Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,4,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(13.5704393013\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 212 x^{12} + 17560 x^{10} + 728073 x^{8} + 16036416 x^{6} + 183184060 x^{4} + 961600400 x^{2} + 1560250000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.3 | ||
Root | \(-3.85861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.4.b.a.139.12 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | − | 4.85861i | − | 0.935039i | −0.883983 | − | 0.467520i | \(-0.845148\pi\) | ||
0.883983 | − | 0.467520i | \(-0.154852\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 8.38650 | + | 7.39369i | 0.750112 | + | 0.661311i | ||||
\(6\) | −9.71722 | −0.661173 | ||||||||
\(7\) | 11.5462i | 0.623435i | 0.950175 | + | 0.311717i | \(0.100904\pi\) | ||||
−0.950175 | + | 0.311717i | \(0.899096\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 3.39393 | 0.125701 | ||||||||
\(10\) | 14.7874 | − | 16.7730i | 0.467618 | − | 0.530409i | ||||
\(11\) | 30.5254 | 0.836704 | 0.418352 | − | 0.908285i | \(-0.362608\pi\) | ||||
0.418352 | + | 0.908285i | \(0.362608\pi\) | |||||||
\(12\) | 19.4344i | 0.467520i | ||||||||
\(13\) | 52.0283i | 1.11000i | 0.831849 | + | 0.555002i | \(0.187283\pi\) | ||||
−0.831849 | + | 0.555002i | \(0.812717\pi\) | |||||||
\(14\) | 23.0923 | 0.440835 | ||||||||
\(15\) | 35.9230 | − | 40.7467i | 0.618352 | − | 0.701384i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 38.0089i | 0.542266i | 0.962542 | + | 0.271133i | \(0.0873983\pi\) | ||||
−0.962542 | + | 0.271133i | \(0.912602\pi\) | |||||||
\(18\) | − | 6.78787i | − | 0.0888842i | ||||||
\(19\) | 109.470 | 1.32179 | 0.660896 | − | 0.750478i | \(-0.270177\pi\) | ||||
0.660896 | + | 0.750478i | \(0.270177\pi\) | |||||||
\(20\) | −33.5460 | − | 29.5747i | −0.375056 | − | 0.330656i | ||||
\(21\) | 56.0983 | 0.582936 | ||||||||
\(22\) | − | 61.0508i | − | 0.591639i | ||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | 38.8689 | 0.330586 | ||||||||
\(25\) | 15.6668 | + | 124.014i | 0.125335 | + | 0.992115i | ||||
\(26\) | 104.057 | 0.784892 | ||||||||
\(27\) | − | 147.672i | − | 1.05258i | ||||||
\(28\) | − | 46.1847i | − | 0.311717i | ||||||
\(29\) | −60.9293 | −0.390148 | −0.195074 | − | 0.980789i | \(-0.562495\pi\) | ||||
−0.195074 | + | 0.980789i | \(0.562495\pi\) | |||||||
\(30\) | −81.4934 | − | 71.8460i | −0.495953 | − | 0.437241i | ||||
\(31\) | −63.1074 | −0.365626 | −0.182813 | − | 0.983148i | \(-0.558520\pi\) | ||||
−0.182813 | + | 0.983148i | \(0.558520\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | − | 148.311i | − | 0.782352i | ||||||
\(34\) | 76.0178 | 0.383440 | ||||||||
\(35\) | −85.3687 | + | 96.8320i | −0.412284 | + | 0.467645i | ||||
\(36\) | −13.5757 | −0.0628506 | ||||||||
\(37\) | − | 386.056i | − | 1.71533i | −0.514208 | − | 0.857666i | \(-0.671914\pi\) | ||
0.514208 | − | 0.857666i | \(-0.328086\pi\) | |||||||
\(38\) | − | 218.939i | − | 0.934648i | ||||||
\(39\) | 252.785 | 1.03790 | ||||||||
\(40\) | −59.1495 | + | 67.0920i | −0.233809 | + | 0.265204i | ||||
\(41\) | −92.0091 | −0.350473 | −0.175237 | − | 0.984526i | \(-0.556069\pi\) | ||||
−0.175237 | + | 0.984526i | \(0.556069\pi\) | |||||||
\(42\) | − | 112.197i | − | 0.412198i | ||||||
\(43\) | − | 181.661i | − | 0.644255i | −0.946696 | − | 0.322128i | \(-0.895602\pi\) | ||
0.946696 | − | 0.322128i | \(-0.104398\pi\) | |||||||
\(44\) | −122.102 | −0.418352 | ||||||||
\(45\) | 28.4632 | + | 25.0937i | 0.0942899 | + | 0.0831276i | ||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 207.423i | 0.643740i | 0.946784 | + | 0.321870i | \(0.104311\pi\) | ||||
−0.946784 | + | 0.321870i | \(0.895689\pi\) | |||||||
\(48\) | − | 77.7377i | − | 0.233760i | ||||||
\(49\) | 209.686 | 0.611329 | ||||||||
\(50\) | 248.029 | − | 31.3337i | 0.701531 | − | 0.0886250i | ||||
\(51\) | 184.670 | 0.507040 | ||||||||
\(52\) | − | 208.113i | − | 0.555002i | ||||||
\(53\) | 136.696i | 0.354277i | 0.984186 | + | 0.177138i | \(0.0566840\pi\) | ||||
−0.984186 | + | 0.177138i | \(0.943316\pi\) | |||||||
\(54\) | −295.344 | −0.744283 | ||||||||
\(55\) | 256.001 | + | 225.695i | 0.627622 | + | 0.553322i | ||||
\(56\) | −92.3694 | −0.220417 | ||||||||
\(57\) | − | 531.870i | − | 1.23593i | ||||||
\(58\) | 121.859i | 0.275876i | ||||||||
\(59\) | 230.608 | 0.508859 | 0.254429 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254429 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(60\) | −143.692 | + | 162.987i | −0.309176 | + | 0.350692i | ||||
\(61\) | −241.396 | −0.506681 | −0.253341 | − | 0.967377i | \(-0.581529\pi\) | ||||
−0.253341 | + | 0.967377i | \(0.581529\pi\) | |||||||
\(62\) | 126.215i | 0.258537i | ||||||||
\(63\) | 39.1869i | 0.0783665i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −384.681 | + | 436.336i | −0.734059 | + | 0.832627i | ||||
\(66\) | −296.622 | −0.553206 | ||||||||
\(67\) | 269.366i | 0.491168i | 0.969375 | + | 0.245584i | \(0.0789797\pi\) | ||||
−0.969375 | + | 0.245584i | \(0.921020\pi\) | |||||||
\(68\) | − | 152.036i | − | 0.271133i | ||||||
\(69\) | 111.748 | 0.194969 | ||||||||
\(70\) | 193.664 | + | 170.737i | 0.330675 | + | 0.291529i | ||||
\(71\) | 186.611 | 0.311925 | 0.155963 | − | 0.987763i | \(-0.450152\pi\) | ||||
0.155963 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(72\) | 27.1515i | 0.0444421i | ||||||||
\(73\) | 59.1574i | 0.0948473i | 0.998875 | + | 0.0474236i | \(0.0151011\pi\) | ||||
−0.998875 | + | 0.0474236i | \(0.984899\pi\) | |||||||
\(74\) | −772.113 | −1.21292 | ||||||||
\(75\) | 602.537 | − | 76.1190i | 0.927666 | − | 0.117193i | ||||
\(76\) | −437.878 | −0.660896 | ||||||||
\(77\) | 352.451i | 0.521631i | ||||||||
\(78\) | − | 505.571i | − | 0.733905i | ||||||
\(79\) | 941.143 | 1.34034 | 0.670170 | − | 0.742208i | \(-0.266221\pi\) | ||||
0.670170 | + | 0.742208i | \(0.266221\pi\) | |||||||
\(80\) | 134.184 | + | 118.299i | 0.187528 | + | 0.165328i | ||||
\(81\) | −625.845 | −0.858498 | ||||||||
\(82\) | 184.018i | 0.247822i | ||||||||
\(83\) | 94.2803i | 0.124682i | 0.998055 | + | 0.0623410i | \(0.0198566\pi\) | ||||
−0.998055 | + | 0.0623410i | \(0.980143\pi\) | |||||||
\(84\) | −224.393 | −0.291468 | ||||||||
\(85\) | −281.026 | + | 318.762i | −0.358606 | + | 0.406760i | ||||
\(86\) | −363.321 | −0.455557 | ||||||||
\(87\) | 296.032i | 0.364804i | ||||||||
\(88\) | 244.203i | 0.295820i | ||||||||
\(89\) | 1380.57 | 1.64427 | 0.822135 | − | 0.569293i | \(-0.192783\pi\) | ||||
0.822135 | + | 0.569293i | \(0.192783\pi\) | |||||||
\(90\) | 50.1873 | − | 56.9265i | 0.0587801 | − | 0.0666731i | ||||
\(91\) | −600.728 | −0.692015 | ||||||||
\(92\) | − | 92.0000i | − | 0.104257i | ||||||
\(93\) | 306.614i | 0.341875i | ||||||||
\(94\) | 414.846 | 0.455193 | ||||||||
\(95\) | 918.067 | + | 809.383i | 0.991491 | + | 0.874116i | ||||
\(96\) | −155.475 | −0.165293 | ||||||||
\(97\) | 1253.69i | 1.31230i | 0.754632 | + | 0.656149i | \(0.227816\pi\) | ||||
−0.754632 | + | 0.656149i | \(0.772184\pi\) | |||||||
\(98\) | − | 419.372i | − | 0.432275i | ||||||
\(99\) | 103.601 | 0.105175 | ||||||||
\(100\) | −62.6673 | − | 496.057i | −0.0626673 | − | 0.496057i | ||||
\(101\) | −1424.98 | −1.40387 | −0.701936 | − | 0.712240i | \(-0.747681\pi\) | ||||
−0.701936 | + | 0.712240i | \(0.747681\pi\) | |||||||
\(102\) | − | 369.341i | − | 0.358531i | ||||||
\(103\) | − | 498.334i | − | 0.476721i | −0.971177 | − | 0.238361i | \(-0.923390\pi\) | ||
0.971177 | − | 0.238361i | \(-0.0766100\pi\) | |||||||
\(104\) | −416.227 | −0.392446 | ||||||||
\(105\) | 470.469 | + | 414.773i | 0.437267 | + | 0.385502i | ||||
\(106\) | 273.392 | 0.250511 | ||||||||
\(107\) | − | 897.019i | − | 0.810450i | −0.914217 | − | 0.405225i | \(-0.867193\pi\) | ||
0.914217 | − | 0.405225i | \(-0.132807\pi\) | |||||||
\(108\) | 590.689i | 0.526288i | ||||||||
\(109\) | −1784.56 | −1.56817 | −0.784084 | − | 0.620655i | \(-0.786867\pi\) | ||||
−0.784084 | + | 0.620655i | \(0.786867\pi\) | |||||||
\(110\) | 451.390 | − | 512.002i | 0.391258 | − | 0.443796i | ||||
\(111\) | −1875.70 | −1.60390 | ||||||||
\(112\) | 184.739i | 0.155859i | ||||||||
\(113\) | − | 1320.30i | − | 1.09915i | −0.835445 | − | 0.549574i | \(-0.814790\pi\) | ||
0.835445 | − | 0.549574i | \(-0.185210\pi\) | |||||||
\(114\) | −1063.74 | −0.873932 | ||||||||
\(115\) | −170.055 | + | 192.890i | −0.137893 | + | 0.156409i | ||||
\(116\) | 243.717 | 0.195074 | ||||||||
\(117\) | 176.581i | 0.139529i | ||||||||
\(118\) | − | 461.217i | − | 0.359817i | ||||||
\(119\) | −438.858 | −0.338067 | ||||||||
\(120\) | 325.974 | + | 287.384i | 0.247977 | + | 0.218621i | ||||
\(121\) | −399.201 | −0.299926 | ||||||||
\(122\) | 482.791i | 0.358278i | ||||||||
\(123\) | 447.036i | 0.327706i | ||||||||
\(124\) | 252.429 | 0.182813 | ||||||||
\(125\) | −785.533 | + | 1155.88i | −0.562082 | + | 0.827082i | ||||
\(126\) | 78.3739 | 0.0554135 | ||||||||
\(127\) | 1464.71i | 1.02340i | 0.859163 | + | 0.511702i | \(0.170985\pi\) | ||||
−0.859163 | + | 0.511702i | \(0.829015\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −882.617 | −0.602404 | ||||||||
\(130\) | 872.671 | + | 769.362i | 0.588757 | + | 0.519058i | ||||
\(131\) | −351.211 | −0.234240 | −0.117120 | − | 0.993118i | \(-0.537366\pi\) | ||||
−0.117120 | + | 0.993118i | \(0.537366\pi\) | |||||||
\(132\) | 593.243i | 0.391176i | ||||||||
\(133\) | 1263.95i | 0.824050i | ||||||||
\(134\) | 538.731 | 0.347308 | ||||||||
\(135\) | 1091.84 | − | 1238.45i | 0.696080 | − | 0.789549i | ||||
\(136\) | −304.071 | −0.191720 | ||||||||
\(137\) | − | 331.895i | − | 0.206976i | −0.994631 | − | 0.103488i | \(-0.967000\pi\) | ||
0.994631 | − | 0.103488i | \(-0.0330003\pi\) | |||||||
\(138\) | − | 223.496i | − | 0.137864i | ||||||
\(139\) | 2215.75 | 1.35207 | 0.676033 | − | 0.736872i | \(-0.263698\pi\) | ||||
0.676033 | + | 0.736872i | \(0.263698\pi\) | |||||||
\(140\) | 341.475 | − | 387.328i | 0.206142 | − | 0.233823i | ||||
\(141\) | 1007.79 | 0.601922 | ||||||||
\(142\) | − | 373.223i | − | 0.220564i | ||||||
\(143\) | 1588.18i | 0.928746i | ||||||||
\(144\) | 54.3029 | 0.0314253 | ||||||||
\(145\) | −510.984 | − | 450.492i | −0.292654 | − | 0.258009i | ||||
\(146\) | 118.315 | 0.0670672 | ||||||||
\(147\) | − | 1018.78i | − | 0.571617i | ||||||
\(148\) | 1544.23i | 0.857666i | ||||||||
\(149\) | −2477.32 | −1.36208 | −0.681041 | − | 0.732245i | \(-0.738473\pi\) | ||||
−0.681041 | + | 0.732245i | \(0.738473\pi\) | |||||||
\(150\) | −152.238 | − | 1205.07i | −0.0828679 | − | 0.655959i | ||||
\(151\) | −1018.32 | −0.548806 | −0.274403 | − | 0.961615i | \(-0.588480\pi\) | ||||
−0.274403 | + | 0.961615i | \(0.588480\pi\) | |||||||
\(152\) | 875.756i | 0.467324i | ||||||||
\(153\) | 129.000i | 0.0681635i | ||||||||
\(154\) | 704.903 | 0.368848 | ||||||||
\(155\) | −529.250 | − | 466.596i | −0.274261 | − | 0.241793i | ||||
\(156\) | −1011.14 | −0.518949 | ||||||||
\(157\) | 1086.32i | 0.552216i | 0.961127 | + | 0.276108i | \(0.0890447\pi\) | ||||
−0.961127 | + | 0.276108i | \(0.910955\pi\) | |||||||
\(158\) | − | 1882.29i | − | 0.947763i | ||||||
\(159\) | 664.153 | 0.331263 | ||||||||
\(160\) | 236.598 | − | 268.368i | 0.116904 | − | 0.132602i | ||||
\(161\) | −265.562 | −0.129995 | ||||||||
\(162\) | 1251.69i | 0.607050i | ||||||||
\(163\) | − | 143.788i | − | 0.0690942i | −0.999403 | − | 0.0345471i | \(-0.989001\pi\) | ||
0.999403 | − | 0.0345471i | \(-0.0109989\pi\) | |||||||
\(164\) | 368.036 | 0.175237 | ||||||||
\(165\) | 1096.56 | − | 1243.81i | 0.517378 | − | 0.586851i | ||||
\(166\) | 188.561 | 0.0881635 | ||||||||
\(167\) | − | 2265.50i | − | 1.04976i | −0.851177 | − | 0.524878i | \(-0.824111\pi\) | ||
0.851177 | − | 0.524878i | \(-0.175889\pi\) | |||||||
\(168\) | 448.786i | 0.206099i | ||||||||
\(169\) | −509.948 | −0.232111 | ||||||||
\(170\) | 637.524 | + | 562.052i | 0.287623 | + | 0.253573i | ||||
\(171\) | 371.532 | 0.166151 | ||||||||
\(172\) | 726.642i | 0.322128i | ||||||||
\(173\) | − | 4159.77i | − | 1.82810i | −0.405602 | − | 0.914050i | \(-0.632938\pi\) | ||
0.405602 | − | 0.914050i | \(-0.367062\pi\) | |||||||
\(174\) | 592.063 | 0.257955 | ||||||||
\(175\) | −1431.89 | + | 180.892i | −0.618519 | + | 0.0781380i | ||||
\(176\) | 488.406 | 0.209176 | ||||||||
\(177\) | − | 1120.44i | − | 0.475803i | ||||||
\(178\) | − | 2761.14i | − | 1.16267i | ||||||
\(179\) | 3483.94 | 1.45476 | 0.727379 | − | 0.686236i | \(-0.240738\pi\) | ||||
0.727379 | + | 0.686236i | \(0.240738\pi\) | |||||||
\(180\) | −113.853 | − | 100.375i | −0.0471450 | − | 0.0415638i | ||||
\(181\) | 2365.09 | 0.971246 | 0.485623 | − | 0.874168i | \(-0.338593\pi\) | ||||
0.485623 | + | 0.874168i | \(0.338593\pi\) | |||||||
\(182\) | 1201.46i | 0.489329i | ||||||||
\(183\) | 1172.85i | 0.473767i | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 2854.38 | − | 3237.66i | 1.13437 | − | 1.28669i | ||||
\(186\) | 613.228 | 0.241742 | ||||||||
\(187\) | 1160.24i | 0.453716i | ||||||||
\(188\) | − | 829.692i | − | 0.321870i | ||||||
\(189\) | 1705.05 | 0.656212 | ||||||||
\(190\) | 1618.77 | − | 1836.13i | 0.618093 | − | 0.701090i | ||||
\(191\) | −4868.10 | −1.84421 | −0.922103 | − | 0.386944i | \(-0.873531\pi\) | ||||
−0.922103 | + | 0.386944i | \(0.873531\pi\) | |||||||
\(192\) | 310.951i | 0.116880i | ||||||||
\(193\) | − | 1452.53i | − | 0.541737i | −0.962616 | − | 0.270869i | \(-0.912689\pi\) | ||
0.962616 | − | 0.270869i | \(-0.0873109\pi\) | |||||||
\(194\) | 2507.38 | 0.927934 | ||||||||
\(195\) | 2119.98 | + | 1869.01i | 0.778540 | + | 0.686374i | ||||
\(196\) | −838.744 | −0.305665 | ||||||||
\(197\) | − | 4235.47i | − | 1.53180i | −0.642960 | − | 0.765900i | \(-0.722294\pi\) | ||
0.642960 | − | 0.765900i | \(-0.277706\pi\) | |||||||
\(198\) | − | 207.202i | − | 0.0743698i | ||||||
\(199\) | −2457.38 | −0.875374 | −0.437687 | − | 0.899128i | \(-0.644202\pi\) | ||||
−0.437687 | + | 0.899128i | \(0.644202\pi\) | |||||||
\(200\) | −992.115 | + | 125.335i | −0.350765 | + | 0.0443125i | ||||
\(201\) | 1308.74 | 0.459261 | ||||||||
\(202\) | 2849.97i | 0.992687i | ||||||||
\(203\) | − | 703.500i | − | 0.243232i | ||||||
\(204\) | −738.682 | −0.253520 | ||||||||
\(205\) | −771.634 | − | 680.286i | −0.262894 | − | 0.231772i | ||||
\(206\) | −996.667 | −0.337093 | ||||||||
\(207\) | 78.0605i | 0.0262105i | ||||||||
\(208\) | 832.453i | 0.277501i | ||||||||
\(209\) | 3341.60 | 1.10595 | ||||||||
\(210\) | 829.546 | − | 940.937i | 0.272591 | − | 0.309194i | ||||
\(211\) | −2325.90 | −0.758871 | −0.379435 | − | 0.925218i | \(-0.623882\pi\) | ||||
−0.379435 | + | 0.925218i | \(0.623882\pi\) | |||||||
\(212\) | − | 546.784i | − | 0.177138i | ||||||
\(213\) | − | 906.671i | − | 0.291662i | ||||||
\(214\) | −1794.04 | −0.573075 | ||||||||
\(215\) | 1343.14 | − | 1523.50i | 0.426053 | − | 0.483263i | ||||
\(216\) | 1181.38 | 0.372141 | ||||||||
\(217\) | − | 728.648i | − | 0.227944i | ||||||
\(218\) | 3569.13i | 1.10886i | ||||||||
\(219\) | 287.423 | 0.0886859 | ||||||||
\(220\) | −1024.00 | − | 902.780i | −0.313811 | − | 0.276661i | ||||
\(221\) | −1977.54 | −0.601918 | ||||||||
\(222\) | 3751.39i | 1.13413i | ||||||||
\(223\) | 5012.72i | 1.50528i | 0.658435 | + | 0.752638i | \(0.271219\pi\) | ||||
−0.658435 | + | 0.752638i | \(0.728781\pi\) | |||||||
\(224\) | 369.477 | 0.110209 | ||||||||
\(225\) | 53.1722 | + | 420.896i | 0.0157547 | + | 0.124710i | ||||
\(226\) | −2640.61 | −0.777215 | ||||||||
\(227\) | − | 3897.60i | − | 1.13962i | −0.821778 | − | 0.569808i | \(-0.807017\pi\) | ||
0.821778 | − | 0.569808i | \(-0.192983\pi\) | |||||||
\(228\) | 2127.48i | 0.617964i | ||||||||
\(229\) | −2346.46 | −0.677111 | −0.338556 | − | 0.940946i | \(-0.609938\pi\) | ||||
−0.338556 | + | 0.940946i | \(0.609938\pi\) | |||||||
\(230\) | 385.779 | + | 340.110i | 0.110598 | + | 0.0975050i | ||||
\(231\) | 1712.42 | 0.487745 | ||||||||
\(232\) | − | 487.434i | − | 0.137938i | ||||||
\(233\) | − | 2476.94i | − | 0.696437i | −0.937413 | − | 0.348218i | \(-0.886787\pi\) | ||
0.937413 | − | 0.348218i | \(-0.113213\pi\) | |||||||
\(234\) | 353.161 | 0.0986619 | ||||||||
\(235\) | −1533.62 | + | 1739.55i | −0.425712 | + | 0.482877i | ||||
\(236\) | −922.434 | −0.254429 | ||||||||
\(237\) | − | 4572.64i | − | 1.25327i | ||||||
\(238\) | 877.715i | 0.239050i | ||||||||
\(239\) | 5126.70 | 1.38753 | 0.693764 | − | 0.720203i | \(-0.255951\pi\) | ||||
0.693764 | + | 0.720203i | \(0.255951\pi\) | |||||||
\(240\) | 574.768 | − | 651.948i | 0.154588 | − | 0.175346i | ||||
\(241\) | −4672.12 | −1.24879 | −0.624394 | − | 0.781110i | \(-0.714654\pi\) | ||||
−0.624394 | + | 0.781110i | \(0.714654\pi\) | |||||||
\(242\) | 798.402i | 0.212079i | ||||||||
\(243\) | − | 946.414i | − | 0.249846i | ||||||
\(244\) | 965.583 | 0.253341 | ||||||||
\(245\) | 1758.53 | + | 1550.35i | 0.458565 | + | 0.404279i | ||||
\(246\) | 894.072 | 0.231723 | ||||||||
\(247\) | 5695.52i | 1.46719i | ||||||||
\(248\) | − | 504.859i | − | 0.129268i | ||||||
\(249\) | 458.071 | 0.116583 | ||||||||
\(250\) | 2311.76 | + | 1571.07i | 0.584835 | + | 0.397452i | ||||
\(251\) | 3001.39 | 0.754764 | 0.377382 | − | 0.926058i | \(-0.376824\pi\) | ||||
0.377382 | + | 0.926058i | \(0.376824\pi\) | |||||||
\(252\) | − | 156.748i | − | 0.0391832i | ||||||
\(253\) | 702.084i | 0.174465i | ||||||||
\(254\) | 2929.43 | 0.723656 | ||||||||
\(255\) | 1548.74 | + | 1365.40i | 0.380336 | + | 0.335311i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 1398.04i | − | 0.339329i | −0.985502 | − | 0.169664i | \(-0.945732\pi\) | ||
0.985502 | − | 0.169664i | \(-0.0542684\pi\) | |||||||
\(258\) | 1765.23i | 0.425964i | ||||||||
\(259\) | 4457.47 | 1.06940 | ||||||||
\(260\) | 1538.72 | − | 1745.34i | 0.367029 | − | 0.416314i | ||||
\(261\) | −206.790 | −0.0490421 | ||||||||
\(262\) | 702.422i | 0.165633i | ||||||||
\(263\) | − | 451.199i | − | 0.105787i | −0.998600 | − | 0.0528937i | \(-0.983156\pi\) | ||
0.998600 | − | 0.0528937i | \(-0.0168445\pi\) | |||||||
\(264\) | 1186.49 | 0.276603 | ||||||||
\(265\) | −1010.69 | + | 1146.40i | −0.234287 | + | 0.265747i | ||||
\(266\) | 2527.91 | 0.582692 | ||||||||
\(267\) | − | 6707.64i | − | 1.53746i | ||||||
\(268\) | − | 1077.46i | − | 0.245584i | ||||||
\(269\) | −4998.42 | −1.13293 | −0.566467 | − | 0.824084i | \(-0.691690\pi\) | ||||
−0.566467 | + | 0.824084i | \(0.691690\pi\) | |||||||
\(270\) | −2476.91 | − | 2183.68i | −0.558295 | − | 0.492203i | ||||
\(271\) | −8357.51 | −1.87337 | −0.936684 | − | 0.350176i | \(-0.886122\pi\) | ||||
−0.936684 | + | 0.350176i | \(0.886122\pi\) | |||||||
\(272\) | 608.143i | 0.135566i | ||||||||
\(273\) | 2918.70i | 0.647062i | ||||||||
\(274\) | −663.790 | −0.146354 | ||||||||
\(275\) | 478.236 | + | 3785.58i | 0.104868 | + | 0.830107i | ||||
\(276\) | −446.992 | −0.0974846 | ||||||||
\(277\) | 632.582i | 0.137214i | 0.997644 | + | 0.0686068i | \(0.0218554\pi\) | ||||
−0.997644 | + | 0.0686068i | \(0.978145\pi\) | |||||||
\(278\) | − | 4431.49i | − | 0.956055i | ||||||
\(279\) | −214.182 | −0.0459597 | ||||||||
\(280\) | −774.656 | − | 682.950i | −0.165338 | − | 0.145765i | ||||
\(281\) | −7414.60 | −1.57408 | −0.787042 | − | 0.616899i | \(-0.788389\pi\) | ||||
−0.787042 | + | 0.616899i | \(0.788389\pi\) | |||||||
\(282\) | − | 2015.57i | − | 0.425623i | ||||||
\(283\) | − | 2450.81i | − | 0.514789i | −0.966306 | − | 0.257395i | \(-0.917136\pi\) | ||
0.966306 | − | 0.257395i | \(-0.0828640\pi\) | |||||||
\(284\) | −746.445 | −0.155963 | ||||||||
\(285\) | 3932.48 | − | 4460.52i | 0.817333 | − | 0.927083i | ||||
\(286\) | 3176.37 | 0.656723 | ||||||||
\(287\) | − | 1062.35i | − | 0.218497i | ||||||
\(288\) | − | 108.606i | − | 0.0222210i | ||||||
\(289\) | 3468.32 | 0.705948 | ||||||||
\(290\) | −900.984 | + | 1021.97i | −0.182440 | + | 0.206938i | ||||
\(291\) | 6091.18 | 1.22705 | ||||||||
\(292\) | − | 236.630i | − | 0.0474236i | ||||||
\(293\) | 8753.49i | 1.74534i | 0.488311 | + | 0.872670i | \(0.337613\pi\) | ||||
−0.488311 | + | 0.872670i | \(0.662387\pi\) | |||||||
\(294\) | −2037.56 | −0.404194 | ||||||||
\(295\) | 1934.00 | + | 1705.05i | 0.381701 | + | 0.336514i | ||||
\(296\) | 3088.45 | 0.606461 | ||||||||
\(297\) | − | 4507.75i | − | 0.880694i | ||||||
\(298\) | 4954.65i | 0.963138i | ||||||||
\(299\) | −1196.65 | −0.231452 | ||||||||
\(300\) | −2410.15 | + | 304.476i | −0.463833 | + | 0.0585964i | ||||
\(301\) | 2097.48 | 0.401651 | ||||||||
\(302\) | 2036.64i | 0.388064i | ||||||||
\(303\) | 6923.43i | 1.31268i | ||||||||
\(304\) | 1751.51 | 0.330448 | ||||||||
\(305\) | −2024.47 | − | 1784.80i | −0.380067 | − | 0.335074i | ||||
\(306\) | 257.999 | 0.0481989 | ||||||||
\(307\) | 7545.31i | 1.40272i | 0.712809 | + | 0.701358i | \(0.247422\pi\) | ||||
−0.712809 | + | 0.701358i | \(0.752578\pi\) | |||||||
\(308\) | − | 1409.81i | − | 0.260815i | ||||||
\(309\) | −2421.21 | −0.445753 | ||||||||
\(310\) | −933.192 | + | 1058.50i | −0.170973 | + | 0.193931i | ||||
\(311\) | −4670.34 | −0.851546 | −0.425773 | − | 0.904830i | \(-0.639998\pi\) | ||||
−0.425773 | + | 0.904830i | \(0.639998\pi\) | |||||||
\(312\) | 2022.28i | 0.366952i | ||||||||
\(313\) | − | 3513.81i | − | 0.634544i | −0.948335 | − | 0.317272i | \(-0.897233\pi\) | ||
0.948335 | − | 0.317272i | \(-0.102767\pi\) | |||||||
\(314\) | 2172.64 | 0.390476 | ||||||||
\(315\) | −289.736 | + | 328.641i | −0.0518246 | + | 0.0587836i | ||||
\(316\) | −3764.57 | −0.670170 | ||||||||
\(317\) | − | 6942.35i | − | 1.23004i | −0.788513 | − | 0.615018i | \(-0.789149\pi\) | ||
0.788513 | − | 0.615018i | \(-0.210851\pi\) | |||||||
\(318\) | − | 1328.31i | − | 0.234238i | ||||||
\(319\) | −1859.89 | −0.326438 | ||||||||
\(320\) | −536.736 | − | 473.196i | −0.0937639 | − | 0.0826639i | ||||
\(321\) | −4358.27 | −0.757803 | ||||||||
\(322\) | 531.124i | 0.0919204i | ||||||||
\(323\) | 4160.82i | 0.716762i | ||||||||
\(324\) | 2503.38 | 0.429249 | ||||||||
\(325\) | −6452.26 | + | 815.119i | −1.10125 | + | 0.139122i | ||||
\(326\) | −287.576 | −0.0488570 | ||||||||
\(327\) | 8670.50i | 1.46630i | ||||||||
\(328\) | − | 736.072i | − | 0.123911i | ||||||
\(329\) | −2394.94 | −0.401330 | ||||||||
\(330\) | −2487.62 | − | 2193.13i | −0.414966 | − | 0.365842i | ||||
\(331\) | 4598.51 | 0.763616 | 0.381808 | − | 0.924242i | \(-0.375302\pi\) | ||||
0.381808 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(332\) | − | 377.121i | − | 0.0623410i | ||||||
\(333\) | − | 1310.25i | − | 0.215619i | ||||||
\(334\) | −4530.99 | −0.742290 | ||||||||
\(335\) | −1991.60 | + | 2259.04i | −0.324815 | + | 0.368431i | ||||
\(336\) | 897.573 | 0.145734 | ||||||||
\(337\) | 638.077i | 0.103140i | 0.998669 | + | 0.0515702i | \(0.0164226\pi\) | ||||
−0.998669 | + | 0.0515702i | \(0.983577\pi\) | |||||||
\(338\) | 1019.90i | 0.164127i | ||||||||
\(339\) | −6414.84 | −1.02775 | ||||||||
\(340\) | 1124.10 | − | 1275.05i | 0.179303 | − | 0.203380i | ||||
\(341\) | −1926.38 | −0.305921 | ||||||||
\(342\) | − | 743.065i | − | 0.117486i | ||||||
\(343\) | 6381.41i | 1.00456i | ||||||||
\(344\) | 1453.28 | 0.227779 | ||||||||
\(345\) | 937.175 | + | 826.229i | 0.146249 | + | 0.128935i | ||||
\(346\) | −8319.54 | −1.29266 | ||||||||
\(347\) | − | 302.348i | − | 0.0467750i | −0.999726 | − | 0.0233875i | \(-0.992555\pi\) | ||
0.999726 | − | 0.0233875i | \(-0.00744515\pi\) | |||||||
\(348\) | − | 1184.13i | − | 0.182402i | ||||||
\(349\) | −8944.40 | −1.37187 | −0.685935 | − | 0.727663i | \(-0.740607\pi\) | ||||
−0.685935 | + | 0.727663i | \(0.740607\pi\) | |||||||
\(350\) | 361.784 | + | 2863.78i | 0.0552519 | + | 0.437359i | ||||
\(351\) | 7683.14 | 1.16836 | ||||||||
\(352\) | − | 976.812i | − | 0.147910i | ||||||
\(353\) | 11231.8i | 1.69351i | 0.531981 | + | 0.846756i | \(0.321448\pi\) | ||||
−0.531981 | + | 0.846756i | \(0.678552\pi\) | |||||||
\(354\) | −2240.87 | −0.336443 | ||||||||
\(355\) | 1565.02 | + | 1379.74i | 0.233979 | + | 0.206280i | ||||
\(356\) | −5522.28 | −0.822135 | ||||||||
\(357\) | 2132.24i | 0.316106i | ||||||||
\(358\) | − | 6967.88i | − | 1.02867i | ||||||
\(359\) | −9283.39 | −1.36479 | −0.682393 | − | 0.730985i | \(-0.739061\pi\) | ||||
−0.682393 | + | 0.730985i | \(0.739061\pi\) | |||||||
\(360\) | −200.749 | + | 227.706i | −0.0293901 | + | 0.0333365i | ||||
\(361\) | 5124.58 | 0.747132 | ||||||||
\(362\) | − | 4730.17i | − | 0.686775i | ||||||
\(363\) | 1939.56i | 0.280442i | ||||||||
\(364\) | 2402.91 | 0.346008 | ||||||||
\(365\) | −437.391 | + | 496.124i | −0.0627236 | + | 0.0711460i | ||||
\(366\) | 2345.69 | 0.335004 | ||||||||
\(367\) | − | 9662.14i | − | 1.37428i | −0.726526 | − | 0.687139i | \(-0.758866\pi\) | ||
0.726526 | − | 0.687139i | \(-0.241134\pi\) | |||||||
\(368\) | 368.000i | 0.0521286i | ||||||||
\(369\) | −312.273 | −0.0440549 | ||||||||
\(370\) | −6475.32 | − | 5708.76i | −0.909827 | − | 0.802119i | ||||
\(371\) | −1578.32 | −0.220868 | ||||||||
\(372\) | − | 1226.46i | − | 0.170938i | ||||||
\(373\) | 2630.59i | 0.365166i | 0.983190 | + | 0.182583i | \(0.0584458\pi\) | ||||
−0.983190 | + | 0.182583i | \(0.941554\pi\) | |||||||
\(374\) | 2320.47 | 0.320826 | ||||||||
\(375\) | 5615.98 | + | 3816.60i | 0.773354 | + | 0.525568i | ||||
\(376\) | −1659.38 | −0.227596 | ||||||||
\(377\) | − | 3170.05i | − | 0.433066i | ||||||
\(378\) | − | 3410.10i | − | 0.464012i | ||||||
\(379\) | −3941.24 | −0.534164 | −0.267082 | − | 0.963674i | \(-0.586059\pi\) | ||||
−0.267082 | + | 0.963674i | \(0.586059\pi\) | |||||||
\(380\) | −3672.27 | − | 3237.53i | −0.495745 | − | 0.437058i | ||||
\(381\) | 7116.46 | 0.956923 | ||||||||
\(382\) | 9736.20i | 1.30405i | ||||||||
\(383\) | − | 8146.17i | − | 1.08681i | −0.839469 | − | 0.543407i | \(-0.817134\pi\) | ||
0.839469 | − | 0.543407i | \(-0.182866\pi\) | |||||||
\(384\) | 621.902 | 0.0826466 | ||||||||
\(385\) | −2605.91 | + | 2955.83i | −0.344960 | + | 0.391281i | ||||
\(386\) | −2905.06 | −0.383066 | ||||||||
\(387\) | − | 616.544i | − | 0.0809837i | ||||||
\(388\) | − | 5014.76i | − | 0.656149i | ||||||
\(389\) | 2668.67 | 0.347833 | 0.173917 | − | 0.984760i | \(-0.444358\pi\) | ||||
0.173917 | + | 0.984760i | \(0.444358\pi\) | |||||||
\(390\) | 3738.03 | − | 4239.97i | 0.485340 | − | 0.550511i | ||||
\(391\) | −874.205 | −0.113070 | ||||||||
\(392\) | 1677.49i | 0.216138i | ||||||||
\(393\) | 1706.40i | 0.219024i | ||||||||
\(394\) | −8470.94 | −1.08315 | ||||||||
\(395\) | 7892.89 | + | 6958.51i | 1.00540 | + | 0.886382i | ||||
\(396\) | −414.404 | −0.0525874 | ||||||||
\(397\) | − | 7028.13i | − | 0.888493i | −0.895905 | − | 0.444247i | \(-0.853471\pi\) | ||
0.895905 | − | 0.444247i | \(-0.146529\pi\) | |||||||
\(398\) | 4914.77i | 0.618983i | ||||||||
\(399\) | 6141.06 | 0.770520 | ||||||||
\(400\) | 250.669 | + | 1984.23i | 0.0313337 | + | 0.248029i | ||||
\(401\) | 9420.36 | 1.17314 | 0.586572 | − | 0.809897i | \(-0.300477\pi\) | ||||
0.586572 | + | 0.809897i | \(0.300477\pi\) | |||||||
\(402\) | − | 2617.48i | − | 0.324747i | ||||||
\(403\) | − | 3283.37i | − | 0.405847i | ||||||
\(404\) | 5699.93 | 0.701936 | ||||||||
\(405\) | −5248.65 | − | 4627.30i | −0.643969 | − | 0.567734i | ||||
\(406\) | −1407.00 | −0.171991 | ||||||||
\(407\) | − | 11784.5i | − | 1.43523i | ||||||
\(408\) | 1477.36i | 0.179266i | ||||||||
\(409\) | −10022.5 | −1.21169 | −0.605847 | − | 0.795581i | \(-0.707165\pi\) | ||||
−0.605847 | + | 0.795581i | \(0.707165\pi\) | |||||||
\(410\) | −1360.57 | + | 1543.27i | −0.163887 | + | 0.185894i | ||||
\(411\) | −1612.55 | −0.193531 | ||||||||
\(412\) | 1993.33i | 0.238361i | ||||||||
\(413\) | 2662.64i | 0.317240i | ||||||||
\(414\) | 156.121 | 0.0185336 | ||||||||
\(415\) | −697.079 | + | 790.682i | −0.0824536 | + | 0.0935254i | ||||
\(416\) | 1664.91 | 0.196223 | ||||||||
\(417\) | − | 10765.4i | − | 1.26423i | ||||||
\(418\) | − | 6683.20i | − | 0.782024i | ||||||
\(419\) | 11177.5 | 1.30324 | 0.651621 | − | 0.758545i | \(-0.274089\pi\) | ||||
0.651621 | + | 0.758545i | \(0.274089\pi\) | |||||||
\(420\) | −1881.87 | − | 1659.09i | −0.218633 | − | 0.192751i | ||||
\(421\) | 8965.60 | 1.03790 | 0.518951 | − | 0.854804i | \(-0.326323\pi\) | ||||
0.518951 | + | 0.854804i | \(0.326323\pi\) | |||||||
\(422\) | 4651.81i | 0.536603i | ||||||||
\(423\) | 703.980i | 0.0809189i | ||||||||
\(424\) | −1093.57 | −0.125256 | ||||||||
\(425\) | −4713.65 | + | 595.480i | −0.537990 | + | 0.0679647i | ||||
\(426\) | −1813.34 | −0.206236 | ||||||||
\(427\) | − | 2787.20i | − | 0.315883i | ||||||
\(428\) | 3588.08i | 0.405225i | ||||||||
\(429\) | 7716.37 | 0.868414 | ||||||||
\(430\) | −3046.99 | − | 2686.28i | −0.341719 | − | 0.301265i | ||||
\(431\) | 16553.1 | 1.84997 | 0.924984 | − | 0.380006i | \(-0.124078\pi\) | ||||
0.924984 | + | 0.380006i | \(0.124078\pi\) | |||||||
\(432\) | − | 2362.76i | − | 0.263144i | ||||||
\(433\) | − | 752.803i | − | 0.0835505i | −0.999127 | − | 0.0417753i | \(-0.986699\pi\) | ||
0.999127 | − | 0.0417753i | \(-0.0133014\pi\) | |||||||
\(434\) | −1457.30 | −0.161181 | ||||||||
\(435\) | −2188.76 | + | 2482.67i | −0.241249 | + | 0.273643i | ||||
\(436\) | 7138.26 | 0.784084 | ||||||||
\(437\) | 2517.80i | 0.275613i | ||||||||
\(438\) | − | 574.845i | − | 0.0627104i | ||||||
\(439\) | 2672.91 | 0.290594 | 0.145297 | − | 0.989388i | \(-0.453586\pi\) | ||||
0.145297 | + | 0.989388i | \(0.453586\pi\) | |||||||
\(440\) | −1805.56 | + | 2048.01i | −0.195629 | + | 0.221898i | ||||
\(441\) | 711.660 | 0.0768448 | ||||||||
\(442\) | 3955.08i | 0.425620i | ||||||||
\(443\) | − | 7311.22i | − | 0.784123i | −0.919939 | − | 0.392062i | \(-0.871762\pi\) | ||
0.919939 | − | 0.392062i | \(-0.128238\pi\) | |||||||
\(444\) | 7502.78 | 0.801951 | ||||||||
\(445\) | 11578.1 | + | 10207.5i | 1.23339 | + | 1.08737i | ||||
\(446\) | 10025.4 | 1.06439 | ||||||||
\(447\) | 12036.3i | 1.27360i | ||||||||
\(448\) | − | 738.955i | − | 0.0779293i | ||||||
\(449\) | −3585.70 | −0.376881 | −0.188441 | − | 0.982085i | \(-0.560343\pi\) | ||||
−0.188441 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(450\) | 841.793 | − | 106.344i | 0.0881833 | − | 0.0111403i | ||||
\(451\) | −2808.61 | −0.293242 | ||||||||
\(452\) | 5281.22i | 0.549574i | ||||||||
\(453\) | 4947.62i | 0.513155i | ||||||||
\(454\) | −7795.21 | −0.805831 | ||||||||
\(455\) | −5038.01 | − | 4441.59i | −0.519089 | − | 0.457638i | ||||
\(456\) | 4254.96 | 0.436966 | ||||||||
\(457\) | − | 1222.55i | − | 0.125139i | −0.998041 | − | 0.0625693i | \(-0.980071\pi\) | ||
0.998041 | − | 0.0625693i | \(-0.0199294\pi\) | |||||||
\(458\) | 4692.92i | 0.478790i | ||||||||
\(459\) | 5612.86 | 0.570775 | ||||||||
\(460\) | 680.219 | − | 771.558i | 0.0689465 | − | 0.0782045i | ||||
\(461\) | 3845.46 | 0.388505 | 0.194252 | − | 0.980952i | \(-0.437772\pi\) | ||||
0.194252 | + | 0.980952i | \(0.437772\pi\) | |||||||
\(462\) | − | 3424.84i | − | 0.344888i | ||||||
\(463\) | − | 5113.70i | − | 0.513291i | −0.966506 | − | 0.256645i | \(-0.917383\pi\) | ||
0.966506 | − | 0.256645i | \(-0.0826173\pi\) | |||||||
\(464\) | −974.869 | −0.0975370 | ||||||||
\(465\) | −2267.01 | + | 2571.42i | −0.226086 | + | 0.256444i | ||||
\(466\) | −4953.88 | −0.492455 | ||||||||
\(467\) | 11547.5i | 1.14422i | 0.820175 | + | 0.572112i | \(0.193876\pi\) | ||||
−0.820175 | + | 0.572112i | \(0.806124\pi\) | |||||||
\(468\) | − | 706.323i | − | 0.0697645i | ||||||
\(469\) | −3110.14 | −0.306211 | ||||||||
\(470\) | 3479.11 | + | 3067.24i | 0.341445 | + | 0.301024i | ||||
\(471\) | 5278.01 | 0.516344 | ||||||||
\(472\) | 1844.87i | 0.179909i | ||||||||
\(473\) | − | 5545.26i | − | 0.539051i | ||||||
\(474\) | −9145.28 | −0.886196 | ||||||||
\(475\) | 1715.04 | + | 13575.8i | 0.165666 | + | 1.31137i | ||||
\(476\) | 1755.43 | 0.169034 | ||||||||
\(477\) | 463.937i | 0.0445330i | ||||||||
\(478\) | − | 10253.4i | − | 0.981130i | ||||||
\(479\) | 4515.48 | 0.430725 | 0.215363 | − | 0.976534i | \(-0.430907\pi\) | ||||
0.215363 | + | 0.976534i | \(0.430907\pi\) | |||||||
\(480\) | −1303.90 | − | 1149.54i | −0.123988 | − | 0.109310i | ||||
\(481\) | 20085.9 | 1.90403 | ||||||||
\(482\) | 9344.24i | 0.883026i | ||||||||
\(483\) | 1290.26i | 0.121551i | ||||||||
\(484\) | 1596.80 | 0.149963 | ||||||||
\(485\) | −9269.38 | + | 10514.1i | −0.867837 | + | 0.984369i | ||||
\(486\) | −1892.83 | −0.176668 | ||||||||
\(487\) | 12101.2i | 1.12599i | 0.826460 | + | 0.562995i | \(0.190351\pi\) | ||||
−0.826460 | + | 0.562995i | \(0.809649\pi\) | |||||||
\(488\) | − | 1931.17i | − | 0.179139i | ||||||
\(489\) | −698.610 | −0.0646058 | ||||||||
\(490\) | 3100.70 | − | 3517.06i | 0.285868 | − | 0.324255i | ||||
\(491\) | 10133.6 | 0.931409 | 0.465705 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465705 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(492\) | − | 1788.14i | − | 0.163853i | ||||||
\(493\) | − | 2315.86i | − | 0.211564i | ||||||
\(494\) | 11391.0 | 1.03746 | ||||||||
\(495\) | 868.851 | + | 765.994i | 0.0788928 | + | 0.0695533i | ||||
\(496\) | −1009.72 | −0.0914066 | ||||||||
\(497\) | 2154.65i | 0.194465i | ||||||||
\(498\) | − | 916.142i | − | 0.0824363i | ||||||
\(499\) | −3383.17 | −0.303510 | −0.151755 | − | 0.988418i | \(-0.548493\pi\) | ||||
−0.151755 | + | 0.988418i | \(0.548493\pi\) | |||||||
\(500\) | 3142.13 | − | 4623.53i | 0.281041 | − | 0.413541i | ||||
\(501\) | −11007.2 | −0.981564 | ||||||||
\(502\) | − | 6002.77i | − | 0.533699i | ||||||
\(503\) | − | 8508.84i | − | 0.754255i | −0.926161 | − | 0.377128i | \(-0.876912\pi\) | ||
0.926161 | − | 0.377128i | \(-0.123088\pi\) | |||||||
\(504\) | −313.495 | −0.0277067 | ||||||||
\(505\) | −11950.6 | − | 10535.9i | −1.05306 | − | 0.928396i | ||||
\(506\) | 1404.17 | 0.123365 | ||||||||
\(507\) | 2477.64i | 0.217033i | ||||||||
\(508\) | − | 5858.85i | − | 0.511702i | ||||||
\(509\) | 8042.61 | 0.700359 | 0.350179 | − | 0.936683i | \(-0.386121\pi\) | ||||
0.350179 | + | 0.936683i | \(0.386121\pi\) | |||||||
\(510\) | 2730.79 | − | 3097.48i | 0.237101 | − | 0.268939i | ||||
\(511\) | −683.042 | −0.0591311 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | − | 16165.6i | − | 1.39128i | ||||||
\(514\) | −2796.09 | −0.239942 | ||||||||
\(515\) | 3684.52 | − | 4179.28i | 0.315261 | − | 0.357594i | ||||
\(516\) | 3530.47 | 0.301202 | ||||||||
\(517\) | 6331.67i | 0.538620i | ||||||||
\(518\) | − | 8914.94i | − | 0.756178i | ||||||
\(519\) | −20210.7 | −1.70935 | ||||||||
\(520\) | −3490.69 | − | 3077.45i | −0.294378 | − | 0.259529i | ||||
\(521\) | 9066.35 | 0.762388 | 0.381194 | − | 0.924495i | \(-0.375513\pi\) | ||||
0.381194 | + | 0.924495i | \(0.375513\pi\) | |||||||
\(522\) | 413.580i | 0.0346780i | ||||||||
\(523\) | − | 13818.5i | − | 1.15533i | −0.816273 | − | 0.577667i | \(-0.803963\pi\) | ||
0.816273 | − | 0.577667i | \(-0.196037\pi\) | |||||||
\(524\) | 1404.84 | 0.117120 | ||||||||
\(525\) | 878.883 | + | 6956.99i | 0.0730621 | + | 0.578339i | ||||
\(526\) | −902.397 | −0.0748030 | ||||||||
\(527\) | − | 2398.64i | − | 0.198267i | ||||||
\(528\) | − | 2372.97i | − | 0.195588i | ||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 2292.80 | + | 2021.38i | 0.187911 | + | 0.165666i | ||||
\(531\) | 782.670 | 0.0639642 | ||||||||
\(532\) | − | 5055.82i | − | 0.412025i | ||||||
\(533\) | − | 4787.08i | − | 0.389027i | ||||||
\(534\) | −13415.3 | −1.08715 | ||||||||
\(535\) | 6632.28 | − | 7522.86i | 0.535960 | − | 0.607928i | ||||
\(536\) | −2154.92 | −0.173654 | ||||||||
\(537\) | − | 16927.1i | − | 1.36026i | ||||||
\(538\) | 9996.85i | 0.801105i | ||||||||
\(539\) | 6400.74 | 0.511502 | ||||||||
\(540\) | −4367.37 | + | 4953.81i | −0.348040 | + | 0.394774i | ||||
\(541\) | 14965.2 | 1.18929 | 0.594643 | − | 0.803990i | \(-0.297293\pi\) | ||||
0.594643 | + | 0.803990i | \(0.297293\pi\) | |||||||
\(542\) | 16715.0i | 1.32467i | ||||||||
\(543\) | − | 11491.0i | − | 0.908153i | ||||||
\(544\) | 1216.29 | 0.0958600 | ||||||||
\(545\) | −14966.3 | − | 13194.5i | −1.17630 | − | 1.03705i | ||||
\(546\) | 5837.40 | 0.457542 | ||||||||
\(547\) | − | 6818.50i | − | 0.532976i | −0.963838 | − | 0.266488i | \(-0.914137\pi\) | ||
0.963838 | − | 0.266488i | \(-0.0858633\pi\) | |||||||
\(548\) | 1327.58i | 0.103488i | ||||||||
\(549\) | −819.281 | −0.0636905 | ||||||||
\(550\) | 7571.17 | − | 956.472i | 0.586974 | − | 0.0741529i | ||||
\(551\) | −6669.90 | −0.515694 | ||||||||
\(552\) | 893.984i | 0.0689320i | ||||||||
\(553\) | 10866.6i | 0.835614i | ||||||||
\(554\) | 1265.16 | 0.0970246 | ||||||||
\(555\) | −15730.5 | − | 13868.3i | −1.20311 | − | 1.06068i | ||||
\(556\) | −8862.98 | −0.676033 | ||||||||
\(557\) | 12318.3i | 0.937060i | 0.883448 | + | 0.468530i | \(0.155216\pi\) | ||||
−0.883448 | + | 0.468530i | \(0.844784\pi\) | |||||||
\(558\) | 428.364i | 0.0324984i | ||||||||
\(559\) | 9451.50 | 0.715127 | ||||||||
\(560\) | −1365.90 | + | 1549.31i | −0.103071 | + | 0.116911i | ||||
\(561\) | 5637.14 | 0.424243 | ||||||||
\(562\) | 14829.2i | 1.11305i | ||||||||
\(563\) | − | 19821.4i | − | 1.48379i | −0.670516 | − | 0.741895i | \(-0.733927\pi\) | ||
0.670516 | − | 0.741895i | \(-0.266073\pi\) | |||||||
\(564\) | −4031.15 | −0.300961 | ||||||||
\(565\) | 9761.91 | − | 11072.7i | 0.726879 | − | 0.824484i | ||||
\(566\) | −4901.61 | −0.364011 | ||||||||
\(567\) | − | 7226.11i | − | 0.535217i | ||||||
\(568\) | 1492.89i | 0.110282i | ||||||||
\(569\) | −4612.33 | −0.339822 | −0.169911 | − | 0.985459i | \(-0.554348\pi\) | ||||
−0.169911 | + | 0.985459i | \(0.554348\pi\) | |||||||
\(570\) | −8921.05 | − | 7864.95i | −0.655547 | − | 0.577941i | ||||
\(571\) | −6497.97 | −0.476238 | −0.238119 | − | 0.971236i | \(-0.576531\pi\) | ||||
−0.238119 | + | 0.971236i | \(0.576531\pi\) | |||||||
\(572\) | − | 6352.74i | − | 0.464373i | ||||||
\(573\) | 23652.2i | 1.72441i | ||||||||
\(574\) | −2124.70 | −0.154501 | ||||||||
\(575\) | −2852.33 | + | 360.337i | −0.206870 | + | 0.0261341i | ||||
\(576\) | −217.212 | −0.0157127 | ||||||||
\(577\) | 160.102i | 0.0115513i | 0.999983 | + | 0.00577567i | \(0.00183846\pi\) | ||||
−0.999983 | + | 0.00577567i | \(0.998162\pi\) | |||||||
\(578\) | − | 6936.64i | − | 0.499180i | ||||||
\(579\) | −7057.27 | −0.506546 | ||||||||
\(580\) | 2043.94 | + | 1801.97i | 0.146327 | + | 0.129005i | ||||
\(581\) | −1088.58 | −0.0777311 | ||||||||
\(582\) | − | 12182.4i | − | 0.867655i | ||||||
\(583\) | 4172.70i | 0.296425i | ||||||||
\(584\) | −473.259 | −0.0335336 | ||||||||
\(585\) | −1305.58 | + | 1480.89i | −0.0922721 | + | 0.104662i | ||||
\(586\) | 17507.0 | 1.23414 | ||||||||
\(587\) | − | 7342.71i | − | 0.516296i | −0.966105 | − | 0.258148i | \(-0.916888\pi\) | ||
0.966105 | − | 0.258148i | \(-0.0831123\pi\) | |||||||
\(588\) | 4075.13i | 0.285809i | ||||||||
\(589\) | −6908.33 | −0.483282 | ||||||||
\(590\) | 3410.09 | − | 3868.00i | 0.237951 | − | 0.269903i | ||||
\(591\) | −20578.5 | −1.43229 | ||||||||
\(592\) | − | 6176.90i | − | 0.428833i | ||||||
\(593\) | − | 12241.1i | − | 0.847692i | −0.905734 | − | 0.423846i | \(-0.860680\pi\) | ||
0.905734 | − | 0.423846i | \(-0.139320\pi\) | |||||||
\(594\) | −9015.50 | −0.622745 | ||||||||
\(595\) | −3680.48 | − | 3244.77i | −0.253588 | − | 0.223568i | ||||
\(596\) | 9909.30 | 0.681041 | ||||||||
\(597\) | 11939.5i | 0.818509i | ||||||||
\(598\) | 2393.30i | 0.163661i | ||||||||
\(599\) | −1597.64 | −0.108978 | −0.0544888 | − | 0.998514i | \(-0.517353\pi\) | ||||
−0.0544888 | + | 0.998514i | \(0.517353\pi\) | |||||||
\(600\) | 608.952 | + | 4820.30i | 0.0414339 | + | 0.327980i | ||||
\(601\) | −861.146 | −0.0584474 | −0.0292237 | − | 0.999573i | \(-0.509304\pi\) | ||||
−0.0292237 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(602\) | − | 4194.97i | − | 0.284010i | ||||||
\(603\) | 914.209i | 0.0617404i | ||||||||
\(604\) | 4073.28 | 0.274403 | ||||||||
\(605\) | −3347.90 | − | 2951.57i | −0.224978 | − | 0.198344i | ||||
\(606\) | 13846.9 | 0.928202 | ||||||||
\(607\) | 24599.3i | 1.64490i | 0.568838 | + | 0.822449i | \(0.307393\pi\) | ||||
−0.568838 | + | 0.822449i | \(0.692607\pi\) | |||||||
\(608\) | − | 3503.03i | − | 0.233662i | ||||||
\(609\) | −3418.03 | −0.227431 | ||||||||
\(610\) | −3569.61 | + | 4048.93i | −0.236933 | + | 0.268748i | ||||
\(611\) | −10791.9 | −0.714554 | ||||||||
\(612\) | − | 515.999i | − | 0.0340817i | ||||||
\(613\) | 6965.05i | 0.458916i | 0.973319 | + | 0.229458i | \(0.0736954\pi\) | ||||
−0.973319 | + | 0.229458i | \(0.926305\pi\) | |||||||
\(614\) | 15090.6 | 0.991870 | ||||||||
\(615\) | −3305.24 | + | 3749.07i | −0.216716 | + | 0.245816i | ||||
\(616\) | −2819.61 | −0.184424 | ||||||||
\(617\) | 7486.04i | 0.488455i | 0.969718 | + | 0.244227i | \(0.0785343\pi\) | ||||
−0.969718 | + | 0.244227i | \(0.921466\pi\) | |||||||
\(618\) | 4842.41i | 0.315195i | ||||||||
\(619\) | 12204.5 | 0.792472 | 0.396236 | − | 0.918149i | \(-0.370316\pi\) | ||||
0.396236 | + | 0.918149i | \(0.370316\pi\) | |||||||
\(620\) | 2117.00 | + | 1866.38i | 0.137130 | + | 0.120896i | ||||
\(621\) | 3396.46 | 0.219477 | ||||||||
\(622\) | 9340.69i | 0.602134i | ||||||||
\(623\) | 15940.3i | 1.02509i | ||||||||
\(624\) | 4044.56 | 0.259475 | ||||||||
\(625\) | −15134.1 | + | 3885.82i | −0.968582 | + | 0.248693i | ||||
\(626\) | −7027.62 | −0.448691 | ||||||||
\(627\) | − | 16235.5i | − | 1.03411i | ||||||
\(628\) | − | 4345.29i | − | 0.276108i | ||||||
\(629\) | 14673.6 | 0.930166 | ||||||||
\(630\) | 657.283 | + | 579.472i | 0.0415663 | + | 0.0366456i | ||||
\(631\) | −9566.26 | −0.603529 | −0.301764 | − | 0.953383i | \(-0.597576\pi\) | ||||
−0.301764 | + | 0.953383i | \(0.597576\pi\) | |||||||
\(632\) | 7529.14i | 0.473882i | ||||||||
\(633\) | 11300.6i | 0.709574i | ||||||||
\(634\) | −13884.7 | −0.869767 | ||||||||
\(635\) | −10829.6 | + | 12283.8i | −0.676788 | + | 0.767667i | ||||
\(636\) | −2656.61 | −0.165631 | ||||||||
\(637\) | 10909.6i | 0.678579i | ||||||||
\(638\) | 3719.78i | 0.230827i | ||||||||
\(639\) | 633.346 | 0.0392094 | ||||||||
\(640\) | −946.392 | + | 1073.47i | −0.0584522 | + | 0.0663011i | ||||
\(641\) | −32146.3 | −1.98081 | −0.990407 | − | 0.138183i | \(-0.955874\pi\) | ||||
−0.990407 | + | 0.138183i | \(0.955874\pi\) | |||||||
\(642\) | 8716.53i | 0.535847i | ||||||||
\(643\) | 12234.1i | 0.750336i | 0.926957 | + | 0.375168i | \(0.122415\pi\) | ||||
−0.926957 | + | 0.375168i | \(0.877585\pi\) | |||||||
\(644\) | 1062.25 | 0.0649975 | ||||||||
\(645\) | −7402.07 | − | 6525.80i | −0.451870 | − | 0.398377i | ||||
\(646\) | 8321.64 | 0.506827 | ||||||||
\(647\) | − | 18206.2i | − | 1.10627i | −0.833091 | − | 0.553136i | \(-0.813431\pi\) | ||
0.833091 | − | 0.553136i | \(-0.186569\pi\) | |||||||
\(648\) | − | 5006.76i | − | 0.303525i | ||||||
\(649\) | 7039.41 | 0.425764 | ||||||||
\(650\) | 1630.24 | + | 12904.5i | 0.0983742 | + | 0.778703i | ||||
\(651\) | −3540.22 | −0.213137 | ||||||||
\(652\) | 575.152i | 0.0345471i | ||||||||
\(653\) | − | 16496.5i | − | 0.988601i | −0.869291 | − | 0.494301i | \(-0.835424\pi\) | ||
0.869291 | − | 0.494301i | \(-0.164576\pi\) | |||||||
\(654\) | 17341.0 | 1.03683 | ||||||||
\(655\) | −2945.43 | − | 2596.74i | −0.175706 | − | 0.154906i | ||||
\(656\) | −1472.14 | −0.0876183 | ||||||||
\(657\) | 200.776i | 0.0119224i | ||||||||
\(658\) | 4789.89i | 0.283783i | ||||||||
\(659\) | −9669.49 | −0.571578 | −0.285789 | − | 0.958293i | \(-0.592256\pi\) | ||||
−0.285789 | + | 0.958293i | \(0.592256\pi\) | |||||||
\(660\) | −4386.26 | + | 4975.24i | −0.258689 | + | 0.293426i | ||||
\(661\) | 19252.4 | 1.13288 | 0.566438 | − | 0.824105i | \(-0.308321\pi\) | ||||
0.566438 | + | 0.824105i | \(0.308321\pi\) | |||||||
\(662\) | − | 9197.02i | − | 0.539958i | ||||||
\(663\) | 9608.10i | 0.562817i | ||||||||
\(664\) | −754.242 | −0.0440817 | ||||||||
\(665\) | −9345.28 | + | 10600.2i | −0.544954 | + | 0.618130i | ||||
\(666\) | −2620.50 | −0.152466 | ||||||||
\(667\) | − | 1401.37i | − | 0.0813515i | ||||||
\(668\) | 9061.98i | 0.524878i | ||||||||
\(669\) | 24354.8 | 1.40749 | ||||||||
\(670\) | 4518.07 | + | 3983.21i | 0.260520 | + | 0.229679i | ||||
\(671\) | −7368.70 | −0.423942 | ||||||||
\(672\) | − | 1795.15i | − | 0.103049i | ||||||
\(673\) | 23690.9i | 1.35693i | 0.734631 | + | 0.678467i | \(0.237355\pi\) | ||||
−0.734631 | + | 0.678467i | \(0.762645\pi\) | |||||||
\(674\) | 1276.15 | 0.0729312 | ||||||||
\(675\) | 18313.5 | − | 2313.56i | 1.04427 | − | 0.131924i | ||||
\(676\) | 2039.79 | 0.116055 | ||||||||
\(677\) | 22913.3i | 1.30079i | 0.759598 | + | 0.650393i | \(0.225396\pi\) | ||||
−0.759598 | + | 0.650393i | \(0.774604\pi\) | |||||||
\(678\) | 12829.7i | 0.726727i | ||||||||
\(679\) | −14475.3 | −0.818131 | ||||||||
\(680\) | −2550.10 | − | 2248.21i | −0.143811 | − | 0.126787i | ||||
\(681\) | −18936.9 | −1.06559 | ||||||||
\(682\) | 3852.75i | 0.216319i | ||||||||
\(683\) | − | 5932.99i | − | 0.332386i | −0.986093 | − | 0.166193i | \(-0.946853\pi\) | ||
0.986093 | − | 0.166193i | \(-0.0531475\pi\) | |||||||
\(684\) | −1486.13 | −0.0830754 | ||||||||
\(685\) | 2453.93 | − | 2783.44i | 0.136876 | − | 0.155255i | ||||
\(686\) | 12762.8 | 0.710330 | ||||||||
\(687\) | 11400.5i | 0.633126i | ||||||||
\(688\) | − | 2906.57i | − | 0.161064i | ||||||
\(689\) | −7112.07 | −0.393249 | ||||||||
\(690\) | 1652.46 | − | 1874.35i | 0.0911711 | − | 0.103413i | ||||
\(691\) | 9480.21 | 0.521917 | 0.260958 | − | 0.965350i | \(-0.415961\pi\) | ||||
0.260958 | + | 0.965350i | \(0.415961\pi\) | |||||||
\(692\) | 16639.1i | 0.914050i | ||||||||
\(693\) | 1196.20i | 0.0655696i | ||||||||
\(694\) | −604.697 | −0.0330749 | ||||||||
\(695\) | 18582.4 | + | 16382.5i | 1.01420 | + | 0.894136i | ||||
\(696\) | −2368.25 | −0.128978 | ||||||||
\(697\) | − | 3497.17i | − | 0.190050i | ||||||
\(698\) | 17888.8i | 0.970059i | ||||||||
\(699\) | −12034.5 | −0.651196 | ||||||||
\(700\) | 5727.56 | − | 723.568i | 0.309259 | − | 0.0390690i | ||||
\(701\) | 16240.3 | 0.875019 | 0.437510 | − | 0.899214i | \(-0.355861\pi\) | ||||
0.437510 | + | 0.899214i | \(0.355861\pi\) | |||||||
\(702\) | − | 15366.3i | − | 0.826158i | ||||||
\(703\) | − | 42261.4i | − | 2.26731i | ||||||
\(704\) | −1953.62 | −0.104588 | ||||||||
\(705\) | 8451.81 | + | 7451.26i | 0.451509 | + | 0.398058i | ||||
\(706\) | 22463.7 | 1.19749 | ||||||||
\(707\) | − | 16453.1i | − | 0.875222i | ||||||
\(708\) | 4481.74i | 0.237901i | ||||||||
\(709\) | −29180.1 | −1.54567 | −0.772837 | − | 0.634605i | \(-0.781163\pi\) | ||||
−0.772837 | + | 0.634605i | \(0.781163\pi\) | |||||||
\(710\) | 2759.49 | − | 3130.03i | 0.145862 | − | 0.165448i | ||||
\(711\) | 3194.17 | 0.168482 | ||||||||
\(712\) | 11044.6i | 0.581337i | ||||||||
\(713\) | − | 1451.47i | − | 0.0762384i | ||||||
\(714\) | 4264.47 | 0.223521 | ||||||||
\(715\) | −11742.5 | + | 13319.3i | −0.614190 | + | 0.696663i | ||||
\(716\) | −13935.8 | −0.727379 | ||||||||
\(717\) | − | 24908.6i | − | 1.29739i | ||||||
\(718\) | 18566.8i | 0.965050i | ||||||||
\(719\) | −18555.0 | −0.962427 | −0.481214 | − | 0.876603i | \(-0.659804\pi\) | ||||
−0.481214 | + | 0.876603i | \(0.659804\pi\) | |||||||
\(720\) | 455.412 | + | 401.499i | 0.0235725 | + | 0.0207819i | ||||
\(721\) | 5753.84 | 0.297204 | ||||||||
\(722\) | − | 10249.2i | − | 0.528302i | ||||||
\(723\) | 22700.0i | 1.16767i | ||||||||
\(724\) | −9460.35 | −0.485623 | ||||||||
\(725\) | −954.569 | − | 7556.11i | −0.0488991 | − | 0.387071i | ||||
\(726\) | 3879.12 | 0.198303 | ||||||||
\(727\) | − | 13806.7i | − | 0.704352i | −0.935934 | − | 0.352176i | \(-0.885442\pi\) | ||
0.935934 | − | 0.352176i | \(-0.114558\pi\) | |||||||
\(728\) | − | 4805.82i | − | 0.244664i | ||||||
\(729\) | −21496.1 | −1.09211 | ||||||||
\(730\) | 992.247 | + | 874.783i | 0.0503078 | + | 0.0443523i | ||||
\(731\) | 6904.72 | 0.349358 | ||||||||
\(732\) | − | 4691.39i | − | 0.236883i | ||||||
\(733\) | 33023.5i | 1.66405i | 0.554736 | + | 0.832027i | \(0.312819\pi\) | ||||
−0.554736 | + | 0.832027i | \(0.687181\pi\) | |||||||
\(734\) | −19324.3 | −0.971761 | ||||||||
\(735\) | 7532.55 | − | 8544.02i | 0.378017 | − | 0.428777i | ||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 8222.49i | 0.410962i | ||||||||
\(738\) | 624.545i | 0.0311515i | ||||||||
\(739\) | 9366.48 | 0.466240 | 0.233120 | − | 0.972448i | \(-0.425106\pi\) | ||||
0.233120 | + | 0.972448i | \(0.425106\pi\) | |||||||
\(740\) | −11417.5 | + | 12950.6i | −0.567184 | + | 0.643345i | ||||
\(741\) | 27672.3 | 1.37189 | ||||||||
\(742\) | 3156.63i | 0.156177i | ||||||||
\(743\) | 4374.71i | 0.216006i | 0.994151 | + | 0.108003i | \(0.0344456\pi\) | ||||
−0.994151 | + | 0.108003i | \(0.965554\pi\) | |||||||
\(744\) | −2452.91 | −0.120871 | ||||||||
\(745\) | −20776.1 | − | 18316.6i | −1.02171 | − | 0.900761i | ||||
\(746\) | 5261.18 | 0.258211 | ||||||||
\(747\) | 319.981i | 0.0156727i | ||||||||
\(748\) | − | 4640.95i | − | 0.226858i | ||||||
\(749\) | 10357.1 | 0.505263 | ||||||||
\(750\) | 7633.19 | − | 11232.0i | 0.371633 | − | 0.546844i | ||||
\(751\) | 7114.96 | 0.345711 | 0.172855 | − | 0.984947i | \(-0.444701\pi\) | ||||
0.172855 | + | 0.984947i | \(0.444701\pi\) | |||||||
\(752\) | 3318.77i | 0.160935i | ||||||||
\(753\) | − | 14582.6i | − | 0.705734i | ||||||
\(754\) | −6340.10 | −0.306224 | ||||||||
\(755\) | −8540.14 | − | 7529.13i | −0.411666 | − | 0.362931i | ||||
\(756\) | −6820.19 | −0.328106 | ||||||||
\(757\) | 16213.0i | 0.778429i | 0.921147 | + | 0.389214i | \(0.127253\pi\) | ||||
−0.921147 | + | 0.389214i | \(0.872747\pi\) | |||||||
\(758\) | 7882.49i | 0.377711i | ||||||||
\(759\) | 3411.15 | 0.163132 | ||||||||
\(760\) | −6475.07 | + | 7344.53i | −0.309047 | + | 0.350545i | ||||
\(761\) | −9766.67 | −0.465232 | −0.232616 | − | 0.972569i | \(-0.574728\pi\) | ||||
−0.232616 | + | 0.972569i | \(0.574728\pi\) | |||||||
\(762\) | − | 14232.9i | − | 0.676647i | ||||||
\(763\) | − | 20604.9i | − | 0.977650i | ||||||
\(764\) | 19472.4 | 0.922103 | ||||||||
\(765\) | −953.784 | + | 1081.86i | −0.0450773 | + | 0.0511302i | ||||
\(766\) | −16292.3 | −0.768494 | ||||||||
\(767\) | 11998.2i | 0.564836i | ||||||||
\(768\) | − | 1243.80i | − | 0.0584400i | ||||||
\(769\) | 42497.5 | 1.99285 | 0.996424 | − | 0.0844951i | \(-0.0269277\pi\) | ||||
0.996424 | + | 0.0844951i | \(0.0269277\pi\) | |||||||
\(770\) | 5911.67 | + | 5211.83i | 0.276677 | + | 0.243924i | ||||
\(771\) | −6792.54 | −0.317286 | ||||||||
\(772\) | 5810.11i | 0.270869i | ||||||||
\(773\) | − | 26248.0i | − | 1.22131i | −0.791896 | − | 0.610656i | \(-0.790906\pi\) | ||
0.791896 | − | 0.610656i | \(-0.209094\pi\) | |||||||
\(774\) | −1233.09 | −0.0572641 | ||||||||
\(775\) | −988.693 | − | 7826.22i | −0.0458257 | − | 0.362743i | ||||
\(776\) | −10029.5 | −0.463967 | ||||||||
\(777\) | − | 21657.1i | − | 0.999928i | ||||||
\(778\) | − | 5337.35i | − | 0.245955i | ||||||
\(779\) | −10072.2 | −0.463252 | ||||||||
\(780\) | −8479.94 | − | 7476.06i | −0.389270 | − | 0.343187i | ||||
\(781\) | 5696.38 | 0.260989 | ||||||||
\(782\) | 1748.41i | 0.0799527i | ||||||||
\(783\) | 8997.56i | 0.410660i | ||||||||
\(784\) | 3354.98 | 0.152832 | ||||||||
\(785\) | −8031.92 | + | 9110.44i | −0.365187 | + | 0.414223i | ||||
\(786\) | 3412.79 | 0.154873 | ||||||||
\(787\) | − | 13044.9i | − | 0.590852i | −0.955366 | − | 0.295426i | \(-0.904538\pi\) | ||
0.955366 | − | 0.295426i | \(-0.0954616\pi\) | |||||||
\(788\) | 16941.9i | 0.765900i | ||||||||
\(789\) | −2192.20 | −0.0989154 | ||||||||
\(790\) | 13917.0 | − | 15785.8i | 0.626766 | − | 0.710928i | ||||
\(791\) | 15244.5 | 0.685247 | ||||||||
\(792\) | 828.809i | 0.0371849i | ||||||||
\(793\) | − | 12559.4i | − | 0.562419i | ||||||
\(794\) | −14056.3 | −0.628260 | ||||||||
\(795\) | 5569.92 | + | 4910.54i | 0.248484 | + | 0.219068i | ||||
\(796\) | 9829.54 | 0.437687 | ||||||||
\(797\) | − | 13044.8i | − | 0.579764i | −0.957062 | − | 0.289882i | \(-0.906384\pi\) | ||
0.957062 | − | 0.289882i | \(-0.0936160\pi\) | |||||||
\(798\) | − | 12282.1i | − | 0.544840i | ||||||
\(799\) | −7883.93 | −0.349078 | ||||||||
\(800\) | 3968.46 | − | 501.339i | 0.175383 | − | 0.0221562i | ||||
\(801\) | 4685.56 | 0.206687 | ||||||||
\(802\) | − | 18840.7i | − | 0.829538i | ||||||
\(803\) | 1805.80i | 0.0793591i | ||||||||
\(804\) | −5234.97 | −0.229631 | ||||||||
\(805\) | −2227.14 | − | 1963.48i | −0.0975108 | − | 0.0859672i | ||||
\(806\) | −6566.74 | −0.286977 | ||||||||
\(807\) | 24285.4i | 1.05934i | ||||||||
\(808\) | − | 11399.9i | − | 0.496344i | ||||||
\(809\) | −14991.2 | −0.651499 | −0.325749 | − | 0.945456i | \(-0.605617\pi\) | ||||
−0.325749 | + | 0.945456i | \(0.605617\pi\) | |||||||
\(810\) | −9254.60 | + | 10497.3i | −0.401449 | + | 0.455355i | ||||
\(811\) | −36807.9 | −1.59371 | −0.796856 | − | 0.604169i | \(-0.793505\pi\) | ||||
−0.796856 | + | 0.604169i | \(0.793505\pi\) | |||||||
\(812\) | 2814.00i | 0.121616i | ||||||||
\(813\) | 40605.9i | 1.75167i | ||||||||
\(814\) | −23569.0 | −1.01486 | ||||||||
\(815\) | 1063.12 | − | 1205.88i | 0.0456928 | − | 0.0518283i | ||||
\(816\) | 2954.73 | 0.126760 | ||||||||
\(817\) | − | 19886.3i | − | 0.851571i | ||||||
\(818\) | 20045.1i | 0.856797i | ||||||||
\(819\) | −2038.83 | −0.0869872 | ||||||||
\(820\) | 3086.54 | + | 2721.14i | 0.131447 | + | 0.115886i | ||||
\(821\) | 533.820 | 0.0226924 | 0.0113462 | − | 0.999936i | \(-0.496388\pi\) | ||||
0.0113462 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(822\) | 3225.10i | 0.136847i | ||||||||
\(823\) | − | 40071.2i | − | 1.69720i | −0.529037 | − | 0.848599i | \(-0.677447\pi\) | ||
0.529037 | − | 0.848599i | \(-0.322553\pi\) | |||||||
\(824\) | 3986.67 | 0.168546 | ||||||||
\(825\) | 18392.7 | − | 2323.56i | 0.776182 | − | 0.0980558i | ||||
\(826\) | 5325.29 | 0.224323 | ||||||||
\(827\) | − | 26949.3i | − | 1.13315i | −0.824009 | − | 0.566577i | \(-0.808267\pi\) | ||
0.824009 | − | 0.566577i | \(-0.191733\pi\) | |||||||
\(828\) | − | 312.242i | − | 0.0131053i | ||||||
\(829\) | 42875.5 | 1.79629 | 0.898147 | − | 0.439696i | \(-0.144914\pi\) | ||||
0.898147 | + | 0.439696i | \(0.144914\pi\) | |||||||
\(830\) | 1581.36 | + | 1394.16i | 0.0661325 | + | 0.0583035i | ||||
\(831\) | 3073.47 | 0.128300 | ||||||||
\(832\) | − | 3329.81i | − | 0.138751i | ||||||
\(833\) | 7969.94i | 0.331503i | ||||||||
\(834\) | −21530.9 | −0.893949 | ||||||||
\(835\) | 16750.4 | − | 18999.6i | 0.694216 | − | 0.787435i | ||||
\(836\) | −13366.4 | −0.552974 | ||||||||
\(837\) | 9319.20i | 0.384849i | ||||||||
\(838\) | − | 22355.1i | − | 0.921531i | ||||||
\(839\) | 32088.5 | 1.32040 | 0.660201 | − | 0.751089i | \(-0.270471\pi\) | ||||
0.660201 | + | 0.751089i | \(0.270471\pi\) | |||||||
\(840\) | −3318.19 | + | 3763.75i | −0.136296 | + | 0.154597i | ||||
\(841\) | −20676.6 | −0.847785 | ||||||||
\(842\) | − | 17931.2i | − | 0.733907i | ||||||
\(843\) | 36024.6i | 1.47183i | ||||||||
\(844\) | 9303.61 | 0.379435 | ||||||||
\(845\) | −4276.68 | − | 3770.39i | −0.174109 | − | 0.153498i | ||||
\(846\) | 1407.96 | 0.0572183 | ||||||||
\(847\) | − | 4609.24i | − | 0.186984i | ||||||
\(848\) | 2187.14i | 0.0885691i | ||||||||
\(849\) | −11907.5 | −0.481348 | ||||||||
\(850\) | 1190.96 | + | 9427.30i | 0.0480583 | + | 0.380416i | ||||
\(851\) | 8879.29 | 0.357671 | ||||||||
\(852\) | 3626.68i | 0.145831i | ||||||||
\(853\) | 5672.84i | 0.227707i | 0.993498 | + | 0.113854i | \(0.0363195\pi\) | ||||
−0.993498 | + | 0.113854i | \(0.963681\pi\) | |||||||
\(854\) | −5574.39 | −0.223363 | ||||||||
\(855\) | 3115.86 | + | 2746.99i | 0.124632 | + | 0.109877i | ||||
\(856\) | 7176.16 | 0.286537 | ||||||||
\(857\) | 11376.7i | 0.453465i | 0.973957 | + | 0.226733i | \(0.0728044\pi\) | ||||
−0.973957 | + | 0.226733i | \(0.927196\pi\) | |||||||
\(858\) | − | 15432.7i | − | 0.614062i | ||||||
\(859\) | 23889.6 | 0.948898 | 0.474449 | − | 0.880283i | \(-0.342647\pi\) | ||||
0.474449 | + | 0.880283i | \(0.342647\pi\) | |||||||
\(860\) | −5372.56 | + | 6093.99i | −0.213027 | + | 0.241632i | ||||
\(861\) | −5161.55 | −0.204303 | ||||||||
\(862\) | − | 33106.3i | − | 1.30813i | ||||||
\(863\) | − | 18232.1i | − | 0.719150i | −0.933116 | − | 0.359575i | \(-0.882922\pi\) | ||
0.933116 | − | 0.359575i | \(-0.117078\pi\) | |||||||
\(864\) | −4725.51 | −0.186071 | ||||||||
\(865\) | 30756.0 | − | 34885.9i | 1.20894 | − | 1.37128i | ||||
\(866\) | −1505.61 | −0.0590792 | ||||||||
\(867\) | − | 16851.2i | − | 0.660089i | ||||||
\(868\) | 2914.59i | 0.113972i | ||||||||
\(869\) | 28728.7 | 1.12147 | ||||||||
\(870\) | 4965.34 | + | 4377.53i | 0.193495 | + | 0.170589i | ||||
\(871\) | −14014.6 | −0.545199 | ||||||||
\(872\) | − | 14276.5i | − | 0.554431i | ||||||
\(873\) | 4254.94i | 0.164957i | ||||||||
\(874\) | 5035.60 | 0.194887 | ||||||||
\(875\) | −13346.0 | − | 9069.90i | −0.515631 | − | 0.350421i | ||||
\(876\) | −1149.69 | −0.0443430 | ||||||||
\(877\) | 12349.2i | 0.475487i | 0.971328 | + | 0.237743i | \(0.0764078\pi\) | ||||
−0.971328 | + | 0.237743i | \(0.923592\pi\) | |||||||
\(878\) | − | 5345.81i | − | 0.205481i | ||||||
\(879\) | 42529.8 | 1.63196 | ||||||||
\(880\) | 4096.02 | + | 3611.12i | 0.156905 | + | 0.138331i | ||||
\(881\) | −37347.4 | −1.42823 | −0.714113 | − | 0.700031i | \(-0.753170\pi\) | ||||
−0.714113 | + | 0.700031i | \(0.753170\pi\) | |||||||
\(882\) | − | 1423.32i | − | 0.0543375i | ||||||
\(883\) | − | 3389.21i | − | 0.129169i | −0.997912 | − | 0.0645844i | \(-0.979428\pi\) | ||
0.997912 | − | 0.0645844i | \(-0.0205722\pi\) | |||||||
\(884\) | 7910.16 | 0.300959 | ||||||||
\(885\) | 8284.15 | − | 9396.54i | 0.314654 | − | 0.356905i | ||||
\(886\) | −14622.4 | −0.554459 | ||||||||
\(887\) | − | 41902.9i | − | 1.58620i | −0.609090 | − | 0.793101i | \(-0.708465\pi\) | ||
0.609090 | − | 0.793101i | \(-0.291535\pi\) | |||||||
\(888\) | − | 15005.6i | − | 0.567065i | ||||||
\(889\) | −16911.8 | −0.638025 | ||||||||
\(890\) | 20415.0 | − | 23156.3i | 0.768890 | − | 0.872136i | ||||
\(891\) | −19104.2 | −0.718309 | ||||||||
\(892\) | − | 20050.9i | − | 0.752638i | ||||||
\(893\) | 22706.5i | 0.850890i | ||||||||
\(894\) | 24072.7 | 0.900572 | ||||||||
\(895\) | 29218.1 | + | 25759.1i | 1.09123 | + | 0.962048i | ||||
\(896\) | −1477.91 | −0.0551044 | ||||||||
\(897\) | 5814.06i | 0.216417i | ||||||||
\(898\) | 7171.40i | 0.266495i | ||||||||
\(899\) | 3845.09 | 0.142648 | ||||||||
\(900\) | −212.689 | − | 1683.59i | −0.00787736 | − | 0.0623550i | ||||
\(901\) | −5195.67 | −0.192112 | ||||||||
\(902\) | 5617.22i | 0.207354i | ||||||||
\(903\) | − | 10190.9i | − | 0.375560i | ||||||
\(904\) | 10562.4 | 0.388608 | ||||||||
\(905\) | 19834.8 | + | 17486.7i | 0.728543 | + | 0.642296i | ||||
\(906\) | 9895.23 | 0.362855 | ||||||||
\(907\) | 37106.0i | 1.35842i | 0.733945 | + | 0.679209i | \(0.237677\pi\) | ||||
−0.733945 | + | 0.679209i | \(0.762323\pi\) | |||||||
\(908\) | 15590.4i | 0.569808i | ||||||||
\(909\) | −4836.30 | −0.176468 | ||||||||
\(910\) | −8883.19 | + | 10076.0i | −0.323599 | + | 0.367051i | ||||
\(911\) | −43702.3 | −1.58938 | −0.794688 | − | 0.607018i | \(-0.792366\pi\) | ||||
−0.794688 | + | 0.607018i | \(0.792366\pi\) | |||||||
\(912\) | − | 8509.91i | − | 0.308982i | ||||||
\(913\) | 2877.94i | 0.104322i | ||||||||
\(914\) | −2445.09 | −0.0884863 | ||||||||
\(915\) | −8671.66 | + | 9836.08i | −0.313307 | + | 0.355378i | ||||
\(916\) | 9385.84 | 0.338556 | ||||||||
\(917\) | − | 4055.14i | − | 0.146033i | ||||||
\(918\) | − | 11225.7i | − | 0.403599i | ||||||
\(919\) | −40160.4 | −1.44153 | −0.720767 | − | 0.693178i | \(-0.756210\pi\) | ||||
−0.720767 | + | 0.693178i | \(0.756210\pi\) | |||||||
\(920\) | −1543.12 | − | 1360.44i | −0.0552990 | − | 0.0487525i | ||||
\(921\) | 36659.7 | 1.31159 | ||||||||
\(922\) | − | 7690.91i | − | 0.274714i | ||||||
\(923\) | 9709.07i | 0.346238i | ||||||||
\(924\) | −6849.69 | −0.243873 | ||||||||
\(925\) | 47876.5 | − | 6048.28i | 1.70181 | − | 0.214991i | ||||
\(926\) | −10227.4 | −0.362952 | ||||||||
\(927\) | − | 1691.31i | − | 0.0599244i | ||||||
\(928\) | 1949.74i | 0.0689691i | ||||||||
\(929\) | −11545.6 | −0.407748 | −0.203874 | − | 0.978997i | \(-0.565353\pi\) | ||||
−0.203874 | + | 0.978997i | \(0.565353\pi\) | |||||||
\(930\) | 5142.84 | + | 4534.01i | 0.181334 | + | 0.159867i | ||||
\(931\) | 22954.2 | 0.808050 | ||||||||
\(932\) | 9907.76i | 0.348218i | ||||||||
\(933\) | 22691.4i | 0.796230i | ||||||||
\(934\) | 23094.9 | 0.809089 | ||||||||
\(935\) | −8578.43 | + | 9730.33i | −0.300048 | + | 0.340338i | ||||
\(936\) | −1412.65 | −0.0493309 | ||||||||
\(937\) | − | 5690.42i | − | 0.198397i | −0.995068 | − | 0.0991985i | \(-0.968372\pi\) | ||
0.995068 | − | 0.0991985i | \(-0.0316279\pi\) | |||||||
\(938\) | 6220.28i | 0.216524i | ||||||||
\(939\) | −17072.2 | −0.593324 | ||||||||
\(940\) | 6134.48 | − | 6958.22i | 0.212856 | − | 0.241438i | ||||
\(941\) | 37839.6 | 1.31088 | 0.655438 | − | 0.755249i | \(-0.272484\pi\) | ||||
0.655438 | + | 0.755249i | \(0.272484\pi\) | |||||||
\(942\) | − | 10556.0i | − | 0.365110i | ||||||
\(943\) | − | 2116.21i | − | 0.0730787i | ||||||
\(944\) | 3689.74 | 0.127215 | ||||||||
\(945\) | 14299.4 | + | 12606.6i | 0.492232 | + | 0.433960i | ||||
\(946\) | −11090.5 | −0.381167 | ||||||||
\(947\) | 47246.5i | 1.62123i | 0.585579 | + | 0.810615i | \(0.300867\pi\) | ||||
−0.585579 | + | 0.810615i | \(0.699133\pi\) | |||||||
\(948\) | 18290.6i | 0.626635i | ||||||||
\(949\) | −3077.86 | −0.105281 | ||||||||
\(950\) | 27151.6 | − | 3430.08i | 0.927277 | − | 0.117144i | ||||
\(951\) | −33730.2 | −1.15013 | ||||||||
\(952\) | − | 3510.86i | − | 0.119525i | ||||||
\(953\) | 7264.72i | 0.246933i | 0.992349 | + | 0.123467i | \(0.0394012\pi\) | ||||
−0.992349 | + | 0.123467i | \(0.960599\pi\) | |||||||
\(954\) | 927.875 | 0.0314896 | ||||||||
\(955\) | −40826.3 | − | 35993.2i | −1.38336 | − | 1.21959i | ||||
\(956\) | −20506.8 | −0.693764 | ||||||||
\(957\) | 9036.48i | 0.305233i | ||||||||
\(958\) | − | 9030.96i | − | 0.304569i | ||||||
\(959\) | 3832.12 | 0.129036 | ||||||||
\(960\) | −2299.07 | + | 2607.79i | −0.0772940 | + | 0.0876730i | ||||
\(961\) | −25808.5 | −0.866317 | ||||||||
\(962\) | − | 40171.7i | − | 1.34635i | ||||||
\(963\) | − | 3044.42i | − | 0.101875i | ||||||
\(964\) | 18688.5 | 0.624394 | ||||||||
\(965\) | 10739.5 | − | 12181.6i | 0.358257 | − | 0.406363i | ||||
\(966\) | 2580.52 | 0.0859492 | ||||||||
\(967\) | 47977.9i | 1.59552i | 0.602976 | + | 0.797759i | \(0.293981\pi\) | ||||
−0.602976 | + | 0.797759i | \(0.706019\pi\) | |||||||
\(968\) | − | 3193.61i | − | 0.106040i | ||||||
\(969\) | 20215.8 | 0.670201 | ||||||||
\(970\) | 21028.1 | + | 18538.8i | 0.696054 | + | 0.613653i | ||||
\(971\) | −14030.3 | −0.463701 | −0.231850 | − | 0.972751i | \(-0.574478\pi\) | ||||
−0.231850 | + | 0.972751i | \(0.574478\pi\) | |||||||
\(972\) | 3785.66i | 0.124923i | ||||||||
\(973\) | 25583.4i | 0.842924i | ||||||||
\(974\) | 24202.4 | 0.796195 | ||||||||
\(975\) | 3960.34 | + | 31349.0i | 0.130085 | + | 1.02971i | ||||
\(976\) | −3862.33 | −0.126670 | ||||||||
\(977\) | − | 29406.7i | − | 0.962950i | −0.876460 | − | 0.481475i | \(-0.840101\pi\) | ||
0.876460 | − | 0.481475i | \(-0.159899\pi\) | |||||||
\(978\) | 1397.22i | 0.0456832i | ||||||||
\(979\) | 42142.4 | 1.37577 | ||||||||
\(980\) | −7034.13 | − | 6201.41i | −0.229283 | − | 0.202139i | ||||
\(981\) | −6056.69 | −0.197121 | ||||||||
\(982\) | − | 20267.2i | − | 0.658606i | ||||||
\(983\) | − | 50249.5i | − | 1.63043i | −0.579161 | − | 0.815213i | \(-0.696620\pi\) | ||
0.579161 | − | 0.815213i | \(-0.303380\pi\) | |||||||
\(984\) | −3576.29 | −0.115862 | ||||||||
\(985\) | 31315.7 | − | 35520.8i | 1.01300 | − | 1.14902i | ||||
\(986\) | −4631.71 | −0.149598 | ||||||||
\(987\) | 11636.1i | 0.375259i | ||||||||
\(988\) | − | 22782.1i | − | 0.733597i | ||||||
\(989\) | 4178.19 | 0.134337 | ||||||||
\(990\) | 1531.99 | − | 1737.70i | 0.0491816 | − | 0.0557856i | ||||
\(991\) | 56812.8 | 1.82111 | 0.910555 | − | 0.413389i | \(-0.135655\pi\) | ||||
0.910555 | + | 0.413389i | \(0.135655\pi\) | |||||||
\(992\) | 2019.44i | 0.0646342i | ||||||||
\(993\) | − | 22342.4i | − | 0.714011i | ||||||
\(994\) | 4309.29 | 0.137507 | ||||||||
\(995\) | −20608.9 | − | 18169.1i | −0.656628 | − | 0.578894i | ||||
\(996\) | −1832.28 | −0.0582913 | ||||||||
\(997\) | 8891.14i | 0.282433i | 0.989979 | + | 0.141216i | \(0.0451013\pi\) | ||||
−0.989979 | + | 0.141216i | \(0.954899\pi\) | |||||||
\(998\) | 6766.35i | 0.214614i | ||||||||
\(999\) | −57009.8 | −1.80552 |
(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 | 230.4.b.a.139.3 | ✓ | 14 | |
5.2 | odd | 4 | 1150.4.a.z.1.3 | 7 | |||
5.3 | odd | 4 | 1150.4.a.y.1.5 | 7 | |||
5.4 | even | 2 | inner | 230.4.b.a.139.12 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.b.a.139.3 | ✓ | 14 | 1.1 | even | 1 | trivial | |
230.4.b.a.139.12 | yes | 14 | 5.4 | even | 2 | inner | |
1150.4.a.y.1.5 | 7 | 5.3 | odd | 4 | |||
1150.4.a.z.1.3 | 7 | 5.2 | odd | 4 |