Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.14 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.d.343.13 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.690218 | + | 1.87713i | −0.345109 | + | 0.938563i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.04720 | − | 2.59125i | −0.761800 | − | 0.647812i | ||||
\(5\) | 8.91109 | 1.78222 | 0.891109 | − | 0.453789i | \(-0.149928\pi\) | ||||
0.891109 | + | 0.453789i | \(0.149928\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.74115i | − | 1.10588i | −0.833222 | − | 0.552939i | \(-0.813506\pi\) | ||
0.833222 | − | 0.552939i | \(-0.186494\pi\) | |||||||
\(8\) | 6.96733 | − | 3.93145i | 0.870916 | − | 0.491431i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.15059 | + | 16.7272i | −0.615059 | + | 1.67272i | ||||
\(11\) | 16.0761i | 1.46146i | 0.682665 | + | 0.730732i | \(0.260821\pi\) | ||||
−0.682665 | + | 0.730732i | \(0.739179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.44347 | −0.495652 | −0.247826 | − | 0.968805i | \(-0.579716\pi\) | ||||
−0.247826 | + | 0.968805i | \(0.579716\pi\) | |||||||
\(14\) | 14.5311 | + | 5.34308i | 1.03794 | + | 0.381648i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.57085 | + | 15.7921i | 0.160678 | + | 0.987007i | ||||
\(17\) | −1.80859 | −0.106388 | −0.0531939 | − | 0.998584i | \(-0.516940\pi\) | ||||
−0.0531939 | + | 0.998584i | \(0.516940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | −27.1539 | − | 23.0909i | −1.35769 | − | 1.15454i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −30.1768 | − | 11.0960i | −1.37167 | − | 0.504364i | ||||
\(23\) | − | 9.27915i | − | 0.403441i | −0.979443 | − | 0.201721i | \(-0.935347\pi\) | ||
0.979443 | − | 0.201721i | \(-0.0646533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.4076 | 2.17630 | ||||||||
\(26\) | 4.44740 | − | 12.0952i | 0.171054 | − | 0.465200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.0592 | + | 23.5888i | −0.716402 | + | 0.842458i | ||||
\(29\) | 40.7713 | 1.40591 | 0.702953 | − | 0.711237i | \(-0.251865\pi\) | ||||
0.702953 | + | 0.711237i | \(0.251865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.0573i | 0.808302i | 0.914692 | + | 0.404151i | \(0.132433\pi\) | ||||
−0.914692 | + | 0.404151i | \(0.867567\pi\) | |||||||
\(32\) | −31.4182 | − | 6.07418i | −0.981819 | − | 0.189818i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.24832 | − | 3.39496i | 0.0367154 | − | 0.0998517i | ||||
\(35\) | − | 68.9821i | − | 1.97092i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 71.0299 | 1.91973 | 0.959864 | − | 0.280466i | \(-0.0904890\pi\) | ||||
0.959864 | + | 0.280466i | \(0.0904890\pi\) | |||||||
\(38\) | −8.18220 | − | 3.00859i | −0.215321 | − | 0.0791734i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 62.0865 | − | 35.0335i | 1.55216 | − | 0.875838i | ||||
\(41\) | 49.0888 | 1.19729 | 0.598643 | − | 0.801016i | \(-0.295707\pi\) | ||||
0.598643 | + | 0.801016i | \(0.295707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 30.1441i | − | 0.701025i | −0.936558 | − | 0.350512i | \(-0.886007\pi\) | ||
0.936558 | − | 0.350512i | \(-0.113993\pi\) | |||||||
\(44\) | 41.6572 | − | 48.9871i | 0.946754 | − | 1.11334i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.4181 | + | 6.40463i | 0.378655 | + | 0.139231i | ||||
\(47\) | − | 82.6289i | − | 1.75806i | −0.476764 | − | 0.879031i | \(-0.658190\pi\) | ||
0.476764 | − | 0.879031i | \(-0.341810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.9254 | −0.222967 | ||||||||
\(50\) | −37.5531 | + | 102.130i | −0.751061 | + | 2.04260i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.6345 | + | 16.6966i | 0.377587 | + | 0.321089i | ||||
\(53\) | −35.2383 | −0.664874 | −0.332437 | − | 0.943125i | \(-0.607871\pi\) | ||||
−0.332437 | + | 0.943125i | \(0.607871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 143.256i | 2.60465i | ||||||||
\(56\) | −30.4339 | − | 53.9351i | −0.543463 | − | 0.963127i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −28.1410 | + | 76.5328i | −0.485190 | + | 1.31953i | ||||
\(59\) | 80.2683i | 1.36048i | 0.732990 | + | 0.680240i | \(0.238124\pi\) | ||||
−0.732990 | + | 0.680240i | \(0.761876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.2987 | 0.840962 | 0.420481 | − | 0.907301i | \(-0.361861\pi\) | ||||
0.420481 | + | 0.907301i | \(0.361861\pi\) | |||||||
\(62\) | −47.0358 | − | 17.2950i | −0.758642 | − | 0.278952i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 33.0874 | − | 54.7834i | 0.516991 | − | 0.855991i | ||||
\(65\) | −57.4184 | −0.883360 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.89367i | 0.0730399i | 0.999333 | + | 0.0365200i | \(0.0116272\pi\) | ||||
−0.999333 | + | 0.0365200i | \(0.988373\pi\) | |||||||
\(68\) | 5.51115 | + | 4.68652i | 0.0810463 | + | 0.0689194i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 129.488 | + | 47.6126i | 1.84983 | + | 0.680181i | ||||
\(71\) | − | 96.5570i | − | 1.35996i | −0.733232 | − | 0.679979i | \(-0.761989\pi\) | ||
0.733232 | − | 0.679979i | \(-0.238011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −117.120 | −1.60439 | −0.802193 | − | 0.597064i | \(-0.796334\pi\) | ||||
−0.802193 | + | 0.597064i | \(0.796334\pi\) | |||||||
\(74\) | −49.0261 | + | 133.332i | −0.662515 | + | 1.80179i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.2950 | − | 13.2824i | 0.148618 | − | 0.174769i | ||||
\(77\) | 124.447 | 1.61620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.35313i | − | 0.0804193i | −0.999191 | − | 0.0402097i | \(-0.987197\pi\) | ||
0.999191 | − | 0.0402097i | \(-0.0128026\pi\) | |||||||
\(80\) | 22.9091 | + | 140.725i | 0.286364 | + | 1.75906i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −33.8819 | + | 92.1458i | −0.413194 | + | 1.12373i | ||||
\(83\) | 91.5054i | 1.10247i | 0.834348 | + | 0.551237i | \(0.185844\pi\) | ||||
−0.834348 | + | 0.551237i | \(0.814156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.1166 | −0.189606 | ||||||||
\(86\) | 56.5842 | + | 20.8060i | 0.657956 | + | 0.241930i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 63.2024 | + | 112.007i | 0.718209 | + | 1.27281i | ||||
\(89\) | 87.1610 | 0.979337 | 0.489668 | − | 0.871909i | \(-0.337118\pi\) | ||||
0.489668 | + | 0.871909i | \(0.337118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.8799i | 0.548130i | ||||||||
\(92\) | −24.0446 | + | 28.2754i | −0.261354 | + | 0.307342i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 155.105 | + | 57.0319i | 1.65005 | + | 0.606723i | ||||
\(95\) | 38.8426i | 0.408869i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −107.608 | −1.10937 | −0.554683 | − | 0.832062i | \(-0.687160\pi\) | ||||
−0.554683 | + | 0.832062i | \(0.687160\pi\) | |||||||
\(98\) | 7.54088 | − | 20.5083i | 0.0769478 | − | 0.209268i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −165.791 | − | 140.984i | −1.65791 | − | 1.40984i | ||||
\(101\) | 179.796 | 1.78016 | 0.890080 | − | 0.455804i | \(-0.150648\pi\) | ||||
0.890080 | + | 0.455804i | \(0.150648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26.0507i | 0.252920i | 0.991972 | + | 0.126460i | \(0.0403615\pi\) | ||||
−0.991972 | + | 0.126460i | \(0.959638\pi\) | |||||||
\(104\) | −44.8938 | + | 25.3322i | −0.431671 | + | 0.243579i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.3221 | − | 66.1468i | 0.229454 | − | 0.624026i | ||||
\(107\) | 24.0268i | 0.224550i | 0.993677 | + | 0.112275i | \(0.0358137\pi\) | ||||
−0.993677 | + | 0.112275i | \(0.964186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.3822 | 0.223690 | 0.111845 | − | 0.993726i | \(-0.464324\pi\) | ||||
0.111845 | + | 0.993726i | \(0.464324\pi\) | |||||||
\(110\) | −268.909 | − | 98.8775i | −2.44462 | − | 0.898887i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 122.249 | − | 19.9013i | 1.09151 | − | 0.177691i | ||||
\(113\) | −80.5460 | −0.712796 | −0.356398 | − | 0.934334i | \(-0.615995\pi\) | ||||
−0.356398 | + | 0.934334i | \(0.615995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 82.6874i | − | 0.719021i | ||||||
\(116\) | −124.238 | − | 105.648i | −1.07102 | − | 0.910763i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −150.674 | − | 55.4026i | −1.27690 | − | 0.469513i | ||||
\(119\) | 14.0006i | 0.117652i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −137.441 | −1.13587 | ||||||||
\(122\) | −35.4073 | + | 96.2941i | −0.290223 | + | 0.789296i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 64.9298 | − | 76.3547i | 0.523628 | − | 0.615764i | ||||
\(125\) | 262.054 | 2.09643 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 156.407i | − | 1.23155i | −0.787921 | − | 0.615776i | \(-0.788843\pi\) | ||
0.787921 | − | 0.615776i | \(-0.211157\pi\) | |||||||
\(128\) | 79.9979 | + | 99.9217i | 0.624983 | + | 0.780638i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 39.6312 | − | 107.782i | 0.304855 | − | 0.829089i | ||||
\(131\) | 15.8524i | 0.121010i | 0.998168 | + | 0.0605052i | \(0.0192712\pi\) | ||||
−0.998168 | + | 0.0605052i | \(0.980729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 33.7429 | 0.253706 | ||||||||
\(134\) | −9.18604 | − | 3.37770i | −0.0685525 | − | 0.0252067i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.6011 | + | 7.11040i | −0.0926550 | + | 0.0522823i | ||||
\(137\) | −79.6097 | −0.581093 | −0.290546 | − | 0.956861i | \(-0.593837\pi\) | ||||
−0.290546 | + | 0.956861i | \(0.593837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 107.505i | 0.773414i | 0.922203 | + | 0.386707i | \(0.126388\pi\) | ||||
−0.922203 | + | 0.386707i | \(0.873612\pi\) | |||||||
\(140\) | −178.750 | + | 210.202i | −1.27678 | + | 1.50144i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 181.250 | + | 66.6453i | 1.27641 | + | 0.469333i | ||||
\(143\) | − | 103.586i | − | 0.724377i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 363.316 | 2.50563 | ||||||||
\(146\) | 80.8384 | − | 219.849i | 0.553688 | − | 1.50582i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −216.442 | − | 184.056i | −1.46245 | − | 1.24362i | ||||
\(149\) | −114.197 | −0.766425 | −0.383212 | − | 0.923660i | \(-0.625182\pi\) | ||||
−0.383212 | + | 0.923660i | \(0.625182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 286.626i | 1.89818i | 0.314999 | + | 0.949092i | \(0.397996\pi\) | ||||
−0.314999 | + | 0.949092i | \(0.602004\pi\) | |||||||
\(152\) | 17.1368 | + | 30.3699i | 0.112742 | + | 0.199802i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −85.8958 | + | 233.603i | −0.557765 | + | 1.51691i | ||||
\(155\) | 223.288i | 1.44057i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −113.974 | −0.725949 | −0.362975 | − | 0.931799i | \(-0.618239\pi\) | ||||
−0.362975 | + | 0.931799i | \(0.618239\pi\) | |||||||
\(158\) | 11.9256 | + | 4.38504i | 0.0754786 | + | 0.0277534i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −279.971 | − | 54.1276i | −1.74982 | − | 0.338297i | ||||
\(161\) | −71.8313 | −0.446157 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.95098i | − | 0.0549140i | −0.999623 | − | 0.0274570i | \(-0.991259\pi\) | ||
0.999623 | − | 0.0274570i | \(-0.00874093\pi\) | |||||||
\(164\) | −149.583 | − | 127.201i | −0.912093 | − | 0.775617i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −171.767 | − | 63.1586i | −1.03474 | − | 0.380474i | ||||
\(167\) | 2.62249i | 0.0157036i | 0.999969 | + | 0.00785178i | \(0.00249932\pi\) | ||||
−0.999969 | + | 0.00785178i | \(0.997501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −127.482 | −0.754329 | ||||||||
\(170\) | 11.1239 | − | 30.2528i | 0.0654349 | − | 0.177958i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −78.1108 | + | 91.8550i | −0.454133 | + | 0.534041i | ||||
\(173\) | −16.2314 | −0.0938230 | −0.0469115 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469115 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 421.177i | − | 2.40673i | ||||||
\(176\) | −253.875 | + | 41.3292i | −1.44247 | + | 0.234825i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −60.1600 | + | 163.612i | −0.337978 | + | 0.919169i | ||||
\(179\) | − | 107.999i | − | 0.603349i | −0.953411 | − | 0.301674i | \(-0.902454\pi\) | ||
0.953411 | − | 0.301674i | \(-0.0975456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 104.811 | 0.579069 | 0.289534 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289534 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(182\) | −93.6308 | − | 34.4280i | −0.514455 | − | 0.189165i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.4805 | − | 64.6509i | −0.198264 | − | 0.351364i | ||||
\(185\) | 632.954 | 3.42138 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 29.0751i | − | 0.155482i | ||||||
\(188\) | −214.112 | + | 251.787i | −1.13889 | + | 1.33929i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −72.9124 | − | 26.8098i | −0.383749 | − | 0.141104i | ||||
\(191\) | − | 295.930i | − | 1.54937i | −0.632345 | − | 0.774687i | \(-0.717907\pi\) | ||
0.632345 | − | 0.774687i | \(-0.282093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −194.495 | −1.00775 | −0.503874 | − | 0.863777i | \(-0.668092\pi\) | ||||
−0.503874 | + | 0.863777i | \(0.668092\pi\) | |||||||
\(194\) | 74.2733 | − | 201.995i | 0.382852 | − | 1.04121i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 33.2918 | + | 28.3104i | 0.169856 | + | 0.144441i | ||||
\(197\) | −130.284 | −0.661340 | −0.330670 | − | 0.943746i | \(-0.607275\pi\) | ||||
−0.330670 | + | 0.943746i | \(0.607275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 270.765i | − | 1.36063i | −0.732921 | − | 0.680313i | \(-0.761844\pi\) | ||
0.732921 | − | 0.680313i | \(-0.238156\pi\) | |||||||
\(200\) | 379.076 | − | 213.901i | 1.89538 | − | 1.06950i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −124.098 | + | 337.500i | −0.614349 | + | 1.67079i | ||||
\(203\) | − | 315.616i | − | 1.55476i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 437.435 | 2.13383 | ||||||||
\(206\) | −48.9005 | − | 17.9807i | −0.237381 | − | 0.0872849i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.5652 | − | 101.756i | −0.0796404 | − | 0.489212i | ||||
\(209\) | −70.0741 | −0.335283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 183.580i | 0.870048i | 0.900419 | + | 0.435024i | \(0.143260\pi\) | ||||
−0.900419 | + | 0.435024i | \(0.856740\pi\) | |||||||
\(212\) | 107.378 | + | 91.3113i | 0.506501 | + | 0.430714i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −45.1013 | − | 16.5837i | −0.210754 | − | 0.0774940i | ||||
\(215\) | − | 268.617i | − | 1.24938i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 193.973 | 0.893883 | ||||||||
\(218\) | −16.8290 | + | 45.7685i | −0.0771974 | + | 0.209947i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 371.211 | − | 436.528i | 1.68732 | − | 1.98422i | ||||
\(221\) | 11.6536 | 0.0527313 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 168.708i | 0.756538i | 0.925696 | + | 0.378269i | \(0.123481\pi\) | ||||
−0.925696 | + | 0.378269i | \(0.876519\pi\) | |||||||
\(224\) | −47.0211 | + | 243.213i | −0.209916 | + | 1.08577i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 55.5943 | − | 151.195i | 0.245992 | − | 0.669004i | ||||
\(227\) | 249.037i | 1.09708i | 0.836124 | + | 0.548540i | \(0.184816\pi\) | ||||
−0.836124 | + | 0.548540i | \(0.815184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −283.680 | −1.23878 | −0.619388 | − | 0.785085i | \(-0.712619\pi\) | ||||
−0.619388 | + | 0.785085i | \(0.712619\pi\) | |||||||
\(230\) | 155.215 | + | 57.0723i | 0.674846 | + | 0.248140i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 284.067 | − | 160.290i | 1.22443 | − | 0.690906i | ||||
\(233\) | 77.8448 | 0.334098 | 0.167049 | − | 0.985949i | \(-0.446576\pi\) | ||||
0.167049 | + | 0.985949i | \(0.446576\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 736.314i | − | 3.13325i | ||||||
\(236\) | 207.995 | − | 244.593i | 0.881335 | − | 1.03641i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.2809 | − | 9.66346i | −0.110424 | − | 0.0406028i | ||||
\(239\) | − | 31.9668i | − | 0.133752i | −0.997761 | − | 0.0668762i | \(-0.978697\pi\) | ||
0.997761 | − | 0.0668762i | \(-0.0213032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 45.2991 | 0.187963 | 0.0939815 | − | 0.995574i | \(-0.470041\pi\) | ||||
0.0939815 | + | 0.995574i | \(0.470041\pi\) | |||||||
\(242\) | 94.8641 | − | 257.994i | 0.392000 | − | 1.06609i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −156.317 | − | 132.928i | −0.640645 | − | 0.544786i | ||||
\(245\) | −97.3570 | −0.397375 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 28.0864i | − | 0.113710i | ||||||
\(248\) | 98.5117 | + | 174.583i | 0.397225 | + | 0.703963i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −180.874 | + | 491.908i | −0.723496 | + | 1.96763i | ||||
\(251\) | 16.0745i | 0.0640416i | 0.999487 | + | 0.0320208i | \(0.0101943\pi\) | ||||
−0.999487 | + | 0.0320208i | \(0.989806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 149.173 | 0.589615 | ||||||||
\(254\) | 293.596 | + | 107.955i | 1.15589 | + | 0.425019i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −242.781 | + | 81.1983i | −0.948365 | + | 0.317181i | ||||
\(257\) | 342.048 | 1.33093 | 0.665463 | − | 0.746431i | \(-0.268234\pi\) | ||||
0.665463 | + | 0.746431i | \(0.268234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 549.853i | − | 2.12299i | ||||||
\(260\) | 174.965 | + | 148.785i | 0.672943 | + | 0.572251i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −29.7569 | − | 10.9416i | −0.113576 | − | 0.0417617i | ||||
\(263\) | − | 306.233i | − | 1.16438i | −0.813052 | − | 0.582192i | \(-0.802195\pi\) | ||
0.813052 | − | 0.582192i | \(-0.197805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −314.012 | −1.18495 | ||||||||
\(266\) | −23.2899 | + | 63.3396i | −0.0875561 | + | 0.238119i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.6807 | − | 14.9120i | 0.0473162 | − | 0.0556418i | ||||
\(269\) | −110.529 | −0.410889 | −0.205444 | − | 0.978669i | \(-0.565864\pi\) | ||||
−0.205444 | + | 0.978669i | \(0.565864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 177.256i | − | 0.654081i | −0.945010 | − | 0.327040i | \(-0.893949\pi\) | ||
0.945010 | − | 0.327040i | \(-0.106051\pi\) | |||||||
\(272\) | −4.64963 | − | 28.5615i | −0.0170942 | − | 0.105006i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 54.9480 | − | 149.437i | 0.200540 | − | 0.545392i | ||||
\(275\) | 874.662i | 3.18059i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −337.347 | −1.21786 | −0.608929 | − | 0.793225i | \(-0.708400\pi\) | ||||
−0.608929 | + | 0.793225i | \(0.708400\pi\) | |||||||
\(278\) | −201.800 | − | 74.2015i | −0.725898 | − | 0.266912i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −271.200 | − | 480.621i | −0.968570 | − | 1.71650i | ||||
\(281\) | −250.838 | −0.892661 | −0.446331 | − | 0.894868i | \(-0.647269\pi\) | ||||
−0.446331 | + | 0.894868i | \(0.647269\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 417.902i | 1.47668i | 0.674427 | + | 0.738342i | \(0.264391\pi\) | ||||
−0.674427 | + | 0.738342i | \(0.735609\pi\) | |||||||
\(284\) | −250.203 | + | 294.229i | −0.880998 | + | 1.03602i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 194.444 | + | 71.4968i | 0.679873 | + | 0.249989i | ||||
\(287\) | − | 380.003i | − | 1.32405i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −285.729 | −0.988682 | ||||||||
\(290\) | −250.767 | + | 681.991i | −0.864715 | + | 2.35169i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 356.889 | + | 303.488i | 1.22222 | + | 1.03934i | ||||
\(293\) | −210.732 | −0.719223 | −0.359612 | − | 0.933102i | \(-0.617091\pi\) | ||||
−0.359612 | + | 0.933102i | \(0.617091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 715.278i | 2.42467i | ||||||||
\(296\) | 494.889 | − | 279.251i | 1.67192 | − | 0.943414i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 78.8210 | − | 214.363i | 0.264500 | − | 0.719338i | ||||
\(299\) | 59.7900i | 0.199966i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −233.350 | −0.775248 | ||||||||
\(302\) | −538.033 | − | 197.834i | −1.78156 | − | 0.655080i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −68.8362 | + | 11.2061i | −0.226435 | + | 0.0368621i | ||||
\(305\) | 457.128 | 1.49878 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 282.598i | 0.920514i | 0.887786 | + | 0.460257i | \(0.152243\pi\) | ||||
−0.887786 | + | 0.460257i | \(0.847757\pi\) | |||||||
\(308\) | −379.216 | − | 322.474i | −1.23122 | − | 1.04699i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −419.140 | − | 154.118i | −1.35207 | − | 0.497153i | ||||
\(311\) | 44.9288i | 0.144466i | 0.997388 | + | 0.0722328i | \(0.0230125\pi\) | ||||
−0.997388 | + | 0.0722328i | \(0.976988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −511.392 | −1.63384 | −0.816921 | − | 0.576750i | \(-0.804321\pi\) | ||||
−0.816921 | + | 0.576750i | \(0.804321\pi\) | |||||||
\(314\) | 78.6669 | − | 213.944i | 0.250531 | − | 0.681349i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4625 | + | 19.3592i | −0.0520966 | + | 0.0612634i | ||||
\(317\) | 419.477 | 1.32327 | 0.661636 | − | 0.749825i | \(-0.269863\pi\) | ||||
0.661636 | + | 0.749825i | \(0.269863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 655.443i | 2.05468i | ||||||||
\(320\) | 294.845 | − | 488.180i | 0.921390 | − | 1.52556i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 49.5792 | − | 134.836i | 0.153973 | − | 0.418746i | ||||
\(323\) | − | 7.88348i | − | 0.0244071i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −350.574 | −1.07869 | ||||||||
\(326\) | 16.8021 | + | 6.17813i | 0.0515402 | + | 0.0189513i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 342.018 | − | 192.990i | 1.04274 | − | 0.588384i | ||||
\(329\) | −639.643 | −1.94420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 355.767i | 1.07482i | 0.843320 | + | 0.537412i | \(0.180598\pi\) | ||||
−0.843320 | + | 0.537412i | \(0.819402\pi\) | |||||||
\(332\) | 237.113 | − | 278.835i | 0.714197 | − | 0.839865i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.92275 | − | 1.81009i | −0.0147388 | − | 0.00541943i | ||||
\(335\) | 43.6080i | 0.130173i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 298.046 | 0.884410 | 0.442205 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442205 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(338\) | 87.9901 | − | 239.299i | 0.260326 | − | 0.707985i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 49.1103 | + | 41.7620i | 0.144442 | + | 0.122829i | ||||
\(341\) | −402.824 | −1.18130 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 294.741i | − | 0.859304i | ||||||
\(344\) | −118.510 | − | 210.024i | −0.344506 | − | 0.610534i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.2032 | − | 30.4683i | 0.0323791 | − | 0.0880587i | ||||
\(347\) | − | 174.610i | − | 0.503199i | −0.967831 | − | 0.251599i | \(-0.919043\pi\) | ||
0.967831 | − | 0.251599i | \(-0.0809565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 41.7325 | 0.119577 | 0.0597887 | − | 0.998211i | \(-0.480957\pi\) | ||||
0.0597887 | + | 0.998211i | \(0.480957\pi\) | |||||||
\(350\) | 790.602 | + | 290.704i | 2.25886 | + | 0.830583i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 97.6491 | − | 505.082i | 0.277412 | − | 1.43489i | ||||
\(353\) | −385.808 | −1.09294 | −0.546470 | − | 0.837478i | \(-0.684029\pi\) | ||||
−0.546470 | + | 0.837478i | \(0.684029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 860.429i | − | 2.42374i | ||||||
\(356\) | −265.597 | − | 225.856i | −0.746059 | − | 0.634426i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 202.729 | + | 74.5431i | 0.566281 | + | 0.208221i | ||||
\(359\) | 702.253i | 1.95614i | 0.208287 | + | 0.978068i | \(0.433211\pi\) | ||||
−0.208287 | + | 0.978068i | \(0.566789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −72.3427 | + | 196.744i | −0.199842 | + | 0.543492i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 129.251 | − | 151.994i | 0.355086 | − | 0.417566i | ||||
\(365\) | −1043.67 | −2.85937 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 384.653i | 1.04810i | 0.851687 | + | 0.524051i | \(0.175580\pi\) | ||||
−0.851687 | + | 0.524051i | \(0.824420\pi\) | |||||||
\(368\) | 146.537 | − | 23.8553i | 0.398200 | − | 0.0648242i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −436.876 | + | 1188.13i | −1.18075 | + | 3.21118i | ||||
\(371\) | 272.785i | 0.735270i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −425.180 | −1.13989 | −0.569946 | − | 0.821682i | \(-0.693036\pi\) | ||||
−0.569946 | + | 0.821682i | \(0.693036\pi\) | |||||||
\(374\) | 54.5777 | + | 20.0682i | 0.145930 | + | 0.0536582i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −324.852 | − | 575.703i | −0.863967 | − | 1.53113i | ||||
\(377\) | −262.708 | −0.696839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 531.642i | − | 1.40275i | −0.712793 | − | 0.701375i | \(-0.752570\pi\) | ||
0.712793 | − | 0.701375i | \(-0.247430\pi\) | |||||||
\(380\) | 100.651 | − | 118.361i | 0.264870 | − | 0.311476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 555.499 | + | 204.256i | 1.45418 | + | 0.534703i | ||||
\(383\) | − | 676.483i | − | 1.76627i | −0.469116 | − | 0.883137i | \(-0.655427\pi\) | ||
0.469116 | − | 0.883137i | \(-0.344573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1108.96 | 2.88042 | ||||||||
\(386\) | 134.244 | − | 365.092i | 0.347783 | − | 0.945834i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 327.905 | + | 278.840i | 0.845115 | + | 0.718661i | ||||
\(389\) | 38.8036 | 0.0997521 | 0.0498760 | − | 0.998755i | \(-0.484117\pi\) | ||||
0.0498760 | + | 0.998755i | \(0.484117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7822i | 0.0429213i | ||||||||
\(392\) | −76.1207 | + | 42.9525i | −0.194185 | + | 0.109573i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 89.9243 | − | 244.559i | 0.228234 | − | 0.620709i | ||||
\(395\) | − | 56.6133i | − | 0.143325i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6954 | −0.0722806 | −0.0361403 | − | 0.999347i | \(-0.511506\pi\) | ||||
−0.0361403 | + | 0.999347i | \(0.511506\pi\) | |||||||
\(398\) | 508.259 | + | 186.887i | 1.27703 | + | 0.469564i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 139.874 | + | 859.211i | 0.349685 | + | 2.14803i | ||||
\(401\) | −402.321 | −1.00329 | −0.501647 | − | 0.865073i | \(-0.667272\pi\) | ||||
−0.501647 | + | 0.865073i | \(0.667272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 161.456i | − | 0.400636i | ||||||
\(404\) | −547.875 | − | 465.897i | −1.35613 | − | 1.15321i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 592.451 | + | 217.844i | 1.45924 | + | 0.536561i | ||||
\(407\) | 1141.88i | 2.80561i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 299.164 | 0.731451 | 0.365726 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365726 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(410\) | −301.925 | + | 821.120i | −0.736402 | + | 2.00273i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 67.5040 | − | 79.3818i | 0.163845 | − | 0.192674i | ||||
\(413\) | 621.369 | 1.50452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 815.413i | 1.96485i | ||||||||
\(416\) | 202.442 | + | 39.1388i | 0.486640 | + | 0.0940837i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 48.3664 | − | 131.538i | 0.115709 | − | 0.314684i | ||||
\(419\) | 55.9282i | 0.133480i | 0.997770 | + | 0.0667401i | \(0.0212598\pi\) | ||||
−0.997770 | + | 0.0667401i | \(0.978740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 657.497 | 1.56175 | 0.780875 | − | 0.624687i | \(-0.214774\pi\) | ||||
0.780875 | + | 0.624687i | \(0.214774\pi\) | |||||||
\(422\) | −344.603 | − | 126.710i | −0.816594 | − | 0.300261i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −245.517 | + | 138.538i | −0.579050 | + | 0.326740i | ||||
\(425\) | −98.4012 | −0.231532 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 397.111i | − | 0.930002i | ||||||
\(428\) | 62.2595 | − | 73.2145i | 0.145466 | − | 0.171062i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 504.227 | + | 185.404i | 1.17262 | + | 0.431172i | ||||
\(431\) | 627.989i | 1.45705i | 0.685019 | + | 0.728525i | \(0.259794\pi\) | ||||
−0.685019 | + | 0.728525i | \(0.740206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −285.023 | −0.658251 | −0.329125 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329125 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(434\) | −133.883 | + | 364.111i | −0.308487 | + | 0.838965i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −74.2975 | − | 63.1804i | −0.170407 | − | 0.144909i | ||||
\(437\) | 40.4469 | 0.0925558 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8089i | 0.0656239i | 0.999462 | + | 0.0328120i | \(0.0104462\pi\) | ||||
−0.999462 | + | 0.0328120i | \(0.989554\pi\) | |||||||
\(440\) | 563.202 | + | 998.109i | 1.28001 | + | 2.26843i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.04354 | + | 21.8753i | −0.0181980 | + | 0.0494917i | ||||
\(443\) | − | 290.870i | − | 0.656591i | −0.944575 | − | 0.328295i | \(-0.893526\pi\) | ||
0.944575 | − | 0.328295i | \(-0.106474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 776.700 | 1.74539 | ||||||||
\(446\) | −316.686 | − | 116.445i | −0.710058 | − | 0.261088i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −424.087 | − | 256.134i | −0.946622 | − | 0.571729i | ||||
\(449\) | 12.6985 | 0.0282817 | 0.0141409 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141409 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 789.156i | 1.74979i | ||||||||
\(452\) | 245.440 | + | 208.715i | 0.543008 | + | 0.461758i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −467.474 | − | 171.890i | −1.02968 | − | 0.378612i | ||||
\(455\) | 444.484i | 0.976888i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 118.476 | 0.259248 | 0.129624 | − | 0.991563i | \(-0.458623\pi\) | ||||
0.129624 | + | 0.991563i | \(0.458623\pi\) | |||||||
\(458\) | 195.801 | − | 532.502i | 0.427512 | − | 1.16267i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −214.264 | + | 251.965i | −0.465791 | + | 0.547750i | ||||
\(461\) | −189.946 | −0.412029 | −0.206015 | − | 0.978549i | \(-0.566049\pi\) | ||||
−0.206015 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 493.864i | − | 1.06666i | −0.845907 | − | 0.533331i | \(-0.820940\pi\) | ||
0.845907 | − | 0.533331i | \(-0.179060\pi\) | |||||||
\(464\) | 104.817 | + | 643.864i | 0.225898 | + | 1.38764i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.7299 | + | 146.125i | −0.115300 | + | 0.313572i | ||||
\(467\) | − | 79.7951i | − | 0.170867i | −0.996344 | − | 0.0854337i | \(-0.972772\pi\) | ||
0.996344 | − | 0.0854337i | \(-0.0272276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.8827 | 0.0807732 | ||||||||
\(470\) | 1382.15 | + | 508.217i | 2.94075 | + | 1.08131i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 315.571 | + | 559.256i | 0.668582 | + | 1.18486i | ||||
\(473\) | 484.599 | 1.02452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 237.157i | 0.499278i | ||||||||
\(476\) | 36.2790 | − | 42.6626i | 0.0762165 | − | 0.0896273i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 60.0057 | + | 22.0640i | 0.125535 | + | 0.0461591i | ||||
\(479\) | 229.249i | 0.478600i | 0.970946 | + | 0.239300i | \(0.0769179\pi\) | ||||
−0.970946 | + | 0.239300i | \(0.923082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −457.679 | −0.951516 | ||||||||
\(482\) | −31.2662 | + | 85.0321i | −0.0648677 | + | 0.176415i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 418.810 | + | 356.144i | 0.865309 | + | 0.735834i | ||||
\(485\) | −958.909 | −1.97713 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 842.418i | − | 1.72981i | −0.501934 | − | 0.864906i | \(-0.667378\pi\) | ||
0.501934 | − | 0.864906i | \(-0.332622\pi\) | |||||||
\(488\) | 357.415 | − | 201.678i | 0.732408 | − | 0.413275i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 67.1975 | − | 182.751i | 0.137138 | − | 0.372962i | ||||
\(491\) | − | 385.037i | − | 0.784190i | −0.919925 | − | 0.392095i | \(-0.871750\pi\) | ||
0.919925 | − | 0.392095i | \(-0.128250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −73.7387 | −0.149571 | ||||||||
\(494\) | 52.7218 | + | 19.3858i | 0.106724 | + | 0.0392424i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −395.708 | + | 64.4187i | −0.797799 | + | 0.129876i | ||||
\(497\) | −747.462 | −1.50395 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 709.613i | 1.42207i | 0.703156 | + | 0.711035i | \(0.251773\pi\) | ||||
−0.703156 | + | 0.711035i | \(0.748227\pi\) | |||||||
\(500\) | −798.530 | − | 679.047i | −1.59706 | − | 1.35809i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.1738 | − | 11.0949i | −0.0601071 | − | 0.0221013i | ||||
\(503\) | − | 607.671i | − | 1.20809i | −0.796949 | − | 0.604047i | \(-0.793554\pi\) | ||
0.796949 | − | 0.604047i | \(-0.206446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1602.18 | 3.17263 | ||||||||
\(506\) | −102.962 | + | 280.016i | −0.203481 | + | 0.553391i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −405.290 | + | 476.604i | −0.797815 | + | 0.938196i | ||||
\(509\) | −42.8187 | −0.0841232 | −0.0420616 | − | 0.999115i | \(-0.513393\pi\) | ||||
−0.0420616 | + | 0.999115i | \(0.513393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 906.645i | 1.77426i | ||||||||
\(512\) | 15.1526 | − | 511.776i | 0.0295949 | − | 0.999562i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −236.088 | + | 642.067i | −0.459314 | + | 1.24916i | ||||
\(515\) | 232.141i | 0.450759i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1328.35 | 2.56934 | ||||||||
\(518\) | 1032.14 | + | 379.518i | 1.99255 | + | 0.732661i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −400.053 | + | 225.738i | −0.769333 | + | 0.434111i | ||||
\(521\) | 261.985 | 0.502849 | 0.251425 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251425 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 509.423i | − | 0.974039i | −0.873391 | − | 0.487020i | \(-0.838084\pi\) | ||
0.873391 | − | 0.487020i | \(-0.161916\pi\) | |||||||
\(524\) | 41.0774 | − | 48.3053i | 0.0783920 | − | 0.0921857i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 574.837 | + | 211.367i | 1.09285 | + | 0.401839i | ||||
\(527\) | − | 45.3186i | − | 0.0859935i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 442.897 | 0.837235 | ||||||||
\(530\) | 216.737 | − | 589.440i | 0.408937 | − | 1.11215i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −102.821 | − | 87.4362i | −0.193273 | − | 0.164354i | ||||
\(533\) | −316.302 | −0.593437 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 214.105i | 0.400196i | ||||||||
\(536\) | 19.2392 | + | 34.0958i | 0.0358941 | + | 0.0636116i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 76.2891 | − | 207.477i | 0.141801 | − | 0.385645i | ||||
\(539\) | − | 175.637i | − | 0.325858i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −990.355 | −1.83060 | −0.915301 | − | 0.402772i | \(-0.868047\pi\) | ||||
−0.915301 | + | 0.402772i | \(0.868047\pi\) | |||||||
\(542\) | 332.732 | + | 122.345i | 0.613896 | + | 0.225729i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 56.8228 | + | 10.9857i | 0.104454 | + | 0.0201944i | ||||
\(545\) | 217.272 | 0.398665 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 547.139i | 1.00025i | 0.865952 | + | 0.500127i | \(0.166713\pi\) | ||||
−0.865952 | + | 0.500127i | \(0.833287\pi\) | |||||||
\(548\) | 242.587 | + | 206.289i | 0.442677 | + | 0.376439i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1641.85 | − | 603.707i | −2.98518 | − | 1.09765i | ||||
\(551\) | 177.718i | 0.322537i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.1805 | −0.0889340 | ||||||||
\(554\) | 232.843 | − | 633.242i | 0.420293 | − | 1.14304i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 278.571 | − | 327.588i | 0.501027 | − | 0.589187i | ||||
\(557\) | −54.9787 | −0.0987050 | −0.0493525 | − | 0.998781i | \(-0.515716\pi\) | ||||
−0.0493525 | + | 0.998781i | \(0.515716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 194.233i | 0.347464i | ||||||||
\(560\) | 1089.37 | − | 177.343i | 1.94531 | − | 0.316683i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 173.133 | − | 470.854i | 0.308065 | − | 0.837818i | ||||
\(563\) | − | 126.028i | − | 0.223851i | −0.993717 | − | 0.111925i | \(-0.964298\pi\) | ||
0.993717 | − | 0.111925i | \(-0.0357018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −717.753 | −1.27036 | ||||||||
\(566\) | −784.454 | − | 288.443i | −1.38596 | − | 0.509617i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −379.609 | − | 672.745i | −0.668326 | − | 1.18441i | ||||
\(569\) | −162.688 | −0.285919 | −0.142959 | − | 0.989729i | \(-0.545662\pi\) | ||||
−0.142959 | + | 0.989729i | \(0.545662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 414.403i | − | 0.725749i | −0.931838 | − | 0.362875i | \(-0.881795\pi\) | ||
0.931838 | − | 0.362875i | \(-0.118205\pi\) | |||||||
\(572\) | −268.417 | + | 315.647i | −0.469260 | + | 0.551830i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 713.314 | + | 262.285i | 1.24271 | + | 0.456942i | ||||
\(575\) | − | 504.856i | − | 0.878011i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −648.643 | −1.12416 | −0.562082 | − | 0.827081i | \(-0.690000\pi\) | ||||
−0.562082 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(578\) | 197.215 | − | 536.349i | 0.341203 | − | 0.927940i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1107.10 | − | 941.444i | −1.90879 | − | 1.62318i | ||||
\(581\) | 708.357 | 1.21920 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 566.495i | − | 0.971689i | ||||||
\(584\) | −816.015 | + | 460.452i | −1.39729 | + | 0.788446i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 145.451 | − | 395.571i | 0.248210 | − | 0.675036i | ||||
\(587\) | − | 1032.50i | − | 1.75895i | −0.475948 | − | 0.879473i | \(-0.657895\pi\) | ||
0.475948 | − | 0.879473i | \(-0.342105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −109.222 | −0.185437 | ||||||||
\(590\) | −1342.67 | − | 493.698i | −2.27571 | − | 0.836775i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 182.607 | + | 1121.71i | 0.308458 | + | 1.89478i | ||||
\(593\) | −820.949 | −1.38440 | −0.692199 | − | 0.721706i | \(-0.743358\pi\) | ||||
−0.692199 | + | 0.721706i | \(0.743358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 124.761i | 0.209682i | ||||||||
\(596\) | 347.982 | + | 295.914i | 0.583862 | + | 0.496499i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −112.233 | − | 41.2681i | −0.187681 | − | 0.0690102i | ||||
\(599\) | 185.031i | 0.308899i | 0.988001 | + | 0.154450i | \(0.0493604\pi\) | ||||
−0.988001 | + | 0.154450i | \(0.950640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −57.8307 | −0.0962241 | −0.0481120 | − | 0.998842i | \(-0.515320\pi\) | ||||
−0.0481120 | + | 0.998842i | \(0.515320\pi\) | |||||||
\(602\) | 161.062 | − | 438.027i | 0.267545 | − | 0.727619i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 742.719 | − | 873.406i | 1.22967 | − | 1.44604i | ||||
\(605\) | −1224.75 | −2.02438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1027.52i | 1.69278i | 0.532565 | + | 0.846389i | \(0.321228\pi\) | ||||
−0.532565 | + | 0.846389i | \(0.678772\pi\) | |||||||
\(608\) | 26.4767 | − | 136.949i | 0.0435473 | − | 0.225245i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −315.517 | + | 858.086i | −0.517242 | + | 1.40670i | ||||
\(611\) | 532.417i | 0.871387i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1130.78 | −1.84466 | −0.922330 | − | 0.386404i | \(-0.873717\pi\) | ||||
−0.922330 | + | 0.386404i | \(0.873717\pi\) | |||||||
\(614\) | −530.471 | − | 195.054i | −0.863960 | − | 0.317677i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 867.066 | − | 489.259i | 1.40758 | − | 0.794251i | ||||
\(617\) | 831.065 | 1.34694 | 0.673472 | − | 0.739212i | \(-0.264802\pi\) | ||||
0.673472 | + | 0.739212i | \(0.264802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 702.202i | − | 1.13441i | −0.823575 | − | 0.567207i | \(-0.808024\pi\) | ||
0.823575 | − | 0.567207i | \(-0.191976\pi\) | |||||||
\(620\) | 578.596 | − | 680.404i | 0.933219 | − | 1.09743i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −84.3370 | − | 31.0107i | −0.135590 | − | 0.0498564i | ||||
\(623\) | − | 674.726i | − | 1.08303i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 974.996 | 1.55999 | ||||||||
\(626\) | 352.972 | − | 959.948i | 0.563853 | − | 1.53346i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 347.302 | + | 295.335i | 0.553028 | + | 0.470279i | ||||
\(629\) | −128.464 | −0.204236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 56.3471i | 0.0892981i | 0.999003 | + | 0.0446490i | \(0.0142170\pi\) | ||||
−0.999003 | + | 0.0446490i | \(0.985783\pi\) | |||||||
\(632\) | −24.9770 | − | 44.2643i | −0.0395206 | − | 0.0700385i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −289.530 | + | 787.411i | −0.456673 | + | 1.24197i | ||||
\(635\) | − | 1393.76i | − | 2.19490i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 70.3973 | 0.110514 | ||||||||
\(638\) | −1230.35 | − | 452.398i | −1.92845 | − | 0.709088i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 712.868 | + | 890.411i | 1.11386 | + | 1.39127i | ||||
\(641\) | −472.269 | −0.736768 | −0.368384 | − | 0.929674i | \(-0.620089\pi\) | ||||
−0.368384 | + | 0.929674i | \(0.620089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 507.477i | − | 0.789233i | −0.918846 | − | 0.394616i | \(-0.870878\pi\) | ||
0.918846 | − | 0.394616i | \(-0.129122\pi\) | |||||||
\(644\) | 218.884 | + | 186.133i | 0.339882 | + | 0.289026i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.7983 | + | 5.44132i | 0.0229076 | + | 0.00842309i | ||||
\(647\) | 1010.69i | 1.56212i | 0.624457 | + | 0.781059i | \(0.285320\pi\) | ||||
−0.624457 | + | 0.781059i | \(0.714680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1290.40 | −1.98829 | ||||||||
\(650\) | 241.972 | − | 658.071i | 0.372265 | − | 1.01242i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.1942 | + | 27.2754i | −0.0355740 | + | 0.0418335i | ||||
\(653\) | 961.670 | 1.47270 | 0.736348 | − | 0.676603i | \(-0.236549\pi\) | ||||
0.736348 | + | 0.676603i | \(0.236549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 141.262i | 0.215667i | ||||||||
\(656\) | 126.200 | + | 775.215i | 0.192378 | + | 1.18173i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 441.493 | − | 1200.69i | 0.670962 | − | 1.82476i | ||||
\(659\) | 373.680i | 0.567041i | 0.958966 | + | 0.283521i | \(0.0915024\pi\) | ||||
−0.958966 | + | 0.283521i | \(0.908498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 254.841 | 0.385538 | 0.192769 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192769 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(662\) | −667.819 | − | 245.556i | −1.00879 | − | 0.370931i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 359.749 | + | 637.548i | 0.541791 | + | 0.960163i | ||||
\(665\) | 300.686 | 0.452159 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 378.323i | − | 0.567201i | ||||||
\(668\) | 6.79553 | − | 7.99126i | 0.0101730 | − | 0.0119630i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −81.8577 | − | 30.0990i | −0.122176 | − | 0.0449239i | ||||
\(671\) | 824.683i | 1.22904i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 166.830 | 0.247891 | 0.123945 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123945 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(674\) | −205.717 | + | 559.470i | −0.305218 | + | 0.830075i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 388.462 | + | 330.337i | 0.574648 | + | 0.488664i | ||||
\(677\) | 43.7097 | 0.0645639 | 0.0322819 | − | 0.999479i | \(-0.489723\pi\) | ||||
0.0322819 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 833.013i | 1.22682i | ||||||||
\(680\) | −112.289 | + | 63.3614i | −0.165131 | + | 0.0931786i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 278.036 | − | 756.152i | 0.407678 | − | 1.10873i | ||||
\(683\) | 398.448i | 0.583379i | 0.956513 | + | 0.291689i | \(0.0942174\pi\) | ||||
−0.956513 | + | 0.291689i | \(0.905783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −709.410 | −1.03563 | ||||||||
\(686\) | 553.266 | + | 203.436i | 0.806511 | + | 0.296553i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 476.038 | − | 77.4959i | 0.691916 | − | 0.112639i | ||||
\(689\) | 227.057 | 0.329546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1092.32i | − | 1.58078i | −0.612605 | − | 0.790389i | \(-0.709878\pi\) | ||
0.612605 | − | 0.790389i | \(-0.290122\pi\) | |||||||
\(692\) | 49.4602 | + | 42.0595i | 0.0714743 | + | 0.0607797i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 327.765 | + | 120.519i | 0.472283 | + | 0.173658i | ||||
\(695\) | 957.983i | 1.37839i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −88.7817 | −0.127377 | ||||||||
\(698\) | −28.8045 | + | 78.3372i | −0.0412672 | + | 0.112231i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1091.38 | + | 1283.41i | −1.55911 | + | 1.83344i | ||||
\(701\) | 828.024 | 1.18120 | 0.590602 | − | 0.806963i | \(-0.298890\pi\) | ||||
0.590602 | + | 0.806963i | \(0.298890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 309.612i | 0.440416i | ||||||||
\(704\) | 880.704 | + | 531.916i | 1.25100 | + | 0.755563i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 266.292 | − | 724.210i | 0.377184 | − | 1.02579i | ||||
\(707\) | − | 1391.83i | − | 1.96864i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1287.71 | −1.81623 | −0.908117 | − | 0.418717i | \(-0.862480\pi\) | ||||
−0.908117 | + | 0.418717i | \(0.862480\pi\) | |||||||
\(710\) | 1615.13 | + | 593.883i | 2.27483 | + | 0.836455i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 607.279 | − | 342.669i | 0.852920 | − | 0.481277i | ||||
\(713\) | 232.511 | 0.326102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 923.063i | − | 1.29100i | ||||||
\(716\) | −279.854 | + | 329.096i | −0.390857 | + | 0.459631i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1318.22 | − | 484.707i | −1.83596 | − | 0.675080i | ||||
\(719\) | − | 915.858i | − | 1.27379i | −0.770949 | − | 0.636897i | \(-0.780218\pi\) | ||
0.770949 | − | 0.636897i | \(-0.219782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 201.663 | 0.279699 | ||||||||
\(722\) | 13.1141 | − | 35.6654i | 0.0181636 | − | 0.0493980i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −319.381 | − | 271.593i | −0.441135 | − | 0.375128i | ||||
\(725\) | 2218.27 | 3.05968 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 913.562i | 1.25662i | 0.777963 | + | 0.628310i | \(0.216253\pi\) | ||||
−0.777963 | + | 0.628310i | \(0.783747\pi\) | |||||||
\(728\) | 196.100 | + | 347.530i | 0.269368 | + | 0.477376i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 720.359 | − | 1959.10i | 0.986793 | − | 2.68370i | ||||
\(731\) | 54.5184i | 0.0745806i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 269.142 | 0.367179 | 0.183590 | − | 0.983003i | \(-0.441228\pi\) | ||||
0.183590 | + | 0.983003i | \(0.441228\pi\) | |||||||
\(734\) | −722.042 | − | 265.494i | −0.983709 | − | 0.361709i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −56.3633 | + | 291.534i | −0.0765805 | + | 0.396107i | ||||
\(737\) | −78.6712 | −0.106745 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 816.781i | − | 1.10525i | −0.833429 | − | 0.552626i | \(-0.813626\pi\) | ||
0.833429 | − | 0.552626i | \(-0.186374\pi\) | |||||||
\(740\) | −1928.74 | − | 1640.14i | −2.60640 | − | 2.21641i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −512.052 | − | 188.281i | −0.690097 | − | 0.253748i | ||||
\(743\) | 889.227i | 1.19681i | 0.801195 | + | 0.598403i | \(0.204198\pi\) | ||||
−0.801195 | + | 0.598403i | \(0.795802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1017.62 | −1.36594 | ||||||||
\(746\) | 293.467 | − | 798.116i | 0.393387 | − | 1.06986i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −75.3409 | + | 88.5977i | −0.100723 | + | 0.118446i | ||||
\(749\) | 185.995 | 0.248325 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 517.950i | − | 0.689680i | −0.938661 | − | 0.344840i | \(-0.887933\pi\) | ||
0.938661 | − | 0.344840i | \(-0.112067\pi\) | |||||||
\(752\) | 1304.89 | − | 212.427i | 1.73522 | − | 0.282482i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 181.326 | − | 493.137i | 0.240485 | − | 0.654027i | ||||
\(755\) | 2554.15i | 3.38298i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −378.920 | −0.500555 | −0.250278 | − | 0.968174i | \(-0.580522\pi\) | ||||
−0.250278 | + | 0.968174i | \(0.580522\pi\) | |||||||
\(758\) | 997.959 | + | 366.949i | 1.31657 | + | 0.484101i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 152.708 | + | 270.629i | 0.200931 | + | 0.356091i | ||||
\(761\) | −702.253 | −0.922803 | −0.461401 | − | 0.887192i | \(-0.652653\pi\) | ||||
−0.461401 | + | 0.887192i | \(0.652653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 188.746i | − | 0.247374i | ||||||
\(764\) | −766.830 | + | 901.759i | −1.00370 | + | 1.18031i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1269.84 | + | 466.920i | 1.65776 | + | 0.609556i | ||||
\(767\) | − | 517.206i | − | 0.674324i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 206.234 | 0.268185 | 0.134092 | − | 0.990969i | \(-0.457188\pi\) | ||||
0.134092 | + | 0.990969i | \(0.457188\pi\) | |||||||
\(770\) | −765.425 | + | 2081.66i | −0.994059 | + | 2.70346i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 592.666 | + | 503.986i | 0.767702 | + | 0.652831i | ||||
\(773\) | −364.309 | −0.471293 | −0.235646 | − | 0.971839i | \(-0.575721\pi\) | ||||
−0.235646 | + | 0.971839i | \(0.575721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1363.31i | 1.75911i | ||||||||
\(776\) | −749.744 | + | 423.057i | −0.966165 | + | 0.545177i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.7829 | + | 72.8392i | −0.0344253 | + | 0.0936236i | ||||
\(779\) | 213.973i | 0.274676i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1552.26 | 1.98753 | ||||||||
\(782\) | −31.5023 | − | 11.5834i | −0.0402843 | − | 0.0148125i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0875 | − | 172.535i | −0.0358259 | − | 0.220070i | ||||
\(785\) | −1015.63 | −1.29380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 844.845i | − | 1.07350i | −0.843741 | − | 0.536750i | \(-0.819652\pi\) | ||
0.843741 | − | 0.536750i | \(-0.180348\pi\) | |||||||
\(788\) | 397.001 | + | 337.598i | 0.503809 | + | 0.428424i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 106.270 | + | 39.0755i | 0.134519 | + | 0.0494627i | ||||
\(791\) | 623.518i | 0.788266i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −330.542 | −0.416824 | ||||||||
\(794\) | 19.8061 | − | 53.8648i | 0.0249447 | − | 0.0678399i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −701.619 | + | 825.074i | −0.881431 | + | 1.03653i | ||||
\(797\) | 1155.32 | 1.44958 | 0.724791 | − | 0.688969i | \(-0.241936\pi\) | ||||
0.724791 | + | 0.688969i | \(0.241936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 149.442i | 0.187037i | ||||||||
\(800\) | −1709.39 | − | 330.482i | −2.13674 | − | 0.413102i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 277.689 | − | 755.206i | 0.346245 | − | 0.941654i | ||||
\(803\) | − | 1882.84i | − | 2.34475i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −640.095 | −0.795150 | ||||||||
\(806\) | 303.074 | + | 111.440i | 0.376022 | + | 0.138263i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1252.70 | − | 706.860i | 1.55037 | − | 0.874826i | ||||
\(809\) | −95.4530 | −0.117989 | −0.0589944 | − | 0.998258i | \(-0.518789\pi\) | ||||
−0.0589944 | + | 0.998258i | \(0.518789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 917.758i | − | 1.13164i | −0.824530 | − | 0.565818i | \(-0.808560\pi\) | ||
0.824530 | − | 0.565818i | \(-0.191440\pi\) | |||||||
\(812\) | −817.841 | + | 961.746i | −1.00719 | + | 1.18442i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2143.46 | − | 788.148i | −2.63324 | − | 0.968241i | ||||
\(815\) | − | 79.7631i | − | 0.0978688i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 131.395 | 0.160826 | ||||||||
\(818\) | −206.488 | + | 561.568i | −0.252430 | + | 0.686513i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1332.95 | − | 1133.50i | −1.62555 | − | 1.38232i | ||||
\(821\) | 958.146 | 1.16705 | 0.583524 | − | 0.812096i | \(-0.301673\pi\) | ||||
0.583524 | + | 0.812096i | \(0.301673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 63.1070i | 0.0766793i | 0.999265 | + | 0.0383396i | \(0.0122069\pi\) | ||||
−0.999265 | + | 0.0383396i | \(0.987793\pi\) | |||||||
\(824\) | 102.417 | + | 181.504i | 0.124293 | + | 0.220272i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −428.880 | + | 1166.39i | −0.519225 | + | 1.41209i | ||||
\(827\) | − | 1430.65i | − | 1.72993i | −0.501836 | − | 0.864963i | \(-0.667342\pi\) | ||
0.501836 | − | 0.864963i | \(-0.332658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −706.756 | −0.852541 | −0.426270 | − | 0.904596i | \(-0.640173\pi\) | ||||
−0.426270 | + | 0.904596i | \(0.640173\pi\) | |||||||
\(830\) | −1530.63 | − | 562.812i | −1.84414 | − | 0.678087i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −213.198 | + | 352.996i | −0.256247 | + | 0.424273i | ||||
\(833\) | 19.7596 | 0.0237210 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.3693i | 0.0279872i | ||||||||
\(836\) | 213.530 | + | 181.579i | 0.255418 | + | 0.217200i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −104.984 | − | 38.6026i | −0.125279 | − | 0.0460652i | ||||
\(839\) | 240.681i | 0.286867i | 0.989660 | + | 0.143433i | \(0.0458142\pi\) | ||||
−0.989660 | + | 0.143433i | \(0.954186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 821.295 | 0.976570 | ||||||||
\(842\) | −453.816 | + | 1234.20i | −0.538974 | + | 1.46580i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 475.702 | − | 559.405i | 0.563628 | − | 0.662802i | ||||
\(845\) | −1136.00 | −1.34438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1063.95i | 1.25614i | ||||||||
\(848\) | −90.5925 | − | 556.488i | −0.106831 | − | 0.656236i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 67.9183 | − | 184.711i | 0.0799038 | − | 0.217308i | ||||
\(851\) | − | 659.098i | − | 0.774498i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1178.74 | 1.38188 | 0.690940 | − | 0.722912i | \(-0.257197\pi\) | ||||
0.690940 | + | 0.722912i | \(0.257197\pi\) | |||||||
\(854\) | 745.427 | + | 274.093i | 0.872865 | + | 0.320952i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 94.4602 | + | 167.403i | 0.110351 | + | 0.195564i | ||||
\(857\) | −424.112 | −0.494880 | −0.247440 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247440 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 695.559i | − | 0.809731i | −0.914376 | − | 0.404866i | \(-0.867318\pi\) | ||
0.914376 | − | 0.404866i | \(-0.132682\pi\) | |||||||
\(860\) | −696.053 | + | 818.529i | −0.809364 | + | 0.951777i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1178.81 | − | 433.449i | −1.36753 | − | 0.502841i | ||||
\(863\) | − | 788.782i | − | 0.914000i | −0.889467 | − | 0.457000i | \(-0.848924\pi\) | ||
0.889467 | − | 0.457000i | \(-0.151076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −144.639 | −0.167213 | ||||||||
\(866\) | 196.728 | − | 535.023i | 0.227168 | − | 0.617810i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −591.073 | − | 502.632i | −0.680960 | − | 0.579069i | ||||
\(869\) | 102.133 | 0.117530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 31.5323i | − | 0.0362024i | ||||||
\(872\) | 169.879 | − | 95.8575i | 0.194815 | − | 0.109928i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27.9172 | + | 75.9239i | −0.0319418 | + | 0.0868694i | ||||
\(875\) | − | 2028.60i | − | 2.31840i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −636.075 | −0.725285 | −0.362642 | − | 0.931928i | \(-0.618125\pi\) | ||||
−0.362642 | + | 0.931928i | \(0.618125\pi\) | |||||||
\(878\) | −54.0779 | − | 19.8844i | −0.0615922 | − | 0.0226474i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2262.31 | + | 368.289i | −2.57080 | + | 0.418510i | ||||
\(881\) | 60.4939 | 0.0686650 | 0.0343325 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343325 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 494.131i | 0.559604i | 0.960058 | + | 0.279802i | \(0.0902689\pi\) | ||||
−0.960058 | + | 0.279802i | \(0.909731\pi\) | |||||||
\(884\) | −35.5109 | − | 30.1975i | −0.0401707 | − | 0.0341600i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 545.999 | + | 200.763i | 0.616251 | + | 0.226595i | ||||
\(887\) | 1459.45i | 1.64538i | 0.568494 | + | 0.822688i | \(0.307526\pi\) | ||||
−0.568494 | + | 0.822688i | \(0.692474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1210.77 | −1.36195 | ||||||||
\(890\) | −536.092 | + | 1457.96i | −0.602350 | + | 1.63816i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 437.164 | − | 514.087i | 0.490095 | − | 0.576331i | ||||
\(893\) | 360.171 | 0.403327 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 962.393i | − | 1.07530i | ||||||
\(896\) | 773.509 | − | 619.275i | 0.863291 | − | 0.691155i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.76472 | + | 23.8366i | −0.00976026 | + | 0.0265442i | ||||
\(899\) | 1021.62i | 1.13640i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.7319 | 0.0707346 | ||||||||
\(902\) | −1481.34 | − | 544.689i | −1.64229 | − | 0.603868i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −561.191 | + | 316.663i | −0.620786 | + | 0.350290i | ||||
\(905\) | 933.985 | 1.03203 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 253.406i | 0.279389i | 0.990195 | + | 0.139695i | \(0.0446120\pi\) | ||||
−0.990195 | + | 0.139695i | \(0.955388\pi\) | |||||||
\(908\) | 645.317 | − | 758.866i | 0.710702 | − | 0.835755i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −834.353 | − | 306.791i | −0.916871 | − | 0.337133i | ||||
\(911\) | − | 11.8641i | − | 0.0130231i | −0.999979 | − | 0.00651156i | \(-0.997927\pi\) | ||
0.999979 | − | 0.00651156i | \(-0.00207271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1471.05 | −1.61123 | ||||||||
\(914\) | −81.7745 | + | 222.395i | −0.0894688 | + | 0.243321i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 864.428 | + | 735.085i | 0.943699 | + | 0.802494i | ||||
\(917\) | 122.715 | 0.133823 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1222.00i | 1.32971i | 0.746974 | + | 0.664853i | \(0.231506\pi\) | ||||
−0.746974 | + | 0.664853i | \(0.768494\pi\) | |||||||
\(920\) | −325.081 | − | 576.111i | −0.353349 | − | 0.626207i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 131.104 | − | 356.552i | 0.142195 | − | 0.386715i | ||||
\(923\) | 622.163i | 0.674066i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3864.57 | 4.17791 | ||||||||
\(926\) | 927.045 | + | 340.874i | 1.00113 | + | 0.368114i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1280.96 | − | 247.652i | −1.38034 | − | 0.266866i | ||||
\(929\) | 772.022 | 0.831024 | 0.415512 | − | 0.909588i | \(-0.363602\pi\) | ||||
0.415512 | + | 0.909588i | \(0.363602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 47.6226i | − | 0.0511521i | ||||||
\(932\) | −237.209 | − | 201.715i | −0.254516 | − | 0.216433i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 149.785 | + | 55.0760i | 0.160370 | + | 0.0589678i | ||||
\(935\) | − | 259.091i | − | 0.277103i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 193.066 | 0.206047 | 0.103023 | − | 0.994679i | \(-0.467148\pi\) | ||||
0.103023 | + | 0.994679i | \(0.467148\pi\) | |||||||
\(938\) | −26.1473 | + | 71.1105i | −0.0278756 | + | 0.0758108i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1907.97 | + | 2243.70i | −2.02976 | + | 2.38691i | ||||
\(941\) | 356.077 | 0.378402 | 0.189201 | − | 0.981938i | \(-0.439410\pi\) | ||||
0.189201 | + | 0.981938i | \(0.439410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 455.502i | − | 0.483035i | ||||||
\(944\) | −1267.61 | + | 206.358i | −1.34280 | + | 0.218599i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −334.479 | + | 909.653i | −0.353572 | + | 0.961578i | ||||
\(947\) | 828.719i | 0.875100i | 0.899194 | + | 0.437550i | \(0.144154\pi\) | ||||
−0.899194 | + | 0.437550i | \(0.855846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 754.661 | 0.795217 | ||||||||
\(950\) | −445.174 | − | 163.690i | −0.468604 | − | 0.172305i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 55.0426 | + | 97.5468i | 0.0578179 | + | 0.102465i | ||||
\(953\) | 72.8231 | 0.0764146 | 0.0382073 | − | 0.999270i | \(-0.487835\pi\) | ||||
0.0382073 | + | 0.999270i | \(0.487835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2637.06i | − | 2.76132i | ||||||
\(956\) | −82.8340 | + | 97.4092i | −0.0866464 | + | 0.101892i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −430.330 | − | 158.232i | −0.449196 | − | 0.165169i | ||||
\(959\) | 616.271i | 0.642618i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 333.129 | 0.346649 | ||||||||
\(962\) | 315.898 | − | 859.122i | 0.328377 | − | 0.893058i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −138.035 | − | 117.381i | −0.143190 | − | 0.121765i | ||||
\(965\) | −1733.17 | −1.79603 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1333.39i | − | 1.37889i | −0.724336 | − | 0.689447i | \(-0.757854\pi\) | ||
0.724336 | − | 0.689447i | \(-0.242146\pi\) | |||||||
\(968\) | −957.596 | + | 540.342i | −0.989252 | + | 0.558204i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 661.856 | − | 1799.99i | 0.682326 | − | 1.85566i | ||||
\(971\) | − | 749.276i | − | 0.771654i | −0.922571 | − | 0.385827i | \(-0.873916\pi\) | ||
0.922571 | − | 0.385827i | \(-0.126084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 832.209 | 0.855302 | ||||||||
\(974\) | 1581.32 | + | 581.452i | 1.62354 | + | 0.596973i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 131.881 | + | 810.115i | 0.135124 | + | 0.830036i | ||||
\(977\) | 943.603 | 0.965817 | 0.482908 | − | 0.875671i | \(-0.339580\pi\) | ||||
0.482908 | + | 0.875671i | \(0.339580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1401.21i | 1.43126i | ||||||||
\(980\) | 296.666 | + | 252.276i | 0.302721 | + | 0.257425i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 722.764 | + | 265.760i | 0.736012 | + | 0.270631i | ||||
\(983\) | − | 650.742i | − | 0.661996i | −0.943632 | − | 0.330998i | \(-0.892615\pi\) | ||
0.943632 | − | 0.330998i | \(-0.107385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1160.97 | −1.17865 | ||||||||
\(986\) | 50.8957 | − | 138.417i | 0.0516184 | − | 0.140382i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −72.7790 | + | 85.5850i | −0.0736629 | + | 0.0866245i | ||||
\(989\) | −279.711 | −0.282823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1136.18i | − | 1.14650i | −0.819380 | − | 0.573251i | \(-0.805682\pi\) | ||
0.819380 | − | 0.573251i | \(-0.194318\pi\) | |||||||
\(992\) | 152.203 | − | 787.257i | 0.153430 | − | 0.793606i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 515.911 | − | 1403.08i | 0.519026 | − | 1.41155i | ||||
\(995\) | − | 2412.81i | − | 2.42493i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1161.15 | −1.16465 | −0.582324 | − | 0.812957i | \(-0.697856\pi\) | ||||
−0.582324 | + | 0.812957i | \(0.697856\pi\) | |||||||
\(998\) | −1332.03 | − | 489.788i | −1.33470 | − | 0.490769i | ||||
\(999\) | 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 | 684.3.g.d.343.14 | yes | 36 | |
3.2 | odd | 2 | inner | 684.3.g.d.343.23 | yes | 36 | |
4.3 | odd | 2 | inner | 684.3.g.d.343.13 | ✓ | 36 | |
12.11 | even | 2 | inner | 684.3.g.d.343.24 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.g.d.343.13 | ✓ | 36 | 4.3 | odd | 2 | inner | |
684.3.g.d.343.14 | yes | 36 | 1.1 | even | 1 | trivial | |
684.3.g.d.343.23 | yes | 36 | 3.2 | odd | 2 | inner | |
684.3.g.d.343.24 | yes | 36 | 12.11 | even | 2 | inner |