Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.57118294509\) |
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: | \( x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.3 | ||
Root | \(-0.452119 + 1.67200i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.229 |
Dual form | 322.2.g.b.45.3 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.07743 | + | 0.622057i | −0.622057 | + | 0.359145i | −0.777670 | − | 0.628673i | \(-0.783598\pi\) |
0.155612 | + | 0.987818i | \(0.450265\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.668984 | + | 1.15871i | −0.299179 | + | 0.518193i | −0.975948 | − | 0.218002i | \(-0.930046\pi\) |
0.676769 | + | 0.736195i | \(0.263379\pi\) | |||||||
\(6\) | 1.24411i | 0.507908i | ||||||||
\(7\) | −2.09536 | − | 1.61539i | −0.791971 | − | 0.610558i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.726090 | + | 1.25762i | −0.242030 | + | 0.419208i | ||||
\(10\) | 0.668984 | + | 1.15871i | 0.211551 | + | 0.366418i | ||||
\(11\) | −5.22660 | + | 3.01758i | −1.57588 | + | 0.909835i | −0.580455 | + | 0.814292i | \(0.697125\pi\) |
−0.995425 | + | 0.0955426i | \(0.969541\pi\) | |||||||
\(12\) | 1.07743 | + | 0.622057i | 0.311029 | + | 0.179572i | ||||
\(13\) | − | 6.52207i | − | 1.80890i | −0.426583 | − | 0.904448i | \(-0.640283\pi\) | ||
0.426583 | − | 0.904448i | \(-0.359717\pi\) | |||||||
\(14\) | −2.44664 | + | 1.00694i | −0.653893 | + | 0.269117i | ||||
\(15\) | − | 1.66459i | − | 0.429794i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.568151 | − | 0.984066i | −0.137797 | − | 0.238671i | 0.788866 | − | 0.614566i | \(-0.210669\pi\) |
−0.926662 | + | 0.375895i | \(0.877335\pi\) | |||||||
\(18\) | 0.726090 | + | 1.25762i | 0.171141 | + | 0.296425i | ||||
\(19\) | −1.77489 | + | 3.07420i | −0.407187 | + | 0.705269i | −0.994573 | − | 0.104038i | \(-0.966824\pi\) |
0.587386 | + | 0.809307i | \(0.300157\pi\) | |||||||
\(20\) | 1.33797 | 0.299179 | ||||||||
\(21\) | 3.26247 | + | 0.437039i | 0.711930 | + | 0.0953697i | ||||
\(22\) | 6.03516i | 1.28670i | ||||||||
\(23\) | −1.35675 | + | 4.59992i | −0.282903 | + | 0.959149i | ||||
\(24\) | 1.07743 | − | 0.622057i | 0.219930 | − | 0.126977i | ||||
\(25\) | 1.60492 | + | 2.77980i | 0.320984 | + | 0.555961i | ||||
\(26\) | −5.64828 | − | 3.26103i | −1.10772 | − | 0.639541i | ||||
\(27\) | − | 5.53902i | − | 1.06598i | ||||||
\(28\) | −0.351285 | + | 2.62233i | −0.0663866 | + | 0.495573i | ||||
\(29\) | −3.18236 | −0.590948 | −0.295474 | − | 0.955351i | \(-0.595478\pi\) | ||||
−0.295474 | + | 0.955351i | \(0.595478\pi\) | |||||||
\(30\) | −1.44157 | − | 0.832293i | −0.263194 | − | 0.151955i | ||||
\(31\) | 2.80352 | − | 1.61862i | 0.503528 | − | 0.290712i | −0.226641 | − | 0.973978i | \(-0.572775\pi\) |
0.730169 | + | 0.683266i | \(0.239441\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 3.75422 | − | 6.50249i | 0.653525 | − | 1.13194i | ||||
\(34\) | −1.13630 | −0.194874 | ||||||||
\(35\) | 3.27353 | − | 1.34726i | 0.553328 | − | 0.227728i | ||||
\(36\) | 1.45218 | 0.242030 | ||||||||
\(37\) | −5.10738 | − | 2.94875i | −0.839649 | − | 0.484771i | 0.0174962 | − | 0.999847i | \(-0.494431\pi\) |
−0.857145 | + | 0.515076i | \(0.827764\pi\) | |||||||
\(38\) | 1.77489 | + | 3.07420i | 0.287925 | + | 0.498701i | ||||
\(39\) | 4.05710 | + | 7.02710i | 0.649656 | + | 1.12524i | ||||
\(40\) | 0.668984 | − | 1.15871i | 0.105776 | − | 0.183209i | ||||
\(41\) | 0.928266i | 0.144971i | 0.997369 | + | 0.0724854i | \(0.0230931\pi\) | ||||
−0.997369 | + | 0.0724854i | \(0.976907\pi\) | |||||||
\(42\) | 2.00972 | − | 2.60687i | 0.310107 | − | 0.402248i | ||||
\(43\) | 0.303546i | 0.0462903i | 0.999732 | + | 0.0231451i | \(0.00736798\pi\) | ||||
−0.999732 | + | 0.0231451i | \(0.992632\pi\) | |||||||
\(44\) | 5.22660 | + | 3.01758i | 0.787940 | + | 0.454917i | ||||
\(45\) | −0.971485 | − | 1.68266i | −0.144820 | − | 0.250836i | ||||
\(46\) | 3.30527 | + | 3.47494i | 0.487335 | + | 0.512352i | ||||
\(47\) | −0.243918 | − | 0.140826i | −0.0355792 | − | 0.0205416i | 0.482105 | − | 0.876113i | \(-0.339872\pi\) |
−0.517684 | + | 0.855572i | \(0.673206\pi\) | |||||||
\(48\) | − | 1.24411i | − | 0.179572i | ||||||
\(49\) | 1.78106 | + | 6.76962i | 0.254437 | + | 0.967089i | ||||
\(50\) | 3.20984 | 0.453940 | ||||||||
\(51\) | 1.22429 | + | 0.706844i | 0.171435 | + | 0.0989780i | ||||
\(52\) | −5.64828 | + | 3.26103i | −0.783275 | + | 0.452224i | ||||
\(53\) | 11.3667 | − | 6.56256i | 1.56133 | − | 0.901437i | 0.564211 | − | 0.825630i | \(-0.309180\pi\) |
0.997123 | − | 0.0758061i | \(-0.0241530\pi\) | |||||||
\(54\) | −4.79693 | − | 2.76951i | −0.652780 | − | 0.376883i | ||||
\(55\) | − | 8.07486i | − | 1.08881i | ||||||
\(56\) | 2.09536 | + | 1.61539i | 0.280004 | + | 0.215865i | ||||
\(57\) | − | 4.41633i | − | 0.584957i | ||||||
\(58\) | −1.59118 | + | 2.75600i | −0.208932 | + | 0.361881i | ||||
\(59\) | −1.10083 | + | 0.635567i | −0.143316 | + | 0.0827438i | −0.569944 | − | 0.821684i | \(-0.693035\pi\) |
0.426627 | + | 0.904428i | \(0.359702\pi\) | |||||||
\(60\) | −1.44157 | + | 0.832293i | −0.186106 | + | 0.107449i | ||||
\(61\) | 7.00107 | − | 12.1262i | 0.896396 | − | 1.55260i | 0.0643281 | − | 0.997929i | \(-0.479510\pi\) |
0.832068 | − | 0.554674i | \(-0.187157\pi\) | |||||||
\(62\) | − | 3.23723i | − | 0.411129i | ||||||
\(63\) | 3.55297 | − | 1.46226i | 0.447632 | − | 0.184227i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.55722 | + | 4.36316i | 0.937357 | + | 0.541183i | ||||
\(66\) | −3.75422 | − | 6.50249i | −0.462112 | − | 0.800402i | ||||
\(67\) | −3.57337 | + | 2.06308i | −0.436556 | + | 0.252046i | −0.702136 | − | 0.712043i | \(-0.747770\pi\) |
0.265580 | + | 0.964089i | \(0.414437\pi\) | |||||||
\(68\) | −0.568151 | + | 0.984066i | −0.0688984 | + | 0.119335i | ||||
\(69\) | −1.39960 | − | 5.80009i | −0.168492 | − | 0.698248i | ||||
\(70\) | 0.470008 | − | 3.50859i | 0.0561767 | − | 0.419357i | ||||
\(71\) | −4.02749 | −0.477975 | −0.238987 | − | 0.971023i | \(-0.576815\pi\) | ||||
−0.238987 | + | 0.971023i | \(0.576815\pi\) | |||||||
\(72\) | 0.726090 | − | 1.25762i | 0.0855705 | − | 0.148212i | ||||
\(73\) | −11.1001 | + | 6.40863i | −1.29917 | + | 0.750074i | −0.980260 | − | 0.197713i | \(-0.936649\pi\) |
−0.318906 | + | 0.947786i | \(0.603315\pi\) | |||||||
\(74\) | −5.10738 | + | 2.94875i | −0.593721 | + | 0.342785i | ||||
\(75\) | −3.45839 | − | 1.99670i | −0.399341 | − | 0.230560i | ||||
\(76\) | 3.54978 | 0.407187 | ||||||||
\(77\) | 15.8262 | + | 2.12006i | 1.80356 | + | 0.241603i | ||||
\(78\) | 8.11420 | 0.918752 | ||||||||
\(79\) | −10.6180 | − | 6.13032i | −1.19462 | − | 0.689715i | −0.235270 | − | 0.971930i | \(-0.575597\pi\) |
−0.959351 | + | 0.282215i | \(0.908931\pi\) | |||||||
\(80\) | −0.668984 | − | 1.15871i | −0.0747947 | − | 0.129548i | ||||
\(81\) | 1.26732 | + | 2.19506i | 0.140813 | + | 0.243896i | ||||
\(82\) | 0.803902 | + | 0.464133i | 0.0887761 | + | 0.0512549i | ||||
\(83\) | 5.99365 | 0.657889 | 0.328944 | − | 0.944349i | \(-0.393307\pi\) | ||||
0.328944 | + | 0.944349i | \(0.393307\pi\) | |||||||
\(84\) | −1.25275 | − | 3.04391i | −0.136686 | − | 0.332117i | ||||
\(85\) | 1.52033 | 0.164903 | ||||||||
\(86\) | 0.262878 | + | 0.151773i | 0.0283469 | + | 0.0163661i | ||||
\(87\) | 3.42878 | − | 1.97961i | 0.367604 | − | 0.212236i | ||||
\(88\) | 5.22660 | − | 3.01758i | 0.557158 | − | 0.321675i | ||||
\(89\) | −4.71966 | + | 8.17470i | −0.500283 | + | 0.866516i | 0.499717 | + | 0.866189i | \(0.333438\pi\) |
−1.00000 | 0.000327275i | \(0.999896\pi\) | ||||||||
\(90\) | −1.94297 | −0.204807 | ||||||||
\(91\) | −10.5357 | + | 13.6661i | −1.10444 | + | 1.43259i | ||||
\(92\) | 4.66202 | − | 1.12497i | 0.486049 | − | 0.117287i | ||||
\(93\) | −2.01374 | + | 3.48790i | −0.208815 | + | 0.361679i | ||||
\(94\) | −0.243918 | + | 0.140826i | −0.0251583 | + | 0.0145251i | ||||
\(95\) | −2.37474 | − | 4.11318i | −0.243644 | − | 0.422003i | ||||
\(96\) | −1.07743 | − | 0.622057i | −0.109965 | − | 0.0634884i | ||||
\(97\) | 14.1845 | 1.44022 | 0.720109 | − | 0.693861i | \(-0.244092\pi\) | ||||
0.720109 | + | 0.693861i | \(0.244092\pi\) | |||||||
\(98\) | 6.75320 | + | 1.84237i | 0.682176 | + | 0.186107i | ||||
\(99\) | − | 8.76414i | − | 0.880829i | ||||||
\(100\) | 1.60492 | − | 2.77980i | 0.160492 | − | 0.277980i | ||||
\(101\) | −8.86258 | + | 5.11681i | −0.881860 | + | 0.509142i | −0.871271 | − | 0.490802i | \(-0.836704\pi\) |
−0.0105887 | + | 0.999944i | \(0.503371\pi\) | |||||||
\(102\) | 1.22429 | − | 0.706844i | 0.121223 | − | 0.0699880i | ||||
\(103\) | −6.03001 | + | 10.4443i | −0.594154 | + | 1.02911i | 0.399511 | + | 0.916728i | \(0.369180\pi\) |
−0.993666 | + | 0.112377i | \(0.964154\pi\) | |||||||
\(104\) | 6.52207i | 0.639541i | ||||||||
\(105\) | −2.68895 | + | 3.48790i | −0.262414 | + | 0.340385i | ||||
\(106\) | − | 13.1251i | − | 1.27482i | ||||||
\(107\) | −7.66359 | − | 4.42458i | −0.740867 | − | 0.427740i | 0.0815172 | − | 0.996672i | \(-0.474023\pi\) |
−0.822385 | + | 0.568932i | \(0.807357\pi\) | |||||||
\(108\) | −4.79693 | + | 2.76951i | −0.461585 | + | 0.266496i | ||||
\(109\) | −6.67380 | + | 3.85312i | −0.639234 | + | 0.369062i | −0.784319 | − | 0.620357i | \(-0.786988\pi\) |
0.145086 | + | 0.989419i | \(0.453654\pi\) | |||||||
\(110\) | −6.99303 | − | 4.03743i | −0.666759 | − | 0.384954i | ||||
\(111\) | 7.33716 | 0.696413 | ||||||||
\(112\) | 2.44664 | − | 1.00694i | 0.231186 | − | 0.0951471i | ||||
\(113\) | 8.89491i | 0.836762i | 0.908272 | + | 0.418381i | \(0.137402\pi\) | ||||
−0.908272 | + | 0.418381i | \(0.862598\pi\) | |||||||
\(114\) | −3.82465 | − | 2.20816i | −0.358212 | − | 0.206814i | ||||
\(115\) | −4.42234 | − | 4.64936i | −0.412386 | − | 0.433555i | ||||
\(116\) | 1.59118 | + | 2.75600i | 0.147737 | + | 0.255888i | ||||
\(117\) | 8.20231 | + | 4.73561i | 0.758304 | + | 0.437807i | ||||
\(118\) | 1.27113i | 0.117017i | ||||||||
\(119\) | −0.399166 | + | 2.97975i | −0.0365914 | + | 0.273154i | ||||
\(120\) | 1.66459i | 0.151955i | ||||||||
\(121\) | 12.7116 | − | 22.0171i | 1.15560 | − | 2.00156i | ||||
\(122\) | −7.00107 | − | 12.1262i | −0.633848 | − | 1.09786i | ||||
\(123\) | −0.577435 | − | 1.00015i | −0.0520655 | − | 0.0901801i | ||||
\(124\) | −2.80352 | − | 1.61862i | −0.251764 | − | 0.145356i | ||||
\(125\) | −10.9845 | −0.982484 | ||||||||
\(126\) | 0.510129 | − | 3.80809i | 0.0454459 | − | 0.339252i | ||||
\(127\) | −11.4514 | −1.01615 | −0.508075 | − | 0.861313i | \(-0.669643\pi\) | ||||
−0.508075 | + | 0.861313i | \(0.669643\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.188823 | − | 0.327051i | −0.0166249 | − | 0.0287952i | ||||
\(130\) | 7.55722 | − | 4.36316i | 0.662812 | − | 0.382675i | ||||
\(131\) | −6.21988 | − | 3.59105i | −0.543433 | − | 0.313751i | 0.203036 | − | 0.979171i | \(-0.434919\pi\) |
−0.746469 | + | 0.665420i | \(0.768252\pi\) | |||||||
\(132\) | −7.50843 | −0.653525 | ||||||||
\(133\) | 8.68504 | − | 3.57442i | 0.753089 | − | 0.309941i | ||||
\(134\) | 4.12617i | 0.356447i | ||||||||
\(135\) | 6.41814 | + | 3.70552i | 0.552386 | + | 0.318920i | ||||
\(136\) | 0.568151 | + | 0.984066i | 0.0487185 | + | 0.0843829i | ||||
\(137\) | −3.87856 | + | 2.23929i | −0.331368 | + | 0.191315i | −0.656448 | − | 0.754371i | \(-0.727942\pi\) |
0.325080 | + | 0.945686i | \(0.394609\pi\) | |||||||
\(138\) | −5.72282 | − | 1.68796i | −0.487159 | − | 0.143688i | ||||
\(139\) | − | 9.07132i | − | 0.769419i | −0.923038 | − | 0.384709i | \(-0.874302\pi\) | ||
0.923038 | − | 0.384709i | \(-0.125698\pi\) | |||||||
\(140\) | −2.80352 | − | 2.16133i | −0.236941 | − | 0.182666i | ||||
\(141\) | 0.350408 | 0.0295097 | ||||||||
\(142\) | −2.01374 | + | 3.48790i | −0.168990 | + | 0.292698i | ||||
\(143\) | 19.6809 | + | 34.0883i | 1.64580 | + | 2.85060i | ||||
\(144\) | −0.726090 | − | 1.25762i | −0.0605075 | − | 0.104802i | ||||
\(145\) | 2.12895 | − | 3.68744i | 0.176799 | − | 0.306225i | ||||
\(146\) | 12.8173i | 1.06076i | ||||||||
\(147\) | −6.13007 | − | 6.18591i | −0.505600 | − | 0.510205i | ||||
\(148\) | 5.89750i | 0.484771i | ||||||||
\(149\) | 15.4017 | + | 8.89220i | 1.26176 | + | 0.728478i | 0.973415 | − | 0.229049i | \(-0.0735616\pi\) |
0.288345 | + | 0.957526i | \(0.406895\pi\) | |||||||
\(150\) | −3.45839 | + | 1.99670i | −0.282377 | + | 0.163030i | ||||
\(151\) | 9.74158 | + | 16.8729i | 0.792759 | + | 1.37310i | 0.924253 | + | 0.381782i | \(0.124689\pi\) |
−0.131494 | + | 0.991317i | \(0.541977\pi\) | |||||||
\(152\) | 1.77489 | − | 3.07420i | 0.143962 | − | 0.249350i | ||||
\(153\) | 1.65011 | 0.133404 | ||||||||
\(154\) | 9.74911 | − | 12.6458i | 0.785606 | − | 1.01903i | ||||
\(155\) | 4.33131i | 0.347899i | ||||||||
\(156\) | 4.05710 | − | 7.02710i | 0.324828 | − | 0.562619i | ||||
\(157\) | −4.10550 | − | 7.11094i | −0.327655 | − | 0.567515i | 0.654391 | − | 0.756156i | \(-0.272925\pi\) |
−0.982046 | + | 0.188642i | \(0.939592\pi\) | |||||||
\(158\) | −10.6180 | + | 6.13032i | −0.844725 | + | 0.487702i | ||||
\(159\) | −8.16457 | + | 14.1415i | −0.647493 | + | 1.12149i | ||||
\(160\) | −1.33797 | −0.105776 | ||||||||
\(161\) | 10.2735 | − | 7.44680i | 0.809667 | − | 0.586890i | ||||
\(162\) | 2.53464 | 0.199140 | ||||||||
\(163\) | −7.48801 | + | 12.9696i | −0.586506 | + | 1.01586i | 0.408180 | + | 0.912902i | \(0.366164\pi\) |
−0.994686 | + | 0.102957i | \(0.967170\pi\) | |||||||
\(164\) | 0.803902 | − | 0.464133i | 0.0627742 | − | 0.0362427i | ||||
\(165\) | 5.02302 | + | 8.70013i | 0.391042 | + | 0.677304i | ||||
\(166\) | 2.99683 | − | 5.19065i | 0.232599 | − | 0.402873i | ||||
\(167\) | 14.5565i | 1.12642i | 0.826315 | + | 0.563208i | \(0.190433\pi\) | ||||
−0.826315 | + | 0.563208i | \(0.809567\pi\) | |||||||
\(168\) | −3.26247 | − | 0.437039i | −0.251705 | − | 0.0337183i | ||||
\(169\) | −29.5374 | −2.27211 | ||||||||
\(170\) | 0.760167 | − | 1.31665i | 0.0583022 | − | 0.100982i | ||||
\(171\) | −2.57746 | − | 4.46429i | −0.197103 | − | 0.341392i | ||||
\(172\) | 0.262878 | − | 0.151773i | 0.0200443 | − | 0.0115726i | ||||
\(173\) | 0.143633 | + | 0.0829263i | 0.0109202 | + | 0.00630477i | 0.505450 | − | 0.862856i | \(-0.331326\pi\) |
−0.494530 | + | 0.869161i | \(0.664660\pi\) | |||||||
\(174\) | − | 3.95921i | − | 0.300147i | ||||||
\(175\) | 1.12757 | − | 8.41725i | 0.0852362 | − | 0.636284i | ||||
\(176\) | − | 6.03516i | − | 0.454917i | ||||||
\(177\) | 0.790718 | − | 1.36956i | 0.0594340 | − | 0.102943i | ||||
\(178\) | 4.71966 | + | 8.17470i | 0.353754 | + | 0.612720i | ||||
\(179\) | −4.07122 | − | 7.05156i | −0.304297 | − | 0.527058i | 0.672807 | − | 0.739818i | \(-0.265088\pi\) |
−0.977105 | + | 0.212759i | \(0.931755\pi\) | |||||||
\(180\) | −0.971485 | + | 1.68266i | −0.0724102 | + | 0.125418i | ||||
\(181\) | −16.7773 | −1.24705 | −0.623524 | − | 0.781804i | \(-0.714300\pi\) | ||||
−0.623524 | + | 0.781804i | \(0.714300\pi\) | |||||||
\(182\) | 6.56734 | + | 15.9572i | 0.486804 | + | 1.18283i | ||||
\(183\) | 17.4203i | 1.28774i | ||||||||
\(184\) | 1.35675 | − | 4.59992i | 0.100021 | − | 0.339110i | ||||
\(185\) | 6.83352 | − | 3.94533i | 0.502410 | − | 0.290067i | ||||
\(186\) | 2.01374 | + | 3.48790i | 0.147655 | + | 0.255746i | ||||
\(187\) | 5.93900 | + | 3.42888i | 0.434302 | + | 0.250745i | ||||
\(188\) | 0.281653i | 0.0205416i | ||||||||
\(189\) | −8.94765 | + | 11.6062i | −0.650846 | + | 0.844230i | ||||
\(190\) | −4.74949 | −0.344564 | ||||||||
\(191\) | 3.11889 | + | 1.80069i | 0.225675 | + | 0.130294i | 0.608575 | − | 0.793496i | \(-0.291741\pi\) |
−0.382900 | + | 0.923790i | \(0.625075\pi\) | |||||||
\(192\) | −1.07743 | + | 0.622057i | −0.0777571 | + | 0.0448931i | ||||
\(193\) | 7.15236 | + | 12.3883i | 0.514838 | + | 0.891726i | 0.999852 | + | 0.0172195i | \(0.00548140\pi\) |
−0.485013 | + | 0.874507i | \(0.661185\pi\) | |||||||
\(194\) | 7.09225 | − | 12.2841i | 0.509194 | − | 0.881950i | ||||
\(195\) | −10.8565 | −0.777453 | ||||||||
\(196\) | 4.97214 | − | 4.92726i | 0.355153 | − | 0.351947i | ||||
\(197\) | −12.0468 | −0.858299 | −0.429149 | − | 0.903233i | \(-0.641187\pi\) | ||||
−0.429149 | + | 0.903233i | \(0.641187\pi\) | |||||||
\(198\) | −7.58997 | − | 4.38207i | −0.539395 | − | 0.311420i | ||||
\(199\) | −9.74098 | − | 16.8719i | −0.690520 | − | 1.19602i | −0.971668 | − | 0.236351i | \(-0.924048\pi\) |
0.281148 | − | 0.959664i | \(-0.409285\pi\) | |||||||
\(200\) | −1.60492 | − | 2.77980i | −0.113485 | − | 0.196562i | ||||
\(201\) | 2.56671 | − | 4.44568i | 0.181042 | − | 0.313574i | ||||
\(202\) | 10.2336i | 0.720036i | ||||||||
\(203\) | 6.66818 | + | 5.14073i | 0.468014 | + | 0.360808i | ||||
\(204\) | − | 1.41369i | − | 0.0989780i | ||||||
\(205\) | −1.07560 | − | 0.620995i | −0.0751229 | − | 0.0433722i | ||||
\(206\) | 6.03001 | + | 10.4443i | 0.420131 | + | 0.727687i | ||||
\(207\) | −4.79984 | − | 5.04624i | −0.333612 | − | 0.350738i | ||||
\(208\) | 5.64828 | + | 3.26103i | 0.391638 | + | 0.226112i | ||||
\(209\) | − | 21.4235i | − | 1.48189i | ||||||
\(210\) | 1.67614 | + | 4.07265i | 0.115665 | + | 0.281039i | ||||
\(211\) | 12.1866 | 0.838961 | 0.419480 | − | 0.907764i | \(-0.362212\pi\) | ||||
0.419480 | + | 0.907764i | \(0.362212\pi\) | |||||||
\(212\) | −11.3667 | − | 6.56256i | −0.780667 | − | 0.450718i | ||||
\(213\) | 4.33935 | − | 2.50533i | 0.297328 | − | 0.171662i | ||||
\(214\) | −7.66359 | + | 4.42458i | −0.523872 | + | 0.302458i | ||||
\(215\) | −0.351723 | − | 0.203067i | −0.0239873 | − | 0.0138491i | ||||
\(216\) | 5.53902i | 0.376883i | ||||||||
\(217\) | −8.48908 | − | 1.13719i | −0.576276 | − | 0.0771975i | ||||
\(218\) | 7.70624i | 0.521932i | ||||||||
\(219\) | 7.97307 | − | 13.8098i | 0.538770 | − | 0.933178i | ||||
\(220\) | −6.99303 | + | 4.03743i | −0.471470 | + | 0.272203i | ||||
\(221\) | −6.41814 | + | 3.70552i | −0.431731 | + | 0.249260i | ||||
\(222\) | 3.66858 | − | 6.35417i | 0.246219 | − | 0.426464i | ||||
\(223\) | − | 16.5496i | − | 1.10824i | −0.832436 | − | 0.554122i | \(-0.813054\pi\) | ||
0.832436 | − | 0.554122i | \(-0.186946\pi\) | |||||||
\(224\) | 0.351285 | − | 2.62233i | 0.0234712 | − | 0.175212i | ||||
\(225\) | −4.66126 | −0.310751 | ||||||||
\(226\) | 7.70322 | + | 4.44745i | 0.512410 | + | 0.295840i | ||||
\(227\) | −8.69075 | − | 15.0528i | −0.576825 | − | 0.999090i | −0.995841 | − | 0.0911113i | \(-0.970958\pi\) |
0.419016 | − | 0.907979i | \(-0.362375\pi\) | |||||||
\(228\) | −3.82465 | + | 2.20816i | −0.253294 | + | 0.146239i | ||||
\(229\) | 0.486122 | − | 0.841988i | 0.0321239 | − | 0.0556402i | −0.849517 | − | 0.527562i | \(-0.823106\pi\) |
0.881640 | + | 0.471922i | \(0.156440\pi\) | |||||||
\(230\) | −6.23764 | + | 1.50518i | −0.411297 | + | 0.0992486i | ||||
\(231\) | −18.3705 | + | 7.56055i | −1.20869 | + | 0.497448i | ||||
\(232\) | 3.18236 | 0.208932 | ||||||||
\(233\) | 3.41466 | − | 5.91436i | 0.223702 | − | 0.387463i | −0.732227 | − | 0.681060i | \(-0.761519\pi\) |
0.955929 | + | 0.293597i | \(0.0948525\pi\) | |||||||
\(234\) | 8.20231 | − | 4.73561i | 0.536202 | − | 0.309576i | ||||
\(235\) | 0.326355 | − | 0.188421i | 0.0212891 | − | 0.0122912i | ||||
\(236\) | 1.10083 | + | 0.635567i | 0.0716582 | + | 0.0413719i | ||||
\(237\) | 15.2536 | 0.990830 | ||||||||
\(238\) | 2.38096 | + | 1.83556i | 0.154335 | + | 0.118982i | ||||
\(239\) | 14.7894 | 0.956647 | 0.478324 | − | 0.878184i | \(-0.341245\pi\) | ||||
0.478324 | + | 0.878184i | \(0.341245\pi\) | |||||||
\(240\) | 1.44157 | + | 0.832293i | 0.0930532 | + | 0.0537243i | ||||
\(241\) | −6.60378 | − | 11.4381i | −0.425387 | − | 0.736791i | 0.571070 | − | 0.820902i | \(-0.306529\pi\) |
−0.996456 | + | 0.0841102i | \(0.973195\pi\) | |||||||
\(242\) | −12.7116 | − | 22.0171i | −0.817132 | − | 1.41531i | ||||
\(243\) | 11.6599 | + | 6.73184i | 0.747982 | + | 0.431848i | ||||
\(244\) | −14.0021 | −0.896396 | ||||||||
\(245\) | −9.03556 | − | 2.46503i | −0.577261 | − | 0.157485i | ||||
\(246\) | −1.15487 | −0.0736318 | ||||||||
\(247\) | 20.0501 | + | 11.5759i | 1.27576 | + | 0.736560i | ||||
\(248\) | −2.80352 | + | 1.61862i | −0.178024 | + | 0.102782i | ||||
\(249\) | −6.45777 | + | 3.72839i | −0.409244 | + | 0.236277i | ||||
\(250\) | −5.49225 | + | 9.51286i | −0.347361 | + | 0.601646i | ||||
\(251\) | −9.65778 | −0.609593 | −0.304797 | − | 0.952417i | \(-0.598589\pi\) | ||||
−0.304797 | + | 0.952417i | \(0.598589\pi\) | |||||||
\(252\) | −3.04284 | − | 2.34583i | −0.191681 | − | 0.147773i | ||||
\(253\) | −6.78940 | − | 28.1360i | −0.426846 | − | 1.76890i | ||||
\(254\) | −5.72571 | + | 9.91722i | −0.359263 | + | 0.622262i | ||||
\(255\) | −1.63806 | + | 0.945735i | −0.102579 | + | 0.0592242i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.82152 | − | 3.36106i | −0.363137 | − | 0.209657i | 0.307319 | − | 0.951607i | \(-0.400568\pi\) |
−0.670456 | + | 0.741949i | \(0.733901\pi\) | |||||||
\(258\) | −0.377645 | −0.0235112 | ||||||||
\(259\) | 5.93844 | + | 14.4291i | 0.368996 | + | 0.896579i | ||||
\(260\) | − | 8.72632i | − | 0.541183i | ||||||
\(261\) | 2.31068 | − | 4.00221i | 0.143027 | − | 0.247730i | ||||
\(262\) | −6.21988 | + | 3.59105i | −0.384265 | + | 0.221856i | ||||
\(263\) | 22.1864 | − | 12.8094i | 1.36808 | − | 0.789859i | 0.377393 | − | 0.926053i | \(-0.376821\pi\) |
0.990682 | + | 0.136195i | \(0.0434873\pi\) | |||||||
\(264\) | −3.75422 | + | 6.50249i | −0.231056 | + | 0.400201i | ||||
\(265\) | 17.5610i | 1.07876i | ||||||||
\(266\) | 1.24698 | − | 9.30868i | 0.0764575 | − | 0.570752i | ||||
\(267\) | − | 11.7436i | − | 0.718697i | ||||||
\(268\) | 3.57337 | + | 2.06308i | 0.218278 | + | 0.126023i | ||||
\(269\) | −19.4220 | + | 11.2133i | −1.18418 | + | 0.683686i | −0.956978 | − | 0.290162i | \(-0.906291\pi\) |
−0.227201 | + | 0.973848i | \(0.572958\pi\) | |||||||
\(270\) | 6.41814 | − | 3.70552i | 0.390596 | − | 0.225511i | ||||
\(271\) | 0.355990 | + | 0.205531i | 0.0216248 | + | 0.0124851i | 0.510773 | − | 0.859715i | \(-0.329359\pi\) |
−0.489149 | + | 0.872200i | \(0.662692\pi\) | |||||||
\(272\) | 1.13630 | 0.0688984 | ||||||||
\(273\) | 2.85040 | − | 21.2781i | 0.172514 | − | 1.28781i | ||||
\(274\) | 4.47858i | 0.270561i | ||||||||
\(275\) | −16.7766 | − | 9.68595i | −1.01166 | − | 0.584085i | ||||
\(276\) | −4.32322 | + | 4.11213i | −0.260227 | + | 0.247521i | ||||
\(277\) | −2.30603 | − | 3.99416i | −0.138556 | − | 0.239986i | 0.788394 | − | 0.615170i | \(-0.210913\pi\) |
−0.926950 | + | 0.375184i | \(0.877579\pi\) | |||||||
\(278\) | −7.85599 | − | 4.53566i | −0.471171 | − | 0.272031i | ||||
\(279\) | 4.70104i | 0.281444i | ||||||||
\(280\) | −3.27353 | + | 1.34726i | −0.195631 | + | 0.0805140i | ||||
\(281\) | 20.5915i | 1.22839i | 0.789156 | + | 0.614193i | \(0.210518\pi\) | ||||
−0.789156 | + | 0.614193i | \(0.789482\pi\) | |||||||
\(282\) | 0.175204 | − | 0.303462i | 0.0104333 | − | 0.0180709i | ||||
\(283\) | −0.174471 | − | 0.302193i | −0.0103712 | − | 0.0179635i | 0.860793 | − | 0.508955i | \(-0.169968\pi\) |
−0.871164 | + | 0.490991i | \(0.836635\pi\) | |||||||
\(284\) | 2.01374 | + | 3.48790i | 0.119494 | + | 0.206969i | ||||
\(285\) | 5.11726 | + | 2.95445i | 0.303121 | + | 0.175007i | ||||
\(286\) | 39.3617 | 2.32751 | ||||||||
\(287\) | 1.49951 | − | 1.94505i | 0.0885131 | − | 0.114813i | ||||
\(288\) | −1.45218 | −0.0855705 | ||||||||
\(289\) | 7.85441 | − | 13.6042i | 0.462024 | − | 0.800249i | ||||
\(290\) | −2.12895 | − | 3.68744i | −0.125016 | − | 0.216534i | ||||
\(291\) | −15.2829 | + | 8.82357i | −0.895898 | + | 0.517247i | ||||
\(292\) | 11.1001 | + | 6.40863i | 0.649583 | + | 0.375037i | ||||
\(293\) | 25.1643 | 1.47011 | 0.735057 | − | 0.678005i | \(-0.237155\pi\) | ||||
0.735057 | + | 0.678005i | \(0.237155\pi\) | |||||||
\(294\) | −8.42219 | + | 2.21584i | −0.491192 | + | 0.129231i | ||||
\(295\) | − | 1.70074i | − | 0.0990208i | ||||||
\(296\) | 5.10738 | + | 2.94875i | 0.296861 | + | 0.171393i | ||||
\(297\) | 16.7144 | + | 28.9503i | 0.969870 | + | 1.67986i | ||||
\(298\) | 15.4017 | − | 8.89220i | 0.892199 | − | 0.515111i | ||||
\(299\) | 30.0010 | + | 8.84884i | 1.73500 | + | 0.511742i | ||||
\(300\) | 3.99341i | 0.230560i | ||||||||
\(301\) | 0.490343 | − | 0.636037i | 0.0282629 | − | 0.0366606i | ||||
\(302\) | 19.4832 | 1.12113 | ||||||||
\(303\) | 6.36590 | − | 11.0261i | 0.365712 | − | 0.633431i | ||||
\(304\) | −1.77489 | − | 3.07420i | −0.101797 | − | 0.176317i | ||||
\(305\) | 9.36722 | + | 16.2245i | 0.536365 | + | 0.929012i | ||||
\(306\) | 0.825057 | − | 1.42904i | 0.0471653 | − | 0.0816928i | ||||
\(307\) | − | 12.9274i | − | 0.737806i | −0.929468 | − | 0.368903i | \(-0.879734\pi\) | ||
0.929468 | − | 0.368903i | \(-0.120266\pi\) | |||||||
\(308\) | −6.07706 | − | 14.7659i | −0.346272 | − | 0.841365i | ||||
\(309\) | − | 15.0040i | − | 0.853550i | ||||||
\(310\) | 3.75103 | + | 2.16566i | 0.213044 | + | 0.123001i | ||||
\(311\) | 3.10046 | − | 1.79005i | 0.175811 | − | 0.101504i | −0.409512 | − | 0.912305i | \(-0.634301\pi\) |
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(312\) | −4.05710 | − | 7.02710i | −0.229688 | − | 0.397831i | ||||
\(313\) | 2.70313 | − | 4.68196i | 0.152790 | − | 0.264640i | −0.779462 | − | 0.626449i | \(-0.784507\pi\) |
0.932252 | + | 0.361809i | \(0.117841\pi\) | |||||||
\(314\) | −8.21100 | −0.463374 | ||||||||
\(315\) | −0.682536 | + | 5.09510i | −0.0384566 | + | 0.287077i | ||||
\(316\) | 12.2606i | 0.689715i | ||||||||
\(317\) | −13.5155 | + | 23.4095i | −0.759106 | + | 1.31481i | 0.184201 | + | 0.982889i | \(0.441030\pi\) |
−0.943307 | + | 0.331921i | \(0.892303\pi\) | |||||||
\(318\) | 8.16457 | + | 14.1415i | 0.457846 | + | 0.793013i | ||||
\(319\) | 16.6329 | − | 9.60301i | 0.931264 | − | 0.537666i | ||||
\(320\) | −0.668984 | + | 1.15871i | −0.0373974 | + | 0.0647741i | ||||
\(321\) | 11.0094 | 0.614483 | ||||||||
\(322\) | −1.31235 | − | 12.6205i | −0.0731346 | − | 0.703315i | ||||
\(323\) | 4.03362 | 0.224436 | ||||||||
\(324\) | 1.26732 | − | 2.19506i | 0.0704066 | − | 0.121948i | ||||
\(325\) | 18.1301 | − | 10.4674i | 1.00568 | − | 0.580627i | ||||
\(326\) | 7.48801 | + | 12.9696i | 0.414722 | + | 0.718320i | ||||
\(327\) | 4.79372 | − | 8.30297i | 0.265093 | − | 0.459155i | ||||
\(328\) | − | 0.928266i | − | 0.0512549i | ||||||
\(329\) | 0.283608 | + | 0.689104i | 0.0156358 | + | 0.0379915i | ||||
\(330\) | 10.0460 | 0.553017 | ||||||||
\(331\) | 3.64113 | − | 6.30662i | 0.200134 | − | 0.346643i | −0.748437 | − | 0.663206i | \(-0.769195\pi\) |
0.948572 | + | 0.316563i | \(0.102529\pi\) | |||||||
\(332\) | −2.99683 | − | 5.19065i | −0.164472 | − | 0.284874i | ||||
\(333\) | 7.41684 | − | 4.28211i | 0.406440 | − | 0.234658i | ||||
\(334\) | 12.6063 | + | 7.27825i | 0.689786 | + | 0.398248i | ||||
\(335\) | − | 5.52068i | − | 0.301627i | ||||||
\(336\) | −2.00972 | + | 2.60687i | −0.109639 | + | 0.142216i | ||||
\(337\) | − | 19.2503i | − | 1.04863i | −0.851524 | − | 0.524316i | \(-0.824321\pi\) | ||
0.851524 | − | 0.524316i | \(-0.175679\pi\) | |||||||
\(338\) | −14.7687 | + | 25.5801i | −0.803311 | + | 1.39138i | ||||
\(339\) | −5.53314 | − | 9.58368i | −0.300519 | − | 0.520514i | ||||
\(340\) | −0.760167 | − | 1.31665i | −0.0412259 | − | 0.0714053i | ||||
\(341\) | −9.76861 | + | 16.9197i | −0.529000 | + | 0.916254i | ||||
\(342\) | −5.15491 | −0.278746 | ||||||||
\(343\) | 7.20359 | − | 17.0619i | 0.388957 | − | 0.921256i | ||||
\(344\) | − | 0.303546i | − | 0.0163661i | ||||||
\(345\) | 7.65695 | + | 2.25843i | 0.412236 | + | 0.121590i | ||||
\(346\) | 0.143633 | − | 0.0829263i | 0.00772173 | − | 0.00445814i | ||||
\(347\) | −14.4944 | − | 25.1050i | −0.778100 | − | 1.34771i | −0.933035 | − | 0.359785i | \(-0.882850\pi\) |
0.154935 | − | 0.987925i | \(-0.450483\pi\) | |||||||
\(348\) | −3.42878 | − | 1.97961i | −0.183802 | − | 0.106118i | ||||
\(349\) | − | 12.4174i | − | 0.664687i | −0.943159 | − | 0.332343i | \(-0.892161\pi\) | ||
0.943159 | − | 0.332343i | \(-0.107839\pi\) | |||||||
\(350\) | −6.72577 | − | 5.18513i | −0.359508 | − | 0.277157i | ||||
\(351\) | −36.1259 | −1.92826 | ||||||||
\(352\) | −5.22660 | − | 3.01758i | −0.278579 | − | 0.160838i | ||||
\(353\) | 6.43499 | − | 3.71525i | 0.342500 | − | 0.197743i | −0.318877 | − | 0.947796i | \(-0.603306\pi\) |
0.661377 | + | 0.750054i | \(0.269972\pi\) | |||||||
\(354\) | −0.790718 | − | 1.36956i | −0.0420262 | − | 0.0727915i | ||||
\(355\) | 2.69432 | − | 4.66671i | 0.143000 | − | 0.247683i | ||||
\(356\) | 9.43933 | 0.500283 | ||||||||
\(357\) | −1.42350 | − | 3.45879i | −0.0753397 | − | 0.183059i | ||||
\(358\) | −8.14244 | −0.430341 | ||||||||
\(359\) | −17.2194 | − | 9.94165i | −0.908808 | − | 0.524700i | −0.0287603 | − | 0.999586i | \(-0.509156\pi\) |
−0.880047 | + | 0.474886i | \(0.842489\pi\) | |||||||
\(360\) | 0.971485 | + | 1.68266i | 0.0512018 | + | 0.0886840i | ||||
\(361\) | 3.19954 | + | 5.54177i | 0.168397 | + | 0.291672i | ||||
\(362\) | −8.38866 | + | 14.5296i | −0.440898 | + | 0.763658i | ||||
\(363\) | 31.6293i | 1.66011i | ||||||||
\(364\) | 17.1030 | + | 2.29110i | 0.896441 | + | 0.120087i | ||||
\(365\) | − | 17.1491i | − | 0.897625i | ||||||
\(366\) | 15.0864 | + | 8.71014i | 0.788579 | + | 0.455286i | ||||
\(367\) | 10.8893 | + | 18.8608i | 0.568416 | + | 0.984525i | 0.996723 | + | 0.0808918i | \(0.0257768\pi\) |
−0.428307 | + | 0.903633i | \(0.640890\pi\) | |||||||
\(368\) | −3.30527 | − | 3.47494i | −0.172299 | − | 0.181144i | ||||
\(369\) | −1.16741 | − | 0.674005i | −0.0607729 | − | 0.0350873i | ||||
\(370\) | − | 7.89066i | − | 0.410216i | ||||||
\(371\) | −34.4183 | − | 4.61066i | −1.78691 | − | 0.239373i | ||||
\(372\) | 4.02749 | 0.208815 | ||||||||
\(373\) | 17.5547 | + | 10.1352i | 0.908948 | + | 0.524781i | 0.880092 | − | 0.474802i | \(-0.157480\pi\) |
0.0288554 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(374\) | 5.93900 | − | 3.42888i | 0.307098 | − | 0.177303i | ||||
\(375\) | 11.8351 | − | 6.83299i | 0.611161 | − | 0.352854i | ||||
\(376\) | 0.243918 | + | 0.140826i | 0.0125791 | + | 0.00726257i | ||||
\(377\) | 20.7555i | 1.06896i | ||||||||
\(378\) | 5.57747 | + | 13.5520i | 0.286874 | + | 0.697040i | ||||
\(379\) | 17.4861i | 0.898200i | 0.893481 | + | 0.449100i | \(0.148255\pi\) | ||||
−0.893481 | + | 0.449100i | \(0.851745\pi\) | |||||||
\(380\) | −2.37474 | + | 4.11318i | −0.121822 | + | 0.211002i | ||||
\(381\) | 12.3382 | − | 7.12344i | 0.632103 | − | 0.364945i | ||||
\(382\) | 3.11889 | − | 1.80069i | 0.159576 | − | 0.0921315i | ||||
\(383\) | 8.88242 | − | 15.3848i | 0.453870 | − | 0.786126i | −0.544752 | − | 0.838597i | \(-0.683376\pi\) |
0.998622 | + | 0.0524707i | \(0.0167096\pi\) | |||||||
\(384\) | 1.24411i | 0.0634884i | ||||||||
\(385\) | −13.0440 | + | 16.9197i | −0.664784 | + | 0.862309i | ||||
\(386\) | 14.3047 | 0.728091 | ||||||||
\(387\) | −0.381746 | − | 0.220401i | −0.0194053 | − | 0.0112036i | ||||
\(388\) | −7.09225 | − | 12.2841i | −0.360055 | − | 0.623633i | ||||
\(389\) | −13.9506 | + | 8.05439i | −0.707324 | + | 0.408374i | −0.810069 | − | 0.586334i | \(-0.800571\pi\) |
0.102746 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(390\) | −5.42827 | + | 9.40204i | −0.274871 | + | 0.476091i | ||||
\(391\) | 5.29746 | − | 1.27831i | 0.267904 | − | 0.0646469i | ||||
\(392\) | −1.78106 | − | 6.76962i | −0.0899572 | − | 0.341918i | ||||
\(393\) | 8.93535 | 0.450729 | ||||||||
\(394\) | −6.02340 | + | 10.4328i | −0.303454 | + | 0.525599i | ||||
\(395\) | 14.2066 | − | 8.20217i | 0.714811 | − | 0.412696i | ||||
\(396\) | −7.58997 | + | 4.38207i | −0.381410 | + | 0.220207i | ||||
\(397\) | −5.91641 | − | 3.41584i | −0.296936 | − | 0.171436i | 0.344130 | − | 0.938922i | \(-0.388174\pi\) |
−0.641066 | + | 0.767486i | \(0.721507\pi\) | |||||||
\(398\) | −19.4820 | −0.976543 | ||||||||
\(399\) | −7.13407 | + | 9.25380i | −0.357150 | + | 0.463269i | ||||
\(400\) | −3.20984 | −0.160492 | ||||||||
\(401\) | −16.3143 | − | 9.41906i | −0.814697 | − | 0.470365i | 0.0338876 | − | 0.999426i | \(-0.489211\pi\) |
−0.848584 | + | 0.529060i | \(0.822545\pi\) | |||||||
\(402\) | −2.56671 | − | 4.44568i | −0.128016 | − | 0.221730i | ||||
\(403\) | −10.5567 | − | 18.2848i | −0.525868 | − | 0.910830i | ||||
\(404\) | 8.86258 | + | 5.11681i | 0.440930 | + | 0.254571i | ||||
\(405\) | −3.39126 | −0.168513 | ||||||||
\(406\) | 7.78609 | − | 3.20445i | 0.386417 | − | 0.159034i | ||||
\(407\) | 35.5924 | 1.76425 | ||||||||
\(408\) | −1.22429 | − | 0.706844i | −0.0606114 | − | 0.0349940i | ||||
\(409\) | 5.12526 | − | 2.95907i | 0.253428 | − | 0.146316i | −0.367905 | − | 0.929863i | \(-0.619925\pi\) |
0.621333 | + | 0.783547i | \(0.286592\pi\) | |||||||
\(410\) | −1.07560 | + | 0.620995i | −0.0531199 | + | 0.0306688i | ||||
\(411\) | 2.78593 | − | 4.82538i | 0.137420 | − | 0.238018i | ||||
\(412\) | 12.0600 | 0.594154 | ||||||||
\(413\) | 3.33333 | + | 0.446530i | 0.164022 | + | 0.0219723i | ||||
\(414\) | −6.77009 | + | 1.63366i | −0.332732 | + | 0.0802902i | ||||
\(415\) | −4.00966 | + | 6.94493i | −0.196826 | + | 0.340913i | ||||
\(416\) | 5.64828 | − | 3.26103i | 0.276930 | − | 0.159885i | ||||
\(417\) | 5.64288 | + | 9.77375i | 0.276333 | + | 0.478623i | ||||
\(418\) | −18.5533 | − | 10.7117i | −0.907471 | − | 0.523928i | ||||
\(419\) | −4.13562 | −0.202038 | −0.101019 | − | 0.994884i | \(-0.532210\pi\) | ||||
−0.101019 | + | 0.994884i | \(0.532210\pi\) | |||||||
\(420\) | 4.36509 | + | 0.584744i | 0.212994 | + | 0.0285326i | ||||
\(421\) | 29.2892i | 1.42747i | 0.700416 | + | 0.713735i | \(0.252998\pi\) | ||||
−0.700416 | + | 0.713735i | \(0.747002\pi\) | |||||||
\(422\) | 6.09331 | − | 10.5539i | 0.296617 | − | 0.513757i | ||||
\(423\) | 0.354213 | − | 0.204505i | 0.0172224 | − | 0.00994338i | ||||
\(424\) | −11.3667 | + | 6.56256i | −0.552015 | + | 0.318706i | ||||
\(425\) | 1.82367 | − | 3.15869i | 0.0884611 | − | 0.153219i | ||||
\(426\) | − | 5.01065i | − | 0.242767i | ||||||
\(427\) | −34.2583 | + | 14.0993i | −1.65787 | + | 0.682315i | ||||
\(428\) | 8.84915i | 0.427740i | ||||||||
\(429\) | −42.4097 | − | 24.4853i | −2.04756 | − | 1.18216i | ||||
\(430\) | −0.351723 | + | 0.203067i | −0.0169616 | + | 0.00979277i | ||||
\(431\) | −4.57492 | + | 2.64133i | −0.220366 | + | 0.127228i | −0.606120 | − | 0.795373i | \(-0.707275\pi\) |
0.385754 | + | 0.922602i | \(0.373941\pi\) | |||||||
\(432\) | 4.79693 | + | 2.76951i | 0.230793 | + | 0.133248i | ||||
\(433\) | −29.0430 | −1.39572 | −0.697860 | − | 0.716235i | \(-0.745864\pi\) | ||||
−0.697860 | + | 0.716235i | \(0.745864\pi\) | |||||||
\(434\) | −5.22938 | + | 6.78316i | −0.251018 | + | 0.325602i | ||||
\(435\) | 5.29730i | 0.253986i | ||||||||
\(436\) | 6.67380 | + | 3.85312i | 0.319617 | + | 0.184531i | ||||
\(437\) | −11.7330 | − | 12.3353i | −0.561264 | − | 0.590076i | ||||
\(438\) | −7.97307 | − | 13.8098i | −0.380968 | − | 0.659856i | ||||
\(439\) | 29.6005 | + | 17.0899i | 1.41276 | + | 0.815655i | 0.995647 | − | 0.0932020i | \(-0.0297102\pi\) |
0.417108 | + | 0.908857i | \(0.363044\pi\) | |||||||
\(440\) | 8.07486i | 0.384954i | ||||||||
\(441\) | −9.80685 | − | 2.67545i | −0.466993 | − | 0.127402i | ||||
\(442\) | 7.41103i | 0.352507i | ||||||||
\(443\) | 0.874186 | − | 1.51413i | 0.0415338 | − | 0.0719387i | −0.844511 | − | 0.535538i | \(-0.820109\pi\) |
0.886045 | + | 0.463599i | \(0.153442\pi\) | |||||||
\(444\) | −3.66858 | − | 6.35417i | −0.174103 | − | 0.301555i | ||||
\(445\) | −6.31476 | − | 10.9375i | −0.299348 | − | 0.518487i | ||||
\(446\) | −14.3324 | − | 8.27481i | −0.678658 | − | 0.391823i | ||||
\(447\) | −22.1258 | −1.04652 | ||||||||
\(448\) | −2.09536 | − | 1.61539i | −0.0989964 | − | 0.0763198i | ||||
\(449\) | 20.7363 | 0.978607 | 0.489303 | − | 0.872114i | \(-0.337251\pi\) | ||||
0.489303 | + | 0.872114i | \(0.337251\pi\) | |||||||
\(450\) | −2.33063 | + | 4.03677i | −0.109867 | + | 0.190295i | ||||
\(451\) | −2.80112 | − | 4.85168i | −0.131900 | − | 0.228457i | ||||
\(452\) | 7.70322 | − | 4.44745i | 0.362329 | − | 0.209191i | ||||
\(453\) | −20.9918 | − | 12.1196i | −0.986283 | − | 0.569431i | ||||
\(454\) | −17.3815 | −0.815754 | ||||||||
\(455\) | −8.78690 | − | 21.3502i | −0.411936 | − | 1.00091i | ||||
\(456\) | 4.41633i | 0.206814i | ||||||||
\(457\) | −10.3635 | − | 5.98335i | −0.484782 | − | 0.279889i | 0.237625 | − | 0.971357i | \(-0.423631\pi\) |
−0.722407 | + | 0.691468i | \(0.756964\pi\) | |||||||
\(458\) | −0.486122 | − | 0.841988i | −0.0227150 | − | 0.0393435i | ||||
\(459\) | −5.45076 | + | 3.14700i | −0.254420 | + | 0.146889i | ||||
\(460\) | −1.81529 | + | 6.15454i | −0.0846385 | + | 0.286957i | ||||
\(461\) | 14.9676i | 0.697109i | 0.937289 | + | 0.348554i | \(0.113327\pi\) | ||||
−0.937289 | + | 0.348554i | \(0.886673\pi\) | |||||||
\(462\) | −2.63760 | + | 19.6896i | −0.122712 | + | 0.916041i | ||||
\(463\) | 8.01243 | 0.372369 | 0.186185 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186185 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(464\) | 1.59118 | − | 2.75600i | 0.0738686 | − | 0.127944i | ||||
\(465\) | −2.69432 | − | 4.66671i | −0.124946 | − | 0.216413i | ||||
\(466\) | −3.41466 | − | 5.91436i | −0.158181 | − | 0.273978i | ||||
\(467\) | 0.207210 | − | 0.358899i | 0.00958855 | − | 0.0166078i | −0.861191 | − | 0.508281i | \(-0.830281\pi\) |
0.870780 | + | 0.491673i | \(0.163614\pi\) | |||||||
\(468\) | − | 9.47121i | − | 0.437807i | ||||||
\(469\) | 10.8202 | + | 1.44946i | 0.499629 | + | 0.0669299i | ||||
\(470\) | − | 0.376843i | − | 0.0173824i | ||||||
\(471\) | 8.84682 | + | 5.10771i | 0.407640 | + | 0.235351i | ||||
\(472\) | 1.10083 | − | 0.635567i | 0.0506700 | − | 0.0292543i | ||||
\(473\) | −0.915973 | − | 1.58651i | −0.0421165 | − | 0.0729479i | ||||
\(474\) | 7.62682 | − | 13.2100i | 0.350311 | − | 0.606757i | ||||
\(475\) | −11.3942 | −0.522803 | ||||||||
\(476\) | 2.78012 | − | 1.14419i | 0.127427 | − | 0.0524438i | ||||
\(477\) | 19.0600i | 0.872698i | ||||||||
\(478\) | 7.39470 | − | 12.8080i | 0.338226 | − | 0.585824i | ||||
\(479\) | 10.3395 | + | 17.9086i | 0.472425 | + | 0.818264i | 0.999502 | − | 0.0315532i | \(-0.0100454\pi\) |
−0.527077 | + | 0.849818i | \(0.676712\pi\) | |||||||
\(480\) | 1.44157 | − | 0.832293i | 0.0657985 | − | 0.0379888i | ||||
\(481\) | −19.2319 | + | 33.3107i | −0.876901 | + | 1.51884i | ||||
\(482\) | −13.2076 | −0.601588 | ||||||||
\(483\) | −6.43672 | + | 14.4142i | −0.292881 | + | 0.655867i | ||||
\(484\) | −25.4232 | −1.15560 | ||||||||
\(485\) | −9.48921 | + | 16.4358i | −0.430883 | + | 0.746311i | ||||
\(486\) | 11.6599 | − | 6.73184i | 0.528903 | − | 0.305363i | ||||
\(487\) | −3.26073 | − | 5.64774i | −0.147758 | − | 0.255924i | 0.782641 | − | 0.622474i | \(-0.213872\pi\) |
−0.930398 | + | 0.366550i | \(0.880539\pi\) | |||||||
\(488\) | −7.00107 | + | 12.1262i | −0.316924 | + | 0.548928i | ||||
\(489\) | − | 18.6319i | − | 0.842563i | ||||||
\(490\) | −6.65256 | + | 6.59251i | −0.300532 | + | 0.297819i | ||||
\(491\) | 14.6314 | 0.660306 | 0.330153 | − | 0.943927i | \(-0.392900\pi\) | ||||
0.330153 | + | 0.943927i | \(0.392900\pi\) | |||||||
\(492\) | −0.577435 | + | 1.00015i | −0.0260328 | + | 0.0450901i | ||||
\(493\) | 1.80806 | + | 3.13165i | 0.0814308 | + | 0.141042i | ||||
\(494\) | 20.0501 | − | 11.5759i | 0.902098 | − | 0.520826i | ||||
\(495\) | 10.1551 | + | 5.86307i | 0.456439 | + | 0.263525i | ||||
\(496\) | 3.23723i | 0.145356i | ||||||||
\(497\) | 8.43903 | + | 6.50594i | 0.378542 | + | 0.291831i | ||||
\(498\) | 7.45679i | 0.334147i | ||||||||
\(499\) | −8.69163 | + | 15.0544i | −0.389091 | + | 0.673925i | −0.992328 | − | 0.123637i | \(-0.960544\pi\) |
0.603237 | + | 0.797562i | \(0.293877\pi\) | |||||||
\(500\) | 5.49225 | + | 9.51286i | 0.245621 | + | 0.425428i | ||||
\(501\) | −9.05497 | − | 15.6837i | −0.404546 | − | 0.700695i | ||||
\(502\) | −4.82889 | + | 8.36388i | −0.215524 | + | 0.373298i | ||||
\(503\) | 17.7000 | 0.789206 | 0.394603 | − | 0.918852i | \(-0.370882\pi\) | ||||
0.394603 | + | 0.918852i | \(0.370882\pi\) | |||||||
\(504\) | −3.55297 | + | 1.46226i | −0.158262 | + | 0.0651342i | ||||
\(505\) | − | 13.6923i | − | 0.609298i | ||||||
\(506\) | −27.7612 | − | 8.18823i | −1.23414 | − | 0.364011i | ||||
\(507\) | 31.8246 | − | 18.3739i | 1.41338 | − | 0.816015i | ||||
\(508\) | 5.72571 | + | 9.91722i | 0.254037 | + | 0.440006i | ||||
\(509\) | −24.1180 | − | 13.9245i | −1.06901 | − | 0.617193i | −0.141099 | − | 0.989995i | \(-0.545064\pi\) |
−0.927911 | + | 0.372802i | \(0.878397\pi\) | |||||||
\(510\) | 1.89147i | 0.0837557i | ||||||||
\(511\) | 33.6111 | + | 4.50251i | 1.48687 | + | 0.199179i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 17.0280 | + | 9.83114i | 0.751806 | + | 0.434056i | ||||
\(514\) | −5.82152 | + | 3.36106i | −0.256776 | + | 0.148250i | ||||
\(515\) | −8.06796 | − | 13.9741i | −0.355517 | − | 0.615773i | ||||
\(516\) | −0.188823 | + | 0.327051i | −0.00831246 | + | 0.0143976i | ||||
\(517\) | 1.69982 | 0.0747580 | ||||||||
\(518\) | 15.4652 | + | 2.07170i | 0.679500 | + | 0.0910254i | ||||
\(519\) | −0.206340 | −0.00905730 | ||||||||
\(520\) | −7.55722 | − | 4.36316i | −0.331406 | − | 0.191337i | ||||
\(521\) | 6.81914 | + | 11.8111i | 0.298752 | + | 0.517453i | 0.975851 | − | 0.218439i | \(-0.0700964\pi\) |
−0.677099 | + | 0.735892i | \(0.736763\pi\) | |||||||
\(522\) | −2.31068 | − | 4.00221i | −0.101136 | − | 0.175172i | ||||
\(523\) | −16.1015 | + | 27.8887i | −0.704071 | + | 1.21949i | 0.262954 | + | 0.964808i | \(0.415303\pi\) |
−0.967026 | + | 0.254679i | \(0.918030\pi\) | |||||||
\(524\) | 7.18209i | 0.313751i | ||||||||
\(525\) | 4.02113 | + | 9.77045i | 0.175497 | + | 0.426417i | ||||
\(526\) | − | 25.6187i | − | 1.11703i | ||||||
\(527\) | −3.18565 | − | 1.83923i | −0.138769 | − | 0.0801183i | ||||
\(528\) | 3.75422 | + | 6.50249i | 0.163381 | + | 0.282985i | ||||
\(529\) | −19.3184 | − | 12.4819i | −0.839932 | − | 0.542691i | ||||
\(530\) | 15.2083 | + | 8.78049i | 0.660605 | + | 0.381400i | ||||
\(531\) | − | 1.84591i | − | 0.0801059i | ||||||
\(532\) | −7.43806 | − | 5.73426i | −0.322481 | − | 0.248612i | ||||
\(533\) | 6.05422 | 0.262237 | ||||||||
\(534\) | −10.1703 | − | 5.87180i | −0.440110 | − | 0.254098i | ||||
\(535\) | 10.2536 | − | 5.91994i | 0.443304 | − | 0.255942i | ||||
\(536\) | 3.57337 | − | 2.06308i | 0.154346 | − | 0.0891117i | ||||
\(537\) | 8.77295 | + | 5.06506i | 0.378581 | + | 0.218574i | ||||
\(538\) | 22.4266i | 0.966878i | ||||||||
\(539\) | −29.7368 | − | 30.0077i | −1.28085 | − | 1.29252i | ||||
\(540\) | − | 7.41103i | − | 0.318920i | ||||||
\(541\) | −4.06544 | + | 7.04155i | −0.174787 | + | 0.302740i | −0.940088 | − | 0.340933i | \(-0.889257\pi\) |
0.765301 | + | 0.643673i | \(0.222590\pi\) | |||||||
\(542\) | 0.355990 | − | 0.205531i | 0.0152911 | − | 0.00882830i | ||||
\(543\) | 18.0765 | − | 10.4365i | 0.775736 | − | 0.447871i | ||||
\(544\) | 0.568151 | − | 0.984066i | 0.0243593 | − | 0.0421915i | ||||
\(545\) | − | 10.3107i | − | 0.441662i | ||||||
\(546\) | −17.0022 | − | 13.1076i | −0.727625 | − | 0.560952i | ||||
\(547\) | 23.6938 | 1.01307 | 0.506536 | − | 0.862219i | \(-0.330926\pi\) | ||||
0.506536 | + | 0.862219i | \(0.330926\pi\) | |||||||
\(548\) | 3.87856 | + | 2.23929i | 0.165684 | + | 0.0956577i | ||||
\(549\) | 10.1668 | + | 17.6094i | 0.433909 | + | 0.751553i | ||||
\(550\) | −16.7766 | + | 9.68595i | −0.715355 | + | 0.413011i | ||||
\(551\) | 5.64833 | − | 9.78319i | 0.240627 | − | 0.416778i | ||||
\(552\) | 1.39960 | + | 5.80009i | 0.0595708 | + | 0.246868i | ||||
\(553\) | 12.3457 | + | 29.9974i | 0.524995 | + | 1.27562i | ||||
\(554\) | −4.61206 | −0.195948 | ||||||||
\(555\) | −4.90844 | + | 8.50168i | −0.208352 | + | 0.360876i | ||||
\(556\) | −7.85599 | + | 4.53566i | −0.333168 | + | 0.192355i | ||||
\(557\) | 19.8469 | − | 11.4586i | 0.840942 | − | 0.485518i | −0.0166424 | − | 0.999862i | \(-0.505298\pi\) |
0.857584 | + | 0.514343i | \(0.171964\pi\) | |||||||
\(558\) | 4.07122 | + | 2.35052i | 0.172349 | + | 0.0995055i | ||||
\(559\) | 1.97975 | 0.0837343 | ||||||||
\(560\) | −0.470008 | + | 3.50859i | −0.0198615 | + | 0.148265i | ||||
\(561\) | −8.53184 | −0.360215 | ||||||||
\(562\) | 17.8328 | + | 10.2958i | 0.752230 | + | 0.434300i | ||||
\(563\) | −11.0559 | − | 19.1493i | −0.465949 | − | 0.807048i | 0.533295 | − | 0.845930i | \(-0.320954\pi\) |
−0.999244 | + | 0.0388818i | \(0.987620\pi\) | |||||||
\(564\) | −0.175204 | − | 0.303462i | −0.00737743 | − | 0.0127781i | ||||
\(565\) | −10.3067 | − | 5.95055i | −0.433604 | − | 0.250342i | ||||
\(566\) | −0.348943 | −0.0146672 | ||||||||
\(567\) | 0.890380 | − | 6.64665i | 0.0373924 | − | 0.279133i | ||||
\(568\) | 4.02749 | 0.168990 | ||||||||
\(569\) | 11.4658 | + | 6.61980i | 0.480673 | + | 0.277517i | 0.720697 | − | 0.693250i | \(-0.243822\pi\) |
−0.240024 | + | 0.970767i | \(0.577155\pi\) | |||||||
\(570\) | 5.11726 | − | 2.95445i | 0.214339 | − | 0.123748i | ||||
\(571\) | −17.6182 | + | 10.1719i | −0.737298 | + | 0.425679i | −0.821086 | − | 0.570805i | \(-0.806631\pi\) |
0.0837883 | + | 0.996484i | \(0.473298\pi\) | |||||||
\(572\) | 19.6809 | − | 34.0883i | 0.822899 | − | 1.42530i | ||||
\(573\) | −4.48054 | −0.187177 | ||||||||
\(574\) | −0.934710 | − | 2.27114i | −0.0390140 | − | 0.0947954i | ||||
\(575\) | −14.9643 | + | 3.61099i | −0.624056 | + | 0.150589i | ||||
\(576\) | −0.726090 | + | 1.25762i | −0.0302537 | + | 0.0524010i | ||||
\(577\) | −14.5048 | + | 8.37436i | −0.603843 | + | 0.348629i | −0.770552 | − | 0.637377i | \(-0.780019\pi\) |
0.166709 | + | 0.986006i | \(0.446686\pi\) | |||||||
\(578\) | −7.85441 | − | 13.6042i | −0.326700 | − | 0.565862i | ||||
\(579\) | −15.4124 | − | 8.89836i | −0.640518 | − | 0.369803i | ||||
\(580\) | −4.25789 | −0.176799 | ||||||||
\(581\) | −12.5589 | − | 9.68205i | −0.521029 | − | 0.401679i | ||||
\(582\) | 17.6471i | 0.731498i | ||||||||
\(583\) | −39.6061 | + | 68.5998i | −1.64032 | + | 2.84111i | ||||
\(584\) | 11.1001 | − | 6.40863i | 0.459325 | − | 0.265191i | ||||
\(585\) | −10.9744 | + | 6.33609i | −0.453737 | + | 0.261965i | ||||
\(586\) | 12.5822 | − | 21.7929i | 0.519764 | − | 0.900258i | ||||
\(587\) | 39.7788i | 1.64185i | 0.571037 | + | 0.820924i | \(0.306541\pi\) | ||||
−0.571037 | + | 0.820924i | \(0.693459\pi\) | |||||||
\(588\) | −2.29212 | + | 8.40175i | −0.0945253 | + | 0.346482i | ||||
\(589\) | 11.4914i | 0.473497i | ||||||||
\(590\) | −1.47288 | − | 0.850369i | −0.0606376 | − | 0.0350091i | ||||
\(591\) | 12.9796 | − | 7.49380i | 0.533911 | − | 0.308254i | ||||
\(592\) | 5.10738 | − | 2.94875i | 0.209912 | − | 0.121193i | ||||
\(593\) | −10.8382 | − | 6.25742i | −0.445070 | − | 0.256961i | 0.260676 | − | 0.965426i | \(-0.416055\pi\) |
−0.705746 | + | 0.708465i | \(0.749388\pi\) | |||||||
\(594\) | 33.4289 | 1.37160 | ||||||||
\(595\) | −3.18565 | − | 2.45593i | −0.130599 | − | 0.100683i | ||||
\(596\) | − | 17.7844i | − | 0.728478i | ||||||
\(597\) | 20.9905 | + | 12.1189i | 0.859086 | + | 0.495993i | ||||
\(598\) | 22.6638 | − | 21.5572i | 0.926792 | − | 0.881539i | ||||
\(599\) | −19.3086 | − | 33.4435i | −0.788928 | − | 1.36646i | −0.926624 | − | 0.375989i | \(-0.877303\pi\) |
0.137696 | − | 0.990475i | \(-0.456030\pi\) | |||||||
\(600\) | 3.45839 | + | 1.99670i | 0.141188 | + | 0.0815151i | ||||
\(601\) | − | 4.35612i | − | 0.177690i | −0.996045 | − | 0.0888449i | \(-0.971682\pi\) | ||
0.996045 | − | 0.0888449i | \(-0.0283176\pi\) | |||||||
\(602\) | −0.305653 | − | 0.742668i | −0.0124575 | − | 0.0302689i | ||||
\(603\) | − | 5.99194i | − | 0.244011i | ||||||
\(604\) | 9.74158 | − | 16.8729i | 0.396379 | − | 0.686549i | ||||
\(605\) | 17.0077 | + | 29.4582i | 0.691462 | + | 1.19765i | ||||
\(606\) | −6.36590 | − | 11.0261i | −0.258597 | − | 0.447903i | ||||
\(607\) | −36.2312 | − | 20.9181i | −1.47058 | − | 0.849039i | −0.471123 | − | 0.882067i | \(-0.656151\pi\) |
−0.999454 | + | 0.0330288i | \(0.989485\pi\) | |||||||
\(608\) | −3.54978 | −0.143962 | ||||||||
\(609\) | −10.3824 | − | 1.39081i | −0.420714 | − | 0.0563586i | ||||
\(610\) | 18.7344 | 0.758535 | ||||||||
\(611\) | −0.918479 | + | 1.59085i | −0.0371577 | + | 0.0643590i | ||||
\(612\) | −0.825057 | − | 1.42904i | −0.0333509 | − | 0.0577655i | ||||
\(613\) | −16.0219 | + | 9.25027i | −0.647120 | + | 0.373615i | −0.787352 | − | 0.616504i | \(-0.788548\pi\) |
0.140232 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(614\) | −11.1955 | − | 6.46370i | −0.451812 | − | 0.260854i | ||||
\(615\) | 1.54518 | 0.0623076 | ||||||||
\(616\) | −15.8262 | − | 2.12006i | −0.637655 | − | 0.0854197i | ||||
\(617\) | 10.0161i | 0.403233i | 0.979465 | + | 0.201616i | \(0.0646194\pi\) | ||||
−0.979465 | + | 0.201616i | \(0.935381\pi\) | |||||||
\(618\) | −12.9939 | − | 7.50202i | −0.522690 | − | 0.301775i | ||||
\(619\) | 9.18249 | + | 15.9045i | 0.369075 | + | 0.639257i | 0.989421 | − | 0.145071i | \(-0.0463411\pi\) |
−0.620346 | + | 0.784328i | \(0.713008\pi\) | |||||||
\(620\) | 3.75103 | − | 2.16566i | 0.150645 | − | 0.0869749i | ||||
\(621\) | 25.4790 | + | 7.51509i | 1.02244 | + | 0.301570i | ||||
\(622\) | − | 3.58010i | − | 0.143549i | ||||||
\(623\) | 23.0947 | − | 9.50485i | 0.925269 | − | 0.380804i | ||||
\(624\) | −8.11420 | −0.324828 | ||||||||
\(625\) | −0.676141 | + | 1.17111i | −0.0270456 | + | 0.0468444i | ||||
\(626\) | −2.70313 | − | 4.68196i | −0.108039 | − | 0.187129i | ||||
\(627\) | 13.3266 | + | 23.0824i | 0.532214 | + | 0.921822i | ||||
\(628\) | −4.10550 | + | 7.11094i | −0.163827 | + | 0.283757i | ||||
\(629\) | 6.70133i | 0.267200i | ||||||||
\(630\) | 4.07122 | + | 3.13865i | 0.162201 | + | 0.125047i | ||||
\(631\) | − | 3.02292i | − | 0.120341i | −0.998188 | − | 0.0601703i | \(-0.980836\pi\) | ||
0.998188 | − | 0.0601703i | \(-0.0191644\pi\) | |||||||
\(632\) | 10.6180 | + | 6.13032i | 0.422362 | + | 0.243851i | ||||
\(633\) | −13.1303 | + | 7.58077i | −0.521882 | + | 0.301309i | ||||
\(634\) | 13.5155 | + | 23.4095i | 0.536769 | + | 0.929711i | ||||
\(635\) | 7.66082 | − | 13.2689i | 0.304010 | − | 0.526561i | ||||
\(636\) | 16.3291 | 0.647493 | ||||||||
\(637\) | 44.1520 | − | 11.6162i | 1.74936 | − | 0.460251i | ||||
\(638\) | − | 19.2060i | − | 0.760374i | ||||||
\(639\) | 2.92432 | − | 5.06506i | 0.115684 | − | 0.200371i | ||||
\(640\) | 0.668984 | + | 1.15871i | 0.0264439 | + | 0.0458022i | ||||
\(641\) | 0.850505 | − | 0.491039i | 0.0335929 | − | 0.0193949i | −0.483109 | − | 0.875560i | \(-0.660493\pi\) |
0.516702 | + | 0.856165i | \(0.327159\pi\) | |||||||
\(642\) | 5.50468 | − | 9.53439i | 0.217252 | − | 0.376292i | ||||
\(643\) | 42.9115 | 1.69227 | 0.846133 | − | 0.532972i | \(-0.178925\pi\) | ||||
0.846133 | + | 0.532972i | \(0.178925\pi\) | |||||||
\(644\) | −11.5859 | − | 5.17373i | −0.456547 | − | 0.203874i | ||||
\(645\) | 0.505278 | 0.0198953 | ||||||||
\(646\) | 2.01681 | − | 3.49321i | 0.0793502 | − | 0.137439i | ||||
\(647\) | 24.5410 | − | 14.1688i | 0.964807 | − | 0.557032i | 0.0671579 | − | 0.997742i | \(-0.478607\pi\) |
0.897649 | + | 0.440711i | \(0.145274\pi\) | |||||||
\(648\) | −1.26732 | − | 2.19506i | −0.0497850 | − | 0.0862301i | ||||
\(649\) | 3.83575 | − | 6.64371i | 0.150566 | − | 0.260789i | ||||
\(650\) | − | 20.9348i | − | 0.821131i | ||||||
\(651\) | 9.85382 | − | 4.05544i | 0.386202 | − | 0.158945i | ||||
\(652\) | 14.9760 | 0.586506 | ||||||||
\(653\) | 14.4667 | − | 25.0571i | 0.566127 | − | 0.980561i | −0.430817 | − | 0.902439i | \(-0.641774\pi\) |
0.996944 | − | 0.0781215i | \(-0.0248922\pi\) | |||||||
\(654\) | −4.79372 | − | 8.30297i | −0.187449 | − | 0.324672i | ||||
\(655\) | 8.32200 | − | 4.80471i | 0.325167 | − | 0.187735i | ||||
\(656\) | −0.803902 | − | 0.464133i | −0.0313871 | − | 0.0181214i | ||||
\(657\) | − | 18.6130i | − | 0.726161i | ||||||
\(658\) | 0.738586 | + | 0.0989404i | 0.0287931 | + | 0.00385710i | ||||
\(659\) | − | 31.7305i | − | 1.23605i | −0.786160 | − | 0.618023i | \(-0.787934\pi\) | ||
0.786160 | − | 0.618023i | \(-0.212066\pi\) | |||||||
\(660\) | 5.02302 | − | 8.70013i | 0.195521 | − | 0.338652i | ||||
\(661\) | 13.8069 | + | 23.9142i | 0.537025 | + | 0.930154i | 0.999062 | + | 0.0432937i | \(0.0137851\pi\) |
−0.462038 | + | 0.886860i | \(0.652882\pi\) | |||||||
\(662\) | −3.64113 | − | 6.30662i | −0.141516 | − | 0.245114i | ||||
\(663\) | 4.61009 | − | 7.98490i | 0.179041 | − | 0.310108i | ||||
\(664\) | −5.99365 | −0.232599 | ||||||||
\(665\) | −1.66842 | + | 12.4547i | −0.0646987 | + | 0.482973i | ||||
\(666\) | − | 8.56422i | − | 0.331857i | ||||||
\(667\) | 4.31767 | − | 14.6386i | 0.167181 | − | 0.566807i | ||||
\(668\) | 12.6063 | − | 7.27825i | 0.487752 | − | 0.281604i | ||||
\(669\) | 10.2948 | + | 17.8311i | 0.398020 | + | 0.689391i | ||||
\(670\) | −4.78105 | − | 2.76034i | −0.184708 | − | 0.106641i | ||||
\(671\) | 84.5052i | 3.26229i | ||||||||
\(672\) | 1.25275 | + | 3.04391i | 0.0483259 | + | 0.117421i | ||||
\(673\) | 5.70731 | 0.220001 | 0.110000 | − | 0.993932i | \(-0.464915\pi\) | ||||
0.110000 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(674\) | −16.6713 | − | 9.62517i | −0.642154 | − | 0.370748i | ||||
\(675\) | 15.3974 | − | 8.88969i | 0.592646 | − | 0.342164i | ||||
\(676\) | 14.7687 | + | 25.5801i | 0.568027 | + | 0.983851i | ||||
\(677\) | −20.5855 | + | 35.6550i | −0.791163 | + | 1.37033i | 0.134084 | + | 0.990970i | \(0.457191\pi\) |
−0.925247 | + | 0.379365i | \(0.876143\pi\) | |||||||
\(678\) | −11.0663 | −0.424998 | ||||||||
\(679\) | −29.7216 | − | 22.9134i | −1.14061 | − | 0.879337i | ||||
\(680\) | −1.52033 | −0.0583022 | ||||||||
\(681\) | 18.7274 | + | 10.8123i | 0.717636 | + | 0.414328i | ||||
\(682\) | 9.76861 | + | 16.9197i | 0.374059 | + | 0.647890i | ||||
\(683\) | −2.95142 | − | 5.11202i | −0.112933 | − | 0.195606i | 0.804019 | − | 0.594604i | \(-0.202691\pi\) |
−0.916952 | + | 0.398998i | \(0.869358\pi\) | |||||||
\(684\) | −2.57746 | + | 4.46429i | −0.0985515 | + | 0.170696i | ||||
\(685\) | − | 5.99220i | − | 0.228950i | ||||||
\(686\) | −11.1742 | − | 14.7694i | −0.426635 | − | 0.563900i | ||||
\(687\) | 1.20958i | 0.0461485i | ||||||||
\(688\) | −0.262878 | − | 0.151773i | −0.0100221 | − | 0.00578628i | ||||
\(689\) | −42.8014 | − | 74.1343i | −1.63061 | − | 2.82429i | ||||
\(690\) | 5.78434 | − | 5.50190i | 0.220206 | − | 0.209454i | ||||
\(691\) | 12.6557 | + | 7.30676i | 0.481445 | + | 0.277962i | 0.721018 | − | 0.692916i | \(-0.243674\pi\) |
−0.239574 | + | 0.970878i | \(0.577008\pi\) | |||||||
\(692\) | − | 0.165853i | − | 0.00630477i | ||||||
\(693\) | −14.1575 | + | 18.3640i | −0.537797 | + | 0.697591i | ||||
\(694\) | −28.9888 | −1.10040 | ||||||||
\(695\) | 10.5111 | + | 6.06857i | 0.398707 | + | 0.230194i | ||||
\(696\) | −3.42878 | + | 1.97961i | −0.129968 | + | 0.0750368i | ||||
\(697\) | 0.913475 | − | 0.527395i | 0.0346003 | − | 0.0199765i | ||||
\(698\) | −10.7538 | − | 6.20868i | −0.407036 | − | 0.235002i | ||||
\(699\) | 8.49645i | 0.321365i | ||||||||
\(700\) | −7.85334 | + | 3.23212i | −0.296828 | + | 0.122163i | ||||
\(701\) | 15.3358i | 0.579225i | 0.957144 | + | 0.289613i | \(0.0935265\pi\) | ||||
−0.957144 | + | 0.289613i | \(0.906474\pi\) | |||||||
\(702\) | −18.0629 | + | 31.2859i | −0.681742 | + | 1.18081i | ||||
\(703\) | 18.1301 | − | 10.4674i | 0.683789 | − | 0.394786i | ||||
\(704\) | −5.22660 | + | 3.01758i | −0.196985 | + | 0.113729i | ||||
\(705\) | −0.234418 | + | 0.406023i | −0.00882868 | + | 0.0152917i | ||||
\(706\) | − | 7.43049i | − | 0.279650i | ||||||
\(707\) | 26.8359 | + | 3.59492i | 1.00927 | + | 0.135201i | ||||
\(708\) | −1.58144 | −0.0594340 | ||||||||
\(709\) | −6.16233 | − | 3.55782i | −0.231431 | − | 0.133617i | 0.379801 | − | 0.925068i | \(-0.375992\pi\) |
−0.611232 | + | 0.791451i | \(0.709326\pi\) | |||||||
\(710\) | −2.69432 | − | 4.66671i | −0.101116 | − | 0.175138i | ||||
\(711\) | 15.4193 | − | 8.90232i | 0.578268 | − | 0.333863i | ||||
\(712\) | 4.71966 | − | 8.17470i | 0.176877 | − | 0.306360i | ||||
\(713\) | 3.64180 | + | 15.0920i | 0.136387 | + | 0.565201i | ||||
\(714\) | −3.70715 | − | 0.496608i | −0.138737 | − | 0.0185851i | ||||
\(715\) | −52.6648 | −1.96955 | ||||||||
\(716\) | −4.07122 | + | 7.05156i | −0.152149 | + | 0.263529i | ||||
\(717\) | −15.9346 | + | 9.19985i | −0.595089 | + | 0.343575i | ||||
\(718\) | −17.2194 | + | 9.94165i | −0.642624 | + | 0.371019i | ||||
\(719\) | −11.2974 | − | 6.52254i | −0.421321 | − | 0.243250i | 0.274321 | − | 0.961638i | \(-0.411547\pi\) |
−0.695642 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(720\) | 1.94297 | 0.0724102 | ||||||||
\(721\) | 29.5066 | − | 12.1437i | 1.09888 | − | 0.452256i | ||||
\(722\) | 6.39908 | 0.238149 | ||||||||
\(723\) | 14.2303 | + | 8.21585i | 0.529230 | + | 0.305551i | ||||
\(724\) | 8.38866 | + | 14.5296i | 0.311762 | + | 0.539988i | ||||
\(725\) | −5.10743 | − | 8.84632i | −0.189685 | − | 0.328544i | ||||
\(726\) | 27.3918 | + | 15.8147i | 1.01661 | + | 0.586938i | ||||
\(727\) | −10.9061 | −0.404485 | −0.202242 | − | 0.979336i | \(-0.564823\pi\) | ||||
−0.202242 | + | 0.979336i | \(0.564823\pi\) | |||||||
\(728\) | 10.5357 | − | 13.6661i | 0.390477 | − | 0.506499i | ||||
\(729\) | −24.3543 | −0.902010 | ||||||||
\(730\) | −14.8516 | − | 8.57455i | −0.549681 | − | 0.317358i | ||||
\(731\) | 0.298709 | − | 0.172460i | 0.0110481 | − | 0.00637865i | ||||
\(732\) | 15.0864 | − | 8.71014i | 0.557609 | − | 0.321936i | ||||
\(733\) | 20.8868 | − | 36.1769i | 0.771470 | − | 1.33623i | −0.165287 | − | 0.986246i | \(-0.552855\pi\) |
0.936757 | − | 0.349980i | \(-0.113812\pi\) | |||||||
\(734\) | 21.7786 | 0.803861 | ||||||||
\(735\) | 11.2686 | − | 2.96473i | 0.415649 | − | 0.109356i | ||||
\(736\) | −4.66202 | + | 1.12497i | −0.171844 | + | 0.0414671i | ||||
\(737\) | 12.4510 | − | 21.5658i | 0.458640 | − | 0.794388i | ||||
\(738\) | −1.16741 | + | 0.674005i | −0.0429730 | + | 0.0248104i | ||||
\(739\) | −2.88980 | − | 5.00528i | −0.106303 | − | 0.184122i | 0.807967 | − | 0.589228i | \(-0.200568\pi\) |
−0.914270 | + | 0.405106i | \(0.867235\pi\) | |||||||
\(740\) | −6.83352 | − | 3.94533i | −0.251205 | − | 0.145033i | ||||
\(741\) | −28.8036 | −1.05813 | ||||||||
\(742\) | −21.2021 | + | 27.5018i | −0.778354 | + | 1.00962i | ||||
\(743\) | − | 2.74633i | − | 0.100753i | −0.998730 | − | 0.0503766i | \(-0.983958\pi\) | ||
0.998730 | − | 0.0503766i | \(-0.0160422\pi\) | |||||||
\(744\) | 2.01374 | − | 3.48790i | 0.0738274 | − | 0.127873i | ||||
\(745\) | −20.6070 | + | 11.8975i | −0.754984 | + | 0.435890i | ||||
\(746\) | 17.5547 | − | 10.1352i | 0.642723 | − | 0.371076i | ||||
\(747\) | −4.35193 | + | 7.53776i | −0.159229 | + | 0.275792i | ||||
\(748\) | − | 6.85776i | − | 0.250745i | ||||||
\(749\) | 8.91058 | + | 21.6507i | 0.325586 | + | 0.791101i | ||||
\(750\) | − | 13.6660i | − | 0.499011i | ||||||
\(751\) | 38.7452 | + | 22.3695i | 1.41383 | + | 0.816275i | 0.995747 | − | 0.0921329i | \(-0.0293685\pi\) |
0.418084 | + | 0.908408i | \(0.362702\pi\) | |||||||
\(752\) | 0.243918 | − | 0.140826i | 0.00889479 | − | 0.00513541i | ||||
\(753\) | 10.4056 | − | 6.00769i | 0.379202 | − | 0.218932i | ||||
\(754\) | 17.9748 | + | 10.3778i | 0.654604 | + | 0.377936i | ||||
\(755\) | −26.0679 | −0.948707 | ||||||||
\(756\) | 14.5251 | + | 1.94577i | 0.528274 | + | 0.0707671i | ||||
\(757\) | 12.3037i | 0.447185i | 0.974683 | + | 0.223593i | \(0.0717785\pi\) | ||||
−0.974683 | + | 0.223593i | \(0.928222\pi\) | |||||||
\(758\) | 15.1434 | + | 8.74305i | 0.550033 | + | 0.317562i | ||||
\(759\) | 24.8174 | + | 26.0914i | 0.900813 | + | 0.947056i | ||||
\(760\) | 2.37474 | + | 4.11318i | 0.0861410 | + | 0.149201i | ||||
\(761\) | 19.1725 | + | 11.0692i | 0.695002 | + | 0.401260i | 0.805483 | − | 0.592618i | \(-0.201906\pi\) |
−0.110481 | + | 0.993878i | \(0.535239\pi\) | |||||||
\(762\) | − | 14.2469i | − | 0.516110i | ||||||
\(763\) | 20.2083 | + | 2.70709i | 0.731589 | + | 0.0980031i | ||||
\(764\) | − | 3.60139i | − | 0.130294i | ||||||
\(765\) | −1.10390 | + | 1.91201i | −0.0399116 | + | 0.0691289i | ||||
\(766\) | −8.88242 | − | 15.3848i | −0.320935 | − | 0.555875i | ||||
\(767\) | 4.14521 | + | 7.17972i | 0.149675 | + | 0.259245i | ||||
\(768\) | 1.07743 | + | 0.622057i | 0.0388786 | + | 0.0224466i | ||||
\(769\) | −0.436260 | −0.0157320 | −0.00786598 | − | 0.999969i | \(-0.502504\pi\) | ||||
−0.00786598 | + | 0.999969i | \(0.502504\pi\) | |||||||
\(770\) | 8.13091 | + | 19.7563i | 0.293018 | + | 0.711968i | ||||
\(771\) | 8.36308 | 0.301189 | ||||||||
\(772\) | 7.15236 | − | 12.3883i | 0.257419 | − | 0.445863i | ||||
\(773\) | −13.4233 | − | 23.2498i | −0.482801 | − | 0.836236i | 0.517004 | − | 0.855983i | \(-0.327047\pi\) |
−0.999805 | + | 0.0197472i | \(0.993714\pi\) | |||||||
\(774\) | −0.381746 | + | 0.220401i | −0.0137216 | + | 0.00792216i | ||||
\(775\) | 8.99887 | + | 5.19550i | 0.323249 | + | 0.186628i | ||||
\(776\) | −14.1845 | −0.509194 | ||||||||
\(777\) | −15.3740 | − | 11.8523i | −0.551539 | − | 0.425200i | ||||
\(778\) | 16.1088i | 0.577527i | ||||||||
\(779\) | −2.85367 | − | 1.64757i | −0.102243 | − | 0.0590303i | ||||
\(780\) | 5.42827 | + | 9.40204i | 0.194363 | + | 0.336647i | ||||
\(781\) | 21.0501 | − | 12.1533i | 0.753231 | − | 0.434878i | ||||
\(782\) | 1.54168 | − | 5.22689i | 0.0551304 | − | 0.186913i | ||||
\(783\) | 17.6271i | 0.629942i | ||||||||
\(784\) | −6.75320 | − | 1.84237i | −0.241186 | − | 0.0657989i | ||||
\(785\) | 10.9861 | 0.392109 | ||||||||
\(786\) | 4.46767 | − | 7.73824i | 0.159357 | − | 0.276014i | ||||
\(787\) | 10.3912 | + | 17.9982i | 0.370408 | + | 0.641565i | 0.989628 | − | 0.143652i | \(-0.0458847\pi\) |
−0.619221 | + | 0.785217i | \(0.712551\pi\) | |||||||
\(788\) | 6.02340 | + | 10.4328i | 0.214575 | + | 0.371654i | ||||
\(789\) | −15.9363 | + | 27.6025i | −0.567347 | + | 0.982674i | ||||
\(790\) | − | 16.4043i | − | 0.583640i | ||||||
\(791\) | 14.3687 | − | 18.6380i | 0.510892 | − | 0.662692i | ||||
\(792\) | 8.76414i | 0.311420i | ||||||||
\(793\) | −79.0880 | − | 45.6615i | −2.80850 | − | 1.62149i | ||||
\(794\) | −5.91641 | + | 3.41584i | −0.209966 | + | 0.121224i | ||||
\(795\) | −10.9239 | − | 18.9208i | −0.387432 | − | 0.671052i | ||||
\(796\) | −9.74098 | + | 16.8719i | −0.345260 | + | 0.598008i | ||||
\(797\) | −15.7307 | −0.557209 | −0.278605 | − | 0.960406i | \(-0.589872\pi\) | ||||
−0.278605 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(798\) | 4.44699 | + | 10.8052i | 0.157422 | + | 0.382499i | ||||
\(799\) | 0.320042i | 0.0113223i | ||||||||
\(800\) | −1.60492 | + | 2.77980i | −0.0567425 | + | 0.0982809i | ||||
\(801\) | −6.85380 | − | 11.8711i | −0.242167 | − | 0.419446i | ||||
\(802\) | −16.3143 | + | 9.41906i | −0.576077 | + | 0.332598i | ||||
\(803\) | 38.6771 | − | 66.9908i | 1.36489 | − | 2.36405i | ||||
\(804\) | −5.13342 | −0.181042 | ||||||||
\(805\) | 1.75589 | + | 16.8859i | 0.0618869 | + | 0.595149i | ||||
\(806\) | −21.1134 | −0.743689 | ||||||||
\(807\) | 13.9506 | − | 24.1632i | 0.491085 | − | 0.850584i | ||||
\(808\) | 8.86258 | − | 5.11681i | 0.311785 | − | 0.180009i | ||||
\(809\) | −5.87066 | − | 10.1683i | −0.206401 | − | 0.357498i | 0.744177 | − | 0.667983i | \(-0.232842\pi\) |
−0.950578 | + | 0.310485i | \(0.899509\pi\) | |||||||
\(810\) | −1.69563 | + | 2.93692i | −0.0595784 | + | 0.103193i | ||||
\(811\) | − | 32.1592i | − | 1.12926i | −0.825343 | − | 0.564631i | \(-0.809018\pi\) | ||
0.825343 | − | 0.564631i | \(-0.190982\pi\) | |||||||
\(812\) | 1.11791 | − | 8.34518i | 0.0392311 | − | 0.292858i | ||||
\(813\) | −0.511408 | −0.0179358 | ||||||||
\(814\) | 17.7962 | − | 30.8239i | 0.623756 | − | 1.08038i | ||||
\(815\) | −10.0187 | − | 17.3529i | −0.350940 | − | 0.607847i | ||||
\(816\) | −1.22429 | + | 0.706844i | −0.0428587 | + | 0.0247445i | ||||
\(817\) | −0.933159 | − | 0.538760i | −0.0326471 | − | 0.0188488i | ||||
\(818\) | − | 5.91813i | − | 0.206923i | ||||||
\(819\) | −9.53696 | − | 23.1727i | −0.333248 | − | 0.809719i | ||||
\(820\) | 1.24199i | 0.0433722i | ||||||||
\(821\) | −1.84632 | + | 3.19792i | −0.0644371 | + | 0.111608i | −0.896444 | − | 0.443157i | \(-0.853859\pi\) |
0.832007 | + | 0.554765i | \(0.187192\pi\) | |||||||
\(822\) | −2.78593 | − | 4.82538i | −0.0971705 | − | 0.168304i | ||||
\(823\) | −9.19610 | − | 15.9281i | −0.320556 | − | 0.555219i | 0.660047 | − | 0.751224i | \(-0.270536\pi\) |
−0.980603 | + | 0.196005i | \(0.937203\pi\) | |||||||
\(824\) | 6.03001 | − | 10.4443i | 0.210065 | − | 0.363844i | ||||
\(825\) | 24.1009 | 0.839085 | ||||||||
\(826\) | 2.05337 | − | 2.66348i | 0.0714459 | − | 0.0926744i | ||||
\(827\) | 2.41961i | 0.0841382i | 0.999115 | + | 0.0420691i | \(0.0133950\pi\) | ||||
−0.999115 | + | 0.0420691i | \(0.986605\pi\) | |||||||
\(828\) | −1.97025 | + | 6.67990i | −0.0684709 | + | 0.232143i | ||||
\(829\) | −9.79002 | + | 5.65227i | −0.340021 | + | 0.196311i | −0.660282 | − | 0.751018i | \(-0.729563\pi\) |
0.320260 | + | 0.947330i | \(0.396230\pi\) | |||||||
\(830\) | 4.00966 | + | 6.94493i | 0.139177 | + | 0.241062i | ||||
\(831\) | 4.96919 | + | 2.86897i | 0.172379 | + | 0.0995233i | ||||
\(832\) | − | 6.52207i | − | 0.226112i | ||||||
\(833\) | 5.64984 | − | 5.59885i | 0.195755 | − | 0.193989i | ||||
\(834\) | 11.2858 | 0.390794 | ||||||||
\(835\) | −16.8668 | − | 9.73806i | −0.583700 | − | 0.337000i | ||||
\(836\) | −18.5533 | + | 10.7117i | −0.641679 | + | 0.370473i | ||||
\(837\) | −8.96554 | − | 15.5288i | −0.309895 | − | 0.536753i | ||||
\(838\) | −2.06781 | + | 3.58155i | −0.0714313 | + | 0.123723i | ||||
\(839\) | 28.2187 | 0.974219 | 0.487110 | − | 0.873341i | \(-0.338051\pi\) | ||||
0.487110 | + | 0.873341i | \(0.338051\pi\) | |||||||
\(840\) | 2.68895 | − | 3.48790i | 0.0927775 | − | 0.120344i | ||||
\(841\) | −18.8726 | −0.650780 | ||||||||
\(842\) | 25.3652 | + | 14.6446i | 0.874143 | + | 0.504687i | ||||
\(843\) | −12.8091 | − | 22.1860i | −0.441169 | − | 0.764126i | ||||
\(844\) | −6.09331 | − | 10.5539i | −0.209740 | − | 0.363281i | ||||
\(845\) | 19.7600 | − | 34.2254i | 0.679766 | − | 1.17739i | ||||
\(846\) | − | 0.409010i | − | 0.0140621i | ||||||
\(847\) | −62.2015 | + | 25.5997i | −2.13727 | + | 0.879615i | ||||
\(848\) | 13.1251i | 0.450718i | ||||||||
\(849\) | 0.375963 | + | 0.217062i | 0.0129030 | + | 0.00744956i | ||||
\(850\) | −1.82367 | − | 3.15869i | −0.0625515 | − | 0.108342i | ||||
\(851\) | 20.4935 | − | 19.4928i | 0.702507 | − | 0.668205i | ||||
\(852\) | −4.33935 | − | 2.50533i | −0.148664 | − | 0.0858311i | ||||
\(853\) | − | 44.0603i | − | 1.50860i | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||
0.656532 | − | 0.754298i | \(-0.272023\pi\) | |||||||
\(854\) | −4.91874 | + | 36.7182i | −0.168316 | + | 1.25647i | ||||
\(855\) | 6.89711 | 0.235876 | ||||||||
\(856\) | 7.66359 | + | 4.42458i | 0.261936 | + | 0.151229i | ||||
\(857\) | −47.2791 | + | 27.2966i | −1.61502 | + | 0.932434i | −0.626842 | + | 0.779147i | \(0.715653\pi\) |
−0.988182 | + | 0.153287i | \(0.951014\pi\) | |||||||
\(858\) | −42.4097 | + | 24.4853i | −1.44784 | + | 0.835913i | ||||
\(859\) | 2.15309 | + | 1.24309i | 0.0734626 | + | 0.0424136i | 0.536281 | − | 0.844039i | \(-0.319829\pi\) |
−0.462819 | + | 0.886453i | \(0.653162\pi\) | |||||||
\(860\) | 0.406134i | 0.0138491i | ||||||||
\(861\) | −0.405688 | + | 3.02844i | −0.0138258 | + | 0.103209i | ||||
\(862\) | 5.28266i | 0.179928i | ||||||||
\(863\) | −21.9157 | + | 37.9590i | −0.746018 | + | 1.29214i | 0.203700 | + | 0.979033i | \(0.434703\pi\) |
−0.949718 | + | 0.313107i | \(0.898630\pi\) | |||||||
\(864\) | 4.79693 | − | 2.76951i | 0.163195 | − | 0.0942207i | ||||
\(865\) | −0.192176 | + | 0.110953i | −0.00653417 | + | 0.00377251i | ||||
\(866\) | −14.5215 | + | 25.1520i | −0.493461 | + | 0.854700i | ||||
\(867\) | 19.5436i | 0.663734i | ||||||||
\(868\) | 3.25970 | + | 7.92035i | 0.110642 | + | 0.268834i | ||||
\(869\) | 73.9949 | 2.51011 | ||||||||
\(870\) | 4.58760 | + | 2.64865i | 0.155534 | + | 0.0897977i | ||||
\(871\) | 13.4556 | + | 23.3057i | 0.455925 | + | 0.789685i | ||||
\(872\) | 6.67380 | − | 3.85312i | 0.226003 | − | 0.130483i | ||||
\(873\) | −10.2992 | + | 17.8388i | −0.348576 | + | 0.603751i | ||||
\(874\) | −16.5491 | + | 3.99341i | −0.559783 | + | 0.135079i | ||||
\(875\) | 23.0165 | + | 17.7442i | 0.778099 | + | 0.599864i | ||||
\(876\) | −15.9461 | −0.538770 | ||||||||
\(877\) | 2.75727 | − | 4.77574i | 0.0931065 | − | 0.161265i | −0.815710 | − | 0.578461i | \(-0.803654\pi\) |
0.908817 | + | 0.417195i | \(0.136987\pi\) | |||||||
\(878\) | 29.6005 | − | 17.0899i | 0.998969 | − | 0.576755i | ||||
\(879\) | −27.1129 | + | 15.6536i | −0.914495 | + | 0.527984i | ||||
\(880\) | 6.99303 | + | 4.03743i | 0.235735 | + | 0.136102i | ||||
\(881\) | −51.6788 | −1.74110 | −0.870552 | − | 0.492076i | \(-0.836238\pi\) | ||||
−0.870552 | + | 0.492076i | \(0.836238\pi\) | |||||||
\(882\) | −7.22043 | + | 7.15526i | −0.243125 | + | 0.240930i | ||||
\(883\) | 53.5374 | 1.80168 | 0.900838 | − | 0.434155i | \(-0.142953\pi\) | ||||
0.900838 | + | 0.434155i | \(0.142953\pi\) | |||||||
\(884\) | 6.41814 | + | 3.70552i | 0.215866 | + | 0.124630i | ||||
\(885\) | 1.05796 | + | 1.83243i | 0.0355628 | + | 0.0615966i | ||||
\(886\) | −0.874186 | − | 1.51413i | −0.0293688 | − | 0.0508683i | ||||
\(887\) | 23.7721 | + | 13.7248i | 0.798190 | + | 0.460835i | 0.842838 | − | 0.538167i | \(-0.180883\pi\) |
−0.0446478 | + | 0.999003i | \(0.514217\pi\) | |||||||
\(888\) | −7.33716 | −0.246219 | ||||||||
\(889\) | 23.9948 | + | 18.4985i | 0.804761 | + | 0.620418i | ||||
\(890\) | −12.6295 | −0.423343 | ||||||||
\(891\) | −13.2475 | − | 7.64847i | −0.443809 | − | 0.256233i | ||||
\(892\) | −14.3324 | + | 8.27481i | −0.479884 | + | 0.277061i | ||||
\(893\) | 0.865856 | − | 0.499902i | 0.0289748 | − | 0.0167286i | ||||
\(894\) | −11.0629 | + | 19.1615i | −0.369999 | + | 0.640858i | ||||
\(895\) | 10.8943 | 0.364157 | ||||||||
\(896\) | −2.44664 | + | 1.00694i | −0.0817366 | + | 0.0336396i | ||||
\(897\) | −37.8286 | + | 9.12827i | −1.26306 | + | 0.304784i | ||||
\(898\) | 10.3682 | − | 17.9582i | 0.345990 | − | 0.599272i | ||||
\(899\) | −8.92181 | + | 5.15101i | −0.297559 | + | 0.171796i | ||||
\(900\) | 2.33063 | + | 4.03677i | 0.0776877 | + | 0.134559i | ||||
\(901\) | −12.9160 | − | 7.45704i | −0.430293 | − | 0.248430i | ||||
\(902\) | −5.60224 | −0.186534 | ||||||||
\(903\) | −0.132661 | + | 0.990310i | −0.00441469 | + | 0.0329554i | ||||
\(904\) | − | 8.89491i | − | 0.295840i | ||||||
\(905\) | 11.2238 | − | 19.4401i | 0.373091 | − | 0.646212i | ||||
\(906\) | −20.9918 | + | 12.1196i | −0.697407 | + | 0.402648i | ||||
\(907\) | −7.07108 | + | 4.08249i | −0.234791 | + | 0.135557i | −0.612781 | − | 0.790253i | \(-0.709949\pi\) |
0.377989 | + | 0.925810i | \(0.376616\pi\) | |||||||
\(908\) | −8.69075 | + | 15.0528i | −0.288413 | + | 0.499545i | ||||
\(909\) | − | 14.8611i | − | 0.492910i | ||||||
\(910\) | −22.8833 | − | 3.06543i | −0.758573 | − | 0.101618i | ||||
\(911\) | − | 5.20076i | − | 0.172309i | −0.996282 | − | 0.0861544i | \(-0.972542\pi\) | ||
0.996282 | − | 0.0861544i | \(-0.0274578\pi\) | |||||||
\(912\) | 3.82465 | + | 2.20816i | 0.126647 | + | 0.0731196i | ||||
\(913\) | −31.3264 | + | 18.0863i | −1.03675 | + | 0.598570i | ||||
\(914\) | −10.3635 | + | 5.98335i | −0.342793 | + | 0.197912i | ||||
\(915\) | −20.1851 | − | 11.6539i | −0.667300 | − | 0.385266i | ||||
\(916\) | −0.972244 | −0.0321239 | ||||||||
\(917\) | 7.23195 | + | 17.5720i | 0.238820 | + | 0.580279i | ||||
\(918\) | 6.29399i | 0.207733i | ||||||||
\(919\) | 13.2238 | + | 7.63479i | 0.436214 | + | 0.251848i | 0.701990 | − | 0.712186i | \(-0.252295\pi\) |
−0.265776 | + | 0.964035i | \(0.585628\pi\) | |||||||
\(920\) | 4.42234 | + | 4.64936i | 0.145800 | + | 0.153285i | ||||
\(921\) | 8.04158 | + | 13.9284i | 0.264979 | + | 0.458957i | ||||
\(922\) | 12.9623 | + | 7.48378i | 0.426890 | + | 0.246465i | ||||
\(923\) | 26.2675i | 0.864607i | ||||||||
\(924\) | 15.7329 | + | 12.1290i | 0.517573 | + | 0.399015i | ||||
\(925\) | − | 18.9300i | − | 0.622415i | ||||||
\(926\) | 4.00621 | − | 6.93897i | 0.131652 | − | 0.228029i | ||||
\(927\) | −8.75665 | − | 15.1670i | −0.287606 | − | 0.498149i | ||||
\(928\) | −1.59118 | − | 2.75600i | −0.0522330 | − | 0.0904701i | ||||
\(929\) | −9.12023 | − | 5.26557i | −0.299225 | − | 0.172758i | 0.342870 | − | 0.939383i | \(-0.388601\pi\) |
−0.642095 | + | 0.766625i | \(0.721934\pi\) | |||||||
\(930\) | −5.38865 | −0.176701 | ||||||||
\(931\) | −23.9723 | − | 6.54000i | −0.785662 | − | 0.214340i | ||||
\(932\) | −6.82932 | −0.223702 | ||||||||
\(933\) | −2.22703 | + | 3.85732i | −0.0729096 | + | 0.126283i | ||||
\(934\) | −0.207210 | − | 0.358899i | −0.00678013 | − | 0.0117435i | ||||
\(935\) | −7.94619 | + | 4.58773i | −0.259868 | + | 0.150035i | ||||
\(936\) | −8.20231 | − | 4.73561i | −0.268101 | − | 0.154788i | ||||
\(937\) | 30.4361 | 0.994304 | 0.497152 | − | 0.867663i | \(-0.334379\pi\) | ||||
0.497152 | + | 0.867663i | \(0.334379\pi\) | |||||||
\(938\) | 6.66535 | − | 8.64580i | 0.217631 | − | 0.282296i | ||||
\(939\) | 6.72601i | 0.219495i | ||||||||
\(940\) | −0.326355 | − | 0.188421i | −0.0106445 | − | 0.00614562i | ||||
\(941\) | −8.00849 | − | 13.8711i | −0.261069 | − | 0.452185i | 0.705457 | − | 0.708753i | \(-0.250742\pi\) |
−0.966526 | + | 0.256567i | \(0.917408\pi\) | |||||||
\(942\) | 8.84682 | − | 5.10771i | 0.288245 | − | 0.166418i | ||||
\(943\) | −4.26995 | − | 1.25943i | −0.139049 | − | 0.0410126i | ||||
\(944\) | − | 1.27113i | − | 0.0413719i | ||||||
\(945\) | −7.46248 | − | 18.1322i | −0.242754 | − | 0.589839i | ||||
\(946\) | −1.83195 | −0.0595617 | ||||||||
\(947\) | 26.9028 | − | 46.5971i | 0.874225 | − | 1.51420i | 0.0166392 | − | 0.999862i | \(-0.494703\pi\) |
0.857586 | − | 0.514341i | \(-0.171963\pi\) | |||||||
\(948\) | −7.62682 | − | 13.2100i | −0.247708 | − | 0.429042i | ||||
\(949\) | 41.7975 | + | 72.3955i | 1.35681 | + | 2.35006i | ||||
\(950\) | −5.69711 | + | 9.86768i | −0.184839 | + | 0.320150i | ||||
\(951\) | − | 33.6296i | − | 1.09052i | ||||||
\(952\) | 0.399166 | − | 2.97975i | 0.0129370 | − | 0.0965743i | ||||
\(953\) | 21.2679i | 0.688936i | 0.938798 | + | 0.344468i | \(0.111941\pi\) | ||||
−0.938798 | + | 0.344468i | \(0.888059\pi\) | |||||||
\(954\) | 16.5065 | + | 9.53001i | 0.534416 | + | 0.308545i | ||||
\(955\) | −4.17298 | + | 2.40927i | −0.135034 | + | 0.0779622i | ||||
\(956\) | −7.39470 | − | 12.8080i | −0.239162 | − | 0.414240i | ||||
\(957\) | −11.9472 | + | 20.6932i | −0.386200 | + | 0.668917i | ||||
\(958\) | 20.6791 | 0.668110 | ||||||||
\(959\) | 11.7443 | + | 1.57326i | 0.379243 | + | 0.0508031i | ||||
\(960\) | − | 1.66459i | − | 0.0537243i | ||||||
\(961\) | −10.2602 | + | 17.7711i | −0.330973 | + | 0.573262i | ||||
\(962\) | 19.2319 | + | 33.3107i | 0.620063 | + | 1.07398i | ||||
\(963\) | 11.1289 | − | 6.42528i | 0.358624 | − | 0.207052i | ||||
\(964\) | −6.60378 | + | 11.4381i | −0.212693 | + | 0.368396i | ||||
\(965\) | −19.1393 | −0.616115 | ||||||||
\(966\) | 9.26467 | + | 12.7814i | 0.298086 | + | 0.411236i | ||||
\(967\) | −23.6682 | −0.761116 | −0.380558 | − | 0.924757i | \(-0.624268\pi\) | ||||
−0.380558 | + | 0.924757i | \(0.624268\pi\) | |||||||
\(968\) | −12.7116 | + | 22.0171i | −0.408566 | + | 0.707657i | ||||
\(969\) | −4.34596 | + | 2.50914i | −0.139612 | + | 0.0806052i | ||||
\(970\) | 9.48921 | + | 16.4358i | 0.304680 | + | 0.527722i | ||||
\(971\) | −28.3288 | + | 49.0669i | −0.909114 | + | 1.57463i | −0.0938170 | + | 0.995589i | \(0.529907\pi\) |
−0.815297 | + | 0.579043i | \(0.803426\pi\) | |||||||
\(972\) | − | 13.4637i | − | 0.431848i | ||||||
\(973\) | −14.6537 | + | 19.0077i | −0.469775 | + | 0.609358i | ||||
\(974\) | −6.52145 | −0.208961 | ||||||||
\(975\) | −13.0226 | + | 22.5559i | −0.417058 | + | 0.722366i | ||||
\(976\) | 7.00107 | + | 12.1262i | 0.224099 | + | 0.388151i | ||||
\(977\) | −31.5941 | + | 18.2409i | −1.01079 | + | 0.583577i | −0.911422 | − | 0.411474i | \(-0.865014\pi\) |
−0.0993638 | + | 0.995051i | \(0.531681\pi\) | |||||||
\(978\) | −16.1357 | − | 9.31594i | −0.515962 | − | 0.297891i | ||||
\(979\) | − | 56.9679i | − | 1.82070i | ||||||
\(980\) | 2.38300 | + | 9.05754i | 0.0761223 | + | 0.289333i | ||||
\(981\) | − | 11.1908i | − | 0.357296i | ||||||
\(982\) | 7.31570 | − | 12.6712i | 0.233453 | − | 0.404353i | ||||
\(983\) | −10.0238 | − | 17.3617i | −0.319708 | − | 0.553751i | 0.660719 | − | 0.750633i | \(-0.270252\pi\) |
−0.980427 | + | 0.196883i | \(0.936918\pi\) | |||||||
\(984\) | 0.577435 | + | 1.00015i | 0.0184079 | + | 0.0318835i | ||||
\(985\) | 8.05912 | − | 13.9588i | 0.256785 | − | 0.444764i | ||||
\(986\) | 3.61611 | 0.115161 | ||||||||
\(987\) | −0.734231 | − | 0.566044i | −0.0233708 | − | 0.0180174i | ||||
\(988\) | − | 23.1519i | − | 0.736560i | ||||||
\(989\) | −1.39628 | − | 0.411837i | −0.0443992 | − | 0.0130956i | ||||
\(990\) | 10.1551 | − | 5.86307i | 0.322751 | − | 0.186341i | ||||
\(991\) | 2.86853 | + | 4.96844i | 0.0911219 | + | 0.157828i | 0.907983 | − | 0.419006i | \(-0.137621\pi\) |
−0.816862 | + | 0.576834i | \(0.804288\pi\) | |||||||
\(992\) | 2.80352 | + | 1.61862i | 0.0890120 | + | 0.0513911i | ||||
\(993\) | 9.05996i | 0.287509i | ||||||||
\(994\) | 9.85382 | − | 4.05544i | 0.312544 | − | 0.128631i | ||||
\(995\) | 26.0663 | 0.826356 | ||||||||
\(996\) | 6.45777 | + | 3.72839i | 0.204622 | + | 0.118139i | ||||
\(997\) | 2.57381 | − | 1.48599i | 0.0815134 | − | 0.0470618i | −0.458689 | − | 0.888597i | \(-0.651681\pi\) |
0.540203 | + | 0.841535i | \(0.318348\pi\) | |||||||
\(998\) | 8.69163 | + | 15.0544i | 0.275129 | + | 0.476537i | ||||
\(999\) | −16.3332 | + | 28.2899i | −0.516759 | + | 0.895053i |
(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 | 322.2.g.b.229.3 | yes | 16 | |
7.2 | even | 3 | 2254.2.c.b.2253.6 | 16 | |||
7.3 | odd | 6 | inner | 322.2.g.b.45.4 | yes | 16 | |
7.5 | odd | 6 | 2254.2.c.b.2253.11 | 16 | |||
23.22 | odd | 2 | inner | 322.2.g.b.229.4 | yes | 16 | |
161.45 | even | 6 | inner | 322.2.g.b.45.3 | ✓ | 16 | |
161.68 | even | 6 | 2254.2.c.b.2253.12 | 16 | |||
161.114 | odd | 6 | 2254.2.c.b.2253.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.b.45.3 | ✓ | 16 | 161.45 | even | 6 | inner | |
322.2.g.b.45.4 | yes | 16 | 7.3 | odd | 6 | inner | |
322.2.g.b.229.3 | yes | 16 | 1.1 | even | 1 | trivial | |
322.2.g.b.229.4 | yes | 16 | 23.22 | odd | 2 | inner | |
2254.2.c.b.2253.5 | 16 | 161.114 | odd | 6 | |||
2254.2.c.b.2253.6 | 16 | 7.2 | even | 3 | |||
2254.2.c.b.2253.11 | 16 | 7.5 | odd | 6 | |||
2254.2.c.b.2253.12 | 16 | 161.68 | even | 6 |