Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(239,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 437.8 | ||
Root | \(0.500000 - 0.410882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.437 |
Dual form | 1014.2.g.d.239.8 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.53819 | − | 0.796225i | 0.888074 | − | 0.459701i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.02097 | + | 2.02097i | −0.903805 | + | 0.903805i | −0.995763 | − | 0.0919576i | \(-0.970688\pi\) |
0.0919576 | + | 0.995763i | \(0.470688\pi\) | |||||||
\(6\) | 0.524648 | − | 1.65068i | 0.214186 | − | 0.673887i | ||||
\(7\) | 2.53819 | − | 2.53819i | 0.959345 | − | 0.959345i | −0.0398600 | − | 0.999205i | \(-0.512691\pi\) |
0.999205 | + | 0.0398600i | \(0.0126912\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.73205 | − | 2.44949i | 0.577350 | − | 0.816497i | ||||
\(10\) | 2.85808i | 0.903805i | ||||||||
\(11\) | −2.97155 | − | 2.97155i | −0.895957 | − | 0.895957i | 0.0991187 | − | 0.995076i | \(-0.468398\pi\) |
−0.995076 | + | 0.0991187i | \(0.968398\pi\) | |||||||
\(12\) | −0.796225 | − | 1.53819i | −0.229850 | − | 0.444037i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 3.58954i | − | 0.959345i | ||||||
\(15\) | −1.49949 | + | 4.71778i | −0.387166 | + | 1.21813i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.45408 | 0.837737 | 0.418869 | − | 0.908047i | \(-0.362427\pi\) | ||||
0.418869 | + | 0.908047i | \(0.362427\pi\) | |||||||
\(18\) | −0.507306 | − | 2.95680i | −0.119573 | − | 0.696923i | ||||
\(19\) | −1.58784 | − | 1.58784i | −0.364276 | − | 0.364276i | 0.501108 | − | 0.865385i | \(-0.332926\pi\) |
−0.865385 | + | 0.501108i | \(0.832926\pi\) | |||||||
\(20\) | 2.02097 | + | 2.02097i | 0.451903 | + | 0.451903i | ||||
\(21\) | 1.88324 | − | 5.92518i | 0.410958 | − | 1.29298i | ||||
\(22\) | −4.20241 | −0.895957 | ||||||||
\(23\) | 3.03237 | 0.632292 | 0.316146 | − | 0.948711i | \(-0.397611\pi\) | ||||
0.316146 | + | 0.948711i | \(0.397611\pi\) | |||||||
\(24\) | −1.65068 | − | 0.524648i | −0.336944 | − | 0.107093i | ||||
\(25\) | − | 3.16864i | − | 0.633728i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.713876 | − | 5.14688i | 0.137386 | − | 0.990518i | ||||
\(28\) | −2.53819 | − | 2.53819i | −0.479673 | − | 0.479673i | ||||
\(29\) | − | 2.01416i | − | 0.374021i | −0.982358 | − | 0.187010i | \(-0.940120\pi\) | ||
0.982358 | − | 0.187010i | \(-0.0598798\pi\) | |||||||
\(30\) | 2.27568 | + | 4.39627i | 0.415480 | + | 0.802646i | ||||
\(31\) | −1.21829 | − | 1.21829i | −0.218812 | − | 0.218812i | 0.589186 | − | 0.807998i | \(-0.299449\pi\) |
−0.807998 | + | 0.589186i | \(0.799449\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.93684 | − | 2.20478i | −1.20755 | − | 0.383804i | ||||
\(34\) | 2.44240 | − | 2.44240i | 0.418869 | − | 0.418869i | ||||
\(35\) | 10.2592i | 1.73412i | ||||||||
\(36\) | −2.44949 | − | 1.73205i | −0.408248 | − | 0.288675i | ||||
\(37\) | 3.42423 | − | 3.42423i | 0.562940 | − | 0.562940i | −0.367202 | − | 0.930141i | \(-0.619684\pi\) |
0.930141 | + | 0.367202i | \(0.119684\pi\) | |||||||
\(38\) | −2.24555 | −0.364276 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.85808 | 0.451903 | ||||||||
\(41\) | −5.61494 | + | 5.61494i | −0.876906 | + | 0.876906i | −0.993213 | − | 0.116307i | \(-0.962894\pi\) |
0.116307 | + | 0.993213i | \(0.462894\pi\) | |||||||
\(42\) | −2.85808 | − | 5.52139i | −0.441012 | − | 0.851969i | ||||
\(43\) | − | 1.95035i | − | 0.297425i | −0.988880 | − | 0.148712i | \(-0.952487\pi\) | ||
0.988880 | − | 0.148712i | \(-0.0475129\pi\) | |||||||
\(44\) | −2.97155 | + | 2.97155i | −0.447978 | + | 0.447978i | ||||
\(45\) | 1.44992 | + | 8.45077i | 0.216142 | + | 1.25977i | ||||
\(46\) | 2.14421 | − | 2.14421i | 0.316146 | − | 0.316146i | ||||
\(47\) | 0.957390 | + | 0.957390i | 0.139650 | + | 0.139650i | 0.773476 | − | 0.633826i | \(-0.218516\pi\) |
−0.633826 | + | 0.773476i | \(0.718516\pi\) | |||||||
\(48\) | −1.53819 | + | 0.796225i | −0.222018 | + | 0.114925i | ||||
\(49\) | − | 5.88481i | − | 0.840687i | ||||||
\(50\) | −2.24057 | − | 2.24057i | −0.316864 | − | 0.316864i | ||||
\(51\) | 5.31303 | − | 2.75023i | 0.743973 | − | 0.385109i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.22186i | − | 0.991999i | −0.868323 | − | 0.495999i | \(-0.834802\pi\) | ||
0.868323 | − | 0.495999i | \(-0.165198\pi\) | |||||||
\(54\) | −3.13461 | − | 4.14418i | −0.426566 | − | 0.563952i | ||||
\(55\) | 12.0108 | 1.61954 | ||||||||
\(56\) | −3.58954 | −0.479673 | ||||||||
\(57\) | −3.70668 | − | 1.17812i | −0.490962 | − | 0.156046i | ||||
\(58\) | −1.42423 | − | 1.42423i | −0.187010 | − | 0.187010i | ||||
\(59\) | 7.27501 | + | 7.27501i | 0.947125 | + | 0.947125i | 0.998671 | − | 0.0515453i | \(-0.0164147\pi\) |
−0.0515453 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(60\) | 4.71778 | + | 1.49949i | 0.609063 | + | 0.193583i | ||||
\(61\) | 0.274207 | 0.0351086 | 0.0175543 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175543 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(62\) | −1.72293 | −0.218812 | ||||||||
\(63\) | −1.82100 | − | 10.6135i | −0.229424 | − | 1.33718i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.46410 | + | 3.34607i | −0.795676 | + | 0.411872i | ||||
\(67\) | 3.00229 | + | 3.00229i | 0.366788 | + | 0.366788i | 0.866304 | − | 0.499516i | \(-0.166489\pi\) |
−0.499516 | + | 0.866304i | \(0.666489\pi\) | |||||||
\(68\) | − | 3.45408i | − | 0.418869i | ||||||
\(69\) | 4.66435 | − | 2.41445i | 0.561522 | − | 0.290665i | ||||
\(70\) | 7.25436 | + | 7.25436i | 0.867061 | + | 0.867061i | ||||
\(71\) | 7.80205 | − | 7.80205i | 0.925933 | − | 0.925933i | −0.0715067 | − | 0.997440i | \(-0.522781\pi\) |
0.997440 | + | 0.0715067i | \(0.0227807\pi\) | |||||||
\(72\) | −2.95680 | + | 0.507306i | −0.348462 | + | 0.0597866i | ||||
\(73\) | −10.0822 | + | 10.0822i | −1.18003 | + | 1.18003i | −0.200296 | + | 0.979735i | \(0.564190\pi\) |
−0.979735 | + | 0.200296i | \(0.935810\pi\) | |||||||
\(74\) | − | 4.84259i | − | 0.562940i | ||||||
\(75\) | −2.52295 | − | 4.87397i | −0.291325 | − | 0.562797i | ||||
\(76\) | −1.58784 | + | 1.58784i | −0.182138 | + | 0.182138i | ||||
\(77\) | −15.0847 | −1.71906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.58051 | 0.177821 | 0.0889105 | − | 0.996040i | \(-0.471661\pi\) | ||||
0.0889105 | + | 0.996040i | \(0.471661\pi\) | |||||||
\(80\) | 2.02097 | − | 2.02097i | 0.225951 | − | 0.225951i | ||||
\(81\) | −3.00000 | − | 8.48528i | −0.333333 | − | 0.942809i | ||||
\(82\) | 7.94072i | 0.876906i | ||||||||
\(83\) | 2.58938 | − | 2.58938i | 0.284221 | − | 0.284221i | −0.550569 | − | 0.834790i | \(-0.685589\pi\) |
0.834790 | + | 0.550569i | \(0.185589\pi\) | |||||||
\(84\) | −5.92518 | − | 1.88324i | −0.646491 | − | 0.205479i | ||||
\(85\) | −6.98059 | + | 6.98059i | −0.757152 | + | 0.757152i | ||||
\(86\) | −1.37910 | − | 1.37910i | −0.148712 | − | 0.148712i | ||||
\(87\) | −1.60373 | − | 3.09816i | −0.171938 | − | 0.332158i | ||||
\(88\) | 4.20241i | 0.447978i | ||||||||
\(89\) | 6.96131 | + | 6.96131i | 0.737897 | + | 0.737897i | 0.972171 | − | 0.234273i | \(-0.0752711\pi\) |
−0.234273 | + | 0.972171i | \(0.575271\pi\) | |||||||
\(90\) | 7.00085 | + | 4.95035i | 0.737954 | + | 0.521812i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.03237i | − | 0.316146i | ||||||
\(93\) | −2.84400 | − | 0.903931i | −0.294910 | − | 0.0937332i | ||||
\(94\) | 1.35395 | 0.139650 | ||||||||
\(95\) | 6.41797 | 0.658470 | ||||||||
\(96\) | −0.524648 | + | 1.65068i | −0.0535466 | + | 0.168472i | ||||
\(97\) | 5.67277 | + | 5.67277i | 0.575983 | + | 0.575983i | 0.933794 | − | 0.357811i | \(-0.116477\pi\) |
−0.357811 | + | 0.933794i | \(0.616477\pi\) | |||||||
\(98\) | −4.16119 | − | 4.16119i | −0.420343 | − | 0.420343i | ||||
\(99\) | −12.4257 | + | 2.13191i | −1.24883 | + | 0.214265i | ||||
\(100\) | −3.16864 | −0.316864 | ||||||||
\(101\) | −2.10685 | −0.209639 | −0.104820 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104820 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(102\) | 1.81217 | − | 5.70158i | 0.179432 | − | 0.564541i | ||||
\(103\) | 14.2629i | 1.40537i | 0.711503 | + | 0.702683i | \(0.248015\pi\) | ||||
−0.711503 | + | 0.702683i | \(0.751985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.16864 | + | 15.7806i | 0.797178 | + | 1.54003i | ||||
\(106\) | −5.10662 | − | 5.10662i | −0.495999 | − | 0.495999i | ||||
\(107\) | 13.8455i | 1.33850i | 0.743039 | + | 0.669248i | \(0.233384\pi\) | ||||
−0.743039 | + | 0.669248i | \(0.766616\pi\) | |||||||
\(108\) | −5.14688 | − | 0.713876i | −0.495259 | − | 0.0686928i | ||||
\(109\) | −5.84220 | − | 5.84220i | −0.559581 | − | 0.559581i | 0.369607 | − | 0.929188i | \(-0.379492\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(110\) | 8.49295 | − | 8.49295i | 0.809771 | − | 0.809771i | ||||
\(111\) | 2.54065 | − | 7.99357i | 0.241148 | − | 0.758716i | ||||
\(112\) | −2.53819 | + | 2.53819i | −0.239836 | + | 0.239836i | ||||
\(113\) | 18.0041i | 1.69368i | 0.531845 | + | 0.846841i | \(0.321499\pi\) | ||||
−0.531845 | + | 0.846841i | \(0.678501\pi\) | |||||||
\(114\) | −3.45408 | + | 1.78796i | −0.323504 | + | 0.167458i | ||||
\(115\) | −6.12832 | + | 6.12832i | −0.571469 | + | 0.571469i | ||||
\(116\) | −2.01416 | −0.187010 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.2884 | 0.947125 | ||||||||
\(119\) | 8.76711 | − | 8.76711i | 0.803679 | − | 0.803679i | ||||
\(120\) | 4.39627 | − | 2.27568i | 0.401323 | − | 0.207740i | ||||
\(121\) | 6.66025i | 0.605478i | ||||||||
\(122\) | 0.193894 | − | 0.193894i | 0.0175543 | − | 0.0175543i | ||||
\(123\) | −4.16608 | + | 13.1076i | −0.375643 | + | 1.18187i | ||||
\(124\) | −1.21829 | + | 1.21829i | −0.109406 | + | 0.109406i | ||||
\(125\) | −3.70112 | − | 3.70112i | −0.331039 | − | 0.331039i | ||||
\(126\) | −8.79254 | − | 6.21727i | −0.783302 | − | 0.553878i | ||||
\(127\) | 20.6932i | 1.83623i | 0.396317 | + | 0.918114i | \(0.370288\pi\) | ||||
−0.396317 | + | 0.918114i | \(0.629712\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −1.55291 | − | 3.00000i | −0.136726 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.68295i | − | 0.409151i | −0.978851 | − | 0.204576i | \(-0.934419\pi\) | ||
0.978851 | − | 0.204576i | \(-0.0655814\pi\) | |||||||
\(132\) | −2.20478 | + | 6.93684i | −0.191902 | + | 0.603774i | ||||
\(133\) | −8.06049 | −0.698933 | ||||||||
\(134\) | 4.24588 | 0.366788 | ||||||||
\(135\) | 8.95897 | + | 11.8444i | 0.771065 | + | 1.01940i | ||||
\(136\) | −2.44240 | − | 2.44240i | −0.209434 | − | 0.209434i | ||||
\(137\) | 3.87494 | + | 3.87494i | 0.331058 | + | 0.331058i | 0.852988 | − | 0.521930i | \(-0.174788\pi\) |
−0.521930 | + | 0.852988i | \(0.674788\pi\) | |||||||
\(138\) | 1.59092 | − | 5.00547i | 0.135428 | − | 0.426094i | ||||
\(139\) | 14.6932 | 1.24626 | 0.623132 | − | 0.782117i | \(-0.285860\pi\) | ||||
0.623132 | + | 0.782117i | \(0.285860\pi\) | |||||||
\(140\) | 10.2592 | 0.867061 | ||||||||
\(141\) | 2.23494 | + | 0.710348i | 0.188216 | + | 0.0598221i | ||||
\(142\) | − | 11.0338i | − | 0.925933i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.73205 | + | 2.44949i | −0.144338 | + | 0.204124i | ||||
\(145\) | 4.07056 | + | 4.07056i | 0.338042 | + | 0.338042i | ||||
\(146\) | 14.2584i | 1.18003i | ||||||||
\(147\) | −4.68563 | − | 9.05195i | −0.386464 | − | 0.746592i | ||||
\(148\) | −3.42423 | − | 3.42423i | −0.281470 | − | 0.281470i | ||||
\(149\) | −7.30774 | + | 7.30774i | −0.598673 | + | 0.598673i | −0.939959 | − | 0.341286i | \(-0.889137\pi\) |
0.341286 | + | 0.939959i | \(0.389137\pi\) | |||||||
\(150\) | −5.23041 | − | 1.66242i | −0.427061 | − | 0.135736i | ||||
\(151\) | 6.48932 | − | 6.48932i | 0.528094 | − | 0.528094i | −0.391910 | − | 0.920004i | \(-0.628186\pi\) |
0.920004 | + | 0.391910i | \(0.128186\pi\) | |||||||
\(152\) | 2.24555i | 0.182138i | ||||||||
\(153\) | 5.98264 | − | 8.46073i | 0.483668 | − | 0.684010i | ||||
\(154\) | −10.6665 | + | 10.6665i | −0.859532 | + | 0.859532i | ||||
\(155\) | 4.92427 | 0.395527 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1431 | −1.12874 | −0.564372 | − | 0.825520i | \(-0.690882\pi\) | ||||
−0.564372 | + | 0.825520i | \(0.690882\pi\) | |||||||
\(158\) | 1.11759 | − | 1.11759i | 0.0889105 | − | 0.0889105i | ||||
\(159\) | −5.75023 | − | 11.1086i | −0.456023 | − | 0.880968i | ||||
\(160\) | − | 2.85808i | − | 0.225951i | ||||||
\(161\) | 7.69672 | − | 7.69672i | 0.606587 | − | 0.606587i | ||||
\(162\) | −8.12132 | − | 3.87868i | −0.638071 | − | 0.304738i | ||||
\(163\) | 0.787963 | − | 0.787963i | 0.0617181 | − | 0.0617181i | −0.675574 | − | 0.737292i | \(-0.736104\pi\) |
0.737292 | + | 0.675574i | \(0.236104\pi\) | |||||||
\(164\) | 5.61494 | + | 5.61494i | 0.438453 | + | 0.438453i | ||||
\(165\) | 18.4749 | − | 9.56333i | 1.43827 | − | 0.744504i | ||||
\(166\) | − | 3.66193i | − | 0.284221i | ||||||
\(167\) | 3.94925 | + | 3.94925i | 0.305602 | + | 0.305602i | 0.843201 | − | 0.537598i | \(-0.180668\pi\) |
−0.537598 | + | 0.843201i | \(0.680668\pi\) | |||||||
\(168\) | −5.52139 | + | 2.85808i | −0.425985 | + | 0.220506i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.87205i | 0.757152i | ||||||||
\(171\) | −6.63963 | + | 1.13918i | −0.507745 | + | 0.0871153i | ||||
\(172\) | −1.95035 | −0.148712 | ||||||||
\(173\) | −17.4953 | −1.33014 | −0.665072 | − | 0.746779i | \(-0.731599\pi\) | ||||
−0.665072 | + | 0.746779i | \(0.731599\pi\) | |||||||
\(174\) | −3.32474 | − | 1.05673i | −0.252048 | − | 0.0801102i | ||||
\(175\) | −8.04261 | − | 8.04261i | −0.607964 | − | 0.607964i | ||||
\(176\) | 2.97155 | + | 2.97155i | 0.223989 | + | 0.223989i | ||||
\(177\) | 16.9829 | + | 5.39779i | 1.27651 | + | 0.405723i | ||||
\(178\) | 9.84478 | 0.737897 | ||||||||
\(179\) | 9.21508 | 0.688768 | 0.344384 | − | 0.938829i | \(-0.388088\pi\) | ||||
0.344384 | + | 0.938829i | \(0.388088\pi\) | |||||||
\(180\) | 8.45077 | − | 1.44992i | 0.629883 | − | 0.108071i | ||||
\(181\) | 13.8110i | 1.02656i | 0.858220 | + | 0.513282i | \(0.171571\pi\) | ||||
−0.858220 | + | 0.513282i | \(0.828429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.421783 | − | 0.218331i | 0.0311791 | − | 0.0161395i | ||||
\(184\) | −2.14421 | − | 2.14421i | −0.158073 | − | 0.158073i | ||||
\(185\) | 13.8405i | 1.01758i | ||||||||
\(186\) | −2.65019 | + | 1.37184i | −0.194321 | + | 0.100588i | ||||
\(187\) | −10.2640 | − | 10.2640i | −0.750577 | − | 0.750577i | ||||
\(188\) | 0.957390 | − | 0.957390i | 0.0698248 | − | 0.0698248i | ||||
\(189\) | −11.2518 | − | 14.8757i | −0.818448 | − | 1.08205i | ||||
\(190\) | 4.53819 | − | 4.53819i | 0.329235 | − | 0.329235i | ||||
\(191\) | − | 22.7030i | − | 1.64273i | −0.570402 | − | 0.821366i | \(-0.693212\pi\) | ||
0.570402 | − | 0.821366i | \(-0.306788\pi\) | |||||||
\(192\) | 0.796225 | + | 1.53819i | 0.0574626 | + | 0.111009i | ||||
\(193\) | 14.1745 | − | 14.1745i | 1.02030 | − | 1.02030i | 0.0205099 | − | 0.999790i | \(-0.493471\pi\) |
0.999790 | − | 0.0205099i | \(-0.00652896\pi\) | |||||||
\(194\) | 8.02251 | 0.575983 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.88481 | −0.420343 | ||||||||
\(197\) | 13.1786 | − | 13.1786i | 0.938935 | − | 0.938935i | −0.0593051 | − | 0.998240i | \(-0.518888\pi\) |
0.998240 | + | 0.0593051i | \(0.0188885\pi\) | |||||||
\(198\) | −7.27879 | + | 10.2938i | −0.517281 | + | 0.731546i | ||||
\(199\) | − | 4.51039i | − | 0.319733i | −0.987139 | − | 0.159866i | \(-0.948894\pi\) | ||
0.987139 | − | 0.159866i | \(-0.0511064\pi\) | |||||||
\(200\) | −2.24057 | + | 2.24057i | −0.158432 | + | 0.158432i | ||||
\(201\) | 7.00859 | + | 2.22759i | 0.494348 | + | 0.157122i | ||||
\(202\) | −1.48977 | + | 1.48977i | −0.104820 | + | 0.104820i | ||||
\(203\) | −5.11233 | − | 5.11233i | −0.358815 | − | 0.358815i | ||||
\(204\) | −2.75023 | − | 5.31303i | −0.192554 | − | 0.371986i | ||||
\(205\) | − | 22.6952i | − | 1.58510i | ||||||
\(206\) | 10.0854 | + | 10.0854i | 0.702683 | + | 0.702683i | ||||
\(207\) | 5.25221 | − | 7.42775i | 0.365054 | − | 0.516264i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.43672i | 0.652752i | ||||||||
\(210\) | 16.9347 | + | 5.38247i | 1.16860 | + | 0.371426i | ||||
\(211\) | −8.57683 | −0.590453 | −0.295227 | − | 0.955427i | \(-0.595395\pi\) | ||||
−0.295227 | + | 0.955427i | \(0.595395\pi\) | |||||||
\(212\) | −7.22186 | −0.495999 | ||||||||
\(213\) | 5.78884 | − | 18.2132i | 0.396645 | − | 1.24795i | ||||
\(214\) | 9.79025 | + | 9.79025i | 0.669248 | + | 0.669248i | ||||
\(215\) | 3.94159 | + | 3.94159i | 0.268814 | + | 0.268814i | ||||
\(216\) | −4.14418 | + | 3.13461i | −0.281976 | + | 0.213283i | ||||
\(217\) | −6.18452 | −0.419833 | ||||||||
\(218\) | −8.26212 | −0.559581 | ||||||||
\(219\) | −7.48062 | + | 23.5360i | −0.505494 | + | 1.59042i | ||||
\(220\) | − | 12.0108i | − | 0.809771i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.85579 | − | 7.44882i | −0.258784 | − | 0.499932i | ||||
\(223\) | 14.9027 | + | 14.9027i | 0.997958 | + | 0.997958i | 0.999998 | − | 0.00203979i | \(-0.000649285\pi\) |
−0.00203979 | + | 0.999998i | \(0.500649\pi\) | |||||||
\(224\) | 3.58954i | 0.239836i | ||||||||
\(225\) | −7.76155 | − | 5.48825i | −0.517437 | − | 0.365883i | ||||
\(226\) | 12.7308 | + | 12.7308i | 0.846841 | + | 0.846841i | ||||
\(227\) | 3.55443 | − | 3.55443i | 0.235916 | − | 0.235916i | −0.579241 | − | 0.815157i | \(-0.696651\pi\) |
0.815157 | + | 0.579241i | \(0.196651\pi\) | |||||||
\(228\) | −1.17812 | + | 3.70668i | −0.0780231 | + | 0.245481i | ||||
\(229\) | 9.92484 | − | 9.92484i | 0.655852 | − | 0.655852i | −0.298544 | − | 0.954396i | \(-0.596501\pi\) |
0.954396 | + | 0.298544i | \(0.0965010\pi\) | |||||||
\(230\) | 8.66676i | 0.571469i | ||||||||
\(231\) | −23.2032 | + | 12.0108i | −1.52666 | + | 0.790255i | ||||
\(232\) | −1.42423 | + | 1.42423i | −0.0935052 | + | 0.0935052i | ||||
\(233\) | 18.7944 | 1.23126 | 0.615630 | − | 0.788035i | \(-0.288902\pi\) | ||||
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.86971 | −0.252432 | ||||||||
\(236\) | 7.27501 | − | 7.27501i | 0.473563 | − | 0.473563i | ||||
\(237\) | 2.43112 | − | 1.25844i | 0.157918 | − | 0.0817445i | ||||
\(238\) | − | 12.3986i | − | 0.803679i | ||||||
\(239\) | −6.82142 | + | 6.82142i | −0.441241 | + | 0.441241i | −0.892429 | − | 0.451188i | \(-0.851000\pi\) |
0.451188 | + | 0.892429i | \(0.351000\pi\) | |||||||
\(240\) | 1.49949 | − | 4.71778i | 0.0967914 | − | 0.304531i | ||||
\(241\) | 5.99419 | − | 5.99419i | 0.386119 | − | 0.386119i | −0.487181 | − | 0.873301i | \(-0.661975\pi\) |
0.873301 | + | 0.487181i | \(0.161975\pi\) | |||||||
\(242\) | 4.70951 | + | 4.70951i | 0.302739 | + | 0.302739i | ||||
\(243\) | −11.3708 | − | 10.6633i | −0.729435 | − | 0.684050i | ||||
\(244\) | − | 0.274207i | − | 0.0175543i | ||||||
\(245\) | 11.8930 | + | 11.8930i | 0.759817 | + | 0.759817i | ||||
\(246\) | 6.32260 | + | 12.2143i | 0.403114 | + | 0.778757i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.72293i | 0.109406i | ||||||||
\(249\) | 1.92122 | − | 6.04468i | 0.121753 | − | 0.383066i | ||||
\(250\) | −5.23418 | −0.331039 | ||||||||
\(251\) | 7.03975 | 0.444345 | 0.222173 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222173 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(252\) | −10.6135 | + | 1.82100i | −0.668590 | + | 0.114712i | ||||
\(253\) | −9.01084 | − | 9.01084i | −0.566507 | − | 0.566507i | ||||
\(254\) | 14.6323 | + | 14.6323i | 0.918114 | + | 0.918114i | ||||
\(255\) | −5.17935 | + | 16.2956i | −0.324343 | + | 1.02047i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.63199 | 0.101801 | 0.0509003 | − | 0.998704i | \(-0.483791\pi\) | ||||
0.0509003 | + | 0.998704i | \(0.483791\pi\) | |||||||
\(258\) | −3.21940 | − | 1.02324i | −0.200431 | − | 0.0637044i | ||||
\(259\) | − | 17.3827i | − | 1.08011i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.93367 | − | 3.48863i | −0.305387 | − | 0.215941i | ||||
\(262\) | −3.31135 | − | 3.31135i | −0.204576 | − | 0.204576i | ||||
\(263\) | 10.5679i | 0.651646i | 0.945431 | + | 0.325823i | \(0.105641\pi\) | ||||
−0.945431 | + | 0.325823i | \(0.894359\pi\) | |||||||
\(264\) | 3.34607 | + | 6.46410i | 0.205936 | + | 0.397838i | ||||
\(265\) | 14.5952 | + | 14.5952i | 0.896574 | + | 0.896574i | ||||
\(266\) | −5.69963 | + | 5.69963i | −0.349467 | + | 0.349467i | ||||
\(267\) | 16.2506 | + | 5.16504i | 0.994519 | + | 0.316095i | ||||
\(268\) | 3.00229 | − | 3.00229i | 0.183394 | − | 0.183394i | ||||
\(269\) | − | 8.61859i | − | 0.525485i | −0.964866 | − | 0.262742i | \(-0.915373\pi\) | ||
0.964866 | − | 0.262742i | \(-0.0846269\pi\) | |||||||
\(270\) | 14.7102 | + | 2.04032i | 0.895235 | + | 0.124170i | ||||
\(271\) | −14.0234 | + | 14.0234i | −0.851858 | + | 0.851858i | −0.990362 | − | 0.138504i | \(-0.955771\pi\) |
0.138504 | + | 0.990362i | \(0.455771\pi\) | |||||||
\(272\) | −3.45408 | −0.209434 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.47999 | 0.331058 | ||||||||
\(275\) | −9.41578 | + | 9.41578i | −0.567793 | + | 0.567793i | ||||
\(276\) | −2.41445 | − | 4.66435i | −0.145333 | − | 0.280761i | ||||
\(277\) | − | 15.5025i | − | 0.931452i | −0.884929 | − | 0.465726i | \(-0.845793\pi\) | ||
0.884929 | − | 0.465726i | \(-0.154207\pi\) | |||||||
\(278\) | 10.3897 | − | 10.3897i | 0.623132 | − | 0.623132i | ||||
\(279\) | −5.09435 | + | 0.874052i | −0.304991 | + | 0.0523281i | ||||
\(280\) | 7.25436 | − | 7.25436i | 0.433531 | − | 0.433531i | ||||
\(281\) | 11.9452 | + | 11.9452i | 0.712591 | + | 0.712591i | 0.967077 | − | 0.254486i | \(-0.0819061\pi\) |
−0.254486 | + | 0.967077i | \(0.581906\pi\) | |||||||
\(282\) | 2.08264 | − | 1.07805i | 0.124019 | − | 0.0641970i | ||||
\(283\) | 1.57972i | 0.0939046i | 0.998897 | + | 0.0469523i | \(0.0149509\pi\) | ||||
−0.998897 | + | 0.0469523i | \(0.985049\pi\) | |||||||
\(284\) | −7.80205 | − | 7.80205i | −0.462967 | − | 0.462967i | ||||
\(285\) | 9.87205 | − | 5.11015i | 0.584770 | − | 0.302699i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.5035i | 1.68251i | ||||||||
\(288\) | 0.507306 | + | 2.95680i | 0.0298933 | + | 0.174231i | ||||
\(289\) | −5.06933 | −0.298196 | ||||||||
\(290\) | 5.75665 | 0.338042 | ||||||||
\(291\) | 13.2426 | + | 4.20899i | 0.776295 | + | 0.246735i | ||||
\(292\) | 10.0822 | + | 10.0822i | 0.590016 | + | 0.590016i | ||||
\(293\) | 2.76136 | + | 2.76136i | 0.161321 | + | 0.161321i | 0.783152 | − | 0.621831i | \(-0.213611\pi\) |
−0.621831 | + | 0.783152i | \(0.713611\pi\) | |||||||
\(294\) | −9.71393 | − | 3.08745i | −0.566528 | − | 0.180064i | ||||
\(295\) | −29.4051 | −1.71203 | ||||||||
\(296\) | −4.84259 | −0.281470 | ||||||||
\(297\) | −17.4155 | + | 13.1729i | −1.01055 | + | 0.764370i | ||||
\(298\) | 10.3347i | 0.598673i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.87397 | + | 2.52295i | −0.281399 | + | 0.145663i | ||||
\(301\) | −4.95035 | − | 4.95035i | −0.285333 | − | 0.285333i | ||||
\(302\) | − | 9.17729i | − | 0.528094i | ||||||
\(303\) | −3.24073 | + | 1.67753i | −0.186175 | + | 0.0963714i | ||||
\(304\) | 1.58784 | + | 1.58784i | 0.0910691 | + | 0.0910691i | ||||
\(305\) | −0.554165 | + | 0.554165i | −0.0317314 | + | 0.0317314i | ||||
\(306\) | −1.75228 | − | 10.2130i | −0.100171 | − | 0.583839i | ||||
\(307\) | −21.7994 | + | 21.7994i | −1.24416 | + | 1.24416i | −0.285899 | + | 0.958260i | \(0.592292\pi\) |
−0.958260 | + | 0.285899i | \(0.907708\pi\) | |||||||
\(308\) | 15.0847i | 0.859532i | ||||||||
\(309\) | 11.3565 | + | 21.9390i | 0.646048 | + | 1.24807i | ||||
\(310\) | 3.48199 | − | 3.48199i | 0.197764 | − | 0.197764i | ||||
\(311\) | −20.9295 | −1.18681 | −0.593403 | − | 0.804906i | \(-0.702216\pi\) | ||||
−0.593403 | + | 0.804906i | \(0.702216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.6685 | −1.84653 | −0.923267 | − | 0.384159i | \(-0.874491\pi\) | ||||
−0.923267 | + | 0.384159i | \(0.874491\pi\) | |||||||
\(314\) | −10.0007 | + | 10.0007i | −0.564372 | + | 0.564372i | ||||
\(315\) | 25.1298 | + | 17.7695i | 1.41591 | + | 1.00120i | ||||
\(316\) | − | 1.58051i | − | 0.0889105i | ||||||
\(317\) | −5.21085 | + | 5.21085i | −0.292671 | + | 0.292671i | −0.838134 | − | 0.545464i | \(-0.816354\pi\) |
0.545464 | + | 0.838134i | \(0.316354\pi\) | |||||||
\(318\) | −11.9210 | − | 3.78893i | −0.668495 | − | 0.212473i | ||||
\(319\) | −5.98519 | + | 5.98519i | −0.335106 | + | 0.335106i | ||||
\(320\) | −2.02097 | − | 2.02097i | −0.112976 | − | 0.112976i | ||||
\(321\) | 11.0241 | + | 21.2970i | 0.615308 | + | 1.18868i | ||||
\(322\) | − | 10.8848i | − | 0.606587i | ||||||
\(323\) | −5.48454 | − | 5.48454i | −0.305168 | − | 0.305168i | ||||
\(324\) | −8.48528 | + | 3.00000i | −0.471405 | + | 0.166667i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.11435i | − | 0.0617181i | ||||||
\(327\) | −13.6381 | − | 4.33470i | −0.754189 | − | 0.239709i | ||||
\(328\) | 7.94072 | 0.438453 | ||||||||
\(329\) | 4.86007 | 0.267944 | ||||||||
\(330\) | 6.30146 | − | 19.8261i | 0.346884 | − | 1.09139i | ||||
\(331\) | −12.8956 | − | 12.8956i | −0.708809 | − | 0.708809i | 0.257476 | − | 0.966285i | \(-0.417109\pi\) |
−0.966285 | + | 0.257476i | \(0.917109\pi\) | |||||||
\(332\) | −2.58938 | − | 2.58938i | −0.142110 | − | 0.142110i | ||||
\(333\) | −2.45667 | − | 14.3186i | −0.134625 | − | 0.784652i | ||||
\(334\) | 5.58509 | 0.305602 | ||||||||
\(335\) | −12.1351 | −0.663010 | ||||||||
\(336\) | −1.88324 | + | 5.92518i | −0.102739 | + | 0.323245i | ||||
\(337\) | − | 4.92484i | − | 0.268273i | −0.990963 | − | 0.134136i | \(-0.957174\pi\) | ||
0.990963 | − | 0.134136i | \(-0.0428260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.3353 | + | 27.6937i | 0.778587 | + | 1.50412i | ||||
\(340\) | 6.98059 | + | 6.98059i | 0.378576 | + | 0.378576i | ||||
\(341\) | 7.24045i | 0.392093i | ||||||||
\(342\) | −3.88941 | + | 5.50045i | −0.210315 | + | 0.297430i | ||||
\(343\) | 2.83057 | + | 2.83057i | 0.152836 | + | 0.152836i | ||||
\(344\) | −1.37910 | + | 1.37910i | −0.0743562 | + | 0.0743562i | ||||
\(345\) | −4.54699 | + | 14.3060i | −0.244802 | + | 0.770212i | ||||
\(346\) | −12.3711 | + | 12.3711i | −0.665072 | + | 0.665072i | ||||
\(347\) | 14.9422i | 0.802137i | 0.916048 | + | 0.401069i | \(0.131361\pi\) | ||||
−0.916048 | + | 0.401069i | \(0.868639\pi\) | |||||||
\(348\) | −3.09816 | + | 1.60373i | −0.166079 | + | 0.0859688i | ||||
\(349\) | 22.0872 | − | 22.0872i | 1.18230 | − | 1.18230i | 0.203155 | − | 0.979147i | \(-0.434880\pi\) |
0.979147 | − | 0.203155i | \(-0.0651196\pi\) | |||||||
\(350\) | −11.3740 | −0.607964 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.20241 | 0.223989 | ||||||||
\(353\) | 7.31540 | − | 7.31540i | 0.389360 | − | 0.389360i | −0.485099 | − | 0.874459i | \(-0.661217\pi\) |
0.874459 | + | 0.485099i | \(0.161217\pi\) | |||||||
\(354\) | 15.8255 | − | 8.19190i | 0.841117 | − | 0.435394i | ||||
\(355\) | 31.5354i | 1.67373i | ||||||||
\(356\) | 6.96131 | − | 6.96131i | 0.368949 | − | 0.368949i | ||||
\(357\) | 6.50488 | − | 20.4661i | 0.344275 | − | 1.08318i | ||||
\(358\) | 6.51605 | − | 6.51605i | 0.344384 | − | 0.344384i | ||||
\(359\) | 9.08944 | + | 9.08944i | 0.479722 | + | 0.479722i | 0.905043 | − | 0.425321i | \(-0.139839\pi\) |
−0.425321 | + | 0.905043i | \(0.639839\pi\) | |||||||
\(360\) | 4.95035 | − | 7.00085i | 0.260906 | − | 0.368977i | ||||
\(361\) | − | 13.9575i | − | 0.734606i | ||||||
\(362\) | 9.76586 | + | 9.76586i | 0.513282 | + | 0.513282i | ||||
\(363\) | 5.30306 | + | 10.2447i | 0.278339 | + | 0.537709i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 40.7516i | − | 2.13304i | ||||||
\(366\) | 0.143862 | − | 0.452628i | 0.00751980 | − | 0.0236593i | ||||
\(367\) | 1.64695 | 0.0859700 | 0.0429850 | − | 0.999076i | \(-0.486313\pi\) | ||||
0.0429850 | + | 0.999076i | \(0.486313\pi\) | |||||||
\(368\) | −3.03237 | −0.158073 | ||||||||
\(369\) | 4.02837 | + | 23.4791i | 0.209709 | + | 1.22227i | ||||
\(370\) | 9.78673 | + | 9.78673i | 0.508788 | + | 0.508788i | ||||
\(371\) | −18.3304 | − | 18.3304i | −0.951669 | − | 0.951669i | ||||
\(372\) | −0.903931 | + | 2.84400i | −0.0468666 | + | 0.147455i | ||||
\(373\) | −19.9516 | −1.03305 | −0.516526 | − | 0.856271i | \(-0.672775\pi\) | ||||
−0.516526 | + | 0.856271i | \(0.672775\pi\) | |||||||
\(374\) | −14.5155 | −0.750577 | ||||||||
\(375\) | −8.63996 | − | 2.74610i | −0.446165 | − | 0.141808i | ||||
\(376\) | − | 1.35395i | − | 0.0698248i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −18.4749 | − | 2.56249i | −0.950248 | − | 0.131800i | ||||
\(379\) | −8.70575 | − | 8.70575i | −0.447184 | − | 0.447184i | 0.447233 | − | 0.894417i | \(-0.352409\pi\) |
−0.894417 | + | 0.447233i | \(0.852409\pi\) | |||||||
\(380\) | − | 6.41797i | − | 0.329235i | ||||||
\(381\) | 16.4765 | + | 31.8301i | 0.844115 | + | 1.63071i | ||||
\(382\) | −16.0534 | − | 16.0534i | −0.821366 | − | 0.821366i | ||||
\(383\) | 20.0436 | − | 20.0436i | 1.02418 | − | 1.02418i | 0.0244774 | − | 0.999700i | \(-0.492208\pi\) |
0.999700 | − | 0.0244774i | \(-0.00779217\pi\) | |||||||
\(384\) | 1.65068 | + | 0.524648i | 0.0842359 | + | 0.0267733i | ||||
\(385\) | 30.4858 | − | 30.4858i | 1.55370 | − | 1.55370i | ||||
\(386\) | − | 20.0457i | − | 1.02030i | ||||||
\(387\) | −4.77735 | − | 3.37810i | −0.242846 | − | 0.171718i | ||||
\(388\) | 5.67277 | − | 5.67277i | 0.287991 | − | 0.287991i | ||||
\(389\) | 15.9504 | 0.808717 | 0.404359 | − | 0.914601i | \(-0.367495\pi\) | ||||
0.404359 | + | 0.914601i | \(0.367495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4740 | 0.529695 | ||||||||
\(392\) | −4.16119 | + | 4.16119i | −0.210172 | + | 0.210172i | ||||
\(393\) | −3.72868 | − | 7.20326i | −0.188087 | − | 0.363357i | ||||
\(394\) | − | 18.6373i | − | 0.938935i | ||||||
\(395\) | −3.19416 | + | 3.19416i | −0.160716 | + | 0.160716i | ||||
\(396\) | 2.13191 | + | 12.4257i | 0.107132 | + | 0.624413i | ||||
\(397\) | −8.97449 | + | 8.97449i | −0.450417 | + | 0.450417i | −0.895493 | − | 0.445076i | \(-0.853177\pi\) |
0.445076 | + | 0.895493i | \(0.353177\pi\) | |||||||
\(398\) | −3.18933 | − | 3.18933i | −0.159866 | − | 0.159866i | ||||
\(399\) | −12.3986 | + | 6.41797i | −0.620705 | + | 0.321300i | ||||
\(400\) | 3.16864i | 0.158432i | ||||||||
\(401\) | −11.6106 | − | 11.6106i | −0.579804 | − | 0.579804i | 0.355045 | − | 0.934849i | \(-0.384465\pi\) |
−0.934849 | + | 0.355045i | \(0.884465\pi\) | |||||||
\(402\) | 6.53097 | − | 3.38068i | 0.325735 | − | 0.168613i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.10685i | 0.104820i | ||||||||
\(405\) | 23.2114 | + | 11.0856i | 1.15338 | + | 0.550847i | ||||
\(406\) | −7.22992 | −0.358815 | ||||||||
\(407\) | −20.3506 | −1.00874 | ||||||||
\(408\) | −5.70158 | − | 1.81217i | −0.282270 | − | 0.0897160i | ||||
\(409\) | 24.0968 | + | 24.0968i | 1.19151 | + | 1.19151i | 0.976643 | + | 0.214868i | \(0.0689322\pi\) |
0.214868 | + | 0.976643i | \(0.431068\pi\) | |||||||
\(410\) | −16.0480 | − | 16.0480i | −0.792552 | − | 0.792552i | ||||
\(411\) | 9.04570 | + | 2.87506i | 0.446192 | + | 0.141816i | ||||
\(412\) | 14.2629 | 0.702683 | ||||||||
\(413\) | 36.9307 | 1.81724 | ||||||||
\(414\) | −1.53834 | − | 8.96609i | −0.0756052 | − | 0.440659i | ||||
\(415\) | 10.4661i | 0.513761i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.6010 | − | 11.6991i | 1.10677 | − | 0.572909i | ||||
\(418\) | 6.67277 | + | 6.67277i | 0.326376 | + | 0.326376i | ||||
\(419\) | − | 32.9024i | − | 1.60739i | −0.595044 | − | 0.803693i | \(-0.702866\pi\) | ||
0.595044 | − | 0.803693i | \(-0.297134\pi\) | |||||||
\(420\) | 15.7806 | − | 8.16864i | 0.770014 | − | 0.398589i | ||||
\(421\) | −17.0945 | − | 17.0945i | −0.833137 | − | 0.833137i | 0.154808 | − | 0.987945i | \(-0.450524\pi\) |
−0.987945 | + | 0.154808i | \(0.950524\pi\) | |||||||
\(422\) | −6.06473 | + | 6.06473i | −0.295227 | + | 0.295227i | ||||
\(423\) | 4.00336 | − | 0.686869i | 0.194650 | − | 0.0333967i | ||||
\(424\) | −5.10662 | + | 5.10662i | −0.248000 | + | 0.248000i | ||||
\(425\) | − | 10.9447i | − | 0.530898i | ||||||
\(426\) | −8.78537 | − | 16.9720i | −0.425652 | − | 0.822297i | ||||
\(427\) | 0.695990 | − | 0.695990i | 0.0336813 | − | 0.0336813i | ||||
\(428\) | 13.8455 | 0.669248 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.57425 | 0.268814 | ||||||||
\(431\) | 1.24152 | − | 1.24152i | 0.0598018 | − | 0.0598018i | −0.676573 | − | 0.736375i | \(-0.736536\pi\) |
0.736375 | + | 0.676573i | \(0.236536\pi\) | |||||||
\(432\) | −0.713876 | + | 5.14688i | −0.0343464 | + | 0.247629i | ||||
\(433\) | − | 10.2438i | − | 0.492286i | −0.969234 | − | 0.246143i | \(-0.920837\pi\) | ||
0.969234 | − | 0.246143i | \(-0.0791633\pi\) | |||||||
\(434\) | −4.37312 | + | 4.37312i | −0.209916 | + | 0.209916i | ||||
\(435\) | 9.50238 | + | 3.02021i | 0.455604 | + | 0.144808i | ||||
\(436\) | −5.84220 | + | 5.84220i | −0.279791 | + | 0.279791i | ||||
\(437\) | −4.81492 | − | 4.81492i | −0.230329 | − | 0.230329i | ||||
\(438\) | 11.3529 | + | 21.9321i | 0.542461 | + | 1.04795i | ||||
\(439\) | 5.40224i | 0.257835i | 0.991655 | + | 0.128917i | \(0.0411502\pi\) | ||||
−0.991655 | + | 0.128917i | \(0.958850\pi\) | |||||||
\(440\) | −8.49295 | − | 8.49295i | −0.404885 | − | 0.404885i | ||||
\(441\) | −14.4148 | − | 10.1928i | −0.686418 | − | 0.485371i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 13.5731i | − | 0.644876i | −0.946591 | − | 0.322438i | \(-0.895498\pi\) | ||
0.946591 | − | 0.322438i | \(-0.104502\pi\) | |||||||
\(444\) | −7.99357 | − | 2.54065i | −0.379358 | − | 0.120574i | ||||
\(445\) | −28.1372 | −1.33383 | ||||||||
\(446\) | 21.0756 | 0.997958 | ||||||||
\(447\) | −5.42208 | + | 17.0593i | −0.256455 | + | 0.806877i | ||||
\(448\) | 2.53819 | + | 2.53819i | 0.119918 | + | 0.119918i | ||||
\(449\) | 1.43493 | + | 1.43493i | 0.0677187 | + | 0.0677187i | 0.740155 | − | 0.672436i | \(-0.234752\pi\) |
−0.672436 | + | 0.740155i | \(0.734752\pi\) | |||||||
\(450\) | −9.36902 | + | 1.60747i | −0.441660 | + | 0.0757769i | ||||
\(451\) | 33.3702 | 1.57134 | ||||||||
\(452\) | 18.0041 | 0.846841 | ||||||||
\(453\) | 4.81484 | − | 15.1488i | 0.226221 | − | 0.711751i | ||||
\(454\) | − | 5.02672i | − | 0.235916i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.78796 | + | 3.45408i | 0.0837291 | + | 0.161752i | ||||
\(457\) | −21.1802 | − | 21.1802i | −0.990770 | − | 0.990770i | 0.00918755 | − | 0.999958i | \(-0.497075\pi\) |
−0.999958 | + | 0.00918755i | \(0.997075\pi\) | |||||||
\(458\) | − | 14.0358i | − | 0.655852i | ||||||
\(459\) | 2.46578 | − | 17.7777i | 0.115093 | − | 0.829794i | ||||
\(460\) | 6.12832 | + | 6.12832i | 0.285735 | + | 0.285735i | ||||
\(461\) | −11.3922 | + | 11.3922i | −0.530589 | + | 0.530589i | −0.920748 | − | 0.390159i | \(-0.872420\pi\) |
0.390159 | + | 0.920748i | \(0.372420\pi\) | |||||||
\(462\) | −7.91417 | + | 24.9001i | −0.368200 | + | 1.15846i | ||||
\(463\) | 4.07041 | − | 4.07041i | 0.189168 | − | 0.189168i | −0.606168 | − | 0.795336i | \(-0.707294\pi\) |
0.795336 | + | 0.606168i | \(0.207294\pi\) | |||||||
\(464\) | 2.01416i | 0.0935052i | ||||||||
\(465\) | 7.57446 | − | 3.92083i | 0.351257 | − | 0.181824i | ||||
\(466\) | 13.2896 | − | 13.2896i | 0.615630 | − | 0.615630i | ||||
\(467\) | −36.8536 | −1.70538 | −0.852690 | − | 0.522417i | \(-0.825030\pi\) | ||||
−0.852690 | + | 0.522417i | \(0.825030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2408 | 0.703753 | ||||||||
\(470\) | −2.73630 | + | 2.73630i | −0.126216 | + | 0.126216i | ||||
\(471\) | −21.7548 | + | 11.2611i | −1.00241 | + | 0.518885i | ||||
\(472\) | − | 10.2884i | − | 0.473563i | ||||||
\(473\) | −5.79555 | + | 5.79555i | −0.266480 | + | 0.266480i | ||||
\(474\) | 0.829210 | − | 2.60891i | 0.0380869 | − | 0.119831i | ||||
\(475\) | −5.03130 | + | 5.03130i | −0.230852 | + | 0.230852i | ||||
\(476\) | −8.76711 | − | 8.76711i | −0.401840 | − | 0.401840i | ||||
\(477\) | −17.6899 | − | 12.5086i | −0.809963 | − | 0.572731i | ||||
\(478\) | 9.64695i | 0.441241i | ||||||||
\(479\) | −10.6370 | − | 10.6370i | −0.486018 | − | 0.486018i | 0.421029 | − | 0.907047i | \(-0.361669\pi\) |
−0.907047 | + | 0.421029i | \(0.861669\pi\) | |||||||
\(480\) | −2.27568 | − | 4.39627i | −0.103870 | − | 0.200661i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 8.47706i | − | 0.386119i | ||||||
\(483\) | 5.71069 | − | 17.9673i | 0.259845 | − | 0.817542i | ||||
\(484\) | 6.66025 | 0.302739 | ||||||||
\(485\) | −22.9290 | −1.04115 | ||||||||
\(486\) | −15.5804 | + | 0.500258i | −0.706743 | + | 0.0226921i | ||||
\(487\) | −11.8303 | − | 11.8303i | −0.536081 | − | 0.536081i | 0.386294 | − | 0.922376i | \(-0.373755\pi\) |
−0.922376 | + | 0.386294i | \(0.873755\pi\) | |||||||
\(488\) | −0.193894 | − | 0.193894i | −0.00877716 | − | 0.00877716i | ||||
\(489\) | 0.584640 | − | 1.83943i | 0.0264383 | − | 0.0831820i | ||||
\(490\) | 16.8193 | 0.759817 | ||||||||
\(491\) | −25.2666 | −1.14026 | −0.570132 | − | 0.821553i | \(-0.693108\pi\) | ||||
−0.570132 | + | 0.821553i | \(0.693108\pi\) | |||||||
\(492\) | 13.1076 | + | 4.16608i | 0.590936 | + | 0.187821i | ||||
\(493\) | − | 6.95708i | − | 0.313331i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.8034 | − | 29.4204i | 0.935043 | − | 1.32235i | ||||
\(496\) | 1.21829 | + | 1.21829i | 0.0547030 | + | 0.0547030i | ||||
\(497\) | − | 39.6062i | − | 1.77658i | ||||||
\(498\) | −2.91572 | − | 5.63274i | −0.130657 | − | 0.252409i | ||||
\(499\) | −1.37946 | − | 1.37946i | −0.0617533 | − | 0.0617533i | 0.675556 | − | 0.737309i | \(-0.263904\pi\) |
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(500\) | −3.70112 | + | 3.70112i | −0.165519 | + | 0.165519i | ||||
\(501\) | 9.21920 | + | 2.93020i | 0.411883 | + | 0.130912i | ||||
\(502\) | 4.97786 | − | 4.97786i | 0.222173 | − | 0.222173i | ||||
\(503\) | − | 11.2904i | − | 0.503414i | −0.967803 | − | 0.251707i | \(-0.919008\pi\) | ||
0.967803 | − | 0.251707i | \(-0.0809919\pi\) | |||||||
\(504\) | −6.21727 | + | 8.79254i | −0.276939 | + | 0.391651i | ||||
\(505\) | 4.25788 | − | 4.25788i | 0.189473 | − | 0.189473i | ||||
\(506\) | −12.7433 | −0.566507 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.6932 | 0.918114 | ||||||||
\(509\) | −26.5900 | + | 26.5900i | −1.17858 | + | 1.17858i | −0.198473 | + | 0.980106i | \(0.563598\pi\) |
−0.980106 | + | 0.198473i | \(0.936402\pi\) | |||||||
\(510\) | 7.86037 | + | 15.1851i | 0.348063 | + | 0.672406i | ||||
\(511\) | 51.1810i | 2.26411i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −9.30596 | + | 7.03892i | −0.410868 | + | 0.310776i | ||||
\(514\) | 1.15399 | − | 1.15399i | 0.0509003 | − | 0.0509003i | ||||
\(515\) | −28.8249 | − | 28.8249i | −1.27018 | − | 1.27018i | ||||
\(516\) | −3.00000 | + | 1.55291i | −0.132068 | + | 0.0683632i | ||||
\(517\) | − | 5.68987i | − | 0.250240i | ||||||
\(518\) | −12.2914 | − | 12.2914i | −0.540054 | − | 0.540054i | ||||
\(519\) | −26.9111 | + | 13.9302i | −1.18127 | + | 0.611468i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2111i | 0.797843i | 0.916985 | + | 0.398922i | \(0.130615\pi\) | ||||
−0.916985 | + | 0.398922i | \(0.869385\pi\) | |||||||
\(522\) | −5.95547 | + | 1.02180i | −0.260664 | + | 0.0447228i | ||||
\(523\) | 33.8098 | 1.47840 | 0.739199 | − | 0.673487i | \(-0.235204\pi\) | ||||
0.739199 | + | 0.673487i | \(0.235204\pi\) | |||||||
\(524\) | −4.68295 | −0.204576 | ||||||||
\(525\) | −18.7748 | − | 5.96732i | −0.819398 | − | 0.260435i | ||||
\(526\) | 7.47265 | + | 7.47265i | 0.325823 | + | 0.325823i | ||||
\(527\) | −4.20809 | − | 4.20809i | −0.183307 | − | 0.183307i | ||||
\(528\) | 6.93684 | + | 2.20478i | 0.301887 | + | 0.0959509i | ||||
\(529\) | −13.8048 | −0.600207 | ||||||||
\(530\) | 20.6407 | 0.896574 | ||||||||
\(531\) | 30.4207 | − | 5.21937i | 1.32015 | − | 0.226502i | ||||
\(532\) | 8.06049i | 0.349467i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15.1431 | − | 7.83866i | 0.655307 | − | 0.339212i | ||||
\(535\) | −27.9814 | − | 27.9814i | −1.20974 | − | 1.20974i | ||||
\(536\) | − | 4.24588i | − | 0.183394i | ||||||
\(537\) | 14.1745 | − | 7.33728i | 0.611676 | − | 0.316627i | ||||
\(538\) | −6.09426 | − | 6.09426i | −0.262742 | − | 0.262742i | ||||
\(539\) | −17.4870 | + | 17.4870i | −0.753219 | + | 0.753219i | ||||
\(540\) | 11.8444 | − | 8.95897i | 0.509702 | − | 0.385533i | ||||
\(541\) | 4.97355 | − | 4.97355i | 0.213829 | − | 0.213829i | −0.592063 | − | 0.805892i | \(-0.701686\pi\) |
0.805892 | + | 0.592063i | \(0.201686\pi\) | |||||||
\(542\) | 19.8320i | 0.851858i | ||||||||
\(543\) | 10.9967 | + | 21.2439i | 0.471912 | + | 0.911665i | ||||
\(544\) | −2.44240 | + | 2.44240i | −0.104717 | + | 0.104717i | ||||
\(545\) | 23.6138 | 1.01150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.15870 | −0.0922995 | −0.0461497 | − | 0.998935i | \(-0.514695\pi\) | ||||
−0.0461497 | + | 0.998935i | \(0.514695\pi\) | |||||||
\(548\) | 3.87494 | − | 3.87494i | 0.165529 | − | 0.165529i | ||||
\(549\) | 0.474941 | − | 0.671668i | 0.0202700 | − | 0.0286661i | ||||
\(550\) | 13.3159i | 0.567793i | ||||||||
\(551\) | −3.19818 | + | 3.19818i | −0.136247 | + | 0.136247i | ||||
\(552\) | −5.00547 | − | 1.59092i | −0.213047 | − | 0.0677142i | ||||
\(553\) | 4.01163 | − | 4.01163i | 0.170592 | − | 0.170592i | ||||
\(554\) | −10.9619 | − | 10.9619i | −0.465726 | − | 0.465726i | ||||
\(555\) | 11.0202 | + | 21.2893i | 0.467780 | + | 0.903682i | ||||
\(556\) | − | 14.6932i | − | 0.623132i | ||||||
\(557\) | −1.59427 | − | 1.59427i | −0.0675516 | − | 0.0675516i | 0.672524 | − | 0.740075i | \(-0.265210\pi\) |
−0.740075 | + | 0.672524i | \(0.765210\pi\) | |||||||
\(558\) | −2.98420 | + | 4.22030i | −0.126331 | + | 0.178659i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 10.2592i | − | 0.433531i | ||||||
\(561\) | −23.9604 | − | 7.61550i | −1.01161 | − | 0.321527i | ||||
\(562\) | 16.8931 | 0.712591 | ||||||||
\(563\) | 36.2979 | 1.52978 | 0.764888 | − | 0.644164i | \(-0.222794\pi\) | ||||
0.764888 | + | 0.644164i | \(0.222794\pi\) | |||||||
\(564\) | 0.710348 | − | 2.23494i | 0.0299111 | − | 0.0941081i | ||||
\(565\) | −36.3857 | − | 36.3857i | −1.53076 | − | 1.53076i | ||||
\(566\) | 1.11703 | + | 1.11703i | 0.0469523 | + | 0.0469523i | ||||
\(567\) | −29.1518 | − | 13.9227i | −1.22426 | − | 0.584698i | ||||
\(568\) | −11.0338 | −0.462967 | ||||||||
\(569\) | −39.0751 | −1.63811 | −0.819057 | − | 0.573712i | \(-0.805503\pi\) | ||||
−0.819057 | + | 0.573712i | \(0.805503\pi\) | |||||||
\(570\) | 3.36717 | − | 10.5940i | 0.141035 | − | 0.443734i | ||||
\(571\) | 31.9061i | 1.33523i | 0.744508 | + | 0.667614i | \(0.232684\pi\) | ||||
−0.744508 | + | 0.667614i | \(0.767316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0767 | − | 34.9215i | −0.755165 | − | 1.45887i | ||||
\(574\) | 20.1550 | + | 20.1550i | 0.841255 | + | 0.841255i | ||||
\(575\) | − | 9.60848i | − | 0.400701i | ||||||
\(576\) | 2.44949 | + | 1.73205i | 0.102062 | + | 0.0721688i | ||||
\(577\) | −9.31011 | − | 9.31011i | −0.387585 | − | 0.387585i | 0.486240 | − | 0.873825i | \(-0.338368\pi\) |
−0.873825 | + | 0.486240i | \(0.838368\pi\) | |||||||
\(578\) | −3.58456 | + | 3.58456i | −0.149098 | + | 0.149098i | ||||
\(579\) | 10.5169 | − | 33.0890i | 0.437069 | − | 1.37513i | ||||
\(580\) | 4.07056 | − | 4.07056i | 0.169021 | − | 0.169021i | ||||
\(581\) | − | 13.1447i | − | 0.545332i | ||||||
\(582\) | 12.3401 | − | 6.38772i | 0.511515 | − | 0.264780i | ||||
\(583\) | −21.4601 | + | 21.4601i | −0.888788 | + | 0.888788i | ||||
\(584\) | 14.2584 | 0.590016 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.90516 | 0.161321 | ||||||||
\(587\) | −20.7092 | + | 20.7092i | −0.854758 | + | 0.854758i | −0.990715 | − | 0.135957i | \(-0.956589\pi\) |
0.135957 | + | 0.990715i | \(0.456589\pi\) | |||||||
\(588\) | −9.05195 | + | 4.68563i | −0.373296 | + | 0.193232i | ||||
\(589\) | 3.86892i | 0.159416i | ||||||||
\(590\) | −20.7926 | + | 20.7926i | −0.856017 | + | 0.856017i | ||||
\(591\) | 9.77803 | − | 30.7643i | 0.402214 | − | 1.26547i | ||||
\(592\) | −3.42423 | + | 3.42423i | −0.140735 | + | 0.140735i | ||||
\(593\) | 12.7368 | + | 12.7368i | 0.523037 | + | 0.523037i | 0.918487 | − | 0.395450i | \(-0.129411\pi\) |
−0.395450 | + | 0.918487i | \(0.629411\pi\) | |||||||
\(594\) | −3.00000 | + | 21.6293i | −0.123091 | + | 0.887461i | ||||
\(595\) | 35.4361i | 1.45274i | ||||||||
\(596\) | 7.30774 | + | 7.30774i | 0.299337 | + | 0.299337i | ||||
\(597\) | −3.59128 | − | 6.93783i | −0.146981 | − | 0.283946i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 15.6579i | − | 0.639764i | −0.947457 | − | 0.319882i | \(-0.896357\pi\) | ||
0.947457 | − | 0.319882i | \(-0.103643\pi\) | |||||||
\(600\) | −1.66242 | + | 5.23041i | −0.0678680 | + | 0.213531i | ||||
\(601\) | 7.99663 | 0.326189 | 0.163095 | − | 0.986610i | \(-0.447852\pi\) | ||||
0.163095 | + | 0.986610i | \(0.447852\pi\) | |||||||
\(602\) | −7.00085 | −0.285333 | ||||||||
\(603\) | 12.5542 | − | 2.15396i | 0.511247 | − | 0.0877160i | ||||
\(604\) | −6.48932 | − | 6.48932i | −0.264047 | − | 0.264047i | ||||
\(605\) | −13.4602 | − | 13.4602i | −0.547234 | − | 0.547234i | ||||
\(606\) | −1.10535 | + | 3.47773i | −0.0449019 | + | 0.141273i | ||||
\(607\) | 4.49161 | 0.182309 | 0.0911545 | − | 0.995837i | \(-0.470944\pi\) | ||||
0.0911545 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(608\) | 2.24555 | 0.0910691 | ||||||||
\(609\) | −11.9343 | − | 3.79316i | −0.483602 | − | 0.153707i | ||||
\(610\) | 0.783707i | 0.0317314i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.46073 | − | 5.98264i | −0.342005 | − | 0.241834i | ||||
\(613\) | 22.3358 | + | 22.3358i | 0.902133 | + | 0.902133i | 0.995620 | − | 0.0934876i | \(-0.0298016\pi\) |
−0.0934876 | + | 0.995620i | \(0.529802\pi\) | |||||||
\(614\) | 30.8290i | 1.24416i | ||||||||
\(615\) | −18.0705 | − | 34.9096i | −0.728674 | − | 1.40769i | ||||
\(616\) | 10.6665 | + | 10.6665i | 0.429766 | + | 0.429766i | ||||
\(617\) | −3.83238 | + | 3.83238i | −0.154286 | + | 0.154286i | −0.780029 | − | 0.625743i | \(-0.784796\pi\) |
0.625743 | + | 0.780029i | \(0.284796\pi\) | |||||||
\(618\) | 23.5435 | + | 7.48300i | 0.947058 | + | 0.301010i | ||||
\(619\) | −7.22455 | + | 7.22455i | −0.290379 | + | 0.290379i | −0.837230 | − | 0.546851i | \(-0.815826\pi\) |
0.546851 | + | 0.837230i | \(0.315826\pi\) | |||||||
\(620\) | − | 4.92427i | − | 0.197764i | ||||||
\(621\) | 2.16473 | − | 15.6072i | 0.0868678 | − | 0.626297i | ||||
\(622\) | −14.7994 | + | 14.7994i | −0.593403 | + | 0.593403i | ||||
\(623\) | 35.3382 | 1.41580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.8029 | 1.23212 | ||||||||
\(626\) | −23.1001 | + | 23.1001i | −0.923267 | + | 0.923267i | ||||
\(627\) | 7.51376 | + | 14.5155i | 0.300071 | + | 0.579692i | ||||
\(628\) | 14.1431i | 0.564372i | ||||||||
\(629\) | 11.8276 | − | 11.8276i | 0.471596 | − | 0.471596i | ||||
\(630\) | 30.3344 | − | 5.20456i | 1.20855 | − | 0.207355i | ||||
\(631\) | −14.8492 | + | 14.8492i | −0.591139 | + | 0.591139i | −0.937939 | − | 0.346800i | \(-0.887268\pi\) |
0.346800 | + | 0.937939i | \(0.387268\pi\) | |||||||
\(632\) | −1.11759 | − | 1.11759i | −0.0444553 | − | 0.0444553i | ||||
\(633\) | −13.1928 | + | 6.82909i | −0.524366 | + | 0.271432i | ||||
\(634\) | 7.36926i | 0.292671i | ||||||||
\(635\) | −41.8204 | − | 41.8204i | −1.65959 | − | 1.65959i | ||||
\(636\) | −11.1086 | + | 5.75023i | −0.440484 | + | 0.228011i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.46434i | 0.335106i | ||||||||
\(639\) | −5.59750 | − | 32.6246i | −0.221434 | − | 1.29061i | ||||
\(640\) | −2.85808 | −0.112976 | ||||||||
\(641\) | 42.6873 | 1.68605 | 0.843024 | − | 0.537876i | \(-0.180773\pi\) | ||||
0.843024 | + | 0.537876i | \(0.180773\pi\) | |||||||
\(642\) | 22.8545 | + | 7.26401i | 0.901995 | + | 0.286688i | ||||
\(643\) | 2.22166 | + | 2.22166i | 0.0876138 | + | 0.0876138i | 0.749555 | − | 0.661942i | \(-0.230267\pi\) |
−0.661942 | + | 0.749555i | \(0.730267\pi\) | |||||||
\(644\) | −7.69672 | − | 7.69672i | −0.303293 | − | 0.303293i | ||||
\(645\) | 9.20130 | + | 2.92452i | 0.362301 | + | 0.115153i | ||||
\(646\) | −7.75631 | −0.305168 | ||||||||
\(647\) | −36.4701 | −1.43379 | −0.716895 | − | 0.697181i | \(-0.754437\pi\) | ||||
−0.716895 | + | 0.697181i | \(0.754437\pi\) | |||||||
\(648\) | −3.87868 | + | 8.12132i | −0.152369 | + | 0.319036i | ||||
\(649\) | − | 43.2361i | − | 1.69717i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.51297 | + | 4.92427i | −0.372843 | + | 0.192998i | ||||
\(652\) | −0.787963 | − | 0.787963i | −0.0308590 | − | 0.0308590i | ||||
\(653\) | − | 45.4283i | − | 1.77775i | −0.458152 | − | 0.888874i | \(-0.651488\pi\) | ||
0.458152 | − | 0.888874i | \(-0.348512\pi\) | |||||||
\(654\) | −12.7087 | + | 6.57851i | −0.496949 | + | 0.257240i | ||||
\(655\) | 9.46410 | + | 9.46410i | 0.369793 | + | 0.369793i | ||||
\(656\) | 5.61494 | − | 5.61494i | 0.219226 | − | 0.219226i | ||||
\(657\) | 7.23336 | + | 42.1591i | 0.282200 | + | 1.64478i | ||||
\(658\) | 3.43659 | − | 3.43659i | 0.133972 | − | 0.133972i | ||||
\(659\) | 13.2626i | 0.516639i | 0.966060 | + | 0.258319i | \(0.0831687\pi\) | ||||
−0.966060 | + | 0.258319i | \(0.916831\pi\) | |||||||
\(660\) | −9.56333 | − | 18.4749i | −0.372252 | − | 0.719136i | ||||
\(661\) | −6.57777 | + | 6.57777i | −0.255846 | + | 0.255846i | −0.823362 | − | 0.567516i | \(-0.807904\pi\) |
0.567516 | + | 0.823362i | \(0.307904\pi\) | |||||||
\(662\) | −18.2372 | −0.708809 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.66193 | −0.142110 | ||||||||
\(665\) | 16.2900 | − | 16.2900i | 0.631700 | − | 0.631700i | ||||
\(666\) | −11.8619 | − | 8.38761i | −0.459638 | − | 0.325013i | ||||
\(667\) | − | 6.10768i | − | 0.236490i | ||||||
\(668\) | 3.94925 | − | 3.94925i | 0.152801 | − | 0.152801i | ||||
\(669\) | 34.7891 | + | 11.0573i | 1.34502 | + | 0.427498i | ||||
\(670\) | −8.58080 | + | 8.58080i | −0.331505 | + | 0.331505i | ||||
\(671\) | −0.814821 | − | 0.814821i | −0.0314558 | − | 0.0314558i | ||||
\(672\) | 2.85808 | + | 5.52139i | 0.110253 | + | 0.212992i | ||||
\(673\) | 26.4742i | 1.02050i | 0.860025 | + | 0.510252i | \(0.170448\pi\) | ||||
−0.860025 | + | 0.510252i | \(0.829552\pi\) | |||||||
\(674\) | −3.48238 | − | 3.48238i | −0.134136 | − | 0.134136i | ||||
\(675\) | −16.3086 | − | 2.26202i | −0.627719 | − | 0.0870650i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0789i | 1.57879i | 0.613885 | + | 0.789396i | \(0.289606\pi\) | ||||
−0.613885 | + | 0.789396i | \(0.710394\pi\) | |||||||
\(678\) | 29.7190 | + | 9.44581i | 1.14135 | + | 0.362764i | ||||
\(679\) | 28.7971 | 1.10513 | ||||||||
\(680\) | 9.87205 | 0.378576 | ||||||||
\(681\) | 2.63726 | − | 8.29751i | 0.101060 | − | 0.317961i | ||||
\(682\) | 5.11977 | + | 5.11977i | 0.196046 | + | 0.196046i | ||||
\(683\) | −4.21174 | − | 4.21174i | −0.161158 | − | 0.161158i | 0.621922 | − | 0.783079i | \(-0.286352\pi\) |
−0.783079 | + | 0.621922i | \(0.786352\pi\) | |||||||
\(684\) | 1.13918 | + | 6.63963i | 0.0435577 | + | 0.253873i | ||||
\(685\) | −15.6623 | −0.598424 | ||||||||
\(686\) | 4.00303 | 0.152836 | ||||||||
\(687\) | 7.36387 | − | 23.1687i | 0.280949 | − | 0.883940i | ||||
\(688\) | 1.95035i | 0.0743562i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 6.90069 | + | 13.3311i | 0.262705 | + | 0.507507i | ||||
\(691\) | 20.2360 | + | 20.2360i | 0.769814 | + | 0.769814i | 0.978074 | − | 0.208260i | \(-0.0667799\pi\) |
−0.208260 | + | 0.978074i | \(0.566780\pi\) | |||||||
\(692\) | 17.4953i | 0.665072i | ||||||||
\(693\) | −26.1275 | + | 36.9499i | −0.992502 | + | 1.40361i | ||||
\(694\) | 10.5657 | + | 10.5657i | 0.401069 | + | 0.401069i | ||||
\(695\) | −29.6946 | + | 29.6946i | −1.12638 | + | 1.12638i | ||||
\(696\) | −1.05673 | + | 3.32474i | −0.0400551 | + | 0.126024i | ||||
\(697\) | −19.3944 | + | 19.3944i | −0.734617 | + | 0.734617i | ||||
\(698\) | − | 31.2360i | − | 1.18230i | ||||||
\(699\) | 28.9093 | − | 14.9646i | 1.09345 | − | 0.566011i | ||||
\(700\) | −8.04261 | + | 8.04261i | −0.303982 | + | 0.303982i | ||||
\(701\) | −0.672924 | −0.0254160 | −0.0127080 | − | 0.999919i | \(-0.504045\pi\) | ||||
−0.0127080 | + | 0.999919i | \(0.504045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.8743 | −0.410131 | ||||||||
\(704\) | 2.97155 | − | 2.97155i | 0.111995 | − | 0.111995i | ||||
\(705\) | −5.95235 | + | 3.08116i | −0.224178 | + | 0.116043i | ||||
\(706\) | − | 10.3455i | − | 0.389360i | ||||||
\(707\) | −5.34758 | + | 5.34758i | −0.201116 | + | 0.201116i | ||||
\(708\) | 5.39779 | − | 16.9829i | 0.202861 | − | 0.638256i | ||||
\(709\) | 21.6346 | − | 21.6346i | 0.812504 | − | 0.812504i | −0.172505 | − | 0.985009i | \(-0.555186\pi\) |
0.985009 | + | 0.172505i | \(0.0551860\pi\) | |||||||
\(710\) | 22.2989 | + | 22.2989i | 0.836864 | + | 0.836864i | ||||
\(711\) | 2.73752 | − | 3.87144i | 0.102665 | − | 0.145190i | ||||
\(712\) | − | 9.84478i | − | 0.368949i | ||||||
\(713\) | −3.69432 | − | 3.69432i | −0.138353 | − | 0.138353i | ||||
\(714\) | −9.87205 | − | 19.0713i | −0.369452 | − | 0.713727i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 9.21508i | − | 0.344384i | ||||||
\(717\) | −5.06125 | + | 15.9240i | −0.189016 | + | 0.594694i | ||||
\(718\) | 12.8544 | 0.479722 | ||||||||
\(719\) | −23.1131 | −0.861974 | −0.430987 | − | 0.902358i | \(-0.641834\pi\) | ||||
−0.430987 | + | 0.902358i | \(0.641834\pi\) | |||||||
\(720\) | −1.44992 | − | 8.45077i | −0.0540354 | − | 0.314942i | ||||
\(721\) | 36.2019 | + | 36.2019i | 1.34823 | + | 1.34823i | ||||
\(722\) | −9.86945 | − | 9.86945i | −0.367303 | − | 0.367303i | ||||
\(723\) | 4.44747 | − | 13.9929i | 0.165403 | − | 0.520402i | ||||
\(724\) | 13.8110 | 0.513282 | ||||||||
\(725\) | −6.38216 | −0.237027 | ||||||||
\(726\) | 10.9939 | + | 3.49429i | 0.408024 | + | 0.129685i | ||||
\(727\) | − | 11.5379i | − | 0.427917i | −0.976843 | − | 0.213959i | \(-0.931364\pi\) | ||
0.976843 | − | 0.213959i | \(-0.0686357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9808 | − | 7.34847i | −0.962250 | − | 0.272166i | ||||
\(730\) | −28.8157 | − | 28.8157i | −1.06652 | − | 1.06652i | ||||
\(731\) | − | 6.73665i | − | 0.249164i | ||||||
\(732\) | −0.218331 | − | 0.421783i | −0.00806974 | − | 0.0155895i | ||||
\(733\) | 0.910162 | + | 0.910162i | 0.0336176 | + | 0.0336176i | 0.723716 | − | 0.690098i | \(-0.242433\pi\) |
−0.690098 | + | 0.723716i | \(0.742433\pi\) | |||||||
\(734\) | 1.16457 | − | 1.16457i | 0.0429850 | − | 0.0429850i | ||||
\(735\) | 27.7632 | + | 8.82419i | 1.02406 | + | 0.325485i | ||||
\(736\) | −2.14421 | + | 2.14421i | −0.0790365 | + | 0.0790365i | ||||
\(737\) | − | 17.8429i | − | 0.657253i | ||||||
\(738\) | 19.4507 | + | 13.7537i | 0.715991 | + | 0.506282i | ||||
\(739\) | 8.82889 | − | 8.82889i | 0.324776 | − | 0.324776i | −0.525820 | − | 0.850596i | \(-0.676241\pi\) |
0.850596 | + | 0.525820i | \(0.176241\pi\) | |||||||
\(740\) | 13.8405 | 0.508788 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.9232 | −0.951669 | ||||||||
\(743\) | 32.3947 | − | 32.3947i | 1.18844 | − | 1.18844i | 0.210948 | − | 0.977497i | \(-0.432345\pi\) |
0.977497 | − | 0.210948i | \(-0.0676549\pi\) | |||||||
\(744\) | 1.37184 | + | 2.65019i | 0.0502941 | + | 0.0971607i | ||||
\(745\) | − | 29.5374i | − | 1.08217i | ||||||
\(746\) | −14.1079 | + | 14.1079i | −0.516526 | + | 0.516526i | ||||
\(747\) | −1.85772 | − | 10.8276i | −0.0679704 | − | 0.396160i | ||||
\(748\) | −10.2640 | + | 10.2640i | −0.375288 | + | 0.375288i | ||||
\(749\) | 35.1425 | + | 35.1425i | 1.28408 | + | 1.28408i | ||||
\(750\) | −8.05116 | + | 4.16759i | −0.293987 | + | 0.152179i | ||||
\(751\) | − | 16.0234i | − | 0.584701i | −0.956311 | − | 0.292350i | \(-0.905563\pi\) | ||
0.956311 | − | 0.292350i | \(-0.0944373\pi\) | |||||||
\(752\) | −0.957390 | − | 0.957390i | −0.0349124 | − | 0.0349124i | ||||
\(753\) | 10.8285 | − | 5.60523i | 0.394611 | − | 0.204266i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.2295i | 0.954588i | ||||||||
\(756\) | −14.8757 | + | 11.2518i | −0.541024 | + | 0.409224i | ||||
\(757\) | −31.2554 | −1.13600 | −0.567998 | − | 0.823030i | \(-0.692282\pi\) | ||||
−0.567998 | + | 0.823030i | \(0.692282\pi\) | |||||||
\(758\) | −12.3118 | −0.447184 | ||||||||
\(759\) | −21.0350 | − | 6.68572i | −0.763523 | − | 0.242676i | ||||
\(760\) | −4.53819 | − | 4.53819i | −0.164617 | − | 0.164617i | ||||
\(761\) | −12.1654 | − | 12.1654i | −0.440994 | − | 0.440994i | 0.451352 | − | 0.892346i | \(-0.350942\pi\) |
−0.892346 | + | 0.451352i | \(0.850942\pi\) | |||||||
\(762\) | 34.1579 | + | 10.8567i | 1.23741 | + | 0.393295i | ||||
\(763\) | −29.6572 | −1.07366 | ||||||||
\(764\) | −22.7030 | −0.821366 | ||||||||
\(765\) | 5.00815 | + | 29.1896i | 0.181070 | + | 1.05535i | ||||
\(766\) | − | 28.3459i | − | 1.02418i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.53819 | − | 0.796225i | 0.0555046 | − | 0.0287313i | ||||
\(769\) | 0.164384 | + | 0.164384i | 0.00592784 | + | 0.00592784i | 0.710064 | − | 0.704137i | \(-0.248666\pi\) |
−0.704137 | + | 0.710064i | \(0.748666\pi\) | |||||||
\(770\) | − | 43.1134i | − | 1.55370i | ||||||
\(771\) | 2.51030 | − | 1.29943i | 0.0904064 | − | 0.0467978i | ||||
\(772\) | −14.1745 | − | 14.1745i | −0.510150 | − | 0.510150i | ||||
\(773\) | 31.2927 | − | 31.2927i | 1.12552 | − | 1.12552i | 0.134621 | − | 0.990897i | \(-0.457018\pi\) |
0.990897 | − | 0.134621i | \(-0.0429818\pi\) | |||||||
\(774\) | −5.76677 | + | 0.989422i | −0.207282 | + | 0.0355640i | ||||
\(775\) | −3.86034 | + | 3.86034i | −0.138667 | + | 0.138667i | ||||
\(776\) | − | 8.02251i | − | 0.287991i | ||||||
\(777\) | −13.8405 | − | 26.7378i | −0.496526 | − | 0.959215i | ||||
\(778\) | 11.2786 | − | 11.2786i | 0.404359 | − | 0.404359i | ||||
\(779\) | 17.8313 | 0.638872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.3684 | −1.65919 | ||||||||
\(782\) | 7.40626 | − | 7.40626i | 0.264847 | − | 0.264847i | ||||
\(783\) | −10.3667 | − | 1.43786i | −0.370474 | − | 0.0513850i | ||||
\(784\) | 5.88481i | 0.210172i | ||||||||
\(785\) | 28.5828 | − | 28.5828i | 1.02017 | − | 1.02017i | ||||
\(786\) | −7.73005 | − | 2.45690i | −0.275722 | − | 0.0876347i | ||||
\(787\) | 14.9399 | − | 14.9399i | 0.532551 | − | 0.532551i | −0.388780 | − | 0.921331i | \(-0.627103\pi\) |
0.921331 | + | 0.388780i | \(0.127103\pi\) | |||||||
\(788\) | −13.1786 | − | 13.1786i | −0.469467 | − | 0.469467i | ||||
\(789\) | 8.41445 | + | 16.2555i | 0.299562 | + | 0.578710i | ||||
\(790\) | 4.51722i | 0.160716i | ||||||||
\(791\) | 45.6978 | + | 45.6978i | 1.62483 | + | 1.62483i | ||||
\(792\) | 10.2938 | + | 7.27879i | 0.365773 | + | 0.258640i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.6918i | 0.450417i | ||||||||
\(795\) | 34.0711 | + | 10.8291i | 1.20838 | + | 0.384068i | ||||
\(796\) | −4.51039 | −0.159866 | ||||||||
\(797\) | 24.0741 | 0.852747 | 0.426373 | − | 0.904547i | \(-0.359791\pi\) | ||||
0.426373 | + | 0.904547i | \(0.359791\pi\) | |||||||
\(798\) | −4.22892 | + | 13.3053i | −0.149702 | + | 0.471002i | ||||
\(799\) | 3.30690 | + | 3.30690i | 0.116990 | + | 0.116990i | ||||
\(800\) | 2.24057 | + | 2.24057i | 0.0792160 | + | 0.0792160i | ||||
\(801\) | 29.1090 | − | 4.99431i | 1.02852 | − | 0.176465i | ||||
\(802\) | −16.4198 | −0.579804 | ||||||||
\(803\) | 59.9195 | 2.11451 | ||||||||
\(804\) | 2.22759 | − | 7.00859i | 0.0785611 | − | 0.247174i | ||||
\(805\) | 31.1097i | 1.09647i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.86234 | − | 13.2570i | −0.241566 | − | 0.466669i | ||||
\(808\) | 1.48977 | + | 1.48977i | 0.0524098 | + | 0.0524098i | ||||
\(809\) | 25.7155i | 0.904109i | 0.891990 | + | 0.452055i | \(0.149309\pi\) | ||||
−0.891990 | + | 0.452055i | \(0.850691\pi\) | |||||||
\(810\) | 24.2516 | − | 8.57425i | 0.852116 | − | 0.301268i | ||||
\(811\) | −5.99463 | − | 5.99463i | −0.210500 | − | 0.210500i | 0.593980 | − | 0.804480i | \(-0.297556\pi\) |
−0.804480 | + | 0.593980i | \(0.797556\pi\) | |||||||
\(812\) | −5.11233 | + | 5.11233i | −0.179408 | + | 0.179408i | ||||
\(813\) | −10.4048 | + | 32.7363i | −0.364913 | + | 1.14811i | ||||
\(814\) | −14.3900 | + | 14.3900i | −0.504370 | + | 0.504370i | ||||
\(815\) | 3.18490i | 0.111562i | ||||||||
\(816\) | −5.31303 | + | 2.75023i | −0.185993 | + | 0.0962772i | ||||
\(817\) | −3.09684 | + | 3.09684i | −0.108345 | + | 0.108345i | ||||
\(818\) | 34.0781 | 1.19151 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.6952 | −0.792552 | ||||||||
\(821\) | −37.5734 | + | 37.5734i | −1.31132 | + | 1.31132i | −0.390879 | + | 0.920442i | \(0.627829\pi\) |
−0.920442 | + | 0.390879i | \(0.872171\pi\) | |||||||
\(822\) | 8.42925 | − | 4.36330i | 0.294004 | − | 0.152188i | ||||
\(823\) | − | 11.4619i | − | 0.399538i | −0.979843 | − | 0.199769i | \(-0.935981\pi\) | ||
0.979843 | − | 0.199769i | \(-0.0640192\pi\) | |||||||
\(824\) | 10.0854 | − | 10.0854i | 0.351341 | − | 0.351341i | ||||
\(825\) | −6.98617 | + | 21.9803i | −0.243227 | + | 0.765257i | ||||
\(826\) | 26.1139 | − | 26.1139i | 0.908620 | − | 0.908620i | ||||
\(827\) | 4.57665 | + | 4.57665i | 0.159146 | + | 0.159146i | 0.782188 | − | 0.623042i | \(-0.214104\pi\) |
−0.623042 | + | 0.782188i | \(0.714104\pi\) | |||||||
\(828\) | −7.42775 | − | 5.25221i | −0.258132 | − | 0.182527i | ||||
\(829\) | − | 49.9553i | − | 1.73502i | −0.497422 | − | 0.867509i | \(-0.665720\pi\) | ||
0.497422 | − | 0.867509i | \(-0.334280\pi\) | |||||||
\(830\) | 7.40065 | + | 7.40065i | 0.256880 | + | 0.256880i | ||||
\(831\) | −12.3434 | − | 23.8457i | −0.428189 | − | 0.827198i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 20.3266i | − | 0.704275i | ||||||
\(834\) | 7.70877 | − | 24.2538i | 0.266933 | − | 0.839842i | ||||
\(835\) | −15.9627 | −0.552410 | ||||||||
\(836\) | 9.43672 | 0.326376 | ||||||||
\(837\) | −7.14013 | + | 5.40071i | −0.246799 | + | 0.186676i | ||||
\(838\) | −23.2655 | − | 23.2655i | −0.803693 | − | 0.803693i | ||||
\(839\) | 8.20115 | + | 8.20115i | 0.283135 | + | 0.283135i | 0.834358 | − | 0.551223i | \(-0.185839\pi\) |
−0.551223 | + | 0.834358i | \(0.685839\pi\) | |||||||
\(840\) | 5.38247 | − | 16.9347i | 0.185713 | − | 0.584302i | ||||
\(841\) | 24.9431 | 0.860108 | ||||||||
\(842\) | −24.1753 | −0.833137 | ||||||||
\(843\) | 27.8850 | + | 8.86291i | 0.960412 | + | 0.305255i | ||||
\(844\) | 8.57683i | 0.295227i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.34512 | − | 3.31649i | 0.0806267 | − | 0.114023i | ||||
\(847\) | 16.9050 | + | 16.9050i | 0.580862 | + | 0.580862i | ||||
\(848\) | 7.22186i | 0.248000i | ||||||||
\(849\) | 1.25781 | + | 2.42991i | 0.0431680 | + | 0.0833942i | ||||
\(850\) | −7.73910 | − | 7.73910i | −0.265449 | − | 0.265449i | ||||
\(851\) | 10.3835 | − | 10.3835i | 0.355942 | − | 0.355942i | ||||
\(852\) | −18.2132 | − | 5.78884i | −0.623975 | − | 0.198322i | ||||
\(853\) | 1.56247 | − | 1.56247i | 0.0534978 | − | 0.0534978i | −0.679852 | − | 0.733350i | \(-0.737956\pi\) |
0.733350 | + | 0.679852i | \(0.237956\pi\) | |||||||
\(854\) | − | 0.984278i | − | 0.0336813i | ||||||
\(855\) | 11.1162 | − | 15.7207i | 0.380168 | − | 0.537638i | ||||
\(856\) | 9.79025 | − | 9.79025i | 0.334624 | − | 0.334624i | ||||
\(857\) | −21.5804 | −0.737174 | −0.368587 | − | 0.929593i | \(-0.620158\pi\) | ||||
−0.368587 | + | 0.929593i | \(0.620158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5544 | 0.360110 | 0.180055 | − | 0.983657i | \(-0.442372\pi\) | ||||
0.180055 | + | 0.983657i | \(0.442372\pi\) | |||||||
\(860\) | 3.94159 | − | 3.94159i | 0.134407 | − | 0.134407i | ||||
\(861\) | 22.6952 | + | 43.8438i | 0.773452 | + | 1.49419i | ||||
\(862\) | − | 1.75577i | − | 0.0598018i | ||||||
\(863\) | 21.4177 | − | 21.4177i | 0.729066 | − | 0.729066i | −0.241368 | − | 0.970434i | \(-0.577596\pi\) |
0.970434 | + | 0.241368i | \(0.0775960\pi\) | |||||||
\(864\) | 3.13461 | + | 4.14418i | 0.106642 | + | 0.140988i | ||||
\(865\) | 35.3575 | − | 35.3575i | 1.20219 | − | 1.20219i | ||||
\(866\) | −7.24346 | − | 7.24346i | −0.246143 | − | 0.246143i | ||||
\(867\) | −7.79759 | + | 4.03633i | −0.264820 | + | 0.137081i | ||||
\(868\) | 6.18452i | 0.209916i | ||||||||
\(869\) | −4.69656 | − | 4.69656i | −0.159320 | − | 0.159320i | ||||
\(870\) | 8.85481 | − | 4.58359i | 0.300206 | − | 0.155398i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.26212i | 0.279791i | ||||||||
\(873\) | 23.7209 | − | 4.06987i | 0.802831 | − | 0.137744i | ||||
\(874\) | −6.80933 | −0.230329 | ||||||||
\(875\) | −18.7883 | −0.635161 | ||||||||
\(876\) | 23.5360 | + | 7.48062i | 0.795208 | + | 0.252747i | ||||
\(877\) | −27.6234 | − | 27.6234i | −0.932775 | − | 0.932775i | 0.0651031 | − | 0.997879i | \(-0.479262\pi\) |
−0.997879 | + | 0.0651031i | \(0.979262\pi\) | |||||||
\(878\) | 3.81996 | + | 3.81996i | 0.128917 | + | 0.128917i | ||||
\(879\) | 6.44617 | + | 2.04883i | 0.217424 | + | 0.0691054i | ||||
\(880\) | −12.0108 | −0.404885 | ||||||||
\(881\) | 6.79415 | 0.228901 | 0.114450 | − | 0.993429i | \(-0.463489\pi\) | ||||
0.114450 | + | 0.993429i | \(0.463489\pi\) | |||||||
\(882\) | −17.4002 | + | 2.98540i | −0.585894 | + | 0.100524i | ||||
\(883\) | 40.6560i | 1.36818i | 0.729397 | + | 0.684091i | \(0.239801\pi\) | ||||
−0.729397 | + | 0.684091i | \(0.760199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.2307 | + | 23.4131i | −1.52041 | + | 0.787023i | ||||
\(886\) | −9.59761 | − | 9.59761i | −0.322438 | − | 0.322438i | ||||
\(887\) | 10.4419i | 0.350606i | 0.984515 | + | 0.175303i | \(0.0560905\pi\) | ||||
−0.984515 | + | 0.175303i | \(0.943909\pi\) | |||||||
\(888\) | −7.44882 | + | 3.85579i | −0.249966 | + | 0.129392i | ||||
\(889\) | 52.5233 | + | 52.5233i | 1.76158 | + | 1.76158i | ||||
\(890\) | −19.8960 | + | 19.8960i | −0.666916 | + | 0.666916i | ||||
\(891\) | −16.2998 | + | 34.1291i | −0.546064 | + | 1.14337i | ||||
\(892\) | 14.9027 | − | 14.9027i | 0.498979 | − | 0.498979i | ||||
\(893\) | − | 3.04037i | − | 0.101742i | ||||||
\(894\) | 8.22875 | + | 15.8967i | 0.275211 | + | 0.531666i | ||||
\(895\) | −18.6234 | + | 18.6234i | −0.622512 | + | 0.622512i | ||||
\(896\) | 3.58954 | 0.119918 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.02930 | 0.0677187 | ||||||||
\(899\) | −2.45384 | + | 2.45384i | −0.0818403 | + | 0.0818403i | ||||
\(900\) | −5.48825 | + | 7.76155i | −0.182942 | + | 0.258718i | ||||
\(901\) | − | 24.9449i | − | 0.831034i | ||||||
\(902\) | 23.5963 | − | 23.5963i | 0.785670 | − | 0.785670i | ||||
\(903\) | −11.5562 | − | 3.67298i | −0.384565 | − | 0.122229i | ||||
\(904\) | 12.7308 | − | 12.7308i | 0.423421 | − | 0.423421i | ||||
\(905\) | −27.9116 | − | 27.9116i | −0.927814 | − | 0.927814i | ||||
\(906\) | −7.30719 | − | 14.1164i | −0.242765 | − | 0.468986i | ||||
\(907\) | 39.2319i | 1.30268i | 0.758788 | + | 0.651338i | \(0.225792\pi\) | ||||
−0.758788 | + | 0.651338i | \(0.774208\pi\) | |||||||
\(908\) | −3.55443 | − | 3.55443i | −0.117958 | − | 0.117958i | ||||
\(909\) | −3.64917 | + | 5.16071i | −0.121035 | + | 0.171170i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0923i | 1.06326i | 0.846975 | + | 0.531632i | \(0.178421\pi\) | ||||
−0.846975 | + | 0.531632i | \(0.821579\pi\) | |||||||
\(912\) | 3.70668 | + | 1.17812i | 0.122741 | + | 0.0390115i | ||||
\(913\) | −15.3889 | −0.509299 | ||||||||
\(914\) | −29.9534 | −0.990770 | ||||||||
\(915\) | −0.411170 | + | 1.29365i | −0.0135929 | + | 0.0427667i | ||||
\(916\) | −9.92484 | − | 9.92484i | −0.327926 | − | 0.327926i | ||||
\(917\) | −11.8862 | − | 11.8862i | −0.392517 | − | 0.392517i | ||||
\(918\) | −10.8272 | − | 14.3143i | −0.357350 | − | 0.472443i | ||||
\(919\) | 33.2842 | 1.09794 | 0.548972 | − | 0.835841i | \(-0.315020\pi\) | ||||
0.548972 | + | 0.835841i | \(0.315020\pi\) | |||||||
\(920\) | 8.66676 | 0.285735 | ||||||||
\(921\) | −16.1744 | + | 50.8889i | −0.532964 | + | 1.67685i | ||||
\(922\) | 16.1111i | 0.530589i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0108 | + | 23.2032i | 0.395128 | + | 0.763328i | ||||
\(925\) | −10.8501 | − | 10.8501i | −0.356751 | − | 0.356751i | ||||
\(926\) | − | 5.75643i | − | 0.189168i | ||||||
\(927\) | 34.9368 | + | 24.7041i | 1.14748 | + | 0.811388i | ||||
\(928\) | 1.42423 | + | 1.42423i | 0.0467526 | + | 0.0467526i | ||||
\(929\) | −15.5309 | + | 15.5309i | −0.509552 | + | 0.509552i | −0.914389 | − | 0.404837i | \(-0.867328\pi\) |
0.404837 | + | 0.914389i | \(0.367328\pi\) | |||||||
\(930\) | 2.58351 | − | 8.12840i | 0.0847166 | − | 0.266541i | ||||
\(931\) | −9.34415 | + | 9.34415i | −0.306242 | + | 0.306242i | ||||
\(932\) | − | 18.7944i | − | 0.615630i | ||||||
\(933\) | −32.1936 | + | 16.6646i | −1.05397 | + | 0.545575i | ||||
\(934\) | −26.0594 | + | 26.0594i | −0.852690 | + | 0.852690i | ||||
\(935\) | 41.4864 | 1.35675 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.9423 | 1.82755 | 0.913777 | − | 0.406216i | \(-0.133152\pi\) | ||||
0.913777 | + | 0.406216i | \(0.133152\pi\) | |||||||
\(938\) | 10.7768 | − | 10.7768i | 0.351877 | − | 0.351877i | ||||
\(939\) | −50.2503 | + | 26.0115i | −1.63986 | + | 0.848853i | ||||
\(940\) | 3.86971i | 0.126216i | ||||||||
\(941\) | −17.1600 | + | 17.1600i | −0.559401 | + | 0.559401i | −0.929137 | − | 0.369736i | \(-0.879448\pi\) |
0.369736 | + | 0.929137i | \(0.379448\pi\) | |||||||
\(942\) | −7.42016 | + | 23.3458i | −0.241762 | + | 0.760647i | ||||
\(943\) | −17.0265 | + | 17.0265i | −0.554461 | + | 0.554461i | ||||
\(944\) | −7.27501 | − | 7.27501i | −0.236781 | − | 0.236781i | ||||
\(945\) | 52.8029 | + | 7.32380i | 1.71768 | + | 0.238243i | ||||
\(946\) | 8.19615i | 0.266480i | ||||||||
\(947\) | 33.7186 | + | 33.7186i | 1.09571 | + | 1.09571i | 0.994907 | + | 0.100799i | \(0.0321400\pi\) |
0.100799 | + | 0.994907i | \(0.467860\pi\) | |||||||
\(948\) | −1.25844 | − | 2.43112i | −0.0408722 | − | 0.0789591i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.11534i | 0.230852i | ||||||||
\(951\) | −3.86626 | + | 12.1643i | −0.125372 | + | 0.394454i | ||||
\(952\) | −12.3986 | −0.401840 | ||||||||
\(953\) | −43.0555 | −1.39471 | −0.697353 | − | 0.716728i | \(-0.745639\pi\) | ||||
−0.697353 | + | 0.716728i | \(0.745639\pi\) | |||||||
\(954\) | −21.3536 | + | 3.66369i | −0.691347 | + | 0.118616i | ||||
\(955\) | 45.8821 | + | 45.8821i | 1.48471 | + | 1.48471i | ||||
\(956\) | 6.82142 | + | 6.82142i | 0.220621 | + | 0.220621i | ||||
\(957\) | −4.44080 | + | 13.9719i | −0.143551 | + | 0.451648i | ||||
\(958\) | −15.0430 | −0.486018 | ||||||||
\(959\) | 19.6706 | 0.635198 | ||||||||
\(960\) | −4.71778 | − | 1.49949i | −0.152266 | − | 0.0483957i | ||||
\(961\) | − | 28.0315i | − | 0.904242i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.9144 | + | 23.9811i | 1.09288 | + | 0.772781i | ||||
\(964\) | −5.99419 | − | 5.99419i | −0.193060 | − | 0.193060i | ||||
\(965\) | 57.2923i | 1.84430i | ||||||||
\(966\) | −8.66676 | − | 16.7429i | −0.278848 | − | 0.538694i | ||||
\(967\) | 4.96226 | + | 4.96226i | 0.159576 | + | 0.159576i | 0.782379 | − | 0.622803i | \(-0.214006\pi\) |
−0.622803 | + | 0.782379i | \(0.714006\pi\) | |||||||
\(968\) | 4.70951 | − | 4.70951i | 0.151369 | − | 0.151369i | ||||
\(969\) | −12.8032 | − | 4.06933i | −0.411298 | − | 0.130726i | ||||
\(970\) | −16.2132 | + | 16.2132i | −0.520576 | + | 0.520576i | ||||
\(971\) | − | 31.7872i | − | 1.02010i | −0.860145 | − | 0.510050i | \(-0.829627\pi\) | ||
0.860145 | − | 0.510050i | \(-0.170373\pi\) | |||||||
\(972\) | −10.6633 | + | 11.3708i | −0.342025 | + | 0.364717i | ||||
\(973\) | 37.2942 | − | 37.2942i | 1.19560 | − | 1.19560i | ||||
\(974\) | −16.7305 | −0.536081 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.274207 | −0.00877716 | ||||||||
\(977\) | −4.92840 | + | 4.92840i | −0.157673 | + | 0.157673i | −0.781535 | − | 0.623861i | \(-0.785563\pi\) |
0.623861 | + | 0.781535i | \(0.285563\pi\) | |||||||
\(978\) | −0.887272 | − | 1.71408i | −0.0283718 | − | 0.0548102i | ||||
\(979\) | − | 41.3718i | − | 1.32225i | ||||||
\(980\) | 11.8930 | − | 11.8930i | 0.379909 | − | 0.379909i | ||||
\(981\) | −24.4294 | + | 4.19142i | −0.779970 | + | 0.133822i | ||||
\(982\) | −17.8662 | + | 17.8662i | −0.570132 | + | 0.570132i | ||||
\(983\) | −10.5636 | − | 10.5636i | −0.336926 | − | 0.336926i | 0.518283 | − | 0.855209i | \(-0.326571\pi\) |
−0.855209 | + | 0.518283i | \(0.826571\pi\) | |||||||
\(984\) | 12.2143 | − | 6.32260i | 0.389379 | − | 0.201557i | ||||
\(985\) | 53.2670i | 1.69723i | ||||||||
\(986\) | −4.91940 | − | 4.91940i | −0.156666 | − | 0.156666i | ||||
\(987\) | 7.47571 | − | 3.86971i | 0.237954 | − | 0.123174i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.91416i | − | 0.188059i | ||||||
\(990\) | −6.09317 | − | 35.5136i | −0.193654 | − | 1.12870i | ||||
\(991\) | 26.3855 | 0.838162 | 0.419081 | − | 0.907949i | \(-0.362352\pi\) | ||||
0.419081 | + | 0.907949i | \(0.362352\pi\) | |||||||
\(992\) | 1.72293 | 0.0547030 | ||||||||
\(993\) | −30.1038 | − | 9.56810i | −0.955315 | − | 0.303635i | ||||
\(994\) | −28.0058 | − | 28.0058i | −0.888290 | − | 0.888290i | ||||
\(995\) | 9.11536 | + | 9.11536i | 0.288976 | + | 0.288976i | ||||
\(996\) | −6.04468 | − | 1.92122i | −0.191533 | − | 0.0608763i | ||||
\(997\) | 29.2650 | 0.926832 | 0.463416 | − | 0.886141i | \(-0.346623\pi\) | ||||
0.463416 | + | 0.886141i | \(0.346623\pi\) | |||||||
\(998\) | −1.95086 | −0.0617533 | ||||||||
\(999\) | −15.1796 | − | 20.0686i | −0.480262 | − | 0.634941i |
(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 | 1014.2.g.d.437.8 | 16 | ||
3.2 | odd | 2 | inner | 1014.2.g.d.437.4 | 16 | ||
13.5 | odd | 4 | inner | 1014.2.g.d.239.4 | 16 | ||
13.7 | odd | 12 | 78.2.k.a.41.3 | yes | 16 | ||
13.8 | odd | 4 | 1014.2.g.c.239.8 | 16 | |||
13.10 | even | 6 | 78.2.k.a.59.1 | yes | 16 | ||
13.12 | even | 2 | 1014.2.g.c.437.4 | 16 | |||
39.5 | even | 4 | inner | 1014.2.g.d.239.8 | 16 | ||
39.8 | even | 4 | 1014.2.g.c.239.4 | 16 | |||
39.20 | even | 12 | 78.2.k.a.41.1 | ✓ | 16 | ||
39.23 | odd | 6 | 78.2.k.a.59.3 | yes | 16 | ||
39.38 | odd | 2 | 1014.2.g.c.437.8 | 16 | |||
52.7 | even | 12 | 624.2.cn.d.353.4 | 16 | |||
52.23 | odd | 6 | 624.2.cn.d.449.3 | 16 | |||
156.23 | even | 6 | 624.2.cn.d.449.4 | 16 | |||
156.59 | odd | 12 | 624.2.cn.d.353.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.k.a.41.1 | ✓ | 16 | 39.20 | even | 12 | ||
78.2.k.a.41.3 | yes | 16 | 13.7 | odd | 12 | ||
78.2.k.a.59.1 | yes | 16 | 13.10 | even | 6 | ||
78.2.k.a.59.3 | yes | 16 | 39.23 | odd | 6 | ||
624.2.cn.d.353.3 | 16 | 156.59 | odd | 12 | |||
624.2.cn.d.353.4 | 16 | 52.7 | even | 12 | |||
624.2.cn.d.449.3 | 16 | 52.23 | odd | 6 | |||
624.2.cn.d.449.4 | 16 | 156.23 | even | 6 | |||
1014.2.g.c.239.4 | 16 | 39.8 | even | 4 | |||
1014.2.g.c.239.8 | 16 | 13.8 | odd | 4 | |||
1014.2.g.c.437.4 | 16 | 13.12 | even | 2 | |||
1014.2.g.c.437.8 | 16 | 39.38 | odd | 2 | |||
1014.2.g.d.239.4 | 16 | 13.5 | odd | 4 | inner | ||
1014.2.g.d.239.8 | 16 | 39.5 | even | 4 | inner | ||
1014.2.g.d.437.4 | 16 | 3.2 | odd | 2 | inner | ||
1014.2.g.d.437.8 | 16 | 1.1 | even | 1 | trivial |