Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(101,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.y (of order \(6\), degree \(2\), 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: | \(10.3805522628\) |
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: | \( x^{16} + 7x^{14} + 21x^{12} + 22x^{10} - 26x^{8} + 198x^{6} + 1701x^{4} + 5103x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(0.979681 - 1.42836i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.101 |
Dual form | 1300.2.y.e.901.2 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.979681 | − | 1.69686i | −0.565619 | − | 0.979681i | −0.996992 | − | 0.0775072i | \(-0.975304\pi\) |
0.431373 | − | 0.902174i | \(-0.358029\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47400 | − | 1.42836i | −0.935084 | − | 0.539871i | −0.0466681 | − | 0.998910i | \(-0.514860\pi\) |
−0.888416 | + | 0.459039i | \(0.848194\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.419550 | + | 0.726682i | −0.139850 | + | 0.242227i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.84746 | − | 2.79868i | 1.46156 | − | 0.843835i | 0.462481 | − | 0.886629i | \(-0.346959\pi\) |
0.999084 | + | 0.0427946i | \(0.0136261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.94331 | + | 2.08253i | 0.816328 | + | 0.577589i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.96363 | − | 3.40111i | 0.476250 | − | 0.824889i | −0.523380 | − | 0.852100i | \(-0.675329\pi\) |
0.999630 | + | 0.0272102i | \(0.00866235\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.09546 | + | 4.09657i | 1.62781 | + | 0.939816i | 0.984745 | + | 0.174005i | \(0.0556709\pi\) |
0.643065 | + | 0.765811i | \(0.277662\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.59737i | 1.22145i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.178504 | + | 0.309177i | 0.0372206 | + | 0.0644679i | 0.884036 | − | 0.467420i | \(-0.154816\pi\) |
−0.846815 | + | 0.531887i | \(0.821483\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.23399 | −0.814831 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.90890 | − | 3.30631i | −0.354473 | − | 0.613966i | 0.632554 | − | 0.774516i | \(-0.282006\pi\) |
−0.987028 | + | 0.160550i | \(0.948673\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.47182i | − | 1.52158i | −0.648996 | − | 0.760792i | \(-0.724811\pi\) | ||
0.648996 | − | 0.760792i | \(-0.275189\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.49793 | − | 5.48363i | −1.65338 | − | 0.954578i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.54609 | + | 3.77939i | −1.07617 | + | 0.621327i | −0.929861 | − | 0.367912i | \(-0.880073\pi\) |
−0.146309 | + | 0.989239i | \(0.546740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.650247 | − | 7.03459i | 0.104123 | − | 1.12644i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.85811 | + | 3.95953i | −1.07106 | + | 0.618375i | −0.928470 | − | 0.371407i | \(-0.878876\pi\) |
−0.142587 | + | 0.989782i | \(0.545542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.67282 | − | 2.89741i | 0.255103 | − | 0.441851i | −0.709820 | − | 0.704383i | \(-0.751224\pi\) |
0.964923 | + | 0.262531i | \(0.0845573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.64753i | − | 1.26137i | −0.776038 | − | 0.630686i | \(-0.782774\pi\) | ||
0.776038 | − | 0.630686i | \(-0.217226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.580450 | + | 1.00537i | 0.0829214 | + | 0.143624i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.69492 | −1.07750 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.581615 | 0.0798909 | 0.0399455 | − | 0.999202i | \(-0.487282\pi\) | ||||
0.0399455 | + | 0.999202i | \(0.487282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 16.0533i | − | 2.12631i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.510653 | + | 0.294826i | 0.0664813 | + | 0.0383830i | 0.532872 | − | 0.846196i | \(-0.321113\pi\) |
−0.466391 | + | 0.884579i | \(0.654446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.90890 | + | 5.03836i | −0.372446 | + | 0.645096i | −0.989941 | − | 0.141479i | \(-0.954814\pi\) |
0.617495 | + | 0.786575i | \(0.288148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07593 | − | 1.19854i | 0.261543 | − | 0.151002i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5655 | − | 6.09997i | 1.29078 | − | 0.745230i | 0.311985 | − | 0.950087i | \(-0.399006\pi\) |
0.978792 | + | 0.204857i | \(0.0656728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.349753 | − | 0.605790i | 0.0421053 | − | 0.0729286i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.11676 | + | 1.22211i | 0.251214 | + | 0.145038i | 0.620320 | − | 0.784349i | \(-0.287003\pi\) |
−0.369106 | + | 0.929387i | \(0.620336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.16506i | 0.487483i | 0.969840 | + | 0.243741i | \(0.0783748\pi\) | ||||
−0.969840 | + | 0.243741i | \(0.921625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.9902 | −1.82225 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.85582 | −1.10887 | −0.554433 | − | 0.832228i | \(-0.687065\pi\) | ||||
−0.554433 | + | 0.832228i | \(0.687065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.40661 | + | 9.36452i | 0.600734 | + | 1.04050i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.09174i | − | 0.668655i | −0.942457 | − | 0.334327i | \(-0.891491\pi\) | ||
0.942457 | − | 0.334327i | \(-0.108509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.74022 | + | 6.47825i | −0.400994 | + | 0.694542i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.510653 | + | 0.294826i | −0.0541291 | + | 0.0312515i | −0.526820 | − | 0.849977i | \(-0.676616\pi\) |
0.472691 | + | 0.881228i | \(0.343283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.30714 | − | 9.35629i | −0.451511 | − | 0.980806i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.3755 | + | 8.29968i | −1.49067 | + | 0.860637i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.08489 | − | 2.35841i | −0.414758 | − | 0.239460i | 0.278074 | − | 0.960560i | \(-0.410304\pi\) |
−0.692832 | + | 0.721099i | \(0.743637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.69675i | 0.472041i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.26701 | − | 2.19453i | −0.126072 | − | 0.218364i | 0.796079 | − | 0.605192i | \(-0.206904\pi\) |
−0.922152 | + | 0.386829i | \(0.873570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.930087 | −0.0916442 | −0.0458221 | − | 0.998950i | \(-0.514591\pi\) | ||||
−0.0458221 | + | 0.998950i | \(0.514591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.295075 | + | 0.511085i | 0.0285260 | + | 0.0494084i | 0.879936 | − | 0.475092i | \(-0.157585\pi\) |
−0.851410 | + | 0.524501i | \(0.824252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.88056i | 0.467473i | 0.972300 | + | 0.233737i | \(0.0750953\pi\) | ||||
−0.972300 | + | 0.233737i | \(0.924905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8262 | + | 7.40518i | 1.21740 | + | 0.702869i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.92299 | − | 6.79482i | 0.369044 | − | 0.639203i | −0.620372 | − | 0.784307i | \(-0.713018\pi\) |
0.989416 | + | 0.145104i | \(0.0463518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.74820 | + | 1.26513i | −0.254071 | + | 0.116961i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.71604 | + | 5.60956i | −0.890668 | + | 0.514227i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1653 | − | 17.6067i | 0.924114 | − | 1.60061i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4375 | + | 7.75816i | 1.21162 | + | 0.699530i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.74022 | + | 6.47825i | 0.331891 | + | 0.574852i | 0.982883 | − | 0.184233i | \(-0.0589801\pi\) |
−0.650992 | + | 0.759085i | \(0.725647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.55533 | −0.577165 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.86041 | 0.249915 | 0.124957 | − | 0.992162i | \(-0.460121\pi\) | ||||
0.124957 | + | 0.992162i | \(0.460121\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7028 | − | 20.2698i | −1.01476 | − | 1.75761i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1725 | + | 8.18250i | 1.21084 | + | 0.699078i | 0.962942 | − | 0.269708i | \(-0.0869272\pi\) |
0.247897 | + | 0.968786i | \(0.420261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.898244 | − | 1.55580i | 0.0761881 | − | 0.131962i | −0.825414 | − | 0.564528i | \(-0.809058\pi\) |
0.901602 | + | 0.432566i | \(0.142392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.6736 | + | 8.47182i | −1.23574 | + | 0.713456i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.0959 | + | 1.85758i | 1.68051 | + | 0.155339i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.13731 | − | 1.96988i | 0.0938039 | − | 0.162473i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.5317 | − | 10.6993i | −1.51818 | − | 0.876521i | −0.999771 | − | 0.0213870i | \(-0.993192\pi\) |
−0.518407 | − | 0.855134i | \(-0.673475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.34466i | − | 0.679079i | −0.940592 | − | 0.339540i | \(-0.889729\pi\) | ||
0.940592 | − | 0.339540i | \(-0.110271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.64768 | + | 2.85387i | 0.133207 | + | 0.230722i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.68191 | −0.214040 | −0.107020 | − | 0.994257i | \(-0.534131\pi\) | ||||
−0.107020 | + | 0.994257i | \(0.534131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.569797 | − | 0.986917i | −0.0451878 | − | 0.0782676i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.01987i | − | 0.0803772i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27615 | − | 3.62354i | −0.491586 | − | 0.283817i | 0.233646 | − | 0.972322i | \(-0.424934\pi\) |
−0.725232 | + | 0.688504i | \(0.758268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0305 | + | 6.36847i | −0.853566 | + | 0.492807i | −0.861853 | − | 0.507159i | \(-0.830696\pi\) |
0.00828625 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.32616 | + | 12.2591i | 0.332781 | + | 0.943004i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.95380 | + | 3.43743i | −0.455298 | + | 0.262867i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.83703 | + | 10.1100i | −0.443781 | + | 0.768651i | −0.997966 | − | 0.0637421i | \(-0.979697\pi\) |
0.554185 | + | 0.832393i | \(0.313030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.15534i | − | 0.0868407i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.510653 | + | 0.884477i | 0.0381680 | + | 0.0661089i | 0.884478 | − | 0.466581i | \(-0.154514\pi\) |
−0.846310 | + | 0.532690i | \(0.821181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8771 | 1.03148 | 0.515739 | − | 0.856745i | \(-0.327517\pi\) | ||||
0.515739 | + | 0.856745i | \(0.327517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3992 | 0.842651 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.9823i | − | 1.60751i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.4749 | + | 6.04767i | 0.761935 | + | 0.439904i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.24135 | + | 5.61418i | −0.234536 | + | 0.406228i | −0.959138 | − | 0.282940i | \(-0.908690\pi\) |
0.724602 | + | 0.689168i | \(0.242024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9831 | + | 10.9599i | −1.36643 | + | 0.788909i | −0.990470 | − | 0.137726i | \(-0.956021\pi\) |
−0.375961 | + | 0.926636i | \(0.622687\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4963 | − | 9.52412i | 1.17531 | − | 0.678566i | 0.220385 | − | 0.975413i | \(-0.429269\pi\) |
0.954925 | + | 0.296847i | \(0.0959353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.84746 | − | 10.1281i | 0.414516 | − | 0.717962i | −0.580862 | − | 0.814002i | \(-0.697284\pi\) |
0.995377 | + | 0.0960401i | \(0.0306177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.7016 | − | 11.9521i | −1.46018 | − | 0.843033i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.9064i | 0.765479i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.299565 | −0.0208212 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 45.8600 | 3.17220 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.59946 | − | 11.4306i | −0.454326 | − | 0.786915i | 0.544323 | − | 0.838876i | \(-0.316786\pi\) |
−0.998649 | + | 0.0519600i | \(0.983453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 4.78913i | − | 0.328146i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.1008 | + | 20.9593i | −0.821459 | + | 1.42281i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.06751 | − | 4.08043i | 0.477578 | − | 0.275730i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8625 | − | 5.92120i | 0.865223 | − | 0.398303i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.28384 | + | 1.31858i | −0.152938 | + | 0.0882985i | −0.574516 | − | 0.818493i | \(-0.694810\pi\) |
0.421578 | + | 0.906792i | \(0.361476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3855 | + | 10.6149i | 1.22029 | + | 0.704535i | 0.964980 | − | 0.262324i | \(-0.0844889\pi\) |
0.255311 | + | 0.966859i | \(0.417822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.0154i | − | 0.661838i | −0.943659 | − | 0.330919i | \(-0.892641\pi\) | ||
0.943659 | − | 0.330919i | \(-0.107359\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.6653 | + | 27.1330i | 1.03070 | + | 1.78522i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.9666 | 1.17703 | 0.588515 | − | 0.808486i | \(-0.299713\pi\) | ||||
0.588515 | + | 0.808486i | \(0.299713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.65556 | + | 16.7239i | 0.627196 | + | 1.08634i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.6771i | − | 0.820014i | −0.912082 | − | 0.410007i | \(-0.865526\pi\) | ||
0.912082 | − | 0.410007i | \(-0.134474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.38988 | + | 4.26655i | 0.476024 | + | 0.274833i | 0.718758 | − | 0.695260i | \(-0.244711\pi\) |
−0.242734 | + | 0.970093i | \(0.578044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.24252 | − | 7.34826i | 0.272158 | − | 0.471391i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3529 | + | 26.8340i | 0.785998 | + | 1.70740i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.3368 | + | 5.96796i | −0.655069 | + | 0.378204i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.86247 | + | 17.0823i | −0.622514 | + | 1.07823i | 0.366502 | + | 0.930417i | \(0.380555\pi\) |
−0.989016 | + | 0.147808i | \(0.952778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.73058 | + | 0.999150i | 0.108800 | + | 0.0628160i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.9885 | + | 20.7648i | 0.747824 | + | 1.29527i | 0.948863 | + | 0.315687i | \(0.102235\pi\) |
−0.201039 | + | 0.979583i | \(0.564432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.5934 | 1.34175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.20351 | 0.198292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.315948 | + | 0.547238i | 0.0194822 | + | 0.0337441i | 0.875602 | − | 0.483033i | \(-0.160465\pi\) |
−0.856120 | + | 0.516777i | \(0.827132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00055 | + | 0.577670i | 0.0612329 | + | 0.0353528i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.68656 | − | 6.38531i | 0.224774 | − | 0.389319i | −0.731478 | − | 0.681865i | \(-0.761169\pi\) |
0.956252 | + | 0.292546i | \(0.0945024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0955 | + | 5.82862i | −0.613255 | + | 0.354063i | −0.774238 | − | 0.632894i | \(-0.781867\pi\) |
0.160983 | + | 0.986957i | \(0.448534\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.6567 | + | 16.4748i | −0.705494 | + | 0.997100i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.460776 | + | 0.798087i | −0.0276853 | + | 0.0479524i | −0.879536 | − | 0.475832i | \(-0.842147\pi\) |
0.851851 | + | 0.523785i | \(0.175480\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.15632 | + | 3.55435i | 0.368569 | + | 0.212793i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.3326i | − | 0.795358i | −0.917525 | − | 0.397679i | \(-0.869816\pi\) | ||
0.917525 | − | 0.397679i | \(-0.130184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.60291 | + | 4.50837i | 0.154727 | + | 0.267995i | 0.932960 | − | 0.359981i | \(-0.117217\pi\) |
−0.778233 | + | 0.627976i | \(0.783884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.6226 | 1.33537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.788317 | + | 1.36541i | 0.0463716 | + | 0.0803180i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.24197i | 0.541774i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0302 | + | 7.52296i | 0.761230 | + | 0.439496i | 0.829737 | − | 0.558155i | \(-0.188490\pi\) |
−0.0685075 | + | 0.997651i | \(0.521824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.5241 | + | 11.8496i | −1.19093 | + | 0.687583i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.118479 | + | 1.28174i | −0.00685180 | + | 0.0741251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.27712 | + | 4.77880i | −0.477085 | + | 0.275445i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.48253 | + | 4.29988i | −0.142618 | + | 0.247021i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.41991i | 0.252258i | 0.992014 | + | 0.126129i | \(0.0402553\pi\) | ||||
−0.992014 | + | 0.126129i | \(0.959745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.911189 | + | 1.57822i | 0.0518357 | + | 0.0897821i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.2076 | 1.82633 | 0.913164 | − | 0.407593i | \(-0.133632\pi\) | ||||
0.913164 | + | 0.407593i | \(0.133632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8549 | −1.06574 | −0.532872 | − | 0.846196i | \(-0.678887\pi\) | ||||
−0.532872 | + | 0.846196i | \(0.678887\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.9904i | − | 1.34743i | −0.738990 | − | 0.673716i | \(-0.764697\pi\) | ||
0.738990 | − | 0.673716i | \(-0.235303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.5066 | − | 10.6848i | −1.03617 | − | 0.598234i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.578158 | − | 1.00140i | 0.0322697 | − | 0.0558927i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.8657 | − | 16.0883i | 1.55049 | − | 0.895175i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.28162 | − | 4.78140i | 0.457975 | − | 0.264412i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3518 | + | 21.3940i | −0.680978 | + | 1.17949i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.24135 | − | 3.60345i | −0.343056 | − | 0.198063i | 0.318567 | − | 0.947900i | \(-0.396798\pi\) |
−0.661622 | + | 0.749837i | \(0.730132\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.34257i | − | 0.347570i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1923 | −1.09995 | −0.549973 | − | 0.835183i | \(-0.685362\pi\) | ||||
−0.549973 | + | 0.835183i | \(0.685362\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.3731 | −0.834953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.7099 | − | 41.0668i | −1.28396 | − | 2.22389i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6807i | 0.900675i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.16701 | − | 7.21747i | 0.223697 | − | 0.387454i | −0.732231 | − | 0.681056i | \(-0.761521\pi\) |
0.955928 | + | 0.293602i | \(0.0948542\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2518 | + | 11.1150i | −1.03052 | + | 0.594973i | −0.917135 | − | 0.398577i | \(-0.869504\pi\) |
−0.113389 | + | 0.993551i | \(0.536171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4619 | − | 8.81739i | −0.665169 | − | 0.470638i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.4565 | − | 11.8106i | 1.08879 | − | 0.628613i | 0.155536 | − | 0.987830i | \(-0.450290\pi\) |
0.933254 | + | 0.359217i | \(0.116956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.0372 | + | 10.9912i | 1.00756 | + | 0.581714i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.91598i | − | 0.153899i | −0.997035 | − | 0.0769497i | \(-0.975482\pi\) | ||
0.997035 | − | 0.0769497i | \(-0.0245181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.0637 | + | 41.6795i | 1.26651 | + | 2.19366i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −39.8348 | −2.09079 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.55944 | − | 13.0933i | −0.394600 | − | 0.683467i | 0.598450 | − | 0.801160i | \(-0.295783\pi\) |
−0.993050 | + | 0.117693i | \(0.962450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.64489i | − | 0.345919i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.43891 | − | 0.830758i | −0.0747047 | − | 0.0431308i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.28840 | + | 9.15978i | −0.273823 | + | 0.474275i | −0.969838 | − | 0.243752i | \(-0.921622\pi\) |
0.696014 | + | 0.718028i | \(0.254955\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.26700 | − | 13.7068i | 0.0652537 | − | 0.705937i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.38724 | + | 3.11032i | −0.276724 | + | 0.159767i | −0.631939 | − | 0.775018i | \(-0.717741\pi\) |
0.355215 | + | 0.934784i | \(0.384408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.32845 | − | 12.6932i | 0.375448 | − | 0.650295i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.2463 | + | 6.49304i | 0.574657 | + | 0.331779i | 0.759007 | − | 0.651082i | \(-0.225685\pi\) |
−0.184350 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.40367 | + | 2.43122i | 0.0713523 | + | 0.123586i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.474689 | 0.0240677 | 0.0120338 | − | 0.999928i | \(-0.496169\pi\) | ||||
0.0120338 | + | 0.999928i | \(0.496169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.40206 | 0.0709052 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.80229 | − | 4.85370i | −0.141357 | − | 0.244837i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6600 | + | 12.5054i | 1.08709 | + | 0.627629i | 0.932799 | − | 0.360397i | \(-0.117359\pi\) |
0.154286 | + | 0.988026i | \(0.450692\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.9300 | + | 39.7159i | −1.14793 | + | 1.98828i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2970 | − | 6.52234i | 0.564147 | − | 0.325710i | −0.190661 | − | 0.981656i | \(-0.561063\pi\) |
0.754808 | + | 0.655946i | \(0.227730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6428 | − | 24.9352i | 0.878850 | − | 1.24211i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1546 | + | 36.6408i | −1.04859 | + | 1.81622i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0173 | − | 5.78349i | −0.495324 | − | 0.285975i | 0.231457 | − | 0.972845i | \(-0.425651\pi\) |
−0.726780 | + | 0.686870i | \(0.758984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 32.0650i | − | 1.58165i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.842237 | − | 1.45880i | −0.0414438 | − | 0.0717827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.51997 | −0.172374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.22688 | − | 14.2494i | −0.401909 | − | 0.696128i | 0.592047 | − | 0.805904i | \(-0.298320\pi\) |
−0.993956 | + | 0.109776i | \(0.964987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.2913i | − | 1.08641i | −0.839599 | − | 0.543206i | \(-0.817210\pi\) | ||
0.839599 | − | 0.543206i | \(-0.182790\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.28400 | + | 3.62807i | 0.305539 | + | 0.176403i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.3932 | − | 8.30993i | 0.696537 | − | 0.402146i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.5355 | − | 35.9197i | −0.798344 | − | 1.73422i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.4893 | + | 13.5616i | −1.13144 | + | 0.653238i | −0.944297 | − | 0.329094i | \(-0.893257\pi\) |
−0.187145 | + | 0.982332i | \(0.559923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0205 | + | 19.0881i | −0.529612 | + | 0.917315i | 0.469792 | + | 0.882777i | \(0.344329\pi\) |
−0.999403 | + | 0.0345372i | \(0.989004\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.92501i | 0.139922i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1843 | + | 22.8358i | 0.629251 | + | 1.08989i | 0.987702 | + | 0.156346i | \(0.0499715\pi\) |
−0.358451 | + | 0.933548i | \(0.616695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.974111 | −0.0463862 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.3081 | 1.91510 | 0.957548 | − | 0.288274i | \(-0.0930815\pi\) | ||||
0.957548 | + | 0.288274i | \(0.0930815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.9276i | 1.98311i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.993353 | + | 0.573512i | 0.0468792 | + | 0.0270657i | 0.523256 | − | 0.852175i | \(-0.324717\pi\) |
−0.476377 | + | 0.879241i | \(0.658050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1630 | + | 38.3874i | −1.04361 | + | 1.80759i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1597 | + | 8.17511i | −0.665281 | + | 0.384100i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.08357 | + | 5.24440i | −0.424912 | + | 0.245323i | −0.697177 | − | 0.716899i | \(-0.745561\pi\) |
0.272265 | + | 0.962222i | \(0.412227\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.31398 | + | 14.4002i | −0.388063 | + | 0.672145i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.20580 | − | 1.27352i | −0.102734 | − | 0.0593138i | 0.447752 | − | 0.894158i | \(-0.352225\pi\) |
−0.550487 | + | 0.834844i | \(0.685558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.25551i | − | 0.151296i | −0.997135 | − | 0.0756482i | \(-0.975897\pi\) | ||
0.997135 | − | 0.0756482i | \(-0.0241026\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.164237 | −0.00759998 | −0.00379999 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00379999 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.8519 | −1.60931 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.62742 | + | 4.55082i | 0.121065 | + | 0.209691i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 18.7268i | − | 0.861059i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.244017 | + | 0.422649i | −0.0111727 | + | 0.0193518i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.34346 | − | 3.66240i | 0.289840 | − | 0.167339i | −0.348030 | − | 0.937483i | \(-0.613149\pi\) |
0.637870 | + | 0.770144i | \(0.279816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.1378 | − | 2.50850i | −1.23738 | − | 0.114378i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.73058 | + | 0.999150i | −0.0787440 | + | 0.0454629i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.6228 | − | 15.9481i | −1.25171 | − | 0.722675i | −0.280261 | − | 0.959924i | \(-0.590421\pi\) |
−0.971449 | + | 0.237248i | \(0.923754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.1996i | 0.642130i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.47434 | + | 6.01773i | 0.156795 | + | 0.271576i | 0.933711 | − | 0.358027i | \(-0.116551\pi\) |
−0.776916 | + | 0.629604i | \(0.783217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.9935 | −0.675272 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.49125 | − | 6.04702i | −0.156604 | − | 0.271246i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.5396i | − | 0.650881i | −0.945563 | − | 0.325440i | \(-0.894487\pi\) | ||
0.945563 | − | 0.325440i | \(-0.105513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6128 | + | 12.4781i | 0.965587 | + | 0.557482i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9369 | + | 25.8715i | −0.666003 | + | 1.15355i | 0.313009 | + | 0.949750i | \(0.398663\pi\) |
−0.979012 | + | 0.203801i | \(0.934670\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.5636 | − | 19.3508i | 0.735616 | − | 0.859401i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6483 | − | 11.3440i | 0.870896 | − | 0.502812i | 0.00325001 | − | 0.999995i | \(-0.498965\pi\) |
0.867646 | + | 0.497183i | \(0.165632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.94922 | − | 10.3043i | 0.263178 | − | 0.455837i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.0421 | − | 17.3448i | −1.32639 | − | 0.765791i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.2017 | − | 41.9185i | −1.06439 | − | 1.84358i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.8737 | 1.00404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0167 | 1.18362 | 0.591812 | − | 0.806076i | \(-0.298413\pi\) | ||||
0.591812 | + | 0.806076i | \(0.298413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3581 | + | 19.6728i | 0.496655 | + | 0.860232i | 0.999993 | − | 0.00385780i | \(-0.00122798\pi\) |
−0.503337 | + | 0.864090i | \(0.667895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.8135 | − | 16.6355i | −1.25514 | − | 0.724654i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4363 | − | 19.8082i | 0.497229 | − | 0.861226i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.428489 | + | 0.247388i | −0.0185948 | + | 0.0107357i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.4314 | − | 2.62807i | −1.23150 | − | 0.113835i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.00055 | − | 1.73301i | 0.0431771 | − | 0.0747849i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.62742 | + | 3.24899i | 0.242390 | + | 0.139944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.2514i | 1.08564i | 0.839848 | + | 0.542821i | \(0.182644\pi\) | ||||
−0.839848 | + | 0.542821i | \(0.817356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5952 | − | 23.5475i | −0.583424 | − | 1.01052i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.9221 | 1.57867 | 0.789337 | − | 0.613960i | \(-0.210424\pi\) | ||||
0.789337 | + | 0.613960i | \(0.210424\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.44086 | − | 4.22769i | −0.104173 | − | 0.180433i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.2797i | − | 1.33256i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.3833 | + | 14.0777i | 1.03688 | + | 0.598645i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2010 | − | 13.3951i | 0.983060 | − | 0.567570i | 0.0798671 | − | 0.996806i | \(-0.474550\pi\) |
0.903192 | + | 0.429236i | \(0.141217\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.9576 | − | 5.04429i | 0.463456 | − | 0.213351i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.3008 | + | 21.5357i | −1.57484 | + | 0.909236i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.19895 | − | 12.4689i | 0.303399 | − | 0.525503i | −0.673504 | − | 0.739183i | \(-0.735212\pi\) |
0.976904 | + | 0.213680i | \(0.0685450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 30.8904i | − | 1.29728i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4173 | + | 26.7035i | 0.646325 | + | 1.11947i | 0.983994 | + | 0.178203i | \(0.0570283\pi\) |
−0.337669 | + | 0.941265i | \(0.609638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5884 | 1.53118 | 0.765588 | − | 0.643331i | \(-0.222448\pi\) | ||||
0.765588 | + | 0.643331i | \(0.222448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.7020 | 0.530632 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17.3008i | − | 0.720241i | −0.932906 | − | 0.360120i | \(-0.882736\pi\) | ||
0.932906 | − | 0.360120i | \(-0.117264\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.1947 | + | 21.4744i | 1.54576 | + | 0.892444i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.70122 | + | 15.0710i | −0.360987 | + | 0.625249i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.81936 | − | 1.62776i | 0.116766 | − | 0.0674147i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.81951 | + | 3.93725i | −0.281471 | + | 0.162508i | −0.634089 | − | 0.773260i | \(-0.718625\pi\) |
0.352618 | + | 0.935767i | \(0.385292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.7053 | − | 60.1114i | 1.43001 | − | 2.47685i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.3222 | − | 18.6612i | −1.32956 | − | 0.767619i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 43.2400i | − | 1.77565i | −0.460179 | − | 0.887826i | \(-0.652215\pi\) | ||
0.460179 | − | 0.887826i | \(-0.347785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.9146 | −0.937832 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.10157 | −0.0858676 | −0.0429338 | − | 0.999078i | \(-0.513670\pi\) | ||||
−0.0429338 | + | 0.999078i | \(0.513670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2987 | + | 29.9623i | 0.705630 | + | 1.22219i | 0.966464 | + | 0.256804i | \(0.0826694\pi\) |
−0.260833 | + | 0.965384i | \(0.583997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2370i | 0.416882i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.00993 | + | 8.67746i | −0.203347 | + | 0.352207i | −0.949605 | − | 0.313450i | \(-0.898515\pi\) |
0.746258 | + | 0.665657i | \(0.231849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.5066 | − | 10.6848i | 0.749926 | − | 0.432970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0087 | − | 25.4524i | 0.728555 | − | 1.02969i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5818 | − | 20.5432i | 1.43714 | − | 0.829731i | 0.439486 | − | 0.898249i | \(-0.355161\pi\) |
0.997650 | + | 0.0685186i | \(0.0218272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.03603 | + | 1.17550i | 0.0819673 | + | 0.0473238i | 0.540423 | − | 0.841393i | \(-0.318264\pi\) |
−0.458456 | + | 0.888717i | \(0.651597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.1595i | − | 0.569117i | −0.958659 | − | 0.284559i | \(-0.908153\pi\) | ||
0.958659 | − | 0.284559i | \(-0.0918471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.755781 | − | 1.30905i | −0.0303285 | − | 0.0525304i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.68447 | 0.0674870 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −44.9281 | − | 77.8178i | −1.79426 | − | 3.10774i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.6853i | 1.18363i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.36835 | − | 3.09942i | −0.213711 | − | 0.123386i | 0.389324 | − | 0.921101i | \(-0.372709\pi\) |
−0.603035 | + | 0.797715i | \(0.706042\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9307 | + | 22.3967i | −0.513951 | + | 0.890189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.385264 | + | 4.16792i | −0.0152647 | + | 0.165139i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.77618 | + | 1.02548i | −0.0702645 | + | 0.0405672i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.85182 | + | 13.5997i | −0.310128 | + | 0.537158i | −0.978390 | − | 0.206769i | \(-0.933705\pi\) |
0.668262 | + | 0.743926i | \(0.267039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.7006 | − | 21.1891i | −1.44733 | − | 0.835616i | −0.449008 | − | 0.893528i | \(-0.648223\pi\) |
−0.998322 | + | 0.0579112i | \(0.981556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.6714 | + | 32.3398i | 0.734048 | + | 1.27141i | 0.955140 | + | 0.296155i | \(0.0957045\pi\) |
−0.221092 | + | 0.975253i | \(0.570962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.30049 | 0.129556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 47.4199 | 1.85853 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.8384 | + | 30.8970i | 0.698069 | + | 1.20909i | 0.969135 | + | 0.246531i | \(0.0792906\pi\) |
−0.271066 | + | 0.962561i | \(0.587376\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.02667 | − | 1.74745i | −0.118082 | − | 0.0681745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.51065 | + | 11.2768i | −0.253619 | + | 0.439281i | −0.964520 | − | 0.264012i | \(-0.914954\pi\) |
0.710900 | + | 0.703293i | \(0.248288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.12096 | + | 1.80189i | −0.121391 | + | 0.0700853i | −0.559466 | − | 0.828853i | \(-0.688994\pi\) |
0.438075 | + | 0.898938i | \(0.355660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6485 | − | 16.0249i | −0.879597 | − | 0.622355i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.681490 | − | 1.18037i | 0.0263874 | − | 0.0457043i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.47488 | + | 2.58357i | 0.173009 | + | 0.0998867i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.5643i | 1.25713i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.89678 | + | 17.1417i | 0.381493 | + | 0.660765i | 0.991276 | − | 0.131804i | \(-0.0420768\pi\) |
−0.609783 | + | 0.792568i | \(0.708743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.2737 | −1.62471 | −0.812355 | − | 0.583163i | \(-0.801815\pi\) | ||||
−0.812355 | + | 0.583163i | \(0.801815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.73734 | + | 11.6694i | 0.258556 | + | 0.447831i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5968i | − | 1.59399i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0755 | − | 8.70386i | −0.576849 | − | 0.333044i | 0.183031 | − | 0.983107i | \(-0.441409\pi\) |
−0.759880 | + | 0.650063i | \(0.774742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.9948 | + | 9.81193i | −0.648390 | + | 0.374348i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.71187 | + | 1.21123i | 0.0652172 | + | 0.0461441i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.3977 | + | 22.7463i | −1.49876 | + | 0.865308i | −0.999999 | − | 0.00143250i | \(-0.999544\pi\) |
−0.498759 | + | 0.866741i | \(0.666211\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.70867 | − | 11.6198i | 0.254841 | − | 0.441398i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.1002i | 1.17801i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.6015 | − | 30.4867i | −0.665751 | − | 1.15311i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.7036 | −0.706427 | −0.353213 | − | 0.935543i | \(-0.614911\pi\) | ||||
−0.353213 | + | 0.935543i | \(0.614911\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −61.9300 | −2.33573 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.23902i | 0.272251i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.95338 | + | 4.01454i | 0.261140 | + | 0.150769i | 0.624854 | − | 0.780741i | \(-0.285158\pi\) |
−0.363715 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.13501 | − | 7.16205i | 0.155075 | − | 0.268598i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.61929 | − | 1.51225i | 0.0980933 | − | 0.0566342i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.5112 | + | 12.4195i | −0.803352 | + | 0.463815i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.01466 | + | 3.48949i | −0.0751341 | + | 0.130136i | −0.901145 | − | 0.433519i | \(-0.857272\pi\) |
0.826010 | + | 0.563655i | \(0.190605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.30103 | + | 1.32850i | 0.0856950 | + | 0.0494760i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.7194i | − | 0.621803i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5996 | 0.763997 | 0.381998 | − | 0.924163i | \(-0.375236\pi\) | ||||
0.381998 | + | 0.924163i | \(0.375236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.8144 | 0.585717 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.56961 | − | 11.3789i | −0.242986 | − | 0.420864i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.93875i | − | 0.219353i | −0.993967 | − | 0.109676i | \(-0.965019\pi\) | ||
0.993967 | − | 0.109676i | \(-0.0349814\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.1438 | − | 59.1388i | 1.25770 | − | 2.17840i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8499 | + | 12.0377i | −0.766975 | + | 0.442813i | −0.831794 | − | 0.555084i | \(-0.812686\pi\) |
0.0648194 | + | 0.997897i | \(0.479353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.4315 | − | 47.2499i | 1.22814 | − | 1.73577i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.859620 | − | 0.496302i | 0.0315364 | − | 0.0182075i | −0.484149 | − | 0.874986i | \(-0.660871\pi\) |
0.515685 | + | 0.856778i | \(0.327537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.42676 | + | 2.55579i | 0.161967 | + | 0.0935114i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.68590i | − | 0.0616014i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8054 | − | 23.9116i | −0.503766 | − | 0.872548i | −0.999991 | − | 0.00435392i | \(-0.998614\pi\) |
0.496225 | − | 0.868194i | \(-0.334719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.6483 | 1.40842 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.20513 | + | 9.01555i | 0.189184 | + | 0.327676i | 0.944978 | − | 0.327133i | \(-0.106082\pi\) |
−0.755795 | + | 0.654809i | \(0.772749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.91539i | − | 0.142120i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.7558 | + | 15.4475i | 0.969896 | + | 0.559970i | 0.899205 | − | 0.437528i | \(-0.144146\pi\) |
0.0706917 | + | 0.997498i | \(0.477479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.97122 | − | 12.0745i | 0.252375 | − | 0.437127i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.889028 | + | 1.93121i | 0.0321009 | + | 0.0697320i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0983 | + | 26.6148i | −1.66235 | + | 0.959756i | −0.690755 | + | 0.723089i | \(0.742722\pi\) |
−0.971591 | + | 0.236666i | \(0.923945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4899 | − | 40.6857i | 0.845968 | − | 1.46526i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.5953 | + | 9.00393i | 0.560923 | + | 0.323849i | 0.753516 | − | 0.657430i | \(-0.228356\pi\) |
−0.192593 | + | 0.981279i | \(0.561690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.1546 | − | 36.6408i | −0.758917 | − | 1.31448i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −64.8820 | −2.32464 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6812 | 0.489554 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.08224 | + | 13.9989i | 0.288836 | + | 0.500278i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.7798 | − | 27.0083i | −1.66752 | − | 0.962742i | −0.968970 | − | 0.247180i | \(-0.920496\pi\) |
−0.698549 | − | 0.715562i | \(-0.746171\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.619056 | − | 1.07224i | 0.0220390 | − | 0.0381726i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4110 | + | 11.2069i | −0.690174 | + | 0.398472i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.0543 | + | 8.77159i | −0.676638 | + | 0.311488i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.31034 | − | 14.3939i | 0.294367 | − | 0.509859i | −0.680470 | − | 0.732776i | \(-0.738224\pi\) |
0.974838 | + | 0.222917i | \(0.0715577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.4112 | − | 16.9805i | −1.04049 | − | 0.600728i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.494776i | − | 0.0174821i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.6567 | + | 20.1899i | 0.411355 | + | 0.712488i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4466 | −0.508545 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.52131 | − | 14.7593i | −0.299593 | − | 0.518911i | 0.676450 | − | 0.736489i | \(-0.263518\pi\) |
−0.976043 | + | 0.217578i | \(0.930184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.60366i | 0.0914268i | 0.998955 | + | 0.0457134i | \(0.0145561\pi\) | ||||
−0.998955 | + | 0.0457134i | \(0.985444\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.7807 | + | 11.4204i | 0.693738 | + | 0.400530i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.7389 | − | 13.7057i | 0.830518 | − | 0.479500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.60611 | + | 0.795511i | 0.300722 | + | 0.0277974i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.7265 | + | 23.5134i | −1.42136 | + | 0.820625i | −0.996416 | − | 0.0845933i | \(-0.973041\pi\) |
−0.424948 | + | 0.905218i | \(0.639708\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.35111 | − | 9.26840i | 0.186528 | − | 0.323076i | −0.757562 | − | 0.652763i | \(-0.773610\pi\) |
0.944090 | + | 0.329687i | \(0.106943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.8240i | − | 0.480707i | −0.970685 | − | 0.240354i | \(-0.922737\pi\) | ||
0.970685 | − | 0.240354i | \(-0.0772634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1310 | + | 41.7961i | 0.838104 | + | 1.45164i | 0.891478 | + | 0.453065i | \(0.149669\pi\) |
−0.0533731 | + | 0.998575i | \(0.516997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.80565 | 0.0626375 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.55915 | 0.157965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.8695i | 1.23983i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.3752 | + | 25.6200i | 1.53200 | + | 0.884502i | 0.999269 | + | 0.0382177i | \(0.0121680\pi\) |
0.532732 | + | 0.846284i | \(0.321165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.21222 | − | 12.4919i | 0.248697 | − | 0.430756i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.6236 | + | 13.0617i | −0.779197 | + | 0.449869i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.2977 | + | 29.0394i | −1.72825 | + | 0.997805i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.10004 | − | 8.83353i | 0.175033 | − | 0.303166i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.33700 | − | 1.34927i | −0.0801113 | − | 0.0462523i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3777i | 0.731960i | 0.930623 | + | 0.365980i | \(0.119266\pi\) | ||||
−0.930623 | + | 0.365980i | \(0.880734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.9615 | 1.26258 | 0.631291 | − | 0.775546i | \(-0.282525\pi\) | ||||
0.631291 | + | 0.775546i | \(0.282525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.3529 | 1.24034 | 0.620172 | − | 0.784465i | \(-0.287063\pi\) | ||||
0.620172 | + | 0.784465i | \(0.287063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.1630 | − | 38.3874i | −0.755312 | − | 1.30824i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41.0328i | − | 1.39677i | −0.715720 | − | 0.698387i | \(-0.753901\pi\) | ||
0.715720 | − | 0.698387i | \(-0.246099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.54460 | − | 2.67532i | 0.0524573 | − | 0.0908588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.7757 | + | 27.5833i | −1.62068 | + | 0.935700i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.8008 | + | 4.04876i | 1.48413 | + | 0.137187i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.42763 | − | 1.97894i | 0.116008 | − | 0.0669771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.5001 | − | 8.37164i | −0.489634 | − | 0.282690i | 0.234789 | − | 0.972046i | \(-0.424560\pi\) |
−0.724423 | + | 0.689356i | \(0.757894\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 29.4804i | − | 0.994350i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.3345 | + | 45.6127i | 0.887232 | + | 1.53673i | 0.843133 | + | 0.537704i | \(0.180708\pi\) |
0.0440990 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.5891 | −1.53419 | −0.767097 | − | 0.641531i | \(-0.778300\pi\) | ||||
−0.767097 | + | 0.641531i | \(0.778300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0366 | + | 17.3838i | 0.336995 | + | 0.583692i | 0.983866 | − | 0.178907i | \(-0.0572562\pi\) |
−0.646871 | + | 0.762599i | \(0.723923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 21.3696i | − | 0.716713i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.4166 | + | 30.2628i | 1.75602 | + | 1.01384i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.4251 | − | 61.3582i | 1.18546 | − | 2.05327i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.29101 | − | 1.05466i | 0.0764945 | − | 0.0352140i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.0104 | + | 16.1718i | −0.934200 | + | 0.539361i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14208 | − | 1.97813i | 0.0380481 | − | 0.0659012i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.2179 | + | 9.36340i | 0.539697 | + | 0.311594i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.1070 | − | 33.0943i | −0.634438 | − | 1.09888i | −0.986634 | − | 0.162953i | \(-0.947898\pi\) |
0.352196 | − | 0.935926i | \(-0.385435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.12630 | 0.0705249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.3853 | −1.20550 | −0.602749 | − | 0.797931i | \(-0.705928\pi\) | ||||
−0.602749 | + | 0.797931i | \(0.705928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.0488 | − | 29.5295i | −0.564234 | − | 0.977282i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.07664 | − | 4.08570i | −0.233691 | − | 0.134922i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6508 | − | 20.1798i | 0.384324 | − | 0.665669i | −0.607351 | − | 0.794434i | \(-0.707768\pi\) |
0.991675 | + | 0.128765i | \(0.0411012\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.49996 | − | 4.33011i | 0.247132 | − | 0.142682i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.68521 | + | 8.00528i | 0.121300 | + | 0.263497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.390218 | − | 0.675877i | 0.0128164 | − | 0.0221987i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.17003 | + | 1.83022i | 0.104005 | + | 0.0600475i | 0.551100 | − | 0.834439i | \(-0.314208\pi\) |
−0.447095 | + | 0.894486i | \(0.647541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.51140i | 0.311724i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.5532 | − | 54.6518i | −1.03301 | − | 1.78922i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.7022 | 1.36235 | 0.681175 | − | 0.732120i | \(-0.261469\pi\) | ||||
0.681175 | + | 0.732120i | \(0.261469\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4718 | + | 31.9941i | 0.602805 | + | 1.04409i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.3086i | 1.70521i | 0.522554 | + | 0.852606i | \(0.324979\pi\) | ||||
−0.522554 | + | 0.852606i | \(0.675021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.44840 | − | 1.41358i | −0.0797307 | − | 0.0460325i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.0703 | − | 18.5158i | 1.04214 | − | 0.601682i | 0.121704 | − | 0.992566i | \(-0.461164\pi\) |
0.920440 | + | 0.390884i | \(0.127831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.67384 | + | 12.2591i | −0.281565 | + | 0.397946i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.7082 | + | 23.5029i | −1.32005 | + | 0.762134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.25776 | + | 12.5708i | −0.235102 | + | 0.407209i | −0.959302 | − | 0.282381i | \(-0.908876\pi\) |
0.724200 | + | 0.689590i | \(0.242209\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.8708i | 1.35349i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.3752 | − | 40.4870i | −0.754824 | − | 1.30739i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −40.7717 | −1.31522 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.495195 | −0.0159574 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2765i | 0.780680i | 0.920671 | + | 0.390340i | \(0.127643\pi\) | ||||
−0.920671 | + | 0.390340i | \(0.872357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −54.5990 | − | 31.5228i | −1.75397 | − | 1.01266i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.3284 | + | 17.8894i | −0.331456 | + | 0.574098i | −0.982798 | − | 0.184686i | \(-0.940873\pi\) |
0.651342 | + | 0.758784i | \(0.274206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.44451 | + | 2.56604i | −0.142485 | + | 0.0822635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.8260 | + | 12.6013i | −0.698277 | + | 0.403150i | −0.806705 | − | 0.590954i | \(-0.798751\pi\) |
0.108429 | + | 0.994104i | \(0.465418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.65025 | + | 2.85831i | −0.0527421 | + | 0.0913520i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.54662 | − | 2.04764i | −0.113235 | − | 0.0653761i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.9686i | 1.40238i | 0.712973 | + | 0.701191i | \(0.247348\pi\) | ||||
−0.712973 | + | 0.701191i | \(0.752652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.4034 | 1.54070 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.19442 | 0.0379803 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8117 | − | 27.3866i | −0.502275 | − | 0.869966i | −0.999997 | − | 0.00262873i | \(-0.999163\pi\) |
0.497722 | − | 0.867337i | \(-0.334170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.1209i | 0.448113i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.53853 | − | 16.5212i | 0.302088 | − | 0.523232i | −0.674521 | − | 0.738256i | \(-0.735650\pi\) |
0.976609 | + | 0.215024i | \(0.0689830\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.7160 | − | 16.0019i | 0.876897 | − | 0.506277i |
(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 | 1300.2.y.e.101.2 | 16 | ||
5.2 | odd | 4 | 260.2.z.a.49.2 | ✓ | 16 | ||
5.3 | odd | 4 | 260.2.z.a.49.7 | yes | 16 | ||
5.4 | even | 2 | inner | 1300.2.y.e.101.7 | 16 | ||
13.4 | even | 6 | inner | 1300.2.y.e.901.2 | 16 | ||
15.2 | even | 4 | 2340.2.cr.a.829.8 | 16 | |||
15.8 | even | 4 | 2340.2.cr.a.829.1 | 16 | |||
20.3 | even | 4 | 1040.2.df.d.49.2 | 16 | |||
20.7 | even | 4 | 1040.2.df.d.49.7 | 16 | |||
65.2 | even | 12 | 3380.2.c.e.2029.3 | 16 | |||
65.3 | odd | 12 | 3380.2.d.d.1689.14 | 16 | |||
65.4 | even | 6 | inner | 1300.2.y.e.901.7 | 16 | ||
65.17 | odd | 12 | 260.2.z.a.69.7 | yes | 16 | ||
65.23 | odd | 12 | 3380.2.d.d.1689.13 | 16 | |||
65.28 | even | 12 | 3380.2.c.e.2029.13 | 16 | |||
65.37 | even | 12 | 3380.2.c.e.2029.4 | 16 | |||
65.42 | odd | 12 | 3380.2.d.d.1689.3 | 16 | |||
65.43 | odd | 12 | 260.2.z.a.69.2 | yes | 16 | ||
65.62 | odd | 12 | 3380.2.d.d.1689.4 | 16 | |||
65.63 | even | 12 | 3380.2.c.e.2029.14 | 16 | |||
195.17 | even | 12 | 2340.2.cr.a.1369.1 | 16 | |||
195.173 | even | 12 | 2340.2.cr.a.1369.8 | 16 | |||
260.43 | even | 12 | 1040.2.df.d.849.7 | 16 | |||
260.147 | even | 12 | 1040.2.df.d.849.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.z.a.49.2 | ✓ | 16 | 5.2 | odd | 4 | ||
260.2.z.a.49.7 | yes | 16 | 5.3 | odd | 4 | ||
260.2.z.a.69.2 | yes | 16 | 65.43 | odd | 12 | ||
260.2.z.a.69.7 | yes | 16 | 65.17 | odd | 12 | ||
1040.2.df.d.49.2 | 16 | 20.3 | even | 4 | |||
1040.2.df.d.49.7 | 16 | 20.7 | even | 4 | |||
1040.2.df.d.849.2 | 16 | 260.147 | even | 12 | |||
1040.2.df.d.849.7 | 16 | 260.43 | even | 12 | |||
1300.2.y.e.101.2 | 16 | 1.1 | even | 1 | trivial | ||
1300.2.y.e.101.7 | 16 | 5.4 | even | 2 | inner | ||
1300.2.y.e.901.2 | 16 | 13.4 | even | 6 | inner | ||
1300.2.y.e.901.7 | 16 | 65.4 | even | 6 | inner | ||
2340.2.cr.a.829.1 | 16 | 15.8 | even | 4 | |||
2340.2.cr.a.829.8 | 16 | 15.2 | even | 4 | |||
2340.2.cr.a.1369.1 | 16 | 195.17 | even | 12 | |||
2340.2.cr.a.1369.8 | 16 | 195.173 | even | 12 | |||
3380.2.c.e.2029.3 | 16 | 65.2 | even | 12 | |||
3380.2.c.e.2029.4 | 16 | 65.37 | even | 12 | |||
3380.2.c.e.2029.13 | 16 | 65.28 | even | 12 | |||
3380.2.c.e.2029.14 | 16 | 65.63 | even | 12 | |||
3380.2.d.d.1689.3 | 16 | 65.42 | odd | 12 | |||
3380.2.d.d.1689.4 | 16 | 65.62 | odd | 12 | |||
3380.2.d.d.1689.13 | 16 | 65.23 | odd | 12 | |||
3380.2.d.d.1689.14 | 16 | 65.3 | odd | 12 |