Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), 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: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 81 x^{14} - 118 x^{13} + 1960 x^{12} - 366 x^{11} + 37625 x^{10} - 83714 x^{9} + 623931 x^{8} + 289492 x^{7} + 241286 x^{6} - 4777608 x^{5} + \cdots + 1148023744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.6 | ||
Root | \(1.75486 - 2.33310i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.145 |
Dual form | 1008.3.cg.q.577.6 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.18217 | + | 1.25988i | 0.436435 | + | 0.251976i | 0.702084 | − | 0.712094i | \(-0.252253\pi\) |
−0.265649 | + | 0.964070i | \(0.585586\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00972 | − | 6.31993i | 0.429960 | − | 0.902848i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.78132 | − | 4.81739i | −0.252848 | − | 0.437945i | 0.711461 | − | 0.702726i | \(-0.248034\pi\) |
−0.964309 | + | 0.264781i | \(0.914700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.50184i | − | 0.500142i | −0.968228 | − | 0.250071i | \(-0.919546\pi\) | ||
0.968228 | − | 0.250071i | \(-0.0804539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.6019 | + | 10.1625i | −1.03541 | + | 0.597793i | −0.918529 | − | 0.395353i | \(-0.870622\pi\) |
−0.116879 | + | 0.993146i | \(0.537289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.98781 | − | 5.76646i | −0.525674 | − | 0.303498i | 0.213579 | − | 0.976926i | \(-0.431488\pi\) |
−0.739253 | + | 0.673428i | \(0.764821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.3094 | − | 28.2488i | 0.709106 | − | 1.22821i | −0.256084 | − | 0.966655i | \(-0.582432\pi\) |
0.965189 | − | 0.261552i | \(-0.0842344\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.32541 | − | 16.1521i | −0.373016 | − | 0.646083i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19.7142 | −0.679801 | −0.339900 | − | 0.940461i | \(-0.610393\pi\) | ||||
−0.339900 | + | 0.940461i | \(0.610393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23235 | − | 3.02090i | 0.168785 | − | 0.0974483i | −0.413228 | − | 0.910628i | \(-0.635599\pi\) |
0.582013 | + | 0.813179i | \(0.302265\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.5301 | − | 9.99931i | 0.415145 | − | 0.285695i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.71348 | + | 9.89604i | −0.154418 | + | 0.267461i | −0.932847 | − | 0.360272i | \(-0.882684\pi\) |
0.778429 | + | 0.627733i | \(0.216017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.9985i | 1.70728i | 0.520862 | + | 0.853641i | \(0.325610\pi\) | ||||
−0.520862 | + | 0.853641i | \(0.674390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −40.6641 | −0.945677 | −0.472838 | − | 0.881149i | \(-0.656771\pi\) | ||||
−0.472838 | + | 0.881149i | \(0.656771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −33.5140 | − | 19.3493i | −0.713063 | − | 0.411687i | 0.0991311 | − | 0.995074i | \(-0.468394\pi\) |
−0.812194 | + | 0.583387i | \(0.801727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30.8831 | − | 38.0425i | −0.630268 | − | 0.776378i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.4735 | + | 28.5330i | 0.310821 | + | 0.538358i | 0.978540 | − | 0.206055i | \(-0.0660627\pi\) |
−0.667719 | + | 0.744413i | \(0.732729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 14.0165i | − | 0.254846i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61.4324 | − | 35.4680i | 1.04123 | − | 0.601153i | 0.121046 | − | 0.992647i | \(-0.461375\pi\) |
0.920181 | + | 0.391494i | \(0.128042\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.8685 | − | 20.7087i | −0.588008 | − | 0.339487i | 0.176301 | − | 0.984336i | \(-0.443587\pi\) |
−0.764310 | + | 0.644849i | \(0.776920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.19153 | − | 14.1881i | 0.126024 | − | 0.218279i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.9001 | − | 82.9655i | −0.714928 | − | 1.23829i | −0.962987 | − | 0.269546i | \(-0.913126\pi\) |
0.248060 | − | 0.968745i | \(-0.420207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 57.6429 | 0.811871 | 0.405936 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405936 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.2999 | − | 16.3389i | 0.387669 | − | 0.223821i | −0.293480 | − | 0.955965i | \(-0.594814\pi\) |
0.681150 | + | 0.732144i | \(0.261480\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −38.8166 | + | 3.07876i | −0.504112 | + | 0.0399839i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31.1447 | − | 53.9442i | 0.394237 | − | 0.682838i | −0.598767 | − | 0.800923i | \(-0.704342\pi\) |
0.993003 | + | 0.118086i | \(0.0376757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 35.3256i | − | 0.425610i | −0.977095 | − | 0.212805i | \(-0.931740\pi\) | ||
0.977095 | − | 0.212805i | \(-0.0682599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −51.2140 | −0.602517 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.60075 | − | 3.81095i | −0.0741658 | − | 0.0428196i | 0.462459 | − | 0.886641i | \(-0.346967\pi\) |
−0.536624 | + | 0.843821i | \(0.680301\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −41.0912 | − | 19.5687i | −0.451552 | − | 0.215041i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.5301 | − | 25.1669i | −0.152948 | − | 0.264914i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 130.272i | − | 1.34301i | −0.740999 | − | 0.671506i | \(-0.765648\pi\) | ||
0.740999 | − | 0.671506i | \(-0.234352\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36.2733 | + | 20.9424i | −0.359141 | + | 0.207350i | −0.668704 | − | 0.743529i | \(-0.733151\pi\) |
0.309563 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −74.4377 | − | 42.9766i | −0.722696 | − | 0.417249i | 0.0930481 | − | 0.995662i | \(-0.470339\pi\) |
−0.815744 | + | 0.578413i | \(0.803672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −80.8938 | + | 140.112i | −0.756016 | + | 1.30946i | 0.188851 | + | 0.982006i | \(0.439524\pi\) |
−0.944867 | + | 0.327453i | \(0.893810\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −43.4215 | − | 75.2082i | −0.398362 | − | 0.689984i | 0.595162 | − | 0.803606i | \(-0.297088\pi\) |
−0.993524 | + | 0.113622i | \(0.963755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 86.5429 | 0.765866 | 0.382933 | − | 0.923776i | \(-0.374914\pi\) | ||||
0.382933 | + | 0.923776i | \(0.374914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 71.1800 | − | 41.0958i | 0.618957 | − | 0.357355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.2493 | + | 141.829i | 0.0945316 | + | 1.19184i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.0285 | − | 77.9916i | 0.372136 | − | 0.644559i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 109.989i | − | 0.879916i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29.4865 | −0.232177 | −0.116089 | − | 0.993239i | \(-0.537036\pi\) | ||||
−0.116089 | + | 0.993239i | \(0.537036\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −169.021 | − | 97.5843i | −1.29024 | − | 0.744918i | −0.311540 | − | 0.950233i | \(-0.600845\pi\) |
−0.978696 | + | 0.205315i | \(0.934178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −66.5042 | + | 45.7668i | −0.500032 | + | 0.344112i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.821473 | − | 1.42283i | −0.00599615 | − | 0.0103856i | 0.863012 | − | 0.505184i | \(-0.168575\pi\) |
−0.869008 | + | 0.494798i | \(0.835242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.93842i | − | 0.0714994i | −0.999361 | − | 0.0357497i | \(-0.988618\pi\) | ||
0.999361 | − | 0.0357497i | \(-0.0113819\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.3219 | + | 18.0837i | −0.219034 | + | 0.126460i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −43.0199 | − | 24.8375i | −0.296689 | − | 0.171293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 145.960 | − | 252.810i | 0.979598 | − | 1.69671i | 0.315758 | − | 0.948840i | \(-0.397741\pi\) |
0.663840 | − | 0.747874i | \(-0.268925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −40.9781 | − | 70.9761i | −0.271378 | − | 0.470041i | 0.697837 | − | 0.716257i | \(-0.254146\pi\) |
−0.969215 | + | 0.246216i | \(0.920813\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.2239 | 0.0982185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −44.0946 | + | 25.4580i | −0.280857 | + | 0.162153i | −0.633812 | − | 0.773488i | \(-0.718511\pi\) |
0.352954 | + | 0.935641i | \(0.385177\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −129.443 | − | 188.095i | −0.803996 | − | 1.16829i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −40.6690 | + | 70.4408i | −0.249503 | + | 0.432152i | −0.963388 | − | 0.268111i | \(-0.913601\pi\) |
0.713885 | + | 0.700263i | \(0.246934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.97762i | 0.0178301i | 0.999960 | + | 0.00891503i | \(0.00283778\pi\) | ||||
−0.999960 | + | 0.00891503i | \(0.997162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 126.726 | 0.749858 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 190.687 | + | 110.093i | 1.10224 | + | 0.636378i | 0.936808 | − | 0.349843i | \(-0.113765\pi\) |
0.165431 | + | 0.986221i | \(0.447099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −130.147 | + | 10.3227i | −0.743697 | + | 0.0589867i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 129.984 | + | 225.139i | 0.726167 | + | 1.25776i | 0.958492 | + | 0.285119i | \(0.0920332\pi\) |
−0.232325 | + | 0.972638i | \(0.574633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 337.053i | 1.86217i | 0.364799 | + | 0.931086i | \(0.381138\pi\) | ||||
−0.364799 | + | 0.931086i | \(0.618862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.9356 | + | 14.3966i | −0.134787 | + | 0.0778194i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 97.9134 | + | 56.5303i | 0.523601 | + | 0.302301i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −102.491 | + | 177.520i | −0.536602 | + | 0.929422i | 0.462482 | + | 0.886629i | \(0.346959\pi\) |
−0.999084 | + | 0.0427932i | \(0.986374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −131.261 | − | 227.351i | −0.680111 | − | 1.17799i | −0.974947 | − | 0.222438i | \(-0.928598\pi\) |
0.294836 | − | 0.955548i | \(-0.404735\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −142.697 | −0.724349 | −0.362175 | − | 0.932110i | \(-0.617966\pi\) | ||||
−0.362175 | + | 0.932110i | \(0.617966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0813 | + | 13.9033i | −0.121011 | + | 0.0698659i | −0.559284 | − | 0.828976i | \(-0.688924\pi\) |
0.438273 | + | 0.898842i | \(0.355590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −59.3344 | + | 124.593i | −0.292287 | + | 0.613757i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −88.1897 | + | 152.749i | −0.430194 | + | 0.745117i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 64.1536i | 0.306955i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 214.007 | 1.01425 | 0.507125 | − | 0.861872i | \(-0.330708\pi\) | ||||
0.507125 | + | 0.861872i | \(0.330708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −88.7361 | − | 51.2318i | −0.412726 | − | 0.238288i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.34396 | − | 42.1602i | −0.0154099 | − | 0.194287i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66.0748 | + | 114.445i | 0.298981 | + | 0.517851i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 125.714i | 0.563738i | 0.959453 | + | 0.281869i | \(0.0909543\pi\) | ||||
−0.959453 | + | 0.281869i | \(0.909046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 193.764 | − | 111.870i | 0.853585 | − | 0.492818i | −0.00827359 | − | 0.999966i | \(-0.502634\pi\) |
0.861859 | + | 0.507148i | \(0.169300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 199.180 | + | 114.997i | 0.869782 | + | 0.502169i | 0.867276 | − | 0.497828i | \(-0.165869\pi\) |
0.00250654 | + | 0.999997i | \(0.499202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 201.147 | − | 348.396i | 0.863291 | − | 1.49526i | −0.00544355 | − | 0.999985i | \(-0.501733\pi\) |
0.868734 | − | 0.495278i | \(-0.164934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −48.7555 | − | 84.4471i | −0.207470 | − | 0.359349i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −52.4038 | −0.219263 | −0.109631 | − | 0.993972i | \(-0.534967\pi\) | ||||
−0.109631 | + | 0.993972i | \(0.534967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 414.018 | − | 239.034i | 1.71792 | − | 0.991840i | 0.795216 | − | 0.606327i | \(-0.207358\pi\) |
0.922702 | − | 0.385513i | \(-0.125976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.4634 | − | 121.924i | −0.0794426 | − | 0.497651i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37.4926 | + | 64.9391i | −0.151792 | + | 0.262912i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 98.1715i | − | 0.391121i | −0.980692 | − | 0.195561i | \(-0.937347\pi\) | ||
0.980692 | − | 0.195561i | \(-0.0626527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −181.447 | −0.717183 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 348.332 | + | 201.110i | 1.35538 | + | 0.782527i | 0.988997 | − | 0.147938i | \(-0.0472636\pi\) |
0.366380 | + | 0.930465i | \(0.380597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 45.3463 | + | 65.8932i | 0.175082 | + | 0.254414i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −183.196 | − | 317.305i | −0.696564 | − | 1.20648i | −0.969651 | − | 0.244494i | \(-0.921378\pi\) |
0.273087 | − | 0.961989i | \(-0.411955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 83.0186i | 0.313278i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −308.338 | + | 178.019i | −1.14624 | + | 0.661780i | −0.947967 | − | 0.318368i | \(-0.896865\pi\) |
−0.198269 | + | 0.980148i | \(0.563532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 275.573 | + | 159.102i | 1.01687 | + | 0.587092i | 0.913197 | − | 0.407519i | \(-0.133606\pi\) |
0.103677 | + | 0.994611i | \(0.466939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51.8740 | + | 89.8484i | −0.188633 | + | 0.326721i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113.444 | + | 196.491i | 0.409546 | + | 0.709354i | 0.994839 | − | 0.101468i | \(-0.0323540\pi\) |
−0.585293 | + | 0.810822i | \(0.699021\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −274.978 | −0.978570 | −0.489285 | − | 0.872124i | \(-0.662742\pi\) | ||||
−0.489285 | + | 0.872124i | \(0.662742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 134.926 | − | 77.8995i | 0.476770 | − | 0.275263i | −0.242299 | − | 0.970202i | \(-0.577902\pi\) |
0.719069 | + | 0.694938i | \(0.244568\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 442.386 | + | 210.676i | 1.54142 | + | 0.734063i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 62.0521 | − | 107.477i | 0.214713 | − | 0.371894i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 484.307i | 1.65293i | 0.562992 | + | 0.826463i | \(0.309650\pi\) | ||||
−0.562992 | + | 0.826463i | \(0.690350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 178.742 | 0.605904 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −183.669 | − | 106.041i | −0.614277 | − | 0.354653i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −122.388 | + | 256.994i | −0.406604 | + | 0.853802i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −52.1809 | − | 90.3800i | −0.171085 | − | 0.296328i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 258.696i | 0.842658i | 0.906908 | + | 0.421329i | \(0.138436\pi\) | ||||
−0.906908 | + | 0.421329i | \(0.861564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 451.891 | − | 260.899i | 1.45303 | − | 0.838905i | 0.454374 | − | 0.890811i | \(-0.349863\pi\) |
0.998652 | + | 0.0519066i | \(0.0165298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 306.163 | + | 176.763i | 0.978155 | + | 0.564738i | 0.901713 | − | 0.432336i | \(-0.142310\pi\) |
0.0764426 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −37.9439 | + | 65.7208i | −0.119697 | + | 0.207321i | −0.919648 | − | 0.392745i | \(-0.871526\pi\) |
0.799951 | + | 0.600066i | \(0.204859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 54.8316 | + | 94.9712i | 0.171886 | + | 0.297715i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 234.406 | 0.725716 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −105.018 | + | 60.6323i | −0.323133 | + | 0.186561i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −223.154 | + | 153.570i | −0.678280 | + | 0.466778i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −200.896 | + | 347.963i | −0.606937 | + | 1.05125i | 0.384805 | + | 0.922998i | \(0.374269\pi\) |
−0.991742 | + | 0.128248i | \(0.959065\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 241.394i | − | 0.720578i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 292.693 | 0.868525 | 0.434262 | − | 0.900786i | \(-0.357009\pi\) | ||||
0.434262 | + | 0.900786i | \(0.357009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.1057 | − | 16.8042i | −0.0853540 | − | 0.0492792i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −333.376 | + | 80.6820i | −0.971941 | + | 0.235224i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −227.335 | − | 393.755i | −0.655143 | − | 1.13474i | −0.981858 | − | 0.189618i | \(-0.939275\pi\) |
0.326715 | − | 0.945123i | \(-0.394058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 583.961i | 1.67324i | 0.547782 | + | 0.836621i | \(0.315472\pi\) | ||||
−0.547782 | + | 0.836621i | \(0.684528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −263.295 | + | 152.013i | −0.745878 | + | 0.430633i | −0.824203 | − | 0.566295i | \(-0.808376\pi\) |
0.0783245 | + | 0.996928i | \(0.475043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 125.787 | + | 72.6230i | 0.354329 | + | 0.204572i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −85.5609 | + | 148.196i | −0.238331 | + | 0.412802i | −0.960236 | − | 0.279191i | \(-0.909934\pi\) |
0.721904 | + | 0.691993i | \(0.243267\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −113.996 | − | 197.447i | −0.315778 | − | 0.546943i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 82.3403 | 0.225590 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 596.765 | − | 344.543i | 1.62606 | − | 0.938808i | 0.640811 | − | 0.767698i | \(-0.278598\pi\) |
0.985252 | − | 0.171110i | \(-0.0547353\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 229.907 | − | 18.2352i | 0.619696 | − | 0.0491515i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −360.676 | + | 624.709i | −0.966960 | + | 1.67482i | −0.262707 | + | 0.964876i | \(0.584615\pi\) |
−0.704254 | + | 0.709948i | \(0.748718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 128.179i | 0.339997i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −282.500 | −0.745383 | −0.372692 | − | 0.927955i | \(-0.621565\pi\) | ||||
−0.372692 | + | 0.927955i | \(0.621565\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −588.573 | − | 339.813i | −1.53674 | − | 0.887240i | −0.999026 | − | 0.0441150i | \(-0.985953\pi\) |
−0.537718 | − | 0.843125i | \(-0.680713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −88.5835 | − | 42.1859i | −0.230087 | − | 0.109574i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 105.767 | + | 183.194i | 0.271895 | + | 0.470935i | 0.969347 | − | 0.245696i | \(-0.0790164\pi\) |
−0.697452 | + | 0.716631i | \(0.745683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 662.977i | 1.69559i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 135.926 | − | 78.4771i | 0.344117 | − | 0.198676i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 46.7416 | + | 26.9863i | 0.117737 | + | 0.0679755i | 0.557712 | − | 0.830035i | \(-0.311679\pi\) |
−0.439975 | + | 0.898010i | \(0.645013\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −88.7998 | + | 153.806i | −0.221446 | + | 0.383556i | −0.955247 | − | 0.295808i | \(-0.904411\pi\) |
0.733801 | + | 0.679364i | \(0.237744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.6414 | − | 34.0199i | −0.0487380 | − | 0.0844166i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 63.5642 | 0.156177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 429.670 | − | 248.070i | 1.05054 | − | 0.606528i | 0.127738 | − | 0.991808i | \(-0.459228\pi\) |
0.922800 | + | 0.385280i | \(0.125895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −39.2610 | − | 494.998i | −0.0950629 | − | 1.19854i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.5060 | − | 77.0866i | 0.107243 | − | 0.185751i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 629.543i | − | 1.50249i | −0.660023 | − | 0.751245i | \(-0.729454\pi\) | ||
0.660023 | − | 0.751245i | \(-0.270546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 342.355 | 0.813196 | 0.406598 | − | 0.913607i | \(-0.366715\pi\) | ||||
0.406598 | + | 0.913607i | \(0.366715\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 328.291 | + | 189.539i | 0.772448 | + | 0.445973i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −238.832 | + | 164.359i | −0.559325 | + | 0.384916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 239.388 | + | 414.633i | 0.555425 | + | 0.962025i | 0.997870 | + | 0.0652291i | \(0.0207778\pi\) |
−0.442445 | + | 0.896796i | \(0.645889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.1130i | − | 0.0626166i | −0.999510 | − | 0.0313083i | \(-0.990033\pi\) | ||
0.999510 | − | 0.0313083i | \(-0.00996737\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −325.791 | + | 188.095i | −0.745517 | + | 0.430424i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 406.217 | + | 234.530i | 0.925325 | + | 0.534236i | 0.885330 | − | 0.464964i | \(-0.153933\pi\) |
0.0399947 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −362.893 | + | 628.550i | −0.819172 | + | 1.41885i | 0.0871206 | + | 0.996198i | \(0.472233\pi\) |
−0.906293 | + | 0.422650i | \(0.861100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.60266 | − | 16.6323i | −0.0215790 | − | 0.0373760i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −333.343 | −0.742412 | −0.371206 | − | 0.928551i | \(-0.621056\pi\) | ||||
−0.371206 | + | 0.928551i | \(0.621056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 337.211 | − | 194.689i | 0.747695 | − | 0.431682i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −65.0139 | − | 94.4723i | −0.142888 | − | 0.207632i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 284.818 | − | 493.319i | 0.623234 | − | 1.07947i | −0.365646 | − | 0.930754i | \(-0.619152\pi\) |
0.988880 | − | 0.148719i | \(-0.0475148\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 137.485i | − | 0.298233i | −0.988820 | − | 0.149116i | \(-0.952357\pi\) | ||
0.988820 | − | 0.149116i | \(-0.0476429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 216.686 | 0.468004 | 0.234002 | − | 0.972236i | \(-0.424818\pi\) | ||||
0.234002 | + | 0.972236i | \(0.424818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 249.762 | + | 144.200i | 0.534821 | + | 0.308779i | 0.742978 | − | 0.669316i | \(-0.233413\pi\) |
−0.208156 | + | 0.978096i | \(0.566746\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −668.503 | + | 53.0226i | −1.42538 | + | 0.113055i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 113.100 | + | 195.895i | 0.239112 | + | 0.414154i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 215.099i | 0.452839i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 202.257 | − | 116.773i | 0.422248 | − | 0.243785i | −0.273791 | − | 0.961789i | \(-0.588278\pi\) |
0.696039 | + | 0.718004i | \(0.254944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.3425 | + | 37.1482i | 0.133768 | + | 0.0772311i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 164.127 | − | 284.277i | 0.338407 | − | 0.586137i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −411.600 | − | 712.913i | −0.845175 | − | 1.46389i | −0.885469 | − | 0.464699i | \(-0.846163\pi\) |
0.0402936 | − | 0.999188i | \(-0.487171\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 506.517 | 1.03160 | 0.515801 | − | 0.856708i | \(-0.327494\pi\) | ||||
0.515801 | + | 0.856708i | \(0.327494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 347.008 | − | 200.345i | 0.703871 | − | 0.406380i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 173.489 | − | 364.299i | 0.349073 | − | 0.732996i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 75.3022 | − | 130.427i | 0.150906 | − | 0.261377i | −0.780655 | − | 0.624963i | \(-0.785114\pi\) |
0.931561 | + | 0.363585i | \(0.118448\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 562.598i | 1.11848i | 0.829004 | + | 0.559242i | \(0.188908\pi\) | ||||
−0.829004 | + | 0.559242i | \(0.811092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −105.539 | −0.208989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 511.698 | + | 295.429i | 1.00530 | + | 0.580411i | 0.909813 | − | 0.415019i | \(-0.136225\pi\) |
0.0954889 | + | 0.995430i | \(0.469559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0862 | − | 228.029i | −0.0353938 | − | 0.446241i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −108.291 | − | 187.565i | −0.210273 | − | 0.364204i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 215.267i | 0.416376i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 70.6996 | − | 40.8184i | 0.135700 | − | 0.0783463i | −0.430613 | − | 0.902537i | \(-0.641703\pi\) |
0.566313 | + | 0.824190i | \(0.308369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −623.961 | − | 360.244i | −1.19304 | − | 0.688803i | −0.234047 | − | 0.972225i | \(-0.575197\pi\) |
−0.958995 | + | 0.283422i | \(0.908530\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −61.3997 | + | 106.347i | −0.116508 | + | 0.201798i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −267.495 | − | 463.315i | −0.505661 | − | 0.875831i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 455.119 | 0.853882 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −353.049 | + | 203.833i | −0.659904 | + | 0.380996i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −97.3697 | + | 254.585i | −0.180649 | + | 0.472328i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −302.518 | + | 523.977i | −0.559183 | + | 0.968534i | 0.438381 | + | 0.898789i | \(0.355552\pi\) |
−0.997565 | + | 0.0697451i | \(0.977781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 218.823i | − | 0.401511i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 570.576 | 1.04310 | 0.521550 | − | 0.853221i | \(-0.325354\pi\) | ||||
0.521550 | + | 0.853221i | \(0.325354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 196.902 | + | 113.681i | 0.357354 | + | 0.206318i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −247.187 | − | 359.189i | −0.446992 | − | 0.649529i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −449.675 | − | 778.859i | −0.807315 | − | 1.39831i | −0.914717 | − | 0.404095i | \(-0.867586\pi\) |
0.107402 | − | 0.994216i | \(-0.465747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 264.392i | 0.472972i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −939.781 | + | 542.583i | −1.66924 | + | 0.963735i | −0.701188 | + | 0.712976i | \(0.747347\pi\) |
−0.968050 | + | 0.250759i | \(0.919320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 188.852 | + | 109.034i | 0.334251 | + | 0.192980i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 269.018 | − | 465.953i | 0.472791 | − | 0.818899i | −0.526724 | − | 0.850037i | \(-0.676580\pi\) |
0.999515 | + | 0.0311379i | \(0.00991310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −373.747 | − | 647.348i | −0.654548 | − | 1.13371i | −0.982007 | − | 0.188845i | \(-0.939526\pi\) |
0.327459 | − | 0.944865i | \(-0.393808\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −608.368 | −1.05803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 373.623 | − | 215.711i | 0.647527 | − | 0.373850i | −0.139981 | − | 0.990154i | \(-0.544704\pi\) |
0.787508 | + | 0.616304i | \(0.211371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −223.256 | − | 106.320i | −0.384261 | − | 0.182995i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 91.6364 | − | 158.719i | 0.157181 | − | 0.272245i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 249.815i | 0.425579i | 0.977098 | + | 0.212790i | \(0.0682549\pi\) | ||||
−0.977098 | + | 0.212790i | \(0.931745\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −69.6796 | −0.118302 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 175.770 | + | 101.481i | 0.296408 | + | 0.171131i | 0.640828 | − | 0.767684i | \(-0.278591\pi\) |
−0.344420 | + | 0.938816i | \(0.611925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −154.140 | + | 323.669i | −0.259059 | + | 0.543981i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5681 | + | 18.3044i | 0.0176428 | + | 0.0305583i | 0.874712 | − | 0.484643i | \(-0.161050\pi\) |
−0.857069 | + | 0.515201i | \(0.827717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 112.712i | 0.187540i | 0.995594 | + | 0.0937701i | \(0.0298919\pi\) | ||||
−0.995594 | + | 0.0937701i | \(0.970108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 196.520 | − | 113.461i | 0.324826 | − | 0.187539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 178.155 | + | 102.858i | 0.293501 | + | 0.169453i | 0.639520 | − | 0.768775i | \(-0.279133\pi\) |
−0.346019 | + | 0.938228i | \(0.612467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −125.806 | + | 217.902i | −0.205902 | + | 0.356633i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −542.469 | − | 939.584i | −0.884941 | − | 1.53276i | −0.845781 | − | 0.533530i | \(-0.820865\pi\) |
−0.0391596 | − | 0.999233i | \(-0.512468\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 454.282 | 0.736276 | 0.368138 | − | 0.929771i | \(-0.379995\pi\) | ||||
0.368138 | + | 0.929771i | \(0.379995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 699.389 | − | 403.793i | 1.12987 | − | 0.652330i | 0.185967 | − | 0.982556i | \(-0.440458\pi\) |
0.943902 | + | 0.330226i | \(0.107125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −43.9514 | + | 30.2464i | −0.0705479 | + | 0.0485496i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −94.5618 | + | 163.786i | −0.151299 | + | 0.262057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 232.253i | − | 0.369241i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1139.48 | −1.80583 | −0.902915 | − | 0.429819i | \(-0.858577\pi\) | ||||
−0.902915 | + | 0.429819i | \(0.858577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −64.3448 | − | 37.1495i | −0.101330 | − | 0.0585031i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −247.346 | + | 200.797i | −0.388299 | + | 0.315223i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.6700 | + | 75.6387i | 0.0681280 | + | 0.118001i | 0.898077 | − | 0.439838i | \(-0.144964\pi\) |
−0.829949 | + | 0.557839i | \(0.811631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 258.078i | − | 0.401366i | −0.979656 | − | 0.200683i | \(-0.935684\pi\) | ||
0.979656 | − | 0.200683i | \(-0.0643161\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.3257 | − | 5.96152i | 0.0159593 | − | 0.00921410i | −0.491999 | − | 0.870596i | \(-0.663734\pi\) |
0.507958 | + | 0.861382i | \(0.330400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −341.727 | − | 197.296i | −0.526544 | − | 0.304000i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 153.685 | − | 266.190i | 0.235352 | − | 0.407641i | −0.724023 | − | 0.689776i | \(-0.757709\pi\) |
0.959375 | + | 0.282135i | \(0.0910425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −245.889 | − | 425.892i | −0.375403 | − | 0.650217i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −135.643 | −0.205832 | −0.102916 | − | 0.994690i | \(-0.532817\pi\) | ||||
−0.102916 | + | 0.994690i | \(0.532817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −177.211 | + | 102.313i | −0.268095 | + | 0.154785i | −0.628022 | − | 0.778196i | \(-0.716135\pi\) |
0.359926 | + | 0.932981i | \(0.382802\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −202.784 | + | 16.0840i | −0.304939 | + | 0.0241864i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −321.528 | + | 556.902i | −0.482051 | + | 0.834936i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 230.390i | 0.343354i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 243.179 | 0.361336 | 0.180668 | − | 0.983544i | \(-0.442174\pi\) | ||||
0.180668 | + | 0.983544i | \(0.442174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −571.368 | − | 329.880i | −0.843971 | − | 0.487267i | 0.0146410 | − | 0.999893i | \(-0.495339\pi\) |
−0.858612 | + | 0.512626i | \(0.828673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −823.312 | − | 392.083i | −1.21254 | − | 0.577442i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 162.302 | + | 281.116i | 0.237631 | + | 0.411589i | 0.960034 | − | 0.279883i | \(-0.0902957\pi\) |
−0.722403 | + | 0.691472i | \(0.756962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.13982i | − | 0.00604354i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 185.517 | − | 107.108i | 0.269255 | − | 0.155455i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 506.305 | + | 292.315i | 0.732714 | + | 0.423033i | 0.819414 | − | 0.573202i | \(-0.194299\pi\) |
−0.0867003 | + | 0.996234i | \(0.527632\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.5212 | − | 21.6874i | 0.0180161 | − | 0.0312048i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −711.359 | − | 1232.11i | −1.02060 | − | 1.76773i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −870.839 | −1.24228 | −0.621141 | − | 0.783699i | \(-0.713330\pi\) | ||||
−0.621141 | + | 0.783699i | \(0.713330\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 114.130 | − | 65.8932i | 0.162348 | − | 0.0937314i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.1820 | + | 292.276i | 0.0327892 | + | 0.413402i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 388.383 | − | 672.700i | 0.547790 | − | 0.948801i | −0.450635 | − | 0.892708i | \(-0.648803\pi\) |
0.998426 | − | 0.0560925i | \(-0.0178642\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 197.077i | − | 0.276405i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −91.1332 | −0.127459 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 188.524 | + | 108.844i | 0.262202 | + | 0.151383i | 0.625339 | − | 0.780353i | \(-0.284961\pi\) |
−0.363136 | + | 0.931736i | \(0.618294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −495.646 | + | 341.094i | −0.687443 | + | 0.473084i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 183.843 | + | 318.426i | 0.253577 | + | 0.439208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 500.204i | − | 0.688038i | −0.938963 | − | 0.344019i | \(-0.888212\pi\) | ||
0.938963 | − | 0.344019i | \(-0.111788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 715.767 | − | 413.248i | 0.979161 | − | 0.565319i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 79.7682 | + | 46.0542i | 0.108824 | + | 0.0628297i | 0.553424 | − | 0.832899i | \(-0.313321\pi\) |
−0.444600 | + | 0.895729i | \(0.646654\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −266.452 | + | 461.508i | −0.361535 | + | 0.626198i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −467.042 | − | 808.941i | −0.631992 | − | 1.09464i | −0.987144 | − | 0.159834i | \(-0.948904\pi\) |
0.355152 | − | 0.934809i | \(-0.384429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −779.457 | −1.04907 | −0.524534 | − | 0.851390i | \(-0.675760\pi\) | ||||
−0.524534 | + | 0.851390i | \(0.675760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 637.021 | − | 367.784i | 0.855062 | − | 0.493670i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 642.031 | + | 932.942i | 0.857185 | + | 1.24558i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 99.7934 | − | 172.847i | 0.132881 | − | 0.230156i | −0.791905 | − | 0.610644i | \(-0.790911\pi\) |
0.924786 | + | 0.380488i | \(0.124244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 206.510i | − | 0.273523i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −541.529 | −0.715361 | −0.357681 | − | 0.933844i | \(-0.616432\pi\) | ||||
−0.357681 | + | 0.933844i | \(0.616432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −929.152 | − | 536.446i | −1.22096 | − | 0.704922i | −0.255838 | − | 0.966720i | \(-0.582351\pi\) |
−0.965123 | + | 0.261797i | \(0.915685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −605.998 | + | 48.0650i | −0.794230 | + | 0.0629948i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −230.607 | − | 399.424i | −0.300661 | − | 0.520761i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.9429i | 0.0181312i | 0.999959 | + | 0.00906558i | \(0.00288570\pi\) | ||||
−0.999959 | + | 0.00906558i | \(0.997114\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1243.17 | − | 717.746i | 1.60824 | − | 0.928520i | 0.618481 | − | 0.785800i | \(-0.287749\pi\) |
0.989763 | − | 0.142720i | \(-0.0455848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −97.5876 | − | 56.3422i | −0.125920 | − | 0.0726997i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 403.644 | − | 699.132i | 0.518157 | − | 0.897474i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −160.323 | − | 277.688i | −0.205280 | − | 0.355555i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −128.296 | −0.163435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1217.14 | − | 702.715i | 1.54655 | − | 0.892904i | 0.548154 | − | 0.836378i | \(-0.315331\pi\) |
0.998401 | − | 0.0565261i | \(-0.0180024\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 260.470 | − | 546.945i | 0.329292 | − | 0.691460i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −134.645 | + | 233.211i | −0.169791 | + | 0.294087i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 269.295i | 0.337885i | 0.985626 | + | 0.168943i | \(0.0540353\pi\) | ||||
−0.985626 | + | 0.168943i | \(0.945965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 786.547 | 0.984415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −157.422 | − | 90.8878i | −0.196043 | − | 0.113185i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.4906 | − | 573.540i | −0.0565101 | − | 0.712472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9829 | + | 19.0229i | 0.0135759 | + | 0.0235141i | 0.872734 | − | 0.488197i | \(-0.162345\pi\) |
−0.859158 | + | 0.511711i | \(0.829012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 453.011i | 0.558583i | 0.960206 | + | 0.279292i | \(0.0900996\pi\) | ||||
−0.960206 | + | 0.279292i | \(0.909900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −177.494 | + | 102.476i | −0.217784 | + | 0.125738i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 406.145 | + | 234.488i | 0.497118 | + | 0.287011i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −433.447 | + | 750.752i | −0.527950 | + | 0.914436i | 0.471519 | + | 0.881856i | \(0.343706\pi\) |
−0.999469 | + | 0.0325803i | \(0.989628\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −265.315 | − | 459.539i | −0.322375 | − | 0.558371i | 0.658602 | − | 0.752491i | \(-0.271148\pi\) |
−0.980978 | + | 0.194121i | \(0.937815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 215.336 | 0.260382 | 0.130191 | − | 0.991489i | \(-0.458441\pi\) | ||||
0.130191 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 473.322 | − | 273.272i | 0.570955 | − | 0.329641i | −0.186576 | − | 0.982441i | \(-0.559739\pi\) |
0.757531 | + | 0.652800i | \(0.226406\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 930.209 | + | 355.772i | 1.11670 | + | 0.427098i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.75144 | + | 6.49769i | −0.00449274 | + | 0.00778166i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 35.6266i | − | 0.0424631i | −0.999775 | − | 0.0212316i | \(-0.993241\pi\) | ||
0.999775 | − | 0.0212316i | \(-0.00675873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −452.349 | −0.537871 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 276.538 | + | 159.659i | 0.327264 | + | 0.188946i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −357.379 | − | 519.310i | −0.421935 | − | 0.613117i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 186.367 | + | 322.798i | 0.218998 | + | 0.379316i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.01022i | − | 0.00352898i | −0.999998 | − | 0.00176449i | \(-0.999438\pi\) | ||
0.999998 | − | 0.00176449i | \(-0.000561654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −997.825 | + | 576.095i | −1.16432 | + | 0.672223i | −0.952336 | − | 0.305050i | \(-0.901327\pi\) |
−0.211987 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1319.48 | − | 761.802i | −1.53606 | − | 0.886847i | −0.999064 | − | 0.0432653i | \(-0.986224\pi\) |
−0.537001 | − | 0.843582i | \(-0.680443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 582.886 | − | 1009.59i | 0.675418 | − | 1.16986i | −0.300929 | − | 0.953647i | \(-0.597297\pi\) |
0.976347 | − | 0.216211i | \(-0.0693700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 277.409 | + | 480.486i | 0.320704 | + | 0.555475i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −346.494 | −0.398727 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −539.428 | + | 311.439i | −0.619321 | + | 0.357565i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −695.126 | − | 331.038i | −0.794430 | − | 0.378329i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 286.492 | − | 496.218i | 0.326672 | − | 0.565813i | −0.655177 | − | 0.755475i | \(-0.727406\pi\) |
0.981849 | + | 0.189662i | \(0.0607393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 741.161i | 0.841272i | 0.907230 | + | 0.420636i | \(0.138193\pi\) | ||||
−0.907230 | + | 0.420636i | \(0.861807\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 902.855 | 1.02249 | 0.511243 | − | 0.859436i | \(-0.329185\pi\) | ||||
0.511243 | + | 0.859436i | \(0.329185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 759.358 | + | 438.416i | 0.856097 | + | 0.494268i | 0.862703 | − | 0.505710i | \(-0.168769\pi\) |
−0.00660618 | + | 0.999978i | \(0.502103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −88.7463 | + | 186.353i | −0.0998271 | + | 0.209621i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 223.154 | + | 386.514i | 0.249893 | + | 0.432827i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 655.055i | 0.731906i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −103.152 | + | 59.5547i | −0.114741 | + | 0.0662455i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −579.932 | − | 334.824i | −0.643653 | − | 0.371613i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −424.646 | + | 735.509i | −0.469222 | + | 0.812717i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −149.904 | − | 259.642i | −0.165275 | − | 0.286264i | 0.771478 | − | 0.636256i | \(-0.219518\pi\) |
−0.936753 | + | 0.349992i | \(0.886184\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1143.71 | 1.25544 | 0.627720 | − | 0.778440i | \(-0.283988\pi\) | ||||
0.627720 | + | 0.778440i | \(0.283988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −170.177 | + | 98.2520i | −0.186394 | + | 0.107614i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1125.43 | + | 774.500i | −1.22730 | + | 0.844601i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.3081 | + | 33.4427i | −0.0210099 | + | 0.0363903i | −0.876339 | − | 0.481694i | \(-0.840021\pi\) |
0.855329 | + | 0.518085i | \(0.173355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 374.785i | − | 0.406051i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 213.122 | 0.230402 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −893.518 | − | 515.873i | −0.961806 | − | 0.555299i | −0.0650776 | − | 0.997880i | \(-0.520730\pi\) |
−0.896728 | + | 0.442581i | \(0.854063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 89.0841 | + | 558.048i | 0.0956865 | + | 0.599407i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 142.443 | + | 246.718i | 0.152345 | + | 0.263869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1219.23i | 1.30120i | 0.759420 | + | 0.650601i | \(0.225483\pi\) | ||||
−0.759420 | + | 0.650601i | \(0.774517\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −381.358 | + | 220.177i | −0.405269 | + | 0.233982i | −0.688755 | − | 0.724994i | \(-0.741842\pi\) |
0.283486 | + | 0.958976i | \(0.408509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1977.37 | + | 1141.64i | 2.09689 | + | 1.21064i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 864.937 | − | 1498.12i | 0.913345 | − | 1.58196i | 0.104038 | − | 0.994573i | \(-0.466824\pi\) |
0.809307 | − | 0.587386i | \(-0.199843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −106.233 | − | 184.001i | −0.111942 | − | 0.193890i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1436.26 | 1.50709 | 0.753545 | − | 0.657397i | \(-0.228342\pi\) | ||||
0.753545 | + | 0.657397i | \(0.228342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −447.306 | + | 258.252i | −0.468384 | + | 0.270421i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.4646 | + | 0.909321i | −0.0119548 | + | 0.000948198i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −462.248 | + | 800.638i | −0.481008 | + | 0.833130i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 661.494i | − | 0.685485i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −446.032 | −0.461254 | −0.230627 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230627 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 166.691 | + | 96.2390i | 0.171669 | + | 0.0991133i | 0.583373 | − | 0.812205i | \(-0.301733\pi\) |
−0.411703 | + | 0.911318i | \(0.635066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.8101 | − | 29.9119i | −0.0645531 | − | 0.0307419i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −218.928 | − | 379.194i | −0.224082 | − | 0.388121i | 0.731962 | − | 0.681346i | \(-0.238605\pi\) |
−0.956044 | + | 0.293225i | \(0.905272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.3979i | 0.0433074i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −792.929 | + | 457.798i | −0.806642 | + | 0.465715i | −0.845788 | − | 0.533518i | \(-0.820870\pi\) |
0.0391462 | + | 0.999233i | \(0.487536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −311.389 | − | 179.781i | −0.316131 | − | 0.182518i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −663.208 | + | 1148.71i | −0.670585 | + | 1.16149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 436.297 | + | 755.688i | 0.440259 | + | 0.762551i | 0.997708 | − | 0.0676598i | \(-0.0215532\pi\) |
−0.557449 | + | 0.830211i | \(0.688220\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −70.0660 | −0.0704181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1505.96 | − | 869.465i | 1.51049 | − | 0.872081i | 0.510564 | − | 0.859840i | \(-0.329437\pi\) |
0.999925 | − | 0.0122411i | \(-0.00389656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.3.cg.q.145.6 | 16 | ||
3.2 | odd | 2 | inner | 1008.3.cg.q.145.3 | 16 | ||
4.3 | odd | 2 | 504.3.by.d.145.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 1008.3.cg.q.577.6 | 16 | ||
12.11 | even | 2 | 504.3.by.d.145.3 | yes | 16 | ||
21.17 | even | 6 | inner | 1008.3.cg.q.577.3 | 16 | ||
28.3 | even | 6 | 504.3.by.d.73.6 | yes | 16 | ||
28.19 | even | 6 | 3528.3.f.i.2449.11 | 16 | |||
28.23 | odd | 6 | 3528.3.f.i.2449.5 | 16 | |||
84.23 | even | 6 | 3528.3.f.i.2449.12 | 16 | |||
84.47 | odd | 6 | 3528.3.f.i.2449.6 | 16 | |||
84.59 | odd | 6 | 504.3.by.d.73.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.3.by.d.73.3 | ✓ | 16 | 84.59 | odd | 6 | ||
504.3.by.d.73.6 | yes | 16 | 28.3 | even | 6 | ||
504.3.by.d.145.3 | yes | 16 | 12.11 | even | 2 | ||
504.3.by.d.145.6 | yes | 16 | 4.3 | odd | 2 | ||
1008.3.cg.q.145.3 | 16 | 3.2 | odd | 2 | inner | ||
1008.3.cg.q.145.6 | 16 | 1.1 | even | 1 | trivial | ||
1008.3.cg.q.577.3 | 16 | 21.17 | even | 6 | inner | ||
1008.3.cg.q.577.6 | 16 | 7.3 | odd | 6 | inner | ||
3528.3.f.i.2449.5 | 16 | 28.23 | odd | 6 | |||
3528.3.f.i.2449.6 | 16 | 84.47 | odd | 6 | |||
3528.3.f.i.2449.11 | 16 | 28.19 | even | 6 | |||
3528.3.f.i.2449.12 | 16 | 84.23 | even | 6 |