Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.8 | ||
Root | \(3.58727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.m.122.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.58727i | 1.79364i | 0.442398 | + | 0.896819i | \(0.354128\pi\) | ||||
−0.442398 | + | 0.896819i | \(0.645872\pi\) | |||||||
\(3\) | −2.74329 | − | 1.21424i | −0.914429 | − | 0.404746i | ||||
\(4\) | −8.86854 | −2.21714 | ||||||||
\(5\) | − | 2.08639i | − | 0.417279i | −0.977993 | − | 0.208639i | \(-0.933097\pi\) | ||
0.977993 | − | 0.208639i | \(-0.0669035\pi\) | |||||||
\(6\) | 4.35581 | − | 9.84093i | 0.725968 | − | 1.64015i | ||||
\(7\) | 8.86303 | 1.26615 | 0.633073 | − | 0.774092i | \(-0.281793\pi\) | ||||
0.633073 | + | 0.774092i | \(0.281793\pi\) | |||||||
\(8\) | − | 17.4648i | − | 2.18310i | ||||||
\(9\) | 6.05125 | + | 6.66201i | 0.672361 | + | 0.740223i | ||||
\(10\) | 7.48447 | 0.748447 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 24.3290 | + | 10.7685i | 2.02741 | + | 0.897377i | ||||
\(13\) | −1.64480 | −0.126523 | −0.0632617 | − | 0.997997i | \(-0.520150\pi\) | ||||
−0.0632617 | + | 0.997997i | \(0.520150\pi\) | |||||||
\(14\) | 31.7941i | 2.27101i | ||||||||
\(15\) | −2.53338 | + | 5.72358i | −0.168892 | + | 0.381572i | ||||
\(16\) | 27.1769 | 1.69855 | ||||||||
\(17\) | 12.4235i | 0.730794i | 0.930852 | + | 0.365397i | \(0.119067\pi\) | ||||
−0.930852 | + | 0.365397i | \(0.880933\pi\) | |||||||
\(18\) | −23.8985 | + | 21.7075i | −1.32769 | + | 1.20597i | ||||
\(19\) | 10.5657 | 0.556088 | 0.278044 | − | 0.960568i | \(-0.410314\pi\) | ||||
0.278044 | + | 0.960568i | \(0.410314\pi\) | |||||||
\(20\) | 18.5033i | 0.925163i | ||||||||
\(21\) | −24.3138 | − | 10.7618i | −1.15780 | − | 0.512468i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.3378i | 0.884251i | 0.896953 | + | 0.442126i | \(0.145775\pi\) | ||||
−0.896953 | + | 0.442126i | \(0.854225\pi\) | |||||||
\(24\) | −21.2064 | + | 47.9109i | −0.883601 | + | 1.99629i | ||||
\(25\) | 20.6470 | 0.825878 | ||||||||
\(26\) | − | 5.90037i | − | 0.226937i | ||||||
\(27\) | −8.51105 | − | 25.6235i | −0.315224 | − | 0.949017i | ||||
\(28\) | −78.6021 | −2.80722 | ||||||||
\(29\) | 11.6087i | 0.400299i | 0.979765 | + | 0.200149i | \(0.0641428\pi\) | ||||
−0.979765 | + | 0.200149i | \(0.935857\pi\) | |||||||
\(30\) | −20.5320 | − | 9.08793i | −0.684402 | − | 0.302931i | ||||
\(31\) | −23.3883 | −0.754460 | −0.377230 | − | 0.926120i | \(-0.623123\pi\) | ||||
−0.377230 | + | 0.926120i | \(0.623123\pi\) | |||||||
\(32\) | 27.6317i | 0.863489i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −44.5665 | −1.31078 | ||||||||
\(35\) | − | 18.4918i | − | 0.528336i | ||||||
\(36\) | −53.6658 | − | 59.0823i | −1.49072 | − | 1.64117i | ||||
\(37\) | 7.24593 | 0.195836 | 0.0979179 | − | 0.995194i | \(-0.468782\pi\) | ||||
0.0979179 | + | 0.995194i | \(0.468782\pi\) | |||||||
\(38\) | 37.9019i | 0.997420i | ||||||||
\(39\) | 4.51217 | + | 1.99719i | 0.115697 | + | 0.0512099i | ||||
\(40\) | −36.4384 | −0.910961 | ||||||||
\(41\) | 38.8768i | 0.948215i | 0.880467 | + | 0.474108i | \(0.157229\pi\) | ||||
−0.880467 | + | 0.474108i | \(0.842771\pi\) | |||||||
\(42\) | 38.6056 | − | 87.2204i | 0.919181 | − | 2.07668i | ||||
\(43\) | −15.8444 | −0.368474 | −0.184237 | − | 0.982882i | \(-0.558981\pi\) | ||||
−0.184237 | + | 0.982882i | \(0.558981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.8996 | − | 12.6253i | 0.308879 | − | 0.280562i | ||||
\(46\) | −72.9572 | −1.58603 | ||||||||
\(47\) | 45.3086i | 0.964013i | 0.876168 | + | 0.482006i | \(0.160092\pi\) | ||||
−0.876168 | + | 0.482006i | \(0.839908\pi\) | |||||||
\(48\) | −74.5539 | − | 32.9992i | −1.55321 | − | 0.687483i | ||||
\(49\) | 29.5532 | 0.603127 | ||||||||
\(50\) | 74.0663i | 1.48133i | ||||||||
\(51\) | 15.0851 | − | 34.0812i | 0.295786 | − | 0.668259i | ||||
\(52\) | 14.5870 | 0.280520 | ||||||||
\(53\) | 40.3160i | 0.760680i | 0.924847 | + | 0.380340i | \(0.124193\pi\) | ||||
−0.924847 | + | 0.380340i | \(0.875807\pi\) | |||||||
\(54\) | 91.9184 | − | 30.5315i | 1.70219 | − | 0.565398i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 154.791i | − | 2.76412i | ||||||
\(57\) | −28.9847 | − | 12.8292i | −0.508503 | − | 0.225074i | ||||
\(58\) | −41.6435 | −0.717991 | ||||||||
\(59\) | 113.181i | 1.91833i | 0.282847 | + | 0.959165i | \(0.408721\pi\) | ||||
−0.282847 | + | 0.959165i | \(0.591279\pi\) | |||||||
\(60\) | 22.4674 | − | 50.7598i | 0.374456 | − | 0.845996i | ||||
\(61\) | 77.5161 | 1.27076 | 0.635378 | − | 0.772202i | \(-0.280844\pi\) | ||||
0.635378 | + | 0.772202i | \(0.280844\pi\) | |||||||
\(62\) | − | 83.9001i | − | 1.35323i | ||||||
\(63\) | 53.6324 | + | 59.0456i | 0.851308 | + | 0.937231i | ||||
\(64\) | 9.58504 | 0.149766 | ||||||||
\(65\) | 3.43171i | 0.0527956i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62.9082 | 0.938929 | 0.469464 | − | 0.882951i | \(-0.344447\pi\) | ||||
0.469464 | + | 0.882951i | \(0.344447\pi\) | |||||||
\(68\) | − | 110.178i | − | 1.62027i | ||||||
\(69\) | 24.6949 | − | 55.7924i | 0.357897 | − | 0.808585i | ||||
\(70\) | 66.3350 | 0.947643 | ||||||||
\(71\) | − | 10.2125i | − | 0.143839i | −0.997410 | − | 0.0719193i | \(-0.977088\pi\) | ||
0.997410 | − | 0.0719193i | \(-0.0229124\pi\) | |||||||
\(72\) | 116.351 | − | 105.684i | 1.61598 | − | 1.46783i | ||||
\(73\) | −74.6222 | −1.02222 | −0.511111 | − | 0.859515i | \(-0.670766\pi\) | ||||
−0.511111 | + | 0.859515i | \(0.670766\pi\) | |||||||
\(74\) | 25.9931i | 0.351258i | ||||||||
\(75\) | −56.6405 | − | 25.0703i | −0.755207 | − | 0.334271i | ||||
\(76\) | −93.7020 | −1.23292 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.16445 | + | 16.1864i | −0.0918519 | + | 0.207518i | ||||
\(79\) | 86.3123 | 1.09256 | 0.546280 | − | 0.837602i | \(-0.316043\pi\) | ||||
0.546280 | + | 0.837602i | \(0.316043\pi\) | |||||||
\(80\) | − | 56.7016i | − | 0.708770i | ||||||
\(81\) | −7.76472 | + | 80.6270i | −0.0958608 | + | 0.995395i | ||||
\(82\) | −139.462 | −1.70075 | ||||||||
\(83\) | 11.8083i | 0.142269i | 0.997467 | + | 0.0711343i | \(0.0226619\pi\) | ||||
−0.997467 | + | 0.0711343i | \(0.977338\pi\) | |||||||
\(84\) | 215.628 | + | 95.4417i | 2.56700 | + | 1.13621i | ||||
\(85\) | 25.9203 | 0.304945 | ||||||||
\(86\) | − | 56.8381i | − | 0.660908i | ||||||
\(87\) | 14.0957 | − | 31.8459i | 0.162019 | − | 0.366045i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.5782i | 0.837957i | 0.907996 | + | 0.418979i | \(0.137612\pi\) | ||||
−0.907996 | + | 0.418979i | \(0.862388\pi\) | |||||||
\(90\) | 45.2904 | + | 49.8616i | 0.503227 | + | 0.554018i | ||||
\(91\) | −14.5779 | −0.160197 | ||||||||
\(92\) | − | 180.366i | − | 1.96050i | ||||||
\(93\) | 64.1607 | + | 28.3989i | 0.689900 | + | 0.305365i | ||||
\(94\) | −162.534 | −1.72909 | ||||||||
\(95\) | − | 22.0441i | − | 0.232044i | ||||||
\(96\) | 33.5514 | − | 75.8016i | 0.349494 | − | 0.789600i | ||||
\(97\) | −77.1678 | −0.795544 | −0.397772 | − | 0.917484i | \(-0.630217\pi\) | ||||
−0.397772 | + | 0.917484i | \(0.630217\pi\) | |||||||
\(98\) | 106.016i | 1.08179i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −183.108 | −1.83108 | ||||||||
\(101\) | 12.7954i | 0.126687i | 0.997992 | + | 0.0633436i | \(0.0201764\pi\) | ||||
−0.997992 | + | 0.0633436i | \(0.979824\pi\) | |||||||
\(102\) | 122.259 | + | 54.1143i | 1.19861 | + | 0.530533i | ||||
\(103\) | 70.5641 | 0.685088 | 0.342544 | − | 0.939502i | \(-0.388711\pi\) | ||||
0.342544 | + | 0.939502i | \(0.388711\pi\) | |||||||
\(104\) | 28.7262i | 0.276213i | ||||||||
\(105\) | −22.4534 | + | 50.7282i | −0.213842 | + | 0.483126i | ||||
\(106\) | −144.625 | −1.36438 | ||||||||
\(107\) | − | 184.220i | − | 1.72168i | −0.508873 | − | 0.860842i | \(-0.669938\pi\) | ||
0.508873 | − | 0.860842i | \(-0.330062\pi\) | |||||||
\(108\) | 75.4806 | + | 227.243i | 0.698895 | + | 2.10410i | ||||
\(109\) | −58.5394 | −0.537058 | −0.268529 | − | 0.963272i | \(-0.586538\pi\) | ||||
−0.268529 | + | 0.963272i | \(0.586538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.8777 | − | 8.79828i | −0.179078 | − | 0.0792638i | ||||
\(112\) | 240.869 | 2.15062 | ||||||||
\(113\) | 151.997i | 1.34511i | 0.740048 | + | 0.672555i | \(0.234803\pi\) | ||||
−0.740048 | + | 0.672555i | \(0.765197\pi\) | |||||||
\(114\) | 46.0220 | − | 103.976i | 0.403702 | − | 0.912070i | ||||
\(115\) | 42.4326 | 0.368979 | ||||||||
\(116\) | − | 102.952i | − | 0.887517i | ||||||
\(117\) | −9.95313 | − | 10.9577i | −0.0850695 | − | 0.0936556i | ||||
\(118\) | −406.013 | −3.44079 | ||||||||
\(119\) | 110.110i | 0.925292i | ||||||||
\(120\) | 99.9611 | + | 44.2449i | 0.833009 | + | 0.368708i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 278.071i | 2.27927i | ||||||||
\(123\) | 47.2057 | − | 106.650i | 0.383786 | − | 0.867076i | ||||
\(124\) | 207.420 | 1.67274 | ||||||||
\(125\) | − | 95.2375i | − | 0.761900i | ||||||
\(126\) | −211.813 | + | 192.394i | −1.68105 | + | 1.52694i | ||||
\(127\) | −14.2743 | −0.112396 | −0.0561979 | − | 0.998420i | \(-0.517898\pi\) | ||||
−0.0561979 | + | 0.998420i | \(0.517898\pi\) | |||||||
\(128\) | 144.911i | 1.13212i | ||||||||
\(129\) | 43.4657 | + | 19.2388i | 0.336943 | + | 0.149138i | ||||
\(130\) | −12.3105 | −0.0946961 | ||||||||
\(131\) | − | 153.686i | − | 1.17318i | −0.809885 | − | 0.586589i | \(-0.800471\pi\) | ||
0.809885 | − | 0.586589i | \(-0.199529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 93.6438 | 0.704088 | ||||||||
\(134\) | 225.669i | 1.68410i | ||||||||
\(135\) | −53.4606 | + | 17.7574i | −0.396005 | + | 0.131536i | ||||
\(136\) | 216.974 | 1.59540 | ||||||||
\(137\) | − | 80.6411i | − | 0.588621i | −0.955710 | − | 0.294311i | \(-0.904910\pi\) | ||
0.955710 | − | 0.294311i | \(-0.0950900\pi\) | |||||||
\(138\) | 200.143 | + | 88.5874i | 1.45031 | + | 0.641938i | ||||
\(139\) | 211.941 | 1.52476 | 0.762379 | − | 0.647130i | \(-0.224031\pi\) | ||||
0.762379 | + | 0.647130i | \(0.224031\pi\) | |||||||
\(140\) | 163.995i | 1.17139i | ||||||||
\(141\) | 55.0154 | − | 124.295i | 0.390180 | − | 0.881521i | ||||
\(142\) | 36.6352 | 0.257994 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 164.454 | + | 181.052i | 1.14204 | + | 1.25731i | ||||
\(145\) | 24.2202 | 0.167036 | ||||||||
\(146\) | − | 267.690i | − | 1.83350i | ||||||
\(147\) | −81.0730 | − | 35.8847i | −0.551517 | − | 0.244113i | ||||
\(148\) | −64.2608 | −0.434194 | ||||||||
\(149\) | − | 226.330i | − | 1.51899i | −0.650513 | − | 0.759495i | \(-0.725446\pi\) | ||
0.650513 | − | 0.759495i | \(-0.274554\pi\) | |||||||
\(150\) | 89.9342 | − | 203.185i | 0.599561 | − | 1.35457i | ||||
\(151\) | 272.729 | 1.80615 | 0.903076 | − | 0.429481i | \(-0.141304\pi\) | ||||
0.903076 | + | 0.429481i | \(0.141304\pi\) | |||||||
\(152\) | − | 184.527i | − | 1.21399i | ||||||
\(153\) | −82.7654 | + | 75.1777i | −0.540951 | + | 0.491357i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 48.7971i | 0.314820i | ||||||||
\(156\) | −40.0164 | − | 17.7121i | −0.256515 | − | 0.113539i | ||||
\(157\) | 6.05930 | 0.0385943 | 0.0192971 | − | 0.999814i | \(-0.493857\pi\) | ||||
0.0192971 | + | 0.999814i | \(0.493857\pi\) | |||||||
\(158\) | 309.626i | 1.95966i | ||||||||
\(159\) | 48.9533 | − | 110.598i | 0.307882 | − | 0.695588i | ||||
\(160\) | 57.6505 | 0.360316 | ||||||||
\(161\) | 180.254i | 1.11959i | ||||||||
\(162\) | −289.231 | − | 27.8542i | −1.78538 | − | 0.171939i | ||||
\(163\) | 161.927 | 0.993416 | 0.496708 | − | 0.867918i | \(-0.334542\pi\) | ||||
0.496708 | + | 0.867918i | \(0.334542\pi\) | |||||||
\(164\) | − | 344.781i | − | 2.10232i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.3596 | −0.255178 | ||||||||
\(167\) | 159.209i | 0.953347i | 0.879081 | + | 0.476673i | \(0.158158\pi\) | ||||
−0.879081 | + | 0.476673i | \(0.841842\pi\) | |||||||
\(168\) | −187.953 | + | 424.636i | −1.11877 | + | 2.52759i | ||||
\(169\) | −166.295 | −0.983992 | ||||||||
\(170\) | 92.9832i | 0.546960i | ||||||||
\(171\) | 63.9355 | + | 70.3886i | 0.373892 | + | 0.411629i | ||||
\(172\) | 140.516 | 0.816956 | ||||||||
\(173\) | − | 38.4198i | − | 0.222080i | −0.993816 | − | 0.111040i | \(-0.964582\pi\) | ||
0.993816 | − | 0.111040i | \(-0.0354181\pi\) | |||||||
\(174\) | 114.240 | + | 50.5651i | 0.656552 | + | 0.290604i | ||||
\(175\) | 182.995 | 1.04568 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 137.429 | − | 310.489i | 0.776437 | − | 1.75418i | ||||
\(178\) | −267.532 | −1.50299 | ||||||||
\(179\) | − | 136.154i | − | 0.760635i | −0.924856 | − | 0.380317i | \(-0.875815\pi\) | ||
0.924856 | − | 0.380317i | \(-0.124185\pi\) | |||||||
\(180\) | −123.269 | + | 111.968i | −0.684827 | + | 0.622044i | ||||
\(181\) | −130.340 | −0.720110 | −0.360055 | − | 0.932931i | \(-0.617242\pi\) | ||||
−0.360055 | + | 0.932931i | \(0.617242\pi\) | |||||||
\(182\) | − | 52.2951i | − | 0.287336i | ||||||
\(183\) | −212.649 | − | 94.1230i | −1.16202 | − | 0.514333i | ||||
\(184\) | 355.195 | 1.93041 | ||||||||
\(185\) | − | 15.1179i | − | 0.0817181i | ||||||
\(186\) | −101.875 | + | 230.162i | −0.547713 | + | 1.23743i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 401.821i | − | 2.13735i | ||||||
\(189\) | −75.4337 | − | 227.101i | −0.399120 | − | 1.20159i | ||||
\(190\) | 79.0784 | 0.416202 | ||||||||
\(191\) | − | 315.580i | − | 1.65225i | −0.563486 | − | 0.826125i | \(-0.690540\pi\) | ||
0.563486 | − | 0.826125i | \(-0.309460\pi\) | |||||||
\(192\) | −26.2945 | − | 11.6385i | −0.136951 | − | 0.0606173i | ||||
\(193\) | 146.410 | 0.758601 | 0.379300 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379300 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(194\) | − | 276.822i | − | 1.42692i | ||||||
\(195\) | 4.16691 | − | 9.41417i | 0.0213688 | − | 0.0482778i | ||||
\(196\) | −262.094 | −1.33721 | ||||||||
\(197\) | 229.459i | 1.16476i | 0.812915 | + | 0.582382i | \(0.197879\pi\) | ||||
−0.812915 | + | 0.582382i | \(0.802121\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −389.358 | −1.95657 | −0.978287 | − | 0.207253i | \(-0.933548\pi\) | ||||
−0.978287 | + | 0.207253i | \(0.933548\pi\) | |||||||
\(200\) | − | 360.595i | − | 1.80297i | ||||||
\(201\) | −172.575 | − | 76.3856i | −0.858584 | − | 0.380028i | ||||
\(202\) | −45.9006 | −0.227231 | ||||||||
\(203\) | 102.888i | 0.506837i | ||||||||
\(204\) | −133.783 | + | 302.251i | −0.655797 | + | 1.48162i | ||||
\(205\) | 81.1124 | 0.395670 | ||||||||
\(206\) | 253.133i | 1.22880i | ||||||||
\(207\) | −135.490 | + | 123.069i | −0.654543 | + | 0.594536i | ||||
\(208\) | −44.7006 | −0.214907 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −181.976 | − | 80.5465i | −0.866553 | − | 0.383555i | ||||
\(211\) | 203.989 | 0.966774 | 0.483387 | − | 0.875407i | \(-0.339406\pi\) | ||||
0.483387 | + | 0.875407i | \(0.339406\pi\) | |||||||
\(212\) | − | 357.544i | − | 1.68653i | ||||||
\(213\) | −12.4005 | + | 28.0159i | −0.0582181 | + | 0.131530i | ||||
\(214\) | 660.848 | 3.08808 | ||||||||
\(215\) | 33.0576i | 0.153756i | ||||||||
\(216\) | −447.509 | + | 148.644i | −2.07180 | + | 0.688166i | ||||
\(217\) | −207.291 | −0.955257 | ||||||||
\(218\) | − | 209.997i | − | 0.963288i | ||||||
\(219\) | 204.710 | + | 90.6091i | 0.934750 | + | 0.413740i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 20.4342i | − | 0.0924626i | ||||||
\(222\) | 31.5618 | − | 71.3066i | 0.142170 | − | 0.321201i | ||||
\(223\) | −16.5198 | −0.0740799 | −0.0370399 | − | 0.999314i | \(-0.511793\pi\) | ||||
−0.0370399 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(224\) | 244.900i | 1.09330i | ||||||||
\(225\) | 124.940 | + | 137.550i | 0.555289 | + | 0.611334i | ||||
\(226\) | −545.256 | −2.41264 | ||||||||
\(227\) | 112.858i | 0.497173i | 0.968610 | + | 0.248587i | \(0.0799661\pi\) | ||||
−0.968610 | + | 0.248587i | \(0.920034\pi\) | |||||||
\(228\) | 257.052 | + | 113.777i | 1.12742 | + | 0.499020i | ||||
\(229\) | −368.618 | −1.60969 | −0.804843 | − | 0.593487i | \(-0.797751\pi\) | ||||
−0.804843 | + | 0.593487i | \(0.797751\pi\) | |||||||
\(230\) | 152.217i | 0.661815i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 202.743 | 0.873892 | ||||||||
\(233\) | 174.540i | 0.749100i | 0.927207 | + | 0.374550i | \(0.122203\pi\) | ||||
−0.927207 | + | 0.374550i | \(0.877797\pi\) | |||||||
\(234\) | 39.3083 | − | 35.7046i | 0.167984 | − | 0.152584i | ||||
\(235\) | 94.5316 | 0.402262 | ||||||||
\(236\) | − | 1003.75i | − | 4.25320i | ||||||
\(237\) | −236.779 | − | 104.804i | −0.999069 | − | 0.442210i | ||||
\(238\) | −394.994 | −1.65964 | ||||||||
\(239\) | − | 345.353i | − | 1.44499i | −0.691375 | − | 0.722496i | \(-0.742995\pi\) | ||
0.691375 | − | 0.722496i | \(-0.257005\pi\) | |||||||
\(240\) | −68.8493 | + | 155.549i | −0.286872 | + | 0.648120i | ||||
\(241\) | −261.447 | −1.08484 | −0.542421 | − | 0.840107i | \(-0.682492\pi\) | ||||
−0.542421 | + | 0.840107i | \(0.682492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 119.201 | − | 211.755i | 0.490540 | − | 0.871419i | ||||
\(244\) | −687.454 | −2.81744 | ||||||||
\(245\) | − | 61.6597i | − | 0.251672i | ||||||
\(246\) | 382.584 | + | 169.340i | 1.55522 | + | 0.688374i | ||||
\(247\) | −17.3785 | −0.0703581 | ||||||||
\(248\) | 408.471i | 1.64706i | ||||||||
\(249\) | 14.3381 | − | 32.3935i | 0.0575826 | − | 0.130095i | ||||
\(250\) | 341.643 | 1.36657 | ||||||||
\(251\) | − | 198.345i | − | 0.790220i | −0.918634 | − | 0.395110i | \(-0.870706\pi\) | ||
0.918634 | − | 0.395110i | \(-0.129294\pi\) | |||||||
\(252\) | −475.641 | − | 523.648i | −1.88746 | − | 2.07797i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 51.2057i | − | 0.201597i | ||||||
\(255\) | −71.1068 | − | 31.4734i | −0.278850 | − | 0.123425i | ||||
\(256\) | −481.495 | −1.88084 | ||||||||
\(257\) | − | 1.86519i | − | 0.00725755i | −0.999993 | − | 0.00362878i | \(-0.998845\pi\) | ||
0.999993 | − | 0.00362878i | \(-0.00115508\pi\) | |||||||
\(258\) | −69.0150 | + | 155.923i | −0.267500 | + | 0.604354i | ||||
\(259\) | 64.2208 | 0.247957 | ||||||||
\(260\) | − | 30.4343i | − | 0.117055i | ||||||
\(261\) | −77.3370 | + | 70.2469i | −0.296310 | + | 0.269145i | ||||
\(262\) | 551.315 | 2.10425 | ||||||||
\(263\) | − | 27.0901i | − | 0.103004i | −0.998673 | − | 0.0515020i | \(-0.983599\pi\) | ||
0.998673 | − | 0.0515020i | \(-0.0164009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 84.1151 | 0.317416 | ||||||||
\(266\) | 335.926i | 1.26288i | ||||||||
\(267\) | 90.5557 | − | 204.589i | 0.339160 | − | 0.766252i | ||||
\(268\) | −557.904 | −2.08173 | ||||||||
\(269\) | 142.848i | 0.531033i | 0.964106 | + | 0.265516i | \(0.0855425\pi\) | ||||
−0.964106 | + | 0.265516i | \(0.914458\pi\) | |||||||
\(270\) | −63.7007 | − | 191.778i | −0.235929 | − | 0.710289i | ||||
\(271\) | −105.327 | −0.388661 | −0.194331 | − | 0.980936i | \(-0.562254\pi\) | ||||
−0.194331 | + | 0.980936i | \(0.562254\pi\) | |||||||
\(272\) | 337.631i | 1.24129i | ||||||||
\(273\) | 39.9915 | + | 17.7011i | 0.146489 | + | 0.0648392i | ||||
\(274\) | 289.282 | 1.05577 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −219.008 | + | 494.797i | −0.793507 | + | 1.79274i | ||||
\(277\) | 244.920 | 0.884186 | 0.442093 | − | 0.896969i | \(-0.354236\pi\) | ||||
0.442093 | + | 0.896969i | \(0.354236\pi\) | |||||||
\(278\) | 760.292i | 2.73486i | ||||||||
\(279\) | −141.528 | − | 155.813i | −0.507270 | − | 0.558469i | ||||
\(280\) | −322.955 | −1.15341 | ||||||||
\(281\) | − | 65.1115i | − | 0.231713i | −0.993266 | − | 0.115857i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115857i | \(-0.0369613\pi\) | |||||||
\(282\) | 445.879 | + | 197.356i | 1.58113 | + | 0.699842i | ||||
\(283\) | −157.576 | −0.556805 | −0.278403 | − | 0.960464i | \(-0.589805\pi\) | ||||
−0.278403 | + | 0.960464i | \(0.589805\pi\) | |||||||
\(284\) | 90.5703i | 0.318910i | ||||||||
\(285\) | −26.7668 | + | 60.4734i | −0.0939187 | + | 0.212187i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 344.566i | 1.20058i | ||||||||
\(288\) | −184.082 | + | 167.206i | −0.639175 | + | 0.580577i | ||||
\(289\) | 134.657 | 0.465940 | ||||||||
\(290\) | 86.8847i | 0.299602i | ||||||||
\(291\) | 211.693 | + | 93.7001i | 0.727469 | + | 0.321993i | ||||
\(292\) | 661.790 | 2.26640 | ||||||||
\(293\) | − | 184.009i | − | 0.628018i | −0.949420 | − | 0.314009i | \(-0.898328\pi\) | ||
0.949420 | − | 0.314009i | \(-0.101672\pi\) | |||||||
\(294\) | 128.728 | − | 290.831i | 0.437851 | − | 0.989221i | ||||
\(295\) | 236.141 | 0.800478 | ||||||||
\(296\) | − | 126.549i | − | 0.427529i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 811.906 | 2.72452 | ||||||||
\(299\) | − | 33.4517i | − | 0.111879i | ||||||
\(300\) | 502.319 | + | 222.337i | 1.67440 | + | 0.741124i | ||||
\(301\) | −140.429 | −0.466542 | ||||||||
\(302\) | 978.353i | 3.23958i | ||||||||
\(303\) | 15.5367 | − | 35.1015i | 0.0512761 | − | 0.115846i | ||||
\(304\) | 287.142 | 0.944544 | ||||||||
\(305\) | − | 161.729i | − | 0.530259i | ||||||
\(306\) | −269.683 | − | 296.902i | −0.881317 | − | 0.970269i | ||||
\(307\) | 386.672 | 1.25952 | 0.629759 | − | 0.776790i | \(-0.283154\pi\) | ||||
0.629759 | + | 0.776790i | \(0.283154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −193.578 | − | 85.6816i | −0.626465 | − | 0.277287i | ||||
\(310\) | −175.049 | −0.564673 | ||||||||
\(311\) | 92.2420i | 0.296598i | 0.988943 | + | 0.148299i | \(0.0473798\pi\) | ||||
−0.988943 | + | 0.148299i | \(0.952620\pi\) | |||||||
\(312\) | 34.8804 | − | 78.8042i | 0.111796 | − | 0.252577i | ||||
\(313\) | −74.3978 | −0.237693 | −0.118846 | − | 0.992913i | \(-0.537920\pi\) | ||||
−0.118846 | + | 0.992913i | \(0.537920\pi\) | |||||||
\(314\) | 21.7364i | 0.0692242i | ||||||||
\(315\) | 123.192 | − | 111.898i | 0.391087 | − | 0.355233i | ||||
\(316\) | −765.464 | −2.42236 | ||||||||
\(317\) | 523.779i | 1.65230i | 0.563450 | + | 0.826150i | \(0.309474\pi\) | ||||
−0.563450 | + | 0.826150i | \(0.690526\pi\) | |||||||
\(318\) | 396.747 | + | 175.609i | 1.24763 | + | 0.552229i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 19.9982i | − | 0.0624943i | ||||||
\(321\) | −223.687 | + | 505.369i | −0.696845 | + | 1.57436i | ||||
\(322\) | −646.622 | −2.00814 | ||||||||
\(323\) | 131.262i | 0.406385i | ||||||||
\(324\) | 68.8617 | − | 715.044i | 0.212536 | − | 2.20692i | ||||
\(325\) | −33.9602 | −0.104493 | ||||||||
\(326\) | 580.876i | 1.78183i | ||||||||
\(327\) | 160.590 | + | 71.0807i | 0.491102 | + | 0.217372i | ||||
\(328\) | 678.976 | 2.07005 | ||||||||
\(329\) | 401.571i | 1.22058i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 251.706 | 0.760441 | 0.380221 | − | 0.924896i | \(-0.375848\pi\) | ||||
0.380221 | + | 0.924896i | \(0.375848\pi\) | |||||||
\(332\) | − | 104.722i | − | 0.315429i | ||||||
\(333\) | 43.8469 | + | 48.2724i | 0.131672 | + | 0.144962i | ||||
\(334\) | −571.126 | −1.70996 | ||||||||
\(335\) | − | 131.251i | − | 0.391795i | ||||||
\(336\) | −660.773 | − | 292.473i | −1.96659 | − | 0.870454i | ||||
\(337\) | −49.6503 | −0.147330 | −0.0736651 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736651 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(338\) | − | 596.544i | − | 1.76492i | ||||||
\(339\) | 184.561 | − | 416.972i | 0.544428 | − | 1.23001i | ||||
\(340\) | −229.875 | −0.676104 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −252.503 | + | 229.354i | −0.738313 | + | 0.670626i | ||||
\(343\) | −172.357 | −0.502499 | ||||||||
\(344\) | 276.719i | 0.804415i | ||||||||
\(345\) | −116.405 | − | 51.5233i | −0.337405 | − | 0.149343i | ||||
\(346\) | 137.822 | 0.398330 | ||||||||
\(347\) | − | 459.779i | − | 1.32501i | −0.749057 | − | 0.662505i | \(-0.769493\pi\) | ||
0.749057 | − | 0.662505i | \(-0.230507\pi\) | |||||||
\(348\) | −125.008 | + | 282.427i | −0.359219 | + | 0.811571i | ||||
\(349\) | −393.749 | −1.12822 | −0.564111 | − | 0.825699i | \(-0.690781\pi\) | ||||
−0.564111 | + | 0.825699i | \(0.690781\pi\) | |||||||
\(350\) | 656.452i | 1.87558i | ||||||||
\(351\) | 13.9990 | + | 42.1456i | 0.0398833 | + | 0.120073i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.9433i | − | 0.0479980i | −0.999712 | − | 0.0239990i | \(-0.992360\pi\) | ||
0.999712 | − | 0.0239990i | \(-0.00763985\pi\) | |||||||
\(354\) | 1113.81 | + | 492.997i | 3.14636 | + | 1.39265i | ||||
\(355\) | −21.3074 | −0.0600208 | ||||||||
\(356\) | − | 661.400i | − | 1.85786i | ||||||
\(357\) | 133.699 | − | 302.063i | 0.374508 | − | 0.846114i | ||||
\(358\) | 488.421 | 1.36430 | ||||||||
\(359\) | − | 75.8881i | − | 0.211387i | −0.994399 | − | 0.105694i | \(-0.966294\pi\) | ||
0.994399 | − | 0.105694i | \(-0.0337063\pi\) | |||||||
\(360\) | −220.498 | − | 242.753i | −0.612495 | − | 0.674314i | ||||
\(361\) | −249.367 | −0.690767 | ||||||||
\(362\) | − | 467.565i | − | 1.29162i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 129.285 | 0.355179 | ||||||||
\(365\) | 155.691i | 0.426552i | ||||||||
\(366\) | 337.645 | − | 762.830i | 0.922527 | − | 2.08423i | ||||
\(367\) | 619.307 | 1.68749 | 0.843743 | − | 0.536748i | \(-0.180347\pi\) | ||||
0.843743 | + | 0.536748i | \(0.180347\pi\) | |||||||
\(368\) | 552.717i | 1.50195i | ||||||||
\(369\) | −258.998 | + | 235.253i | −0.701891 | + | 0.637543i | ||||
\(370\) | 54.2319 | 0.146573 | ||||||||
\(371\) | 357.322i | 0.963132i | ||||||||
\(372\) | −569.012 | − | 251.857i | −1.52960 | − | 0.677035i | ||||
\(373\) | −365.674 | −0.980359 | −0.490179 | − | 0.871622i | \(-0.663069\pi\) | ||||
−0.490179 | + | 0.871622i | \(0.663069\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −115.641 | + | 261.264i | −0.308376 | + | 0.696704i | ||||
\(376\) | 791.305 | 2.10454 | ||||||||
\(377\) | − | 19.0940i | − | 0.0506472i | ||||||
\(378\) | 814.675 | − | 270.601i | 2.15523 | − | 0.715877i | ||||
\(379\) | −409.884 | −1.08149 | −0.540744 | − | 0.841187i | \(-0.681857\pi\) | ||||
−0.540744 | + | 0.841187i | \(0.681857\pi\) | |||||||
\(380\) | 195.499i | 0.514472i | ||||||||
\(381\) | 39.1584 | + | 17.3324i | 0.102778 | + | 0.0454918i | ||||
\(382\) | 1132.07 | 2.96354 | ||||||||
\(383\) | 52.9616i | 0.138281i | 0.997607 | + | 0.0691404i | \(0.0220257\pi\) | ||||
−0.997607 | + | 0.0691404i | \(0.977974\pi\) | |||||||
\(384\) | 175.956 | − | 397.532i | 0.458219 | − | 1.03524i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 525.213i | 1.36065i | ||||||||
\(387\) | −95.8783 | − | 105.555i | −0.247748 | − | 0.272753i | ||||
\(388\) | 684.366 | 1.76383 | ||||||||
\(389\) | 90.6661i | 0.233075i | 0.993186 | + | 0.116537i | \(0.0371795\pi\) | ||||
−0.993186 | + | 0.116537i | \(0.962821\pi\) | |||||||
\(390\) | 33.7712 | + | 14.9479i | 0.0865929 | + | 0.0383279i | ||||
\(391\) | −252.666 | −0.646205 | ||||||||
\(392\) | − | 516.141i | − | 1.31669i | ||||||
\(393\) | −186.612 | + | 421.606i | −0.474839 | + | 1.07279i | ||||
\(394\) | −823.131 | −2.08916 | ||||||||
\(395\) | − | 180.081i | − | 0.455902i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −335.768 | −0.845763 | −0.422882 | − | 0.906185i | \(-0.638981\pi\) | ||||
−0.422882 | + | 0.906185i | \(0.638981\pi\) | |||||||
\(398\) | − | 1396.74i | − | 3.50939i | ||||||
\(399\) | −256.892 | − | 113.706i | −0.643839 | − | 0.284977i | ||||
\(400\) | 561.119 | 1.40280 | ||||||||
\(401\) | − | 18.9212i | − | 0.0471849i | −0.999722 | − | 0.0235925i | \(-0.992490\pi\) | ||
0.999722 | − | 0.0235925i | \(-0.00751041\pi\) | |||||||
\(402\) | 274.016 | − | 619.075i | 0.681632 | − | 1.53999i | ||||
\(403\) | 38.4691 | 0.0954569 | ||||||||
\(404\) | − | 113.477i | − | 0.280883i | ||||||
\(405\) | 168.220 | + | 16.2003i | 0.415357 | + | 0.0400007i | ||||
\(406\) | −369.087 | −0.909082 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −595.221 | − | 263.458i | −1.45888 | − | 0.645730i | ||||
\(409\) | −119.263 | −0.291596 | −0.145798 | − | 0.989314i | \(-0.546575\pi\) | ||||
−0.145798 | + | 0.989314i | \(0.546575\pi\) | |||||||
\(410\) | 290.972i | 0.709689i | ||||||||
\(411\) | −97.9175 | + | 221.222i | −0.238242 | + | 0.538252i | ||||
\(412\) | −625.800 | −1.51893 | ||||||||
\(413\) | 1003.13i | 2.42889i | ||||||||
\(414\) | −441.482 | − | 486.042i | −1.06638 | − | 1.17401i | ||||
\(415\) | 24.6367 | 0.0593657 | ||||||||
\(416\) | − | 45.4487i | − | 0.109252i | ||||||
\(417\) | −581.416 | − | 257.347i | −1.39428 | − | 0.617140i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 412.874i | − | 0.985381i | −0.870205 | − | 0.492690i | \(-0.836014\pi\) | ||
0.870205 | − | 0.492690i | \(-0.163986\pi\) | |||||||
\(420\) | 199.129 | − | 449.885i | 0.474117 | − | 1.07116i | ||||
\(421\) | 604.942 | 1.43692 | 0.718458 | − | 0.695570i | \(-0.244848\pi\) | ||||
0.718458 | + | 0.695570i | \(0.244848\pi\) | |||||||
\(422\) | 731.766i | 1.73404i | ||||||||
\(423\) | −301.846 | + | 274.174i | −0.713585 | + | 0.648165i | ||||
\(424\) | 704.111 | 1.66064 | ||||||||
\(425\) | 256.507i | 0.603547i | ||||||||
\(426\) | −100.501 | − | 44.4839i | −0.235918 | − | 0.104422i | ||||
\(427\) | 687.027 | 1.60896 | ||||||||
\(428\) | 1633.76i | 3.81721i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −118.587 | −0.275783 | ||||||||
\(431\) | − | 443.420i | − | 1.02882i | −0.857545 | − | 0.514409i | \(-0.828011\pi\) | ||
0.857545 | − | 0.514409i | \(-0.171989\pi\) | |||||||
\(432\) | −231.304 | − | 696.365i | −0.535425 | − | 1.61196i | ||||
\(433\) | 218.980 | 0.505727 | 0.252864 | − | 0.967502i | \(-0.418628\pi\) | ||||
0.252864 | + | 0.967502i | \(0.418628\pi\) | |||||||
\(434\) | − | 743.609i | − | 1.71338i | ||||||
\(435\) | −66.4431 | − | 29.4092i | −0.152743 | − | 0.0676072i | ||||
\(436\) | 519.159 | 1.19073 | ||||||||
\(437\) | 214.882i | 0.491721i | ||||||||
\(438\) | −325.040 | + | 734.352i | −0.742100 | + | 1.67660i | ||||
\(439\) | 171.641 | 0.390982 | 0.195491 | − | 0.980705i | \(-0.437370\pi\) | ||||
0.195491 | + | 0.980705i | \(0.437370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 178.834 | + | 196.884i | 0.405519 | + | 0.446449i | ||||
\(442\) | 73.3032 | 0.165844 | ||||||||
\(443\) | 592.539i | 1.33756i | 0.743461 | + | 0.668780i | \(0.233183\pi\) | ||||
−0.743461 | + | 0.668780i | \(0.766817\pi\) | |||||||
\(444\) | 176.286 | + | 78.0279i | 0.397040 | + | 0.175739i | ||||
\(445\) | 155.599 | 0.349662 | ||||||||
\(446\) | − | 59.2611i | − | 0.132872i | ||||||
\(447\) | −274.818 | + | 620.887i | −0.614805 | + | 1.38901i | ||||
\(448\) | 84.9525 | 0.189626 | ||||||||
\(449\) | − | 436.128i | − | 0.971331i | −0.874145 | − | 0.485665i | \(-0.838577\pi\) | ||
0.874145 | − | 0.485665i | \(-0.161423\pi\) | |||||||
\(450\) | −493.430 | + | 448.194i | −1.09651 | + | 0.995986i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 1347.99i | − | 2.98229i | ||||||
\(453\) | −748.174 | − | 331.158i | −1.65160 | − | 0.731033i | ||||
\(454\) | −404.854 | −0.891749 | ||||||||
\(455\) | 30.4153i | 0.0668469i | ||||||||
\(456\) | −224.060 | + | 506.211i | −0.491360 | + | 1.11011i | ||||
\(457\) | 238.541 | 0.521973 | 0.260986 | − | 0.965343i | \(-0.415952\pi\) | ||||
0.260986 | + | 0.965343i | \(0.415952\pi\) | |||||||
\(458\) | − | 1322.34i | − | 2.88719i | ||||||
\(459\) | 318.333 | − | 105.737i | 0.693536 | − | 0.230364i | ||||
\(460\) | −376.315 | −0.818077 | ||||||||
\(461\) | − | 711.175i | − | 1.54268i | −0.636424 | − | 0.771339i | \(-0.719587\pi\) | ||
0.636424 | − | 0.771339i | \(-0.280413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −461.487 | −0.996732 | −0.498366 | − | 0.866967i | \(-0.666066\pi\) | ||||
−0.498366 | + | 0.866967i | \(0.666066\pi\) | |||||||
\(464\) | 315.487i | 0.679929i | ||||||||
\(465\) | 59.2513 | − | 133.865i | 0.127422 | − | 0.287881i | ||||
\(466\) | −626.124 | −1.34361 | ||||||||
\(467\) | − | 48.3844i | − | 0.103607i | −0.998657 | − | 0.0518035i | \(-0.983503\pi\) | ||
0.998657 | − | 0.0518035i | \(-0.0164969\pi\) | |||||||
\(468\) | 88.2697 | + | 97.1789i | 0.188611 | + | 0.207647i | ||||
\(469\) | 557.557 | 1.18882 | ||||||||
\(470\) | 339.111i | 0.721512i | ||||||||
\(471\) | −16.6224 | − | 7.35744i | −0.0352917 | − | 0.0156209i | ||||
\(472\) | 1976.69 | 4.18790 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 375.960 | − | 849.393i | 0.793164 | − | 1.79197i | ||||
\(475\) | 218.149 | 0.459261 | ||||||||
\(476\) | − | 976.513i | − | 2.05150i | ||||||
\(477\) | −268.586 | + | 243.962i | −0.563073 | + | 0.511452i | ||||
\(478\) | 1238.88 | 2.59179 | ||||||||
\(479\) | 171.425i | 0.357880i | 0.983860 | + | 0.178940i | \(0.0572668\pi\) | ||||
−0.983860 | + | 0.178940i | \(0.942733\pi\) | |||||||
\(480\) | −158.152 | − | 70.0015i | −0.329483 | − | 0.145836i | ||||
\(481\) | −11.9181 | −0.0247778 | ||||||||
\(482\) | − | 937.883i | − | 1.94581i | ||||||
\(483\) | 218.872 | − | 494.489i | 0.453150 | − | 1.02379i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 161.002i | 0.331964i | ||||||||
\(486\) | 759.622 | + | 427.608i | 1.56301 | + | 0.879851i | ||||
\(487\) | −495.498 | −1.01745 | −0.508725 | − | 0.860929i | \(-0.669883\pi\) | ||||
−0.508725 | + | 0.860929i | \(0.669883\pi\) | |||||||
\(488\) | − | 1353.80i | − | 2.77418i | ||||||
\(489\) | −444.212 | − | 196.618i | −0.908409 | − | 0.402081i | ||||
\(490\) | 221.190 | 0.451408 | ||||||||
\(491\) | − | 330.249i | − | 0.672604i | −0.941754 | − | 0.336302i | \(-0.890824\pi\) | ||
0.941754 | − | 0.336302i | \(-0.109176\pi\) | |||||||
\(492\) | −418.646 | + | 945.833i | −0.850906 | + | 1.92242i | ||||
\(493\) | −144.220 | −0.292536 | ||||||||
\(494\) | − | 62.3413i | − | 0.126197i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −635.619 | −1.28149 | ||||||||
\(497\) | − | 90.5140i | − | 0.182121i | ||||||
\(498\) | 116.205 | + | 51.4346i | 0.233342 | + | 0.103282i | ||||
\(499\) | 109.801 | 0.220042 | 0.110021 | − | 0.993929i | \(-0.464908\pi\) | ||||
0.110021 | + | 0.993929i | \(0.464908\pi\) | |||||||
\(500\) | 844.618i | 1.68924i | ||||||||
\(501\) | 193.318 | − | 436.756i | 0.385863 | − | 0.871768i | ||||
\(502\) | 711.519 | 1.41737 | ||||||||
\(503\) | 571.702i | 1.13658i | 0.822827 | + | 0.568292i | \(0.192396\pi\) | ||||
−0.822827 | + | 0.568292i | \(0.807604\pi\) | |||||||
\(504\) | 1031.22 | − | 936.679i | 2.04607 | − | 1.85849i | ||||
\(505\) | 26.6963 | 0.0528639 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 456.194 | + | 201.921i | 0.899791 | + | 0.398267i | ||||
\(508\) | 126.592 | 0.249197 | ||||||||
\(509\) | − | 540.924i | − | 1.06272i | −0.847146 | − | 0.531360i | \(-0.821681\pi\) | ||
0.847146 | − | 0.531360i | \(-0.178319\pi\) | |||||||
\(510\) | 112.904 | − | 255.080i | 0.221380 | − | 0.500156i | ||||
\(511\) | −661.379 | −1.29428 | ||||||||
\(512\) | − | 1147.61i | − | 2.24143i | ||||||
\(513\) | −89.9250 | − | 270.729i | −0.175292 | − | 0.527737i | ||||
\(514\) | 6.69095 | 0.0130174 | ||||||||
\(515\) | − | 147.224i | − | 0.285873i | ||||||
\(516\) | −385.477 | − | 170.620i | −0.747049 | − | 0.330660i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 230.378i | 0.444745i | ||||||||
\(519\) | −46.6507 | + | 105.396i | −0.0898858 | + | 0.203076i | ||||
\(520\) | 59.9341 | 0.115258 | ||||||||
\(521\) | 337.888i | 0.648537i | 0.945965 | + | 0.324269i | \(0.105118\pi\) | ||||
−0.945965 | + | 0.324269i | \(0.894882\pi\) | |||||||
\(522\) | −251.995 | − | 277.429i | −0.482749 | − | 0.531474i | ||||
\(523\) | 307.433 | 0.587827 | 0.293913 | − | 0.955832i | \(-0.405042\pi\) | ||||
0.293913 | + | 0.955832i | \(0.405042\pi\) | |||||||
\(524\) | 1362.97i | 2.60109i | ||||||||
\(525\) | −502.007 | − | 222.199i | −0.956203 | − | 0.423236i | ||||
\(526\) | 97.1795 | 0.184752 | ||||||||
\(527\) | − | 290.564i | − | 0.551355i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 115.375 | 0.218100 | ||||||||
\(530\) | 301.744i | 0.569329i | ||||||||
\(531\) | −754.016 | + | 684.889i | −1.41999 | + | 1.28981i | ||||
\(532\) | −830.484 | −1.56106 | ||||||||
\(533\) | − | 63.9448i | − | 0.119971i | ||||||
\(534\) | 733.918 | + | 324.848i | 1.37438 | + | 0.608330i | ||||
\(535\) | −384.356 | −0.718422 | ||||||||
\(536\) | − | 1098.68i | − | 2.04978i | ||||||
\(537\) | −165.323 | + | 373.509i | −0.307864 | + | 0.695547i | ||||
\(538\) | −512.434 | −0.952480 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 474.118 | − | 157.482i | 0.877996 | − | 0.291634i | ||||
\(541\) | −82.7018 | −0.152868 | −0.0764342 | − | 0.997075i | \(-0.524354\pi\) | ||||
−0.0764342 | + | 0.997075i | \(0.524354\pi\) | |||||||
\(542\) | − | 377.838i | − | 0.697118i | ||||||
\(543\) | 357.560 | + | 158.264i | 0.658490 | + | 0.291462i | ||||
\(544\) | −343.282 | −0.631033 | ||||||||
\(545\) | 122.136i | 0.224103i | ||||||||
\(546\) | −63.4987 | + | 143.461i | −0.116298 | + | 0.262748i | ||||
\(547\) | −396.695 | −0.725220 | −0.362610 | − | 0.931941i | \(-0.618114\pi\) | ||||
−0.362610 | + | 0.931941i | \(0.618114\pi\) | |||||||
\(548\) | 715.169i | 1.30505i | ||||||||
\(549\) | 469.069 | + | 516.413i | 0.854407 | + | 0.940642i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 122.653i | 0.222601i | ||||||||
\(552\) | −974.402 | − | 431.291i | −1.76522 | − | 0.781325i | ||||
\(553\) | 764.988 | 1.38334 | ||||||||
\(554\) | 878.594i | 1.58591i | ||||||||
\(555\) | −18.3567 | + | 41.4726i | −0.0330751 | + | 0.0747254i | ||||
\(556\) | −1879.61 | −3.38060 | ||||||||
\(557\) | − | 383.089i | − | 0.687771i | −0.939012 | − | 0.343886i | \(-0.888257\pi\) | ||
0.939012 | − | 0.343886i | \(-0.111743\pi\) | |||||||
\(558\) | 558.943 | − | 507.701i | 1.00169 | − | 0.909858i | ||||
\(559\) | 26.0609 | 0.0466206 | ||||||||
\(560\) | − | 502.548i | − | 0.897407i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 233.573 | 0.415610 | ||||||||
\(563\) | 144.837i | 0.257259i | 0.991693 | + | 0.128629i | \(0.0410577\pi\) | ||||
−0.991693 | + | 0.128629i | \(0.958942\pi\) | |||||||
\(564\) | −487.907 | + | 1102.31i | −0.865083 | + | 1.95445i | ||||
\(565\) | 317.126 | 0.561285 | ||||||||
\(566\) | − | 565.268i | − | 0.998707i | ||||||
\(567\) | −68.8189 | + | 714.599i | −0.121374 | + | 1.26032i | ||||
\(568\) | −178.360 | −0.314014 | ||||||||
\(569\) | 923.151i | 1.62241i | 0.584763 | + | 0.811204i | \(0.301188\pi\) | ||||
−0.584763 | + | 0.811204i | \(0.698812\pi\) | |||||||
\(570\) | −216.935 | − | 96.0200i | −0.380587 | − | 0.168456i | ||||
\(571\) | 421.725 | 0.738573 | 0.369287 | − | 0.929316i | \(-0.379602\pi\) | ||||
0.369287 | + | 0.929316i | \(0.379602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −383.189 | + | 865.726i | −0.668742 | + | 1.51087i | ||||
\(574\) | −1236.05 | −2.15340 | ||||||||
\(575\) | 419.913i | 0.730284i | ||||||||
\(576\) | 58.0015 | + | 63.8556i | 0.100697 | + | 0.110860i | ||||
\(577\) | 460.408 | 0.797934 | 0.398967 | − | 0.916965i | \(-0.369369\pi\) | ||||
0.398967 | + | 0.916965i | \(0.369369\pi\) | |||||||
\(578\) | 483.051i | 0.835728i | ||||||||
\(579\) | −401.644 | − | 177.776i | −0.693686 | − | 0.307041i | ||||
\(580\) | −214.798 | −0.370342 | ||||||||
\(581\) | 104.657i | 0.180133i | ||||||||
\(582\) | −336.128 | + | 759.403i | −0.577539 | + | 1.30482i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1303.26i | 2.23161i | ||||||||
\(585\) | −22.8621 | + | 20.7661i | −0.0390805 | + | 0.0354977i | ||||
\(586\) | 660.091 | 1.12644 | ||||||||
\(587\) | 42.4644i | 0.0723413i | 0.999346 | + | 0.0361707i | \(0.0115160\pi\) | ||||
−0.999346 | + | 0.0361707i | \(0.988484\pi\) | |||||||
\(588\) | 718.999 | + | 318.245i | 1.22279 | + | 0.541232i | ||||
\(589\) | −247.112 | −0.419546 | ||||||||
\(590\) | 847.103i | 1.43577i | ||||||||
\(591\) | 278.617 | − | 629.471i | 0.471434 | − | 1.06509i | ||||
\(592\) | 196.921 | 0.332638 | ||||||||
\(593\) | 106.267i | 0.179203i | 0.995978 | + | 0.0896015i | \(0.0285593\pi\) | ||||
−0.995978 | + | 0.0896015i | \(0.971441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 229.732 | 0.386105 | ||||||||
\(596\) | 2007.21i | 3.36781i | ||||||||
\(597\) | 1068.12 | + | 472.774i | 1.78915 | + | 0.791916i | ||||
\(598\) | 120.000 | 0.200670 | ||||||||
\(599\) | 728.012i | 1.21538i | 0.794174 | + | 0.607690i | \(0.207904\pi\) | ||||
−0.794174 | + | 0.607690i | \(0.792096\pi\) | |||||||
\(600\) | −437.848 | + | 989.215i | −0.729747 | + | 1.64869i | ||||
\(601\) | −118.594 | −0.197327 | −0.0986635 | − | 0.995121i | \(-0.531457\pi\) | ||||
−0.0986635 | + | 0.995121i | \(0.531457\pi\) | |||||||
\(602\) | − | 503.758i | − | 0.836807i | ||||||
\(603\) | 380.674 | + | 419.095i | 0.631299 | + | 0.695017i | ||||
\(604\) | −2418.71 | −4.00448 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 125.919 | + | 55.7343i | 0.207787 | + | 0.0919708i | ||||
\(607\) | 713.203 | 1.17496 | 0.587482 | − | 0.809237i | \(-0.300119\pi\) | ||||
0.587482 | + | 0.809237i | \(0.300119\pi\) | |||||||
\(608\) | 291.947i | 0.480176i | ||||||||
\(609\) | 124.930 | − | 282.251i | 0.205140 | − | 0.463466i | ||||
\(610\) | 580.167 | 0.951093 | ||||||||
\(611\) | − | 74.5238i | − | 0.121970i | ||||||
\(612\) | 734.009 | − | 666.716i | 1.19936 | − | 1.08941i | ||||
\(613\) | 687.465 | 1.12148 | 0.560739 | − | 0.827993i | \(-0.310517\pi\) | ||||
0.560739 | + | 0.827993i | \(0.310517\pi\) | |||||||
\(614\) | 1387.10i | 2.25912i | ||||||||
\(615\) | −222.515 | − | 98.4898i | −0.361812 | − | 0.160146i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 762.156i | 1.23526i | 0.786468 | + | 0.617631i | \(0.211907\pi\) | ||||
−0.786468 | + | 0.617631i | \(0.788093\pi\) | |||||||
\(618\) | 307.363 | − | 694.416i | 0.497352 | − | 1.12365i | ||||
\(619\) | −530.698 | −0.857348 | −0.428674 | − | 0.903459i | \(-0.641019\pi\) | ||||
−0.428674 | + | 0.903459i | \(0.641019\pi\) | |||||||
\(620\) | − | 432.759i | − | 0.697999i | ||||||
\(621\) | 521.124 | − | 173.096i | 0.839170 | − | 0.278737i | ||||
\(622\) | −330.897 | −0.531989 | ||||||||
\(623\) | 660.988i | 1.06098i | ||||||||
\(624\) | 122.627 | + | 54.2772i | 0.196517 | + | 0.0869827i | ||||
\(625\) | 317.471 | 0.507954 | ||||||||
\(626\) | − | 266.885i | − | 0.426334i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −53.7372 | −0.0855688 | ||||||||
\(629\) | 90.0197i | 0.143116i | ||||||||
\(630\) | 401.410 | + | 441.925i | 0.637159 | + | 0.701468i | ||||
\(631\) | 676.449 | 1.07203 | 0.536013 | − | 0.844210i | \(-0.319930\pi\) | ||||
0.536013 | + | 0.844210i | \(0.319930\pi\) | |||||||
\(632\) | − | 1507.43i | − | 2.38517i | ||||||
\(633\) | −559.602 | − | 247.692i | −0.884047 | − | 0.391298i | ||||
\(634\) | −1878.94 | −2.96363 | ||||||||
\(635\) | 29.7817i | 0.0469004i | ||||||||
\(636\) | −434.144 | + | 980.847i | −0.682617 | + | 1.54221i | ||||
\(637\) | −48.6093 | −0.0763097 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 68.0360 | − | 61.7987i | 0.106473 | − | 0.0967115i | ||||
\(640\) | 302.341 | 0.472408 | ||||||||
\(641\) | − | 785.884i | − | 1.22603i | −0.790072 | − | 0.613014i | \(-0.789957\pi\) | ||
0.790072 | − | 0.613014i | \(-0.210043\pi\) | |||||||
\(642\) | −1812.90 | − | 802.427i | −2.82383 | − | 1.24989i | ||||
\(643\) | −849.706 | −1.32147 | −0.660736 | − | 0.750619i | \(-0.729756\pi\) | ||||
−0.660736 | + | 0.750619i | \(0.729756\pi\) | |||||||
\(644\) | − | 1598.59i | − | 2.48229i | ||||||
\(645\) | 40.1398 | − | 90.6865i | 0.0622323 | − | 0.140599i | ||||
\(646\) | −470.875 | −0.728908 | ||||||||
\(647\) | − | 1169.38i | − | 1.80738i | −0.428184 | − | 0.903692i | \(-0.640846\pi\) | ||
0.428184 | − | 0.903692i | \(-0.359154\pi\) | |||||||
\(648\) | 1408.13 | + | 135.609i | 2.17305 | + | 0.209274i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 121.825i | − | 0.187423i | ||||||
\(651\) | 568.658 | + | 251.700i | 0.873515 | + | 0.386636i | ||||
\(652\) | −1436.05 | −2.20254 | ||||||||
\(653\) | 535.533i | 0.820111i | 0.912060 | + | 0.410056i | \(0.134491\pi\) | ||||
−0.912060 | + | 0.410056i | \(0.865509\pi\) | |||||||
\(654\) | −254.986 | + | 576.082i | −0.389887 | + | 0.880859i | ||||
\(655\) | −320.650 | −0.489542 | ||||||||
\(656\) | 1056.55i | 1.61059i | ||||||||
\(657\) | −451.558 | − | 497.134i | −0.687303 | − | 0.756673i | ||||
\(658\) | −1440.55 | −2.18928 | ||||||||
\(659\) | − | 138.756i | − | 0.210555i | −0.994443 | − | 0.105278i | \(-0.966427\pi\) | ||
0.994443 | − | 0.105278i | \(-0.0335731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1690 | 0.0411029 | 0.0205515 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205515 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(662\) | 902.939i | 1.36396i | ||||||||
\(663\) | −24.8120 | + | 56.0570i | −0.0374239 | + | 0.0845505i | ||||
\(664\) | 206.229 | 0.310586 | ||||||||
\(665\) | − | 195.378i | − | 0.293801i | ||||||
\(666\) | −173.166 | + | 157.291i | −0.260010 | + | 0.236173i | ||||
\(667\) | −236.094 | −0.353965 | ||||||||
\(668\) | − | 1411.95i | − | 2.11370i | ||||||
\(669\) | 45.3186 | + | 20.0590i | 0.0677408 | + | 0.0299835i | ||||
\(670\) | 470.835 | 0.702738 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 297.367 | − | 671.831i | 0.442511 | − | 0.999749i | ||||
\(673\) | −657.485 | −0.976946 | −0.488473 | − | 0.872579i | \(-0.662446\pi\) | ||||
−0.488473 | + | 0.872579i | \(0.662446\pi\) | |||||||
\(674\) | − | 178.109i | − | 0.264257i | ||||||
\(675\) | −175.727 | − | 529.047i | −0.260337 | − | 0.783773i | ||||
\(676\) | 1474.79 | 2.18164 | ||||||||
\(677\) | − | 611.265i | − | 0.902902i | −0.892296 | − | 0.451451i | \(-0.850907\pi\) | ||
0.892296 | − | 0.451451i | \(-0.149093\pi\) | |||||||
\(678\) | 1495.79 | + | 662.071i | 2.20619 | + | 0.976506i | ||||
\(679\) | −683.940 | −1.00728 | ||||||||
\(680\) | − | 452.693i | − | 0.665725i | ||||||
\(681\) | 137.037 | − | 309.603i | 0.201229 | − | 0.454630i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 990.520i | − | 1.45025i | −0.688618 | − | 0.725124i | \(-0.741782\pi\) | ||
0.688618 | − | 0.725124i | \(-0.258218\pi\) | |||||||
\(684\) | −567.015 | − | 624.244i | −0.828969 | − | 0.912637i | ||||
\(685\) | −168.249 | −0.245619 | ||||||||
\(686\) | − | 618.293i | − | 0.901302i | ||||||
\(687\) | 1011.23 | + | 447.590i | 1.47194 | + | 0.651514i | ||||
\(688\) | −430.600 | −0.625872 | ||||||||
\(689\) | − | 66.3120i | − | 0.0962439i | ||||||
\(690\) | 184.828 | − | 417.576i | 0.267867 | − | 0.605183i | ||||
\(691\) | 573.077 | 0.829345 | 0.414672 | − | 0.909971i | \(-0.363896\pi\) | ||||
0.414672 | + | 0.909971i | \(0.363896\pi\) | |||||||
\(692\) | 340.727i | 0.492380i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1649.35 | 2.37659 | ||||||||
\(695\) | − | 442.193i | − | 0.636249i | ||||||
\(696\) | −556.182 | − | 246.178i | −0.799112 | − | 0.353704i | ||||
\(697\) | −482.986 | −0.692950 | ||||||||
\(698\) | − | 1412.49i | − | 2.02362i | ||||||
\(699\) | 211.933 | − | 478.814i | 0.303195 | − | 0.684999i | ||||
\(700\) | −1622.89 | −2.31842 | ||||||||
\(701\) | − | 819.026i | − | 1.16837i | −0.811621 | − | 0.584184i | \(-0.801415\pi\) | ||
0.811621 | − | 0.584184i | \(-0.198585\pi\) | |||||||
\(702\) | −151.188 | + | 50.2183i | −0.215367 | + | 0.0715361i | ||||
\(703\) | 76.5580 | 0.108902 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −259.327 | − | 114.784i | −0.367840 | − | 0.162814i | ||||
\(706\) | 60.7802 | 0.0860910 | ||||||||
\(707\) | 113.406i | 0.160405i | ||||||||
\(708\) | −1218.80 | + | 2753.59i | −1.72146 | + | 3.88925i | ||||
\(709\) | 179.842 | 0.253656 | 0.126828 | − | 0.991925i | \(-0.459520\pi\) | ||||
0.126828 | + | 0.991925i | \(0.459520\pi\) | |||||||
\(710\) | − | 76.4354i | − | 0.107656i | ||||||
\(711\) | 522.297 | + | 575.013i | 0.734596 | + | 0.808739i | ||||
\(712\) | 1302.49 | 1.82934 | ||||||||
\(713\) | − | 475.665i | − | 0.667132i | ||||||
\(714\) | 1083.58 | + | 479.617i | 1.51762 | + | 0.671732i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1207.48i | 1.68643i | ||||||||
\(717\) | −419.341 | + | 947.403i | −0.584855 | + | 1.32134i | ||||
\(718\) | 272.231 | 0.379152 | ||||||||
\(719\) | − | 666.337i | − | 0.926755i | −0.886161 | − | 0.463378i | \(-0.846637\pi\) | ||
0.886161 | − | 0.463378i | \(-0.153363\pi\) | |||||||
\(720\) | 377.747 | − | 343.116i | 0.524648 | − | 0.476550i | ||||
\(721\) | 625.411 | 0.867422 | ||||||||
\(722\) | − | 894.547i | − | 1.23898i | ||||||
\(723\) | 717.225 | + | 317.459i | 0.992012 | + | 0.439086i | ||||
\(724\) | 1155.92 | 1.59658 | ||||||||
\(725\) | 239.684i | 0.330598i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 162.429 | 0.223424 | 0.111712 | − | 0.993741i | \(-0.464367\pi\) | ||||
0.111712 | + | 0.993741i | \(0.464367\pi\) | |||||||
\(728\) | 254.601i | 0.349726i | ||||||||
\(729\) | −584.124 | + | 436.165i | −0.801267 | + | 0.598306i | ||||
\(730\) | −558.508 | −0.765079 | ||||||||
\(731\) | − | 196.842i | − | 0.269278i | ||||||
\(732\) | 1885.88 | + | 834.733i | 2.57635 | + | 1.14035i | ||||
\(733\) | 1169.88 | 1.59602 | 0.798008 | − | 0.602646i | \(-0.205887\pi\) | ||||
0.798008 | + | 0.602646i | \(0.205887\pi\) | |||||||
\(734\) | 2221.62i | 3.02674i | ||||||||
\(735\) | −74.8695 | + | 169.150i | −0.101863 | + | 0.230136i | ||||
\(736\) | −561.967 | −0.763542 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −843.919 | − | 929.096i | −1.14352 | − | 1.25894i | ||||
\(739\) | −242.377 | −0.327979 | −0.163990 | − | 0.986462i | \(-0.552436\pi\) | ||||
−0.163990 | + | 0.986462i | \(0.552436\pi\) | |||||||
\(740\) | 134.073i | 0.181180i | ||||||||
\(741\) | 47.6741 | + | 21.1016i | 0.0643375 | + | 0.0284772i | ||||
\(742\) | −1281.81 | −1.72751 | ||||||||
\(743\) | 823.655i | 1.10855i | 0.832333 | + | 0.554277i | \(0.187005\pi\) | ||||
−0.832333 | + | 0.554277i | \(0.812995\pi\) | |||||||
\(744\) | 495.981 | − | 1120.55i | 0.666641 | − | 1.50612i | ||||
\(745\) | −472.213 | −0.633842 | ||||||||
\(746\) | − | 1311.77i | − | 1.75841i | ||||||
\(747\) | −78.6669 | + | 71.4549i | −0.105310 | + | 0.0956559i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1632.75i | − | 2.17990i | ||||||
\(750\) | −937.226 | − | 414.836i | −1.24963 | − | 0.553115i | ||||
\(751\) | −6.13817 | −0.00817333 | −0.00408666 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408666 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(752\) | 1231.35i | 1.63743i | ||||||||
\(753\) | −240.838 | + | 544.118i | −0.319839 | + | 0.722600i | ||||
\(754\) | 68.4954 | 0.0908427 | ||||||||
\(755\) | − | 569.020i | − | 0.753669i | ||||||
\(756\) | 668.987 | + | 2014.06i | 0.884903 | + | 2.66410i | ||||
\(757\) | −1102.27 | −1.45610 | −0.728052 | − | 0.685522i | \(-0.759574\pi\) | ||||
−0.728052 | + | 0.685522i | \(0.759574\pi\) | |||||||
\(758\) | − | 1470.37i | − | 1.93980i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −384.996 | −0.506574 | ||||||||
\(761\) | − | 1200.28i | − | 1.57724i | −0.614882 | − | 0.788619i | \(-0.710796\pi\) | ||
0.614882 | − | 0.788619i | \(-0.289204\pi\) | |||||||
\(762\) | −62.1759 | + | 140.472i | −0.0815957 | + | 0.184346i | ||||
\(763\) | −518.836 | −0.679995 | ||||||||
\(764\) | 2798.73i | 3.66326i | ||||||||
\(765\) | 156.850 | + | 172.681i | 0.205033 | + | 0.225727i | ||||
\(766\) | −189.988 | −0.248026 | ||||||||
\(767\) | − | 186.161i | − | 0.242714i | ||||||
\(768\) | 1320.88 | + | 584.649i | 1.71989 | + | 0.761262i | ||||
\(769\) | −1038.16 | −1.35001 | −0.675007 | − | 0.737811i | \(-0.735859\pi\) | ||||
−0.675007 | + | 0.737811i | \(0.735859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.26479 | + | 5.11676i | −0.00293747 | + | 0.00663652i | ||||
\(772\) | −1298.44 | −1.68192 | ||||||||
\(773\) | − | 586.211i | − | 0.758359i | −0.925323 | − | 0.379179i | \(-0.876206\pi\) | ||
0.925323 | − | 0.379179i | \(-0.123794\pi\) | |||||||
\(774\) | 378.656 | − | 343.942i | 0.489220 | − | 0.444369i | ||||
\(775\) | −482.896 | −0.623092 | ||||||||
\(776\) | 1347.72i | 1.73675i | ||||||||
\(777\) | −176.176 | − | 77.9794i | −0.226739 | − | 0.100360i | ||||
\(778\) | −325.244 | −0.418052 | ||||||||
\(779\) | 410.760i | 0.527291i | ||||||||
\(780\) | −36.9545 | + | 83.4899i | −0.0473775 | + | 0.107038i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 906.383i | − | 1.15906i | ||||||
\(783\) | 297.454 | − | 98.8020i | 0.379890 | − | 0.126184i | ||||
\(784\) | 803.164 | 1.02444 | ||||||||
\(785\) | − | 12.6421i | − | 0.0161046i | ||||||
\(786\) | −1512.41 | − | 669.427i | −1.92419 | − | 0.851689i | ||||
\(787\) | 373.464 | 0.474541 | 0.237271 | − | 0.971444i | \(-0.423747\pi\) | ||||
0.237271 | + | 0.971444i | \(0.423747\pi\) | |||||||
\(788\) | − | 2034.96i | − | 2.58244i | ||||||
\(789\) | −32.8938 | + | 74.3158i | −0.0416905 | + | 0.0941899i | ||||
\(790\) | 646.002 | 0.817724 | ||||||||
\(791\) | 1347.16i | 1.70311i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −127.499 | −0.160780 | ||||||||
\(794\) | − | 1204.49i | − | 1.51699i | ||||||
\(795\) | −230.752 | − | 102.136i | −0.290254 | − | 0.128473i | ||||
\(796\) | 3453.04 | 4.33799 | ||||||||
\(797\) | − | 836.809i | − | 1.04995i | −0.851118 | − | 0.524974i | \(-0.824075\pi\) | ||
0.851118 | − | 0.524974i | \(-0.175925\pi\) | |||||||
\(798\) | 407.894 | − | 921.541i | 0.511145 | − | 1.15481i | ||||
\(799\) | −562.891 | −0.704495 | ||||||||
\(800\) | 570.510i | 0.713137i | ||||||||
\(801\) | −496.841 | + | 451.291i | −0.620275 | + | 0.563410i | ||||
\(802\) | 67.8754 | 0.0846326 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1530.49 | + | 677.429i | 1.90360 | + | 0.842573i | ||||
\(805\) | 376.081 | 0.467182 | ||||||||
\(806\) | 137.999i | 0.171215i | ||||||||
\(807\) | 173.451 | − | 391.873i | 0.214933 | − | 0.485592i | ||||
\(808\) | 223.469 | 0.276571 | ||||||||
\(809\) | − | 518.833i | − | 0.641326i | −0.947193 | − | 0.320663i | \(-0.896094\pi\) | ||
0.947193 | − | 0.320663i | \(-0.103906\pi\) | |||||||
\(810\) | −58.1148 | + | 603.450i | −0.0717467 | + | 0.745000i | ||||
\(811\) | 782.670 | 0.965068 | 0.482534 | − | 0.875877i | \(-0.339716\pi\) | ||||
0.482534 | + | 0.875877i | \(0.339716\pi\) | |||||||
\(812\) | − | 912.466i | − | 1.12373i | ||||||
\(813\) | 288.943 | + | 127.892i | 0.355403 | + | 0.157309i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 337.843i | − | 0.414531i | ||||||
\(816\) | 409.965 | − | 926.220i | 0.502408 | − | 1.13507i | ||||
\(817\) | −167.406 | −0.204904 | ||||||||
\(818\) | − | 427.828i | − | 0.523017i | ||||||
\(819\) | −88.2148 | − | 97.1184i | −0.107710 | − | 0.118582i | ||||
\(820\) | −719.348 | −0.877254 | ||||||||
\(821\) | − | 551.621i | − | 0.671889i | −0.941882 | − | 0.335944i | \(-0.890945\pi\) | ||
0.941882 | − | 0.335944i | \(-0.109055\pi\) | |||||||
\(822\) | −793.583 | − | 351.257i | −0.965429 | − | 0.427320i | ||||
\(823\) | −46.1726 | −0.0561028 | −0.0280514 | − | 0.999606i | \(-0.508930\pi\) | ||||
−0.0280514 | + | 0.999606i | \(0.508930\pi\) | |||||||
\(824\) | − | 1232.39i | − | 1.49562i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3598.50 | −4.35654 | ||||||||
\(827\) | 596.211i | 0.720932i | 0.932772 | + | 0.360466i | \(0.117382\pi\) | ||||
−0.932772 | + | 0.360466i | \(0.882618\pi\) | |||||||
\(828\) | 1201.60 | − | 1091.44i | 1.45121 | − | 1.31817i | ||||
\(829\) | −1387.07 | −1.67319 | −0.836593 | − | 0.547825i | \(-0.815456\pi\) | ||||
−0.836593 | + | 0.547825i | \(0.815456\pi\) | |||||||
\(830\) | 88.3788i | 0.106480i | ||||||||
\(831\) | −671.885 | − | 297.391i | −0.808526 | − | 0.357871i | ||||
\(832\) | −15.7655 | −0.0189489 | ||||||||
\(833\) | 367.154i | 0.440761i | ||||||||
\(834\) | 923.176 | − | 2085.70i | 1.10693 | − | 2.50084i | ||||
\(835\) | 332.172 | 0.397811 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 199.059 | + | 599.288i | 0.237824 | + | 0.715995i | ||||
\(838\) | 1481.09 | 1.76742 | ||||||||
\(839\) | − | 1665.00i | − | 1.98451i | −0.124217 | − | 0.992255i | \(-0.539642\pi\) | ||
0.124217 | − | 0.992255i | \(-0.460358\pi\) | |||||||
\(840\) | 885.958 | + | 392.144i | 1.05471 | + | 0.466838i | ||||
\(841\) | 706.239 | 0.839761 | ||||||||
\(842\) | 2170.09i | 2.57731i | ||||||||
\(843\) | −79.0609 | + | 178.620i | −0.0937851 | + | 0.211886i | ||||
\(844\) | −1809.09 | −2.14347 | ||||||||
\(845\) | 346.956i | 0.410599i | ||||||||
\(846\) | −983.537 | − | 1082.81i | −1.16257 | − | 1.27991i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1095.66i | 1.29206i | ||||||||
\(849\) | 432.276 | + | 191.335i | 0.509159 | + | 0.225365i | ||||
\(850\) | −920.163 | −1.08254 | ||||||||
\(851\) | 147.366i | 0.173168i | ||||||||
\(852\) | 109.974 | − | 248.460i | 0.129077 | − | 0.291620i | ||||
\(853\) | −812.549 | −0.952578 | −0.476289 | − | 0.879289i | \(-0.658018\pi\) | ||||
−0.476289 | + | 0.879289i | \(0.658018\pi\) | |||||||
\(854\) | 2464.55i | 2.88589i | ||||||||
\(855\) | 146.858 | − | 133.395i | 0.171764 | − | 0.156017i | ||||
\(856\) | −3217.37 | −3.75861 | ||||||||
\(857\) | 551.421i | 0.643431i | 0.946836 | + | 0.321716i | \(0.104260\pi\) | ||||
−0.946836 | + | 0.321716i | \(0.895740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1196.04 | −1.39236 | −0.696180 | − | 0.717868i | \(-0.745118\pi\) | ||||
−0.696180 | + | 0.717868i | \(0.745118\pi\) | |||||||
\(860\) | − | 293.173i | − | 0.340898i | ||||||
\(861\) | 418.386 | − | 945.245i | 0.485930 | − | 1.09784i | ||||
\(862\) | 1590.67 | 1.84533 | ||||||||
\(863\) | − | 716.382i | − | 0.830106i | −0.909797 | − | 0.415053i | \(-0.863763\pi\) | ||
0.909797 | − | 0.415053i | \(-0.136237\pi\) | |||||||
\(864\) | 708.019 | − | 235.175i | 0.819466 | − | 0.272193i | ||||
\(865\) | −80.1588 | −0.0926691 | ||||||||
\(866\) | 785.541i | 0.907091i | ||||||||
\(867\) | −369.402 | − | 163.505i | −0.426070 | − | 0.188588i | ||||
\(868\) | 1838.37 | 2.11793 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 105.499 | − | 238.350i | 0.121263 | − | 0.273965i | ||||
\(871\) | −103.472 | −0.118797 | ||||||||
\(872\) | 1022.38i | 1.17245i | ||||||||
\(873\) | −466.962 | − | 514.093i | −0.534893 | − | 0.588880i | ||||
\(874\) | −770.841 | −0.881970 | ||||||||
\(875\) | − | 844.093i | − | 0.964677i | ||||||
\(876\) | −1815.48 | − | 803.571i | −2.07247 | − | 0.917318i | ||||
\(877\) | 991.635 | 1.13071 | 0.565357 | − | 0.824847i | \(-0.308739\pi\) | ||||
0.565357 | + | 0.824847i | \(0.308739\pi\) | |||||||
\(878\) | 615.724i | 0.701280i | ||||||||
\(879\) | −223.431 | + | 504.790i | −0.254188 | + | 0.574278i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1256.55i | − | 1.42628i | −0.701021 | − | 0.713140i | \(-0.747272\pi\) | ||
0.701021 | − | 0.713140i | \(-0.252728\pi\) | |||||||
\(882\) | −706.276 | + | 641.527i | −0.800767 | + | 0.727354i | ||||
\(883\) | 278.326 | 0.315205 | 0.157603 | − | 0.987503i | \(-0.449624\pi\) | ||||
0.157603 | + | 0.987503i | \(0.449624\pi\) | |||||||
\(884\) | 181.222i | 0.205002i | ||||||||
\(885\) | −647.803 | − | 286.732i | −0.731981 | − | 0.323990i | ||||
\(886\) | −2125.60 | −2.39910 | ||||||||
\(887\) | 1174.00i | 1.32357i | 0.749695 | + | 0.661784i | \(0.230200\pi\) | ||||
−0.749695 | + | 0.661784i | \(0.769800\pi\) | |||||||
\(888\) | −153.660 | + | 347.159i | −0.173041 | + | 0.390945i | ||||
\(889\) | −126.513 | −0.142310 | ||||||||
\(890\) | 558.178i | 0.627166i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 146.507 | 0.164245 | ||||||||
\(893\) | 478.716i | 0.536076i | ||||||||
\(894\) | −2227.29 | − | 985.848i | −2.49138 | − | 1.10274i | ||||
\(895\) | −284.070 | −0.317397 | ||||||||
\(896\) | 1284.35i | 1.43342i | ||||||||
\(897\) | −40.6183 | + | 91.7676i | −0.0452824 | + | 0.102305i | ||||
\(898\) | 1564.51 | 1.74222 | ||||||||
\(899\) | − | 271.506i | − | 0.302009i | ||||||
\(900\) | −1108.03 | − | 1219.87i | −1.23115 | − | 1.35541i | ||||
\(901\) | −500.866 | −0.555900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 385.237 | + | 170.514i | 0.426619 | + | 0.188831i | ||||
\(904\) | 2654.60 | 2.93651 | ||||||||
\(905\) | 271.940i | 0.300487i | ||||||||
\(906\) | 1187.95 | − | 2683.90i | 1.31121 | − | 2.96237i | ||||
\(907\) | 145.616 | 0.160547 | 0.0802736 | − | 0.996773i | \(-0.474421\pi\) | ||||
0.0802736 | + | 0.996773i | \(0.474421\pi\) | |||||||
\(908\) | − | 1000.89i | − | 1.10230i | ||||||
\(909\) | −85.2431 | + | 77.4282i | −0.0937768 | + | 0.0851796i | ||||
\(910\) | −109.108 | −0.119899 | ||||||||
\(911\) | 1076.70i | 1.18189i | 0.806713 | + | 0.590943i | \(0.201244\pi\) | ||||
−0.806713 | + | 0.590943i | \(0.798756\pi\) | |||||||
\(912\) | −787.712 | − | 348.658i | −0.863719 | − | 0.382301i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 855.714i | 0.936230i | ||||||||
\(915\) | −196.378 | + | 443.669i | −0.214620 | + | 0.484884i | ||||
\(916\) | 3269.11 | 3.56889 | ||||||||
\(917\) | − | 1362.13i | − | 1.48541i | ||||||
\(918\) | 379.308 | + | 1141.95i | 0.413189 | + | 1.24395i | ||||
\(919\) | 316.112 | 0.343974 | 0.171987 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171987 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(920\) | − | 741.077i | − | 0.805518i | ||||||
\(921\) | −1060.75 | − | 469.512i | −1.15174 | − | 0.509785i | ||||
\(922\) | 2551.18 | 2.76701 | ||||||||
\(923\) | 16.7976i | 0.0181990i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 149.606 | 0.161737 | ||||||||
\(926\) | − | 1655.48i | − | 1.78778i | ||||||
\(927\) | 427.001 | + | 470.098i | 0.460627 | + | 0.507118i | ||||
\(928\) | −320.767 | −0.345654 | ||||||||
\(929\) | 1118.65i | 1.20414i | 0.798442 | + | 0.602072i | \(0.205658\pi\) | ||||
−0.798442 | + | 0.602072i | \(0.794342\pi\) | |||||||
\(930\) | 480.209 | + | 212.551i | 0.516353 | + | 0.228549i | ||||
\(931\) | 312.249 | 0.335391 | ||||||||
\(932\) | − | 1547.92i | − | 1.66086i | ||||||
\(933\) | 112.004 | − | 253.046i | 0.120047 | − | 0.271218i | ||||
\(934\) | 173.568 | 0.185833 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −191.374 | + | 173.829i | −0.204459 | + | 0.185715i | ||||
\(937\) | 1051.22 | 1.12189 | 0.560947 | − | 0.827852i | \(-0.310437\pi\) | ||||
0.560947 | + | 0.827852i | \(0.310437\pi\) | |||||||
\(938\) | 2000.11i | 2.13231i | ||||||||
\(939\) | 204.094 | + | 90.3366i | 0.217353 | + | 0.0962051i | ||||
\(940\) | −838.357 | −0.891869 | ||||||||
\(941\) | 320.555i | 0.340654i | 0.985388 | + | 0.170327i | \(0.0544824\pi\) | ||||
−0.985388 | + | 0.170327i | \(0.945518\pi\) | |||||||
\(942\) | 26.3932 | − | 59.6292i | 0.0280182 | − | 0.0633006i | ||||
\(943\) | −790.668 | −0.838461 | ||||||||
\(944\) | 3075.92i | 3.25839i | ||||||||
\(945\) | −473.823 | + | 157.384i | −0.501400 | + | 0.166544i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 689.980i | 0.728596i | 0.931283 | + | 0.364298i | \(0.118691\pi\) | ||||
−0.931283 | + | 0.364298i | \(0.881309\pi\) | |||||||
\(948\) | 2099.89 | + | 929.456i | 2.21507 | + | 0.980439i | ||||
\(949\) | 122.739 | 0.129335 | ||||||||
\(950\) | 782.560i | 0.823747i | ||||||||
\(951\) | 635.993 | − | 1436.88i | 0.668762 | − | 1.51091i | ||||
\(952\) | 1923.04 | 2.02000 | ||||||||
\(953\) | − | 1342.08i | − | 1.40827i | −0.710067 | − | 0.704134i | \(-0.751335\pi\) | ||
0.710067 | − | 0.704134i | \(-0.248665\pi\) | |||||||
\(954\) | −875.160 | − | 963.491i | −0.917359 | − | 1.00995i | ||||
\(955\) | −658.424 | −0.689449 | ||||||||
\(956\) | 3062.78i | 3.20374i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −614.947 | −0.641907 | ||||||||
\(959\) | − | 714.724i | − | 0.745281i | ||||||
\(960\) | −24.2825 | + | 54.8607i | −0.0252943 | + | 0.0571466i | ||||
\(961\) | −413.990 | −0.430790 | ||||||||
\(962\) | − | 42.7536i | − | 0.0444424i | ||||||
\(963\) | 1227.28 | − | 1114.76i | 1.27443 | − | 1.15759i | ||||
\(964\) | 2318.65 | 2.40524 | ||||||||
\(965\) | − | 305.469i | − | 0.316548i | ||||||
\(966\) | 1773.87 | + | 785.153i | 1.83630 | + | 0.812787i | ||||
\(967\) | 1283.30 | 1.32709 | 0.663546 | − | 0.748135i | \(-0.269051\pi\) | ||||
0.663546 | + | 0.748135i | \(0.269051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 159.384 | − | 360.091i | 0.164483 | − | 0.371611i | ||||
\(970\) | −577.560 | −0.595423 | ||||||||
\(971\) | 850.821i | 0.876231i | 0.898919 | + | 0.438116i | \(0.144354\pi\) | ||||
−0.898919 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(972\) | −1057.14 | + | 1877.96i | −1.08759 | + | 1.93205i | ||||
\(973\) | 1878.44 | 1.93057 | ||||||||
\(974\) | − | 1777.49i | − | 1.82494i | ||||||
\(975\) | 93.1626 | + | 41.2358i | 0.0955514 | + | 0.0422931i | ||||
\(976\) | 2106.64 | 2.15845 | ||||||||
\(977\) | 1212.63i | 1.24118i | 0.784136 | + | 0.620589i | \(0.213107\pi\) | ||||
−0.784136 | + | 0.620589i | \(0.786893\pi\) | |||||||
\(978\) | 705.322 | − | 1593.51i | 0.721188 | − | 1.62936i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 546.831i | 0.557991i | ||||||||
\(981\) | −354.236 | − | 389.990i | −0.361097 | − | 0.397543i | ||||
\(982\) | 1184.69 | 1.20641 | ||||||||
\(983\) | 454.656i | 0.462519i | 0.972892 | + | 0.231260i | \(0.0742846\pi\) | ||||
−0.972892 | + | 0.231260i | \(0.925715\pi\) | |||||||
\(984\) | −1862.63 | − | 824.438i | −1.89291 | − | 0.837844i | ||||
\(985\) | 478.741 | 0.486031 | ||||||||
\(986\) | − | 517.357i | − | 0.524703i | ||||||
\(987\) | 487.603 | − | 1101.63i | 0.494026 | − | 1.11614i | ||||
\(988\) | 154.122 | 0.155993 | ||||||||
\(989\) | − | 322.239i | − | 0.325823i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 697.554 | 0.703889 | 0.351945 | − | 0.936021i | \(-0.385521\pi\) | ||||
0.351945 | + | 0.936021i | \(0.385521\pi\) | |||||||
\(992\) | − | 646.256i | − | 0.651468i | ||||||
\(993\) | −690.502 | − | 305.631i | −0.695369 | − | 0.307786i | ||||
\(994\) | 324.699 | 0.326659 | ||||||||
\(995\) | 812.355i | 0.816437i | ||||||||
\(996\) | −127.158 | + | 287.283i | −0.127669 | + | 0.288437i | ||||
\(997\) | 653.975 | 0.655943 | 0.327971 | − | 0.944688i | \(-0.393635\pi\) | ||||
0.327971 | + | 0.944688i | \(0.393635\pi\) | |||||||
\(998\) | 393.885i | 0.394675i | ||||||||
\(999\) | −61.6705 | − | 185.666i | −0.0617322 | − | 0.185852i |
(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 | 363.3.b.m.122.8 | 8 | ||
3.2 | odd | 2 | inner | 363.3.b.m.122.1 | 8 | ||
11.2 | odd | 10 | 363.3.h.j.323.1 | 16 | |||
11.3 | even | 5 | 363.3.h.o.251.4 | 16 | |||
11.4 | even | 5 | 363.3.h.o.269.1 | 16 | |||
11.5 | even | 5 | 33.3.h.b.14.1 | ✓ | 16 | ||
11.6 | odd | 10 | 363.3.h.j.245.4 | 16 | |||
11.7 | odd | 10 | 363.3.h.n.269.4 | 16 | |||
11.8 | odd | 10 | 363.3.h.n.251.1 | 16 | |||
11.9 | even | 5 | 33.3.h.b.26.4 | yes | 16 | ||
11.10 | odd | 2 | 363.3.b.l.122.1 | 8 | |||
33.2 | even | 10 | 363.3.h.j.323.4 | 16 | |||
33.5 | odd | 10 | 33.3.h.b.14.4 | yes | 16 | ||
33.8 | even | 10 | 363.3.h.n.251.4 | 16 | |||
33.14 | odd | 10 | 363.3.h.o.251.1 | 16 | |||
33.17 | even | 10 | 363.3.h.j.245.1 | 16 | |||
33.20 | odd | 10 | 33.3.h.b.26.1 | yes | 16 | ||
33.26 | odd | 10 | 363.3.h.o.269.4 | 16 | |||
33.29 | even | 10 | 363.3.h.n.269.1 | 16 | |||
33.32 | even | 2 | 363.3.b.l.122.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.h.b.14.1 | ✓ | 16 | 11.5 | even | 5 | ||
33.3.h.b.14.4 | yes | 16 | 33.5 | odd | 10 | ||
33.3.h.b.26.1 | yes | 16 | 33.20 | odd | 10 | ||
33.3.h.b.26.4 | yes | 16 | 11.9 | even | 5 | ||
363.3.b.l.122.1 | 8 | 11.10 | odd | 2 | |||
363.3.b.l.122.8 | 8 | 33.32 | even | 2 | |||
363.3.b.m.122.1 | 8 | 3.2 | odd | 2 | inner | ||
363.3.b.m.122.8 | 8 | 1.1 | even | 1 | trivial | ||
363.3.h.j.245.1 | 16 | 33.17 | even | 10 | |||
363.3.h.j.245.4 | 16 | 11.6 | odd | 10 | |||
363.3.h.j.323.1 | 16 | 11.2 | odd | 10 | |||
363.3.h.j.323.4 | 16 | 33.2 | even | 10 | |||
363.3.h.n.251.1 | 16 | 11.8 | odd | 10 | |||
363.3.h.n.251.4 | 16 | 33.8 | even | 10 | |||
363.3.h.n.269.1 | 16 | 33.29 | even | 10 | |||
363.3.h.n.269.4 | 16 | 11.7 | odd | 10 | |||
363.3.h.o.251.1 | 16 | 33.14 | odd | 10 | |||
363.3.h.o.251.4 | 16 | 11.3 | even | 5 | |||
363.3.h.o.269.1 | 16 | 11.4 | even | 5 | |||
363.3.h.o.269.4 | 16 | 33.26 | odd | 10 |