Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(0.453245 + 1.39494i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.p.372.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.453245 | − | 1.39494i | −0.320493 | − | 0.986375i | −0.973434 | − | 0.228967i | \(-0.926465\pi\) |
0.652942 | − | 0.757408i | \(-0.273535\pi\) | |||||||
\(3\) | 1.30902 | + | 0.951057i | 0.755761 | + | 0.549093i | 0.897607 | − | 0.440796i | \(-0.145304\pi\) |
−0.141846 | + | 0.989889i | \(0.545304\pi\) | |||||||
\(4\) | −0.122406 | + | 0.0889332i | −0.0612030 | + | 0.0444666i | ||||
\(5\) | 0.144228 | − | 0.443888i | 0.0645007 | − | 0.198513i | −0.913613 | − | 0.406586i | \(-0.866719\pi\) |
0.978113 | + | 0.208073i | \(0.0667192\pi\) | |||||||
\(6\) | 0.733366 | − | 2.25707i | 0.299395 | − | 0.921444i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −2.19369 | − | 1.59381i | −0.775585 | − | 0.563495i | ||||
\(9\) | −0.118034 | − | 0.363271i | −0.0393447 | − | 0.121090i | ||||
\(10\) | −0.684570 | −0.216480 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.244812 | −0.0706712 | ||||||||
\(13\) | −0.488963 | − | 1.50487i | −0.135614 | − | 0.417376i | 0.860071 | − | 0.510174i | \(-0.170419\pi\) |
−0.995685 | + | 0.0927976i | \(0.970419\pi\) | |||||||
\(14\) | −1.18661 | − | 0.862123i | −0.317135 | − | 0.230412i | ||||
\(15\) | 0.610960 | − | 0.443888i | 0.157749 | − | 0.114611i | ||||
\(16\) | −1.32250 | + | 4.07025i | −0.330626 | + | 1.01756i | ||||
\(17\) | 1.61533 | − | 4.97148i | 0.391776 | − | 1.20576i | −0.539669 | − | 0.841877i | \(-0.681451\pi\) |
0.931444 | − | 0.363884i | \(-0.118549\pi\) | |||||||
\(18\) | −0.453245 | + | 0.329302i | −0.106831 | + | 0.0776172i | ||||
\(19\) | −3.41560 | − | 2.48158i | −0.783593 | − | 0.569314i | 0.122462 | − | 0.992473i | \(-0.460921\pi\) |
−0.906055 | + | 0.423159i | \(0.860921\pi\) | |||||||
\(20\) | 0.0218220 | + | 0.0671613i | 0.00487955 | + | 0.0150177i | ||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.80505 | −0.376380 | −0.188190 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188190 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(24\) | −1.35577 | − | 4.17264i | −0.276746 | − | 0.851736i | ||||
\(25\) | 3.86885 | + | 2.81088i | 0.773770 | + | 0.562177i | ||||
\(26\) | −1.87759 | + | 1.36415i | −0.368226 | + | 0.267532i | ||||
\(27\) | 1.69098 | − | 5.20431i | 0.325430 | − | 1.00157i | ||||
\(28\) | −0.0467549 | + | 0.143897i | −0.00883585 | + | 0.0271940i | ||||
\(29\) | −2.20010 | + | 1.59846i | −0.408548 | + | 0.296827i | −0.773014 | − | 0.634389i | \(-0.781252\pi\) |
0.364466 | + | 0.931217i | \(0.381252\pi\) | |||||||
\(30\) | −0.896114 | − | 0.651065i | −0.163607 | − | 0.118868i | ||||
\(31\) | 0.399825 | + | 1.23053i | 0.0718107 | + | 0.221010i | 0.980520 | − | 0.196419i | \(-0.0629312\pi\) |
−0.908709 | + | 0.417429i | \(0.862931\pi\) | |||||||
\(32\) | 0.854102 | 0.150985 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.66708 | −1.31489 | ||||||||
\(35\) | −0.144228 | − | 0.443888i | −0.0243790 | − | 0.0750308i | ||||
\(36\) | 0.0467549 | + | 0.0339695i | 0.00779249 | + | 0.00566158i | ||||
\(37\) | 1.57128 | − | 1.14160i | 0.258317 | − | 0.187678i | −0.451088 | − | 0.892480i | \(-0.648964\pi\) |
0.709405 | + | 0.704801i | \(0.248964\pi\) | |||||||
\(38\) | −1.91356 | + | 5.88935i | −0.310421 | + | 0.955378i | ||||
\(39\) | 0.791158 | − | 2.43493i | 0.126687 | − | 0.389902i | ||||
\(40\) | −1.02386 | + | 0.743880i | −0.161887 | + | 0.117618i | ||||
\(41\) | 0.842285 | + | 0.611956i | 0.131543 | + | 0.0955715i | 0.651611 | − | 0.758553i | \(-0.274093\pi\) |
−0.520068 | + | 0.854125i | \(0.674093\pi\) | |||||||
\(42\) | −0.733366 | − | 2.25707i | −0.113161 | − | 0.348273i | ||||
\(43\) | 8.70820 | 1.32799 | 0.663994 | − | 0.747738i | \(-0.268860\pi\) | ||||
0.663994 | + | 0.747738i | \(0.268860\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.178276 | −0.0265758 | ||||||||
\(46\) | 0.818132 | + | 2.51795i | 0.120627 | + | 0.371252i | ||||
\(47\) | 5.17390 | + | 3.75906i | 0.754691 | + | 0.548315i | 0.897277 | − | 0.441467i | \(-0.145542\pi\) |
−0.142586 | + | 0.989782i | \(0.545542\pi\) | |||||||
\(48\) | −5.60222 | + | 4.07025i | −0.808610 | + | 0.587490i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 2.16749 | − | 6.67085i | 0.306530 | − | 0.943401i | ||||
\(51\) | 6.84266 | − | 4.97148i | 0.958163 | − | 0.696147i | ||||
\(52\) | 0.193685 | + | 0.140720i | 0.0268593 | + | 0.0195144i | ||||
\(53\) | −4.08039 | − | 12.5582i | −0.560485 | − | 1.72500i | −0.680999 | − | 0.732284i | \(-0.738454\pi\) |
0.120514 | − | 0.992712i | \(-0.461546\pi\) | |||||||
\(54\) | −8.02616 | −1.09222 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.71154 | −0.362345 | ||||||||
\(57\) | −2.11096 | − | 6.49687i | −0.279603 | − | 0.860531i | ||||
\(58\) | 3.22695 | + | 2.34452i | 0.423720 | + | 0.307850i | ||||
\(59\) | 6.96069 | − | 5.05724i | 0.906205 | − | 0.658396i | −0.0338475 | − | 0.999427i | \(-0.510776\pi\) |
0.940052 | + | 0.341031i | \(0.110776\pi\) | |||||||
\(60\) | −0.0353088 | + | 0.108669i | −0.00455834 | + | 0.0140291i | ||||
\(61\) | −4.70947 | + | 14.4942i | −0.602985 | + | 1.85580i | −0.0928967 | + | 0.995676i | \(0.529613\pi\) |
−0.510089 | + | 0.860122i | \(0.670387\pi\) | |||||||
\(62\) | 1.53531 | − | 1.11547i | 0.194984 | − | 0.141664i | ||||
\(63\) | −0.309017 | − | 0.224514i | −0.0389325 | − | 0.0282861i | ||||
\(64\) | 2.25789 | + | 6.94907i | 0.282236 | + | 0.868634i | ||||
\(65\) | −0.738517 | −0.0916018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.67583 | −0.571243 | −0.285622 | − | 0.958342i | \(-0.592200\pi\) | ||||
−0.285622 | + | 0.958342i | \(0.592200\pi\) | |||||||
\(68\) | 0.244403 | + | 0.752196i | 0.0296382 | + | 0.0912171i | ||||
\(69\) | −2.36285 | − | 1.71671i | −0.284453 | − | 0.206667i | ||||
\(70\) | −0.553829 | + | 0.402380i | −0.0661952 | + | 0.0480937i | ||||
\(71\) | 3.01078 | − | 9.26624i | 0.357314 | − | 1.09970i | −0.597341 | − | 0.801987i | \(-0.703776\pi\) |
0.954655 | − | 0.297713i | \(-0.0962239\pi\) | |||||||
\(72\) | −0.320054 | + | 0.985026i | −0.0377188 | + | 0.116086i | ||||
\(73\) | 10.7761 | − | 7.82931i | 1.26125 | − | 0.916351i | 0.262431 | − | 0.964951i | \(-0.415476\pi\) |
0.998818 | + | 0.0485994i | \(0.0154758\pi\) | |||||||
\(74\) | −2.30464 | − | 1.67442i | −0.267910 | − | 0.194648i | ||||
\(75\) | 2.39108 | + | 7.35899i | 0.276098 | + | 0.849743i | ||||
\(76\) | 0.638786 | 0.0732737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.75519 | −0.425191 | ||||||||
\(79\) | 1.10700 | + | 3.40699i | 0.124547 | + | 0.383316i | 0.993818 | − | 0.111019i | \(-0.0354116\pi\) |
−0.869271 | + | 0.494335i | \(0.835412\pi\) | |||||||
\(80\) | 1.61599 | + | 1.17409i | 0.180674 | + | 0.131267i | ||||
\(81\) | 6.23607 | − | 4.53077i | 0.692896 | − | 0.503419i | ||||
\(82\) | 0.471883 | − | 1.45231i | 0.0521108 | − | 0.160381i | ||||
\(83\) | −5.33329 | + | 16.4142i | −0.585404 | + | 1.80169i | 0.0122356 | + | 0.999925i | \(0.496105\pi\) |
−0.597640 | + | 0.801765i | \(0.703895\pi\) | |||||||
\(84\) | −0.198057 | + | 0.143897i | −0.0216098 | + | 0.0157004i | ||||
\(85\) | −1.97381 | − | 1.43405i | −0.214089 | − | 0.155545i | ||||
\(86\) | −3.94695 | − | 12.1475i | −0.425611 | − | 1.30989i | ||||
\(87\) | −4.40020 | −0.471750 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.91982 | −0.945499 | −0.472750 | − | 0.881197i | \(-0.656738\pi\) | ||||
−0.472750 | + | 0.881197i | \(0.656738\pi\) | |||||||
\(90\) | 0.0808026 | + | 0.248685i | 0.00851734 | + | 0.0262137i | ||||
\(91\) | −1.28012 | − | 0.930062i | −0.134193 | − | 0.0974970i | ||||
\(92\) | 0.220949 | − | 0.160529i | 0.0230356 | − | 0.0167363i | ||||
\(93\) | −0.646930 | + | 1.99105i | −0.0670835 | + | 0.206462i | ||||
\(94\) | 2.89864 | − | 8.92109i | 0.298972 | − | 0.920140i | ||||
\(95\) | −1.59417 | + | 1.15823i | −0.163559 | + | 0.118832i | ||||
\(96\) | 1.11803 | + | 0.812299i | 0.114109 | + | 0.0829049i | ||||
\(97\) | −0.835464 | − | 2.57129i | −0.0848285 | − | 0.261075i | 0.899641 | − | 0.436630i | \(-0.143828\pi\) |
−0.984470 | + | 0.175555i | \(0.943828\pi\) | |||||||
\(98\) | −1.46673 | −0.148162 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.723551 | −0.0723551 | ||||||||
\(101\) | 0.0552464 | + | 0.170031i | 0.00549722 | + | 0.0169187i | 0.953768 | − | 0.300545i | \(-0.0971687\pi\) |
−0.948270 | + | 0.317464i | \(0.897169\pi\) | |||||||
\(102\) | −10.0363 | − | 7.29183i | −0.993746 | − | 0.721999i | ||||
\(103\) | −13.6540 | + | 9.92019i | −1.34537 | + | 0.977465i | −0.346137 | + | 0.938184i | \(0.612507\pi\) |
−0.999228 | + | 0.0392811i | \(0.987493\pi\) | |||||||
\(104\) | −1.32584 | + | 4.08053i | −0.130010 | + | 0.400129i | ||||
\(105\) | 0.233366 | − | 0.718226i | 0.0227742 | − | 0.0700917i | ||||
\(106\) | −15.6685 | + | 11.3838i | −1.52186 | + | 1.10570i | ||||
\(107\) | 12.5205 | + | 9.09669i | 1.21040 | + | 0.879410i | 0.995267 | − | 0.0971734i | \(-0.0309801\pi\) |
0.215137 | + | 0.976584i | \(0.430980\pi\) | |||||||
\(108\) | 0.255849 | + | 0.787424i | 0.0246191 | + | 0.0757699i | ||||
\(109\) | 11.0349 | 1.05695 | 0.528476 | − | 0.848948i | \(-0.322764\pi\) | ||||
0.528476 | + | 0.848948i | \(0.322764\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.14256 | 0.298278 | ||||||||
\(112\) | 1.32250 | + | 4.07025i | 0.124965 | + | 0.384602i | ||||
\(113\) | −1.43202 | − | 1.04043i | −0.134713 | − | 0.0978750i | 0.518388 | − | 0.855146i | \(-0.326532\pi\) |
−0.653101 | + | 0.757271i | \(0.726532\pi\) | |||||||
\(114\) | −8.10599 | + | 5.88935i | −0.759195 | + | 0.551588i | ||||
\(115\) | −0.260339 | + | 0.801242i | −0.0242768 | + | 0.0747162i | ||||
\(116\) | 0.127149 | − | 0.391323i | 0.0118055 | − | 0.0363335i | ||||
\(117\) | −0.488963 | + | 0.355252i | −0.0452046 | + | 0.0328431i | ||||
\(118\) | −10.2095 | − | 7.41761i | −0.939857 | − | 0.682846i | ||||
\(119\) | −1.61533 | − | 4.97148i | −0.148077 | − | 0.455735i | ||||
\(120\) | −2.04773 | −0.186931 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 22.3532 | 2.02376 | ||||||||
\(123\) | 0.520561 | + | 1.60212i | 0.0469374 | + | 0.144458i | ||||
\(124\) | −0.158376 | − | 0.115067i | −0.0142226 | − | 0.0103333i | ||||
\(125\) | 3.69369 | − | 2.68362i | 0.330373 | − | 0.240030i | ||||
\(126\) | −0.173124 | + | 0.532822i | −0.0154231 | + | 0.0474675i | ||||
\(127\) | −2.63908 | + | 8.12224i | −0.234180 | + | 0.720732i | 0.763049 | + | 0.646341i | \(0.223702\pi\) |
−0.997229 | + | 0.0743917i | \(0.976298\pi\) | |||||||
\(128\) | 10.0522 | − | 7.30332i | 0.888494 | − | 0.645528i | ||||
\(129\) | 11.3992 | + | 8.28199i | 1.00364 | + | 0.729189i | ||||
\(130\) | 0.334729 | + | 1.03019i | 0.0293577 | + | 0.0903537i | ||||
\(131\) | −9.66708 | −0.844617 | −0.422308 | − | 0.906452i | \(-0.638780\pi\) | ||||
−0.422308 | + | 0.906452i | \(0.638780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.22192 | −0.366087 | ||||||||
\(134\) | 2.11930 | + | 6.52252i | 0.183079 | + | 0.563460i | ||||
\(135\) | −2.06625 | − | 1.50122i | −0.177834 | − | 0.129204i | ||||
\(136\) | −11.4671 | + | 8.33134i | −0.983296 | + | 0.714406i | ||||
\(137\) | −4.32958 | + | 13.3251i | −0.369901 | + | 1.13844i | 0.576954 | + | 0.816777i | \(0.304241\pi\) |
−0.946855 | + | 0.321661i | \(0.895759\pi\) | |||||||
\(138\) | −1.32376 | + | 4.07413i | −0.112686 | + | 0.346813i | ||||
\(139\) | −7.74848 | + | 5.62960i | −0.657218 | + | 0.477497i | −0.865722 | − | 0.500525i | \(-0.833140\pi\) |
0.208504 | + | 0.978021i | \(0.433140\pi\) | |||||||
\(140\) | 0.0571308 | + | 0.0415079i | 0.00482843 | + | 0.00350806i | ||||
\(141\) | 3.19765 | + | 9.84135i | 0.269291 | + | 0.828791i | ||||
\(142\) | −14.2905 | −1.19923 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.63470 | 0.136225 | ||||||||
\(145\) | 0.392224 | + | 1.20714i | 0.0325724 | + | 0.100248i | ||||
\(146\) | −15.8057 | − | 11.4835i | −1.30809 | − | 0.950381i | ||||
\(147\) | 1.30902 | − | 0.951057i | 0.107966 | − | 0.0784418i | ||||
\(148\) | −0.0908078 | + | 0.279478i | −0.00746436 | + | 0.0229729i | ||||
\(149\) | 4.62367 | − | 14.2302i | 0.378786 | − | 1.16578i | −0.562103 | − | 0.827067i | \(-0.690008\pi\) |
0.940889 | − | 0.338715i | \(-0.109992\pi\) | |||||||
\(150\) | 9.18164 | − | 6.67085i | 0.749678 | − | 0.544673i | ||||
\(151\) | 2.32376 | + | 1.68831i | 0.189105 | + | 0.137393i | 0.678310 | − | 0.734776i | \(-0.262713\pi\) |
−0.489204 | + | 0.872169i | \(0.662713\pi\) | |||||||
\(152\) | 3.53760 | + | 10.8876i | 0.286937 | + | 0.883103i | ||||
\(153\) | −1.99666 | −0.161420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.603886 | 0.0485053 | ||||||||
\(156\) | 0.119704 | + | 0.368411i | 0.00958399 | + | 0.0294965i | ||||
\(157\) | 15.2761 | + | 11.0988i | 1.21917 | + | 0.885777i | 0.996031 | − | 0.0890105i | \(-0.0283705\pi\) |
0.223136 | + | 0.974787i | \(0.428370\pi\) | |||||||
\(158\) | 4.25082 | − | 3.08840i | 0.338177 | − | 0.245700i | ||||
\(159\) | 6.60222 | − | 20.3195i | 0.523590 | − | 1.61144i | ||||
\(160\) | 0.123185 | − | 0.379126i | 0.00973867 | − | 0.0299725i | ||||
\(161\) | −1.46032 | + | 1.06098i | −0.115089 | + | 0.0836173i | ||||
\(162\) | −9.14664 | − | 6.64542i | −0.718628 | − | 0.522114i | ||||
\(163\) | 3.58310 | + | 11.0276i | 0.280650 | + | 0.863751i | 0.987669 | + | 0.156557i | \(0.0500394\pi\) |
−0.707019 | + | 0.707194i | \(0.749961\pi\) | |||||||
\(164\) | −0.157524 | −0.0123006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.3142 | 1.96476 | ||||||||
\(167\) | 1.95451 | + | 6.01535i | 0.151244 | + | 0.465482i | 0.997761 | − | 0.0668802i | \(-0.0213045\pi\) |
−0.846517 | + | 0.532362i | \(0.821305\pi\) | |||||||
\(168\) | −3.54946 | − | 2.57883i | −0.273847 | − | 0.198961i | ||||
\(169\) | 8.49166 | − | 6.16956i | 0.653205 | − | 0.474581i | ||||
\(170\) | −1.10581 | + | 3.40333i | −0.0848116 | + | 0.261023i | ||||
\(171\) | −0.498330 | + | 1.53370i | −0.0381082 | + | 0.117285i | ||||
\(172\) | −1.06594 | + | 0.774448i | −0.0812769 | + | 0.0590511i | ||||
\(173\) | −1.08332 | − | 0.787082i | −0.0823637 | − | 0.0598407i | 0.545841 | − | 0.837889i | \(-0.316210\pi\) |
−0.628205 | + | 0.778048i | \(0.716210\pi\) | |||||||
\(174\) | 1.99437 | + | 6.13803i | 0.151193 | + | 0.465323i | ||||
\(175\) | 4.78216 | 0.361497 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.9214 | 1.04639 | ||||||||
\(178\) | 4.04286 | + | 12.4427i | 0.303026 | + | 0.932617i | ||||
\(179\) | −14.3915 | − | 10.4560i | −1.07567 | − | 0.781518i | −0.0987452 | − | 0.995113i | \(-0.531483\pi\) |
−0.976922 | + | 0.213595i | \(0.931483\pi\) | |||||||
\(180\) | 0.0218220 | − | 0.0158546i | 0.00162652 | − | 0.00118173i | ||||
\(181\) | −0.297823 | + | 0.916606i | −0.0221370 | + | 0.0681308i | −0.961515 | − | 0.274753i | \(-0.911404\pi\) |
0.939378 | + | 0.342884i | \(0.111404\pi\) | |||||||
\(182\) | −0.717177 | + | 2.20724i | −0.0531607 | + | 0.163612i | ||||
\(183\) | −19.9496 | + | 14.4942i | −1.47472 | + | 1.07145i | ||||
\(184\) | 3.95972 | + | 2.87690i | 0.291914 | + | 0.212088i | ||||
\(185\) | −0.280121 | − | 0.862123i | −0.0205949 | − | 0.0633846i | ||||
\(186\) | 3.07062 | 0.225149 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.967622 | −0.0705711 | ||||||||
\(189\) | −1.69098 | − | 5.20431i | −0.123001 | − | 0.378558i | ||||
\(190\) | 2.33822 | + | 1.69882i | 0.169632 | + | 0.123245i | ||||
\(191\) | 13.0162 | − | 9.45679i | 0.941816 | − | 0.684269i | −0.00704142 | − | 0.999975i | \(-0.502241\pi\) |
0.948857 | + | 0.315706i | \(0.102241\pi\) | |||||||
\(192\) | −3.65334 | + | 11.2438i | −0.263657 | + | 0.811454i | ||||
\(193\) | 3.75377 | − | 11.5529i | 0.270202 | − | 0.831597i | −0.720247 | − | 0.693718i | \(-0.755971\pi\) |
0.990449 | − | 0.137879i | \(-0.0440286\pi\) | |||||||
\(194\) | −3.20814 | + | 2.33085i | −0.230331 | + | 0.167345i | ||||
\(195\) | −0.966732 | − | 0.702372i | −0.0692291 | − | 0.0502979i | ||||
\(196\) | 0.0467549 | + | 0.143897i | 0.00333964 | + | 0.0102784i | ||||
\(197\) | −2.30179 | −0.163996 | −0.0819978 | − | 0.996633i | \(-0.526130\pi\) | ||||
−0.0819978 | + | 0.996633i | \(0.526130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2797 | 1.43759 | 0.718795 | − | 0.695222i | \(-0.244694\pi\) | ||||
0.718795 | + | 0.695222i | \(0.244694\pi\) | |||||||
\(200\) | −4.00704 | − | 12.3324i | −0.283340 | − | 0.872032i | ||||
\(201\) | −6.12074 | − | 4.44698i | −0.431723 | − | 0.313665i | ||||
\(202\) | 0.212144 | − | 0.154131i | 0.0149264 | − | 0.0108446i | ||||
\(203\) | −0.840363 | + | 2.58637i | −0.0589819 | + | 0.181528i | ||||
\(204\) | −0.395453 | + | 1.21708i | −0.0276872 | + | 0.0852125i | ||||
\(205\) | 0.393121 | − | 0.285619i | 0.0274568 | − | 0.0199485i | ||||
\(206\) | 20.0267 | + | 14.5503i | 1.39533 | + | 1.01376i | ||||
\(207\) | 0.213058 | + | 0.655724i | 0.0148085 | + | 0.0455760i | ||||
\(208\) | 6.77186 | 0.469544 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.10766 | −0.0764357 | ||||||||
\(211\) | 1.65797 | + | 5.10270i | 0.114139 | + | 0.351284i | 0.991767 | − | 0.128059i | \(-0.0408748\pi\) |
−0.877627 | + | 0.479344i | \(0.840875\pi\) | |||||||
\(212\) | 1.61630 | + | 1.17431i | 0.111008 | + | 0.0806521i | ||||
\(213\) | 12.7539 | − | 9.26624i | 0.873882 | − | 0.634912i | ||||
\(214\) | 7.01452 | − | 21.5885i | 0.479503 | − | 1.47576i | ||||
\(215\) | 1.25597 | − | 3.86547i | 0.0856563 | − | 0.263623i | ||||
\(216\) | −12.0041 | + | 8.72152i | −0.816778 | + | 0.593424i | ||||
\(217\) | 1.04675 | + | 0.760512i | 0.0710584 | + | 0.0516269i | ||||
\(218\) | −5.00151 | − | 15.3931i | −0.338745 | − | 1.04255i | ||||
\(219\) | 21.5522 | 1.45637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.27128 | −0.556387 | ||||||||
\(222\) | −1.42435 | − | 4.38370i | −0.0955960 | − | 0.294214i | ||||
\(223\) | 20.5676 | + | 14.9433i | 1.37731 | + | 1.00068i | 0.997126 | + | 0.0757654i | \(0.0241400\pi\) |
0.380186 | + | 0.924910i | \(0.375860\pi\) | |||||||
\(224\) | 0.690983 | − | 0.502029i | 0.0461682 | − | 0.0335432i | ||||
\(225\) | 0.564458 | − | 1.73722i | 0.0376305 | − | 0.115815i | ||||
\(226\) | −0.802279 | + | 2.46916i | −0.0533668 | + | 0.164246i | ||||
\(227\) | 17.5636 | − | 12.7607i | 1.16573 | − | 0.846956i | 0.175243 | − | 0.984525i | \(-0.443929\pi\) |
0.990492 | + | 0.137569i | \(0.0439290\pi\) | |||||||
\(228\) | 0.836181 | + | 0.607521i | 0.0553775 | + | 0.0402341i | ||||
\(229\) | 6.34433 | + | 19.5258i | 0.419245 | + | 1.29030i | 0.908399 | + | 0.418105i | \(0.137306\pi\) |
−0.489154 | + | 0.872198i | \(0.662694\pi\) | |||||||
\(230\) | 1.23569 | 0.0814787 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.37396 | 0.484124 | ||||||||
\(233\) | 0.214475 | + | 0.660086i | 0.0140507 | + | 0.0432437i | 0.957836 | − | 0.287315i | \(-0.0927627\pi\) |
−0.943785 | + | 0.330559i | \(0.892763\pi\) | |||||||
\(234\) | 0.717177 | + | 0.521060i | 0.0468833 | + | 0.0340627i | ||||
\(235\) | 2.41483 | − | 1.75447i | 0.157526 | − | 0.114449i | ||||
\(236\) | −0.402274 | + | 1.23807i | −0.0261858 | + | 0.0805917i | ||||
\(237\) | −1.79116 | + | 5.51262i | −0.116348 | + | 0.358083i | ||||
\(238\) | −6.20280 | + | 4.50660i | −0.402068 | + | 0.292119i | ||||
\(239\) | −0.280374 | − | 0.203703i | −0.0181359 | − | 0.0131765i | 0.578680 | − | 0.815554i | \(-0.303568\pi\) |
−0.596816 | + | 0.802378i | \(0.703568\pi\) | |||||||
\(240\) | 0.998739 | + | 3.07380i | 0.0644683 | + | 0.198413i | ||||
\(241\) | −10.4372 | −0.672317 | −0.336158 | − | 0.941806i | \(-0.609128\pi\) | ||||
−0.336158 | + | 0.941806i | \(0.609128\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −0.712552 | − | 2.19301i | −0.0456165 | − | 0.140393i | ||||
\(245\) | −0.377594 | − | 0.274338i | −0.0241236 | − | 0.0175268i | ||||
\(246\) | 1.99893 | − | 1.45231i | 0.127447 | − | 0.0925957i | ||||
\(247\) | −2.06436 | + | 6.35345i | −0.131352 | + | 0.404260i | ||||
\(248\) | 1.08414 | − | 3.33665i | 0.0688431 | − | 0.211877i | ||||
\(249\) | −22.5922 | + | 16.4142i | −1.43172 | + | 1.04021i | ||||
\(250\) | −5.41765 | − | 3.93615i | −0.342642 | − | 0.248944i | ||||
\(251\) | −2.16158 | − | 6.65266i | −0.136438 | − | 0.419912i | 0.859373 | − | 0.511349i | \(-0.170854\pi\) |
−0.995811 | + | 0.0914367i | \(0.970854\pi\) | |||||||
\(252\) | 0.0577923 | 0.00364057 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.5262 | 0.785965 | ||||||||
\(255\) | −1.21988 | − | 3.75440i | −0.0763918 | − | 0.235110i | ||||
\(256\) | −2.92136 | − | 2.12249i | −0.182585 | − | 0.132656i | ||||
\(257\) | 8.04845 | − | 5.84754i | 0.502048 | − | 0.364760i | −0.307750 | − | 0.951467i | \(-0.599576\pi\) |
0.809799 | + | 0.586708i | \(0.199576\pi\) | |||||||
\(258\) | 6.38630 | − | 19.6550i | 0.397594 | − | 1.22367i | ||||
\(259\) | 0.600175 | − | 1.84715i | 0.0372931 | − | 0.114776i | ||||
\(260\) | 0.0903990 | − | 0.0656787i | 0.00560631 | − | 0.00407322i | ||||
\(261\) | 0.840363 | + | 0.610559i | 0.0520171 | + | 0.0377927i | ||||
\(262\) | 4.38156 | + | 13.4850i | 0.270694 | + | 0.833109i | ||||
\(263\) | 14.1803 | 0.874397 | 0.437199 | − | 0.899365i | \(-0.355971\pi\) | ||||
0.437199 | + | 0.899365i | \(0.355971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.16293 | −0.378586 | ||||||||
\(266\) | 1.91356 | + | 5.88935i | 0.117328 | + | 0.361099i | ||||
\(267\) | −11.6762 | − | 8.48325i | −0.714572 | − | 0.519167i | ||||
\(268\) | 0.572349 | − | 0.415836i | 0.0349618 | − | 0.0254012i | ||||
\(269\) | −5.68686 | + | 17.5024i | −0.346734 | + | 1.06714i | 0.613915 | + | 0.789372i | \(0.289594\pi\) |
−0.960649 | + | 0.277766i | \(0.910406\pi\) | |||||||
\(270\) | −1.15760 | + | 3.56272i | −0.0704491 | + | 0.216820i | ||||
\(271\) | −0.591060 | + | 0.429431i | −0.0359044 | + | 0.0260861i | −0.605593 | − | 0.795775i | \(-0.707064\pi\) |
0.569688 | + | 0.821861i | \(0.307064\pi\) | |||||||
\(272\) | 18.0989 | + | 13.1496i | 1.09741 | + | 0.797312i | ||||
\(273\) | −0.791158 | − | 2.43493i | −0.0478831 | − | 0.147369i | ||||
\(274\) | 20.5501 | 1.24148 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.441899 | 0.0265992 | ||||||||
\(277\) | 4.65515 | + | 14.3271i | 0.279701 | + | 0.860832i | 0.987937 | + | 0.154856i | \(0.0494913\pi\) |
−0.708236 | + | 0.705976i | \(0.750509\pi\) | |||||||
\(278\) | 11.3649 | + | 8.25712i | 0.681624 | + | 0.495229i | ||||
\(279\) | 0.399825 | − | 0.290490i | 0.0239369 | − | 0.0173912i | ||||
\(280\) | −0.391081 | + | 1.20362i | −0.0233715 | + | 0.0719302i | ||||
\(281\) | −3.30528 | + | 10.1726i | −0.197177 | + | 0.606847i | 0.802768 | + | 0.596292i | \(0.203360\pi\) |
−0.999944 | + | 0.0105553i | \(0.996640\pi\) | |||||||
\(282\) | 12.2788 | − | 8.92109i | 0.731193 | − | 0.531243i | ||||
\(283\) | −7.36926 | − | 5.35408i | −0.438057 | − | 0.318267i | 0.346805 | − | 0.937937i | \(-0.387266\pi\) |
−0.784862 | + | 0.619670i | \(0.787266\pi\) | |||||||
\(284\) | 0.455538 | + | 1.40200i | 0.0270312 | + | 0.0831936i | ||||
\(285\) | −3.18834 | −0.188861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04112 | 0.0614555 | ||||||||
\(288\) | −0.100813 | − | 0.310271i | −0.00594047 | − | 0.0182829i | ||||
\(289\) | −8.35303 | − | 6.06883i | −0.491355 | − | 0.356990i | ||||
\(290\) | 1.50612 | − | 1.09426i | 0.0884425 | − | 0.0642572i | ||||
\(291\) | 1.35181 | − | 4.16044i | 0.0792444 | − | 0.243889i | ||||
\(292\) | −0.622777 | + | 1.91671i | −0.0364452 | + | 0.112167i | ||||
\(293\) | −9.61840 | + | 6.98818i | −0.561913 | + | 0.408254i | −0.832159 | − | 0.554538i | \(-0.812895\pi\) |
0.270245 | + | 0.962791i | \(0.412895\pi\) | |||||||
\(294\) | −1.91998 | − | 1.39494i | −0.111975 | − | 0.0813548i | ||||
\(295\) | −1.24092 | − | 3.81916i | −0.0722493 | − | 0.222360i | ||||
\(296\) | −5.26638 | −0.306102 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.9460 | −1.27130 | ||||||||
\(299\) | 0.882604 | + | 2.71638i | 0.0510423 | + | 0.157092i | ||||
\(300\) | −0.947141 | − | 0.688138i | −0.0546832 | − | 0.0397297i | ||||
\(301\) | 7.04508 | − | 5.11855i | 0.406072 | − | 0.295029i | ||||
\(302\) | 1.30187 | − | 4.00674i | 0.0749142 | − | 0.230562i | ||||
\(303\) | −0.0893905 | + | 0.275116i | −0.00513535 | + | 0.0158050i | ||||
\(304\) | 14.6178 | − | 10.6205i | 0.838389 | − | 0.609125i | ||||
\(305\) | 5.75459 | + | 4.18095i | 0.329507 | + | 0.239401i | ||||
\(306\) | 0.904976 | + | 2.78523i | 0.0517341 | + | 0.159221i | ||||
\(307\) | 2.22072 | 0.126743 | 0.0633716 | − | 0.997990i | \(-0.479815\pi\) | ||||
0.0633716 | + | 0.997990i | \(0.479815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.3079 | −1.55349 | ||||||||
\(310\) | −0.273708 | − | 0.842387i | −0.0155456 | − | 0.0478444i | ||||
\(311\) | 17.3231 | + | 12.5860i | 0.982304 | + | 0.713686i | 0.958222 | − | 0.286024i | \(-0.0923337\pi\) |
0.0240820 | + | 0.999710i | \(0.492334\pi\) | |||||||
\(312\) | −5.61636 | + | 4.08053i | −0.317964 | + | 0.231014i | ||||
\(313\) | −9.75096 | + | 30.0104i | −0.551157 | + | 1.69629i | 0.154726 | + | 0.987957i | \(0.450550\pi\) |
−0.705883 | + | 0.708329i | \(0.749450\pi\) | |||||||
\(314\) | 8.55832 | − | 26.3398i | 0.482974 | − | 1.48644i | ||||
\(315\) | −0.144228 | + | 0.104788i | −0.00812633 | + | 0.00590412i | ||||
\(316\) | −0.438497 | − | 0.318587i | −0.0246674 | − | 0.0179219i | ||||
\(317\) | −4.07923 | − | 12.5546i | −0.229112 | − | 0.705135i | −0.997848 | − | 0.0655687i | \(-0.979114\pi\) |
0.768736 | − | 0.639567i | \(-0.220886\pi\) | |||||||
\(318\) | −31.3370 | −1.75729 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.41026 | 0.190639 | ||||||||
\(321\) | 7.73811 | + | 23.8154i | 0.431899 | + | 1.32925i | ||||
\(322\) | 2.14190 | + | 1.55618i | 0.119363 | + | 0.0867225i | ||||
\(323\) | −17.8545 | + | 12.9720i | −0.993449 | + | 0.721783i | ||||
\(324\) | −0.360397 | + | 1.10919i | −0.0200220 | + | 0.0616215i | ||||
\(325\) | 2.33830 | − | 7.19654i | 0.129705 | − | 0.399192i | ||||
\(326\) | 13.7589 | − | 9.99644i | 0.762036 | − | 0.553652i | ||||
\(327\) | 14.4449 | + | 10.4948i | 0.798803 | + | 0.580365i | ||||
\(328\) | −0.872370 | − | 2.68488i | −0.0481686 | − | 0.148248i | ||||
\(329\) | 6.39530 | 0.352584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.47653 | 0.520877 | 0.260439 | − | 0.965490i | \(-0.416133\pi\) | ||||
0.260439 | + | 0.965490i | \(0.416133\pi\) | |||||||
\(332\) | −0.806938 | − | 2.48350i | −0.0442865 | − | 0.136300i | ||||
\(333\) | −0.600175 | − | 0.436053i | −0.0328894 | − | 0.0238955i | ||||
\(334\) | 7.50521 | − | 5.45286i | 0.410667 | − | 0.298367i | ||||
\(335\) | −0.674385 | + | 2.07554i | −0.0368456 | + | 0.113399i | ||||
\(336\) | −2.13986 | + | 6.58580i | −0.116739 | + | 0.359285i | ||||
\(337\) | 15.5340 | − | 11.2861i | 0.846191 | − | 0.614794i | −0.0779019 | − | 0.996961i | \(-0.524822\pi\) |
0.924093 | + | 0.382167i | \(0.124822\pi\) | |||||||
\(338\) | −12.4550 | − | 9.04908i | −0.677462 | − | 0.492205i | ||||
\(339\) | −0.885039 | − | 2.72387i | −0.0480687 | − | 0.147940i | ||||
\(340\) | 0.369141 | 0.0200195 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.36530 | 0.127901 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | −19.1031 | − | 13.8792i | −1.02997 | − | 0.748315i | ||||
\(345\) | −1.10282 | + | 0.801242i | −0.0593736 | + | 0.0431374i | ||||
\(346\) | −0.606924 | + | 1.86792i | −0.0326284 | + | 0.100420i | ||||
\(347\) | 0.941979 | − | 2.89911i | 0.0505681 | − | 0.155632i | −0.922584 | − | 0.385797i | \(-0.873926\pi\) |
0.973152 | + | 0.230165i | \(0.0739265\pi\) | |||||||
\(348\) | 0.538610 | − | 0.391323i | 0.0288726 | − | 0.0209771i | ||||
\(349\) | −15.6918 | − | 11.4007i | −0.839962 | − | 0.610268i | 0.0823980 | − | 0.996600i | \(-0.473742\pi\) |
−0.922360 | + | 0.386331i | \(0.873742\pi\) | |||||||
\(350\) | −2.16749 | − | 6.67085i | −0.115857 | − | 0.356572i | ||||
\(351\) | −8.65865 | −0.462165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7585 | −0.572619 | −0.286309 | − | 0.958137i | \(-0.592428\pi\) | ||||
−0.286309 | + | 0.958137i | \(0.592428\pi\) | |||||||
\(354\) | −6.30980 | − | 19.4196i | −0.335362 | − | 1.03214i | ||||
\(355\) | −3.67894 | − | 2.67290i | −0.195258 | − | 0.141863i | ||||
\(356\) | 1.09184 | − | 0.793268i | 0.0578674 | − | 0.0420431i | ||||
\(357\) | 2.61366 | − | 8.04402i | 0.138330 | − | 0.425735i | ||||
\(358\) | −8.06269 | + | 24.8144i | −0.426126 | + | 1.31148i | ||||
\(359\) | −0.491256 | + | 0.356918i | −0.0259275 | + | 0.0188374i | −0.600674 | − | 0.799494i | \(-0.705101\pi\) |
0.574746 | + | 0.818332i | \(0.305101\pi\) | |||||||
\(360\) | 0.391081 | + | 0.284137i | 0.0206118 | + | 0.0149753i | ||||
\(361\) | −0.363217 | − | 1.11787i | −0.0191167 | − | 0.0588351i | ||||
\(362\) | 1.41360 | 0.0742973 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.239408 | 0.0125484 | ||||||||
\(365\) | −1.92112 | − | 5.91260i | −0.100556 | − | 0.309480i | ||||
\(366\) | 29.2607 | + | 21.2592i | 1.52948 | + | 1.11123i | ||||
\(367\) | −22.3797 | + | 16.2598i | −1.16821 | + | 0.848755i | −0.990794 | − | 0.135380i | \(-0.956774\pi\) |
−0.177418 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(368\) | 2.38719 | − | 7.34702i | 0.124441 | − | 0.382990i | ||||
\(369\) | 0.122888 | − | 0.378210i | 0.00639728 | − | 0.0196888i | ||||
\(370\) | −1.07565 | + | 0.781506i | −0.0559204 | + | 0.0406286i | ||||
\(371\) | −10.6826 | − | 7.76137i | −0.554613 | − | 0.402950i | ||||
\(372\) | −0.0978819 | − | 0.301250i | −0.00507494 | − | 0.0156191i | ||||
\(373\) | −29.4513 | −1.52493 | −0.762465 | − | 0.647029i | \(-0.776011\pi\) | ||||
−0.762465 | + | 0.647029i | \(0.776011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.38737 | 0.381482 | ||||||||
\(376\) | −5.35870 | − | 16.4924i | −0.276354 | − | 0.850530i | ||||
\(377\) | 3.48125 | + | 2.52928i | 0.179294 | + | 0.130264i | ||||
\(378\) | −6.49330 | + | 4.71766i | −0.333979 | + | 0.242650i | ||||
\(379\) | 7.83162 | − | 24.1032i | 0.402283 | − | 1.23810i | −0.520859 | − | 0.853643i | \(-0.674388\pi\) |
0.923143 | − | 0.384458i | \(-0.125612\pi\) | |||||||
\(380\) | 0.0921308 | − | 0.283550i | 0.00472621 | − | 0.0145458i | ||||
\(381\) | −11.1793 | + | 8.12224i | −0.572733 | + | 0.416115i | ||||
\(382\) | −19.0912 | − | 13.8706i | −0.976791 | − | 0.709680i | ||||
\(383\) | −9.86759 | − | 30.3693i | −0.504210 | − | 1.55180i | −0.802094 | − | 0.597197i | \(-0.796281\pi\) |
0.297884 | − | 0.954602i | \(-0.403719\pi\) | |||||||
\(384\) | 20.1043 | 1.02594 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.8171 | −0.906865 | ||||||||
\(387\) | −1.02786 | − | 3.16344i | −0.0522493 | − | 0.160807i | ||||
\(388\) | 0.330939 | + | 0.240441i | 0.0168009 | + | 0.0122066i | ||||
\(389\) | −14.3614 | + | 10.4342i | −0.728153 | + | 0.529034i | −0.888979 | − | 0.457949i | \(-0.848584\pi\) |
0.160825 | + | 0.986983i | \(0.448584\pi\) | |||||||
\(390\) | −0.541603 | + | 1.66688i | −0.0274252 | + | 0.0844060i | ||||
\(391\) | −2.91576 | + | 8.97379i | −0.147456 | + | 0.453824i | ||||
\(392\) | −2.19369 | + | 1.59381i | −0.110798 | + | 0.0804993i | ||||
\(393\) | −12.6544 | − | 9.19394i | −0.638329 | − | 0.463773i | ||||
\(394\) | 1.04327 | + | 3.21087i | 0.0525594 | + | 0.161761i | ||||
\(395\) | 1.67198 | 0.0841265 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3047 | −0.667742 | −0.333871 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333871 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(398\) | −9.19168 | − | 28.2891i | −0.460737 | − | 1.41800i | ||||
\(399\) | −5.52656 | − | 4.01528i | −0.276674 | − | 0.201016i | ||||
\(400\) | −16.5576 | + | 12.0298i | −0.827878 | + | 0.601489i | ||||
\(401\) | −1.07835 | + | 3.31883i | −0.0538504 | + | 0.165734i | −0.974365 | − | 0.224975i | \(-0.927770\pi\) |
0.920514 | + | 0.390709i | \(0.127770\pi\) | |||||||
\(402\) | −3.42909 | + | 10.5537i | −0.171028 | + | 0.526369i | ||||
\(403\) | 1.65630 | − | 1.20337i | 0.0825061 | − | 0.0599442i | ||||
\(404\) | −0.0218839 | − | 0.0158996i | −0.00108876 | − | 0.000791033i | ||||
\(405\) | −1.11174 | − | 3.42158i | −0.0552428 | − | 0.170020i | ||||
\(406\) | 3.98873 | 0.197958 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −22.9342 | −1.13541 | ||||||||
\(409\) | −9.15478 | − | 28.1755i | −0.452675 | − | 1.39319i | −0.873843 | − | 0.486208i | \(-0.838380\pi\) |
0.421168 | − | 0.906982i | \(-0.361620\pi\) | |||||||
\(410\) | −0.576603 | − | 0.418927i | −0.0284764 | − | 0.0206893i | ||||
\(411\) | −18.3404 | + | 13.3251i | −0.904665 | + | 0.657277i | ||||
\(412\) | 0.789094 | − | 2.42858i | 0.0388759 | − | 0.119648i | ||||
\(413\) | 2.65875 | − | 8.18278i | 0.130828 | − | 0.402648i | ||||
\(414\) | 0.818132 | − | 0.594407i | 0.0402090 | − | 0.0292135i | ||||
\(415\) | 6.51685 | + | 4.73477i | 0.319900 | + | 0.232421i | ||||
\(416\) | −0.417624 | − | 1.28531i | −0.0204757 | − | 0.0630177i | ||||
\(417\) | −15.4970 | −0.758890 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6452 | −0.568907 | −0.284454 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284454 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(420\) | 0.0353088 | + | 0.108669i | 0.00172289 | + | 0.00530252i | ||||
\(421\) | −16.0872 | − | 11.6880i | −0.784041 | − | 0.569639i | 0.122148 | − | 0.992512i | \(-0.461022\pi\) |
−0.906189 | + | 0.422873i | \(0.861022\pi\) | |||||||
\(422\) | 6.36652 | − | 4.62555i | 0.309917 | − | 0.225168i | ||||
\(423\) | 0.754862 | − | 2.32323i | 0.0367027 | − | 0.112959i | ||||
\(424\) | −11.0642 | + | 34.0520i | −0.537323 | + | 1.65371i | ||||
\(425\) | 20.2237 | − | 14.6934i | 0.980995 | − | 0.712735i | ||||
\(426\) | −18.7065 | − | 13.5911i | −0.906335 | − | 0.658491i | ||||
\(427\) | 4.70947 | + | 14.4942i | 0.227907 | + | 0.701426i | ||||
\(428\) | −2.34159 | −0.113185 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.96138 | −0.287483 | ||||||||
\(431\) | 9.34664 | + | 28.7660i | 0.450212 | + | 1.38561i | 0.876666 | + | 0.481100i | \(0.159763\pi\) |
−0.426454 | + | 0.904509i | \(0.640237\pi\) | |||||||
\(432\) | 18.9465 | + | 13.7654i | 0.911564 | + | 0.662290i | ||||
\(433\) | 4.61722 | − | 3.35460i | 0.221889 | − | 0.161212i | −0.471287 | − | 0.881980i | \(-0.656211\pi\) |
0.693177 | + | 0.720768i | \(0.256211\pi\) | |||||||
\(434\) | 0.586436 | − | 1.80486i | 0.0281498 | − | 0.0866362i | ||||
\(435\) | −0.634632 | + | 1.95320i | −0.0304283 | + | 0.0936485i | ||||
\(436\) | −1.35074 | + | 0.981369i | −0.0646886 | + | 0.0469990i | ||||
\(437\) | 6.16535 | + | 4.47939i | 0.294929 | + | 0.214278i | ||||
\(438\) | −9.76845 | − | 30.0642i | −0.466754 | − | 1.43652i | ||||
\(439\) | 6.84875 | 0.326873 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 3.74892 | + | 11.5380i | 0.178318 | + | 0.548806i | ||||
\(443\) | −0.0814641 | − | 0.0591871i | −0.00387047 | − | 0.00281206i | 0.585848 | − | 0.810421i | \(-0.300761\pi\) |
−0.589719 | + | 0.807609i | \(0.700761\pi\) | |||||||
\(444\) | −0.384668 | + | 0.279478i | −0.0182555 | + | 0.0132634i | ||||
\(445\) | −1.28649 | + | 3.95940i | −0.0609854 | + | 0.187694i | ||||
\(446\) | 11.5229 | − | 35.4637i | 0.545623 | − | 1.67925i | ||||
\(447\) | 19.5862 | − | 14.2302i | 0.926394 | − | 0.673065i | ||||
\(448\) | 5.91123 | + | 4.29476i | 0.279279 | + | 0.202908i | ||||
\(449\) | −9.51919 | − | 29.2971i | −0.449238 | − | 1.38261i | −0.877768 | − | 0.479086i | \(-0.840968\pi\) |
0.428530 | − | 0.903528i | \(-0.359032\pi\) | |||||||
\(450\) | −2.67917 | −0.126297 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.267817 | 0.0125970 | ||||||||
\(453\) | 1.43617 | + | 4.42006i | 0.0674770 | + | 0.207673i | ||||
\(454\) | −25.7610 | − | 18.7165i | −1.20903 | − | 0.878409i | ||||
\(455\) | −0.597473 | + | 0.434090i | −0.0280100 | + | 0.0203504i | ||||
\(456\) | −5.72396 | + | 17.6165i | −0.268049 | + | 0.824970i | ||||
\(457\) | 7.14928 | − | 22.0032i | 0.334429 | − | 1.02927i | −0.632573 | − | 0.774501i | \(-0.718001\pi\) |
0.967002 | − | 0.254767i | \(-0.0819988\pi\) | |||||||
\(458\) | 24.3619 | − | 17.7000i | 1.13836 | − | 0.827065i | ||||
\(459\) | −23.1416 | − | 16.8134i | −1.08016 | − | 0.784781i | ||||
\(460\) | −0.0393899 | − | 0.121230i | −0.00183656 | − | 0.00565236i | ||||
\(461\) | −2.77839 | −0.129403 | −0.0647013 | − | 0.997905i | \(-0.520609\pi\) | ||||
−0.0647013 | + | 0.997905i | \(0.520609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0950 | −1.21274 | −0.606369 | − | 0.795184i | \(-0.707374\pi\) | ||||
−0.606369 | + | 0.795184i | \(0.707374\pi\) | |||||||
\(464\) | −3.59651 | − | 11.0689i | −0.166964 | − | 0.513862i | ||||
\(465\) | 0.790497 | + | 0.574329i | 0.0366584 | + | 0.0266339i | ||||
\(466\) | 0.823574 | − | 0.598362i | 0.0381513 | − | 0.0277186i | ||||
\(467\) | −0.821457 | + | 2.52818i | −0.0380125 | + | 0.116990i | −0.968262 | − | 0.249937i | \(-0.919590\pi\) |
0.930250 | + | 0.366927i | \(0.119590\pi\) | |||||||
\(468\) | 0.0282583 | − | 0.0869700i | 0.00130624 | − | 0.00402019i | ||||
\(469\) | −3.78282 | + | 2.74838i | −0.174675 | + | 0.126908i | ||||
\(470\) | −3.54190 | − | 2.57334i | −0.163376 | − | 0.118699i | ||||
\(471\) | 9.44116 | + | 29.0569i | 0.435026 | + | 1.33887i | ||||
\(472\) | −23.3298 | −1.07384 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.50163 | 0.390493 | ||||||||
\(475\) | −6.23902 | − | 19.2017i | −0.286266 | − | 0.881036i | ||||
\(476\) | 0.639856 | + | 0.464883i | 0.0293278 | + | 0.0213079i | ||||
\(477\) | −4.08039 | + | 2.96458i | −0.186828 | + | 0.135739i | ||||
\(478\) | −0.157077 | + | 0.483433i | −0.00718453 | + | 0.0221117i | ||||
\(479\) | −2.55935 | + | 7.87687i | −0.116940 | + | 0.359904i | −0.992347 | − | 0.123483i | \(-0.960593\pi\) |
0.875407 | + | 0.483387i | \(0.160593\pi\) | |||||||
\(480\) | 0.521822 | − | 0.379126i | 0.0238178 | − | 0.0173047i | ||||
\(481\) | −2.48626 | − | 1.80637i | −0.113364 | − | 0.0823636i | ||||
\(482\) | 4.73059 | + | 14.5593i | 0.215473 | + | 0.663156i | ||||
\(483\) | −2.92064 | −0.132894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.26186 | −0.0572983 | ||||||||
\(486\) | 1.78772 | + | 5.50204i | 0.0810927 | + | 0.249578i | ||||
\(487\) | 15.8531 | + | 11.5180i | 0.718375 | + | 0.521930i | 0.885865 | − | 0.463944i | \(-0.153566\pi\) |
−0.167490 | + | 0.985874i | \(0.553566\pi\) | |||||||
\(488\) | 33.4321 | − | 24.2898i | 1.51340 | − | 1.09955i | ||||
\(489\) | −5.79757 | + | 17.8431i | −0.262175 | + | 0.806892i | ||||
\(490\) | −0.211544 | + | 0.651065i | −0.00955658 | + | 0.0294121i | ||||
\(491\) | 23.2039 | − | 16.8587i | 1.04718 | − | 0.760821i | 0.0755055 | − | 0.997145i | \(-0.475943\pi\) |
0.971674 | + | 0.236325i | \(0.0759430\pi\) | |||||||
\(492\) | −0.206202 | − | 0.149814i | −0.00929629 | − | 0.00675415i | ||||
\(493\) | 4.39285 | + | 13.5198i | 0.197844 | + | 0.608901i | ||||
\(494\) | 9.79837 | 0.440850 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.53735 | −0.248634 | ||||||||
\(497\) | −3.01078 | − | 9.26624i | −0.135052 | − | 0.415648i | ||||
\(498\) | 33.1367 | + | 24.0752i | 1.48489 | + | 1.07884i | ||||
\(499\) | −22.6120 | + | 16.4285i | −1.01225 | + | 0.735443i | −0.964680 | − | 0.263425i | \(-0.915148\pi\) |
−0.0475702 | + | 0.998868i | \(0.515148\pi\) | |||||||
\(500\) | −0.213467 | + | 0.656982i | −0.00954651 | + | 0.0293811i | ||||
\(501\) | −3.16246 | + | 9.73304i | −0.141288 | + | 0.434840i | ||||
\(502\) | −8.30037 | + | 6.03057i | −0.370464 | + | 0.269158i | ||||
\(503\) | 6.55090 | + | 4.75951i | 0.292090 | + | 0.212216i | 0.724174 | − | 0.689618i | \(-0.242221\pi\) |
−0.432083 | + | 0.901834i | \(0.642221\pi\) | |||||||
\(504\) | 0.320054 | + | 0.985026i | 0.0142564 | + | 0.0438765i | ||||
\(505\) | 0.0834428 | 0.00371316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.9833 | 0.754256 | ||||||||
\(508\) | −0.399298 | − | 1.22891i | −0.0177160 | − | 0.0545242i | ||||
\(509\) | −13.1871 | − | 9.58099i | −0.584508 | − | 0.424670i | 0.255839 | − | 0.966720i | \(-0.417648\pi\) |
−0.840346 | + | 0.542050i | \(0.817648\pi\) | |||||||
\(510\) | −4.68428 | + | 3.40333i | −0.207423 | + | 0.150702i | ||||
\(511\) | 4.11611 | − | 12.6681i | 0.182086 | − | 0.560403i | ||||
\(512\) | 6.04250 | − | 18.5969i | 0.267043 | − | 0.821875i | ||||
\(513\) | −18.6907 | + | 13.5796i | −0.825213 | + | 0.599552i | ||||
\(514\) | −11.8049 | − | 8.57677i | −0.520692 | − | 0.378305i | ||||
\(515\) | 2.43417 | + | 7.49161i | 0.107262 | + | 0.330120i | ||||
\(516\) | −2.13187 | −0.0938505 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.84870 | −0.125165 | ||||||||
\(519\) | −0.669532 | − | 2.06061i | −0.0293892 | − | 0.0904506i | ||||
\(520\) | 1.62007 | + | 1.17705i | 0.0710450 | + | 0.0516172i | ||||
\(521\) | −6.21815 | + | 4.51775i | −0.272422 | + | 0.197926i | −0.715605 | − | 0.698505i | \(-0.753849\pi\) |
0.443183 | + | 0.896431i | \(0.353849\pi\) | |||||||
\(522\) | 0.470806 | − | 1.44899i | 0.0206066 | − | 0.0634207i | ||||
\(523\) | 8.07243 | − | 24.8444i | 0.352983 | − | 1.08637i | −0.604187 | − | 0.796842i | \(-0.706502\pi\) |
0.957170 | − | 0.289527i | \(-0.0934979\pi\) | |||||||
\(524\) | 1.18331 | − | 0.859724i | 0.0516931 | − | 0.0375572i | ||||
\(525\) | 6.25993 | + | 4.54811i | 0.273206 | + | 0.198496i | ||||
\(526\) | −6.42717 | − | 19.7808i | −0.280238 | − | 0.862484i | ||||
\(527\) | 6.76343 | 0.294619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7418 | −0.858338 | ||||||||
\(530\) | 2.79332 | + | 8.59694i | 0.121334 | + | 0.373427i | ||||
\(531\) | −2.65875 | − | 1.93169i | −0.115380 | − | 0.0838283i | ||||
\(532\) | 0.516788 | − | 0.375469i | 0.0224056 | − | 0.0162786i | ||||
\(533\) | 0.509070 | − | 1.56676i | 0.0220503 | − | 0.0678637i | ||||
\(534\) | −6.54149 | + | 20.1326i | −0.283078 | + | 0.871225i | ||||
\(535\) | 5.84373 | − | 4.24572i | 0.252646 | − | 0.183558i | ||||
\(536\) | 10.2573 | + | 7.45236i | 0.443047 | + | 0.321893i | ||||
\(537\) | −8.89441 | − | 27.3742i | −0.383822 | − | 1.18128i | ||||
\(538\) | 26.9924 | 1.16372 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.386429 | 0.0166292 | ||||||||
\(541\) | −7.99664 | − | 24.6111i | −0.343802 | − | 1.05811i | −0.962222 | − | 0.272266i | \(-0.912227\pi\) |
0.618420 | − | 0.785848i | \(-0.287773\pi\) | |||||||
\(542\) | 0.866927 | + | 0.629859i | 0.0372377 | + | 0.0270548i | ||||
\(543\) | −1.26160 | + | 0.916606i | −0.0541405 | + | 0.0393353i | ||||
\(544\) | 1.37966 | − | 4.24615i | 0.0591524 | − | 0.182052i | ||||
\(545\) | 1.59154 | − | 4.89826i | 0.0681742 | − | 0.209819i | ||||
\(546\) | −3.03801 | + | 2.20724i | −0.130015 | + | 0.0944613i | ||||
\(547\) | 30.8210 | + | 22.3927i | 1.31781 | + | 0.957445i | 0.999957 | + | 0.00930483i | \(0.00296186\pi\) |
0.317853 | + | 0.948140i | \(0.397038\pi\) | |||||||
\(548\) | −0.655075 | − | 2.01611i | −0.0279834 | − | 0.0861240i | ||||
\(549\) | 5.82122 | 0.248444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4814 | 0.489123 | ||||||||
\(552\) | 2.44724 | + | 7.53183i | 0.104162 | + | 0.320576i | ||||
\(553\) | 2.89815 | + | 2.10563i | 0.123242 | + | 0.0895406i | ||||
\(554\) | 17.8756 | − | 12.9874i | 0.759460 | − | 0.551780i | ||||
\(555\) | 0.453245 | − | 1.39494i | 0.0192392 | − | 0.0592121i | ||||
\(556\) | 0.447803 | − | 1.37819i | 0.0189911 | − | 0.0584485i | ||||
\(557\) | −27.9452 | + | 20.3034i | −1.18408 | + | 0.860282i | −0.992626 | − | 0.121220i | \(-0.961319\pi\) |
−0.191451 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(558\) | −0.586436 | − | 0.426071i | −0.0248258 | − | 0.0180370i | ||||
\(559\) | −4.25799 | − | 13.1047i | −0.180094 | − | 0.554271i | ||||
\(560\) | 1.99748 | 0.0844088 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6883 | 0.661773 | ||||||||
\(563\) | 6.02025 | + | 18.5284i | 0.253723 | + | 0.780880i | 0.994079 | + | 0.108664i | \(0.0346573\pi\) |
−0.740355 | + | 0.672216i | \(0.765343\pi\) | |||||||
\(564\) | −1.26663 | − | 0.920264i | −0.0533349 | − | 0.0387501i | ||||
\(565\) | −0.668371 | + | 0.485600i | −0.0281186 | + | 0.0204293i | ||||
\(566\) | −4.12857 | + | 12.7064i | −0.173537 | + | 0.534091i | ||||
\(567\) | 2.38197 | − | 7.33094i | 0.100033 | − | 0.307870i | ||||
\(568\) | −21.3733 | + | 15.5286i | −0.896804 | + | 0.651566i | ||||
\(569\) | −13.8575 | − | 10.0680i | −0.580935 | − | 0.422074i | 0.258126 | − | 0.966111i | \(-0.416895\pi\) |
−0.839061 | + | 0.544037i | \(0.816895\pi\) | |||||||
\(570\) | 1.44510 | + | 4.44756i | 0.0605286 | + | 0.186288i | ||||
\(571\) | −3.85581 | −0.161360 | −0.0806802 | − | 0.996740i | \(-0.525709\pi\) | ||||
−0.0806802 | + | 0.996740i | \(0.525709\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.0323 | 1.08751 | ||||||||
\(574\) | −0.471883 | − | 1.45231i | −0.0196960 | − | 0.0606181i | ||||
\(575\) | −6.98348 | − | 5.07380i | −0.291231 | − | 0.211592i | ||||
\(576\) | 2.25789 | − | 1.64045i | 0.0940787 | − | 0.0683522i | ||||
\(577\) | −3.02276 | + | 9.30309i | −0.125839 | + | 0.387293i | −0.994053 | − | 0.108897i | \(-0.965268\pi\) |
0.868214 | + | 0.496190i | \(0.165268\pi\) | |||||||
\(578\) | −4.67972 | + | 14.4027i | −0.194651 | + | 0.599073i | ||||
\(579\) | 15.9012 | − | 11.5529i | 0.660832 | − | 0.480123i | ||||
\(580\) | −0.155365 | − | 0.112880i | −0.00645120 | − | 0.00468707i | ||||
\(581\) | 5.33329 | + | 16.4142i | 0.221262 | + | 0.680975i | ||||
\(582\) | −6.41628 | −0.265964 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −36.1178 | −1.49457 | ||||||||
\(585\) | 0.0871702 | + | 0.268282i | 0.00360404 | + | 0.0110921i | ||||
\(586\) | 14.1076 | + | 10.2498i | 0.582780 | + | 0.423415i | ||||
\(587\) | 4.93413 | − | 3.58485i | 0.203653 | − | 0.147963i | −0.481284 | − | 0.876565i | \(-0.659830\pi\) |
0.684937 | + | 0.728602i | \(0.259830\pi\) | |||||||
\(588\) | −0.0756511 | + | 0.232830i | −0.00311980 | + | 0.00960175i | ||||
\(589\) | 1.68803 | − | 5.19522i | 0.0695540 | − | 0.214065i | ||||
\(590\) | −4.76508 | + | 3.46203i | −0.196175 | + | 0.142530i | ||||
\(591\) | −3.01308 | − | 2.18913i | −0.123941 | − | 0.0900487i | ||||
\(592\) | 2.56858 | + | 7.90527i | 0.105568 | + | 0.324904i | ||||
\(593\) | 13.2330 | 0.543413 | 0.271706 | − | 0.962380i | \(-0.412412\pi\) | ||||
0.271706 | + | 0.962380i | \(0.412412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.43976 | −0.100020 | ||||||||
\(596\) | 0.699571 | + | 2.15306i | 0.0286555 | + | 0.0881927i | ||||
\(597\) | 26.5465 | + | 19.2872i | 1.08648 | + | 0.789371i | ||||
\(598\) | 3.38916 | − | 2.46237i | 0.138593 | − | 0.100694i | ||||
\(599\) | −1.83097 | + | 5.63515i | −0.0748115 | + | 0.230246i | −0.981469 | − | 0.191622i | \(-0.938625\pi\) |
0.906657 | + | 0.421868i | \(0.138625\pi\) | |||||||
\(600\) | 6.48352 | − | 19.9542i | 0.264689 | − | 0.814628i | ||||
\(601\) | −10.3075 | + | 7.48886i | −0.420453 | + | 0.305477i | −0.777820 | − | 0.628487i | \(-0.783674\pi\) |
0.357367 | + | 0.933964i | \(0.383674\pi\) | |||||||
\(602\) | −10.3333 | − | 7.50755i | −0.421152 | − | 0.305985i | ||||
\(603\) | 0.551906 | + | 1.69859i | 0.0224754 | + | 0.0691721i | ||||
\(604\) | −0.434590 | −0.0176832 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.424287 | 0.0172355 | ||||||||
\(607\) | 2.58382 | + | 7.95217i | 0.104874 | + | 0.322769i | 0.989701 | − | 0.143151i | \(-0.0457235\pi\) |
−0.884827 | + | 0.465920i | \(0.845724\pi\) | |||||||
\(608\) | −2.91727 | − | 2.11952i | −0.118311 | − | 0.0859581i | ||||
\(609\) | −3.55983 | + | 2.58637i | −0.144252 | + | 0.104805i | ||||
\(610\) | 3.22396 | − | 9.92233i | 0.130534 | − | 0.401743i | ||||
\(611\) | 3.12706 | − | 9.62410i | 0.126507 | − | 0.389350i | ||||
\(612\) | 0.244403 | − | 0.177569i | 0.00987942 | − | 0.00717782i | ||||
\(613\) | 5.40661 | + | 3.92813i | 0.218371 | + | 0.158656i | 0.691593 | − | 0.722287i | \(-0.256909\pi\) |
−0.473222 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(614\) | −1.00653 | − | 3.09778i | −0.0406203 | − | 0.125016i | ||||
\(615\) | 0.786243 | 0.0317044 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8669 | 0.477741 | 0.238871 | − | 0.971051i | \(-0.423223\pi\) | ||||
0.238871 | + | 0.971051i | \(0.423223\pi\) | |||||||
\(618\) | 12.3772 | + | 38.0931i | 0.497883 | + | 1.53233i | ||||
\(619\) | −16.6825 | − | 12.1205i | −0.670524 | − | 0.487165i | 0.199676 | − | 0.979862i | \(-0.436011\pi\) |
−0.870201 | + | 0.492697i | \(0.836011\pi\) | |||||||
\(620\) | −0.0739193 | + | 0.0537055i | −0.00296867 | + | 0.00215686i | ||||
\(621\) | −3.05232 | + | 9.39406i | −0.122485 | + | 0.376971i | ||||
\(622\) | 9.70514 | − | 29.8693i | 0.389141 | − | 1.19765i | ||||
\(623\) | −7.21629 | + | 5.24294i | −0.289114 | + | 0.210054i | ||||
\(624\) | 8.86448 | + | 6.44042i | 0.354863 | + | 0.257823i | ||||
\(625\) | 6.73035 | + | 20.7139i | 0.269214 | + | 0.828556i | ||||
\(626\) | 46.2824 | 1.84982 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.85694 | −0.114004 | ||||||||
\(629\) | −3.13731 | − | 9.65565i | −0.125093 | − | 0.384996i | ||||
\(630\) | 0.211544 | + | 0.153696i | 0.00842811 | + | 0.00612338i | ||||
\(631\) | 12.5232 | − | 9.09861i | 0.498539 | − | 0.362210i | −0.309920 | − | 0.950763i | \(-0.600302\pi\) |
0.808459 | + | 0.588553i | \(0.200302\pi\) | |||||||
\(632\) | 3.00167 | − | 9.23819i | 0.119400 | − | 0.367475i | ||||
\(633\) | −2.68265 | + | 8.25634i | −0.106626 | + | 0.328160i | ||||
\(634\) | −15.6641 | + | 11.3806i | −0.622099 | + | 0.451981i | ||||
\(635\) | 3.22474 | + | 2.34291i | 0.127970 | + | 0.0929756i | ||||
\(636\) | 0.998930 | + | 3.07439i | 0.0396101 | + | 0.121907i | ||||
\(637\) | −1.58232 | −0.0626937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.72153 | −0.147222 | ||||||||
\(640\) | −1.79206 | − | 5.51538i | −0.0708372 | − | 0.218015i | ||||
\(641\) | 19.0754 | + | 13.8591i | 0.753432 | + | 0.547401i | 0.896889 | − | 0.442256i | \(-0.145822\pi\) |
−0.143457 | + | 0.989657i | \(0.545822\pi\) | |||||||
\(642\) | 29.7140 | − | 21.5885i | 1.17272 | − | 0.852029i | ||||
\(643\) | 8.86281 | − | 27.2769i | 0.349515 | − | 1.07570i | −0.609607 | − | 0.792704i | \(-0.708673\pi\) |
0.959122 | − | 0.282993i | \(-0.0913273\pi\) | |||||||
\(644\) | 0.0843952 | − | 0.259742i | 0.00332564 | − | 0.0102353i | ||||
\(645\) | 5.32036 | − | 3.86547i | 0.209489 | − | 0.152203i | ||||
\(646\) | 26.1877 | + | 19.0265i | 1.03034 | + | 0.748587i | ||||
\(647\) | 1.67723 | + | 5.16198i | 0.0659387 | + | 0.202938i | 0.978597 | − | 0.205784i | \(-0.0659744\pi\) |
−0.912659 | + | 0.408722i | \(0.865974\pi\) | |||||||
\(648\) | −20.9011 | −0.821074 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.0986 | −0.435323 | ||||||||
\(651\) | 0.646930 | + | 1.99105i | 0.0253552 | + | 0.0780353i | ||||
\(652\) | −1.41932 | − | 1.03119i | −0.0555847 | − | 0.0403846i | ||||
\(653\) | 9.98496 | − | 7.25450i | 0.390742 | − | 0.283890i | −0.375018 | − | 0.927018i | \(-0.622363\pi\) |
0.765759 | + | 0.643127i | \(0.222363\pi\) | |||||||
\(654\) | 8.09262 | − | 24.9065i | 0.316446 | − | 0.973922i | ||||
\(655\) | −1.39426 | + | 4.29110i | −0.0544784 | + | 0.167667i | ||||
\(656\) | −3.60474 | + | 2.61900i | −0.140741 | + | 0.102255i | ||||
\(657\) | −4.11611 | − | 2.99053i | −0.160585 | − | 0.116672i | ||||
\(658\) | −2.89864 | − | 8.92109i | −0.113001 | − | 0.347780i | ||||
\(659\) | 16.2115 | 0.631512 | 0.315756 | − | 0.948840i | \(-0.397742\pi\) | ||||
0.315756 | + | 0.948840i | \(0.397742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7050 | 1.69993 | 0.849964 | − | 0.526840i | \(-0.176623\pi\) | ||||
0.849964 | + | 0.526840i | \(0.176623\pi\) | |||||||
\(662\) | −4.29519 | − | 13.2192i | −0.166937 | − | 0.513780i | ||||
\(663\) | −10.8272 | − | 7.86645i | −0.420495 | − | 0.305508i | ||||
\(664\) | 37.8606 | − | 27.5073i | 1.46927 | − | 1.06749i | ||||
\(665\) | −0.608919 | + | 1.87406i | −0.0236129 | + | 0.0726730i | ||||
\(666\) | −0.336243 | + | 1.03485i | −0.0130292 | + | 0.0400996i | ||||
\(667\) | 3.97129 | − | 2.88531i | 0.153769 | − | 0.111720i | ||||
\(668\) | −0.774208 | − | 0.562495i | −0.0299550 | − | 0.0217636i | ||||
\(669\) | 12.7115 | + | 39.1220i | 0.491455 | + | 1.51254i | ||||
\(670\) | 3.20093 | 0.123663 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.38197 | 0.0533105 | ||||||||
\(673\) | −1.81115 | − | 5.57416i | −0.0698149 | − | 0.214868i | 0.910062 | − | 0.414473i | \(-0.136034\pi\) |
−0.979876 | + | 0.199605i | \(0.936034\pi\) | |||||||
\(674\) | −22.7842 | − | 16.5537i | −0.877616 | − | 0.637625i | ||||
\(675\) | 21.1709 | − | 15.3815i | 0.814867 | − | 0.592036i | ||||
\(676\) | −0.490753 | + | 1.51038i | −0.0188751 | + | 0.0580916i | ||||
\(677\) | −6.34347 | + | 19.5232i | −0.243799 | + | 0.750338i | 0.752032 | + | 0.659127i | \(0.229074\pi\) |
−0.995832 | + | 0.0912112i | \(0.970926\pi\) | |||||||
\(678\) | −3.39851 | + | 2.46916i | −0.130519 | + | 0.0948275i | ||||
\(679\) | −2.18727 | − | 1.58915i | −0.0839398 | − | 0.0609858i | ||||
\(680\) | 2.04431 | + | 6.29173i | 0.0783955 | + | 0.241277i | ||||
\(681\) | 35.1271 | 1.34607 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.7055 | 1.48103 | 0.740513 | − | 0.672042i | \(-0.234583\pi\) | ||||
0.740513 | + | 0.672042i | \(0.234583\pi\) | |||||||
\(684\) | −0.0753984 | − | 0.232052i | −0.00288293 | − | 0.00887275i | ||||
\(685\) | 5.29040 | + | 3.84370i | 0.202136 | + | 0.146860i | ||||
\(686\) | −1.18661 | + | 0.862123i | −0.0453050 | + | 0.0329160i | ||||
\(687\) | −10.2653 | + | 31.5935i | −0.391647 | + | 1.20537i | ||||
\(688\) | −11.5166 | + | 35.4445i | −0.439067 | + | 1.35131i | ||||
\(689\) | −16.9033 | + | 12.2809i | −0.643963 | + | 0.467867i | ||||
\(690\) | 1.61753 | + | 1.17521i | 0.0615785 | + | 0.0447394i | ||||
\(691\) | −7.14757 | − | 21.9980i | −0.271906 | − | 0.836842i | −0.990021 | − | 0.140917i | \(-0.954995\pi\) |
0.718115 | − | 0.695924i | \(-0.245005\pi\) | |||||||
\(692\) | 0.202603 | 0.00770182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.47105 | −0.169719 | ||||||||
\(695\) | 1.38137 | + | 4.25141i | 0.0523982 | + | 0.161265i | ||||
\(696\) | 9.65264 | + | 7.01306i | 0.365882 | + | 0.265829i | ||||
\(697\) | 4.40290 | − | 3.19889i | 0.166772 | − | 0.121167i | ||||
\(698\) | −8.79119 | + | 27.0565i | −0.332752 | + | 1.02410i | ||||
\(699\) | −0.347028 | + | 1.06804i | −0.0131258 | + | 0.0403971i | ||||
\(700\) | −0.585365 | + | 0.425293i | −0.0221247 | + | 0.0160746i | ||||
\(701\) | −28.7288 | − | 20.8727i | −1.08507 | − | 0.788350i | −0.106510 | − | 0.994312i | \(-0.533968\pi\) |
−0.978560 | + | 0.205962i | \(0.933968\pi\) | |||||||
\(702\) | 3.92449 | + | 12.0783i | 0.148120 | + | 0.455868i | ||||
\(703\) | −8.19985 | −0.309263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.82965 | 0.181895 | ||||||||
\(706\) | 4.87625 | + | 15.0076i | 0.183520 | + | 0.564817i | ||||
\(707\) | 0.144637 | + | 0.105085i | 0.00543963 | + | 0.00395212i | ||||
\(708\) | −1.70406 | + | 1.23807i | −0.0640425 | + | 0.0465296i | ||||
\(709\) | 13.5363 | − | 41.6605i | 0.508367 | − | 1.56459i | −0.286667 | − | 0.958030i | \(-0.592547\pi\) |
0.795035 | − | 0.606564i | \(-0.207453\pi\) | |||||||
\(710\) | −2.06109 | + | 6.34340i | −0.0773515 | + | 0.238063i | ||||
\(711\) | 1.10700 | − | 0.804280i | 0.0415156 | − | 0.0301629i | ||||
\(712\) | 19.5673 | + | 14.2165i | 0.733315 | + | 0.532784i | ||||
\(713\) | −0.721705 | − | 2.22118i | −0.0270281 | − | 0.0831839i | ||||
\(714\) | −12.4056 | −0.464268 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.69149 | 0.100586 | ||||||||
\(717\) | −0.173280 | − | 0.533302i | −0.00647127 | − | 0.0199165i | ||||
\(718\) | 0.720541 | + | 0.523503i | 0.0268903 | + | 0.0195370i | ||||
\(719\) | −12.8314 | + | 9.32255i | −0.478530 | + | 0.347672i | −0.800756 | − | 0.598990i | \(-0.795569\pi\) |
0.322226 | + | 0.946663i | \(0.395569\pi\) | |||||||
\(720\) | 0.235770 | − | 0.725626i | 0.00878664 | − | 0.0270425i | ||||
\(721\) | −5.21535 | + | 16.0512i | −0.194230 | + | 0.597778i | ||||
\(722\) | −1.39474 | + | 1.01333i | −0.0519067 | + | 0.0377124i | ||||
\(723\) | −13.6624 | − | 9.92633i | −0.508111 | − | 0.369164i | ||||
\(724\) | −0.0450613 | − | 0.138685i | −0.00167469 | − | 0.00515417i | ||||
\(725\) | −13.0049 | −0.482992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7719 | 0.510770 | 0.255385 | − | 0.966839i | \(-0.417798\pi\) | ||||
0.255385 | + | 0.966839i | \(0.417798\pi\) | |||||||
\(728\) | 1.32584 | + | 4.08053i | 0.0491390 | + | 0.151234i | ||||
\(729\) | −23.8713 | − | 17.3435i | −0.884123 | − | 0.642353i | ||||
\(730\) | −7.37701 | + | 5.35971i | −0.273035 | + | 0.198372i | ||||
\(731\) | 14.0666 | − | 43.2927i | 0.520273 | − | 1.60124i | ||||
\(732\) | 1.15293 | − | 3.54837i | 0.0426137 | − | 0.131151i | ||||
\(733\) | 15.8306 | − | 11.5016i | 0.584717 | − | 0.424822i | −0.255705 | − | 0.966755i | \(-0.582307\pi\) |
0.840422 | + | 0.541933i | \(0.182307\pi\) | |||||||
\(734\) | 32.8250 | + | 23.8488i | 1.21159 | + | 0.880275i | ||||
\(735\) | −0.233366 | − | 0.718226i | −0.00860783 | − | 0.0264922i | ||||
\(736\) | −1.54170 | −0.0568278 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.583280 | −0.0214708 | ||||||||
\(739\) | −3.44683 | − | 10.6083i | −0.126794 | − | 0.390231i | 0.867430 | − | 0.497560i | \(-0.165770\pi\) |
−0.994224 | + | 0.107328i | \(0.965770\pi\) | |||||||
\(740\) | 0.110960 | + | 0.0806171i | 0.00407897 | + | 0.00296354i | ||||
\(741\) | −8.74477 | + | 6.35345i | −0.321247 | + | 0.233400i | ||||
\(742\) | −5.98484 | + | 18.4195i | −0.219711 | + | 0.676199i | ||||
\(743\) | 6.38273 | − | 19.6440i | 0.234160 | − | 0.720669i | −0.763072 | − | 0.646313i | \(-0.776310\pi\) |
0.997232 | − | 0.0743560i | \(-0.0236901\pi\) | |||||||
\(744\) | 4.59250 | − | 3.33665i | 0.168369 | − | 0.122327i | ||||
\(745\) | −5.64975 | − | 4.10478i | −0.206991 | − | 0.150388i | ||||
\(746\) | 13.3487 | + | 41.0829i | 0.488729 | + | 1.50415i | ||||
\(747\) | 6.59231 | 0.241200 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4762 | 0.565489 | ||||||||
\(750\) | −3.34829 | − | 10.3050i | −0.122262 | − | 0.376284i | ||||
\(751\) | −21.5191 | − | 15.6345i | −0.785243 | − | 0.570513i | 0.121305 | − | 0.992615i | \(-0.461292\pi\) |
−0.906548 | + | 0.422103i | \(0.861292\pi\) | |||||||
\(752\) | −22.1428 | + | 16.0877i | −0.807465 | + | 0.586658i | ||||
\(753\) | 3.49751 | − | 10.7642i | 0.127456 | − | 0.392271i | ||||
\(754\) | 1.95034 | − | 6.00253i | 0.0710273 | − | 0.218599i | ||||
\(755\) | 1.08457 | − | 0.787990i | 0.0394717 | − | 0.0286779i | ||||
\(756\) | 0.669822 | + | 0.486655i | 0.0243612 | + | 0.0176995i | ||||
\(757\) | 6.52024 | + | 20.0672i | 0.236982 | + | 0.729356i | 0.996852 | + | 0.0792809i | \(0.0252624\pi\) |
−0.759870 | + | 0.650075i | \(0.774738\pi\) | |||||||
\(758\) | −37.1723 | −1.35016 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.34311 | 0.193815 | ||||||||
\(761\) | −2.47134 | − | 7.60601i | −0.0895861 | − | 0.275718i | 0.896219 | − | 0.443612i | \(-0.146303\pi\) |
−0.985805 | + | 0.167895i | \(0.946303\pi\) | |||||||
\(762\) | 16.3970 | + | 11.9132i | 0.594002 | + | 0.431568i | ||||
\(763\) | 8.92742 | − | 6.48615i | 0.323194 | − | 0.234814i | ||||
\(764\) | −0.752233 | + | 2.31514i | −0.0272148 | + | 0.0837587i | ||||
\(765\) | −0.287974 | + | 0.886294i | −0.0104117 | + | 0.0320440i | ||||
\(766\) | −37.8911 | + | 27.5295i | −1.36906 | + | 0.994681i | ||||
\(767\) | −11.0140 | − | 8.00215i | −0.397693 | − | 0.288941i | ||||
\(768\) | −1.80550 | − | 5.55675i | −0.0651503 | − | 0.200512i | ||||
\(769\) | −52.0476 | −1.87689 | −0.938443 | − | 0.345435i | \(-0.887731\pi\) | ||||
−0.938443 | + | 0.345435i | \(0.887731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0969 | 0.579716 | ||||||||
\(772\) | 0.567954 | + | 1.74798i | 0.0204411 | + | 0.0629112i | ||||
\(773\) | 1.27905 | + | 0.929285i | 0.0460042 | + | 0.0334240i | 0.610550 | − | 0.791978i | \(-0.290949\pi\) |
−0.564545 | + | 0.825402i | \(0.690949\pi\) | |||||||
\(774\) | −3.94695 | + | 2.86763i | −0.141870 | + | 0.103075i | ||||
\(775\) | −1.91203 | + | 5.88461i | −0.0686820 | + | 0.211382i | ||||
\(776\) | −2.26540 | + | 6.97217i | −0.0813230 | + | 0.250286i | ||||
\(777\) | 2.54238 | − | 1.84715i | 0.0912075 | − | 0.0662661i | ||||
\(778\) | 21.0644 | + | 15.3042i | 0.755194 | + | 0.548681i | ||||
\(779\) | −1.35829 | − | 4.18040i | −0.0486659 | − | 0.149778i | ||||
\(780\) | 0.180798 | 0.00647361 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.8395 | 0.494899 | ||||||||
\(783\) | 4.59858 | + | 14.1530i | 0.164340 | + | 0.505786i | ||||
\(784\) | 3.46236 | + | 2.51555i | 0.123656 | + | 0.0898411i | ||||
\(785\) | 7.12985 | − | 5.18014i | 0.254475 | − | 0.184887i | ||||
\(786\) | −7.08951 | + | 21.8193i | −0.252874 | + | 0.778267i | ||||
\(787\) | 7.22813 | − | 22.2459i | 0.257655 | − | 0.792980i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) |
0.993295 | − | 0.115608i | \(-0.0368815\pi\) | |||||||
\(788\) | 0.281753 | − | 0.204705i | 0.0100370 | − | 0.00729232i | ||||
\(789\) | 18.5623 | + | 13.4863i | 0.660836 | + | 0.480125i | ||||
\(790\) | −0.757817 | − | 2.33232i | −0.0269619 | − | 0.0829803i | ||||
\(791\) | −1.77008 | −0.0629367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.1147 | 0.856339 | ||||||||
\(794\) | 6.03028 | + | 18.5593i | 0.214006 | + | 0.658644i | ||||
\(795\) | −8.06738 | − | 5.86129i | −0.286120 | − | 0.207879i | ||||
\(796\) | −2.48236 | + | 1.80354i | −0.0879849 | + | 0.0639248i | ||||
\(797\) | −14.2617 | + | 43.8930i | −0.505175 | + | 1.55477i | 0.295301 | + | 0.955404i | \(0.404580\pi\) |
−0.800476 | + | 0.599365i | \(0.795420\pi\) | |||||||
\(798\) | −3.09621 | + | 9.52916i | −0.109605 | + | 0.337329i | ||||
\(799\) | 27.0457 | − | 19.6498i | 0.956807 | − | 0.695161i | ||||
\(800\) | 3.30439 | + | 2.40078i | 0.116828 | + | 0.0848804i | ||||
\(801\) | 1.05284 | + | 3.24031i | 0.0372003 | + | 0.114491i | ||||
\(802\) | 5.11834 | 0.180735 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.14470 | 0.0403704 | ||||||||
\(805\) | 0.260339 | + | 0.801242i | 0.00917576 | + | 0.0282401i | ||||
\(806\) | −2.42934 | − | 1.76502i | −0.0855700 | − | 0.0621702i | ||||
\(807\) | −24.0899 | + | 17.5024i | −0.848006 | + | 0.616112i | ||||
\(808\) | 0.149803 | − | 0.461046i | 0.00527005 | − | 0.0162195i | ||||
\(809\) | 10.4294 | − | 32.0983i | 0.366677 | − | 1.12851i | −0.582248 | − | 0.813011i | \(-0.697827\pi\) |
0.948924 | − | 0.315503i | \(-0.102173\pi\) | |||||||
\(810\) | −4.26903 | + | 3.10163i | −0.149998 | + | 0.108980i | ||||
\(811\) | 24.8894 | + | 18.0832i | 0.873985 | + | 0.634987i | 0.931653 | − | 0.363349i | \(-0.118367\pi\) |
−0.0576684 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(812\) | −0.127149 | − | 0.391323i | −0.00446204 | − | 0.0137328i | ||||
\(813\) | −1.18212 | −0.0414588 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.41182 | 0.189568 | ||||||||
\(816\) | 11.1857 | + | 34.4261i | 0.391579 | + | 1.20515i | ||||
\(817\) | −29.7438 | − | 21.6101i | −1.04060 | − | 0.756043i | ||||
\(818\) | −35.1539 | + | 25.5408i | −1.22913 | + | 0.893014i | ||||
\(819\) | −0.186767 | + | 0.574810i | −0.00652617 | + | 0.0200855i | ||||
\(820\) | −0.0227194 | + | 0.0699231i | −0.000793395 | + | 0.00244182i | ||||
\(821\) | −9.77159 | + | 7.09948i | −0.341031 | + | 0.247774i | −0.745097 | − | 0.666956i | \(-0.767597\pi\) |
0.404066 | + | 0.914730i | \(0.367597\pi\) | |||||||
\(822\) | 26.9004 | + | 19.5443i | 0.938260 | + | 0.681686i | ||||
\(823\) | −7.66939 | − | 23.6040i | −0.267338 | − | 0.822782i | −0.991146 | − | 0.132780i | \(-0.957610\pi\) |
0.723807 | − | 0.690002i | \(-0.242390\pi\) | |||||||
\(824\) | 45.7634 | 1.59424 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.6196 | −0.439092 | ||||||||
\(827\) | 1.59864 | + | 4.92010i | 0.0555901 | + | 0.171089i | 0.974997 | − | 0.222220i | \(-0.0713303\pi\) |
−0.919406 | + | 0.393309i | \(0.871330\pi\) | |||||||
\(828\) | −0.0843952 | − | 0.0613167i | −0.00293294 | − | 0.00213090i | ||||
\(829\) | −25.5273 | + | 18.5467i | −0.886601 | + | 0.644153i | −0.934989 | − | 0.354675i | \(-0.884591\pi\) |
0.0483887 | + | 0.998829i | \(0.484591\pi\) | |||||||
\(830\) | 3.65101 | − | 11.2367i | 0.126728 | − | 0.390030i | ||||
\(831\) | −7.53220 | + | 23.1817i | −0.261289 | + | 0.804165i | ||||
\(832\) | 9.35344 | − | 6.79567i | 0.324272 | − | 0.235598i | ||||
\(833\) | −4.22899 | − | 3.07254i | −0.146526 | − | 0.106457i | ||||
\(834\) | 7.02392 | + | 21.6174i | 0.243219 | + | 0.748550i | ||||
\(835\) | 2.95204 | 0.102160 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.08018 | 0.244727 | ||||||||
\(838\) | 5.27815 | + | 16.2445i | 0.182331 | + | 0.561156i | ||||
\(839\) | 4.72176 | + | 3.43056i | 0.163013 | + | 0.118436i | 0.666301 | − | 0.745683i | \(-0.267876\pi\) |
−0.503288 | + | 0.864119i | \(0.667876\pi\) | |||||||
\(840\) | −1.65664 | + | 1.20362i | −0.0571597 | + | 0.0415289i | ||||
\(841\) | −6.67615 | + | 20.5471i | −0.230212 | + | 0.708520i | ||||
\(842\) | −9.01271 | + | 27.7383i | −0.310598 | + | 0.955924i | ||||
\(843\) | −14.0014 | + | 10.1726i | −0.482234 | + | 0.350363i | ||||
\(844\) | −0.656745 | − | 0.477153i | −0.0226061 | − | 0.0164243i | ||||
\(845\) | −1.51386 | − | 4.65917i | −0.0520783 | − | 0.160280i | ||||
\(846\) | −3.58291 | −0.123183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56.5112 | 1.94060 | ||||||||
\(849\) | −4.55445 | − | 14.0172i | −0.156308 | − | 0.481068i | ||||
\(850\) | −29.6628 | − | 21.5513i | −1.01743 | − | 0.739203i | ||||
\(851\) | −2.83624 | + | 2.06065i | −0.0972252 | + | 0.0706382i | ||||
\(852\) | −0.737076 | + | 2.26849i | −0.0252518 | + | 0.0777171i | ||||
\(853\) | −6.28731 | + | 19.3504i | −0.215273 | + | 0.662544i | 0.783861 | + | 0.620937i | \(0.213248\pi\) |
−0.999134 | + | 0.0416068i | \(0.986752\pi\) | |||||||
\(854\) | 18.0841 | − | 13.1389i | 0.618826 | − | 0.449603i | ||||
\(855\) | 0.608919 | + | 0.442406i | 0.0208246 | + | 0.0151300i | ||||
\(856\) | −12.9677 | − | 39.9106i | −0.443228 | − | 1.36411i | ||||
\(857\) | −15.1087 | −0.516104 | −0.258052 | − | 0.966131i | \(-0.583081\pi\) | ||||
−0.258052 | + | 0.966131i | \(0.583081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.9641 | −1.15884 | −0.579420 | − | 0.815029i | \(-0.696721\pi\) | ||||
−0.579420 | + | 0.815029i | \(0.696721\pi\) | |||||||
\(860\) | 0.190031 | + | 0.584854i | 0.00647999 | + | 0.0199434i | ||||
\(861\) | 1.36285 | + | 0.990166i | 0.0464457 | + | 0.0337448i | ||||
\(862\) | 35.8907 | − | 26.0761i | 1.22244 | − | 0.888156i | ||||
\(863\) | −0.858245 | + | 2.64141i | −0.0292150 | + | 0.0899145i | −0.964601 | − | 0.263714i | \(-0.915052\pi\) |
0.935386 | + | 0.353629i | \(0.115052\pi\) | |||||||
\(864\) | 1.44427 | − | 4.44501i | 0.0491351 | − | 0.151222i | ||||
\(865\) | −0.505622 | + | 0.367356i | −0.0171917 | + | 0.0124905i | ||||
\(866\) | −6.77222 | − | 4.92030i | −0.230129 | − | 0.167199i | ||||
\(867\) | −5.16246 | − | 15.8884i | −0.175326 | − | 0.539599i | ||||
\(868\) | −0.195764 | −0.00664466 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.01224 | 0.102125 | ||||||||
\(871\) | 2.28630 | + | 7.03652i | 0.0774685 | + | 0.238423i | ||||
\(872\) | −24.2071 | − | 17.5875i | −0.819756 | − | 0.595587i | ||||
\(873\) | −0.835464 | + | 0.607000i | −0.0282762 | + | 0.0205438i | ||||
\(874\) | 3.45409 | − | 10.6306i | 0.116836 | − | 0.359585i | ||||
\(875\) | 1.41086 | − | 4.34219i | 0.0476958 | − | 0.146793i | ||||
\(876\) | −2.63812 | + | 1.91671i | −0.0891340 | + | 0.0647596i | ||||
\(877\) | −40.1906 | − | 29.2002i | −1.35714 | − | 0.986020i | −0.998621 | − | 0.0524978i | \(-0.983282\pi\) |
−0.358519 | − | 0.933522i | \(-0.616718\pi\) | |||||||
\(878\) | −3.10416 | − | 9.55362i | −0.104760 | − | 0.322419i | ||||
\(879\) | −19.2368 | −0.648841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.3064 | −0.919975 | −0.459988 | − | 0.887925i | \(-0.652146\pi\) | ||||
−0.459988 | + | 0.887925i | \(0.652146\pi\) | |||||||
\(882\) | 0.173124 | + | 0.532822i | 0.00582940 | + | 0.0179410i | ||||
\(883\) | 14.4093 | + | 10.4690i | 0.484913 | + | 0.352310i | 0.803225 | − | 0.595676i | \(-0.203116\pi\) |
−0.318312 | + | 0.947986i | \(0.603116\pi\) | |||||||
\(884\) | 1.01245 | − | 0.735591i | 0.0340525 | − | 0.0247406i | ||||
\(885\) | 2.00785 | − | 6.17954i | 0.0674933 | − | 0.207723i | ||||
\(886\) | −0.0456396 | + | 0.140464i | −0.00153329 | + | 0.00471899i | ||||
\(887\) | 13.3268 | − | 9.68251i | 0.447471 | − | 0.325107i | −0.341125 | − | 0.940018i | \(-0.610808\pi\) |
0.788597 | + | 0.614911i | \(0.210808\pi\) | |||||||
\(888\) | −6.89378 | − | 5.00863i | −0.231340 | − | 0.168078i | ||||
\(889\) | 2.63908 | + | 8.12224i | 0.0885118 | + | 0.272411i | ||||
\(890\) | 6.10625 | 0.204682 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.84656 | −0.128792 | ||||||||
\(893\) | −8.34359 | − | 25.6789i | −0.279208 | − | 0.859313i | ||||
\(894\) | −28.7277 | − | 20.8719i | −0.960797 | − | 0.698060i | ||||
\(895\) | −6.71695 | + | 4.88015i | −0.224523 | + | 0.163125i | ||||
\(896\) | 3.83958 | − | 11.8170i | 0.128271 | − | 0.394779i | ||||
\(897\) | −1.42808 | + | 4.39519i | −0.0476823 | + | 0.146751i | ||||
\(898\) | −36.5532 | + | 26.5575i | −1.21980 | + | 0.886235i | ||||
\(899\) | −2.84662 | − | 2.06819i | −0.0949401 | − | 0.0689780i | ||||
\(900\) | 0.0854037 | + | 0.262845i | 0.00284679 | + | 0.00876152i | ||||
\(901\) | −69.0238 | −2.29952 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.0902 | 0.468891 | ||||||||
\(904\) | 1.48317 | + | 4.56473i | 0.0493295 | + | 0.151821i | ||||
\(905\) | 0.363916 | + | 0.264401i | 0.0120970 | + | 0.00878898i | ||||
\(906\) | 5.51481 | − | 4.00674i | 0.183217 | − | 0.133115i | ||||
\(907\) | 8.80318 | − | 27.0934i | 0.292305 | − | 0.899621i | −0.691809 | − | 0.722081i | \(-0.743186\pi\) |
0.984113 | − | 0.177541i | \(-0.0568141\pi\) | |||||||
\(908\) | −1.01504 | + | 3.12397i | −0.0336852 | + | 0.103673i | ||||
\(909\) | 0.0552464 | − | 0.0401388i | 0.00183241 | − | 0.00133132i | ||||
\(910\) | 0.876333 | + | 0.636693i | 0.0290501 | + | 0.0211062i | ||||
\(911\) | −3.47190 | − | 10.6854i | −0.115029 | − | 0.354023i | 0.876924 | − | 0.480629i | \(-0.159592\pi\) |
−0.991953 | + | 0.126606i | \(0.959592\pi\) | |||||||
\(912\) | 29.2356 | 0.968088 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −33.9337 | −1.12243 | ||||||||
\(915\) | 3.55653 | + | 10.9459i | 0.117575 | + | 0.361860i | ||||
\(916\) | −2.51308 | − | 1.82586i | −0.0830344 | − | 0.0603280i | ||||
\(917\) | −7.82083 | + | 5.68217i | −0.258267 | + | 0.187642i | ||||
\(918\) | −12.9649 | + | 39.9019i | −0.427906 | + | 1.31696i | ||||
\(919\) | 0.241174 | − | 0.742259i | 0.00795561 | − | 0.0244848i | −0.947000 | − | 0.321234i | \(-0.895902\pi\) |
0.954956 | + | 0.296749i | \(0.0959025\pi\) | |||||||
\(920\) | 1.84813 | − | 1.34274i | 0.0609309 | − | 0.0442689i | ||||
\(921\) | 2.90696 | + | 2.11203i | 0.0957876 | + | 0.0695938i | ||||
\(922\) | 1.25929 | + | 3.87570i | 0.0414726 | + | 0.127640i | ||||
\(923\) | −15.4167 | −0.507446 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.28795 | 0.305386 | ||||||||
\(926\) | 11.8274 | + | 36.4011i | 0.388673 | + | 1.19621i | ||||
\(927\) | 5.21535 | + | 3.78917i | 0.171295 | + | 0.124453i | ||||
\(928\) | −1.87911 | + | 1.36525i | −0.0616847 | + | 0.0448166i | ||||
\(929\) | 8.21871 | − | 25.2946i | 0.269647 | − | 0.829889i | −0.720939 | − | 0.692999i | \(-0.756289\pi\) |
0.990586 | − | 0.136890i | \(-0.0437108\pi\) | |||||||
\(930\) | 0.442869 | − | 1.36301i | 0.0145223 | − | 0.0446949i | ||||
\(931\) | −3.41560 | + | 2.48158i | −0.111942 | + | 0.0813306i | ||||
\(932\) | −0.0849566 | − | 0.0617246i | −0.00278285 | − | 0.00202186i | ||||
\(933\) | 10.7063 | + | 32.9505i | 0.350508 | + | 1.07875i | ||||
\(934\) | 3.89900 | 0.127579 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.63883 | 0.0535669 | ||||||||
\(937\) | 12.9693 | + | 39.9155i | 0.423690 | + | 1.30398i | 0.904243 | + | 0.427018i | \(0.140436\pi\) |
−0.480554 | + | 0.876965i | \(0.659564\pi\) | |||||||
\(938\) | 5.54839 | + | 4.03114i | 0.181161 | + | 0.131621i | ||||
\(939\) | −41.3057 | + | 30.0104i | −1.34796 | + | 0.979351i | ||||
\(940\) | −0.139558 | + | 0.429516i | −0.00455189 | + | 0.0140093i | ||||
\(941\) | −15.1520 | + | 46.6331i | −0.493942 | + | 1.52020i | 0.324658 | + | 0.945832i | \(0.394751\pi\) |
−0.818599 | + | 0.574365i | \(0.805249\pi\) | |||||||
\(942\) | 36.2536 | − | 26.3398i | 1.18121 | − | 0.858197i | ||||
\(943\) | −1.52037 | − | 1.10461i | −0.0495101 | − | 0.0359712i | ||||
\(944\) | 11.3787 | + | 35.0199i | 0.370344 | + | 1.13980i | ||||
\(945\) | −2.55402 | −0.0830823 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2953 | −0.886978 | −0.443489 | − | 0.896280i | \(-0.646259\pi\) | ||||
−0.443489 | + | 0.896280i | \(0.646259\pi\) | |||||||
\(948\) | −0.271006 | − | 0.834071i | −0.00880187 | − | 0.0270894i | ||||
\(949\) | −17.0512 | − | 12.3884i | −0.553506 | − | 0.402146i | ||||
\(950\) | −23.9576 | + | 17.4062i | −0.777286 | + | 0.564731i | ||||
\(951\) | 6.60033 | − | 20.3137i | 0.214030 | − | 0.658718i | ||||
\(952\) | −4.38004 | + | 13.4804i | −0.141958 | + | 0.436902i | ||||
\(953\) | −15.9706 | + | 11.6033i | −0.517339 | + | 0.375869i | −0.815601 | − | 0.578615i | \(-0.803593\pi\) |
0.298261 | + | 0.954484i | \(0.403593\pi\) | |||||||
\(954\) | 5.98484 | + | 4.34824i | 0.193766 | + | 0.140780i | ||||
\(955\) | −2.32046 | − | 7.14165i | −0.0750884 | − | 0.231098i | ||||
\(956\) | 0.0524354 | 0.00169588 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.1478 | 0.392478 | ||||||||
\(959\) | 4.32958 | + | 13.3251i | 0.139809 | + | 0.430289i | ||||
\(960\) | 4.46409 | + | 3.24335i | 0.144078 | + | 0.104679i | ||||
\(961\) | 23.7252 | − | 17.2373i | 0.765328 | − | 0.556043i | ||||
\(962\) | −1.39291 | + | 4.28693i | −0.0449091 | + | 0.138216i | ||||
\(963\) | 1.82672 | − | 5.62206i | 0.0588652 | − | 0.181169i | ||||
\(964\) | 1.27757 | − | 0.928210i | 0.0411478 | − | 0.0298956i | ||||
\(965\) | −4.58681 | − | 3.33251i | −0.147655 | − | 0.107277i | ||||
\(966\) | 1.32376 | + | 4.07413i | 0.0425914 | + | 0.131083i | ||||
\(967\) | −12.6734 | −0.407551 | −0.203775 | − | 0.979018i | \(-0.565321\pi\) | ||||
−0.203775 | + | 0.979018i | \(0.565321\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.7089 | −1.14714 | ||||||||
\(970\) | 0.571934 | + | 1.76023i | 0.0183637 | + | 0.0565176i | ||||
\(971\) | −13.5135 | − | 9.81814i | −0.433669 | − | 0.315079i | 0.349445 | − | 0.936957i | \(-0.386370\pi\) |
−0.783114 | + | 0.621878i | \(0.786370\pi\) | |||||||
\(972\) | 0.482803 | − | 0.350777i | 0.0154859 | − | 0.0112512i | ||||
\(973\) | −2.95966 | + | 9.10889i | −0.0948823 | + | 0.292018i | ||||
\(974\) | 8.88160 | − | 27.3347i | 0.284585 | − | 0.875862i | ||||
\(975\) | 9.90519 | − | 7.19654i | 0.317220 | − | 0.230474i | ||||
\(976\) | −52.7669 | − | 38.3374i | −1.68903 | − | 1.22715i | ||||
\(977\) | 8.45013 | + | 26.0068i | 0.270344 | + | 0.832032i | 0.990414 | + | 0.138131i | \(0.0441096\pi\) |
−0.720070 | + | 0.693901i | \(0.755890\pi\) | |||||||
\(978\) | 27.5178 | 0.879924 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.0706175 | 0.00225579 | ||||||||
\(981\) | −1.30249 | − | 4.00866i | −0.0415854 | − | 0.127987i | ||||
\(982\) | −34.0340 | − | 24.7271i | −1.08607 | − | 0.789074i | ||||
\(983\) | 44.5012 | − | 32.3320i | 1.41937 | − | 1.03123i | 0.427492 | − | 0.904019i | \(-0.359397\pi\) |
0.991876 | − | 0.127212i | \(-0.0406028\pi\) | |||||||
\(984\) | 1.41152 | − | 4.34422i | 0.0449977 | − | 0.138489i | ||||
\(985\) | −0.331982 | + | 1.02174i | −0.0105778 | + | 0.0325552i | ||||
\(986\) | 16.8683 | − | 12.2556i | 0.537197 | − | 0.390297i | ||||
\(987\) | 8.37155 | + | 6.08229i | 0.266469 | + | 0.193601i | ||||
\(988\) | −0.312342 | − | 0.961291i | −0.00993693 | − | 0.0305827i | ||||
\(989\) | −15.7188 | −0.499828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.2327 | 1.69099 | 0.845497 | − | 0.533980i | \(-0.179304\pi\) | ||||
0.845497 | + | 0.533980i | \(0.179304\pi\) | |||||||
\(992\) | 0.341491 | + | 1.05100i | 0.0108424 | + | 0.0333693i | ||||
\(993\) | 12.4049 | + | 9.01272i | 0.393659 | + | 0.286010i | ||||
\(994\) | −11.5613 | + | 8.39976i | −0.366701 | + | 0.266424i | ||||
\(995\) | 2.92490 | − | 9.00193i | 0.0927257 | − | 0.285380i | ||||
\(996\) | 1.30565 | − | 4.01839i | 0.0413712 | − | 0.127327i | ||||
\(997\) | −26.4990 | + | 19.2527i | −0.839232 | + | 0.609738i | −0.922156 | − | 0.386818i | \(-0.873574\pi\) |
0.0829239 | + | 0.996556i | \(0.473574\pi\) | |||||||
\(998\) | 33.1657 | + | 24.0963i | 1.04984 | + | 0.762754i | ||||
\(999\) | −3.28424 | − | 10.1079i | −0.103909 | − | 0.319798i |
(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 | 847.2.f.p.148.1 | 8 | ||
11.2 | odd | 10 | 847.2.f.s.372.2 | 8 | |||
11.3 | even | 5 | 847.2.a.l.1.1 | 4 | |||
11.4 | even | 5 | 77.2.f.a.36.2 | yes | 8 | ||
11.5 | even | 5 | 77.2.f.a.15.2 | ✓ | 8 | ||
11.6 | odd | 10 | 847.2.f.q.323.1 | 8 | |||
11.7 | odd | 10 | 847.2.f.q.729.1 | 8 | |||
11.8 | odd | 10 | 847.2.a.k.1.4 | 4 | |||
11.9 | even | 5 | inner | 847.2.f.p.372.1 | 8 | ||
11.10 | odd | 2 | 847.2.f.s.148.2 | 8 | |||
33.5 | odd | 10 | 693.2.m.g.631.1 | 8 | |||
33.8 | even | 10 | 7623.2.a.co.1.1 | 4 | |||
33.14 | odd | 10 | 7623.2.a.ch.1.4 | 4 | |||
33.26 | odd | 10 | 693.2.m.g.190.1 | 8 | |||
77.4 | even | 15 | 539.2.q.c.520.2 | 16 | |||
77.5 | odd | 30 | 539.2.q.b.312.2 | 16 | |||
77.16 | even | 15 | 539.2.q.c.312.2 | 16 | |||
77.26 | odd | 30 | 539.2.q.b.410.1 | 16 | |||
77.27 | odd | 10 | 539.2.f.d.246.2 | 8 | |||
77.37 | even | 15 | 539.2.q.c.410.1 | 16 | |||
77.38 | odd | 30 | 539.2.q.b.422.1 | 16 | |||
77.41 | even | 10 | 5929.2.a.bb.1.4 | 4 | |||
77.48 | odd | 10 | 539.2.f.d.344.2 | 8 | |||
77.59 | odd | 30 | 539.2.q.b.520.2 | 16 | |||
77.60 | even | 15 | 539.2.q.c.422.1 | 16 | |||
77.69 | odd | 10 | 5929.2.a.bi.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.2 | ✓ | 8 | 11.5 | even | 5 | ||
77.2.f.a.36.2 | yes | 8 | 11.4 | even | 5 | ||
539.2.f.d.246.2 | 8 | 77.27 | odd | 10 | |||
539.2.f.d.344.2 | 8 | 77.48 | odd | 10 | |||
539.2.q.b.312.2 | 16 | 77.5 | odd | 30 | |||
539.2.q.b.410.1 | 16 | 77.26 | odd | 30 | |||
539.2.q.b.422.1 | 16 | 77.38 | odd | 30 | |||
539.2.q.b.520.2 | 16 | 77.59 | odd | 30 | |||
539.2.q.c.312.2 | 16 | 77.16 | even | 15 | |||
539.2.q.c.410.1 | 16 | 77.37 | even | 15 | |||
539.2.q.c.422.1 | 16 | 77.60 | even | 15 | |||
539.2.q.c.520.2 | 16 | 77.4 | even | 15 | |||
693.2.m.g.190.1 | 8 | 33.26 | odd | 10 | |||
693.2.m.g.631.1 | 8 | 33.5 | odd | 10 | |||
847.2.a.k.1.4 | 4 | 11.8 | odd | 10 | |||
847.2.a.l.1.1 | 4 | 11.3 | even | 5 | |||
847.2.f.p.148.1 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.p.372.1 | 8 | 11.9 | even | 5 | inner | ||
847.2.f.q.323.1 | 8 | 11.6 | odd | 10 | |||
847.2.f.q.729.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.s.148.2 | 8 | 11.10 | odd | 2 | |||
847.2.f.s.372.2 | 8 | 11.2 | odd | 10 | |||
5929.2.a.bb.1.4 | 4 | 77.41 | even | 10 | |||
5929.2.a.bi.1.1 | 4 | 77.69 | odd | 10 | |||
7623.2.a.ch.1.4 | 4 | 33.14 | odd | 10 | |||
7623.2.a.co.1.1 | 4 | 33.8 | even | 10 |