Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1889,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.d (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: | \(15.0917259820\) |
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: |
\( x^{16} - 3 x^{15} + 3 x^{14} + 5 x^{12} + 15 x^{11} - 12 x^{10} + 381 x^{9} - 1356 x^{8} + 1905 x^{7} + \cdots + 390625 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.13 | ||
Root | \(1.98399 + 1.03140i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.1889 |
Dual form | 1890.2.d.e.1889.14 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.88521 | − | 1.20249i | 0.843093 | − | 0.537768i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61764 | + | 0.384656i | 0.989375 | + | 0.145386i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.88521 | + | 1.20249i | −0.596157 | + | 0.380260i | ||||
\(11\) | − | 0.149444i | − | 0.0450589i | −0.999746 | − | 0.0225295i | \(-0.992828\pi\) | ||
0.999746 | − | 0.0225295i | \(-0.00717196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.72182 | −1.58695 | −0.793474 | − | 0.608604i | \(-0.791730\pi\) | ||||
−0.793474 | + | 0.608604i | \(0.791730\pi\) | |||||||
\(14\) | −2.61764 | − | 0.384656i | −0.699594 | − | 0.102804i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.33796i | − | 1.53718i | −0.639741 | − | 0.768590i | \(-0.720958\pi\) | ||
0.639741 | − | 0.768590i | \(-0.279042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.66504i | 1.29965i | 0.760085 | + | 0.649824i | \(0.225158\pi\) | ||||
−0.760085 | + | 0.649824i | \(0.774842\pi\) | |||||||
\(20\) | 1.88521 | − | 1.20249i | 0.421546 | − | 0.268884i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.149444i | 0.0318615i | ||||||||
\(23\) | 4.59603 | 0.958338 | 0.479169 | − | 0.877723i | \(-0.340938\pi\) | ||||
0.479169 | + | 0.877723i | \(0.340938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.10805 | − | 4.53389i | 0.421610 | − | 0.906777i | ||||
\(26\) | 5.72182 | 1.12214 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.61764 | + | 0.384656i | 0.494687 | + | 0.0726932i | ||||
\(29\) | − | 5.06799i | − | 0.941101i | −0.882373 | − | 0.470551i | \(-0.844055\pi\) | ||
0.882373 | − | 0.470551i | \(-0.155945\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.39709i | − | 1.32856i | −0.747486 | − | 0.664278i | \(-0.768739\pi\) | ||
0.747486 | − | 0.664278i | \(-0.231261\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.33796i | 1.08695i | ||||||||
\(35\) | 5.39735 | − | 2.42252i | 0.912319 | − | 0.409480i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.76125i | − | 0.947144i | −0.880755 | − | 0.473572i | \(-0.842964\pi\) | ||
0.880755 | − | 0.473572i | \(-0.157036\pi\) | |||||||
\(38\) | − | 5.66504i | − | 0.918990i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.88521 | + | 1.20249i | −0.298078 | + | 0.190130i | ||||
\(41\) | 4.02927 | 0.629266 | 0.314633 | − | 0.949213i | \(-0.398119\pi\) | ||||
0.314633 | + | 0.949213i | \(0.398119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14923i | 0.632752i | 0.948634 | + | 0.316376i | \(0.102466\pi\) | ||||
−0.948634 | + | 0.316376i | \(0.897534\pi\) | |||||||
\(44\) | − | 0.149444i | − | 0.0225295i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.59603 | −0.677647 | ||||||||
\(47\) | − | 12.0976i | − | 1.76461i | −0.470675 | − | 0.882306i | \(-0.655990\pi\) | ||
0.470675 | − | 0.882306i | \(-0.344010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.70408 | + | 2.01378i | 0.957726 | + | 0.287683i | ||||
\(50\) | −2.10805 | + | 4.53389i | −0.298124 | + | 0.641188i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.72182 | −0.793474 | ||||||||
\(53\) | −9.38164 | −1.28867 | −0.644334 | − | 0.764745i | \(-0.722865\pi\) | ||||
−0.644334 | + | 0.764745i | \(0.722865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.179704 | − | 0.281733i | −0.0242313 | − | 0.0379889i | ||||
\(56\) | −2.61764 | − | 0.384656i | −0.349797 | − | 0.0514019i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.06799i | 0.665459i | ||||||||
\(59\) | 11.2159 | 1.46019 | 0.730096 | − | 0.683345i | \(-0.239475\pi\) | ||||
0.730096 | + | 0.683345i | \(0.239475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 7.39709i | 0.939431i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.7868 | + | 6.88041i | −1.33794 | + | 0.853410i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6717i | 1.91461i | 0.289084 | + | 0.957304i | \(0.406649\pi\) | ||||
−0.289084 | + | 0.957304i | \(0.593351\pi\) | |||||||
\(68\) | − | 6.33796i | − | 0.768590i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.39735 | + | 2.42252i | −0.645107 | + | 0.289546i | ||||
\(71\) | 3.23047i | 0.383387i | 0.981455 | + | 0.191693i | \(0.0613979\pi\) | ||||
−0.981455 | + | 0.191693i | \(0.938602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.74686 | 1.02374 | 0.511871 | − | 0.859062i | \(-0.328952\pi\) | ||||
0.511871 | + | 0.859062i | \(0.328952\pi\) | |||||||
\(74\) | 5.76125i | 0.669732i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.66504i | 0.649824i | ||||||||
\(77\) | 0.0574844 | − | 0.391190i | 0.00655096 | − | 0.0445802i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.05057 | −0.230707 | −0.115353 | − | 0.993325i | \(-0.536800\pi\) | ||||
−0.115353 | + | 0.993325i | \(0.536800\pi\) | |||||||
\(80\) | 1.88521 | − | 1.20249i | 0.210773 | − | 0.134442i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.02927 | −0.444958 | ||||||||
\(83\) | − | 8.07001i | − | 0.885799i | −0.896571 | − | 0.442899i | \(-0.853950\pi\) | ||
0.896571 | − | 0.442899i | \(-0.146050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.62131 | − | 11.9484i | −0.826647 | − | 1.29599i | ||||
\(86\) | − | 4.14923i | − | 0.447423i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.149444i | 0.0159307i | ||||||||
\(89\) | −2.31080 | −0.244945 | −0.122472 | − | 0.992472i | \(-0.539082\pi\) | ||||
−0.122472 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9777 | − | 2.20093i | −1.57009 | − | 0.230721i | ||||
\(92\) | 4.59603 | 0.479169 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0976i | 1.24777i | ||||||||
\(95\) | 6.81213 | + | 10.6798i | 0.698910 | + | 1.09572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.70014 | −0.680296 | −0.340148 | − | 0.940372i | \(-0.610477\pi\) | ||||
−0.340148 | + | 0.940372i | \(0.610477\pi\) | |||||||
\(98\) | −6.70408 | − | 2.01378i | −0.677214 | − | 0.203423i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.10805 | − | 4.53389i | 0.210805 | − | 0.453389i | ||||
\(101\) | 7.28201 | 0.724587 | 0.362293 | − | 0.932064i | \(-0.381994\pi\) | ||||
0.362293 | + | 0.932064i | \(0.381994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.84830 | 0.576250 | 0.288125 | − | 0.957593i | \(-0.406968\pi\) | ||||
0.288125 | + | 0.957593i | \(0.406968\pi\) | |||||||
\(104\) | 5.72182 | 0.561071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.38164 | 0.911225 | ||||||||
\(107\) | −4.16554 | −0.402698 | −0.201349 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201349 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1432 | −1.54624 | −0.773119 | − | 0.634261i | \(-0.781305\pi\) | ||||
−0.773119 | + | 0.634261i | \(0.781305\pi\) | |||||||
\(110\) | 0.179704 | + | 0.281733i | 0.0171341 | + | 0.0268622i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.61764 | + | 0.384656i | 0.247344 | + | 0.0363466i | ||||
\(113\) | 12.1432 | 1.14234 | 0.571168 | − | 0.820833i | \(-0.306490\pi\) | ||||
0.571168 | + | 0.820833i | \(0.306490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.66449 | − | 5.52666i | 0.807968 | − | 0.515364i | ||||
\(116\) | − | 5.06799i | − | 0.470551i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2159 | −1.03251 | ||||||||
\(119\) | 2.43794 | − | 16.5905i | 0.223485 | − | 1.52085i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9777 | 0.997970 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 7.39709i | − | 0.664278i | ||||||
\(125\) | −1.47781 | − | 11.0822i | −0.132180 | − | 0.991226i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.74821i | − | 0.687543i | −0.939053 | − | 0.343771i | \(-0.888296\pi\) | ||
0.939053 | − | 0.343771i | \(-0.111704\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.7868 | − | 6.88041i | 0.946069 | − | 0.603452i | ||||
\(131\) | −9.36577 | −0.818291 | −0.409145 | − | 0.912469i | \(-0.634173\pi\) | ||||
−0.409145 | + | 0.912469i | \(0.634173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17909 | + | 14.8290i | −0.188951 | + | 1.28584i | ||||
\(134\) | − | 15.6717i | − | 1.35383i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.33796i | 0.543475i | ||||||||
\(137\) | −2.56951 | −0.219528 | −0.109764 | − | 0.993958i | \(-0.535009\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.7066i | − | 1.24740i | −0.781665 | − | 0.623698i | \(-0.785629\pi\) | ||
0.781665 | − | 0.623698i | \(-0.214371\pi\) | |||||||
\(140\) | 5.39735 | − | 2.42252i | 0.456159 | − | 0.204740i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 3.23047i | − | 0.271095i | ||||||
\(143\) | 0.855090i | 0.0715062i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.09419 | − | 9.55423i | −0.506095 | − | 0.793436i | ||||
\(146\) | −8.74686 | −0.723895 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 5.76125i | − | 0.473572i | ||||||
\(149\) | − | 2.61325i | − | 0.214086i | −0.994254 | − | 0.107043i | \(-0.965862\pi\) | ||
0.994254 | − | 0.107043i | \(-0.0341382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.02652 | 0.0835369 | 0.0417685 | − | 0.999127i | \(-0.486701\pi\) | ||||
0.0417685 | + | 0.999127i | \(0.486701\pi\) | |||||||
\(152\) | − | 5.66504i | − | 0.459495i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0574844 | + | 0.391190i | −0.00463223 | + | 0.0315230i | ||||
\(155\) | −8.89490 | − | 13.9451i | −0.714455 | − | 1.12010i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2216 | 1.61386 | 0.806932 | − | 0.590645i | \(-0.201127\pi\) | ||||
0.806932 | + | 0.590645i | \(0.201127\pi\) | |||||||
\(158\) | 2.05057 | 0.163134 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.88521 | + | 1.20249i | −0.149039 | + | 0.0950649i | ||||
\(161\) | 12.0307 | + | 1.76789i | 0.948156 | + | 0.139329i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.46879i | 0.428349i | 0.976795 | + | 0.214174i | \(0.0687061\pi\) | ||||
−0.976795 | + | 0.214174i | \(0.931294\pi\) | |||||||
\(164\) | 4.02927 | 0.314633 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.07001i | 0.626354i | ||||||||
\(167\) | − | 9.70748i | − | 0.751187i | −0.926784 | − | 0.375594i | \(-0.877439\pi\) | ||
0.926784 | − | 0.375594i | \(-0.122561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.7392 | 1.51840 | ||||||||
\(170\) | 7.62131 | + | 11.9484i | 0.584528 | + | 0.916400i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.14923i | 0.316376i | ||||||||
\(173\) | 19.3174i | 1.46868i | 0.678785 | + | 0.734338i | \(0.262507\pi\) | ||||
−0.678785 | + | 0.734338i | \(0.737493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.26211 | − | 11.0572i | 0.548964 | − | 0.835846i | ||||
\(176\) | − | 0.149444i | − | 0.0112647i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.31080 | 0.173202 | ||||||||
\(179\) | − | 10.9851i | − | 0.821065i | −0.911846 | − | 0.410533i | \(-0.865343\pi\) | ||
0.911846 | − | 0.410533i | \(-0.134657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.83362i | 0.507939i | 0.967212 | + | 0.253970i | \(0.0817363\pi\) | ||||
−0.967212 | + | 0.253970i | \(0.918264\pi\) | |||||||
\(182\) | 14.9777 | + | 2.20093i | 1.11022 | + | 0.163144i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.59603 | −0.338824 | ||||||||
\(185\) | −6.92783 | − | 10.8612i | −0.509344 | − | 0.798530i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.947167 | −0.0692637 | ||||||||
\(188\) | − | 12.0976i | − | 0.882306i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.81213 | − | 10.6798i | −0.494204 | − | 0.774794i | ||||
\(191\) | 16.2182i | 1.17351i | 0.809765 | + | 0.586754i | \(0.199595\pi\) | ||||
−0.809765 | + | 0.586754i | \(0.800405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8379i | 1.49994i | 0.661471 | + | 0.749971i | \(0.269933\pi\) | ||||
−0.661471 | + | 0.749971i | \(0.730067\pi\) | |||||||
\(194\) | 6.70014 | 0.481042 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70408 | + | 2.01378i | 0.478863 | + | 0.143842i | ||||
\(197\) | −5.64659 | −0.402303 | −0.201152 | − | 0.979560i | \(-0.564468\pi\) | ||||
−0.201152 | + | 0.979560i | \(0.564468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.3142i | − | 1.29826i | −0.760679 | − | 0.649129i | \(-0.775134\pi\) | ||
0.760679 | − | 0.649129i | \(-0.224866\pi\) | |||||||
\(200\) | −2.10805 | + | 4.53389i | −0.149062 | + | 0.320594i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.28201 | −0.512360 | ||||||||
\(203\) | 1.94943 | − | 13.2662i | 0.136823 | − | 0.931102i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.59603 | − | 4.84514i | 0.530530 | − | 0.338399i | ||||
\(206\) | −5.84830 | −0.407470 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.72182 | −0.396737 | ||||||||
\(209\) | 0.846603 | 0.0585608 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.54546 | 0.175237 | 0.0876184 | − | 0.996154i | \(-0.472074\pi\) | ||||
0.0876184 | + | 0.996154i | \(0.472074\pi\) | |||||||
\(212\) | −9.38164 | −0.644334 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.16554 | 0.284750 | ||||||||
\(215\) | 4.98939 | + | 7.82218i | 0.340274 | + | 0.533468i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.84534 | − | 19.3629i | 0.193154 | − | 1.31444i | ||||
\(218\) | 16.1432 | 1.09336 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.179704 | − | 0.281733i | −0.0121156 | − | 0.0189944i | ||||
\(221\) | 36.2647i | 2.43943i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.7080 | 1.98940 | 0.994698 | − | 0.102843i | \(-0.0327939\pi\) | ||||
0.994698 | + | 0.102843i | \(0.0327939\pi\) | |||||||
\(224\) | −2.61764 | − | 0.384656i | −0.174898 | − | 0.0257009i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.1432 | −0.807754 | ||||||||
\(227\) | 20.7727i | 1.37873i | 0.724413 | + | 0.689366i | \(0.242111\pi\) | ||||
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.7942i | − | 0.977627i | −0.872388 | − | 0.488813i | \(-0.837430\pi\) | ||
0.872388 | − | 0.488813i | \(-0.162570\pi\) | |||||||
\(230\) | −8.66449 | + | 5.52666i | −0.571319 | + | 0.364417i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.06799i | 0.332730i | ||||||||
\(233\) | −13.7110 | −0.898237 | −0.449119 | − | 0.893472i | \(-0.648262\pi\) | ||||
−0.449119 | + | 0.893472i | \(0.648262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.5472 | − | 22.8065i | −0.948953 | − | 1.48773i | ||||
\(236\) | 11.2159 | 0.730096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.43794 | + | 16.5905i | −0.158028 | + | 1.07540i | ||||
\(239\) | − | 2.77836i | − | 0.179717i | −0.995955 | − | 0.0898587i | \(-0.971358\pi\) | ||
0.995955 | − | 0.0898587i | \(-0.0286415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.0438i | − | 1.09789i | −0.835860 | − | 0.548943i | \(-0.815031\pi\) | ||
0.835860 | − | 0.548943i | \(-0.184969\pi\) | |||||||
\(242\) | −10.9777 | −0.705671 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0602 | − | 4.26516i | 0.962158 | − | 0.272491i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 32.4143i | − | 2.06247i | ||||||
\(248\) | 7.39709i | 0.469715i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.47781 | + | 11.0822i | 0.0934650 | + | 0.700902i | ||||
\(251\) | 17.5560 | 1.10813 | 0.554063 | − | 0.832475i | \(-0.313077\pi\) | ||||
0.554063 | + | 0.832475i | \(0.313077\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.686847i | − | 0.0431817i | ||||||
\(254\) | 7.74821i | 0.486166i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.74771i | 0.358533i | 0.983801 | + | 0.179266i | \(0.0573724\pi\) | ||||
−0.983801 | + | 0.179266i | \(0.942628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.21610 | − | 15.0809i | 0.137702 | − | 0.937081i | ||||
\(260\) | −10.7868 | + | 6.88041i | −0.668972 | + | 0.426705i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.36577 | 0.578619 | ||||||||
\(263\) | −26.5514 | −1.63723 | −0.818614 | − | 0.574345i | \(-0.805257\pi\) | ||||
−0.818614 | + | 0.574345i | \(0.805257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.6864 | + | 11.2813i | −1.08647 | + | 0.693005i | ||||
\(266\) | 2.17909 | − | 14.8290i | 0.133609 | − | 0.909226i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.6717i | 0.957304i | ||||||||
\(269\) | −32.1200 | −1.95839 | −0.979196 | − | 0.202915i | \(-0.934958\pi\) | ||||
−0.979196 | + | 0.202915i | \(0.934958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.4482i | − | 0.634683i | −0.948311 | − | 0.317342i | \(-0.897210\pi\) | ||
0.948311 | − | 0.317342i | \(-0.102790\pi\) | |||||||
\(272\) | − | 6.33796i | − | 0.384295i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.56951 | 0.155230 | ||||||||
\(275\) | −0.677560 | − | 0.315035i | −0.0408584 | − | 0.0189973i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.1223i | 1.56954i | 0.619790 | + | 0.784768i | \(0.287218\pi\) | ||||
−0.619790 | + | 0.784768i | \(0.712782\pi\) | |||||||
\(278\) | 14.7066i | 0.882043i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.39735 | + | 2.42252i | −0.322553 | + | 0.144773i | ||||
\(281\) | − | 8.68642i | − | 0.518188i | −0.965852 | − | 0.259094i | \(-0.916576\pi\) | ||
0.965852 | − | 0.259094i | \(-0.0834240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.70267 | −0.160657 | −0.0803285 | − | 0.996768i | \(-0.525597\pi\) | ||||
−0.0803285 | + | 0.996768i | \(0.525597\pi\) | |||||||
\(284\) | 3.23047i | 0.191693i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.855090i | − | 0.0505625i | ||||||
\(287\) | 10.5472 | + | 1.54988i | 0.622580 | + | 0.0914867i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.1697 | −1.36292 | ||||||||
\(290\) | 6.09419 | + | 9.55423i | 0.357863 | + | 0.561044i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.74686 | 0.511871 | ||||||||
\(293\) | 5.74771i | 0.335785i | 0.985805 | + | 0.167893i | \(0.0536962\pi\) | ||||
−0.985805 | + | 0.167893i | \(0.946304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.1444 | − | 13.4870i | 1.23108 | − | 0.785245i | ||||
\(296\) | 5.76125i | 0.334866i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.61325i | 0.151381i | ||||||||
\(299\) | −26.2976 | −1.52083 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.59603 | + | 10.8612i | −0.0919935 | + | 0.626029i | ||||
\(302\) | −1.02652 | −0.0590695 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.66504i | 0.324912i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.82304 | 0.332338 | 0.166169 | − | 0.986097i | \(-0.446860\pi\) | ||||
0.166169 | + | 0.986097i | \(0.446860\pi\) | |||||||
\(308\) | 0.0574844 | − | 0.391190i | 0.00327548 | − | 0.0222901i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.89490 | + | 13.9451i | 0.505196 | + | 0.792027i | ||||
\(311\) | −17.3290 | −0.982636 | −0.491318 | − | 0.870980i | \(-0.663485\pi\) | ||||
−0.491318 | + | 0.870980i | \(0.663485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.43305 | 0.0810009 | 0.0405005 | − | 0.999180i | \(-0.487105\pi\) | ||||
0.0405005 | + | 0.999180i | \(0.487105\pi\) | |||||||
\(314\) | −20.2216 | −1.14117 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.05057 | −0.115353 | ||||||||
\(317\) | 3.31552 | 0.186218 | 0.0931091 | − | 0.995656i | \(-0.470319\pi\) | ||||
0.0931091 | + | 0.995656i | \(0.470319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.757378 | −0.0424050 | ||||||||
\(320\) | 1.88521 | − | 1.20249i | 0.105387 | − | 0.0672210i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0307 | − | 1.76789i | −0.670447 | − | 0.0985207i | ||||
\(323\) | 35.9048 | 1.99779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0619 | + | 25.9421i | −0.669073 | + | 1.43901i | ||||
\(326\) | − | 5.46879i | − | 0.302888i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.02927 | −0.222479 | ||||||||
\(329\) | 4.65341 | − | 31.6671i | 0.256551 | − | 1.74586i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3087 | 0.841444 | 0.420722 | − | 0.907190i | \(-0.361777\pi\) | ||||
0.420722 | + | 0.907190i | \(0.361777\pi\) | |||||||
\(332\) | − | 8.07001i | − | 0.442899i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.70748i | 0.531170i | ||||||||
\(335\) | 18.8451 | + | 29.5446i | 1.02962 | + | 1.61419i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.7701i | − | 0.641158i | −0.947222 | − | 0.320579i | \(-0.896123\pi\) | ||
0.947222 | − | 0.320579i | \(-0.103877\pi\) | |||||||
\(338\) | −19.7392 | −1.07367 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.62131 | − | 11.9484i | −0.413324 | − | 0.647993i | ||||
\(341\) | −1.10545 | −0.0598633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7743 | + | 7.85013i | 0.905724 | + | 0.423867i | ||||
\(344\) | − | 4.14923i | − | 0.223711i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 19.3174i | − | 1.03851i | ||||||
\(347\) | 18.6483 | 1.00109 | 0.500547 | − | 0.865709i | \(-0.333132\pi\) | ||||
0.500547 | + | 0.865709i | \(0.333132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.668016i | 0.0357581i | 0.999840 | + | 0.0178790i | \(0.00569138\pi\) | ||||
−0.999840 | + | 0.0178790i | \(0.994309\pi\) | |||||||
\(350\) | −7.26211 | + | 11.0572i | −0.388176 | + | 0.591032i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.149444i | 0.00796537i | ||||||||
\(353\) | 1.16368i | 0.0619363i | 0.999520 | + | 0.0309682i | \(0.00985905\pi\) | ||||
−0.999520 | + | 0.0309682i | \(0.990141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.88460 | + | 6.09013i | 0.206173 | + | 0.323230i | ||||
\(356\) | −2.31080 | −0.122472 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.9851i | 0.580581i | ||||||||
\(359\) | 27.8864i | 1.47179i | 0.677097 | + | 0.735893i | \(0.263238\pi\) | ||||
−0.677097 | + | 0.735893i | \(0.736762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0926 | −0.689086 | ||||||||
\(362\) | − | 6.83362i | − | 0.359167i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.9777 | − | 2.20093i | −0.785043 | − | 0.115360i | ||||
\(365\) | 16.4897 | − | 10.5180i | 0.863110 | − | 0.550536i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.6042 | −1.44093 | −0.720464 | − | 0.693492i | \(-0.756071\pi\) | ||||
−0.720464 | + | 0.693492i | \(0.756071\pi\) | |||||||
\(368\) | 4.59603 | 0.239584 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.92783 | + | 10.8612i | 0.360161 | + | 0.564646i | ||||
\(371\) | −24.5578 | − | 3.60871i | −1.27498 | − | 0.187355i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6305i | 1.79310i | 0.442941 | + | 0.896551i | \(0.353935\pi\) | ||||
−0.442941 | + | 0.896551i | \(0.646065\pi\) | |||||||
\(374\) | 0.947167 | 0.0489769 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.0976i | 0.623885i | ||||||||
\(377\) | 28.9981i | 1.49348i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1921 | −0.677630 | −0.338815 | − | 0.940853i | \(-0.610026\pi\) | ||||
−0.338815 | + | 0.940853i | \(0.610026\pi\) | |||||||
\(380\) | 6.81213 | + | 10.6798i | 0.349455 | + | 0.547862i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 16.2182i | − | 0.829796i | ||||||
\(383\) | 15.2023i | 0.776799i | 0.921491 | + | 0.388399i | \(0.126972\pi\) | ||||
−0.921491 | + | 0.388399i | \(0.873028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.362030 | − | 0.806600i | −0.0184508 | − | 0.0411081i | ||||
\(386\) | − | 20.8379i | − | 1.06062i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.70014 | −0.340148 | ||||||||
\(389\) | − | 27.0512i | − | 1.37155i | −0.727813 | − | 0.685776i | \(-0.759463\pi\) | ||
0.727813 | − | 0.685776i | \(-0.240537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.1294i | − | 1.47314i | ||||||
\(392\) | −6.70408 | − | 2.01378i | −0.338607 | − | 0.101711i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.64659 | 0.284471 | ||||||||
\(395\) | −3.86575 | + | 2.46578i | −0.194507 | + | 0.124067i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.23781 | 0.0621241 | 0.0310621 | − | 0.999517i | \(-0.490111\pi\) | ||||
0.0310621 | + | 0.999517i | \(0.490111\pi\) | |||||||
\(398\) | 18.3142i | 0.918007i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.10805 | − | 4.53389i | 0.105403 | − | 0.226694i | ||||
\(401\) | 36.2582i | 1.81065i | 0.424719 | + | 0.905325i | \(0.360373\pi\) | ||||
−0.424719 | + | 0.905325i | \(0.639627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.3248i | 2.10835i | ||||||||
\(404\) | 7.28201 | 0.362293 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.94943 | + | 13.2662i | −0.0967487 | + | 0.658389i | ||||
\(407\) | −0.860983 | −0.0426773 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1246i | 1.58846i | 0.607616 | + | 0.794231i | \(0.292126\pi\) | ||||
−0.607616 | + | 0.794231i | \(0.707874\pi\) | |||||||
\(410\) | −7.59603 | + | 4.84514i | −0.375141 | + | 0.239285i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.84830 | 0.288125 | ||||||||
\(413\) | 29.3593 | + | 4.31428i | 1.44468 | + | 0.212292i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.70408 | − | 15.2137i | −0.476355 | − | 0.746810i | ||||
\(416\) | 5.72182 | 0.280535 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.846603 | −0.0414087 | ||||||||
\(419\) | 12.6549 | 0.618232 | 0.309116 | − | 0.951024i | \(-0.399967\pi\) | ||||
0.309116 | + | 0.951024i | \(0.399967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2468 | −1.18172 | −0.590859 | − | 0.806775i | \(-0.701211\pi\) | ||||
−0.590859 | + | 0.806775i | \(0.701211\pi\) | |||||||
\(422\) | −2.54546 | −0.123911 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.38164 | 0.455613 | ||||||||
\(425\) | −28.7356 | − | 13.3607i | −1.39388 | − | 0.648091i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.16554 | −0.201349 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.98939 | − | 7.82218i | −0.240610 | − | 0.377219i | ||||
\(431\) | 5.73916i | 0.276446i | 0.990401 | + | 0.138223i | \(0.0441390\pi\) | ||||
−0.990401 | + | 0.138223i | \(0.955861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.54573 | −0.410682 | −0.205341 | − | 0.978691i | \(-0.565830\pi\) | ||||
−0.205341 | + | 0.978691i | \(0.565830\pi\) | |||||||
\(434\) | −2.84534 | + | 19.3629i | −0.136581 | + | 0.929449i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1432 | −0.773119 | ||||||||
\(437\) | 26.0367i | 1.24550i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.38350i | − | 0.400123i | −0.979783 | − | 0.200061i | \(-0.935886\pi\) | ||
0.979783 | − | 0.200061i | \(-0.0641142\pi\) | |||||||
\(440\) | 0.179704 | + | 0.281733i | 0.00856705 | + | 0.0134311i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 36.2647i | − | 1.72493i | ||||||
\(443\) | −6.61158 | −0.314126 | −0.157063 | − | 0.987589i | \(-0.550202\pi\) | ||||
−0.157063 | + | 0.987589i | \(0.550202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.35636 | + | 2.77871i | −0.206511 | + | 0.131724i | ||||
\(446\) | −29.7080 | −1.40671 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.61764 | + | 0.384656i | 0.123672 | + | 0.0181733i | ||||
\(449\) | − | 19.5221i | − | 0.921304i | −0.887581 | − | 0.460652i | \(-0.847616\pi\) | ||
0.887581 | − | 0.460652i | \(-0.152384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.602148i | − | 0.0283541i | ||||||
\(452\) | 12.1432 | 0.571168 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 20.7727i | − | 0.974911i | ||||||
\(455\) | −30.8827 | + | 13.8612i | −1.44780 | + | 0.649824i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.2220i | − | 0.758833i | −0.925226 | − | 0.379416i | \(-0.876125\pi\) | ||
0.925226 | − | 0.379416i | \(-0.123875\pi\) | |||||||
\(458\) | 14.7942i | 0.691286i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.66449 | − | 5.52666i | 0.403984 | − | 0.257682i | ||||
\(461\) | −28.9692 | −1.34923 | −0.674614 | − | 0.738170i | \(-0.735690\pi\) | ||||
−0.674614 | + | 0.738170i | \(0.735690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6872i | 0.821994i | 0.911637 | + | 0.410997i | \(0.134819\pi\) | ||||
−0.911637 | + | 0.410997i | \(0.865181\pi\) | |||||||
\(464\) | − | 5.06799i | − | 0.235275i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7110 | 0.635150 | ||||||||
\(467\) | 6.31118i | 0.292047i | 0.989281 | + | 0.146023i | \(0.0466474\pi\) | ||||
−0.989281 | + | 0.146023i | \(0.953353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.02823 | + | 41.0230i | −0.278358 | + | 1.89426i | ||||
\(470\) | 14.5472 | + | 22.8065i | 0.671011 | + | 1.05199i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.2159 | −0.516256 | ||||||||
\(473\) | 0.620076 | 0.0285111 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.6846 | + | 11.9422i | 1.17849 | + | 0.547945i | ||||
\(476\) | 2.43794 | − | 16.5905i | 0.111743 | − | 0.760424i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.77836i | 0.127079i | ||||||||
\(479\) | −10.0152 | −0.457605 | −0.228802 | − | 0.973473i | \(-0.573481\pi\) | ||||
−0.228802 | + | 0.973473i | \(0.573481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.9649i | 1.50307i | ||||||||
\(482\) | 17.0438i | 0.776322i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9777 | 0.498985 | ||||||||
\(485\) | −12.6312 | + | 8.05682i | −0.573552 | + | 0.365842i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.76766i | 0.351986i | 0.984391 | + | 0.175993i | \(0.0563137\pi\) | ||||
−0.984391 | + | 0.175993i | \(0.943686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.0602 | + | 4.26516i | −0.680349 | + | 0.192680i | ||||
\(491\) | − | 12.1397i | − | 0.547859i | −0.961750 | − | 0.273929i | \(-0.911677\pi\) | ||
0.961750 | − | 0.273929i | \(-0.0883234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.1207 | −1.44664 | ||||||||
\(494\) | 32.4143i | 1.45839i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.39709i | − | 0.332139i | ||||||
\(497\) | −1.24262 | + | 8.45622i | −0.0557392 | + | 0.379313i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.5231 | 1.14257 | 0.571286 | − | 0.820751i | \(-0.306445\pi\) | ||||
0.571286 | + | 0.820751i | \(0.306445\pi\) | |||||||
\(500\) | −1.47781 | − | 11.0822i | −0.0660898 | − | 0.495613i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.5560 | −0.783563 | ||||||||
\(503\) | − | 6.65636i | − | 0.296792i | −0.988928 | − | 0.148396i | \(-0.952589\pi\) | ||
0.988928 | − | 0.148396i | \(-0.0474111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.7281 | − | 8.75651i | 0.610894 | − | 0.389660i | ||||
\(506\) | 0.686847i | 0.0305341i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 7.74821i | − | 0.343771i | ||||||
\(509\) | 40.0580 | 1.77554 | 0.887769 | − | 0.460289i | \(-0.152254\pi\) | ||||
0.887769 | + | 0.460289i | \(0.152254\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8961 | + | 3.36454i | 1.01287 | + | 0.148838i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 5.74771i | − | 0.253521i | ||||||
\(515\) | 11.0253 | − | 7.03250i | 0.485832 | − | 0.309889i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.80791 | −0.0795116 | ||||||||
\(518\) | −2.21610 | + | 15.0809i | −0.0973700 | + | 0.662616i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.7868 | − | 6.88041i | 0.473035 | − | 0.301726i | ||||
\(521\) | 4.26743 | 0.186960 | 0.0934798 | − | 0.995621i | \(-0.470201\pi\) | ||||
0.0934798 | + | 0.995621i | \(0.470201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.36664 | −0.278394 | −0.139197 | − | 0.990265i | \(-0.544452\pi\) | ||||
−0.139197 | + | 0.990265i | \(0.544452\pi\) | |||||||
\(524\) | −9.36577 | −0.409145 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.5514 | 1.15769 | ||||||||
\(527\) | −46.8824 | −2.04223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.87653 | −0.0815884 | ||||||||
\(530\) | 17.6864 | − | 11.2813i | 0.768247 | − | 0.490028i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.17909 | + | 14.8290i | −0.0944756 | + | 0.642920i | ||||
\(533\) | −23.0548 | −0.998612 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.85292 | + | 5.00900i | −0.339511 | + | 0.216558i | ||||
\(536\) | − | 15.6717i | − | 0.676916i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32.1200 | 1.38479 | ||||||||
\(539\) | 0.300947 | − | 1.00188i | 0.0129627 | − | 0.0431541i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.1432 | 1.12398 | 0.561992 | − | 0.827143i | \(-0.310035\pi\) | ||||
0.561992 | + | 0.827143i | \(0.310035\pi\) | |||||||
\(542\) | 10.4482i | 0.448789i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.33796i | 0.271738i | ||||||||
\(545\) | −30.4334 | + | 19.4120i | −1.30362 | + | 0.831518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.8954i | − | 1.06445i | −0.846603 | − | 0.532225i | \(-0.821356\pi\) | ||
0.846603 | − | 0.532225i | \(-0.178644\pi\) | |||||||
\(548\) | −2.56951 | −0.109764 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.677560 | + | 0.315035i | 0.0288913 | + | 0.0134331i | ||||
\(551\) | 28.7103 | 1.22310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.36765 | − | 0.788764i | −0.228256 | − | 0.0335416i | ||||
\(554\) | − | 26.1223i | − | 1.10983i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 14.7066i | − | 0.623698i | ||||||
\(557\) | 8.37992 | 0.355069 | 0.177534 | − | 0.984115i | \(-0.443188\pi\) | ||||
0.177534 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.7411i | − | 1.00414i | ||||||
\(560\) | 5.39735 | − | 2.42252i | 0.228080 | − | 0.102370i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.68642i | 0.366414i | ||||||||
\(563\) | 10.0061i | 0.421707i | 0.977518 | + | 0.210853i | \(0.0676243\pi\) | ||||
−0.977518 | + | 0.210853i | \(0.932376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.8925 | − | 14.6020i | 0.963095 | − | 0.614312i | ||||
\(566\) | 2.70267 | 0.113602 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 3.23047i | − | 0.135548i | ||||||
\(569\) | 23.8840i | 1.00127i | 0.865659 | + | 0.500634i | \(0.166900\pi\) | ||||
−0.865659 | + | 0.500634i | \(0.833100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0686 | −0.672449 | −0.336225 | − | 0.941782i | \(-0.609150\pi\) | ||||
−0.336225 | + | 0.941782i | \(0.609150\pi\) | |||||||
\(572\) | 0.855090i | 0.0357531i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.5472 | − | 1.54988i | −0.440231 | − | 0.0646909i | ||||
\(575\) | 9.68866 | − | 20.8379i | 0.404045 | − | 0.868999i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.4786 | −1.01906 | −0.509529 | − | 0.860453i | \(-0.670180\pi\) | ||||
−0.509529 | + | 0.860453i | \(0.670180\pi\) | |||||||
\(578\) | 23.1697 | 0.963733 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.09419 | − | 9.55423i | −0.253047 | − | 0.396718i | ||||
\(581\) | 3.10418 | − | 21.1244i | 0.128783 | − | 0.876387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.40203i | 0.0580660i | ||||||||
\(584\) | −8.74686 | −0.361948 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 5.74771i | − | 0.237436i | ||||||
\(587\) | − | 7.26576i | − | 0.299890i | −0.988694 | − | 0.149945i | \(-0.952090\pi\) | ||
0.988694 | − | 0.149945i | \(-0.0479097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.9048 | 1.72666 | ||||||||
\(590\) | −21.1444 | + | 13.4870i | −0.870503 | + | 0.555252i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 5.76125i | − | 0.236786i | ||||||
\(593\) | 9.67345i | 0.397241i | 0.980076 | + | 0.198621i | \(0.0636461\pi\) | ||||
−0.980076 | + | 0.198621i | \(0.936354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.3538 | − | 34.2082i | −0.629445 | − | 1.40240i | ||||
\(596\) | − | 2.61325i | − | 0.107043i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.2976 | 1.07539 | ||||||||
\(599\) | 23.7290i | 0.969542i | 0.874641 | + | 0.484771i | \(0.161097\pi\) | ||||
−0.874641 | + | 0.484771i | \(0.838903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.7532i | 1.66236i | 0.556005 | + | 0.831179i | \(0.312334\pi\) | ||||
−0.556005 | + | 0.831179i | \(0.687666\pi\) | |||||||
\(602\) | 1.59603 | − | 10.8612i | 0.0650492 | − | 0.442669i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.02652 | 0.0417685 | ||||||||
\(605\) | 20.6952 | − | 13.2005i | 0.841381 | − | 0.536677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1985 | 0.535710 | 0.267855 | − | 0.963459i | \(-0.413685\pi\) | ||||
0.267855 | + | 0.963459i | \(0.413685\pi\) | |||||||
\(608\) | − | 5.66504i | − | 0.229748i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 69.2202i | 2.80035i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.0175i | 1.13162i | 0.824537 | + | 0.565808i | \(0.191436\pi\) | ||||
−0.824537 | + | 0.565808i | \(0.808564\pi\) | |||||||
\(614\) | −5.82304 | −0.234999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0574844 | + | 0.391190i | −0.00231611 | + | 0.0157615i | ||||
\(617\) | 41.0463 | 1.65246 | 0.826230 | − | 0.563333i | \(-0.190481\pi\) | ||||
0.826230 | + | 0.563333i | \(0.190481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.8602i | 1.88347i | 0.336355 | + | 0.941735i | \(0.390806\pi\) | ||||
−0.336355 | + | 0.941735i | \(0.609194\pi\) | |||||||
\(620\) | −8.89490 | − | 13.9451i | −0.357228 | − | 0.560048i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.3290 | 0.694829 | ||||||||
\(623\) | −6.04885 | − | 0.888865i | −0.242342 | − | 0.0356116i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.1122 | − | 19.1153i | −0.644489 | − | 0.764613i | ||||
\(626\) | −1.43305 | −0.0572763 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.2216 | 0.806932 | ||||||||
\(629\) | −36.5146 | −1.45593 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.1150 | −0.402671 | −0.201335 | − | 0.979522i | \(-0.564528\pi\) | ||||
−0.201335 | + | 0.979522i | \(0.564528\pi\) | |||||||
\(632\) | 2.05057 | 0.0815672 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.31552 | −0.131676 | ||||||||
\(635\) | −9.31712 | − | 14.6070i | −0.369739 | − | 0.579662i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.3595 | − | 11.5225i | −1.51986 | − | 0.456538i | ||||
\(638\) | 0.757378 | 0.0299849 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.88521 | + | 1.20249i | −0.0745196 | + | 0.0475325i | ||||
\(641\) | 21.7604i | 0.859484i | 0.902952 | + | 0.429742i | \(0.141395\pi\) | ||||
−0.902952 | + | 0.429742i | \(0.858605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.9750 | −0.708866 | −0.354433 | − | 0.935081i | \(-0.615326\pi\) | ||||
−0.354433 | + | 0.935081i | \(0.615326\pi\) | |||||||
\(644\) | 12.0307 | + | 1.76789i | 0.474078 | + | 0.0696647i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −35.9048 | −1.41265 | ||||||||
\(647\) | − | 26.3383i | − | 1.03546i | −0.855543 | − | 0.517732i | \(-0.826777\pi\) | ||
0.855543 | − | 0.517732i | \(-0.173223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.67615i | − | 0.0657947i | ||||||
\(650\) | 12.0619 | − | 25.9421i | 0.473106 | − | 1.01753i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.46879i | 0.214174i | ||||||||
\(653\) | −8.28222 | −0.324108 | −0.162054 | − | 0.986782i | \(-0.551812\pi\) | ||||
−0.162054 | + | 0.986782i | \(0.551812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6565 | + | 11.2622i | −0.689895 | + | 0.440051i | ||||
\(656\) | 4.02927 | 0.157317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.65341 | + | 31.6671i | −0.181409 | + | 1.23451i | ||||
\(659\) | − | 0.515309i | − | 0.0200736i | −0.999950 | − | 0.0100368i | \(-0.996805\pi\) | ||
0.999950 | − | 0.0100368i | \(-0.00319486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.37717i | 0.364730i | 0.983231 | + | 0.182365i | \(0.0583752\pi\) | ||||
−0.983231 | + | 0.182365i | \(0.941625\pi\) | |||||||
\(662\) | −15.3087 | −0.594991 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.07001i | 0.313177i | ||||||||
\(665\) | 13.7237 | + | 30.5762i | 0.532180 | + | 1.18569i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 23.2926i | − | 0.901893i | ||||||
\(668\) | − | 9.70748i | − | 0.375594i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.8451 | − | 29.5446i | −0.728048 | − | 1.14141i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8974i | 0.458613i | 0.973354 | + | 0.229306i | \(0.0736457\pi\) | ||||
−0.973354 | + | 0.229306i | \(0.926354\pi\) | |||||||
\(674\) | 11.7701i | 0.453367i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.7392 | 0.759201 | ||||||||
\(677\) | − | 7.55519i | − | 0.290370i | −0.989405 | − | 0.145185i | \(-0.953622\pi\) | ||
0.989405 | − | 0.145185i | \(-0.0463777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5385 | − | 2.57725i | −0.673068 | − | 0.0989058i | ||||
\(680\) | 7.62131 | + | 11.9484i | 0.292264 | + | 0.458200i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.10545 | 0.0423298 | ||||||||
\(683\) | 2.71271 | 0.103799 | 0.0518995 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0518995 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.84407 | + | 3.08980i | −0.185082 | + | 0.118055i | ||||
\(686\) | −16.7743 | − | 7.85013i | −0.640444 | − | 0.299719i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.14923i | 0.158188i | ||||||||
\(689\) | 53.6801 | 2.04505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.7710i | 0.828209i | 0.910229 | + | 0.414104i | \(0.135905\pi\) | ||||
−0.910229 | + | 0.414104i | \(0.864095\pi\) | |||||||
\(692\) | 19.3174i | 0.734338i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6483 | −0.707880 | ||||||||
\(695\) | −17.6845 | − | 27.7250i | −0.670810 | − | 1.05167i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 25.5373i | − | 0.967296i | ||||||
\(698\) | − | 0.668016i | − | 0.0252848i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.26211 | − | 11.0572i | 0.274482 | − | 0.417923i | ||||
\(701\) | − | 17.6523i | − | 0.666717i | −0.942800 | − | 0.333359i | \(-0.891818\pi\) | ||
0.942800 | − | 0.333359i | \(-0.108182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.6377 | 1.23095 | ||||||||
\(704\) | − | 0.149444i | − | 0.00563237i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.16368i | − | 0.0437956i | ||||||
\(707\) | 19.0617 | + | 2.80107i | 0.716888 | + | 0.105345i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.2443 | 0.835404 | 0.417702 | − | 0.908584i | \(-0.362836\pi\) | ||||
0.417702 | + | 0.908584i | \(0.362836\pi\) | |||||||
\(710\) | −3.88460 | − | 6.09013i | −0.145786 | − | 0.228558i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.31080 | 0.0866010 | ||||||||
\(713\) | − | 33.9972i | − | 1.27321i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.02823 | + | 1.61203i | 0.0384538 | + | 0.0602863i | ||||
\(716\) | − | 10.9851i | − | 0.410533i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 27.8864i | − | 1.04071i | ||||||
\(719\) | −13.6286 | −0.508262 | −0.254131 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254131 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3087 | + | 2.24958i | 0.570127 | + | 0.0837789i | ||||
\(722\) | 13.0926 | 0.487257 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.83362i | 0.253970i | ||||||||
\(725\) | −22.9777 | − | 10.6836i | −0.853369 | − | 0.396778i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.1615 | 1.26698 | 0.633490 | − | 0.773751i | \(-0.281622\pi\) | ||||
0.633490 | + | 0.773751i | \(0.281622\pi\) | |||||||
\(728\) | 14.9777 | + | 2.20093i | 0.555109 | + | 0.0815721i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.4897 | + | 10.5180i | −0.610311 | + | 0.389288i | ||||
\(731\) | 26.2976 | 0.972653 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.783653 | 0.0289449 | 0.0144724 | − | 0.999895i | \(-0.495393\pi\) | ||||
0.0144724 | + | 0.999895i | \(0.495393\pi\) | |||||||
\(734\) | 27.6042 | 1.01889 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.59603 | −0.169412 | ||||||||
\(737\) | 2.34204 | 0.0862702 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1921 | 0.632420 | 0.316210 | − | 0.948689i | \(-0.397590\pi\) | ||||
0.316210 | + | 0.948689i | \(0.397590\pi\) | |||||||
\(740\) | −6.92783 | − | 10.8612i | −0.254672 | − | 0.399265i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.5578 | + | 3.60871i | 0.901544 | + | 0.132480i | ||||
\(743\) | −39.4123 | −1.44590 | −0.722949 | − | 0.690901i | \(-0.757214\pi\) | ||||
−0.722949 | + | 0.690901i | \(0.757214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.14240 | − | 4.92653i | −0.115128 | − | 0.180494i | ||||
\(746\) | − | 34.6305i | − | 1.26791i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.947167 | −0.0346319 | ||||||||
\(749\) | −10.9039 | − | 1.60230i | −0.398419 | − | 0.0585468i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.93560 | −0.289574 | −0.144787 | − | 0.989463i | \(-0.546250\pi\) | ||||
−0.144787 | + | 0.989463i | \(0.546250\pi\) | |||||||
\(752\) | − | 12.0976i | − | 0.441153i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 28.9981i | − | 1.05605i | ||||||
\(755\) | 1.93521 | − | 1.23438i | 0.0704294 | − | 0.0449235i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7949i | 0.864840i | 0.901672 | + | 0.432420i | \(0.142340\pi\) | ||||
−0.901672 | + | 0.432420i | \(0.857660\pi\) | |||||||
\(758\) | 13.1921 | 0.479157 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.81213 | − | 10.6798i | −0.247102 | − | 0.387397i | ||||
\(761\) | −36.7800 | −1.33327 | −0.666637 | − | 0.745383i | \(-0.732267\pi\) | ||||
−0.666637 | + | 0.745383i | \(0.732267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.2571 | − | 6.20959i | −1.52981 | − | 0.224802i | ||||
\(764\) | 16.2182i | 0.586754i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 15.2023i | − | 0.549280i | ||||||
\(767\) | −64.1756 | −2.31725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4381i | 0.881261i | 0.897688 | + | 0.440631i | \(0.145245\pi\) | ||||
−0.897688 | + | 0.440631i | \(0.854755\pi\) | |||||||
\(770\) | 0.362030 | + | 0.806600i | 0.0130467 | + | 0.0290678i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.8379i | 0.749971i | ||||||||
\(773\) | − | 31.9157i | − | 1.14793i | −0.818880 | − | 0.573964i | \(-0.805405\pi\) | ||
0.818880 | − | 0.573964i | \(-0.194595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.5375 | − | 15.5934i | −1.20470 | − | 0.560133i | ||||
\(776\) | 6.70014 | 0.240521 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.0512i | 0.969833i | ||||||||
\(779\) | 22.8260i | 0.817825i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.482774 | 0.0172750 | ||||||||
\(782\) | 29.1294i | 1.04167i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.70408 | + | 2.01378i | 0.239431 | + | 0.0719208i | ||||
\(785\) | 38.1221 | − | 24.3163i | 1.36064 | − | 0.867885i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.4244 | 1.36968 | 0.684841 | − | 0.728693i | \(-0.259872\pi\) | ||||
0.684841 | + | 0.728693i | \(0.259872\pi\) | |||||||
\(788\) | −5.64659 | −0.201152 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.86575 | − | 2.46578i | 0.137537 | − | 0.0877285i | ||||
\(791\) | 31.7865 | + | 4.67096i | 1.13020 | + | 0.166080i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.23781 | −0.0439284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 18.3142i | − | 0.649129i | ||||||
\(797\) | − | 36.4968i | − | 1.29278i | −0.763006 | − | 0.646391i | \(-0.776278\pi\) | ||
0.763006 | − | 0.646391i | \(-0.223722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −76.6739 | −2.71253 | ||||||||
\(800\) | −2.10805 | + | 4.53389i | −0.0745309 | + | 0.160297i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 36.2582i | − | 1.28032i | ||||||
\(803\) | − | 1.30716i | − | 0.0461288i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.8064 | − | 11.1340i | 0.874310 | − | 0.392421i | ||||
\(806\) | − | 42.3248i | − | 1.49083i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.28201 | −0.256180 | ||||||||
\(809\) | − | 27.1786i | − | 0.955548i | −0.878483 | − | 0.477774i | \(-0.841444\pi\) | ||
0.878483 | − | 0.477774i | \(-0.158556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.1896i | − | 0.392919i | −0.980512 | − | 0.196459i | \(-0.937056\pi\) | ||
0.980512 | − | 0.196459i | \(-0.0629443\pi\) | |||||||
\(812\) | 1.94943 | − | 13.2662i | 0.0684117 | − | 0.465551i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.860983 | 0.0301774 | ||||||||
\(815\) | 6.57615 | + | 10.3098i | 0.230352 | + | 0.361138i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.5055 | −0.822355 | ||||||||
\(818\) | − | 32.1246i | − | 1.12321i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.59603 | − | 4.84514i | 0.265265 | − | 0.169200i | ||||
\(821\) | 26.1287i | 0.911898i | 0.890006 | + | 0.455949i | \(0.150700\pi\) | ||||
−0.890006 | + | 0.455949i | \(0.849300\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5532i | 0.751298i | 0.926762 | + | 0.375649i | \(0.122580\pi\) | ||||
−0.926762 | + | 0.375649i | \(0.877420\pi\) | |||||||
\(824\) | −5.84830 | −0.203735 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.3593 | − | 4.31428i | −1.02154 | − | 0.150113i | ||||
\(827\) | 43.9107 | 1.52692 | 0.763462 | − | 0.645853i | \(-0.223498\pi\) | ||||
0.763462 | + | 0.645853i | \(0.223498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8397i | 1.00165i | 0.865550 | + | 0.500823i | \(0.166969\pi\) | ||||
−0.865550 | + | 0.500823i | \(0.833031\pi\) | |||||||
\(830\) | 9.70408 | + | 15.2137i | 0.336833 | + | 0.528075i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.72182 | −0.198368 | ||||||||
\(833\) | 12.7633 | − | 42.4902i | 0.442221 | − | 1.47220i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6731 | − | 18.3007i | −0.403965 | − | 0.633320i | ||||
\(836\) | 0.846603 | 0.0292804 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.6549 | −0.437156 | ||||||||
\(839\) | 27.7255 | 0.957189 | 0.478595 | − | 0.878036i | \(-0.341146\pi\) | ||||
0.478595 | + | 0.878036i | \(0.341146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31552 | 0.114328 | ||||||||
\(842\) | 24.2468 | 0.835600 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.54546 | 0.0876184 | ||||||||
\(845\) | 37.2126 | − | 23.7362i | 1.28015 | − | 0.816549i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.7356 | + | 4.22263i | 0.987366 | + | 0.145091i | ||||
\(848\) | −9.38164 | −0.322167 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 28.7356 | + | 13.3607i | 0.985622 | + | 0.458270i | ||||
\(851\) | − | 26.4789i | − | 0.907684i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.2528 | 0.830400 | 0.415200 | − | 0.909730i | \(-0.363712\pi\) | ||||
0.415200 | + | 0.909730i | \(0.363712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.16554 | 0.142375 | ||||||||
\(857\) | 0.779409i | 0.0266241i | 0.999911 | + | 0.0133120i | \(0.00423748\pi\) | ||||
−0.999911 | + | 0.0133120i | \(0.995763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16.0573i | − | 0.547869i | −0.961748 | − | 0.273935i | \(-0.911675\pi\) | ||
0.961748 | − | 0.273935i | \(-0.0883252\pi\) | |||||||
\(860\) | 4.98939 | + | 7.82218i | 0.170137 | + | 0.266734i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 5.73916i | − | 0.195477i | ||||||
\(863\) | −18.5430 | −0.631211 | −0.315605 | − | 0.948891i | \(-0.602208\pi\) | ||||
−0.315605 | + | 0.948891i | \(0.602208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.2289 | + | 36.4174i | 0.789807 | + | 1.23823i | ||||
\(866\) | 8.54573 | 0.290396 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.84534 | − | 19.3629i | 0.0965770 | − | 0.657220i | ||||
\(869\) | 0.306444i | 0.0103954i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 89.6709i | − | 3.03838i | ||||||
\(872\) | 16.1432 | 0.546678 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 26.0367i | − | 0.880703i | ||||||
\(875\) | 0.394475 | − | 29.5778i | 0.0133357 | − | 0.999911i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.5808i | 0.897570i | 0.893640 | + | 0.448785i | \(0.148143\pi\) | ||||
−0.893640 | + | 0.448785i | \(0.851857\pi\) | |||||||
\(878\) | 8.38350i | 0.282930i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.179704 | − | 0.281733i | −0.00605782 | − | 0.00949722i | ||||
\(881\) | 15.7648 | 0.531129 | 0.265565 | − | 0.964093i | \(-0.414442\pi\) | ||||
0.265565 | + | 0.964093i | \(0.414442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.3087i | 1.76033i | 0.474670 | + | 0.880164i | \(0.342567\pi\) | ||||
−0.474670 | + | 0.880164i | \(0.657433\pi\) | |||||||
\(884\) | 36.2647i | 1.21971i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.61158 | 0.222120 | ||||||||
\(887\) | − | 33.6308i | − | 1.12921i | −0.825361 | − | 0.564606i | \(-0.809028\pi\) | ||
0.825361 | − | 0.564606i | \(-0.190972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.98040 | − | 20.2820i | 0.0999594 | − | 0.680237i | ||||
\(890\) | 4.35636 | − | 2.77871i | 0.146025 | − | 0.0931426i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.7080 | 0.994698 | ||||||||
\(893\) | 68.5332 | 2.29338 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.2094 | − | 20.7093i | −0.441543 | − | 0.692234i | ||||
\(896\) | −2.61764 | − | 0.384656i | −0.0874492 | − | 0.0128505i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5221i | 0.651460i | ||||||||
\(899\) | −37.4883 | −1.25031 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.4604i | 1.98091i | ||||||||
\(902\) | 0.602148i | 0.0200494i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.1432 | −0.403877 | ||||||||
\(905\) | 8.21734 | + | 12.8828i | 0.273154 | + | 0.428240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 35.2451i | − | 1.17030i | −0.810927 | − | 0.585148i | \(-0.801037\pi\) | ||
0.810927 | − | 0.585148i | \(-0.198963\pi\) | |||||||
\(908\) | 20.7727i | 0.689366i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.8827 | − | 13.8612i | 1.02375 | − | 0.459495i | ||||
\(911\) | − | 31.1169i | − | 1.03095i | −0.856905 | − | 0.515474i | \(-0.827616\pi\) | ||
0.856905 | − | 0.515474i | \(-0.172384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.20601 | −0.0399132 | ||||||||
\(914\) | 16.2220i | 0.536576i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 14.7942i | − | 0.488813i | ||||||
\(917\) | −24.5162 | − | 3.60260i | −0.809597 | − | 0.118968i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.2177 | 1.82146 | 0.910732 | − | 0.412998i | \(-0.135518\pi\) | ||||
0.910732 | + | 0.412998i | \(0.135518\pi\) | |||||||
\(920\) | −8.66449 | + | 5.52666i | −0.285660 | + | 0.182209i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.9692 | 0.954049 | ||||||||
\(923\) | − | 18.4842i | − | 0.608414i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.1209 | − | 12.1450i | −0.858849 | − | 0.399326i | ||||
\(926\) | − | 17.6872i | − | 0.581238i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.06799i | 0.166365i | ||||||||
\(929\) | −37.5882 | −1.23323 | −0.616615 | − | 0.787265i | \(-0.711496\pi\) | ||||
−0.616615 | + | 0.787265i | \(0.711496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.4082 | + | 37.9789i | −0.373887 | + | 1.24471i | ||||
\(932\) | −13.7110 | −0.449119 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 6.31118i | − | 0.206508i | ||||||
\(935\) | −1.78561 | + | 1.13896i | −0.0583958 | + | 0.0372479i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.0452 | −1.14488 | −0.572438 | − | 0.819948i | \(-0.694002\pi\) | ||||
−0.572438 | + | 0.819948i | \(0.694002\pi\) | |||||||
\(938\) | 6.02823 | − | 41.0230i | 0.196829 | − | 1.33945i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.5472 | − | 22.8065i | −0.474477 | − | 0.743866i | ||||
\(941\) | 13.4203 | 0.437489 | 0.218745 | − | 0.975782i | \(-0.429804\pi\) | ||||
0.218745 | + | 0.975782i | \(0.429804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.5186 | 0.603050 | ||||||||
\(944\) | 11.2159 | 0.365048 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.620076 | −0.0201604 | ||||||||
\(947\) | −51.7451 | −1.68149 | −0.840745 | − | 0.541431i | \(-0.817883\pi\) | ||||
−0.840745 | + | 0.541431i | \(0.817883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.0480 | −1.62463 | ||||||||
\(950\) | −25.6846 | − | 11.9422i | −0.833319 | − | 0.387456i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.43794 | + | 16.5905i | −0.0790140 | + | 0.537701i | ||||
\(953\) | −29.5796 | −0.958177 | −0.479089 | − | 0.877767i | \(-0.659033\pi\) | ||||
−0.479089 | + | 0.877767i | \(0.659033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5022 | + | 30.5748i | 0.631076 | + | 0.989376i | ||||
\(956\) | − | 2.77836i | − | 0.0898587i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.0152 | 0.323575 | ||||||||
\(959\) | −6.72605 | − | 0.988378i | −0.217195 | − | 0.0319164i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.7169 | −0.765061 | ||||||||
\(962\) | − | 32.9649i | − | 1.06283i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 17.0438i | − | 0.548943i | ||||||
\(965\) | 25.0573 | + | 39.2838i | 0.806621 | + | 1.26459i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8966i | 0.961409i | 0.876883 | + | 0.480704i | \(0.159619\pi\) | ||||
−0.876883 | + | 0.480704i | \(0.840381\pi\) | |||||||
\(968\) | −10.9777 | −0.352836 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.6312 | − | 8.05682i | 0.405563 | − | 0.258689i | ||||
\(971\) | 24.7109 | 0.793010 | 0.396505 | − | 0.918033i | \(-0.370223\pi\) | ||||
0.396505 | + | 0.918033i | \(0.370223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.65698 | − | 38.4966i | 0.181355 | − | 1.23414i | ||||
\(974\) | − | 7.76766i | − | 0.248892i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.32936 | 0.0425299 | 0.0212649 | − | 0.999774i | \(-0.493231\pi\) | ||||
0.0212649 | + | 0.999774i | \(0.493231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.345335i | 0.0110369i | ||||||||
\(980\) | 15.0602 | − | 4.26516i | 0.481079 | − | 0.136245i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.1397i | 0.387395i | ||||||||
\(983\) | 36.7355i | 1.17168i | 0.810427 | + | 0.585840i | \(0.199235\pi\) | ||||
−0.810427 | + | 0.585840i | \(0.800765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6450 | + | 6.78995i | −0.339179 | + | 0.216346i | ||||
\(986\) | 32.1207 | 1.02293 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 32.4143i | − | 1.03124i | ||||||
\(989\) | 19.0700i | 0.606390i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0805 | −0.860241 | −0.430120 | − | 0.902772i | \(-0.641529\pi\) | ||||
−0.430120 | + | 0.902772i | \(0.641529\pi\) | |||||||
\(992\) | 7.39709i | 0.234858i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.24262 | − | 8.45622i | 0.0394136 | − | 0.268215i | ||||
\(995\) | −22.0226 | − | 34.5261i | −0.698162 | − | 1.09455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.3312 | −1.65735 | −0.828673 | − | 0.559733i | \(-0.810904\pi\) | ||||
−0.828673 | + | 0.559733i | \(0.810904\pi\) | |||||||
\(998\) | −25.5231 | −0.807920 | ||||||||
\(999\) | 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 | 1890.2.d.e.1889.13 | yes | 16 | |
3.2 | odd | 2 | 1890.2.d.f.1889.4 | yes | 16 | ||
5.4 | even | 2 | 1890.2.d.f.1889.14 | yes | 16 | ||
7.6 | odd | 2 | inner | 1890.2.d.e.1889.4 | yes | 16 | |
15.14 | odd | 2 | inner | 1890.2.d.e.1889.3 | ✓ | 16 | |
21.20 | even | 2 | 1890.2.d.f.1889.13 | yes | 16 | ||
35.34 | odd | 2 | 1890.2.d.f.1889.3 | yes | 16 | ||
105.104 | even | 2 | inner | 1890.2.d.e.1889.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.d.e.1889.3 | ✓ | 16 | 15.14 | odd | 2 | inner | |
1890.2.d.e.1889.4 | yes | 16 | 7.6 | odd | 2 | inner | |
1890.2.d.e.1889.13 | yes | 16 | 1.1 | even | 1 | trivial | |
1890.2.d.e.1889.14 | yes | 16 | 105.104 | even | 2 | inner | |
1890.2.d.f.1889.3 | yes | 16 | 35.34 | odd | 2 | ||
1890.2.d.f.1889.4 | yes | 16 | 3.2 | odd | 2 | ||
1890.2.d.f.1889.13 | yes | 16 | 21.20 | even | 2 | ||
1890.2.d.f.1889.14 | yes | 16 | 5.4 | even | 2 |