Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(49,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.j (of order \(6\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} - 36 x^{13} + 67 x^{12} + 34 x^{11} - 24 x^{10} + 182 x^{9} - 495 x^{8} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(-1.49012 + 0.399276i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.49 |
Dual form | 950.2.j.i.349.5 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −2.82754 | − | 1.63248i | −1.63248 | − | 0.942513i | −0.983325 | − | 0.181856i | \(-0.941790\pi\) |
−0.649154 | − | 0.760657i | \(-0.724877\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.63248 | − | 2.82754i | −0.666457 | − | 1.15434i | ||||
\(7\) | − | 2.62013i | − | 0.990316i | −0.868803 | − | 0.495158i | \(-0.835110\pi\) | ||
0.868803 | − | 0.495158i | \(-0.164890\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.82998 | + | 6.63372i | 1.27666 | + | 2.21124i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.03983 | 1.51957 | 0.759783 | − | 0.650177i | \(-0.225305\pi\) | ||||
0.759783 | + | 0.650177i | \(0.225305\pi\) | |||||||
\(12\) | − | 3.26496i | − | 0.942513i | ||||||
\(13\) | −4.02254 | + | 2.32241i | −1.11565 | + | 0.644122i | −0.940287 | − | 0.340382i | \(-0.889444\pi\) |
−0.175365 | + | 0.984504i | \(0.556110\pi\) | |||||||
\(14\) | 1.31007 | − | 2.26910i | 0.350130 | − | 0.606442i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.16962 | + | 1.82998i | 0.768745 | + | 0.443835i | 0.832427 | − | 0.554135i | \(-0.186951\pi\) |
−0.0636816 | + | 0.997970i | \(0.520284\pi\) | |||||||
\(18\) | 7.65996i | 1.80547i | ||||||||
\(19\) | −0.697500 | − | 4.30273i | −0.160017 | − | 0.987114i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.27731 | + | 7.40852i | −0.933385 | + | 1.61667i | ||||
\(22\) | 4.36462 | + | 2.51991i | 0.930540 | + | 0.537248i | ||||
\(23\) | 4.05703 | − | 2.34233i | 0.845950 | − | 0.488409i | −0.0133324 | − | 0.999911i | \(-0.504244\pi\) |
0.859282 | + | 0.511502i | \(0.170911\pi\) | |||||||
\(24\) | 1.63248 | − | 2.82754i | 0.333229 | − | 0.577169i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.64483 | −0.910926 | ||||||||
\(27\) | − | 15.2146i | − | 2.92805i | ||||||
\(28\) | 2.26910 | − | 1.31007i | 0.428819 | − | 0.247579i | ||||
\(29\) | −4.01991 | − | 6.96270i | −0.746479 | − | 1.29294i | −0.949500 | − | 0.313766i | \(-0.898409\pi\) |
0.203021 | − | 0.979174i | \(-0.434924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28009 | −0.589121 | −0.294561 | − | 0.955633i | \(-0.595173\pi\) | ||||
−0.294561 | + | 0.955633i | \(0.595173\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −14.2503 | − | 8.22742i | −2.48066 | − | 1.43221i | ||||
\(34\) | 1.82998 | + | 3.16962i | 0.313839 | + | 0.543585i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.82998 | + | 6.63372i | −0.638330 | + | 1.10562i | ||||
\(37\) | − | 5.75505i | − | 0.946124i | −0.881029 | − | 0.473062i | \(-0.843149\pi\) | ||
0.881029 | − | 0.473062i | \(-0.156851\pi\) | |||||||
\(38\) | 1.54731 | − | 4.07502i | 0.251007 | − | 0.661056i | ||||
\(39\) | 15.1652 | 2.42837 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.90735 | − | 5.03568i | 0.454052 | − | 0.786441i | −0.544581 | − | 0.838708i | \(-0.683311\pi\) |
0.998633 | + | 0.0522673i | \(0.0166448\pi\) | |||||||
\(42\) | −7.40852 | + | 4.27731i | −1.14316 | + | 0.660003i | ||||
\(43\) | −0.502555 | − | 0.290150i | −0.0766390 | − | 0.0442475i | 0.461191 | − | 0.887301i | \(-0.347422\pi\) |
−0.537830 | + | 0.843053i | \(0.680756\pi\) | |||||||
\(44\) | 2.51991 | + | 4.36462i | 0.379891 | + | 0.657991i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.68466 | 0.690715 | ||||||||
\(47\) | 4.00115 | − | 2.31007i | 0.583628 | − | 0.336958i | −0.178946 | − | 0.983859i | \(-0.557269\pi\) |
0.762574 | + | 0.646901i | \(0.223935\pi\) | |||||||
\(48\) | 2.82754 | − | 1.63248i | 0.408120 | − | 0.235628i | ||||
\(49\) | 0.134919 | 0.0192741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.97481 | − | 10.3487i | −0.836641 | − | 1.44910i | ||||
\(52\) | −4.02254 | − | 2.32241i | −0.557826 | − | 0.322061i | ||||
\(53\) | 4.00115 | − | 2.31007i | 0.549600 | − | 0.317312i | −0.199361 | − | 0.979926i | \(-0.563886\pi\) |
0.748961 | + | 0.662614i | \(0.230553\pi\) | |||||||
\(54\) | 7.60729 | − | 13.1762i | 1.03522 | − | 1.79306i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.62013 | 0.350130 | ||||||||
\(57\) | −5.05191 | + | 13.3048i | −0.669142 | + | 1.76226i | ||||
\(58\) | − | 8.03983i | − | 1.05568i | ||||||
\(59\) | −1.88743 | + | 3.26913i | −0.245723 | + | 0.425605i | −0.962335 | − | 0.271868i | \(-0.912359\pi\) |
0.716612 | + | 0.697472i | \(0.245692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0650203 | − | 0.112618i | −0.00832500 | − | 0.0144193i | 0.861833 | − | 0.507192i | \(-0.169317\pi\) |
−0.870158 | + | 0.492773i | \(0.835983\pi\) | |||||||
\(62\) | −2.84064 | − | 1.64004i | −0.360762 | − | 0.208286i | ||||
\(63\) | 17.3812 | − | 10.0350i | 2.18983 | − | 1.26430i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.22742 | − | 14.2503i | −1.01273 | − | 1.75409i | ||||
\(67\) | 0.328977 | − | 0.189935i | 0.0401909 | − | 0.0232043i | −0.479770 | − | 0.877394i | \(-0.659280\pi\) |
0.519961 | + | 0.854190i | \(0.325947\pi\) | |||||||
\(68\) | 3.65996i | 0.443835i | ||||||||
\(69\) | −15.2952 | −1.84133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.56746 | − | 7.91107i | 0.542058 | − | 0.938871i | −0.456728 | − | 0.889606i | \(-0.650979\pi\) |
0.998786 | − | 0.0492651i | \(-0.0156879\pi\) | |||||||
\(72\) | −6.63372 | + | 3.82998i | −0.781791 | + | 0.451367i | ||||
\(73\) | −7.36574 | − | 4.25261i | −0.862094 | − | 0.497730i | 0.00261883 | − | 0.999997i | \(-0.499166\pi\) |
−0.864713 | + | 0.502266i | \(0.832500\pi\) | |||||||
\(74\) | 2.87752 | − | 4.98402i | 0.334505 | − | 0.579380i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.37752 | − | 2.75542i | 0.387429 | − | 0.316068i | ||||
\(77\) | − | 13.2050i | − | 1.50485i | ||||||
\(78\) | 13.1334 | + | 7.58259i | 1.48707 | + | 0.858559i | ||||
\(79\) | −3.98237 | + | 6.89767i | −0.448052 | + | 0.776049i | −0.998259 | − | 0.0589793i | \(-0.981215\pi\) |
0.550207 | + | 0.835028i | \(0.314549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −13.3475 | + | 23.1186i | −1.48306 | + | 2.56874i | ||||
\(82\) | 5.03568 | − | 2.90735i | 0.556098 | − | 0.321063i | ||||
\(83\) | − | 7.86996i | − | 0.863840i | −0.901912 | − | 0.431920i | \(-0.857836\pi\) | ||
0.901912 | − | 0.431920i | \(-0.142164\pi\) | |||||||
\(84\) | −8.55462 | −0.933385 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.290150 | − | 0.502555i | −0.0312877 | − | 0.0541919i | ||||
\(87\) | 26.2497i | 2.81426i | ||||||||
\(88\) | 5.03983i | 0.537248i | ||||||||
\(89\) | −4.14483 | − | 7.17905i | −0.439351 | − | 0.760978i | 0.558289 | − | 0.829647i | \(-0.311458\pi\) |
−0.997640 | + | 0.0686686i | \(0.978125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.08503 | + | 10.5396i | 0.637884 | + | 1.10485i | ||||
\(92\) | 4.05703 | + | 2.34233i | 0.422975 | + | 0.244205i | ||||
\(93\) | 9.27458 | + | 5.35468i | 0.961729 | + | 0.555254i | ||||
\(94\) | 4.62013 | 0.476530 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.26496 | 0.333229 | ||||||||
\(97\) | 14.0208 | + | 8.09494i | 1.42360 | + | 0.821917i | 0.996605 | − | 0.0823367i | \(-0.0262383\pi\) |
0.426997 | + | 0.904253i | \(0.359572\pi\) | |||||||
\(98\) | 0.116843 | + | 0.0674593i | 0.0118029 | + | 0.00681442i | ||||
\(99\) | 19.3024 | + | 33.4328i | 1.93997 | + | 3.36012i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.23270 | − | 7.33124i | −0.421169 | − | 0.729486i | 0.574885 | − | 0.818234i | \(-0.305047\pi\) |
−0.996054 | + | 0.0887481i | \(0.971713\pi\) | |||||||
\(102\) | − | 11.9496i | − | 1.18319i | ||||||
\(103\) | − | 11.8498i | − | 1.16760i | −0.811898 | − | 0.583800i | \(-0.801565\pi\) | ||
0.811898 | − | 0.583800i | \(-0.198435\pi\) | |||||||
\(104\) | −2.32241 | − | 4.02254i | −0.227731 | − | 0.394443i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.62013 | 0.448747 | ||||||||
\(107\) | 16.8100i | 1.62508i | 0.582902 | + | 0.812542i | \(0.301917\pi\) | ||||
−0.582902 | + | 0.812542i | \(0.698083\pi\) | |||||||
\(108\) | 13.1762 | − | 7.60729i | 1.26788 | − | 0.732012i | ||||
\(109\) | 10.0023 | − | 17.3245i | 0.958045 | − | 1.65938i | 0.230806 | − | 0.973000i | \(-0.425864\pi\) |
0.727240 | − | 0.686384i | \(-0.240803\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.39500 | + | 16.2726i | −0.891734 | + | 1.54453i | ||||
\(112\) | 2.26910 | + | 1.31007i | 0.214410 | + | 0.123790i | ||||
\(113\) | 14.3505i | 1.34998i | 0.737827 | + | 0.674990i | \(0.235852\pi\) | ||||
−0.737827 | + | 0.674990i | \(0.764148\pi\) | |||||||
\(114\) | −11.0275 | + | 8.99633i | −1.03282 | + | 0.842583i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.01991 | − | 6.96270i | 0.373240 | − | 0.646470i | ||||
\(117\) | −30.8125 | − | 17.7896i | −2.84862 | − | 1.64465i | ||||
\(118\) | −3.26913 | + | 1.88743i | −0.300948 | + | 0.173752i | ||||
\(119\) | 4.79478 | − | 8.30481i | 0.439537 | − | 0.761301i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3999 | 1.30908 | ||||||||
\(122\) | − | 0.130041i | − | 0.0117733i | ||||||
\(123\) | −16.4413 | + | 9.49238i | −1.48246 | + | 0.855899i | ||||
\(124\) | −1.64004 | − | 2.84064i | −0.147280 | − | 0.255097i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20.0701 | 1.78799 | ||||||||
\(127\) | 6.82869 | − | 3.94254i | 0.605948 | − | 0.349844i | −0.165430 | − | 0.986222i | \(-0.552901\pi\) |
0.771378 | + | 0.636377i | \(0.219568\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0.947329 | + | 1.64082i | 0.0834077 | + | 0.144466i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.20228 | + | 2.08242i | −0.105044 | + | 0.181942i | −0.913756 | − | 0.406263i | \(-0.866832\pi\) |
0.808712 | + | 0.588205i | \(0.200165\pi\) | |||||||
\(132\) | − | 16.4548i | − | 1.43221i | ||||||
\(133\) | −11.2737 | + | 1.82754i | −0.977555 | + | 0.158468i | ||||
\(134\) | 0.379870 | 0.0328158 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82998 | + | 3.16962i | −0.156919 | + | 0.271792i | ||||
\(137\) | −15.0992 | + | 8.71751i | −1.29001 | + | 0.744787i | −0.978656 | − | 0.205507i | \(-0.934116\pi\) |
−0.311353 | + | 0.950294i | \(0.600782\pi\) | |||||||
\(138\) | −13.2460 | − | 7.64761i | −1.12758 | − | 0.651008i | ||||
\(139\) | 4.78487 | + | 8.28764i | 0.405848 | + | 0.702949i | 0.994420 | − | 0.105496i | \(-0.0336430\pi\) |
−0.588572 | + | 0.808445i | \(0.700310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0845 | −1.27035 | ||||||||
\(142\) | 7.91107 | − | 4.56746i | 0.663882 | − | 0.383293i | ||||
\(143\) | −20.2729 | + | 11.7046i | −1.69531 | + | 0.978786i | ||||
\(144\) | −7.65996 | −0.638330 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.25261 | − | 7.36574i | −0.351948 | − | 0.609593i | ||||
\(147\) | −0.381488 | − | 0.220252i | −0.0314646 | − | 0.0181661i | ||||
\(148\) | 4.98402 | − | 2.87752i | 0.409684 | − | 0.236531i | ||||
\(149\) | −8.56218 | + | 14.8301i | −0.701441 | + | 1.21493i | 0.266519 | + | 0.963830i | \(0.414126\pi\) |
−0.967961 | + | 0.251102i | \(0.919207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.44440 | −0.443059 | −0.221529 | − | 0.975154i | \(-0.571105\pi\) | ||||
−0.221529 | + | 0.975154i | \(0.571105\pi\) | |||||||
\(152\) | 4.30273 | − | 0.697500i | 0.348998 | − | 0.0565747i | ||||
\(153\) | 28.0351i | 2.26651i | ||||||||
\(154\) | 6.60250 | − | 11.4359i | 0.532045 | − | 0.921529i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.58259 | + | 13.1334i | 0.607093 | + | 1.05152i | ||||
\(157\) | −0.0213902 | − | 0.0123496i | −0.00170712 | − | 0.000985608i | 0.499146 | − | 0.866518i | \(-0.333647\pi\) |
−0.500853 | + | 0.865532i | \(0.666980\pi\) | |||||||
\(158\) | −6.89767 | + | 3.98237i | −0.548749 | + | 0.316821i | ||||
\(159\) | −15.0845 | −1.19628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.13721 | − | 10.6300i | −0.483680 | − | 0.837758i | ||||
\(162\) | −23.1186 | + | 13.3475i | −1.81637 | + | 1.04868i | ||||
\(163\) | − | 10.8347i | − | 0.848640i | −0.905512 | − | 0.424320i | \(-0.860513\pi\) | ||
0.905512 | − | 0.424320i | \(-0.139487\pi\) | |||||||
\(164\) | 5.81470 | 0.454052 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.93498 | − | 6.81558i | 0.305414 | − | 0.528992i | ||||
\(167\) | 5.44278 | − | 3.14239i | 0.421175 | − | 0.243165i | −0.274405 | − | 0.961614i | \(-0.588481\pi\) |
0.695580 | + | 0.718449i | \(0.255148\pi\) | |||||||
\(168\) | −7.40852 | − | 4.27731i | −0.571579 | − | 0.330002i | ||||
\(169\) | 4.28722 | − | 7.42568i | 0.329786 | − | 0.571206i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25.8717 | − | 21.1064i | 1.97846 | − | 1.61405i | ||||
\(172\) | − | 0.580301i | − | 0.0442475i | ||||||
\(173\) | 0.324914 | + | 0.187589i | 0.0247028 | + | 0.0142622i | 0.512301 | − | 0.858806i | \(-0.328793\pi\) |
−0.487598 | + | 0.873068i | \(0.662127\pi\) | |||||||
\(174\) | −13.1249 | + | 22.7329i | −0.994993 | + | 1.72338i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.51991 | + | 4.36462i | −0.189946 | + | 0.328996i | ||||
\(177\) | 10.6736 | − | 6.16240i | 0.802276 | − | 0.463194i | ||||
\(178\) | − | 8.28966i | − | 0.621336i | ||||||
\(179\) | 8.04940 | 0.601640 | 0.300820 | − | 0.953681i | \(-0.402740\pi\) | ||||
0.300820 | + | 0.953681i | \(0.402740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5251 | + | 18.2301i | 0.782327 | + | 1.35503i | 0.930583 | + | 0.366081i | \(0.119301\pi\) |
−0.148256 | + | 0.988949i | \(0.547366\pi\) | |||||||
\(182\) | 12.1701i | 0.902105i | ||||||||
\(183\) | 0.424577i | 0.0313857i | ||||||||
\(184\) | 2.34233 | + | 4.05703i | 0.172679 | + | 0.299088i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.35468 | + | 9.27458i | 0.392624 | + | 0.680045i | ||||
\(187\) | 15.9743 | + | 9.22278i | 1.16816 | + | 0.674437i | ||||
\(188\) | 4.00115 | + | 2.31007i | 0.291814 | + | 0.168479i | ||||
\(189\) | −39.8642 | −2.89969 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.03983 | 0.581742 | 0.290871 | − | 0.956762i | \(-0.406055\pi\) | ||||
0.290871 | + | 0.956762i | \(0.406055\pi\) | |||||||
\(192\) | 2.82754 | + | 1.63248i | 0.204060 | + | 0.117814i | ||||
\(193\) | 17.5325 | + | 10.1224i | 1.26202 | + | 0.728628i | 0.973465 | − | 0.228836i | \(-0.0734919\pi\) |
0.288555 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(194\) | 8.09494 | + | 14.0208i | 0.581183 | + | 1.00664i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0674593 | + | 0.116843i | 0.00481852 | + | 0.00834593i | ||||
\(197\) | 2.92004i | 0.208044i | 0.994575 | + | 0.104022i | \(0.0331713\pi\) | ||||
−0.994575 | + | 0.104022i | \(0.966829\pi\) | |||||||
\(198\) | 38.6049i | 2.74353i | ||||||||
\(199\) | −7.80244 | − | 13.5142i | −0.553101 | − | 0.957998i | −0.998049 | − | 0.0624418i | \(-0.980111\pi\) |
0.444948 | − | 0.895556i | \(-0.353222\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.24026 | −0.0874812 | ||||||||
\(202\) | − | 8.46539i | − | 0.595623i | ||||||
\(203\) | −18.2432 | + | 10.5327i | −1.28042 | + | 0.739251i | ||||
\(204\) | 5.97481 | − | 10.3487i | 0.418320 | − | 0.724552i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.92492 | − | 10.2623i | 0.412809 | − | 0.715006i | ||||
\(207\) | 31.0767 | + | 17.9421i | 2.15998 | + | 1.24707i | ||||
\(208\) | − | 4.64483i | − | 0.322061i | ||||||
\(209\) | −3.51528 | − | 21.6850i | −0.243157 | − | 1.49998i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.572585 | + | 0.991747i | −0.0394184 | + | 0.0682747i | −0.885062 | − | 0.465474i | \(-0.845884\pi\) |
0.845643 | + | 0.533749i | \(0.179217\pi\) | |||||||
\(212\) | 4.00115 | + | 2.31007i | 0.274800 | + | 0.158656i | ||||
\(213\) | −25.8293 | + | 14.9126i | −1.76980 | + | 1.02179i | ||||
\(214\) | −8.40500 | + | 14.5579i | −0.574554 | + | 0.995157i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.2146 | 1.03522 | ||||||||
\(217\) | 8.59426i | 0.583416i | ||||||||
\(218\) | 17.3245 | − | 10.0023i | 1.17336 | − | 0.677440i | ||||
\(219\) | 13.8846 | + | 24.0488i | 0.938234 | + | 1.62507i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.9999 | −1.14354 | ||||||||
\(222\) | −16.2726 | + | 9.39500i | −1.09215 | + | 0.630551i | ||||
\(223\) | 13.2757 | + | 7.66474i | 0.889008 | + | 0.513269i | 0.873618 | − | 0.486612i | \(-0.161768\pi\) |
0.0153903 | + | 0.999882i | \(0.495101\pi\) | |||||||
\(224\) | 1.31007 | + | 2.26910i | 0.0875324 | + | 0.151611i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.17524 | + | 12.4279i | −0.477290 | + | 0.826690i | ||||
\(227\) | − | 19.2850i | − | 1.27999i | −0.768380 | − | 0.639994i | \(-0.778937\pi\) | ||
0.768380 | − | 0.639994i | \(-0.221063\pi\) | |||||||
\(228\) | −14.0482 | + | 2.27731i | −0.930368 | + | 0.150818i | ||||
\(229\) | −14.3752 | −0.949939 | −0.474969 | − | 0.880002i | \(-0.657541\pi\) | ||||
−0.474969 | + | 0.880002i | \(0.657541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.5569 | + | 37.3377i | −1.41834 | + | 2.45664i | ||||
\(232\) | 6.96270 | − | 4.01991i | 0.457123 | − | 0.263920i | ||||
\(233\) | 11.9732 | + | 6.91272i | 0.784389 | + | 0.452867i | 0.837984 | − | 0.545695i | \(-0.183734\pi\) |
−0.0535944 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(234\) | −17.7896 | − | 30.8125i | −1.16294 | − | 2.01428i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.77487 | −0.245723 | ||||||||
\(237\) | 22.5206 | − | 13.0023i | 1.46287 | − | 0.844589i | ||||
\(238\) | 8.30481 | − | 4.79478i | 0.538321 | − | 0.310800i | ||||
\(239\) | 14.9696 | 0.968305 | 0.484152 | − | 0.874984i | \(-0.339128\pi\) | ||||
0.484152 | + | 0.874984i | \(0.339128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.66469 | + | 16.7397i | 0.622557 | + | 1.07830i | 0.989008 | + | 0.147863i | \(0.0472395\pi\) |
−0.366451 | + | 0.930437i | \(0.619427\pi\) | |||||||
\(242\) | 12.4707 | + | 7.19994i | 0.801644 | + | 0.462830i | ||||
\(243\) | 35.9528 | − | 20.7573i | 2.30637 | − | 1.33158i | ||||
\(244\) | 0.0650203 | − | 0.112618i | 0.00416250 | − | 0.00720966i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.9848 | −1.21042 | ||||||||
\(247\) | 12.7984 | + | 15.6880i | 0.814346 | + | 0.998205i | ||||
\(248\) | − | 3.28009i | − | 0.208286i | ||||||
\(249\) | −12.8475 | + | 22.2526i | −0.814180 | + | 1.41020i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.16246 | − | 8.94164i | −0.325851 | − | 0.564391i | 0.655833 | − | 0.754906i | \(-0.272318\pi\) |
−0.981684 | + | 0.190515i | \(0.938984\pi\) | |||||||
\(252\) | 17.3812 | + | 10.0350i | 1.09491 | + | 0.632148i | ||||
\(253\) | 20.4468 | − | 11.8049i | 1.28548 | − | 0.742170i | ||||
\(254\) | 7.88509 | 0.494755 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −24.9149 | + | 14.3846i | −1.55415 | + | 0.897287i | −0.556349 | + | 0.830949i | \(0.687798\pi\) |
−0.997797 | + | 0.0663376i | \(0.978869\pi\) | |||||||
\(258\) | 1.89466i | 0.117956i | ||||||||
\(259\) | −15.0790 | −0.936962 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.7924 | − | 53.3340i | 1.90600 | − | 3.30129i | ||||
\(262\) | −2.08242 | + | 1.20228i | −0.128652 | + | 0.0742774i | ||||
\(263\) | 7.91107 | + | 4.56746i | 0.487818 | + | 0.281642i | 0.723669 | − | 0.690148i | \(-0.242454\pi\) |
−0.235851 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(264\) | 8.22742 | − | 14.2503i | 0.506363 | − | 0.877046i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.6771 | − | 4.05416i | −0.654655 | − | 0.248577i | ||||
\(267\) | 27.0654i | 1.65638i | ||||||||
\(268\) | 0.328977 | + | 0.189935i | 0.0200955 | + | 0.0116021i | ||||
\(269\) | 8.45474 | − | 14.6440i | 0.515495 | − | 0.892863i | −0.484343 | − | 0.874878i | \(-0.660941\pi\) |
0.999838 | − | 0.0179853i | \(-0.00572519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.94483 | − | 13.7609i | 0.482614 | − | 0.835912i | −0.517187 | − | 0.855873i | \(-0.673021\pi\) |
0.999801 | + | 0.0199603i | \(0.00635399\pi\) | |||||||
\(272\) | −3.16962 | + | 1.82998i | −0.192186 | + | 0.110959i | ||||
\(273\) | − | 39.7347i | − | 2.40486i | ||||||
\(274\) | −17.4350 | −1.05329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.64761 | − | 13.2460i | −0.460332 | − | 0.797318i | ||||
\(277\) | − | 11.4852i | − | 0.690079i | −0.938588 | − | 0.345040i | \(-0.887865\pi\) | ||
0.938588 | − | 0.345040i | \(-0.112135\pi\) | |||||||
\(278\) | 9.56975i | 0.573955i | ||||||||
\(279\) | −12.5627 | − | 21.7592i | −0.752108 | − | 1.30269i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.14483 | + | 12.3752i | 0.426225 | + | 0.738243i | 0.996534 | − | 0.0831872i | \(-0.0265099\pi\) |
−0.570309 | + | 0.821430i | \(0.693177\pi\) | |||||||
\(282\) | −13.0636 | − | 7.54227i | −0.777926 | − | 0.449136i | ||||
\(283\) | −2.74037 | − | 1.58215i | −0.162898 | − | 0.0940493i | 0.416335 | − | 0.909211i | \(-0.363314\pi\) |
−0.579233 | + | 0.815162i | \(0.696648\pi\) | |||||||
\(284\) | 9.13492 | 0.542058 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.4091 | −1.38421 | ||||||||
\(287\) | −13.1941 | − | 7.61763i | −0.778825 | − | 0.449655i | ||||
\(288\) | −6.63372 | − | 3.82998i | −0.390896 | − | 0.225684i | ||||
\(289\) | −1.80235 | − | 3.12176i | −0.106021 | − | 0.183633i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.4296 | − | 45.7775i | −1.54933 | − | 2.68352i | ||||
\(292\) | − | 8.50522i | − | 0.497730i | ||||||
\(293\) | 14.7094i | 0.859330i | 0.902988 | + | 0.429665i | \(0.141368\pi\) | ||||
−0.902988 | + | 0.429665i | \(0.858632\pi\) | |||||||
\(294\) | −0.220252 | − | 0.381488i | −0.0128454 | − | 0.0222488i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.75505 | 0.334505 | ||||||||
\(297\) | − | 76.6789i | − | 4.44936i | ||||||
\(298\) | −14.8301 | + | 8.56218i | −0.859087 | + | 0.495994i | ||||
\(299\) | −10.8797 | + | 18.8442i | −0.629190 | + | 1.08979i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.760232 | + | 1.31676i | −0.0438190 | + | 0.0758968i | ||||
\(302\) | −4.71499 | − | 2.72220i | −0.271317 | − | 0.156645i | ||||
\(303\) | 27.6392i | 1.58783i | ||||||||
\(304\) | 4.07502 | + | 1.54731i | 0.233719 | + | 0.0887445i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.0176 | + | 24.2791i | −0.801331 | + | 1.38795i | ||||
\(307\) | −22.6425 | − | 13.0727i | −1.29228 | − | 0.746097i | −0.313221 | − | 0.949680i | \(-0.601408\pi\) |
−0.979058 | + | 0.203583i | \(0.934741\pi\) | |||||||
\(308\) | 11.4359 | − | 6.60250i | 0.651619 | − | 0.376213i | ||||
\(309\) | −19.3446 | + | 33.5059i | −1.10048 | + | 1.90608i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.65039 | 0.377109 | 0.188555 | − | 0.982063i | \(-0.439620\pi\) | ||||
0.188555 | + | 0.982063i | \(0.439620\pi\) | |||||||
\(312\) | 15.1652i | 0.858559i | ||||||||
\(313\) | −15.0513 | + | 8.68988i | −0.850750 | + | 0.491181i | −0.860904 | − | 0.508768i | \(-0.830101\pi\) |
0.0101536 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(314\) | −0.0123496 | − | 0.0213902i | −0.000696930 | − | 0.00120712i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.96475 | −0.448052 | ||||||||
\(317\) | −1.19104 | + | 0.687647i | −0.0668954 | + | 0.0386221i | −0.533075 | − | 0.846068i | \(-0.678964\pi\) |
0.466179 | + | 0.884690i | \(0.345630\pi\) | |||||||
\(318\) | −13.0636 | − | 7.54227i | −0.732570 | − | 0.422949i | ||||
\(319\) | −20.2597 | − | 35.0908i | −1.13432 | − | 1.96471i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.4420 | − | 47.5309i | 1.53166 | − | 2.65292i | ||||
\(322\) | − | 12.2744i | − | 0.684026i | ||||||
\(323\) | 5.66310 | − | 14.9144i | 0.315103 | − | 0.829861i | ||||
\(324\) | −26.6951 | −1.48306 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.41735 | − | 9.38313i | 0.300039 | − | 0.519684i | ||||
\(327\) | −56.5637 | + | 32.6571i | −3.12798 | + | 1.80594i | ||||
\(328\) | 5.03568 | + | 2.90735i | 0.278049 | + | 0.160532i | ||||
\(329\) | −6.05267 | − | 10.4835i | −0.333695 | − | 0.577976i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7399 | 0.645284 | 0.322642 | − | 0.946521i | \(-0.395429\pi\) | ||||
0.322642 | + | 0.946521i | \(0.395429\pi\) | |||||||
\(332\) | 6.81558 | − | 3.93498i | 0.374054 | − | 0.215960i | ||||
\(333\) | 38.1774 | − | 22.0417i | 2.09211 | − | 1.20788i | ||||
\(334\) | 6.28478 | 0.343888 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.27731 | − | 7.40852i | −0.233346 | − | 0.404168i | ||||
\(337\) | 11.1545 | + | 6.44005i | 0.607624 | + | 0.350812i | 0.772035 | − | 0.635580i | \(-0.219239\pi\) |
−0.164411 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(338\) | 7.42568 | − | 4.28722i | 0.403904 | − | 0.233194i | ||||
\(339\) | 23.4269 | − | 40.5765i | 1.27237 | − | 2.20381i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.5311 | −0.895209 | ||||||||
\(342\) | 32.9587 | − | 5.34282i | 1.78220 | − | 0.288907i | ||||
\(343\) | − | 18.6944i | − | 1.00940i | ||||||
\(344\) | 0.290150 | − | 0.502555i | 0.0156439 | − | 0.0270960i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.187589 | + | 0.324914i | 0.0100849 | + | 0.0174675i | ||||
\(347\) | −4.27339 | − | 2.46724i | −0.229408 | − | 0.132449i | 0.380891 | − | 0.924620i | \(-0.375617\pi\) |
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(348\) | −22.7329 | + | 13.1249i | −1.21861 | + | 0.703566i | ||||
\(349\) | −1.26594 | −0.0677644 | −0.0338822 | − | 0.999426i | \(-0.510787\pi\) | ||||
−0.0338822 | + | 0.999426i | \(0.510787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.3346 | + | 61.2012i | 1.88602 | + | 3.26668i | ||||
\(352\) | −4.36462 | + | 2.51991i | −0.232635 | + | 0.134312i | ||||
\(353\) | − | 2.16060i | − | 0.114997i | −0.998346 | − | 0.0574986i | \(-0.981688\pi\) | ||
0.998346 | − | 0.0574986i | \(-0.0183125\pi\) | |||||||
\(354\) | 12.3248 | 0.655056 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.14483 | − | 7.17905i | 0.219676 | − | 0.380489i | ||||
\(357\) | −27.1149 | + | 15.6548i | −1.43507 | + | 0.828539i | ||||
\(358\) | 6.97098 | + | 4.02470i | 0.368428 | + | 0.212712i | ||||
\(359\) | −2.36981 | + | 4.10463i | −0.125074 | + | 0.216634i | −0.921762 | − | 0.387757i | \(-0.873250\pi\) |
0.796688 | + | 0.604391i | \(0.206583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0270 | + | 6.00231i | −0.948789 | + | 0.315911i | ||||
\(362\) | 21.0503i | 1.10638i | ||||||||
\(363\) | −40.7162 | − | 23.5075i | −2.13705 | − | 1.23382i | ||||
\(364\) | −6.08503 | + | 10.5396i | −0.318942 | + | 0.552424i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.212289 | + | 0.367695i | −0.0110965 | + | 0.0192197i | ||||
\(367\) | −19.8271 | + | 11.4472i | −1.03497 | + | 0.597538i | −0.918403 | − | 0.395645i | \(-0.870521\pi\) |
−0.116563 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(368\) | 4.68466i | 0.244205i | ||||||||
\(369\) | 44.5404 | 2.31868 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.05267 | − | 10.4835i | −0.314239 | − | 0.544278i | ||||
\(372\) | 10.7094i | 0.555254i | ||||||||
\(373\) | − | 19.2393i | − | 0.996172i | −0.867128 | − | 0.498086i | \(-0.834036\pi\) | ||
0.867128 | − | 0.498086i | \(-0.165964\pi\) | |||||||
\(374\) | 9.22278 | + | 15.9743i | 0.476899 | + | 0.826013i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.31007 | + | 4.00115i | 0.119133 | + | 0.206344i | ||||
\(377\) | 32.3405 | + | 18.6718i | 1.66562 | + | 0.961647i | ||||
\(378\) | −34.5234 | − | 19.9321i | −1.77569 | − | 1.02520i | ||||
\(379\) | 6.45953 | 0.331804 | 0.165902 | − | 0.986142i | \(-0.446947\pi\) | ||||
0.165902 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.7445 | −1.31893 | ||||||||
\(382\) | 6.96270 | + | 4.01991i | 0.356243 | + | 0.205677i | ||||
\(383\) | 7.91107 | + | 4.56746i | 0.404237 | + | 0.233386i | 0.688310 | − | 0.725416i | \(-0.258353\pi\) |
−0.284074 | + | 0.958802i | \(0.591686\pi\) | |||||||
\(384\) | 1.63248 | + | 2.82754i | 0.0833071 | + | 0.144292i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1224 | + | 17.5325i | 0.515218 | + | 0.892383i | ||||
\(387\) | − | 4.44508i | − | 0.225956i | ||||||
\(388\) | 16.1899i | 0.821917i | ||||||||
\(389\) | −13.3424 | − | 23.1098i | −0.676488 | − | 1.17171i | −0.976032 | − | 0.217629i | \(-0.930168\pi\) |
0.299544 | − | 0.954082i | \(-0.403165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1457 | 0.867093 | ||||||||
\(392\) | 0.134919i | 0.00681442i | ||||||||
\(393\) | 6.79901 | − | 3.92541i | 0.342965 | − | 0.198011i | ||||
\(394\) | −1.46002 | + | 2.52883i | −0.0735548 | + | 0.127401i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −19.3024 | + | 33.4328i | −0.969984 | + | 1.68006i | ||||
\(397\) | 12.7732 | + | 7.37459i | 0.641067 | + | 0.370120i | 0.785025 | − | 0.619464i | \(-0.212650\pi\) |
−0.143958 | + | 0.989584i | \(0.545983\pi\) | |||||||
\(398\) | − | 15.6049i | − | 0.782202i | ||||||
\(399\) | 34.8603 | + | 13.2367i | 1.74520 | + | 0.662662i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.82720 | + | 10.0930i | −0.290996 | + | 0.504021i | −0.974046 | − | 0.226352i | \(-0.927320\pi\) |
0.683049 | + | 0.730372i | \(0.260653\pi\) | |||||||
\(402\) | −1.07410 | − | 0.620130i | −0.0535711 | − | 0.0309293i | ||||
\(403\) | 13.1943 | − | 7.61773i | 0.657254 | − | 0.379466i | ||||
\(404\) | 4.23270 | − | 7.33124i | 0.210584 | − | 0.364743i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.0654 | −1.04546 | ||||||||
\(407\) | − | 29.0045i | − | 1.43770i | ||||||
\(408\) | 10.3487 | − | 5.97481i | 0.512336 | − | 0.295797i | ||||
\(409\) | 19.7824 | + | 34.2641i | 0.978176 | + | 1.69425i | 0.669030 | + | 0.743235i | \(0.266710\pi\) |
0.309145 | + | 0.951015i | \(0.399957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.9246 | 2.80788 | ||||||||
\(412\) | 10.2623 | − | 5.92492i | 0.505585 | − | 0.291900i | ||||
\(413\) | 8.56555 | + | 4.94532i | 0.421483 | + | 0.243344i | ||||
\(414\) | 17.9421 | + | 31.0767i | 0.881808 | + | 1.52734i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.32241 | − | 4.02254i | 0.113866 | − | 0.197221i | ||||
\(417\) | − | 31.2448i | − | 1.53007i | ||||||
\(418\) | 7.79819 | − | 20.5374i | 0.381422 | − | 1.00452i | ||||
\(419\) | −17.3292 | −0.846586 | −0.423293 | − | 0.905993i | \(-0.639126\pi\) | ||||
−0.423293 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.1652 | + | 21.0707i | −0.592895 | + | 1.02692i | 0.400946 | + | 0.916102i | \(0.368682\pi\) |
−0.993840 | + | 0.110822i | \(0.964652\pi\) | |||||||
\(422\) | −0.991747 | + | 0.572585i | −0.0482775 | + | 0.0278730i | ||||
\(423\) | 30.6486 | + | 17.6950i | 1.49019 | + | 0.860361i | ||||
\(424\) | 2.31007 | + | 4.00115i | 0.112187 | + | 0.194313i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −29.8251 | −1.44503 | ||||||||
\(427\) | −0.295075 | + | 0.170362i | −0.0142797 | + | 0.00824438i | ||||
\(428\) | −14.5579 | + | 8.40500i | −0.703682 | + | 0.406271i | ||||
\(429\) | 76.4299 | 3.69007 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.1173 | − | 24.4519i | −0.680006 | − | 1.17781i | −0.974978 | − | 0.222299i | \(-0.928644\pi\) |
0.294972 | − | 0.955506i | \(-0.404690\pi\) | |||||||
\(432\) | 13.1762 | + | 7.60729i | 0.633941 | + | 0.366006i | ||||
\(433\) | −20.2475 | + | 11.6899i | −0.973031 | + | 0.561780i | −0.900159 | − | 0.435562i | \(-0.856550\pi\) |
−0.0728720 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(434\) | −4.29713 | + | 7.44285i | −0.206269 | + | 0.357268i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.0046 | 0.958045 | ||||||||
\(437\) | −12.9082 | − | 15.8225i | −0.617483 | − | 0.756895i | ||||
\(438\) | 27.7692i | 1.32686i | ||||||||
\(439\) | 13.3775 | − | 23.1705i | 0.638472 | − | 1.10587i | −0.347297 | − | 0.937755i | \(-0.612900\pi\) |
0.985768 | − | 0.168110i | \(-0.0537664\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.516736 | + | 0.895013i | 0.0246065 | + | 0.0426197i | ||||
\(442\) | −14.7223 | − | 8.49994i | −0.700270 | − | 0.404301i | ||||
\(443\) | −15.3285 | + | 8.84989i | −0.728277 | + | 0.420471i | −0.817792 | − | 0.575514i | \(-0.804802\pi\) |
0.0895142 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(444\) | −18.7900 | −0.891734 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.66474 | + | 13.2757i | 0.362936 | + | 0.628624i | ||||
\(447\) | 48.4198 | − | 27.9552i | 2.29018 | − | 1.32223i | ||||
\(448\) | 2.62013i | 0.123790i | ||||||||
\(449\) | −28.3541 | −1.33811 | −0.669056 | − | 0.743212i | \(-0.733301\pi\) | ||||
−0.669056 | + | 0.743212i | \(0.733301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6525 | − | 25.3790i | 0.689961 | − | 1.19505i | ||||
\(452\) | −12.4279 | + | 7.17524i | −0.584558 | + | 0.337495i | ||||
\(453\) | 15.3942 | + | 8.88787i | 0.723285 | + | 0.417589i | ||||
\(454\) | 9.64248 | − | 16.7013i | 0.452544 | − | 0.783830i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.3048 | − | 5.05191i | −0.623054 | − | 0.236578i | ||||
\(457\) | − | 11.5898i | − | 0.542146i | −0.962559 | − | 0.271073i | \(-0.912622\pi\) | ||
0.962559 | − | 0.271073i | \(-0.0873785\pi\) | |||||||
\(458\) | −12.4493 | − | 7.18759i | −0.581716 | − | 0.335854i | ||||
\(459\) | 27.8424 | − | 48.2244i | 1.29957 | − | 2.25092i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8899 | + | 30.9862i | −0.833214 | + | 1.44317i | 0.0622614 | + | 0.998060i | \(0.480169\pi\) |
−0.895476 | + | 0.445110i | \(0.853165\pi\) | |||||||
\(462\) | −37.3377 | + | 21.5569i | −1.73711 | + | 1.00292i | ||||
\(463\) | 23.5039i | 1.09232i | 0.837681 | + | 0.546160i | \(0.183911\pi\) | ||||
−0.837681 | + | 0.546160i | \(0.816089\pi\) | |||||||
\(464\) | 8.03983 | 0.373240 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.91272 | + | 11.9732i | 0.320226 | + | 0.554647i | ||||
\(467\) | 1.12047i | 0.0518492i | 0.999664 | + | 0.0259246i | \(0.00825299\pi\) | ||||
−0.999664 | + | 0.0259246i | \(0.991747\pi\) | |||||||
\(468\) | − | 35.5792i | − | 1.64465i | ||||||
\(469\) | −0.497654 | − | 0.861963i | −0.0229795 | − | 0.0398017i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0403210 | + | 0.0698381i | 0.00185790 | + | 0.00321797i | ||||
\(472\) | −3.26913 | − | 1.88743i | −0.150474 | − | 0.0868762i | ||||
\(473\) | −2.53279 | − | 1.46231i | −0.116458 | − | 0.0672370i | ||||
\(474\) | 26.0046 | 1.19443 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.58957 | 0.439537 | ||||||||
\(477\) | 30.6486 | + | 17.6950i | 1.40331 | + | 0.810199i | ||||
\(478\) | 12.9641 | + | 7.48481i | 0.592963 | + | 0.342347i | ||||
\(479\) | 13.6547 | + | 23.6506i | 0.623898 | + | 1.08062i | 0.988753 | + | 0.149559i | \(0.0477854\pi\) |
−0.364854 | + | 0.931065i | \(0.618881\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3656 | + | 23.1499i | 0.609419 | + | 1.05555i | ||||
\(482\) | 19.3294i | 0.880429i | ||||||||
\(483\) | 40.0755i | 1.82350i | ||||||||
\(484\) | 7.19994 | + | 12.4707i | 0.327270 | + | 0.566848i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 41.5147 | 1.88314 | ||||||||
\(487\) | − | 6.32003i | − | 0.286388i | −0.989695 | − | 0.143194i | \(-0.954263\pi\) | ||
0.989695 | − | 0.143194i | \(-0.0457373\pi\) | |||||||
\(488\) | 0.112618 | − | 0.0650203i | 0.00509800 | − | 0.00294333i | ||||
\(489\) | −17.6874 | + | 30.6355i | −0.799854 | + | 1.38539i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9025 | − | 22.3478i | 0.582282 | − | 1.00854i | −0.412926 | − | 0.910764i | \(-0.635493\pi\) |
0.995208 | − | 0.0977776i | \(-0.0311734\pi\) | |||||||
\(492\) | −16.4413 | − | 9.49238i | −0.741230 | − | 0.427949i | ||||
\(493\) | − | 29.4254i | − | 1.32526i | ||||||
\(494\) | 3.23977 | + | 19.9855i | 0.145764 | + | 0.899188i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.64004 | − | 2.84064i | 0.0736402 | − | 0.127549i | ||||
\(497\) | −20.7280 | − | 11.9673i | −0.929779 | − | 0.536808i | ||||
\(498\) | −22.2526 | + | 12.8475i | −0.997163 | + | 0.575712i | ||||
\(499\) | −14.4572 | + | 25.0406i | −0.647192 | + | 1.12097i | 0.336598 | + | 0.941648i | \(0.390724\pi\) |
−0.983790 | + | 0.179322i | \(0.942610\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.5196 | −0.916746 | ||||||||
\(502\) | − | 10.3249i | − | 0.460823i | ||||||
\(503\) | −0.995971 | + | 0.575024i | −0.0444082 | + | 0.0256391i | −0.522040 | − | 0.852921i | \(-0.674829\pi\) |
0.477632 | + | 0.878560i | \(0.341495\pi\) | |||||||
\(504\) | 10.0350 | + | 17.3812i | 0.446996 | + | 0.774220i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.6099 | 1.04959 | ||||||||
\(507\) | −24.2445 | + | 13.9976i | −1.07674 | + | 0.621655i | ||||
\(508\) | 6.82869 | + | 3.94254i | 0.302974 | + | 0.174922i | ||||
\(509\) | 20.3673 | + | 35.2772i | 0.902765 | + | 1.56364i | 0.823889 | + | 0.566751i | \(0.191800\pi\) |
0.0788760 | + | 0.996884i | \(0.474867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1424 | + | 19.2992i | −0.492910 | + | 0.853746i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −65.4642 | + | 10.6122i | −2.89032 | + | 0.468539i | ||||
\(514\) | −28.7692 | −1.26895 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.947329 | + | 1.64082i | −0.0417038 | + | 0.0722332i | ||||
\(517\) | 20.1651 | − | 11.6423i | 0.886861 | − | 0.512029i | ||||
\(518\) | −13.0588 | − | 7.53949i | −0.573770 | − | 0.331266i | ||||
\(519\) | −0.612472 | − | 1.06083i | −0.0268845 | − | 0.0465654i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4246 | −0.500520 | −0.250260 | − | 0.968179i | \(-0.580516\pi\) | ||||
−0.250260 | + | 0.968179i | \(0.580516\pi\) | |||||||
\(522\) | 53.3340 | − | 30.7924i | 2.33436 | − | 1.34775i | ||||
\(523\) | −11.3570 | + | 6.55696i | −0.496607 | + | 0.286716i | −0.727311 | − | 0.686308i | \(-0.759230\pi\) |
0.230704 | + | 0.973024i | \(0.425897\pi\) | |||||||
\(524\) | −2.40457 | −0.105044 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.56746 | + | 7.91107i | 0.199151 | + | 0.344939i | ||||
\(527\) | −10.3966 | − | 6.00250i | −0.452884 | − | 0.261473i | ||||
\(528\) | 14.2503 | − | 8.22742i | 0.620165 | − | 0.358052i | ||||
\(529\) | −0.526988 | + | 0.912769i | −0.0229125 | + | 0.0396856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.9153 | −1.25482 | ||||||||
\(532\) | −7.21955 | − | 8.84955i | −0.313007 | − | 0.383677i | ||||
\(533\) | 27.0083i | 1.16986i | ||||||||
\(534\) | −13.5327 | + | 23.4393i | −0.585617 | + | 1.01432i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.189935 | + | 0.328977i | 0.00820394 | + | 0.0142096i | ||||
\(537\) | −22.7600 | − | 13.1405i | −0.982166 | − | 0.567054i | ||||
\(538\) | 14.6440 | − | 8.45474i | 0.631350 | − | 0.364510i | ||||
\(539\) | 0.679967 | 0.0292883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4949 | + | 25.1059i | 0.623183 | + | 1.07939i | 0.988889 | + | 0.148655i | \(0.0474943\pi\) |
−0.365706 | + | 0.930730i | \(0.619172\pi\) | |||||||
\(542\) | 13.7609 | − | 7.94483i | 0.591079 | − | 0.341260i | ||||
\(543\) | − | 68.7283i | − | 2.94941i | ||||||
\(544\) | −3.65996 | −0.156919 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.8674 | − | 34.4113i | 0.850245 | − | 1.47267i | ||||
\(547\) | −30.8724 | + | 17.8242i | −1.32001 | + | 0.762108i | −0.983730 | − | 0.179654i | \(-0.942502\pi\) |
−0.336280 | + | 0.941762i | \(0.609169\pi\) | |||||||
\(548\) | −15.0992 | − | 8.71751i | −0.645004 | − | 0.372393i | ||||
\(549\) | 0.498053 | − | 0.862653i | 0.0212564 | − | 0.0368171i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.1547 | + | 22.1531i | −1.15683 | + | 0.943753i | ||||
\(552\) | − | 15.2952i | − | 0.651008i | ||||||
\(553\) | 18.0728 | + | 10.4343i | 0.768534 | + | 0.443713i | ||||
\(554\) | 5.74261 | − | 9.94648i | 0.243980 | − | 0.422586i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.78487 | + | 8.28764i | −0.202924 | + | 0.351474i | ||||
\(557\) | 10.8726 | − | 6.27731i | 0.460688 | − | 0.265978i | −0.251646 | − | 0.967819i | \(-0.580972\pi\) |
0.712333 | + | 0.701841i | \(0.247638\pi\) | |||||||
\(558\) | − | 25.1253i | − | 1.06364i | ||||||
\(559\) | 2.69540 | 0.114003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.1120 | − | 52.1555i | −1.27133 | − | 2.20201i | ||||
\(562\) | 14.2897i | 0.602773i | ||||||||
\(563\) | 2.88509i | 0.121592i | 0.998150 | + | 0.0607960i | \(0.0193639\pi\) | ||||
−0.998150 | + | 0.0607960i | \(0.980636\pi\) | |||||||
\(564\) | −7.54227 | − | 13.0636i | −0.317587 | − | 0.550076i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.58215 | − | 2.74037i | −0.0665029 | − | 0.115186i | ||||
\(567\) | 60.5738 | + | 34.9723i | 2.54386 | + | 1.46870i | ||||
\(568\) | 7.91107 | + | 4.56746i | 0.331941 | + | 0.191646i | ||||
\(569\) | 10.9249 | 0.457996 | 0.228998 | − | 0.973427i | \(-0.426455\pi\) | ||||
0.228998 | + | 0.973427i | \(0.426455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.27911 | 0.262772 | 0.131386 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131386 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(572\) | −20.2729 | − | 11.7046i | −0.847653 | − | 0.489393i | ||||
\(573\) | −22.7329 | − | 13.1249i | −0.949681 | − | 0.548299i | ||||
\(574\) | −7.61763 | − | 13.1941i | −0.317954 | − | 0.550712i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.82998 | − | 6.63372i | −0.159582 | − | 0.276405i | ||||
\(577\) | − | 25.9848i | − | 1.08176i | −0.841100 | − | 0.540880i | \(-0.818091\pi\) | ||
0.841100 | − | 0.540880i | \(-0.181909\pi\) | |||||||
\(578\) | − | 3.60470i | − | 0.149936i | ||||||
\(579\) | −33.0493 | − | 57.2430i | −1.37348 | − | 2.37894i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.6203 | −0.855475 | ||||||||
\(582\) | − | 52.8593i | − | 2.19109i | ||||||
\(583\) | 20.1651 | − | 11.6423i | 0.835154 | − | 0.482176i | ||||
\(584\) | 4.25261 | − | 7.36574i | 0.175974 | − | 0.304796i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.35468 | + | 12.7387i | −0.303819 | + | 0.526230i | ||||
\(587\) | −31.4448 | − | 18.1547i | −1.29787 | − | 0.749324i | −0.317832 | − | 0.948147i | \(-0.602955\pi\) |
−0.980035 | + | 0.198823i | \(0.936288\pi\) | |||||||
\(588\) | − | 0.440504i | − | 0.0181661i | ||||||
\(589\) | 2.28786 | + | 14.1133i | 0.0942697 | + | 0.581530i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.76691 | − | 8.25652i | 0.196084 | − | 0.339628i | ||||
\(592\) | 4.98402 | + | 2.87752i | 0.204842 | + | 0.118266i | ||||
\(593\) | 27.4783 | − | 15.8646i | 1.12840 | − | 0.651482i | 0.184868 | − | 0.982763i | \(-0.440814\pi\) |
0.943532 | + | 0.331281i | \(0.107481\pi\) | |||||||
\(594\) | 38.3394 | − | 66.4058i | 1.57309 | − | 2.72466i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.1244 | −0.701441 | ||||||||
\(597\) | 50.9493i | 2.08522i | ||||||||
\(598\) | −18.8442 | + | 10.8797i | −0.770598 | + | 0.444905i | ||||
\(599\) | −0.174654 | − | 0.302510i | −0.00713619 | − | 0.0123602i | 0.862435 | − | 0.506167i | \(-0.168938\pi\) |
−0.869571 | + | 0.493807i | \(0.835605\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.7305 | 1.37590 | 0.687949 | − | 0.725759i | \(-0.258511\pi\) | ||||
0.687949 | + | 0.725759i | \(0.258511\pi\) | |||||||
\(602\) | −1.31676 | + | 0.760232i | −0.0536671 | + | 0.0309847i | ||||
\(603\) | 2.51995 | + | 1.45489i | 0.102620 | + | 0.0592479i | ||||
\(604\) | −2.72220 | − | 4.71499i | −0.110765 | − | 0.191850i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.8196 | + | 23.9362i | −0.561382 | + | 0.972342i | ||||
\(607\) | 28.0561i | 1.13876i | 0.822073 | + | 0.569382i | \(0.192817\pi\) | ||||
−0.822073 | + | 0.569382i | \(0.807183\pi\) | |||||||
\(608\) | 2.75542 | + | 3.37752i | 0.111747 | + | 0.136977i | ||||
\(609\) | 68.7777 | 2.78701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7299 | + | 18.5847i | −0.434084 | + | 0.751855i | ||||
\(612\) | −24.2791 | + | 14.0176i | −0.981426 | + | 0.566627i | ||||
\(613\) | 35.8969 | + | 20.7251i | 1.44986 | + | 0.837078i | 0.998473 | − | 0.0552496i | \(-0.0175955\pi\) |
0.451389 | + | 0.892327i | \(0.350929\pi\) | |||||||
\(614\) | −13.0727 | − | 22.6425i | −0.527570 | − | 0.913779i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.2050 | 0.532045 | ||||||||
\(617\) | −5.09985 | + | 2.94440i | −0.205312 | + | 0.118537i | −0.599131 | − | 0.800651i | \(-0.704487\pi\) |
0.393819 | + | 0.919188i | \(0.371154\pi\) | |||||||
\(618\) | −33.5059 | + | 19.3446i | −1.34780 | + | 0.778155i | ||||
\(619\) | −13.7152 | −0.551261 | −0.275631 | − | 0.961264i | \(-0.588887\pi\) | ||||
−0.275631 | + | 0.961264i | \(0.588887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.6375 | − | 61.7260i | −1.43009 | − | 2.47698i | ||||
\(622\) | 5.75941 | + | 3.32519i | 0.230931 | + | 0.133328i | ||||
\(623\) | −18.8101 | + | 10.8600i | −0.753609 | + | 0.435096i | ||||
\(624\) | −7.58259 | + | 13.1334i | −0.303547 | + | 0.525758i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.3798 | −0.694635 | ||||||||
\(627\) | −25.4608 | + | 67.0539i | −1.01681 | + | 2.67787i | ||||
\(628\) | − | 0.0246993i | − | 0.000985608i | ||||||
\(629\) | 10.5316 | − | 18.2413i | 0.419923 | − | 0.727328i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.14468 | + | 14.1070i | 0.324235 | + | 0.561591i | 0.981357 | − | 0.192193i | \(-0.0615600\pi\) |
−0.657123 | + | 0.753784i | \(0.728227\pi\) | |||||||
\(632\) | −6.89767 | − | 3.98237i | −0.274375 | − | 0.158410i | ||||
\(633\) | 3.23801 | − | 1.86947i | 0.128699 | − | 0.0743047i | ||||
\(634\) | −1.37529 | −0.0546199 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.54227 | − | 13.0636i | −0.299070 | − | 0.518005i | ||||
\(637\) | −0.542716 | + | 0.313337i | −0.0215032 | + | 0.0124149i | ||||
\(638\) | − | 40.5194i | − | 1.60418i | ||||||
\(639\) | 69.9731 | 2.76809 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.8124 | + | 25.6559i | −0.585056 | + | 1.01335i | 0.409812 | + | 0.912170i | \(0.365594\pi\) |
−0.994868 | + | 0.101177i | \(0.967739\pi\) | |||||||
\(642\) | 47.5309 | − | 27.4420i | 1.87590 | − | 1.08305i | ||||
\(643\) | 10.4105 | + | 6.01050i | 0.410549 | + | 0.237031i | 0.691026 | − | 0.722830i | \(-0.257159\pi\) |
−0.280476 | + | 0.959861i | \(0.590492\pi\) | |||||||
\(644\) | 6.13721 | − | 10.6300i | 0.241840 | − | 0.418879i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.3616 | − | 10.0847i | 0.486361 | − | 0.396778i | ||||
\(647\) | − | 3.16079i | − | 0.124263i | −0.998068 | − | 0.0621317i | \(-0.980210\pi\) | ||
0.998068 | − | 0.0621317i | \(-0.0197899\pi\) | |||||||
\(648\) | −23.1186 | − | 13.3475i | −0.908186 | − | 0.524341i | ||||
\(649\) | −9.51235 | + | 16.4759i | −0.373392 | + | 0.646735i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.0300 | − | 24.3006i | 0.549877 | − | 0.952415i | ||||
\(652\) | 9.38313 | − | 5.41735i | 0.367472 | − | 0.212160i | ||||
\(653\) | − | 19.6097i | − | 0.767387i | −0.923461 | − | 0.383693i | \(-0.874652\pi\) | ||
0.923461 | − | 0.383693i | \(-0.125348\pi\) | |||||||
\(654\) | −65.3141 | −2.55398 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.90735 | + | 5.03568i | 0.113513 | + | 0.196610i | ||||
\(657\) | − | 65.1496i | − | 2.54173i | ||||||
\(658\) | − | 12.1053i | − | 0.471915i | ||||||
\(659\) | −9.03748 | − | 15.6534i | −0.352050 | − | 0.609769i | 0.634558 | − | 0.772875i | \(-0.281182\pi\) |
−0.986609 | + | 0.163106i | \(0.947849\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.26715 | + | 12.5871i | 0.282660 | + | 0.489581i | 0.972039 | − | 0.234820i | \(-0.0754500\pi\) |
−0.689379 | + | 0.724400i | \(0.742117\pi\) | |||||||
\(662\) | 10.1671 | + | 5.86996i | 0.395154 | + | 0.228142i | ||||
\(663\) | 48.0678 | + | 27.7520i | 1.86680 | + | 1.07780i | ||||
\(664\) | 7.86996 | 0.305414 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 44.0834 | 1.70820 | ||||||||
\(667\) | −32.6179 | − | 18.8319i | −1.26297 | − | 0.729175i | ||||
\(668\) | 5.44278 | + | 3.14239i | 0.210587 | + | 0.121583i | ||||
\(669\) | −25.0251 | − | 43.3447i | −0.967525 | − | 1.67580i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.327691 | − | 0.567578i | −0.0126504 | − | 0.0219111i | ||||
\(672\) | − | 8.55462i | − | 0.330002i | ||||||
\(673\) | 6.13522i | 0.236495i | 0.992984 | + | 0.118248i | \(0.0377277\pi\) | ||||
−0.992984 | + | 0.118248i | \(0.962272\pi\) | |||||||
\(674\) | 6.44005 | + | 11.1545i | 0.248061 | + | 0.429655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.57444 | 0.329786 | ||||||||
\(677\) | 13.6380i | 0.524150i | 0.965047 | + | 0.262075i | \(0.0844068\pi\) | ||||
−0.965047 | + | 0.262075i | \(0.915593\pi\) | |||||||
\(678\) | 40.5765 | − | 23.4269i | 1.55833 | − | 0.899703i | ||||
\(679\) | 21.2098 | − | 36.7364i | 0.813957 | − | 1.40982i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.4823 | + | 54.5290i | −1.20640 | + | 2.08955i | ||||
\(682\) | −14.3163 | − | 8.26554i | −0.548201 | − | 0.316504i | ||||
\(683\) | 16.7550i | 0.641114i | 0.947229 | + | 0.320557i | \(0.103870\pi\) | ||||
−0.947229 | + | 0.320557i | \(0.896130\pi\) | |||||||
\(684\) | 31.2145 | + | 11.8524i | 1.19352 | + | 0.453186i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.34721 | − | 16.1898i | 0.356878 | − | 0.618131i | ||||
\(687\) | 40.6464 | + | 23.4672i | 1.55076 | + | 0.895329i | ||||
\(688\) | 0.502555 | − | 0.290150i | 0.0191597 | − | 0.0110619i | ||||
\(689\) | −10.7299 | + | 18.5847i | −0.408775 | + | 0.708019i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5889 | 0.821280 | 0.410640 | − | 0.911798i | \(-0.365305\pi\) | ||||
0.410640 | + | 0.911798i | \(0.365305\pi\) | |||||||
\(692\) | 0.375179i | 0.0142622i | ||||||||
\(693\) | 87.5983 | − | 50.5749i | 3.32758 | − | 1.92118i | ||||
\(694\) | −2.46724 | − | 4.27339i | −0.0936553 | − | 0.162216i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −26.2497 | −0.994993 | ||||||||
\(697\) | 18.4304 | − | 10.6408i | 0.698100 | − | 0.403048i | ||||
\(698\) | −1.09634 | − | 0.632972i | −0.0414970 | − | 0.0239583i | ||||
\(699\) | −22.5697 | − | 39.0919i | −0.853666 | − | 1.47859i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.8628 | − | 32.6713i | 0.712437 | − | 1.23398i | −0.251503 | − | 0.967857i | \(-0.580925\pi\) |
0.963940 | − | 0.266121i | \(-0.0857419\pi\) | |||||||
\(702\) | 70.6691i | 2.66723i | ||||||||
\(703\) | −24.7624 | + | 4.01415i | −0.933933 | + | 0.151396i | ||||
\(704\) | −5.03983 | −0.189946 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.08030 | − | 1.87114i | 0.0406577 | − | 0.0704211i | ||||
\(707\) | −19.2088 | + | 11.0902i | −0.722422 | + | 0.417090i | ||||
\(708\) | 10.6736 | + | 6.16240i | 0.401138 | + | 0.231597i | ||||
\(709\) | −10.4795 | − | 18.1511i | −0.393567 | − | 0.681678i | 0.599350 | − | 0.800487i | \(-0.295426\pi\) |
−0.992917 | + | 0.118809i | \(0.962092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −61.0096 | −2.28804 | ||||||||
\(712\) | 7.17905 | − | 4.14483i | 0.269046 | − | 0.155334i | ||||
\(713\) | −13.3074 | + | 7.68305i | −0.498367 | + | 0.287732i | ||||
\(714\) | −31.3096 | −1.17173 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.02470 | + | 6.97098i | 0.150410 | + | 0.260518i | ||||
\(717\) | −42.3272 | − | 24.4376i | −1.58074 | − | 0.912639i | ||||
\(718\) | −4.10463 | + | 2.36981i | −0.153183 | + | 0.0884405i | ||||
\(719\) | −22.1401 | + | 38.3477i | −0.825686 | + | 1.43013i | 0.0757084 | + | 0.997130i | \(0.475878\pi\) |
−0.901394 | + | 0.433000i | \(0.857455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.0481 | −1.15629 | ||||||||
\(722\) | −18.6130 | − | 3.81534i | −0.692704 | − | 0.141992i | ||||
\(723\) | − | 63.1096i | − | 2.34707i | ||||||
\(724\) | −10.5251 | + | 18.2301i | −0.391164 | + | 0.677515i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −23.5075 | − | 40.7162i | −0.872445 | − | 1.51112i | ||||
\(727\) | 41.9448 | + | 24.2169i | 1.55565 | + | 0.898154i | 0.997665 | + | 0.0683017i | \(0.0217580\pi\) |
0.557983 | + | 0.829852i | \(0.311575\pi\) | |||||||
\(728\) | −10.5396 | + | 6.08503i | −0.390623 | + | 0.225526i | ||||
\(729\) | −55.4584 | −2.05402 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.06194 | − | 1.83933i | −0.0392772 | − | 0.0680301i | ||||
\(732\) | −0.367695 | + | 0.212289i | −0.0135904 | + | 0.00784641i | ||||
\(733\) | 9.62940i | 0.355670i | 0.984060 | + | 0.177835i | \(0.0569093\pi\) | ||||
−0.984060 | + | 0.177835i | \(0.943091\pi\) | |||||||
\(734\) | −22.8944 | −0.845046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.34233 | + | 4.05703i | −0.0863394 | + | 0.149544i | ||||
\(737\) | 1.65799 | − | 0.957240i | 0.0610728 | − | 0.0352604i | ||||
\(738\) | 38.5731 | + | 22.2702i | 1.41989 | + | 0.819777i | ||||
\(739\) | −20.3423 | + | 35.2338i | −0.748303 | + | 1.29610i | 0.200333 | + | 0.979728i | \(0.435798\pi\) |
−0.948636 | + | 0.316370i | \(0.897536\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5777 | − | 65.2517i | −0.388582 | − | 2.39708i | ||||
\(742\) | − | 12.1053i | − | 0.444401i | ||||||
\(743\) | 2.48123 | + | 1.43254i | 0.0910276 | + | 0.0525548i | 0.544823 | − | 0.838551i | \(-0.316597\pi\) |
−0.453795 | + | 0.891106i | \(0.649930\pi\) | |||||||
\(744\) | −5.35468 | + | 9.27458i | −0.196312 | + | 0.340022i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.61964 | − | 16.6617i | 0.352200 | − | 0.610028i | ||||
\(747\) | 52.2071 | − | 30.1418i | 1.91016 | − | 1.10283i | ||||
\(748\) | 18.4456i | 0.674437i | ||||||||
\(749\) | 44.0444 | 1.60935 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.1148 | + | 22.7155i | 0.478566 | + | 0.828900i | 0.999698 | − | 0.0245758i | \(-0.00782351\pi\) |
−0.521132 | + | 0.853476i | \(0.674490\pi\) | |||||||
\(752\) | 4.62013i | 0.168479i | ||||||||
\(753\) | 33.7104i | 1.22848i | ||||||||
\(754\) | 18.6718 | + | 32.3405i | 0.679987 | + | 1.17777i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −19.9321 | − | 34.5234i | −0.724923 | − | 1.25560i | ||||
\(757\) | −5.70182 | − | 3.29195i | −0.207236 | − | 0.119648i | 0.392790 | − | 0.919628i | \(-0.371510\pi\) |
−0.600026 | + | 0.799980i | \(0.704843\pi\) | |||||||
\(758\) | 5.59412 | + | 3.22976i | 0.203187 | + | 0.117310i | ||||
\(759\) | −77.0853 | −2.79802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.7549 | −1.00612 | −0.503058 | − | 0.864253i | \(-0.667792\pi\) | ||||
−0.503058 | + | 0.864253i | \(0.667792\pi\) | |||||||
\(762\) | −22.2954 | − | 12.8722i | −0.807677 | − | 0.466312i | ||||
\(763\) | −45.3924 | − | 26.2073i | −1.64331 | − | 0.948768i | ||||
\(764\) | 4.01991 | + | 6.96270i | 0.145435 | + | 0.251902i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.56746 | + | 7.91107i | 0.165029 | + | 0.285839i | ||||
\(767\) | − | 17.5336i | − | 0.633103i | ||||||
\(768\) | 3.26496i | 0.117814i | ||||||||
\(769\) | 8.32285 | + | 14.4156i | 0.300130 | + | 0.519840i | 0.976165 | − | 0.217029i | \(-0.0696367\pi\) |
−0.676035 | + | 0.736869i | \(0.736303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 93.9303 | 3.38282 | ||||||||
\(772\) | 20.2448i | 0.728628i | ||||||||
\(773\) | 20.9664 | − | 12.1049i | 0.754108 | − | 0.435385i | −0.0730682 | − | 0.997327i | \(-0.523279\pi\) |
0.827176 | + | 0.561942i | \(0.189946\pi\) | |||||||
\(774\) | 2.22254 | − | 3.84955i | 0.0798876 | − | 0.138369i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.09494 | + | 14.0208i | −0.290591 | + | 0.503319i | ||||
\(777\) | 42.6364 | + | 24.6161i | 1.52957 | + | 0.883098i | ||||
\(778\) | − | 26.6848i | − | 0.956698i | ||||||
\(779\) | −23.6950 | − | 8.99716i | −0.848963 | − | 0.322357i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.0192 | − | 39.8704i | 0.823692 | − | 1.42668i | ||||
\(782\) | 14.8486 | + | 8.57283i | 0.530984 | + | 0.306564i | ||||
\(783\) | −105.934 | + | 61.1613i | −3.78579 | + | 2.18573i | ||||
\(784\) | −0.0674593 | + | 0.116843i | −0.00240926 | + | 0.00417296i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.85082 | 0.280030 | ||||||||
\(787\) | − | 1.63409i | − | 0.0582490i | −0.999576 | − | 0.0291245i | \(-0.990728\pi\) | ||
0.999576 | − | 0.0291245i | \(-0.00927193\pi\) | |||||||
\(788\) | −2.52883 | + | 1.46002i | −0.0900858 | + | 0.0520111i | ||||
\(789\) | −14.9126 | − | 25.8293i | −0.530902 | − | 0.919548i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.6001 | 1.33691 | ||||||||
\(792\) | −33.4328 | + | 19.3024i | −1.18798 | + | 0.685882i | ||||
\(793\) | 0.523094 | + | 0.302008i | 0.0185756 | + | 0.0107246i | ||||
\(794\) | 7.37459 | + | 12.7732i | 0.261715 | + | 0.453303i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.80244 | − | 13.5142i | 0.276550 | − | 0.478999i | ||||
\(797\) | − | 12.2802i | − | 0.434987i | −0.976062 | − | 0.217494i | \(-0.930212\pi\) | ||
0.976062 | − | 0.217494i | \(-0.0697881\pi\) | |||||||
\(798\) | 23.5715 | + | 28.8934i | 0.834424 | + | 1.02282i | ||||
\(799\) | 16.9095 | 0.598215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.7492 | − | 54.9913i | 1.12180 | − | 1.94302i | ||||
\(802\) | −10.0930 | + | 5.82720i | −0.356396 | + | 0.205766i | ||||
\(803\) | −37.1221 | − | 21.4324i | −1.31001 | − | 0.756334i | ||||
\(804\) | −0.620130 | − | 1.07410i | −0.0218703 | − | 0.0378805i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.2355 | 0.536646 | ||||||||
\(807\) | −47.8122 | + | 27.6044i | −1.68307 | + | 0.971721i | ||||
\(808\) | 7.33124 | − | 4.23270i | 0.257912 | − | 0.148906i | ||||
\(809\) | −49.2846 | −1.73275 | −0.866376 | − | 0.499392i | \(-0.833557\pi\) | ||||
−0.866376 | + | 0.499392i | \(0.833557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5927 | − | 20.0791i | −0.407073 | − | 0.705071i | 0.587487 | − | 0.809233i | \(-0.300117\pi\) |
−0.994560 | + | 0.104162i | \(0.966784\pi\) | |||||||
\(812\) | −18.2432 | − | 10.5327i | −0.640210 | − | 0.369625i | ||||
\(813\) | −44.9286 | + | 25.9396i | −1.57572 | + | 0.909740i | ||||
\(814\) | 14.5022 | − | 25.1186i | 0.508303 | − | 0.880407i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.9496 | 0.418320 | ||||||||
\(817\) | −0.897907 | + | 2.36474i | −0.0314138 | + | 0.0827318i | ||||
\(818\) | 39.5648i | 1.38335i | ||||||||
\(819\) | −46.6111 | + | 80.7327i | −1.62872 | + | 2.82103i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5793 | − | 23.5201i | −0.473921 | − | 0.820856i | 0.525633 | − | 0.850712i | \(-0.323829\pi\) |
−0.999554 | + | 0.0298556i | \(0.990495\pi\) | |||||||
\(822\) | 49.2982 | + | 28.4623i | 1.71947 | + | 0.992737i | ||||
\(823\) | 7.77209 | − | 4.48722i | 0.270918 | − | 0.156415i | −0.358387 | − | 0.933573i | \(-0.616673\pi\) |
0.629305 | + | 0.777159i | \(0.283340\pi\) | |||||||
\(824\) | 11.8498 | 0.412809 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.94532 | + | 8.56555i | 0.172070 | + | 0.298034i | ||||
\(827\) | 20.7890 | − | 12.0025i | 0.722904 | − | 0.417369i | −0.0929165 | − | 0.995674i | \(-0.529619\pi\) |
0.815821 | + | 0.578305i | \(0.196286\pi\) | |||||||
\(828\) | 35.8843i | 1.24707i | ||||||||
\(829\) | −25.7361 | −0.893852 | −0.446926 | − | 0.894571i | \(-0.647481\pi\) | ||||
−0.446926 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7494 | + | 32.4749i | −0.650409 | + | 1.12654i | ||||
\(832\) | 4.02254 | − | 2.32241i | 0.139456 | − | 0.0805152i | ||||
\(833\) | 0.427641 | + | 0.246898i | 0.0148169 | + | 0.00855452i | ||||
\(834\) | 15.6224 | − | 27.0588i | 0.540960 | − | 0.936970i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.0221 | − | 13.8868i | 0.588723 | − | 0.480286i | ||||
\(837\) | 49.9052i | 1.72498i | ||||||||
\(838\) | −15.0075 | − | 8.66459i | −0.518426 | − | 0.299313i | ||||
\(839\) | −16.3570 | + | 28.3311i | −0.564705 | + | 0.978098i | 0.432372 | + | 0.901695i | \(0.357677\pi\) |
−0.997077 | + | 0.0764027i | \(0.975657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8194 | + | 30.8642i | −0.614463 | + | 1.06428i | ||||
\(842\) | −21.0707 | + | 12.1652i | −0.726145 | + | 0.419240i | ||||
\(843\) | − | 46.6552i | − | 1.60689i | ||||||
\(844\) | −1.14517 | −0.0394184 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.6950 | + | 30.6486i | 0.608367 | + | 1.05372i | ||||
\(847\) | − | 37.7296i | − | 1.29640i | ||||||
\(848\) | 4.62013i | 0.158656i | ||||||||
\(849\) | 5.16567 | + | 8.94720i | 0.177285 | + | 0.307067i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.4802 | − | 23.3484i | −0.462096 | − | 0.800374i | ||||
\(852\) | −25.8293 | − | 14.9126i | −0.884898 | − | 0.510896i | ||||
\(853\) | 26.8384 | + | 15.4952i | 0.918929 | + | 0.530544i | 0.883293 | − | 0.468821i | \(-0.155321\pi\) |
0.0356360 | + | 0.999365i | \(0.488654\pi\) | |||||||
\(854\) | −0.340723 | −0.0116593 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.8100 | −0.574554 | ||||||||
\(857\) | 18.1865 | + | 10.5000i | 0.621240 | + | 0.358673i | 0.777352 | − | 0.629066i | \(-0.216563\pi\) |
−0.156112 | + | 0.987739i | \(0.549896\pi\) | |||||||
\(858\) | 66.1902 | + | 38.2150i | 2.25970 | + | 1.30464i | ||||
\(859\) | 14.1575 | + | 24.5215i | 0.483048 | + | 0.836664i | 0.999811 | − | 0.0194647i | \(-0.00619620\pi\) |
−0.516762 | + | 0.856129i | \(0.672863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.8713 | + | 43.0783i | 0.847610 | + | 1.46810i | ||||
\(862\) | − | 28.2346i | − | 0.961674i | ||||||
\(863\) | 10.9254i | 0.371905i | 0.982559 | + | 0.185953i | \(0.0595371\pi\) | ||||
−0.982559 | + | 0.185953i | \(0.940463\pi\) | |||||||
\(864\) | 7.60729 | + | 13.1762i | 0.258805 | + | 0.448264i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.3798 | −0.794476 | ||||||||
\(867\) | 11.7692i | 0.399703i | ||||||||
\(868\) | −7.44285 | + | 4.29713i | −0.252627 | + | 0.145854i | ||||
\(869\) | −20.0705 | + | 34.7631i | −0.680845 | + | 1.17926i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.882216 | + | 1.52804i | −0.0298927 | + | 0.0517757i | ||||
\(872\) | 17.3245 | + | 10.0023i | 0.586681 | + | 0.338720i | ||||
\(873\) | 124.014i | 4.19723i | ||||||||
\(874\) | −3.26755 | − | 20.1568i | −0.110526 | − | 0.681815i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.8846 | + | 24.0488i | −0.469117 | + | 0.812535i | ||||
\(877\) | −29.2972 | − | 16.9148i | −0.989297 | − | 0.571171i | −0.0842330 | − | 0.996446i | \(-0.526844\pi\) |
−0.905064 | + | 0.425275i | \(0.860177\pi\) | |||||||
\(878\) | 23.1705 | − | 13.3775i | 0.781965 | − | 0.451468i | ||||
\(879\) | 24.0127 | − | 41.5913i | 0.809929 | − | 1.40284i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3696 | 0.989488 | 0.494744 | − | 0.869039i | \(-0.335262\pi\) | ||||
0.494744 | + | 0.869039i | \(0.335262\pi\) | |||||||
\(882\) | 1.03347i | 0.0347988i | ||||||||
\(883\) | 35.6803 | − | 20.6000i | 1.20074 | − | 0.693245i | 0.240017 | − | 0.970769i | \(-0.422847\pi\) |
0.960719 | + | 0.277523i | \(0.0895135\pi\) | |||||||
\(884\) | −8.49994 | − | 14.7223i | −0.285884 | − | 0.495166i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.6998 | −0.594636 | ||||||||
\(887\) | −22.4221 | + | 12.9454i | −0.752861 | + | 0.434665i | −0.826727 | − | 0.562604i | \(-0.809800\pi\) |
0.0738656 | + | 0.997268i | \(0.476466\pi\) | |||||||
\(888\) | −16.2726 | − | 9.39500i | −0.546073 | − | 0.315276i | ||||
\(889\) | −10.3300 | − | 17.8920i | −0.346456 | − | 0.600080i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −67.2694 | + | 116.514i | −2.25361 | + | 3.90336i | ||||
\(892\) | 15.3295i | 0.513269i | ||||||||
\(893\) | −12.7304 | − | 15.6046i | −0.426006 | − | 0.522188i | ||||
\(894\) | 55.9104 | 1.86992 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.31007 | + | 2.26910i | −0.0437662 | + | 0.0758053i | ||||
\(897\) | 61.5256 | − | 35.5218i | 2.05428 | − | 1.18604i | ||||
\(898\) | −24.5553 | − | 14.1770i | −0.819423 | − | 0.473094i | ||||
\(899\) | 13.1857 | + | 22.8383i | 0.439767 | + | 0.761699i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.9095 | 0.563337 | ||||||||
\(902\) | 25.3790 | − | 14.6525i | 0.845027 | − | 0.487876i | ||||
\(903\) | 4.29917 | − | 2.48213i | 0.143067 | − | 0.0826000i | ||||
\(904\) | −14.3505 | −0.477290 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.88787 | + | 15.3942i | 0.295280 | + | 0.511439i | ||||
\(907\) | −22.0706 | − | 12.7425i | −0.732842 | − | 0.423106i | 0.0866192 | − | 0.996241i | \(-0.472394\pi\) |
−0.819461 | + | 0.573135i | \(0.805727\pi\) | |||||||
\(908\) | 16.7013 | − | 9.64248i | 0.554251 | − | 0.319997i | ||||
\(909\) | 32.4223 | − | 56.1570i | 1.07538 | − | 1.86261i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.1197 | 0.335280 | 0.167640 | − | 0.985848i | \(-0.446385\pi\) | ||||
0.167640 | + | 0.985848i | \(0.446385\pi\) | |||||||
\(912\) | −8.99633 | − | 11.0275i | −0.297898 | − | 0.365156i | ||||
\(913\) | − | 39.6633i | − | 1.31266i | ||||||
\(914\) | 5.79488 | − | 10.0370i | 0.191678 | − | 0.331995i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.18759 | − | 12.4493i | −0.237485 | − | 0.411335i | ||||
\(917\) | 5.45621 | + | 3.15014i | 0.180180 | + | 0.104027i | ||||
\(918\) | 48.2244 | − | 27.8424i | 1.59164 | − | 0.918935i | ||||
\(919\) | 15.0939 | 0.497902 | 0.248951 | − | 0.968516i | \(-0.419914\pi\) | ||||
0.248951 | + | 0.968516i | \(0.419914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.6818 | + | 73.9270i | 1.40641 | + | 2.43598i | ||||
\(922\) | −30.9862 | + | 17.8899i | −1.02048 | + | 0.589172i | ||||
\(923\) | 42.4301i | 1.39660i | ||||||||
\(924\) | −43.1138 | −1.41834 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.7520 | + | 20.3550i | −0.386194 | + | 0.668907i | ||||
\(927\) | 78.6085 | − | 45.3846i | 2.58184 | − | 1.49063i | ||||
\(928\) | 6.96270 | + | 4.01991i | 0.228562 | + | 0.131960i | ||||
\(929\) | −5.40003 | + | 9.35312i | −0.177169 | + | 0.306866i | −0.940910 | − | 0.338657i | \(-0.890027\pi\) |
0.763741 | + | 0.645523i | \(0.223361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0941058 | − | 0.580519i | −0.00308419 | − | 0.0190257i | ||||
\(932\) | 13.8254i | 0.452867i | ||||||||
\(933\) | −18.8042 | − | 10.8566i | −0.615623 | − | 0.355430i | ||||
\(934\) | −0.560236 | + | 0.970357i | −0.0183315 | + | 0.0317510i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.7896 | − | 30.8125i | 0.581471 | − | 1.00714i | ||||
\(937\) | 39.3163 | − | 22.6993i | 1.28441 | − | 0.741554i | 0.306758 | − | 0.951788i | \(-0.400756\pi\) |
0.977651 | + | 0.210234i | \(0.0674226\pi\) | |||||||
\(938\) | − | 0.995309i | − | 0.0324980i | ||||||
\(939\) | 56.7442 | 1.85178 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.155325 | − | 0.269031i | −0.00506346 | − | 0.00877016i | 0.863483 | − | 0.504379i | \(-0.168278\pi\) |
−0.868546 | + | 0.495609i | \(0.834945\pi\) | |||||||
\(942\) | 0.0806421i | 0.00262746i | ||||||||
\(943\) | − | 27.2399i | − | 0.887053i | ||||||
\(944\) | −1.88743 | − | 3.26913i | −0.0614308 | − | 0.106401i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.46231 | − | 2.53279i | −0.0475438 | − | 0.0823482i | ||||
\(947\) | −3.65897 | − | 2.11251i | −0.118901 | − | 0.0686473i | 0.439370 | − | 0.898306i | \(-0.355202\pi\) |
−0.558271 | + | 0.829659i | \(0.688535\pi\) | |||||||
\(948\) | 22.5206 | + | 13.0023i | 0.731436 | + | 0.422295i | ||||
\(949\) | 39.5053 | 1.28240 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.49028 | 0.145607 | ||||||||
\(952\) | 8.30481 | + | 4.79478i | 0.269160 | + | 0.155400i | ||||
\(953\) | −29.3008 | − | 16.9168i | −0.949145 | − | 0.547989i | −0.0563297 | − | 0.998412i | \(-0.517940\pi\) |
−0.892815 | + | 0.450423i | \(0.851273\pi\) | |||||||
\(954\) | 17.6950 | + | 30.6486i | 0.572897 | + | 0.992287i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.48481 | + | 12.9641i | 0.242076 | + | 0.419288i | ||||
\(957\) | 132.294i | 4.27646i | ||||||||
\(958\) | 27.3094i | 0.882326i | ||||||||
\(959\) | 22.8410 | + | 39.5618i | 0.737574 | + | 1.27752i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2410 | −0.652936 | ||||||||
\(962\) | 26.7312i | 0.861849i | ||||||||
\(963\) | −111.513 | + | 64.3820i | −3.59345 | + | 2.07468i | ||||
\(964\) | −9.66469 | + | 16.7397i | −0.311279 | + | 0.539150i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.0377 | + | 34.7064i | −0.644703 | + | 1.11666i | ||||
\(967\) | −33.9875 | − | 19.6227i | −1.09296 | − | 0.631024i | −0.158601 | − | 0.987343i | \(-0.550698\pi\) |
−0.934364 | + | 0.356319i | \(0.884032\pi\) | |||||||
\(968\) | 14.3999i | 0.462830i | ||||||||
\(969\) | −40.3601 | + | 32.9262i | −1.29655 | + | 1.05774i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3469 | + | 35.2419i | −0.652963 | + | 1.13097i | 0.329437 | + | 0.944178i | \(0.393141\pi\) |
−0.982400 | + | 0.186788i | \(0.940192\pi\) | |||||||
\(972\) | 35.9528 | + | 20.7573i | 1.15319 | + | 0.665792i | ||||
\(973\) | 21.7147 | − | 12.5370i | 0.696142 | − | 0.401918i | ||||
\(974\) | 3.16002 | − | 5.47331i | 0.101253 | − | 0.175376i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.130041 | 0.00416250 | ||||||||
\(977\) | − | 26.7081i | − | 0.854467i | −0.904141 | − | 0.427233i | \(-0.859488\pi\) | ||
0.904141 | − | 0.427233i | \(-0.140512\pi\) | |||||||
\(978\) | −30.6355 | + | 17.6874i | −0.979617 | + | 0.565582i | ||||
\(979\) | −20.8892 | − | 36.1812i | −0.667623 | − | 1.15636i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 153.234 | 4.89239 | ||||||||
\(982\) | 22.3478 | − | 12.9025i | 0.713147 | − | 0.411736i | ||||
\(983\) | −21.6233 | − | 12.4842i | −0.689677 | − | 0.398185i | 0.113814 | − | 0.993502i | \(-0.463693\pi\) |
−0.803491 | + | 0.595317i | \(0.797026\pi\) | |||||||
\(984\) | −9.49238 | − | 16.4413i | −0.302606 | − | 0.524129i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.7127 | − | 25.4832i | 0.468549 | − | 0.811550i | ||||
\(987\) | 39.5234i | 1.25805i | ||||||||
\(988\) | −7.18700 | + | 18.9278i | −0.228649 | + | 0.602173i | ||||
\(989\) | −2.71851 | −0.0864436 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.53968 | − | 13.0591i | 0.239506 | − | 0.414836i | −0.721067 | − | 0.692866i | \(-0.756348\pi\) |
0.960573 | + | 0.278029i | \(0.0896813\pi\) | |||||||
\(992\) | 2.84064 | − | 1.64004i | 0.0901904 | − | 0.0520715i | ||||
\(993\) | −33.1951 | − | 19.1652i | −1.05341 | − | 0.608189i | ||||
\(994\) | −11.9673 | − | 20.7280i | −0.379581 | − | 0.657453i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.6951 | −0.814180 | ||||||||
\(997\) | −35.6158 | + | 20.5628i | −1.12796 | + | 0.651229i | −0.943422 | − | 0.331595i | \(-0.892413\pi\) |
−0.184541 | + | 0.982825i | \(0.559080\pi\) | |||||||
\(998\) | −25.0406 | + | 14.4572i | −0.792646 | + | 0.457634i | ||||
\(999\) | −87.5606 | −2.77030 |
(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 | 950.2.j.i.49.5 | 16 | ||
5.2 | odd | 4 | 950.2.e.l.201.1 | ✓ | 8 | ||
5.3 | odd | 4 | 950.2.e.m.201.4 | yes | 8 | ||
5.4 | even | 2 | inner | 950.2.j.i.49.4 | 16 | ||
19.7 | even | 3 | inner | 950.2.j.i.349.4 | 16 | ||
95.7 | odd | 12 | 950.2.e.l.501.1 | yes | 8 | ||
95.64 | even | 6 | inner | 950.2.j.i.349.5 | 16 | ||
95.83 | odd | 12 | 950.2.e.m.501.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.e.l.201.1 | ✓ | 8 | 5.2 | odd | 4 | ||
950.2.e.l.501.1 | yes | 8 | 95.7 | odd | 12 | ||
950.2.e.m.201.4 | yes | 8 | 5.3 | odd | 4 | ||
950.2.e.m.501.4 | yes | 8 | 95.83 | odd | 12 | ||
950.2.j.i.49.4 | 16 | 5.4 | even | 2 | inner | ||
950.2.j.i.49.5 | 16 | 1.1 | even | 1 | trivial | ||
950.2.j.i.349.4 | 16 | 19.7 | even | 3 | inner | ||
950.2.j.i.349.5 | 16 | 95.64 | even | 6 | inner |