Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not 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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.5 | ||
Root | \(-10.8764i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.l.193.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 45.8569 | − | 79.4265i | 0.820314 | − | 1.42083i | −0.0851348 | − | 0.996369i | \(-0.527132\pi\) |
0.905449 | − | 0.424456i | \(-0.139535\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −108.828 | − | 70.4522i | −0.839450 | − | 0.543437i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −271.590 | − | 470.408i | −0.676757 | − | 1.17218i | −0.975952 | − | 0.217986i | \(-0.930051\pi\) |
0.299195 | − | 0.954192i | \(-0.403282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.2573 | −0.0463737 | −0.0231868 | − | 0.999731i | \(-0.507381\pi\) | ||||
−0.0231868 | + | 0.999731i | \(0.507381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −825.425 | −0.947217 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −509.837 | − | 883.064i | −0.427868 | − | 0.741088i | 0.568816 | − | 0.822465i | \(-0.307402\pi\) |
−0.996683 | + | 0.0813766i | \(0.974068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 91.8396 | − | 159.071i | 0.0583641 | − | 0.101090i | −0.835367 | − | 0.549693i | \(-0.814745\pi\) |
0.893731 | + | 0.448603i | \(0.148078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −59.3955 | + | 1165.26i | −0.0293904 | + | 0.576602i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2311.12 | + | 4002.98i | −0.910969 | + | 1.57784i | −0.0982706 | + | 0.995160i | \(0.531331\pi\) |
−0.812698 | + | 0.582685i | \(0.802002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2643.22 | − | 4578.19i | −0.845830 | − | 1.46502i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3335.60 | 0.736510 | 0.368255 | − | 0.929725i | \(-0.379955\pi\) | ||||
0.368255 | + | 0.929725i | \(0.379955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4139.23 | − | 7169.36i | −0.773598 | − | 1.33991i | −0.935579 | − | 0.353117i | \(-0.885122\pi\) |
0.161981 | − | 0.986794i | \(-0.448212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2444.31 | + | 4233.68i | −0.390726 | + | 0.676757i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10586.3 | + | 5413.09i | −1.46074 | + | 0.746922i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −958.872 | + | 1660.81i | −0.115148 | + | 0.199442i | −0.917839 | − | 0.396953i | \(-0.870068\pi\) |
0.802691 | + | 0.596395i | \(0.203401\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 127.158 | + | 220.243i | 0.0133869 | + | 0.0231868i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18886.2 | 1.75462 | 0.877312 | − | 0.479921i | \(-0.159335\pi\) | ||||
0.877312 | + | 0.479921i | \(0.159335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1285.40 | 0.106015 | 0.0530073 | − | 0.998594i | \(-0.483119\pi\) | ||||
0.0530073 | + | 0.998594i | \(0.483119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3714.41 | + | 6433.55i | 0.273438 | + | 0.473608i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12651.9 | − | 21913.7i | 0.835430 | − | 1.44701i | −0.0582505 | − | 0.998302i | \(-0.518552\pi\) |
0.893680 | − | 0.448705i | \(-0.148114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6879.98 | + | 15334.3i | 0.409352 | + | 0.912377i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4588.54 | + | 7947.58i | −0.247029 | + | 0.427868i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2942.99 | + | 5097.40i | 0.143912 | + | 0.249264i | 0.928967 | − | 0.370163i | \(-0.120698\pi\) |
−0.785054 | + | 0.619427i | \(0.787365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49817.2 | −2.22061 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1653.11 | −0.0673931 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18354.7 | + | 31791.4i | 0.686465 | + | 1.18899i | 0.972974 | + | 0.230915i | \(0.0741718\pi\) |
−0.286509 | + | 0.958078i | \(0.592495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18278.8 | − | 31659.8i | 0.628959 | − | 1.08939i | −0.358802 | − | 0.933414i | \(-0.616815\pi\) |
0.987761 | − | 0.155976i | \(-0.0498522\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9349.61 | − | 4780.74i | 0.296785 | − | 0.151755i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1295.79 | + | 2244.38i | −0.0380410 | + | 0.0658889i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13987.2 | + | 24226.6i | 0.380666 | + | 0.659333i | 0.991158 | − | 0.132690i | \(-0.0423614\pi\) |
−0.610491 | + | 0.792023i | \(0.709028\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41600.2 | 1.05190 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33470.8 | −0.787989 | −0.393995 | − | 0.919113i | \(-0.628907\pi\) | ||||
−0.393995 | + | 0.919113i | \(0.628907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15693.4 | − | 27181.8i | −0.344675 | − | 0.596995i | 0.640620 | − | 0.767858i | \(-0.278678\pi\) |
−0.985295 | + | 0.170864i | \(0.945344\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23789.0 | + | 41203.7i | −0.488340 | + | 0.845830i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3584.72 | + | 70327.7i | −0.0689015 | + | 1.35176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38693.2 | + | 67018.6i | −0.697537 | + | 1.20817i | 0.271781 | + | 0.962359i | \(0.412387\pi\) |
−0.969318 | + | 0.245810i | \(0.920946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −70029.7 | −1.11580 | −0.557901 | − | 0.829908i | \(-0.688393\pi\) | ||||
−0.557901 | + | 0.829908i | \(0.688393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −93518.3 | −1.40394 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15010.2 | − | 25998.4i | −0.212612 | − | 0.368255i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −71716.7 | + | 124217.i | −0.959722 | + | 1.66229i | −0.236550 | + | 0.971619i | \(0.576017\pi\) |
−0.723172 | + | 0.690668i | \(0.757317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3075.17 | + | 1990.79i | 0.0389284 | + | 0.0252012i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −37253.1 | + | 64524.2i | −0.446637 | + | 0.773598i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8422.97 | − | 14589.0i | −0.0957538 | − | 0.165850i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −50694.0 | −0.547051 | −0.273525 | − | 0.961865i | \(-0.588190\pi\) | ||||
−0.273525 | + | 0.961865i | \(0.588190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43997.7 | 0.451171 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 23915.0 | + | 41422.0i | 0.233275 | + | 0.404043i | 0.958770 | − | 0.284184i | \(-0.0917226\pi\) |
−0.725495 | + | 0.688227i | \(0.758389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 39537.9 | − | 68481.7i | 0.367215 | − | 0.636036i | −0.621914 | − | 0.783086i | \(-0.713645\pi\) |
0.989129 | + | 0.147050i | \(0.0469779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 89829.2 | + | 58153.0i | 0.795141 | + | 0.514753i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −47288.4 | + | 81906.0i | −0.399296 | + | 0.691602i | −0.993639 | − | 0.112610i | \(-0.964079\pi\) |
0.594343 | + | 0.804212i | \(0.297412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14426.0 | − | 24986.5i | −0.116300 | − | 0.201437i | 0.801999 | − | 0.597326i | \(-0.203770\pi\) |
−0.918299 | + | 0.395889i | \(0.870437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17259.7 | 0.132961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −54891.9 | −0.404401 | −0.202200 | − | 0.979344i | \(-0.564809\pi\) | ||||
−0.202200 | + | 0.979344i | \(0.564809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 211962. | + | 367129.i | 1.49456 | + | 2.58866i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1144.42 | − | 1982.19i | 0.00772895 | − | 0.0133869i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6729.34 | + | 132021.i | −0.0435617 | + | 0.854626i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −66997.2 | + | 116043.i | −0.416000 | + | 0.720533i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −84987.7 | − | 147203.i | −0.506516 | − | 0.877312i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −198234. | −1.13476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 146580. | 0.806426 | 0.403213 | − | 0.915106i | \(-0.367893\pi\) | ||||
0.403213 | + | 0.915106i | \(0.367893\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5784.28 | − | 10018.7i | −0.0306038 | − | 0.0530073i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 89310.5 | − | 154690.i | 0.454699 | − | 0.787562i | −0.543972 | − | 0.839104i | \(-0.683080\pi\) |
0.998671 | + | 0.0515415i | \(0.0164134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21201.6 | + | 10841.0i | −0.103930 | + | 0.0531424i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 33429.7 | − | 57902.0i | 0.157869 | − | 0.273438i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −160490. | − | 277977.i | −0.730545 | − | 1.26534i | −0.956650 | − | 0.291239i | \(-0.905933\pi\) |
0.226105 | − | 0.974103i | \(-0.427401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 199000. | 0.873609 | 0.436804 | − | 0.899557i | \(-0.356110\pi\) | ||||
0.436804 | + | 0.899557i | \(0.356110\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −227734. | −0.964671 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7674.40 | + | 13292.5i | 0.0313837 | + | 0.0543582i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152960. | − | 264935.i | 0.604169 | − | 1.04645i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 88559.3 | − | 122629.i | 0.338019 | − | 0.468056i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −167594. | + | 290282.i | −0.618434 | + | 1.07116i | 0.371338 | + | 0.928498i | \(0.378899\pi\) |
−0.989772 | + | 0.142661i | \(0.954434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16420.0 | + | 28440.3i | 0.0586045 | + | 0.101506i | 0.893839 | − | 0.448388i | \(-0.148002\pi\) |
−0.835235 | + | 0.549894i | \(0.814668\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 82593.6 | 0.285245 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −759250. | −2.53837 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 64878.8 | + | 112373.i | 0.210065 | + | 0.363843i | 0.951735 | − | 0.306922i | \(-0.0992991\pi\) |
−0.741670 | + | 0.670765i | \(0.765966\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26486.9 | − | 45876.6i | 0.0830879 | − | 0.143912i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 533533. | − | 272812.i | 1.62217 | − | 0.829467i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8020.18 | + | 13891.4i | −0.0236437 | + | 0.0409521i | −0.877605 | − | 0.479384i | \(-0.840860\pi\) |
0.853961 | + | 0.520336i | \(0.174193\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 224178. | + | 388287.i | 0.641036 | + | 1.11031i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 411005. | 1.14040 | 0.570199 | − | 0.821507i | \(-0.306866\pi\) | ||||
0.570199 | + | 0.821507i | \(0.306866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −370495. | −0.997849 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7439.01 | + | 12884.7i | 0.0194547 | + | 0.0336966i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −170401. | + | 295143.i | −0.432869 | + | 0.749752i | −0.997119 | − | 0.0758523i | \(-0.975832\pi\) |
0.564250 | + | 0.825604i | \(0.309166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34887.8 | + | 684455.i | −0.0861150 | + | 1.68947i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 165193. | − | 286122.i | 0.396331 | − | 0.686465i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −336758. | − | 583282.i | −0.785570 | − | 1.36065i | −0.928658 | − | 0.370938i | \(-0.879036\pi\) |
0.143087 | − | 0.989710i | \(-0.454297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −395635. | −0.897631 | −0.448815 | − | 0.893624i | \(-0.648154\pi\) | ||||
−0.448815 | + | 0.893624i | \(0.648154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −329018. | −0.726260 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 87941.9 | + | 152320.i | 0.188915 | + | 0.327210i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −276934. | + | 479664.i | −0.579125 | + | 1.00307i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −79335.5 | − | 51359.7i | −0.161552 | − | 0.104585i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 150062. | − | 259915.i | 0.297637 | − | 0.515522i | −0.677958 | − | 0.735101i | \(-0.737135\pi\) |
0.975595 | + | 0.219578i | \(0.0704682\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 164830. | + | 285494.i | 0.318524 | + | 0.551700i | 0.980180 | − | 0.198107i | \(-0.0634795\pi\) |
−0.661656 | + | 0.749807i | \(0.730146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23324.2 | 0.0439259 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −436497. | −0.801338 | −0.400669 | − | 0.916223i | \(-0.631222\pi\) | ||||
−0.400669 | + | 0.916223i | \(0.631222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 217471. | + | 376672.i | 0.389287 | + | 0.674264i | 0.992354 | − | 0.123426i | \(-0.0393882\pi\) |
−0.603067 | + | 0.797691i | \(0.706055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 125885. | − | 218039.i | 0.219778 | − | 0.380666i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −363005. | − | 235000.i | −0.618263 | − | 0.400247i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 866061. | − | 1.50006e6i | 1.43934 | − | 2.49301i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −187201. | − | 324242.i | −0.303656 | − | 0.525948i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −99771.1 | −0.157993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 416977. | 0.644771 | 0.322386 | − | 0.946608i | \(-0.395515\pi\) | ||||
0.322386 | + | 0.946608i | \(0.395515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 150619. | + | 260879.i | 0.227473 | + | 0.393995i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 58944.3 | − | 102095.i | 0.0869653 | − | 0.150628i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −54633.7 | + | 1.07184e6i | −0.0787610 | + | 1.54519i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −141241. | + | 244636.i | −0.198998 | + | 0.344675i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14406.6 | + | 24953.0i | 0.0198418 | + | 0.0343670i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 661253. | 0.890442 | 0.445221 | − | 0.895421i | \(-0.353125\pi\) | ||||
0.445221 | + | 0.895421i | \(0.353125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 428201. | 0.563886 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −492697. | − | 853376.i | −0.634622 | − | 1.09920i | −0.986595 | − | 0.163188i | \(-0.947822\pi\) |
0.351973 | − | 0.936010i | \(-0.385511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 456147. | − | 790070.i | 0.574799 | − | 0.995581i | −0.421264 | − | 0.906938i | \(-0.638413\pi\) |
0.996063 | − | 0.0886435i | \(-0.0282532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 564281. | − | 288534.i | 0.695770 | − | 0.355769i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 168915. | − | 292569.i | 0.203834 | − | 0.353052i | −0.745926 | − | 0.666028i | \(-0.767993\pi\) |
0.949761 | + | 0.312977i | \(0.101326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.16035e6 | − | 2.00979e6i | −1.37063 | − | 2.37400i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 696478. | 0.805446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −483102. | −0.547071 | −0.273536 | − | 0.961862i | \(-0.588193\pi\) | ||||
−0.273536 | + | 0.961862i | \(0.588193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −640764. | − | 1.10984e6i | −0.710650 | − | 1.23088i | −0.964614 | − | 0.263668i | \(-0.915068\pi\) |
0.253964 | − | 0.967214i | \(-0.418266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.53345e6 | + | 156732.i | 1.63212 | + | 0.166818i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2595.14 | + | 4494.91i | −0.00270656 | + | 0.00468790i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 315134. | + | 545827.i | 0.322104 | + | 0.557901i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 215401. | 0.215806 | 0.107903 | − | 0.994161i | \(-0.465586\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.51072e6 | 2.46602 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 420832. | + | 728903.i | 0.405283 | + | 0.701971i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −284938. | + | 493527.i | −0.269102 | + | 0.466099i | −0.968630 | − | 0.248507i | \(-0.920060\pi\) |
0.699528 | + | 0.714605i | \(0.253394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 221360. | − | 113188.i | 0.205045 | − | 0.104846i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −135092. | + | 233986.i | −0.122752 | + | 0.212612i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.05525e6 | + | 1.82774e6i | 0.940731 | + | 1.62939i | 0.764081 | + | 0.645120i | \(0.223193\pi\) |
0.176649 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 539825. | 0.472214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.29090e6 | 1.10819 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −320637. | − | 555360.i | −0.270168 | − | 0.467944i | 0.698737 | − | 0.715379i | \(-0.253746\pi\) |
−0.968905 | + | 0.247435i | \(0.920412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.02062e6 | − | 1.76777e6i | 0.844191 | − | 1.46218i | −0.0421304 | − | 0.999112i | \(-0.513414\pi\) |
0.886322 | − | 0.463070i | \(-0.153252\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1678.35 | − | 32927.1i | 0.00136294 | − | 0.0267391i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.43575e6 | + | 2.48678e6i | −1.14484 | + | 1.98293i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −792401. | − | 1.37248e6i | −0.620505 | − | 1.07475i | −0.989392 | − | 0.145272i | \(-0.953594\pi\) |
0.368886 | − | 0.929475i | \(-0.379739\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 670555. | 0.515732 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −37483.9 | −0.0283191 | −0.0141595 | − | 0.999900i | \(-0.504507\pi\) | ||||
−0.0141595 | + | 0.999900i | \(0.504507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −565224. | − | 978997.i | −0.419522 | − | 0.726633i | 0.576369 | − | 0.817189i | \(-0.304469\pi\) |
−0.995891 | + | 0.0905559i | \(0.971136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −75806.7 | + | 131301.i | −0.0552835 | + | 0.0957538i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.05534e6 | − | 1.33057e6i | −1.47292 | − | 0.953528i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 190060. | − | 329194.i | 0.133859 | − | 0.231850i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 228123. | + | 395121.i | 0.157920 | + | 0.273525i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.70066e6 | −1.83781 | −0.918906 | − | 0.394477i | \(-0.870926\pi\) | ||||
−0.918906 | + | 0.394477i | \(0.870926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.36677e6 | 2.25247 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −197989. | − | 342928.i | −0.130242 | − | 0.225586i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65306.0 | − | 113113.i | 0.0422450 | − | 0.0731705i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −139887. | − | 90559.0i | −0.0889940 | − | 0.0576123i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 215235. | − | 372798.i | 0.134681 | − | 0.233275i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.67642e6 | − | 2.90364e6i | −1.03189 | − | 1.78728i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −568937. | −0.344523 | −0.172262 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172262 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −711683. | −0.424024 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −392425. | − | 679701.i | −0.230068 | − | 0.398489i | 0.727760 | − | 0.685832i | \(-0.240562\pi\) |
−0.957828 | + | 0.287343i | \(0.907228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.71402e6 | + | 2.96877e6i | −0.988905 | + | 1.71283i | −0.365807 | + | 0.930691i | \(0.619207\pi\) |
−0.623099 | + | 0.782143i | \(0.714126\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 49026.5 | − | 961838.i | 0.0278391 | − | 0.546167i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.40936e6 | − | 2.44108e6i | 0.787723 | − | 1.36438i | −0.139636 | − | 0.990203i | \(-0.544593\pi\) |
0.927359 | − | 0.374173i | \(-0.122074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −905916. | − | 1.56909e6i | −0.498438 | − | 0.863320i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 851192. | 0.461068 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −187293. | −0.0998885 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74690.1 | + | 129367.i | 0.0392242 | + | 0.0679384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −129834. | + | 224878.i | −0.0671456 | + | 0.116300i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92074e6 | + | 1.49346e6i | −1.48766 | + | 0.760686i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10243e6 | + | 1.90947e6i | −0.553072 | + | 0.957949i | 0.444979 | + | 0.895541i | \(0.353211\pi\) |
−0.998051 | + | 0.0624078i | \(0.980122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −77668.6 | − | 134526.i | −0.0383827 | − | 0.0664807i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.56564e6 | 1.24906 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 998199. | 0.478787 | 0.239393 | − | 0.970923i | \(-0.423051\pi\) | ||||
0.239393 | + | 0.970923i | \(0.423051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 247013. | + | 427840.i | 0.116740 | + | 0.202200i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.24835e6 | + | 3.89426e6i | −1.04708 | + | 1.81359i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 331603. | − | 2.15351e6i | 0.152189 | − | 0.988351i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.90766e6 | − | 3.30416e6i | 0.862885 | − | 1.49456i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.48383e6 | − | 2.57007e6i | −0.661548 | − | 1.14583i | −0.980209 | − | 0.197966i | \(-0.936567\pi\) |
0.318661 | − | 0.947869i | \(-0.396767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.12310e6 | −0.933055 | −0.466528 | − | 0.884507i | \(-0.654495\pi\) | ||||
−0.466528 | + | 0.884507i | \(0.654495\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20599.5 | −0.00892462 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −731166. | − | 1.26642e6i | −0.312305 | − | 0.540929i | 0.666556 | − | 0.745455i | \(-0.267768\pi\) |
−0.978861 | + | 0.204527i | \(0.934435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.53487e6 | + | 2.65847e6i | −0.646398 | + | 1.11959i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.05928e6 | − | 541645.i | 0.439888 | − | 0.224928i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 827058. | − | 1.43251e6i | 0.338688 | − | 0.586625i | −0.645498 | − | 0.763762i | \(-0.723350\pi\) |
0.984186 | + | 0.177137i | \(0.0566835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.22118e6 | + | 2.11515e6i | 0.493187 | + | 0.854225i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.20595e6 | 0.480356 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.87860e6 | −1.13097 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −83460.8 | − | 144558.i | −0.0323458 | − | 0.0560245i | 0.849399 | − | 0.527751i | \(-0.176964\pi\) |
−0.881745 | + | 0.471726i | \(0.843631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −764889. | + | 1.32483e6i | −0.292437 | + | 0.506516i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38844.4 | − | 762079.i | 0.0146519 | − | 0.287452i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.06059e6 | + | 1.83699e6i | −0.394707 | + | 0.683652i | −0.993064 | − | 0.117578i | \(-0.962487\pi\) |
0.598357 | + | 0.801230i | \(0.295820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 892051. | + | 1.54508e6i | 0.327576 | + | 0.567378i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −94254.8 | −0.0341547 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.85242e6 | 1.02004 | 0.510018 | − | 0.860164i | \(-0.329639\pi\) | ||||
0.510018 | + | 0.860164i | \(0.329639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −659609. | − | 1.14248e6i | −0.232795 | − | 0.403213i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.46122e6 | + | 2.53091e6i | −0.509002 | + | 0.881617i | 0.490944 | + | 0.871191i | \(0.336652\pi\) |
−0.999946 | + | 0.0104256i | \(0.996681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.42150e6 | + | 3.50973e6i | 1.86409 | + | 1.20676i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −52058.5 | + | 90168.1i | −0.0176691 | + | 0.0306038i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.61135e6 | + | 2.79095e6i | 0.539904 | + | 0.935142i | 0.998909 | + | 0.0467079i | \(0.0148730\pi\) |
−0.459004 | + | 0.888434i | \(0.651794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.71319e6 | 1.55910 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.60759e6 | −0.525041 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.54871e6 | + | 6.14654e6i | 1.14440 | + | 1.98216i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 323031. | − | 559505.i | 0.102865 | − | 0.178167i | −0.809999 | − | 0.586431i | \(-0.800532\pi\) |
0.912864 | + | 0.408264i | \(0.133866\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 179905. | + | 116465.i | 0.0565731 | + | 0.0366239i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.22390e6 | − | 3.85190e6i | 0.690643 | − | 1.19623i | −0.280984 | − | 0.959712i | \(-0.590661\pi\) |
0.971627 | − | 0.236517i | \(-0.0760057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 116963. | + | 202586.i | 0.0358746 | + | 0.0621366i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −601735. | −0.182292 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.04168e6 | 0.311709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −68279.3 | − | 118263.i | −0.0201828 | − | 0.0349576i | 0.855758 | − | 0.517377i | \(-0.173091\pi\) |
−0.875940 | + | 0.482419i | \(0.839758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.44441e6 | + | 2.50180e6i | −0.421781 | + | 0.730545i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 242264. | − | 4.75291e6i | 0.0698898 | − | 1.37115i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.21135e6 | + | 5.56222e6i | −0.915308 | + | 1.58536i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −895502. | − | 1.55105e6i | −0.252189 | − | 0.436804i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.72474e6 | −1.59302 | −0.796509 | − | 0.604626i | \(-0.793323\pi\) | ||||
−0.796509 | + | 0.604626i | \(0.793323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.80110e6 | 1.87014 | 0.935070 | − | 0.354463i | \(-0.115336\pi\) | ||||
0.935070 | + | 0.354463i | \(0.115336\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.02480e6 | + | 1.77501e6i | 0.278477 | + | 0.482336i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.69522e6 | + | 4.66826e6i | −0.723806 | + | 1.25367i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.21974e6 | + | 2.15768e6i | −1.11999 | + | 0.572688i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 69069.6 | − | 119632.i | 0.0181194 | − | 0.0313837i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.85483e6 | − | 4.94471e6i | −0.740265 | − | 1.28218i | −0.952375 | − | 0.304930i | \(-0.901367\pi\) |
0.212110 | − | 0.977246i | \(-0.431967\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.13874e6 | −0.804519 | −0.402259 | − | 0.915526i | \(-0.631775\pi\) | ||||
−0.402259 | + | 0.915526i | \(0.631775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.75328e6 | −0.697634 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 424505. | + | 735265.i | 0.106336 | + | 0.184179i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −206778. | + | 358150.i | −0.0512086 | + | 0.0886959i | −0.890493 | − | 0.454996i | \(-0.849641\pi\) |
0.839285 | + | 0.543692i | \(0.182974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.35431e6 | − | 138423.i | −0.331606 | − | 0.0338931i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.22503e6 | + | 2.12181e6i | −0.296577 | + | 0.513687i | −0.975351 | − | 0.220661i | \(-0.929178\pi\) |
0.678773 | + | 0.734348i | \(0.262512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.57742e6 | + | 1.13924e7i | 1.57455 | + | 2.72719i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.01670e6 | 0.714106 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −902207. | −0.211198 | −0.105599 | − | 0.994409i | \(-0.533676\pi\) | ||||
−0.105599 | + | 0.994409i | \(0.533676\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.12930e6 | − | 8.88421e6i | −1.18745 | − | 2.05673i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 147780. | − | 255963.i | 0.0338353 | − | 0.0586045i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 299139. | − | 152959.i | 0.0677400 | − | 0.0346375i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.63007e6 | + | 4.55541e6i | −0.589083 | + | 1.02032i | 0.405270 | + | 0.914197i | \(0.367177\pi\) |
−0.994353 | + | 0.106124i | \(0.966156\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −371671. | − | 643754.i | −0.0823431 | − | 0.142623i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.79974e6 | −0.613573 | −0.306786 | − | 0.951778i | \(-0.599254\pi\) | ||||
−0.306786 | + | 0.951778i | \(0.599254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.54186e6 | 0.334266 | 0.167133 | − | 0.985934i | \(-0.446549\pi\) | ||||
0.167133 | + | 0.985934i | \(0.446549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.41662e6 | + | 5.91777e6i | 0.732765 | + | 1.26919i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.65218e6 | + | 6.32577e6i | −0.774926 | + | 1.34221i | 0.159910 | + | 0.987132i | \(0.448880\pi\) |
−0.934836 | + | 0.355080i | \(0.884454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 184617. | − | 3.62195e6i | 0.0387561 | − | 0.760345i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 583909. | − | 1.01136e6i | 0.121281 | − | 0.210065i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −349101. | − | 604661.i | −0.0717462 | − | 0.124268i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −971008. | −0.197464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −476764. | −0.0959416 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.69966e6 | + | 6.40801e6i | 0.736756 | + | 1.27610i | 0.953949 | + | 0.299970i | \(0.0969766\pi\) |
−0.217193 | + | 0.976129i | \(0.569690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27095.1 | − | 46930.1i | 0.00533983 | − | 0.00924887i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.52726e6 | − | 2.93083e6i | −0.883014 | − | 0.571640i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.32467e6 | + | 4.02645e6i | −0.448753 | + | 0.777263i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.25178e6 | − | 3.90020e6i | −0.430234 | − | 0.745187i | 0.566660 | − | 0.823952i | \(-0.308236\pi\) |
−0.996893 | + | 0.0787655i | \(0.974902\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 144363. | 0.0273014 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.10273e6 | −1.51680 | −0.758399 | − | 0.651791i | \(-0.774018\pi\) | ||||
−0.758399 | + | 0.651791i | \(0.774018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.70061e6 | − | 2.94554e6i | −0.315128 | − | 0.545819i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.01760e6 | − | 3.49458e6i | 0.370102 | − | 0.641036i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.64255e6 | + | 2.35809e6i | 0.661477 | + | 0.428223i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 635251. | − | 1.10029e6i | 0.114207 | − | 0.197813i | −0.803255 | − | 0.595635i | \(-0.796901\pi\) |
0.917463 | + | 0.397822i | \(0.130234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.84952e6 | − | 3.20347e6i | −0.329205 | − | 0.570199i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.90365e6 | −0.511710 | −0.255855 | − | 0.966715i | \(-0.582357\pi\) | ||||
−0.255855 | + | 0.966715i | \(0.582357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.38668e6 | 0.765433 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.66723e6 | + | 2.88772e6i | 0.288054 | + | 0.498925i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.46536e6 | − | 7.73423e6i | 0.763945 | − | 1.32319i | −0.176858 | − | 0.984236i | \(-0.556593\pi\) |
0.940803 | − | 0.338955i | \(-0.110073\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −207137. | + | 4.06377e6i | −0.0350918 | + | 0.688456i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 66951.1 | − | 115963.i | 0.0112322 | − | 0.0194547i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.62618e6 | − | 6.28072e6i | −0.602464 | − | 1.04350i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.37445e7 | −2.26153 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.06722e6 | 0.499835 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −262540. | − | 454732.i | −0.0423741 | − | 0.0733942i | 0.844060 | − | 0.536248i | \(-0.180159\pi\) |
−0.886435 | + | 0.462854i | \(0.846825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.36105e6 | − | 2.35741e6i | 0.217581 | − | 0.376861i | −0.736487 | − | 0.676452i | \(-0.763517\pi\) |
0.954068 | + | 0.299590i | \(0.0968500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.49179e6 | − | 2.80812e6i | 0.869592 | − | 0.444649i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.22067e6 | + | 7.31041e6i | −0.661995 | + | 1.14661i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.46441e6 | − | 1.29287e7i | −1.15973 | − | 2.00871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.97347e6 | −0.457643 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −533671. | −0.0813683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.33701e6 | + | 7.51191e6i | 0.655097 | + | 1.13466i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.03082e6 | + | 5.24953e6i | −0.453549 | + | 0.785570i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.34485e6 | − | 7.40105e6i | 0.792436 | − | 1.09729i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −922098. | + | 1.59712e6i | −0.135451 | + | 0.234609i | −0.925770 | − | 0.378088i | \(-0.876582\pi\) |
0.790318 | + | 0.612696i | \(0.209915\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.78036e6 | + | 3.08367e6i | 0.259124 | + | 0.448815i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.64612e6 | −0.381609 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.41792e6 | −1.06002 | −0.530010 | − | 0.847992i | \(-0.677812\pi\) | ||||
−0.530010 | + | 0.847992i | \(0.677812\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.48058e6 | + | 2.56444e6i | 0.209653 | + | 0.363130i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 306340. | − | 530596.i | 0.0429857 | − | 0.0744535i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.93251e6 | − | 4.56747e6i | 1.24211 | − | 0.635130i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 791477. | − | 1.37088e6i | 0.109070 | − | 0.188915i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.81148e6 | + | 6.60168e6i | 0.520542 | + | 0.901606i | 0.999715 | + | 0.0238850i | \(0.00760354\pi\) |
−0.479172 | + | 0.877721i | \(0.659063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36321.8 | −0.00491629 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.98481e6 | 0.668716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.19628e6 | − | 2.07201e6i | −0.159060 | − | 0.275500i | 0.775470 | − | 0.631384i | \(-0.217513\pi\) |
−0.934530 | + | 0.355885i | \(0.884180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.51717e6 | + | 4.35987e6i | −0.331735 | + | 0.574583i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −43299.3 | + | 849477.i | −0.00565618 | + | 0.110967i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.40156e6 | − | 4.15963e6i | 0.310966 | − | 0.538609i | −0.667606 | − | 0.744515i | \(-0.732681\pi\) |
0.978572 | + | 0.205906i | \(0.0660141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.10893e6 | − | 3.65278e6i | −0.270690 | − | 0.468849i | 0.698349 | − | 0.715758i | \(-0.253919\pi\) |
−0.969039 | + | 0.246909i | \(0.920585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.70111e6 | −0.343681 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.44352e7 | 3.08210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.24750e6 | − | 7.35688e6i | −0.531121 | − | 0.919929i | −0.999340 | − | 0.0363167i | \(-0.988437\pi\) |
0.468219 | − | 0.883612i | \(-0.344896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.48347e6 | − | 2.56944e6i | 0.183900 | − | 0.318524i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.62118e6 | + | 4.93375e6i | 0.936659 | + | 0.606368i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.59857e6 | − | 2.76881e6i | 0.194788 | − | 0.337382i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −104959. | − | 181794.i | −0.0126803 | − | 0.0219630i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.35441e6 | 0.162238 | 0.0811192 | − | 0.996704i | \(-0.474151\pi\) | ||||
0.0811192 | + | 0.996704i | \(0.474151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.52058e6 | −0.180602 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.96424e6 | + | 3.40216e6i | 0.231326 | + | 0.400669i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.20201e6 | + | 3.81399e6i | −0.257147 | + | 0.445392i | −0.965476 | − | 0.260490i | \(-0.916116\pi\) |
0.708329 | + | 0.705882i | \(0.249449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01774e7 | + | 6.58857e6i | 1.17854 | + | 0.762955i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.95724e6 | − | 3.39004e6i | 0.224755 | − | 0.389287i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.40934e6 | − | 4.17309e6i | −0.274366 | − | 0.475216i | 0.695609 | − | 0.718421i | \(-0.255135\pi\) |
−0.969975 | + | 0.243205i | \(0.921801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.64290e6 | 0.976053 | 0.488027 | − | 0.872829i | \(-0.337717\pi\) | ||||
0.488027 | + | 0.872829i | \(0.337717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.26593e6 | −0.253777 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.14458e6 | + | 1.06427e7i | 0.682501 | + | 1.18213i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 125066. | − | 216621.i | 0.0137775 | − | 0.0238633i | −0.859054 | − | 0.511884i | \(-0.828948\pi\) |
0.872832 | + | 0.488021i | \(0.162281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −198119. | + | 3.88685e6i | −0.0216463 | + | 0.424673i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −357507. | + | 619220.i | −0.0387419 | + | 0.0671030i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.05759e6 | − | 1.22241e7i | −0.758587 | − | 1.31391i | −0.943571 | − | 0.331169i | \(-0.892557\pi\) |
0.184985 | − | 0.982741i | \(-0.440776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.55891e7 | −1.66201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.14663e7 | −1.21258 | −0.606291 | − | 0.795243i | \(-0.707343\pi\) | ||||
−0.606291 | + | 0.795243i | \(0.707343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −322987. | − | 559430.i | −0.0338812 | − | 0.0586839i | 0.848588 | − | 0.529055i | \(-0.177453\pi\) |
−0.882469 | + | 0.470371i | \(0.844120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.68481e6 | + | 2.91817e6i | −0.175316 | + | 0.303656i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.65561e7 | − | 8.46566e6i | 1.70899 | − | 0.873858i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −830333. | + | 1.43818e6i | −0.0850260 | + | 0.147269i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 448970. | + | 777638.i | 0.0456088 | + | 0.0789967i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.95547e6 | 0.197072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.83763e7 | 1.83732 | 0.918658 | − | 0.395053i | \(-0.129274\pi\) | ||||
0.918658 | + | 0.395053i | \(0.129274\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.87639e6 | − | 3.25001e6i | −0.186129 | − | 0.322386i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.72170e6 | − | 1.16423e7i | 0.661523 | − | 1.14579i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −194409. | − | 433306.i | −0.0189832 | − | 0.0423103i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.35557e6 | − | 2.34791e6i | 0.131332 | − | 0.227473i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.57166e6 | − | 9.65039e6i | −0.535599 | − | 0.927684i | −0.999134 | − | 0.0416055i | \(-0.986753\pi\) |
0.463536 | − | 0.886078i | \(-0.346581\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 323686. | 0.0308743 | 0.0154371 | − | 0.999881i | \(-0.495086\pi\) | ||||
0.0154371 | + | 0.999881i | \(0.495086\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.06100e6 | −0.100419 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.31428e6 | + | 7.47256e6i | 0.405180 | + | 0.701792i | 0.994342 | − | 0.106222i | \(-0.0338755\pi\) |
−0.589162 | + | 0.808015i | \(0.700542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.96995e6 | − | 1.72685e7i | 0.929140 | − | 1.60932i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.60004e6 | − | 4.39747e6i | 0.795331 | − | 0.406678i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.60795e6 | + | 7.98120e6i | −0.422887 | + | 0.732462i | −0.996221 | − | 0.0868600i | \(-0.972317\pi\) |
0.573333 | + | 0.819322i | \(0.305650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.19101e6 | − | 1.41872e7i | −0.745992 | − | 1.29210i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.54233e6 | 0.229783 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.19016e6 | 0.734647 | 0.367324 | − | 0.930093i | \(-0.380274\pi\) | ||||
0.367324 | + | 0.930093i | \(0.380274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.60129e6 | − | 4.50557e6i | −0.231572 | − | 0.401094i | 0.726699 | − | 0.686956i | \(-0.241054\pi\) |
−0.958271 | + | 0.285862i | \(0.907720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 129659. | − | 224577.i | 0.0114557 | − | 0.0198418i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −111175. | + | 2.18111e6i | −0.00974881 | + | 0.191259i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.70897e6 | + | 1.33523e7i | −0.670937 | + | 1.16210i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.97564e6 | − | 5.15396e6i | −0.257048 | − | 0.445221i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.98574e7 | −1.70261 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.57148e6 | −0.133743 | −0.0668715 | − | 0.997762i | \(-0.521302\pi\) | ||||
−0.0668715 | + | 0.997762i | \(0.521302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.92691e6 | − | 3.33750e6i | −0.162780 | − | 0.281943i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.71371e6 | − | 1.68246e7i | 0.814542 | − | 1.41083i | −0.0951147 | − | 0.995466i | \(-0.530322\pi\) |
0.909656 | − | 0.415361i | \(-0.136345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.51692e6 | + | 3.57151e6i | 0.459221 | + | 0.297288i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.43427e6 | + | 7.68039e6i | −0.366399 | + | 0.634622i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.08715e6 | + | 1.05433e7i | 0.499301 | + | 0.864814i | 1.00000 | 0.000807242i | \(-0.000256953\pi\) | |
−0.500699 | + | 0.865622i | \(0.666924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.94384e7 | −2.39711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.21065e6 | −0.663721 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −83160.7 | − | 144039.i | −0.00667375 | − | 0.0115593i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 831962. | − | 1.44100e6i | 0.0662839 | − | 0.114807i | −0.830979 | − | 0.556304i | \(-0.812219\pi\) |
0.897263 | + | 0.441497i | \(0.145552\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.78817e6 | − | 3.09973e6i | −0.378736 | − | 0.245183i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.12555e6 | − | 1.58059e7i | 0.716633 | − | 1.24125i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.62887e6 | − | 1.66777e7i | −0.750746 | − | 1.30033i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.04046e6 | −0.235368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.62394e7 | 1.24817 | 0.624087 | − | 0.781355i | \(-0.285471\pi\) | ||||
0.624087 | + | 0.781355i | \(0.285471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 176125. | + | 305057.i | 0.0134410 | + | 0.0232805i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.04432e7 | + | 1.80881e7i | −0.791333 | + | 1.37063i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 315654. | − | 6.19273e6i | 0.0237500 | − | 0.465944i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.31112e6 | + | 9.19913e6i | −0.396799 | + | 0.687276i | −0.993329 | − | 0.115315i | \(-0.963212\pi\) |
0.596530 | + | 0.802591i | \(0.296546\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.13415e6 | − | 5.42851e6i | −0.232512 | − | 0.402723i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.82651e7 | 2.81890 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40770e6 | 0.102978 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.17396e6 | + | 3.76541e6i | 0.157926 | + | 0.273536i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.18925e6 | − | 7.25599e6i | 0.302214 | − | 0.523449i | −0.674423 | − | 0.738345i | \(-0.735608\pi\) |
0.976637 | + | 0.214895i | \(0.0689411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.12751e6 | + | 4.66718e6i | −0.653904 | + | 0.334361i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.76688e6 | + | 9.98853e6i | −0.410294 | + | 0.710650i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.81671e6 | − | 1.52710e7i | −0.622962 | − | 1.07900i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.58477e6 | 0.532239 | 0.266119 | − | 0.963940i | \(-0.414258\pi\) | ||||
0.266119 | + | 0.963940i | \(0.414258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −655343. | − | 1.13509e6i | −0.0453602 | − | 0.0785662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.11733e6 | + | 8.86347e6i | −0.351790 | + | 0.609318i | −0.986563 | − | 0.163380i | \(-0.947760\pi\) |
0.634773 | + | 0.772699i | \(0.281094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.67890e6 | − | 1.26573e7i | −0.387745 | − | 0.864219i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.59759e6 | − | 1.31594e7i | 0.515237 | − | 0.892417i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.49404e6 | + | 1.64442e7i | 0.639499 | + | 1.10764i | 0.985543 | + | 0.169427i | \(0.0541916\pi\) |
−0.346044 | + | 0.938218i | \(0.612475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 46712.4 | 0.00312527 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.42011e7 | −1.60829 | −0.804143 | − | 0.594436i | \(-0.797375\pi\) | ||||
−0.804143 | + | 0.594436i | \(0.797375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.53707e7 | + | 2.66229e7i | 1.01462 | + | 1.75737i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.83620e6 | − | 4.91245e6i | 0.185967 | − | 0.322104i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.09168e7 | − | 5.58207e6i | 0.711032 | − | 0.363572i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.98715e6 | − | 6.90594e6i | 0.257966 | − | 0.446810i | −0.707731 | − | 0.706482i | \(-0.750281\pi\) |
0.965697 | + | 0.259672i | \(0.0836144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −969305. | − | 1.67889e6i | −0.0622978 | − | 0.107903i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.01188e6 | 0.192296 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.00632e7 | 1.90676 | 0.953378 | − | 0.301778i | \(-0.0975800\pi\) | ||||
0.953378 | + | 0.301778i | \(0.0975800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.12982e7 | − | 1.95691e7i | −0.711878 | − | 1.23301i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.23479e6 | + | 5.60282e6i | −0.202481 | + | 0.350708i | −0.949327 | − | 0.314289i | \(-0.898234\pi\) |
0.746846 | + | 0.664997i | \(0.231567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −190408. | + | 3.73556e6i | −0.0118406 | + | 0.232298i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.78749e6 | − | 6.56013e6i | 0.233990 | − | 0.405283i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −518655. | − | 898336.i | −0.0318339 | − | 0.0551379i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.52170e6 | 0.214752 | 0.107376 | − | 0.994219i | \(-0.465755\pi\) | ||||
0.107376 | + | 0.994219i | \(0.465755\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.12888e6 | 0.310732 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.22474e7 | + | 2.12131e7i | 0.737216 | + | 1.27690i | 0.953744 | + | 0.300619i | \(0.0971934\pi\) |
−0.216528 | + | 0.976276i | \(0.569473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.18818e7 | + | 3.79004e7i | −1.30866 | + | 2.26667i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.87833e6 | − | 1.21598e6i | −0.111614 | − | 0.0722562i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.73450e6 | − | 3.00424e6i | 0.102407 | − | 0.177374i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.09035e6 | + | 1.57449e7i | 0.533277 | + | 0.923663i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.43165e6 | 0.141741 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.19006e7 | 0.689277 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.91530e6 | + | 8.51356e6i | 0.282887 | + | 0.489975i | 0.972095 | − | 0.234589i | \(-0.0753744\pi\) |
−0.689207 | + | 0.724564i | \(0.742041\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.49724e6 | − | 1.64497e7i | 0.543131 | − | 0.940731i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.97376e6 | + | 3.86725e6i | 0.339474 | + | 0.219766i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −516508. | + | 894618.i | −0.0291672 | + | 0.0505190i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.42921e6 | − | 4.20752e6i | −0.136316 | − | 0.236107i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.59743e6 | 0.144843 | 0.0724215 | − | 0.997374i | \(-0.476927\pi\) | ||||
0.0724215 | + | 0.997374i | \(0.476927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.58016e7 | −1.42981 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.80906e6 | − | 1.00616e7i | −0.319907 | − | 0.554096i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.52435e6 | + | 1.47646e7i | −0.466522 | + | 0.808041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.79769e6 | − | 5.48870e7i | 0.152163 | − | 2.98525i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.88574e6 | + | 4.99824e6i | −0.155981 | + | 0.270168i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.45127e7 | − | 2.51368e7i | −0.779611 | − | 1.35033i | −0.932166 | − | 0.362031i | \(-0.882083\pi\) |
0.152555 | − | 0.988295i | \(-0.451250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −196756. | −0.0105045 | −0.00525227 | − | 0.999986i | \(-0.501672\pi\) | ||||
−0.00525227 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.83712e7 | −0.974788 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 735562. | + | 1.27403e6i | 0.0387905 | + | 0.0671871i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 118050. | − | 204469.i | 0.00618745 | − | 0.0107170i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −264194. | + | 135091.i | −0.0137630 | + | 0.00703746i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.64732e6 | + | 1.15135e7i | −0.344183 | + | 0.596142i | −0.985205 | − | 0.171381i | \(-0.945177\pi\) |
0.641022 | + | 0.767522i | \(0.278511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.66709e7 | − | 2.88749e7i | −0.857946 | − | 1.48601i | −0.873884 | − | 0.486134i | \(-0.838407\pi\) |
0.0159382 | − | 0.999873i | \(-0.494927\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.58434e7 | 1.32195 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.68644e7 | 1.36588 | 0.682942 | − | 0.730473i | \(-0.260700\pi\) | ||||
0.682942 | + | 0.730473i | \(0.260700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.28567e6 | + | 1.08871e7i | 0.317662 | + | 0.550206i | 0.980000 | − | 0.198999i | \(-0.0637690\pi\) |
−0.662338 | + | 0.749205i | \(0.730436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.13161e6 | + | 1.23523e7i | −0.358249 | + | 0.620505i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00335e7 | − | 1.38935e7i | 0.501003 | − | 0.693742i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.88475e7 | − | 3.26447e7i | 0.935484 | − | 1.62031i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.01750e6 | − | 5.22646e6i | −0.148879 | − | 0.257866i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.61488e6 | −0.0792018 | −0.0396009 | − | 0.999216i | \(-0.512609\pi\) | ||||
−0.0396009 | + | 0.999216i | \(0.512609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.38495e6 | −0.457554 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 168677. | + | 292158.i | 0.00817501 | + | 0.0141595i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.69897e7 | + | 2.94271e7i | −0.818550 | + | 1.41777i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.54666e7 | − | 7.90856e6i | 0.740776 | − | 0.378782i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.08702e6 | + | 8.81097e6i | −0.242211 | + | 0.419522i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.43214e6 | − | 7.67670e6i | −0.209792 | − | 0.363371i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.64014e7 | −0.771807 | −0.385903 | − | 0.922539i | \(-0.626110\pi\) | ||||
−0.385903 | + | 0.922539i | \(0.626110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.36452e6 | 0.0638359 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.87706e6 | + | 3.25116e6i | 0.0873022 | + | 0.151212i | 0.906370 | − | 0.422485i | \(-0.138842\pi\) |
−0.819068 | + | 0.573697i | \(0.805509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.63044e7 | + | 2.82401e7i | −0.753916 | + | 1.30582i | 0.191996 | + | 0.981396i | \(0.438504\pi\) |
−0.945912 | + | 0.324425i | \(0.894829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.12175e6 | + | 2.20073e7i | −0.0515690 | + | 1.01172i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.43895e6 | − | 5.95644e6i | 0.157181 | − | 0.272245i | −0.776670 | − | 0.629907i | \(-0.783093\pi\) |
0.933851 | + | 0.357662i | \(0.116426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.56281e7 | + | 2.70687e7i | 0.710178 | + | 1.23006i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.42109e6 | −0.154567 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.20348e7 | 1.88825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −395240. | − | 684576.i | −0.0176529 | − | 0.0305757i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.05311e6 | − | 3.55609e6i | 0.0911751 | − | 0.157920i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.15733e7 | + | 1.39660e7i | 0.952570 | + | 0.616668i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 329879. | − | 571367.i | 0.0144829 | − | 0.0250851i | −0.858693 | − | 0.512490i | \(-0.828723\pi\) |
0.873176 | + | 0.487405i | \(0.162056\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.21530e7 | + | 2.10496e7i | 0.530531 | + | 0.918906i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.91651e7 | −1.70004 | −0.850022 | − | 0.526748i | \(-0.823411\pi\) | ||||
−0.850022 | + | 0.526748i | \(0.823411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.30226e7 | −0.562078 | −0.281039 | − | 0.959696i | \(-0.590679\pi\) | ||||
−0.281039 | + | 0.959696i | \(0.590679\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.51505e7 | − | 2.62414e7i | −0.650231 | − | 1.12623i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.10805e6 | − | 7.11535e6i | 0.175318 | − | 0.303660i | −0.764953 | − | 0.644086i | \(-0.777238\pi\) |
0.940271 | + | 0.340426i | \(0.110571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.59519e7 | − | 1.03269e7i | −0.676954 | − | 0.438242i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78190e6 | + | 3.08635e6i | −0.0751952 | + | 0.130242i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.32388e6 | − | 4.02509e6i | −0.0975183 | − | 0.168907i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.17707e7 | −2.57766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17551e6 | −0.0487803 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38068e7 | − | 2.39141e7i | −0.569762 | − | 0.986857i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.00089e6 | − | 5.19769e6i | 0.123151 | − | 0.213304i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −76346.7 | + | 1.49783e6i | −0.00311581 | + | 0.0611282i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.81426e7 | + | 3.14239e7i | −0.736339 | + | 1.27538i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.40624e7 | − | 2.43567e7i | −0.567597 | − | 0.983107i | −0.996803 | − | 0.0799006i | \(-0.974540\pi\) |
0.429205 | − | 0.903207i | \(-0.358794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.87423e6 | −0.155516 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.65678e7 | −1.06062 | −0.530310 | − | 0.847804i | \(-0.677925\pi\) | ||||
−0.530310 | + | 0.847804i | \(0.677925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.90194e7 | + | 3.29426e7i | 0.755127 | + | 1.30792i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.50878e7 | + | 2.61328e7i | −0.595761 | + | 1.03189i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.06177e7 | + | 1.05425e7i | −0.809688 | + | 0.414018i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.86095e7 | − | 3.22326e7i | 0.726851 | − | 1.25894i | −0.231356 | − | 0.972869i | \(-0.574316\pi\) |
0.958208 | − | 0.286074i | \(-0.0923503\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.56022e6 | + | 4.43443e6i | 0.0994552 | + | 0.172262i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 945793. | 0.0365420 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.01380e7 | 0.389582 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.20257e6 | + | 5.54702e6i | 0.122405 | + | 0.212012i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.45083e7 | + | 2.51291e7i | −0.551539 | + | 0.955294i | 0.446625 | + | 0.894721i | \(0.352626\pi\) |
−0.998164 | + | 0.0605722i | \(0.980707\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07110e6 | + | 313894.i | 0.116123 | + | 0.0118688i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.53183e6 | + | 6.11731e6i | −0.132830 | + | 0.230068i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.53987e7 | + | 4.39918e7i | 0.950128 | + | 1.64567i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.84662e7 | −1.80339 | −0.901696 | − | 0.432370i | \(-0.857677\pi\) | ||||
−0.901696 | + | 0.432370i | \(0.857677\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.08523e7 | 1.14189 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.46201e7 | + | 2.53227e7i | 0.538239 | + | 0.932258i | 0.998999 | + | 0.0447331i | \(0.0142437\pi\) |
−0.460759 | + | 0.887525i | \(0.652423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.36482e7 | + | 7.56010e7i | −1.59841 | + | 2.76852i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.71740e6 | + | 3.94615e6i | −0.281120 | + | 0.143745i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.60062e7 | + | 2.77236e7i | −0.579982 | + | 1.00456i | 0.415499 | + | 0.909594i | \(0.363607\pi\) |
−0.995481 | + | 0.0949641i | \(0.969726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 443452. | + | 768082.i | 0.0159838 | + | 0.0276848i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.53685e7 | −0.909584 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.89025e7 | 0.674196 | 0.337098 | − | 0.941470i | \(-0.390555\pi\) | ||||
0.337098 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.37627e7 | − | 2.38378e7i | −0.488311 | − | 0.845780i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.15324e6 | + | 1.41218e7i | −0.287773 | + | 0.498438i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.11831e6 | + | 4.15585e7i | −0.0743777 | + | 1.45920i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99519e7 | + | 3.45577e7i | −0.696908 | + | 1.20708i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.83036e6 | − | 6.63438e6i | −0.133099 | − | 0.230534i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.02344e7 | 1.04516 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.66513e7 | 1.94825 | 0.974123 | − | 0.226017i | \(-0.0725705\pi\) | ||||
0.974123 | + | 0.226017i | \(0.0725705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 842819. | + | 1.45980e6i | 0.0288353 | + | 0.0499442i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.72939e6 | + | 1.16556e7i | −0.229049 | + | 0.396724i | −0.957526 | − | 0.288346i | \(-0.906895\pi\) |
0.728478 | + | 0.685069i | \(0.240228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.16568e7 | − | 1.40200e7i | −0.733351 | − | 0.474752i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 672211. | − | 1.16430e6i | 0.0226461 | − | 0.0392242i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.86448e7 | − | 4.96142e7i | −0.960084 | − | 1.66291i | −0.722280 | − | 0.691601i | \(-0.756906\pi\) |
−0.237804 | − | 0.971313i | \(-0.576428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.79103e7 | 2.59799 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33700e6 | 0.0775331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.74148e6 | + | 1.68727e7i | 0.321544 | + | 0.556931i | 0.980807 | − | 0.194982i | \(-0.0624647\pi\) |
−0.659262 | + | 0.751913i | \(0.729131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00164e7 | + | 3.46695e7i | −0.657349 | + | 1.13856i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47837e7 | + | 1.60443e7i | 0.809793 | + | 0.524238i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.97071e6 | + | 5.14542e6i | −0.0965761 | + | 0.167275i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.03075e7 | − | 3.51736e7i | −0.656859 | − | 1.13771i | −0.981424 | − | 0.191849i | \(-0.938552\pi\) |
0.324566 | − | 0.945863i | \(-0.394782\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.98438e7 | 0.638633 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.98903e7 | 1.27735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.66000e7 | − | 4.60725e7i | −0.847506 | − | 1.46792i | −0.883427 | − | 0.468570i | \(-0.844770\pi\) |
0.0359201 | − | 0.999355i | \(-0.488564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −699018. | + | 1.21073e6i | −0.0221602 | + | 0.0383827i |
(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 | 336.6.q.l.289.5 | 10 | ||
4.3 | odd | 2 | 168.6.q.c.121.5 | yes | 10 | ||
7.4 | even | 3 | inner | 336.6.q.l.193.5 | 10 | ||
12.11 | even | 2 | 504.6.s.c.289.1 | 10 | |||
28.11 | odd | 6 | 168.6.q.c.25.5 | ✓ | 10 | ||
84.11 | even | 6 | 504.6.s.c.361.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.q.c.25.5 | ✓ | 10 | 28.11 | odd | 6 | ||
168.6.q.c.121.5 | yes | 10 | 4.3 | odd | 2 | ||
336.6.q.l.193.5 | 10 | 7.4 | even | 3 | inner | ||
336.6.q.l.289.5 | 10 | 1.1 | even | 1 | trivial | ||
504.6.s.c.289.1 | 10 | 12.11 | even | 2 | |||
504.6.s.c.361.1 | 10 | 84.11 | even | 6 |