Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(36,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 36.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 385.36 |
Dual form | 385.2.n.b.246.1 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80902 | − | 1.31433i | 1.27917 | − | 0.929370i | 0.279641 | − | 0.960105i | \(-0.409785\pi\) |
0.999528 | + | 0.0307347i | \(0.00978469\pi\) | |||||||
\(3\) | 0.190983 | + | 0.587785i | 0.110264 | + | 0.339358i | 0.990930 | − | 0.134380i | \(-0.0429043\pi\) |
−0.880666 | + | 0.473738i | \(0.842904\pi\) | |||||||
\(4\) | 0.927051 | − | 2.85317i | 0.463525 | − | 1.42658i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 1.11803 | + | 0.812299i | 0.456435 | + | 0.331620i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | −0.690983 | − | 2.12663i | −0.244299 | − | 0.751876i | ||||
\(9\) | 2.11803 | − | 1.53884i | 0.706011 | − | 0.512947i | ||||
\(10\) | 2.23607 | 0.707107 | ||||||||
\(11\) | 3.04508 | − | 1.31433i | 0.918128 | − | 0.396285i | ||||
\(12\) | 1.85410 | 0.535233 | ||||||||
\(13\) | −3.73607 | + | 2.71441i | −1.03620 | + | 0.752843i | −0.969540 | − | 0.244933i | \(-0.921234\pi\) |
−0.0666589 | + | 0.997776i | \(0.521234\pi\) | |||||||
\(14\) | 0.690983 | + | 2.12663i | 0.184673 | + | 0.568365i | ||||
\(15\) | −0.190983 | + | 0.587785i | −0.0493116 | + | 0.151765i | ||||
\(16\) | 0.809017 | + | 0.587785i | 0.202254 | + | 0.146946i | ||||
\(17\) | −4.54508 | − | 3.30220i | −1.10235 | − | 0.800901i | −0.120904 | − | 0.992664i | \(-0.538579\pi\) |
−0.981441 | + | 0.191764i | \(0.938579\pi\) | |||||||
\(18\) | 1.80902 | − | 5.56758i | 0.426389 | − | 1.31229i | ||||
\(19\) | −1.00000 | − | 3.07768i | −0.229416 | − | 0.706069i | −0.997813 | − | 0.0660962i | \(-0.978946\pi\) |
0.768398 | − | 0.639973i | \(-0.221054\pi\) | |||||||
\(20\) | 2.42705 | − | 1.76336i | 0.542705 | − | 0.394298i | ||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 3.78115 | − | 6.37988i | 0.806145 | − | 1.36020i | ||||
\(23\) | −4.47214 | −0.932505 | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | 1.11803 | − | 0.812299i | 0.228218 | − | 0.165810i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −3.19098 | + | 9.82084i | −0.625803 | + | 1.92602i | ||||
\(27\) | 2.80902 | + | 2.04087i | 0.540596 | + | 0.392766i | ||||
\(28\) | 2.42705 | + | 1.76336i | 0.458670 | + | 0.333243i | ||||
\(29\) | 0.263932 | − | 0.812299i | 0.0490109 | − | 0.150840i | −0.923556 | − | 0.383464i | \(-0.874731\pi\) |
0.972567 | + | 0.232624i | \(0.0747311\pi\) | |||||||
\(30\) | 0.427051 | + | 1.31433i | 0.0779685 | + | 0.239962i | ||||
\(31\) | −2.61803 | + | 1.90211i | −0.470213 | + | 0.341630i | −0.797524 | − | 0.603287i | \(-0.793857\pi\) |
0.327311 | + | 0.944917i | \(0.393857\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 1.35410 | + | 1.53884i | 0.235719 | + | 0.267878i | ||||
\(34\) | −12.5623 | −2.15442 | ||||||||
\(35\) | −0.809017 | + | 0.587785i | −0.136749 | + | 0.0993538i | ||||
\(36\) | −2.42705 | − | 7.46969i | −0.404508 | − | 1.24495i | ||||
\(37\) | −2.23607 | + | 6.88191i | −0.367607 | + | 1.13138i | 0.580725 | + | 0.814100i | \(0.302769\pi\) |
−0.948332 | + | 0.317279i | \(0.897231\pi\) | |||||||
\(38\) | −5.85410 | − | 4.25325i | −0.949661 | − | 0.689969i | ||||
\(39\) | −2.30902 | − | 1.67760i | −0.369739 | − | 0.268631i | ||||
\(40\) | 0.690983 | − | 2.12663i | 0.109254 | − | 0.336249i | ||||
\(41\) | 0.763932 | + | 2.35114i | 0.119306 | + | 0.367187i | 0.992821 | − | 0.119611i | \(-0.0381648\pi\) |
−0.873515 | + | 0.486798i | \(0.838165\pi\) | |||||||
\(42\) | −1.11803 | + | 0.812299i | −0.172516 | + | 0.125340i | ||||
\(43\) | −5.23607 | −0.798493 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(44\) | −0.927051 | − | 9.90659i | −0.139758 | − | 1.49348i | ||||
\(45\) | 2.61803 | 0.390273 | ||||||||
\(46\) | −8.09017 | + | 5.87785i | −1.19283 | + | 0.866642i | ||||
\(47\) | −0.354102 | − | 1.08981i | −0.0516511 | − | 0.158966i | 0.921904 | − | 0.387419i | \(-0.126633\pi\) |
−0.973555 | + | 0.228453i | \(0.926633\pi\) | |||||||
\(48\) | −0.190983 | + | 0.587785i | −0.0275660 | + | 0.0848395i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 1.80902 | + | 1.31433i | 0.255834 | + | 0.185874i | ||||
\(51\) | 1.07295 | − | 3.30220i | 0.150243 | − | 0.462400i | ||||
\(52\) | 4.28115 | + | 13.1760i | 0.593689 | + | 1.82719i | ||||
\(53\) | 1.23607 | − | 0.898056i | 0.169787 | − | 0.123357i | −0.499647 | − | 0.866229i | \(-0.666537\pi\) |
0.669434 | + | 0.742872i | \(0.266537\pi\) | |||||||
\(54\) | 7.76393 | 1.05654 | ||||||||
\(55\) | 3.23607 | + | 0.726543i | 0.436351 | + | 0.0979670i | ||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 1.61803 | − | 1.17557i | 0.214314 | − | 0.155708i | ||||
\(58\) | −0.590170 | − | 1.81636i | −0.0774931 | − | 0.238499i | ||||
\(59\) | −2.85410 | + | 8.78402i | −0.371572 | + | 1.14358i | 0.574190 | + | 0.818722i | \(0.305317\pi\) |
−0.945762 | + | 0.324860i | \(0.894683\pi\) | |||||||
\(60\) | 1.50000 | + | 1.08981i | 0.193649 | + | 0.140694i | ||||
\(61\) | 3.85410 | + | 2.80017i | 0.493467 | + | 0.358525i | 0.806516 | − | 0.591212i | \(-0.201350\pi\) |
−0.313049 | + | 0.949737i | \(0.601350\pi\) | |||||||
\(62\) | −2.23607 | + | 6.88191i | −0.283981 | + | 0.874003i | ||||
\(63\) | 0.809017 | + | 2.48990i | 0.101927 | + | 0.313698i | ||||
\(64\) | 10.5172 | − | 7.64121i | 1.31465 | − | 0.955151i | ||||
\(65\) | −4.61803 | −0.572797 | ||||||||
\(66\) | 4.47214 | + | 1.00406i | 0.550482 | + | 0.123591i | ||||
\(67\) | 8.18034 | 0.999388 | 0.499694 | − | 0.866202i | \(-0.333446\pi\) | ||||
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(68\) | −13.6353 | + | 9.90659i | −1.65352 | + | 1.20135i | ||||
\(69\) | −0.854102 | − | 2.62866i | −0.102822 | − | 0.316453i | ||||
\(70\) | −0.690983 | + | 2.12663i | −0.0825883 | + | 0.254181i | ||||
\(71\) | −13.2082 | − | 9.59632i | −1.56753 | − | 1.13887i | −0.929478 | − | 0.368876i | \(-0.879743\pi\) |
−0.638047 | − | 0.769997i | \(-0.720257\pi\) | |||||||
\(72\) | −4.73607 | − | 3.44095i | −0.558151 | − | 0.405520i | ||||
\(73\) | 1.97214 | − | 6.06961i | 0.230821 | − | 0.710394i | −0.766827 | − | 0.641854i | \(-0.778166\pi\) |
0.997648 | − | 0.0685406i | \(-0.0218343\pi\) | |||||||
\(74\) | 5.00000 | + | 15.3884i | 0.581238 | + | 1.78887i | ||||
\(75\) | −0.500000 | + | 0.363271i | −0.0577350 | + | 0.0419470i | ||||
\(76\) | −9.70820 | −1.11361 | ||||||||
\(77\) | 0.309017 | + | 3.30220i | 0.0352158 | + | 0.376320i | ||||
\(78\) | −6.38197 | −0.722615 | ||||||||
\(79\) | −8.73607 | + | 6.34712i | −0.982884 | + | 0.714107i | −0.958351 | − | 0.285592i | \(-0.907810\pi\) |
−0.0245330 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(80\) | 0.309017 | + | 0.951057i | 0.0345492 | + | 0.106331i | ||||
\(81\) | 1.76393 | − | 5.42882i | 0.195992 | − | 0.603203i | ||||
\(82\) | 4.47214 | + | 3.24920i | 0.493865 | + | 0.358814i | ||||
\(83\) | −7.73607 | − | 5.62058i | −0.849144 | − | 0.616939i | 0.0757660 | − | 0.997126i | \(-0.475860\pi\) |
−0.924910 | + | 0.380187i | \(0.875860\pi\) | |||||||
\(84\) | −0.572949 | + | 1.76336i | −0.0625139 | + | 0.192398i | ||||
\(85\) | −1.73607 | − | 5.34307i | −0.188303 | − | 0.579537i | ||||
\(86\) | −9.47214 | + | 6.88191i | −1.02141 | + | 0.742095i | ||||
\(87\) | 0.527864 | 0.0565930 | ||||||||
\(88\) | −4.89919 | − | 5.56758i | −0.522255 | − | 0.593506i | ||||
\(89\) | 12.7639 | 1.35297 | 0.676487 | − | 0.736455i | \(-0.263501\pi\) | ||||
0.676487 | + | 0.736455i | \(0.263501\pi\) | |||||||
\(90\) | 4.73607 | − | 3.44095i | 0.499225 | − | 0.362708i | ||||
\(91\) | −1.42705 | − | 4.39201i | −0.149596 | − | 0.460408i | ||||
\(92\) | −4.14590 | + | 12.7598i | −0.432240 | + | 1.33030i | ||||
\(93\) | −1.61803 | − | 1.17557i | −0.167782 | − | 0.121901i | ||||
\(94\) | −2.07295 | − | 1.50609i | −0.213808 | − | 0.155341i | ||||
\(95\) | 1.00000 | − | 3.07768i | 0.102598 | − | 0.315764i | ||||
\(96\) | 1.28115 | + | 3.94298i | 0.130757 | + | 0.402429i | ||||
\(97\) | 12.3992 | − | 9.00854i | 1.25895 | − | 0.914678i | 0.260241 | − | 0.965544i | \(-0.416198\pi\) |
0.998706 | + | 0.0508653i | \(0.0161979\pi\) | |||||||
\(98\) | −2.23607 | −0.225877 | ||||||||
\(99\) | 4.42705 | − | 7.46969i | 0.444935 | − | 0.750733i | ||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 11.0902 | − | 8.05748i | 1.10351 | − | 0.801749i | 0.121883 | − | 0.992544i | \(-0.461107\pi\) |
0.981630 | + | 0.190795i | \(0.0611066\pi\) | |||||||
\(102\) | −2.39919 | − | 7.38394i | −0.237555 | − | 0.731119i | ||||
\(103\) | −5.35410 | + | 16.4782i | −0.527555 | + | 1.62365i | 0.231651 | + | 0.972799i | \(0.425587\pi\) |
−0.759207 | + | 0.650850i | \(0.774413\pi\) | |||||||
\(104\) | 8.35410 | + | 6.06961i | 0.819187 | + | 0.595174i | ||||
\(105\) | −0.500000 | − | 0.363271i | −0.0487950 | − | 0.0354516i | ||||
\(106\) | 1.05573 | − | 3.24920i | 0.102541 | − | 0.315590i | ||||
\(107\) | −2.23607 | − | 6.88191i | −0.216169 | − | 0.665299i | −0.999069 | − | 0.0431514i | \(-0.986260\pi\) |
0.782900 | − | 0.622148i | \(-0.213740\pi\) | |||||||
\(108\) | 8.42705 | − | 6.12261i | 0.810893 | − | 0.589149i | ||||
\(109\) | −11.5279 | −1.10417 | −0.552085 | − | 0.833788i | \(-0.686167\pi\) | ||||
−0.552085 | + | 0.833788i | \(0.686167\pi\) | |||||||
\(110\) | 6.80902 | − | 2.93893i | 0.649214 | − | 0.280216i | ||||
\(111\) | −4.47214 | −0.424476 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | 3.23607 | + | 9.95959i | 0.304424 | + | 0.936920i | 0.979892 | + | 0.199530i | \(0.0639417\pi\) |
−0.675468 | + | 0.737389i | \(0.736058\pi\) | |||||||
\(114\) | 1.38197 | − | 4.25325i | 0.129433 | − | 0.398354i | ||||
\(115\) | −3.61803 | − | 2.62866i | −0.337383 | − | 0.245123i | ||||
\(116\) | −2.07295 | − | 1.50609i | −0.192468 | − | 0.139837i | ||||
\(117\) | −3.73607 | + | 11.4984i | −0.345400 | + | 1.06303i | ||||
\(118\) | 6.38197 | + | 19.6417i | 0.587508 | + | 1.80816i | ||||
\(119\) | 4.54508 | − | 3.30220i | 0.416647 | − | 0.302712i | ||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | 7.54508 | − | 8.00448i | 0.685917 | − | 0.727680i | ||||
\(122\) | 10.6525 | 0.964430 | ||||||||
\(123\) | −1.23607 | + | 0.898056i | −0.111452 | + | 0.0809750i | ||||
\(124\) | 3.00000 | + | 9.23305i | 0.269408 | + | 0.829152i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 4.73607 | + | 3.44095i | 0.421922 | + | 0.306545i | ||||
\(127\) | −7.47214 | − | 5.42882i | −0.663045 | − | 0.481730i | 0.204645 | − | 0.978836i | \(-0.434396\pi\) |
−0.867690 | + | 0.497106i | \(0.834396\pi\) | |||||||
\(128\) | 4.83688 | − | 14.8864i | 0.427524 | − | 1.31578i | ||||
\(129\) | −1.00000 | − | 3.07768i | −0.0880451 | − | 0.270975i | ||||
\(130\) | −8.35410 | + | 6.06961i | −0.732703 | + | 0.532340i | ||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 5.64590 | − | 2.43690i | 0.491412 | − | 0.212105i | ||||
\(133\) | 3.23607 | 0.280603 | ||||||||
\(134\) | 14.7984 | − | 10.7516i | 1.27838 | − | 0.928801i | ||||
\(135\) | 1.07295 | + | 3.30220i | 0.0923447 | + | 0.284208i | ||||
\(136\) | −3.88197 | + | 11.9475i | −0.332876 | + | 1.02449i | ||||
\(137\) | 9.23607 | + | 6.71040i | 0.789091 | + | 0.573308i | 0.907693 | − | 0.419634i | \(-0.137842\pi\) |
−0.118603 | + | 0.992942i | \(0.537842\pi\) | |||||||
\(138\) | −5.00000 | − | 3.63271i | −0.425628 | − | 0.309237i | ||||
\(139\) | 1.70820 | − | 5.25731i | 0.144888 | − | 0.445919i | −0.852109 | − | 0.523365i | \(-0.824676\pi\) |
0.996997 | + | 0.0774457i | \(0.0246764\pi\) | |||||||
\(140\) | 0.927051 | + | 2.85317i | 0.0783501 | + | 0.241137i | ||||
\(141\) | 0.572949 | − | 0.416272i | 0.0482510 | − | 0.0350564i | ||||
\(142\) | −36.5066 | −3.06356 | ||||||||
\(143\) | −7.80902 | + | 13.1760i | −0.653023 | + | 1.10184i | ||||
\(144\) | 2.61803 | 0.218169 | ||||||||
\(145\) | 0.690983 | − | 0.502029i | 0.0573830 | − | 0.0416912i | ||||
\(146\) | −4.40983 | − | 13.5721i | −0.364960 | − | 1.12323i | ||||
\(147\) | 0.190983 | − | 0.587785i | 0.0157520 | − | 0.0484797i | ||||
\(148\) | 17.5623 | + | 12.7598i | 1.44361 | + | 1.04885i | ||||
\(149\) | 14.4443 | + | 10.4944i | 1.18332 | + | 0.859733i | 0.992542 | − | 0.121900i | \(-0.0388988\pi\) |
0.190778 | + | 0.981633i | \(0.438899\pi\) | |||||||
\(150\) | −0.427051 | + | 1.31433i | −0.0348686 | + | 0.107314i | ||||
\(151\) | −0.118034 | − | 0.363271i | −0.00960547 | − | 0.0295626i | 0.946139 | − | 0.323761i | \(-0.104947\pi\) |
−0.955744 | + | 0.294198i | \(0.904947\pi\) | |||||||
\(152\) | −5.85410 | + | 4.25325i | −0.474830 | + | 0.344984i | ||||
\(153\) | −14.7082 | −1.18909 | ||||||||
\(154\) | 4.89919 | + | 5.56758i | 0.394788 | + | 0.448649i | ||||
\(155\) | −3.23607 | −0.259927 | ||||||||
\(156\) | −6.92705 | + | 5.03280i | −0.554608 | + | 0.402946i | ||||
\(157\) | −4.97214 | − | 15.3027i | −0.396820 | − | 1.22129i | −0.927535 | − | 0.373735i | \(-0.878077\pi\) |
0.530716 | − | 0.847550i | \(-0.321923\pi\) | |||||||
\(158\) | −7.46149 | + | 22.9641i | −0.593604 | + | 1.82693i | ||||
\(159\) | 0.763932 | + | 0.555029i | 0.0605838 | + | 0.0440167i | ||||
\(160\) | 5.42705 | + | 3.94298i | 0.429046 | + | 0.311720i | ||||
\(161\) | 1.38197 | − | 4.25325i | 0.108914 | − | 0.335203i | ||||
\(162\) | −3.94427 | − | 12.1392i | −0.309891 | − | 0.953747i | ||||
\(163\) | 17.9443 | − | 13.0373i | 1.40550 | − | 1.02116i | 0.411547 | − | 0.911389i | \(-0.364989\pi\) |
0.993957 | − | 0.109770i | \(-0.0350113\pi\) | |||||||
\(164\) | 7.41641 | 0.579124 | ||||||||
\(165\) | 0.190983 | + | 2.04087i | 0.0148680 | + | 0.158882i | ||||
\(166\) | −21.3820 | −1.65956 | ||||||||
\(167\) | 9.70820 | − | 7.05342i | 0.751243 | − | 0.545810i | −0.144969 | − | 0.989436i | \(-0.546308\pi\) |
0.896212 | + | 0.443626i | \(0.146308\pi\) | |||||||
\(168\) | 0.427051 | + | 1.31433i | 0.0329477 | + | 0.101403i | ||||
\(169\) | 2.57295 | − | 7.91872i | 0.197919 | − | 0.609133i | ||||
\(170\) | −10.1631 | − | 7.38394i | −0.779476 | − | 0.566322i | ||||
\(171\) | −6.85410 | − | 4.97980i | −0.524146 | − | 0.380815i | ||||
\(172\) | −4.85410 | + | 14.9394i | −0.370122 | + | 1.13912i | ||||
\(173\) | −0.482779 | − | 1.48584i | −0.0367050 | − | 0.112966i | 0.931025 | − | 0.364955i | \(-0.118916\pi\) |
−0.967730 | + | 0.251988i | \(0.918916\pi\) | |||||||
\(174\) | 0.954915 | − | 0.693786i | 0.0723919 | − | 0.0525958i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.23607 | + | 0.726543i | 0.243928 | + | 0.0547652i | ||||
\(177\) | −5.70820 | −0.429055 | ||||||||
\(178\) | 23.0902 | − | 16.7760i | 1.73068 | − | 1.25741i | ||||
\(179\) | 6.06231 | + | 18.6579i | 0.453118 | + | 1.39455i | 0.873331 | + | 0.487128i | \(0.161956\pi\) |
−0.420212 | + | 0.907426i | \(0.638044\pi\) | |||||||
\(180\) | 2.42705 | − | 7.46969i | 0.180902 | − | 0.556758i | ||||
\(181\) | −4.47214 | − | 3.24920i | −0.332411 | − | 0.241511i | 0.409042 | − | 0.912516i | \(-0.365863\pi\) |
−0.741453 | + | 0.671005i | \(0.765863\pi\) | |||||||
\(182\) | −8.35410 | − | 6.06961i | −0.619247 | − | 0.449909i | ||||
\(183\) | −0.909830 | + | 2.80017i | −0.0672566 | + | 0.206994i | ||||
\(184\) | 3.09017 | + | 9.51057i | 0.227810 | + | 0.701128i | ||||
\(185\) | −5.85410 | + | 4.25325i | −0.430402 | + | 0.312705i | ||||
\(186\) | −4.47214 | −0.327913 | ||||||||
\(187\) | −18.1803 | − | 4.08174i | −1.32948 | − | 0.298486i | ||||
\(188\) | −3.43769 | −0.250720 | ||||||||
\(189\) | −2.80902 | + | 2.04087i | −0.204326 | + | 0.148451i | ||||
\(190\) | −2.23607 | − | 6.88191i | −0.162221 | − | 0.499266i | ||||
\(191\) | 7.13525 | − | 21.9601i | 0.516289 | − | 1.58897i | −0.264636 | − | 0.964348i | \(-0.585252\pi\) |
0.780924 | − | 0.624625i | \(-0.214748\pi\) | |||||||
\(192\) | 6.50000 | + | 4.72253i | 0.469097 | + | 0.340819i | ||||
\(193\) | −3.23607 | − | 2.35114i | −0.232937 | − | 0.169239i | 0.465194 | − | 0.885209i | \(-0.345985\pi\) |
−0.698131 | + | 0.715970i | \(0.745985\pi\) | |||||||
\(194\) | 10.5902 | − | 32.5932i | 0.760330 | − | 2.34005i | ||||
\(195\) | −0.881966 | − | 2.71441i | −0.0631589 | − | 0.194383i | ||||
\(196\) | −2.42705 | + | 1.76336i | −0.173361 | + | 0.125954i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | −1.80902 | − | 19.3314i | −0.128561 | − | 1.37382i | ||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 1.80902 | − | 1.31433i | 0.127917 | − | 0.0929370i | ||||
\(201\) | 1.56231 | + | 4.80828i | 0.110197 | + | 0.339150i | ||||
\(202\) | 9.47214 | − | 29.1522i | 0.666457 | − | 2.05114i | ||||
\(203\) | 0.690983 | + | 0.502029i | 0.0484975 | + | 0.0352355i | ||||
\(204\) | −8.42705 | − | 6.12261i | −0.590012 | − | 0.428669i | ||||
\(205\) | −0.763932 | + | 2.35114i | −0.0533553 | + | 0.164211i | ||||
\(206\) | 11.9721 | + | 36.8464i | 0.834138 | + | 2.56721i | ||||
\(207\) | −9.47214 | + | 6.88191i | −0.658359 | + | 0.478326i | ||||
\(208\) | −4.61803 | −0.320203 | ||||||||
\(209\) | −7.09017 | − | 8.05748i | −0.490437 | − | 0.557348i | ||||
\(210\) | −1.38197 | −0.0953647 | ||||||||
\(211\) | −6.20820 | + | 4.51052i | −0.427390 | + | 0.310517i | −0.780605 | − | 0.625025i | \(-0.785089\pi\) |
0.353214 | + | 0.935542i | \(0.385089\pi\) | |||||||
\(212\) | −1.41641 | − | 4.35926i | −0.0972793 | − | 0.299395i | ||||
\(213\) | 3.11803 | − | 9.59632i | 0.213644 | − | 0.657529i | ||||
\(214\) | −13.0902 | − | 9.51057i | −0.894826 | − | 0.650129i | ||||
\(215\) | −4.23607 | − | 3.07768i | −0.288897 | − | 0.209896i | ||||
\(216\) | 2.39919 | − | 7.38394i | 0.163244 | − | 0.502413i | ||||
\(217\) | −1.00000 | − | 3.07768i | −0.0678844 | − | 0.208927i | ||||
\(218\) | −20.8541 | + | 15.1514i | −1.41242 | + | 1.02618i | ||||
\(219\) | 3.94427 | 0.266529 | ||||||||
\(220\) | 5.07295 | − | 8.55951i | 0.342018 | − | 0.577082i | ||||
\(221\) | 25.9443 | 1.74520 | ||||||||
\(222\) | −8.09017 | + | 5.87785i | −0.542977 | + | 0.394496i | ||||
\(223\) | 0.472136 | + | 1.45309i | 0.0316166 | + | 0.0973058i | 0.965620 | − | 0.259959i | \(-0.0837092\pi\) |
−0.934003 | + | 0.357265i | \(0.883709\pi\) | |||||||
\(224\) | −2.07295 | + | 6.37988i | −0.138505 | + | 0.426274i | ||||
\(225\) | 2.11803 | + | 1.53884i | 0.141202 | + | 0.102589i | ||||
\(226\) | 18.9443 | + | 13.7638i | 1.26015 | + | 0.915556i | ||||
\(227\) | −3.33688 | + | 10.2699i | −0.221477 | + | 0.681635i | 0.777154 | + | 0.629311i | \(0.216663\pi\) |
−0.998630 | + | 0.0523238i | \(0.983337\pi\) | |||||||
\(228\) | −1.85410 | − | 5.70634i | −0.122791 | − | 0.377912i | ||||
\(229\) | 20.0344 | − | 14.5559i | 1.32391 | − | 0.961879i | 0.324039 | − | 0.946044i | \(-0.394959\pi\) |
0.999875 | − | 0.0158354i | \(-0.00504076\pi\) | |||||||
\(230\) | −10.0000 | −0.659380 | ||||||||
\(231\) | −1.88197 | + | 0.812299i | −0.123824 | + | 0.0534454i | ||||
\(232\) | −1.90983 | −0.125386 | ||||||||
\(233\) | −5.38197 | + | 3.91023i | −0.352584 | + | 0.256168i | −0.749952 | − | 0.661492i | \(-0.769924\pi\) |
0.397368 | + | 0.917659i | \(0.369924\pi\) | |||||||
\(234\) | 8.35410 | + | 25.7113i | 0.546125 | + | 1.68080i | ||||
\(235\) | 0.354102 | − | 1.08981i | 0.0230991 | − | 0.0710916i | ||||
\(236\) | 22.4164 | + | 16.2865i | 1.45918 | + | 1.06016i | ||||
\(237\) | −5.39919 | − | 3.92274i | −0.350715 | − | 0.254809i | ||||
\(238\) | 3.88197 | − | 11.9475i | 0.251630 | − | 0.774439i | ||||
\(239\) | 7.71885 | + | 23.7562i | 0.499291 | + | 1.53666i | 0.810162 | + | 0.586207i | \(0.199379\pi\) |
−0.310871 | + | 0.950452i | \(0.600621\pi\) | |||||||
\(240\) | −0.500000 | + | 0.363271i | −0.0322749 | + | 0.0234491i | ||||
\(241\) | −17.1246 | −1.10309 | −0.551547 | − | 0.834144i | \(-0.685962\pi\) | ||||
−0.551547 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(242\) | 3.12868 | − | 24.3970i | 0.201119 | − | 1.56830i | ||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 11.5623 | − | 8.40051i | 0.740201 | − | 0.537787i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | −1.05573 | + | 3.24920i | −0.0673108 | + | 0.207161i | ||||
\(247\) | 12.0902 | + | 8.78402i | 0.769279 | + | 0.558914i | ||||
\(248\) | 5.85410 | + | 4.25325i | 0.371736 | + | 0.270082i | ||||
\(249\) | 1.82624 | − | 5.62058i | 0.115733 | − | 0.356190i | ||||
\(250\) | 0.690983 | + | 2.12663i | 0.0437016 | + | 0.134500i | ||||
\(251\) | 6.23607 | − | 4.53077i | 0.393617 | − | 0.285980i | −0.373319 | − | 0.927703i | \(-0.621780\pi\) |
0.766936 | + | 0.641723i | \(0.221780\pi\) | |||||||
\(252\) | 7.85410 | 0.494762 | ||||||||
\(253\) | −13.6180 | + | 5.87785i | −0.856158 | + | 0.369537i | ||||
\(254\) | −20.6525 | −1.29585 | ||||||||
\(255\) | 2.80902 | − | 2.04087i | 0.175907 | − | 0.127804i | ||||
\(256\) | −2.78115 | − | 8.55951i | −0.173822 | − | 0.534969i | ||||
\(257\) | −0.736068 | + | 2.26538i | −0.0459147 | + | 0.141311i | −0.971386 | − | 0.237508i | \(-0.923670\pi\) |
0.925471 | + | 0.378818i | \(0.123670\pi\) | |||||||
\(258\) | −5.85410 | − | 4.25325i | −0.364460 | − | 0.264796i | ||||
\(259\) | −5.85410 | − | 4.25325i | −0.363756 | − | 0.264284i | ||||
\(260\) | −4.28115 | + | 13.1760i | −0.265506 | + | 0.817143i | ||||
\(261\) | −0.690983 | − | 2.12663i | −0.0427708 | − | 0.131635i | ||||
\(262\) | 14.4721 | − | 10.5146i | 0.894092 | − | 0.649596i | ||||
\(263\) | 14.1803 | 0.874397 | 0.437199 | − | 0.899365i | \(-0.355971\pi\) | ||||
0.437199 | + | 0.899365i | \(0.355971\pi\) | |||||||
\(264\) | 2.33688 | − | 3.94298i | 0.143825 | − | 0.242674i | ||||
\(265\) | 1.52786 | 0.0938559 | ||||||||
\(266\) | 5.85410 | − | 4.25325i | 0.358938 | − | 0.260784i | ||||
\(267\) | 2.43769 | + | 7.50245i | 0.149184 | + | 0.459143i | ||||
\(268\) | 7.58359 | − | 23.3399i | 0.463242 | − | 1.42571i | ||||
\(269\) | 15.0902 | + | 10.9637i | 0.920064 | + | 0.668466i | 0.943540 | − | 0.331259i | \(-0.107473\pi\) |
−0.0234760 | + | 0.999724i | \(0.507473\pi\) | |||||||
\(270\) | 6.28115 | + | 4.56352i | 0.382259 | + | 0.277727i | ||||
\(271\) | 7.18034 | − | 22.0988i | 0.436175 | − | 1.34241i | −0.455704 | − | 0.890132i | \(-0.650612\pi\) |
0.891878 | − | 0.452276i | \(-0.149388\pi\) | |||||||
\(272\) | −1.73607 | − | 5.34307i | −0.105265 | − | 0.323971i | ||||
\(273\) | 2.30902 | − | 1.67760i | 0.139748 | − | 0.101533i | ||||
\(274\) | 25.5279 | 1.54219 | ||||||||
\(275\) | 2.19098 | + | 2.48990i | 0.132121 | + | 0.150147i | ||||
\(276\) | −8.29180 | −0.499107 | ||||||||
\(277\) | 7.61803 | − | 5.53483i | 0.457723 | − | 0.332555i | −0.334914 | − | 0.942249i | \(-0.608707\pi\) |
0.792638 | + | 0.609693i | \(0.208707\pi\) | |||||||
\(278\) | −3.81966 | − | 11.7557i | −0.229088 | − | 0.705060i | ||||
\(279\) | −2.61803 | + | 8.05748i | −0.156738 | + | 0.482389i | ||||
\(280\) | 1.80902 | + | 1.31433i | 0.108109 | + | 0.0785461i | ||||
\(281\) | 6.85410 | + | 4.97980i | 0.408881 | + | 0.297070i | 0.773149 | − | 0.634225i | \(-0.218681\pi\) |
−0.364267 | + | 0.931294i | \(0.618681\pi\) | |||||||
\(282\) | 0.489357 | − | 1.50609i | 0.0291408 | − | 0.0896861i | ||||
\(283\) | −2.29837 | − | 7.07367i | −0.136624 | − | 0.420486i | 0.859215 | − | 0.511615i | \(-0.170952\pi\) |
−0.995839 | + | 0.0911289i | \(0.970952\pi\) | |||||||
\(284\) | −39.6246 | + | 28.7890i | −2.35129 | + | 1.70831i | ||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 3.19098 | + | 34.0993i | 0.188687 | + | 2.01633i | ||||
\(287\) | −2.47214 | −0.145926 | ||||||||
\(288\) | 14.2082 | − | 10.3229i | 0.837226 | − | 0.608281i | ||||
\(289\) | 4.50000 | + | 13.8496i | 0.264706 | + | 0.814681i | ||||
\(290\) | 0.590170 | − | 1.81636i | 0.0346560 | − | 0.106660i | ||||
\(291\) | 7.66312 | + | 5.56758i | 0.449220 | + | 0.326377i | ||||
\(292\) | −15.4894 | − | 11.2537i | −0.906446 | − | 0.658572i | ||||
\(293\) | −2.90983 | + | 8.95554i | −0.169994 | + | 0.523188i | −0.999370 | − | 0.0355036i | \(-0.988696\pi\) |
0.829375 | + | 0.558692i | \(0.188696\pi\) | |||||||
\(294\) | −0.427051 | − | 1.31433i | −0.0249061 | − | 0.0766532i | ||||
\(295\) | −7.47214 | + | 5.42882i | −0.435045 | + | 0.316078i | ||||
\(296\) | 16.1803 | 0.940463 | ||||||||
\(297\) | 11.2361 | + | 2.52265i | 0.651983 | + | 0.146379i | ||||
\(298\) | 39.9230 | 2.31268 | ||||||||
\(299\) | 16.7082 | − | 12.1392i | 0.966260 | − | 0.702029i | ||||
\(300\) | 0.572949 | + | 1.76336i | 0.0330792 | + | 0.101807i | ||||
\(301\) | 1.61803 | − | 4.97980i | 0.0932619 | − | 0.287031i | ||||
\(302\) | −0.690983 | − | 0.502029i | −0.0397616 | − | 0.0288885i | ||||
\(303\) | 6.85410 | + | 4.97980i | 0.393758 | + | 0.286082i | ||||
\(304\) | 1.00000 | − | 3.07768i | 0.0573539 | − | 0.176517i | ||||
\(305\) | 1.47214 | + | 4.53077i | 0.0842943 | + | 0.259431i | ||||
\(306\) | −26.6074 | + | 19.3314i | −1.52104 | + | 1.10510i | ||||
\(307\) | −20.5623 | −1.17355 | −0.586776 | − | 0.809749i | \(-0.699603\pi\) | ||||
−0.586776 | + | 0.809749i | \(0.699603\pi\) | |||||||
\(308\) | 9.70820 | + | 2.17963i | 0.553176 | + | 0.124196i | ||||
\(309\) | −10.7082 | −0.609168 | ||||||||
\(310\) | −5.85410 | + | 4.25325i | −0.332491 | + | 0.241569i | ||||
\(311\) | 4.05573 | + | 12.4822i | 0.229979 | + | 0.707803i | 0.997748 | + | 0.0670761i | \(0.0213670\pi\) |
−0.767769 | + | 0.640727i | \(0.778633\pi\) | |||||||
\(312\) | −1.97214 | + | 6.06961i | −0.111650 | + | 0.343624i | ||||
\(313\) | 14.5623 | + | 10.5801i | 0.823110 | + | 0.598025i | 0.917602 | − | 0.397501i | \(-0.130123\pi\) |
−0.0944915 | + | 0.995526i | \(0.530123\pi\) | |||||||
\(314\) | −29.1074 | − | 21.1478i | −1.64263 | − | 1.19344i | ||||
\(315\) | −0.809017 | + | 2.48990i | −0.0455829 | + | 0.140290i | ||||
\(316\) | 10.0106 | + | 30.8096i | 0.563143 | + | 1.73317i | ||||
\(317\) | 17.4164 | − | 12.6538i | 0.978203 | − | 0.710706i | 0.0208967 | − | 0.999782i | \(-0.493348\pi\) |
0.957306 | + | 0.289076i | \(0.0933479\pi\) | |||||||
\(318\) | 2.11146 | 0.118405 | ||||||||
\(319\) | −0.263932 | − | 2.82041i | −0.0147774 | − | 0.157913i | ||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | 3.61803 | − | 2.62866i | 0.201939 | − | 0.146717i | ||||
\(322\) | −3.09017 | − | 9.51057i | −0.172208 | − | 0.530003i | ||||
\(323\) | −5.61803 | + | 17.2905i | −0.312596 | + | 0.962071i | ||||
\(324\) | −13.8541 | − | 10.0656i | −0.769672 | − | 0.559200i | ||||
\(325\) | −3.73607 | − | 2.71441i | −0.207240 | − | 0.150569i | ||||
\(326\) | 15.3262 | − | 47.1693i | 0.848842 | − | 2.61247i | ||||
\(327\) | −2.20163 | − | 6.77591i | −0.121750 | − | 0.374709i | ||||
\(328\) | 4.47214 | − | 3.24920i | 0.246932 | − | 0.179407i | ||||
\(329\) | 1.14590 | 0.0631754 | ||||||||
\(330\) | 3.02786 | + | 3.44095i | 0.166678 | + | 0.189418i | ||||
\(331\) | −18.5066 | −1.01721 | −0.508607 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508607 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(332\) | −23.2082 | + | 16.8617i | −1.27372 | + | 0.925409i | ||||
\(333\) | 5.85410 | + | 18.0171i | 0.320803 | + | 0.987330i | ||||
\(334\) | 8.29180 | − | 25.5195i | 0.453707 | − | 1.39637i | ||||
\(335\) | 6.61803 | + | 4.80828i | 0.361582 | + | 0.262705i | ||||
\(336\) | −0.500000 | − | 0.363271i | −0.0272772 | − | 0.0198181i | ||||
\(337\) | −9.70820 | + | 29.8788i | −0.528840 | + | 1.62760i | 0.227756 | + | 0.973718i | \(0.426861\pi\) |
−0.756596 | + | 0.653883i | \(0.773139\pi\) | |||||||
\(338\) | −5.75329 | − | 17.7068i | −0.312938 | − | 0.963123i | ||||
\(339\) | −5.23607 | + | 3.80423i | −0.284384 | + | 0.206617i | ||||
\(340\) | −16.8541 | −0.914042 | ||||||||
\(341\) | −5.47214 | + | 9.23305i | −0.296333 | + | 0.499998i | ||||
\(342\) | −18.9443 | −1.02439 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | 3.61803 | + | 11.1352i | 0.195071 | + | 0.600368i | ||||
\(345\) | 0.854102 | − | 2.62866i | 0.0459833 | − | 0.141522i | ||||
\(346\) | −2.82624 | − | 2.05338i | −0.151939 | − | 0.110391i | ||||
\(347\) | 1.23607 | + | 0.898056i | 0.0663556 | + | 0.0482102i | 0.620469 | − | 0.784231i | \(-0.286942\pi\) |
−0.554113 | + | 0.832441i | \(0.686942\pi\) | |||||||
\(348\) | 0.489357 | − | 1.50609i | 0.0262323 | − | 0.0807347i | ||||
\(349\) | 1.20163 | + | 3.69822i | 0.0643216 | + | 0.197961i | 0.978053 | − | 0.208358i | \(-0.0668120\pi\) |
−0.913731 | + | 0.406320i | \(0.866812\pi\) | |||||||
\(350\) | −1.80902 | + | 1.31433i | −0.0966960 | + | 0.0702538i | ||||
\(351\) | −16.0344 | −0.855855 | ||||||||
\(352\) | 20.4271 | − | 8.81678i | 1.08877 | − | 0.469936i | ||||
\(353\) | −13.5623 | −0.721849 | −0.360924 | − | 0.932595i | \(-0.617539\pi\) | ||||
−0.360924 | + | 0.932595i | \(0.617539\pi\) | |||||||
\(354\) | −10.3262 | + | 7.50245i | −0.548833 | + | 0.398751i | ||||
\(355\) | −5.04508 | − | 15.5272i | −0.267765 | − | 0.824097i | ||||
\(356\) | 11.8328 | − | 36.4177i | 0.627138 | − | 1.93013i | ||||
\(357\) | 2.80902 | + | 2.04087i | 0.148669 | + | 0.108014i | ||||
\(358\) | 35.4894 | + | 25.7845i | 1.87567 | + | 1.36275i | ||||
\(359\) | −4.01064 | + | 12.3435i | −0.211674 | + | 0.651465i | 0.787699 | + | 0.616060i | \(0.211272\pi\) |
−0.999373 | + | 0.0354047i | \(0.988728\pi\) | |||||||
\(360\) | −1.80902 | − | 5.56758i | −0.0953436 | − | 0.293437i | ||||
\(361\) | 6.89919 | − | 5.01255i | 0.363115 | − | 0.263819i | ||||
\(362\) | −12.3607 | −0.649663 | ||||||||
\(363\) | 6.14590 | + | 2.90617i | 0.322576 | + | 0.152534i | ||||
\(364\) | −13.8541 | −0.726152 | ||||||||
\(365\) | 5.16312 | − | 3.75123i | 0.270250 | − | 0.196348i | ||||
\(366\) | 2.03444 | + | 6.26137i | 0.106342 | + | 0.327287i | ||||
\(367\) | −9.71885 | + | 29.9115i | −0.507320 | + | 1.56137i | 0.289516 | + | 0.957173i | \(0.406506\pi\) |
−0.796836 | + | 0.604196i | \(0.793494\pi\) | |||||||
\(368\) | −3.61803 | − | 2.62866i | −0.188603 | − | 0.137028i | ||||
\(369\) | 5.23607 | + | 3.80423i | 0.272579 | + | 0.198040i | ||||
\(370\) | −5.00000 | + | 15.3884i | −0.259938 | + | 0.800006i | ||||
\(371\) | 0.472136 | + | 1.45309i | 0.0245121 | + | 0.0754404i | ||||
\(372\) | −4.85410 | + | 3.52671i | −0.251673 | + | 0.182851i | ||||
\(373\) | 11.1246 | 0.576011 | 0.288005 | − | 0.957629i | \(-0.407008\pi\) | ||||
0.288005 | + | 0.957629i | \(0.407008\pi\) | |||||||
\(374\) | −38.2533 | + | 16.5110i | −1.97803 | + | 0.853763i | ||||
\(375\) | −0.618034 | −0.0319151 | ||||||||
\(376\) | −2.07295 | + | 1.50609i | −0.106904 | + | 0.0776704i | ||||
\(377\) | 1.21885 | + | 3.75123i | 0.0627738 | + | 0.193198i | ||||
\(378\) | −2.39919 | + | 7.38394i | −0.123401 | + | 0.379789i | ||||
\(379\) | −20.0172 | − | 14.5434i | −1.02822 | − | 0.747042i | −0.0602648 | − | 0.998182i | \(-0.519195\pi\) |
−0.967951 | + | 0.251140i | \(0.919195\pi\) | |||||||
\(380\) | −7.85410 | − | 5.70634i | −0.402907 | − | 0.292729i | ||||
\(381\) | 1.76393 | − | 5.42882i | 0.0903690 | − | 0.278127i | ||||
\(382\) | −15.9549 | − | 49.1042i | −0.816324 | − | 2.51239i | ||||
\(383\) | −21.6803 | + | 15.7517i | −1.10781 | + | 0.804874i | −0.982318 | − | 0.187220i | \(-0.940052\pi\) |
−0.125496 | + | 0.992094i | \(0.540052\pi\) | |||||||
\(384\) | 9.67376 | 0.493662 | ||||||||
\(385\) | −1.69098 | + | 2.85317i | −0.0861805 | + | 0.145411i | ||||
\(386\) | −8.94427 | −0.455251 | ||||||||
\(387\) | −11.0902 | + | 8.05748i | −0.563745 | + | 0.409585i | ||||
\(388\) | −14.2082 | − | 43.7284i | −0.721312 | − | 2.21997i | ||||
\(389\) | −10.3713 | + | 31.9196i | −0.525847 | + | 1.61839i | 0.236788 | + | 0.971561i | \(0.423905\pi\) |
−0.762635 | + | 0.646829i | \(0.776095\pi\) | |||||||
\(390\) | −5.16312 | − | 3.75123i | −0.261445 | − | 0.189951i | ||||
\(391\) | 20.3262 | + | 14.7679i | 1.02794 | + | 0.746844i | ||||
\(392\) | −0.690983 | + | 2.12663i | −0.0348999 | + | 0.107411i | ||||
\(393\) | 1.52786 | + | 4.70228i | 0.0770705 | + | 0.237199i | ||||
\(394\) | −21.7082 | + | 15.7719i | −1.09364 | + | 0.794579i | ||||
\(395\) | −10.7984 | −0.543325 | ||||||||
\(396\) | −17.2082 | − | 19.5559i | −0.864745 | − | 0.982722i | ||||
\(397\) | 35.1591 | 1.76458 | 0.882291 | − | 0.470704i | \(-0.156000\pi\) | ||||
0.882291 | + | 0.470704i | \(0.156000\pi\) | |||||||
\(398\) | −32.5623 | + | 23.6579i | −1.63220 | + | 1.18586i | ||||
\(399\) | 0.618034 | + | 1.90211i | 0.0309404 | + | 0.0952248i | ||||
\(400\) | −0.309017 | + | 0.951057i | −0.0154508 | + | 0.0475528i | ||||
\(401\) | −12.5451 | − | 9.11454i | −0.626472 | − | 0.455158i | 0.228704 | − | 0.973496i | \(-0.426551\pi\) |
−0.855176 | + | 0.518338i | \(0.826551\pi\) | |||||||
\(402\) | 9.14590 | + | 6.64488i | 0.456156 | + | 0.331417i | ||||
\(403\) | 4.61803 | − | 14.2128i | 0.230041 | − | 0.707992i | ||||
\(404\) | −12.7082 | − | 39.1118i | −0.632257 | − | 1.94589i | ||||
\(405\) | 4.61803 | − | 3.35520i | 0.229472 | − | 0.166721i | ||||
\(406\) | 1.90983 | 0.0947833 | ||||||||
\(407\) | 2.23607 | + | 23.8949i | 0.110838 | + | 1.18443i | ||||
\(408\) | −7.76393 | −0.384372 | ||||||||
\(409\) | 2.61803 | − | 1.90211i | 0.129453 | − | 0.0940534i | −0.521174 | − | 0.853450i | \(-0.674506\pi\) |
0.650628 | + | 0.759397i | \(0.274506\pi\) | |||||||
\(410\) | 1.70820 | + | 5.25731i | 0.0843622 | + | 0.259640i | ||||
\(411\) | −2.18034 | + | 6.71040i | −0.107548 | + | 0.330999i | ||||
\(412\) | 42.0517 | + | 30.5523i | 2.07174 | + | 1.50520i | ||||
\(413\) | −7.47214 | − | 5.42882i | −0.367680 | − | 0.267135i | ||||
\(414\) | −8.09017 | + | 24.8990i | −0.397610 | + | 1.22372i | ||||
\(415\) | −2.95492 | − | 9.09429i | −0.145051 | − | 0.446421i | ||||
\(416\) | −25.0623 | + | 18.2088i | −1.22878 | + | 0.892761i | ||||
\(417\) | 3.41641 | 0.167302 | ||||||||
\(418\) | −23.4164 | − | 5.25731i | −1.14533 | − | 0.257143i | ||||
\(419\) | −35.3050 | −1.72476 | −0.862380 | − | 0.506262i | \(-0.831027\pi\) | ||||
−0.862380 | + | 0.506262i | \(0.831027\pi\) | |||||||
\(420\) | −1.50000 | + | 1.08981i | −0.0731925 | + | 0.0531775i | ||||
\(421\) | −10.6631 | − | 32.8177i | −0.519689 | − | 1.59944i | −0.774586 | − | 0.632469i | \(-0.782042\pi\) |
0.254897 | − | 0.966968i | \(-0.417958\pi\) | |||||||
\(422\) | −5.30244 | + | 16.3192i | −0.258119 | + | 0.794408i | ||||
\(423\) | −2.42705 | − | 1.76336i | −0.118007 | − | 0.0857373i | ||||
\(424\) | −2.76393 | − | 2.00811i | −0.134228 | − | 0.0975226i | ||||
\(425\) | 1.73607 | − | 5.34307i | 0.0842117 | − | 0.259177i | ||||
\(426\) | −6.97214 | − | 21.4580i | −0.337801 | − | 1.03964i | ||||
\(427\) | −3.85410 | + | 2.80017i | −0.186513 | + | 0.135510i | ||||
\(428\) | −21.7082 | −1.04931 | ||||||||
\(429\) | −9.23607 | − | 2.07363i | −0.445922 | − | 0.100116i | ||||
\(430\) | −11.7082 | −0.564620 | ||||||||
\(431\) | 4.30902 | − | 3.13068i | 0.207558 | − | 0.150800i | −0.479150 | − | 0.877733i | \(-0.659055\pi\) |
0.686708 | + | 0.726933i | \(0.259055\pi\) | |||||||
\(432\) | 1.07295 | + | 3.30220i | 0.0516223 | + | 0.158877i | ||||
\(433\) | 3.71885 | − | 11.4454i | 0.178716 | − | 0.550032i | −0.821067 | − | 0.570831i | \(-0.806621\pi\) |
0.999784 | + | 0.0207989i | \(0.00662098\pi\) | |||||||
\(434\) | −5.85410 | − | 4.25325i | −0.281006 | − | 0.204163i | ||||
\(435\) | 0.427051 | + | 0.310271i | 0.0204755 | + | 0.0148763i | ||||
\(436\) | −10.6869 | + | 32.8910i | −0.511811 | + | 1.57519i | ||||
\(437\) | 4.47214 | + | 13.7638i | 0.213931 | + | 0.658413i | ||||
\(438\) | 7.13525 | − | 5.18407i | 0.340936 | − | 0.247704i | ||||
\(439\) | 4.29180 | 0.204836 | 0.102418 | − | 0.994741i | \(-0.467342\pi\) | ||||
0.102418 | + | 0.994741i | \(0.467342\pi\) | |||||||
\(440\) | −0.690983 | − | 7.38394i | −0.0329413 | − | 0.352015i | ||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 46.9336 | − | 34.0993i | 2.23241 | − | 1.62194i | ||||
\(443\) | −1.03444 | − | 3.18368i | −0.0491478 | − | 0.151261i | 0.923471 | − | 0.383669i | \(-0.125340\pi\) |
−0.972618 | + | 0.232408i | \(0.925340\pi\) | |||||||
\(444\) | −4.14590 | + | 12.7598i | −0.196756 | + | 0.605552i | ||||
\(445\) | 10.3262 | + | 7.50245i | 0.489511 | + | 0.355650i | ||||
\(446\) | 2.76393 | + | 2.00811i | 0.130876 | + | 0.0950870i | ||||
\(447\) | −3.40983 | + | 10.4944i | −0.161279 | + | 0.496367i | ||||
\(448\) | 4.01722 | + | 12.3637i | 0.189796 | + | 0.584132i | ||||
\(449\) | 7.50000 | − | 5.44907i | 0.353947 | − | 0.257157i | −0.396576 | − | 0.918002i | \(-0.629802\pi\) |
0.750523 | + | 0.660844i | \(0.229802\pi\) | |||||||
\(450\) | 5.85410 | 0.275965 | ||||||||
\(451\) | 5.41641 | + | 6.15537i | 0.255049 | + | 0.289845i | ||||
\(452\) | 31.4164 | 1.47770 | ||||||||
\(453\) | 0.190983 | − | 0.138757i | 0.00897316 | − | 0.00651939i | ||||
\(454\) | 7.46149 | + | 22.9641i | 0.350185 | + | 1.07776i | ||||
\(455\) | 1.42705 | − | 4.39201i | 0.0669012 | − | 0.205901i | ||||
\(456\) | −3.61803 | − | 2.62866i | −0.169430 | − | 0.123098i | ||||
\(457\) | 30.5623 | + | 22.2048i | 1.42964 | + | 1.03870i | 0.990083 | + | 0.140485i | \(0.0448662\pi\) |
0.439562 | + | 0.898212i | \(0.355134\pi\) | |||||||
\(458\) | 17.1115 | − | 52.6636i | 0.799566 | − | 2.46081i | ||||
\(459\) | −6.02786 | − | 18.5519i | −0.281357 | − | 0.865927i | ||||
\(460\) | −10.8541 | + | 7.88597i | −0.506075 | + | 0.367685i | ||||
\(461\) | 16.2918 | 0.758785 | 0.379392 | − | 0.925236i | \(-0.376133\pi\) | ||||
0.379392 | + | 0.925236i | \(0.376133\pi\) | |||||||
\(462\) | −2.33688 | + | 3.94298i | −0.108722 | + | 0.183444i | ||||
\(463\) | −17.1246 | −0.795848 | −0.397924 | − | 0.917418i | \(-0.630269\pi\) | ||||
−0.397924 | + | 0.917418i | \(0.630269\pi\) | |||||||
\(464\) | 0.690983 | − | 0.502029i | 0.0320781 | − | 0.0233061i | ||||
\(465\) | −0.618034 | − | 1.90211i | −0.0286606 | − | 0.0882084i | ||||
\(466\) | −4.59675 | + | 14.1473i | −0.212940 | + | 0.655363i | ||||
\(467\) | 26.1525 | + | 19.0009i | 1.21019 | + | 0.879256i | 0.995248 | − | 0.0973702i | \(-0.0310431\pi\) |
0.214944 | + | 0.976626i | \(0.431043\pi\) | |||||||
\(468\) | 29.3435 | + | 21.3193i | 1.35640 | + | 0.985484i | ||||
\(469\) | −2.52786 | + | 7.77997i | −0.116726 | + | 0.359245i | ||||
\(470\) | −0.791796 | − | 2.43690i | −0.0365228 | − | 0.112406i | ||||
\(471\) | 8.04508 | − | 5.84510i | 0.370698 | − | 0.269328i | ||||
\(472\) | 20.6525 | 0.950607 | ||||||||
\(473\) | −15.9443 | + | 6.88191i | −0.733118 | + | 0.316431i | ||||
\(474\) | −14.9230 | −0.685435 | ||||||||
\(475\) | 2.61803 | − | 1.90211i | 0.120124 | − | 0.0872749i | ||||
\(476\) | −5.20820 | − | 16.0292i | −0.238718 | − | 0.734697i | ||||
\(477\) | 1.23607 | − | 3.80423i | 0.0565957 | − | 0.174184i | ||||
\(478\) | 45.1869 | + | 32.8302i | 2.06680 | + | 1.50162i | ||||
\(479\) | −18.3262 | − | 13.3148i | −0.837347 | − | 0.608368i | 0.0842812 | − | 0.996442i | \(-0.473141\pi\) |
−0.921628 | + | 0.388074i | \(0.873141\pi\) | |||||||
\(480\) | −1.28115 | + | 3.94298i | −0.0584764 | + | 0.179972i | ||||
\(481\) | −10.3262 | − | 31.7809i | −0.470836 | − | 1.44908i | ||||
\(482\) | −30.9787 | + | 22.5074i | −1.41104 | + | 1.02518i | ||||
\(483\) | 2.76393 | 0.125763 | ||||||||
\(484\) | −15.8435 | − | 28.9480i | −0.720157 | − | 1.31582i | ||||
\(485\) | 15.3262 | 0.695929 | ||||||||
\(486\) | 25.2254 | − | 18.3273i | 1.14425 | − | 0.831345i | ||||
\(487\) | −0.562306 | − | 1.73060i | −0.0254805 | − | 0.0784210i | 0.937508 | − | 0.347965i | \(-0.113127\pi\) |
−0.962988 | + | 0.269544i | \(0.913127\pi\) | |||||||
\(488\) | 3.29180 | − | 10.1311i | 0.149013 | − | 0.458614i | ||||
\(489\) | 11.0902 | + | 8.05748i | 0.501515 | + | 0.364372i | ||||
\(490\) | −1.80902 | − | 1.31433i | −0.0817231 | − | 0.0593753i | ||||
\(491\) | 0.652476 | − | 2.00811i | 0.0294458 | − | 0.0906249i | −0.935254 | − | 0.353979i | \(-0.884829\pi\) |
0.964699 | + | 0.263354i | \(0.0848286\pi\) | |||||||
\(492\) | 1.41641 | + | 4.35926i | 0.0638566 | + | 0.196530i | ||||
\(493\) | −3.88197 | + | 2.82041i | −0.174835 | + | 0.127025i | ||||
\(494\) | 33.4164 | 1.50348 | ||||||||
\(495\) | 7.97214 | − | 3.44095i | 0.358321 | − | 0.154659i | ||||
\(496\) | −3.23607 | −0.145304 | ||||||||
\(497\) | 13.2082 | − | 9.59632i | 0.592469 | − | 0.430454i | ||||
\(498\) | −4.08359 | − | 12.5680i | −0.182990 | − | 0.563186i | ||||
\(499\) | −7.11803 | + | 21.9071i | −0.318647 | + | 0.980695i | 0.655580 | + | 0.755126i | \(0.272424\pi\) |
−0.974227 | + | 0.225569i | \(0.927576\pi\) | |||||||
\(500\) | 2.42705 | + | 1.76336i | 0.108541 | + | 0.0788597i | ||||
\(501\) | 6.00000 | + | 4.35926i | 0.268060 | + | 0.194757i | ||||
\(502\) | 5.32624 | − | 16.3925i | 0.237722 | − | 0.731632i | ||||
\(503\) | 0.954915 | + | 2.93893i | 0.0425776 | + | 0.131040i | 0.970086 | − | 0.242763i | \(-0.0780536\pi\) |
−0.927508 | + | 0.373803i | \(0.878054\pi\) | |||||||
\(504\) | 4.73607 | − | 3.44095i | 0.210961 | − | 0.153272i | ||||
\(505\) | 13.7082 | 0.610007 | ||||||||
\(506\) | −16.9098 | + | 28.5317i | −0.751734 | + | 1.26839i | ||||
\(507\) | 5.14590 | 0.228537 | ||||||||
\(508\) | −22.4164 | + | 16.2865i | −0.994567 | + | 0.722595i | ||||
\(509\) | 8.14590 | + | 25.0705i | 0.361061 | + | 1.11123i | 0.952411 | + | 0.304816i | \(0.0985949\pi\) |
−0.591351 | + | 0.806414i | \(0.701405\pi\) | |||||||
\(510\) | 2.39919 | − | 7.38394i | 0.106238 | − | 0.326966i | ||||
\(511\) | 5.16312 | + | 3.75123i | 0.228403 | + | 0.165944i | ||||
\(512\) | 9.04508 | + | 6.57164i | 0.399740 | + | 0.290428i | ||||
\(513\) | 3.47214 | − | 10.6861i | 0.153299 | − | 0.471804i | ||||
\(514\) | 1.64590 | + | 5.06555i | 0.0725975 | + | 0.223432i | ||||
\(515\) | −14.0172 | + | 10.1841i | −0.617673 | + | 0.448765i | ||||
\(516\) | −9.70820 | −0.427380 | ||||||||
\(517\) | −2.51064 | − | 2.85317i | −0.110418 | − | 0.125482i | ||||
\(518\) | −16.1803 | −0.710923 | ||||||||
\(519\) | 0.781153 | − | 0.567541i | 0.0342888 | − | 0.0249123i | ||||
\(520\) | 3.19098 | + | 9.82084i | 0.139934 | + | 0.430672i | ||||
\(521\) | −4.38197 | + | 13.4863i | −0.191977 | + | 0.590846i | 0.808021 | + | 0.589153i | \(0.200539\pi\) |
−0.999999 | + | 0.00169226i | \(0.999461\pi\) | |||||||
\(522\) | −4.04508 | − | 2.93893i | −0.177049 | − | 0.128633i | ||||
\(523\) | −0.927051 | − | 0.673542i | −0.0405371 | − | 0.0294519i | 0.567332 | − | 0.823489i | \(-0.307976\pi\) |
−0.607869 | + | 0.794037i | \(0.707976\pi\) | |||||||
\(524\) | 7.41641 | − | 22.8254i | 0.323987 | − | 0.997130i | ||||
\(525\) | −0.190983 | − | 0.587785i | −0.00833518 | − | 0.0256531i | ||||
\(526\) | 25.6525 | − | 18.6376i | 1.11850 | − | 0.812639i | ||||
\(527\) | 18.1803 | 0.791948 | ||||||||
\(528\) | 0.190983 | + | 2.04087i | 0.00831147 | + | 0.0888175i | ||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 2.76393 | − | 2.00811i | 0.120058 | − | 0.0872269i | ||||
\(531\) | 7.47214 | + | 22.9969i | 0.324263 | + | 0.997979i | ||||
\(532\) | 3.00000 | − | 9.23305i | 0.130066 | − | 0.400304i | ||||
\(533\) | −9.23607 | − | 6.71040i | −0.400059 | − | 0.290660i | ||||
\(534\) | 14.2705 | + | 10.3681i | 0.617545 | + | 0.448673i | ||||
\(535\) | 2.23607 | − | 6.88191i | 0.0966736 | − | 0.297531i | ||||
\(536\) | −5.65248 | − | 17.3965i | −0.244150 | − | 0.751416i | ||||
\(537\) | −9.80902 | + | 7.12667i | −0.423290 | + | 0.307538i | ||||
\(538\) | 41.7082 | 1.79817 | ||||||||
\(539\) | −3.23607 | − | 0.726543i | −0.139387 | − | 0.0312944i | ||||
\(540\) | 10.4164 | 0.448251 | ||||||||
\(541\) | −4.97214 | + | 3.61247i | −0.213769 | + | 0.155312i | −0.689517 | − | 0.724269i | \(-0.742177\pi\) |
0.475748 | + | 0.879581i | \(0.342177\pi\) | |||||||
\(542\) | −16.0557 | − | 49.4145i | −0.689653 | − | 2.12253i | ||||
\(543\) | 1.05573 | − | 3.24920i | 0.0453056 | − | 0.139436i | ||||
\(544\) | −30.4894 | − | 22.1518i | −1.30722 | − | 0.949751i | ||||
\(545\) | −9.32624 | − | 6.77591i | −0.399492 | − | 0.290248i | ||||
\(546\) | 1.97214 | − | 6.06961i | 0.0843996 | − | 0.259755i | ||||
\(547\) | −5.58359 | − | 17.1845i | −0.238737 | − | 0.734757i | −0.996604 | − | 0.0823478i | \(-0.973758\pi\) |
0.757866 | − | 0.652410i | \(-0.226242\pi\) | |||||||
\(548\) | 27.7082 | − | 20.1312i | 1.18364 | − | 0.859962i | ||||
\(549\) | 12.4721 | 0.532298 | ||||||||
\(550\) | 7.23607 | + | 1.62460i | 0.308547 | + | 0.0692731i | ||||
\(551\) | −2.76393 | −0.117747 | ||||||||
\(552\) | −5.00000 | + | 3.63271i | −0.212814 | + | 0.154619i | ||||
\(553\) | −3.33688 | − | 10.2699i | −0.141899 | − | 0.436719i | ||||
\(554\) | 6.50658 | − | 20.0252i | 0.276438 | − | 0.850789i | ||||
\(555\) | −3.61803 | − | 2.62866i | −0.153577 | − | 0.111580i | ||||
\(556\) | −13.4164 | − | 9.74759i | −0.568982 | − | 0.413390i | ||||
\(557\) | −5.47214 | + | 16.8415i | −0.231862 | + | 0.713597i | 0.765660 | + | 0.643245i | \(0.222412\pi\) |
−0.997522 | + | 0.0703523i | \(0.977588\pi\) | |||||||
\(558\) | 5.85410 | + | 18.0171i | 0.247824 | + | 0.762724i | ||||
\(559\) | 19.5623 | − | 14.2128i | 0.827397 | − | 0.601139i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −1.07295 | − | 11.4657i | −0.0452999 | − | 0.484081i | ||||
\(562\) | 18.9443 | 0.799116 | ||||||||
\(563\) | 19.1074 | − | 13.8823i | 0.805281 | − | 0.585071i | −0.107178 | − | 0.994240i | \(-0.534181\pi\) |
0.912458 | + | 0.409169i | \(0.134181\pi\) | |||||||
\(564\) | −0.656541 | − | 2.02063i | −0.0276454 | − | 0.0850837i | ||||
\(565\) | −3.23607 | + | 9.95959i | −0.136142 | + | 0.419003i | ||||
\(566\) | −13.4549 | − | 9.77557i | −0.565552 | − | 0.410898i | ||||
\(567\) | 4.61803 | + | 3.35520i | 0.193939 | + | 0.140905i | ||||
\(568\) | −11.2812 | + | 34.7198i | −0.473347 | + | 1.45681i | ||||
\(569\) | −11.6803 | − | 35.9484i | −0.489665 | − | 1.50703i | −0.825108 | − | 0.564974i | \(-0.808886\pi\) |
0.335443 | − | 0.942060i | \(-0.391114\pi\) | |||||||
\(570\) | 3.61803 | − | 2.62866i | 0.151543 | − | 0.110102i | ||||
\(571\) | −35.9787 | −1.50566 | −0.752831 | − | 0.658214i | \(-0.771312\pi\) | ||||
−0.752831 | + | 0.658214i | \(0.771312\pi\) | |||||||
\(572\) | 30.3541 | + | 34.4953i | 1.26917 | + | 1.44232i | ||||
\(573\) | 14.2705 | 0.596159 | ||||||||
\(574\) | −4.47214 | + | 3.24920i | −0.186663 | + | 0.135619i | ||||
\(575\) | −1.38197 | − | 4.25325i | −0.0576320 | − | 0.177373i | ||||
\(576\) | 10.5172 | − | 32.3687i | 0.438218 | − | 1.34869i | ||||
\(577\) | −26.8713 | − | 19.5232i | −1.11867 | − | 0.812760i | −0.134661 | − | 0.990892i | \(-0.542995\pi\) |
−0.984007 | + | 0.178132i | \(0.942995\pi\) | |||||||
\(578\) | 26.3435 | + | 19.1396i | 1.09574 | + | 0.796104i | ||||
\(579\) | 0.763932 | − | 2.35114i | 0.0317479 | − | 0.0977101i | ||||
\(580\) | −0.791796 | − | 2.43690i | −0.0328775 | − | 0.101187i | ||||
\(581\) | 7.73607 | − | 5.62058i | 0.320946 | − | 0.233181i | ||||
\(582\) | 21.1803 | 0.877953 | ||||||||
\(583\) | 2.58359 | − | 4.35926i | 0.107001 | − | 0.180542i | ||||
\(584\) | −14.2705 | −0.590518 | ||||||||
\(585\) | −9.78115 | + | 7.10642i | −0.404401 | + | 0.293814i | ||||
\(586\) | 6.50658 | + | 20.0252i | 0.268784 | + | 0.827233i | ||||
\(587\) | 2.07953 | − | 6.40013i | 0.0858313 | − | 0.264161i | −0.898925 | − | 0.438103i | \(-0.855650\pi\) |
0.984756 | + | 0.173942i | \(0.0556504\pi\) | |||||||
\(588\) | −1.50000 | − | 1.08981i | −0.0618590 | − | 0.0449432i | ||||
\(589\) | 8.47214 | + | 6.15537i | 0.349088 | + | 0.253627i | ||||
\(590\) | −6.38197 | + | 19.6417i | −0.262741 | + | 0.808635i | ||||
\(591\) | −2.29180 | − | 7.05342i | −0.0942719 | − | 0.290139i | ||||
\(592\) | −5.85410 | + | 4.25325i | −0.240602 | + | 0.174808i | ||||
\(593\) | 9.79837 | 0.402371 | 0.201185 | − | 0.979553i | \(-0.435521\pi\) | ||||
0.201185 | + | 0.979553i | \(0.435521\pi\) | |||||||
\(594\) | 23.6418 | − | 10.2044i | 0.970036 | − | 0.418690i | ||||
\(595\) | 5.61803 | 0.230317 | ||||||||
\(596\) | 43.3328 | − | 31.4831i | 1.77498 | − | 1.28960i | ||||
\(597\) | −3.43769 | − | 10.5801i | −0.140695 | − | 0.433016i | ||||
\(598\) | 14.2705 | − | 43.9201i | 0.583565 | − | 1.79603i | ||||
\(599\) | −21.2533 | − | 15.4414i | −0.868386 | − | 0.630919i | 0.0617675 | − | 0.998091i | \(-0.480326\pi\) |
−0.930153 | + | 0.367171i | \(0.880326\pi\) | |||||||
\(600\) | 1.11803 | + | 0.812299i | 0.0456435 | + | 0.0331620i | ||||
\(601\) | −4.76393 | + | 14.6619i | −0.194325 | + | 0.598070i | 0.805659 | + | 0.592380i | \(0.201811\pi\) |
−0.999984 | + | 0.00569073i | \(0.998189\pi\) | |||||||
\(602\) | −3.61803 | − | 11.1352i | −0.147460 | − | 0.453835i | ||||
\(603\) | 17.3262 | − | 12.5882i | 0.705579 | − | 0.512633i | ||||
\(604\) | −1.14590 | −0.0466259 | ||||||||
\(605\) | 10.8090 | − | 2.04087i | 0.439449 | − | 0.0829732i | ||||
\(606\) | 18.9443 | 0.769558 | ||||||||
\(607\) | 1.54508 | − | 1.12257i | 0.0627131 | − | 0.0455637i | −0.555987 | − | 0.831191i | \(-0.687660\pi\) |
0.618700 | + | 0.785627i | \(0.287660\pi\) | |||||||
\(608\) | −6.70820 | − | 20.6457i | −0.272054 | − | 0.837295i | ||||
\(609\) | −0.163119 | + | 0.502029i | −0.00660991 | + | 0.0203432i | ||||
\(610\) | 8.61803 | + | 6.26137i | 0.348934 | + | 0.253515i | ||||
\(611\) | 4.28115 | + | 3.11044i | 0.173197 | + | 0.125835i | ||||
\(612\) | −13.6353 | + | 41.9650i | −0.551173 | + | 1.69633i | ||||
\(613\) | −12.6180 | − | 38.8343i | −0.509638 | − | 1.56850i | −0.792832 | − | 0.609441i | \(-0.791394\pi\) |
0.283194 | − | 0.959063i | \(-0.408606\pi\) | |||||||
\(614\) | −37.1976 | + | 27.0256i | −1.50117 | + | 1.09066i | ||||
\(615\) | −1.52786 | −0.0616094 | ||||||||
\(616\) | 6.80902 | − | 2.93893i | 0.274343 | − | 0.118413i | ||||
\(617\) | −2.76393 | −0.111272 | −0.0556359 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556359 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(618\) | −19.3713 | + | 14.0741i | −0.779229 | + | 0.566143i | ||||
\(619\) | −6.94427 | − | 21.3723i | −0.279114 | − | 0.859024i | −0.988101 | − | 0.153803i | \(-0.950848\pi\) |
0.708988 | − | 0.705221i | \(-0.249152\pi\) | |||||||
\(620\) | −3.00000 | + | 9.23305i | −0.120483 | + | 0.370808i | ||||
\(621\) | −12.5623 | − | 9.12705i | −0.504108 | − | 0.366256i | ||||
\(622\) | 23.7426 | + | 17.2500i | 0.951993 | + | 0.691664i | ||||
\(623\) | −3.94427 | + | 12.1392i | −0.158024 | + | 0.486348i | ||||
\(624\) | −0.881966 | − | 2.71441i | −0.0353069 | − | 0.108663i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 40.2492 | 1.60868 | ||||||||
\(627\) | 3.38197 | − | 5.70634i | 0.135063 | − | 0.227889i | ||||
\(628\) | −48.2705 | −1.92620 | ||||||||
\(629\) | 32.8885 | − | 23.8949i | 1.31135 | − | 0.952753i | ||||
\(630\) | 1.80902 | + | 5.56758i | 0.0720730 | + | 0.221818i | ||||
\(631\) | −2.93769 | + | 9.04129i | −0.116948 | + | 0.359928i | −0.992348 | − | 0.123470i | \(-0.960598\pi\) |
0.875401 | + | 0.483398i | \(0.160598\pi\) | |||||||
\(632\) | 19.5344 | + | 14.1926i | 0.777038 | + | 0.564551i | ||||
\(633\) | −3.83688 | − | 2.78766i | −0.152502 | − | 0.110799i | ||||
\(634\) | 14.8754 | − | 45.7817i | 0.590777 | − | 1.81823i | ||||
\(635\) | −2.85410 | − | 8.78402i | −0.113262 | − | 0.348583i | ||||
\(636\) | 2.29180 | − | 1.66509i | 0.0908756 | − | 0.0660250i | ||||
\(637\) | 4.61803 | 0.182973 | ||||||||
\(638\) | −4.18441 | − | 4.75528i | −0.165662 | − | 0.188263i | ||||
\(639\) | −42.7426 | −1.69087 | ||||||||
\(640\) | 12.6631 | − | 9.20029i | 0.500554 | − | 0.363674i | ||||
\(641\) | 6.48278 | + | 19.9519i | 0.256054 | + | 0.788054i | 0.993620 | + | 0.112779i | \(0.0359752\pi\) |
−0.737566 | + | 0.675275i | \(0.764025\pi\) | |||||||
\(642\) | 3.09017 | − | 9.51057i | 0.121959 | − | 0.375352i | ||||
\(643\) | −8.73607 | − | 6.34712i | −0.344517 | − | 0.250306i | 0.402048 | − | 0.915618i | \(-0.368298\pi\) |
−0.746565 | + | 0.665312i | \(0.768298\pi\) | |||||||
\(644\) | −10.8541 | − | 7.88597i | −0.427712 | − | 0.310751i | ||||
\(645\) | 1.00000 | − | 3.07768i | 0.0393750 | − | 0.121184i | ||||
\(646\) | 12.5623 | + | 38.6628i | 0.494257 | + | 1.52117i | ||||
\(647\) | 37.9058 | − | 27.5402i | 1.49023 | − | 1.08272i | 0.516153 | − | 0.856497i | \(-0.327364\pi\) |
0.974077 | − | 0.226219i | \(-0.0726363\pi\) | |||||||
\(648\) | −12.7639 | −0.501415 | ||||||||
\(649\) | 2.85410 | + | 30.4993i | 0.112033 | + | 1.19720i | ||||
\(650\) | −10.3262 | −0.405028 | ||||||||
\(651\) | 1.61803 | − | 1.17557i | 0.0634158 | − | 0.0460742i | ||||
\(652\) | −20.5623 | − | 63.2843i | −0.805282 | − | 2.47840i | ||||
\(653\) | −11.7984 | + | 36.3117i | −0.461706 | + | 1.42099i | 0.401372 | + | 0.915915i | \(0.368533\pi\) |
−0.863078 | + | 0.505070i | \(0.831467\pi\) | |||||||
\(654\) | −12.8885 | − | 9.36408i | −0.503982 | − | 0.366164i | ||||
\(655\) | 6.47214 | + | 4.70228i | 0.252887 | + | 0.183733i | ||||
\(656\) | −0.763932 | + | 2.35114i | −0.0298265 | + | 0.0917966i | ||||
\(657\) | −5.16312 | − | 15.8904i | −0.201432 | − | 0.619945i | ||||
\(658\) | 2.07295 | − | 1.50609i | 0.0808120 | − | 0.0587133i | ||||
\(659\) | −4.03444 | −0.157160 | −0.0785798 | − | 0.996908i | \(-0.525039\pi\) | ||||
−0.0785798 | + | 0.996908i | \(0.525039\pi\) | |||||||
\(660\) | 6.00000 | + | 1.34708i | 0.233550 | + | 0.0524352i | ||||
\(661\) | −6.58359 | −0.256072 | −0.128036 | − | 0.991770i | \(-0.540867\pi\) | ||||
−0.128036 | + | 0.991770i | \(0.540867\pi\) | |||||||
\(662\) | −33.4787 | + | 24.3237i | −1.30119 | + | 0.945368i | ||||
\(663\) | 4.95492 | + | 15.2497i | 0.192433 | + | 0.592248i | ||||
\(664\) | −6.60739 | + | 20.3355i | −0.256416 | + | 0.789169i | ||||
\(665\) | 2.61803 | + | 1.90211i | 0.101523 | + | 0.0737608i | ||||
\(666\) | 34.2705 | + | 24.8990i | 1.32796 | + | 0.964816i | ||||
\(667\) | −1.18034 | + | 3.63271i | −0.0457029 | + | 0.140659i | ||||
\(668\) | −11.1246 | − | 34.2380i | −0.430424 | − | 1.32471i | ||||
\(669\) | −0.763932 | + | 0.555029i | −0.0295353 | + | 0.0214587i | ||||
\(670\) | 18.2918 | 0.706674 | ||||||||
\(671\) | 15.4164 | + | 3.46120i | 0.595144 | + | 0.133618i | ||||
\(672\) | −4.14590 | −0.159931 | ||||||||
\(673\) | −17.7082 | + | 12.8658i | −0.682601 | + | 0.495939i | −0.874220 | − | 0.485531i | \(-0.838626\pi\) |
0.191618 | + | 0.981469i | \(0.438626\pi\) | |||||||
\(674\) | 21.7082 | + | 66.8110i | 0.836169 | + | 2.57346i | ||||
\(675\) | −1.07295 | + | 3.30220i | −0.0412978 | + | 0.127102i | ||||
\(676\) | −20.2082 | − | 14.6821i | −0.777239 | − | 0.564697i | ||||
\(677\) | −39.5238 | − | 28.7157i | −1.51902 | − | 1.10363i | −0.961969 | − | 0.273158i | \(-0.911932\pi\) |
−0.557054 | − | 0.830476i | \(-0.688068\pi\) | |||||||
\(678\) | −4.47214 | + | 13.7638i | −0.171751 | + | 0.528596i | ||||
\(679\) | 4.73607 | + | 14.5761i | 0.181754 | + | 0.559380i | ||||
\(680\) | −10.1631 | + | 7.38394i | −0.389738 | + | 0.283161i | ||||
\(681\) | −6.67376 | −0.255739 | ||||||||
\(682\) | 2.23607 | + | 23.8949i | 0.0856235 | + | 0.914984i | ||||
\(683\) | 34.7639 | 1.33020 | 0.665102 | − | 0.746752i | \(-0.268388\pi\) | ||||
0.665102 | + | 0.746752i | \(0.268388\pi\) | |||||||
\(684\) | −20.5623 | + | 14.9394i | −0.786219 | + | 0.571222i | ||||
\(685\) | 3.52786 | + | 10.8576i | 0.134793 | + | 0.414849i | ||||
\(686\) | 0.690983 | − | 2.12663i | 0.0263819 | − | 0.0811950i | ||||
\(687\) | 12.3820 | + | 8.99602i | 0.472401 | + | 0.343220i | ||||
\(688\) | −4.23607 | − | 3.07768i | −0.161499 | − | 0.117336i | ||||
\(689\) | −2.18034 | + | 6.71040i | −0.0830643 | + | 0.255646i | ||||
\(690\) | −1.90983 | − | 5.87785i | −0.0727060 | − | 0.223766i | ||||
\(691\) | 21.7082 | − | 15.7719i | 0.825819 | − | 0.599993i | −0.0925544 | − | 0.995708i | \(-0.529503\pi\) |
0.918373 | + | 0.395715i | \(0.129503\pi\) | |||||||
\(692\) | −4.68692 | −0.178170 | ||||||||
\(693\) | 5.73607 | + | 6.51864i | 0.217895 | + | 0.247623i | ||||
\(694\) | 3.41641 | 0.129685 | ||||||||
\(695\) | 4.47214 | − | 3.24920i | 0.169638 | − | 0.123249i | ||||
\(696\) | −0.364745 | − | 1.12257i | −0.0138256 | − | 0.0425509i | ||||
\(697\) | 4.29180 | − | 13.2088i | 0.162563 | − | 0.500319i | ||||
\(698\) | 7.03444 | + | 5.11082i | 0.266258 | + | 0.193447i | ||||
\(699\) | −3.32624 | − | 2.41665i | −0.125810 | − | 0.0914062i | ||||
\(700\) | −0.927051 | + | 2.85317i | −0.0350392 | + | 0.107840i | ||||
\(701\) | −15.8541 | − | 48.7939i | −0.598801 | − | 1.84292i | −0.534814 | − | 0.844970i | \(-0.679618\pi\) |
−0.0639871 | − | 0.997951i | \(-0.520382\pi\) | |||||||
\(702\) | −29.0066 | + | 21.0745i | −1.09478 | + | 0.795406i | ||||
\(703\) | 23.4164 | 0.883167 | ||||||||
\(704\) | 21.9828 | − | 37.0912i | 0.828507 | − | 1.39793i | ||||
\(705\) | 0.708204 | 0.0266725 | ||||||||
\(706\) | −24.5344 | + | 17.8253i | −0.923366 | + | 0.670865i | ||||
\(707\) | 4.23607 | + | 13.0373i | 0.159314 | + | 0.490317i | ||||
\(708\) | −5.29180 | + | 16.2865i | −0.198878 | + | 0.612083i | ||||
\(709\) | −0.208204 | − | 0.151269i | −0.00781926 | − | 0.00568103i | 0.583869 | − | 0.811848i | \(-0.301538\pi\) |
−0.591688 | + | 0.806167i | \(0.701538\pi\) | |||||||
\(710\) | −29.5344 | − | 21.4580i | −1.10841 | − | 0.805305i | ||||
\(711\) | −8.73607 | + | 26.8869i | −0.327628 | + | 1.00834i | ||||
\(712\) | −8.81966 | − | 27.1441i | −0.330531 | − | 1.01727i | ||||
\(713\) | 11.7082 | − | 8.50651i | 0.438476 | − | 0.318571i | ||||
\(714\) | 7.76393 | 0.290558 | ||||||||
\(715\) | −14.0623 | + | 6.06961i | −0.525900 | + | 0.226991i | ||||
\(716\) | 58.8541 | 2.19948 | ||||||||
\(717\) | −12.4894 | + | 9.07405i | −0.466424 | + | 0.338877i | ||||
\(718\) | 8.96807 | + | 27.6009i | 0.334685 | + | 1.03006i | ||||
\(719\) | 6.76393 | − | 20.8172i | 0.252252 | − | 0.776352i | −0.742107 | − | 0.670282i | \(-0.766173\pi\) |
0.994359 | − | 0.106070i | \(-0.0338268\pi\) | |||||||
\(720\) | 2.11803 | + | 1.53884i | 0.0789345 | + | 0.0573492i | ||||
\(721\) | −14.0172 | − | 10.1841i | −0.522029 | − | 0.379276i | ||||
\(722\) | 5.89261 | − | 18.1356i | 0.219300 | − | 0.674937i | ||||
\(723\) | −3.27051 | − | 10.0656i | −0.121632 | − | 0.374343i | ||||
\(724\) | −13.4164 | + | 9.74759i | −0.498617 | + | 0.362266i | ||||
\(725\) | 0.854102 | 0.0317206 | ||||||||
\(726\) | 14.9377 | − | 2.82041i | 0.554390 | − | 0.104675i | ||||
\(727\) | −41.5623 | −1.54146 | −0.770730 | − | 0.637162i | \(-0.780108\pi\) | ||||
−0.770730 | + | 0.637162i | \(0.780108\pi\) | |||||||
\(728\) | −8.35410 | + | 6.06961i | −0.309624 | + | 0.224955i | ||||
\(729\) | −2.62868 | − | 8.09024i | −0.0973584 | − | 0.299638i | ||||
\(730\) | 4.40983 | − | 13.5721i | 0.163215 | − | 0.502325i | ||||
\(731\) | 23.7984 | + | 17.2905i | 0.880215 | + | 0.639513i | ||||
\(732\) | 7.14590 | + | 5.19180i | 0.264120 | + | 0.191894i | ||||
\(733\) | 10.7746 | − | 33.1607i | 0.397968 | − | 1.22482i | −0.528658 | − | 0.848835i | \(-0.677305\pi\) |
0.926626 | − | 0.375985i | \(-0.122695\pi\) | |||||||
\(734\) | 21.7320 | + | 66.8842i | 0.802143 | + | 2.46874i | ||||
\(735\) | 0.500000 | − | 0.363271i | 0.0184428 | − | 0.0133995i | ||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | 24.9098 | − | 10.7516i | 0.917565 | − | 0.396042i | ||||
\(738\) | 14.4721 | 0.532727 | ||||||||
\(739\) | −9.70820 | + | 7.05342i | −0.357122 | + | 0.259464i | −0.751851 | − | 0.659333i | \(-0.770839\pi\) |
0.394729 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(740\) | 6.70820 | + | 20.6457i | 0.246598 | + | 0.758952i | ||||
\(741\) | −2.85410 | + | 8.78402i | −0.104848 | + | 0.322689i | ||||
\(742\) | 2.76393 | + | 2.00811i | 0.101467 | + | 0.0737202i | ||||
\(743\) | −4.32624 | − | 3.14320i | −0.158714 | − | 0.115313i | 0.505594 | − | 0.862772i | \(-0.331274\pi\) |
−0.664308 | + | 0.747459i | \(0.731274\pi\) | |||||||
\(744\) | −1.38197 | + | 4.25325i | −0.0506653 | + | 0.155932i | ||||
\(745\) | 5.51722 | + | 16.9803i | 0.202135 | + | 0.622109i | ||||
\(746\) | 20.1246 | − | 14.6214i | 0.736814 | − | 0.535327i | ||||
\(747\) | −25.0344 | −0.915962 | ||||||||
\(748\) | −28.5000 | + | 48.0876i | −1.04206 | + | 1.75826i | ||||
\(749\) | 7.23607 | 0.264400 | ||||||||
\(750\) | −1.11803 | + | 0.812299i | −0.0408248 | + | 0.0296610i | ||||
\(751\) | 11.5344 | + | 35.4994i | 0.420898 | + | 1.29539i | 0.906868 | + | 0.421415i | \(0.138466\pi\) |
−0.485970 | + | 0.873975i | \(0.661534\pi\) | |||||||
\(752\) | 0.354102 | − | 1.08981i | 0.0129128 | − | 0.0397414i | ||||
\(753\) | 3.85410 | + | 2.80017i | 0.140451 | + | 0.102044i | ||||
\(754\) | 7.13525 | + | 5.18407i | 0.259851 | + | 0.188793i | ||||
\(755\) | 0.118034 | − | 0.363271i | 0.00429570 | − | 0.0132208i | ||||
\(756\) | 3.21885 | + | 9.90659i | 0.117068 | + | 0.360299i | ||||
\(757\) | −3.38197 | + | 2.45714i | −0.122920 | + | 0.0893063i | −0.647547 | − | 0.762026i | \(-0.724205\pi\) |
0.524627 | + | 0.851332i | \(0.324205\pi\) | |||||||
\(758\) | −55.3262 | −2.00954 | ||||||||
\(759\) | −6.05573 | − | 6.88191i | −0.219809 | − | 0.249797i | ||||
\(760\) | −7.23607 | −0.262480 | ||||||||
\(761\) | −39.5066 | + | 28.7032i | −1.43211 | + | 1.04049i | −0.442494 | + | 0.896772i | \(0.645906\pi\) |
−0.989619 | + | 0.143719i | \(0.954094\pi\) | |||||||
\(762\) | −3.94427 | − | 12.1392i | −0.142886 | − | 0.439758i | ||||
\(763\) | 3.56231 | − | 10.9637i | 0.128964 | − | 0.396911i | ||||
\(764\) | −56.0410 | − | 40.7162i | −2.02749 | − | 1.47306i | ||||
\(765\) | −11.8992 | − | 8.64527i | −0.430216 | − | 0.312570i | ||||
\(766\) | −18.5172 | + | 56.9901i | −0.669054 | + | 2.05914i | ||||
\(767\) | −13.1803 | − | 40.5649i | −0.475914 | − | 1.46471i | ||||
\(768\) | 4.50000 | − | 3.26944i | 0.162380 | − | 0.117976i | ||||
\(769\) | 11.7082 | 0.422209 | 0.211104 | − | 0.977464i | \(-0.432294\pi\) | ||||
0.211104 | + | 0.977464i | \(0.432294\pi\) | |||||||
\(770\) | 0.690983 | + | 7.38394i | 0.0249013 | + | 0.266099i | ||||
\(771\) | −1.47214 | −0.0530177 | ||||||||
\(772\) | −9.70820 | + | 7.05342i | −0.349406 | + | 0.253858i | ||||
\(773\) | −8.46149 | − | 26.0418i | −0.304339 | − | 0.936658i | −0.979923 | − | 0.199376i | \(-0.936109\pi\) |
0.675584 | − | 0.737283i | \(-0.263891\pi\) | |||||||
\(774\) | −9.47214 | + | 29.1522i | −0.340469 | + | 1.04786i | ||||
\(775\) | −2.61803 | − | 1.90211i | −0.0940426 | − | 0.0683259i | ||||
\(776\) | −27.7254 | − | 20.1437i | −0.995285 | − | 0.723117i | ||||
\(777\) | 1.38197 | − | 4.25325i | 0.0495778 | − | 0.152585i | ||||
\(778\) | 23.1910 | + | 71.3745i | 0.831437 | + | 2.55890i | ||||
\(779\) | 6.47214 | − | 4.70228i | 0.231888 | − | 0.168477i | ||||
\(780\) | −8.56231 | −0.306580 | ||||||||
\(781\) | −52.8328 | − | 11.8617i | −1.89051 | − | 0.424445i | ||||
\(782\) | 56.1803 | 2.00900 | ||||||||
\(783\) | 2.39919 | − | 1.74311i | 0.0857399 | − | 0.0622937i | ||||
\(784\) | −0.309017 | − | 0.951057i | −0.0110363 | − | 0.0339663i | ||||
\(785\) | 4.97214 | − | 15.3027i | 0.177463 | − | 0.546175i | ||||
\(786\) | 8.94427 | + | 6.49839i | 0.319032 | + | 0.231790i | ||||
\(787\) | −32.3885 | − | 23.5317i | −1.15453 | − | 0.838813i | −0.165451 | − | 0.986218i | \(-0.552908\pi\) |
−0.989076 | + | 0.147405i | \(0.952908\pi\) | |||||||
\(788\) | −11.1246 | + | 34.2380i | −0.396298 | + | 1.21968i | ||||
\(789\) | 2.70820 | + | 8.33499i | 0.0964146 | + | 0.296734i | ||||
\(790\) | −19.5344 | + | 14.1926i | −0.695004 | + | 0.504950i | ||||
\(791\) | −10.4721 | −0.372346 | ||||||||
\(792\) | −18.9443 | − | 4.25325i | −0.673155 | − | 0.151133i | ||||
\(793\) | −22.0000 | −0.781243 | ||||||||
\(794\) | 63.6033 | − | 46.2105i | 2.25720 | − | 1.63995i | ||||
\(795\) | 0.291796 | + | 0.898056i | 0.0103489 | + | 0.0318508i | ||||
\(796\) | −16.6869 | + | 51.3571i | −0.591452 | + | 1.82030i | ||||
\(797\) | −35.6803 | − | 25.9233i | −1.26386 | − | 0.918250i | −0.264922 | − | 0.964270i | \(-0.585346\pi\) |
−0.998941 | + | 0.0460200i | \(0.985346\pi\) | |||||||
\(798\) | 3.61803 | + | 2.62866i | 0.128077 | + | 0.0930534i | ||||
\(799\) | −1.98936 | + | 6.12261i | −0.0703784 | + | 0.216602i | ||||
\(800\) | 2.07295 | + | 6.37988i | 0.0732898 | + | 0.225563i | ||||
\(801\) | 27.0344 | − | 19.6417i | 0.955215 | − | 0.694004i | ||||
\(802\) | −34.6738 | −1.22437 | ||||||||
\(803\) | −1.97214 | − | 21.0745i | −0.0695952 | − | 0.743703i | ||||
\(804\) | 15.1672 | 0.534905 | ||||||||
\(805\) | 3.61803 | − | 2.62866i | 0.127519 | − | 0.0926479i | ||||
\(806\) | −10.3262 | − | 31.7809i | −0.363726 | − | 1.11943i | ||||
\(807\) | −3.56231 | + | 10.9637i | −0.125399 | + | 0.385939i | ||||
\(808\) | −24.7984 | − | 18.0171i | −0.872404 | − | 0.633838i | ||||
\(809\) | 2.50000 | + | 1.81636i | 0.0878953 | + | 0.0638597i | 0.630865 | − | 0.775893i | \(-0.282700\pi\) |
−0.542970 | + | 0.839752i | \(0.682700\pi\) | |||||||
\(810\) | 3.94427 | − | 12.1392i | 0.138588 | − | 0.426529i | ||||
\(811\) | 9.70820 | + | 29.8788i | 0.340901 | + | 1.04919i | 0.963742 | + | 0.266837i | \(0.0859785\pi\) |
−0.622841 | + | 0.782349i | \(0.714021\pi\) | |||||||
\(812\) | 2.07295 | − | 1.50609i | 0.0727462 | − | 0.0528532i | ||||
\(813\) | 14.3607 | 0.503651 | ||||||||
\(814\) | 35.4508 | + | 40.2874i | 1.24255 | + | 1.41207i | ||||
\(815\) | 22.1803 | 0.776943 | ||||||||
\(816\) | 2.80902 | − | 2.04087i | 0.0983353 | − | 0.0714448i | ||||
\(817\) | 5.23607 | + | 16.1150i | 0.183187 | + | 0.563791i | ||||
\(818\) | 2.23607 | − | 6.88191i | 0.0781823 | − | 0.240620i | ||||
\(819\) | −9.78115 | − | 7.10642i | −0.341781 | − | 0.248319i | ||||
\(820\) | 6.00000 | + | 4.35926i | 0.209529 | + | 0.152232i | ||||
\(821\) | 3.91641 | − | 12.0535i | 0.136684 | − | 0.420669i | −0.859165 | − | 0.511699i | \(-0.829016\pi\) |
0.995848 | + | 0.0910307i | \(0.0290161\pi\) | |||||||
\(822\) | 4.87539 | + | 15.0049i | 0.170049 | + | 0.523356i | ||||
\(823\) | 16.1803 | − | 11.7557i | 0.564011 | − | 0.409778i | −0.268914 | − | 0.963164i | \(-0.586665\pi\) |
0.832925 | + | 0.553386i | \(0.186665\pi\) | |||||||
\(824\) | 38.7426 | 1.34966 | ||||||||
\(825\) | −1.04508 | + | 1.76336i | −0.0363852 | + | 0.0613922i | ||||
\(826\) | −20.6525 | −0.718592 | ||||||||
\(827\) | 30.6525 | − | 22.2703i | 1.06589 | − | 0.774415i | 0.0907218 | − | 0.995876i | \(-0.471083\pi\) |
0.975169 | + | 0.221461i | \(0.0710826\pi\) | |||||||
\(828\) | 10.8541 | + | 33.4055i | 0.377206 | + | 1.16092i | ||||
\(829\) | 10.4721 | − | 32.2299i | 0.363712 | − | 1.11939i | −0.587071 | − | 0.809535i | \(-0.699719\pi\) |
0.950783 | − | 0.309856i | \(-0.100281\pi\) | |||||||
\(830\) | −17.2984 | − | 12.5680i | −0.600435 | − | 0.436242i | ||||
\(831\) | 4.70820 | + | 3.42071i | 0.163326 | + | 0.118663i | ||||
\(832\) | −18.5517 | + | 57.0961i | −0.643163 | + | 1.97945i | ||||
\(833\) | 1.73607 | + | 5.34307i | 0.0601512 | + | 0.185126i | ||||
\(834\) | 6.18034 | − | 4.49028i | 0.214008 | − | 0.155486i | ||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | −29.5623 | + | 12.7598i | −1.02243 | + | 0.441306i | ||||
\(837\) | −11.2361 | −0.388375 | ||||||||
\(838\) | −63.8673 | + | 46.4023i | −2.20626 | + | 1.60294i | ||||
\(839\) | 2.36068 | + | 7.26543i | 0.0814997 | + | 0.250830i | 0.983501 | − | 0.180903i | \(-0.0579021\pi\) |
−0.902001 | + | 0.431734i | \(0.857902\pi\) | |||||||
\(840\) | −0.427051 | + | 1.31433i | −0.0147347 | + | 0.0453486i | ||||
\(841\) | 22.8713 | + | 16.6170i | 0.788666 | + | 0.573000i | ||||
\(842\) | −62.4230 | − | 45.3530i | −2.15124 | − | 1.56297i | ||||
\(843\) | −1.61803 | + | 4.97980i | −0.0557281 | + | 0.171513i | ||||
\(844\) | 7.11397 | + | 21.8945i | 0.244873 | + | 0.753641i | ||||
\(845\) | 6.73607 | − | 4.89404i | 0.231728 | − | 0.168360i | ||||
\(846\) | −6.70820 | −0.230633 | ||||||||
\(847\) | 5.28115 | + | 9.64932i | 0.181463 | + | 0.331555i | ||||
\(848\) | 1.52786 | 0.0524671 | ||||||||
\(849\) | 3.71885 | − | 2.70190i | 0.127631 | − | 0.0927290i | ||||
\(850\) | −3.88197 | − | 11.9475i | −0.133150 | − | 0.409795i | ||||
\(851\) | 10.0000 | − | 30.7768i | 0.342796 | − | 1.05502i | ||||
\(852\) | −24.4894 | − | 17.7926i | −0.838992 | − | 0.609563i | ||||
\(853\) | −14.9164 | − | 10.8374i | −0.510728 | − | 0.371066i | 0.302372 | − | 0.953190i | \(-0.402222\pi\) |
−0.813100 | + | 0.582124i | \(0.802222\pi\) | |||||||
\(854\) | −3.29180 | + | 10.1311i | −0.112643 | + | 0.346679i | ||||
\(855\) | −2.61803 | − | 8.05748i | −0.0895349 | − | 0.275560i | ||||
\(856\) | −13.0902 | + | 9.51057i | −0.447413 | + | 0.325064i | ||||
\(857\) | −57.1935 | −1.95369 | −0.976846 | − | 0.213942i | \(-0.931370\pi\) | ||||
−0.976846 | + | 0.213942i | \(0.931370\pi\) | |||||||
\(858\) | −19.4336 | + | 8.38800i | −0.663453 | + | 0.286361i | ||||
\(859\) | −11.0557 | −0.377217 | −0.188608 | − | 0.982052i | \(-0.560398\pi\) | ||||
−0.188608 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(860\) | −12.7082 | + | 9.23305i | −0.433346 | + | 0.314844i | ||||
\(861\) | −0.472136 | − | 1.45309i | −0.0160904 | − | 0.0495210i | ||||
\(862\) | 3.68034 | − | 11.3269i | 0.125353 | − | 0.385796i | ||||
\(863\) | −2.47214 | − | 1.79611i | −0.0841525 | − | 0.0611404i | 0.544914 | − | 0.838492i | \(-0.316562\pi\) |
−0.629066 | + | 0.777352i | \(0.716562\pi\) | |||||||
\(864\) | 18.8435 | + | 13.6906i | 0.641067 | + | 0.465763i | ||||
\(865\) | 0.482779 | − | 1.48584i | 0.0164150 | − | 0.0505201i | ||||
\(866\) | −8.31559 | − | 25.5928i | −0.282575 | − | 0.869678i | ||||
\(867\) | −7.28115 | + | 5.29007i | −0.247281 | + | 0.179660i | ||||
\(868\) | −9.70820 | −0.329518 | ||||||||
\(869\) | −18.2599 | + | 30.8096i | −0.619424 | + | 1.04514i | ||||
\(870\) | 1.18034 | 0.0400173 | ||||||||
\(871\) | −30.5623 | + | 22.2048i | −1.03556 | + | 0.752381i | ||||
\(872\) | 7.96556 | + | 24.5155i | 0.269748 | + | 0.830198i | ||||
\(873\) | 12.3992 | − | 38.1608i | 0.419649 | − | 1.29155i | ||||
\(874\) | 26.1803 | + | 19.0211i | 0.885563 | + | 0.643399i | ||||
\(875\) | −0.809017 | − | 0.587785i | −0.0273498 | − | 0.0198708i | ||||
\(876\) | 3.65654 | − | 11.2537i | 0.123543 | − | 0.380226i | ||||
\(877\) | 17.0000 | + | 52.3206i | 0.574049 | + | 1.76674i | 0.639394 | + | 0.768879i | \(0.279185\pi\) |
−0.0653450 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(878\) | 7.76393 | − | 5.64083i | 0.262020 | − | 0.190369i | ||||
\(879\) | −5.81966 | −0.196292 | ||||||||
\(880\) | 2.19098 | + | 2.48990i | 0.0738580 | + | 0.0839345i | ||||
\(881\) | −5.23607 | −0.176408 | −0.0882038 | − | 0.996102i | \(-0.528113\pi\) | ||||
−0.0882038 | + | 0.996102i | \(0.528113\pi\) | |||||||
\(882\) | −4.73607 | + | 3.44095i | −0.159472 | + | 0.115863i | ||||
\(883\) | −3.14590 | − | 9.68208i | −0.105868 | − | 0.325828i | 0.884065 | − | 0.467363i | \(-0.154796\pi\) |
−0.989933 | + | 0.141536i | \(0.954796\pi\) | |||||||
\(884\) | 24.0517 | − | 74.0234i | 0.808945 | − | 2.48968i | ||||
\(885\) | −4.61803 | − | 3.35520i | −0.155234 | − | 0.112784i | ||||
\(886\) | −6.05573 | − | 4.39974i | −0.203446 | − | 0.147812i | ||||
\(887\) | −6.53444 | + | 20.1109i | −0.219405 | + | 0.675259i | 0.779406 | + | 0.626519i | \(0.215521\pi\) |
−0.998811 | + | 0.0487407i | \(0.984479\pi\) | |||||||
\(888\) | 3.09017 | + | 9.51057i | 0.103699 | + | 0.319154i | ||||
\(889\) | 7.47214 | − | 5.42882i | 0.250607 | − | 0.182077i | ||||
\(890\) | 28.5410 | 0.956697 | ||||||||
\(891\) | −1.76393 | − | 18.8496i | −0.0590939 | − | 0.631486i | ||||
\(892\) | 4.58359 | 0.153470 | ||||||||
\(893\) | −3.00000 | + | 2.17963i | −0.100391 | + | 0.0729385i | ||||
\(894\) | 7.62461 | + | 23.4661i | 0.255005 | + | 0.784825i | ||||
\(895\) | −6.06231 | + | 18.6579i | −0.202641 | + | 0.623663i | ||||
\(896\) | 12.6631 | + | 9.20029i | 0.423045 | + | 0.307360i | ||||
\(897\) | 10.3262 | + | 7.50245i | 0.344783 | + | 0.250500i | ||||
\(898\) | 6.40576 | − | 19.7149i | 0.213763 | − | 0.657895i | ||||
\(899\) | 0.854102 | + | 2.62866i | 0.0284859 | + | 0.0876706i | ||||
\(900\) | 6.35410 | − | 4.61653i | 0.211803 | − | 0.153884i | ||||
\(901\) | −8.58359 | −0.285961 | ||||||||
\(902\) | 17.8885 | + | 4.01623i | 0.595623 | + | 0.133726i | ||||
\(903\) | 3.23607 | 0.107690 | ||||||||
\(904\) | 18.9443 | − | 13.7638i | 0.630077 | − | 0.457778i | ||||
\(905\) | −1.70820 | − | 5.25731i | −0.0567826 | − | 0.174759i | ||||
\(906\) | 0.163119 | − | 0.502029i | 0.00541926 | − | 0.0166788i | ||||
\(907\) | −22.5623 | − | 16.3925i | −0.749169 | − | 0.544303i | 0.146400 | − | 0.989225i | \(-0.453231\pi\) |
−0.895569 | + | 0.444922i | \(0.853231\pi\) | |||||||
\(908\) | 26.2082 | + | 19.0414i | 0.869750 | + | 0.631910i | ||||
\(909\) | 11.0902 | − | 34.1320i | 0.367838 | − | 1.13209i | ||||
\(910\) | −3.19098 | − | 9.82084i | −0.105780 | − | 0.325558i | ||||
\(911\) | 1.21885 | − | 0.885544i | 0.0403822 | − | 0.0293394i | −0.567411 | − | 0.823435i | \(-0.692055\pi\) |
0.607793 | + | 0.794095i | \(0.292055\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | −30.9443 | − | 6.94742i | −1.02411 | − | 0.229926i | ||||
\(914\) | 84.4721 | 2.79409 | ||||||||
\(915\) | −2.38197 | + | 1.73060i | −0.0787454 | + | 0.0572119i | ||||
\(916\) | −22.9574 | − | 70.6557i | −0.758535 | − | 2.33453i | ||||
\(917\) | −2.47214 | + | 7.60845i | −0.0816371 | + | 0.251253i | ||||
\(918\) | −35.2877 | − | 25.6380i | −1.16467 | − | 0.846181i | ||||
\(919\) | −1.83688 | − | 1.33457i | −0.0605931 | − | 0.0440235i | 0.557076 | − | 0.830461i | \(-0.311923\pi\) |
−0.617670 | + | 0.786438i | \(0.711923\pi\) | |||||||
\(920\) | −3.09017 | + | 9.51057i | −0.101880 | + | 0.313554i | ||||
\(921\) | −3.92705 | − | 12.0862i | −0.129401 | − | 0.398254i | ||||
\(922\) | 29.4721 | − | 21.4128i | 0.970613 | − | 0.705192i | ||||
\(923\) | 75.3951 | 2.48166 | ||||||||
\(924\) | 0.572949 | + | 6.12261i | 0.0188486 | + | 0.201419i | ||||
\(925\) | −7.23607 | −0.237920 | ||||||||
\(926\) | −30.9787 | + | 22.5074i | −1.01802 | + | 0.739638i | ||||
\(927\) | 14.0172 | + | 43.1406i | 0.460386 | + | 1.41692i | ||||
\(928\) | 1.77051 | − | 5.44907i | 0.0581198 | − | 0.178874i | ||||
\(929\) | 14.4721 | + | 10.5146i | 0.474815 | + | 0.344974i | 0.799315 | − | 0.600912i | \(-0.205196\pi\) |
−0.324500 | + | 0.945886i | \(0.605196\pi\) | |||||||
\(930\) | −3.61803 | − | 2.62866i | −0.118640 | − | 0.0861970i | ||||
\(931\) | −1.00000 | + | 3.07768i | −0.0327737 | + | 0.100867i | ||||
\(932\) | 6.16718 | + | 18.9806i | 0.202013 | + | 0.621732i | ||||
\(933\) | −6.56231 | + | 4.76779i | −0.214840 | + | 0.156091i | ||||
\(934\) | 72.2837 | 2.36519 | ||||||||
\(935\) | −12.3090 | − | 13.9883i | −0.402548 | − | 0.457467i | ||||
\(936\) | 27.0344 | 0.883648 | ||||||||
\(937\) | −0.444272 | + | 0.322782i | −0.0145137 | + | 0.0105448i | −0.595018 | − | 0.803712i | \(-0.702855\pi\) |
0.580505 | + | 0.814257i | \(0.302855\pi\) | |||||||
\(938\) | 5.65248 | + | 17.3965i | 0.184560 | + | 0.568017i | ||||
\(939\) | −3.43769 | + | 10.5801i | −0.112185 | + | 0.345270i | ||||
\(940\) | −2.78115 | − | 2.02063i | −0.0907112 | − | 0.0659055i | ||||
\(941\) | 24.7082 | + | 17.9516i | 0.805464 | + | 0.585204i | 0.912512 | − | 0.409050i | \(-0.134140\pi\) |
−0.107048 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(942\) | 6.87132 | − | 21.1478i | 0.223880 | − | 0.689031i | ||||
\(943\) | −3.41641 | − | 10.5146i | −0.111254 | − | 0.342403i | ||||
\(944\) | −7.47214 | + | 5.42882i | −0.243197 | + | 0.176693i | ||||
\(945\) | −3.47214 | −0.112949 | ||||||||
\(946\) | −19.7984 | + | 33.4055i | −0.643701 | + | 1.08611i | ||||
\(947\) | 34.0689 | 1.10709 | 0.553545 | − | 0.832819i | \(-0.313275\pi\) | ||||
0.553545 | + | 0.832819i | \(0.313275\pi\) | |||||||
\(948\) | −16.1976 | + | 11.7682i | −0.526072 | + | 0.382214i | ||||
\(949\) | 9.10739 | + | 28.0297i | 0.295638 | + | 0.909881i | ||||
\(950\) | 2.23607 | − | 6.88191i | 0.0725476 | − | 0.223279i | ||||
\(951\) | 10.7639 | + | 7.82045i | 0.349044 | + | 0.253596i | ||||
\(952\) | −10.1631 | − | 7.38394i | −0.329389 | − | 0.239315i | ||||
\(953\) | 13.2705 | − | 40.8424i | 0.429874 | − | 1.32302i | −0.468375 | − | 0.883530i | \(-0.655160\pi\) |
0.898249 | − | 0.439486i | \(-0.144840\pi\) | |||||||
\(954\) | −2.76393 | − | 8.50651i | −0.0894856 | − | 0.275408i | ||||
\(955\) | 18.6803 | − | 13.5721i | 0.604482 | − | 0.439182i | ||||
\(956\) | 74.9361 | 2.42361 | ||||||||
\(957\) | 1.60739 | − | 0.693786i | 0.0519596 | − | 0.0224269i | ||||
\(958\) | −50.6525 | −1.63651 | ||||||||
\(959\) | −9.23607 | + | 6.71040i | −0.298248 | + | 0.216690i | ||||
\(960\) | 2.48278 | + | 7.64121i | 0.0801314 | + | 0.246619i | ||||
\(961\) | −6.34346 | + | 19.5232i | −0.204628 | + | 0.629779i | ||||
\(962\) | −60.4508 | − | 43.9201i | −1.94901 | − | 1.41604i | ||||
\(963\) | −15.3262 | − | 11.1352i | −0.493881 | − | 0.358826i | ||||
\(964\) | −15.8754 | + | 48.8594i | −0.511312 | + | 1.57366i | ||||
\(965\) | −1.23607 | − | 3.80423i | −0.0397904 | − | 0.122462i | ||||
\(966\) | 5.00000 | − | 3.63271i | 0.160872 | − | 0.116881i | ||||
\(967\) | −16.7639 | −0.539092 | −0.269546 | − | 0.962988i | \(-0.586874\pi\) | ||||
−0.269546 | + | 0.962988i | \(0.586874\pi\) | |||||||
\(968\) | −22.2361 | − | 10.5146i | −0.714694 | − | 0.337953i | ||||
\(969\) | −11.2361 | −0.360955 | ||||||||
\(970\) | 27.7254 | − | 20.1437i | 0.890210 | − | 0.646775i | ||||
\(971\) | −0.798374 | − | 2.45714i | −0.0256210 | − | 0.0788534i | 0.937428 | − | 0.348178i | \(-0.113200\pi\) |
−0.963049 | + | 0.269325i | \(0.913200\pi\) | |||||||
\(972\) | 12.9271 | − | 39.7854i | 0.414635 | − | 1.27612i | ||||
\(973\) | 4.47214 | + | 3.24920i | 0.143370 | + | 0.104164i | ||||
\(974\) | −3.29180 | − | 2.39163i | −0.105476 | − | 0.0766328i | ||||
\(975\) | 0.881966 | − | 2.71441i | 0.0282455 | − | 0.0869308i | ||||
\(976\) | 1.47214 | + | 4.53077i | 0.0471219 | + | 0.145026i | ||||
\(977\) | −33.3607 | + | 24.2380i | −1.06730 | + | 0.775441i | −0.975425 | − | 0.220330i | \(-0.929287\pi\) |
−0.0918772 | + | 0.995770i | \(0.529287\pi\) | |||||||
\(978\) | 30.6525 | 0.980158 | ||||||||
\(979\) | 38.8673 | − | 16.7760i | 1.24220 | − | 0.536163i | ||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | −24.4164 | + | 17.7396i | −0.779556 | + | 0.566381i | ||||
\(982\) | −1.45898 | − | 4.49028i | −0.0465579 | − | 0.143291i | ||||
\(983\) | −8.64590 | + | 26.6093i | −0.275761 | + | 0.848706i | 0.713256 | + | 0.700904i | \(0.247220\pi\) |
−0.989017 | + | 0.147802i | \(0.952780\pi\) | |||||||
\(984\) | 2.76393 | + | 2.00811i | 0.0881109 | + | 0.0640163i | ||||
\(985\) | −9.70820 | − | 7.05342i | −0.309329 | − | 0.224741i | ||||
\(986\) | −3.31559 | + | 10.2044i | −0.105590 | + | 0.324973i | ||||
\(987\) | 0.218847 | + | 0.673542i | 0.00696598 | + | 0.0214391i | ||||
\(988\) | 36.2705 | − | 26.3521i | 1.15392 | − | 0.838371i | ||||
\(989\) | 23.4164 | 0.744598 | ||||||||
\(990\) | 9.89919 | − | 16.7027i | 0.314617 | − | 0.530848i | ||||
\(991\) | 13.8541 | 0.440090 | 0.220045 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220045 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(992\) | −17.5623 | + | 12.7598i | −0.557604 | + | 0.405123i | ||||
\(993\) | −3.53444 | − | 10.8779i | −0.112162 | − | 0.345200i | ||||
\(994\) | 11.2812 | − | 34.7198i | 0.357816 | − | 1.10125i | ||||
\(995\) | −14.5623 | − | 10.5801i | −0.461656 | − | 0.335413i | ||||
\(996\) | −14.3435 | − | 10.4211i | −0.454490 | − | 0.330206i | ||||
\(997\) | −7.79180 | + | 23.9807i | −0.246769 | + | 0.759476i | 0.748572 | + | 0.663054i | \(0.230740\pi\) |
−0.995341 | + | 0.0964222i | \(0.969260\pi\) | |||||||
\(998\) | 15.9164 | + | 48.9857i | 0.503825 | + | 1.55061i | ||||
\(999\) | −20.3262 | + | 14.7679i | −0.643094 | + | 0.467235i |
(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 | 385.2.n.b.36.1 | ✓ | 4 | |
11.2 | odd | 10 | 4235.2.a.k.1.2 | 2 | |||
11.4 | even | 5 | inner | 385.2.n.b.246.1 | yes | 4 | |
11.9 | even | 5 | 4235.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.b.36.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
385.2.n.b.246.1 | yes | 4 | 11.4 | even | 5 | inner | |
4235.2.a.j.1.1 | 2 | 11.9 | even | 5 | |||
4235.2.a.k.1.2 | 2 | 11.2 | odd | 10 |