Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(55,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.14 | ||
Root | \(-1.16433 + 0.802711i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.55 |
Dual form | 756.2.b.f.55.13 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16433 | + | 0.802711i | 0.823303 | + | 0.567602i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.711311 | + | 1.86923i | 0.355655 | + | 0.934617i | ||||
\(5\) | 0.944421i | 0.422358i | 0.977447 | + | 0.211179i | \(0.0677303\pi\) | ||||
−0.977447 | + | 0.211179i | \(0.932270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59468 | + | 0.517335i | 0.980697 | + | 0.195534i | ||||
\(8\) | −0.672257 | + | 2.74738i | −0.237679 | + | 0.971344i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.758097 | + | 1.09961i | −0.239731 | + | 0.347729i | ||||
\(11\) | 3.44501i | 1.03871i | 0.854559 | + | 0.519354i | \(0.173828\pi\) | ||||
−0.854559 | + | 0.519354i | \(0.826172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.04974i | − | 0.568496i | −0.958751 | − | 0.284248i | \(-0.908256\pi\) | ||
0.958751 | − | 0.284248i | \(-0.0917440\pi\) | |||||||
\(14\) | 2.60578 | + | 2.68512i | 0.696425 | + | 0.717630i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.98807 | + | 2.65921i | −0.747018 | + | 0.664803i | ||||
\(17\) | − | 4.37401i | − | 1.06085i | −0.847731 | − | 0.530426i | \(-0.822032\pi\) | ||
0.847731 | − | 0.530426i | \(-0.177968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09657 | −0.251570 | −0.125785 | − | 0.992058i | \(-0.540145\pi\) | ||||
−0.125785 | + | 0.992058i | \(0.540145\pi\) | |||||||
\(20\) | −1.76534 | + | 0.671777i | −0.394743 | + | 0.150214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.76534 | + | 4.01111i | −0.589574 | + | 0.855172i | ||||
\(23\) | 3.80465i | 0.793325i | 0.917965 | + | 0.396662i | \(0.129832\pi\) | ||||
−0.917965 | + | 0.396662i | \(0.870168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.10807 | 0.821614 | ||||||||
\(26\) | 1.64535 | − | 2.38657i | 0.322680 | − | 0.468045i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.878604 | + | 5.21805i | 0.166041 | + | 0.986119i | ||||
\(29\) | −4.94141 | −0.917598 | −0.458799 | − | 0.888540i | \(-0.651720\pi\) | ||||
−0.458799 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.40936 | −0.791944 | −0.395972 | − | 0.918263i | \(-0.629592\pi\) | ||||
−0.395972 | + | 0.918263i | \(0.629592\pi\) | |||||||
\(32\) | −5.61367 | + | 0.697633i | −0.992366 | + | 0.123325i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.51106 | − | 5.09277i | 0.602142 | − | 0.873403i | ||||
\(35\) | −0.488582 | + | 2.45047i | −0.0825854 | + | 0.414205i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.97615 | 1.14687 | 0.573436 | − | 0.819251i | \(-0.305610\pi\) | ||||
0.573436 | + | 0.819251i | \(0.305610\pi\) | |||||||
\(38\) | −1.27676 | − | 0.880227i | −0.207118 | − | 0.142792i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.59468 | − | 0.634894i | −0.410255 | − | 0.100385i | ||||
\(41\) | 7.38669i | 1.15361i | 0.816883 | + | 0.576804i | \(0.195700\pi\) | ||||
−0.816883 | + | 0.576804i | \(0.804300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.99177i | − | 0.761239i | −0.924732 | − | 0.380619i | \(-0.875711\pi\) | ||
0.924732 | − | 0.380619i | \(-0.124289\pi\) | |||||||
\(44\) | −6.43953 | + | 2.45047i | −0.970795 | + | 0.369422i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.05403 | + | 4.42985i | −0.450293 | + | 0.653146i | ||||
\(47\) | 9.82139 | 1.43260 | 0.716299 | − | 0.697794i | \(-0.245835\pi\) | ||||
0.716299 | + | 0.697794i | \(0.245835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46473 | + | 2.68464i | 0.923533 | + | 0.383519i | ||||
\(50\) | 4.78313 | + | 3.29759i | 0.676437 | + | 0.466350i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.83145 | − | 1.45800i | 0.531326 | − | 0.202189i | ||||
\(53\) | −1.34451 | −0.184683 | −0.0923416 | − | 0.995727i | \(-0.529435\pi\) | ||||
−0.0923416 | + | 0.995727i | \(0.529435\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.25354 | −0.438707 | ||||||||
\(56\) | −3.16560 | + | 6.78078i | −0.423022 | + | 0.906120i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.75342 | − | 3.96653i | −0.755461 | − | 0.520831i | ||||
\(59\) | −9.08422 | −1.18266 | −0.591332 | − | 0.806428i | \(-0.701398\pi\) | ||||
−0.591332 | + | 0.806428i | \(0.701398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.06524i | − | 1.16068i | −0.814373 | − | 0.580342i | \(-0.802919\pi\) | ||
0.814373 | − | 0.580342i | \(-0.197081\pi\) | |||||||
\(62\) | −5.13393 | − | 3.53944i | −0.652010 | − | 0.449509i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.09614 | − | 3.69388i | −0.887018 | − | 0.461735i | ||||
\(65\) | 1.93582 | 0.240109 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.7607i | − | 1.43680i | −0.695632 | − | 0.718399i | \(-0.744875\pi\) | ||
0.695632 | − | 0.718399i | \(-0.255125\pi\) | |||||||
\(68\) | 8.17604 | − | 3.11128i | 0.991491 | − | 0.377298i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.53589 | + | 2.46096i | −0.303097 | + | 0.294141i | ||||
\(71\) | − | 0.593808i | − | 0.0704720i | −0.999379 | − | 0.0352360i | \(-0.988782\pi\) | ||
0.999379 | − | 0.0352360i | \(-0.0112183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0018i | 1.75583i | 0.478818 | + | 0.877914i | \(0.341065\pi\) | ||||
−0.478818 | + | 0.877914i | \(0.658935\pi\) | |||||||
\(74\) | 8.12251 | + | 5.59983i | 0.944223 | + | 0.650967i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.780001 | − | 2.04974i | −0.0894722 | − | 0.235122i | ||||
\(77\) | −1.78222 | + | 8.93869i | −0.203103 | + | 1.01866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.27553i | − | 1.04358i | −0.853074 | − | 0.521789i | \(-0.825265\pi\) | ||
0.853074 | − | 0.521789i | \(-0.174735\pi\) | |||||||
\(80\) | −2.51142 | − | 2.82200i | −0.280785 | − | 0.315509i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.92937 | + | 8.60052i | −0.654790 | + | 0.949768i | ||||
\(83\) | 2.26282 | 0.248377 | 0.124189 | − | 0.992259i | \(-0.460367\pi\) | ||||
0.124189 | + | 0.992259i | \(0.460367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.13090 | 0.448059 | ||||||||
\(86\) | 4.00695 | − | 5.81205i | 0.432081 | − | 0.626730i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.46473 | − | 2.31593i | −1.00894 | − | 0.246879i | ||||
\(89\) | − | 12.5590i | − | 1.33125i | −0.746288 | − | 0.665624i | \(-0.768166\pi\) | ||
0.746288 | − | 0.665624i | \(-0.231834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06040 | − | 5.31843i | 0.111160 | − | 0.557523i | ||||
\(92\) | −7.11178 | + | 2.70629i | −0.741455 | + | 0.282150i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.4353 | + | 7.88374i | 1.17946 | + | 0.813145i | ||||
\(95\) | − | 1.03562i | − | 0.106253i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.8330i | − | 1.91220i | −0.293044 | − | 0.956099i | \(-0.594668\pi\) | ||
0.293044 | − | 0.956099i | \(-0.405332\pi\) | |||||||
\(98\) | 5.37207 | + | 8.31510i | 0.542661 | + | 0.839952i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.92211 | + | 7.67894i | 0.292211 | + | 0.767894i | ||||
\(101\) | − | 8.33111i | − | 0.828976i | −0.910055 | − | 0.414488i | \(-0.863961\pi\) | ||
0.910055 | − | 0.414488i | \(-0.136039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.50215 | 0.837742 | 0.418871 | − | 0.908046i | \(-0.362426\pi\) | ||||
0.418871 | + | 0.908046i | \(0.362426\pi\) | |||||||
\(104\) | 5.63141 | + | 1.37795i | 0.552205 | + | 0.135119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.56545 | − | 1.07926i | −0.152050 | − | 0.104827i | ||||
\(107\) | 2.87772i | 0.278199i | 0.990278 | + | 0.139100i | \(0.0444208\pi\) | ||||
−0.990278 | + | 0.139100i | \(0.955579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.97615 | 0.668194 | 0.334097 | − | 0.942539i | \(-0.391569\pi\) | ||||
0.334097 | + | 0.942539i | \(0.391569\pi\) | |||||||
\(110\) | −3.78818 | − | 2.61165i | −0.361189 | − | 0.249011i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.12880 | + | 5.35397i | −0.862590 | + | 0.505903i | ||||
\(113\) | 12.6043 | 1.18571 | 0.592857 | − | 0.805308i | \(-0.298000\pi\) | ||||
0.592857 | + | 0.805308i | \(0.298000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59319 | −0.335067 | ||||||||
\(116\) | −3.51488 | − | 9.23666i | −0.326349 | − | 0.857603i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5770 | − | 7.29200i | −0.973691 | − | 0.671283i | ||||
\(119\) | 2.26282 | − | 11.3491i | 0.207433 | − | 1.04037i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.868079 | −0.0789163 | ||||||||
\(122\) | 7.27676 | − | 10.5549i | 0.658807 | − | 0.955595i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.13643 | − | 8.24213i | −0.281659 | − | 0.740165i | ||||
\(125\) | 8.60185i | 0.769373i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.80359i | − | 0.692457i | −0.938150 | − | 0.346228i | \(-0.887462\pi\) | ||
0.938150 | − | 0.346228i | \(-0.112538\pi\) | |||||||
\(128\) | −5.29710 | − | 9.99703i | −0.468202 | − | 0.883621i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.25393 | + | 1.55390i | 0.197682 | + | 0.136286i | ||||
\(131\) | −4.28566 | −0.374440 | −0.187220 | − | 0.982318i | \(-0.559948\pi\) | ||||
−0.187220 | + | 0.982318i | \(0.559948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.84524 | − | 0.567293i | −0.246714 | − | 0.0491905i | ||||
\(134\) | 9.44044 | − | 13.6933i | 0.815529 | − | 1.18292i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0170 | + | 2.94045i | 1.03045 | + | 0.252142i | ||||
\(137\) | 7.31387 | 0.624866 | 0.312433 | − | 0.949940i | \(-0.398856\pi\) | ||||
0.312433 | + | 0.949940i | \(0.398856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.44290 | −0.716117 | −0.358059 | − | 0.933699i | \(-0.616561\pi\) | ||||
−0.358059 | + | 0.933699i | \(0.616561\pi\) | |||||||
\(140\) | −4.92804 | + | 0.829773i | −0.416495 | + | 0.0701286i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.476656 | − | 0.691386i | 0.0400001 | − | 0.0580198i | ||||
\(143\) | 7.06138 | 0.590502 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.66678i | − | 0.387555i | ||||||
\(146\) | −12.0421 | + | 17.4670i | −0.996612 | + | 1.44558i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.96221 | + | 13.0401i | 0.407891 | + | 1.07189i | ||||
\(149\) | −2.71211 | −0.222185 | −0.111093 | − | 0.993810i | \(-0.535435\pi\) | ||||
−0.111093 | + | 0.993810i | \(0.535435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2805i | 1.24351i | 0.783211 | + | 0.621756i | \(0.213580\pi\) | ||||
−0.783211 | + | 0.621756i | \(0.786420\pi\) | |||||||
\(152\) | 0.737175 | − | 3.01268i | 0.0597928 | − | 0.244361i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.25027 | + | 8.97695i | −0.745408 | + | 0.723383i | ||||
\(155\) | − | 4.16429i | − | 0.334484i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6823i | 0.932347i | 0.884693 | + | 0.466173i | \(0.154368\pi\) | ||||
−0.884693 | + | 0.466173i | \(0.845632\pi\) | |||||||
\(158\) | 7.44557 | − | 10.7997i | 0.592338 | − | 0.859182i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.658859 | − | 5.30167i | −0.0520874 | − | 0.419134i | ||||
\(161\) | −1.96828 | + | 9.87185i | −0.155122 | + | 0.778011i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.15169i | 0.638490i | 0.947672 | + | 0.319245i | \(0.103429\pi\) | ||||
−0.947672 | + | 0.319245i | \(0.896571\pi\) | |||||||
\(164\) | −13.8075 | + | 5.25423i | −1.07818 | + | 0.410287i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.63467 | + | 1.81639i | 0.204490 | + | 0.140980i | ||||
\(167\) | −22.8828 | −1.77072 | −0.885361 | − | 0.464904i | \(-0.846089\pi\) | ||||
−0.885361 | + | 0.464904i | \(0.846089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.79855 | 0.676812 | ||||||||
\(170\) | 4.80972 | + | 3.31592i | 0.368889 | + | 0.254320i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.33080 | − | 3.55070i | 0.711467 | − | 0.270739i | ||||
\(173\) | − | 21.2156i | − | 1.61300i | −0.591237 | − | 0.806498i | \(-0.701360\pi\) | ||
0.591237 | − | 0.806498i | \(-0.298640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6591 | + | 2.12525i | 0.805754 | + | 0.160654i | ||||
\(176\) | −9.16101 | − | 10.2939i | −0.690537 | − | 0.775935i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.0812 | − | 14.6227i | 0.755619 | − | 1.09602i | ||||
\(179\) | − | 21.7448i | − | 1.62529i | −0.582762 | − | 0.812643i | \(-0.698028\pi\) | ||
0.582762 | − | 0.812643i | \(-0.301972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.31447i | 0.543680i | 0.962342 | + | 0.271840i | \(0.0876322\pi\) | ||||
−0.962342 | + | 0.271840i | \(0.912368\pi\) | |||||||
\(182\) | 5.50381 | − | 5.34119i | 0.407970 | − | 0.395915i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.4528 | − | 2.55770i | −0.770591 | − | 0.188556i | ||||
\(185\) | 6.58842i | 0.484391i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0685 | 1.10192 | ||||||||
\(188\) | 6.98606 | + | 18.3585i | 0.509511 | + | 1.33893i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.831305 | − | 1.20580i | 0.0603092 | − | 0.0874781i | ||||
\(191\) | − | 15.0890i | − | 1.09180i | −0.837850 | − | 0.545900i | \(-0.816188\pi\) | ||
0.837850 | − | 0.545900i | \(-0.183812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.37089 | −0.314624 | −0.157312 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157312 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(194\) | 15.1174 | − | 21.9277i | 1.08537 | − | 1.57432i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.419782 | + | 13.9937i | −0.0299844 | + | 0.999550i | ||||
\(197\) | −15.6005 | −1.11149 | −0.555746 | − | 0.831352i | \(-0.687567\pi\) | ||||
−0.555746 | + | 0.831352i | \(0.687567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3171 | −1.44024 | −0.720120 | − | 0.693849i | \(-0.755913\pi\) | ||||
−0.720120 | + | 0.693849i | \(0.755913\pi\) | |||||||
\(200\) | −2.76168 | + | 11.2864i | −0.195280 | + | 0.798069i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.68747 | − | 9.70013i | 0.470529 | − | 0.682499i | ||||
\(203\) | −12.8214 | − | 2.55637i | −0.899885 | − | 0.179422i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.97615 | −0.487235 | ||||||||
\(206\) | 9.89928 | + | 6.82477i | 0.689715 | + | 0.475504i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.45070 | + | 6.12478i | 0.377938 | + | 0.424677i | ||||
\(209\) | − | 3.77769i | − | 0.261308i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.7839i | 1.98157i | 0.135459 | + | 0.990783i | \(0.456749\pi\) | ||||
−0.135459 | + | 0.990783i | \(0.543251\pi\) | |||||||
\(212\) | −0.956367 | − | 2.51321i | −0.0656836 | − | 0.172608i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.30997 | + | 3.35060i | −0.157906 | + | 0.229042i | ||||
\(215\) | 4.71434 | 0.321515 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4409 | − | 2.28111i | −0.776657 | − | 0.154852i | ||||
\(218\) | 8.12251 | + | 5.59983i | 0.550126 | + | 0.379268i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.31428 | − | 6.08163i | −0.156029 | − | 0.410023i | ||||
\(221\) | −8.96558 | −0.603091 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3145 | −0.824643 | −0.412321 | − | 0.911038i | \(-0.635282\pi\) | ||||
−0.412321 | + | 0.911038i | \(0.635282\pi\) | |||||||
\(224\) | −14.9266 | − | 1.09401i | −0.997325 | − | 0.0730969i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6755 | + | 10.1176i | 0.976202 | + | 0.673014i | ||||
\(227\) | 24.9056 | 1.65304 | 0.826522 | − | 0.562905i | \(-0.190316\pi\) | ||||
0.826522 | + | 0.562905i | \(0.190316\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.63253i | − | 0.636535i | −0.948001 | − | 0.318268i | \(-0.896899\pi\) | ||
0.948001 | − | 0.318268i | \(-0.103101\pi\) | |||||||
\(230\) | −4.18365 | − | 2.88430i | −0.275862 | − | 0.190185i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.32190 | − | 13.5759i | 0.218093 | − | 0.891303i | ||||
\(233\) | 25.9431 | 1.69959 | 0.849794 | − | 0.527115i | \(-0.176726\pi\) | ||||
0.849794 | + | 0.527115i | \(0.176726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.27553i | 0.605069i | ||||||||
\(236\) | −6.46170 | − | 16.9805i | −0.420621 | − | 1.10534i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.7447 | − | 11.3977i | 0.761299 | − | 0.738804i | ||||
\(239\) | − | 7.45731i | − | 0.482373i | −0.970479 | − | 0.241187i | \(-0.922463\pi\) | ||
0.970479 | − | 0.241187i | \(-0.0775366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0962i | 1.48776i | 0.668314 | + | 0.743879i | \(0.267016\pi\) | ||||
−0.668314 | + | 0.743879i | \(0.732984\pi\) | |||||||
\(242\) | −1.01073 | − | 0.696817i | −0.0649720 | − | 0.0447931i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.9451 | − | 6.44820i | 1.08480 | − | 0.412804i | ||||
\(245\) | −2.53543 | + | 6.10543i | −0.161983 | + | 0.390062i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24768i | 0.143017i | ||||||||
\(248\) | 2.96422 | − | 12.1142i | 0.188228 | − | 0.769250i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.90480 | + | 10.0154i | −0.436698 | + | 0.633427i | ||||
\(251\) | 1.28566 | 0.0811502 | 0.0405751 | − | 0.999176i | \(-0.487081\pi\) | ||||
0.0405751 | + | 0.999176i | \(0.487081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1071 | −0.824033 | ||||||||
\(254\) | 6.26402 | − | 9.08592i | 0.393040 | − | 0.570101i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.85717 | − | 15.8919i | 0.116073 | − | 0.993241i | ||||
\(257\) | − | 16.4054i | − | 1.02334i | −0.859181 | − | 0.511672i | \(-0.829026\pi\) | ||
0.859181 | − | 0.511672i | \(-0.170974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.1009 | + | 3.60900i | 1.12473 | + | 0.224253i | ||||
\(260\) | 1.37697 | + | 3.61850i | 0.0853961 | + | 0.224410i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.98991 | − | 3.44015i | −0.308277 | − | 0.212533i | ||||
\(263\) | 23.3095i | 1.43732i | 0.695360 | + | 0.718661i | \(0.255245\pi\) | ||||
−0.695360 | + | 0.718661i | \(0.744755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.26979i | − | 0.0780024i | ||||||
\(266\) | −2.85742 | − | 2.94442i | −0.175200 | − | 0.180534i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.9835 | − | 8.36551i | 1.34286 | − | 0.511005i | ||||
\(269\) | 14.6853i | 0.895378i | 0.894189 | + | 0.447689i | \(0.147753\pi\) | ||||
−0.894189 | + | 0.447689i | \(0.852247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4778 | 1.18319 | 0.591597 | − | 0.806234i | \(-0.298498\pi\) | ||||
0.591597 | + | 0.806234i | \(0.298498\pi\) | |||||||
\(272\) | 11.6314 | + | 13.0698i | 0.705258 | + | 0.792476i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.51574 | + | 5.87093i | 0.514454 | + | 0.354676i | ||||
\(275\) | 14.1523i | 0.853417i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8828 | −1.25472 | −0.627362 | − | 0.778728i | \(-0.715865\pi\) | ||||
−0.627362 | + | 0.778728i | \(0.715865\pi\) | |||||||
\(278\) | −9.83029 | − | 6.77721i | −0.589582 | − | 0.406470i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.40391 | − | 2.98966i | −0.382707 | − | 0.178667i | ||||
\(281\) | 13.9070 | 0.829622 | 0.414811 | − | 0.909908i | \(-0.363848\pi\) | ||||
0.414811 | + | 0.909908i | \(0.363848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.0609 | −1.25194 | −0.625971 | − | 0.779846i | \(-0.715297\pi\) | ||||
−0.625971 | + | 0.779846i | \(0.715297\pi\) | |||||||
\(284\) | 1.10997 | − | 0.422382i | 0.0658643 | − | 0.0250637i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.22175 | + | 5.66825i | 0.486162 | + | 0.335170i | ||||
\(287\) | −3.82139 | + | 19.1661i | −0.225570 | + | 1.13134i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.13192 | −0.125407 | ||||||||
\(290\) | 3.74607 | − | 5.43365i | 0.219977 | − | 0.319075i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.0419 | + | 10.6709i | −1.64103 | + | 0.624470i | ||||
\(293\) | 16.9330i | 0.989234i | 0.869111 | + | 0.494617i | \(0.164692\pi\) | ||||
−0.869111 | + | 0.494617i | \(0.835308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.57933i | − | 0.499508i | ||||||
\(296\) | −4.68976 | + | 19.1661i | −0.272587 | + | 1.11401i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.15779 | − | 2.17704i | −0.182926 | − | 0.126113i | ||||
\(299\) | 7.79855 | 0.451002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.58242 | − | 12.9521i | 0.148848 | − | 0.746544i | ||||
\(302\) | −12.2658 | + | 17.7915i | −0.705820 | + | 1.02379i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.27663 | − | 2.91601i | 0.187927 | − | 0.167245i | ||||
\(305\) | 8.56140 | 0.490225 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.41866 | 0.423405 | 0.211703 | − | 0.977334i | \(-0.432099\pi\) | ||||
0.211703 | + | 0.977334i | \(0.432099\pi\) | |||||||
\(308\) | −17.9762 | + | 3.02680i | −1.02429 | + | 0.172468i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.34272 | − | 4.84860i | 0.189854 | − | 0.275382i | ||||
\(311\) | −9.23999 | −0.523952 | −0.261976 | − | 0.965074i | \(-0.584374\pi\) | ||||
−0.261976 | + | 0.965074i | \(0.584374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.80283i | − | 0.384519i | −0.981344 | − | 0.192259i | \(-0.938419\pi\) | ||
0.981344 | − | 0.192259i | \(-0.0615815\pi\) | |||||||
\(314\) | −9.37749 | + | 13.6020i | −0.529202 | + | 0.767604i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.3381 | − | 6.59779i | 0.975347 | − | 0.371154i | ||||
\(317\) | −32.7972 | −1.84208 | −0.921038 | − | 0.389472i | \(-0.872658\pi\) | ||||
−0.921038 | + | 0.389472i | \(0.872658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.0232i | − | 0.953117i | ||||||
\(320\) | 3.48858 | − | 6.70175i | 0.195018 | − | 0.374639i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.2160 | + | 9.91410i | −0.569313 | + | 0.552491i | ||||
\(323\) | 4.79639i | 0.266879i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 8.42048i | − | 0.467084i | ||||||
\(326\) | −6.54345 | + | 9.49123i | −0.362408 | + | 0.525670i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.2940 | − | 4.96575i | −1.12055 | − | 0.274188i | ||||
\(329\) | 25.4834 | + | 5.08095i | 1.40494 | + | 0.280122i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.58896i | 0.472092i | 0.971742 | + | 0.236046i | \(0.0758516\pi\) | ||||
−0.971742 | + | 0.236046i | \(0.924148\pi\) | |||||||
\(332\) | 1.60957 | + | 4.22975i | 0.0883367 | + | 0.232138i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.6430 | − | 18.3682i | −1.45784 | − | 1.00507i | ||||
\(335\) | 11.1071 | 0.606843 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.4652 | −1.44165 | −0.720825 | − | 0.693117i | \(-0.756237\pi\) | ||||
−0.720825 | + | 0.693117i | \(0.756237\pi\) | |||||||
\(338\) | 10.2444 | + | 7.06269i | 0.557221 | + | 0.384160i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.93836 | + | 7.72163i | 0.159355 | + | 0.418764i | ||||
\(341\) | − | 15.1903i | − | 0.822600i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.3850 | + | 10.3102i | 0.830715 | + | 0.556699i | ||||
\(344\) | 13.7143 | + | 3.35575i | 0.739424 | + | 0.180930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.0300 | − | 24.7019i | 0.915540 | − | 1.32798i | ||||
\(347\) | 12.6572i | 0.679475i | 0.940520 | + | 0.339738i | \(0.110338\pi\) | ||||
−0.940520 | + | 0.339738i | \(0.889662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.0876i | 1.44997i | 0.688767 | + | 0.724983i | \(0.258152\pi\) | ||||
−0.688767 | + | 0.724983i | \(0.741848\pi\) | |||||||
\(350\) | 10.7047 | + | 11.0307i | 0.572192 | + | 0.589614i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.40335 | − | 19.3391i | −0.128099 | − | 1.03078i | ||||
\(353\) | − | 3.28343i | − | 0.174759i | −0.996175 | − | 0.0873796i | \(-0.972151\pi\) | ||
0.996175 | − | 0.0873796i | \(-0.0278493\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.560805 | 0.0297644 | ||||||||
\(356\) | 23.4756 | − | 8.93332i | 1.24421 | − | 0.473465i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4548 | − | 25.3181i | 0.922516 | − | 1.33810i | ||||
\(359\) | − | 3.16696i | − | 0.167146i | −0.996502 | − | 0.0835730i | \(-0.973367\pi\) | ||
0.996502 | − | 0.0835730i | \(-0.0266332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7975 | −0.936713 | ||||||||
\(362\) | −5.87140 | + | 8.51643i | −0.308594 | + | 0.447613i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.6957 | − | 1.80091i | 0.560605 | − | 0.0943935i | ||||
\(365\) | −14.1680 | −0.741588 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1586 | −1.20887 | −0.604436 | − | 0.796654i | \(-0.706601\pi\) | ||||
−0.604436 | + | 0.796654i | \(0.706601\pi\) | |||||||
\(368\) | −10.1174 | − | 11.3686i | −0.527405 | − | 0.592628i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.28860 | + | 7.67107i | −0.274941 | + | 0.398800i | ||||
\(371\) | −3.48858 | − | 0.695563i | −0.181118 | − | 0.0361119i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0375 | −1.14106 | −0.570530 | − | 0.821277i | \(-0.693262\pi\) | ||||
−0.570530 | + | 0.821277i | \(0.693262\pi\) | |||||||
\(374\) | 17.5446 | + | 12.0956i | 0.907211 | + | 0.625450i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.60250 | + | 26.9830i | −0.340498 | + | 1.39154i | ||||
\(377\) | 10.1286i | 0.521651i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.37455i | − | 0.327438i | −0.986507 | − | 0.163719i | \(-0.947651\pi\) | ||
0.986507 | − | 0.163719i | \(-0.0523491\pi\) | |||||||
\(380\) | 1.93582 | − | 0.736649i | 0.0993055 | − | 0.0377893i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.1121 | − | 17.5685i | 0.619709 | − | 0.898883i | ||||
\(383\) | −8.34704 | −0.426514 | −0.213257 | − | 0.976996i | \(-0.568407\pi\) | ||||
−0.213257 | + | 0.976996i | \(0.568407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44189 | − | 1.68317i | −0.430239 | − | 0.0857822i | ||||
\(386\) | −5.08915 | − | 3.50856i | −0.259031 | − | 0.178581i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.2032 | − | 13.3961i | 1.78717 | − | 0.680084i | ||||
\(389\) | −15.4480 | −0.783245 | −0.391623 | − | 0.920126i | \(-0.628086\pi\) | ||||
−0.391623 | + | 0.920126i | \(0.628086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6416 | 0.841600 | ||||||||
\(392\) | −11.7217 | + | 15.9563i | −0.592033 | + | 0.805914i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.1641 | − | 12.5227i | −0.915095 | − | 0.630885i | ||||
\(395\) | 8.76001 | 0.440764 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.43356i | − | 0.0719482i | −0.999353 | − | 0.0359741i | \(-0.988547\pi\) | ||
0.999353 | − | 0.0359741i | \(-0.0114534\pi\) | |||||||
\(398\) | −23.6557 | − | 16.3088i | −1.18575 | − | 0.817484i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.2752 | + | 10.9242i | −0.613761 | + | 0.546211i | ||||
\(401\) | −21.1657 | −1.05697 | −0.528483 | − | 0.848944i | \(-0.677239\pi\) | ||||
−0.528483 | + | 0.848944i | \(0.677239\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.03805i | 0.450217i | ||||||||
\(404\) | 15.5728 | − | 5.92601i | 0.774776 | − | 0.294830i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.8763 | − | 13.2683i | −0.639038 | − | 0.658495i | ||||
\(407\) | 24.0329i | 1.19127i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5348i | 1.01538i | 0.861539 | + | 0.507691i | \(0.169501\pi\) | ||||
−0.861539 | + | 0.507691i | \(0.830499\pi\) | |||||||
\(410\) | −8.12251 | − | 5.59983i | −0.401142 | − | 0.276556i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.04767 | + | 15.8925i | 0.297947 | + | 0.782968i | ||||
\(413\) | −23.5706 | − | 4.69958i | −1.15984 | − | 0.231251i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.13706i | 0.104904i | ||||||||
\(416\) | 1.42997 | + | 11.5066i | 0.0701099 | + | 0.564157i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.03239 | − | 4.39846i | 0.148319 | − | 0.215136i | ||||
\(419\) | 3.97716 | 0.194297 | 0.0971486 | − | 0.995270i | \(-0.469028\pi\) | ||||
0.0971486 | + | 0.995270i | \(0.469028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.31959 | 0.113050 | 0.0565250 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565250 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(422\) | −23.1052 | + | 33.5139i | −1.12474 | + | 1.63143i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.903858 | − | 3.69388i | 0.0438952 | − | 0.179391i | ||||
\(425\) | − | 17.9687i | − | 0.871611i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.68976 | − | 23.5214i | 0.226953 | − | 1.13828i | ||||
\(428\) | −5.37912 | + | 2.04695i | −0.260010 | + | 0.0989431i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.48903 | + | 3.78425i | 0.264704 | + | 0.182493i | ||||
\(431\) | − | 6.89002i | − | 0.331880i | −0.986136 | − | 0.165940i | \(-0.946934\pi\) | ||
0.986136 | − | 0.165940i | \(-0.0530659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.26241i | 0.108724i | 0.998521 | + | 0.0543621i | \(0.0173125\pi\) | ||||
−0.998521 | + | 0.0543621i | \(0.982687\pi\) | |||||||
\(434\) | −11.4898 | − | 11.8397i | −0.551530 | − | 0.568323i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.96221 | + | 13.0401i | 0.237647 | + | 0.624505i | ||||
\(437\) | − | 4.17206i | − | 0.199577i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.94512 | −0.236018 | −0.118009 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118009 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(440\) | 2.18721 | − | 8.93869i | 0.104271 | − | 0.426135i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4389 | − | 7.19677i | −0.496526 | − | 0.342316i | ||||
\(443\) | − | 11.1415i | − | 0.529348i | −0.964338 | − | 0.264674i | \(-0.914736\pi\) | ||
0.964338 | − | 0.264674i | \(-0.0852644\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.8610 | 0.562263 | ||||||||
\(446\) | −14.3381 | − | 9.88501i | −0.678931 | − | 0.468069i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.5012 | − | 13.2555i | −0.779611 | − | 0.626265i | ||||
\(449\) | −4.12154 | −0.194508 | −0.0972538 | − | 0.995260i | \(-0.531006\pi\) | ||||
−0.0972538 | + | 0.995260i | \(0.531006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.4472 | −1.19826 | ||||||||
\(452\) | 8.96558 | + | 23.5604i | 0.421706 | + | 1.10819i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.9982 | + | 19.9920i | 1.36096 | + | 0.938271i | ||||
\(455\) | 5.02284 | + | 1.00147i | 0.235474 | + | 0.0469495i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.45050 | 0.254964 | 0.127482 | − | 0.991841i | \(-0.459311\pi\) | ||||
0.127482 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(458\) | 7.73213 | − | 11.2154i | 0.361299 | − | 0.524061i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.55588 | − | 6.71652i | −0.119168 | − | 0.313159i | ||||
\(461\) | 25.7035i | 1.19713i | 0.801074 | + | 0.598566i | \(0.204262\pi\) | ||||
−0.801074 | + | 0.598566i | \(0.795738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.6023i | 1.32926i | 0.747171 | + | 0.664632i | \(0.231412\pi\) | ||||
−0.747171 | + | 0.664632i | \(0.768588\pi\) | |||||||
\(464\) | 14.7653 | − | 13.1403i | 0.685462 | − | 0.610022i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.2062 | + | 20.8248i | 1.39928 | + | 0.964690i | ||||
\(467\) | 6.66562 | 0.308448 | 0.154224 | − | 0.988036i | \(-0.450712\pi\) | ||||
0.154224 | + | 0.988036i | \(0.450712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.08422 | − | 30.5152i | 0.280943 | − | 1.40906i | ||||
\(470\) | −7.44557 | + | 10.7997i | −0.343439 | + | 0.498155i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.10692 | − | 24.9577i | 0.281094 | − | 1.14877i | ||||
\(473\) | 17.1967 | 0.790705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.50478 | −0.206693 | ||||||||
\(476\) | 22.8238 | − | 3.84302i | 1.04613 | − | 0.176145i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.98606 | − | 8.68274i | 0.273796 | − | 0.397139i | ||||
\(479\) | −21.8214 | −0.997045 | −0.498522 | − | 0.866877i | \(-0.666124\pi\) | ||||
−0.498522 | + | 0.866877i | \(0.666124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.2993i | − | 0.651992i | ||||||
\(482\) | −18.5396 | + | 26.8915i | −0.844455 | + | 1.22488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.617474 | − | 1.62264i | −0.0280670 | − | 0.0737565i | ||||
\(485\) | 17.7863 | 0.807632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.03966i | 0.318998i | 0.987198 | + | 0.159499i | \(0.0509878\pi\) | ||||
−0.987198 | + | 0.159499i | \(0.949012\pi\) | |||||||
\(488\) | 24.9056 | + | 6.09417i | 1.12742 | + | 0.275870i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.85296 | + | 5.07350i | −0.354761 | + | 0.229197i | ||||
\(491\) | 2.31042i | 0.104268i | 0.998640 | + | 0.0521340i | \(0.0166023\pi\) | ||||
−0.998640 | + | 0.0521340i | \(0.983398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.6138i | 0.973435i | ||||||||
\(494\) | −1.80424 | + | 2.61704i | −0.0811765 | + | 0.117746i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.1755 | − | 11.7254i | 0.591597 | − | 0.526487i | ||||
\(497\) | 0.307197 | − | 1.54074i | 0.0137797 | − | 0.0691117i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1665i | 0.499882i | 0.968261 | + | 0.249941i | \(0.0804113\pi\) | ||||
−0.968261 | + | 0.249941i | \(0.919589\pi\) | |||||||
\(500\) | −16.0789 | + | 6.11859i | −0.719069 | + | 0.273632i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.49693 | + | 1.03201i | 0.0668112 | + | 0.0460610i | ||||
\(503\) | −2.76001 | −0.123063 | −0.0615314 | − | 0.998105i | \(-0.519598\pi\) | ||||
−0.0615314 | + | 0.998105i | \(0.519598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.86808 | 0.350125 | ||||||||
\(506\) | −15.2609 | − | 10.5212i | −0.678429 | − | 0.467723i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.5867 | − | 5.55078i | 0.647182 | − | 0.246276i | ||||
\(509\) | 13.2133i | 0.585671i | 0.956163 | + | 0.292835i | \(0.0945988\pi\) | ||||
−0.956163 | + | 0.292835i | \(0.905401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.76095 | + | 38.9249i | −0.343324 | + | 1.72194i | ||||
\(512\) | 14.9189 | − | 17.0125i | 0.659329 | − | 0.751855i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.1688 | − | 19.1013i | 0.580852 | − | 0.842522i | ||||
\(515\) | 8.02961i | 0.353827i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.8348i | 1.48805i | ||||||||
\(518\) | 18.1783 | + | 18.7318i | 0.798710 | + | 0.823029i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.30137 | + | 5.31843i | −0.0570688 | + | 0.233228i | ||||
\(521\) | − | 39.7699i | − | 1.74235i | −0.490970 | − | 0.871176i | \(-0.663358\pi\) | ||
0.490970 | − | 0.871176i | \(-0.336642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6727 | 1.34122 | 0.670612 | − | 0.741808i | \(-0.266031\pi\) | ||||
0.670612 | + | 0.741808i | \(0.266031\pi\) | |||||||
\(524\) | −3.04844 | − | 8.01090i | −0.133172 | − | 0.349958i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.7108 | + | 27.1398i | −0.815828 | + | 1.18335i | ||||
\(527\) | 19.2866i | 0.840136i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.52463 | 0.370636 | ||||||||
\(530\) | 1.01927 | − | 1.47845i | 0.0442743 | − | 0.0642196i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.963449 | − | 5.72195i | −0.0417708 | − | 0.248078i | ||||
\(533\) | 15.1408 | 0.655821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.71778 | −0.117500 | ||||||||
\(536\) | 32.3110 | + | 7.90621i | 1.39562 | + | 0.341496i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.7880 | + | 17.0985i | −0.508218 | + | 0.737167i | ||||
\(539\) | −9.24859 | + | 22.2710i | −0.398365 | + | 0.959282i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.132937 | 0.00571541 | 0.00285771 | − | 0.999996i | \(-0.499090\pi\) | ||||
0.00285771 | + | 0.999996i | \(0.499090\pi\) | |||||||
\(542\) | 22.6786 | + | 15.6351i | 0.974128 | + | 0.671584i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.05145 | + | 24.5542i | 0.130830 | + | 1.05275i | ||||
\(545\) | 6.58842i | 0.282217i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.9144i | − | 1.62110i | −0.585669 | − | 0.810550i | \(-0.699168\pi\) | ||
0.585669 | − | 0.810550i | \(-0.300832\pi\) | |||||||
\(548\) | 5.20244 | + | 13.6713i | 0.222237 | + | 0.584011i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.3602 | + | 16.4779i | −0.484402 | + | 0.702621i | ||||
\(551\) | 5.41860 | 0.230840 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.79855 | − | 24.0670i | 0.204055 | − | 1.02343i | ||||
\(554\) | −24.3144 | − | 16.7628i | −1.03302 | − | 0.712184i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00553 | − | 15.7818i | −0.254691 | − | 0.669296i | ||||
\(557\) | −23.1661 | −0.981578 | −0.490789 | − | 0.871279i | \(-0.663291\pi\) | ||||
−0.490789 | + | 0.871279i | \(0.663291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2319 | −0.432761 | ||||||||
\(560\) | −5.05641 | − | 8.62143i | −0.213672 | − | 0.364322i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.1923 | + | 11.1633i | 0.683030 | + | 0.470895i | ||||
\(563\) | 25.3014 | 1.06633 | 0.533163 | − | 0.846013i | \(-0.321003\pi\) | ||||
0.533163 | + | 0.846013i | \(0.321003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9038i | 0.500796i | ||||||||
\(566\) | −24.5218 | − | 16.9058i | −1.03073 | − | 0.710605i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.63141 | + | 0.399191i | 0.0684525 | + | 0.0167497i | ||||
\(569\) | 27.1120 | 1.13659 | 0.568297 | − | 0.822824i | \(-0.307603\pi\) | ||||
0.568297 | + | 0.822824i | \(0.307603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.90401i | 0.247075i | 0.992340 | + | 0.123538i | \(0.0394239\pi\) | ||||
−0.992340 | + | 0.123538i | \(0.960576\pi\) | |||||||
\(572\) | 5.02284 | + | 13.1994i | 0.210015 | + | 0.551894i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.8342 | + | 19.2481i | −0.827863 | + | 0.803401i | ||||
\(575\) | 15.6298i | 0.651806i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23.3360i | − | 0.971489i | −0.874101 | − | 0.485745i | \(-0.838548\pi\) | ||
0.874101 | − | 0.485745i | \(-0.161452\pi\) | |||||||
\(578\) | −2.48225 | − | 1.71132i | −0.103248 | − | 0.0711813i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.72330 | − | 3.31953i | 0.362215 | − | 0.137836i | ||||
\(581\) | 5.87131 | + | 1.17064i | 0.243583 | + | 0.0485662i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.63186i | − | 0.191832i | ||||||
\(584\) | −41.2156 | − | 10.0851i | −1.70551 | − | 0.417323i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5923 | + | 19.7155i | −0.561492 | + | 0.814440i | ||||
\(587\) | −11.3470 | −0.468342 | −0.234171 | − | 0.972195i | \(-0.575238\pi\) | ||||
−0.234171 | + | 0.972195i | \(0.575238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.83516 | 0.199229 | ||||||||
\(590\) | 6.88672 | − | 9.98914i | 0.283522 | − | 0.411246i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.8452 | + | 18.5511i | −0.856734 | + | 0.762444i | ||||
\(593\) | 27.5698i | 1.13216i | 0.824351 | + | 0.566078i | \(0.191540\pi\) | ||||
−0.824351 | + | 0.566078i | \(0.808460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.7184 | + | 2.13706i | 0.439411 | + | 0.0876109i | ||||
\(596\) | −1.92916 | − | 5.06958i | −0.0790213 | − | 0.207658i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.08006 | + | 6.25998i | 0.371311 | + | 0.255990i | ||||
\(599\) | − | 29.6098i | − | 1.20982i | −0.796292 | − | 0.604912i | \(-0.793208\pi\) | ||
0.796292 | − | 0.604912i | \(-0.206792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.3660i | 0.993910i | 0.867776 | + | 0.496955i | \(0.165549\pi\) | ||||
−0.867776 | + | 0.496955i | \(0.834451\pi\) | |||||||
\(602\) | 13.4035 | − | 13.0075i | 0.546287 | − | 0.530146i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −28.5629 | + | 10.8692i | −1.16221 | + | 0.442262i | ||||
\(605\) | − | 0.819833i | − | 0.0333309i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.7025 | 1.53030 | 0.765148 | − | 0.643854i | \(-0.222666\pi\) | ||||
0.765148 | + | 0.643854i | \(0.222666\pi\) | |||||||
\(608\) | 6.15577 | − | 0.765002i | 0.249650 | − | 0.0310249i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.96827 | + | 6.87233i | 0.403603 | + | 0.278253i | ||||
\(611\) | − | 20.1313i | − | 0.814426i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 8.63774 | + | 5.95504i | 0.348591 | + | 0.240326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23.3598 | − | 10.9055i | −0.941195 | − | 0.439396i | ||||
\(617\) | 39.0969 | 1.57398 | 0.786991 | − | 0.616965i | \(-0.211638\pi\) | ||||
0.786991 | + | 0.616965i | \(0.211638\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.0479 | −0.926375 | −0.463188 | − | 0.886260i | \(-0.653294\pi\) | ||||
−0.463188 | + | 0.886260i | \(0.653294\pi\) | |||||||
\(620\) | 7.78404 | − | 2.96211i | 0.312615 | − | 0.118961i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.7584 | − | 7.41704i | −0.431371 | − | 0.297396i | ||||
\(623\) | 6.49719 | − | 32.5865i | 0.260304 | − | 1.30555i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4166 | 0.496663 | ||||||||
\(626\) | 5.46071 | − | 7.92071i | 0.218254 | − | 0.316575i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.8369 | + | 8.30973i | −0.871387 | + | 0.331594i | ||||
\(629\) | − | 30.5137i | − | 1.21666i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2224i | 0.446758i | 0.974732 | + | 0.223379i | \(0.0717088\pi\) | ||||
−0.974732 | + | 0.223379i | \(0.928291\pi\) | |||||||
\(632\) | 25.4834 | + | 6.23554i | 1.01367 | + | 0.248036i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38.1867 | − | 26.3267i | −1.51659 | − | 1.04557i | ||||
\(635\) | 7.36988 | 0.292465 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50281 | − | 13.2510i | 0.218029 | − | 0.525025i | ||||
\(638\) | 13.6647 | − | 19.8206i | 0.540991 | − | 0.784704i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.44141 | − | 5.00270i | 0.373205 | − | 0.197749i | ||||
\(641\) | 19.9506 | 0.788003 | 0.394002 | − | 0.919110i | \(-0.371090\pi\) | ||||
0.394002 | + | 0.919110i | \(0.371090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4554 | −1.08273 | −0.541367 | − | 0.840787i | \(-0.682093\pi\) | ||||
−0.541367 | + | 0.840787i | \(0.682093\pi\) | |||||||
\(644\) | −19.8529 | + | 3.34278i | −0.782312 | + | 0.131724i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.85012 | + | 5.58457i | −0.151481 | + | 0.219722i | ||||
\(647\) | −43.2298 | −1.69954 | −0.849770 | − | 0.527154i | \(-0.823259\pi\) | ||||
−0.849770 | + | 0.527154i | \(0.823259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.2952i | − | 1.22844i | ||||||
\(650\) | 6.75921 | − | 9.80419i | 0.265118 | − | 0.384552i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.2374 | + | 5.79839i | −0.596743 | + | 0.227082i | ||||
\(653\) | −48.4533 | −1.89613 | −0.948063 | − | 0.318084i | \(-0.896961\pi\) | ||||
−0.948063 | + | 0.318084i | \(0.896961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.04747i | − | 0.158148i | ||||||
\(656\) | −19.6428 | − | 22.0720i | −0.766922 | − | 0.861766i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.5924 | + | 26.3717i | 0.997696 | + | 1.02807i | ||||
\(659\) | − | 22.6111i | − | 0.880804i | −0.897801 | − | 0.440402i | \(-0.854836\pi\) | ||
0.897801 | − | 0.440402i | \(-0.145164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.2022i | − | 0.941358i | −0.882305 | − | 0.470679i | \(-0.844009\pi\) | ||
0.882305 | − | 0.470679i | \(-0.155991\pi\) | |||||||
\(662\) | −6.89445 | + | 10.0004i | −0.267961 | + | 0.388675i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.52120 | + | 6.21683i | −0.0590340 | + | 0.241260i | ||||
\(665\) | 0.535763 | − | 2.68711i | 0.0207760 | − | 0.104202i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.8004i | − | 0.727953i | ||||||
\(668\) | −16.2768 | − | 42.7733i | −0.629767 | − | 1.65495i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.9322 | + | 8.91575i | 0.499616 | + | 0.344445i | ||||
\(671\) | 31.2298 | 1.20561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.45050 | 0.210101 | 0.105051 | − | 0.994467i | \(-0.466500\pi\) | ||||
0.105051 | + | 0.994467i | \(0.466500\pi\) | |||||||
\(674\) | −30.8141 | − | 21.2439i | −1.18692 | − | 0.818284i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.25851 | + | 16.4466i | 0.240712 | + | 0.632560i | ||||
\(677\) | 36.8454i | 1.41608i | 0.706171 | + | 0.708041i | \(0.250421\pi\) | ||||
−0.706171 | + | 0.708041i | \(0.749579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.74295 | − | 48.8655i | 0.373900 | − | 1.87529i | ||||
\(680\) | −2.77703 | + | 11.3491i | −0.106494 | + | 0.435220i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.1934 | − | 17.6864i | 0.466909 | − | 0.677249i | ||||
\(683\) | − | 34.0857i | − | 1.30425i | −0.758110 | − | 0.652127i | \(-0.773877\pi\) | ||
0.758110 | − | 0.652127i | \(-0.226123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.90738i | 0.263917i | ||||||||
\(686\) | 9.63711 | + | 24.3542i | 0.367946 | + | 0.929847i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.2742 | + | 14.9158i | 0.506074 | + | 0.568659i | ||||
\(689\) | 2.75591i | 0.104992i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.6652 | 1.39481 | 0.697405 | − | 0.716678i | \(-0.254338\pi\) | ||||
0.697405 | + | 0.716678i | \(0.254338\pi\) | |||||||
\(692\) | 39.6570 | − | 15.0909i | 1.50753 | − | 0.573671i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.1601 | + | 14.7371i | −0.385672 | + | 0.559414i | ||||
\(695\) | − | 7.97366i | − | 0.302458i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.3094 | 1.22381 | ||||||||
\(698\) | −21.7435 | + | 31.5388i | −0.823004 | + | 1.19376i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.60937 | + | 21.4361i | 0.136421 | + | 0.810209i | ||||
\(701\) | −36.2856 | −1.37049 | −0.685245 | − | 0.728313i | \(-0.740305\pi\) | ||||
−0.685245 | + | 0.728313i | \(0.740305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.64982 | −0.288518 | ||||||||
\(704\) | 12.7255 | − | 24.4463i | 0.479609 | − | 0.921353i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.63564 | − | 3.82298i | 0.0991937 | − | 0.143880i | ||||
\(707\) | 4.30997 | − | 21.6166i | 0.162093 | − | 0.812975i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.2060 | 1.43485 | 0.717427 | − | 0.696633i | \(-0.245319\pi\) | ||||
0.717427 | + | 0.696633i | \(0.245319\pi\) | |||||||
\(710\) | 0.652960 | + | 0.450164i | 0.0245051 | + | 0.0168944i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.5042 | + | 8.44284i | 1.29310 | + | 0.316409i | ||||
\(713\) | − | 16.7761i | − | 0.628269i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.66892i | 0.249403i | ||||||||
\(716\) | 40.6462 | − | 15.4673i | 1.51902 | − | 0.578042i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.54216 | − | 3.68738i | 0.0948724 | − | 0.137612i | ||||
\(719\) | 14.3470 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413793\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0604 | + | 4.39846i | 0.821571 | + | 0.163807i | ||||
\(722\) | −20.7221 | − | 14.2863i | −0.771198 | − | 0.531680i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.6725 | + | 5.20286i | −0.508133 | + | 0.193363i | ||||
\(725\) | −20.2997 | −0.753911 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.7557 | −0.435994 | −0.217997 | − | 0.975949i | \(-0.569952\pi\) | ||||
−0.217997 | + | 0.975949i | \(0.569952\pi\) | |||||||
\(728\) | 13.8989 | + | 6.48867i | 0.515126 | + | 0.240486i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.4962 | − | 11.3728i | −0.610552 | − | 0.420927i | ||||
\(731\) | −21.8340 | −0.807561 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.71652i | 0.248080i | 0.992277 | + | 0.124040i | \(0.0395852\pi\) | ||||
−0.992277 | + | 0.124040i | \(0.960415\pi\) | |||||||
\(734\) | −26.9642 | − | 18.5897i | −0.995268 | − | 0.686158i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.65425 | − | 21.3581i | −0.0978369 | − | 0.787269i | ||||
\(737\) | 40.5157 | 1.49241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 29.1879i | − | 1.07369i | −0.843679 | − | 0.536847i | \(-0.819615\pi\) | ||
0.843679 | − | 0.536847i | \(-0.180385\pi\) | |||||||
\(740\) | −12.3153 | + | 4.68642i | −0.452720 | + | 0.172276i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.50351 | − | 3.61019i | −0.128618 | − | 0.132534i | ||||
\(743\) | − | 40.8022i | − | 1.49689i | −0.663197 | − | 0.748445i | \(-0.730801\pi\) | ||
0.663197 | − | 0.748445i | \(-0.269199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.56138i | − | 0.0938416i | ||||||
\(746\) | −25.6589 | − | 17.6898i | −0.939438 | − | 0.647668i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.7184 | + | 28.1665i | 0.391903 | + | 1.02987i | ||||
\(749\) | −1.48874 | + | 7.46675i | −0.0543974 | + | 0.272829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.2771i | − | 0.411509i | −0.978604 | − | 0.205755i | \(-0.934035\pi\) | ||
0.978604 | − | 0.205755i | \(-0.0659648\pi\) | |||||||
\(752\) | −29.3470 | + | 26.1172i | −1.07018 | + | 0.952395i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.13036 | + | 11.7930i | −0.296090 | + | 0.429477i | ||||
\(755\) | −14.4313 | −0.525207 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1446 | 0.695822 | 0.347911 | − | 0.937528i | \(-0.386891\pi\) | ||||
0.347911 | + | 0.937528i | \(0.386891\pi\) | |||||||
\(758\) | 5.11692 | − | 7.42205i | 0.185855 | − | 0.269581i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.84524 | + | 0.696204i | 0.103208 | + | 0.0252540i | ||||
\(761\) | 3.93458i | 0.142628i | 0.997454 | + | 0.0713142i | \(0.0227193\pi\) | ||||
−0.997454 | + | 0.0713142i | \(0.977281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.1009 | + | 3.60900i | 0.655296 | + | 0.130655i | ||||
\(764\) | 28.2049 | − | 10.7330i | 1.02042 | − | 0.388305i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.71868 | − | 6.70026i | −0.351150 | − | 0.242090i | ||||
\(767\) | 18.6203i | 0.672340i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.12867i | − | 0.112823i | −0.998408 | − | 0.0564114i | \(-0.982034\pi\) | ||
0.998408 | − | 0.0564114i | \(-0.0179658\pi\) | |||||||
\(770\) | −8.47802 | − | 8.73616i | −0.305527 | − | 0.314829i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.10906 | − | 8.17022i | −0.111898 | − | 0.294053i | ||||
\(773\) | 24.0844i | 0.866257i | 0.901332 | + | 0.433129i | \(0.142590\pi\) | ||||
−0.901332 | + | 0.433129i | \(0.857410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.1139 | −0.650672 | ||||||||
\(776\) | 51.7412 | + | 12.6606i | 1.85740 | + | 0.454489i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.9865 | − | 12.4003i | −0.644848 | − | 0.444572i | ||||
\(779\) | − | 8.10001i | − | 0.290213i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04567 | 0.0731999 | ||||||||
\(782\) | 19.3762 | + | 13.3584i | 0.692892 | + | 0.477694i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.4561 | + | 9.16920i | −0.944861 | + | 0.327472i | ||||
\(785\) | −11.0330 | −0.393784 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.4943 | −1.76428 | −0.882141 | − | 0.470985i | \(-0.843899\pi\) | ||||
−0.882141 | + | 0.470985i | \(0.843899\pi\) | |||||||
\(788\) | −11.0968 | − | 29.1611i | −0.395308 | − | 1.03882i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.1995 | + | 7.03176i | 0.362882 | + | 0.250179i | ||||
\(791\) | 32.7042 | + | 6.52065i | 1.16283 | + | 0.231848i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.5814 | −0.659845 | ||||||||
\(794\) | 1.15073 | − | 1.66913i | 0.0408380 | − | 0.0592352i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.4518 | − | 37.9774i | −0.512229 | − | 1.34607i | ||||
\(797\) | − | 45.8276i | − | 1.62330i | −0.584146 | − | 0.811649i | \(-0.698570\pi\) | ||
0.584146 | − | 0.811649i | \(-0.301430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.9588i | − | 1.51977i | ||||||
\(800\) | −23.0613 | + | 2.86592i | −0.815342 | + | 0.101326i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.6438 | − | 16.9899i | −0.870203 | − | 0.599936i | ||||
\(803\) | −51.6813 | −1.82379 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.32319 | − | 1.85888i | −0.328599 | − | 0.0655170i | ||||
\(806\) | −7.25494 | + | 10.5232i | −0.255544 | + | 0.370665i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.8887 | + | 5.60064i | 0.805221 | + | 0.197030i | ||||
\(809\) | 37.1473 | 1.30603 | 0.653016 | − | 0.757344i | \(-0.273504\pi\) | ||||
0.653016 | + | 0.757344i | \(0.273504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.84971 | 0.170296 | 0.0851481 | − | 0.996368i | \(-0.472864\pi\) | ||||
0.0851481 | + | 0.996368i | \(0.472864\pi\) | |||||||
\(812\) | −4.34155 | − | 25.7846i | −0.152358 | − | 0.904860i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.2915 | + | 27.9821i | −0.676165 | + | 0.980773i | ||||
\(815\) | −7.69863 | −0.269671 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.47382i | 0.191505i | ||||||||
\(818\) | −16.4835 | + | 23.9093i | −0.576334 | + | 0.835968i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.96221 | − | 13.0401i | −0.173288 | − | 0.455378i | ||||
\(821\) | 2.21993 | 0.0774761 | 0.0387381 | − | 0.999249i | \(-0.487666\pi\) | ||||
0.0387381 | + | 0.999249i | \(0.487666\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.5018i | − | 0.923794i | −0.886934 | − | 0.461897i | \(-0.847169\pi\) | ||
0.886934 | − | 0.461897i | \(-0.152831\pi\) | |||||||
\(824\) | −5.71563 | + | 23.3586i | −0.199113 | + | 0.813735i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.6715 | − | 24.3922i | −0.823637 | − | 0.848715i | ||||
\(827\) | 29.2189i | 1.01604i | 0.861345 | + | 0.508021i | \(0.169623\pi\) | ||||
−0.861345 | + | 0.508021i | \(0.830377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0069i | 1.59788i | 0.601408 | + | 0.798942i | \(0.294607\pi\) | ||||
−0.601408 | + | 0.798942i | \(0.705393\pi\) | |||||||
\(830\) | −1.71544 | + | 2.48824i | −0.0595438 | + | 0.0863679i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.57151 | + | 14.5453i | −0.262495 | + | 0.504266i | ||||
\(833\) | 11.7426 | − | 28.2768i | 0.406857 | − | 0.979732i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 21.6110i | − | 0.747879i | ||||||
\(836\) | 7.06138 | − | 2.68711i | 0.244223 | − | 0.0929356i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.63072 | + | 3.19251i | 0.159965 | + | 0.110284i | ||||
\(839\) | −24.3927 | −0.842130 | −0.421065 | − | 0.907030i | \(-0.638344\pi\) | ||||
−0.421065 | + | 0.907030i | \(0.638344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.58242 | −0.158014 | ||||||||
\(842\) | 2.70076 | + | 1.86196i | 0.0930745 | + | 0.0641675i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −53.8039 | + | 20.4743i | −1.85201 | + | 0.704755i | ||||
\(845\) | 8.30954i | 0.285857i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.25239 | − | 0.449088i | −0.0773930 | − | 0.0154308i | ||||
\(848\) | 4.01751 | − | 3.57535i | 0.137962 | − | 0.122778i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.4237 | − | 20.9214i | 0.494728 | − | 0.717599i | ||||
\(851\) | 26.5418i | 0.909841i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.1876i | − | 0.656971i | −0.944509 | − | 0.328485i | \(-0.893462\pi\) | ||
0.944509 | − | 0.328485i | \(-0.106538\pi\) | |||||||
\(854\) | 24.3413 | − | 23.6220i | 0.832942 | − | 0.808330i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.90616 | − | 1.93456i | −0.270227 | − | 0.0661220i | ||||
\(857\) | 23.1818i | 0.791877i | 0.918277 | + | 0.395938i | \(0.129581\pi\) | ||||
−0.918277 | + | 0.395938i | \(0.870419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0789 | −0.650965 | −0.325482 | − | 0.945548i | \(-0.605527\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605527\pi\) | |||||||
\(860\) | 3.35336 | + | 8.81220i | 0.114349 | + | 0.300494i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.53069 | − | 8.02223i | 0.188376 | − | 0.273238i | ||||
\(863\) | − | 41.0656i | − | 1.39789i | −0.715177 | − | 0.698944i | \(-0.753654\pi\) | ||
0.715177 | − | 0.698944i | \(-0.246346\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0365 | 0.681262 | ||||||||
\(866\) | −1.81606 | + | 2.63418i | −0.0617121 | + | 0.0895130i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.87408 | − | 23.0083i | −0.131495 | − | 0.780951i | ||||
\(869\) | 31.9543 | 1.08397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.1064 | −0.816814 | ||||||||
\(872\) | −4.68976 | + | 19.1661i | −0.158815 | + | 0.649046i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.34896 | − | 4.85764i | 0.113280 | − | 0.164312i | ||||
\(875\) | −4.45004 | + | 22.3191i | −0.150439 | + | 0.754522i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8807 | 0.705092 | 0.352546 | − | 0.935794i | \(-0.385316\pi\) | ||||
0.352546 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(878\) | −5.75774 | − | 3.96950i | −0.194314 | − | 0.133964i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.72182 | − | 8.65185i | 0.327722 | − | 0.291654i | ||||
\(881\) | − | 5.65474i | − | 0.190513i | −0.995453 | − | 0.0952565i | \(-0.969633\pi\) | ||
0.995453 | − | 0.0952565i | \(-0.0303671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.0230i | − | 0.539217i | −0.962970 | − | 0.269608i | \(-0.913106\pi\) | ||
0.962970 | − | 0.269608i | \(-0.0868943\pi\) | |||||||
\(884\) | −6.37732 | − | 16.7588i | −0.214492 | − | 0.563659i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.94340 | − | 12.9723i | 0.300459 | − | 0.435814i | ||||
\(887\) | 54.5611 | 1.83198 | 0.915992 | − | 0.401197i | \(-0.131406\pi\) | ||||
0.915992 | + | 0.401197i | \(0.131406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.03707 | − | 20.2478i | 0.135399 | − | 0.679090i | ||||
\(890\) | 13.8100 | + | 9.52091i | 0.462913 | + | 0.319142i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.75947 | − | 23.0188i | −0.293289 | − | 0.770725i | ||||
\(893\) | −10.7698 | −0.360398 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.5363 | 0.686452 | ||||||||
\(896\) | −8.57248 | − | 28.6795i | −0.286386 | − | 0.958114i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.79882 | − | 3.30841i | −0.160139 | − | 0.110403i | ||||
\(899\) | 21.7885 | 0.726686 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.88091i | 0.195921i | ||||||||
\(902\) | −29.6288 | − | 20.4267i | −0.986533 | − | 0.680136i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.47333 | + | 34.6288i | −0.281819 | + | 1.15174i | ||||
\(905\) | −6.90794 | −0.229628 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.0129i | 1.09618i | 0.836420 | + | 0.548089i | \(0.184644\pi\) | ||||
−0.836420 | + | 0.548089i | \(0.815356\pi\) | |||||||
\(908\) | 17.7156 | + | 46.5544i | 0.587914 | + | 1.54496i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.04433 | + | 5.19792i | 0.167218 | + | 0.172309i | ||||
\(911\) | − | 10.4172i | − | 0.345137i | −0.984998 | − | 0.172569i | \(-0.944793\pi\) | ||
0.984998 | − | 0.172569i | \(-0.0552066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.79545i | 0.257992i | ||||||||
\(914\) | 6.34616 | + | 4.37517i | 0.209912 | + | 0.144718i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.0055 | − | 6.85172i | 0.594917 | − | 0.226387i | ||||
\(917\) | −11.1199 | − | 2.21712i | −0.367212 | − | 0.0732158i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 45.5590i | − | 1.50285i | −0.659817 | − | 0.751427i | \(-0.729366\pi\) | ||
0.659817 | − | 0.751427i | \(-0.270634\pi\) | |||||||
\(920\) | 2.41555 | − | 9.87185i | 0.0796383 | − | 0.325465i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.6325 | + | 29.9273i | −0.679494 | + | 0.985602i | ||||
\(923\) | −1.21715 | −0.0400631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.6585 | 0.942285 | ||||||||
\(926\) | −22.9594 | + | 33.3024i | −0.754493 | + | 1.09439i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 27.7395 | − | 3.44729i | 0.910593 | − | 0.113163i | ||||
\(929\) | 21.9033i | 0.718624i | 0.933218 | + | 0.359312i | \(0.116989\pi\) | ||||
−0.933218 | + | 0.359312i | \(0.883011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.08902 | − | 2.94389i | −0.232333 | − | 0.0964820i | ||||
\(932\) | 18.4536 | + | 48.4937i | 0.604468 | + | 1.58846i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.76095 | + | 5.35056i | 0.253946 | + | 0.175076i | ||||
\(935\) | 14.2310i | 0.465403i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9676i | 0.652312i | 0.945316 | + | 0.326156i | \(0.105753\pi\) | ||||
−0.945316 | + | 0.326156i | \(0.894247\pi\) | |||||||
\(938\) | 31.5789 | − | 30.6458i | 1.03109 | − | 1.00062i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.3381 | + | 6.59779i | −0.565508 | + | 0.215196i | ||||
\(941\) | − | 31.5818i | − | 1.02954i | −0.857330 | − | 0.514768i | \(-0.827878\pi\) | ||
0.857330 | − | 0.514768i | \(-0.172122\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.1038 | −0.915185 | ||||||||
\(944\) | 27.1443 | − | 24.1569i | 0.883472 | − | 0.786239i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.0226 | + | 13.8040i | 0.650990 | + | 0.448806i | ||||
\(947\) | 50.1762i | 1.63051i | 0.579104 | + | 0.815253i | \(0.303402\pi\) | ||||
−0.579104 | + | 0.815253i | \(0.696598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.7498 | 0.998182 | ||||||||
\(950\) | −5.24503 | − | 3.61603i | −0.170171 | − | 0.117320i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 29.6592 | + | 13.8464i | 0.961259 | + | 0.448763i | ||||
\(953\) | −21.7989 | −0.706134 | −0.353067 | − | 0.935598i | \(-0.614861\pi\) | ||||
−0.353067 | + | 0.935598i | \(0.614861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.2504 | 0.461131 | ||||||||
\(956\) | 13.9395 | − | 5.30446i | 0.450834 | − | 0.171559i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.4072 | − | 17.5163i | −0.820870 | − | 0.565925i | ||||
\(959\) | 18.9772 | + | 3.78372i | 0.612805 | + | 0.122183i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5575 | −0.372824 | ||||||||
\(962\) | 11.4782 | − | 16.6491i | 0.370072 | − | 0.536787i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −43.1723 | + | 16.4286i | −1.39048 | + | 0.529129i | ||||
\(965\) | − | 4.12796i | − | 0.132884i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5444i | 1.40029i | 0.713999 | + | 0.700147i | \(0.246882\pi\) | ||||
−0.713999 | + | 0.700147i | \(0.753118\pi\) | |||||||
\(968\) | 0.583572 | − | 2.38494i | 0.0187567 | − | 0.0766549i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.7090 | + | 14.2772i | 0.664926 | + | 0.458414i | ||||
\(971\) | −53.3926 | −1.71345 | −0.856725 | − | 0.515773i | \(-0.827505\pi\) | ||||
−0.856725 | + | 0.515773i | \(0.827505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.9066 | − | 4.36781i | −0.702294 | − | 0.140025i | ||||
\(974\) | −5.65081 | + | 8.19646i | −0.181064 | + | 0.262632i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.1064 | + | 27.0876i | 0.771627 | + | 0.867053i | ||||
\(977\) | −29.8010 | −0.953419 | −0.476710 | − | 0.879061i | \(-0.658171\pi\) | ||||
−0.476710 | + | 0.879061i | \(0.658171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.2657 | 1.38278 | ||||||||
\(980\) | −13.2160 | − | 0.396451i | −0.422168 | − | 0.0126642i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.85460 | + | 2.69009i | −0.0591827 | + | 0.0858441i | ||||
\(983\) | 5.46417 | 0.174280 | 0.0871400 | − | 0.996196i | \(-0.472227\pi\) | ||||
0.0871400 | + | 0.996196i | \(0.472227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 14.7335i | − | 0.469448i | ||||||
\(986\) | −17.3496 | + | 25.1655i | −0.552524 | + | 0.801432i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.20145 | + | 1.59880i | −0.133666 | + | 0.0508646i | ||||
\(989\) | 18.9920 | 0.603909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.95872i | − | 0.0622207i | −0.999516 | − | 0.0311103i | \(-0.990096\pi\) | ||
0.999516 | − | 0.0311103i | \(-0.00990433\pi\) | |||||||
\(992\) | 24.7527 | − | 3.07611i | 0.785899 | − | 0.0976667i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.59445 | − | 1.54733i | 0.0505728 | − | 0.0490785i | ||||
\(995\) | − | 19.1879i | − | 0.608297i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 31.2177i | − | 0.988676i | −0.869270 | − | 0.494338i | \(-0.835411\pi\) | ||
0.869270 | − | 0.494338i | \(-0.164589\pi\) | |||||||
\(998\) | −8.96349 | + | 13.0015i | −0.283734 | + | 0.411555i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.b.f.55.14 | yes | 16 | |
3.2 | odd | 2 | 756.2.b.e.55.3 | ✓ | 16 | ||
4.3 | odd | 2 | 756.2.b.e.55.13 | yes | 16 | ||
7.6 | odd | 2 | 756.2.b.e.55.14 | yes | 16 | ||
12.11 | even | 2 | inner | 756.2.b.f.55.4 | yes | 16 | |
21.20 | even | 2 | inner | 756.2.b.f.55.3 | yes | 16 | |
28.27 | even | 2 | inner | 756.2.b.f.55.13 | yes | 16 | |
84.83 | odd | 2 | 756.2.b.e.55.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.b.e.55.3 | ✓ | 16 | 3.2 | odd | 2 | ||
756.2.b.e.55.4 | yes | 16 | 84.83 | odd | 2 | ||
756.2.b.e.55.13 | yes | 16 | 4.3 | odd | 2 | ||
756.2.b.e.55.14 | yes | 16 | 7.6 | odd | 2 | ||
756.2.b.f.55.3 | yes | 16 | 21.20 | even | 2 | inner | |
756.2.b.f.55.4 | yes | 16 | 12.11 | even | 2 | inner | |
756.2.b.f.55.13 | yes | 16 | 28.27 | even | 2 | inner | |
756.2.b.f.55.14 | yes | 16 | 1.1 | even | 1 | trivial |