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 | 343.12 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.d.343.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07034 | + | 1.68949i | −0.535172 | + | 0.844743i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.70873 | − | 3.61666i | −0.427183 | − | 0.904165i | ||||
\(5\) | −6.66582 | −1.33316 | −0.666582 | − | 0.745432i | \(-0.732243\pi\) | ||||
−0.666582 | + | 0.745432i | \(0.732243\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 12.1510i | − | 1.73586i | −0.496687 | − | 0.867930i | \(-0.665450\pi\) | ||
0.496687 | − | 0.867930i | \(-0.334550\pi\) | |||||||
\(8\) | 7.93923 | + | 0.984190i | 0.992404 | + | 0.123024i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.13471 | − | 11.2618i | 0.713471 | − | 1.12618i | ||||
\(11\) | 4.93767i | 0.448880i | 0.974488 | + | 0.224440i | \(0.0720552\pi\) | ||||
−0.974488 | + | 0.224440i | \(0.927945\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.2570 | 0.865922 | 0.432961 | − | 0.901413i | \(-0.357469\pi\) | ||||
0.432961 | + | 0.901413i | \(0.357469\pi\) | |||||||
\(14\) | 20.5290 | + | 13.0058i | 1.46636 | + | 0.928983i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.1605 | + | 12.3598i | −0.635030 | + | 0.772488i | ||||
\(17\) | 17.2061 | 1.01212 | 0.506062 | − | 0.862497i | \(-0.331101\pi\) | ||||
0.506062 | + | 0.862497i | \(0.331101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | 11.3901 | + | 24.1080i | 0.569505 | + | 1.20540i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.34214 | − | 5.28501i | −0.379188 | − | 0.240228i | ||||
\(23\) | − | 16.0420i | − | 0.697480i | −0.937220 | − | 0.348740i | \(-0.886610\pi\) | ||
0.937220 | − | 0.348740i | \(-0.113390\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.4331 | 0.777325 | ||||||||
\(26\) | −12.0488 | + | 19.0185i | −0.463417 | + | 0.731482i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −43.9461 | + | 20.7628i | −1.56950 | + | 0.741529i | ||||
\(29\) | −50.3944 | −1.73774 | −0.868869 | − | 0.495043i | \(-0.835152\pi\) | ||||
−0.868869 | + | 0.495043i | \(0.835152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.35866i | 0.205118i | 0.994727 | + | 0.102559i | \(0.0327031\pi\) | ||||
−0.994727 | + | 0.102559i | \(0.967297\pi\) | |||||||
\(32\) | −10.0065 | − | 30.3952i | −0.312704 | − | 0.949851i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.4164 | + | 29.0695i | −0.541660 | + | 0.854985i | ||||
\(35\) | 80.9965i | 2.31419i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.0832 | −0.975221 | −0.487610 | − | 0.873061i | \(-0.662131\pi\) | ||||
−0.487610 | + | 0.873061i | \(0.662131\pi\) | |||||||
\(38\) | 7.36430 | + | 4.66552i | 0.193797 | + | 0.122777i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −52.9215 | − | 6.56043i | −1.32304 | − | 0.164011i | ||||
\(41\) | 11.8766 | 0.289673 | 0.144837 | − | 0.989456i | \(-0.453734\pi\) | ||||
0.144837 | + | 0.989456i | \(0.453734\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 59.2181i | − | 1.37716i | −0.725158 | − | 0.688582i | \(-0.758233\pi\) | ||
0.725158 | − | 0.688582i | \(-0.241767\pi\) | |||||||
\(44\) | 17.8579 | − | 8.43716i | 0.405861 | − | 0.191754i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27.1028 | + | 17.1705i | 0.589192 | + | 0.373271i | ||||
\(47\) | − | 35.3518i | − | 0.752165i | −0.926586 | − | 0.376083i | \(-0.877271\pi\) | ||
0.926586 | − | 0.376083i | \(-0.122729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −98.6473 | −2.01321 | ||||||||
\(50\) | −20.8001 | + | 32.8320i | −0.416002 | + | 0.656640i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.2352 | − | 40.7127i | −0.369907 | − | 0.782937i | ||||
\(53\) | −38.6046 | −0.728388 | −0.364194 | − | 0.931323i | \(-0.618655\pi\) | ||||
−0.364194 | + | 0.931323i | \(0.618655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 32.9136i | − | 0.598430i | ||||||
\(56\) | 11.9589 | − | 96.4697i | 0.213552 | − | 1.72267i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 53.9393 | − | 85.1406i | 0.929988 | − | 1.46794i | ||||
\(59\) | 89.8121i | 1.52224i | 0.648612 | + | 0.761119i | \(0.275350\pi\) | ||||
−0.648612 | + | 0.761119i | \(0.724650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −85.8862 | −1.40797 | −0.703985 | − | 0.710215i | \(-0.748598\pi\) | ||||
−0.703985 | + | 0.710215i | \(0.748598\pi\) | |||||||
\(62\) | −10.7429 | − | 6.80595i | −0.173272 | − | 0.109773i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 62.0627 | + | 15.6274i | 0.969730 | + | 0.244178i | ||||
\(65\) | −75.0370 | −1.15442 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 103.436i | 1.54383i | 0.635729 | + | 0.771913i | \(0.280700\pi\) | ||||
−0.635729 | + | 0.771913i | \(0.719300\pi\) | |||||||
\(68\) | −29.4006 | − | 62.2286i | −0.432362 | − | 0.915127i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −136.842 | − | 86.6940i | −1.95489 | − | 1.23849i | ||||
\(71\) | 67.2102i | 0.946623i | 0.880895 | + | 0.473311i | \(0.156941\pi\) | ||||
−0.880895 | + | 0.473311i | \(0.843059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 109.478 | 1.49970 | 0.749848 | − | 0.661610i | \(-0.230126\pi\) | ||||
0.749848 | + | 0.661610i | \(0.230126\pi\) | |||||||
\(74\) | 38.6214 | − | 60.9620i | 0.521910 | − | 0.823811i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.7647 | + | 7.44819i | −0.207430 | + | 0.0980025i | ||||
\(77\) | 59.9978 | 0.779192 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 66.3475i | 0.839841i | 0.907561 | + | 0.419921i | \(0.137942\pi\) | ||||
−0.907561 | + | 0.419921i | \(0.862058\pi\) | |||||||
\(80\) | 67.7279 | − | 82.3882i | 0.846599 | − | 1.02985i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.7120 | + | 20.0654i | −0.155025 | + | 0.244700i | ||||
\(83\) | − | 4.01466i | − | 0.0483694i | −0.999708 | − | 0.0241847i | \(-0.992301\pi\) | ||
0.999708 | − | 0.0241847i | \(-0.00769898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −114.693 | −1.34933 | ||||||||
\(86\) | 100.048 | + | 63.3836i | 1.16335 | + | 0.737019i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.85961 | + | 39.2013i | −0.0552228 | + | 0.445470i | ||||
\(89\) | −53.9336 | −0.605996 | −0.302998 | − | 0.952991i | \(-0.597988\pi\) | ||||
−0.302998 | + | 0.952991i | \(0.597988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 136.784i | − | 1.50312i | ||||||
\(92\) | −58.0186 | + | 27.4115i | −0.630637 | + | 0.297951i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 59.7263 | + | 37.8385i | 0.635386 | + | 0.402537i | ||||
\(95\) | 29.0556i | 0.305849i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −62.8736 | −0.648181 | −0.324090 | − | 0.946026i | \(-0.605058\pi\) | ||||
−0.324090 | + | 0.946026i | \(0.605058\pi\) | |||||||
\(98\) | 105.586 | − | 166.663i | 1.07741 | − | 1.70065i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −33.2060 | − | 70.2830i | −0.332060 | − | 0.702830i | ||||
\(101\) | −73.2286 | −0.725036 | −0.362518 | − | 0.931977i | \(-0.618083\pi\) | ||||
−0.362518 | + | 0.931977i | \(0.618083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 53.3144i | − | 0.517615i | −0.965929 | − | 0.258808i | \(-0.916670\pi\) | ||
0.965929 | − | 0.258808i | \(-0.0833296\pi\) | |||||||
\(104\) | 89.3718 | + | 11.0790i | 0.859344 | + | 0.106529i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 41.3201 | − | 65.2219i | 0.389813 | − | 0.615301i | ||||
\(107\) | 54.1071i | 0.505673i | 0.967509 | + | 0.252837i | \(0.0813635\pi\) | ||||
−0.967509 | + | 0.252837i | \(0.918636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −114.140 | −1.04716 | −0.523578 | − | 0.851978i | \(-0.675403\pi\) | ||||
−0.523578 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(110\) | 55.6072 | + | 35.2289i | 0.505520 | + | 0.320263i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 150.184 | + | 123.460i | 1.34093 | + | 1.10232i | ||||
\(113\) | −55.4302 | −0.490533 | −0.245266 | − | 0.969456i | \(-0.578875\pi\) | ||||
−0.245266 | + | 0.969456i | \(0.578875\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 106.933i | 0.929855i | ||||||||
\(116\) | 86.1104 | + | 182.259i | 0.742331 | + | 1.57120i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −151.736 | − | 96.1297i | −1.28590 | − | 0.814659i | ||||
\(119\) | − | 209.072i | − | 1.75690i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 96.6194 | 0.798507 | ||||||||
\(122\) | 91.9277 | − | 145.104i | 0.753505 | − | 1.18937i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.9971 | − | 10.8652i | 0.185461 | − | 0.0876229i | ||||
\(125\) | 37.1077 | 0.296862 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 39.6329i | 0.312070i | 0.987752 | + | 0.156035i | \(0.0498712\pi\) | ||||
−0.987752 | + | 0.156035i | \(0.950129\pi\) | |||||||
\(128\) | −92.8307 | + | 88.1275i | −0.725240 | + | 0.688496i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 80.3154 | − | 126.774i | 0.617811 | − | 0.975185i | ||||
\(131\) | − | 166.297i | − | 1.26944i | −0.772743 | − | 0.634720i | \(-0.781116\pi\) | ||
0.772743 | − | 0.634720i | \(-0.218884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −52.9651 | −0.398234 | ||||||||
\(134\) | −174.754 | − | 110.712i | −1.30414 | − | 0.826211i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 136.603 | + | 16.9341i | 1.00444 | + | 0.124515i | ||||
\(137\) | −167.858 | −1.22524 | −0.612621 | − | 0.790377i | \(-0.709885\pi\) | ||||
−0.612621 | + | 0.790377i | \(0.709885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0197i | 0.0792785i | 0.999214 | + | 0.0396393i | \(0.0126209\pi\) | ||||
−0.999214 | + | 0.0396393i | \(0.987379\pi\) | |||||||
\(140\) | 292.937 | − | 138.401i | 2.09241 | − | 0.988580i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −113.551 | − | 71.9380i | −0.799653 | − | 0.506606i | ||||
\(143\) | 55.5833i | 0.388695i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 335.920 | 2.31669 | ||||||||
\(146\) | −117.179 | + | 184.961i | −0.802595 | + | 1.26686i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61.6564 | + | 130.501i | 0.416598 | + | 0.881761i | ||||
\(149\) | −243.481 | −1.63410 | −0.817051 | − | 0.576565i | \(-0.804393\pi\) | ||||
−0.817051 | + | 0.576565i | \(0.804393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 116.761i | 0.773250i | 0.922237 | + | 0.386625i | \(0.126359\pi\) | ||||
−0.922237 | + | 0.386625i | \(0.873641\pi\) | |||||||
\(152\) | 4.28998 | − | 34.6063i | 0.0282236 | − | 0.227673i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −64.2182 | + | 101.365i | −0.417001 | + | 0.658217i | ||||
\(155\) | − | 42.3857i | − | 0.273456i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −41.8235 | −0.266392 | −0.133196 | − | 0.991090i | \(-0.542524\pi\) | ||||
−0.133196 | + | 0.991090i | \(0.542524\pi\) | |||||||
\(158\) | −112.093 | − | 71.0145i | −0.709450 | − | 0.449459i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 66.7017 | + | 202.609i | 0.416886 | + | 1.26631i | ||||
\(161\) | −194.927 | −1.21073 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 285.363i | − | 1.75069i | −0.483497 | − | 0.875346i | \(-0.660634\pi\) | ||
0.483497 | − | 0.875346i | \(-0.339366\pi\) | |||||||
\(164\) | −20.2939 | − | 42.9536i | −0.123743 | − | 0.261912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.78271 | + | 4.29706i | 0.0408597 | + | 0.0258859i | ||||
\(167\) | − | 67.9780i | − | 0.407054i | −0.979069 | − | 0.203527i | \(-0.934760\pi\) | ||
0.979069 | − | 0.203527i | \(-0.0652405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42.2802 | −0.250179 | ||||||||
\(170\) | 122.761 | − | 193.772i | 0.722121 | − | 1.13983i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −214.172 | + | 101.188i | −1.24518 | + | 0.588301i | ||||
\(173\) | −323.430 | −1.86954 | −0.934768 | − | 0.355259i | \(-0.884393\pi\) | ||||
−0.934768 | + | 0.355259i | \(0.884393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 236.132i | − | 1.34933i | ||||||
\(176\) | −61.0287 | − | 50.1691i | −0.346754 | − | 0.285052i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 57.7275 | − | 91.1201i | 0.324312 | − | 0.511911i | ||||
\(179\) | 281.726i | 1.57389i | 0.617024 | + | 0.786944i | \(0.288338\pi\) | ||||
−0.617024 | + | 0.786944i | \(0.711662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 278.611 | 1.53929 | 0.769645 | − | 0.638473i | \(-0.220433\pi\) | ||||
0.769645 | + | 0.638473i | \(0.220433\pi\) | |||||||
\(182\) | 231.095 | + | 146.406i | 1.26975 | + | 0.804427i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.7884 | − | 127.361i | 0.0858066 | − | 0.692182i | ||||
\(185\) | 240.524 | 1.30013 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 84.9581i | 0.454321i | ||||||||
\(188\) | −127.855 | + | 60.4067i | −0.680082 | + | 0.321312i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −49.0891 | − | 31.0995i | −0.258364 | − | 0.163682i | ||||
\(191\) | − | 99.7898i | − | 0.522459i | −0.965277 | − | 0.261230i | \(-0.915872\pi\) | ||
0.965277 | − | 0.261230i | \(-0.0841280\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 252.868 | 1.31020 | 0.655100 | − | 0.755543i | \(-0.272627\pi\) | ||||
0.655100 | + | 0.755543i | \(0.272627\pi\) | |||||||
\(194\) | 67.2963 | − | 106.224i | 0.346888 | − | 0.547547i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 168.562 | + | 356.774i | 0.860009 | + | 1.82027i | ||||
\(197\) | 12.7366 | 0.0646529 | 0.0323265 | − | 0.999477i | \(-0.489708\pi\) | ||||
0.0323265 | + | 0.999477i | \(0.489708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 248.822i | 1.25036i | 0.780480 | + | 0.625181i | \(0.214975\pi\) | ||||
−0.780480 | + | 0.625181i | \(0.785025\pi\) | |||||||
\(200\) | 154.284 | + | 19.1259i | 0.771420 | + | 0.0956294i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 78.3797 | − | 123.719i | 0.388018 | − | 0.612469i | ||||
\(203\) | 612.343i | 3.01647i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −79.1673 | −0.386182 | ||||||||
\(206\) | 90.0739 | + | 57.0647i | 0.437252 | + | 0.277013i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −114.376 | + | 139.134i | −0.549886 | + | 0.668914i | ||||
\(209\) | 21.5228 | 0.102980 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 262.582i | 1.24446i | 0.782833 | + | 0.622232i | \(0.213774\pi\) | ||||
−0.782833 | + | 0.622232i | \(0.786226\pi\) | |||||||
\(212\) | 65.9648 | + | 139.620i | 0.311155 | + | 0.658583i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −91.4132 | − | 57.9131i | −0.427164 | − | 0.270622i | ||||
\(215\) | 394.737i | 1.83599i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 77.2642 | 0.356056 | ||||||||
\(218\) | 122.169 | − | 192.838i | 0.560408 | − | 0.884578i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −119.037 | + | 56.2406i | −0.541079 | + | 0.255639i | ||||
\(221\) | 193.689 | 0.876420 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 297.653i | − | 1.33477i | −0.744714 | − | 0.667384i | \(-0.767414\pi\) | ||
0.744714 | − | 0.667384i | \(-0.232586\pi\) | |||||||
\(224\) | −369.333 | + | 121.590i | −1.64881 | + | 0.542810i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 59.3293 | − | 93.6486i | 0.262519 | − | 0.414374i | ||||
\(227\) | − | 70.5415i | − | 0.310756i | −0.987855 | − | 0.155378i | \(-0.950340\pi\) | ||
0.987855 | − | 0.155378i | \(-0.0496595\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 332.538 | 1.45213 | 0.726064 | − | 0.687627i | \(-0.241347\pi\) | ||||
0.726064 | + | 0.687627i | \(0.241347\pi\) | |||||||
\(230\) | −180.662 | − | 114.455i | −0.785489 | − | 0.497632i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −400.093 | − | 49.5976i | −1.72454 | − | 0.213783i | ||||
\(233\) | 421.259 | 1.80798 | 0.903989 | − | 0.427555i | \(-0.140625\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 235.648i | 1.00276i | ||||||||
\(236\) | 324.820 | − | 153.465i | 1.37636 | − | 0.650274i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 353.224 | + | 223.778i | 1.48413 | + | 0.940245i | ||||
\(239\) | − | 234.793i | − | 0.982396i | −0.871048 | − | 0.491198i | \(-0.836559\pi\) | ||
0.871048 | − | 0.491198i | \(-0.163441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −264.431 | −1.09722 | −0.548612 | − | 0.836077i | \(-0.684844\pi\) | ||||
−0.548612 | + | 0.836077i | \(0.684844\pi\) | |||||||
\(242\) | −103.416 | + | 163.237i | −0.427338 | + | 0.674534i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 146.756 | + | 310.621i | 0.601460 | + | 1.27304i | ||||
\(245\) | 657.565 | 2.68394 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 49.0681i | − | 0.198656i | ||||||
\(248\) | −6.25813 | + | 50.4829i | −0.0252344 | + | 0.203560i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −39.7180 | + | 62.6930i | −0.158872 | + | 0.250772i | ||||
\(251\) | 141.609i | 0.564178i | 0.959388 | + | 0.282089i | \(0.0910274\pi\) | ||||
−0.959388 | + | 0.282089i | \(0.908973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 79.2104 | 0.313084 | ||||||||
\(254\) | −66.9592 | − | 42.4208i | −0.263619 | − | 0.167011i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −49.5295 | − | 251.163i | −0.193474 | − | 0.981105i | ||||
\(257\) | −403.482 | −1.56997 | −0.784985 | − | 0.619515i | \(-0.787329\pi\) | ||||
−0.784985 | + | 0.619515i | \(0.787329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 438.447i | 1.69285i | ||||||||
\(260\) | 128.218 | + | 271.384i | 0.493147 | + | 1.04378i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 280.956 | + | 177.994i | 1.07235 | + | 0.679368i | ||||
\(263\) | 329.342i | 1.25225i | 0.779722 | + | 0.626126i | \(0.215360\pi\) | ||||
−0.779722 | + | 0.626126i | \(0.784640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 257.331 | 0.971060 | ||||||||
\(266\) | 56.6908 | − | 89.4838i | 0.213123 | − | 0.336405i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 374.094 | − | 176.745i | 1.39587 | − | 0.659495i | ||||
\(269\) | −251.084 | −0.933397 | −0.466698 | − | 0.884417i | \(-0.654557\pi\) | ||||
−0.466698 | + | 0.884417i | \(0.654557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 150.264i | − | 0.554479i | −0.960801 | − | 0.277240i | \(-0.910580\pi\) | ||
0.960801 | − | 0.277240i | \(-0.0894196\pi\) | |||||||
\(272\) | −174.822 | + | 212.664i | −0.642729 | + | 0.781853i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 179.666 | − | 283.594i | 0.655715 | − | 1.03502i | ||||
\(275\) | 95.9545i | 0.348925i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −177.410 | −0.640469 | −0.320235 | − | 0.947338i | \(-0.603762\pi\) | ||||
−0.320235 | + | 0.947338i | \(0.603762\pi\) | |||||||
\(278\) | −18.6177 | − | 11.7949i | −0.0669700 | − | 0.0424276i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −79.7159 | + | 643.050i | −0.284700 | + | 2.29661i | ||||
\(281\) | −152.887 | −0.544083 | −0.272042 | − | 0.962285i | \(-0.587699\pi\) | ||||
−0.272042 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 351.150i | 1.24081i | 0.784280 | + | 0.620407i | \(0.213033\pi\) | ||||
−0.784280 | + | 0.620407i | \(0.786967\pi\) | |||||||
\(284\) | 243.077 | − | 114.844i | 0.855903 | − | 0.404381i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −93.9073 | − | 59.4933i | −0.328347 | − | 0.208018i | ||||
\(287\) | − | 144.313i | − | 0.502832i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.04985 | 0.0243940 | ||||||||
\(290\) | −359.549 | + | 567.532i | −1.23983 | + | 1.95701i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −187.068 | − | 395.944i | −0.640645 | − | 1.35597i | ||||
\(293\) | −141.826 | −0.484049 | −0.242025 | − | 0.970270i | \(-0.577811\pi\) | ||||
−0.242025 | + | 0.970270i | \(0.577811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 598.671i | − | 2.02939i | ||||||
\(296\) | −286.473 | − | 35.5127i | −0.967813 | − | 0.119975i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 260.608 | − | 411.358i | 0.874525 | − | 1.38040i | ||||
\(299\) | − | 180.585i | − | 0.603963i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −719.560 | −2.39056 | ||||||||
\(302\) | −197.266 | − | 124.974i | −0.653197 | − | 0.413821i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 53.8751 | + | 44.2885i | 0.177221 | + | 0.145686i | ||||
\(305\) | 572.501 | 1.87705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 367.051i | 1.19561i | 0.801643 | + | 0.597804i | \(0.203960\pi\) | ||||
−0.801643 | + | 0.597804i | \(0.796040\pi\) | |||||||
\(308\) | −102.520 | − | 216.992i | −0.332857 | − | 0.704518i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 71.6100 | + | 45.3672i | 0.231000 | + | 0.146346i | ||||
\(311\) | − | 365.139i | − | 1.17408i | −0.809558 | − | 0.587040i | \(-0.800293\pi\) | ||
0.809558 | − | 0.587040i | \(-0.199707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 422.596 | 1.35015 | 0.675073 | − | 0.737751i | \(-0.264112\pi\) | ||||
0.675073 | + | 0.737751i | \(0.264112\pi\) | |||||||
\(314\) | 44.7655 | − | 70.6602i | 0.142565 | − | 0.225032i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 239.956 | − | 113.370i | 0.759355 | − | 0.358766i | ||||
\(317\) | 141.440 | 0.446182 | 0.223091 | − | 0.974798i | \(-0.428385\pi\) | ||||
0.223091 | + | 0.974798i | \(0.428385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 248.831i | − | 0.780035i | ||||||
\(320\) | −413.699 | − | 104.170i | −1.29281 | − | 0.325530i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 208.639 | − | 329.327i | 0.647947 | − | 1.02275i | ||||
\(323\) | − | 74.9996i | − | 0.232197i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 218.759 | 0.673103 | ||||||||
\(326\) | 482.117 | + | 305.436i | 1.47889 | + | 0.936921i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 94.2911 | + | 11.6888i | 0.287473 | + | 0.0356367i | ||||
\(329\) | −429.560 | −1.30565 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 276.637i | − | 0.835760i | −0.908502 | − | 0.417880i | \(-0.862773\pi\) | ||
0.908502 | − | 0.417880i | \(-0.137227\pi\) | |||||||
\(332\) | −14.5197 | + | 6.85997i | −0.0437339 | + | 0.0206626i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 114.848 | + | 72.7598i | 0.343856 | + | 0.217844i | ||||
\(335\) | − | 689.487i | − | 2.05817i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −380.293 | −1.12847 | −0.564234 | − | 0.825615i | \(-0.690828\pi\) | ||||
−0.564234 | + | 0.825615i | \(0.690828\pi\) | |||||||
\(338\) | 45.2543 | − | 71.4318i | 0.133889 | − | 0.211337i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 195.979 | + | 414.805i | 0.576409 | + | 1.22001i | ||||
\(341\) | −31.3970 | −0.0920733 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 603.265i | 1.75879i | ||||||||
\(344\) | 58.2818 | − | 470.146i | 0.169424 | − | 1.36670i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 346.181 | − | 546.430i | 1.00052 | − | 1.57928i | ||||
\(347\) | − | 537.101i | − | 1.54784i | −0.633283 | − | 0.773920i | \(-0.718293\pi\) | ||
0.633283 | − | 0.773920i | \(-0.281707\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 117.919 | 0.337877 | 0.168938 | − | 0.985627i | \(-0.445966\pi\) | ||||
0.168938 | + | 0.985627i | \(0.445966\pi\) | |||||||
\(350\) | 398.942 | + | 252.743i | 1.13984 | + | 0.722122i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 150.082 | − | 49.4090i | 0.426368 | − | 0.140366i | ||||
\(353\) | 384.382 | 1.08890 | 0.544451 | − | 0.838793i | \(-0.316738\pi\) | ||||
0.544451 | + | 0.838793i | \(0.316738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 448.011i | − | 1.26200i | ||||||
\(356\) | 92.1581 | + | 195.060i | 0.258871 | + | 0.547920i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −475.972 | − | 301.543i | −1.32953 | − | 0.842300i | ||||
\(359\) | − | 222.659i | − | 0.620221i | −0.950701 | − | 0.310110i | \(-0.899634\pi\) | ||
0.950701 | − | 0.310110i | \(-0.100366\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −298.210 | + | 470.710i | −0.823784 | + | 1.30030i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −494.701 | + | 233.727i | −1.35907 | + | 0.642107i | ||||
\(365\) | −729.759 | −1.99934 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 70.5386i | − | 0.192203i | −0.995372 | − | 0.0961016i | \(-0.969363\pi\) | ||
0.995372 | − | 0.0961016i | \(-0.0306374\pi\) | |||||||
\(368\) | 198.276 | + | 162.995i | 0.538795 | + | 0.442920i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −257.443 | + | 406.362i | −0.695792 | + | 1.09828i | ||||
\(371\) | 469.085i | 1.26438i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 256.364 | 0.687302 | 0.343651 | − | 0.939097i | \(-0.388336\pi\) | ||||
0.343651 | + | 0.939097i | \(0.388336\pi\) | |||||||
\(374\) | −143.536 | − | 90.9343i | −0.383785 | − | 0.243140i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.7928 | − | 280.666i | 0.0925342 | − | 0.746451i | ||||
\(377\) | −567.289 | −1.50475 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 337.173i | − | 0.889638i | −0.895620 | − | 0.444819i | \(-0.853268\pi\) | ||
0.895620 | − | 0.444819i | \(-0.146732\pi\) | |||||||
\(380\) | 105.084 | − | 49.6483i | 0.276538 | − | 0.130653i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 168.593 | + | 106.809i | 0.441344 | + | 0.279605i | ||||
\(383\) | − | 53.8050i | − | 0.140483i | −0.997530 | − | 0.0702415i | \(-0.977623\pi\) | ||
0.997530 | − | 0.0702415i | \(-0.0223770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −399.934 | −1.03879 | ||||||||
\(386\) | −270.656 | + | 427.218i | −0.701181 | + | 1.10678i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 107.434 | + | 227.392i | 0.276892 | + | 0.586063i | ||||
\(389\) | 768.174 | 1.97474 | 0.987370 | − | 0.158434i | \(-0.0506445\pi\) | ||||
0.987370 | + | 0.158434i | \(0.0506445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 276.021i | − | 0.705936i | ||||||
\(392\) | −783.183 | − | 97.0876i | −1.99792 | − | 0.247673i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.6326 | + | 21.5184i | −0.0346004 | + | 0.0546151i | ||||
\(395\) | − | 442.260i | − | 1.11965i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 132.666 | 0.334172 | 0.167086 | − | 0.985942i | \(-0.446564\pi\) | ||||
0.167086 | + | 0.985942i | \(0.446564\pi\) | |||||||
\(398\) | −420.381 | − | 266.325i | −1.05623 | − | 0.669158i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −197.450 | + | 240.190i | −0.493625 | + | 0.600474i | ||||
\(401\) | 112.782 | 0.281253 | 0.140626 | − | 0.990063i | \(-0.455088\pi\) | ||||
0.140626 | + | 0.990063i | \(0.455088\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 71.5794i | 0.177616i | ||||||||
\(404\) | 125.128 | + | 264.843i | 0.309723 | + | 0.655552i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1034.55 | − | 655.417i | −2.54814 | − | 1.61433i | ||||
\(407\) | − | 178.167i | − | 0.437757i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −808.855 | −1.97764 | −0.988820 | − | 0.149112i | \(-0.952358\pi\) | ||||
−0.988820 | + | 0.149112i | \(0.952358\pi\) | |||||||
\(410\) | 84.7361 | − | 133.752i | 0.206673 | − | 0.326224i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −192.820 | + | 91.0999i | −0.468010 | + | 0.221116i | ||||
\(413\) | 1091.31 | 2.64239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.7610i | 0.0644843i | ||||||||
\(416\) | −112.643 | − | 342.159i | −0.270777 | − | 0.822497i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.0368 | + | 36.3625i | −0.0551120 | + | 0.0869917i | ||||
\(419\) | − | 566.901i | − | 1.35299i | −0.736449 | − | 0.676493i | \(-0.763499\pi\) | ||
0.736449 | − | 0.676493i | \(-0.236501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −300.257 | −0.713199 | −0.356599 | − | 0.934257i | \(-0.616064\pi\) | ||||
−0.356599 | + | 0.934257i | \(0.616064\pi\) | |||||||
\(422\) | −443.629 | − | 281.053i | −1.05125 | − | 0.666002i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −306.491 | − | 37.9942i | −0.722855 | − | 0.0896090i | ||||
\(425\) | 334.368 | 0.786749 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1043.60i | 2.44404i | ||||||||
\(428\) | 195.687 | − | 92.4544i | 0.457212 | − | 0.216015i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −666.903 | − | 422.504i | −1.55094 | − | 0.982567i | ||||
\(431\) | − | 756.625i | − | 1.75551i | −0.479110 | − | 0.877755i | \(-0.659041\pi\) | ||
0.479110 | − | 0.877755i | \(-0.340959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −707.649 | −1.63429 | −0.817146 | − | 0.576430i | \(-0.804445\pi\) | ||||
−0.817146 | + | 0.576430i | \(0.804445\pi\) | |||||||
\(434\) | −82.6992 | + | 130.537i | −0.190551 | + | 0.300776i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 195.035 | + | 412.806i | 0.447327 | + | 0.946802i | ||||
\(437\) | −69.9256 | −0.160013 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.253i | 0.524495i | 0.965001 | + | 0.262247i | \(0.0844636\pi\) | ||||
−0.965001 | + | 0.262247i | \(0.915536\pi\) | |||||||
\(440\) | 32.3933 | − | 261.309i | 0.0736211 | − | 0.593884i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −207.314 | + | 327.235i | −0.469035 | + | 0.740350i | ||||
\(443\) | − | 63.6893i | − | 0.143768i | −0.997413 | − | 0.0718841i | \(-0.977099\pi\) | ||
0.997413 | − | 0.0718841i | \(-0.0229012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 359.512 | 0.807891 | ||||||||
\(446\) | 502.881 | + | 318.591i | 1.12754 | + | 0.714330i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 189.889 | − | 754.126i | 0.423860 | − | 1.68332i | ||||
\(449\) | 212.618 | 0.473536 | 0.236768 | − | 0.971566i | \(-0.423912\pi\) | ||||
0.236768 | + | 0.971566i | \(0.423912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.6428i | 0.130028i | ||||||||
\(452\) | 94.7153 | + | 200.472i | 0.209547 | + | 0.443523i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 119.179 | + | 75.5037i | 0.262509 | + | 0.166308i | ||||
\(455\) | 911.777i | 2.00390i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −436.548 | −0.955247 | −0.477624 | − | 0.878565i | \(-0.658502\pi\) | ||||
−0.477624 | + | 0.878565i | \(0.658502\pi\) | |||||||
\(458\) | −355.929 | + | 561.818i | −0.777138 | + | 1.22668i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 386.742 | − | 182.720i | 0.840742 | − | 0.397218i | ||||
\(461\) | 101.372 | 0.219895 | 0.109948 | − | 0.993937i | \(-0.464932\pi\) | ||||
0.109948 | + | 0.993937i | \(0.464932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 527.038i | 1.13831i | 0.822230 | + | 0.569155i | \(0.192730\pi\) | ||||
−0.822230 | + | 0.569155i | \(0.807270\pi\) | |||||||
\(464\) | 512.031 | − | 622.865i | 1.10351 | − | 1.34238i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −450.892 | + | 711.712i | −0.967579 | + | 1.52728i | ||||
\(467\) | 460.432i | 0.985936i | 0.870048 | + | 0.492968i | \(0.164088\pi\) | ||||
−0.870048 | + | 0.492968i | \(0.835912\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1256.86 | 2.67986 | ||||||||
\(470\) | −398.125 | − | 252.225i | −0.847074 | − | 0.536648i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −88.3921 | + | 713.039i | −0.187271 | + | 1.51068i | ||||
\(473\) | 292.400 | 0.618181 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 84.7070i | − | 0.178331i | ||||||
\(476\) | −756.141 | + | 357.247i | −1.58853 | + | 0.750519i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 396.679 | + | 251.309i | 0.829872 | + | 0.525750i | ||||
\(479\) | 175.329i | 0.366031i | 0.983110 | + | 0.183016i | \(0.0585859\pi\) | ||||
−0.983110 | + | 0.183016i | \(0.941414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −406.188 | −0.844465 | ||||||||
\(482\) | 283.032 | − | 446.753i | 0.587204 | − | 0.926873i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −165.097 | − | 349.440i | −0.341109 | − | 0.721982i | ||||
\(485\) | 419.104 | 0.864131 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 726.060i | − | 1.49088i | −0.666571 | − | 0.745441i | \(-0.732239\pi\) | ||
0.666571 | − | 0.745441i | \(-0.267761\pi\) | |||||||
\(488\) | −681.870 | − | 84.5283i | −1.39727 | − | 0.173214i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −703.820 | + | 1110.95i | −1.43637 | + | 2.26724i | ||||
\(491\) | − | 812.931i | − | 1.65566i | −0.560976 | − | 0.827832i | \(-0.689574\pi\) | ||
0.560976 | − | 0.827832i | \(-0.310426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −867.091 | −1.75880 | ||||||||
\(494\) | 82.8999 | + | 52.5197i | 0.167813 | + | 0.106315i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −78.5918 | − | 64.6070i | −0.158451 | − | 0.130256i | ||||
\(497\) | 816.672 | 1.64320 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 454.585i | − | 0.910993i | −0.890238 | − | 0.455496i | \(-0.849462\pi\) | ||
0.890238 | − | 0.455496i | \(-0.150538\pi\) | |||||||
\(500\) | −63.4072 | − | 134.206i | −0.126814 | − | 0.268412i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −239.246 | − | 151.570i | −0.476586 | − | 0.301932i | ||||
\(503\) | 709.318i | 1.41018i | 0.709120 | + | 0.705088i | \(0.249092\pi\) | ||||
−0.709120 | + | 0.705088i | \(0.750908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 488.128 | 0.966591 | ||||||||
\(506\) | −84.7823 | + | 133.825i | −0.167554 | + | 0.264476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 143.339 | − | 67.7219i | 0.282163 | − | 0.133311i | ||||
\(509\) | 112.989 | 0.221983 | 0.110991 | − | 0.993821i | \(-0.464597\pi\) | ||||
0.110991 | + | 0.993821i | \(0.464597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1330.27i | − | 2.60326i | ||||||
\(512\) | 477.350 | + | 185.151i | 0.932324 | + | 0.361623i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 431.864 | − | 681.678i | 0.840203 | − | 1.32622i | ||||
\(515\) | 355.384i | 0.690066i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 174.555 | 0.337631 | ||||||||
\(518\) | −740.751 | − | 469.289i | −1.43002 | − | 0.905963i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −595.736 | − | 73.8507i | −1.14565 | − | 0.142021i | ||||
\(521\) | −194.174 | −0.372694 | −0.186347 | − | 0.982484i | \(-0.559665\pi\) | ||||
−0.186347 | + | 0.982484i | \(0.559665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 448.356i | − | 0.857278i | −0.903476 | − | 0.428639i | \(-0.858993\pi\) | ||
0.903476 | − | 0.428639i | \(-0.141007\pi\) | |||||||
\(524\) | −601.438 | + | 284.156i | −1.14778 | + | 0.542283i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −556.419 | − | 352.509i | −1.05783 | − | 0.670170i | ||||
\(527\) | 109.408i | 0.207605i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 271.653 | 0.513522 | ||||||||
\(530\) | −275.432 | + | 434.757i | −0.519684 | + | 0.820297i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 90.5031 | + | 191.557i | 0.170119 | + | 0.360069i | ||||
\(533\) | 133.695 | 0.250834 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 360.668i | − | 0.674145i | ||||||
\(536\) | −101.801 | + | 821.204i | −0.189927 | + | 1.53210i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 268.746 | − | 424.203i | 0.499527 | − | 0.788481i | ||||
\(539\) | − | 487.088i | − | 0.903689i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 260.593 | 0.481687 | 0.240844 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240844 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(542\) | 253.869 | + | 160.834i | 0.468393 | + | 0.296741i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −172.173 | − | 522.983i | −0.316495 | − | 0.961366i | ||||
\(545\) | 760.837 | 1.39603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 698.050i | − | 1.27614i | −0.769978 | − | 0.638071i | \(-0.779733\pi\) | ||
0.769978 | − | 0.638071i | \(-0.220267\pi\) | |||||||
\(548\) | 286.825 | + | 607.086i | 0.523403 | + | 1.10782i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −162.114 | − | 102.704i | −0.294752 | − | 0.186735i | ||||
\(551\) | 219.664i | 0.398664i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 806.189 | 1.45785 | ||||||||
\(554\) | 189.890 | − | 299.732i | 0.342761 | − | 0.541032i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 39.8546 | − | 18.8297i | 0.0716809 | − | 0.0338664i | ||||
\(557\) | −344.964 | −0.619324 | −0.309662 | − | 0.950847i | \(-0.600216\pi\) | ||||
−0.309662 | + | 0.950847i | \(0.600216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 666.617i | − | 1.19252i | ||||||
\(560\) | −1001.10 | − | 822.963i | −1.78768 | − | 1.46958i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 163.642 | − | 258.301i | 0.291178 | − | 0.459611i | ||||
\(563\) | 1075.78i | 1.91080i | 0.295314 | + | 0.955400i | \(0.404576\pi\) | ||||
−0.295314 | + | 0.955400i | \(0.595424\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 369.488 | 0.653960 | ||||||||
\(566\) | −593.264 | − | 375.851i | −1.04817 | − | 0.664048i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −66.1476 | + | 533.597i | −0.116457 | + | 0.939432i | ||||
\(569\) | −206.716 | −0.363298 | −0.181649 | − | 0.983363i | \(-0.558143\pi\) | ||||
−0.181649 | + | 0.983363i | \(0.558143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 908.816i | 1.59162i | 0.605545 | + | 0.795811i | \(0.292955\pi\) | ||||
−0.605545 | + | 0.795811i | \(0.707045\pi\) | |||||||
\(572\) | 201.026 | − | 94.9770i | 0.351444 | − | 0.166044i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 243.815 | + | 154.464i | 0.424764 | + | 0.269101i | ||||
\(575\) | − | 311.747i | − | 0.542169i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −766.400 | −1.32825 | −0.664125 | − | 0.747622i | \(-0.731196\pi\) | ||||
−0.664125 | + | 0.747622i | \(0.731196\pi\) | |||||||
\(578\) | −7.54576 | + | 11.9106i | −0.0130550 | + | 0.0206066i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −573.997 | − | 1214.91i | −0.989649 | − | 2.09467i | ||||
\(581\) | −48.7822 | −0.0839625 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 190.617i | − | 0.326958i | ||||||
\(584\) | 869.170 | + | 107.747i | 1.48830 | + | 0.184498i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 151.803 | − | 239.614i | 0.259049 | − | 0.408897i | ||||
\(587\) | − | 730.808i | − | 1.24499i | −0.782625 | − | 0.622494i | \(-0.786120\pi\) | ||
0.782625 | − | 0.622494i | \(-0.213880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7168 | 0.0470573 | ||||||||
\(590\) | 1011.45 | + | 640.783i | 1.71432 | + | 1.08607i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 366.622 | − | 445.981i | 0.619294 | − | 0.753346i | ||||
\(593\) | −770.478 | −1.29929 | −0.649644 | − | 0.760239i | \(-0.725082\pi\) | ||||
−0.649644 | + | 0.760239i | \(0.725082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1393.63i | 2.34224i | ||||||||
\(596\) | 416.044 | + | 880.589i | 0.698060 | + | 1.47750i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 305.096 | + | 193.288i | 0.510194 | + | 0.323224i | ||||
\(599\) | − | 312.936i | − | 0.522430i | −0.965281 | − | 0.261215i | \(-0.915877\pi\) | ||
0.965281 | − | 0.261215i | \(-0.0841232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 70.1694 | 0.116754 | 0.0583772 | − | 0.998295i | \(-0.481407\pi\) | ||||
0.0583772 | + | 0.998295i | \(0.481407\pi\) | |||||||
\(602\) | 770.176 | − | 1215.69i | 1.27936 | − | 2.01941i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 422.284 | − | 199.513i | 0.699145 | − | 0.330319i | ||||
\(605\) | −644.047 | −1.06454 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 128.626i | − | 0.211904i | −0.994371 | − | 0.105952i | \(-0.966211\pi\) | ||
0.994371 | − | 0.105952i | \(-0.0337889\pi\) | |||||||
\(608\) | −132.490 | + | 43.6174i | −0.217911 | + | 0.0717392i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −612.773 | + | 967.234i | −1.00455 | + | 1.58563i | ||||
\(611\) | − | 397.954i | − | 0.651316i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 113.004 | 0.184346 | 0.0921731 | − | 0.995743i | \(-0.470619\pi\) | ||||
0.0921731 | + | 0.995743i | \(0.470619\pi\) | |||||||
\(614\) | −620.129 | − | 392.871i | −1.00998 | − | 0.639855i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 476.336 | + | 59.0492i | 0.773273 | + | 0.0958591i | ||||
\(617\) | −335.800 | −0.544246 | −0.272123 | − | 0.962262i | \(-0.587726\pi\) | ||||
−0.272123 | + | 0.962262i | \(0.587726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 173.951i | − | 0.281019i | −0.990079 | − | 0.140510i | \(-0.955126\pi\) | ||
0.990079 | − | 0.140510i | \(-0.0448741\pi\) | |||||||
\(620\) | −153.295 | + | 72.4257i | −0.247249 | + | 0.116816i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 616.897 | + | 390.824i | 0.991796 | + | 0.628334i | ||||
\(623\) | 655.348i | 1.05192i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −733.182 | −1.17309 | ||||||||
\(626\) | −452.322 | + | 713.970i | −0.722560 | + | 1.14053i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 71.4651 | + | 151.261i | 0.113798 | + | 0.240862i | ||||
\(629\) | −620.851 | −0.987044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0362i | 0.0507705i | 0.999678 | + | 0.0253852i | \(0.00808124\pi\) | ||||
−0.999678 | + | 0.0253852i | \(0.991919\pi\) | |||||||
\(632\) | −65.2985 | + | 526.748i | −0.103320 | + | 0.833462i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −151.389 | + | 238.961i | −0.238784 | + | 0.376909i | ||||
\(635\) | − | 264.186i | − | 0.416040i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1110.47 | −1.74328 | ||||||||
\(638\) | 420.397 | + | 266.335i | 0.658929 | + | 0.417452i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 618.793 | − | 587.442i | 0.966864 | − | 0.917878i | ||||
\(641\) | 711.508 | 1.11000 | 0.554999 | − | 0.831851i | \(-0.312719\pi\) | ||||
0.554999 | + | 0.831851i | \(0.312719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 261.269i | 0.406329i | 0.979145 | + | 0.203164i | \(0.0651226\pi\) | ||||
−0.979145 | + | 0.203164i | \(0.934877\pi\) | |||||||
\(644\) | 333.078 | + | 704.985i | 0.517202 | + | 1.09470i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 126.711 | + | 80.2754i | 0.196147 | + | 0.124265i | ||||
\(647\) | 658.867i | 1.01834i | 0.860666 | + | 0.509170i | \(0.170048\pi\) | ||||
−0.860666 | + | 0.509170i | \(0.829952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −443.463 | −0.683302 | ||||||||
\(650\) | −234.147 | + | 369.590i | −0.360226 | + | 0.568599i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1032.06 | + | 487.608i | −1.58292 | + | 0.747866i | ||||
\(653\) | 89.8604 | 0.137612 | 0.0688058 | − | 0.997630i | \(-0.478081\pi\) | ||||
0.0688058 | + | 0.997630i | \(0.478081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1108.50i | 1.69237i | ||||||||
\(656\) | −120.672 | + | 146.792i | −0.183951 | + | 0.223769i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 459.777 | − | 725.736i | 0.698748 | − | 1.10294i | ||||
\(659\) | − | 317.095i | − | 0.481176i | −0.970627 | − | 0.240588i | \(-0.922660\pi\) | ||
0.970627 | − | 0.240588i | \(-0.0773403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −338.063 | −0.511442 | −0.255721 | − | 0.966751i | \(-0.582313\pi\) | ||||
−0.255721 | + | 0.966751i | \(0.582313\pi\) | |||||||
\(662\) | 467.374 | + | 296.096i | 0.706003 | + | 0.447275i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.95119 | − | 31.8733i | 0.00595058 | − | 0.0480019i | ||||
\(665\) | 353.055 | 0.530911 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 808.429i | 1.21204i | ||||||||
\(668\) | −245.853 | + | 116.156i | −0.368044 | + | 0.173886i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1164.88 | + | 737.988i | 1.73863 | + | 1.10147i | ||||
\(671\) | − | 424.078i | − | 0.632009i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 300.946 | 0.447170 | 0.223585 | − | 0.974684i | \(-0.428224\pi\) | ||||
0.223585 | + | 0.974684i | \(0.428224\pi\) | |||||||
\(674\) | 407.045 | − | 642.501i | 0.603924 | − | 0.953265i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 72.2455 | + | 152.913i | 0.106872 | + | 0.226203i | ||||
\(677\) | 366.287 | 0.541044 | 0.270522 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270522 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 763.978i | 1.12515i | ||||||||
\(680\) | −910.572 | − | 112.879i | −1.33908 | − | 0.165999i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.6056 | − | 53.0448i | 0.0492750 | − | 0.0777783i | ||||
\(683\) | 157.941i | 0.231247i | 0.993293 | + | 0.115623i | \(0.0368866\pi\) | ||||
−0.993293 | + | 0.115623i | \(0.963113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1118.91 | 1.63345 | ||||||||
\(686\) | −1019.21 | − | 645.701i | −1.48573 | − | 0.941254i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 731.924 | + | 601.684i | 1.06384 | + | 0.874540i | ||||
\(689\) | −434.571 | −0.630727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 340.395i | 0.492613i | 0.969192 | + | 0.246306i | \(0.0792170\pi\) | ||||
−0.969192 | + | 0.246306i | \(0.920783\pi\) | |||||||
\(692\) | 552.654 | + | 1169.74i | 0.798633 | + | 1.69037i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 907.424 | + | 574.882i | 1.30753 | + | 0.828360i | ||||
\(695\) | − | 73.4554i | − | 0.105691i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 204.350 | 0.293185 | ||||||||
\(698\) | −126.214 | + | 199.223i | −0.180822 | + | 0.285419i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −854.011 | + | 403.487i | −1.22002 | + | 0.576410i | ||||
\(701\) | −68.5225 | −0.0977496 | −0.0488748 | − | 0.998805i | \(-0.515564\pi\) | ||||
−0.0488748 | + | 0.998805i | \(0.515564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 157.283i | 0.223731i | ||||||||
\(704\) | −77.1631 | + | 306.446i | −0.109607 | + | 0.435292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −411.421 | + | 649.409i | −0.582749 | + | 0.919843i | ||||
\(707\) | 889.802i | 1.25856i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −508.634 | −0.717396 | −0.358698 | − | 0.933454i | \(-0.616779\pi\) | ||||
−0.358698 | + | 0.933454i | \(0.616779\pi\) | |||||||
\(710\) | 756.909 | + | 479.525i | 1.06607 | + | 0.675388i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −428.191 | − | 53.0809i | −0.601392 | − | 0.0745519i | ||||
\(713\) | 102.006 | 0.143066 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 370.508i | − | 0.518194i | ||||||
\(716\) | 1018.91 | − | 481.394i | 1.42305 | − | 0.672338i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 376.180 | + | 238.322i | 0.523927 | + | 0.331925i | ||||
\(719\) | − | 1118.37i | − | 1.55545i | −0.628605 | − | 0.777725i | \(-0.716374\pi\) | ||
0.628605 | − | 0.777725i | \(-0.283626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −647.824 | −0.898508 | ||||||||
\(722\) | 20.3365 | − | 32.1002i | 0.0281669 | − | 0.0444602i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −476.072 | − | 1007.64i | −0.657558 | − | 1.39177i | ||||
\(725\) | −979.320 | −1.35079 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 421.983i | − | 0.580444i | −0.956959 | − | 0.290222i | \(-0.906271\pi\) | ||
0.956959 | − | 0.290222i | \(-0.0937291\pi\) | |||||||
\(728\) | 134.621 | − | 1085.96i | 0.184919 | − | 1.49170i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 781.093 | − | 1232.92i | 1.06999 | − | 1.68893i | ||||
\(731\) | − | 1018.91i | − | 1.39386i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 484.508 | 0.660994 | 0.330497 | − | 0.943807i | \(-0.392784\pi\) | ||||
0.330497 | + | 0.943807i | \(0.392784\pi\) | |||||||
\(734\) | 119.174 | + | 75.5005i | 0.162362 | + | 0.102862i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −487.601 | + | 160.525i | −0.662502 | + | 0.218105i | ||||
\(737\) | −510.735 | −0.692991 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 523.500i | − | 0.708390i | −0.935172 | − | 0.354195i | \(-0.884755\pi\) | ||
0.935172 | − | 0.354195i | \(-0.115245\pi\) | |||||||
\(740\) | −410.991 | − | 869.893i | −0.555393 | − | 1.17553i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −792.513 | − | 502.082i | −1.06808 | − | 0.676660i | ||||
\(743\) | 1021.39i | 1.37468i | 0.726336 | + | 0.687340i | \(0.241222\pi\) | ||||
−0.726336 | + | 0.687340i | \(0.758778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1623.00 | 2.17853 | ||||||||
\(746\) | −274.397 | + | 433.123i | −0.367824 | + | 0.580594i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 307.265 | − | 145.171i | 0.410782 | − | 0.194078i | ||||
\(749\) | 657.456 | 0.877778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 263.896i | − | 0.351393i | −0.984444 | − | 0.175697i | \(-0.943782\pi\) | ||
0.984444 | − | 0.175697i | \(-0.0562177\pi\) | |||||||
\(752\) | 436.941 | + | 359.191i | 0.581038 | + | 0.477647i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 607.194 | − | 958.427i | 0.805297 | − | 1.27112i | ||||
\(755\) | − | 778.305i | − | 1.03087i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 233.092 | 0.307916 | 0.153958 | − | 0.988077i | \(-0.450798\pi\) | ||||
0.153958 | + | 0.988077i | \(0.450798\pi\) | |||||||
\(758\) | 569.649 | + | 360.891i | 0.751516 | + | 0.476109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.5963 | + | 230.679i | −0.0376266 | + | 0.303525i | ||||
\(761\) | −835.785 | −1.09827 | −0.549136 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549136 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1386.92i | 1.81772i | ||||||||
\(764\) | −360.906 | + | 170.514i | −0.472390 | + | 0.223186i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 90.9029 | + | 57.5898i | 0.118672 | + | 0.0751826i | ||||
\(767\) | 1011.01i | 1.31814i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −467.786 | −0.608304 | −0.304152 | − | 0.952623i | \(-0.598373\pi\) | ||||
−0.304152 | + | 0.952623i | \(0.598373\pi\) | |||||||
\(770\) | 428.067 | − | 675.684i | 0.555931 | − | 0.877511i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −432.084 | − | 914.539i | −0.559695 | − | 1.18464i | ||||
\(773\) | 85.5085 | 0.110619 | 0.0553095 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553095 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 123.569i | 0.159443i | ||||||||
\(776\) | −499.168 | − | 61.8795i | −0.643257 | − | 0.0797416i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −822.209 | + | 1297.82i | −1.05682 | + | 1.66815i | ||||
\(779\) | − | 51.7689i | − | 0.0664556i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −331.862 | −0.424919 | ||||||||
\(782\) | 466.334 | + | 295.437i | 0.596335 | + | 0.377797i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1002.30 | − | 1219.26i | 1.27845 | − | 1.55518i | ||||
\(785\) | 278.788 | 0.355144 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7664i | 0.0251162i | 0.999921 | + | 0.0125581i | \(0.00399747\pi\) | ||||
−0.999921 | + | 0.0125581i | \(0.996003\pi\) | |||||||
\(788\) | −21.7635 | − | 46.0641i | −0.0276186 | − | 0.0584569i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 747.193 | + | 473.370i | 0.945813 | + | 0.599203i | ||||
\(791\) | 673.533i | 0.851496i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −966.819 | −1.21919 | ||||||||
\(794\) | −141.999 | + | 224.138i | −0.178839 | + | 0.282290i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 899.905 | − | 425.170i | 1.13053 | − | 0.534133i | ||||
\(797\) | 462.093 | 0.579791 | 0.289895 | − | 0.957058i | \(-0.406380\pi\) | ||||
0.289895 | + | 0.957058i | \(0.406380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 608.266i | − | 0.761284i | ||||||
\(800\) | −194.458 | − | 590.674i | −0.243073 | − | 0.738343i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −120.716 | + | 190.544i | −0.150519 | + | 0.237586i | ||||
\(803\) | 540.566i | 0.673183i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1299.35 | 1.61410 | ||||||||
\(806\) | −120.932 | − | 76.6145i | −0.150040 | − | 0.0950552i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −581.379 | − | 72.0708i | −0.719528 | − | 0.0891966i | ||||
\(809\) | 1230.01 | 1.52041 | 0.760206 | − | 0.649682i | \(-0.225098\pi\) | ||||
0.760206 | + | 0.649682i | \(0.225098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 512.789i | 0.632292i | 0.948711 | + | 0.316146i | \(0.102389\pi\) | ||||
−0.948711 | + | 0.316146i | \(0.897611\pi\) | |||||||
\(812\) | 2214.64 | − | 1046.33i | 2.72739 | − | 1.28858i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 301.011 | + | 190.700i | 0.369792 | + | 0.234275i | ||||
\(815\) | 1902.18i | 2.33396i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −258.126 | −0.315943 | ||||||||
\(818\) | 865.752 | − | 1366.55i | 1.05838 | − | 1.67060i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 135.276 | + | 286.321i | 0.164970 | + | 0.349172i | ||||
\(821\) | −289.781 | −0.352961 | −0.176481 | − | 0.984304i | \(-0.556471\pi\) | ||||
−0.176481 | + | 0.984304i | \(0.556471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1455.81i | − | 1.76891i | −0.466629 | − | 0.884453i | \(-0.654532\pi\) | ||
0.466629 | − | 0.884453i | \(-0.345468\pi\) | |||||||
\(824\) | 52.4715 | − | 423.275i | 0.0636790 | − | 0.513683i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1168.07 | + | 1843.75i | −1.41413 | + | 2.23214i | ||||
\(827\) | − | 453.430i | − | 0.548282i | −0.961689 | − | 0.274141i | \(-0.911606\pi\) | ||
0.961689 | − | 0.274141i | \(-0.0883936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1194.07 | −1.44038 | −0.720190 | − | 0.693777i | \(-0.755945\pi\) | ||||
−0.720190 | + | 0.693777i | \(0.755945\pi\) | |||||||
\(830\) | −45.2123 | − | 28.6434i | −0.0544727 | − | 0.0345102i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 698.640 | + | 175.918i | 0.839711 | + | 0.211440i | ||||
\(833\) | −1697.33 | −2.03762 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 453.129i | 0.542670i | ||||||||
\(836\) | −36.7767 | − | 77.8408i | −0.0439913 | − | 0.0931110i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 957.773 | + | 606.779i | 1.14293 | + | 0.724080i | ||||
\(839\) | − | 139.199i | − | 0.165911i | −0.996553 | − | 0.0829554i | \(-0.973564\pi\) | ||
0.996553 | − | 0.0829554i | \(-0.0264359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1698.59 | 2.01973 | ||||||||
\(842\) | 321.378 | − | 507.280i | 0.381684 | − | 0.602470i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 949.670 | − | 448.682i | 1.12520 | − | 0.531614i | ||||
\(845\) | 281.832 | 0.333529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1174.02i | − | 1.38610i | ||||||
\(848\) | 392.241 | − | 477.145i | 0.462548 | − | 0.562671i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −357.889 | + | 564.911i | −0.421046 | + | 0.664601i | ||||
\(851\) | 578.848i | 0.680197i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 389.779 | 0.456951 | 0.228476 | − | 0.973550i | \(-0.426626\pi\) | ||||
0.228476 | + | 0.973550i | \(0.426626\pi\) | |||||||
\(854\) | −1763.16 | − | 1117.01i | −2.06459 | − | 1.30798i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −53.2516 | + | 429.568i | −0.0622098 | + | 0.501832i | ||||
\(857\) | 1341.14 | 1.56493 | 0.782464 | − | 0.622696i | \(-0.213963\pi\) | ||||
0.782464 | + | 0.622696i | \(0.213963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 551.747i | − | 0.642313i | −0.947026 | − | 0.321157i | \(-0.895928\pi\) | ||
0.947026 | − | 0.321157i | \(-0.104072\pi\) | |||||||
\(860\) | 1427.63 | − | 674.499i | 1.66003 | − | 0.784301i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1278.31 | + | 809.848i | 1.48296 | + | 0.939499i | ||||
\(863\) | − | 1298.16i | − | 1.50425i | −0.659023 | − | 0.752123i | \(-0.729030\pi\) | ||
0.659023 | − | 0.752123i | \(-0.270970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2155.92 | 2.49240 | ||||||||
\(866\) | 757.427 | − | 1195.56i | 0.874627 | − | 1.38056i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −132.024 | − | 279.438i | −0.152101 | − | 0.321934i | ||||
\(869\) | −327.602 | −0.376987 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1164.38i | 1.33683i | ||||||||
\(872\) | −906.184 | − | 112.335i | −1.03920 | − | 0.128825i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74.8444 | − | 118.138i | 0.0856343 | − | 0.135170i | ||||
\(875\) | − | 450.897i | − | 0.515311i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 943.666 | 1.07602 | 0.538008 | − | 0.842940i | \(-0.319177\pi\) | ||||
0.538008 | + | 0.842940i | \(0.319177\pi\) | |||||||
\(878\) | −389.010 | − | 246.450i | −0.443063 | − | 0.280695i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 406.806 | + | 334.418i | 0.462280 | + | 0.380021i | ||||
\(881\) | −1220.11 | −1.38492 | −0.692460 | − | 0.721456i | \(-0.743473\pi\) | ||||
−0.692460 | + | 0.721456i | \(0.743473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1315.99i | 1.49036i | 0.666862 | + | 0.745181i | \(0.267637\pi\) | ||||
−0.666862 | + | 0.745181i | \(0.732363\pi\) | |||||||
\(884\) | −330.962 | − | 700.507i | −0.374392 | − | 0.792429i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 107.602 | + | 68.1695i | 0.121447 | + | 0.0769407i | ||||
\(887\) | 588.646i | 0.663637i | 0.943343 | + | 0.331819i | \(0.107662\pi\) | ||||
−0.943343 | + | 0.331819i | \(0.892338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 481.580 | 0.541710 | ||||||||
\(890\) | −384.801 | + | 607.390i | −0.432361 | + | 0.682461i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1076.51 | + | 508.609i | −1.20685 | + | 0.570190i | ||||
\(893\) | −154.095 | −0.172559 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1877.93i | − | 2.09825i | ||||||
\(896\) | 1070.84 | + | 1127.99i | 1.19513 | + | 1.25892i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −227.574 | + | 359.215i | −0.253423 | + | 0.400016i | ||||
\(899\) | − | 320.441i | − | 0.356441i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −664.234 | −0.737219 | ||||||||
\(902\) | −99.0762 | − | 62.7679i | −0.109841 | − | 0.0695875i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −440.073 | − | 54.5538i | −0.486807 | − | 0.0603472i | ||||
\(905\) | −1857.17 | −2.05212 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 446.540i | 0.492326i | 0.969228 | + | 0.246163i | \(0.0791699\pi\) | ||||
−0.969228 | + | 0.246163i | \(0.920830\pi\) | |||||||
\(908\) | −255.125 | + | 120.537i | −0.280975 | + | 0.132749i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1540.43 | − | 975.914i | −1.69278 | − | 1.07243i | ||||
\(911\) | 1089.84i | 1.19632i | 0.801378 | + | 0.598158i | \(0.204100\pi\) | ||||
−0.801378 | + | 0.598158i | \(0.795900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.8231 | 0.0217120 | ||||||||
\(914\) | 467.256 | − | 737.542i | 0.511221 | − | 0.806939i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −568.217 | − | 1202.68i | −0.620324 | − | 1.31296i | ||||
\(917\) | −2020.67 | −2.20357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1127.18i | 1.22653i | 0.789879 | + | 0.613263i | \(0.210144\pi\) | ||||
−0.789879 | + | 0.613263i | \(0.789856\pi\) | |||||||
\(920\) | −105.243 | + | 848.968i | −0.114394 | + | 0.922791i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −108.503 | + | 171.266i | −0.117682 | + | 0.185755i | ||||
\(923\) | 756.585i | 0.819702i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −701.209 | −0.758064 | ||||||||
\(926\) | −890.423 | − | 564.111i | −0.961580 | − | 0.609192i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 504.273 | + | 1531.75i | 0.543397 | + | 1.65059i | ||||
\(929\) | −1581.94 | −1.70284 | −0.851421 | − | 0.524482i | \(-0.824259\pi\) | ||||
−0.851421 | + | 0.524482i | \(0.824259\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 429.993i | 0.461862i | ||||||||
\(932\) | −719.818 | − | 1523.55i | −0.772337 | − | 1.63471i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −777.894 | − | 492.820i | −0.832863 | − | 0.527645i | ||||
\(935\) | − | 566.315i | − | 0.605685i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 176.071 | 0.187909 | 0.0939547 | − | 0.995576i | \(-0.470049\pi\) | ||||
0.0939547 | + | 0.995576i | \(0.470049\pi\) | |||||||
\(938\) | −1345.27 | + | 2123.44i | −1.43419 | + | 2.26380i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 852.260 | − | 402.660i | 0.906660 | − | 0.428361i | ||||
\(941\) | 1629.91 | 1.73210 | 0.866052 | − | 0.499954i | \(-0.166650\pi\) | ||||
0.866052 | + | 0.499954i | \(0.166650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 190.525i | − | 0.202041i | ||||||
\(944\) | −1110.06 | − | 912.533i | −1.17591 | − | 0.966667i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −312.968 | + | 494.005i | −0.330833 | + | 0.522204i | ||||
\(947\) | − | 1141.57i | − | 1.20546i | −0.797945 | − | 0.602731i | \(-0.794079\pi\) | ||
0.797945 | − | 0.602731i | \(-0.205921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1232.39 | 1.29862 | ||||||||
\(950\) | 143.111 | + | 90.6656i | 0.150644 | + | 0.0954375i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 205.766 | − | 1659.87i | 0.216141 | − | 1.74356i | ||||
\(953\) | 824.746 | 0.865421 | 0.432711 | − | 0.901533i | \(-0.357557\pi\) | ||||
0.432711 | + | 0.901533i | \(0.357557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 665.180i | 0.696524i | ||||||||
\(956\) | −849.165 | + | 401.197i | −0.888248 | + | 0.419663i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −296.216 | − | 187.662i | −0.309203 | − | 0.195890i | ||||
\(959\) | 2039.65i | 2.12685i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 920.567 | 0.957927 | ||||||||
\(962\) | 434.760 | − | 686.249i | 0.451934 | − | 0.713357i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 451.842 | + | 956.358i | 0.468716 | + | 0.992073i | ||||
\(965\) | −1685.57 | −1.74671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 286.436i | 0.296211i | 0.988972 | + | 0.148105i | \(0.0473175\pi\) | ||||
−0.988972 | + | 0.148105i | \(0.952683\pi\) | |||||||
\(968\) | 767.083 | + | 95.0918i | 0.792442 | + | 0.0982353i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −448.585 | + | 708.070i | −0.462458 | + | 0.729969i | ||||
\(971\) | − | 509.431i | − | 0.524646i | −0.964980 | − | 0.262323i | \(-0.915511\pi\) | ||
0.964980 | − | 0.262323i | \(-0.0844886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 133.901 | 0.137616 | ||||||||
\(974\) | 1226.67 | + | 777.133i | 1.25941 | + | 0.797878i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 872.644 | − | 1061.54i | 0.894103 | − | 1.08764i | ||||
\(977\) | −92.0031 | −0.0941690 | −0.0470845 | − | 0.998891i | \(-0.514993\pi\) | ||||
−0.0470845 | + | 0.998891i | \(0.514993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 266.307i | − | 0.272019i | ||||||
\(980\) | −1123.60 | − | 2378.19i | −1.14653 | − | 2.42672i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1373.44 | + | 870.115i | 1.39861 | + | 0.886065i | ||||
\(983\) | − | 699.319i | − | 0.711413i | −0.934598 | − | 0.355706i | \(-0.884240\pi\) | ||
0.934598 | − | 0.355706i | \(-0.115760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −84.9000 | −0.0861929 | ||||||||
\(986\) | 928.085 | − | 1464.94i | 0.941262 | − | 1.48574i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −177.463 | + | 83.8441i | −0.179618 | + | 0.0848625i | ||||
\(989\) | −949.978 | −0.960544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1338.85i | − | 1.35101i | −0.737356 | − | 0.675505i | \(-0.763926\pi\) | ||
0.737356 | − | 0.675505i | \(-0.236074\pi\) | |||||||
\(992\) | 193.273 | − | 63.6281i | 0.194832 | − | 0.0641412i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −874.120 | + | 1379.76i | −0.879396 | + | 1.38809i | ||||
\(995\) | − | 1658.60i | − | 1.66694i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1147.47 | −1.15092 | −0.575461 | − | 0.817829i | \(-0.695177\pi\) | ||||
−0.575461 | + | 0.817829i | \(0.695177\pi\) | |||||||
\(998\) | 768.016 | + | 486.562i | 0.769555 | + | 0.487538i | ||||
\(999\) | 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.343.12 | yes | 36 | |
3.2 | odd | 2 | inner | 684.3.g.d.343.25 | yes | 36 | |
4.3 | odd | 2 | inner | 684.3.g.d.343.11 | ✓ | 36 | |
12.11 | even | 2 | inner | 684.3.g.d.343.26 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.g.d.343.11 | ✓ | 36 | 4.3 | odd | 2 | inner | |
684.3.g.d.343.12 | yes | 36 | 1.1 | even | 1 | trivial | |
684.3.g.d.343.25 | yes | 36 | 3.2 | odd | 2 | inner | |
684.3.g.d.343.26 | yes | 36 | 12.11 | even | 2 | inner |