Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Root | \(2.27790i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.293 |
Dual form | 1300.2.bs.d.457.3 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.243028 | + | 0.0651192i | −0.140312 | + | 0.0375966i | −0.328292 | − | 0.944576i | \(-0.606473\pi\) |
0.187979 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.30824 | − | 2.48736i | 1.62836 | − | 0.940134i | 0.643778 | − | 0.765212i | \(-0.277366\pi\) |
0.984582 | − | 0.174922i | \(-0.0559675\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.54325 | + | 1.46835i | −0.847751 | + | 0.489449i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.07571 | + | 4.01459i | 0.324337 | + | 1.21044i | 0.914976 | + | 0.403508i | \(0.132209\pi\) |
−0.590639 | + | 0.806936i | \(0.701124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.20328 | + | 1.65499i | −0.888430 | + | 0.459012i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.65147 | + | 6.16338i | −0.400541 | + | 1.49484i | 0.411592 | + | 0.911368i | \(0.364973\pi\) |
−0.812133 | + | 0.583472i | \(0.801694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.01061 | + | 0.270792i | 0.231850 | + | 0.0621239i | 0.372873 | − | 0.927882i | \(-0.378373\pi\) |
−0.141024 | + | 0.990006i | \(0.545039\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.885048 | + | 0.885048i | −0.193133 | + | 0.193133i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.195793 | − | 0.730708i | −0.0408256 | − | 0.152363i | 0.942504 | − | 0.334194i | \(-0.108464\pi\) |
−0.983330 | + | 0.181831i | \(0.941798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.05619 | − | 1.05619i | 0.203264 | − | 0.203264i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.59295 | + | 3.80644i | 1.22428 | + | 0.706839i | 0.965828 | − | 0.259185i | \(-0.0834539\pi\) |
0.258453 | + | 0.966024i | \(0.416787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.17449 | + | 2.17449i | 0.390551 | + | 0.390551i | 0.874884 | − | 0.484333i | \(-0.160938\pi\) |
−0.484333 | + | 0.874884i | \(0.660938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.522853 | − | 0.905608i | −0.0910171 | − | 0.157646i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.36518 | − | 3.09759i | −0.882030 | − | 0.509240i | −0.0107029 | − | 0.999943i | \(-0.503407\pi\) |
−0.871327 | + | 0.490702i | \(0.836740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.670715 | − | 0.610805i | 0.107400 | − | 0.0978070i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.57347 | + | 0.689559i | −0.401908 | + | 0.107691i | −0.454110 | − | 0.890946i | \(-0.650043\pi\) |
0.0522020 | + | 0.998637i | \(0.483376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90779 | + | 0.779141i | 0.443435 | + | 0.118818i | 0.473626 | − | 0.880726i | \(-0.342945\pi\) |
−0.0301912 | + | 0.999544i | \(0.509612\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.62865i | 0.237563i | 0.992920 | + | 0.118781i | \(0.0378988\pi\) | ||||
−0.992920 | + | 0.118781i | \(0.962101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.87394 | − | 15.3701i | 1.26771 | − | 2.19573i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.60542i | − | 0.224804i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.32012 | + | 5.32012i | 0.730775 | + | 0.730775i | 0.970773 | − | 0.239998i | \(-0.0771468\pi\) |
−0.239998 | + | 0.970773i | \(0.577147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.263240 | −0.0348670 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.52700 | − | 9.43090i | 0.328988 | − | 1.22780i | −0.581254 | − | 0.813722i | \(-0.697438\pi\) |
0.910242 | − | 0.414077i | \(-0.135895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.39215 | + | 9.33947i | 0.690394 | + | 1.19580i | 0.971709 | + | 0.236182i | \(0.0758961\pi\) |
−0.281315 | + | 0.959615i | \(0.590771\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.30463 | + | 12.6520i | −0.920297 | + | 1.59400i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.04802 | − | 5.27932i | 0.372375 | − | 0.644972i | −0.617556 | − | 0.786527i | \(-0.711877\pi\) |
0.989930 | + | 0.141555i | \(0.0452103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0951662 | + | 0.164833i | 0.0114567 | + | 0.0198435i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.15621 | + | 4.31503i | −0.137217 | + | 0.512100i | 0.862762 | + | 0.505610i | \(0.168733\pi\) |
−0.999979 | + | 0.00649007i | \(0.997934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.98834 | −0.700882 | −0.350441 | − | 0.936585i | \(-0.613968\pi\) | ||||
−0.350441 | + | 0.936585i | \(0.613968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.6201 | + | 14.6201i | 1.66612 | + | 1.66612i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0944i | 1.58574i | 0.609390 | + | 0.792871i | \(0.291415\pi\) | ||||
−0.609390 | + | 0.792871i | \(0.708585\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.21714 | − | 7.30430i | 0.468571 | − | 0.811589i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.32705i | 0.914013i | 0.889463 | + | 0.457006i | \(0.151078\pi\) | ||||
−0.889463 | + | 0.457006i | \(0.848922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.85015 | − | 0.495745i | −0.198356 | − | 0.0531494i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.99308 | + | 0.534044i | −0.211266 | + | 0.0566086i | −0.362900 | − | 0.931828i | \(-0.618213\pi\) |
0.151634 | + | 0.988437i | \(0.451547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.68392 | + | 15.0978i | −1.01515 | + | 1.58268i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.670065 | − | 0.386862i | −0.0694825 | − | 0.0401157i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.17921 | − | 7.23861i | −0.424335 | − | 0.734970i | 0.572023 | − | 0.820237i | \(-0.306159\pi\) |
−0.996358 | + | 0.0852678i | \(0.972825\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.63060 | − | 8.63060i | −0.867408 | − | 0.867408i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46818 | + | 0.847656i | 0.146090 | + | 0.0843449i | 0.571263 | − | 0.820767i | \(-0.306454\pi\) |
−0.425173 | + | 0.905112i | \(0.639787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.53574 | − | 1.53574i | 0.151321 | − | 0.151321i | −0.627387 | − | 0.778708i | \(-0.715875\pi\) |
0.778708 | + | 0.627387i | \(0.215875\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.68950 | + | 13.7694i | 0.356677 | + | 1.33114i | 0.878361 | + | 0.477998i | \(0.158637\pi\) |
−0.521684 | + | 0.853139i | \(0.674696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.49190 | − | 3.49190i | 0.334464 | − | 0.334464i | −0.519815 | − | 0.854279i | \(-0.673999\pi\) |
0.854279 | + | 0.519815i | \(0.173999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.50560 | + | 0.403425i | 0.142905 | + | 0.0382914i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.02987 | − | 3.84351i | 0.0968817 | − | 0.361567i | −0.900416 | − | 0.435029i | \(-0.856738\pi\) |
0.997298 | + | 0.0734619i | \(0.0234047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.71665 | − | 8.91260i | 0.528504 | − | 0.823970i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.21563 | + | 30.6611i | 0.753125 | + | 2.81070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.43349 | + | 3.13702i | −0.493953 | + | 0.285184i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.580521 | − | 0.335164i | 0.0523439 | − | 0.0302207i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9209 | + | 3.73009i | −1.23528 | + | 0.330992i | −0.816633 | − | 0.577157i | \(-0.804162\pi\) |
−0.418646 | + | 0.908149i | \(0.637495\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.757413 | −0.0666865 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6069 | 1.18884 | 0.594418 | − | 0.804156i | \(-0.297382\pi\) | ||||
0.594418 | + | 0.804156i | \(0.297382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.02750 | − | 1.34712i | 0.435940 | − | 0.116810i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.63357 | − | 4.98459i | 0.737616 | − | 0.425863i | −0.0835860 | − | 0.996501i | \(-0.526637\pi\) |
0.821202 | + | 0.570638i | \(0.193304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3180 | + | 8.26649i | −1.21443 | + | 0.701154i | −0.963722 | − | 0.266907i | \(-0.913998\pi\) |
−0.250713 | + | 0.968062i | \(0.580665\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.106056 | − | 0.395808i | −0.00893155 | − | 0.0333330i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0899 | − | 11.0796i | −0.843760 | − | 0.926519i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.15573 | + | 4.31323i | −0.0953228 | + | 0.355749i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.94306 | − | 1.32449i | −0.404951 | − | 0.108506i | 0.0505933 | − | 0.998719i | \(-0.483889\pi\) |
−0.455545 | + | 0.890213i | \(0.650555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2431 | − | 10.2431i | 0.833572 | − | 0.833572i | −0.154432 | − | 0.988003i | \(-0.549355\pi\) |
0.988003 | + | 0.154432i | \(0.0493547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.84988 | − | 18.1000i | −0.392089 | − | 1.46330i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.17805 | − | 9.17805i | 0.732488 | − | 0.732488i | −0.238624 | − | 0.971112i | \(-0.576696\pi\) |
0.971112 | + | 0.238624i | \(0.0766963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.63938 | − | 0.946497i | −0.130011 | − | 0.0750621i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.66106 | − | 2.66106i | −0.209721 | − | 0.209721i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.301606 | − | 0.522396i | −0.0236236 | − | 0.0409172i | 0.853972 | − | 0.520319i | \(-0.174187\pi\) |
−0.877596 | + | 0.479402i | \(0.840854\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.55141 | − | 5.51451i | −0.739111 | − | 0.426726i | 0.0826352 | − | 0.996580i | \(-0.473666\pi\) |
−0.821746 | + | 0.569854i | \(0.807000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.52200 | − | 10.6028i | 0.578615 | − | 0.815601i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.96785 | + | 0.795234i | −0.226957 | + | 0.0608130i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.32352 | + | 0.622584i | 0.176654 | + | 0.0473342i | 0.346062 | − | 0.938212i | \(-0.387519\pi\) |
−0.169408 | + | 0.985546i | \(0.554186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.45653i | 0.184644i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.18307 | − | 7.24528i | 0.312657 | − | 0.541538i | −0.666280 | − | 0.745702i | \(-0.732114\pi\) |
0.978937 | + | 0.204164i | \(0.0654476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.76362i | − | 0.354077i | −0.984204 | − | 0.177038i | \(-0.943348\pi\) | ||
0.984204 | − | 0.177038i | \(-0.0566517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.91862 | − | 1.91862i | −0.141829 | − | 0.141829i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5199 | −1.93933 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.92319 | − | 7.17745i | 0.139892 | − | 0.522083i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.87644 | − | 15.3744i | −0.642277 | − | 1.11246i | −0.984923 | − | 0.172992i | \(-0.944657\pi\) |
0.342647 | − | 0.939464i | \(-0.388677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.533644 | + | 0.924299i | −0.0384126 | + | 0.0665325i | −0.884593 | − | 0.466365i | \(-0.845563\pi\) |
0.846180 | + | 0.532897i | \(0.178897\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.86172 | − | 3.22459i | 0.132642 | − | 0.229742i | −0.792052 | − | 0.610453i | \(-0.790987\pi\) |
0.924694 | + | 0.380711i | \(0.124321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.66514 | − | 15.0085i | −0.614256 | − | 1.06392i | −0.990515 | − | 0.137407i | \(-0.956123\pi\) |
0.376259 | − | 0.926515i | \(-0.377210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.396969 | + | 1.48151i | −0.0280000 | + | 0.104498i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 37.8720 | 2.65809 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.57088 | + | 1.57088i | 0.109184 | + | 0.109184i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.34847i | 0.300790i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.27838 | + | 5.67831i | −0.225693 | + | 0.390911i | −0.956527 | − | 0.291644i | \(-0.905798\pi\) |
0.730834 | + | 0.682555i | \(0.239131\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.12397i | − | 0.0770128i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.7770 | + | 3.95948i | 1.00313 | + | 0.268787i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.45533 | − | 0.389956i | 0.0983424 | − | 0.0263508i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.91022 | − | 22.4762i | −0.330297 | − | 1.51191i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.31040 | − | 2.48861i | −0.288646 | − | 0.166650i | 0.348685 | − | 0.937240i | \(-0.386628\pi\) |
−0.637331 | + | 0.770590i | \(0.719962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56183 | − | 6.16926i | −0.236407 | − | 0.409468i | 0.723274 | − | 0.690561i | \(-0.242636\pi\) |
−0.959681 | + | 0.281093i | \(0.909303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5515 | + | 15.5515i | 1.02767 | + | 1.02767i | 0.999606 | + | 0.0280672i | \(0.00893525\pi\) |
0.0280672 | + | 0.999606i | \(0.491065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.50515 | − | 2.60105i | −0.296417 | − | 0.171137i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.10223 | − | 1.10223i | 0.0722092 | − | 0.0722092i | −0.670080 | − | 0.742289i | \(-0.733740\pi\) |
0.742289 | + | 0.670080i | \(0.233740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.917815 | − | 3.42533i | −0.0596185 | − | 0.222499i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.75486 | − | 3.75486i | 0.242882 | − | 0.242882i | −0.575160 | − | 0.818041i | \(-0.695060\pi\) |
0.818041 | + | 0.575160i | \(0.195060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.3970 | − | 6.26920i | −1.50713 | − | 0.403834i | −0.591650 | − | 0.806195i | \(-0.701523\pi\) |
−0.915481 | + | 0.402361i | \(0.868190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.70901 | + | 6.37812i | −0.109633 | + | 0.409157i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.68542 | + | 0.805129i | −0.234498 | + | 0.0512291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.542251 | − | 2.02371i | −0.0343637 | − | 0.128247i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.3191 | − | 10.5765i | 1.15629 | − | 0.667584i | 0.205878 | − | 0.978578i | \(-0.433995\pi\) |
0.950412 | + | 0.310993i | \(0.100662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.72288 | − | 1.57205i | 0.171186 | − | 0.0988341i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.6872 | + | 4.20336i | −0.978538 | + | 0.262198i | −0.712429 | − | 0.701745i | \(-0.752405\pi\) |
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.8193 | −1.91502 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.3567 | −1.38385 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.6930 | + | 6.61647i | −1.52264 | + | 0.407989i | −0.920609 | − | 0.390486i | \(-0.872307\pi\) |
−0.602028 | + | 0.798475i | \(0.705640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.449598 | − | 0.259576i | 0.0275149 | − | 0.0158858i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.52850 | + | 1.45983i | −0.154166 | + | 0.0890076i | −0.575098 | − | 0.818084i | \(-0.695036\pi\) |
0.420933 | + | 0.907092i | \(0.361703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.61686 | + | 17.2303i | 0.280454 | + | 1.04667i | 0.952098 | + | 0.305794i | \(0.0989220\pi\) |
−0.671643 | + | 0.740875i | \(0.734411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.37031 | − | 4.29980i | 0.0829348 | − | 0.260236i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.632426 | − | 2.36025i | 0.0379988 | − | 0.141813i | −0.944320 | − | 0.329027i | \(-0.893279\pi\) |
0.982319 | + | 0.187214i | \(0.0599458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.72321 | − | 2.33738i | −0.522245 | − | 0.139935i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.70513 | − | 7.70513i | 0.459649 | − | 0.459649i | −0.438891 | − | 0.898540i | \(-0.644629\pi\) |
0.898540 | + | 0.438891i | \(0.144629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.35341 | + | 19.9792i | 0.318227 | + | 1.18764i | 0.920947 | + | 0.389687i | \(0.127417\pi\) |
−0.602721 | + | 0.797952i | \(0.705917\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.37193 | + | 9.37193i | −0.553207 | + | 0.553207i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.5375 | − | 11.8573i | −1.20809 | − | 0.697490i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.48704 | + | 1.48704i | 0.0871718 | + | 0.0871718i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.32754 | + | 5.76347i | 0.194397 | + | 0.336705i | 0.946703 | − | 0.322109i | \(-0.104392\pi\) |
−0.752306 | + | 0.658814i | \(0.771058\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.37632 | + | 3.10402i | 0.311966 | + | 0.180114i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.83649 | + | 2.01663i | 0.106207 | + | 0.116625i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.4655 | − | 3.87601i | 0.833776 | − | 0.223410i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.412009 | − | 0.110397i | −0.0236693 | − | 0.00634216i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2894i | − | 1.15798i | −0.815336 | − | 0.578988i | \(-0.803448\pi\) | ||
0.815336 | − | 0.578988i | \(-0.196552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.273222 | + | 0.473235i | −0.0155431 | + | 0.0269214i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.7888i | − | 0.952005i | −0.879444 | − | 0.476003i | \(-0.842085\pi\) | ||
0.879444 | − | 0.476003i | \(-0.157915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.96737 | + | 3.96737i | 0.224249 | + | 0.224249i | 0.810285 | − | 0.586036i | \(-0.199312\pi\) |
−0.586036 | + | 0.810285i | \(0.699312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0049 | 0.786596 | 0.393298 | − | 0.919411i | \(-0.371334\pi\) | ||||
0.393298 | + | 0.919411i | \(0.371334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.18922 | + | 30.5626i | −0.458508 | + | 1.71118i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.79330 | − | 3.10609i | −0.100092 | − | 0.173365i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.33799 | + | 5.78157i | −0.185731 | + | 0.321695i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.621241 | + | 1.07602i | −0.0343547 | + | 0.0595041i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.05104 | + | 7.01661i | 0.223341 | + | 0.386838i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.64068 | − | 17.3193i | 0.255075 | − | 0.951953i | −0.712974 | − | 0.701191i | \(-0.752652\pi\) |
0.968049 | − | 0.250762i | \(-0.0806812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1934 | 0.996990 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.10238 | + | 5.10238i | 0.277944 | + | 0.277944i | 0.832288 | − | 0.554344i | \(-0.187031\pi\) |
−0.554344 | + | 0.832288i | \(0.687031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00115i | 0.0543748i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.39058 | + | 11.0688i | −0.346069 | + | 0.599410i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 53.4677i | − | 2.88699i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.64882 | + | 1.51360i | 0.303245 | + | 0.0812541i | 0.407233 | − | 0.913324i | \(-0.366494\pi\) |
−0.103988 | + | 0.994579i | \(0.533160\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5635 | + | 2.83049i | −0.565453 | + | 0.151513i | −0.530210 | − | 0.847866i | \(-0.677887\pi\) |
−0.0352425 | + | 0.999379i | \(0.511220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.63529 | + | 5.13127i | −0.0872852 | + | 0.273887i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.17880 | − | 2.41263i | −0.222415 | − | 0.128411i | 0.384653 | − | 0.923061i | \(-0.374321\pi\) |
−0.607068 | + | 0.794650i | \(0.707654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.99326 | − | 6.91652i | −0.211346 | − | 0.366061i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0711 | + | 14.0711i | 0.742643 | + | 0.742643i | 0.973086 | − | 0.230443i | \(-0.0740175\pi\) |
−0.230443 | + | 0.973086i | \(0.574017\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5065 | − | 8.95267i | −0.816131 | − | 0.471193i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.11621 | − | 1.11621i | 0.0585858 | − | 0.0585858i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.521841 | − | 1.94754i | −0.0272399 | − | 0.101661i | 0.950968 | − | 0.309291i | \(-0.100092\pi\) |
−0.978207 | + | 0.207630i | \(0.933425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.53247 | − | 5.53247i | 0.288009 | − | 0.288009i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 36.1534 | + | 9.68728i | 1.87699 | + | 0.502939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.91290 | − | 10.8711i | 0.150824 | − | 0.562884i | −0.848603 | − | 0.529031i | \(-0.822556\pi\) |
0.999427 | − | 0.0338529i | \(-0.0107778\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.4187 | − | 1.28181i | −1.41214 | − | 0.0660167i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.25775 | − | 19.6222i | −0.270072 | − | 1.00792i | −0.959072 | − | 0.283162i | \(-0.908617\pi\) |
0.689000 | − | 0.724762i | \(-0.258050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.14027 | − | 1.81303i | 0.160881 | − | 0.0928846i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.8722 | − | 15.5147i | 1.37310 | − | 0.792762i | 0.381786 | − | 0.924251i | \(-0.375309\pi\) |
0.991318 | + | 0.131489i | \(0.0419758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.53931 | + | 2.28810i | −0.434078 | + | 0.116311i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.63490 | −0.0828926 | −0.0414463 | − | 0.999141i | \(-0.513197\pi\) | ||||
−0.0414463 | + | 0.999141i | \(0.513197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82698 | 0.244111 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.30685 | + | 0.886068i | −0.166808 | + | 0.0446962i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6174 | + | 13.6355i | −1.18532 | + | 0.684347i | −0.957240 | − | 0.289295i | \(-0.906579\pi\) |
−0.228084 | + | 0.973642i | \(0.573246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.13410 | + | 0.654774i | −0.0567761 | + | 0.0327797i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.48832 | − | 24.2147i | −0.324011 | − | 1.20923i | −0.915302 | − | 0.402768i | \(-0.868048\pi\) |
0.591291 | − | 0.806458i | \(-0.298618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.5643 | − | 3.36674i | −0.526245 | − | 0.167709i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.66418 | − | 24.8711i | 0.330331 | − | 1.23281i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8874 | + | 5.06087i | 0.933923 | + | 0.250244i | 0.693527 | − | 0.720431i | \(-0.256056\pi\) |
0.240396 | + | 0.970675i | \(0.422723\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.77361 | + | 1.77361i | −0.0874856 | + | 0.0874856i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5711 | − | 46.9161i | −0.618585 | − | 2.30859i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.94136 | − | 2.94136i | 0.144039 | − | 0.144039i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.39265 | − | 2.53610i | −0.214595 | − | 0.123896i | 0.388850 | − | 0.921301i | \(-0.372872\pi\) |
−0.603445 | + | 0.797405i | \(0.706206\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3139 | − | 17.3139i | −0.843829 | − | 0.843829i | 0.145526 | − | 0.989354i | \(-0.453513\pi\) |
−0.989354 | + | 0.145526i | \(0.953513\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.39142 | − | 4.14207i | −0.116275 | − | 0.201394i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.4613 | + | 26.8244i | 2.24842 | + | 1.29813i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.17362 | + | 2.03560i | 0.153224 | + | 0.0982796i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.0567 | + | 9.12548i | −1.64046 | + | 0.439559i | −0.956918 | − | 0.290357i | \(-0.906226\pi\) |
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.36406 | − | 1.97319i | −0.353894 | − | 0.0948256i | 0.0774922 | − | 0.996993i | \(-0.475309\pi\) |
−0.431386 | + | 0.902167i | \(0.641975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.791479i | − | 0.0378616i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.65410 | − | 11.5252i | 0.317583 | − | 0.550070i | −0.662400 | − | 0.749150i | \(-0.730462\pi\) |
0.979983 | + | 0.199080i | \(0.0637955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 52.1201i | 2.48191i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.68354 | + | 3.68354i | 0.175010 | + | 0.175010i | 0.789177 | − | 0.614166i | \(-0.210508\pi\) |
−0.614166 | + | 0.789177i | \(0.710508\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.28755 | 0.0608991 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.69575 | + | 32.4530i | −0.410378 | + | 1.53155i | 0.383539 | + | 0.923525i | \(0.374705\pi\) |
−0.793917 | + | 0.608026i | \(0.791961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.53659 | − | 9.58965i | −0.260708 | − | 0.451559i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.82234 | + | 3.15638i | −0.0856210 | + | 0.148300i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.7773 | − | 22.1309i | 0.597697 | − | 1.03524i | −0.395464 | − | 0.918482i | \(-0.629416\pi\) |
0.993160 | − | 0.116759i | \(-0.0372506\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.76544 | + | 8.25399i | 0.222432 | + | 0.385263i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.88759 | − | 14.5087i | 0.181063 | − | 0.675736i | −0.814376 | − | 0.580337i | \(-0.802921\pi\) |
0.995439 | − | 0.0953989i | \(-0.0304126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4587 | 0.857850 | 0.428925 | − | 0.903340i | \(-0.358893\pi\) | ||||
0.428925 | + | 0.903340i | \(0.358893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.6509 | − | 19.6509i | −0.909333 | − | 0.909333i | 0.0868854 | − | 0.996218i | \(-0.472309\pi\) |
−0.996218 | + | 0.0868854i | \(0.972309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.3261i | − | 1.40033i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.63286 | + | 2.82819i | −0.0752381 | + | 0.130316i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.5117i | 0.575289i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.3422 | − | 5.71863i | −0.977193 | − | 0.261838i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.7117 | + | 4.20993i | −0.717885 | + | 0.192357i | −0.599228 | − | 0.800579i | \(-0.704526\pi\) |
−0.118657 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3127 | + | 1.04311i | 1.01737 | + | 0.0475615i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.819997 | + | 0.473426i | 0.0373112 | + | 0.0215416i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1697 | + | 34.9350i | 0.913977 | + | 1.58306i | 0.808392 | + | 0.588645i | \(0.200338\pi\) |
0.105586 | + | 0.994410i | \(0.466328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.107317 | + | 0.107317i | 0.00485303 | + | 0.00485303i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.241005 | + | 0.139144i | 0.0108764 | + | 0.00627949i | 0.505428 | − | 0.862869i | \(-0.331334\pi\) |
−0.494552 | + | 0.869148i | \(0.664668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.3487 | + | 34.3487i | −1.54699 | + | 1.54699i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.75182 | + | 21.4661i | 0.258004 | + | 0.962886i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.97274 | + | 5.97274i | −0.267377 | + | 0.267377i | −0.828042 | − | 0.560666i | \(-0.810545\pi\) |
0.560666 | + | 0.828042i | \(0.310545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.68036 | + | 0.718201i | 0.119750 | + | 0.0320869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.52299 | + | 31.8082i | −0.380021 | + | 1.41826i | 0.465846 | + | 0.884866i | \(0.345750\pi\) |
−0.845867 | + | 0.533393i | \(0.820917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.13761 | + | 3.06661i | −0.0505231 | + | 0.136193i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.47308 | − | 31.6220i | −0.375562 | − | 1.40162i | −0.852521 | − | 0.522693i | \(-0.824928\pi\) |
0.476959 | − | 0.878926i | \(-0.341739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.7992 | + | 14.8952i | −1.14129 | + | 0.658923i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.35340 | − | 0.781389i | 0.0597543 | − | 0.0344992i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.53835 | + | 1.75195i | −0.287556 | + | 0.0770505i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.605222 | −0.0265663 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.2134 | 1.06081 | 0.530405 | − | 0.847744i | \(-0.322040\pi\) | ||||
0.530405 | + | 0.847744i | \(0.322040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0608 | + | 9.12656i | −1.48937 | + | 0.399076i | −0.909525 | − | 0.415648i | \(-0.863555\pi\) |
−0.579848 | + | 0.814725i | \(0.696888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9934 | + | 9.81113i | −0.740243 | + | 0.427379i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4230 | − | 11.2139i | 0.844478 | − | 0.487559i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.42104 | + | 27.6957i | 0.322046 | + | 1.20189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.10232 | − | 6.46792i | 0.307636 | − | 0.280157i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.544796 | + | 2.03321i | −0.0235097 | + | 0.0877393i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 71.2504 | + | 19.0915i | 3.06897 | + | 0.822328i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.9720 | − | 16.9720i | 0.729682 | − | 0.729682i | −0.240874 | − | 0.970556i | \(-0.577434\pi\) |
0.970556 | + | 0.240874i | \(0.0774342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.310203 | + | 1.15769i | 0.0133121 | + | 0.0496814i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.4672 | − | 23.4672i | 1.00339 | − | 1.00339i | 0.00339103 | − | 0.999994i | \(-0.498921\pi\) |
0.999994 | − | 0.00339103i | \(-0.00107940\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.4272 | − | 15.8351i | −1.17056 | − | 0.675826i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.63215 | + | 5.63215i | 0.239937 | + | 0.239937i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.0578 | + | 60.7219i | 1.49081 | + | 2.58216i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.3777 | + | 13.4971i | 0.990547 | + | 0.571893i | 0.905438 | − | 0.424479i | \(-0.139543\pi\) |
0.0851092 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.6040 | + | 2.31657i | −0.448499 | + | 0.0979806i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.44509 | − | 1.72696i | 0.272112 | − | 0.0729122i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.8306 | + | 7.45719i | 1.17292 | + | 0.314283i | 0.792115 | − | 0.610372i | \(-0.208980\pi\) |
0.380806 | + | 0.924655i | \(0.375647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 41.9582i | − | 1.76208i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.73227 | + | 9.92858i | −0.240309 | + | 0.416228i | −0.960802 | − | 0.277234i | \(-0.910582\pi\) |
0.720493 | + | 0.693462i | \(0.243915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.41332i | − | 0.268389i | −0.990955 | − | 0.134195i | \(-0.957155\pi\) | ||
0.990955 | − | 0.134195i | \(-0.0428447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.15840 | + | 3.15840i | 0.131944 | + | 0.131944i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3236 | 0.471407 | 0.235704 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235704 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0695010 | − | 0.259381i | 0.00288836 | − | 0.0107795i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7124 | + | 35.8749i | 0.859295 | + | 1.48834i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.6352 | + | 27.0810i | −0.647544 | + | 1.12158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.2749 | + | 29.9211i | −0.713013 | + | 1.23497i | 0.250708 | + | 0.968063i | \(0.419336\pi\) |
−0.963721 | + | 0.266911i | \(0.913997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.60873 | + | 2.78640i | 0.0662865 | + | 0.114812i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.242467 | + | 0.904898i | −0.00997375 | + | 0.0372225i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.05726 | −0.371937 | −0.185969 | − | 0.982556i | \(-0.559542\pi\) | ||||
−0.185969 | + | 0.982556i | \(0.559542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.08321 | + | 3.08321i | 0.126187 | + | 0.126187i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.99982i | 0.245146i | 0.992459 | + | 0.122573i | \(0.0391146\pi\) | ||||
−0.992459 | + | 0.122573i | \(0.960885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2508 | + | 33.3433i | −0.785256 | + | 1.36010i | 0.143590 | + | 0.989637i | \(0.454135\pi\) |
−0.928846 | + | 0.370466i | \(0.879198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.9022i | 0.729034i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.53668 | − | 1.75150i | −0.265316 | − | 0.0710911i | 0.123709 | − | 0.992319i | \(-0.460521\pi\) |
−0.389024 | + | 0.921227i | \(0.627188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.20396 | + | 2.46619i | −0.372963 | + | 0.0999352i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.69540 | − | 5.21702i | −0.109044 | − | 0.211058i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.1115 | + | 10.4567i | 0.731517 | + | 0.422342i | 0.818977 | − | 0.573826i | \(-0.194542\pi\) |
−0.0874596 | + | 0.996168i | \(0.527875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.32411 | − | 10.9537i | −0.254599 | − | 0.440978i | 0.710188 | − | 0.704012i | \(-0.248610\pi\) |
−0.964786 | + | 0.263034i | \(0.915277\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.45857 | + | 1.45857i | 0.0586247 | + | 0.0586247i | 0.735811 | − | 0.677187i | \(-0.236801\pi\) |
−0.677187 | + | 0.735811i | \(0.736801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.978562 | − | 0.564973i | −0.0392683 | − | 0.0226716i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.25830 | + | 7.25830i | −0.290798 | + | 0.290798i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.283169 | − | 1.05680i | −0.0113087 | − | 0.0422046i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.9521 | − | 27.9521i | 1.11452 | − | 1.11452i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4552 | − | 3.60532i | −0.535644 | − | 0.143525i | −0.0191508 | − | 0.999817i | \(-0.506096\pi\) |
−0.516493 | + | 0.856291i | \(0.672763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.426970 | − | 1.59347i | 0.0169705 | − | 0.0633349i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.98828 | + | 63.9211i | −0.118400 | + | 2.53264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.39544 | − | 12.6719i | −0.134321 | − | 0.501294i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.8804 | − | 14.3647i | 0.982716 | − | 0.567371i | 0.0796269 | − | 0.996825i | \(-0.474627\pi\) |
0.903089 | + | 0.429453i | \(0.141294\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.92050 | − | 5.15025i | 0.351790 | − | 0.203106i | −0.313683 | − | 0.949528i | \(-0.601563\pi\) |
0.665473 | + | 0.746422i | \(0.268230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.63436 | − | 2.31357i | 0.339452 | − | 0.0909558i | −0.0850664 | − | 0.996375i | \(-0.527110\pi\) |
0.424518 | + | 0.905420i | \(0.360444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.5795 | 1.59288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.84906 | −0.150857 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.13021 | + | 2.44643i | −0.357293 | + | 0.0957363i | −0.433000 | − | 0.901394i | \(-0.642545\pi\) |
0.0757076 | + | 0.997130i | \(0.475878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.2299 | − | 8.79296i | 0.594173 | − | 0.343046i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.4663 | − | 19.8991i | 1.34262 | − | 0.775160i | 0.355426 | − | 0.934704i | \(-0.384336\pi\) |
0.987191 | + | 0.159544i | \(0.0510025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.86551 | + | 18.1583i | 0.189246 | + | 0.706277i | 0.993682 | + | 0.112236i | \(0.0358014\pi\) |
−0.804435 | + | 0.594040i | \(0.797532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.65696 | + | 5.14260i | 0.103188 | + | 0.199722i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.49055 | − | 5.56280i | 0.0577142 | − | 0.215392i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.20961 | + | 0.324113i | 0.0467660 | + | 0.0125309i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.6938 | + | 31.6938i | −1.22352 | + | 1.22352i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5669 | − | 43.1681i | −0.445870 | − | 1.66401i | −0.713630 | − | 0.700522i | \(-0.752950\pi\) |
0.267761 | − | 0.963485i | \(-0.413716\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.55951 | − | 1.55951i | 0.0599367 | − | 0.0599367i | −0.676503 | − | 0.736440i | \(-0.736505\pi\) |
0.736440 | + | 0.676503i | \(0.236505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0101 | − | 20.7904i | −1.38194 | − | 0.797864i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.26736 | + | 1.26736i | 0.0485654 | + | 0.0485654i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.814127 | + | 1.41011i | 0.0311517 | + | 0.0539563i | 0.881181 | − | 0.472779i | \(-0.156749\pi\) |
−0.850029 | + | 0.526735i | \(0.823416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.79216 | − | 2.76675i | −0.182832 | − | 0.105558i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.8466 | − | 8.23708i | −0.984677 | − | 0.313808i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.4385 | − | 8.15597i | 1.15793 | − | 0.310268i | 0.371794 | − | 0.928315i | \(-0.378743\pi\) |
0.786141 | + | 0.618047i | \(0.212076\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −58.6501 | − | 15.7153i | −2.22793 | − | 0.596973i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 17.0001i | − | 0.643923i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.196096 | + | 0.339648i | −0.00741702 | + | 0.0128467i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.9348i | 1.65939i | 0.558215 | + | 0.829697i | \(0.311487\pi\) | ||||
−0.558215 | + | 0.829697i | \(0.688513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.58330 | − | 4.58330i | −0.172862 | − | 0.172862i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.43371 | 0.317182 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.94108 | + | 14.7083i | −0.148011 | + | 0.552383i | 0.851592 | + | 0.524205i | \(0.175637\pi\) |
−0.999603 | + | 0.0281782i | \(0.991029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.6955 | − | 35.8456i | −0.776140 | − | 1.34431i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.16317 | − | 2.01467i | 0.0435611 | − | 0.0754500i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.668023 | + | 1.15705i | −0.0249478 | + | 0.0432108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.45929 | + | 16.3840i | 0.352772 | + | 0.611019i | 0.986734 | − | 0.162345i | \(-0.0519057\pi\) |
−0.633962 | + | 0.773364i | \(0.718572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.79639 | − | 10.4363i | 0.104143 | − | 0.388668i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.09436 | 0.226652 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.2973 | − | 12.2973i | −0.456082 | − | 0.456082i | 0.441285 | − | 0.897367i | \(-0.354523\pi\) |
−0.897367 | + | 0.441285i | \(0.854523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.6415i | 0.875611i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.60429 | + | 16.6351i | −0.355228 | + | 0.615272i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 28.9122i | − | 1.06790i | −0.845517 | − | 0.533948i | \(-0.820708\pi\) | ||
0.845517 | − | 0.533948i | \(-0.179292\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.4731 | + | 6.55754i | 0.901477 | + | 0.241550i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.63268 | − | 0.973373i | 0.133630 | − | 0.0358061i | −0.191384 | − | 0.981515i | \(-0.561298\pi\) |
0.325014 | + | 0.945709i | \(0.394631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.843232 | − | 0.435661i | 0.0309769 | − | 0.0160044i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.7182 | − | 17.7352i | −1.12694 | − | 0.650641i | −0.183779 | − | 0.982968i | \(-0.558833\pi\) |
−0.943164 | + | 0.332327i | \(0.892166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2270 | − | 21.1778i | −0.447363 | − | 0.774855i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.1447 | + | 50.1447i | 1.83225 | + | 1.83225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5593 | − | 7.25111i | −0.458295 | − | 0.264597i | 0.253032 | − | 0.967458i | \(-0.418572\pi\) |
−0.711327 | + | 0.702861i | \(0.751906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.76332 | + | 3.76332i | −0.137143 | + | 0.137143i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.92051 | − | 37.0239i | −0.360567 | − | 1.34566i | −0.873332 | − | 0.487126i | \(-0.838045\pi\) |
0.512765 | − | 0.858529i | \(-0.328621\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.559364 | + | 0.559364i | −0.0203036 | + | 0.0203036i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.7432 | + | 9.84532i | 1.33194 | + | 0.356892i | 0.853438 | − | 0.521194i | \(-0.174513\pi\) |
0.478502 | + | 0.878086i | \(0.341180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.35832 | − | 23.7296i | 0.230187 | − | 0.859068i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.51338 | + | 34.3920i | 0.271292 | + | 1.24182i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.83503 | − | 29.2407i | −0.282538 | − | 1.05445i | −0.950619 | − | 0.310359i | \(-0.899551\pi\) |
0.668081 | − | 0.744089i | \(-0.267116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.53870 | − | 2.04307i | 0.127443 | − | 0.0735793i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.0681 | − | 9.27689i | 0.577928 | − | 0.333667i | −0.182382 | − | 0.983228i | \(-0.558381\pi\) |
0.760309 | + | 0.649561i | \(0.225047\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.48995 | − | 2.00693i | 0.268701 | − | 0.0719981i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.78750 | −0.0998724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5668 | −0.664373 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.9838 | − | 2.94309i | 0.392527 | − | 0.105177i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8837 | − | 15.5213i | 0.958302 | − | 0.553276i | 0.0626520 | − | 0.998035i | \(-0.480044\pi\) |
0.895650 | + | 0.444759i | \(0.146711\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.57024 | − | 3.21598i | 0.198306 | − | 0.114492i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.12330 | − | 19.1204i | −0.182164 | − | 0.679844i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7293 | − | 20.9930i | −1.16225 | − | 0.745483i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.19057 | + | 23.1035i | −0.219281 | + | 0.818368i | 0.765334 | + | 0.643633i | \(0.222574\pi\) |
−0.984615 | + | 0.174735i | \(0.944093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0380 | − | 2.68967i | −0.355119 | − | 0.0951537i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.28475 | − | 4.28475i | 0.151394 | − | 0.151394i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.44169 | − | 24.0407i | −0.227322 | − | 0.848378i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.519434 | − | 0.519434i | 0.0182850 | − | 0.0182850i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.8616 | + | 18.9726i | 1.15535 | + | 0.667043i | 0.950186 | − | 0.311684i | \(-0.100893\pi\) |
0.205166 | + | 0.978727i | \(0.434227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4061 | + | 26.4061i | 0.927242 | + | 0.927242i | 0.997527 | − | 0.0702846i | \(-0.0223907\pi\) |
−0.0702846 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.24405 | − | 3.88681i | −0.0787023 | − | 0.136316i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.72766 | + | 1.57481i | 0.0954287 | + | 0.0550958i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.45982 | − | 52.6170i | 0.0859530 | − | 1.83859i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.49104 | − | 2.54312i | 0.331240 | − | 0.0887554i | −0.0893662 | − | 0.995999i | \(-0.528484\pi\) |
0.420606 | + | 0.907243i | \(0.361817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0556 | + | 3.49823i | 0.455089 | + | 0.121941i | 0.479080 | − | 0.877771i | \(-0.340970\pi\) |
−0.0239906 | + | 0.999712i | \(0.507637\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5815i | 0.680916i | 0.940260 | + | 0.340458i | \(0.110582\pi\) | ||||
−0.940260 | + | 0.340458i | \(0.889418\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.60308 | + | 11.4369i | −0.229335 | + | 0.397219i | −0.957611 | − | 0.288064i | \(-0.906988\pi\) |
0.728277 | + | 0.685283i | \(0.240322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.614789i | 0.0213268i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 80.0768 | + | 80.0768i | 2.77450 | + | 2.77450i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.59337 | 0.158770 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.51806 | + | 13.1296i | −0.121457 | + | 0.453283i | −0.999689 | − | 0.0249523i | \(-0.992057\pi\) |
0.878232 | + | 0.478235i | \(0.158723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4780 | + | 25.0767i | 0.499242 | + | 0.864713i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.37081 | + | 2.37431i | −0.0472132 | + | 0.0817757i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.6058 | + | 27.0301i | −0.536223 | + | 0.928765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.60206 | − | 4.50689i | −0.0893023 | − | 0.154676i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.21297 | + | 4.52686i | −0.0415801 | + | 0.155179i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.37110 | −0.0469457 | −0.0234728 | − | 0.999724i | \(-0.507472\pi\) | ||||
−0.0234728 | + | 0.999724i | \(0.507472\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5377 | − | 19.5377i | −0.667395 | − | 0.667395i | 0.289718 | − | 0.957112i | \(-0.406439\pi\) |
−0.957112 | + | 0.289718i | \(0.906439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.82578i | 0.232893i | 0.993197 | + | 0.116446i | \(0.0371503\pi\) | ||||
−0.993197 | + | 0.116446i | \(0.962850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66735 | − | 2.88793i | 0.0568231 | − | 0.0984205i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6002i | 0.837401i | 0.908124 | + | 0.418701i | \(0.137514\pi\) | ||||
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.76333 | + | 1.54428i | 0.195733 | + | 0.0524465i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −56.5831 | + | 15.1614i | −1.91945 | + | 0.514315i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.02641 | + | 21.9556i | −0.0347787 | + | 0.743937i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2576 | + | 12.2731i | 0.719461 | + | 0.415381i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.4286 | − | 33.6513i | −0.656057 | − | 1.13632i | −0.981628 | − | 0.190806i | \(-0.938890\pi\) |
0.325571 | − | 0.945518i | \(-0.394444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.18400 | − | 1.18400i | −0.0399353 | − | 0.0399353i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.9837 | − | 14.4243i | −0.841721 | − | 0.485968i | 0.0161277 | − | 0.999870i | \(-0.494866\pi\) |
−0.857849 | + | 0.513902i | \(0.828200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2512 | + | 38.2512i | −1.28725 | + | 1.28725i | −0.350806 | + | 0.936448i | \(0.614092\pi\) |
−0.936448 | + | 0.350806i | \(0.885908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6937 | + | 43.6417i | 0.392638 | + | 1.46534i | 0.825767 | + | 0.564012i | \(0.190743\pi\) |
−0.433129 | + | 0.901332i | \(0.642591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.6964 | + | 50.6964i | −1.70030 | + | 1.70030i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.8601 | + | 9.07280i | 1.13436 | + | 0.303950i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.441025 | + | 1.64593i | −0.0147583 | + | 0.0550789i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.577641 | − | 0.370506i | −0.0192869 | − | 0.0123708i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.05925 | + | 22.6134i | 0.202087 | + | 0.754200i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.5760 | + | 24.0039i | −1.38510 | + | 0.799687i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.26311 | + | 1.88396i | −0.108590 | + | 0.0626943i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3497 | − | 5.98857i | 0.742108 | − | 0.198847i | 0.132093 | − | 0.991237i | \(-0.457830\pi\) |
0.610015 | + | 0.792390i | \(0.291163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.97862 | −0.165130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.3382 | 1.66778 | 0.833890 | − | 0.551931i | \(-0.186109\pi\) | ||||
0.833890 | + | 0.551931i | \(0.186109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.4297 | + | 8.95745i | −1.10636 | + | 0.296448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 58.6216 | − | 33.8452i | 1.93586 | − | 1.11767i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.9629 | − | 16.1444i | 0.922412 | − | 0.532555i | 0.0380085 | − | 0.999277i | \(-0.487899\pi\) |
0.884404 | + | 0.466722i | \(0.154565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.32123 | + | 4.93089i | 0.0435359 | + | 0.162478i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.43769 | − | 15.7358i | −0.113153 | − | 0.517949i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.65078 | + | 6.16079i | −0.0542187 | + | 0.202347i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.2130 | − | 4.88016i | −0.597549 | − | 0.160113i | −0.0526479 | − | 0.998613i | \(-0.516766\pi\) |
−0.544901 | + | 0.838500i | \(0.683433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1302 | − | 13.1302i | 0.430324 | − | 0.430324i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.09327 | + | 4.08015i | 0.0357921 | + | 0.133578i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.7938 | + | 28.7938i | −0.940651 | + | 0.940651i | −0.998335 | − | 0.0576835i | \(-0.981629\pi\) |
0.0576835 | + | 0.998335i | \(0.481629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22253 | − | 0.705830i | −0.0398959 | − | 0.0230339i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7400 | − | 15.7400i | −0.513111 | − | 0.513111i | 0.402367 | − | 0.915478i | \(-0.368187\pi\) |
−0.915478 | + | 0.402367i | \(0.868187\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00773 | + | 1.74544i | 0.0328163 | + | 0.0568394i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.4702 | + | 26.8296i | 1.51008 | + | 0.871845i | 0.999931 | + | 0.0117590i | \(0.00374310\pi\) |
0.510149 | + | 0.860086i | \(0.329590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.1823 | − | 9.91065i | 0.622684 | − | 0.321713i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.40360 | + | 0.911991i | −0.110369 | + | 0.0295733i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.7036 | + | 4.74366i | 0.573475 | + | 0.153662i | 0.533890 | − | 0.845554i | \(-0.320730\pi\) |
0.0395854 | + | 0.999216i | \(0.487396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.96085i | − | 0.257338i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.7970 | − | 42.9496i | 0.800736 | − | 1.38692i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 21.5431i | − | 0.694940i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.6016 | − | 29.6016i | −0.953898 | − | 0.953898i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.0099 | −0.932894 | −0.466447 | − | 0.884549i | \(-0.654466\pi\) | ||||
−0.466447 | + | 0.884549i | \(0.654466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.434734 | − | 1.62245i | 0.0139657 | − | 0.0521206i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.94826 | + | 13.7668i | 0.255072 | + | 0.441797i | 0.964915 | − | 0.262562i | \(-0.0845676\pi\) |
−0.709843 | + | 0.704360i | \(0.751234\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.1235 | + | 71.2280i | −1.31836 | + | 2.28346i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.9877 | + | 36.3517i | −0.671454 | + | 1.16299i | 0.306037 | + | 0.952020i | \(0.400997\pi\) |
−0.977492 | + | 0.210974i | \(0.932337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.28793 | − | 7.42692i | −0.137043 | − | 0.237365i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.75347 | + | 14.0081i | −0.119839 | + | 0.447245i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.2861 | 1.09356 | 0.546779 | − | 0.837277i | \(-0.315854\pi\) | ||||
0.546779 | + | 0.837277i | \(0.315854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.44143 | − | 1.44143i | −0.0458813 | − | 0.0458813i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.27730i | − | 0.0724139i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4379 | − | 35.3995i | 0.649231 | − | 1.12450i | −0.334076 | − | 0.942546i | \(-0.608424\pi\) |
0.983307 | − | 0.181955i | \(-0.0582424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.51127i | 0.143161i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5952 | − | 9.26975i | −1.09564 | − | 0.293576i | −0.334652 | − | 0.942342i | \(-0.608619\pi\) |
−0.760988 | + | 0.648766i | \(0.775285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.93830 | + | 2.39501i | −0.282795 | + | 0.0757748i |
(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.bs.d.293.3 | 20 | ||
5.2 | odd | 4 | 1300.2.bn.d.657.3 | 20 | |||
5.3 | odd | 4 | 260.2.bf.c.137.3 | yes | 20 | ||
5.4 | even | 2 | 260.2.bk.c.33.3 | yes | 20 | ||
13.2 | odd | 12 | 1300.2.bn.d.93.3 | 20 | |||
65.2 | even | 12 | inner | 1300.2.bs.d.457.3 | 20 | ||
65.28 | even | 12 | 260.2.bk.c.197.3 | yes | 20 | ||
65.54 | odd | 12 | 260.2.bf.c.93.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.93.3 | ✓ | 20 | 65.54 | odd | 12 | ||
260.2.bf.c.137.3 | yes | 20 | 5.3 | odd | 4 | ||
260.2.bk.c.33.3 | yes | 20 | 5.4 | even | 2 | ||
260.2.bk.c.197.3 | yes | 20 | 65.28 | even | 12 | ||
1300.2.bn.d.93.3 | 20 | 13.2 | odd | 12 | |||
1300.2.bn.d.657.3 | 20 | 5.2 | odd | 4 | |||
1300.2.bs.d.293.3 | 20 | 1.1 | even | 1 | trivial | ||
1300.2.bs.d.457.3 | 20 | 65.2 | even | 12 | inner |