Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 293.7 | ||
Character | \(\chi\) | \(=\) | 750.293 |
Dual form | 750.2.l.a.407.7 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.156434 | + | 0.987688i | 0.110616 | + | 0.698401i | ||||
\(3\) | −0.876876 | + | 1.49368i | −0.506264 | + | 0.862378i | ||||
\(4\) | −0.951057 | + | 0.309017i | −0.475528 | + | 0.154508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.61247 | − | 0.632416i | −0.658287 | − | 0.258183i | ||||
\(7\) | 1.43195 | − | 1.43195i | 0.541225 | − | 0.541225i | −0.382663 | − | 0.923888i | \(-0.624993\pi\) |
0.923888 | + | 0.382663i | \(0.124993\pi\) | |||||||
\(8\) | −0.453990 | − | 0.891007i | −0.160510 | − | 0.315018i | ||||
\(9\) | −1.46218 | − | 2.61955i | −0.487393 | − | 0.873183i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.22713 | − | 4.44177i | 0.973017 | − | 1.33924i | 0.0325093 | − | 0.999471i | \(-0.489650\pi\) |
0.940508 | − | 0.339772i | \(-0.110350\pi\) | |||||||
\(12\) | 0.372385 | − | 1.69155i | 0.107498 | − | 0.488307i | ||||
\(13\) | 6.34051 | + | 1.00424i | 1.75854 | + | 0.278526i | 0.950528 | − | 0.310638i | \(-0.100543\pi\) |
0.808014 | + | 0.589164i | \(0.200543\pi\) | |||||||
\(14\) | 1.63832 | + | 1.19031i | 0.437860 | + | 0.318124i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | −0.199309 | + | 0.101553i | −0.0483396 | + | 0.0246303i | −0.477993 | − | 0.878364i | \(-0.658636\pi\) |
0.429654 | + | 0.902994i | \(0.358636\pi\) | |||||||
\(18\) | 2.35856 | − | 1.85396i | 0.555919 | − | 0.436984i | ||||
\(19\) | −2.05900 | − | 0.669009i | −0.472366 | − | 0.153481i | 0.0631534 | − | 0.998004i | \(-0.479884\pi\) |
−0.535520 | + | 0.844523i | \(0.679884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.883235 | + | 3.39451i | 0.192738 | + | 0.740743i | ||||
\(22\) | 4.89192 | + | 2.49256i | 1.04296 | + | 0.531415i | ||||
\(23\) | 2.14504 | − | 0.339741i | 0.447271 | − | 0.0708408i | 0.0712640 | − | 0.997457i | \(-0.477297\pi\) |
0.376007 | + | 0.926617i | \(0.377297\pi\) | |||||||
\(24\) | 1.72897 | + | 0.103184i | 0.352925 | + | 0.0210623i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.41955i | 1.25898i | ||||||||
\(27\) | 5.19492 | + | 0.112987i | 0.999764 | + | 0.0217444i | ||||
\(28\) | −0.919366 | + | 1.80436i | −0.173744 | + | 0.340992i | ||||
\(29\) | −2.33841 | − | 7.19688i | −0.434231 | − | 1.33643i | −0.893872 | − | 0.448322i | \(-0.852022\pi\) |
0.459641 | − | 0.888105i | \(-0.347978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.944961 | + | 2.90829i | −0.169720 | + | 0.522344i | −0.999353 | − | 0.0359646i | \(-0.988550\pi\) |
0.829633 | + | 0.558309i | \(0.188550\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 3.80480 | + | 8.71519i | 0.662330 | + | 1.51712i | ||||
\(34\) | −0.131482 | − | 0.180969i | −0.0225489 | − | 0.0310359i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.20010 | + | 2.03950i | 0.366683 | + | 0.339917i | ||||
\(37\) | −1.02386 | + | 6.46438i | −0.168321 | + | 1.06274i | 0.748411 | + | 0.663235i | \(0.230817\pi\) |
−0.916732 | + | 0.399502i | \(0.869183\pi\) | |||||||
\(38\) | 0.338674 | − | 2.13830i | 0.0549402 | − | 0.346879i | ||||
\(39\) | −7.05986 | + | 8.59013i | −1.13048 | + | 1.37552i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.896615 | − | 1.23409i | −0.140028 | − | 0.192732i | 0.733243 | − | 0.679966i | \(-0.238006\pi\) |
−0.873271 | + | 0.487235i | \(0.838006\pi\) | |||||||
\(42\) | −3.21455 | + | 1.40338i | −0.496016 | + | 0.216546i | ||||
\(43\) | 2.14384 | + | 2.14384i | 0.326933 | + | 0.326933i | 0.851419 | − | 0.524486i | \(-0.175742\pi\) |
−0.524486 | + | 0.851419i | \(0.675742\pi\) | |||||||
\(44\) | −1.69660 | + | 5.22161i | −0.255773 | + | 0.787187i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.671116 | + | 2.06548i | 0.0989506 | + | 0.304539i | ||||
\(47\) | 2.37459 | − | 4.66039i | 0.346369 | − | 0.679788i | −0.650444 | − | 0.759554i | \(-0.725417\pi\) |
0.996814 | + | 0.0797657i | \(0.0254172\pi\) | |||||||
\(48\) | 0.168558 | + | 1.72383i | 0.0243292 | + | 0.248813i | ||||
\(49\) | 2.89906i | 0.414151i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0230812 | − | 0.386754i | 0.00323202 | − | 0.0541564i | ||||
\(52\) | −6.34051 | + | 1.00424i | −0.879271 | + | 0.139263i | ||||
\(53\) | −10.9216 | − | 5.56485i | −1.50020 | − | 0.764390i | −0.505082 | − | 0.863072i | \(-0.668538\pi\) |
−0.995119 | + | 0.0986812i | \(0.968538\pi\) | |||||||
\(54\) | 0.701069 | + | 5.14864i | 0.0954034 | + | 0.700641i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.92596 | − | 0.625783i | −0.257368 | − | 0.0836238i | ||||
\(57\) | 2.80477 | − | 2.48885i | 0.371501 | − | 0.329657i | ||||
\(58\) | 6.74246 | − | 3.43546i | 0.885329 | − | 0.451098i | ||||
\(59\) | 4.61185 | − | 3.35071i | 0.600412 | − | 0.436225i | −0.245613 | − | 0.969368i | \(-0.578989\pi\) |
0.846025 | + | 0.533143i | \(0.178989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.55529 | + | 1.85653i | 0.327171 | + | 0.237704i | 0.739229 | − | 0.673454i | \(-0.235190\pi\) |
−0.412058 | + | 0.911158i | \(0.635190\pi\) | |||||||
\(62\) | −3.02031 | − | 0.478370i | −0.383580 | − | 0.0607530i | ||||
\(63\) | −5.84481 | − | 1.65729i | −0.736377 | − | 0.208799i | ||||
\(64\) | −0.587785 | + | 0.809017i | −0.0734732 | + | 0.101127i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.01269 | + | 5.12131i | −0.986294 | + | 0.630390i | ||||
\(67\) | 1.13368 | + | 2.22498i | 0.138501 | + | 0.271824i | 0.949830 | − | 0.312766i | \(-0.101255\pi\) |
−0.811329 | + | 0.584590i | \(0.801255\pi\) | |||||||
\(68\) | 0.158173 | − | 0.158173i | 0.0191813 | − | 0.0191813i | ||||
\(69\) | −1.37347 | + | 3.50192i | −0.165346 | + | 0.421581i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.77333 | − | 1.87587i | 0.685168 | − | 0.222625i | 0.0543113 | − | 0.998524i | \(-0.482704\pi\) |
0.630856 | + | 0.775900i | \(0.282704\pi\) | |||||||
\(72\) | −1.67022 | + | 2.49206i | −0.196837 | + | 0.293692i | ||||
\(73\) | 0.478324 | + | 3.02002i | 0.0559836 | + | 0.353467i | 0.999740 | + | 0.0228237i | \(0.00726563\pi\) |
−0.943756 | + | 0.330643i | \(0.892734\pi\) | |||||||
\(74\) | −6.54496 | −0.760836 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.16496 | 0.248338 | ||||||||
\(77\) | −1.73929 | − | 10.9815i | −0.198211 | − | 1.25145i | ||||
\(78\) | −9.58877 | − | 5.62915i | −1.08571 | − | 0.637375i | ||||
\(79\) | 11.0020 | − | 3.57478i | 1.23783 | − | 0.402194i | 0.384282 | − | 0.923216i | \(-0.374449\pi\) |
0.853543 | + | 0.521022i | \(0.174449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.72407 | + | 7.66049i | −0.524897 | + | 0.851166i | ||||
\(82\) | 1.07863 | − | 1.07863i | 0.119115 | − | 0.119115i | ||||
\(83\) | 4.74686 | + | 9.31624i | 0.521036 | + | 1.02259i | 0.990223 | + | 0.139492i | \(0.0445469\pi\) |
−0.469187 | + | 0.883099i | \(0.655453\pi\) | |||||||
\(84\) | −1.88897 | − | 2.95544i | −0.206103 | − | 0.322465i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.78208 | + | 2.45282i | −0.192166 | + | 0.264494i | ||||
\(87\) | 12.8003 | + | 2.81793i | 1.37234 | + | 0.302113i | ||||
\(88\) | −5.42273 | − | 0.858876i | −0.578065 | − | 0.0915565i | ||||
\(89\) | 7.34358 | + | 5.33542i | 0.778418 | + | 0.565554i | 0.904504 | − | 0.426466i | \(-0.140241\pi\) |
−0.126086 | + | 0.992019i | \(0.540241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5173 | − | 7.64126i | 1.10251 | − | 0.801022i | ||||
\(92\) | −1.93507 | + | 0.985966i | −0.201745 | + | 0.102794i | ||||
\(93\) | −3.51545 | − | 3.96168i | −0.364535 | − | 0.410807i | ||||
\(94\) | 4.97448 | + | 1.61631i | 0.513079 | + | 0.166709i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.67624 | + | 0.436149i | −0.171080 | + | 0.0445142i | ||||
\(97\) | 2.14637 | + | 1.09363i | 0.217931 | + | 0.111041i | 0.559548 | − | 0.828798i | \(-0.310975\pi\) |
−0.341617 | + | 0.939839i | \(0.610975\pi\) | |||||||
\(98\) | −2.86337 | + | 0.453513i | −0.289244 | + | 0.0458117i | ||||
\(99\) | −16.3541 | − | 1.95898i | −1.64365 | − | 0.196884i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.60118i | 0.756346i | 0.925735 | + | 0.378173i | \(0.123448\pi\) | ||||
−0.925735 | + | 0.378173i | \(0.876552\pi\) | |||||||
\(102\) | 0.385604 | − | 0.0377047i | 0.0381804 | − | 0.00373332i | ||||
\(103\) | 3.87657 | − | 7.60819i | 0.381970 | − | 0.749657i | −0.617344 | − | 0.786693i | \(-0.711791\pi\) |
0.999314 | + | 0.0370356i | \(0.0117915\pi\) | |||||||
\(104\) | −1.98375 | − | 6.10535i | −0.194523 | − | 0.598679i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78781 | − | 11.6577i | 0.367905 | − | 1.13230i | ||||
\(107\) | 3.60945 | + | 3.60945i | 0.348939 | + | 0.348939i | 0.859714 | − | 0.510775i | \(-0.170642\pi\) |
−0.510775 | + | 0.859714i | \(0.670642\pi\) | |||||||
\(108\) | −4.97558 | + | 1.49786i | −0.478776 | + | 0.144132i | ||||
\(109\) | −5.74999 | − | 7.91418i | −0.550749 | − | 0.758041i | 0.439365 | − | 0.898309i | \(-0.355204\pi\) |
−0.990114 | + | 0.140268i | \(0.955204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.75794 | − | 7.19777i | −0.831266 | − | 0.683182i | ||||
\(112\) | 0.316792 | − | 2.00015i | 0.0299340 | − | 0.188996i | ||||
\(113\) | −2.06024 | + | 13.0078i | −0.193811 | + | 1.22367i | 0.678454 | + | 0.734642i | \(0.262650\pi\) |
−0.872266 | + | 0.489033i | \(0.837350\pi\) | |||||||
\(114\) | 2.89697 | + | 2.38090i | 0.271326 | + | 0.222992i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.44791 | + | 6.12203i | 0.412978 | + | 0.568416i | ||||
\(117\) | −6.64031 | − | 18.0777i | −0.613897 | − | 1.67128i | ||||
\(118\) | 4.03091 | + | 4.03091i | 0.371075 | + | 0.371075i | ||||
\(119\) | −0.139982 | + | 0.430819i | −0.0128321 | + | 0.0394931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.91572 | − | 18.2067i | −0.537793 | − | 1.65516i | ||||
\(122\) | −1.43393 | + | 2.81426i | −0.129822 | + | 0.254791i | ||||
\(123\) | 2.62955 | − | 0.257120i | 0.237099 | − | 0.0231837i | ||||
\(124\) | − | 3.05796i | − | 0.274613i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.722558 | − | 6.03211i | 0.0643706 | − | 0.537383i | ||||
\(127\) | −11.3429 | + | 1.79653i | −1.00652 | + | 0.159417i | −0.637863 | − | 0.770150i | \(-0.720181\pi\) |
−0.368654 | + | 0.929567i | \(0.620181\pi\) | |||||||
\(128\) | −0.891007 | − | 0.453990i | −0.0787546 | − | 0.0401275i | ||||
\(129\) | −5.08211 | + | 1.32234i | −0.447455 | + | 0.116425i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.82350 | − | 3.19185i | −0.858284 | − | 0.278873i | −0.153372 | − | 0.988169i | \(-0.549013\pi\) |
−0.704911 | + | 0.709295i | \(0.749013\pi\) | |||||||
\(132\) | −6.31172 | − | 7.11289i | −0.549365 | − | 0.619098i | ||||
\(133\) | −3.90636 | + | 1.99039i | −0.338724 | + | 0.172589i | ||||
\(134\) | −2.02024 | + | 1.46779i | −0.174522 | + | 0.126797i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.180969 | + | 0.131482i | 0.0155180 | + | 0.0112745i | ||||
\(137\) | −13.3238 | − | 2.11029i | −1.13833 | − | 0.180294i | −0.441317 | − | 0.897351i | \(-0.645489\pi\) |
−0.697014 | + | 0.717057i | \(0.745489\pi\) | |||||||
\(138\) | −3.67366 | − | 0.808736i | −0.312723 | − | 0.0688442i | ||||
\(139\) | 6.69452 | − | 9.21421i | 0.567822 | − | 0.781539i | −0.424473 | − | 0.905441i | \(-0.639541\pi\) |
0.992295 | + | 0.123901i | \(0.0395406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.87893 | + | 7.63347i | 0.410880 | + | 0.642854i | ||||
\(142\) | 2.75592 | + | 5.40880i | 0.231272 | + | 0.453896i | ||||
\(143\) | 24.9223 | − | 24.9223i | 2.08411 | − | 2.08411i | ||||
\(144\) | −2.72266 | − | 1.25981i | −0.226888 | − | 0.104984i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.90801 | + | 0.944871i | −0.240669 | + | 0.0781981i | ||||
\(147\) | −4.33028 | − | 2.54211i | −0.357155 | − | 0.209670i | ||||
\(148\) | −1.02386 | − | 6.46438i | −0.0841605 | − | 0.531369i | ||||
\(149\) | 5.97158 | 0.489211 | 0.244606 | − | 0.969623i | \(-0.421342\pi\) | ||||
0.244606 | + | 0.969623i | \(0.421342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.02183 | −0.245913 | −0.122956 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122956 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(152\) | 0.338674 | + | 2.13830i | 0.0274701 | + | 0.173439i | ||||
\(153\) | 0.557449 | + | 0.373612i | 0.0450671 | + | 0.0302047i | ||||
\(154\) | 10.5742 | − | 3.43576i | 0.852091 | − | 0.276861i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.05983 | − | 10.3513i | 0.325046 | − | 0.828768i | ||||
\(157\) | −4.40896 | + | 4.40896i | −0.351873 | + | 0.351873i | −0.860806 | − | 0.508933i | \(-0.830040\pi\) |
0.508933 | + | 0.860806i | \(0.330040\pi\) | |||||||
\(158\) | 5.25186 | + | 10.3074i | 0.417816 | + | 0.820010i | ||||
\(159\) | 17.8890 | − | 11.4338i | 1.41869 | − | 0.906757i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.58509 | − | 3.55807i | 0.203734 | − | 0.280415i | ||||
\(162\) | −8.30519 | − | 3.46754i | −0.652517 | − | 0.272436i | ||||
\(163\) | 5.66023 | + | 0.896493i | 0.443344 | + | 0.0702187i | 0.374116 | − | 0.927382i | \(-0.377946\pi\) |
0.0692282 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(164\) | 1.23409 | + | 0.896615i | 0.0963659 | + | 0.0700139i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.45897 | + | 6.14580i | −0.656544 | + | 0.477007i | ||||
\(167\) | 8.68941 | − | 4.42748i | 0.672407 | − | 0.342608i | −0.0842276 | − | 0.996447i | \(-0.526842\pi\) |
0.756634 | + | 0.653838i | \(0.226842\pi\) | |||||||
\(168\) | 2.62355 | − | 2.32804i | 0.202411 | − | 0.179613i | ||||
\(169\) | 26.8299 | + | 8.71756i | 2.06384 | + | 0.670581i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.25812 | + | 6.37185i | 0.0962109 | + | 0.487268i | ||||
\(172\) | −2.70140 | − | 1.37643i | −0.205980 | − | 0.104952i | ||||
\(173\) | −17.3254 | + | 2.74408i | −1.31723 | + | 0.208629i | −0.775192 | − | 0.631726i | \(-0.782347\pi\) |
−0.542037 | + | 0.840354i | \(0.682347\pi\) | |||||||
\(174\) | −0.780818 | + | 13.0836i | −0.0591937 | + | 0.991863i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.49033i | − | 0.413849i | ||||||
\(177\) | 0.960873 | + | 9.82680i | 0.0722237 | + | 0.738627i | ||||
\(178\) | −4.12095 | + | 8.08781i | −0.308878 | + | 0.606207i | ||||
\(179\) | −3.59155 | − | 11.0537i | −0.268445 | − | 0.826190i | −0.990880 | − | 0.134750i | \(-0.956977\pi\) |
0.722434 | − | 0.691440i | \(-0.243023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.22208 | + | 3.76116i | −0.0908362 | + | 0.279565i | −0.986146 | − | 0.165879i | \(-0.946954\pi\) |
0.895310 | + | 0.445444i | \(0.146954\pi\) | |||||||
\(182\) | 9.19245 | + | 9.19245i | 0.681390 | + | 0.681390i | ||||
\(183\) | −5.01373 | + | 2.18885i | −0.370626 | + | 0.161804i | ||||
\(184\) | −1.27654 | − | 1.75700i | −0.0941076 | − | 0.129528i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.36297 | − | 4.09191i | 0.246585 | − | 0.300034i | ||||
\(187\) | −0.192122 | + | 1.21301i | −0.0140494 | + | 0.0887042i | ||||
\(188\) | −0.818228 | + | 5.16609i | −0.0596754 | + | 0.376776i | ||||
\(189\) | 7.60064 | − | 7.27706i | 0.552865 | − | 0.529328i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89270 | − | 13.6161i | −0.715810 | − | 0.985228i | −0.999653 | − | 0.0263574i | \(-0.991609\pi\) |
0.283842 | − | 0.958871i | \(-0.408391\pi\) | |||||||
\(192\) | −0.693000 | − | 1.58737i | −0.0500130 | − | 0.114559i | ||||
\(193\) | −11.0921 | − | 11.0921i | −0.798428 | − | 0.798428i | 0.184419 | − | 0.982848i | \(-0.440960\pi\) |
−0.982848 | + | 0.184419i | \(0.940960\pi\) | |||||||
\(194\) | −0.744401 | + | 2.29103i | −0.0534449 | + | 0.164486i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.895859 | − | 2.75717i | −0.0639899 | − | 0.196941i | ||||
\(197\) | −8.05955 | + | 15.8178i | −0.574219 | + | 1.12697i | 0.403091 | + | 0.915160i | \(0.367936\pi\) |
−0.977311 | + | 0.211809i | \(0.932064\pi\) | |||||||
\(198\) | −0.623483 | − | 16.4592i | −0.0443090 | − | 1.16970i | ||||
\(199\) | 2.78155i | 0.197179i | 0.995128 | + | 0.0985894i | \(0.0314330\pi\) | ||||
−0.995128 | + | 0.0985894i | \(0.968567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.31751 | − | 0.257666i | −0.304533 | − | 0.0181743i | ||||
\(202\) | −7.50760 | + | 1.18909i | −0.528233 | + | 0.0836639i | ||||
\(203\) | −13.6540 | − | 6.95707i | −0.958324 | − | 0.488290i | ||||
\(204\) | 0.0975621 | + | 0.374958i | 0.00683072 | + | 0.0262523i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.12095 | + | 2.63866i | 0.565813 | + | 0.183844i | ||||
\(207\) | −4.02640 | − | 5.12227i | −0.279854 | − | 0.356022i | ||||
\(208\) | 5.71986 | − | 2.91441i | 0.396601 | − | 0.202078i | ||||
\(209\) | −9.61624 | + | 6.98661i | −0.665169 | + | 0.483274i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4724 | − | 8.33520i | −0.789794 | − | 0.573819i | 0.118108 | − | 0.993001i | \(-0.462317\pi\) |
−0.907902 | + | 0.419182i | \(0.862317\pi\) | |||||||
\(212\) | 12.1067 | + | 1.91752i | 0.831493 | + | 0.131695i | ||||
\(213\) | −2.26054 | + | 10.2684i | −0.154889 | + | 0.703581i | ||||
\(214\) | −3.00037 | + | 4.12966i | −0.205101 | + | 0.282298i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.25777 | − | 4.68001i | −0.153622 | − | 0.318434i | ||||
\(217\) | 2.81138 | + | 5.51765i | 0.190849 | + | 0.374562i | ||||
\(218\) | 6.91725 | − | 6.91725i | 0.468495 | − | 0.468495i | ||||
\(219\) | −4.93039 | − | 1.93372i | −0.333165 | − | 0.130669i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.36571 | + | 0.443745i | −0.0918674 | + | 0.0298495i | ||||
\(222\) | 5.73911 | − | 9.77609i | 0.385184 | − | 0.656128i | ||||
\(223\) | −0.849459 | − | 5.36327i | −0.0568840 | − | 0.359151i | −0.999668 | − | 0.0257485i | \(-0.991803\pi\) |
0.942784 | − | 0.333403i | \(-0.108197\pi\) | |||||||
\(224\) | 2.02508 | 0.135306 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.1700 | −0.876055 | ||||||||
\(227\) | 3.12180 | + | 19.7103i | 0.207201 | + | 1.30822i | 0.843649 | + | 0.536896i | \(0.180403\pi\) |
−0.636448 | + | 0.771320i | \(0.719597\pi\) | |||||||
\(228\) | −1.89840 | + | 3.23376i | −0.125725 | + | 0.214161i | ||||
\(229\) | −10.9433 | + | 3.55568i | −0.723151 | + | 0.234966i | −0.647389 | − | 0.762160i | \(-0.724139\pi\) |
−0.0757621 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.9280 | + | 7.03142i | 1.17957 | + | 0.462633i | ||||
\(232\) | −5.35085 | + | 5.35085i | −0.351300 | + | 0.351300i | ||||
\(233\) | 2.20854 | + | 4.33449i | 0.144686 | + | 0.283962i | 0.951964 | − | 0.306208i | \(-0.0990605\pi\) |
−0.807279 | + | 0.590171i | \(0.799060\pi\) | |||||||
\(234\) | 16.8163 | − | 9.38652i | 1.09932 | − | 0.613616i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.35071 | + | 4.61185i | −0.218112 | + | 0.300206i | ||||
\(237\) | −4.30783 | + | 19.5682i | −0.279824 | + | 1.27109i | ||||
\(238\) | −0.447413 | − | 0.0708632i | −0.0290015 | − | 0.00459338i | ||||
\(239\) | 13.5737 | + | 9.86185i | 0.878008 | + | 0.637910i | 0.932724 | − | 0.360592i | \(-0.117425\pi\) |
−0.0547159 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7609 | − | 9.99786i | 0.886416 | − | 0.644019i | −0.0485253 | − | 0.998822i | \(-0.515452\pi\) |
0.934941 | + | 0.354803i | \(0.115452\pi\) | |||||||
\(242\) | 17.0571 | − | 8.69105i | 1.09648 | − | 0.558682i | ||||
\(243\) | −7.29993 | − | 13.7736i | −0.468291 | − | 0.883574i | ||||
\(244\) | −3.00392 | − | 0.976034i | −0.192307 | − | 0.0624842i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.665307 | + | 2.55696i | 0.0424184 | + | 0.163026i | ||||
\(247\) | −12.3833 | − | 6.30958i | −0.787928 | − | 0.401469i | ||||
\(248\) | 3.02031 | − | 0.478370i | 0.191790 | − | 0.0303765i | ||||
\(249\) | −18.0779 | − | 1.07888i | −1.14564 | − | 0.0683711i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.1027i | − | 1.71071i | −0.518046 | − | 0.855353i | \(-0.673340\pi\) | ||
0.518046 | − | 0.855353i | \(-0.326660\pi\) | |||||||
\(252\) | 6.07088 | − | 0.229968i | 0.382429 | − | 0.0144866i | ||||
\(253\) | 5.41327 | − | 10.6241i | 0.340330 | − | 0.667934i | ||||
\(254\) | −3.54883 | − | 10.9222i | −0.222673 | − | 0.685318i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −11.8188 | − | 11.8188i | −0.737238 | − | 0.737238i | 0.234805 | − | 0.972043i | \(-0.424555\pi\) |
−0.972043 | + | 0.234805i | \(0.924555\pi\) | |||||||
\(258\) | −2.10108 | − | 4.81268i | −0.130807 | − | 0.299624i | ||||
\(259\) | 7.79053 | + | 10.7227i | 0.484080 | + | 0.666279i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.4334 | + | 16.6487i | −0.955303 | + | 1.03053i | ||||
\(262\) | 1.61582 | − | 10.2019i | 0.0998256 | − | 0.630274i | ||||
\(263\) | 1.14180 | − | 7.20902i | 0.0704062 | − | 0.444527i | −0.927152 | − | 0.374686i | \(-0.877751\pi\) |
0.997558 | − | 0.0698415i | \(-0.0222493\pi\) | |||||||
\(264\) | 6.03795 | − | 7.34671i | 0.371610 | − | 0.452159i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.57697 | − | 3.54690i | −0.158004 | − | 0.217474i | ||||
\(267\) | −14.4088 | + | 6.29048i | −0.881807 | + | 0.384971i | ||||
\(268\) | −1.76575 | − | 1.76575i | −0.107860 | − | 0.107860i | ||||
\(269\) | −9.50784 | + | 29.2621i | −0.579703 | + | 1.78414i | 0.0398701 | + | 0.999205i | \(0.487306\pi\) |
−0.619573 | + | 0.784939i | \(0.712694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.91027 | + | 15.1123i | 0.298278 | + | 0.918004i | 0.982101 | + | 0.188356i | \(0.0603160\pi\) |
−0.683823 | + | 0.729648i | \(0.739684\pi\) | |||||||
\(272\) | −0.101553 | + | 0.199309i | −0.00615756 | + | 0.0120849i | ||||
\(273\) | 2.19126 | + | 22.4099i | 0.132621 | + | 1.35631i | ||||
\(274\) | − | 13.4899i | − | 0.814956i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.224092 | − | 3.75495i | 0.0134888 | − | 0.226021i | ||||
\(277\) | 9.49399 | − | 1.50370i | 0.570438 | − | 0.0903486i | 0.135449 | − | 0.990784i | \(-0.456752\pi\) |
0.434989 | + | 0.900436i | \(0.356752\pi\) | |||||||
\(278\) | 10.1480 | + | 5.17068i | 0.608638 | + | 0.310117i | ||||
\(279\) | 9.00011 | − | 1.77707i | 0.538822 | − | 0.106390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6851 | + | 6.39607i | 1.17431 | + | 0.381558i | 0.830251 | − | 0.557389i | \(-0.188197\pi\) |
0.344062 | + | 0.938947i | \(0.388197\pi\) | |||||||
\(282\) | −6.77626 | + | 6.01300i | −0.403520 | + | 0.358069i | ||||
\(283\) | −10.8711 | + | 5.53912i | −0.646222 | + | 0.329267i | −0.746199 | − | 0.665723i | \(-0.768123\pi\) |
0.0999766 | + | 0.994990i | \(0.468123\pi\) | |||||||
\(284\) | −4.91108 | + | 3.56811i | −0.291419 | + | 0.211728i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.5141 | + | 20.7167i | 1.68608 | + | 1.22501i | ||||
\(287\) | −3.05105 | − | 0.483239i | −0.180098 | − | 0.0285247i | ||||
\(288\) | 0.818384 | − | 2.88622i | 0.0482238 | − | 0.170072i | ||||
\(289\) | −9.96294 | + | 13.7128i | −0.586055 | + | 0.806636i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.51564 | + | 2.24702i | −0.206091 | + | 0.131723i | ||||
\(292\) | −1.38815 | − | 2.72440i | −0.0812354 | − | 0.159433i | ||||
\(293\) | −0.153372 | + | 0.153372i | −0.00896009 | + | 0.00896009i | −0.711573 | − | 0.702613i | \(-0.752017\pi\) |
0.702613 | + | 0.711573i | \(0.252017\pi\) | |||||||
\(294\) | 1.83341 | − | 4.67464i | 0.106927 | − | 0.272630i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.22462 | − | 2.02250i | 0.361799 | − | 0.117556i | ||||
\(297\) | 17.2666 | − | 22.7100i | 1.00191 | − | 1.31777i | ||||
\(298\) | 0.934161 | + | 5.89806i | 0.0541145 | + | 0.341666i | ||||
\(299\) | 13.9418 | 0.806276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.13974 | 0.353889 | ||||||||
\(302\) | −0.472718 | − | 2.98463i | −0.0272019 | − | 0.171746i | ||||
\(303\) | −11.3538 | − | 6.66529i | −0.652256 | − | 0.382911i | ||||
\(304\) | −2.05900 | + | 0.669009i | −0.118092 | + | 0.0383703i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.281808 | + | 0.609032i | −0.0161099 | + | 0.0348160i | ||||
\(307\) | 4.76351 | − | 4.76351i | 0.271868 | − | 0.271868i | −0.557984 | − | 0.829852i | \(-0.688425\pi\) |
0.829852 | + | 0.557984i | \(0.188425\pi\) | |||||||
\(308\) | 5.04762 | + | 9.90651i | 0.287615 | + | 0.564476i | ||||
\(309\) | 7.96496 | + | 12.4618i | 0.453111 | + | 0.708927i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8640 | + | 24.5877i | −1.01298 | + | 1.39424i | −0.0959647 | + | 0.995385i | \(0.530594\pi\) |
−0.917012 | + | 0.398859i | \(0.869406\pi\) | |||||||
\(312\) | 10.8590 | + | 2.39054i | 0.614768 | + | 0.135338i | ||||
\(313\) | −8.62568 | − | 1.36617i | −0.487552 | − | 0.0772206i | −0.0921812 | − | 0.995742i | \(-0.529384\pi\) |
−0.395371 | + | 0.918522i | \(0.629384\pi\) | |||||||
\(314\) | −5.04439 | − | 3.66496i | −0.284671 | − | 0.206826i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.35889 | + | 6.79963i | −0.526479 | + | 0.382509i | ||||
\(317\) | −8.99167 | + | 4.58149i | −0.505023 | + | 0.257322i | −0.687889 | − | 0.725816i | \(-0.741462\pi\) |
0.182866 | + | 0.983138i | \(0.441462\pi\) | |||||||
\(318\) | 14.0915 | + | 15.8801i | 0.790210 | + | 0.890514i | ||||
\(319\) | −39.5132 | − | 12.8386i | −2.21231 | − | 0.718825i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.55642 | + | 2.22634i | −0.477573 | + | 0.124262i | ||||
\(322\) | 3.91866 | + | 1.99666i | 0.218378 | + | 0.111269i | ||||
\(323\) | 0.478317 | − | 0.0757580i | 0.0266143 | − | 0.00421529i | ||||
\(324\) | 2.12563 | − | 8.74538i | 0.118091 | − | 0.485854i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.73079i | 0.317399i | ||||||||
\(327\) | 16.8633 | − | 1.64891i | 0.932543 | − | 0.0911849i | ||||
\(328\) | −0.692523 | + | 1.35915i | −0.0382382 | + | 0.0750467i | ||||
\(329\) | −3.27315 | − | 10.0737i | −0.180455 | − | 0.555382i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.78449 | + | 23.9582i | −0.427874 | + | 1.31686i | 0.472341 | + | 0.881416i | \(0.343409\pi\) |
−0.900215 | + | 0.435445i | \(0.856591\pi\) | |||||||
\(332\) | −7.39341 | − | 7.39341i | −0.405766 | − | 0.405766i | ||||
\(333\) | 18.4308 | − | 6.77003i | 1.01000 | − | 0.370995i | ||||
\(334\) | 5.73229 | + | 7.88982i | 0.313657 | + | 0.431712i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.70980 | + | 2.22707i | 0.147832 | + | 0.121496i | ||||
\(337\) | 4.74900 | − | 29.9840i | 0.258694 | − | 1.63333i | −0.426157 | − | 0.904649i | \(-0.640133\pi\) |
0.684852 | − | 0.728683i | \(-0.259867\pi\) | |||||||
\(338\) | −4.41311 | + | 27.8633i | −0.240042 | + | 1.51556i | ||||
\(339\) | −17.6230 | − | 14.4836i | −0.957151 | − | 0.786642i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.86844 | + | 13.5827i | 0.534406 | + | 0.735546i | ||||
\(342\) | −6.09659 | + | 2.23941i | −0.329666 | + | 0.121093i | ||||
\(343\) | 14.1749 | + | 14.1749i | 0.765374 | + | 0.765374i | ||||
\(344\) | 0.936894 | − | 2.88346i | 0.0505139 | − | 0.155466i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.42059 | − | 16.6829i | −0.291413 | − | 0.896877i | ||||
\(347\) | −11.2852 | + | 22.1485i | −0.605823 | + | 1.18899i | 0.360765 | + | 0.932657i | \(0.382516\pi\) |
−0.966587 | + | 0.256337i | \(0.917484\pi\) | |||||||
\(348\) | −13.0446 | + | 1.27552i | −0.699266 | + | 0.0683749i | ||||
\(349\) | − | 7.66380i | − | 0.410234i | −0.978737 | − | 0.205117i | \(-0.934243\pi\) | ||
0.978737 | − | 0.205117i | \(-0.0657575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.8250 | + | 5.93334i | 1.75207 | + | 0.316698i | ||||
\(352\) | 5.42273 | − | 0.858876i | 0.289033 | − | 0.0457783i | ||||
\(353\) | −2.41473 | − | 1.23037i | −0.128523 | − | 0.0654859i | 0.388547 | − | 0.921429i | \(-0.372977\pi\) |
−0.517070 | + | 0.855943i | \(0.672977\pi\) | |||||||
\(354\) | −9.55550 | + | 2.48629i | −0.507869 | + | 0.132145i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.63290 | − | 2.80500i | −0.457543 | − | 0.148665i | ||||
\(357\) | −0.520760 | − | 0.586863i | −0.0275616 | − | 0.0310601i | ||||
\(358\) | 10.3557 | − | 5.27651i | 0.547317 | − | 0.278872i | ||||
\(359\) | −3.19128 | + | 2.31860i | −0.168429 | + | 0.122371i | −0.668807 | − | 0.743436i | \(-0.733195\pi\) |
0.500377 | + | 0.865807i | \(0.333195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5794 | − | 8.41294i | −0.609443 | − | 0.442787i | ||||
\(362\) | −3.90603 | − | 0.618655i | −0.205297 | − | 0.0325158i | ||||
\(363\) | 32.3824 | + | 7.12882i | 1.69964 | + | 0.374166i | ||||
\(364\) | −7.64126 | + | 10.5173i | −0.400511 | + | 0.551256i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.94622 | − | 4.60960i | −0.154002 | − | 0.240947i | ||||
\(367\) | 12.7890 | + | 25.0999i | 0.667581 | + | 1.31020i | 0.937724 | + | 0.347381i | \(0.112929\pi\) |
−0.270143 | + | 0.962820i | \(0.587071\pi\) | |||||||
\(368\) | 1.53568 | − | 1.53568i | 0.0800527 | − | 0.0800527i | ||||
\(369\) | −1.92173 | + | 4.15318i | −0.100042 | + | 0.216206i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.6077 | + | 7.67062i | −1.22565 | + | 0.398239i | ||||
\(372\) | 4.56762 | + | 2.68145i | 0.236820 | + | 0.139027i | ||||
\(373\) | 4.08750 | + | 25.8075i | 0.211643 | + | 1.33626i | 0.833235 | + | 0.552919i | \(0.186486\pi\) |
−0.621592 | + | 0.783341i | \(0.713514\pi\) | |||||||
\(374\) | −1.22813 | −0.0635052 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.23048 | −0.269742 | ||||||||
\(377\) | −7.59932 | − | 47.9802i | −0.391385 | − | 2.47111i | ||||
\(378\) | 8.37647 | + | 6.36868i | 0.430839 | + | 0.327570i | ||||
\(379\) | −20.6572 | + | 6.71194i | −1.06109 | + | 0.344769i | −0.787012 | − | 0.616938i | \(-0.788373\pi\) |
−0.274079 | + | 0.961707i | \(0.588373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.26283 | − | 18.5180i | 0.372086 | − | 0.948705i | ||||
\(382\) | 11.9009 | − | 11.9009i | 0.608905 | − | 0.608905i | ||||
\(383\) | −10.8440 | − | 21.2826i | −0.554104 | − | 1.08749i | −0.982909 | − | 0.184093i | \(-0.941065\pi\) |
0.428805 | − | 0.903397i | \(-0.358935\pi\) | |||||||
\(384\) | 1.45942 | − | 0.932788i | 0.0744757 | − | 0.0476011i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.22037 | − | 12.6908i | 0.469304 | − | 0.645942i | ||||
\(387\) | 2.48122 | − | 8.75058i | 0.126128 | − | 0.444817i | ||||
\(388\) | −2.37927 | − | 0.376840i | −0.120789 | − | 0.0191311i | ||||
\(389\) | 14.6439 | + | 10.6394i | 0.742476 | + | 0.539440i | 0.893486 | − | 0.449092i | \(-0.148252\pi\) |
−0.151010 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.393024 | + | 0.285549i | −0.0198761 | + | 0.0144408i | ||||
\(392\) | 2.58308 | − | 1.31615i | 0.130465 | − | 0.0664754i | ||||
\(393\) | 13.3816 | − | 11.8743i | 0.675013 | − | 0.598982i | ||||
\(394\) | −16.8838 | − | 5.48588i | −0.850594 | − | 0.276375i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.1590 | − | 3.19059i | 0.812020 | − | 0.160333i | ||||
\(397\) | 12.5321 | + | 6.38543i | 0.628969 | + | 0.320476i | 0.739257 | − | 0.673424i | \(-0.235177\pi\) |
−0.110287 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(398\) | −2.74730 | + | 0.435130i | −0.137710 | + | 0.0218111i | ||||
\(399\) | 0.452380 | − | 7.58019i | 0.0226473 | − | 0.379484i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.841787i | 0.0420368i | 0.999779 | + | 0.0210184i | \(0.00669086\pi\) | ||||
−0.999779 | + | 0.0210184i | \(0.993309\pi\) | |||||||
\(402\) | −0.420913 | − | 4.30466i | −0.0209933 | − | 0.214697i | ||||
\(403\) | −8.91216 | + | 17.4911i | −0.443946 | + | 0.871293i | ||||
\(404\) | −2.34889 | − | 7.22915i | −0.116862 | − | 0.359664i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.73546 | − | 14.5742i | 0.235017 | − | 0.723307i | ||||
\(407\) | 25.4091 | + | 25.4091i | 1.25948 | + | 1.25948i | ||||
\(408\) | −0.355079 | + | 0.155017i | −0.0175790 | + | 0.00767450i | ||||
\(409\) | −8.95042 | − | 12.3192i | −0.442570 | − | 0.609145i | 0.528211 | − | 0.849113i | \(-0.322863\pi\) |
−0.970781 | + | 0.239968i | \(0.922863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8354 | − | 18.0511i | 0.731779 | − | 0.890396i | ||||
\(412\) | −1.33577 | + | 8.43375i | −0.0658089 | + | 0.415501i | ||||
\(413\) | 1.80589 | − | 11.4020i | 0.0888622 | − | 0.561054i | ||||
\(414\) | 4.42934 | − | 4.77812i | 0.217690 | − | 0.234832i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.77332 | + | 5.19352i | 0.185002 | + | 0.254633i | ||||
\(417\) | 7.89285 | + | 18.0792i | 0.386515 | + | 0.885343i | ||||
\(418\) | −8.40490 | − | 8.40490i | −0.411097 | − | 0.411097i | ||||
\(419\) | 0.0964938 | − | 0.296977i | 0.00471403 | − | 0.0145083i | −0.948672 | − | 0.316262i | \(-0.897572\pi\) |
0.953386 | + | 0.301754i | \(0.0975721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.7686 | + | 36.2199i | 0.573565 | + | 1.76525i | 0.641015 | + | 0.767528i | \(0.278514\pi\) |
−0.0674500 | + | 0.997723i | \(0.521486\pi\) | |||||||
\(422\) | 6.43790 | − | 12.6351i | 0.313392 | − | 0.615067i | ||||
\(423\) | −15.6802 | + | 0.593975i | −0.762398 | + | 0.0288800i | ||||
\(424\) | 12.2576i | 0.595283i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.4956 | − | 0.626372i | −0.508515 | − | 0.0303478i | ||||
\(427\) | 6.31749 | − | 1.00059i | 0.305725 | − | 0.0484220i | ||||
\(428\) | −4.54817 | − | 2.31741i | −0.219844 | − | 0.112016i | ||||
\(429\) | 15.3722 | + | 59.0797i | 0.742179 | + | 2.85240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.0434 | − | 7.48726i | −1.10996 | − | 0.360648i | −0.304033 | − | 0.952661i | \(-0.598333\pi\) |
−0.805928 | + | 0.592013i | \(0.798333\pi\) | |||||||
\(432\) | 4.26919 | − | 2.96209i | 0.205402 | − | 0.142514i | ||||
\(433\) | −4.82804 | + | 2.46001i | −0.232021 | + | 0.118220i | −0.566136 | − | 0.824312i | \(-0.691562\pi\) |
0.334116 | + | 0.942532i | \(0.391562\pi\) | |||||||
\(434\) | −5.00992 | + | 3.63992i | −0.240484 | + | 0.174722i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.91418 | + | 5.74999i | 0.379021 | + | 0.275375i | ||||
\(437\) | −4.64392 | − | 0.735524i | −0.222149 | − | 0.0351849i | ||||
\(438\) | 1.13863 | − | 5.17219i | 0.0544058 | − | 0.247137i | ||||
\(439\) | 15.7160 | − | 21.6312i | 0.750083 | − | 1.03240i | −0.247892 | − | 0.968788i | \(-0.579738\pi\) |
0.997975 | − | 0.0636130i | \(-0.0202623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.59423 | − | 4.23894i | 0.361630 | − | 0.201854i | ||||
\(442\) | −0.651925 | − | 1.27948i | −0.0310089 | − | 0.0608585i | ||||
\(443\) | −16.9801 | + | 16.9801i | −0.806749 | + | 0.806749i | −0.984140 | − | 0.177391i | \(-0.943234\pi\) |
0.177391 | + | 0.984140i | \(0.443234\pi\) | |||||||
\(444\) | 10.5535 | + | 4.13914i | 0.500848 | + | 0.196435i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.16436 | − | 1.67800i | 0.244539 | − | 0.0794557i | ||||
\(447\) | −5.23633 | + | 8.91965i | −0.247670 | + | 0.421885i | ||||
\(448\) | 0.316792 | + | 2.00015i | 0.0149670 | + | 0.0944980i | ||||
\(449\) | −6.98488 | −0.329637 | −0.164818 | − | 0.986324i | \(-0.552704\pi\) | ||||
−0.164818 | + | 0.986324i | \(0.552704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.37502 | −0.394364 | ||||||||
\(452\) | −2.06024 | − | 13.0078i | −0.0969055 | − | 0.611837i | ||||
\(453\) | 2.64977 | − | 4.51366i | 0.124497 | − | 0.212070i | ||||
\(454\) | −18.9792 | + | 6.16673i | −0.890739 | + | 0.289419i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.49092 | − | 1.36915i | −0.163477 | − | 0.0641165i | ||||
\(457\) | 4.53549 | − | 4.53549i | 0.212161 | − | 0.212161i | −0.593024 | − | 0.805185i | \(-0.702066\pi\) |
0.805185 | + | 0.593024i | \(0.202066\pi\) | |||||||
\(458\) | −5.22381 | − | 10.2523i | −0.244092 | − | 0.479058i | ||||
\(459\) | −1.04687 | + | 0.505042i | −0.0488637 | + | 0.0235733i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.73628 | − | 2.38979i | 0.0808667 | − | 0.111303i | −0.766667 | − | 0.642045i | \(-0.778086\pi\) |
0.847534 | + | 0.530741i | \(0.178086\pi\) | |||||||
\(462\) | −4.14030 | + | 18.8072i | −0.192624 | + | 0.874990i | ||||
\(463\) | 28.2610 | + | 4.47610i | 1.31340 | + | 0.208022i | 0.773547 | − | 0.633739i | \(-0.218481\pi\) |
0.539851 | + | 0.841761i | \(0.318481\pi\) | |||||||
\(464\) | −6.12203 | − | 4.44791i | −0.284208 | − | 0.206489i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.93564 | + | 2.85941i | −0.182315 | + | 0.132460i | ||||
\(467\) | 4.07796 | − | 2.07783i | 0.188706 | − | 0.0961504i | −0.357085 | − | 0.934072i | \(-0.616229\pi\) |
0.545791 | + | 0.837922i | \(0.316229\pi\) | |||||||
\(468\) | 11.9016 | + | 15.1409i | 0.550152 | + | 0.699889i | ||||
\(469\) | 4.80942 | + | 1.56267i | 0.222078 | + | 0.0721576i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.71948 | − | 10.4517i | −0.125307 | − | 0.481588i | ||||
\(472\) | −5.07924 | − | 2.58800i | −0.233791 | − | 0.119122i | ||||
\(473\) | 16.4409 | − | 2.60399i | 0.755955 | − | 0.119731i | ||||
\(474\) | −20.0012 | − | 1.19365i | −0.918684 | − | 0.0548264i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.452990i | − | 0.0207628i | ||||||
\(477\) | 1.39198 | + | 36.7465i | 0.0637343 | + | 1.68251i | ||||
\(478\) | −7.61704 | + | 14.9493i | −0.348395 | + | 0.683765i | ||||
\(479\) | −8.54601 | − | 26.3019i | −0.390477 | − | 1.20176i | −0.932428 | − | 0.361355i | \(-0.882314\pi\) |
0.541951 | − | 0.840410i | \(-0.317686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.9836 | + | 39.9593i | −0.591999 | + | 1.82199i | ||||
\(482\) | 12.0274 | + | 12.0274i | 0.547835 | + | 0.547835i | ||||
\(483\) | 3.04783 | + | 6.98129i | 0.138681 | + | 0.317660i | ||||
\(484\) | 11.2524 | + | 15.4876i | 0.511472 | + | 0.703980i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.4620 | − | 9.36471i | 0.565289 | − | 0.424792i | ||||
\(487\) | 4.73443 | − | 29.8920i | 0.214538 | − | 1.35454i | −0.611644 | − | 0.791133i | \(-0.709491\pi\) |
0.826182 | − | 0.563404i | \(-0.190509\pi\) | |||||||
\(488\) | 0.494100 | − | 3.11963i | 0.0223669 | − | 0.141219i | ||||
\(489\) | −6.30240 | + | 7.66848i | −0.285004 | + | 0.346781i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.84555 | + | 6.66933i | 0.218677 | + | 0.300982i | 0.904235 | − | 0.427035i | \(-0.140442\pi\) |
−0.685558 | + | 0.728018i | \(0.740442\pi\) | |||||||
\(492\) | −2.42140 | + | 1.05711i | −0.109165 | + | 0.0476583i | ||||
\(493\) | 1.19693 | + | 1.19693i | 0.0539071 | + | 0.0539071i | ||||
\(494\) | 4.29473 | − | 13.2178i | 0.193229 | − | 0.594698i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.944961 | + | 2.90829i | 0.0424300 | + | 0.130586i | ||||
\(497\) | 5.58095 | − | 10.9532i | 0.250340 | − | 0.491320i | ||||
\(498\) | −1.76242 | − | 18.0241i | −0.0789757 | − | 0.807680i | ||||
\(499\) | 38.0463i | 1.70318i | 0.524205 | + | 0.851592i | \(0.324363\pi\) | ||||
−0.524205 | + | 0.851592i | \(0.675637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00629 | + | 16.8616i | −0.0449576 | + | 0.753320i | ||||
\(502\) | 26.7690 | − | 4.23979i | 1.19476 | − | 0.189231i | ||||
\(503\) | 33.9723 | + | 17.3097i | 1.51475 | + | 0.771804i | 0.996513 | − | 0.0834338i | \(-0.0265887\pi\) |
0.518236 | + | 0.855237i | \(0.326589\pi\) | |||||||
\(504\) | 1.17683 | + | 5.96016i | 0.0524203 | + | 0.265487i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.3402 | + | 3.68464i | 0.504132 | + | 0.163802i | ||||
\(507\) | −36.5477 | + | 32.4311i | −1.62314 | + | 1.44032i | ||||
\(508\) | 10.2325 | − | 5.21374i | 0.453996 | − | 0.231322i | ||||
\(509\) | −5.62616 | + | 4.08765i | −0.249375 | + | 0.181182i | −0.705450 | − | 0.708760i | \(-0.749255\pi\) |
0.456075 | + | 0.889942i | \(0.349255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00944 | + | 3.63957i | 0.221605 | + | 0.161005i | ||||
\(512\) | 0.987688 | + | 0.156434i | 0.0436501 | + | 0.00691349i | ||||
\(513\) | −10.6207 | − | 3.70809i | −0.468917 | − | 0.163716i | ||||
\(514\) | 9.82444 | − | 13.5222i | 0.433337 | − | 0.596438i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.42475 | − | 2.82808i | 0.194789 | − | 0.124499i | ||||
\(517\) | −13.0373 | − | 25.5871i | −0.573379 | − | 1.12532i | ||||
\(518\) | −9.37203 | + | 9.37203i | −0.411783 | + | 0.411783i | ||||
\(519\) | 11.0935 | − | 28.2849i | 0.486950 | − | 1.24157i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.6631 | − | 6.71385i | 0.905267 | − | 0.294139i | 0.180858 | − | 0.983509i | \(-0.442113\pi\) |
0.724409 | + | 0.689370i | \(0.242113\pi\) | |||||||
\(522\) | −18.8580 | − | 12.6390i | −0.825394 | − | 0.553192i | ||||
\(523\) | −6.72718 | − | 42.4737i | −0.294159 | − | 1.85725i | −0.483513 | − | 0.875337i | \(-0.660639\pi\) |
0.189354 | − | 0.981909i | \(-0.439361\pi\) | |||||||
\(524\) | 10.3290 | 0.451226 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.29888 | 0.318246 | ||||||||
\(527\) | −0.107007 | − | 0.675613i | −0.00466128 | − | 0.0294302i | ||||
\(528\) | 8.20081 | + | 4.81433i | 0.356894 | + | 0.209517i | ||||
\(529\) | −17.3885 | + | 5.64988i | −0.756023 | + | 0.245647i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.5207 | − | 7.18164i | −0.673541 | − | 0.311657i | ||||
\(532\) | 3.10010 | − | 3.10010i | 0.134407 | − | 0.134407i | ||||
\(533\) | −4.44569 | − | 8.72515i | −0.192564 | − | 0.377928i | ||||
\(534\) | −8.46707 | − | 13.2474i | −0.366406 | − | 0.573271i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.46779 | − | 2.02024i | 0.0633987 | − | 0.0872609i | ||||
\(537\) | 19.6600 | + | 4.32805i | 0.848392 | + | 0.186769i | ||||
\(538\) | −30.3892 | − | 4.81318i | −1.31017 | − | 0.207511i | ||||
\(539\) | 12.8769 | + | 9.35565i | 0.554649 | + | 0.402976i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.60979 | + | 6.25538i | −0.370164 | + | 0.268940i | −0.757279 | − | 0.653092i | \(-0.773472\pi\) |
0.387115 | + | 0.922031i | \(0.373472\pi\) | |||||||
\(542\) | −14.1581 | + | 7.21390i | −0.608141 | + | 0.309863i | ||||
\(543\) | −4.54638 | − | 5.12347i | −0.195104 | − | 0.219869i | ||||
\(544\) | −0.212742 | − | 0.0691240i | −0.00912123 | − | 0.00296367i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −21.7912 | + | 5.66997i | −0.932579 | + | 0.242652i | ||||
\(547\) | 12.7347 | + | 6.48863i | 0.544495 | + | 0.277434i | 0.704526 | − | 0.709678i | \(-0.251160\pi\) |
−0.160031 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(548\) | 13.3238 | − | 2.11029i | 0.569166 | − | 0.0901470i | ||||
\(549\) | 1.12697 | − | 9.40828i | 0.0480980 | − | 0.401536i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.3828i | 0.697929i | ||||||||
\(552\) | 3.74377 | − | 0.366069i | 0.159346 | − | 0.0155809i | ||||
\(553\) | 10.6354 | − | 20.8732i | 0.452265 | − | 0.887619i | ||||
\(554\) | 2.97037 | + | 9.14187i | 0.126199 | + | 0.388401i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.51952 | + | 10.8320i | −0.149261 | + | 0.459377i | ||||
\(557\) | −3.60663 | − | 3.60663i | −0.152818 | − | 0.152818i | 0.626557 | − | 0.779375i | \(-0.284463\pi\) |
−0.779375 | + | 0.626557i | \(0.784463\pi\) | |||||||
\(558\) | 3.16312 | + | 8.61131i | 0.133905 | + | 0.364546i | ||||
\(559\) | 11.4401 | + | 15.7460i | 0.483866 | + | 0.665985i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.64339 | − | 1.35063i | −0.0693839 | − | 0.0570236i | ||||
\(562\) | −3.23790 | + | 20.4433i | −0.136583 | + | 0.862349i | ||||
\(563\) | 3.98324 | − | 25.1492i | 0.167874 | − | 1.05991i | −0.749534 | − | 0.661965i | \(-0.769723\pi\) |
0.917408 | − | 0.397948i | \(-0.130277\pi\) | |||||||
\(564\) | −6.99901 | − | 5.75219i | −0.294712 | − | 0.242211i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.17155 | − | 9.87079i | −0.301443 | − | 0.414900i | ||||
\(567\) | 4.20480 | + | 17.7340i | 0.176585 | + | 0.744759i | ||||
\(568\) | −4.29245 | − | 4.29245i | −0.180107 | − | 0.180107i | ||||
\(569\) | 9.49637 | − | 29.2268i | 0.398108 | − | 1.22525i | −0.528406 | − | 0.848992i | \(-0.677210\pi\) |
0.926514 | − | 0.376260i | \(-0.122790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.95564 | − | 21.4073i | −0.291085 | − | 0.895866i | −0.984509 | − | 0.175336i | \(-0.943899\pi\) |
0.693424 | − | 0.720530i | \(-0.256101\pi\) | |||||||
\(572\) | −16.0011 | + | 31.4039i | −0.669039 | + | 1.31306i | ||||
\(573\) | 29.0128 | − | 2.83690i | 1.21203 | − | 0.118513i | ||||
\(574\) | − | 3.08908i | − | 0.128936i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.97871 | + | 0.356805i | 0.124113 | + | 0.0148669i | ||||
\(577\) | −41.1545 | + | 6.51823i | −1.71328 | + | 0.271358i | −0.934508 | − | 0.355943i | \(-0.884160\pi\) |
−0.778777 | + | 0.627301i | \(0.784160\pi\) | |||||||
\(578\) | −15.1025 | − | 7.69512i | −0.628182 | − | 0.320075i | ||||
\(579\) | 26.2945 | − | 6.84170i | 1.09276 | − | 0.284332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.1376 | + | 6.54311i | 0.835449 | + | 0.271454i | ||||
\(582\) | −2.76933 | − | 3.12085i | −0.114792 | − | 0.129363i | ||||
\(583\) | −59.9633 | + | 30.5528i | −2.48343 | + | 1.26537i | ||||
\(584\) | 2.47370 | − | 1.79725i | 0.102363 | − | 0.0743708i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.175477 | − | 0.127491i | −0.00724887 | − | 0.00526661i | ||||
\(587\) | −24.5435 | − | 3.88731i | −1.01302 | − | 0.160447i | −0.372212 | − | 0.928148i | \(-0.621400\pi\) |
−0.640808 | + | 0.767701i | \(0.721400\pi\) | |||||||
\(588\) | 4.90389 | + | 1.07957i | 0.202233 | + | 0.0445205i | ||||
\(589\) | 3.89134 | − | 5.35598i | 0.160340 | − | 0.220689i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.5595 | − | 25.9086i | −0.681167 | − | 1.06574i | ||||
\(592\) | 2.97135 | + | 5.83160i | 0.122122 | + | 0.239677i | ||||
\(593\) | −25.7915 | + | 25.7915i | −1.05913 | + | 1.05913i | −0.0609902 | + | 0.998138i | \(0.519426\pi\) |
−0.998138 | + | 0.0609902i | \(0.980574\pi\) | |||||||
\(594\) | 25.1315 | + | 13.5014i | 1.03116 | + | 0.553968i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.67931 | + | 1.84532i | −0.232634 | + | 0.0755873i | ||||
\(597\) | −4.15475 | − | 2.43907i | −0.170043 | − | 0.0998246i | ||||
\(598\) | 2.18098 | + | 13.7702i | 0.0891870 | + | 0.563104i | ||||
\(599\) | 36.9040 | 1.50786 | 0.753929 | − | 0.656956i | \(-0.228156\pi\) | ||||
0.753929 | + | 0.656956i | \(0.228156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4696 | 0.834972 | 0.417486 | − | 0.908683i | \(-0.362911\pi\) | ||||
0.417486 | + | 0.908683i | \(0.362911\pi\) | |||||||
\(602\) | 0.960467 | + | 6.06415i | 0.0391457 | + | 0.247156i | ||||
\(603\) | 4.17079 | − | 6.22305i | 0.169848 | − | 0.253422i | ||||
\(604\) | 2.87393 | − | 0.933797i | 0.116939 | − | 0.0379956i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.80711 | − | 12.2567i | 0.195276 | − | 0.497893i | ||||
\(607\) | 4.57545 | − | 4.57545i | 0.185712 | − | 0.185712i | −0.608128 | − | 0.793839i | \(-0.708079\pi\) |
0.793839 | + | 0.608128i | \(0.208079\pi\) | |||||||
\(608\) | −0.982870 | − | 1.92899i | −0.0398607 | − | 0.0782309i | ||||
\(609\) | 22.3645 | − | 14.2943i | 0.906256 | − | 0.579234i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7363 | − | 27.1646i | 0.798444 | − | 1.09896i | ||||
\(612\) | −0.645618 | − | 0.183064i | −0.0260976 | − | 0.00739994i | ||||
\(613\) | −29.0842 | − | 4.60648i | −1.17470 | − | 0.186054i | −0.461581 | − | 0.887098i | \(-0.652718\pi\) |
−0.713118 | + | 0.701044i | \(0.752718\pi\) | |||||||
\(614\) | 5.45004 | + | 3.95968i | 0.219946 | + | 0.159800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.99493 | + | 6.53520i | −0.362416 | + | 0.263311i | ||||
\(617\) | 22.4860 | − | 11.4572i | 0.905254 | − | 0.461250i | 0.0615777 | − | 0.998102i | \(-0.480387\pi\) |
0.843676 | + | 0.536852i | \(0.180387\pi\) | |||||||
\(618\) | −11.0624 | + | 9.81635i | −0.444994 | + | 0.394872i | ||||
\(619\) | 2.83846 | + | 0.922271i | 0.114087 | + | 0.0370692i | 0.365504 | − | 0.930810i | \(-0.380897\pi\) |
−0.251417 | + | 0.967879i | \(0.580897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1817 | − | 1.52256i | 0.448706 | − | 0.0610984i | ||||
\(622\) | −27.0796 | − | 13.7977i | −1.08579 | − | 0.553239i | ||||
\(623\) | 18.1557 | − | 2.87557i | 0.727391 | − | 0.115207i | ||||
\(624\) | −0.662395 | + | 11.0992i | −0.0265170 | + | 0.444325i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 8.73320i | − | 0.349049i | ||||||
\(627\) | −2.00353 | − | 20.4900i | −0.0800133 | − | 0.818292i | ||||
\(628\) | 2.83072 | − | 5.55561i | 0.112958 | − | 0.221693i | ||||
\(629\) | −0.452414 | − | 1.39239i | −0.0180389 | − | 0.0555181i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.27752 | − | 28.5533i | 0.369332 | − | 1.13669i | −0.577891 | − | 0.816114i | \(-0.696124\pi\) |
0.947223 | − | 0.320574i | \(-0.103876\pi\) | |||||||
\(632\) | −8.17997 | − | 8.17997i | −0.325382 | − | 0.325382i | ||||
\(633\) | 22.5100 | − | 9.82723i | 0.894694 | − | 0.390597i | ||||
\(634\) | −5.93169 | − | 8.16427i | −0.235577 | − | 0.324245i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.4802 | + | 16.4022i | −0.534526 | + | 0.650388i | ||||
\(637\) | −2.91135 | + | 18.3815i | −0.115352 | + | 0.728303i | ||||
\(638\) | 6.49933 | − | 41.0351i | 0.257311 | − | 1.62460i | ||||
\(639\) | −13.3556 | − | 12.3807i | −0.528338 | − | 0.489771i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4719 | − | 14.4133i | −0.413614 | − | 0.569291i | 0.550481 | − | 0.834847i | \(-0.314444\pi\) |
−0.964095 | + | 0.265557i | \(0.914444\pi\) | |||||||
\(642\) | −3.53745 | − | 8.10280i | −0.139612 | − | 0.319792i | ||||
\(643\) | −10.8997 | − | 10.8997i | −0.429840 | − | 0.429840i | 0.458734 | − | 0.888574i | \(-0.348303\pi\) |
−0.888574 | + | 0.458734i | \(0.848303\pi\) | |||||||
\(644\) | −1.35906 | + | 4.18276i | −0.0535545 | + | 0.164824i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.149651 | + | 0.460577i | 0.00588792 | + | 0.0181212i | ||||
\(647\) | 0.982107 | − | 1.92749i | 0.0386106 | − | 0.0757776i | −0.870895 | − | 0.491469i | \(-0.836460\pi\) |
0.909506 | + | 0.415691i | \(0.136460\pi\) | |||||||
\(648\) | 8.97023 | + | 0.731385i | 0.352384 | + | 0.0287315i | ||||
\(649\) | − | 31.2980i | − | 1.22855i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.7069 | − | 0.638977i | −0.419635 | − | 0.0250435i | ||||
\(652\) | −5.66023 | + | 0.896493i | −0.221672 | + | 0.0351094i | ||||
\(653\) | −5.67905 | − | 2.89362i | −0.222238 | − | 0.113236i | 0.339327 | − | 0.940668i | \(-0.389801\pi\) |
−0.561565 | + | 0.827432i | \(0.689801\pi\) | |||||||
\(654\) | 4.26661 | + | 16.3977i | 0.166838 | + | 0.641202i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.45075 | − | 0.471379i | −0.0566424 | − | 0.0184042i | ||||
\(657\) | 7.21170 | − | 5.66880i | 0.281355 | − | 0.221161i | ||||
\(658\) | 9.43766 | − | 4.80873i | 0.367918 | − | 0.187464i | ||||
\(659\) | −27.9601 | + | 20.3142i | −1.08917 | + | 0.791330i | −0.979259 | − | 0.202611i | \(-0.935057\pi\) |
−0.109913 | + | 0.993941i | \(0.535057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8226 | − | 24.5736i | −1.31555 | − | 0.955801i | −0.999976 | − | 0.00689972i | \(-0.997804\pi\) |
−0.315572 | − | 0.948902i | \(-0.602196\pi\) | |||||||
\(662\) | −24.8810 | − | 3.94076i | −0.967027 | − | 0.153162i | ||||
\(663\) | 0.534741 | − | 2.42904i | 0.0207676 | − | 0.0943362i | ||||
\(664\) | 6.14580 | − | 8.45897i | 0.238503 | − | 0.328272i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.56989 | + | 17.1448i | 0.370826 | + | 0.664349i | ||||
\(667\) | −7.46104 | − | 14.6431i | −0.288893 | − | 0.566984i | ||||
\(668\) | −6.89596 | + | 6.89596i | −0.266813 | + | 0.266813i | ||||
\(669\) | 8.75590 | + | 3.43410i | 0.338523 | + | 0.132770i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4925 | − | 5.35875i | 0.636687 | − | 0.206872i | ||||
\(672\) | −1.77574 | + | 3.02482i | −0.0685007 | + | 0.116685i | ||||
\(673\) | 0.934113 | + | 5.89775i | 0.0360074 | + | 0.227342i | 0.999129 | − | 0.0417241i | \(-0.0132851\pi\) |
−0.963122 | + | 0.269066i | \(0.913285\pi\) | |||||||
\(674\) | 30.3577 | 1.16934 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.2106 | −1.08502 | ||||||||
\(677\) | 3.42993 | + | 21.6557i | 0.131823 | + | 0.832297i | 0.961651 | + | 0.274277i | \(0.0884386\pi\) |
−0.829828 | + | 0.558020i | \(0.811561\pi\) | |||||||
\(678\) | 11.5484 | − | 19.6718i | 0.443515 | − | 0.755490i | ||||
\(679\) | 4.63951 | − | 1.50747i | 0.178048 | − | 0.0578514i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.1783 | − | 12.6205i | −1.23308 | − | 0.483617i | ||||
\(682\) | −11.8717 | + | 11.8717i | −0.454593 | + | 0.454593i | ||||
\(683\) | 5.64753 | + | 11.0839i | 0.216097 | + | 0.424114i | 0.973453 | − | 0.228888i | \(-0.0735091\pi\) |
−0.757356 | + | 0.653002i | \(0.773509\pi\) | |||||||
\(684\) | −3.16555 | − | 5.67121i | −0.121038 | − | 0.216844i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.7830 | + | 16.2179i | −0.449875 | + | 0.619200i | ||||
\(687\) | 4.28482 | − | 19.4637i | 0.163476 | − | 0.742585i | ||||
\(688\) | 2.99453 | + | 0.474286i | 0.114165 | + | 0.0180820i | ||||
\(689\) | −63.6603 | − | 46.2519i | −2.42526 | − | 1.76206i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.87945 | − | 4.99821i | 0.261706 | − | 0.190141i | −0.449193 | − | 0.893435i | \(-0.648288\pi\) |
0.710899 | + | 0.703294i | \(0.248288\pi\) | |||||||
\(692\) | 15.6295 | − | 7.96363i | 0.594145 | − | 0.302732i | ||||
\(693\) | −26.2233 | + | 20.6130i | −0.996141 | + | 0.783023i | ||||
\(694\) | −23.6412 | − | 7.68150i | −0.897408 | − | 0.291586i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.30044 | − | 12.6845i | −0.125103 | − | 0.480805i | ||||
\(697\) | 0.304029 | + | 0.154911i | 0.0115159 | + | 0.00586765i | ||||
\(698\) | 7.56945 | − | 1.19888i | 0.286508 | − | 0.0453784i | ||||
\(699\) | −8.41097 | − | 0.501961i | −0.318132 | − | 0.0189859i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8483i | 0.749660i | 0.927093 | + | 0.374830i | \(0.122299\pi\) | ||||
−0.927093 | + | 0.374830i | \(0.877701\pi\) | |||||||
\(702\) | −0.725327 | + | 33.3491i | −0.0273757 | + | 1.25868i | ||||
\(703\) | 6.43284 | − | 12.6252i | 0.242619 | − | 0.476167i | ||||
\(704\) | 1.69660 | + | 5.22161i | 0.0639432 | + | 0.196797i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.837472 | − | 2.57747i | 0.0315187 | − | 0.0970045i | ||||
\(707\) | 10.8845 | + | 10.8845i | 0.409353 | + | 0.409353i | ||||
\(708\) | −3.95049 | − | 9.04891i | −0.148469 | − | 0.340079i | ||||
\(709\) | −2.74291 | − | 3.77529i | −0.103012 | − | 0.141784i | 0.754399 | − | 0.656416i | \(-0.227928\pi\) |
−0.857411 | + | 0.514632i | \(0.827928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.4512 | − | 23.5934i | −0.954496 | − | 0.884821i | ||||
\(712\) | 1.41998 | − | 8.96541i | 0.0532160 | − | 0.335993i | ||||
\(713\) | −1.03891 | + | 6.55944i | −0.0389076 | + | 0.245653i | ||||
\(714\) | 0.498173 | − | 0.606155i | 0.0186436 | − | 0.0226848i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.83154 | + | 9.40281i | 0.255307 | + | 0.351399i | ||||
\(717\) | −26.6329 | + | 11.6271i | −0.994624 | + | 0.434224i | ||||
\(718\) | −2.78928 | − | 2.78928i | −0.104095 | − | 0.104095i | ||||
\(719\) | −5.35309 | + | 16.4751i | −0.199637 | + | 0.614418i | 0.800255 | + | 0.599660i | \(0.204698\pi\) |
−0.999891 | + | 0.0147577i | \(0.995302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.34349 | − | 16.4456i | −0.199002 | − | 0.612465i | ||||
\(722\) | 6.49795 | − | 12.7529i | 0.241829 | − | 0.474615i | ||||
\(723\) | 2.86706 | + | 29.3213i | 0.106627 | + | 1.09047i | ||||
\(724\) | − | 3.95472i | − | 0.146976i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.97532 | + | 33.0989i | −0.0733111 | + | 1.22842i | ||||
\(727\) | 5.26211 | − | 0.833437i | 0.195161 | − | 0.0309105i | −0.0580887 | − | 0.998311i | \(-0.518501\pi\) |
0.253250 | + | 0.967401i | \(0.418501\pi\) | |||||||
\(728\) | −11.5832 | − | 5.90192i | −0.429301 | − | 0.218740i | ||||
\(729\) | 26.9745 | + | 1.17392i | 0.999054 | + | 0.0434785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.645002 | − | 0.209574i | −0.0238563 | − | 0.00775137i | ||||
\(732\) | 4.09195 | − | 3.63105i | 0.151243 | − | 0.134207i | ||||
\(733\) | 14.8502 | − | 7.56657i | 0.548506 | − | 0.279478i | −0.157697 | − | 0.987488i | \(-0.550407\pi\) |
0.706202 | + | 0.708010i | \(0.250407\pi\) | |||||||
\(734\) | −22.7902 | + | 16.5580i | −0.841201 | + | 0.611168i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75700 | + | 1.27654i | 0.0647640 | + | 0.0470538i | ||||
\(737\) | 13.5414 | + | 2.14474i | 0.498803 | + | 0.0790026i | ||||
\(738\) | −4.40267 | − | 1.24837i | −0.162065 | − | 0.0459533i | ||||
\(739\) | −4.33206 | + | 5.96257i | −0.159357 | + | 0.219337i | −0.881228 | − | 0.472691i | \(-0.843283\pi\) |
0.721871 | + | 0.692028i | \(0.243283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.2831 | − | 12.9639i | 0.745118 | − | 0.476242i | ||||
\(742\) | −11.2692 | − | 22.1171i | −0.413707 | − | 0.811946i | ||||
\(743\) | −24.6348 | + | 24.6348i | −0.903763 | + | 0.903763i | −0.995759 | − | 0.0919959i | \(-0.970675\pi\) |
0.0919959 | + | 0.995759i | \(0.470675\pi\) | |||||||
\(744\) | −1.93390 | + | 4.93086i | −0.0709003 | + | 0.180774i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.8503 | + | 8.07436i | −0.909835 | + | 0.295623i | ||||
\(747\) | 17.4636 | − | 26.0566i | 0.638959 | − | 0.953363i | ||||
\(748\) | −0.192122 | − | 1.21301i | −0.00702468 | − | 0.0443521i | ||||
\(749\) | 10.3371 | 0.377709 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0915 | −0.587188 | −0.293594 | − | 0.955930i | \(-0.594851\pi\) | ||||
−0.293594 | + | 0.955930i | \(0.594851\pi\) | |||||||
\(752\) | −0.818228 | − | 5.16609i | −0.0298377 | − | 0.188388i | ||||
\(753\) | 40.4828 | + | 23.7657i | 1.47528 | + | 0.866069i | ||||
\(754\) | 46.2007 | − | 15.0115i | 1.68253 | − | 0.546687i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.97991 | + | 9.26962i | −0.181117 | + | 0.337133i | ||||
\(757\) | 5.11239 | − | 5.11239i | 0.185813 | − | 0.185813i | −0.608070 | − | 0.793883i | \(-0.708056\pi\) |
0.793883 | + | 0.608070i | \(0.208056\pi\) | |||||||
\(758\) | −9.86081 | − | 19.3529i | −0.358161 | − | 0.702930i | ||||
\(759\) | 11.1223 | + | 17.4018i | 0.403715 | + | 0.631644i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.3299 | − | 23.8525i | 0.628208 | − | 0.864654i | −0.369711 | − | 0.929147i | \(-0.620543\pi\) |
0.997918 | + | 0.0644935i | \(0.0205432\pi\) | |||||||
\(762\) | 19.4261 | + | 4.27656i | 0.703735 | + | 0.154923i | ||||
\(763\) | −19.5664 | − | 3.09901i | −0.708350 | − | 0.112192i | ||||
\(764\) | 13.6161 | + | 9.89270i | 0.492614 | + | 0.357905i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3242 | − | 14.0399i | 0.698212 | − | 0.507281i | ||||
\(767\) | 32.6064 | − | 16.6138i | 1.17735 | − | 0.599890i | ||||
\(768\) | 1.14961 | + | 1.29553i | 0.0414829 | + | 0.0467485i | ||||
\(769\) | 44.5425 | + | 14.4727i | 1.60624 | + | 0.521900i | 0.968641 | − | 0.248466i | \(-0.0799264\pi\) |
0.637602 | + | 0.770366i | \(0.279926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0172 | − | 7.28994i | 1.00901 | − | 0.262541i | ||||
\(772\) | 13.9769 | + | 7.12158i | 0.503039 | + | 0.256311i | ||||
\(773\) | −37.2215 | + | 5.89531i | −1.33876 | + | 0.212039i | −0.784411 | − | 0.620242i | \(-0.787034\pi\) |
−0.554353 | + | 0.832281i | \(0.687034\pi\) | |||||||
\(774\) | 9.03100 | + | 1.08178i | 0.324613 | + | 0.0388838i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.40893i | − | 0.0864756i | ||||||
\(777\) | −22.8477 | + | 2.23407i | −0.819657 | + | 0.0801468i | ||||
\(778\) | −8.21763 | + | 16.1280i | −0.294616 | + | 0.578217i | ||||
\(779\) | 1.02051 | + | 3.14082i | 0.0365637 | + | 0.112532i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2991 | − | 31.6974i | 0.368532 | − | 1.13422i | ||||
\(782\) | −0.343516 | − | 0.343516i | −0.0122841 | − | 0.0122841i | ||||
\(783\) | −11.3347 | − | 37.6514i | −0.405069 | − | 1.34555i | ||||
\(784\) | 1.70402 | + | 2.34539i | 0.0608580 | + | 0.0837639i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.8215 | + | 11.3593i | 0.492997 | + | 0.405173i | ||||
\(787\) | −0.968005 | + | 6.11175i | −0.0345057 | + | 0.217860i | −0.998916 | − | 0.0465501i | \(-0.985177\pi\) |
0.964410 | + | 0.264410i | \(0.0851773\pi\) | |||||||
\(788\) | 2.77713 | − | 17.5341i | 0.0989313 | − | 0.624627i | ||||
\(789\) | 9.76677 | + | 8.02689i | 0.347706 | + | 0.285765i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.6764 | + | 21.5767i | 0.557388 | + | 0.767179i | ||||
\(792\) | 5.67913 | + | 15.4609i | 0.201799 | + | 0.549381i | ||||
\(793\) | 14.3375 | + | 14.3375i | 0.509138 | + | 0.509138i | ||||
\(794\) | −4.34636 | + | 13.3767i | −0.154247 | + | 0.474722i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.859546 | − | 2.64541i | −0.0304658 | − | 0.0937641i | ||||
\(797\) | 5.46214 | − | 10.7200i | 0.193479 | − | 0.379724i | −0.773804 | − | 0.633426i | \(-0.781648\pi\) |
0.967282 | + | 0.253702i | \(0.0816483\pi\) | |||||||
\(798\) | 7.55763 | − | 0.738992i | 0.267537 | − | 0.0261600i | ||||
\(799\) | 1.17001i | 0.0413919i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.23878 | − | 27.0382i | 0.114437 | − | 0.955348i | ||||
\(802\) | −0.831423 | + | 0.131684i | −0.0293586 | + | 0.00464994i | ||||
\(803\) | 14.9579 | + | 7.62141i | 0.527851 | + | 0.268954i | ||||
\(804\) | 4.18582 | − | 1.08913i | 0.147622 | − | 0.0384106i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.6699 | − | 6.06622i | −0.657620 | − | 0.213674i | ||||
\(807\) | −35.3712 | − | 39.8610i | −1.24512 | − | 1.40317i | ||||
\(808\) | 6.77270 | − | 3.45086i | 0.238263 | − | 0.121401i | ||||
\(809\) | −31.1568 | + | 22.6367i | −1.09542 | + | 0.795866i | −0.980305 | − | 0.197487i | \(-0.936722\pi\) |
−0.115110 | + | 0.993353i | \(0.536722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9742 | + | 9.42631i | 0.455586 | + | 0.331002i | 0.791797 | − | 0.610784i | \(-0.209146\pi\) |
−0.336211 | + | 0.941787i | \(0.609146\pi\) | |||||||
\(812\) | 15.1356 | + | 2.39724i | 0.531155 | + | 0.0841267i | ||||
\(813\) | −26.8786 | − | 5.91718i | −0.942674 | − | 0.207525i | ||||
\(814\) | −21.1214 | + | 29.0712i | −0.740306 | + | 1.01894i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.208655 | − | 0.326458i | −0.00730440 | − | 0.0114283i | ||||
\(817\) | −2.97992 | − | 5.84842i | −0.104254 | − | 0.204610i | ||||
\(818\) | 10.7674 | − | 10.7674i | 0.376472 | − | 0.376472i | ||||
\(819\) | −35.3948 | − | 16.3777i | −1.23679 | − | 0.572282i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.82793 | + | 1.89361i | −0.203396 | + | 0.0660875i | −0.408943 | − | 0.912560i | \(-0.634103\pi\) |
0.205547 | + | 0.978647i | \(0.434103\pi\) | |||||||
\(822\) | 20.1497 | + | 11.8290i | 0.702800 | + | 0.412583i | ||||
\(823\) | −3.12202 | − | 19.7116i | −0.108827 | − | 0.687105i | −0.980426 | − | 0.196886i | \(-0.936917\pi\) |
0.871600 | − | 0.490218i | \(-0.163083\pi\) | |||||||
\(824\) | −8.53887 | −0.297466 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.5441 | 0.401670 | ||||||||
\(827\) | −2.58216 | − | 16.3031i | −0.0897904 | − | 0.566914i | −0.991035 | − | 0.133603i | \(-0.957345\pi\) |
0.901244 | − | 0.433311i | \(-0.142655\pi\) | |||||||
\(828\) | 5.41220 | + | 3.62734i | 0.188087 | + | 0.126059i | ||||
\(829\) | −6.29526 | + | 2.04545i | −0.218643 | + | 0.0710415i | −0.416290 | − | 0.909232i | \(-0.636670\pi\) |
0.197647 | + | 0.980273i | \(0.436670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.07900 | + | 15.4996i | −0.210878 | + | 0.537674i | ||||
\(832\) | −4.53931 | + | 4.53931i | −0.157372 | + | 0.157372i | ||||
\(833\) | −0.294409 | − | 0.577809i | −0.0102007 | − | 0.0200199i | ||||
\(834\) | −16.6219 | + | 10.6239i | −0.575570 | + | 0.367875i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.98661 | − | 9.61624i | 0.241637 | − | 0.332585i | ||||
\(837\) | −5.23760 | + | 15.0016i | −0.181038 | + | 0.518530i | ||||
\(838\) | 0.308416 | + | 0.0488483i | 0.0106541 | + | 0.00168744i | ||||
\(839\) | −7.33822 | − | 5.33153i | −0.253343 | − | 0.184065i | 0.453864 | − | 0.891071i | \(-0.350045\pi\) |
−0.707207 | + | 0.707006i | \(0.750045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8654 | + | 16.6127i | −0.788462 | + | 0.572851i | ||||
\(842\) | −33.9330 | + | 17.2897i | −1.16941 | + | 0.595843i | ||||
\(843\) | −26.8151 | + | 23.7947i | −0.923560 | + | 0.819534i | ||||
\(844\) | 13.4866 | + | 4.38208i | 0.464229 | + | 0.150837i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.03959 | − | 15.3942i | −0.104503 | − | 0.529265i | ||||
\(847\) | −34.5421 | − | 17.6001i | −1.18688 | − | 0.604745i | ||||
\(848\) | −12.1067 | + | 1.91752i | −0.415746 | + | 0.0658477i | ||||
\(849\) | 1.25894 | − | 21.0952i | 0.0432069 | − | 0.723984i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.2142i | 0.487256i | ||||||||
\(852\) | −1.02322 | − | 10.4644i | −0.0350549 | − | 0.358504i | ||||
\(853\) | −5.41209 | + | 10.6218i | −0.185306 | + | 0.363684i | −0.964907 | − | 0.262593i | \(-0.915422\pi\) |
0.779600 | + | 0.626277i | \(0.215422\pi\) | |||||||
\(854\) | 1.97655 | + | 6.08318i | 0.0676360 | + | 0.208162i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.57739 | − | 4.85470i | 0.0539140 | − | 0.165930i | ||||
\(857\) | −7.62449 | − | 7.62449i | −0.260448 | − | 0.260448i | 0.564788 | − | 0.825236i | \(-0.308958\pi\) |
−0.825236 | + | 0.564788i | \(0.808958\pi\) | |||||||
\(858\) | −55.9476 | + | 24.4251i | −1.91002 | + | 0.833859i | ||||
\(859\) | −19.5703 | − | 26.9362i | −0.667730 | − | 0.919051i | 0.331976 | − | 0.943288i | \(-0.392285\pi\) |
−0.999706 | + | 0.0242364i | \(0.992285\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.39720 | − | 4.13356i | 0.115776 | − | 0.140871i | ||||
\(862\) | 3.79029 | − | 23.9310i | 0.129098 | − | 0.815092i | ||||
\(863\) | −3.76211 | + | 23.7530i | −0.128064 | + | 0.808562i | 0.837126 | + | 0.547010i | \(0.184234\pi\) |
−0.965189 | + | 0.261552i | \(0.915766\pi\) | |||||||
\(864\) | 3.59347 | + | 3.75326i | 0.122252 | + | 0.127688i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.18499 | − | 4.38377i | −0.108230 | − | 0.148966i | ||||
\(867\) | −11.7463 | − | 26.9059i | −0.398926 | − | 0.913772i | ||||
\(868\) | −4.37883 | − | 4.37883i | −0.148627 | − | 0.148627i | ||||
\(869\) | 19.6267 | − | 60.4048i | 0.665790 | − | 2.04909i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95372 | + | 15.2460i | 0.167850 | + | 0.516590i | ||||
\(872\) | −4.44115 | + | 8.71624i | −0.150396 | + | 0.295169i | ||||
\(873\) | −0.273559 | − | 7.22161i | −0.00925856 | − | 0.244415i | ||||
\(874\) | − | 4.70180i | − | 0.159041i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.28663 | + | 0.315502i | 0.178619 | + | 0.0106598i | ||||
\(877\) | −13.7146 | + | 2.17218i | −0.463110 | + | 0.0733494i | −0.383630 | − | 0.923487i | \(-0.625326\pi\) |
−0.0794802 | + | 0.996836i | \(0.525326\pi\) | |||||||
\(878\) | 23.8234 | + | 12.1386i | 0.804001 | + | 0.409659i | ||||
\(879\) | −0.0946011 | − | 0.363578i | −0.00319081 | − | 0.0122632i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0334 | − | 8.78367i | −0.910777 | − | 0.295930i | −0.184099 | − | 0.982908i | \(-0.558937\pi\) |
−0.726678 | + | 0.686978i | \(0.758937\pi\) | |||||||
\(882\) | 5.37475 | + | 6.83761i | 0.180977 | + | 0.230234i | ||||
\(883\) | 15.6986 | − | 7.99886i | 0.528301 | − | 0.269183i | −0.169430 | − | 0.985542i | \(-0.554193\pi\) |
0.697732 | + | 0.716359i | \(0.254193\pi\) | |||||||
\(884\) | 1.16174 | − | 0.844053i | 0.0390735 | − | 0.0283886i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.4273 | − | 14.1148i | −0.652674 | − | 0.474195i | ||||
\(887\) | 9.80527 | + | 1.55300i | 0.329229 | + | 0.0521447i | 0.318861 | − | 0.947802i | \(-0.396700\pi\) |
0.0103679 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(888\) | −2.43724 | + | 11.0711i | −0.0817885 | + | 0.371522i | ||||
\(889\) | −13.6698 | + | 18.8149i | −0.458471 | + | 0.631032i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.7809 | + | 45.7047i | 0.629185 | + | 1.53116i | ||||
\(892\) | 2.46523 | + | 4.83828i | 0.0825419 | + | 0.161998i | ||||
\(893\) | −8.00712 | + | 8.00712i | −0.267948 | + | 0.267948i | ||||
\(894\) | −9.62898 | − | 3.77653i | −0.322041 | − | 0.126306i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.92596 | + | 0.625783i | −0.0643419 | + | 0.0209060i | ||||
\(897\) | −12.2252 | + | 20.8247i | −0.408189 | + | 0.695315i | ||||
\(898\) | −1.09268 | − | 6.89889i | −0.0364631 | − | 0.230219i | ||||
\(899\) | 23.1403 | 0.771773 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.74191 | 0.0913462 | ||||||||
\(902\) | −1.31014 | − | 8.27191i | −0.0436229 | − | 0.275424i | ||||
\(903\) | −5.38379 | + | 9.17082i | −0.179161 | + | 0.305186i | ||||
\(904\) | 12.5254 | − | 4.06975i | 0.416589 | − | 0.135358i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.87260 | + | 1.91105i | 0.161881 | + | 0.0634905i | ||||
\(907\) | −16.5638 | + | 16.5638i | −0.549992 | + | 0.549992i | −0.926438 | − | 0.376446i | \(-0.877146\pi\) |
0.376446 | + | 0.926438i | \(0.377146\pi\) | |||||||
\(908\) | −9.05981 | − | 17.7809i | −0.300660 | − | 0.590079i | ||||
\(909\) | 19.9117 | − | 11.1143i | 0.660428 | − | 0.368638i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0445 | + | 34.4709i | −0.829763 | + | 1.14207i | 0.158205 | + | 0.987406i | \(0.449429\pi\) |
−0.987967 | + | 0.154664i | \(0.950571\pi\) | |||||||
\(912\) | 0.806197 | − | 3.66213i | 0.0266959 | − | 0.121265i | ||||
\(913\) | 56.6993 | + | 8.98029i | 1.87647 | + | 0.297204i | ||||
\(914\) | 5.18916 | + | 3.77014i | 0.171642 | + | 0.124705i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.30889 | − | 6.76331i | 0.307574 | − | 0.223466i | ||||
\(917\) | −18.6373 | + | 9.49617i | −0.615458 | + | 0.313591i | ||||
\(918\) | −0.662590 | − | 0.954976i | −0.0218687 | − | 0.0315189i | ||||
\(919\) | −6.21323 | − | 2.01880i | −0.204955 | − | 0.0665940i | 0.204740 | − | 0.978816i | \(-0.434365\pi\) |
−0.409696 | + | 0.912222i | \(0.634365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.93817 | + | 11.2922i | 0.0968159 | + | 0.372090i | ||||
\(922\) | 2.63198 | + | 1.34106i | 0.0866796 | + | 0.0441655i | ||||
\(923\) | 38.4897 | − | 6.09617i | 1.26690 | − | 0.200658i | ||||
\(924\) | −19.2233 | − | 1.14723i | −0.632401 | − | 0.0377412i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.6132i | 0.940289i | ||||||||
\(927\) | −25.5983 | + | 0.969677i | −0.840757 | + | 0.0318484i | ||||
\(928\) | 3.43546 | − | 6.74246i | 0.112774 | − | 0.221332i | ||||
\(929\) | −8.15479 | − | 25.0979i | −0.267550 | − | 0.823434i | −0.991095 | − | 0.133157i | \(-0.957489\pi\) |
0.723545 | − | 0.690277i | \(-0.242511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.93950 | − | 5.96916i | 0.0635644 | − | 0.195631i | ||||
\(932\) | −3.43987 | − | 3.43987i | −0.112677 | − | 0.112677i | ||||
\(933\) | −21.0618 | − | 48.2436i | −0.689531 | − | 1.57943i | ||||
\(934\) | 2.69018 | + | 3.70271i | 0.0880254 | + | 0.121157i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.0927 | + | 14.1236i | −0.427947 | + | 0.461646i | ||||
\(937\) | −6.92001 | + | 43.6912i | −0.226067 | + | 1.42733i | 0.569763 | + | 0.821809i | \(0.307035\pi\) |
−0.795829 | + | 0.605521i | \(0.792965\pi\) | |||||||
\(938\) | −0.791077 | + | 4.99466i | −0.0258296 | + | 0.163081i | ||||
\(939\) | 9.60427 | − | 11.6861i | 0.313424 | − | 0.381360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.24570 | + | 4.46733i | 0.105807 | + | 0.145631i | 0.858637 | − | 0.512584i | \(-0.171312\pi\) |
−0.752830 | + | 0.658215i | \(0.771312\pi\) | |||||||
\(942\) | 9.89759 | − | 4.32100i | 0.322481 | − | 0.140786i | ||||
\(943\) | −2.34254 | − | 2.34254i | −0.0762837 | − | 0.0762837i | ||||
\(944\) | 1.76157 | − | 5.42156i | 0.0573342 | − | 0.176457i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.14385 | + | 15.8312i | 0.167241 | + | 0.514715i | ||||
\(947\) | −1.68564 | + | 3.30825i | −0.0547759 | + | 0.107504i | −0.916772 | − | 0.399412i | \(-0.869214\pi\) |
0.861996 | + | 0.506916i | \(0.169214\pi\) | |||||||
\(948\) | −1.94991 | − | 19.9416i | −0.0633302 | − | 0.647674i | ||||
\(949\) | 19.6288i | 0.637179i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.04129 | − | 17.4481i | 0.0337662 | − | 0.565794i | ||||
\(952\) | 0.447413 | − | 0.0708632i | 0.0145007 | − | 0.00229669i | ||||
\(953\) | 38.9868 | + | 19.8647i | 1.26290 | + | 0.643482i | 0.951749 | − | 0.306877i | \(-0.0992840\pi\) |
0.311156 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(954\) | −36.0764 | + | 7.12326i | −1.16802 | + | 0.230624i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.9568 | − | 5.18468i | −0.516080 | − | 0.167685i | ||||
\(957\) | 53.8250 | − | 47.7623i | 1.73991 | − | 1.54394i | ||||
\(958\) | 24.6412 | − | 12.5553i | 0.796121 | − | 0.405644i | ||||
\(959\) | −22.1008 | + | 16.0572i | −0.713673 | + | 0.518514i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.5143 | + | 12.7249i | 0.564978 | + | 0.410481i | ||||
\(962\) | −41.4984 | − | 6.57270i | −1.33796 | − | 0.211912i | ||||
\(963\) | 4.17747 | − | 14.7328i | 0.134617 | − | 0.474758i | ||||
\(964\) | −9.99786 | + | 13.7609i | −0.322009 | + | 0.443208i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.41855 | + | 4.10242i | −0.206514 | + | 0.131993i | ||||
\(967\) | 11.3768 | + | 22.3283i | 0.365854 | + | 0.718028i | 0.998403 | − | 0.0564917i | \(-0.0179914\pi\) |
−0.632549 | + | 0.774520i | \(0.717991\pi\) | |||||||
\(968\) | −13.5366 | + | 13.5366i | −0.435084 | + | 0.435084i | ||||
\(969\) | −0.306266 | + | 0.780885i | −0.00983869 | + | 0.0250856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.2601 | + | 8.53244i | −0.842728 | + | 0.273819i | −0.698397 | − | 0.715711i | \(-0.746103\pi\) |
−0.144331 | + | 0.989529i | \(0.546103\pi\) | |||||||
\(972\) | 11.1989 | + | 10.8436i | 0.359205 | + | 0.347810i | ||||
\(973\) | −3.60807 | − | 22.7804i | −0.115669 | − | 0.730308i | ||||
\(974\) | 30.2646 | 0.969741 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.15851 | 0.101102 | ||||||||
\(977\) | 1.45735 | + | 9.20136i | 0.0466248 | + | 0.294378i | 0.999972 | − | 0.00749885i | \(-0.00238698\pi\) |
−0.953347 | + | 0.301876i | \(0.902387\pi\) | |||||||
\(978\) | −8.55998 | − | 5.02519i | −0.273718 | − | 0.160688i | ||||
\(979\) | 47.3974 | − | 15.4004i | 1.51483 | − | 0.492197i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.3241 | + | 26.6343i | −0.393477 | + | 0.850368i | ||||
\(982\) | −5.82921 | + | 5.82921i | −0.186017 | + | 0.186017i | ||||
\(983\) | 21.0084 | + | 41.2314i | 0.670065 | + | 1.31508i | 0.936311 | + | 0.351172i | \(0.114217\pi\) |
−0.266245 | + | 0.963905i | \(0.585783\pi\) | |||||||
\(984\) | −1.42289 | − | 2.22622i | −0.0453600 | − | 0.0709692i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.994954 | + | 1.36944i | −0.0316858 | + | 0.0436118i | ||||
\(987\) | 17.9171 | + | 3.94435i | 0.570307 | + | 0.125550i | ||||
\(988\) | 13.7269 | + | 2.17413i | 0.436712 | + | 0.0691684i | ||||
\(989\) | 5.32698 | + | 3.87028i | 0.169388 | + | 0.123068i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5452 | + | 13.4739i | −0.589107 | + | 0.428011i | −0.841996 | − | 0.539484i | \(-0.818619\pi\) |
0.252889 | + | 0.967495i | \(0.418619\pi\) | |||||||
\(992\) | −2.72466 | + | 1.38828i | −0.0865081 | + | 0.0440781i | ||||
\(993\) | −28.9599 | − | 32.6359i | −0.919015 | − | 1.03567i | ||||
\(994\) | 11.6914 | + | 3.79878i | 0.370830 | + | 0.120490i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.5265 | − | 4.56031i | 0.555349 | − | 0.144499i | ||||
\(997\) | 42.9560 | + | 21.8872i | 1.36043 | + | 0.693173i | 0.973447 | − | 0.228914i | \(-0.0735173\pi\) |
0.386983 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(998\) | −37.5779 | + | 5.95175i | −1.18951 | + | 0.188399i | ||||
\(999\) | −6.04925 | + | 33.4663i | −0.191390 | + | 1.05883i |
(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 | 750.2.l.a.293.7 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.a.293.2 | 80 | ||
5.2 | odd | 4 | 750.2.l.b.707.5 | 80 | |||
5.3 | odd | 4 | 150.2.l.a.137.6 | yes | 80 | ||
5.4 | even | 2 | 750.2.l.c.293.4 | 80 | |||
15.2 | even | 4 | 750.2.l.b.707.10 | 80 | |||
15.8 | even | 4 | 150.2.l.a.137.1 | yes | 80 | ||
15.14 | odd | 2 | 750.2.l.c.293.9 | 80 | |||
25.2 | odd | 20 | inner | 750.2.l.a.407.2 | 80 | ||
25.11 | even | 5 | 750.2.l.b.593.10 | 80 | |||
25.14 | even | 10 | 150.2.l.a.23.1 | ✓ | 80 | ||
25.23 | odd | 20 | 750.2.l.c.407.9 | 80 | |||
75.2 | even | 20 | inner | 750.2.l.a.407.7 | 80 | ||
75.11 | odd | 10 | 750.2.l.b.593.5 | 80 | |||
75.14 | odd | 10 | 150.2.l.a.23.6 | yes | 80 | ||
75.23 | even | 20 | 750.2.l.c.407.4 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.23.1 | ✓ | 80 | 25.14 | even | 10 | ||
150.2.l.a.23.6 | yes | 80 | 75.14 | odd | 10 | ||
150.2.l.a.137.1 | yes | 80 | 15.8 | even | 4 | ||
150.2.l.a.137.6 | yes | 80 | 5.3 | odd | 4 | ||
750.2.l.a.293.2 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.a.293.7 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.a.407.2 | 80 | 25.2 | odd | 20 | inner | ||
750.2.l.a.407.7 | 80 | 75.2 | even | 20 | inner | ||
750.2.l.b.593.5 | 80 | 75.11 | odd | 10 | |||
750.2.l.b.593.10 | 80 | 25.11 | even | 5 | |||
750.2.l.b.707.5 | 80 | 5.2 | odd | 4 | |||
750.2.l.b.707.10 | 80 | 15.2 | even | 4 | |||
750.2.l.c.293.4 | 80 | 5.4 | even | 2 | |||
750.2.l.c.293.9 | 80 | 15.14 | odd | 2 | |||
750.2.l.c.407.4 | 80 | 75.23 | even | 20 | |||
750.2.l.c.407.9 | 80 | 25.23 | odd | 20 |