Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(109,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.e (of order \(3\), 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: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.163 |
Dual form | 189.2.e.e.109.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34981 | + | 2.33795i | −0.954463 | + | 1.65318i | −0.218870 | + | 0.975754i | \(0.570237\pi\) |
−0.735593 | + | 0.677424i | \(0.763096\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.64400 | − | 4.57954i | −1.32200 | − | 2.28977i | ||||
\(5\) | 0.794182 | − | 1.37556i | 0.355169 | − | 0.615171i | −0.631978 | − | 0.774986i | \(-0.717757\pi\) |
0.987147 | + | 0.159816i | \(0.0510900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23855 | − | 2.33795i | 0.468128 | − | 0.883661i | ||||
\(8\) | 8.87636 | 3.13827 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.14400 | + | 3.71351i | 0.677991 | + | 1.17432i | ||||
\(11\) | −0.150186 | − | 0.260130i | −0.0452828 | − | 0.0784320i | 0.842496 | − | 0.538703i | \(-0.181086\pi\) |
−0.887778 | + | 0.460271i | \(0.847752\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81089 | 0.779601 | 0.389801 | − | 0.920899i | \(-0.372544\pi\) | ||||
0.389801 | + | 0.920899i | \(0.372544\pi\) | |||||||
\(14\) | 3.79418 | + | 6.05146i | 1.01404 | + | 1.61732i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.69344 | + | 11.5934i | −1.67336 | + | 2.89834i | ||||
\(17\) | −2.93818 | − | 5.08907i | −0.712613 | − | 1.23428i | −0.963873 | − | 0.266362i | \(-0.914178\pi\) |
0.251260 | − | 0.967920i | \(-0.419155\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.14400 | − | 1.98146i | 0.262451 | − | 0.454578i | −0.704442 | − | 0.709762i | \(-0.748803\pi\) |
0.966893 | + | 0.255184i | \(0.0821360\pi\) | |||||||
\(20\) | −8.39926 | −1.87813 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.810892 | 0.172883 | ||||||||
\(23\) | −0.944368 | + | 1.63569i | −0.196914 | + | 0.341066i | −0.947526 | − | 0.319678i | \(-0.896425\pi\) |
0.750612 | + | 0.660743i | \(0.229759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23855 | + | 2.14523i | 0.247710 | + | 0.429046i | ||||
\(26\) | −3.79418 | + | 6.57172i | −0.744100 | + | 1.28882i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.9814 | + | 0.509538i | −2.64224 | + | 0.0962937i | ||||
\(29\) | 2.52290 | 0.468491 | 0.234245 | − | 0.972178i | \(-0.424738\pi\) | ||||
0.234245 | + | 0.972178i | \(0.424738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.40545 | + | 4.16635i | 0.432031 | + | 0.748299i | 0.997048 | − | 0.0767797i | \(-0.0244638\pi\) |
−0.565017 | + | 0.825079i | \(0.691130\pi\) | |||||||
\(32\) | −9.19344 | − | 15.9235i | −1.62519 | − | 2.81490i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.8640 | 2.72065 | ||||||||
\(35\) | −2.23236 | − | 3.56046i | −0.377338 | − | 0.601827i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.23855 | − | 3.87728i | 0.368015 | − | 0.637421i | −0.621240 | − | 0.783620i | \(-0.713371\pi\) |
0.989255 | + | 0.146199i | \(0.0467041\pi\) | |||||||
\(38\) | 3.08836 | + | 5.34920i | 0.500999 | + | 0.867755i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.04944 | − | 12.2100i | 1.11461 | − | 1.93057i | ||||
\(41\) | 8.90978 | 1.39147 | 0.695737 | − | 0.718297i | \(-0.255078\pi\) | ||||
0.695737 | + | 0.718297i | \(0.255078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.09888 | −1.38757 | −0.693783 | − | 0.720184i | \(-0.744058\pi\) | ||||
−0.693783 | + | 0.720184i | \(0.744058\pi\) | |||||||
\(44\) | −0.794182 | + | 1.37556i | −0.119727 | + | 0.207374i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.54944 | − | 4.41576i | −0.375895 | − | 0.651069i | ||||
\(47\) | 1.60507 | − | 2.78007i | 0.234124 | − | 0.405515i | −0.724894 | − | 0.688861i | \(-0.758111\pi\) |
0.959018 | + | 0.283346i | \(0.0914444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.93199 | − | 5.79133i | −0.561713 | − | 0.827332i | ||||
\(50\) | −6.68725 | −0.945720 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.43199 | − | 12.8726i | −1.03063 | − | 1.78511i | ||||
\(53\) | −1.00619 | − | 1.74277i | −0.138211 | − | 0.239388i | 0.788609 | − | 0.614895i | \(-0.210802\pi\) |
−0.926819 | + | 0.375507i | \(0.877468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.477100 | −0.0643321 | ||||||||
\(56\) | 10.9938 | − | 20.7524i | 1.46911 | − | 2.77316i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.40545 | + | 5.89841i | −0.447157 | + | 0.774499i | ||||
\(59\) | 2.44437 | + | 4.23377i | 0.318230 | + | 0.551190i | 0.980119 | − | 0.198412i | \(-0.0635784\pi\) |
−0.661889 | + | 0.749602i | \(0.730245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.78799 | + | 6.56099i | −0.485003 | + | 0.840049i | −0.999852 | − | 0.0172317i | \(-0.994515\pi\) |
0.514849 | + | 0.857281i | \(0.327848\pi\) | |||||||
\(62\) | −12.9876 | −1.64943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 22.8640 | 2.85800 | ||||||||
\(65\) | 2.23236 | − | 3.86656i | 0.276890 | − | 0.479588i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.356004 | − | 0.616617i | −0.0434928 | − | 0.0753317i | 0.843460 | − | 0.537193i | \(-0.180515\pi\) |
−0.886952 | + | 0.461861i | \(0.847182\pi\) | |||||||
\(68\) | −15.5371 | + | 26.9110i | −1.88415 | + | 3.26344i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.3374 | − | 0.413181i | 1.35508 | − | 0.0493845i | ||||
\(71\) | −12.8640 | −1.52667 | −0.763337 | − | 0.646001i | \(-0.776440\pi\) | ||||
−0.763337 | + | 0.646001i | \(0.776440\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.83743 | + | 10.1107i | 0.683220 | + | 1.18337i | 0.973993 | + | 0.226580i | \(0.0727543\pi\) |
−0.290773 | + | 0.956792i | \(0.593912\pi\) | |||||||
\(74\) | 6.04325 | + | 10.4672i | 0.702514 | + | 1.21679i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.0989 | −1.38784 | ||||||||
\(77\) | −0.794182 | + | 0.0289431i | −0.0905054 | + | 0.00329837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.833104 | + | 1.44298i | −0.0937315 | + | 0.162348i | −0.909078 | − | 0.416625i | \(-0.863213\pi\) |
0.815347 | + | 0.578973i | \(0.196546\pi\) | |||||||
\(80\) | 10.6316 | + | 18.4145i | 1.18865 | + | 2.05880i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.0265 | + | 20.8306i | −1.32811 | + | 2.30035i | ||||
\(83\) | −5.43268 | −0.596314 | −0.298157 | − | 0.954517i | \(-0.596372\pi\) | ||||
−0.298157 | + | 0.954517i | \(0.596372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.33379 | −1.01239 | ||||||||
\(86\) | 12.2818 | − | 21.2727i | 1.32438 | − | 2.29389i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.33310 | − | 2.30900i | −0.142109 | − | 0.246141i | ||||
\(89\) | 4.67673 | − | 8.10033i | 0.495732 | − | 0.858633i | −0.504256 | − | 0.863554i | \(-0.668233\pi\) |
0.999988 | + | 0.00492107i | \(0.00156643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.48143 | − | 6.57172i | 0.364953 | − | 0.688903i | ||||
\(92\) | 9.98762 | 1.04128 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.33310 | + | 7.50516i | 0.446926 | + | 0.774098i | ||||
\(95\) | −1.81708 | − | 3.14728i | −0.186429 | − | 0.322904i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5760 | −1.27690 | −0.638449 | − | 0.769664i | \(-0.720424\pi\) | ||||
−0.638449 | + | 0.769664i | \(0.720424\pi\) | |||||||
\(98\) | 18.8473 | − | 1.37556i | 1.90386 | − | 0.138953i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.54944 | − | 11.3440i | 0.654944 | − | 1.13440i | ||||
\(101\) | 7.30470 | + | 12.6521i | 0.726845 | + | 1.25893i | 0.958210 | + | 0.286066i | \(0.0923475\pi\) |
−0.231365 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.59888 | + | 7.96550i | −0.453142 | + | 0.784864i | −0.998579 | − | 0.0532872i | \(-0.983030\pi\) |
0.545438 | + | 0.838151i | \(0.316363\pi\) | |||||||
\(104\) | 24.9505 | 2.44660 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43268 | 0.527668 | ||||||||
\(107\) | −6.25526 | + | 10.8344i | −0.604719 | + | 1.04740i | 0.387377 | + | 0.921921i | \(0.373381\pi\) |
−0.992096 | + | 0.125482i | \(0.959952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.52290 | + | 2.63774i | 0.145867 | + | 0.252650i | 0.929696 | − | 0.368327i | \(-0.120069\pi\) |
−0.783829 | + | 0.620977i | \(0.786736\pi\) | |||||||
\(110\) | 0.643996 | − | 1.11543i | 0.0614026 | − | 0.106352i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.8145 | + | 30.0079i | 1.77781 | + | 2.83548i | ||||
\(113\) | 9.95420 | 0.936412 | 0.468206 | − | 0.883619i | \(-0.344900\pi\) | ||||
0.468206 | + | 0.883619i | \(0.344900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | + | 2.59808i | 0.139876 | + | 0.242272i | ||||
\(116\) | −6.67054 | − | 11.5537i | −0.619344 | − | 1.07274i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.1978 | −1.21495 | ||||||||
\(119\) | −15.5371 | + | 0.566231i | −1.42428 | + | 0.0519064i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.45489 | − | 9.44814i | 0.495899 | − | 0.858922i | ||||
\(122\) | −10.2262 | − | 17.7122i | −0.925834 | − | 1.60359i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.7200 | − | 22.0317i | 1.14229 | − | 1.97850i | ||||
\(125\) | 11.8764 | 1.06225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4400 | −1.19260 | −0.596302 | − | 0.802760i | \(-0.703364\pi\) | ||||
−0.596302 | + | 0.802760i | \(0.703364\pi\) | |||||||
\(128\) | −12.4752 | + | 21.6078i | −1.10267 | + | 1.90987i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.02654 | + | 10.4383i | 0.528563 | + | 0.915497i | ||||
\(131\) | −5.63781 | + | 9.76497i | −0.492577 | + | 0.853169i | −0.999963 | − | 0.00854976i | \(-0.997278\pi\) |
0.507386 | + | 0.861719i | \(0.330612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.21565 | − | 5.12874i | −0.278832 | − | 0.444718i | ||||
\(134\) | 1.92216 | 0.166049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26.0803 | − | 45.1724i | −2.23637 | − | 3.87350i | ||||
\(137\) | −1.88874 | − | 3.27139i | −0.161366 | − | 0.279493i | 0.773993 | − | 0.633194i | \(-0.218256\pi\) |
−0.935359 | + | 0.353701i | \(0.884923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7193 | 1.41811 | 0.709056 | − | 0.705152i | \(-0.249121\pi\) | ||||
0.709056 | + | 0.705152i | \(0.249121\pi\) | |||||||
\(140\) | −10.4029 | + | 19.6370i | −0.879205 | + | 1.65963i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.3640 | − | 30.0753i | 1.45715 | − | 2.52386i | ||||
\(143\) | −0.422156 | − | 0.731196i | −0.0353025 | − | 0.0611457i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00364 | − | 3.47041i | 0.166393 | − | 0.288202i | ||||
\(146\) | −31.5178 | −2.60843 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.6749 | −1.94606 | ||||||||
\(149\) | −5.44437 | + | 9.42992i | −0.446020 | + | 0.772529i | −0.998123 | − | 0.0612468i | \(-0.980492\pi\) |
0.552103 | + | 0.833776i | \(0.313826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.04944 | + | 10.4779i | 0.492297 | + | 0.852683i | 0.999961 | − | 0.00887237i | \(-0.00282420\pi\) |
−0.507664 | + | 0.861555i | \(0.669491\pi\) | |||||||
\(152\) | 10.1545 | − | 17.5881i | 0.823640 | − | 1.42659i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00433 | − | 1.89582i | 0.0809313 | − | 0.152770i | ||||
\(155\) | 7.64145 | 0.613776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0945538 | + | 0.163772i | 0.00754622 | + | 0.0130704i | 0.869774 | − | 0.493451i | \(-0.164265\pi\) |
−0.862228 | + | 0.506521i | \(0.830931\pi\) | |||||||
\(158\) | −2.24907 | − | 3.89550i | −0.178926 | − | 0.309910i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.2051 | −2.30886 | ||||||||
\(161\) | 2.65452 | + | 4.23377i | 0.209205 | + | 0.333668i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.47779 | − | 7.75576i | 0.350727 | − | 0.607478i | −0.635650 | − | 0.771978i | \(-0.719268\pi\) |
0.986377 | + | 0.164500i | \(0.0526010\pi\) | |||||||
\(164\) | −23.5574 | − | 40.8026i | −1.83953 | − | 3.18615i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.33310 | − | 12.7013i | 0.569159 | − | 0.985813i | ||||
\(167\) | −4.34108 | −0.335923 | −0.167961 | − | 0.985794i | \(-0.553718\pi\) | ||||
−0.167961 | + | 0.985794i | \(0.553718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.09888 | −0.392222 | ||||||||
\(170\) | 12.5989 | − | 21.8219i | 0.966290 | − | 1.67366i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 24.0574 | + | 41.6687i | 1.83436 | + | 3.17721i | ||||
\(173\) | 3.15019 | − | 5.45628i | 0.239504 | − | 0.414833i | −0.721068 | − | 0.692864i | \(-0.756348\pi\) |
0.960572 | + | 0.278031i | \(0.0896818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.54944 | − | 0.238687i | 0.495091 | − | 0.0180431i | ||||
\(176\) | 4.02104 | 0.303097 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.6254 | + | 21.8679i | 0.946316 | + | 1.63907i | ||||
\(179\) | 6.97091 | + | 12.0740i | 0.521030 | + | 0.902451i | 0.999701 | + | 0.0244564i | \(0.00778548\pi\) |
−0.478671 | + | 0.877995i | \(0.658881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3411 | 1.36328 | 0.681641 | − | 0.731687i | \(-0.261267\pi\) | ||||
0.681641 | + | 0.731687i | \(0.261267\pi\) | |||||||
\(182\) | 10.6650 | + | 17.0100i | 0.790545 | + | 1.26086i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.38255 | + | 14.5190i | −0.617969 | + | 1.07035i | ||||
\(185\) | −3.55563 | − | 6.15854i | −0.261415 | − | 0.452785i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.882546 | + | 1.52861i | −0.0645382 | + | 0.111783i | ||||
\(188\) | −16.9752 | −1.23805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.81089 | 0.711757 | ||||||||
\(191\) | −3.80401 | + | 6.58875i | −0.275249 | + | 0.476745i | −0.970198 | − | 0.242314i | \(-0.922094\pi\) |
0.694949 | + | 0.719059i | \(0.255427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.83310 | − | 6.63913i | −0.275913 | − | 0.477895i | 0.694452 | − | 0.719539i | \(-0.255647\pi\) |
−0.970365 | + | 0.241644i | \(0.922313\pi\) | |||||||
\(194\) | 16.9752 | − | 29.4020i | 1.21875 | − | 2.11094i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.1254 | + | 33.3189i | −1.15182 | + | 2.37992i | ||||
\(197\) | 18.3869 | 1.31001 | 0.655005 | − | 0.755624i | \(-0.272666\pi\) | ||||
0.655005 | + | 0.755624i | \(0.272666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.97710 | − | 5.15649i | −0.211041 | − | 0.365534i | 0.741000 | − | 0.671505i | \(-0.234352\pi\) |
−0.952041 | + | 0.305972i | \(0.901019\pi\) | |||||||
\(200\) | 10.9938 | + | 19.0418i | 0.777380 | + | 1.34646i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −39.4400 | −2.77499 | ||||||||
\(203\) | 3.12474 | − | 5.89841i | 0.219314 | − | 0.413987i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.07598 | − | 12.2560i | 0.494208 | − | 0.855994i | ||||
\(206\) | −12.4153 | − | 21.5039i | −0.865013 | − | 1.49825i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.8145 | + | 32.5877i | −1.30455 | + | 2.25955i | ||||
\(209\) | −0.687248 | −0.0475380 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.67487 | 0.459517 | 0.229758 | − | 0.973248i | \(-0.426206\pi\) | ||||
0.229758 | + | 0.973248i | \(0.426206\pi\) | |||||||
\(212\) | −5.32072 | + | 9.21576i | −0.365429 | + | 0.632941i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.8869 | − | 29.2489i | −1.15436 | − | 1.99942i | ||||
\(215\) | −7.22617 | + | 12.5161i | −0.492821 | + | 0.853591i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.7200 | − | 0.463566i | 0.863489 | − | 0.0314689i | ||||
\(218\) | −8.22253 | −0.556900 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.26145 | + | 2.18490i | 0.0850469 | + | 0.147306i | ||||
\(221\) | −8.25890 | − | 14.3048i | −0.555554 | − | 0.962248i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.34108 | 0.424630 | 0.212315 | − | 0.977201i | \(-0.431900\pi\) | ||||
0.212315 | + | 0.977201i | \(0.431900\pi\) | |||||||
\(224\) | −48.6148 | + | 1.77172i | −3.24821 | + | 0.118378i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.4363 | + | 23.2724i | −0.893771 | + | 1.54806i | ||||
\(227\) | 13.5433 | + | 23.4576i | 0.898897 | + | 1.55694i | 0.828906 | + | 0.559388i | \(0.188964\pi\) |
0.0699913 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.09820 | + | 7.09828i | −0.270816 | + | 0.469068i | −0.969071 | − | 0.246782i | \(-0.920627\pi\) |
0.698255 | + | 0.715849i | \(0.253960\pi\) | |||||||
\(230\) | −8.09888 | −0.534025 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.3942 | 1.47025 | ||||||||
\(233\) | −13.7101 | + | 23.7467i | −0.898182 | + | 1.55570i | −0.0683649 | + | 0.997660i | \(0.521778\pi\) |
−0.829817 | + | 0.558036i | \(0.811555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.54944 | − | 4.41576i | −0.166307 | − | 0.288053i | ||||
\(236\) | 12.9258 | − | 22.3881i | 0.841398 | − | 1.45734i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 19.6483 | − | 37.0891i | 1.27361 | − | 2.40413i | ||||
\(239\) | −27.8640 | −1.80237 | −0.901185 | − | 0.433434i | \(-0.857302\pi\) | ||||
−0.901185 | + | 0.433434i | \(0.857302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2651 | + | 19.5117i | 0.725648 | + | 1.25686i | 0.958707 | + | 0.284397i | \(0.0917934\pi\) |
−0.233058 | + | 0.972463i | \(0.574873\pi\) | |||||||
\(242\) | 14.7262 | + | 25.5065i | 0.946634 | + | 1.63962i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 40.0617 | 2.56469 | ||||||||
\(245\) | −11.0891 | + | 0.809332i | −0.708454 | + | 0.0517063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.21565 | − | 5.56967i | 0.204607 | − | 0.354390i | ||||
\(248\) | 21.3516 | + | 36.9821i | 1.35583 | + | 2.34836i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.0309 | + | 27.7663i | −1.01388 | + | 1.75609i | ||||
\(251\) | 31.2509 | 1.97254 | 0.986268 | − | 0.165152i | \(-0.0528114\pi\) | ||||
0.986268 | + | 0.165152i | \(0.0528114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.567323 | 0.0356673 | ||||||||
\(254\) | 18.1414 | − | 31.4219i | 1.13830 | − | 1.97159i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.8145 | − | 18.7313i | −0.675908 | − | 1.17071i | ||||
\(257\) | 5.10074 | − | 8.83475i | 0.318176 | − | 0.551096i | −0.661932 | − | 0.749564i | \(-0.730263\pi\) |
0.980107 | + | 0.198468i | \(0.0635965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.29232 | − | 10.0358i | −0.390986 | − | 0.623595i | ||||
\(260\) | −23.6094 | −1.46419 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.2200 | − | 26.3618i | −0.940294 | − | 1.62864i | ||||
\(263\) | −14.2305 | − | 24.6480i | −0.877490 | − | 1.51986i | −0.854086 | − | 0.520132i | \(-0.825883\pi\) |
−0.0234042 | − | 0.999726i | \(-0.507450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.19639 | −0.196353 | ||||||||
\(266\) | 16.3312 | − | 0.595175i | 1.00133 | − | 0.0364925i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.88255 | + | 3.26067i | −0.114995 | + | 0.199177i | ||||
\(269\) | −7.43818 | − | 12.8833i | −0.453514 | − | 0.785509i | 0.545088 | − | 0.838379i | \(-0.316496\pi\) |
−0.998601 | + | 0.0528702i | \(0.983163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0222115 | + | 0.0384714i | −0.00134925 | + | 0.00233697i | −0.866699 | − | 0.498831i | \(-0.833763\pi\) |
0.865350 | + | 0.501168i | \(0.167096\pi\) | |||||||
\(272\) | 78.6661 | 4.76983 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1978 | 0.616070 | ||||||||
\(275\) | 0.372026 | − | 0.644367i | 0.0224340 | − | 0.0388568i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.83743 | − | 13.5748i | −0.470906 | − | 0.815633i | 0.528540 | − | 0.848908i | \(-0.322739\pi\) |
−0.999446 | + | 0.0332754i | \(0.989406\pi\) | |||||||
\(278\) | −22.5679 | + | 39.0888i | −1.35353 | + | 2.34439i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.8152 | − | 31.6039i | −1.18419 | − | 1.88869i | ||||
\(281\) | 11.9098 | 0.710478 | 0.355239 | − | 0.934776i | \(-0.384400\pi\) | ||||
0.355239 | + | 0.934776i | \(0.384400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00364 | − | 5.20246i | −0.178548 | − | 0.309254i | 0.762835 | − | 0.646593i | \(-0.223807\pi\) |
−0.941383 | + | 0.337339i | \(0.890473\pi\) | |||||||
\(284\) | 34.0123 | + | 58.9110i | 2.01826 | + | 3.49573i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27933 | 0.134780 | ||||||||
\(287\) | 11.0352 | − | 20.8306i | 0.651387 | − | 1.22959i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.76578 | + | 15.1828i | −0.515634 | + | 0.893105i | ||||
\(290\) | 5.40909 | + | 9.36882i | 0.317633 | + | 0.550156i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.8683 | − | 53.4655i | 1.80643 | − | 3.12883i | ||||
\(293\) | −4.95558 | −0.289508 | −0.144754 | − | 0.989468i | \(-0.546239\pi\) | ||||
−0.144754 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.76509 | 0.452101 | ||||||||
\(296\) | 19.8702 | − | 34.4161i | 1.15493 | − | 2.00040i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.6978 | − | 25.4573i | −0.851419 | − | 1.47470i | ||||
\(299\) | −2.65452 | + | 4.59776i | −0.153515 | + | 0.265895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2694 | + | 21.2727i | −0.649559 | + | 1.22614i | ||||
\(302\) | −32.6625 | −1.87952 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.3145 | + | 26.5256i | 0.878349 | + | 1.52134i | ||||
\(305\) | 6.01671 | + | 10.4212i | 0.344516 | + | 0.596719i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0531 | −1.25864 | −0.629318 | − | 0.777148i | \(-0.716666\pi\) | ||||
−0.629318 | + | 0.777148i | \(0.716666\pi\) | |||||||
\(308\) | 2.23236 | + | 3.56046i | 0.127201 | + | 0.202876i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.3145 | + | 17.8653i | −0.585826 | + | 1.01468i | ||||
\(311\) | −3.98762 | − | 6.90676i | −0.226117 | − | 0.391646i | 0.730537 | − | 0.682873i | \(-0.239270\pi\) |
−0.956654 | + | 0.291227i | \(0.905937\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2651 | − | 19.5117i | 0.636741 | − | 1.10287i | −0.349403 | − | 0.936973i | \(-0.613616\pi\) |
0.986143 | − | 0.165895i | \(-0.0530511\pi\) | |||||||
\(314\) | −0.510520 | −0.0288103 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.81089 | 0.495651 | ||||||||
\(317\) | 9.96905 | − | 17.2669i | 0.559918 | − | 0.969806i | −0.437585 | − | 0.899177i | \(-0.644166\pi\) |
0.997503 | − | 0.0706288i | \(-0.0225006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.378904 | − | 0.656281i | −0.0212146 | − | 0.0367447i | ||||
\(320\) | 18.1582 | − | 31.4509i | 1.01507 | − | 1.75816i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.4814 | + | 0.491316i | −0.751291 | + | 0.0273800i | ||||
\(323\) | −13.4451 | −0.748103 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.48143 | + | 6.03001i | 0.193115 | + | 0.334485i | ||||
\(326\) | 12.0884 | + | 20.9377i | 0.669513 | + | 1.15963i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 79.0864 | 4.36681 | ||||||||
\(329\) | −4.51169 | − | 7.19583i | −0.248738 | − | 0.396719i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8152 | + | 20.4646i | −0.649423 | + | 1.12483i | 0.333837 | + | 0.942631i | \(0.391656\pi\) |
−0.983261 | + | 0.182204i | \(0.941677\pi\) | |||||||
\(332\) | 14.3640 | + | 24.8791i | 0.788326 | + | 1.36542i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.85965 | − | 10.1492i | 0.320626 | − | 0.555340i | ||||
\(335\) | −1.13093 | −0.0617892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3855 | −0.674681 | −0.337341 | − | 0.941383i | \(-0.609527\pi\) | ||||
−0.337341 | + | 0.941383i | \(0.609527\pi\) | |||||||
\(338\) | 6.88255 | − | 11.9209i | 0.374361 | − | 0.648413i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 24.6785 | + | 42.7444i | 1.33838 | + | 2.31814i | ||||
\(341\) | 0.722528 | − | 1.25146i | 0.0391271 | − | 0.0677701i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4098 | + | 2.01993i | −0.994035 | + | 0.109066i | ||||
\(344\) | −80.7649 | −4.35455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.50433 | + | 14.7299i | 0.457196 | + | 0.791886i | ||||
\(347\) | 1.92216 | + | 3.32927i | 0.103187 | + | 0.178725i | 0.912996 | − | 0.407969i | \(-0.133763\pi\) |
−0.809809 | + | 0.586693i | \(0.800429\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.1891 | −0.652468 | −0.326234 | − | 0.945289i | \(-0.605780\pi\) | ||||
−0.326234 | + | 0.945289i | \(0.605780\pi\) | |||||||
\(350\) | −8.28249 | + | 15.6344i | −0.442718 | + | 0.835695i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.76145 | + | 4.78297i | −0.147186 | + | 0.254933i | ||||
\(353\) | 1.78180 | + | 3.08617i | 0.0948358 | + | 0.164260i | 0.909540 | − | 0.415616i | \(-0.136434\pi\) |
−0.814704 | + | 0.579877i | \(0.803101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2163 | + | 17.6952i | −0.542227 | + | 0.939165i | ||||
\(356\) | −49.4610 | −2.62143 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −37.6377 | −1.98922 | ||||||||
\(359\) | 0.483978 | − | 0.838275i | 0.0255434 | − | 0.0442425i | −0.852971 | − | 0.521958i | \(-0.825202\pi\) |
0.878515 | + | 0.477716i | \(0.158535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.88255 | + | 11.9209i | 0.362239 | + | 0.627417i | ||||
\(362\) | −24.7570 | + | 42.8805i | −1.30120 | + | 2.25375i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −39.3003 | + | 1.43226i | −2.05990 | + | 0.0750707i | ||||
\(365\) | 18.5439 | 0.970634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4771 | − | 18.1469i | −0.546900 | − | 0.947259i | −0.998485 | − | 0.0550305i | \(-0.982474\pi\) |
0.451585 | − | 0.892228i | \(-0.350859\pi\) | |||||||
\(368\) | −12.6421 | − | 21.8968i | −0.659017 | − | 1.14145i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.1978 | 0.998044 | ||||||||
\(371\) | −5.32072 | + | 0.193908i | −0.276238 | + | 0.0100672i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | + | 1.73205i | −0.0517780 | + | 0.0896822i | −0.890753 | − | 0.454488i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183156\pi\) | |||||||
\(374\) | −2.38255 | − | 4.12669i | −0.123199 | − | 0.213386i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.2472 | − | 24.6769i | 0.734744 | − | 1.27261i | ||||
\(377\) | 7.09160 | 0.365236 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.14331 | −0.366927 | −0.183464 | − | 0.983027i | \(-0.558731\pi\) | ||||
−0.183464 | + | 0.983027i | \(0.558731\pi\) | |||||||
\(380\) | −9.60872 | + | 16.6428i | −0.492917 | + | 0.853757i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.2694 | − | 17.7872i | −0.525429 | − | 0.910070i | ||||
\(383\) | 5.98831 | − | 10.3721i | 0.305988 | − | 0.529987i | −0.671493 | − | 0.741011i | \(-0.734346\pi\) |
0.977481 | + | 0.211024i | \(0.0676798\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.590912 | + | 1.11543i | −0.0301157 | + | 0.0568478i | ||||
\(386\) | 20.6959 | 1.05339 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.2509 | + | 57.5922i | 1.68806 | + | 2.92380i | ||||
\(389\) | −6.88942 | − | 11.9328i | −0.349308 | − | 0.605019i | 0.636819 | − | 0.771013i | \(-0.280250\pi\) |
−0.986127 | + | 0.165995i | \(0.946917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0989 | 0.561295 | ||||||||
\(392\) | −34.9017 | − | 51.4059i | −1.76280 | − | 2.59639i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.8189 | + | 42.9875i | −1.25036 | + | 2.16568i | ||||
\(395\) | 1.32327 | + | 2.29197i | 0.0665810 | + | 0.115322i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.19344 | + | 7.26325i | −0.210463 | + | 0.364532i | −0.951859 | − | 0.306535i | \(-0.900830\pi\) |
0.741397 | + | 0.671067i | \(0.234164\pi\) | |||||||
\(398\) | 16.0741 | 0.805723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33.1606 | −1.65803 | ||||||||
\(401\) | −13.8083 | + | 23.9168i | −0.689556 | + | 1.19435i | 0.282426 | + | 0.959289i | \(0.408861\pi\) |
−0.971982 | + | 0.235057i | \(0.924472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.76145 | + | 11.7112i | 0.336812 | + | 0.583375i | ||||
\(404\) | 38.6272 | − | 66.9043i | 1.92178 | − | 3.32861i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.57234 | + | 15.2672i | 0.475067 | + | 0.757699i | ||||
\(407\) | −1.34479 | −0.0666590 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2658 | − | 26.4411i | −0.754844 | − | 1.30743i | −0.945452 | − | 0.325762i | \(-0.894379\pi\) |
0.190607 | − | 0.981666i | \(-0.438954\pi\) | |||||||
\(410\) | 19.1025 | + | 33.0865i | 0.943407 | + | 1.63403i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 48.6377 | 2.39621 | ||||||||
\(413\) | 12.9258 | − | 0.471067i | 0.636037 | − | 0.0231797i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.31453 | + | 7.47299i | −0.211792 | + | 0.366835i | ||||
\(416\) | −25.8418 | − | 44.7592i | −1.26700 | − | 2.19450i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.927658 | − | 1.60675i | 0.0453732 | − | 0.0785887i | ||||
\(419\) | 21.0000 | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.7293 | 1.69260 | 0.846302 | − | 0.532703i | \(-0.178824\pi\) | ||||
0.846302 | + | 0.532703i | \(0.178824\pi\) | |||||||
\(422\) | −9.00983 | + | 15.6055i | −0.438592 | + | 0.759663i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.93130 | − | 15.4695i | −0.433742 | − | 0.751264i | ||||
\(425\) | 7.27816 | − | 12.6061i | 0.353043 | − | 0.611488i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6476 | + | 16.9822i | 0.515275 | + | 0.821828i | ||||
\(428\) | 66.1555 | 3.19775 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.5080 | − | 33.7888i | −0.940758 | − | 1.62944i | ||||
\(431\) | −15.8022 | − | 27.3701i | −0.761163 | − | 1.31837i | −0.942251 | − | 0.334906i | \(-0.891295\pi\) |
0.181088 | − | 0.983467i | \(-0.442038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.48576 | −0.311686 | −0.155843 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155843 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(434\) | −16.0858 | + | 30.3644i | −0.772144 | + | 1.45754i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.05308 | − | 13.9484i | 0.385673 | − | 0.668005i | ||||
\(437\) | 2.16071 | + | 3.74245i | 0.103361 | + | 0.179026i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.78799 | − | 13.4892i | 0.371701 | − | 0.643804i | −0.618127 | − | 0.786078i | \(-0.712108\pi\) |
0.989827 | + | 0.142274i | \(0.0454415\pi\) | |||||||
\(440\) | −4.23491 | −0.201891 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 44.5919 | 2.12102 | ||||||||
\(443\) | 12.5371 | − | 21.7148i | 0.595654 | − | 1.03170i | −0.397800 | − | 0.917472i | \(-0.630226\pi\) |
0.993454 | − | 0.114231i | \(-0.0364403\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.42835 | − | 12.8663i | −0.352137 | − | 0.609920i | ||||
\(446\) | −8.55927 | + | 14.8251i | −0.405293 | + | 0.701989i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.3182 | − | 53.4548i | 1.33791 | − | 2.52550i | ||||
\(449\) | −15.2967 | −0.721894 | −0.360947 | − | 0.932586i | \(-0.617546\pi\) | ||||
−0.360947 | + | 0.932586i | \(0.617546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33812 | − | 2.31770i | −0.0630098 | − | 0.109136i | ||||
\(452\) | −26.3189 | − | 45.5856i | −1.23794 | − | 2.14417i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −73.1235 | −3.43186 | ||||||||
\(455\) | −6.27492 | − | 10.0081i | −0.294173 | − | 0.469185i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2200 | + | 17.7015i | −0.478071 | + | 0.828042i | −0.999684 | − | 0.0251395i | \(-0.991997\pi\) |
0.521613 | + | 0.853182i | \(0.325330\pi\) | |||||||
\(458\) | −11.0636 | − | 19.1627i | −0.516968 | − | 0.895415i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.93199 | − | 13.7386i | 0.369831 | − | 0.640566i | ||||
\(461\) | −40.8182 | −1.90109 | −0.950546 | − | 0.310584i | \(-0.899475\pi\) | ||||
−0.950546 | + | 0.310584i | \(0.899475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.90840 | 0.460482 | 0.230241 | − | 0.973134i | \(-0.426048\pi\) | ||||
0.230241 | + | 0.973134i | \(0.426048\pi\) | |||||||
\(464\) | −16.8869 | + | 29.2489i | −0.783954 | + | 1.35785i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −37.0123 | − | 64.1072i | −1.71456 | − | 2.96971i | ||||
\(467\) | 8.86948 | − | 15.3624i | 0.410430 | − | 0.710886i | −0.584506 | − | 0.811389i | \(-0.698712\pi\) |
0.994937 | + | 0.100503i | \(0.0320451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.88255 | + | 0.0686074i | −0.0869279 | + | 0.00316799i | ||||
\(470\) | 13.7651 | 0.634936 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.6971 | + | 37.5804i | 0.998689 | + | 1.72978i | ||||
\(473\) | 1.36652 | + | 2.36689i | 0.0628329 | + | 0.108830i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.66758 | 0.260047 | ||||||||
\(476\) | 43.6730 | + | 69.6554i | 2.00175 | + | 3.19265i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 37.6112 | − | 65.1445i | 1.72030 | − | 2.97964i | ||||
\(479\) | 11.8047 | + | 20.4463i | 0.539371 | + | 0.934217i | 0.998938 | + | 0.0460744i | \(0.0146711\pi\) |
−0.459567 | + | 0.888143i | \(0.651996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.29232 | − | 10.8986i | 0.286905 | − | 0.496934i | ||||
\(482\) | −60.8231 | −2.77042 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −57.6908 | −2.62231 | ||||||||
\(485\) | −9.98762 | + | 17.2991i | −0.453514 | + | 0.785510i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.4363 | − | 30.2006i | −0.790115 | − | 1.36852i | −0.925895 | − | 0.377780i | \(-0.876687\pi\) |
0.135780 | − | 0.990739i | \(-0.456646\pi\) | |||||||
\(488\) | −33.6236 | + | 58.2377i | −1.52207 | + | 2.63630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.0760 | − | 27.0181i | 0.590713 | − | 1.22055i | ||||
\(491\) | 23.2051 | 1.04723 | 0.523615 | − | 0.851955i | \(-0.324583\pi\) | ||||
0.523615 | + | 0.851955i | \(0.324583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.41273 | − | 12.8392i | −0.333853 | − | 0.578250i | ||||
\(494\) | 8.68106 | + | 15.0360i | 0.390579 | + | 0.676503i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −64.4028 | −2.89177 | ||||||||
\(497\) | −15.9327 | + | 30.0753i | −0.714678 | + | 1.34906i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.66257 | − | 4.61170i | 0.119193 | − | 0.206448i | −0.800255 | − | 0.599660i | \(-0.795303\pi\) |
0.919448 | + | 0.393212i | \(0.128636\pi\) | |||||||
\(500\) | −31.4010 | − | 54.3882i | −1.40430 | − | 2.43231i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −42.1828 | + | 73.0628i | −1.88271 | + | 3.26095i | ||||
\(503\) | −10.4313 | −0.465109 | −0.232554 | − | 0.972583i | \(-0.574708\pi\) | ||||
−0.232554 | + | 0.972583i | \(0.574708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.2051 | 1.03261 | ||||||||
\(506\) | −0.765781 | + | 1.32637i | −0.0340431 | + | 0.0589644i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 35.5352 | + | 61.5488i | 1.57662 | + | 2.73079i | ||||
\(509\) | −0.750930 | + | 1.30065i | −0.0332844 | + | 0.0576502i | −0.882188 | − | 0.470898i | \(-0.843930\pi\) |
0.848903 | + | 0.528548i | \(0.177263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.8683 | − | 1.12496i | 1.36553 | − | 0.0497654i | ||||
\(512\) | 8.48948 | 0.375186 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.7701 | + | 23.8505i | 0.607374 | + | 1.05200i | ||||
\(515\) | 7.30470 | + | 12.6521i | 0.321884 | + | 0.557519i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.964238 | −0.0424072 | ||||||||
\(518\) | 31.9567 | − | 1.16463i | 1.40410 | − | 0.0511707i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.8152 | − | 34.3210i | 0.868955 | − | 1.50507i | ||||
\(521\) | −18.8709 | − | 32.6853i | −0.826747 | − | 1.43197i | −0.900577 | − | 0.434697i | \(-0.856855\pi\) |
0.0738295 | − | 0.997271i | \(-0.476478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.97779 | − | 15.5500i | 0.392571 | − | 0.679953i | −0.600217 | − | 0.799837i | \(-0.704919\pi\) |
0.992788 | + | 0.119884i | \(0.0382523\pi\) | |||||||
\(524\) | 59.6253 | 2.60475 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 76.8341 | 3.35013 | ||||||||
\(527\) | 14.1353 | − | 24.4830i | 0.615742 | − | 1.06650i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.71634 | + | 16.8292i | 0.422449 | + | 0.731704i | ||||
\(530\) | 4.31453 | − | 7.47299i | 0.187411 | − | 0.324606i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9851 | + | 28.2865i | −0.649685 | + | 1.22638i | ||||
\(533\) | 25.0444 | 1.08479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.93563 | + | 17.2090i | 0.429555 | + | 0.744011i | ||||
\(536\) | −3.16002 | − | 5.47331i | −0.136492 | − | 0.236411i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.1606 | 1.73145 | ||||||||
\(539\) | −0.915967 | + | 1.89260i | −0.0394535 | + | 0.0815202i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.18547 | + | 7.24944i | −0.179947 | + | 0.311678i | −0.941862 | − | 0.335999i | \(-0.890926\pi\) |
0.761915 | + | 0.647677i | \(0.224259\pi\) | |||||||
\(542\) | −0.0599627 | − | 0.103858i | −0.00257562 | − | 0.00446110i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −54.0239 | + | 93.5722i | −2.31626 | + | 4.01187i | ||||
\(545\) | 4.83784 | 0.207230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1075 | 1.28731 | 0.643653 | − | 0.765318i | \(-0.277418\pi\) | ||||
0.643653 | + | 0.765318i | \(0.277418\pi\) | |||||||
\(548\) | −9.98762 | + | 17.2991i | −0.426650 | + | 0.738979i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00433 | + | 1.73955i | 0.0428248 | + | 0.0741747i | ||||
\(551\) | 2.88619 | − | 4.99902i | 0.122956 | − | 0.212966i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.34176 | + | 3.73495i | 0.0995820 | + | 0.158826i | ||||
\(554\) | 42.3163 | 1.79785 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −44.2057 | − | 76.5666i | −1.87474 | − | 3.24715i | ||||
\(557\) | −8.26764 | − | 14.3200i | −0.350311 | − | 0.606757i | 0.635993 | − | 0.771695i | \(-0.280591\pi\) |
−0.986304 | + | 0.164938i | \(0.947257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5760 | −1.08175 | ||||||||
\(560\) | 56.2199 | − | 2.04887i | 2.37572 | − | 0.0865807i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.0760 | + | 27.8444i | −0.678124 | + | 1.17455i | ||||
\(563\) | 11.1156 | + | 19.2528i | 0.468466 | + | 0.811408i | 0.999350 | − | 0.0360368i | \(-0.0114733\pi\) |
−0.530884 | + | 0.847444i | \(0.678140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.90545 | − | 13.6926i | 0.332585 | − | 0.576053i | ||||
\(566\) | 16.2174 | 0.681670 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −114.185 | −4.79111 | ||||||||
\(569\) | −1.15638 | + | 2.00290i | −0.0484778 | + | 0.0839660i | −0.889246 | − | 0.457429i | \(-0.848770\pi\) |
0.840768 | + | 0.541395i | \(0.182104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.04944 | + | 5.28179i | 0.127615 | + | 0.221036i | 0.922752 | − | 0.385394i | \(-0.125934\pi\) |
−0.795137 | + | 0.606430i | \(0.792601\pi\) | |||||||
\(572\) | −2.23236 | + | 3.86656i | −0.0933397 | + | 0.161669i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 33.8053 | + | 53.9171i | 1.41101 | + | 2.25046i | ||||
\(575\) | −4.67859 | −0.195111 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1032 | − | 17.4993i | −0.420602 | − | 0.728505i | 0.575396 | − | 0.817875i | \(-0.304848\pi\) |
−0.995998 | + | 0.0893702i | \(0.971515\pi\) | |||||||
\(578\) | −23.6643 | − | 40.9879i | −0.984307 | − | 1.70487i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.1905 | −0.879887 | ||||||||
\(581\) | −6.72864 | + | 12.7013i | −0.279151 | + | 0.526939i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.302231 | + | 0.523480i | −0.0125171 | + | 0.0216803i | ||||
\(584\) | 51.8151 | + | 89.7465i | 2.14413 | + | 3.71374i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.68911 | − | 11.5859i | 0.276324 | − | 0.478608i | ||||
\(587\) | 38.6822 | 1.59658 | 0.798292 | − | 0.602271i | \(-0.205737\pi\) | ||||
0.798292 | + | 0.602271i | \(0.205737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.0073 | 0.453547 | ||||||||
\(590\) | −10.4814 | + | 18.1544i | −0.431514 | + | 0.747404i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 29.9672 | + | 51.9047i | 1.23164 | + | 2.13327i | ||||
\(593\) | −11.8578 | + | 20.5383i | −0.486941 | + | 0.843406i | −0.999887 | − | 0.0150142i | \(-0.995221\pi\) |
0.512946 | + | 0.858421i | \(0.328554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.5604 | + | 21.8219i | −0.473929 | + | 0.894611i | ||||
\(596\) | 57.5795 | 2.35855 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.16621 | − | 12.4122i | −0.293048 | − | 0.507574i | ||||
\(599\) | 17.2403 | + | 29.8611i | 0.704421 | + | 1.22009i | 0.966900 | + | 0.255155i | \(0.0821265\pi\) |
−0.262479 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.28071 | −0.296986 | −0.148493 | − | 0.988913i | \(-0.547442\pi\) | ||||
−0.148493 | + | 0.988913i | \(0.547442\pi\) | |||||||
\(602\) | −34.5228 | − | 55.0615i | −1.40705 | − | 2.24414i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 31.9894 | − | 55.4073i | 1.30163 | − | 2.25449i | ||||
\(605\) | −8.66435 | − | 15.0071i | −0.352256 | − | 0.610125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5796 | − | 21.7886i | 0.510591 | − | 0.884370i | −0.489333 | − | 0.872097i | \(-0.662760\pi\) |
0.999925 | − | 0.0122732i | \(-0.00390679\pi\) | |||||||
\(608\) | −42.0690 | −1.70612 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.4858 | −1.31531 | ||||||||
\(611\) | 4.51169 | − | 7.81448i | 0.182523 | − | 0.316140i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7731 | + | 32.5159i | 0.758237 | + | 1.31330i | 0.943749 | + | 0.330663i | \(0.107272\pi\) |
−0.185512 | + | 0.982642i | \(0.559394\pi\) | |||||||
\(614\) | 29.7676 | − | 51.5589i | 1.20132 | − | 2.08075i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.04944 | + | 0.256909i | −0.284030 | + | 0.0103512i | ||||
\(617\) | −13.7280 | −0.552667 | −0.276333 | − | 0.961062i | \(-0.589119\pi\) | ||||
−0.276333 | + | 0.961062i | \(0.589119\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.90545 | − | 10.2285i | −0.237360 | − | 0.411119i | 0.722596 | − | 0.691271i | \(-0.242949\pi\) |
−0.959956 | + | 0.280151i | \(0.909615\pi\) | |||||||
\(620\) | −20.2040 | − | 34.9943i | −0.811411 | − | 1.40540i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.5302 | 0.863282 | ||||||||
\(623\) | −13.1458 | − | 20.9666i | −0.526675 | − | 0.840009i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.23924 | − | 5.61053i | 0.129570 | − | 0.224421i | ||||
\(626\) | 30.4116 | + | 52.6744i | 1.21549 | + | 2.10529i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.500000 | − | 0.866025i | 0.0199522 | − | 0.0345582i | ||||
\(629\) | −26.3090 | −1.04901 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6304 | 1.17957 | 0.589785 | − | 0.807561i | \(-0.299213\pi\) | ||||
0.589785 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(632\) | −7.39493 | + | 12.8084i | −0.294154 | + | 0.509490i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.9127 | + | 46.6142i | 1.06884 | + | 1.85129i | ||||
\(635\) | −10.6738 | + | 18.4875i | −0.423576 | + | 0.733655i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0524 | − | 16.2788i | −0.437912 | − | 0.644989i | ||||
\(638\) | 2.04580 | 0.0809940 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.8152 | + | 34.3210i | 0.783265 | + | 1.35666i | ||||
\(641\) | 7.32623 | + | 12.6894i | 0.289368 | + | 0.501201i | 0.973659 | − | 0.228008i | \(-0.0732214\pi\) |
−0.684291 | + | 0.729209i | \(0.739888\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.03714 | 0.0803369 | 0.0401685 | − | 0.999193i | \(-0.487211\pi\) | ||||
0.0401685 | + | 0.999193i | \(0.487211\pi\) | |||||||
\(644\) | 12.3702 | − | 23.3505i | 0.487453 | − | 0.920139i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.1483 | − | 31.4338i | 0.714036 | − | 1.23675i | ||||
\(647\) | −5.89307 | − | 10.2071i | −0.231680 | − | 0.401282i | 0.726622 | − | 0.687037i | \(-0.241089\pi\) |
−0.958303 | + | 0.285755i | \(0.907756\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.734219 | − | 1.27171i | 0.0288206 | − | 0.0499188i | ||||
\(650\) | −18.7971 | −0.737284 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −47.3570 | −1.85464 | ||||||||
\(653\) | −17.0920 | + | 29.6042i | −0.668862 | + | 1.15850i | 0.309361 | + | 0.950945i | \(0.399885\pi\) |
−0.978223 | + | 0.207558i | \(0.933448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.95489 | + | 15.5103i | 0.349896 | + | 0.606038i | ||||
\(656\) | −59.6370 | + | 103.294i | −2.32844 | + | 4.03297i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.9134 | − | 0.835055i | 0.893258 | − | 0.0325538i | ||||
\(659\) | −24.8640 | −0.968563 | −0.484282 | − | 0.874912i | \(-0.660919\pi\) | ||||
−0.484282 | + | 0.874912i | \(0.660919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.7694 | − | 22.1173i | −0.496673 | − | 0.860263i | 0.503320 | − | 0.864100i | \(-0.332112\pi\) |
−0.999993 | + | 0.00383747i | \(0.998778\pi\) | |||||||
\(662\) | −31.8967 | − | 55.2467i | −1.23970 | − | 2.14722i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −48.2224 | −1.87139 | ||||||||
\(665\) | −9.60872 | + | 0.350179i | −0.372610 | + | 0.0135794i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.38255 | + | 4.12669i | −0.0922525 | + | 0.159786i | ||||
\(668\) | 11.4778 | + | 19.8801i | 0.444089 | + | 0.769185i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.52654 | − | 2.64405i | 0.0589755 | − | 0.102149i | ||||
\(671\) | 2.27561 | 0.0878490 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.81955 | −0.147233 | −0.0736165 | − | 0.997287i | \(-0.523454\pi\) | ||||
−0.0736165 | + | 0.997287i | \(0.523454\pi\) | |||||||
\(674\) | 16.7181 | − | 28.9566i | 0.643958 | − | 1.11537i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.4814 | + | 23.3505i | 0.518517 | + | 0.898097i | ||||
\(677\) | −8.61126 | + | 14.9151i | −0.330958 | + | 0.573236i | −0.982700 | − | 0.185205i | \(-0.940705\pi\) |
0.651742 | + | 0.758441i | \(0.274038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.5760 | + | 29.4020i | −0.597751 | + | 1.12834i | ||||
\(680\) | −82.8501 | −3.17715 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.95056 | + | 3.37847i | 0.0746907 | + | 0.129368i | ||||
\(683\) | 16.8585 | + | 29.1997i | 0.645072 | + | 1.11730i | 0.984285 | + | 0.176587i | \(0.0565058\pi\) |
−0.339213 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 20.1273 | − | 45.7676i | 0.768463 | − | 1.74742i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 60.9028 | − | 105.487i | 2.32190 | − | 4.02165i | ||||
\(689\) | −2.82829 | − | 4.89874i | −0.107749 | − | 0.186627i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7465 | − | 22.0776i | 0.484901 | − | 0.839872i | −0.514949 | − | 0.857221i | \(-0.672189\pi\) |
0.999850 | + | 0.0173484i | \(0.00552246\pi\) | |||||||
\(692\) | −33.3163 | −1.26650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.3782 | −0.393952 | ||||||||
\(695\) | 13.2782 | − | 22.9984i | 0.503669 | − | 0.872381i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.1785 | − | 45.3425i | −0.991582 | − | 1.71747i | ||||
\(698\) | 16.4530 | − | 28.4975i | 0.622756 | − | 1.07865i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.4098 | − | 29.3623i | −0.695824 | − | 1.10979i | ||||
\(701\) | −10.1606 | −0.383762 | −0.191881 | − | 0.981418i | \(-0.561459\pi\) | ||||
−0.191881 | + | 0.981418i | \(0.561459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.12178 | − | 8.87119i | −0.193172 | − | 0.334583i | ||||
\(704\) | −3.43385 | − | 5.94760i | −0.129418 | − | 0.224159i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.62041 | −0.362069 | ||||||||
\(707\) | 38.6272 | − | 1.40773i | 1.45273 | − | 0.0529430i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.97346 | − | 13.8104i | 0.299449 | − | 0.518662i | −0.676561 | − | 0.736387i | \(-0.736530\pi\) |
0.976010 | + | 0.217725i | \(0.0698637\pi\) | |||||||
\(710\) | −27.5803 | − | 47.7705i | −1.03507 | − | 1.79280i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.5123 | − | 71.9014i | 1.55574 | − | 2.69462i | ||||
\(713\) | −9.08650 | −0.340292 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.34108 | −0.0501534 | ||||||||
\(716\) | 36.8621 | − | 63.8471i | 1.37760 | − | 2.38608i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.30656 | + | 2.26303i | 0.0487604 | + | 0.0844556i | ||||
\(719\) | −8.20877 | + | 14.2180i | −0.306136 | + | 0.530242i | −0.977513 | − | 0.210873i | \(-0.932369\pi\) |
0.671378 | + | 0.741115i | \(0.265703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9270 | + | 20.6176i | 0.481425 | + | 0.767840i | ||||
\(722\) | −37.1606 | −1.38298 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −48.4937 | − | 83.9936i | −1.80226 | − | 3.12160i | ||||
\(725\) | 3.12474 | + | 5.41220i | 0.116050 | + | 0.201004i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.8282 | −1.32879 | −0.664397 | − | 0.747379i | \(-0.731312\pi\) | ||||
−0.664397 | + | 0.747379i | \(0.731312\pi\) | |||||||
\(728\) | 30.9024 | − | 58.3329i | 1.14532 | − | 2.16196i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.0309 | + | 43.3547i | −0.926434 | + | 1.60463i | ||||
\(731\) | 26.7341 | + | 46.3049i | 0.988798 | + | 1.71265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6440 | + | 34.0244i | −0.725568 | + | 1.25672i | 0.233172 | + | 0.972435i | \(0.425089\pi\) |
−0.958740 | + | 0.284284i | \(0.908244\pi\) | |||||||
\(734\) | 56.5685 | 2.08798 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.7280 | 1.28009 | ||||||||
\(737\) | −0.106934 | + | 0.185214i | −0.00393895 | + | 0.00682246i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.04511 | − | 1.81019i | −0.0384451 | − | 0.0665888i | 0.846163 | − | 0.532925i | \(-0.178907\pi\) |
−0.884608 | + | 0.466336i | \(0.845574\pi\) | |||||||
\(740\) | −18.8022 | + | 32.5663i | −0.691181 | + | 1.19716i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.72864 | − | 12.7013i | 0.247016 | − | 0.466280i | ||||
\(743\) | −30.7266 | −1.12725 | −0.563624 | − | 0.826031i | \(-0.690593\pi\) | ||||
−0.563624 | + | 0.826031i | \(0.690593\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.64764 | + | 14.9781i | 0.316825 | + | 0.548757i | ||||
\(746\) | −2.69963 | − | 4.67589i | −0.0988404 | − | 0.171197i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.33379 | 0.341277 | ||||||||
\(749\) | 17.5829 | + | 28.0434i | 0.642464 | + | 1.02469i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3869 | + | 17.9906i | −0.379023 | + | 0.656486i | −0.990920 | − | 0.134451i | \(-0.957073\pi\) |
0.611898 | + | 0.790937i | \(0.290406\pi\) | |||||||
\(752\) | 21.4869 | + | 37.2165i | 0.783548 | + | 1.35714i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.57234 | + | 16.5798i | −0.348604 | + | 0.603800i | ||||
\(755\) | 19.2174 | 0.699394 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9257 | 0.615176 | 0.307588 | − | 0.951520i | \(-0.400478\pi\) | ||||
0.307588 | + | 0.951520i | \(0.400478\pi\) | |||||||
\(758\) | 9.64214 | − | 16.7007i | 0.350218 | − | 0.606596i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.1291 | − | 27.9364i | −0.585063 | − | 1.01336i | ||||
\(761\) | 16.4196 | − | 28.4396i | 0.595210 | − | 1.03093i | −0.398307 | − | 0.917252i | \(-0.630402\pi\) |
0.993517 | − | 0.113682i | \(-0.0362646\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.05308 | − | 0.293486i | 0.291541 | − | 0.0106249i | ||||
\(764\) | 40.2312 | 1.45551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.1662 | + | 28.0007i | 0.584109 | + | 1.01171i | ||||
\(767\) | 6.87085 | + | 11.9007i | 0.248092 | + | 0.429708i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7293 | 1.14419 | 0.572094 | − | 0.820188i | \(-0.306131\pi\) | ||||
0.572094 | + | 0.820188i | \(0.306131\pi\) | |||||||
\(770\) | −1.81020 | − | 2.88715i | −0.0652352 | − | 0.104046i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.2694 | + | 35.1077i | −0.729512 | + | 1.26355i | ||||
\(773\) | 3.18656 | + | 5.51928i | 0.114613 | + | 0.198515i | 0.917625 | − | 0.397448i | \(-0.130104\pi\) |
−0.803012 | + | 0.595963i | \(0.796771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.95853 | + | 10.3205i | −0.214037 | + | 0.370722i | ||||
\(776\) | −111.629 | −4.00724 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.1978 | 1.33360 | ||||||||
\(779\) | 10.1927 | − | 17.6544i | 0.365193 | − | 0.632533i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.93199 | + | 3.34630i | 0.0691320 | + | 0.119740i | ||||
\(782\) | −14.9814 | + | 25.9486i | −0.535735 | + | 0.927920i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 93.4595 | − | 6.82112i | 3.33784 | − | 0.243612i | ||||
\(785\) | 0.300372 | 0.0107207 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.93996 | + | 17.2165i | 0.354321 | + | 0.613703i | 0.987002 | − | 0.160711i | \(-0.0513786\pi\) |
−0.632680 | + | 0.774413i | \(0.718045\pi\) | |||||||
\(788\) | −48.6148 | − | 84.2034i | −1.73183 | − | 2.99962i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.14468 | −0.254196 | ||||||||
\(791\) | 12.3288 | − | 23.2724i | 0.438361 | − | 0.827471i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.6476 | + | 18.4422i | −0.378109 | + | 0.654903i | ||||
\(794\) | −11.3207 | − | 19.6081i | −0.401757 | − | 0.695864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.7429 | + | 27.2675i | −0.557992 | + | 0.966470i | ||||
\(797\) | 5.81955 | 0.206139 | 0.103070 | − | 0.994674i | \(-0.467134\pi\) | ||||
0.103070 | + | 0.994674i | \(0.467134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8640 | −0.667360 | ||||||||
\(800\) | 22.7731 | − | 39.4441i | 0.805149 | − | 1.39456i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.2774 | − | 64.5663i | −1.31631 | − | 2.27992i | ||||
\(803\) | 1.75340 | − | 3.03698i | 0.0618762 | − | 0.107173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.93199 | − | 0.289073i | 0.279566 | − | 0.0101885i | ||||
\(806\) | −36.5068 | −1.28590 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 64.8391 | + | 112.305i | 2.28103 | + | 3.95087i | ||||
\(809\) | 1.06113 | + | 1.83794i | 0.0373075 | + | 0.0646184i | 0.884076 | − | 0.467343i | \(-0.154789\pi\) |
−0.846769 | + | 0.531961i | \(0.821455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4327 | −0.647259 | −0.323629 | − | 0.946184i | \(-0.604903\pi\) | ||||
−0.323629 | + | 0.946184i | \(0.604903\pi\) | |||||||
\(812\) | −35.2738 | + | 1.28551i | −1.23787 | + | 0.0451127i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.81522 | − | 3.14406i | 0.0636235 | − | 0.110199i | ||||
\(815\) | −7.11236 | − | 12.3190i | −0.249135 | − | 0.431515i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4091 | + | 18.0291i | −0.364168 | + | 0.630757i | ||||
\(818\) | 82.4239 | 2.88188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −74.8355 | −2.61337 | ||||||||
\(821\) | −22.5778 | + | 39.1058i | −0.787969 | + | 1.36480i | 0.139239 | + | 0.990259i | \(0.455534\pi\) |
−0.927209 | + | 0.374544i | \(0.877799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5259 | − | 21.6954i | −0.436624 | − | 0.756255i | 0.560803 | − | 0.827949i | \(-0.310493\pi\) |
−0.997427 | + | 0.0716948i | \(0.977159\pi\) | |||||||
\(824\) | −40.8213 | + | 70.7046i | −1.42208 | + | 2.46311i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3461 | + | 30.8557i | −0.568753 | + | 1.07361i | ||||
\(827\) | 14.2953 | 0.497095 | 0.248548 | − | 0.968620i | \(-0.420047\pi\) | ||||
0.248548 | + | 0.968620i | \(0.420047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.9127 | − | 27.5617i | −0.552672 | − | 0.957256i | −0.998081 | − | 0.0619285i | \(-0.980275\pi\) |
0.445409 | − | 0.895327i | \(-0.353058\pi\) | |||||||
\(830\) | −11.6476 | − | 20.1743i | −0.404295 | − | 0.700260i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64.2682 | 2.22810 | ||||||||
\(833\) | −17.9196 | + | 37.0261i | −0.620878 | + | 1.28288i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.44760 | + | 5.97143i | −0.119309 | + | 0.206650i | ||||
\(836\) | 1.81708 | + | 3.14728i | 0.0628451 | + | 0.108851i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.3461 | + | 49.0969i | −0.979200 | + | 1.69602i | ||||
\(839\) | −16.4785 | −0.568900 | −0.284450 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284450 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6350 | −0.780516 | ||||||||
\(842\) | −46.8781 | + | 81.1953i | −1.61553 | + | 2.79818i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.6483 | − | 30.5678i | −0.607480 | − | 1.05219i | ||||
\(845\) | −4.04944 | + | 7.01384i | −0.139305 | + | 0.241283i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.3331 | − | 24.4552i | −0.526852 | − | 0.840292i | ||||
\(848\) | 26.9395 | 0.925106 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.6483 | + | 34.0319i | 0.673932 | + | 1.16728i | ||||
\(851\) | 4.22803 | + | 7.32316i | 0.144935 | + | 0.251035i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.9986 | −0.924415 | −0.462208 | − | 0.886772i | \(-0.652943\pi\) | ||||
−0.462208 | + | 0.886772i | \(0.652943\pi\) | |||||||
\(854\) | −54.0759 | + | 1.97074i | −1.85044 | + | 0.0674373i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −55.5239 | + | 96.1702i | −1.89777 | + | 3.28703i | ||||
\(857\) | −19.5815 | − | 33.9161i | −0.668891 | − | 1.15855i | −0.978215 | − | 0.207596i | \(-0.933436\pi\) |
0.309324 | − | 0.950957i | \(-0.399897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.73422 | + | 8.19991i | −0.161529 | + | 0.279777i | −0.935417 | − | 0.353545i | \(-0.884976\pi\) |
0.773888 | + | 0.633323i | \(0.218309\pi\) | |||||||
\(860\) | 76.4239 | 2.60603 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 85.3199 | 2.90601 | ||||||||
\(863\) | 1.00619 | − | 1.74277i | 0.0342511 | − | 0.0593246i | −0.848392 | − | 0.529369i | \(-0.822429\pi\) |
0.882643 | + | 0.470044i | \(0.155762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00364 | − | 8.66656i | −0.170129 | − | 0.294672i | ||||
\(866\) | 8.75457 | − | 15.1634i | 0.297492 | − | 0.515272i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −35.7545 | − | 57.0259i | −1.21359 | − | 1.93559i | ||||
\(869\) | 0.500482 | 0.0169777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00069 | − | 1.73324i | −0.0339070 | − | 0.0587287i | ||||
\(872\) | 13.5178 | + | 23.4135i | 0.457771 | + | 0.792882i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.6662 | −0.394615 | ||||||||
\(875\) | 14.7095 | − | 27.7663i | 0.497271 | − | 0.938672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3497 | + | 38.7109i | −0.754697 | + | 1.30717i | 0.190828 | + | 0.981624i | \(0.438883\pi\) |
−0.945525 | + | 0.325550i | \(0.894451\pi\) | |||||||
\(878\) | 21.0247 | + | 36.4158i | 0.709549 | + | 1.22897i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.19344 | − | 5.53120i | 0.107651 | − | 0.186457i | ||||
\(881\) | −12.7047 | −0.428033 | −0.214017 | − | 0.976830i | \(-0.568655\pi\) | ||||
−0.214017 | + | 0.976830i | \(0.568655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0014 | −0.572142 | −0.286071 | − | 0.958208i | \(-0.592349\pi\) | ||||
−0.286071 | + | 0.958208i | \(0.592349\pi\) | |||||||
\(884\) | −43.6730 | + | 75.6439i | −1.46888 | + | 2.54418i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.8454 | + | 58.6220i | 1.13706 | + | 1.96944i | ||||
\(887\) | 0.600744 | − | 1.04052i | 0.0201710 | − | 0.0349372i | −0.855764 | − | 0.517367i | \(-0.826912\pi\) |
0.875935 | + | 0.482430i | \(0.160246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6461 | + | 31.4219i | −0.558291 | + | 1.05386i | ||||
\(890\) | 40.1075 | 1.34441 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.7658 | − | 29.0392i | −0.561360 | − | 0.972304i | ||||
\(893\) | −3.67240 | − | 6.36078i | −0.122892 | − | 0.212855i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.1447 | 0.740215 | ||||||||
\(896\) | 35.0666 | + | 55.9287i | 1.17149 | + | 1.86845i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.6476 | − | 35.7628i | 0.689021 | − | 1.19342i | ||||
\(899\) | 6.06870 | + | 10.5113i | 0.202402 | + | 0.350571i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.91273 | + | 10.2411i | −0.196982 | + | 0.341182i | ||||
\(902\) | 7.22487 | 0.240562 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 88.3570 | 2.93871 | ||||||||
\(905\) | 14.5662 | − | 25.2293i | 0.484195 | − | 0.838651i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.53156 | − | 14.7771i | −0.283286 | − | 0.490665i | 0.688906 | − | 0.724850i | \(-0.258091\pi\) |
−0.972192 | + | 0.234185i | \(0.924758\pi\) | |||||||
\(908\) | 71.6166 | − | 124.044i | 2.37668 | − | 4.11653i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 31.8683 | − | 1.16141i | 1.05642 | − | 0.0385002i | ||||
\(911\) | −22.0014 | −0.728938 | −0.364469 | − | 0.931215i | \(-0.618750\pi\) | ||||
−0.364469 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.815912 | + | 1.41320i | 0.0270027 | + | 0.0467701i | ||||
\(914\) | −27.5901 | − | 47.7875i | −0.912601 | − | 1.58067i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.3425 | 1.43207 | ||||||||
\(917\) | 15.8473 | + | 25.2753i | 0.523323 | + | 0.834664i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7953 | − | 25.6262i | 0.488051 | − | 0.845329i | −0.511854 | − | 0.859072i | \(-0.671041\pi\) |
0.999906 | + | 0.0137429i | \(0.00437462\pi\) | |||||||
\(920\) | 13.3145 | + | 23.0614i | 0.438967 | + | 0.760313i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 55.0969 | − | 95.4307i | 1.81452 | − | 3.14284i | ||||
\(923\) | −36.1593 | −1.19020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0902 | 0.364644 | ||||||||
\(926\) | −13.3745 | + | 23.1653i | −0.439513 | + | 0.761259i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.1941 | − | 40.1734i | −0.761385 | − | 1.31876i | ||||
\(929\) | −1.34981 | + | 2.33795i | −0.0442860 | + | 0.0767055i | −0.887319 | − | 0.461157i | \(-0.847435\pi\) |
0.843033 | + | 0.537862i | \(0.180768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9735 | + | 1.16582i | −0.523509 | + | 0.0382082i | ||||
\(932\) | 144.998 | 4.74958 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.9443 | + | 41.4727i | 0.783481 | + | 1.35703i | ||||
\(935\) | 1.40180 | + | 2.42800i | 0.0458439 | + | 0.0794040i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.4472 | 1.28869 | 0.644343 | − | 0.764737i | \(-0.277131\pi\) | ||||
0.644343 | + | 0.764737i | \(0.277131\pi\) | |||||||
\(938\) | 2.38069 | − | 4.49390i | 0.0777322 | − | 0.146731i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.4814 | + | 23.3505i | −0.439716 | + | 0.761610i | ||||
\(941\) | −19.8622 | − | 34.4023i | −0.647489 | − | 1.12148i | −0.983721 | − | 0.179705i | \(-0.942486\pi\) |
0.336232 | − | 0.941779i | \(-0.390848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.41411 | + | 14.5737i | −0.274001 | + | 0.474584i | ||||
\(944\) | −65.4449 | −2.13005 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.37822 | −0.239886 | ||||||||
\(947\) | 7.86515 | − | 13.6228i | 0.255583 | − | 0.442683i | −0.709471 | − | 0.704735i | \(-0.751066\pi\) |
0.965054 | + | 0.262052i | \(0.0843993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.4084 | + | 28.4202i | 0.532639 | + | 0.922558i | ||||
\(950\) | −7.65019 | + | 13.2505i | −0.248205 | + | 0.429903i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −137.913 | + | 5.02607i | −4.46977 | + | 0.162896i | ||||
\(953\) | 30.2064 | 0.978482 | 0.489241 | − | 0.872149i | \(-0.337274\pi\) | ||||
0.489241 | + | 0.872149i | \(0.337274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.04216 | + | 10.4653i | 0.195520 | + | 0.338650i | ||||
\(956\) | 73.6722 | + | 127.604i | 2.38273 | + | 4.12701i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −63.7366 | −2.05924 | ||||||||
\(959\) | −9.98762 | + | 0.363988i | −0.322517 | + | 0.0117538i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.92766 | − | 6.80290i | 0.126699 | − | 0.219448i | ||||
\(962\) | 16.9869 | + | 29.4222i | 0.547681 | + | 0.948611i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 59.5697 | − | 103.178i | 1.91861 | − | 3.32313i | ||||
\(965\) | −12.1767 | −0.391983 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.18911 | −0.199028 | −0.0995141 | − | 0.995036i | \(-0.531729\pi\) | ||||
−0.0995141 | + | 0.995036i | \(0.531729\pi\) | |||||||
\(968\) | 48.4195 | − | 83.8651i | 1.55626 | − | 2.69553i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.9629 | − | 46.7010i | −0.865725 | − | 1.49948i | ||||
\(971\) | 1.08582 | − | 1.88069i | 0.0348455 | − | 0.0603542i | −0.848077 | − | 0.529873i | \(-0.822239\pi\) |
0.882922 | + | 0.469519i | \(0.155573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.7077 | − | 39.0888i | 0.663858 | − | 1.25313i | ||||
\(974\) | 94.1432 | 3.01654 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −50.7094 | − | 87.8312i | −1.62317 | − | 2.81141i | ||||
\(977\) | 5.72803 | + | 9.92124i | 0.183256 | + | 0.317409i | 0.942987 | − | 0.332828i | \(-0.108003\pi\) |
−0.759732 | + | 0.650237i | \(0.774670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.80951 | −0.0897925 | ||||||||
\(980\) | 33.0258 | + | 48.6428i | 1.05497 | + | 1.55384i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.3225 | + | 54.2522i | −0.999541 | + | 1.73126i | ||||
\(983\) | −22.4010 | − | 38.7997i | −0.714482 | − | 1.23752i | −0.963159 | − | 0.268933i | \(-0.913329\pi\) |
0.248677 | − | 0.968587i | \(-0.420004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6025 | − | 25.2923i | 0.465275 | − | 0.805880i | ||||
\(986\) | 40.0232 | 1.27460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −34.0087 | −1.08196 | ||||||||
\(989\) | 8.59269 | − | 14.8830i | 0.273232 | − | 0.473251i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1476 | + | 21.0403i | 0.385882 | + | 0.668368i | 0.991891 | − | 0.127090i | \(-0.0405637\pi\) |
−0.606009 | + | 0.795458i | \(0.707230\pi\) | |||||||
\(992\) | 44.2286 | − | 76.6063i | 1.40426 | − | 2.43225i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −48.8083 | − | 77.8458i | −1.54810 | − | 2.46912i | ||||
\(995\) | −9.45744 | −0.299821 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.66257 | + | 9.80785i | 0.179335 | + | 0.310618i | 0.941653 | − | 0.336585i | \(-0.109272\pi\) |
−0.762318 | + | 0.647203i | \(0.775939\pi\) | |||||||
\(998\) | 7.18794 | + | 12.4499i | 0.227530 | + | 0.394094i | ||||
\(999\) | 0 | 0 |
(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 | 189.2.e.e.163.1 | yes | 6 | |
3.2 | odd | 2 | 189.2.e.f.163.3 | yes | 6 | ||
7.2 | even | 3 | 1323.2.a.ba.1.3 | 3 | |||
7.4 | even | 3 | inner | 189.2.e.e.109.1 | ✓ | 6 | |
7.5 | odd | 6 | 1323.2.a.z.1.3 | 3 | |||
9.2 | odd | 6 | 567.2.h.h.352.1 | 6 | |||
9.4 | even | 3 | 567.2.g.h.541.1 | 6 | |||
9.5 | odd | 6 | 567.2.g.i.541.3 | 6 | |||
9.7 | even | 3 | 567.2.h.i.352.3 | 6 | |||
21.2 | odd | 6 | 1323.2.a.x.1.1 | 3 | |||
21.5 | even | 6 | 1323.2.a.y.1.1 | 3 | |||
21.11 | odd | 6 | 189.2.e.f.109.3 | yes | 6 | ||
63.4 | even | 3 | 567.2.h.i.298.3 | 6 | |||
63.11 | odd | 6 | 567.2.g.i.109.3 | 6 | |||
63.25 | even | 3 | 567.2.g.h.109.1 | 6 | |||
63.32 | odd | 6 | 567.2.h.h.298.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.e.109.1 | ✓ | 6 | 7.4 | even | 3 | inner | |
189.2.e.e.163.1 | yes | 6 | 1.1 | even | 1 | trivial | |
189.2.e.f.109.3 | yes | 6 | 21.11 | odd | 6 | ||
189.2.e.f.163.3 | yes | 6 | 3.2 | odd | 2 | ||
567.2.g.h.109.1 | 6 | 63.25 | even | 3 | |||
567.2.g.h.541.1 | 6 | 9.4 | even | 3 | |||
567.2.g.i.109.3 | 6 | 63.11 | odd | 6 | |||
567.2.g.i.541.3 | 6 | 9.5 | odd | 6 | |||
567.2.h.h.298.1 | 6 | 63.32 | odd | 6 | |||
567.2.h.h.352.1 | 6 | 9.2 | odd | 6 | |||
567.2.h.i.298.3 | 6 | 63.4 | even | 3 | |||
567.2.h.i.352.3 | 6 | 9.7 | even | 3 | |||
1323.2.a.x.1.1 | 3 | 21.2 | odd | 6 | |||
1323.2.a.y.1.1 | 3 | 21.5 | even | 6 | |||
1323.2.a.z.1.3 | 3 | 7.5 | odd | 6 | |||
1323.2.a.ba.1.3 | 3 | 7.2 | even | 3 |