Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,2,Mod(164,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.164");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(1.31753163335\) |
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: | \( x^{16} - 24x^{14} + 244x^{12} - 1224x^{10} + 2880x^{8} - 2208x^{6} + 3976x^{4} + 432x^{2} + 2116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 164.3 | ||
Root | \(-2.48916 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.164 |
Dual form | 165.2.d.c.164.16 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.39417i | − | 1.69293i | −0.532441 | − | 0.846467i | \(-0.678725\pi\) | ||
0.532441 | − | 0.846467i | \(-0.321275\pi\) | |||||||
\(3\) | 0.796225 | − | 1.53819i | 0.459701 | − | 0.888074i | ||||
\(4\) | −3.73205 | −1.86603 | ||||||||
\(5\) | 2.17533 | + | 0.517638i | 0.972836 | + | 0.231495i | ||||
\(6\) | −3.68269 | − | 1.90630i | −1.50345 | − | 0.778243i | ||||
\(7\) | −3.38587 | −1.27974 | −0.639869 | − | 0.768484i | \(-0.721011\pi\) | ||||
−0.639869 | + | 0.768484i | \(0.721011\pi\) | |||||||
\(8\) | 4.14682i | 1.46612i | ||||||||
\(9\) | −1.73205 | − | 2.44949i | −0.577350 | − | 0.816497i | ||||
\(10\) | 1.23931 | − | 5.20810i | 0.391905 | − | 1.64695i | ||||
\(11\) | 2.69591 | + | 1.93185i | 0.812848 | + | 0.582475i | ||||
\(12\) | −2.97155 | + | 5.74060i | −0.857813 | + | 1.65717i | ||||
\(13\) | 3.38587 | 0.939071 | 0.469535 | − | 0.882914i | \(-0.344421\pi\) | ||||
0.469535 | + | 0.882914i | \(0.344421\pi\) | |||||||
\(14\) | 8.10634i | 2.16651i | ||||||||
\(15\) | 2.52828 | − | 2.93391i | 0.652798 | − | 0.757532i | ||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | − | 1.75265i | − | 0.425081i | −0.977152 | − | 0.212541i | \(-0.931826\pi\) | ||
0.977152 | − | 0.212541i | \(-0.0681738\pi\) | |||||||
\(18\) | −5.86450 | + | 4.14682i | −1.38227 | + | 0.977416i | ||||
\(19\) | 3.81260i | 0.874670i | 0.899299 | + | 0.437335i | \(0.144078\pi\) | ||||
−0.899299 | + | 0.437335i | \(0.855922\pi\) | |||||||
\(20\) | −8.11843 | − | 1.93185i | −1.81534 | − | 0.431975i | ||||
\(21\) | −2.69591 | + | 5.20810i | −0.588297 | + | 1.13650i | ||||
\(22\) | 4.62518 | − | 6.45448i | 0.986092 | − | 1.37610i | ||||
\(23\) | 2.75821 | 0.575126 | 0.287563 | − | 0.957762i | \(-0.407155\pi\) | ||||
0.287563 | + | 0.957762i | \(0.407155\pi\) | |||||||
\(24\) | 6.37860 | + | 3.30181i | 1.30203 | + | 0.673978i | ||||
\(25\) | 4.46410 | + | 2.25207i | 0.892820 | + | 0.450413i | ||||
\(26\) | − | 8.10634i | − | 1.58978i | ||||||
\(27\) | −5.14688 | + | 0.713876i | −0.990518 | + | 0.137386i | ||||
\(28\) | 12.6362 | 2.38802 | ||||||||
\(29\) | 1.97355 | 0.366478 | 0.183239 | − | 0.983068i | \(-0.441342\pi\) | ||||
0.183239 | + | 0.983068i | \(0.441342\pi\) | |||||||
\(30\) | −7.02428 | − | 6.05312i | −1.28245 | − | 1.10514i | ||||
\(31\) | −3.46410 | −0.622171 | −0.311086 | − | 0.950382i | \(-0.600693\pi\) | ||||
−0.311086 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(32\) | 2.39417i | 0.423233i | ||||||||
\(33\) | 5.11811 | − | 2.60864i | 0.890948 | − | 0.454105i | ||||
\(34\) | −4.19615 | −0.719634 | ||||||||
\(35\) | −7.36537 | − | 1.75265i | −1.24498 | − | 0.296253i | ||||
\(36\) | 6.46410 | + | 9.14162i | 1.07735 | + | 1.52360i | ||||
\(37\) | − | 8.40482i | − | 1.38174i | −0.722977 | − | 0.690872i | \(-0.757227\pi\) | ||
0.722977 | − | 0.690872i | \(-0.242773\pi\) | |||||||
\(38\) | 9.12801 | 1.48076 | ||||||||
\(39\) | 2.69591 | − | 5.20810i | 0.431692 | − | 0.833964i | ||||
\(40\) | −2.14655 | + | 9.02070i | −0.339400 | + | 1.42630i | ||||
\(41\) | 7.36537 | 1.15028 | 0.575139 | − | 0.818056i | \(-0.304948\pi\) | ||||
0.575139 | + | 0.818056i | \(0.304948\pi\) | |||||||
\(42\) | 12.4691 | + | 6.45448i | 1.92402 | + | 0.995947i | ||||
\(43\) | −8.34312 | −1.27231 | −0.636157 | − | 0.771560i | \(-0.719477\pi\) | ||||
−0.636157 | + | 0.771560i | \(0.719477\pi\) | |||||||
\(44\) | −10.0613 | − | 7.20977i | −1.51680 | − | 1.08691i | ||||
\(45\) | −2.49983 | − | 6.22502i | −0.372653 | − | 0.927971i | ||||
\(46\) | − | 6.60361i | − | 0.973650i | ||||||
\(47\) | 1.59245 | 0.232283 | 0.116141 | − | 0.993233i | \(-0.462947\pi\) | ||||
0.116141 | + | 0.993233i | \(0.462947\pi\) | |||||||
\(48\) | 1.96198 | − | 3.79025i | 0.283187 | − | 0.547076i | ||||
\(49\) | 4.46410 | 0.637729 | ||||||||
\(50\) | 5.39183 | − | 10.6878i | 0.762519 | − | 1.51149i | ||||
\(51\) | −2.69591 | − | 1.39551i | −0.377503 | − | 0.195410i | ||||
\(52\) | −12.6362 | −1.75233 | ||||||||
\(53\) | −8.70131 | −1.19522 | −0.597608 | − | 0.801788i | \(-0.703882\pi\) | ||||
−0.597608 | + | 0.801788i | \(0.703882\pi\) | |||||||
\(54\) | 1.70914 | + | 12.3225i | 0.232585 | + | 1.67688i | ||||
\(55\) | 4.86450 | + | 5.59792i | 0.655928 | + | 0.754823i | ||||
\(56\) | − | 14.0406i | − | 1.87625i | ||||||
\(57\) | 5.86450 | + | 3.03569i | 0.776771 | + | 0.402086i | ||||
\(58\) | − | 4.72500i | − | 0.620423i | ||||||
\(59\) | 4.89898i | 0.637793i | 0.947790 | + | 0.318896i | \(0.103312\pi\) | ||||
−0.947790 | + | 0.318896i | \(0.896688\pi\) | |||||||
\(60\) | −9.43565 | + | 10.9495i | −1.21814 | + | 1.41357i | ||||
\(61\) | 10.4162i | 1.33366i | 0.745210 | + | 0.666829i | \(0.232349\pi\) | ||||
−0.745210 | + | 0.666829i | \(0.767651\pi\) | |||||||
\(62\) | 8.29365i | 1.05329i | ||||||||
\(63\) | 5.86450 | + | 8.29365i | 0.738857 | + | 1.04490i | ||||
\(64\) | 10.6603 | 1.33253 | ||||||||
\(65\) | 7.36537 | + | 1.75265i | 0.913562 | + | 0.217390i | ||||
\(66\) | −6.24552 | − | 12.2536i | −0.768770 | − | 1.50832i | ||||
\(67\) | 13.1298i | 1.60406i | 0.597281 | + | 0.802032i | \(0.296248\pi\) | ||||
−0.597281 | + | 0.802032i | \(0.703752\pi\) | |||||||
\(68\) | 6.54099i | 0.793212i | ||||||||
\(69\) | 2.19615 | − | 4.24264i | 0.264386 | − | 0.510754i | ||||
\(70\) | −4.19615 | + | 17.6340i | −0.501536 | + | 2.10766i | ||||
\(71\) | 3.58630i | 0.425616i | 0.977094 | + | 0.212808i | \(0.0682608\pi\) | ||||
−0.977094 | + | 0.212808i | \(0.931739\pi\) | |||||||
\(72\) | 10.1576 | − | 7.18251i | 1.19709 | − | 0.846467i | ||||
\(73\) | −3.38587 | −0.396286 | −0.198143 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198143 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(74\) | −20.1226 | −2.33920 | ||||||||
\(75\) | 7.01853 | − | 5.07348i | 0.810430 | − | 0.585835i | ||||
\(76\) | − | 14.2288i | − | 1.63216i | ||||||
\(77\) | −9.12801 | − | 6.54099i | −1.04023 | − | 0.745416i | ||||
\(78\) | −12.4691 | − | 6.45448i | −1.41185 | − | 0.730825i | ||||
\(79\) | − | 11.4378i | − | 1.28685i | −0.765508 | − | 0.643426i | \(-0.777512\pi\) | ||
0.765508 | − | 0.643426i | \(-0.222488\pi\) | |||||||
\(80\) | 5.36023 | + | 1.27551i | 0.599292 | + | 0.142607i | ||||
\(81\) | −3.00000 | + | 8.48528i | −0.333333 | + | 0.942809i | ||||
\(82\) | − | 17.6340i | − | 1.94734i | ||||||
\(83\) | 10.0463i | 1.10273i | 0.834266 | + | 0.551363i | \(0.185892\pi\) | ||||
−0.834266 | + | 0.551363i | \(0.814108\pi\) | |||||||
\(84\) | 10.0613 | − | 19.4369i | 1.09778 | − | 2.12074i | ||||
\(85\) | 0.907241 | − | 3.81260i | 0.0984041 | − | 0.413534i | ||||
\(86\) | 19.9749i | 2.15394i | ||||||||
\(87\) | 1.57139 | − | 3.03569i | 0.168470 | − | 0.325460i | ||||
\(88\) | −8.01105 | + | 11.1795i | −0.853981 | + | 1.19174i | ||||
\(89\) | − | 9.52056i | − | 1.00918i | −0.863360 | − | 0.504589i | \(-0.831644\pi\) | ||
0.863360 | − | 0.504589i | \(-0.168356\pi\) | |||||||
\(90\) | −14.9038 | + | 5.98502i | −1.57099 | + | 0.630876i | ||||
\(91\) | −11.4641 | −1.20176 | ||||||||
\(92\) | −10.2938 | −1.07320 | ||||||||
\(93\) | −2.75821 | + | 5.32844i | −0.286013 | + | 0.552534i | ||||
\(94\) | − | 3.81260i | − | 0.393239i | ||||||
\(95\) | −1.97355 | + | 8.29365i | −0.202482 | + | 0.850910i | ||||
\(96\) | 3.68269 | + | 1.90630i | 0.375863 | + | 0.194561i | ||||
\(97\) | 8.40482i | 0.853380i | 0.904398 | + | 0.426690i | \(0.140321\pi\) | ||||
−0.904398 | + | 0.426690i | \(0.859679\pi\) | |||||||
\(98\) | − | 10.6878i | − | 1.07963i | ||||||
\(99\) | 0.0625918 | − | 9.94968i | 0.00629071 | − | 0.999980i | ||||
\(100\) | −16.6603 | − | 8.40482i | −1.66603 | − | 0.840482i | ||||
\(101\) | −1.97355 | −0.196375 | −0.0981876 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981876 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(102\) | −3.34108 | + | 6.45448i | −0.330816 | + | 0.639088i | ||||
\(103\) | − | 0.824313i | − | 0.0812220i | −0.999175 | − | 0.0406110i | \(-0.987070\pi\) | ||
0.999175 | − | 0.0406110i | \(-0.0129304\pi\) | |||||||
\(104\) | 14.0406i | 1.37679i | ||||||||
\(105\) | −8.56041 | + | 9.93383i | −0.835410 | + | 0.969442i | ||||
\(106\) | 20.8324i | 2.02342i | ||||||||
\(107\) | − | 6.54099i | − | 0.632342i | −0.948702 | − | 0.316171i | \(-0.897603\pi\) | ||
0.948702 | − | 0.316171i | \(-0.102397\pi\) | |||||||
\(108\) | 19.2084 | − | 2.66422i | 1.84833 | − | 0.256365i | ||||
\(109\) | − | 2.79101i | − | 0.267331i | −0.991027 | − | 0.133665i | \(-0.957325\pi\) | ||
0.991027 | − | 0.133665i | \(-0.0426747\pi\) | |||||||
\(110\) | 13.4024 | − | 11.6464i | 1.27787 | − | 1.11044i | ||||
\(111\) | −12.9282 | − | 6.69213i | −1.22709 | − | 0.635189i | ||||
\(112\) | −8.34312 | −0.788351 | ||||||||
\(113\) | 5.51641 | 0.518940 | 0.259470 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259470 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(114\) | 7.26795 | − | 14.0406i | 0.680706 | − | 1.31502i | ||||
\(115\) | 6.00000 | + | 1.42775i | 0.559503 | + | 0.133139i | ||||
\(116\) | −7.36537 | −0.683858 | ||||||||
\(117\) | −5.86450 | − | 8.29365i | −0.542173 | − | 0.766748i | ||||
\(118\) | 11.7290 | 1.07974 | ||||||||
\(119\) | 5.93426i | 0.543992i | ||||||||
\(120\) | 12.1664 | + | 10.4843i | 1.11064 | + | 0.957083i | ||||
\(121\) | 3.53590 | + | 10.4162i | 0.321445 | + | 0.946928i | ||||
\(122\) | 24.9382 | 2.25780 | ||||||||
\(123\) | 5.86450 | − | 11.3293i | 0.528784 | − | 1.02153i | ||||
\(124\) | 12.9282 | 1.16099 | ||||||||
\(125\) | 8.54513 | + | 7.20977i | 0.764300 | + | 0.644861i | ||||
\(126\) | 19.8564 | − | 14.0406i | 1.76895 | − | 1.25084i | ||||
\(127\) | −16.9293 | −1.50224 | −0.751118 | − | 0.660168i | \(-0.770485\pi\) | ||||
−0.751118 | + | 0.660168i | \(0.770485\pi\) | |||||||
\(128\) | − | 20.7341i | − | 1.83265i | ||||||
\(129\) | −6.64300 | + | 12.8333i | −0.584884 | + | 1.12991i | ||||
\(130\) | 4.19615 | − | 17.6340i | 0.368027 | − | 1.54660i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −19.1010 | + | 9.73556i | −1.66253 | + | 0.847372i | ||||
\(133\) | − | 12.9090i | − | 1.11935i | ||||||
\(134\) | 31.4350 | 2.71557 | ||||||||
\(135\) | −11.5657 | − | 1.11131i | −0.995415 | − | 0.0956461i | ||||
\(136\) | 7.26795 | 0.623222 | ||||||||
\(137\) | 4.35066 | 0.371702 | 0.185851 | − | 0.982578i | \(-0.440496\pi\) | ||||
0.185851 | + | 0.982578i | \(0.440496\pi\) | |||||||
\(138\) | −10.1576 | − | 5.25796i | −0.864673 | − | 0.447588i | ||||
\(139\) | − | 1.02158i | − | 0.0866495i | −0.999061 | − | 0.0433247i | \(-0.986205\pi\) | ||
0.999061 | − | 0.0433247i | \(-0.0137950\pi\) | |||||||
\(140\) | 27.4879 | + | 6.54099i | 2.32316 | + | 0.552815i | ||||
\(141\) | 1.26795 | − | 2.44949i | 0.106781 | − | 0.206284i | ||||
\(142\) | 8.58622 | 0.720539 | ||||||||
\(143\) | 9.12801 | + | 6.54099i | 0.763322 | + | 0.546985i | ||||
\(144\) | −4.26795 | − | 6.03579i | −0.355662 | − | 0.502983i | ||||
\(145\) | 4.29311 | + | 1.02158i | 0.356523 | + | 0.0848378i | ||||
\(146\) | 8.10634i | 0.670886i | ||||||||
\(147\) | 3.55443 | − | 6.86663i | 0.293164 | − | 0.566350i | ||||
\(148\) | 31.3672i | 2.57837i | ||||||||
\(149\) | −3.41828 | −0.280037 | −0.140018 | − | 0.990149i | \(-0.544716\pi\) | ||||
−0.140018 | + | 0.990149i | \(0.544716\pi\) | |||||||
\(150\) | −12.1468 | − | 16.8036i | −0.991780 | − | 1.37200i | ||||
\(151\) | − | 21.8540i | − | 1.77845i | −0.457467 | − | 0.889227i | \(-0.651243\pi\) | ||
0.457467 | − | 0.889227i | \(-0.348757\pi\) | |||||||
\(152\) | −15.8102 | −1.28237 | ||||||||
\(153\) | −4.29311 | + | 3.03569i | −0.347077 | + | 0.245421i | ||||
\(154\) | −15.6603 | + | 21.8540i | −1.26194 | + | 1.76105i | ||||
\(155\) | −7.53556 | − | 1.79315i | −0.605270 | − | 0.144029i | ||||
\(156\) | −10.0613 | + | 19.4369i | −0.805548 | + | 1.55620i | ||||
\(157\) | 4.50413i | 0.359469i | 0.983715 | + | 0.179734i | \(0.0575238\pi\) | ||||
−0.983715 | + | 0.179734i | \(0.942476\pi\) | |||||||
\(158\) | −27.3840 | −2.17856 | ||||||||
\(159\) | −6.92820 | + | 13.3843i | −0.549442 | + | 1.06144i | ||||
\(160\) | −1.23931 | + | 5.20810i | −0.0979763 | + | 0.411737i | ||||
\(161\) | −9.33892 | −0.736010 | ||||||||
\(162\) | 20.3152 | + | 7.18251i | 1.59611 | + | 0.564311i | ||||
\(163\) | 0.824313i | 0.0645652i | 0.999479 | + | 0.0322826i | \(0.0102777\pi\) | ||||
−0.999479 | + | 0.0322826i | \(0.989722\pi\) | |||||||
\(164\) | −27.4879 | −2.14645 | ||||||||
\(165\) | 12.4839 | − | 3.02531i | 0.971869 | − | 0.235520i | ||||
\(166\) | 24.0526 | 1.86684 | ||||||||
\(167\) | − | 12.6124i | − | 0.975974i | −0.872851 | − | 0.487987i | \(-0.837731\pi\) | ||
0.872851 | − | 0.487987i | \(-0.162269\pi\) | |||||||
\(168\) | −21.5971 | − | 11.1795i | −1.66625 | − | 0.862516i | ||||
\(169\) | −1.53590 | −0.118146 | ||||||||
\(170\) | −9.12801 | − | 2.17209i | −0.700086 | − | 0.166592i | ||||
\(171\) | 9.33892 | − | 6.60361i | 0.714165 | − | 0.504991i | ||||
\(172\) | 31.1370 | 2.37417 | ||||||||
\(173\) | − | 18.3400i | − | 1.39436i | −0.716896 | − | 0.697180i | \(-0.754438\pi\) | ||
0.716896 | − | 0.697180i | \(-0.245562\pi\) | |||||||
\(174\) | −7.26795 | − | 3.76217i | −0.550982 | − | 0.285209i | ||||
\(175\) | −15.1149 | − | 7.62519i | −1.14258 | − | 0.576411i | ||||
\(176\) | 6.64300 | + | 4.76028i | 0.500735 | + | 0.358820i | ||||
\(177\) | 7.53556 | + | 3.90069i | 0.566407 | + | 0.293194i | ||||
\(178\) | −22.7938 | −1.70847 | ||||||||
\(179\) | − | 5.17638i | − | 0.386901i | −0.981110 | − | 0.193450i | \(-0.938032\pi\) | ||
0.981110 | − | 0.193450i | \(-0.0619679\pi\) | |||||||
\(180\) | 9.32949 | + | 23.2321i | 0.695379 | + | 1.73162i | ||||
\(181\) | −2.53590 | −0.188492 | −0.0942459 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942459 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(182\) | 27.4470i | 2.03451i | ||||||||
\(183\) | 16.0221 | + | 8.29365i | 1.18439 | + | 0.613084i | ||||
\(184\) | 11.4378i | 0.843205i | ||||||||
\(185\) | 4.35066 | − | 18.2832i | 0.319867 | − | 1.34421i | ||||
\(186\) | 12.7572 | + | 6.60361i | 0.935403 | + | 0.484200i | ||||
\(187\) | 3.38587 | − | 4.72500i | 0.247599 | − | 0.345527i | ||||
\(188\) | −5.94311 | −0.433446 | ||||||||
\(189\) | 17.4267 | − | 2.41709i | 1.26760 | − | 0.175817i | ||||
\(190\) | 19.8564 | + | 4.72500i | 1.44054 | + | 0.342788i | ||||
\(191\) | − | 4.62158i | − | 0.334406i | −0.985923 | − | 0.167203i | \(-0.946527\pi\) | ||
0.985923 | − | 0.167203i | \(-0.0534735\pi\) | |||||||
\(192\) | 8.48796 | − | 16.3975i | 0.612566 | − | 1.18339i | ||||
\(193\) | −16.9293 | −1.21860 | −0.609300 | − | 0.792940i | \(-0.708550\pi\) | ||||
−0.609300 | + | 0.792940i | \(0.708550\pi\) | |||||||
\(194\) | 20.1226 | 1.44472 | ||||||||
\(195\) | 8.56041 | − | 9.93383i | 0.613024 | − | 0.711376i | ||||
\(196\) | −16.6603 | −1.19002 | ||||||||
\(197\) | 20.9060i | 1.48949i | 0.667348 | + | 0.744746i | \(0.267429\pi\) | ||||
−0.667348 | + | 0.744746i | \(0.732571\pi\) | |||||||
\(198\) | −23.8212 | − | 0.149855i | −1.69290 | − | 0.0106498i | ||||
\(199\) | −2.92820 | −0.207575 | −0.103787 | − | 0.994600i | \(-0.533096\pi\) | ||||
−0.103787 | + | 0.994600i | \(0.533096\pi\) | |||||||
\(200\) | −9.33892 | + | 18.5118i | −0.660361 | + | 1.30899i | ||||
\(201\) | 20.1962 | + | 10.4543i | 1.42453 | + | 0.737389i | ||||
\(202\) | 4.72500i | 0.332450i | ||||||||
\(203\) | −6.68216 | −0.468996 | ||||||||
\(204\) | 10.0613 | + | 5.20810i | 0.704431 | + | 0.364640i | ||||
\(205\) | 16.0221 | + | 3.81260i | 1.11903 | + | 0.266283i | ||||
\(206\) | −1.97355 | −0.137503 | ||||||||
\(207\) | −4.77735 | − | 6.75620i | −0.332049 | − | 0.469588i | ||||
\(208\) | 8.34312 | 0.578491 | ||||||||
\(209\) | −7.36537 | + | 10.2784i | −0.509473 | + | 0.710974i | ||||
\(210\) | 23.7833 | + | 20.4951i | 1.64120 | + | 1.41429i | ||||
\(211\) | 14.2288i | 0.979551i | 0.871848 | + | 0.489776i | \(0.162921\pi\) | ||||
−0.871848 | + | 0.489776i | \(0.837079\pi\) | |||||||
\(212\) | 32.4737 | 2.23031 | ||||||||
\(213\) | 5.51641 | + | 2.85550i | 0.377978 | + | 0.195656i | ||||
\(214\) | −15.6603 | −1.07051 | ||||||||
\(215\) | −18.1490 | − | 4.31872i | −1.23775 | − | 0.294534i | ||||
\(216\) | −2.96032 | − | 21.3432i | −0.201424 | − | 1.45222i | ||||
\(217\) | 11.7290 | 0.796216 | ||||||||
\(218\) | −6.68216 | −0.452573 | ||||||||
\(219\) | −2.69591 | + | 5.20810i | −0.182173 | + | 0.351931i | ||||
\(220\) | −18.1545 | − | 20.8917i | −1.22398 | − | 1.40852i | ||||
\(221\) | − | 5.93426i | − | 0.399181i | ||||||
\(222\) | −16.0221 | + | 30.9523i | −1.07533 | + | 2.07738i | ||||
\(223\) | − | 18.2374i | − | 1.22127i | −0.791914 | − | 0.610633i | \(-0.790915\pi\) | ||
0.791914 | − | 0.610633i | \(-0.209085\pi\) | |||||||
\(224\) | − | 8.10634i | − | 0.541628i | ||||||
\(225\) | −2.21564 | − | 14.8355i | −0.147709 | − | 0.989031i | ||||
\(226\) | − | 13.2072i | − | 0.878532i | ||||||
\(227\) | − | 10.0463i | − | 0.666797i | −0.942786 | − | 0.333398i | \(-0.891805\pi\) | ||
0.942786 | − | 0.333398i | \(-0.108195\pi\) | |||||||
\(228\) | −21.8866 | − | 11.3293i | −1.44948 | − | 0.750304i | ||||
\(229\) | −13.3205 | −0.880244 | −0.440122 | − | 0.897938i | \(-0.645065\pi\) | ||||
−0.440122 | + | 0.897938i | \(0.645065\pi\) | |||||||
\(230\) | 3.41828 | − | 14.3650i | 0.225395 | − | 0.947201i | ||||
\(231\) | −17.3292 | + | 8.83249i | −1.14018 | + | 0.581135i | ||||
\(232\) | 8.18395i | 0.537302i | ||||||||
\(233\) | 7.82403i | 0.512569i | 0.966601 | + | 0.256285i | \(0.0824984\pi\) | ||||
−0.966601 | + | 0.256285i | \(0.917502\pi\) | |||||||
\(234\) | −19.8564 | + | 14.0406i | −1.29805 | + | 0.917863i | ||||
\(235\) | 3.46410 | + | 0.824313i | 0.225973 | + | 0.0537723i | ||||
\(236\) | − | 18.2832i | − | 1.19014i | ||||||
\(237\) | −17.5935 | − | 9.10706i | −1.14282 | − | 0.591567i | ||||
\(238\) | 14.2076 | 0.920943 | ||||||||
\(239\) | −24.0697 | −1.55694 | −0.778469 | − | 0.627684i | \(-0.784003\pi\) | ||||
−0.778469 | + | 0.627684i | \(0.784003\pi\) | |||||||
\(240\) | 6.22993 | − | 7.22945i | 0.402140 | − | 0.466659i | ||||
\(241\) | − | 2.79101i | − | 0.179785i | −0.995951 | − | 0.0898925i | \(-0.971348\pi\) | ||
0.995951 | − | 0.0898925i | \(-0.0286524\pi\) | |||||||
\(242\) | 24.9382 | − | 8.46554i | 1.60309 | − | 0.544186i | ||||
\(243\) | 10.6633 | + | 11.3708i | 0.684050 | + | 0.729435i | ||||
\(244\) | − | 38.8738i | − | 2.48864i | ||||||
\(245\) | 9.71088 | + | 2.31079i | 0.620406 | + | 0.147631i | ||||
\(246\) | −27.1244 | − | 14.0406i | −1.72939 | − | 0.895196i | ||||
\(247\) | 12.9090i | 0.821377i | ||||||||
\(248\) | − | 14.3650i | − | 0.912180i | ||||||
\(249\) | 15.4531 | + | 7.99912i | 0.979301 | + | 0.506924i | ||||
\(250\) | 17.2614 | − | 20.4585i | 1.09171 | − | 1.29391i | ||||
\(251\) | − | 16.9706i | − | 1.07117i | −0.844481 | − | 0.535586i | \(-0.820091\pi\) | ||
0.844481 | − | 0.535586i | \(-0.179909\pi\) | |||||||
\(252\) | −21.8866 | − | 30.9523i | −1.37873 | − | 1.94981i | ||||
\(253\) | 7.43588 | + | 5.32844i | 0.467490 | + | 0.334996i | ||||
\(254\) | 40.5317i | 2.54319i | ||||||||
\(255\) | −5.14213 | − | 4.43119i | −0.322013 | − | 0.277492i | ||||
\(256\) | −28.3205 | −1.77003 | ||||||||
\(257\) | −12.1986 | −0.760926 | −0.380463 | − | 0.924796i | \(-0.624235\pi\) | ||||
−0.380463 | + | 0.924796i | \(0.624235\pi\) | |||||||
\(258\) | 30.7251 | + | 15.9045i | 1.91286 | + | 0.990170i | ||||
\(259\) | 28.4576i | 1.76827i | ||||||||
\(260\) | −27.4879 | − | 6.54099i | −1.70473 | − | 0.405655i | ||||
\(261\) | −3.41828 | − | 4.83418i | −0.211586 | − | 0.299228i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.469622i | 0.0289582i | 0.999895 | + | 0.0144791i | \(0.00460899\pi\) | ||||
−0.999895 | + | 0.0144791i | \(0.995391\pi\) | |||||||
\(264\) | 10.8176 | + | 21.2239i | 0.665774 | + | 1.30624i | ||||
\(265\) | −18.9282 | − | 4.50413i | −1.16275 | − | 0.276687i | ||||
\(266\) | −30.9062 | −1.89498 | ||||||||
\(267\) | −14.6444 | − | 7.58051i | −0.896224 | − | 0.463920i | ||||
\(268\) | − | 49.0012i | − | 2.99322i | ||||||
\(269\) | − | 8.48528i | − | 0.517357i | −0.965964 | − | 0.258678i | \(-0.916713\pi\) | ||
0.965964 | − | 0.258678i | \(-0.0832870\pi\) | |||||||
\(270\) | −2.66066 | + | 27.6902i | −0.161923 | + | 1.68517i | ||||
\(271\) | − | 19.8108i | − | 1.20342i | −0.798714 | − | 0.601711i | \(-0.794486\pi\) | ||
0.798714 | − | 0.601711i | \(-0.205514\pi\) | |||||||
\(272\) | − | 4.31872i | − | 0.261861i | ||||||
\(273\) | −9.12801 | + | 17.6340i | −0.552452 | + | 1.06726i | ||||
\(274\) | − | 10.4162i | − | 0.629266i | ||||||
\(275\) | 7.68418 | + | 14.6954i | 0.463373 | + | 0.886163i | ||||
\(276\) | −8.19615 | + | 15.8338i | −0.493350 | + | 0.953080i | ||||
\(277\) | 20.0721 | 1.20602 | 0.603008 | − | 0.797735i | \(-0.293969\pi\) | ||||
0.603008 | + | 0.797735i | \(0.293969\pi\) | |||||||
\(278\) | −2.44584 | −0.146692 | ||||||||
\(279\) | 6.00000 | + | 8.48528i | 0.359211 | + | 0.508001i | ||||
\(280\) | 7.26795 | − | 30.5429i | 0.434343 | − | 1.82529i | ||||
\(281\) | 32.8798 | 1.96144 | 0.980721 | − | 0.195411i | \(-0.0626042\pi\) | ||||
0.980721 | + | 0.195411i | \(0.0626042\pi\) | |||||||
\(282\) | −5.86450 | − | 3.03569i | −0.349226 | − | 0.180772i | ||||
\(283\) | −6.52864 | −0.388087 | −0.194044 | − | 0.980993i | \(-0.562160\pi\) | ||||
−0.194044 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(284\) | − | 13.3843i | − | 0.794210i | ||||||
\(285\) | 11.1858 | + | 9.63930i | 0.662590 | + | 0.570983i | ||||
\(286\) | 15.6603 | − | 21.8540i | 0.926010 | − | 1.29225i | ||||
\(287\) | −24.9382 | −1.47205 | ||||||||
\(288\) | 5.86450 | − | 4.14682i | 0.345569 | − | 0.244354i | ||||
\(289\) | 13.9282 | 0.819306 | ||||||||
\(290\) | 2.44584 | − | 10.2784i | 0.143625 | − | 0.603570i | ||||
\(291\) | 12.9282 | + | 6.69213i | 0.757865 | + | 0.392300i | ||||
\(292\) | 12.6362 | 0.739479 | ||||||||
\(293\) | 1.75265i | 0.102391i | 0.998689 | + | 0.0511956i | \(0.0163032\pi\) | ||||
−0.998689 | + | 0.0511956i | \(0.983697\pi\) | |||||||
\(294\) | −16.4399 | − | 8.50991i | −0.958794 | − | 0.496308i | ||||
\(295\) | −2.53590 | + | 10.6569i | −0.147646 | + | 0.620468i | ||||
\(296\) | 34.8533 | 2.02581 | ||||||||
\(297\) | −15.2546 | − | 8.01846i | −0.885164 | − | 0.465278i | ||||
\(298\) | 8.18395i | 0.474083i | ||||||||
\(299\) | 9.33892 | 0.540084 | ||||||||
\(300\) | −26.1935 | + | 18.9345i | −1.51228 | + | 1.09318i | ||||
\(301\) | 28.2487 | 1.62823 | ||||||||
\(302\) | −52.3222 | −3.01080 | ||||||||
\(303\) | −1.57139 | + | 3.03569i | −0.0902738 | + | 0.174396i | ||||
\(304\) | 9.39463i | 0.538819i | ||||||||
\(305\) | −5.39183 | + | 22.6587i | −0.308735 | + | 1.29743i | ||||
\(306\) | 7.26795 | + | 10.2784i | 0.415481 | + | 0.587579i | ||||
\(307\) | 8.34312 | 0.476167 | 0.238084 | − | 0.971245i | \(-0.423481\pi\) | ||||
0.238084 | + | 0.971245i | \(0.423481\pi\) | |||||||
\(308\) | 34.0662 | + | 24.4113i | 1.94110 | + | 1.39096i | ||||
\(309\) | −1.26795 | − | 0.656339i | −0.0721311 | − | 0.0373378i | ||||
\(310\) | −4.29311 | + | 18.0414i | −0.243832 | + | 1.02468i | ||||
\(311\) | − | 14.6969i | − | 0.833387i | −0.909047 | − | 0.416693i | \(-0.863189\pi\) | ||
0.909047 | − | 0.416693i | \(-0.136811\pi\) | |||||||
\(312\) | 21.5971 | + | 11.1795i | 1.22269 | + | 0.632913i | ||||
\(313\) | − | 15.7645i | − | 0.891060i | −0.895267 | − | 0.445530i | \(-0.853015\pi\) | ||
0.895267 | − | 0.445530i | \(-0.146985\pi\) | |||||||
\(314\) | 10.7837 | 0.608557 | ||||||||
\(315\) | 8.46409 | + | 21.0771i | 0.476897 | + | 1.18756i | ||||
\(316\) | 42.6864i | 2.40130i | ||||||||
\(317\) | −0.853392 | −0.0479312 | −0.0239656 | − | 0.999713i | \(-0.507629\pi\) | ||||
−0.0239656 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(318\) | 32.0442 | + | 16.5873i | 1.79695 | + | 0.930169i | ||||
\(319\) | 5.32051 | + | 3.81260i | 0.297891 | + | 0.213464i | ||||
\(320\) | 23.1895 | + | 5.51815i | 1.29634 | + | 0.308474i | ||||
\(321\) | −10.0613 | − | 5.20810i | −0.561566 | − | 0.290688i | ||||
\(322\) | 22.3590i | 1.24602i | ||||||||
\(323\) | 6.68216 | 0.371806 | ||||||||
\(324\) | 11.1962 | − | 31.6675i | 0.622008 | − | 1.75931i | ||||
\(325\) | 15.1149 | + | 7.62519i | 0.838421 | + | 0.422970i | ||||
\(326\) | 1.97355 | 0.109305 | ||||||||
\(327\) | −4.29311 | − | 2.22228i | −0.237409 | − | 0.122892i | ||||
\(328\) | 30.5429i | 1.68645i | ||||||||
\(329\) | −5.39183 | −0.297261 | ||||||||
\(330\) | −7.24311 | − | 29.8886i | −0.398720 | − | 1.64531i | ||||
\(331\) | 15.4641 | 0.849984 | 0.424992 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424992 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(332\) | − | 37.4933i | − | 2.05771i | ||||||
\(333\) | −20.5875 | + | 14.5576i | −1.12819 | + | 0.797750i | ||||
\(334\) | −30.1962 | −1.65226 | ||||||||
\(335\) | −6.79650 | + | 28.5617i | −0.371332 | + | 1.56049i | ||||
\(336\) | −6.64300 | + | 12.8333i | −0.362406 | + | 0.700114i | ||||
\(337\) | −20.0721 | −1.09340 | −0.546699 | − | 0.837329i | \(-0.684116\pi\) | ||||
−0.546699 | + | 0.837329i | \(0.684116\pi\) | |||||||
\(338\) | 3.67720i | 0.200013i | ||||||||
\(339\) | 4.39230 | − | 8.48528i | 0.238557 | − | 0.460857i | ||||
\(340\) | −3.38587 | + | 14.2288i | −0.183624 | + | 0.771665i | ||||
\(341\) | −9.33892 | − | 6.69213i | −0.505731 | − | 0.362399i | ||||
\(342\) | −15.8102 | − | 22.3590i | −0.854916 | − | 1.20903i | ||||
\(343\) | 8.58622 | 0.463612 | ||||||||
\(344\) | − | 34.5975i | − | 1.86537i | ||||||
\(345\) | 6.97350 | − | 8.09232i | 0.375441 | − | 0.435676i | ||||
\(346\) | −43.9090 | −2.36056 | ||||||||
\(347\) | 18.6837i | 1.00300i | 0.865159 | + | 0.501498i | \(0.167217\pi\) | ||||
−0.865159 | + | 0.501498i | \(0.832783\pi\) | |||||||
\(348\) | −5.86450 | + | 11.3293i | −0.314370 | + | 0.607316i | ||||
\(349\) | − | 5.58203i | − | 0.298799i | −0.988777 | − | 0.149400i | \(-0.952266\pi\) | ||
0.988777 | − | 0.149400i | \(-0.0477341\pi\) | |||||||
\(350\) | −18.2560 | + | 36.1875i | −0.975825 | + | 1.93431i | ||||
\(351\) | −17.4267 | + | 2.41709i | −0.930166 | + | 0.129015i | ||||
\(352\) | −4.62518 | + | 6.45448i | −0.246523 | + | 0.344025i | ||||
\(353\) | −11.8862 | −0.632639 | −0.316320 | − | 0.948653i | \(-0.602447\pi\) | ||||
−0.316320 | + | 0.948653i | \(0.602447\pi\) | |||||||
\(354\) | 9.33892 | − | 18.0414i | 0.496358 | − | 0.958890i | ||||
\(355\) | −1.85641 | + | 7.80138i | −0.0985278 | + | 0.414054i | ||||
\(356\) | 35.5312i | 1.88315i | ||||||||
\(357\) | 9.12801 | + | 4.72500i | 0.483105 | + | 0.250074i | ||||
\(358\) | −12.3931 | −0.654998 | ||||||||
\(359\) | 20.1226 | 1.06203 | 0.531014 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531014 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(360\) | 25.8141 | − | 10.3664i | 1.36052 | − | 0.546355i | ||||
\(361\) | 4.46410 | 0.234953 | ||||||||
\(362\) | 6.07137i | 0.319104i | ||||||||
\(363\) | 18.8375 | + | 2.85477i | 0.988711 | + | 0.149837i | ||||
\(364\) | 42.7846 | 2.24252 | ||||||||
\(365\) | −7.36537 | − | 1.75265i | −0.385521 | − | 0.0917381i | ||||
\(366\) | 19.8564 | − | 38.3596i | 1.03791 | − | 2.00509i | ||||
\(367\) | 35.0470i | 1.82944i | 0.404088 | + | 0.914720i | \(0.367589\pi\) | ||||
−0.404088 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(368\) | 6.79650 | 0.354292 | ||||||||
\(369\) | −12.7572 | − | 18.0414i | −0.664113 | − | 0.939198i | ||||
\(370\) | −43.7732 | − | 10.4162i | −2.27566 | − | 0.541513i | ||||
\(371\) | 29.4615 | 1.52956 | ||||||||
\(372\) | 10.2938 | − | 19.8860i | 0.533707 | − | 1.03104i | ||||
\(373\) | 8.34312 | 0.431991 | 0.215995 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215995 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(374\) | −11.3125 | − | 8.10634i | −0.584954 | − | 0.419169i | ||||
\(375\) | 17.8938 | − | 7.40342i | 0.924034 | − | 0.382311i | ||||
\(376\) | 6.60361i | 0.340555i | ||||||||
\(377\) | 6.68216 | 0.344149 | ||||||||
\(378\) | −5.78692 | − | 41.7224i | −0.297647 | − | 2.14597i | ||||
\(379\) | 10.9282 | 0.561344 | 0.280672 | − | 0.959804i | \(-0.409443\pi\) | ||||
0.280672 | + | 0.959804i | \(0.409443\pi\) | |||||||
\(380\) | 7.36537 | − | 30.9523i | 0.377836 | − | 1.58782i | ||||
\(381\) | −13.4796 | + | 26.0405i | −0.690579 | + | 1.33410i | ||||
\(382\) | −11.0648 | −0.566127 | ||||||||
\(383\) | 27.3840 | 1.39926 | 0.699629 | − | 0.714506i | \(-0.253349\pi\) | ||||
0.699629 | + | 0.714506i | \(0.253349\pi\) | |||||||
\(384\) | −31.8930 | − | 16.5090i | −1.62753 | − | 0.842473i | ||||
\(385\) | −16.4705 | − | 18.9538i | −0.839416 | − | 0.965976i | ||||
\(386\) | 40.5317i | 2.06301i | ||||||||
\(387\) | 14.4507 | + | 20.4364i | 0.734571 | + | 1.03884i | ||||
\(388\) | − | 31.3672i | − | 1.59243i | ||||||
\(389\) | 37.8792i | 1.92055i | 0.279056 | + | 0.960275i | \(0.409978\pi\) | ||||
−0.279056 | + | 0.960275i | \(0.590022\pi\) | |||||||
\(390\) | −23.7833 | − | 20.4951i | −1.20431 | − | 1.03781i | ||||
\(391\) | − | 4.83418i | − | 0.244475i | ||||||
\(392\) | 18.5118i | 0.934989i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 50.0526 | 2.52161 | ||||||||
\(395\) | 5.92064 | − | 24.8809i | 0.297900 | − | 1.25190i | ||||
\(396\) | −0.233596 | + | 37.1327i | −0.0117386 | + | 1.86599i | ||||
\(397\) | − | 20.7103i | − | 1.03942i | −0.854342 | − | 0.519711i | \(-0.826040\pi\) | ||
0.854342 | − | 0.519711i | \(-0.173960\pi\) | |||||||
\(398\) | 7.01062i | 0.351410i | ||||||||
\(399\) | −19.8564 | − | 10.2784i | −0.994064 | − | 0.514565i | ||||
\(400\) | 11.0000 | + | 5.54932i | 0.550000 | + | 0.277466i | ||||
\(401\) | − | 11.0363i | − | 0.551127i | −0.961283 | − | 0.275563i | \(-0.911136\pi\) | ||
0.961283 | − | 0.275563i | \(-0.0888644\pi\) | |||||||
\(402\) | 25.0294 | − | 48.3530i | 1.24835 | − | 2.41163i | ||||
\(403\) | −11.7290 | −0.584263 | ||||||||
\(404\) | 7.36537 | 0.366441 | ||||||||
\(405\) | −10.9183 | + | 16.9054i | −0.542534 | + | 0.840034i | ||||
\(406\) | 15.9982i | 0.793979i | ||||||||
\(407\) | 16.2369 | − | 22.6587i | 0.804832 | − | 1.12315i | ||||
\(408\) | 5.78692 | − | 11.1795i | 0.286495 | − | 0.553467i | ||||
\(409\) | 23.6234i | 1.16810i | 0.811716 | + | 0.584052i | \(0.198534\pi\) | ||||
−0.811716 | + | 0.584052i | \(0.801466\pi\) | |||||||
\(410\) | 9.12801 | − | 38.3596i | 0.450800 | − | 1.89445i | ||||
\(411\) | 3.46410 | − | 6.69213i | 0.170872 | − | 0.330098i | ||||
\(412\) | 3.07638i | 0.151562i | ||||||||
\(413\) | − | 16.5873i | − | 0.816208i | ||||||
\(414\) | −16.1755 | + | 11.4378i | −0.794981 | + | 0.562137i | ||||
\(415\) | −5.20035 | + | 21.8540i | −0.255275 | + | 1.07277i | ||||
\(416\) | 8.10634i | 0.397446i | ||||||||
\(417\) | −1.57139 | − | 0.813410i | −0.0769511 | − | 0.0398328i | ||||
\(418\) | 24.6083 | + | 17.6340i | 1.20363 | + | 0.862505i | ||||
\(419\) | − | 35.5312i | − | 1.73581i | −0.496728 | − | 0.867906i | \(-0.665465\pi\) | ||
0.496728 | − | 0.867906i | \(-0.334535\pi\) | |||||||
\(420\) | 31.9479 | − | 37.0735i | 1.55890 | − | 1.80900i | ||||
\(421\) | −32.7846 | −1.59782 | −0.798912 | − | 0.601448i | \(-0.794591\pi\) | ||||
−0.798912 | + | 0.601448i | \(0.794591\pi\) | |||||||
\(422\) | 34.0662 | 1.65832 | ||||||||
\(423\) | −2.75821 | − | 3.90069i | −0.134109 | − | 0.189658i | ||||
\(424\) | − | 36.0828i | − | 1.75234i | ||||||
\(425\) | 3.94709 | − | 7.82403i | 0.191462 | − | 0.379521i | ||||
\(426\) | 6.83656 | − | 13.2072i | 0.331233 | − | 0.639892i | ||||
\(427\) | − | 35.2679i | − | 1.70673i | ||||||
\(428\) | 24.4113i | 1.17997i | ||||||||
\(429\) | 17.3292 | − | 8.83249i | 0.836663 | − | 0.426437i | ||||
\(430\) | −10.3397 | + | 43.4519i | −0.498627 | + | 2.09543i | ||||
\(431\) | 16.1755 | 0.779145 | 0.389573 | − | 0.920996i | \(-0.372623\pi\) | ||||
0.389573 | + | 0.920996i | \(0.372623\pi\) | |||||||
\(432\) | −12.6824 | + | 1.75906i | −0.610184 | + | 0.0846330i | ||||
\(433\) | − | 19.5035i | − | 0.937276i | −0.883390 | − | 0.468638i | \(-0.844745\pi\) | ||
0.883390 | − | 0.468638i | \(-0.155255\pi\) | |||||||
\(434\) | − | 28.0812i | − | 1.34794i | ||||||
\(435\) | 4.98967 | − | 5.79020i | 0.239236 | − | 0.277619i | ||||
\(436\) | 10.4162i | 0.498846i | ||||||||
\(437\) | 10.5159i | 0.503045i | ||||||||
\(438\) | 12.4691 | + | 6.45448i | 0.595796 | + | 0.308407i | ||||
\(439\) | 6.60361i | 0.315173i | 0.987505 | + | 0.157587i | \(0.0503713\pi\) | ||||
−0.987505 | + | 0.157587i | \(0.949629\pi\) | |||||||
\(440\) | −23.2136 | + | 20.1722i | −1.10666 | + | 0.961672i | ||||
\(441\) | −7.73205 | − | 10.9348i | −0.368193 | − | 0.520703i | ||||
\(442\) | −14.2076 | −0.675787 | ||||||||
\(443\) | −1.28009 | −0.0608188 | −0.0304094 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304094 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(444\) | 48.2487 | + | 24.9754i | 2.28978 | + | 1.18528i | ||||
\(445\) | 4.92820 | − | 20.7103i | 0.233619 | − | 0.981764i | ||||
\(446\) | −43.6634 | −2.06752 | ||||||||
\(447\) | −2.72172 | + | 5.25796i | −0.128733 | + | 0.248693i | ||||
\(448\) | −36.0942 | −1.70529 | ||||||||
\(449\) | 18.5606i | 0.875931i | 0.898992 | + | 0.437965i | \(0.144301\pi\) | ||||
−0.898992 | + | 0.437965i | \(0.855699\pi\) | |||||||
\(450\) | −35.5186 | + | 5.30462i | −1.67436 | + | 0.250062i | ||||
\(451\) | 19.8564 | + | 14.2288i | 0.935002 | + | 0.670008i | ||||
\(452\) | −20.5875 | −0.968356 | ||||||||
\(453\) | −33.6156 | − | 17.4007i | −1.57940 | − | 0.817557i | ||||
\(454\) | −24.0526 | −1.12884 | ||||||||
\(455\) | −24.9382 | − | 5.93426i | −1.16912 | − | 0.278202i | ||||
\(456\) | −12.5885 | + | 24.3190i | −0.589509 | + | 1.13884i | ||||
\(457\) | 28.6583 | 1.34058 | 0.670290 | − | 0.742099i | \(-0.266170\pi\) | ||||
0.670290 | + | 0.742099i | \(0.266170\pi\) | |||||||
\(458\) | 31.8916i | 1.49019i | ||||||||
\(459\) | 1.25118 | + | 9.02070i | 0.0584000 | + | 0.421050i | ||||
\(460\) | −22.3923 | − | 5.32844i | −1.04405 | − | 0.248440i | ||||
\(461\) | −31.4350 | −1.46408 | −0.732038 | − | 0.681264i | \(-0.761431\pi\) | ||||
−0.732038 | + | 0.681264i | \(0.761431\pi\) | |||||||
\(462\) | 21.1465 | + | 41.4891i | 0.983824 | + | 1.93025i | ||||
\(463\) | 7.58051i | 0.352296i | 0.984364 | + | 0.176148i | \(0.0563637\pi\) | ||||
−0.984364 | + | 0.176148i | \(0.943636\pi\) | |||||||
\(464\) | 4.86302 | 0.225760 | ||||||||
\(465\) | −8.75821 | + | 10.1634i | −0.406152 | + | 0.471314i | ||||
\(466\) | 18.7321 | 0.867745 | ||||||||
\(467\) | 29.7155 | 1.37507 | 0.687535 | − | 0.726151i | \(-0.258693\pi\) | ||||
0.687535 | + | 0.726151i | \(0.258693\pi\) | |||||||
\(468\) | 21.8866 | + | 30.9523i | 1.01171 | + | 1.43077i | ||||
\(469\) | − | 44.4559i | − | 2.05278i | ||||||
\(470\) | 1.97355 | − | 8.29365i | 0.0910329 | − | 0.382557i | ||||
\(471\) | 6.92820 | + | 3.58630i | 0.319235 | + | 0.165248i | ||||
\(472\) | −20.3152 | −0.935083 | ||||||||
\(473\) | −22.4923 | − | 16.1177i | −1.03420 | − | 0.741091i | ||||
\(474\) | −21.8038 | + | 42.1218i | −1.00148 | + | 1.93472i | ||||
\(475\) | −8.58622 | + | 17.0198i | −0.393963 | + | 0.780923i | ||||
\(476\) | − | 22.1469i | − | 1.01510i | ||||||
\(477\) | 15.0711 | + | 21.3138i | 0.690059 | + | 0.975891i | ||||
\(478\) | 57.6269i | 2.63579i | ||||||||
\(479\) | 1.44474 | 0.0660117 | 0.0330058 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330058 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(480\) | 7.02428 | + | 6.05312i | 0.320613 | + | 0.276286i | ||||
\(481\) | − | 28.4576i | − | 1.29756i | ||||||
\(482\) | −6.68216 | −0.304364 | ||||||||
\(483\) | −7.43588 | + | 14.3650i | −0.338344 | + | 0.653631i | ||||
\(484\) | −13.1962 | − | 38.8738i | −0.599825 | − | 1.76699i | ||||
\(485\) | −4.35066 | + | 18.2832i | −0.197553 | + | 0.830199i | ||||
\(486\) | 27.2235 | − | 25.5297i | 1.23488 | − | 1.15805i | ||||
\(487\) | − | 12.6881i | − | 0.574952i | −0.957788 | − | 0.287476i | \(-0.907184\pi\) | ||
0.957788 | − | 0.287476i | \(-0.0928161\pi\) | |||||||
\(488\) | −43.1942 | −1.95531 | ||||||||
\(489\) | 1.26795 | + | 0.656339i | 0.0573386 | + | 0.0296807i | ||||
\(490\) | 5.53242 | − | 23.2495i | 0.249929 | − | 1.05031i | ||||
\(491\) | −16.1755 | −0.729989 | −0.364995 | − | 0.931010i | \(-0.618929\pi\) | ||||
−0.364995 | + | 0.931010i | \(0.618929\pi\) | |||||||
\(492\) | −21.8866 | + | 42.2817i | −0.986724 | + | 1.90620i | ||||
\(493\) | − | 3.45894i | − | 0.155783i | ||||||
\(494\) | 30.9062 | 1.39054 | ||||||||
\(495\) | 5.28649 | − | 21.6114i | 0.237610 | − | 0.971361i | ||||
\(496\) | −8.53590 | −0.383273 | ||||||||
\(497\) | − | 12.1427i | − | 0.544677i | ||||||
\(498\) | 19.1513 | − | 36.9974i | 0.858188 | − | 1.65789i | ||||
\(499\) | −10.9282 | −0.489214 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(500\) | −31.8909 | − | 26.9072i | −1.42620 | − | 1.20333i | ||||
\(501\) | −19.4002 | − | 10.0423i | −0.866737 | − | 0.448656i | ||||
\(502\) | −40.6304 | −1.81342 | ||||||||
\(503\) | 17.0569i | 0.760530i | 0.924877 | + | 0.380265i | \(0.124167\pi\) | ||||
−0.924877 | + | 0.380265i | \(0.875833\pi\) | |||||||
\(504\) | −34.3923 | + | 24.3190i | −1.53196 | + | 1.08326i | ||||
\(505\) | −4.29311 | − | 1.02158i | −0.191041 | − | 0.0454598i | ||||
\(506\) | 12.7572 | − | 17.8028i | 0.567127 | − | 0.791430i | ||||
\(507\) | −1.22292 | + | 2.36250i | −0.0543118 | + | 0.104922i | ||||
\(508\) | 63.1812 | 2.80321 | ||||||||
\(509\) | − | 2.62536i | − | 0.116367i | −0.998306 | − | 0.0581834i | \(-0.981469\pi\) | ||
0.998306 | − | 0.0581834i | \(-0.0185308\pi\) | |||||||
\(510\) | −10.6090 | + | 12.3111i | −0.469776 | + | 0.545146i | ||||
\(511\) | 11.4641 | 0.507142 | ||||||||
\(512\) | 26.3359i | 1.16389i | ||||||||
\(513\) | −2.72172 | − | 19.6230i | −0.120167 | − | 0.866376i | ||||
\(514\) | 29.2055i | 1.28820i | ||||||||
\(515\) | 0.426696 | − | 1.79315i | 0.0188025 | − | 0.0790157i | ||||
\(516\) | 24.7920 | − | 47.8945i | 1.09141 | − | 2.10844i | ||||
\(517\) | 4.29311 | + | 3.07638i | 0.188811 | + | 0.135299i | ||||
\(518\) | 68.1324 | 2.99356 | ||||||||
\(519\) | −28.2103 | − | 14.6027i | −1.23830 | − | 0.640989i | ||||
\(520\) | −7.26795 | + | 30.5429i | −0.318721 | + | 1.33940i | ||||
\(521\) | 26.4911i | 1.16060i | 0.814404 | + | 0.580299i | \(0.197064\pi\) | ||||
−0.814404 | + | 0.580299i | \(0.802936\pi\) | |||||||
\(522\) | −11.5738 | + | 8.18395i | −0.506574 | + | 0.358202i | ||||
\(523\) | 28.6583 | 1.25314 | 0.626571 | − | 0.779365i | \(-0.284458\pi\) | ||||
0.626571 | + | 0.779365i | \(0.284458\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.7638 | + | 17.1781i | −1.03714 | + | 0.749715i | ||||
\(526\) | 1.12436 | 0.0490242 | ||||||||
\(527\) | 6.07137i | 0.264473i | ||||||||
\(528\) | 12.6115 | − | 6.42794i | 0.548847 | − | 0.279740i | ||||
\(529\) | −15.3923 | −0.669231 | ||||||||
\(530\) | −10.7837 | + | 45.3173i | −0.468412 | + | 1.96846i | ||||
\(531\) | 12.0000 | − | 8.48528i | 0.520756 | − | 0.368230i | ||||
\(532\) | 48.1769i | 2.08873i | ||||||||
\(533\) | 24.9382 | 1.08019 | ||||||||
\(534\) | −18.1490 | + | 35.0612i | −0.785385 | + | 1.51725i | ||||
\(535\) | 3.38587 | − | 14.2288i | 0.146384 | − | 0.615165i | ||||
\(536\) | −54.4471 | −2.35176 | ||||||||
\(537\) | −7.96225 | − | 4.12157i | −0.343597 | − | 0.177859i | ||||
\(538\) | −20.3152 | −0.875851 | ||||||||
\(539\) | 12.0348 | + | 8.62398i | 0.518377 | + | 0.371461i | ||||
\(540\) | 43.1637 | + | 4.14746i | 1.85747 | + | 0.178478i | ||||
\(541\) | − | 20.8324i | − | 0.895656i | −0.894120 | − | 0.447828i | \(-0.852198\pi\) | ||
0.894120 | − | 0.447828i | \(-0.147802\pi\) | |||||||
\(542\) | −47.4305 | −2.03732 | ||||||||
\(543\) | −2.01915 | + | 3.90069i | −0.0866499 | + | 0.167395i | ||||
\(544\) | 4.19615 | 0.179909 | ||||||||
\(545\) | 1.44474 | − | 6.07137i | 0.0618857 | − | 0.260069i | ||||
\(546\) | 42.2187 | + | 21.8540i | 1.80679 | + | 0.935265i | ||||
\(547\) | −6.52864 | −0.279145 | −0.139572 | − | 0.990212i | \(-0.544573\pi\) | ||||
−0.139572 | + | 0.990212i | \(0.544573\pi\) | |||||||
\(548\) | −16.2369 | −0.693605 | ||||||||
\(549\) | 25.5144 | − | 18.0414i | 1.08893 | − | 0.769988i | ||||
\(550\) | 35.1832 | − | 18.3972i | 1.50022 | − | 0.784460i | ||||
\(551\) | 7.52433i | 0.320547i | ||||||||
\(552\) | 17.5935 | + | 9.10706i | 0.748828 | + | 0.387622i | ||||
\(553\) | 38.7269i | 1.64683i | ||||||||
\(554\) | − | 48.0561i | − | 2.04171i | ||||||
\(555\) | −24.6590 | − | 21.2497i | −1.04672 | − | 0.902000i | ||||
\(556\) | 3.81260i | 0.161690i | ||||||||
\(557\) | 1.75265i | 0.0742623i | 0.999310 | + | 0.0371312i | \(0.0118219\pi\) | ||||
−0.999310 | + | 0.0371312i | \(0.988178\pi\) | |||||||
\(558\) | 20.3152 | − | 14.3650i | 0.860011 | − | 0.608120i | ||||
\(559\) | −28.2487 | −1.19479 | ||||||||
\(560\) | −18.1490 | − | 4.31872i | −0.766936 | − | 0.182499i | ||||
\(561\) | −4.57204 | − | 8.97027i | −0.193032 | − | 0.378725i | ||||
\(562\) | − | 78.7198i | − | 3.32059i | ||||||
\(563\) | 28.2604i | 1.19103i | 0.803342 | + | 0.595517i | \(0.203053\pi\) | ||||
−0.803342 | + | 0.595517i | \(0.796947\pi\) | |||||||
\(564\) | −4.73205 | + | 9.14162i | −0.199255 | + | 0.384932i | ||||
\(565\) | 12.0000 | + | 2.85550i | 0.504844 | + | 0.120132i | ||||
\(566\) | 15.6307i | 0.657006i | ||||||||
\(567\) | 10.1576 | − | 28.7300i | 0.426579 | − | 1.20655i | ||||
\(568\) | −14.8718 | −0.624005 | ||||||||
\(569\) | 7.36537 | 0.308772 | 0.154386 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154386 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(570\) | 23.0781 | − | 26.7807i | 0.966636 | − | 1.12172i | ||||
\(571\) | 32.2702i | 1.35047i | 0.737604 | + | 0.675233i | \(0.235957\pi\) | ||||
−0.737604 | + | 0.675233i | \(0.764043\pi\) | |||||||
\(572\) | −34.0662 | − | 24.4113i | −1.42438 | − | 1.02069i | ||||
\(573\) | −7.10886 | − | 3.67982i | −0.296977 | − | 0.153727i | ||||
\(574\) | 59.7062i | 2.49209i | ||||||||
\(575\) | 12.3129 | + | 6.21166i | 0.513484 | + | 0.259044i | ||||
\(576\) | −18.4641 | − | 26.1122i | −0.769338 | − | 1.08801i | ||||
\(577\) | 4.94588i | 0.205900i | 0.994687 | + | 0.102950i | \(0.0328281\pi\) | ||||
−0.994687 | + | 0.102950i | \(0.967172\pi\) | |||||||
\(578\) | − | 33.3465i | − | 1.38703i | ||||||
\(579\) | −13.4796 | + | 26.0405i | −0.560192 | + | 1.08221i | ||||
\(580\) | −16.0221 | − | 3.81260i | −0.665281 | − | 0.158309i | ||||
\(581\) | − | 34.0155i | − | 1.41120i | ||||||
\(582\) | 16.0221 | − | 30.9523i | 0.664137 | − | 1.28301i | ||||
\(583\) | −23.4580 | − | 16.8096i | −0.971530 | − | 0.696184i | ||||
\(584\) | − | 14.0406i | − | 0.581004i | ||||||
\(585\) | −8.46409 | − | 21.0771i | −0.349947 | − | 0.871430i | ||||
\(586\) | 4.19615 | 0.173341 | ||||||||
\(587\) | 21.0142 | 0.867350 | 0.433675 | − | 0.901069i | \(-0.357217\pi\) | ||||
0.433675 | + | 0.901069i | \(0.357217\pi\) | |||||||
\(588\) | −13.2653 | + | 25.6266i | −0.547052 | + | 1.05682i | ||||
\(589\) | − | 13.2072i | − | 0.544194i | ||||||
\(590\) | 25.5144 | + | 6.07137i | 1.05041 | + | 0.249954i | ||||
\(591\) | 32.1574 | + | 16.6459i | 1.32278 | + | 0.684721i | ||||
\(592\) | − | 20.7103i | − | 0.851189i | ||||||
\(593\) | − | 43.5647i | − | 1.78899i | −0.447081 | − | 0.894494i | \(-0.647536\pi\) | ||
0.447081 | − | 0.894494i | \(-0.352464\pi\) | |||||||
\(594\) | −19.1976 | + | 36.5222i | −0.787686 | + | 1.49852i | ||||
\(595\) | −3.07180 | + | 12.9090i | −0.125931 | + | 0.529215i | ||||
\(596\) | 12.7572 | 0.522555 | ||||||||
\(597\) | −2.33151 | + | 4.50413i | −0.0954223 | + | 0.184342i | ||||
\(598\) | − | 22.3590i | − | 0.914326i | ||||||
\(599\) | 13.1069i | 0.535532i | 0.963484 | + | 0.267766i | \(0.0862854\pi\) | ||||
−0.963484 | + | 0.267766i | \(0.913715\pi\) | |||||||
\(600\) | 21.0388 | + | 29.1046i | 0.858907 | + | 1.18819i | ||||
\(601\) | − | 10.4162i | − | 0.424886i | −0.977173 | − | 0.212443i | \(-0.931858\pi\) | ||
0.977173 | − | 0.212443i | \(-0.0681420\pi\) | |||||||
\(602\) | − | 67.6322i | − | 2.75648i | ||||||
\(603\) | 32.1614 | − | 22.7415i | 1.30971 | − | 0.926106i | ||||
\(604\) | 81.5602i | 3.31864i | ||||||||
\(605\) | 2.29991 | + | 24.4890i | 0.0935047 | + | 0.995619i | ||||
\(606\) | 7.26795 | + | 3.76217i | 0.295240 | + | 0.152828i | ||||
\(607\) | −25.5156 | −1.03564 | −0.517822 | − | 0.855488i | \(-0.673257\pi\) | ||||
−0.517822 | + | 0.855488i | \(0.673257\pi\) | |||||||
\(608\) | −9.12801 | −0.370190 | ||||||||
\(609\) | −5.32051 | + | 10.2784i | −0.215598 | + | 0.416503i | ||||
\(610\) | 54.2487 | + | 12.9090i | 2.19647 | + | 0.522668i | ||||
\(611\) | 5.39183 | 0.218130 | ||||||||
\(612\) | 16.0221 | − | 11.3293i | 0.647655 | − | 0.457961i | ||||
\(613\) | −2.05758 | −0.0831047 | −0.0415523 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415523 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(614\) | − | 19.9749i | − | 0.806120i | ||||||
\(615\) | 18.6217 | − | 21.6093i | 0.750899 | − | 0.871372i | ||||
\(616\) | 27.1244 | − | 37.8522i | 1.09287 | − | 1.52511i | ||||
\(617\) | 38.8435 | 1.56378 | 0.781891 | − | 0.623415i | \(-0.214255\pi\) | ||||
0.781891 | + | 0.623415i | \(0.214255\pi\) | |||||||
\(618\) | −1.57139 | + | 3.03569i | −0.0632104 | + | 0.122113i | ||||
\(619\) | 22.3923 | 0.900023 | 0.450011 | − | 0.893023i | \(-0.351420\pi\) | ||||
0.450011 | + | 0.893023i | \(0.351420\pi\) | |||||||
\(620\) | 28.1231 | + | 6.69213i | 1.12945 | + | 0.268762i | ||||
\(621\) | −14.1962 | + | 1.96902i | −0.569672 | + | 0.0790139i | ||||
\(622\) | −35.1870 | −1.41087 | ||||||||
\(623\) | 32.2354i | 1.29148i | ||||||||
\(624\) | 6.64300 | − | 12.8333i | 0.265933 | − | 0.513743i | ||||
\(625\) | 14.8564 | + | 20.1069i | 0.594256 | + | 0.804276i | ||||
\(626\) | −37.7428 | −1.50851 | ||||||||
\(627\) | 9.94568 | + | 19.5133i | 0.397192 | + | 0.779285i | ||||
\(628\) | − | 16.8096i | − | 0.670778i | ||||||
\(629\) | −14.7307 | −0.587353 | ||||||||
\(630\) | 50.4621 | − | 20.2645i | 2.01046 | − | 0.807356i | ||||
\(631\) | −30.6410 | −1.21980 | −0.609900 | − | 0.792479i | \(-0.708790\pi\) | ||||
−0.609900 | + | 0.792479i | \(0.708790\pi\) | |||||||
\(632\) | 47.4305 | 1.88668 | ||||||||
\(633\) | 21.8866 | + | 11.3293i | 0.869914 | + | 0.450301i | ||||
\(634\) | 2.04316i | 0.0811444i | ||||||||
\(635\) | −36.8269 | − | 8.76327i | −1.46143 | − | 0.347760i | ||||
\(636\) | 25.8564 | − | 49.9507i | 1.02527 | − | 1.98068i | ||||
\(637\) | 15.1149 | 0.598872 | ||||||||
\(638\) | 9.12801 | − | 12.7382i | 0.361381 | − | 0.504310i | ||||
\(639\) | 8.78461 | − | 6.21166i | 0.347514 | − | 0.245729i | ||||
\(640\) | 10.7328 | − | 45.1035i | 0.424250 | − | 1.78287i | ||||
\(641\) | 27.8038i | 1.09818i | 0.835762 | + | 0.549092i | \(0.185026\pi\) | ||||
−0.835762 | + | 0.549092i | \(0.814974\pi\) | |||||||
\(642\) | −12.4691 | + | 24.0884i | −0.492116 | + | 0.950695i | ||||
\(643\) | − | 4.12157i | − | 0.162539i | −0.996692 | − | 0.0812693i | \(-0.974103\pi\) | ||
0.996692 | − | 0.0812693i | \(-0.0258974\pi\) | |||||||
\(644\) | 34.8533 | 1.37341 | ||||||||
\(645\) | −21.0937 | + | 24.4780i | −0.830564 | + | 0.963819i | ||||
\(646\) | − | 15.9982i | − | 0.629442i | ||||||
\(647\) | −44.7866 | −1.76074 | −0.880372 | − | 0.474283i | \(-0.842707\pi\) | ||||
−0.880372 | + | 0.474283i | \(0.842707\pi\) | |||||||
\(648\) | −35.1870 | − | 12.4405i | −1.38227 | − | 0.488708i | ||||
\(649\) | −9.46410 | + | 13.2072i | −0.371498 | + | 0.518429i | ||||
\(650\) | 18.2560 | − | 36.1875i | 0.716060 | − | 1.41939i | ||||
\(651\) | 9.33892 | − | 18.0414i | 0.366021 | − | 0.707098i | ||||
\(652\) | − | 3.07638i | − | 0.120480i | ||||||
\(653\) | −25.7916 | −1.00930 | −0.504651 | − | 0.863323i | \(-0.668379\pi\) | ||||
−0.504651 | + | 0.863323i | \(0.668379\pi\) | |||||||
\(654\) | −5.32051 | + | 10.2784i | −0.208048 | + | 0.401919i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18.1490 | 0.708600 | ||||||||
\(657\) | 5.86450 | + | 8.29365i | 0.228796 | + | 0.323566i | ||||
\(658\) | 12.9090i | 0.503243i | ||||||||
\(659\) | 36.2981 | 1.41397 | 0.706986 | − | 0.707228i | \(-0.250055\pi\) | ||||
0.706986 | + | 0.707228i | \(0.250055\pi\) | |||||||
\(660\) | −46.5905 | + | 11.2906i | −1.81353 | + | 0.439486i | ||||
\(661\) | −11.4641 | −0.445902 | −0.222951 | − | 0.974830i | \(-0.571569\pi\) | ||||
−0.222951 | + | 0.974830i | \(0.571569\pi\) | |||||||
\(662\) | − | 37.0237i | − | 1.43897i | ||||||
\(663\) | −9.12801 | − | 4.72500i | −0.354502 | − | 0.183504i | ||||
\(664\) | −41.6603 | −1.61673 | ||||||||
\(665\) | 6.68216 | − | 28.0812i | 0.259123 | − | 1.08894i | ||||
\(666\) | 34.8533 | + | 49.2900i | 1.35054 | + | 1.90995i | ||||
\(667\) | 5.44344 | 0.210771 | ||||||||
\(668\) | 47.0700i | 1.82119i | ||||||||
\(669\) | −28.0526 | − | 14.5211i | −1.08457 | − | 0.561417i | ||||
\(670\) | 68.3815 | + | 16.2720i | 2.64181 | + | 0.628641i | ||||
\(671\) | −20.1226 | + | 28.0812i | −0.776823 | + | 1.08406i | ||||
\(672\) | −12.4691 | − | 6.45448i | −0.481006 | − | 0.248987i | ||||
\(673\) | −8.82931 | −0.340345 | −0.170172 | − | 0.985414i | \(-0.554432\pi\) | ||||
−0.170172 | + | 0.985414i | \(0.554432\pi\) | |||||||
\(674\) | 48.0561i | 1.85105i | ||||||||
\(675\) | −24.5839 | − | 8.40429i | −0.946235 | − | 0.323481i | ||||
\(676\) | 5.73205 | 0.220463 | ||||||||
\(677\) | 30.4827i | 1.17155i | 0.810475 | + | 0.585773i | \(0.199209\pi\) | ||||
−0.810475 | + | 0.585773i | \(0.800791\pi\) | |||||||
\(678\) | −20.3152 | − | 10.5159i | −0.780201 | − | 0.403862i | ||||
\(679\) | − | 28.4576i | − | 1.09210i | ||||||
\(680\) | 15.8102 | + | 3.76217i | 0.606292 | + | 0.144273i | ||||
\(681\) | −15.4531 | − | 7.99912i | −0.592165 | − | 0.306527i | ||||
\(682\) | −16.0221 | + | 22.3590i | −0.613518 | + | 0.856169i | ||||
\(683\) | −37.2511 | −1.42537 | −0.712687 | − | 0.701483i | \(-0.752522\pi\) | ||||
−0.712687 | + | 0.701483i | \(0.752522\pi\) | |||||||
\(684\) | −34.8533 | + | 24.6450i | −1.33265 | + | 0.942326i | ||||
\(685\) | 9.46410 | + | 2.25207i | 0.361605 | + | 0.0860470i | ||||
\(686\) | − | 20.5569i | − | 0.784865i | ||||||
\(687\) | −10.6061 | + | 20.4895i | −0.404649 | + | 0.781722i | ||||
\(688\) | −20.5583 | −0.783778 | ||||||||
\(689\) | −29.4615 | −1.12239 | ||||||||
\(690\) | −19.3744 | − | 16.6958i | −0.737571 | − | 0.635597i | ||||
\(691\) | −2.14359 | −0.0815461 | −0.0407731 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407731 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(692\) | 68.4456i | 2.60191i | ||||||||
\(693\) | −0.211928 | + | 33.6883i | −0.00805046 | + | 1.27971i | ||||
\(694\) | 44.7321 | 1.69801 | ||||||||
\(695\) | 0.528810 | − | 2.22228i | 0.0200589 | − | 0.0842958i | ||||
\(696\) | 12.5885 | + | 6.51626i | 0.477164 | + | 0.246998i | ||||
\(697\) | − | 12.9090i | − | 0.488961i | ||||||
\(698\) | −13.3643 | −0.505847 | ||||||||
\(699\) | 12.0348 | + | 6.22969i | 0.455199 | + | 0.235628i | ||||
\(700\) | 56.4094 | + | 28.4576i | 2.13208 | + | 1.07560i | ||||
\(701\) | 43.6634 | 1.64914 | 0.824572 | − | 0.565756i | \(-0.191416\pi\) | ||||
0.824572 | + | 0.565756i | \(0.191416\pi\) | |||||||
\(702\) | 5.78692 | + | 41.7224i | 0.218413 | + | 1.57471i | ||||
\(703\) | 32.0442 | 1.20857 | ||||||||
\(704\) | 28.7391 | + | 20.5940i | 1.08315 | + | 0.776167i | ||||
\(705\) | 4.02615 | − | 4.67210i | 0.151634 | − | 0.175962i | ||||
\(706\) | 28.4576i | 1.07102i | ||||||||
\(707\) | 6.68216 | 0.251309 | ||||||||
\(708\) | −28.1231 | − | 14.5576i | −1.05693 | − | 0.547107i | ||||
\(709\) | −42.9282 | −1.61220 | −0.806101 | − | 0.591778i | \(-0.798426\pi\) | ||||
−0.806101 | + | 0.591778i | \(0.798426\pi\) | |||||||
\(710\) | 18.6778 | + | 4.44455i | 0.700967 | + | 0.166801i | ||||
\(711\) | −28.0168 | + | 19.8108i | −1.05071 | + | 0.742964i | ||||
\(712\) | 39.4801 | 1.47958 | ||||||||
\(713\) | −9.55470 | −0.357826 | ||||||||
\(714\) | 11.3125 | − | 21.8540i | 0.423358 | − | 0.817865i | ||||
\(715\) | 16.4705 | + | 18.9538i | 0.615963 | + | 0.708832i | ||||
\(716\) | 19.3185i | 0.721967i | ||||||||
\(717\) | −19.1649 | + | 37.0237i | −0.715725 | + | 1.38268i | ||||
\(718\) | − | 48.1769i | − | 1.79794i | ||||||
\(719\) | − | 37.6018i | − | 1.40231i | −0.713009 | − | 0.701154i | \(-0.752668\pi\) | ||
0.713009 | − | 0.701154i | \(-0.247332\pi\) | |||||||
\(720\) | −6.15983 | − | 15.3391i | −0.229563 | − | 0.571654i | ||||
\(721\) | 2.79101i | 0.103943i | ||||||||
\(722\) | − | 10.6878i | − | 0.397759i | ||||||
\(723\) | −4.29311 | − | 2.22228i | −0.159662 | − | 0.0826474i | ||||
\(724\) | 9.46410 | 0.351731 | ||||||||
\(725\) | 8.81011 | + | 4.44455i | 0.327199 | + | 0.165067i | ||||
\(726\) | 6.83480 | − | 45.1001i | 0.253663 | − | 1.67382i | ||||
\(727\) | 18.6791i | 0.692771i | 0.938092 | + | 0.346386i | \(0.112591\pi\) | ||||
−0.938092 | + | 0.346386i | \(0.887409\pi\) | |||||||
\(728\) | − | 47.5396i | − | 1.76194i | ||||||
\(729\) | 25.9808 | − | 7.34847i | 0.962250 | − | 0.272166i | ||||
\(730\) | −4.19615 | + | 17.6340i | −0.155307 | + | 0.652662i | ||||
\(731\) | 14.6226i | 0.540837i | ||||||||
\(732\) | −59.7953 | − | 30.9523i | −2.21010 | − | 1.14403i | ||||
\(733\) | −3.38587 | −0.125060 | −0.0625299 | − | 0.998043i | \(-0.519917\pi\) | ||||
−0.0625299 | + | 0.998043i | \(0.519917\pi\) | |||||||
\(734\) | 83.9086 | 3.09712 | ||||||||
\(735\) | 11.2865 | − | 13.0973i | 0.416308 | − | 0.483100i | ||||
\(736\) | 6.60361i | 0.243412i | ||||||||
\(737\) | −25.3649 | + | 35.3969i | −0.934327 | + | 1.30386i | ||||
\(738\) | −43.1942 | + | 30.5429i | −1.59000 | + | 1.12430i | ||||
\(739\) | − | 4.56045i | − | 0.167759i | −0.996476 | − | 0.0838794i | \(-0.973269\pi\) | ||
0.996476 | − | 0.0838794i | \(-0.0267310\pi\) | |||||||
\(740\) | −16.2369 | + | 68.2340i | −0.596879 | + | 2.50833i | ||||
\(741\) | 19.8564 | + | 10.2784i | 0.729443 | + | 0.377588i | ||||
\(742\) | − | 70.5358i | − | 2.58945i | ||||||
\(743\) | − | 22.1890i | − | 0.814037i | −0.913420 | − | 0.407019i | \(-0.866568\pi\) | ||
0.913420 | − | 0.407019i | \(-0.133432\pi\) | |||||||
\(744\) | −22.0961 | − | 11.4378i | −0.810083 | − | 0.419330i | ||||
\(745\) | −7.43588 | − | 1.76943i | −0.272430 | − | 0.0648270i | ||||
\(746\) | − | 19.9749i | − | 0.731331i | ||||||
\(747\) | 24.6083 | − | 17.4007i | 0.900371 | − | 0.636659i | ||||
\(748\) | −12.6362 | + | 17.6340i | −0.462026 | + | 0.644761i | ||||
\(749\) | 22.1469i | 0.809232i | ||||||||
\(750\) | −17.7251 | − | 42.8409i | −0.647228 | − | 1.56433i | ||||
\(751\) | 23.7128 | 0.865293 | 0.432646 | − | 0.901564i | \(-0.357580\pi\) | ||||
0.432646 | + | 0.901564i | \(0.357580\pi\) | |||||||
\(752\) | 3.92396 | 0.143092 | ||||||||
\(753\) | −26.1039 | − | 13.5124i | −0.951280 | − | 0.492419i | ||||
\(754\) | − | 15.9982i | − | 0.582622i | ||||||
\(755\) | 11.3125 | − | 47.5396i | 0.411703 | − | 1.73014i | ||||
\(756\) | −65.0372 | + | 9.02070i | −2.36538 | + | 0.328080i | ||||
\(757\) | − | 27.4665i | − | 0.998288i | −0.866519 | − | 0.499144i | \(-0.833648\pi\) | ||
0.866519 | − | 0.499144i | \(-0.166352\pi\) | |||||||
\(758\) | − | 26.1640i | − | 0.950318i | ||||||
\(759\) | 14.1168 | − | 7.19515i | 0.512407 | − | 0.261167i | ||||
\(760\) | −34.3923 | − | 8.18395i | −1.24754 | − | 0.296863i | ||||
\(761\) | 24.5985 | 0.891694 | 0.445847 | − | 0.895109i | \(-0.352903\pi\) | ||||
0.445847 | + | 0.895109i | \(0.352903\pi\) | |||||||
\(762\) | 62.3454 | + | 32.2724i | 2.25854 | + | 1.16910i | ||||
\(763\) | 9.45001i | 0.342113i | ||||||||
\(764\) | 17.2480i | 0.624009i | ||||||||
\(765\) | −10.9103 | + | 4.38134i | −0.394463 | + | 0.158408i | ||||
\(766\) | − | 65.5620i | − | 2.36885i | ||||||
\(767\) | 16.5873i | 0.598933i | ||||||||
\(768\) | −22.5495 | + | 43.5623i | −0.813685 | + | 1.57192i | ||||
\(769\) | − | 9.66836i | − | 0.348650i | −0.984688 | − | 0.174325i | \(-0.944226\pi\) | ||
0.984688 | − | 0.174325i | \(-0.0557743\pi\) | |||||||
\(770\) | −45.3786 | + | 39.4333i | −1.63533 | + | 1.42108i | ||||
\(771\) | −9.71281 | + | 18.7637i | −0.349798 | + | 0.675759i | ||||
\(772\) | 63.1812 | 2.27394 | ||||||||
\(773\) | 8.38895 | 0.301729 | 0.150865 | − | 0.988554i | \(-0.451794\pi\) | ||||
0.150865 | + | 0.988554i | \(0.451794\pi\) | |||||||
\(774\) | 48.9282 | − | 34.5975i | 1.75869 | − | 1.24358i | ||||
\(775\) | −15.4641 | − | 7.80138i | −0.555487 | − | 0.280234i | ||||
\(776\) | −34.8533 | −1.25116 | ||||||||
\(777\) | 43.7732 | + | 22.6587i | 1.57035 | + | 0.812875i | ||||
\(778\) | 90.6892 | 3.25136 | ||||||||
\(779\) | 28.0812i | 1.00611i | ||||||||
\(780\) | −31.9479 | + | 37.0735i | −1.14392 | + | 1.32745i | ||||
\(781\) | −6.92820 | + | 9.66836i | −0.247911 | + | 0.345961i | ||||
\(782\) | −11.5738 | −0.413880 | ||||||||
\(783\) | −10.1576 | + | 1.40887i | −0.363003 | + | 0.0503488i | ||||
\(784\) | 11.0000 | 0.392857 | ||||||||
\(785\) | −2.33151 | + | 9.79796i | −0.0832151 | + | 0.349704i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9721 | 0.426759 | 0.213379 | − | 0.976969i | \(-0.431553\pi\) | ||||
0.213379 | + | 0.976969i | \(0.431553\pi\) | |||||||
\(788\) | − | 78.0223i | − | 2.77943i | ||||||
\(789\) | 0.722368 | + | 0.373925i | 0.0257170 | + | 0.0133121i | ||||
\(790\) | −59.5692 | − | 14.1750i | −2.11938 | − | 0.504324i | ||||
\(791\) | −18.6778 | −0.664107 | ||||||||
\(792\) | 41.2596 | + | 0.259557i | 1.46609 | + | 0.00922296i | ||||
\(793\) | 35.2679i | 1.25240i | ||||||||
\(794\) | −49.5841 | −1.75967 | ||||||||
\(795\) | −21.9993 | + | 25.5289i | −0.780235 | + | 0.905415i | ||||
\(796\) | 10.9282 | 0.387340 | ||||||||
\(797\) | 7.22319 | 0.255859 | 0.127929 | − | 0.991783i | \(-0.459167\pi\) | ||||
0.127929 | + | 0.991783i | \(0.459167\pi\) | |||||||
\(798\) | −24.6083 | + | 47.5396i | −0.871125 | + | 1.68288i | ||||
\(799\) | − | 2.79101i | − | 0.0987390i | ||||||
\(800\) | −5.39183 | + | 10.6878i | −0.190630 | + | 0.377871i | ||||
\(801\) | −23.3205 | + | 16.4901i | −0.823990 | + | 0.582649i | ||||
\(802\) | −26.4228 | −0.933021 | ||||||||
\(803\) | −9.12801 | − | 6.54099i | −0.322120 | − | 0.230827i | ||||
\(804\) | −75.3731 | − | 39.0160i | −2.65820 | − | 1.37599i | ||||
\(805\) | −20.3152 | − | 4.83418i | −0.716017 | − | 0.170382i | ||||
\(806\) | 28.0812i | 0.989118i | ||||||||
\(807\) | −13.0520 | − | 6.75620i | −0.459451 | − | 0.237829i | ||||
\(808\) | − | 8.18395i | − | 0.287910i | ||||||
\(809\) | −53.0023 | −1.86346 | −0.931732 | − | 0.363148i | \(-0.881702\pi\) | ||||
−0.931732 | + | 0.363148i | \(0.881702\pi\) | |||||||
\(810\) | 40.4743 | + | 26.1402i | 1.42212 | + | 0.918474i | ||||
\(811\) | 22.6019i | 0.793658i | 0.917892 | + | 0.396829i | \(0.129889\pi\) | ||||
−0.917892 | + | 0.396829i | \(0.870111\pi\) | |||||||
\(812\) | 24.9382 | 0.875158 | ||||||||
\(813\) | −30.4728 | − | 15.7739i | −1.06873 | − | 0.553214i | ||||
\(814\) | −54.2487 | − | 38.8738i | −1.90142 | − | 1.36253i | ||||
\(815\) | −0.426696 | + | 1.79315i | −0.0149465 | + | 0.0628113i | ||||
\(816\) | −6.64300 | − | 3.43867i | −0.232552 | − | 0.120378i | ||||
\(817\) | − | 31.8090i | − | 1.11285i | ||||||
\(818\) | 56.5585 | 1.97752 | ||||||||
\(819\) | 19.8564 | + | 28.0812i | 0.693839 | + | 0.981237i | ||||
\(820\) | −59.7953 | − | 14.2288i | −2.08814 | − | 0.496891i | ||||
\(821\) | 24.9856 | 0.872003 | 0.436002 | − | 0.899946i | \(-0.356394\pi\) | ||||
0.436002 | + | 0.899946i | \(0.356394\pi\) | |||||||
\(822\) | −16.0221 | − | 8.29365i | −0.558835 | − | 0.289274i | ||||
\(823\) | 31.1463i | 1.08569i | 0.839832 | + | 0.542847i | \(0.182654\pi\) | ||||
−0.839832 | + | 0.542847i | \(0.817346\pi\) | |||||||
\(824\) | 3.41828 | 0.119081 | ||||||||
\(825\) | 28.7226 | − | 0.118903i | 0.999991 | − | 0.00413968i | ||||
\(826\) | −39.7128 | −1.38179 | ||||||||
\(827\) | 10.9855i | 0.382005i | 0.981590 | + | 0.191002i | \(0.0611738\pi\) | ||||
−0.981590 | + | 0.191002i | \(0.938826\pi\) | |||||||
\(828\) | 17.8293 | + | 25.2145i | 0.619612 | + | 0.876263i | ||||
\(829\) | 32.1051 | 1.11506 | 0.557528 | − | 0.830158i | \(-0.311750\pi\) | ||||
0.557528 | + | 0.830158i | \(0.311750\pi\) | |||||||
\(830\) | 52.3222 | + | 12.4505i | 1.81613 | + | 0.432164i | ||||
\(831\) | 15.9819 | − | 30.8747i | 0.554407 | − | 1.07103i | ||||
\(832\) | 36.0942 | 1.25134 | ||||||||
\(833\) | − | 7.82403i | − | 0.271086i | ||||||
\(834\) | −1.94744 | + | 3.76217i | −0.0674344 | + | 0.130273i | ||||
\(835\) | 6.52864 | − | 27.4360i | 0.225933 | − | 0.949463i | ||||
\(836\) | 27.4879 | − | 38.3596i | 0.950690 | − | 1.32670i | ||||
\(837\) | 17.8293 | − | 2.47294i | 0.616271 | − | 0.0854773i | ||||
\(838\) | −85.0677 | −2.93862 | ||||||||
\(839\) | − | 38.8401i | − | 1.34091i | −0.741950 | − | 0.670455i | \(-0.766099\pi\) | ||
0.741950 | − | 0.670455i | \(-0.233901\pi\) | |||||||
\(840\) | −41.1938 | − | 35.4985i | −1.42132 | − | 1.22482i | ||||
\(841\) | −25.1051 | −0.865694 | ||||||||
\(842\) | 78.4919i | 2.70501i | ||||||||
\(843\) | 26.1797 | − | 50.5753i | 0.901677 | − | 1.74191i | ||||
\(844\) | − | 53.1026i | − | 1.82787i | ||||||
\(845\) | −3.34108 | − | 0.795040i | −0.114937 | − | 0.0273502i | ||||
\(846\) | −9.33892 | + | 6.60361i | −0.321079 | + | 0.227037i | ||||
\(847\) | −11.9721 | − | 35.2679i | −0.411366 | − | 1.21182i | ||||
\(848\) | −21.4409 | −0.736284 | ||||||||
\(849\) | −5.19827 | + | 10.0423i | −0.178404 | + | 0.344650i | ||||
\(850\) | −18.7321 | − | 9.45001i | −0.642504 | − | 0.324133i | ||||
\(851\) | − | 23.1822i | − | 0.794676i | ||||||
\(852\) | −20.5875 | − | 10.6569i | −0.705317 | − | 0.365099i | ||||
\(853\) | −0.243094 | −0.00832339 | −0.00416170 | − | 0.999991i | \(-0.501325\pi\) | ||||
−0.00416170 | + | 0.999991i | \(0.501325\pi\) | |||||||
\(854\) | −84.4374 | −2.88939 | ||||||||
\(855\) | 23.7335 | − | 9.53084i | 0.811668 | − | 0.325948i | ||||
\(856\) | 27.1244 | 0.927091 | ||||||||
\(857\) | − | 2.69190i | − | 0.0919535i | −0.998943 | − | 0.0459768i | \(-0.985360\pi\) | ||
0.998943 | − | 0.0459768i | \(-0.0146400\pi\) | |||||||
\(858\) | −21.1465 | − | 41.4891i | −0.721929 | − | 1.41642i | ||||
\(859\) | 32.5359 | 1.11011 | 0.555055 | − | 0.831813i | \(-0.312697\pi\) | ||||
0.555055 | + | 0.831813i | \(0.312697\pi\) | |||||||
\(860\) | 67.7331 | + | 16.1177i | 2.30968 | + | 0.549608i | ||||
\(861\) | −19.8564 | + | 38.3596i | −0.676705 | + | 1.30729i | ||||
\(862\) | − | 38.7269i | − | 1.31904i | ||||||
\(863\) | 29.7155 | 1.01153 | 0.505764 | − | 0.862672i | \(-0.331211\pi\) | ||||
0.505764 | + | 0.862672i | \(0.331211\pi\) | |||||||
\(864\) | −1.70914 | − | 12.3225i | −0.0581461 | − | 0.419220i | ||||
\(865\) | 9.49346 | − | 39.8954i | 0.322787 | − | 1.35648i | ||||
\(866\) | −46.6946 | −1.58675 | ||||||||
\(867\) | 11.0900 | − | 21.4242i | 0.376636 | − | 0.727604i | ||||
\(868\) | −43.7732 | −1.48576 | ||||||||
\(869\) | 22.0961 | − | 30.8353i | 0.749559 | − | 1.04602i | ||||
\(870\) | −13.8627 | − | 11.9461i | −0.469991 | − | 0.405011i | ||||
\(871\) | 44.4559i | 1.50633i | ||||||||
\(872\) | 11.5738 | 0.391940 | ||||||||
\(873\) | 20.5875 | − | 14.5576i | 0.696782 | − | 0.492699i | ||||
\(874\) | 25.1769 | 0.851622 | ||||||||
\(875\) | −28.9327 | − | 24.4113i | −0.978103 | − | 0.825253i | ||||
\(876\) | 10.0613 | − | 19.4369i | 0.339939 | − | 0.656712i | ||||
\(877\) | −23.2149 | −0.783911 | −0.391956 | − | 0.919984i | \(-0.628201\pi\) | ||||
−0.391956 | + | 0.919984i | \(0.628201\pi\) | |||||||
\(878\) | 15.8102 | 0.533567 | ||||||||
\(879\) | 2.69591 | + | 1.39551i | 0.0909309 | + | 0.0470693i | ||||
\(880\) | 11.9866 | + | 13.7938i | 0.404069 | + | 0.464990i | ||||
\(881\) | − | 45.0518i | − | 1.51783i | −0.651188 | − | 0.758916i | \(-0.725729\pi\) | ||
0.651188 | − | 0.758916i | \(-0.274271\pi\) | |||||||
\(882\) | −26.1797 | + | 18.5118i | −0.881516 | + | 0.623326i | ||||
\(883\) | 12.0846i | 0.406680i | 0.979108 | + | 0.203340i | \(0.0651797\pi\) | ||||
−0.979108 | + | 0.203340i | \(0.934820\pi\) | |||||||
\(884\) | 22.1469i | 0.744882i | ||||||||
\(885\) | 14.3732 | + | 12.3860i | 0.483148 | + | 0.416350i | ||||
\(886\) | 3.06475i | 0.102962i | ||||||||
\(887\) | − | 10.0463i | − | 0.337322i | −0.985674 | − | 0.168661i | \(-0.946056\pi\) | ||
0.985674 | − | 0.168661i | \(-0.0539443\pi\) | |||||||
\(888\) | 27.7511 | − | 53.6110i | 0.931266 | − | 1.79907i | ||||
\(889\) | 57.3205 | 1.92247 | ||||||||
\(890\) | −49.5841 | − | 11.7990i | −1.66206 | − | 0.395502i | ||||
\(891\) | −24.4800 | + | 17.0800i | −0.820112 | + | 0.572203i | ||||
\(892\) | 68.0629i | 2.27891i | ||||||||
\(893\) | 6.07137i | 0.203171i | ||||||||
\(894\) | 12.5885 | + | 6.51626i | 0.421021 | + | 0.217937i | ||||
\(895\) | 2.67949 | − | 11.2603i | 0.0895655 | − | 0.376391i | ||||
\(896\) | 70.2030i | 2.34532i | ||||||||
\(897\) | 7.43588 | − | 14.3650i | 0.248277 | − | 0.479634i | ||||
\(898\) | 44.4373 | 1.48289 | ||||||||
\(899\) | −6.83656 | −0.228012 | ||||||||
\(900\) | 8.26888 | + | 55.3667i | 0.275629 | + | 1.84556i | ||||
\(901\) | 15.2504i | 0.508064i | ||||||||
\(902\) | 34.0662 | − | 47.5396i | 1.13428 | − | 1.58290i | ||||
\(903\) | 22.4923 | − | 43.4519i | 0.748498 | − | 1.44599i | ||||
\(904\) | 22.8756i | 0.760831i | ||||||||
\(905\) | −5.51641 | − | 1.31268i | −0.183372 | − | 0.0436349i | ||||
\(906\) | −41.6603 | + | 80.4814i | −1.38407 | + | 2.67382i | ||||
\(907\) | 31.7498i | 1.05423i | 0.849793 | + | 0.527117i | \(0.176727\pi\) | ||||
−0.849793 | + | 0.527117i | \(0.823273\pi\) | |||||||
\(908\) | 37.4933i | 1.24426i | ||||||||
\(909\) | 3.41828 | + | 4.83418i | 0.113377 | + | 0.160340i | ||||
\(910\) | −14.2076 | + | 59.7062i | −0.470978 | + | 1.97924i | ||||
\(911\) | 28.7647i | 0.953019i | 0.879169 | + | 0.476509i | \(0.158098\pi\) | ||||
−0.879169 | + | 0.476509i | \(0.841902\pi\) | |||||||
\(912\) | 14.4507 | + | 7.48024i | 0.478511 | + | 0.247695i | ||||
\(913\) | −19.4080 | + | 27.0840i | −0.642310 | + | 0.896348i | ||||
\(914\) | − | 68.6129i | − | 2.26951i | ||||||
\(915\) | 30.5602 | + | 26.3351i | 1.01029 | + | 0.870610i | ||||
\(916\) | 49.7128 | 1.64256 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 21.5971 | − | 2.99553i | 0.712810 | − | 0.0988673i | ||||
\(919\) | 19.8108i | 0.653499i | 0.945111 | + | 0.326750i | \(0.105953\pi\) | ||||
−0.945111 | + | 0.326750i | \(0.894047\pi\) | |||||||
\(920\) | −5.92064 | + | 24.8809i | −0.195198 | + | 0.820301i | ||||
\(921\) | 6.64300 | − | 12.8333i | 0.218894 | − | 0.422872i | ||||
\(922\) | 75.2608i | 2.47858i | ||||||||
\(923\) | 12.1427i | 0.399683i | ||||||||
\(924\) | 64.6736 | − | 32.9633i | 2.12760 | − | 1.08441i | ||||
\(925\) | 18.9282 | − | 37.5200i | 0.622355 | − | 1.23365i | ||||
\(926\) | 18.1490 | 0.596414 | ||||||||
\(927\) | −2.01915 | + | 1.42775i | −0.0663175 | + | 0.0468935i | ||||
\(928\) | 4.72500i | 0.155106i | ||||||||
\(929\) | − | 41.4655i | − | 1.36044i | −0.733009 | − | 0.680219i | \(-0.761885\pi\) | ||
0.733009 | − | 0.680219i | \(-0.238115\pi\) | |||||||
\(930\) | 24.3328 | + | 20.9686i | 0.797904 | + | 0.687589i | ||||
\(931\) | 17.0198i | 0.557802i | ||||||||
\(932\) | − | 29.1997i | − | 0.956467i | ||||||
\(933\) | −22.6067 | − | 11.7021i | −0.740109 | − | 0.383109i | ||||
\(934\) | − | 71.1440i | − | 2.32790i | ||||||
\(935\) | 9.81121 | − | 8.52578i | 0.320861 | − | 0.278823i | ||||
\(936\) | 34.3923 | − | 24.3190i | 1.12415 | − | 0.794892i | ||||
\(937\) | −46.6729 | −1.52474 | −0.762368 | − | 0.647144i | \(-0.775963\pi\) | ||||
−0.762368 | + | 0.647144i | \(0.775963\pi\) | |||||||
\(938\) | −106.435 | −3.47522 | ||||||||
\(939\) | −24.2487 | − | 12.5521i | −0.791327 | − | 0.409621i | ||||
\(940\) | −12.9282 | − | 3.07638i | −0.421671 | − | 0.100340i | ||||
\(941\) | 46.1658 | 1.50496 | 0.752481 | − | 0.658614i | \(-0.228857\pi\) | ||||
0.752481 | + | 0.658614i | \(0.228857\pi\) | |||||||
\(942\) | 8.58622 | − | 16.5873i | 0.279754 | − | 0.540443i | ||||
\(943\) | 20.3152 | 0.661554 | ||||||||
\(944\) | 12.0716i | 0.392897i | ||||||||
\(945\) | 39.1599 | + | 3.76274i | 1.27387 | + | 0.122402i | ||||
\(946\) | −38.5885 | + | 53.8505i | −1.25462 | + | 1.75083i | ||||
\(947\) | −23.6581 | −0.768785 | −0.384392 | − | 0.923170i | \(-0.625589\pi\) | ||||
−0.384392 | + | 0.923170i | \(0.625589\pi\) | |||||||
\(948\) | 65.6598 | + | 33.9880i | 2.13253 | + | 1.10388i | ||||
\(949\) | −11.4641 | −0.372140 | ||||||||
\(950\) | 40.7483 | + | 20.5569i | 1.32205 | + | 0.666953i | ||||
\(951\) | −0.679492 | + | 1.31268i | −0.0220340 | + | 0.0425665i | ||||
\(952\) | −24.6083 | −0.797560 | ||||||||
\(953\) | 10.3901i | 0.336568i | 0.985739 | + | 0.168284i | \(0.0538226\pi\) | ||||
−0.985739 | + | 0.168284i | \(0.946177\pi\) | |||||||
\(954\) | 51.0288 | − | 36.0828i | 1.65212 | − | 1.16822i | ||||
\(955\) | 2.39230 | − | 10.0534i | 0.0774132 | − | 0.325322i | ||||
\(956\) | 89.8292 | 2.90528 | ||||||||
\(957\) | 10.1008 | − | 5.14826i | 0.326513 | − | 0.166420i | ||||
\(958\) | − | 3.45894i | − | 0.111753i | ||||||
\(959\) | −14.7307 | −0.475681 | ||||||||
\(960\) | 26.9521 | − | 31.2762i | 0.869874 | − | 1.00944i | ||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | −68.1324 | −2.19668 | ||||||||
\(963\) | −16.0221 | + | 11.3293i | −0.516305 | + | 0.365083i | ||||
\(964\) | 10.4162i | 0.335484i | ||||||||
\(965\) | −36.8269 | − | 8.76327i | −1.18550 | − | 0.282100i | ||||
\(966\) | 34.3923 | + | 17.8028i | 1.10655 | + | 0.572795i | ||||
\(967\) | −8.34312 | −0.268297 | −0.134148 | − | 0.990961i | \(-0.542830\pi\) | ||||
−0.134148 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(968\) | −43.1942 | + | 14.6627i | −1.38831 | + | 0.471279i | ||||
\(969\) | 5.32051 | − | 10.2784i | 0.170919 | − | 0.330191i | ||||
\(970\) | 43.7732 | + | 10.4162i | 1.40547 | + | 0.334444i | ||||
\(971\) | − | 50.2281i | − | 1.61190i | −0.591985 | − | 0.805949i | \(-0.701656\pi\) | ||
0.591985 | − | 0.805949i | \(-0.298344\pi\) | |||||||
\(972\) | −39.7959 | − | 42.4363i | −1.27646 | − | 1.36114i | ||||
\(973\) | 3.45894i | 0.110889i | ||||||||
\(974\) | −30.3774 | −0.973355 | ||||||||
\(975\) | 23.7638 | − | 17.1781i | 0.761051 | − | 0.550141i | ||||
\(976\) | 25.6666i | 0.821568i | ||||||||
\(977\) | 39.1559 | 1.25271 | 0.626354 | − | 0.779539i | \(-0.284546\pi\) | ||||
0.626354 | + | 0.779539i | \(0.284546\pi\) | |||||||
\(978\) | 1.57139 | − | 3.03569i | 0.0502474 | − | 0.0970705i | ||||
\(979\) | 18.3923 | − | 25.6666i | 0.587821 | − | 0.820308i | ||||
\(980\) | −36.2415 | − | 8.62398i | −1.15769 | − | 0.275483i | ||||
\(981\) | −6.83656 | + | 4.83418i | −0.218275 | + | 0.154343i | ||||
\(982\) | 38.7269i | 1.23582i | ||||||||
\(983\) | −8.27462 | −0.263919 | −0.131960 | − | 0.991255i | \(-0.542127\pi\) | ||||
−0.131960 | + | 0.991255i | \(0.542127\pi\) | |||||||
\(984\) | 46.9808 | + | 24.3190i | 1.49769 | + | 0.775262i | ||||
\(985\) | −10.8217 | + | 45.4774i | −0.344810 | + | 1.44903i | ||||
\(986\) | −8.28130 | −0.263730 | ||||||||
\(987\) | −4.29311 | + | 8.29365i | −0.136651 | + | 0.263990i | ||||
\(988\) | − | 48.1769i | − | 1.53271i | ||||||
\(989\) | −23.0120 | −0.731740 | ||||||||
\(990\) | −51.7414 | − | 12.6568i | −1.64445 | − | 0.402258i | ||||
\(991\) | −48.2487 | −1.53267 | −0.766335 | − | 0.642441i | \(-0.777922\pi\) | ||||
−0.766335 | + | 0.642441i | \(0.777922\pi\) | |||||||
\(992\) | − | 8.29365i | − | 0.263324i | ||||||
\(993\) | 12.3129 | − | 23.7867i | 0.390738 | − | 0.754848i | ||||
\(994\) | −29.0718 | −0.922101 | ||||||||
\(995\) | −6.36980 | − | 1.51575i | −0.201936 | − | 0.0480525i | ||||
\(996\) | −57.6718 | − | 29.8531i | −1.82740 | − | 0.945932i | ||||
\(997\) | 29.9866 | 0.949686 | 0.474843 | − | 0.880071i | \(-0.342505\pi\) | ||||
0.474843 | + | 0.880071i | \(0.342505\pi\) | |||||||
\(998\) | 26.1640i | 0.828206i | ||||||||
\(999\) | 6.00000 | + | 43.2586i | 0.189832 | + | 1.36864i |
(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 | 165.2.d.c.164.3 | yes | 16 | |
3.2 | odd | 2 | inner | 165.2.d.c.164.13 | yes | 16 | |
5.2 | odd | 4 | 825.2.f.f.626.13 | 16 | |||
5.3 | odd | 4 | 825.2.f.f.626.4 | 16 | |||
5.4 | even | 2 | inner | 165.2.d.c.164.14 | yes | 16 | |
11.10 | odd | 2 | inner | 165.2.d.c.164.15 | yes | 16 | |
15.2 | even | 4 | 825.2.f.f.626.2 | 16 | |||
15.8 | even | 4 | 825.2.f.f.626.15 | 16 | |||
15.14 | odd | 2 | inner | 165.2.d.c.164.4 | yes | 16 | |
33.32 | even | 2 | inner | 165.2.d.c.164.1 | ✓ | 16 | |
55.32 | even | 4 | 825.2.f.f.626.1 | 16 | |||
55.43 | even | 4 | 825.2.f.f.626.16 | 16 | |||
55.54 | odd | 2 | inner | 165.2.d.c.164.2 | yes | 16 | |
165.32 | odd | 4 | 825.2.f.f.626.14 | 16 | |||
165.98 | odd | 4 | 825.2.f.f.626.3 | 16 | |||
165.164 | even | 2 | inner | 165.2.d.c.164.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.d.c.164.1 | ✓ | 16 | 33.32 | even | 2 | inner | |
165.2.d.c.164.2 | yes | 16 | 55.54 | odd | 2 | inner | |
165.2.d.c.164.3 | yes | 16 | 1.1 | even | 1 | trivial | |
165.2.d.c.164.4 | yes | 16 | 15.14 | odd | 2 | inner | |
165.2.d.c.164.13 | yes | 16 | 3.2 | odd | 2 | inner | |
165.2.d.c.164.14 | yes | 16 | 5.4 | even | 2 | inner | |
165.2.d.c.164.15 | yes | 16 | 11.10 | odd | 2 | inner | |
165.2.d.c.164.16 | yes | 16 | 165.164 | even | 2 | inner | |
825.2.f.f.626.1 | 16 | 55.32 | even | 4 | |||
825.2.f.f.626.2 | 16 | 15.2 | even | 4 | |||
825.2.f.f.626.3 | 16 | 165.98 | odd | 4 | |||
825.2.f.f.626.4 | 16 | 5.3 | odd | 4 | |||
825.2.f.f.626.13 | 16 | 5.2 | odd | 4 | |||
825.2.f.f.626.14 | 16 | 165.32 | odd | 4 | |||
825.2.f.f.626.15 | 16 | 15.8 | even | 4 | |||
825.2.f.f.626.16 | 16 | 55.43 | even | 4 |