Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(26,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.h (of order \(5\), degree \(4\), 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: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} - 256 x^{7} + 472 x^{6} - 48 x^{5} + 432 x^{4} + 88 x^{3} + 128 x^{2} + 64 x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 126.1 | ||
Root | \(0.545543 - 1.67901i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.126 |
Dual form | 275.2.h.c.251.1 |
$q$-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 \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.854560 | − | 2.63006i | −0.604265 | − | 1.85974i | −0.501766 | − | 0.865004i | \(-0.667316\pi\) |
−0.102499 | − | 0.994733i | \(-0.532684\pi\) | |||||||
\(3\) | −1.32800 | − | 0.964848i | −0.766721 | − | 0.557055i | 0.134244 | − | 0.990948i | \(-0.457139\pi\) |
−0.900964 | + | 0.433893i | \(0.857139\pi\) | |||||||
\(4\) | −4.56893 | + | 3.31953i | −2.28447 | + | 1.65976i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.40276 | + | 4.31724i | −0.572673 | + | 1.76251i | ||||
\(7\) | −1.53545 | + | 1.11557i | −0.580346 | + | 0.421646i | −0.838849 | − | 0.544365i | \(-0.816771\pi\) |
0.258503 | + | 0.966010i | \(0.416771\pi\) | |||||||
\(8\) | 8.16046 | + | 5.92892i | 2.88516 | + | 2.09619i | ||||
\(9\) | −0.0944009 | − | 0.290536i | −0.0314670 | − | 0.0968453i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.102720 | + | 3.31503i | 0.0309712 | + | 0.999520i | ||||
\(12\) | 9.27038 | 2.67613 | ||||||||
\(13\) | −0.638270 | − | 1.96439i | −0.177024 | − | 0.544825i | 0.822696 | − | 0.568482i | \(-0.192469\pi\) |
−0.999720 | + | 0.0236571i | \(0.992469\pi\) | |||||||
\(14\) | 4.24616 | + | 3.08501i | 1.13483 | + | 0.824504i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.12949 | − | 15.7870i | 1.28237 | − | 3.94674i | ||||
\(17\) | −1.12040 | + | 3.44822i | −0.271736 | + | 0.836317i | 0.718329 | + | 0.695704i | \(0.244907\pi\) |
−0.990065 | + | 0.140613i | \(0.955093\pi\) | |||||||
\(18\) | −0.683457 | + | 0.496561i | −0.161092 | + | 0.117040i | ||||
\(19\) | 1.03575 | + | 0.752517i | 0.237618 | + | 0.172639i | 0.700221 | − | 0.713926i | \(-0.253085\pi\) |
−0.462604 | + | 0.886565i | \(0.653085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.11543 | 0.679843 | ||||||||
\(22\) | 8.63097 | − | 3.10305i | 1.84013 | − | 0.661573i | ||||
\(23\) | −3.36725 | −0.702121 | −0.351061 | − | 0.936353i | \(-0.614179\pi\) | ||||
−0.351061 | + | 0.936353i | \(0.614179\pi\) | |||||||
\(24\) | −5.11658 | − | 15.7472i | −1.04442 | − | 3.21438i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.62104 | + | 3.35738i | −0.906261 | + | 0.658437i | ||||
\(27\) | −1.67671 | + | 5.16038i | −0.322683 | + | 0.993116i | ||||
\(28\) | 3.31221 | − | 10.1939i | 0.625949 | − | 1.92647i | ||||
\(29\) | −0.910336 | + | 0.661398i | −0.169045 | + | 0.122819i | −0.669091 | − | 0.743180i | \(-0.733316\pi\) |
0.500046 | + | 0.865999i | \(0.333316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.42251 | + | 4.37805i | 0.255491 | + | 0.786321i | 0.993732 | + | 0.111784i | \(0.0356566\pi\) |
−0.738241 | + | 0.674537i | \(0.764343\pi\) | |||||||
\(32\) | −25.7304 | −4.54853 | ||||||||
\(33\) | 3.06209 | − | 4.50147i | 0.533042 | − | 0.783605i | ||||
\(34\) | 10.0265 | 1.71953 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.39575 | + | 1.01407i | 0.232625 | + | 0.169012i | ||||
\(37\) | −1.45794 | + | 1.05926i | −0.239684 | + | 0.174141i | −0.701142 | − | 0.713021i | \(-0.747326\pi\) |
0.461459 | + | 0.887162i | \(0.347326\pi\) | |||||||
\(38\) | 1.09406 | − | 3.36716i | 0.177480 | − | 0.546226i | ||||
\(39\) | −1.04772 | + | 3.22455i | −0.167769 | + | 0.516341i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.73360 | − | 2.71262i | −0.583090 | − | 0.423639i | 0.256747 | − | 0.966479i | \(-0.417349\pi\) |
−0.839837 | + | 0.542839i | \(0.817349\pi\) | |||||||
\(42\) | −2.66232 | − | 8.19379i | −0.410805 | − | 1.26433i | ||||
\(43\) | 0.0110430 | 0.00168404 | 0.000842018 | − | 1.00000i | \(-0.499732\pi\) | ||||
0.000842018 | 1.00000i | \(0.499732\pi\) | ||||||||
\(44\) | −11.4737 | − | 14.8052i | −1.72972 | − | 2.23197i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.87752 | + | 8.85610i | 0.424267 | + | 1.30576i | ||||
\(47\) | 7.46408 | + | 5.42297i | 1.08875 | + | 0.791022i | 0.979187 | − | 0.202958i | \(-0.0650556\pi\) |
0.109561 | + | 0.993980i | \(0.465056\pi\) | |||||||
\(48\) | −22.0440 | + | 16.0159i | −3.18177 | + | 2.31169i | ||||
\(49\) | −1.05001 | + | 3.23159i | −0.150001 | + | 0.461656i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.81489 | − | 3.49822i | 0.674220 | − | 0.489849i | ||||
\(52\) | 9.43707 | + | 6.85643i | 1.30869 | + | 0.950816i | ||||
\(53\) | 2.02220 | + | 6.22368i | 0.277770 | + | 0.854888i | 0.988473 | + | 0.151396i | \(0.0483769\pi\) |
−0.710703 | + | 0.703492i | \(0.751623\pi\) | |||||||
\(54\) | 15.0050 | 2.04192 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.1441 | −2.55824 | ||||||||
\(57\) | −0.649412 | − | 1.99868i | −0.0860167 | − | 0.264732i | ||||
\(58\) | 2.51746 | + | 1.82904i | 0.330558 | + | 0.240165i | ||||
\(59\) | −4.43142 | + | 3.21961i | −0.576921 | + | 0.419158i | −0.837613 | − | 0.546264i | \(-0.816049\pi\) |
0.260692 | + | 0.965422i | \(0.416049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.27166 | − | 6.99144i | 0.290856 | − | 0.895162i | −0.693726 | − | 0.720239i | \(-0.744032\pi\) |
0.984582 | − | 0.174923i | \(-0.0559678\pi\) | |||||||
\(62\) | 10.2989 | − | 7.48261i | 1.30797 | − | 0.950293i | ||||
\(63\) | 0.469061 | + | 0.340793i | 0.0590962 | + | 0.0429359i | ||||
\(64\) | 11.7292 | + | 36.0987i | 1.46615 | + | 4.51234i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.4559 | − | 4.20672i | −1.77940 | − | 0.517812i | ||||
\(67\) | −7.01002 | −0.856410 | −0.428205 | − | 0.903682i | \(-0.640854\pi\) | ||||
−0.428205 | + | 0.903682i | \(0.640854\pi\) | |||||||
\(68\) | −6.32745 | − | 19.4739i | −0.767316 | − | 2.36155i | ||||
\(69\) | 4.47171 | + | 3.24889i | 0.538331 | + | 0.391120i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.68735 | + | 11.3485i | −0.437607 | + | 1.34682i | 0.452783 | + | 0.891621i | \(0.350431\pi\) |
−0.890391 | + | 0.455197i | \(0.849569\pi\) | |||||||
\(72\) | 0.952211 | − | 2.93060i | 0.112219 | − | 0.345375i | ||||
\(73\) | −2.44810 | + | 1.77865i | −0.286529 | + | 0.208175i | −0.721760 | − | 0.692143i | \(-0.756667\pi\) |
0.435231 | + | 0.900319i | \(0.356667\pi\) | |||||||
\(74\) | 4.03181 | + | 2.92928i | 0.468688 | + | 0.340522i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.23028 | −0.829370 | ||||||||
\(77\) | −3.85587 | − | 4.97548i | −0.439418 | − | 0.567009i | ||||
\(78\) | 9.37610 | 1.06163 | ||||||||
\(79\) | −1.89180 | − | 5.82235i | −0.212844 | − | 0.655066i | −0.999300 | − | 0.0374192i | \(-0.988086\pi\) |
0.786456 | − | 0.617646i | \(-0.211914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.46422 | − | 4.69653i | 0.718247 | − | 0.521837i | ||||
\(82\) | −3.94377 | + | 12.1377i | −0.435517 | + | 1.34038i | ||||
\(83\) | −4.52716 | + | 13.9332i | −0.496921 | + | 1.52936i | 0.317021 | + | 0.948418i | \(0.397317\pi\) |
−0.813942 | + | 0.580946i | \(0.802683\pi\) | |||||||
\(84\) | −14.2342 | + | 10.3418i | −1.55308 | + | 1.12838i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.00943687 | − | 0.0290437i | −0.00101760 | − | 0.00313186i | ||||
\(87\) | 1.84707 | 0.198027 | ||||||||
\(88\) | −18.8163 | + | 27.6612i | −2.00583 | + | 2.94870i | ||||
\(89\) | −13.8156 | −1.46445 | −0.732227 | − | 0.681060i | \(-0.761519\pi\) | ||||
−0.732227 | + | 0.681060i | \(0.761519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.17145 | + | 2.30419i | 0.332458 | + | 0.241545i | ||||
\(92\) | 15.3848 | − | 11.1777i | 1.60397 | − | 1.16535i | ||||
\(93\) | 2.33505 | − | 7.18656i | 0.242134 | − | 0.745211i | ||||
\(94\) | 7.88426 | − | 24.2653i | 0.813200 | − | 2.50277i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 34.1699 | + | 24.8259i | 3.48745 | + | 2.53378i | ||||
\(97\) | −5.34722 | − | 16.4571i | −0.542928 | − | 1.67096i | −0.725866 | − | 0.687836i | \(-0.758561\pi\) |
0.182938 | − | 0.983124i | \(-0.441439\pi\) | |||||||
\(98\) | 9.39658 | 0.949198 | ||||||||
\(99\) | 0.953440 | − | 0.342786i | 0.0958243 | − | 0.0344513i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.60266 | − | 14.1655i | −0.457982 | − | 1.40952i | −0.867599 | − | 0.497265i | \(-0.834338\pi\) |
0.409617 | − | 0.912258i | \(-0.365662\pi\) | |||||||
\(102\) | −13.3152 | − | 9.67404i | −1.31840 | − | 0.957873i | ||||
\(103\) | −0.344090 | + | 0.249996i | −0.0339042 | + | 0.0246329i | −0.604608 | − | 0.796523i | \(-0.706670\pi\) |
0.570704 | + | 0.821156i | \(0.306670\pi\) | |||||||
\(104\) | 6.43816 | − | 19.8146i | 0.631313 | − | 1.94298i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.6406 | − | 10.6370i | 1.42202 | − | 1.03316i | ||||
\(107\) | −6.82802 | − | 4.96085i | −0.660090 | − | 0.479583i | 0.206603 | − | 0.978425i | \(-0.433759\pi\) |
−0.866693 | + | 0.498841i | \(0.833759\pi\) | |||||||
\(108\) | −9.46924 | − | 29.1433i | −0.911178 | − | 2.80432i | ||||
\(109\) | 0.922589 | 0.0883680 | 0.0441840 | − | 0.999023i | \(-0.485931\pi\) | ||||
0.0441840 | + | 0.999023i | \(0.485931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.95816 | 0.280776 | ||||||||
\(112\) | 9.73537 | + | 29.9624i | 0.919906 | + | 2.83118i | ||||
\(113\) | −2.19418 | − | 1.59417i | −0.206411 | − | 0.149967i | 0.479777 | − | 0.877390i | \(-0.340718\pi\) |
−0.686189 | + | 0.727424i | \(0.740718\pi\) | |||||||
\(114\) | −4.70171 | + | 3.41599i | −0.440355 | + | 0.319937i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.96374 | − | 6.04377i | 0.182329 | − | 0.561150i | ||||
\(117\) | −0.510474 | + | 0.370881i | −0.0471933 | + | 0.0342880i | ||||
\(118\) | 12.2547 | + | 8.90356i | 1.12814 | + | 0.819639i | ||||
\(119\) | −2.12642 | − | 6.54445i | −0.194929 | − | 0.599929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9789 | + | 0.681040i | −0.998082 | + | 0.0619127i | ||||
\(122\) | −20.3292 | −1.84052 | ||||||||
\(123\) | 2.34095 | + | 7.20470i | 0.211076 | + | 0.649626i | ||||
\(124\) | −21.0324 | − | 15.2809i | −1.88877 | − | 1.37227i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.495467 | − | 1.52489i | 0.0441397 | − | 0.135848i | ||||
\(127\) | −2.51456 | + | 7.73903i | −0.223131 | + | 0.686728i | 0.775345 | + | 0.631539i | \(0.217576\pi\) |
−0.998476 | + | 0.0551893i | \(0.982424\pi\) | |||||||
\(128\) | 43.2860 | − | 31.4491i | 3.82598 | − | 2.77973i | ||||
\(129\) | −0.0146650 | − | 0.0106548i | −0.00129118 | − | 0.000938101i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.69256 | 0.235250 | 0.117625 | − | 0.993058i | \(-0.462472\pi\) | ||||
0.117625 | + | 0.993058i | \(0.462472\pi\) | |||||||
\(132\) | 0.952252 | + | 30.7316i | 0.0828829 | + | 2.67484i | ||||
\(133\) | −2.42983 | −0.210693 | ||||||||
\(134\) | 5.99048 | + | 18.4368i | 0.517498 | + | 1.59270i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.5872 | + | 21.4963i | −2.53708 | + | 1.84330i | ||||
\(137\) | 2.62279 | − | 8.07211i | 0.224080 | − | 0.689647i | −0.774304 | − | 0.632814i | \(-0.781900\pi\) |
0.998384 | − | 0.0568330i | \(-0.0181003\pi\) | |||||||
\(138\) | 4.72344 | − | 14.5373i | 0.402086 | − | 1.23749i | ||||
\(139\) | 17.8961 | − | 13.0023i | 1.51793 | − | 1.10284i | 0.555427 | − | 0.831565i | \(-0.312555\pi\) |
0.962502 | − | 0.271275i | \(-0.0874452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.67995 | − | 14.4034i | −0.394123 | − | 1.21299i | ||||
\(142\) | 32.9983 | 2.76916 | ||||||||
\(143\) | 6.44647 | − | 2.31767i | 0.539081 | − | 0.193813i | ||||
\(144\) | −5.07091 | −0.422575 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.77002 | + | 4.91871i | 0.560291 | + | 0.407075i | ||||
\(147\) | 4.51240 | − | 3.27845i | 0.372176 | − | 0.270402i | ||||
\(148\) | 3.14501 | − | 9.67934i | 0.258518 | − | 0.795637i | ||||
\(149\) | −4.96839 | + | 15.2911i | −0.407026 | + | 1.25270i | 0.512165 | + | 0.858887i | \(0.328844\pi\) |
−0.919191 | + | 0.393811i | \(0.871156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7865 | − | 13.6492i | −1.52882 | − | 1.11075i | −0.956889 | − | 0.290454i | \(-0.906194\pi\) |
−0.571933 | − | 0.820300i | \(-0.693806\pi\) | |||||||
\(152\) | 3.99059 | + | 12.2818i | 0.323680 | + | 0.996183i | ||||
\(153\) | 1.10760 | 0.0895441 | ||||||||
\(154\) | −9.79076 | + | 14.3930i | −0.788962 | + | 1.15982i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.91700 | − | 18.2107i | −0.473740 | − | 1.45802i | ||||
\(157\) | 13.1364 | + | 9.54418i | 1.04840 | + | 0.761709i | 0.971908 | − | 0.235361i | \(-0.0756274\pi\) |
0.0764941 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(158\) | −13.6965 | + | 9.95109i | −1.08964 | + | 0.791666i | ||||
\(159\) | 3.31943 | − | 10.2162i | 0.263248 | − | 0.810194i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.17025 | − | 3.75641i | 0.407473 | − | 0.296047i | ||||
\(162\) | −17.8762 | − | 12.9878i | −1.40449 | − | 1.02042i | ||||
\(163\) | 3.78855 | + | 11.6599i | 0.296742 | + | 0.913277i | 0.982631 | + | 0.185571i | \(0.0594136\pi\) |
−0.685889 | + | 0.727706i | \(0.740586\pi\) | |||||||
\(164\) | 26.0631 | 2.03519 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 40.5139 | 3.14449 | ||||||||
\(167\) | 1.95812 | + | 6.02648i | 0.151524 | + | 0.466343i | 0.997792 | − | 0.0664141i | \(-0.0211558\pi\) |
−0.846268 | + | 0.532757i | \(0.821156\pi\) | |||||||
\(168\) | 25.4234 | + | 18.4712i | 1.96146 | + | 1.42508i | ||||
\(169\) | 7.06577 | − | 5.13358i | 0.543521 | − | 0.394891i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.120858 | − | 0.371961i | 0.00924221 | − | 0.0284446i | ||||
\(172\) | −0.0504546 | + | 0.0366574i | −0.00384712 | + | 0.00279510i | ||||
\(173\) | 1.70469 | + | 1.23853i | 0.129605 | + | 0.0941637i | 0.650699 | − | 0.759336i | \(-0.274476\pi\) |
−0.521094 | + | 0.853499i | \(0.674476\pi\) | |||||||
\(174\) | −1.57844 | − | 4.85792i | −0.119661 | − | 0.368278i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 52.8612 | + | 15.3828i | 3.98456 | + | 1.15952i | ||||
\(177\) | 8.99135 | 0.675831 | ||||||||
\(178\) | 11.8063 | + | 36.3360i | 0.884919 | + | 2.72350i | ||||
\(179\) | 7.90157 | + | 5.74083i | 0.590591 | + | 0.429090i | 0.842527 | − | 0.538654i | \(-0.181067\pi\) |
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.97245 | + | 18.3813i | −0.443928 | + | 1.36627i | 0.439726 | + | 0.898132i | \(0.355076\pi\) |
−0.883655 | + | 0.468139i | \(0.844924\pi\) | |||||||
\(182\) | 3.34999 | − | 10.3102i | 0.248317 | − | 0.764242i | ||||
\(183\) | −9.76243 | + | 7.09282i | −0.721660 | + | 0.524317i | ||||
\(184\) | −27.4784 | − | 19.9642i | −2.02573 | − | 1.47178i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.8965 | −1.53221 | ||||||||
\(187\) | −11.5461 | − | 3.35995i | −0.844331 | − | 0.245704i | ||||
\(188\) | −52.1046 | −3.80012 | ||||||||
\(189\) | −3.18226 | − | 9.79400i | −0.231476 | − | 0.712409i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7719 | + | 8.55279i | −0.851785 | + | 0.618858i | −0.925638 | − | 0.378411i | \(-0.876471\pi\) |
0.0738525 | + | 0.997269i | \(0.476471\pi\) | |||||||
\(192\) | 19.2534 | − | 59.2559i | 1.38950 | − | 4.27643i | ||||
\(193\) | 6.86801 | − | 21.1376i | 0.494370 | − | 1.52151i | −0.323566 | − | 0.946206i | \(-0.604882\pi\) |
0.817936 | − | 0.575309i | \(-0.195118\pi\) | |||||||
\(194\) | −38.7136 | + | 28.1271i | −2.77947 | + | 2.01941i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.92993 | − | 18.2504i | −0.423566 | − | 1.30360i | ||||
\(197\) | 9.00781 | 0.641780 | 0.320890 | − | 0.947116i | \(-0.396018\pi\) | ||||
0.320890 | + | 0.947116i | \(0.396018\pi\) | |||||||
\(198\) | −1.71632 | − | 2.21468i | −0.121974 | − | 0.157390i | ||||
\(199\) | 0.459925 | 0.0326032 | 0.0163016 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0163016 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.30929 | + | 6.76360i | 0.656627 | + | 0.477067i | ||||
\(202\) | −33.3230 | + | 24.2106i | −2.34460 | + | 1.70345i | ||||
\(203\) | 0.659941 | − | 2.03109i | 0.0463187 | − | 0.142554i | ||||
\(204\) | −10.3865 | + | 31.9663i | −0.727199 | + | 2.23809i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.951553 | + | 0.691343i | 0.0662978 | + | 0.0481682i | ||||
\(207\) | 0.317872 | + | 0.978309i | 0.0220936 | + | 0.0679972i | ||||
\(208\) | −34.2858 | −2.37729 | ||||||||
\(209\) | −2.38823 | + | 3.51085i | −0.165197 | + | 0.242850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.242564 | + | 0.746536i | 0.0166988 | + | 0.0513936i | 0.959059 | − | 0.283207i | \(-0.0913985\pi\) |
−0.942360 | + | 0.334601i | \(0.891398\pi\) | |||||||
\(212\) | −29.8989 | − | 21.7229i | −2.05347 | − | 1.49193i | ||||
\(213\) | 15.8463 | − | 11.5130i | 1.08577 | − | 0.788861i | ||||
\(214\) | −7.21240 | + | 22.1975i | −0.493029 | + | 1.51739i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −44.2782 | + | 32.1700i | −3.01275 | + | 2.18889i | ||||
\(217\) | −7.06822 | − | 5.13536i | −0.479822 | − | 0.348611i | ||||
\(218\) | −0.788407 | − | 2.42647i | −0.0533977 | − | 0.164341i | ||||
\(219\) | 4.96721 | 0.335653 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.48878 | 0.503750 | ||||||||
\(222\) | −2.52793 | − | 7.78016i | −0.169663 | − | 0.522170i | ||||
\(223\) | −10.8039 | − | 7.84950i | −0.723483 | − | 0.525641i | 0.164012 | − | 0.986458i | \(-0.447556\pi\) |
−0.887495 | + | 0.460817i | \(0.847556\pi\) | |||||||
\(224\) | 39.5077 | − | 28.7041i | 2.63972 | − | 1.91787i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.31770 | + | 7.13316i | −0.154171 | + | 0.474491i | ||||
\(227\) | 13.9787 | − | 10.1561i | 0.927801 | − | 0.674087i | −0.0176523 | − | 0.999844i | \(-0.505619\pi\) |
0.945453 | + | 0.325757i | \(0.105619\pi\) | |||||||
\(228\) | 9.60180 | + | 6.97612i | 0.635895 | + | 0.462005i | ||||
\(229\) | 3.64367 | + | 11.2141i | 0.240780 | + | 0.741045i | 0.996302 | + | 0.0859217i | \(0.0273835\pi\) |
−0.755522 | + | 0.655124i | \(0.772616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.320017 | + | 10.3278i | 0.0210556 | + | 0.679517i | ||||
\(232\) | −11.3501 | −0.745173 | ||||||||
\(233\) | −0.780690 | − | 2.40272i | −0.0511447 | − | 0.157407i | 0.922222 | − | 0.386661i | \(-0.126372\pi\) |
−0.973367 | + | 0.229254i | \(0.926372\pi\) | |||||||
\(234\) | 1.41167 | + | 1.02564i | 0.0922838 | + | 0.0670481i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.55927 | − | 29.4204i | 0.622255 | − | 1.91510i | ||||
\(237\) | −3.10538 | + | 9.55737i | −0.201716 | + | 0.620818i | ||||
\(238\) | −15.3952 | + | 11.1853i | −0.997922 | + | 0.725032i | ||||
\(239\) | −20.0190 | − | 14.5446i | −1.29492 | − | 0.940815i | −0.295028 | − | 0.955489i | \(-0.595329\pi\) |
−0.999892 | + | 0.0146739i | \(0.995329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8935 | 1.21704 | 0.608520 | − | 0.793539i | \(-0.291764\pi\) | ||||
0.608520 | + | 0.793539i | \(0.291764\pi\) | |||||||
\(242\) | 11.1733 | + | 28.2932i | 0.718247 | + | 1.81876i | ||||
\(243\) | 3.16193 | 0.202838 | ||||||||
\(244\) | 12.8292 | + | 39.4843i | 0.821306 | + | 2.52772i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16.9484 | − | 12.3137i | 1.08059 | − | 0.785093i | ||||
\(247\) | 0.817151 | − | 2.51493i | 0.0519941 | − | 0.160021i | ||||
\(248\) | −14.3487 | + | 44.1609i | −0.911146 | + | 2.80422i | ||||
\(249\) | 19.4555 | − | 14.1352i | 1.23294 | − | 0.895783i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.11446 | + | 3.42996i | 0.0703443 | + | 0.216497i | 0.980048 | − | 0.198760i | \(-0.0636915\pi\) |
−0.909704 | + | 0.415258i | \(0.863691\pi\) | |||||||
\(252\) | −3.27438 | −0.206267 | ||||||||
\(253\) | −0.345884 | − | 11.1626i | −0.0217455 | − | 0.701784i | ||||
\(254\) | 22.5030 | 1.41196 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −58.2889 | − | 42.3493i | −3.64305 | − | 2.64683i | ||||
\(257\) | 10.6382 | − | 7.72911i | 0.663593 | − | 0.482129i | −0.204281 | − | 0.978912i | \(-0.565486\pi\) |
0.867874 | + | 0.496784i | \(0.165486\pi\) | |||||||
\(258\) | −0.0154906 | + | 0.0476752i | −0.000964402 | + | 0.00296813i | ||||
\(259\) | 1.05692 | − | 3.25287i | 0.0656739 | − | 0.202123i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.278096 | + | 0.202049i | 0.0172137 | + | 0.0125065i | ||||
\(262\) | −2.30096 | − | 7.08162i | −0.142154 | − | 0.437504i | ||||
\(263\) | −6.24673 | −0.385190 | −0.192595 | − | 0.981278i | \(-0.561690\pi\) | ||||
−0.192595 | + | 0.981278i | \(0.561690\pi\) | |||||||
\(264\) | 51.6769 | − | 18.5792i | 3.18050 | − | 1.14347i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.07644 | + | 6.39061i | 0.127314 | + | 0.391834i | ||||
\(267\) | 18.3472 | + | 13.3300i | 1.12283 | + | 0.815782i | ||||
\(268\) | 32.0283 | − | 23.2699i | 1.95644 | − | 1.42144i | ||||
\(269\) | −6.92064 | + | 21.2995i | −0.421959 | + | 1.29866i | 0.483918 | + | 0.875114i | \(0.339213\pi\) |
−0.905876 | + | 0.423542i | \(0.860787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.00497 | − | 5.08941i | 0.425521 | − | 0.309159i | −0.354334 | − | 0.935119i | \(-0.615292\pi\) |
0.779856 | + | 0.625959i | \(0.215292\pi\) | |||||||
\(272\) | 48.6899 | + | 35.3752i | 2.95226 | + | 2.14494i | ||||
\(273\) | −1.98849 | − | 6.11994i | −0.120349 | − | 0.370395i | ||||
\(274\) | −23.4715 | −1.41797 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −31.2157 | −1.87897 | ||||||||
\(277\) | 0.804194 | + | 2.47505i | 0.0483193 | + | 0.148712i | 0.972305 | − | 0.233715i | \(-0.0750884\pi\) |
−0.923986 | + | 0.382427i | \(0.875088\pi\) | |||||||
\(278\) | −49.4902 | − | 35.9567i | −2.96822 | − | 2.15654i | ||||
\(279\) | 1.13769 | − | 0.826583i | 0.0681120 | − | 0.0494862i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.39755 | + | 19.6896i | −0.381646 | + | 1.17459i | 0.557238 | + | 0.830353i | \(0.311861\pi\) |
−0.938884 | + | 0.344233i | \(0.888139\pi\) | |||||||
\(282\) | −33.8826 | + | 24.6171i | −2.01768 | + | 1.46593i | ||||
\(283\) | 8.74594 | + | 6.35430i | 0.519892 | + | 0.377724i | 0.816563 | − | 0.577256i | \(-0.195877\pi\) |
−0.296671 | + | 0.954980i | \(0.595877\pi\) | |||||||
\(284\) | −20.8243 | − | 64.0907i | −1.23570 | − | 3.80308i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.6045 | − | 14.9740i | −0.686189 | − | 0.885434i | ||||
\(287\) | 8.75886 | 0.517019 | ||||||||
\(288\) | 2.42897 | + | 7.47560i | 0.143128 | + | 0.440504i | ||||
\(289\) | 3.11834 | + | 2.26561i | 0.183432 | + | 0.133271i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.77745 | + | 27.0142i | −0.514543 | + | 1.58360i | ||||
\(292\) | 5.28095 | − | 16.2531i | 0.309044 | − | 0.951140i | ||||
\(293\) | 0.423178 | − | 0.307457i | 0.0247223 | − | 0.0179618i | −0.575355 | − | 0.817903i | \(-0.695136\pi\) |
0.600078 | + | 0.799942i | \(0.295136\pi\) | |||||||
\(294\) | −12.4787 | − | 9.06627i | −0.727770 | − | 0.528756i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.1777 | −1.05656 | ||||||||
\(297\) | −17.2791 | − | 5.02828i | −1.00263 | − | 0.291770i | ||||
\(298\) | 44.4624 | 2.57564 | ||||||||
\(299\) | 2.14922 | + | 6.61461i | 0.124292 | + | 0.382533i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0169559 | + | 0.0123192i | −0.000977323 | + | 0.000710067i | ||||
\(302\) | −19.8440 | + | 61.0737i | −1.14190 | + | 3.51440i | ||||
\(303\) | −7.55525 | + | 23.2527i | −0.434038 | + | 1.33583i | ||||
\(304\) | 17.1928 | − | 12.4913i | 0.986076 | − | 0.716426i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.946510 | − | 2.91306i | −0.0541083 | − | 0.166528i | ||||
\(307\) | −20.0401 | −1.14375 | −0.571873 | − | 0.820342i | \(-0.693783\pi\) | ||||
−0.571873 | + | 0.820342i | \(0.693783\pi\) | |||||||
\(308\) | 34.1335 | + | 9.93297i | 1.94493 | + | 0.565983i | ||||
\(309\) | 0.698160 | 0.0397169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3892 | + | 9.00127i | 0.702527 | + | 0.510415i | 0.880754 | − | 0.473574i | \(-0.157036\pi\) |
−0.178227 | + | 0.983989i | \(0.557036\pi\) | |||||||
\(312\) | −27.6679 | + | 20.1019i | −1.56639 | + | 1.13805i | ||||
\(313\) | 8.78365 | − | 27.0333i | 0.496481 | − | 1.52801i | −0.318154 | − | 0.948039i | \(-0.603063\pi\) |
0.814635 | − | 0.579974i | \(-0.196937\pi\) | |||||||
\(314\) | 13.8759 | − | 42.7058i | 0.783065 | − | 2.41003i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.9709 | + | 20.3221i | 1.57349 | + | 1.14321i | ||||
\(317\) | 5.82421 | + | 17.9251i | 0.327120 | + | 1.00677i | 0.970474 | + | 0.241204i | \(0.0775424\pi\) |
−0.643354 | + | 0.765569i | \(0.722458\pi\) | |||||||
\(318\) | −29.7058 | −1.66582 | ||||||||
\(319\) | −2.28607 | − | 2.94986i | −0.127995 | − | 0.165160i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.28114 | + | 13.1760i | 0.238950 | + | 0.735413i | ||||
\(322\) | −14.2979 | − | 10.3880i | −0.796790 | − | 0.578902i | ||||
\(323\) | −3.75530 | + | 2.72838i | −0.208950 | + | 0.151811i | ||||
\(324\) | −13.9443 | + | 42.9163i | −0.774686 | + | 2.38424i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.4289 | − | 19.9282i | 1.51914 | − | 1.10372i | ||||
\(327\) | −1.22520 | − | 0.890158i | −0.0677535 | − | 0.0492258i | ||||
\(328\) | −14.3850 | − | 44.2724i | −0.794277 | − | 2.44453i | ||||
\(329\) | −17.5104 | −0.965381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0888 | −0.664461 | −0.332230 | − | 0.943198i | \(-0.607801\pi\) | ||||
−0.332230 | + | 0.943198i | \(0.607801\pi\) | |||||||
\(332\) | −25.5672 | − | 78.6878i | −1.40318 | − | 4.31855i | ||||
\(333\) | 0.445383 | + | 0.323589i | 0.0244068 | + | 0.0177326i | ||||
\(334\) | 14.1767 | − | 10.3000i | 0.775715 | − | 0.563590i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.9806 | − | 49.1832i | 0.871812 | − | 2.68316i | ||||
\(337\) | 18.8783 | − | 13.7159i | 1.02837 | − | 0.747151i | 0.0603846 | − | 0.998175i | \(-0.480767\pi\) |
0.967981 | + | 0.251024i | \(0.0807673\pi\) | |||||||
\(338\) | −19.5398 | − | 14.1965i | −1.06282 | − | 0.772186i | ||||
\(339\) | 1.37574 | + | 4.23411i | 0.0747202 | + | 0.229965i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.3673 | + | 5.16540i | −0.778031 | + | 0.279722i | ||||
\(342\) | −1.08156 | −0.0584842 | ||||||||
\(343\) | −6.09826 | − | 18.7685i | −0.329275 | − | 1.01340i | ||||
\(344\) | 0.0901157 | + | 0.0654729i | 0.00485871 | + | 0.00353006i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.80065 | − | 5.54185i | 0.0968038 | − | 0.297931i | ||||
\(347\) | 6.37801 | − | 19.6295i | 0.342389 | − | 1.05377i | −0.620577 | − | 0.784145i | \(-0.713102\pi\) |
0.962967 | − | 0.269621i | \(-0.0868983\pi\) | |||||||
\(348\) | −8.43916 | + | 6.13141i | −0.452387 | + | 0.328678i | ||||
\(349\) | 20.6326 | + | 14.9904i | 1.10444 | + | 0.802419i | 0.981778 | − | 0.190030i | \(-0.0608585\pi\) |
0.122657 | + | 0.992449i | \(0.460859\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.2072 | 0.598197 | ||||||||
\(352\) | −2.64302 | − | 85.2971i | −0.140874 | − | 4.54635i | ||||
\(353\) | −3.41010 | −0.181501 | −0.0907506 | − | 0.995874i | \(-0.528927\pi\) | ||||
−0.0907506 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(354\) | −7.68365 | − | 23.6478i | −0.408381 | − | 1.25687i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 63.1227 | − | 45.8614i | 3.34550 | − | 2.43065i | ||||
\(357\) | −3.49052 | + | 10.7427i | −0.184738 | + | 0.568564i | ||||
\(358\) | 8.34638 | − | 25.6875i | 0.441120 | − | 1.35763i | ||||
\(359\) | −3.86662 | + | 2.80926i | −0.204072 | + | 0.148267i | −0.685128 | − | 0.728423i | \(-0.740254\pi\) |
0.481055 | + | 0.876690i | \(0.340254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.36482 | − | 16.5112i | −0.282359 | − | 0.869012i | ||||
\(362\) | 53.4478 | 2.80916 | ||||||||
\(363\) | 15.2371 | + | 9.68854i | 0.799738 | + | 0.508517i | ||||
\(364\) | −22.1390 | −1.16040 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 26.9972 | + | 19.6146i | 1.41116 | + | 1.02527i | ||||
\(367\) | −10.6250 | + | 7.71953i | −0.554622 | + | 0.402956i | −0.829487 | − | 0.558526i | \(-0.811367\pi\) |
0.274865 | + | 0.961483i | \(0.411367\pi\) | |||||||
\(368\) | −17.2723 | + | 53.1587i | −0.900381 | + | 2.77109i | ||||
\(369\) | −0.435658 | + | 1.34082i | −0.0226794 | + | 0.0698001i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0479 | − | 7.30025i | −0.521663 | − | 0.379010i | ||||
\(372\) | 13.1872 | + | 40.5862i | 0.683727 | + | 2.10429i | ||||
\(373\) | −24.9476 | −1.29174 | −0.645869 | − | 0.763448i | \(-0.723505\pi\) | ||||
−0.645869 | + | 0.763448i | \(0.723505\pi\) | |||||||
\(374\) | 1.02992 | + | 33.2382i | 0.0532559 | + | 1.71870i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.7580 | + | 88.5079i | 1.48308 | + | 4.56445i | ||||
\(377\) | 1.88029 | + | 1.36611i | 0.0968397 | + | 0.0703582i | ||||
\(378\) | −23.0394 | + | 16.7391i | −1.18502 | + | 0.860968i | ||||
\(379\) | −0.630173 | + | 1.93947i | −0.0323698 | + | 0.0996240i | −0.965936 | − | 0.258781i | \(-0.916679\pi\) |
0.933566 | + | 0.358405i | \(0.116679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.8063 | − | 7.85125i | 0.553625 | − | 0.402232i | ||||
\(382\) | 32.5542 | + | 23.6520i | 1.66562 | + | 1.21014i | ||||
\(383\) | 9.94983 | + | 30.6224i | 0.508413 | + | 1.56473i | 0.794957 | + | 0.606666i | \(0.207493\pi\) |
−0.286544 | + | 0.958067i | \(0.592507\pi\) | |||||||
\(384\) | −87.8273 | −4.48192 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −61.4623 | −3.12835 | ||||||||
\(387\) | −0.00104247 | − | 0.00320838i | −5.29915e−5 | − | 0.000163091i | ||||
\(388\) | 79.0607 | + | 57.4410i | 4.01370 | + | 2.91612i | ||||
\(389\) | −2.25775 | + | 1.64035i | −0.114473 | + | 0.0831692i | −0.643549 | − | 0.765405i | \(-0.722539\pi\) |
0.529076 | + | 0.848574i | \(0.322539\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.77266 | − | 11.6110i | 0.190791 | − | 0.587196i | ||||
\(392\) | −27.7284 | + | 20.1458i | −1.40049 | + | 1.01752i | ||||
\(393\) | −3.57572 | − | 2.59791i | −0.180371 | − | 0.131047i | ||||
\(394\) | −7.69772 | − | 23.6911i | −0.387805 | − | 1.19354i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.21832 | + | 4.73113i | −0.161727 | + | 0.237748i | ||||
\(397\) | 26.6387 | 1.33696 | 0.668480 | − | 0.743730i | \(-0.266945\pi\) | ||||
0.668480 | + | 0.743730i | \(0.266945\pi\) | |||||||
\(398\) | −0.393033 | − | 1.20963i | −0.0197010 | − | 0.0606333i | ||||
\(399\) | 3.22681 | + | 2.34442i | 0.161543 | + | 0.117368i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.62283 | + | 17.3053i | −0.280791 | + | 0.864186i | 0.706838 | + | 0.707376i | \(0.250121\pi\) |
−0.987629 | + | 0.156810i | \(0.949879\pi\) | |||||||
\(402\) | 9.83335 | − | 30.2639i | 0.490443 | − | 1.50943i | ||||
\(403\) | 7.69226 | − | 5.58876i | 0.383179 | − | 0.278396i | ||||
\(404\) | 68.0521 | + | 49.4427i | 3.38572 | + | 2.45987i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.90585 | −0.293103 | ||||||||
\(407\) | −3.66123 | − | 4.72431i | −0.181480 | − | 0.234176i | ||||
\(408\) | 60.0324 | 2.97205 | ||||||||
\(409\) | 2.34693 | + | 7.22312i | 0.116048 | + | 0.357160i | 0.992164 | − | 0.124940i | \(-0.0398740\pi\) |
−0.876116 | + | 0.482101i | \(0.839874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.2714 | + | 8.18916i | −0.555978 | + | 0.403942i | ||||
\(412\) | 0.742258 | − | 2.28443i | 0.0365684 | − | 0.112546i | ||||
\(413\) | 3.21252 | − | 9.88711i | 0.158078 | − | 0.486513i | ||||
\(414\) | 2.30137 | − | 1.67205i | 0.113106 | − | 0.0821766i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.4229 | + | 50.5446i | 0.805201 | + | 2.47815i | ||||
\(417\) | −36.3113 | −1.77817 | ||||||||
\(418\) | 11.2746 | + | 3.28096i | 0.551461 | + | 0.160477i | ||||
\(419\) | 29.8323 | 1.45740 | 0.728701 | − | 0.684832i | \(-0.240125\pi\) | ||||
0.728701 | + | 0.684832i | \(0.240125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4942 | − | 14.8899i | −0.998828 | − | 0.725691i | −0.0369918 | − | 0.999316i | \(-0.511778\pi\) |
−0.961837 | + | 0.273624i | \(0.911778\pi\) | |||||||
\(422\) | 1.75615 | − | 1.27592i | 0.0854881 | − | 0.0621108i | ||||
\(423\) | 0.870953 | − | 2.68052i | 0.0423472 | − | 0.130331i | ||||
\(424\) | −20.3977 | + | 62.7775i | −0.990598 | + | 3.04875i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −43.8217 | − | 31.8383i | −2.12317 | − | 1.54257i | ||||
\(427\) | 4.31143 | + | 13.2692i | 0.208645 | + | 0.642142i | ||||
\(428\) | 47.6644 | 2.30395 | ||||||||
\(429\) | −10.7971 | − | 3.14200i | −0.521289 | − | 0.151697i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.34030 | − | 19.5134i | −0.305401 | − | 0.939929i | −0.979527 | − | 0.201312i | \(-0.935479\pi\) |
0.674126 | − | 0.738617i | \(-0.264521\pi\) | |||||||
\(432\) | 72.8660 | + | 52.9403i | 3.50577 | + | 2.54709i | ||||
\(433\) | −11.1286 | + | 8.08542i | −0.534807 | + | 0.388560i | −0.822153 | − | 0.569267i | \(-0.807227\pi\) |
0.287346 | + | 0.957827i | \(0.407227\pi\) | |||||||
\(434\) | −7.46612 | + | 22.9784i | −0.358385 | + | 1.10300i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.21525 | + | 3.06256i | −0.201874 | + | 0.146670i | ||||
\(437\) | −3.48764 | − | 2.53392i | −0.166836 | − | 0.121214i | ||||
\(438\) | −4.24478 | − | 13.0641i | −0.202823 | − | 0.624226i | ||||
\(439\) | −24.1841 | −1.15425 | −0.577123 | − | 0.816657i | \(-0.695825\pi\) | ||||
−0.577123 | + | 0.816657i | \(0.695825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.03801 | 0.0494293 | ||||||||
\(442\) | −6.39961 | − | 19.6960i | −0.304398 | − | 0.936842i | ||||
\(443\) | −1.37342 | − | 0.997848i | −0.0652532 | − | 0.0474092i | 0.554680 | − | 0.832063i | \(-0.312840\pi\) |
−0.619934 | + | 0.784654i | \(0.712840\pi\) | |||||||
\(444\) | −13.5157 | + | 9.81970i | −0.641425 | + | 0.466022i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.4121 | + | 35.1228i | −0.540379 | + | 1.66311i | ||||
\(447\) | 21.3516 | − | 15.5129i | 1.00990 | − | 0.733733i | ||||
\(448\) | −58.2802 | − | 42.3430i | −2.75348 | − | 2.00052i | ||||
\(449\) | 0.804184 | + | 2.47502i | 0.0379518 | + | 0.116804i | 0.968238 | − | 0.250032i | \(-0.0804412\pi\) |
−0.930286 | + | 0.366836i | \(0.880441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.60890 | − | 12.6556i | 0.405377 | − | 0.595931i | ||||
\(452\) | 15.3170 | 0.720449 | ||||||||
\(453\) | 11.7790 | + | 36.2522i | 0.553428 | + | 1.70328i | ||||
\(454\) | −38.6570 | − | 28.0859i | −1.81426 | − | 1.31814i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.55054 | − | 20.1605i | 0.306757 | − | 0.944102i | ||||
\(457\) | −4.31421 | + | 13.2778i | −0.201810 | + | 0.621108i | 0.798019 | + | 0.602632i | \(0.205881\pi\) |
−0.999829 | + | 0.0184756i | \(0.994119\pi\) | |||||||
\(458\) | 26.3800 | − | 19.1662i | 1.23265 | − | 0.895576i | ||||
\(459\) | −15.9156 | − | 11.5633i | −0.742875 | − | 0.539730i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5365 | 1.23593 | 0.617963 | − | 0.786207i | \(-0.287958\pi\) | ||||
0.617963 | + | 0.786207i | \(0.287958\pi\) | |||||||
\(462\) | 26.8892 | − | 9.66736i | 1.25100 | − | 0.449766i | ||||
\(463\) | −23.6363 | −1.09847 | −0.549237 | − | 0.835667i | \(-0.685081\pi\) | ||||
−0.549237 | + | 0.835667i | \(0.685081\pi\) | |||||||
\(464\) | 5.77190 | + | 17.7641i | 0.267954 | + | 0.824676i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.65215 | + | 4.10653i | −0.261831 | + | 0.190231i | ||||
\(467\) | −3.12854 | + | 9.62866i | −0.144772 | + | 0.445561i | −0.996982 | − | 0.0776386i | \(-0.975262\pi\) |
0.852210 | + | 0.523200i | \(0.175262\pi\) | |||||||
\(468\) | 1.10117 | − | 3.38906i | 0.0509017 | − | 0.156659i | ||||
\(469\) | 10.7635 | − | 7.82016i | 0.497014 | − | 0.361102i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.23650 | − | 25.3493i | −0.379518 | − | 1.16804i | ||||
\(472\) | −55.2512 | −2.54314 | ||||||||
\(473\) | 0.00113433 | + | 0.0366078i | 5.21566e−5 | + | 0.00168323i | ||||
\(474\) | 27.7902 | 1.27645 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 31.4400 | + | 22.8425i | 1.44105 | + | 1.04698i | ||||
\(477\) | 1.61731 | − | 1.17504i | 0.0740513 | − | 0.0538015i | ||||
\(478\) | −21.1459 | + | 65.0805i | −0.967192 | + | 2.97671i | ||||
\(479\) | 0.210601 | − | 0.648162i | 0.00962259 | − | 0.0296153i | −0.946130 | − | 0.323787i | \(-0.895044\pi\) |
0.955753 | + | 0.294172i | \(0.0950438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.01135 | + | 2.18788i | 0.137306 | + | 0.0997586i | ||||
\(482\) | −16.1457 | − | 49.6912i | −0.735414 | − | 2.26337i | ||||
\(483\) | −10.4905 | −0.477332 | ||||||||
\(484\) | 47.9011 | − | 39.5564i | 2.17732 | − | 1.79802i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.70206 | − | 8.31608i | −0.122568 | − | 0.377225i | ||||
\(487\) | −8.59541 | − | 6.24493i | −0.389495 | − | 0.282985i | 0.375754 | − | 0.926720i | \(-0.377384\pi\) |
−0.765249 | + | 0.643735i | \(0.777384\pi\) | |||||||
\(488\) | 59.9895 | − | 43.5849i | 2.71560 | − | 1.97300i | ||||
\(489\) | 6.21889 | − | 19.1398i | 0.281228 | − | 0.865530i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.34180 | − | 6.78722i | 0.421590 | − | 0.306303i | −0.356687 | − | 0.934224i | \(-0.616094\pi\) |
0.778277 | + | 0.627921i | \(0.216094\pi\) | |||||||
\(492\) | −34.6118 | − | 25.1470i | −1.56042 | − | 1.13371i | ||||
\(493\) | −1.26071 | − | 3.88007i | −0.0567796 | − | 0.174750i | ||||
\(494\) | −7.31274 | −0.329016 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 76.4128 | 3.43104 | ||||||||
\(497\) | −6.99829 | − | 21.5385i | −0.313916 | − | 0.966135i | ||||
\(498\) | −53.8024 | − | 39.0897i | −2.41094 | − | 1.75165i | ||||
\(499\) | 7.47146 | − | 5.42833i | 0.334469 | − | 0.243006i | −0.407856 | − | 0.913046i | \(-0.633723\pi\) |
0.742324 | + | 0.670041i | \(0.233723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.21425 | − | 9.89246i | 0.143602 | − | 0.441962i | ||||
\(502\) | 8.06865 | − | 5.86222i | 0.360122 | − | 0.261644i | ||||
\(503\) | 15.6117 | + | 11.3426i | 0.696092 | + | 0.505740i | 0.878657 | − | 0.477453i | \(-0.158440\pi\) |
−0.182565 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(504\) | 1.80722 | + | 5.56205i | 0.0805000 | + | 0.247754i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −29.0627 | + | 10.4488i | −1.29199 | + | 0.464505i | ||||
\(507\) | −14.3365 | −0.636704 | ||||||||
\(508\) | −14.2010 | − | 43.7063i | −0.630069 | − | 1.93915i | ||||
\(509\) | −2.62203 | − | 1.90502i | −0.116219 | − | 0.0844384i | 0.528157 | − | 0.849147i | \(-0.322883\pi\) |
−0.644377 | + | 0.764708i | \(0.722883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.77473 | − | 5.46206i | 0.0785095 | − | 0.241627i | ||||
\(512\) | −28.5026 | + | 87.7221i | −1.25965 | + | 3.87681i | ||||
\(513\) | −5.61993 | + | 4.08312i | −0.248126 | + | 0.180274i | ||||
\(514\) | −29.4190 | − | 21.3742i | −1.29762 | − | 0.942775i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.102372 | 0.00450669 | ||||||||
\(517\) | −17.2106 | + | 25.3007i | −0.756922 | + | 1.11272i | ||||
\(518\) | −9.45846 | −0.415581 | ||||||||
\(519\) | −1.06883 | − | 3.28953i | −0.0469166 | − | 0.144395i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.45689 | − | 6.87083i | 0.414314 | − | 0.301017i | −0.361032 | − | 0.932553i | \(-0.617576\pi\) |
0.775346 | + | 0.631537i | \(0.217576\pi\) | |||||||
\(522\) | 0.293752 | − | 0.904075i | 0.0128572 | − | 0.0395703i | ||||
\(523\) | −3.39708 | + | 10.4551i | −0.148544 | + | 0.457171i | −0.997450 | − | 0.0713730i | \(-0.977262\pi\) |
0.848906 | + | 0.528544i | \(0.177262\pi\) | |||||||
\(524\) | −12.3021 | + | 8.93803i | −0.537422 | + | 0.390460i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.33821 | + | 16.4293i | 0.232757 | + | 0.716352i | ||||
\(527\) | −16.6903 | −0.727039 | ||||||||
\(528\) | −55.3575 | − | 71.4313i | −2.40913 | − | 3.10865i | ||||
\(529\) | −11.6616 | −0.507026 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.35374 | + | 0.983552i | 0.0587474 | + | 0.0426825i | ||||
\(532\) | 11.1017 | − | 8.06588i | 0.481321 | − | 0.349700i | ||||
\(533\) | −2.94560 | + | 9.06563i | −0.127588 | + | 0.392676i | ||||
\(534\) | 19.3800 | − | 59.6455i | 0.838654 | − | 2.58111i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −57.2050 | − | 41.5618i | −2.47088 | − | 1.79520i | ||||
\(537\) | −4.95425 | − | 15.2476i | −0.213792 | − | 0.657984i | ||||
\(538\) | 61.9333 | 2.67013 | ||||||||
\(539\) | −10.8207 | − | 3.14886i | −0.466080 | − | 0.135631i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.93398 | − | 21.3406i | −0.298115 | − | 0.917504i | −0.982157 | − | 0.188061i | \(-0.939780\pi\) |
0.684042 | − | 0.729442i | \(-0.260220\pi\) | |||||||
\(542\) | −19.3716 | − | 14.0743i | −0.832083 | − | 0.604544i | ||||
\(543\) | 25.6666 | − | 18.6478i | 1.10146 | − | 0.800256i | ||||
\(544\) | 28.8282 | − | 88.7241i | 1.23600 | − | 3.80401i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.3965 | + | 10.4597i | −0.616115 | + | 0.447634i | ||||
\(547\) | −21.6722 | − | 15.7458i | −0.926638 | − | 0.673242i | 0.0185290 | − | 0.999828i | \(-0.494102\pi\) |
−0.945167 | + | 0.326586i | \(0.894102\pi\) | |||||||
\(548\) | 14.8122 | + | 45.5874i | 0.632747 | + | 1.94740i | ||||
\(549\) | −2.24571 | −0.0958446 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.44060 | −0.0613714 | ||||||||
\(552\) | 17.2288 | + | 53.0248i | 0.733307 | + | 2.25689i | ||||
\(553\) | 9.40000 | + | 6.82950i | 0.399729 | + | 0.290420i | ||||
\(554\) | 5.82232 | − | 4.23016i | 0.247367 | − | 0.179722i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −38.6048 | + | 118.813i | −1.63721 | + | 5.03880i | ||||
\(557\) | −4.99921 | + | 3.63214i | −0.211824 | + | 0.153899i | −0.688638 | − | 0.725105i | \(-0.741791\pi\) |
0.476815 | + | 0.879004i | \(0.341791\pi\) | |||||||
\(558\) | −3.14620 | − | 2.28584i | −0.133189 | − | 0.0967675i | ||||
\(559\) | −0.00704839 | − | 0.0216927i | −0.000298115 | − | 0.000917504i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0913 | + | 15.6022i | 0.510496 | + | 0.658725i | ||||
\(562\) | 57.2521 | 2.41503 | ||||||||
\(563\) | −9.10209 | − | 28.0133i | −0.383607 | − | 1.18062i | −0.937486 | − | 0.348024i | \(-0.886853\pi\) |
0.553878 | − | 0.832598i | \(-0.313147\pi\) | |||||||
\(564\) | 69.1948 | + | 50.2730i | 2.91363 | + | 2.11687i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.23828 | − | 28.4325i | 0.388314 | − | 1.19511i | ||||
\(567\) | −4.68618 | + | 14.4226i | −0.196801 | + | 0.605691i | ||||
\(568\) | −97.3747 | + | 70.7469i | −4.08575 | + | 2.96847i | ||||
\(569\) | −31.0867 | − | 22.5858i | −1.30322 | − | 0.946845i | −0.303239 | − | 0.952915i | \(-0.598068\pi\) |
−0.999982 | + | 0.00606937i | \(0.998068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.3745 | 0.978193 | 0.489096 | − | 0.872230i | \(-0.337327\pi\) | ||||
0.489096 | + | 0.872230i | \(0.337327\pi\) | |||||||
\(572\) | −21.7599 | + | 31.9885i | −0.909828 | + | 1.33751i | ||||
\(573\) | 23.8852 | 0.997819 | ||||||||
\(574\) | −7.48497 | − | 23.0364i | −0.312417 | − | 0.961520i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.38073 | − | 6.81550i | 0.390864 | − | 0.283979i | ||||
\(577\) | 5.77115 | − | 17.7618i | 0.240256 | − | 0.739432i | −0.756124 | − | 0.654428i | \(-0.772910\pi\) |
0.996381 | − | 0.0850044i | \(-0.0270904\pi\) | |||||||
\(578\) | 3.29388 | − | 10.1375i | 0.137007 | − | 0.421666i | ||||
\(579\) | −29.5152 | + | 21.4441i | −1.22661 | + | 0.891185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.59220 | − | 26.4441i | −0.356464 | − | 1.09708i | ||||
\(582\) | 78.5499 | 3.25600 | ||||||||
\(583\) | −20.4240 | + | 7.34294i | −0.845875 | + | 0.304114i | ||||
\(584\) | −30.5231 | −1.26306 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.17026 | − | 0.850245i | −0.0483431 | − | 0.0351233i | ||||
\(587\) | −15.1091 | + | 10.9774i | −0.623621 | + | 0.453087i | −0.854184 | − | 0.519970i | \(-0.825943\pi\) |
0.230563 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(588\) | −9.73396 | + | 29.9581i | −0.401422 | + | 1.23545i | ||||
\(589\) | −1.82119 | + | 5.60504i | −0.0750407 | + | 0.230951i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9624 | − | 8.69117i | −0.492066 | − | 0.357507i | ||||
\(592\) | 9.24392 | + | 28.4499i | 0.379923 | + | 1.16928i | ||||
\(593\) | −10.2335 | −0.420240 | −0.210120 | − | 0.977676i | \(-0.567385\pi\) | ||||
−0.210120 | + | 0.977676i | \(0.567385\pi\) | |||||||
\(594\) | 1.54131 | + | 49.7421i | 0.0632408 | + | 2.04094i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.0590 | − | 86.3569i | −1.14934 | − | 3.53731i | ||||
\(597\) | −0.610779 | − | 0.443757i | −0.0249975 | − | 0.0181618i | ||||
\(598\) | 15.5602 | − | 11.3052i | 0.636305 | − | 0.462303i | ||||
\(599\) | 6.79277 | − | 20.9060i | 0.277545 | − | 0.854196i | −0.710990 | − | 0.703203i | \(-0.751753\pi\) |
0.988535 | − | 0.150994i | \(-0.0482473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0923 | + | 10.9652i | −0.615627 | + | 0.447279i | −0.851391 | − | 0.524531i | \(-0.824241\pi\) |
0.235764 | + | 0.971810i | \(0.424241\pi\) | |||||||
\(602\) | 0.0468901 | + | 0.0340677i | 0.00191110 | + | 0.00138850i | ||||
\(603\) | 0.661752 | + | 2.03666i | 0.0269486 | + | 0.0829393i | ||||
\(604\) | 131.143 | 5.33613 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 67.6124 | 2.74657 | ||||||||
\(607\) | 1.02449 | + | 3.15306i | 0.0415829 | + | 0.127979i | 0.969693 | − | 0.244327i | \(-0.0785671\pi\) |
−0.928110 | + | 0.372306i | \(0.878567\pi\) | |||||||
\(608\) | −26.6503 | − | 19.3626i | −1.08081 | − | 0.785256i | ||||
\(609\) | −2.83609 | + | 2.06054i | −0.114924 | + | 0.0834973i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.88875 | − | 18.1237i | 0.238233 | − | 0.733207i | ||||
\(612\) | −5.06055 | + | 3.67670i | −0.204560 | + | 0.148622i | ||||
\(613\) | 18.0980 | + | 13.1489i | 0.730970 | + | 0.531081i | 0.889870 | − | 0.456214i | \(-0.150795\pi\) |
−0.158900 | + | 0.987295i | \(0.550795\pi\) | |||||||
\(614\) | 17.1254 | + | 52.7066i | 0.691126 | + | 2.12707i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.96648 | − | 63.4634i | −0.0792318 | − | 2.55701i | ||||
\(617\) | −11.3963 | −0.458798 | −0.229399 | − | 0.973332i | \(-0.573676\pi\) | ||||
−0.229399 | + | 0.973332i | \(0.573676\pi\) | |||||||
\(618\) | −0.596620 | − | 1.83621i | −0.0239996 | − | 0.0738631i | ||||
\(619\) | 16.5704 | + | 12.0391i | 0.666019 | + | 0.483891i | 0.868690 | − | 0.495356i | \(-0.164962\pi\) |
−0.202671 | + | 0.979247i | \(0.564962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.64591 | − | 17.3763i | 0.226563 | − | 0.697288i | ||||
\(622\) | 13.0866 | − | 40.2765i | 0.524726 | − | 1.61494i | ||||
\(623\) | 21.2132 | − | 15.4123i | 0.849890 | − | 0.617481i | ||||
\(624\) | 45.5315 | + | 33.0806i | 1.82272 | + | 1.32428i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −78.6055 | −3.14171 | ||||||||
\(627\) | 6.55900 | − | 2.35813i | 0.261941 | − | 0.0941745i | ||||
\(628\) | −91.7017 | −3.65930 | ||||||||
\(629\) | −2.01908 | − | 6.21409i | −0.0805060 | − | 0.247772i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1408 | + | 10.2739i | −0.562937 | + | 0.408998i | −0.832533 | − | 0.553976i | \(-0.813110\pi\) |
0.269596 | + | 0.962974i | \(0.413110\pi\) | |||||||
\(632\) | 19.0823 | − | 58.7294i | 0.759054 | − | 2.33613i | ||||
\(633\) | 0.398168 | − | 1.22544i | 0.0158258 | − | 0.0487067i | ||||
\(634\) | 42.1670 | − | 30.6361i | 1.67467 | − | 1.21672i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 18.7465 | + | 57.6959i | 0.743348 | + | 2.28779i | ||||
\(637\) | 7.01830 | 0.278075 | ||||||||
\(638\) | −5.80473 | + | 8.53333i | −0.229812 | + | 0.337838i | ||||
\(639\) | 3.64523 | 0.144203 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.17247 | − | 3.03148i | −0.164803 | − | 0.119736i | 0.502327 | − | 0.864678i | \(-0.332477\pi\) |
−0.667130 | + | 0.744942i | \(0.732477\pi\) | |||||||
\(642\) | 30.9953 | − | 22.5194i | 1.22328 | − | 0.888769i | ||||
\(643\) | 5.82659 | − | 17.9324i | 0.229778 | − | 0.707185i | −0.767993 | − | 0.640458i | \(-0.778744\pi\) |
0.997771 | − | 0.0667267i | \(-0.0212556\pi\) | |||||||
\(644\) | −11.1531 | + | 34.3256i | −0.439492 | + | 1.35262i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.3849 | + | 7.54511i | 0.408590 | + | 0.296858i | ||||
\(647\) | 7.59827 | + | 23.3851i | 0.298719 | + | 0.919362i | 0.981947 | + | 0.189157i | \(0.0605754\pi\) |
−0.683228 | + | 0.730205i | \(0.739425\pi\) | |||||||
\(648\) | 80.5964 | 3.16612 | ||||||||
\(649\) | −11.1283 | − | 14.3596i | −0.436825 | − | 0.563663i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.43175 | + | 13.6395i | 0.173694 | + | 0.534575i | ||||
\(652\) | −56.0151 | − | 40.6974i | −2.19372 | − | 1.59383i | ||||
\(653\) | −33.4097 | + | 24.2736i | −1.30742 | + | 0.949898i | −0.999999 | − | 0.00167469i | \(-0.999467\pi\) |
−0.307424 | + | 0.951573i | \(0.599467\pi\) | |||||||
\(654\) | −1.29417 | + | 3.98304i | −0.0506060 | + | 0.155749i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −61.9754 | + | 45.0277i | −2.41973 | + | 1.75804i | ||||
\(657\) | 0.747865 | + | 0.543356i | 0.0291770 | + | 0.0211983i | ||||
\(658\) | 14.9637 | + | 46.0536i | 0.583346 | + | 1.79536i | ||||
\(659\) | −4.73658 | −0.184511 | −0.0922555 | − | 0.995735i | \(-0.529408\pi\) | ||||
−0.0922555 | + | 0.995735i | \(0.529408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7556 | 0.418344 | 0.209172 | − | 0.977879i | \(-0.432923\pi\) | ||||
0.209172 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(662\) | 10.3306 | + | 31.7943i | 0.401511 | + | 1.23572i | ||||
\(663\) | −9.94509 | − | 7.22553i | −0.386235 | − | 0.280616i | ||||
\(664\) | −119.552 | + | 86.8599i | −4.63953 | + | 3.37082i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.470455 | − | 1.44791i | 0.0182298 | − | 0.0561054i | ||||
\(667\) | 3.06533 | − | 2.22710i | 0.118690 | − | 0.0862335i | ||||
\(668\) | −28.9516 | − | 21.0346i | −1.12017 | − | 0.813852i | ||||
\(669\) | 6.77401 | + | 20.8482i | 0.261898 | + | 0.806040i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.4102 | + | 6.81246i | 0.903741 | + | 0.262992i | ||||
\(672\) | −80.1613 | −3.09229 | ||||||||
\(673\) | 11.6621 | + | 35.8921i | 0.449539 | + | 1.38354i | 0.877428 | + | 0.479708i | \(0.159257\pi\) |
−0.427889 | + | 0.903831i | \(0.640743\pi\) | |||||||
\(674\) | −52.2063 | − | 37.9301i | −2.01091 | − | 1.46101i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.2420 | + | 46.9100i | −0.586230 | + | 1.80423i | ||||
\(677\) | −7.19149 | + | 22.1331i | −0.276392 | + | 0.850646i | 0.712456 | + | 0.701716i | \(0.247583\pi\) |
−0.988848 | + | 0.148929i | \(0.952417\pi\) | |||||||
\(678\) | 9.96032 | − | 7.23659i | 0.382524 | − | 0.277920i | ||||
\(679\) | 26.5694 | + | 19.3038i | 1.01964 | + | 0.740811i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.3629 | −1.08687 | ||||||||
\(682\) | 25.8630 | + | 33.3727i | 0.990346 | + | 1.27791i | ||||
\(683\) | 12.6153 | 0.482712 | 0.241356 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241356 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(684\) | 0.682545 | + | 2.10066i | 0.0260977 | + | 0.0803206i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −44.1511 | + | 32.0776i | −1.68570 | + | 1.22473i | ||||
\(687\) | 5.98107 | − | 18.4078i | 0.228192 | − | 0.702303i | ||||
\(688\) | 0.0566448 | − | 0.174335i | 0.00215956 | − | 0.00664645i | ||||
\(689\) | 10.9350 | − | 7.94478i | 0.416592 | − | 0.302672i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.26469 | + | 6.97000i | 0.0861529 | + | 0.265151i | 0.984847 | − | 0.173424i | \(-0.0554831\pi\) |
−0.898694 | + | 0.438576i | \(0.855483\pi\) | |||||||
\(692\) | −11.9000 | −0.452368 | ||||||||
\(693\) | −1.08156 | + | 1.58996i | −0.0410850 | + | 0.0603976i | ||||
\(694\) | −57.0772 | −2.16662 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.0730 | + | 10.9512i | 0.571340 | + | 0.415103i | ||||
\(697\) | 13.5368 | − | 9.83506i | 0.512743 | − | 0.372530i | ||||
\(698\) | 21.7940 | − | 67.0752i | 0.824917 | − | 2.53883i | ||||
\(699\) | −1.28150 | + | 3.94405i | −0.0484708 | + | 0.149178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7236 | + | 21.5954i | 1.12264 | + | 0.815649i | 0.984608 | − | 0.174778i | \(-0.0559209\pi\) |
0.138036 | + | 0.990427i | \(0.455921\pi\) | |||||||
\(702\) | −9.57724 | − | 29.4757i | −0.361470 | − | 1.11249i | ||||
\(703\) | −2.30717 | −0.0870166 | ||||||||
\(704\) | −118.464 | + | 42.5907i | −4.46476 | + | 1.60520i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.91413 | + | 8.96878i | 0.109675 | + | 0.337545i | ||||
\(707\) | 22.8698 | + | 16.6159i | 0.860107 | + | 0.624904i | ||||
\(708\) | −41.0809 | + | 29.8470i | −1.54391 | + | 1.12172i | ||||
\(709\) | −8.01840 | + | 24.6781i | −0.301137 | + | 0.926806i | 0.679953 | + | 0.733256i | \(0.262000\pi\) |
−0.981090 | + | 0.193550i | \(0.938000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.51302 | + | 1.09927i | −0.0567425 | + | 0.0412258i | ||||
\(712\) | −112.742 | − | 81.9118i | −4.22518 | − | 3.06978i | ||||
\(713\) | −4.78997 | − | 14.7420i | −0.179386 | − | 0.552093i | ||||
\(714\) | 31.2369 | 1.16901 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −55.1586 | −2.06137 | ||||||||
\(717\) | 12.5518 | + | 38.6305i | 0.468756 | + | 1.44268i | ||||
\(718\) | 10.6928 | + | 7.76877i | 0.399052 | + | 0.289928i | ||||
\(719\) | 2.19677 | − | 1.59605i | 0.0819259 | − | 0.0595226i | −0.546068 | − | 0.837741i | \(-0.683876\pi\) |
0.627994 | + | 0.778218i | \(0.283876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.249445 | − | 0.767714i | 0.00928983 | − | 0.0285912i | ||||
\(722\) | −38.8410 | + | 28.2197i | −1.44551 | + | 1.05023i | ||||
\(723\) | −25.0906 | − | 18.2294i | −0.933129 | − | 0.677958i | ||||
\(724\) | −33.7295 | − | 103.809i | −1.25355 | − | 3.85802i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.4605 | − | 48.3539i | 0.462453 | − | 1.79458i | ||||
\(727\) | −18.6564 | −0.691926 | −0.345963 | − | 0.938248i | \(-0.612448\pi\) | ||||
−0.345963 | + | 0.938248i | \(0.612448\pi\) | |||||||
\(728\) | 12.2191 | + | 37.6066i | 0.452871 | + | 1.39379i | ||||
\(729\) | −23.5917 | − | 17.1404i | −0.873767 | − | 0.634829i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0123725 | + | 0.0380786i | −0.000457613 | + | 0.00140839i | ||||
\(732\) | 21.0591 | − | 64.8133i | 0.778367 | − | 2.39557i | ||||
\(733\) | −27.1407 | + | 19.7188i | −1.00246 | + | 0.728332i | −0.962615 | − | 0.270874i | \(-0.912687\pi\) |
−0.0398480 | + | 0.999206i | \(0.512687\pi\) | |||||||
\(734\) | 29.3826 | + | 21.3477i | 1.08453 | + | 0.787958i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 86.6408 | 3.19362 | ||||||||
\(737\) | −0.720068 | − | 23.2384i | −0.0265240 | − | 0.855999i | ||||
\(738\) | 3.89873 | 0.143514 | ||||||||
\(739\) | 13.7840 | + | 42.4228i | 0.507053 | + | 1.56055i | 0.797291 | + | 0.603595i | \(0.206266\pi\) |
−0.290238 | + | 0.956955i | \(0.593734\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.51170 | + | 2.55140i | −0.129006 | + | 0.0937280i | ||||
\(742\) | −10.6136 | + | 32.6652i | −0.389637 | + | 1.19918i | ||||
\(743\) | 4.17597 | − | 12.8523i | 0.153202 | − | 0.471506i | −0.844773 | − | 0.535125i | \(-0.820264\pi\) |
0.997974 | + | 0.0636194i | \(0.0202644\pi\) | |||||||
\(744\) | 61.6636 | − | 44.8013i | 2.26070 | − | 1.64249i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.3192 | + | 65.6139i | 0.780553 | + | 2.40229i | ||||
\(747\) | 4.47546 | 0.163748 | ||||||||
\(748\) | 63.9066 | − | 22.9761i | 2.33666 | − | 0.840088i | ||||
\(749\) | 16.0183 | 0.585295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4965 | + | 14.8915i | 0.747926 | + | 0.543400i | 0.895183 | − | 0.445698i | \(-0.147045\pi\) |
−0.147257 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(752\) | 123.899 | − | 90.0180i | 4.51814 | − | 3.28262i | ||||
\(753\) | 1.82939 | − | 5.63028i | 0.0666666 | − | 0.205179i | ||||
\(754\) | 1.98614 | − | 6.11270i | 0.0723308 | − | 0.222611i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 47.0510 | + | 34.1845i | 1.71123 | + | 1.24328i | ||||
\(757\) | 5.48060 | + | 16.8676i | 0.199196 | + | 0.613062i | 0.999902 | + | 0.0140044i | \(0.00445787\pi\) |
−0.800706 | + | 0.599057i | \(0.795542\pi\) | |||||||
\(758\) | 5.63946 | 0.204834 | ||||||||
\(759\) | −10.3108 | + | 15.1576i | −0.374260 | + | 0.550186i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.43998 | + | 22.8979i | 0.269699 | + | 0.830048i | 0.990573 | + | 0.136982i | \(0.0437404\pi\) |
−0.720875 | + | 0.693066i | \(0.756260\pi\) | |||||||
\(762\) | −29.8840 | − | 21.7120i | −1.08258 | − | 0.786541i | ||||
\(763\) | −1.41659 | + | 1.02921i | −0.0512840 | + | 0.0372600i | ||||
\(764\) | 25.3939 | − | 78.1543i | 0.918718 | − | 2.82752i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 72.0362 | − | 52.3374i | 2.60278 | − | 1.89103i | ||||
\(767\) | 9.15303 | + | 6.65006i | 0.330497 | + | 0.240120i | ||||
\(768\) | 36.5469 | + | 112.480i | 1.31877 | + | 4.05876i | ||||
\(769\) | 25.1389 | 0.906532 | 0.453266 | − | 0.891375i | \(-0.350259\pi\) | ||||
0.453266 | + | 0.891375i | \(0.350259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.5849 | −0.777363 | ||||||||
\(772\) | 38.7872 | + | 119.375i | 1.39598 | + | 4.29639i | ||||
\(773\) | 37.4614 | + | 27.2173i | 1.34739 | + | 0.978937i | 0.999137 | + | 0.0415374i | \(0.0132256\pi\) |
0.348255 | + | 0.937400i | \(0.386774\pi\) | |||||||
\(774\) | −0.00754739 | + | 0.00548350i | −0.000271285 | + | 0.000197100i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 53.9368 | − | 166.000i | 1.93622 | − | 5.95907i | ||||
\(777\) | −4.54211 | + | 3.30004i | −0.162947 | + | 0.118388i | ||||
\(778\) | 6.24362 | + | 4.53625i | 0.223845 | + | 0.162633i | ||||
\(779\) | −1.82579 | − | 5.61919i | −0.0654155 | − | 0.201328i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.9994 | − | 11.0580i | −1.35972 | − | 0.395685i | ||||
\(782\) | −33.7618 | −1.20732 | ||||||||
\(783\) | −1.88670 | − | 5.80666i | −0.0674251 | − | 0.207513i | ||||
\(784\) | 45.6309 | + | 33.1528i | 1.62968 | + | 1.18403i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.77701 | + | 11.6245i | −0.134722 | + | 0.414630i | ||||
\(787\) | −5.85893 | + | 18.0319i | −0.208848 | + | 0.642769i | 0.790685 | + | 0.612223i | \(0.209724\pi\) |
−0.999533 | + | 0.0305456i | \(0.990276\pi\) | |||||||
\(788\) | −41.1561 | + | 29.9017i | −1.46613 | + | 1.06520i | ||||
\(789\) | 8.29565 | + | 6.02714i | 0.295333 | + | 0.214572i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.14747 | 0.183023 | ||||||||
\(792\) | 9.81286 | + | 2.85558i | 0.348685 | + | 0.101469i | ||||
\(793\) | −15.1839 | −0.539195 | ||||||||
\(794\) | −22.7644 | − | 70.0616i | −0.807878 | − | 2.48639i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.10137 | + | 1.52673i | −0.0744809 | + | 0.0541136i | ||||
\(797\) | 3.66796 | − | 11.2888i | 0.129926 | − | 0.399871i | −0.864841 | − | 0.502047i | \(-0.832581\pi\) |
0.994766 | + | 0.102176i | \(0.0325805\pi\) | |||||||
\(798\) | 3.40846 | − | 10.4902i | 0.120658 | − | 0.371348i | ||||
\(799\) | −27.0623 | + | 19.6619i | −0.957396 | + | 0.695589i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.30421 | + | 4.01394i | 0.0460819 | + | 0.141826i | ||||
\(802\) | 50.3191 | 1.77683 | ||||||||
\(803\) | −6.14776 | − | 7.93284i | −0.216950 | − | 0.279944i | ||||
\(804\) | −64.9855 | −2.29186 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.2723 | − | 15.4552i | −0.749285 | − | 0.544387i | ||||
\(807\) | 29.7414 | − | 21.6084i | 1.04695 | − | 0.760652i | ||||
\(808\) | 46.4265 | − | 142.886i | 1.63328 | − | 5.02671i | ||||
\(809\) | −2.17500 | + | 6.69397i | −0.0764690 | + | 0.235347i | −0.981983 | − | 0.188969i | \(-0.939486\pi\) |
0.905514 | + | 0.424316i | \(0.139486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5326 | + | 20.7302i | 1.00192 | + | 0.727935i | 0.962498 | − | 0.271288i | \(-0.0874496\pi\) |
0.0394182 | + | 0.999223i | \(0.487450\pi\) | |||||||
\(812\) | 3.72702 | + | 11.4706i | 0.130793 | + | 0.402539i | ||||
\(813\) | −14.2131 | −0.498475 | ||||||||
\(814\) | −9.29651 | + | 13.6665i | −0.325843 | + | 0.479010i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −30.5283 | − | 93.9566i | −1.06871 | − | 3.28914i | ||||
\(817\) | 0.0114378 | + | 0.00831002i | 0.000400157 | + | 0.000290731i | ||||
\(818\) | 16.9917 | − | 12.3452i | 0.594100 | − | 0.431639i | ||||
\(819\) | 0.370064 | − | 1.13894i | 0.0129311 | − | 0.0397977i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.5952 | + | 30.2207i | −1.45168 | + | 1.05471i | −0.466246 | + | 0.884655i | \(0.654394\pi\) |
−0.985435 | + | 0.170053i | \(0.945606\pi\) | |||||||
\(822\) | 31.1701 | + | 22.6464i | 1.08718 | + | 0.789885i | ||||
\(823\) | −11.9306 | − | 36.7186i | −0.415875 | − | 1.27993i | −0.911466 | − | 0.411376i | \(-0.865048\pi\) |
0.495591 | − | 0.868556i | \(-0.334952\pi\) | |||||||
\(824\) | −4.29015 | −0.149454 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.7490 | −1.00031 | ||||||||
\(827\) | 5.45382 | + | 16.7851i | 0.189648 | + | 0.583677i | 0.999997 | − | 0.00227034i | \(-0.000722673\pi\) |
−0.810349 | + | 0.585947i | \(0.800723\pi\) | |||||||
\(828\) | −4.69986 | − | 3.41464i | −0.163331 | − | 0.118667i | ||||
\(829\) | 20.5573 | − | 14.9357i | 0.713984 | − | 0.518740i | −0.170472 | − | 0.985362i | \(-0.554529\pi\) |
0.884457 | + | 0.466623i | \(0.154529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.32008 | − | 4.06279i | 0.0457931 | − | 0.140937i | ||||
\(832\) | 63.4257 | − | 46.0814i | 2.19889 | − | 1.59759i | ||||
\(833\) | −9.96681 | − | 7.24131i | −0.345330 | − | 0.250897i | ||||
\(834\) | 31.0301 | + | 95.5010i | 1.07449 | + | 3.30693i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.742693 | − | 23.9686i | −0.0256866 | − | 0.828972i | ||||
\(837\) | −24.9776 | −0.863351 | ||||||||
\(838\) | −25.4935 | − | 78.4608i | −0.880657 | − | 2.71038i | ||||
\(839\) | 44.0635 | + | 32.0140i | 1.52124 | + | 1.10525i | 0.960868 | + | 0.277005i | \(0.0893419\pi\) |
0.560372 | + | 0.828241i | \(0.310658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.57023 | + | 26.3764i | −0.295525 | + | 0.909533i | ||||
\(842\) | −21.6480 | + | 66.6255i | −0.746038 | + | 2.29607i | ||||
\(843\) | 27.4934 | − | 19.9752i | 0.946924 | − | 0.687981i | ||||
\(844\) | −3.58640 | − | 2.60567i | −0.123449 | − | 0.0896910i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.79421 | −0.267971 | ||||||||
\(847\) | 16.0978 | − | 13.2934i | 0.553127 | − | 0.456768i | ||||
\(848\) | 108.626 | 3.73022 | ||||||||
\(849\) | −5.48367 | − | 16.8770i | −0.188199 | − | 0.579217i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.90926 | − | 3.56678i | 0.168287 | − | 0.122268i | ||||
\(852\) | −34.1831 | + | 105.205i | −1.17109 | + | 3.60425i | ||||
\(853\) | 0.526298 | − | 1.61978i | 0.0180201 | − | 0.0554601i | −0.941642 | − | 0.336616i | \(-0.890718\pi\) |
0.959662 | + | 0.281156i | \(0.0907177\pi\) | |||||||
\(854\) | 31.2145 | − | 22.6787i | 1.06814 | − | 0.776048i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.3073 | − | 80.9656i | −0.899166 | − | 2.76735i | ||||
\(857\) | −34.5112 | −1.17888 | −0.589440 | − | 0.807812i | \(-0.700652\pi\) | ||||
−0.589440 | + | 0.807812i | \(0.700652\pi\) | |||||||
\(858\) | 0.963112 | + | 31.0821i | 0.0328801 | + | 1.06113i | ||||
\(859\) | −41.1808 | −1.40507 | −0.702535 | − | 0.711650i | \(-0.747948\pi\) | ||||
−0.702535 | + | 0.711650i | \(0.747948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6318 | − | 8.45097i | −0.396409 | − | 0.288008i | ||||
\(862\) | −45.9034 | + | 33.3508i | −1.56348 | + | 1.13593i | ||||
\(863\) | 5.64904 | − | 17.3860i | 0.192296 | − | 0.591825i | −0.807702 | − | 0.589591i | \(-0.799289\pi\) |
0.999998 | − | 0.00223395i | \(-0.000711090\pi\) | |||||||
\(864\) | 43.1424 | − | 132.779i | 1.46773 | − | 4.51722i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.7752 | + | 22.3595i | 1.04579 | + | 0.759808i | ||||
\(867\) | −1.95519 | − | 6.01744i | −0.0664016 | − | 0.204363i | ||||
\(868\) | 49.3412 | 1.67475 | ||||||||
\(869\) | 19.1070 | − | 6.86944i | 0.648159 | − | 0.233030i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.47428 | + | 13.7704i | 0.151605 | + | 0.466593i | ||||
\(872\) | 7.52875 | + | 5.46996i | 0.254956 | + | 0.185236i | ||||
\(873\) | −4.27658 | + | 3.10712i | −0.144740 | + | 0.105160i | ||||
\(874\) | −3.68397 | + | 11.3381i | −0.124612 | + | 0.383517i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.6948 | + | 16.4888i | −0.766788 | + | 0.557104i | ||||
\(877\) | 33.5709 | + | 24.3907i | 1.13361 | + | 0.823614i | 0.986216 | − | 0.165464i | \(-0.0529122\pi\) |
0.147392 | + | 0.989078i | \(0.452912\pi\) | |||||||
\(878\) | 20.6668 | + | 63.6059i | 0.697471 | + | 2.14659i | ||||
\(879\) | −0.858629 | −0.0289608 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.7389 | 1.67575 | 0.837873 | − | 0.545866i | \(-0.183799\pi\) | ||||
0.837873 | + | 0.545866i | \(0.183799\pi\) | |||||||
\(882\) | −0.887046 | − | 2.73005i | −0.0298684 | − | 0.0919254i | ||||
\(883\) | −15.3859 | − | 11.1785i | −0.517776 | − | 0.376186i | 0.297990 | − | 0.954569i | \(-0.403684\pi\) |
−0.815765 | + | 0.578383i | \(0.803684\pi\) | |||||||
\(884\) | −34.2157 | + | 24.8592i | −1.15080 | + | 0.836105i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.45074 | + | 4.46491i | −0.0487384 | + | 0.150001i | ||||
\(887\) | 2.73133 | − | 1.98443i | 0.0917090 | − | 0.0666305i | −0.540986 | − | 0.841032i | \(-0.681949\pi\) |
0.632695 | + | 0.774401i | \(0.281949\pi\) | |||||||
\(888\) | 24.1400 | + | 17.5387i | 0.810085 | + | 0.588561i | ||||
\(889\) | −4.77244 | − | 14.6881i | −0.160063 | − | 0.492622i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.2332 | + | 20.9467i | 0.543831 | + | 0.701740i | ||||
\(892\) | 75.4189 | 2.52521 | ||||||||
\(893\) | 3.65005 | + | 11.2337i | 0.122144 | + | 0.375921i | ||||
\(894\) | −59.0461 | − | 42.8995i | −1.97480 | − | 1.43477i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −31.3798 | + | 96.5771i | −1.04833 | + | 3.22641i | ||||
\(897\) | 3.52794 | − | 10.8579i | 0.117794 | − | 0.362534i | ||||
\(898\) | 5.82225 | − | 4.23011i | 0.194291 | − | 0.141161i | ||||
\(899\) | −4.19060 | − | 3.04465i | −0.139764 | − | 0.101545i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.7263 | −0.790437 | ||||||||
\(902\) | −40.6420 | − | 11.8270i | −1.35323 | − | 0.393795i | ||||
\(903\) | 0.0344036 | 0.00114488 | ||||||||
\(904\) | −8.45385 | − | 26.0183i | −0.281171 | − | 0.865355i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 85.2797 | − | 61.9593i | 2.83323 | − | 2.05846i | ||||
\(907\) | 10.3770 | − | 31.9372i | 0.344563 | − | 1.06046i | −0.617254 | − | 0.786764i | \(-0.711755\pi\) |
0.961817 | − | 0.273692i | \(-0.0882449\pi\) | |||||||
\(908\) | −30.1543 | + | 92.8055i | −1.00071 | + | 3.07986i | ||||
\(909\) | −3.68110 | + | 2.67448i | −0.122094 | + | 0.0887068i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.7638 | + | 45.4384i | 0.489147 | + | 1.50544i | 0.825883 | + | 0.563841i | \(0.190677\pi\) |
−0.336736 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(912\) | −34.8843 | −1.15513 | ||||||||
\(913\) | −46.6540 | − | 13.5765i | −1.54402 | − | 0.449316i | ||||
\(914\) | 38.6081 | 1.27704 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.8730 | − | 39.1410i | −1.78001 | − | 1.29326i | ||||
\(917\) | −4.13430 | + | 3.00374i | −0.136527 | + | 0.0991923i | ||||
\(918\) | −16.8115 | + | 51.7405i | −0.554863 | + | 1.70769i | ||||
\(919\) | 3.79764 | − | 11.6879i | 0.125273 | − | 0.385550i | −0.868678 | − | 0.495377i | \(-0.835030\pi\) |
0.993951 | + | 0.109827i | \(0.0350298\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.6132 | + | 19.3356i | 0.876934 | + | 0.637130i | ||||
\(922\) | −22.6770 | − | 69.7926i | −0.746827 | − | 2.29850i | ||||
\(923\) | 24.6464 | 0.811246 | ||||||||
\(924\) | −35.7454 | − | 46.1246i | −1.17594 | − | 1.51739i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.1987 | + | 62.1651i | 0.663769 | + | 2.04287i | ||||
\(927\) | 0.105115 | + | 0.0763708i | 0.00345244 | + | 0.00250835i | ||||
\(928\) | 23.4233 | − | 17.0180i | 0.768908 | − | 0.558644i | ||||
\(929\) | 16.3005 | − | 50.1679i | 0.534804 | − | 1.64596i | −0.209269 | − | 0.977858i | \(-0.567109\pi\) |
0.744073 | − | 0.668098i | \(-0.232891\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.51937 | + | 2.55697i | −0.115343 | + | 0.0838014i | ||||
\(932\) | 11.5428 | + | 8.38633i | 0.378097 | + | 0.274703i | ||||
\(933\) | −7.76797 | − | 23.9074i | −0.254312 | − | 0.782692i | ||||
\(934\) | 27.9975 | 0.916107 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.36462 | −0.208034 | ||||||||
\(937\) | −12.5153 | − | 38.5181i | −0.408857 | − | 1.25833i | −0.917632 | − | 0.397432i | \(-0.869901\pi\) |
0.508775 | − | 0.860900i | \(-0.330099\pi\) | |||||||
\(938\) | −29.7656 | − | 21.6260i | −0.971882 | − | 0.706114i | ||||
\(939\) | −37.7477 | + | 27.4253i | −1.23185 | + | 0.894991i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.10825 | − | 6.48852i | 0.0687269 | − | 0.211520i | −0.910794 | − | 0.412860i | \(-0.864530\pi\) |
0.979521 | + | 0.201341i | \(0.0645298\pi\) | |||||||
\(942\) | −59.6318 | + | 43.3250i | −1.94291 | + | 1.41161i | ||||
\(943\) | 12.5720 | + | 9.13407i | 0.409400 | + | 0.297446i | ||||
\(944\) | 28.0969 | + | 86.4735i | 0.914478 | + | 2.81447i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0953115 | − | 0.0342669i | 0.00309884 | − | 0.00111411i | ||||
\(947\) | −31.5841 | −1.02634 | −0.513172 | − | 0.858286i | \(-0.671530\pi\) | ||||
−0.513172 | + | 0.858286i | \(0.671530\pi\) | |||||||
\(948\) | −17.5377 | − | 53.9754i | −0.569597 | − | 1.75304i | ||||
\(949\) | 5.05652 | + | 3.67378i | 0.164142 | + | 0.119256i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.56043 | − | 29.4240i | 0.310018 | − | 0.954138i | ||||
\(952\) | 21.4490 | − | 66.0132i | 0.695165 | − | 2.13950i | ||||
\(953\) | −17.5279 | + | 12.7347i | −0.567784 | + | 0.412519i | −0.834299 | − | 0.551312i | \(-0.814128\pi\) |
0.266516 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(954\) | −4.47252 | − | 3.24948i | −0.144803 | − | 0.105206i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 139.747 | 4.51973 | ||||||||
\(957\) | 0.189731 | + | 6.12311i | 0.00613314 | + | 0.197932i | ||||
\(958\) | −1.88468 | −0.0608912 | ||||||||
\(959\) | 4.97785 | + | 15.3202i | 0.160743 | + | 0.494716i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.93576 | − | 5.76566i | 0.255992 | − | 0.185989i | ||||
\(962\) | 3.18088 | − | 9.78973i | 0.102556 | − | 0.315634i | ||||
\(963\) | −0.796734 | + | 2.45209i | −0.0256744 | + | 0.0790176i | ||||
\(964\) | −86.3233 | + | 62.7175i | −2.78029 | + | 2.02000i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.96472 | + | 27.5906i | 0.288435 | + | 0.887712i | ||||
\(967\) | 9.03757 | 0.290629 | 0.145314 | − | 0.989386i | \(-0.453581\pi\) | ||||
0.145314 | + | 0.989386i | \(0.453581\pi\) | |||||||
\(968\) | −93.6307 | − | 59.5354i | −3.00940 | − | 1.91354i | ||||
\(969\) | 7.61950 | 0.244774 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.7379 | − | 20.1528i | −0.890151 | − | 0.646733i | 0.0457664 | − | 0.998952i | \(-0.485427\pi\) |
−0.935917 | + | 0.352220i | \(0.885427\pi\) | |||||||
\(972\) | −14.4467 | + | 10.4961i | −0.463377 | + | 0.336663i | ||||
\(973\) | −12.9736 | + | 39.9288i | −0.415916 | + | 1.28006i | ||||
\(974\) | −9.07928 | + | 27.9431i | −0.290919 | + | 0.895356i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −98.7211 | − | 71.7251i | −3.15998 | − | 2.29586i | ||||
\(977\) | −5.30858 | − | 16.3381i | −0.169837 | − | 0.522703i | 0.829523 | − | 0.558472i | \(-0.188612\pi\) |
−0.999360 | + | 0.0357684i | \(0.988612\pi\) | |||||||
\(978\) | −55.6532 | −1.77959 | ||||||||
\(979\) | −1.41914 | − | 45.7993i | −0.0453559 | − | 1.46375i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0870932 | − | 0.268045i | −0.00278067 | − | 0.00855802i | ||||
\(982\) | −25.8340 | − | 18.7695i | −0.824395 | − | 0.598958i | ||||
\(983\) | −3.12224 | + | 2.26844i | −0.0995839 | + | 0.0723519i | −0.636463 | − | 0.771307i | \(-0.719603\pi\) |
0.536879 | + | 0.843659i | \(0.319603\pi\) | |||||||
\(984\) | −23.6129 | + | 72.6730i | −0.752751 | + | 2.31673i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.12748 | + | 6.63150i | −0.290678 | + | 0.211190i | ||||
\(987\) | 23.2538 | + | 16.8949i | 0.740178 | + | 0.537771i | ||||
\(988\) | 4.61487 | + | 14.2031i | 0.146819 | + | 0.451861i | ||||
\(989\) | −0.0371845 | −0.00118240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.5631 | −1.00263 | −0.501317 | − | 0.865264i | \(-0.667151\pi\) | ||||
−0.501317 | + | 0.865264i | \(0.667151\pi\) | |||||||
\(992\) | −36.6019 | − | 112.649i | −1.16211 | − | 3.57661i | ||||
\(993\) | 16.0539 | + | 11.6639i | 0.509456 | + | 0.370141i | ||||
\(994\) | −50.6673 | + | 36.8119i | −1.60707 | + | 1.16760i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −41.9685 | + | 129.166i | −1.32982 | + | 4.09277i | ||||
\(997\) | −7.49529 | + | 5.44564i | −0.237378 | + | 0.172465i | −0.700114 | − | 0.714031i | \(-0.746868\pi\) |
0.462736 | + | 0.886496i | \(0.346868\pi\) | |||||||
\(998\) | −20.6617 | − | 15.0116i | −0.654034 | − | 0.475184i | ||||
\(999\) | −3.02162 | − | 9.29959i | −0.0955999 | − | 0.294226i |
(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 | 275.2.h.c.126.1 | ✓ | 16 | |
5.2 | odd | 4 | 275.2.z.c.49.8 | 32 | |||
5.3 | odd | 4 | 275.2.z.c.49.1 | 32 | |||
5.4 | even | 2 | 275.2.h.e.126.4 | yes | 16 | ||
11.3 | even | 5 | 3025.2.a.bi.1.1 | 8 | |||
11.8 | odd | 10 | 3025.2.a.bm.1.8 | 8 | |||
11.9 | even | 5 | inner | 275.2.h.c.251.1 | yes | 16 | |
55.9 | even | 10 | 275.2.h.e.251.4 | yes | 16 | ||
55.14 | even | 10 | 3025.2.a.bn.1.8 | 8 | |||
55.19 | odd | 10 | 3025.2.a.bj.1.1 | 8 | |||
55.42 | odd | 20 | 275.2.z.c.174.1 | 32 | |||
55.53 | odd | 20 | 275.2.z.c.174.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.h.c.126.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
275.2.h.c.251.1 | yes | 16 | 11.9 | even | 5 | inner | |
275.2.h.e.126.4 | yes | 16 | 5.4 | even | 2 | ||
275.2.h.e.251.4 | yes | 16 | 55.9 | even | 10 | ||
275.2.z.c.49.1 | 32 | 5.3 | odd | 4 | |||
275.2.z.c.49.8 | 32 | 5.2 | odd | 4 | |||
275.2.z.c.174.1 | 32 | 55.42 | odd | 20 | |||
275.2.z.c.174.8 | 32 | 55.53 | odd | 20 | |||
3025.2.a.bi.1.1 | 8 | 11.3 | even | 5 | |||
3025.2.a.bj.1.1 | 8 | 55.19 | odd | 10 | |||
3025.2.a.bm.1.8 | 8 | 11.8 | odd | 10 | |||
3025.2.a.bn.1.8 | 8 | 55.14 | even | 10 |