | 0.991541i | \(-0.458568\pi\) | ||||
0.129796 | + | 0.991541i | \(0.458568\pi\) | |||||||
\(864\) | 29.9553 | 1.01910 | ||||||||
\(865\) | 22.0859 | 0.750945 | ||||||||
\(866\) | −6.67856 | −0.226947 | ||||||||
\(867\) | −13.4373 | −0.456355 | ||||||||
\(868\) | 2.33942 | 0.0794050 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.95782 | −0.134183 | ||||||||
\(871\) | 0.00202640 | 6.86619e−5 0 | ||||||||
\(872\) | −6.06682 | −0.205448 | ||||||||
\(873\) | −0.298109 | −0.0100895 | ||||||||
\(874\) | 8.47867 | 0.286795 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.164165 | −0.00554661 | ||||||||
\(877\) | −25.0934 | −0.847344 | −0.423672 | − | 0.905816i | \(-0.639259\pi\) | ||||
−0.423672 | + | 0.905816i | \(0.639259\pi\) | |||||||
\(878\) | −23.0898 | −0.779243 | ||||||||
\(879\) | 13.4940 | 0.455142 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4989 | 0.926463 | 0.463231 | − | 0.886237i | \(-0.346690\pi\) | ||||
0.463231 | + | 0.886237i | \(0.346690\pi\) | |||||||
\(882\) | 0.591771 | 0.0199260 | ||||||||
\(883\) | −26.9277 | −0.906190 | −0.453095 | − | 0.891462i | \(-0.649680\pi\) | ||||
−0.453095 | + | 0.891462i | \(0.649680\pi\) | |||||||
\(884\) | 4.45694 | 0.149903 | ||||||||
\(885\) | 13.6696 | 0.459497 | ||||||||
\(886\) | 9.44697 | 0.317377 | ||||||||
\(887\) | −34.6125 | −1.16217 | −0.581087 | − | 0.813841i | \(-0.697372\pi\) | ||||
−0.581087 | + | 0.813841i | \(0.697372\pi\) | |||||||
\(888\) | −29.5324 | −0.991041 | ||||||||
\(889\) | 15.6786 | 0.525843 | ||||||||
\(890\) | 0.486324 | 0.0163016 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.2705 | −0.745670 | ||||||||
\(893\) | −12.3696 | −0.413932 | ||||||||
\(894\) | −7.44911 | −0.249136 | ||||||||
\(895\) | 14.5651 | 0.486859 | ||||||||
\(896\) | 4.96470 | 0.165859 | ||||||||
\(897\) | 13.8527 | 0.462527 | ||||||||
\(898\) | −26.7322 | −0.892064 | ||||||||
\(899\) | 5.73495 | 0.191271 | ||||||||
\(900\) | 0.699796 | 0.0233265 | ||||||||
\(901\) | −21.0293 | −0.700587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.07127 | 0.268595 | ||||||||
\(904\) | 53.7494 | 1.78768 | ||||||||
\(905\) | −4.14710 | −0.137854 | ||||||||
\(906\) | 13.7943 | 0.458285 | ||||||||
\(907\) | 19.9016 | 0.660823 | 0.330411 | − | 0.943837i | \(-0.392813\pi\) | ||||
0.330411 | + | 0.943837i | \(0.392813\pi\) | |||||||
\(908\) | −14.7039 | −0.487965 | ||||||||
\(909\) | 6.10261 | 0.202411 | ||||||||
\(910\) | 1.31025 | 0.0434343 | ||||||||
\(911\) | 50.4666 | 1.67203 | 0.836016 | − | 0.548704i | \(-0.184879\pi\) | ||||
0.836016 | + | 0.548704i | \(0.184879\pi\) | |||||||
\(912\) | 1.14412 | 0.0378856 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.8641 | −0.557816 | ||||||||
\(915\) | 2.61854 | 0.0865662 | ||||||||
\(916\) | 28.6685 | 0.947232 | ||||||||
\(917\) | −14.8387 | −0.490016 | ||||||||
\(918\) | −15.1341 | −0.499500 | ||||||||
\(919\) | −6.02847 | −0.198861 | −0.0994304 | − | 0.995045i | \(-0.531702\pi\) | ||||
−0.0994304 | + | 0.995045i | \(0.531702\pi\) | |||||||
\(920\) | −18.9502 | −0.624770 | ||||||||
\(921\) | −24.1759 | −0.796622 | ||||||||
\(922\) | −21.0398 | −0.692909 | ||||||||
\(923\) | 9.67025 | 0.318300 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.54173 | −0.215091 | ||||||||
\(926\) | 29.9234 | 0.983345 | ||||||||
\(927\) | −0.454229 | −0.0149188 | ||||||||
\(928\) | 14.6328 | 0.480345 | ||||||||
\(929\) | 30.9289 | 1.01474 | 0.507371 | − | 0.861727i | \(-0.330617\pi\) | ||||
0.507371 | + | 0.861727i | \(0.330617\pi\) | |||||||
\(930\) | −3.04651 | −0.0998990 | ||||||||
\(931\) | −1.39301 | −0.0456542 | ||||||||
\(932\) | −13.2531 | −0.434120 | ||||||||
\(933\) | 6.98332 | 0.228624 | ||||||||
\(934\) | −12.6425 | −0.413674 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.56387 | −0.0838028 | ||||||||
\(937\) | −17.9725 | −0.587135 | −0.293568 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293568 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(938\) | −0.00137112 | −4.47687e−5 0 | ||||||||
\(939\) | −4.13719 | −0.135012 | ||||||||
\(940\) | 9.88711 | 0.322482 | ||||||||
\(941\) | 11.1858 | 0.364646 | 0.182323 | − | 0.983239i | \(-0.441638\pi\) | ||||
0.182323 | + | 0.983239i | \(0.441638\pi\) | |||||||
\(942\) | 7.17167 | 0.233665 | ||||||||
\(943\) | −48.7679 | −1.58810 | ||||||||
\(944\) | 4.73420 | 0.154085 | ||||||||
\(945\) | 5.58777 | 0.181770 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.2130 | 1.17677 | 0.588383 | − | 0.808583i | \(-0.299765\pi\) | ||||
0.588383 | + | 0.808583i | \(0.299765\pi\) | |||||||
\(948\) | 15.8570 | 0.515011 | ||||||||
\(949\) | 0.133229 | 0.00432480 | ||||||||
\(950\) | 1.31162 | 0.0425545 | ||||||||
\(951\) | −21.6124 | −0.700829 | ||||||||
\(952\) | −8.43256 | −0.273301 | ||||||||
\(953\) | 28.0283 | 0.907926 | 0.453963 | − | 0.891020i | \(-0.350010\pi\) | ||||
0.453963 | + | 0.891020i | \(0.350010\pi\) | |||||||
\(954\) | 4.32626 | 0.140068 | ||||||||
\(955\) | 13.3933 | 0.433398 | ||||||||
\(956\) | −19.3958 | −0.627306 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.09262 | 0.293769 | ||||||||
\(959\) | 13.0351 | 0.420924 | ||||||||
\(960\) | −9.41586 | −0.303896 | ||||||||
\(961\) | −26.5856 | −0.857598 | ||||||||
\(962\) | 8.57128 | 0.276349 | ||||||||
\(963\) | 7.60291 | 0.245000 | ||||||||
\(964\) | 2.56718 | 0.0826832 | ||||||||
\(965\) | 14.7344 | 0.474317 | ||||||||
\(966\) | −9.37313 | −0.301575 | ||||||||
\(967\) | −60.9621 | −1.96041 | −0.980205 | − | 0.197985i | \(-0.936560\pi\) | ||||
−0.980205 | + | 0.197985i | \(0.936560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.17068 | 0.198231 | ||||||||
\(970\) | 0.446608 | 0.0143397 | ||||||||
\(971\) | −26.9575 | −0.865107 | −0.432554 | − | 0.901608i | \(-0.642387\pi\) | ||||
−0.432554 | + | 0.901608i | \(0.642387\pi\) | |||||||
\(972\) | −7.14329 | −0.229121 | ||||||||
\(973\) | −18.9218 | −0.606605 | ||||||||
\(974\) | 32.1567 | 1.03037 | ||||||||
\(975\) | 2.14296 | 0.0686295 | ||||||||
\(976\) | 0.906883 | 0.0290286 | ||||||||
\(977\) | −3.67207 | −0.117480 | −0.0587400 | − | 0.998273i | \(-0.518708\pi\) | ||||
−0.0587400 | + | 0.998273i | \(0.518708\pi\) | |||||||
\(978\) | 27.7656 | 0.887845 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.11345 | 0.0355678 | ||||||||
\(981\) | 1.30067 | 0.0415273 | ||||||||
\(982\) | 1.45597 | 0.0464618 | ||||||||
\(983\) | 25.0044 | 0.797515 | 0.398758 | − | 0.917056i | \(-0.369442\pi\) | ||||
0.398758 | + | 0.917056i | \(0.369442\pi\) | |||||||
\(984\) | −34.0581 | −1.08573 | ||||||||
\(985\) | 3.94112 | 0.125575 | ||||||||
\(986\) | −7.39281 | −0.235435 | ||||||||
\(987\) | 13.6745 | 0.435264 | ||||||||
\(988\) | 2.15837 | 0.0686669 | ||||||||
\(989\) | 33.8805 | 1.07734 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.78499 | −0.183766 | −0.0918831 | − | 0.995770i | \(-0.529289\pi\) | ||||
−0.0918831 | + | 0.995770i | \(0.529289\pi\) | |||||||
\(992\) | 11.2635 | 0.357617 | ||||||||
\(993\) | 33.1631 | 1.05240 | ||||||||
\(994\) | −6.54318 | −0.207537 | ||||||||
\(995\) | 10.2444 | 0.324769 | ||||||||
\(996\) | 22.7132 | 0.719695 | ||||||||
\(997\) | −2.01189 | −0.0637171 | −0.0318585 | − | 0.999492i | \(-0.510143\pi\) | ||||
−0.0318585 | + | 0.999492i | \(0.510143\pi\) | |||||||
\(998\) | 14.0972 | 0.446240 | ||||||||
\(999\) | 36.5537 | 1.15651 |
(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 | 4235.2.a.bb.1.2 | yes | 5 | |
11.10 | odd | 2 | 4235.2.a.ba.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.ba.1.4 | ✓ | 5 | 11.10 | odd | 2 | ||
4235.2.a.bb.1.2 | yes | 5 | 1.1 | even | 1 | trivial |