Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [357,2,Mod(16,357)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(357, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("357.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 357 = 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 357.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.85065935216\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.1 |
$q$-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 \(\left(\mathbb{Z}/357\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(190\) | \(239\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34373 | + | 2.32741i | −0.950161 | + | 1.64573i | −0.205088 | + | 0.978744i | \(0.565748\pi\) |
−0.745073 | + | 0.666983i | \(0.767585\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −2.61122 | − | 4.52277i | −1.30561 | − | 2.26138i | ||||
\(5\) | 2.98396 | + | 1.72279i | 1.33447 | + | 0.770454i | 0.985981 | − | 0.166860i | \(-0.0533628\pi\) |
0.348485 | + | 0.937314i | \(0.386696\pi\) | |||||||
\(6\) | − | 2.68746i | − | 1.09715i | ||||||
\(7\) | −0.462813 | − | 2.60496i | −0.174927 | − | 0.984581i | ||||
\(8\) | 8.66019 | 3.06184 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −8.01926 | + | 4.62992i | −2.53591 | + | 1.46411i | ||||
\(11\) | 0.636072 | − | 0.367236i | 0.191783 | − | 0.110726i | −0.401034 | − | 0.916063i | \(-0.631349\pi\) |
0.592817 | + | 0.805337i | \(0.298016\pi\) | |||||||
\(12\) | 4.52277 | + | 2.61122i | 1.30561 | + | 0.753795i | ||||
\(13\) | 6.64148 | 1.84202 | 0.921008 | − | 0.389543i | \(-0.127367\pi\) | ||||
0.921008 | + | 0.389543i | \(0.127367\pi\) | |||||||
\(14\) | 6.68470 | + | 2.42320i | 1.78656 | + | 0.647629i | ||||
\(15\) | −3.44558 | −0.889644 | ||||||||
\(16\) | −6.41451 | + | 11.1103i | −1.60363 | + | 2.77757i | ||||
\(17\) | 2.64411 | + | 3.16365i | 0.641290 | + | 0.767299i | ||||
\(18\) | 1.34373 | + | 2.32741i | 0.316720 | + | 0.548576i | ||||
\(19\) | 0.832031 | − | 1.44112i | 0.190881 | − | 0.330616i | −0.754661 | − | 0.656114i | \(-0.772199\pi\) |
0.945542 | + | 0.325499i | \(0.105532\pi\) | |||||||
\(20\) | − | 17.9943i | − | 4.02365i | ||||||
\(21\) | 1.70329 | + | 2.02455i | 0.371688 | + | 0.441794i | ||||
\(22\) | 1.97387i | 0.420830i | ||||||||
\(23\) | −4.08650 | − | 2.35934i | −0.852095 | − | 0.491957i | 0.00926217 | − | 0.999957i | \(-0.497052\pi\) |
−0.861357 | + | 0.508000i | \(0.830385\pi\) | |||||||
\(24\) | −7.49994 | + | 4.33009i | −1.53092 | + | 0.883877i | ||||
\(25\) | 3.43600 | + | 5.95132i | 0.687199 | + | 1.19026i | ||||
\(26\) | −8.92436 | + | 15.4574i | −1.75021 | + | 3.03146i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −10.5731 | + | 8.89532i | −1.99813 | + | 1.68106i | ||||
\(29\) | − | 4.36957i | − | 0.811409i | −0.914004 | − | 0.405704i | \(-0.867026\pi\) | ||
0.914004 | − | 0.405704i | \(-0.132974\pi\) | |||||||
\(30\) | 4.62992 | − | 8.01926i | 0.845305 | − | 1.46411i | ||||
\(31\) | −2.56750 | + | 1.48235i | −0.461136 | + | 0.266237i | −0.712522 | − | 0.701650i | \(-0.752447\pi\) |
0.251386 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(32\) | −8.57856 | − | 14.8585i | −1.51649 | − | 2.62664i | ||||
\(33\) | −0.367236 | + | 0.636072i | −0.0639276 | + | 0.110726i | ||||
\(34\) | −10.9161 | + | 1.90282i | −1.87209 | + | 0.326331i | ||||
\(35\) | 3.10678 | − | 8.57041i | 0.525141 | − | 1.44866i | ||||
\(36\) | −5.22244 | −0.870407 | ||||||||
\(37\) | −0.711530 | − | 0.410802i | −0.116975 | − | 0.0675354i | 0.440371 | − | 0.897816i | \(-0.354847\pi\) |
−0.557346 | + | 0.830280i | \(0.688180\pi\) | |||||||
\(38\) | 2.23605 | + | 3.87295i | 0.362735 | + | 0.628276i | ||||
\(39\) | −5.75169 | + | 3.32074i | −0.921008 | + | 0.531744i | ||||
\(40\) | 25.8416 | + | 14.9197i | 4.08592 | + | 2.35901i | ||||
\(41\) | 7.21438i | 1.12670i | 0.826220 | + | 0.563348i | \(0.190487\pi\) | ||||
−0.826220 | + | 0.563348i | \(0.809513\pi\) | |||||||
\(42\) | −7.00072 | + | 1.24379i | −1.08023 | + | 0.191921i | ||||
\(43\) | 3.15651 | 0.481363 | 0.240682 | − | 0.970604i | \(-0.422629\pi\) | ||||
0.240682 | + | 0.970604i | \(0.422629\pi\) | |||||||
\(44\) | −3.32185 | − | 1.91787i | −0.500788 | − | 0.289130i | ||||
\(45\) | 2.98396 | − | 1.72279i | 0.444822 | − | 0.256818i | ||||
\(46\) | 10.9823 | − | 6.34064i | 1.61925 | − | 0.934877i | ||||
\(47\) | 2.84941 | − | 4.93533i | 0.415629 | − | 0.719891i | −0.579865 | − | 0.814713i | \(-0.696895\pi\) |
0.995494 | + | 0.0948214i | \(0.0302280\pi\) | |||||||
\(48\) | − | 12.8290i | − | 1.85171i | ||||||
\(49\) | −6.57161 | + | 2.41122i | −0.938801 | + | 0.344460i | ||||
\(50\) | −18.4682 | −2.61180 | ||||||||
\(51\) | −3.87169 | − | 1.41775i | −0.542145 | − | 0.198525i | ||||
\(52\) | −17.3424 | − | 30.0379i | −2.40496 | − | 4.16551i | ||||
\(53\) | 0.253341 | + | 0.438799i | 0.0347991 | + | 0.0602737i | 0.882900 | − | 0.469560i | \(-0.155588\pi\) |
−0.848101 | + | 0.529834i | \(0.822254\pi\) | |||||||
\(54\) | −2.32741 | − | 1.34373i | −0.316720 | − | 0.182859i | ||||
\(55\) | 2.53068 | 0.341237 | ||||||||
\(56\) | −4.00805 | − | 22.5594i | −0.535598 | − | 3.01463i | ||||
\(57\) | 1.66406i | 0.220410i | ||||||||
\(58\) | 10.1698 | + | 5.87152i | 1.33536 | + | 0.770969i | ||||
\(59\) | 5.46350 | + | 9.46306i | 0.711287 | + | 1.23199i | 0.964374 | + | 0.264542i | \(0.0852209\pi\) |
−0.253087 | + | 0.967444i | \(0.581446\pi\) | |||||||
\(60\) | 8.99716 | + | 15.5835i | 1.16153 | + | 2.01183i | ||||
\(61\) | −7.47769 | − | 4.31725i | −0.957420 | − | 0.552767i | −0.0620420 | − | 0.998074i | \(-0.519761\pi\) |
−0.895378 | + | 0.445307i | \(0.853095\pi\) | |||||||
\(62\) | − | 7.96749i | − | 1.01187i | ||||||
\(63\) | −2.48737 | − | 0.901671i | −0.313379 | − | 0.113600i | ||||
\(64\) | 20.4510 | 2.55638 | ||||||||
\(65\) | 19.8179 | + | 11.4419i | 2.45811 | + | 1.41919i | ||||
\(66\) | −0.986933 | − | 1.70942i | −0.121483 | − | 0.210415i | ||||
\(67\) | 1.05396 | + | 1.82551i | 0.128762 | + | 0.223022i | 0.923197 | − | 0.384327i | \(-0.125566\pi\) |
−0.794435 | + | 0.607349i | \(0.792233\pi\) | |||||||
\(68\) | 7.40413 | − | 20.2197i | 0.897882 | − | 2.45200i | ||||
\(69\) | 4.71869 | 0.568063 | ||||||||
\(70\) | 15.7722 | + | 18.7471i | 1.88514 | + | 2.24070i | ||||
\(71\) | 13.8398i | 1.64248i | 0.570583 | + | 0.821240i | \(0.306717\pi\) | ||||
−0.570583 | + | 0.821240i | \(0.693283\pi\) | |||||||
\(72\) | 4.33009 | − | 7.49994i | 0.510307 | − | 0.883877i | ||||
\(73\) | 1.85921 | − | 1.07342i | 0.217605 | − | 0.125634i | −0.387236 | − | 0.921981i | \(-0.626570\pi\) |
0.604841 | + | 0.796347i | \(0.293237\pi\) | |||||||
\(74\) | 1.91221 | − | 1.10401i | 0.222290 | − | 0.128339i | ||||
\(75\) | −5.95132 | − | 3.43600i | −0.687199 | − | 0.396755i | ||||
\(76\) | −8.69047 | −0.996866 | ||||||||
\(77\) | −1.25102 | − | 1.48698i | −0.142567 | − | 0.169457i | ||||
\(78\) | − | 17.8487i | − | 2.02097i | ||||||
\(79\) | 10.0684 | + | 5.81300i | 1.13279 | + | 0.654014i | 0.944634 | − | 0.328126i | \(-0.106417\pi\) |
0.188151 | + | 0.982140i | \(0.439750\pi\) | |||||||
\(80\) | −38.2813 | + | 22.1017i | −4.27997 | + | 2.47104i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −16.7908 | − | 9.69418i | −1.85423 | − | 1.07054i | ||||
\(83\) | 3.50718 | 0.384963 | 0.192481 | − | 0.981301i | \(-0.438346\pi\) | ||||
0.192481 | + | 0.981301i | \(0.438346\pi\) | |||||||
\(84\) | 4.70893 | − | 12.9901i | 0.513786 | − | 1.41734i | ||||
\(85\) | 2.43959 | + | 13.9954i | 0.264611 | + | 1.51802i | ||||
\(86\) | −4.24150 | + | 7.34649i | −0.457373 | + | 0.792193i | ||||
\(87\) | 2.18479 | + | 3.78416i | 0.234234 | + | 0.405704i | ||||
\(88\) | 5.50850 | − | 3.18034i | 0.587209 | − | 0.339025i | ||||
\(89\) | 0.872197 | − | 1.51069i | 0.0924527 | − | 0.160133i | −0.816090 | − | 0.577925i | \(-0.803863\pi\) |
0.908543 | + | 0.417792i | \(0.137196\pi\) | |||||||
\(90\) | 9.25985i | 0.976074i | ||||||||
\(91\) | −3.07377 | − | 17.3008i | −0.322218 | − | 1.81361i | ||||
\(92\) | 24.6431i | 2.56922i | ||||||||
\(93\) | 1.48235 | − | 2.56750i | 0.153712 | − | 0.266237i | ||||
\(94\) | 7.65768 | + | 13.2635i | 0.789829 | + | 1.36802i | ||||
\(95\) | 4.96549 | − | 2.86683i | 0.509449 | − | 0.294130i | ||||
\(96\) | 14.8585 | + | 8.57856i | 1.51649 | + | 0.875546i | ||||
\(97\) | − | 12.5471i | − | 1.27397i | −0.770877 | − | 0.636984i | \(-0.780182\pi\) | ||
0.770877 | − | 0.636984i | \(-0.219818\pi\) | |||||||
\(98\) | 3.21858 | − | 18.5348i | 0.325126 | − | 1.87230i | ||||
\(99\) | − | 0.734473i | − | 0.0738173i | ||||||
\(100\) | 17.9443 | − | 31.0804i | 1.79443 | − | 3.10804i | ||||
\(101\) | −0.346754 | − | 0.600595i | −0.0345033 | − | 0.0597615i | 0.848258 | − | 0.529583i | \(-0.177652\pi\) |
−0.882761 | + | 0.469822i | \(0.844318\pi\) | |||||||
\(102\) | 8.50219 | − | 7.10593i | 0.841843 | − | 0.703592i | ||||
\(103\) | −1.53373 | + | 2.65650i | −0.151123 | + | 0.261753i | −0.931641 | − | 0.363381i | \(-0.881622\pi\) |
0.780518 | + | 0.625134i | \(0.214956\pi\) | |||||||
\(104\) | 57.5165 | 5.63996 | ||||||||
\(105\) | 1.59466 | + | 8.97558i | 0.155623 | + | 0.875927i | ||||
\(106\) | −1.36169 | −0.132259 | ||||||||
\(107\) | 0.0528559 | + | 0.0305163i | 0.00510977 | + | 0.00295013i | 0.502553 | − | 0.864547i | \(-0.332394\pi\) |
−0.497443 | + | 0.867497i | \(0.665728\pi\) | |||||||
\(108\) | 4.52277 | − | 2.61122i | 0.435204 | − | 0.251265i | ||||
\(109\) | −1.11532 | + | 0.643932i | −0.106829 | + | 0.0616775i | −0.552462 | − | 0.833538i | \(-0.686312\pi\) |
0.445634 | + | 0.895215i | \(0.352978\pi\) | |||||||
\(110\) | −3.40055 | + | 5.88993i | −0.324230 | + | 0.561583i | ||||
\(111\) | 0.821604 | 0.0779832 | ||||||||
\(112\) | 31.9105 | + | 11.5676i | 3.01526 | + | 1.09303i | ||||
\(113\) | − | 9.90093i | − | 0.931401i | −0.884942 | − | 0.465701i | \(-0.845802\pi\) | ||
0.884942 | − | 0.465701i | \(-0.154198\pi\) | |||||||
\(114\) | −3.87295 | − | 2.23605i | −0.362735 | − | 0.209425i | ||||
\(115\) | −8.12930 | − | 14.0804i | −0.758061 | − | 1.31300i | ||||
\(116\) | −19.7626 | + | 11.4099i | −1.83491 | + | 1.05938i | ||||
\(117\) | 3.32074 | − | 5.75169i | 0.307003 | − | 0.531744i | ||||
\(118\) | −29.3659 | −2.70335 | ||||||||
\(119\) | 7.01746 | − | 8.35196i | 0.643289 | − | 0.765623i | ||||
\(120\) | −29.8393 | −2.72395 | ||||||||
\(121\) | −5.23027 | + | 9.05910i | −0.475480 | + | 0.823555i | ||||
\(122\) | 20.0960 | − | 11.6024i | 1.81941 | − | 1.05043i | ||||
\(123\) | −3.60719 | − | 6.24783i | −0.325249 | − | 0.563348i | ||||
\(124\) | 13.4086 | + | 7.74146i | 1.20413 | + | 0.695204i | ||||
\(125\) | 6.45009i | 0.576914i | ||||||||
\(126\) | 5.44091 | − | 4.57752i | 0.484714 | − | 0.407797i | ||||
\(127\) | −11.9764 | −1.06273 | −0.531365 | − | 0.847143i | \(-0.678321\pi\) | ||||
−0.531365 | + | 0.847143i | \(0.678321\pi\) | |||||||
\(128\) | −10.3236 | + | 17.8809i | −0.912482 | + | 1.58047i | ||||
\(129\) | −2.73362 | + | 1.57826i | −0.240682 | + | 0.138958i | ||||
\(130\) | −53.2598 | + | 30.7496i | −4.67119 | + | 2.69692i | ||||
\(131\) | −14.7194 | − | 8.49826i | −1.28604 | − | 0.742497i | −0.308096 | − | 0.951355i | \(-0.599692\pi\) |
−0.977946 | + | 0.208858i | \(0.933025\pi\) | |||||||
\(132\) | 3.83574 | 0.333859 | ||||||||
\(133\) | −4.13913 | − | 1.50044i | −0.358908 | − | 0.130104i | ||||
\(134\) | −5.66495 | −0.489377 | ||||||||
\(135\) | −1.72279 | + | 2.98396i | −0.148274 | + | 0.256818i | ||||
\(136\) | 22.8985 | + | 27.3978i | 1.96353 | + | 2.34935i | ||||
\(137\) | −3.54214 | − | 6.13517i | −0.302626 | − | 0.524163i | 0.674104 | − | 0.738636i | \(-0.264530\pi\) |
−0.976730 | + | 0.214473i | \(0.931197\pi\) | |||||||
\(138\) | −6.34064 | + | 10.9823i | −0.539751 | + | 0.934877i | ||||
\(139\) | − | 5.98507i | − | 0.507647i | −0.967251 | − | 0.253823i | \(-0.918312\pi\) | ||
0.967251 | − | 0.253823i | \(-0.0816882\pi\) | |||||||
\(140\) | −46.8745 | + | 8.32801i | −3.96161 | + | 0.703845i | ||||
\(141\) | 5.69882i | 0.479928i | ||||||||
\(142\) | −32.2108 | − | 18.5969i | −2.70307 | − | 1.56062i | ||||
\(143\) | 4.22446 | − | 2.43899i | 0.353267 | − | 0.203959i | ||||
\(144\) | 6.41451 | + | 11.1103i | 0.534543 | + | 0.925855i | ||||
\(145\) | 7.52784 | − | 13.0386i | 0.625153 | − | 1.08280i | ||||
\(146\) | 5.76953i | 0.477490i | ||||||||
\(147\) | 4.48557 | − | 5.37398i | 0.369964 | − | 0.443238i | ||||
\(148\) | 4.29078i | 0.352700i | ||||||||
\(149\) | −6.14891 | + | 10.6502i | −0.503738 | + | 0.872500i | 0.496252 | + | 0.868178i | \(0.334709\pi\) |
−0.999991 | + | 0.00432206i | \(0.998624\pi\) | |||||||
\(150\) | 15.9939 | − | 9.23410i | 1.30590 | − | 0.753961i | ||||
\(151\) | −8.84711 | − | 15.3236i | −0.719968 | − | 1.24702i | −0.961012 | − | 0.276507i | \(-0.910823\pi\) |
0.241044 | − | 0.970514i | \(-0.422510\pi\) | |||||||
\(152\) | 7.20555 | − | 12.4804i | 0.584447 | − | 1.01229i | ||||
\(153\) | 4.06186 | − | 0.708036i | 0.328382 | − | 0.0572413i | ||||
\(154\) | 5.14184 | − | 0.913531i | 0.414341 | − | 0.0736144i | ||||
\(155\) | −10.2151 | −0.820494 | ||||||||
\(156\) | 30.0379 | + | 17.3424i | 2.40496 | + | 1.38850i | ||||
\(157\) | −7.11934 | − | 12.3311i | −0.568185 | − | 0.984126i | −0.996746 | − | 0.0806125i | \(-0.974312\pi\) |
0.428560 | − | 0.903513i | \(-0.359021\pi\) | |||||||
\(158\) | −27.0585 | + | 15.6222i | −2.15266 | + | 1.24284i | ||||
\(159\) | −0.438799 | − | 0.253341i | −0.0347991 | − | 0.0200912i | ||||
\(160\) | − | 59.1162i | − | 4.67354i | ||||||
\(161\) | −4.25470 | + | 11.7371i | −0.335318 | + | 0.925013i | ||||
\(162\) | 2.68746 | 0.211147 | ||||||||
\(163\) | 7.69049 | + | 4.44011i | 0.602366 | + | 0.347776i | 0.769972 | − | 0.638078i | \(-0.220270\pi\) |
−0.167606 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(164\) | 32.6290 | − | 18.8383i | 2.54789 | − | 1.47103i | ||||
\(165\) | −2.19163 | + | 1.26534i | −0.170619 | + | 0.0985066i | ||||
\(166\) | −4.71270 | + | 8.16264i | −0.365777 | + | 0.633544i | ||||
\(167\) | 15.3605i | 1.18863i | 0.804231 | + | 0.594316i | \(0.202577\pi\) | ||||
−0.804231 | + | 0.594316i | \(0.797423\pi\) | |||||||
\(168\) | 14.7508 | + | 17.5330i | 1.13805 | + | 1.35270i | ||||
\(169\) | 31.1093 | 2.39302 | ||||||||
\(170\) | −35.8513 | − | 13.1282i | −2.74967 | − | 1.00688i | ||||
\(171\) | −0.832031 | − | 1.44112i | −0.0636270 | − | 0.110205i | ||||
\(172\) | −8.24235 | − | 14.2762i | −0.628473 | − | 1.08855i | ||||
\(173\) | −13.5001 | − | 7.79431i | −1.02640 | − | 0.592590i | −0.110446 | − | 0.993882i | \(-0.535228\pi\) |
−0.915950 | + | 0.401292i | \(0.868561\pi\) | |||||||
\(174\) | −11.7430 | −0.890238 | ||||||||
\(175\) | 13.9127 | − | 11.7050i | 1.05170 | − | 0.884813i | ||||
\(176\) | 9.42257i | 0.710253i | ||||||||
\(177\) | −9.46306 | − | 5.46350i | −0.711287 | − | 0.410662i | ||||
\(178\) | 2.34399 | + | 4.05992i | 0.175690 | + | 0.304304i | ||||
\(179\) | −2.50601 | − | 4.34053i | −0.187308 | − | 0.324427i | 0.757044 | − | 0.653364i | \(-0.226643\pi\) |
−0.944352 | + | 0.328937i | \(0.893310\pi\) | |||||||
\(180\) | −15.5835 | − | 8.99716i | −1.16153 | − | 0.670609i | ||||
\(181\) | − | 8.58767i | − | 0.638317i | −0.947701 | − | 0.319158i | \(-0.896600\pi\) | ||
0.947701 | − | 0.319158i | \(-0.103400\pi\) | |||||||
\(182\) | 44.3963 | + | 16.0937i | 3.29087 | + | 1.19294i | ||||
\(183\) | 8.63449 | 0.638280 | ||||||||
\(184\) | −35.3899 | − | 20.4324i | −2.60898 | − | 1.50629i | ||||
\(185\) | −1.41545 | − | 2.45163i | −0.104066 | − | 0.180247i | ||||
\(186\) | 3.98374 | + | 6.90005i | 0.292102 | + | 0.505936i | ||||
\(187\) | 2.84365 | + | 1.04130i | 0.207948 | + | 0.0761474i | ||||
\(188\) | −29.7618 | −2.17060 | ||||||||
\(189\) | 2.60496 | − | 0.462813i | 0.189483 | − | 0.0336647i | ||||
\(190\) | 15.4090i | 1.11788i | ||||||||
\(191\) | 6.42844 | − | 11.1344i | 0.465146 | − | 0.805656i | −0.534062 | − | 0.845445i | \(-0.679335\pi\) |
0.999208 | + | 0.0397890i | \(0.0126686\pi\) | |||||||
\(192\) | −17.7111 | + | 10.2255i | −1.27819 | + | 0.737963i | ||||
\(193\) | 13.3779 | − | 7.72374i | 0.962963 | − | 0.555967i | 0.0658790 | − | 0.997828i | \(-0.479015\pi\) |
0.897084 | + | 0.441861i | \(0.145682\pi\) | |||||||
\(194\) | 29.2023 | + | 16.8600i | 2.09660 | + | 1.21047i | ||||
\(195\) | −22.8837 | −1.63874 | ||||||||
\(196\) | 28.0653 | + | 23.4256i | 2.00466 | + | 1.67326i | ||||
\(197\) | 21.6200i | 1.54036i | 0.637825 | + | 0.770182i | \(0.279834\pi\) | ||||
−0.637825 | + | 0.770182i | \(0.720166\pi\) | |||||||
\(198\) | 1.70942 | + | 0.986933i | 0.121483 | + | 0.0701383i | ||||
\(199\) | 1.04803 | − | 0.605080i | 0.0742928 | − | 0.0428930i | −0.462393 | − | 0.886675i | \(-0.653009\pi\) |
0.536686 | + | 0.843782i | \(0.319676\pi\) | |||||||
\(200\) | 29.7564 | + | 51.5396i | 2.10409 | + | 3.64440i | ||||
\(201\) | −1.82551 | − | 1.05396i | −0.128762 | − | 0.0743405i | ||||
\(202\) | 1.86378 | 0.131135 | ||||||||
\(203\) | −11.3825 | + | 2.02229i | −0.798898 | + | 0.141937i | ||||
\(204\) | 3.69768 | + | 21.2128i | 0.258889 | + | 1.48519i | ||||
\(205\) | −12.4288 | + | 21.5274i | −0.868068 | + | 1.50354i | ||||
\(206\) | −4.12184 | − | 7.13924i | −0.287182 | − | 0.497414i | ||||
\(207\) | −4.08650 | + | 2.35934i | −0.284032 | + | 0.163986i | ||||
\(208\) | −42.6019 | + | 73.7886i | −2.95391 | + | 5.11632i | ||||
\(209\) | − | 1.22221i | − | 0.0845419i | ||||||
\(210\) | −23.0326 | − | 8.34934i | −1.58940 | − | 0.576159i | ||||
\(211\) | 8.26993i | 0.569325i | 0.958628 | + | 0.284663i | \(0.0918816\pi\) | ||||
−0.958628 | + | 0.284663i | \(0.908118\pi\) | |||||||
\(212\) | 1.32306 | − | 2.29161i | 0.0908681 | − | 0.157388i | ||||
\(213\) | −6.91989 | − | 11.9856i | −0.474143 | − | 0.821240i | ||||
\(214\) | −0.142048 | + | 0.0820115i | −0.00971020 | + | 0.00560619i | ||||
\(215\) | 9.41889 | + | 5.43800i | 0.642363 | + | 0.370868i | ||||
\(216\) | 8.66019i | 0.589251i | ||||||||
\(217\) | 5.04972 | + | 6.00217i | 0.342797 | + | 0.407454i | ||||
\(218\) | − | 3.46108i | − | 0.234414i | ||||||
\(219\) | −1.07342 | + | 1.85921i | −0.0725348 | + | 0.125634i | ||||
\(220\) | −6.60817 | − | 11.4457i | −0.445523 | − | 0.771668i | ||||
\(221\) | 17.5608 | + | 21.0114i | 1.18127 | + | 1.41338i | ||||
\(222\) | −1.10401 | + | 1.91221i | −0.0740965 | + | 0.128339i | ||||
\(223\) | −7.78894 | −0.521586 | −0.260793 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260793 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(224\) | −34.7355 | + | 29.2235i | −2.32086 | + | 1.95258i | ||||
\(225\) | 6.87199 | 0.458133 | ||||||||
\(226\) | 23.0435 | + | 13.3042i | 1.53283 | + | 0.884981i | ||||
\(227\) | 19.2546 | − | 11.1166i | 1.27797 | − | 0.737837i | 0.301496 | − | 0.953468i | \(-0.402514\pi\) |
0.976475 | + | 0.215631i | \(0.0691808\pi\) | |||||||
\(228\) | 7.52617 | − | 4.34524i | 0.498433 | − | 0.287770i | ||||
\(229\) | 9.08552 | − | 15.7366i | 0.600388 | − | 1.03990i | −0.392374 | − | 0.919806i | \(-0.628346\pi\) |
0.992762 | − | 0.120097i | \(-0.0383206\pi\) | |||||||
\(230\) | 43.6943 | 2.88112 | ||||||||
\(231\) | 1.82690 | + | 0.662253i | 0.120201 | + | 0.0435730i | ||||
\(232\) | − | 37.8413i | − | 2.48440i | ||||||
\(233\) | 2.24023 | + | 1.29340i | 0.146763 | + | 0.0847334i | 0.571583 | − | 0.820544i | \(-0.306329\pi\) |
−0.424821 | + | 0.905278i | \(0.639663\pi\) | |||||||
\(234\) | 8.92436 | + | 15.4574i | 0.583404 | + | 1.01049i | ||||
\(235\) | 17.0050 | − | 9.81786i | 1.10929 | − | 0.640447i | ||||
\(236\) | 28.5328 | − | 49.4203i | 1.85733 | − | 3.21699i | ||||
\(237\) | −11.6260 | −0.755190 | ||||||||
\(238\) | 10.0089 | + | 27.5553i | 0.648778 | + | 1.78614i | ||||
\(239\) | −22.0029 | −1.42325 | −0.711624 | − | 0.702560i | \(-0.752040\pi\) | ||||
−0.711624 | + | 0.702560i | \(0.752040\pi\) | |||||||
\(240\) | 22.1017 | − | 38.2813i | 1.42666 | − | 2.47104i | ||||
\(241\) | −18.3874 | + | 10.6160i | −1.18444 | + | 0.683835i | −0.957037 | − | 0.289967i | \(-0.906356\pi\) |
−0.227400 | + | 0.973801i | \(0.573022\pi\) | |||||||
\(242\) | −14.0562 | − | 24.3460i | −0.903564 | − | 1.56502i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 45.0931i | 2.88679i | ||||||||
\(245\) | −23.7634 | − | 4.12652i | −1.51819 | − | 0.263634i | ||||
\(246\) | 19.3884 | 1.23616 | ||||||||
\(247\) | 5.52592 | − | 9.57118i | 0.351606 | − | 0.608999i | ||||
\(248\) | −22.2350 | + | 12.8374i | −1.41192 | + | 0.815175i | ||||
\(249\) | −3.03731 | + | 1.75359i | −0.192481 | + | 0.111129i | ||||
\(250\) | −15.0120 | − | 8.66718i | −0.949442 | − | 0.548161i | ||||
\(251\) | −8.84862 | −0.558520 | −0.279260 | − | 0.960216i | \(-0.590089\pi\) | ||||
−0.279260 | + | 0.960216i | \(0.590089\pi\) | |||||||
\(252\) | 2.41702 | + | 13.6042i | 0.152258 | + | 0.856987i | ||||
\(253\) | −3.46575 | −0.217890 | ||||||||
\(254\) | 16.0930 | − | 27.8739i | 1.00977 | − | 1.74896i | ||||
\(255\) | −9.11047 | − | 10.9006i | −0.570520 | − | 0.682623i | ||||
\(256\) | −7.29311 | − | 12.6320i | −0.455819 | − | 0.789502i | ||||
\(257\) | −7.74761 | + | 13.4193i | −0.483283 | + | 0.837070i | −0.999816 | − | 0.0191971i | \(-0.993889\pi\) |
0.516533 | + | 0.856267i | \(0.327222\pi\) | |||||||
\(258\) | − | 8.48300i | − | 0.528128i | ||||||
\(259\) | −0.740816 | + | 2.04363i | −0.0460321 | + | 0.126985i | ||||
\(260\) | − | 119.509i | − | 7.41163i | ||||||
\(261\) | −3.78416 | − | 2.18479i | −0.234234 | − | 0.135235i | ||||
\(262\) | 39.5579 | − | 22.8387i | 2.44389 | − | 1.41098i | ||||
\(263\) | −4.05408 | − | 7.02187i | −0.249985 | − | 0.432987i | 0.713536 | − | 0.700618i | \(-0.247092\pi\) |
−0.963521 | + | 0.267631i | \(0.913759\pi\) | |||||||
\(264\) | −3.18034 | + | 5.50850i | −0.195736 | + | 0.339025i | ||||
\(265\) | 1.74581i | 0.107244i | ||||||||
\(266\) | 9.05401 | − | 7.61727i | 0.555137 | − | 0.467045i | ||||
\(267\) | 1.74439i | 0.106755i | ||||||||
\(268\) | 5.50424 | − | 9.53363i | 0.336225 | − | 0.582359i | ||||
\(269\) | 0.439196 | − | 0.253570i | 0.0267783 | − | 0.0154604i | −0.486551 | − | 0.873652i | \(-0.661745\pi\) |
0.513329 | + | 0.858192i | \(0.328412\pi\) | |||||||
\(270\) | −4.62992 | − | 8.01926i | −0.281768 | − | 0.488037i | ||||
\(271\) | 0.0889435 | − | 0.154055i | 0.00540293 | − | 0.00935815i | −0.863311 | − | 0.504672i | \(-0.831614\pi\) |
0.868714 | + | 0.495314i | \(0.164947\pi\) | |||||||
\(272\) | −52.1097 | + | 9.08341i | −3.15961 | + | 0.550763i | ||||
\(273\) | 11.3124 | + | 13.4460i | 0.684655 | + | 0.813791i | ||||
\(274\) | 19.0387 | 1.15017 | ||||||||
\(275\) | 4.37108 | + | 2.52365i | 0.263586 | + | 0.152182i | ||||
\(276\) | −12.3215 | − | 21.3415i | −0.741670 | − | 1.28461i | ||||
\(277\) | −25.0775 | + | 14.4785i | −1.50676 | + | 0.869930i | −0.506794 | + | 0.862067i | \(0.669169\pi\) |
−0.999969 | + | 0.00786258i | \(0.997497\pi\) | |||||||
\(278\) | 13.9297 | + | 8.04232i | 0.835448 | + | 0.482346i | ||||
\(279\) | 2.96469i | 0.177491i | ||||||||
\(280\) | 26.9053 | − | 74.2214i | 1.60790 | − | 4.43557i | ||||
\(281\) | −3.87418 | −0.231114 | −0.115557 | − | 0.993301i | \(-0.536865\pi\) | ||||
−0.115557 | + | 0.993301i | \(0.536865\pi\) | |||||||
\(282\) | −13.2635 | − | 7.65768i | −0.789829 | − | 0.456008i | ||||
\(283\) | −0.795522 | + | 0.459295i | −0.0472889 | + | 0.0273022i | −0.523458 | − | 0.852051i | \(-0.675358\pi\) |
0.476169 | + | 0.879354i | \(0.342025\pi\) | |||||||
\(284\) | 62.5941 | − | 36.1387i | 3.71428 | − | 2.14444i | ||||
\(285\) | −2.86683 | + | 4.96549i | −0.169816 | + | 0.294130i | ||||
\(286\) | 13.1094i | 0.775175i | ||||||||
\(287\) | 18.7931 | − | 3.33891i | 1.10932 | − | 0.197090i | ||||
\(288\) | −17.1571 | −1.01099 | ||||||||
\(289\) | −3.01741 | + | 16.7301i | −0.177495 | + | 0.984122i | ||||
\(290\) | 20.2308 | + | 35.0407i | 1.18799 | + | 2.05766i | ||||
\(291\) | 6.27357 | + | 10.8661i | 0.367763 | + | 0.636984i | ||||
\(292\) | −9.70964 | − | 5.60586i | −0.568214 | − | 0.328058i | ||||
\(293\) | 18.8923 | 1.10370 | 0.551849 | − | 0.833944i | \(-0.313922\pi\) | ||||
0.551849 | + | 0.833944i | \(0.313922\pi\) | |||||||
\(294\) | 6.48005 | + | 17.6609i | 0.377924 | + | 1.03001i | ||||
\(295\) | 37.6498i | 2.19206i | ||||||||
\(296\) | −6.16198 | − | 3.55762i | −0.358158 | − | 0.206783i | ||||
\(297\) | 0.367236 | + | 0.636072i | 0.0213092 | + | 0.0369086i | ||||
\(298\) | −16.5250 | − | 28.6221i | −0.957265 | − | 1.65803i | ||||
\(299\) | −27.1404 | − | 15.6695i | −1.56957 | − | 0.906193i | ||||
\(300\) | 35.8886i | 2.07203i | ||||||||
\(301\) | −1.46087 | − | 8.22258i | −0.0842034 | − | 0.473941i | ||||
\(302\) | 47.5525 | 2.73634 | ||||||||
\(303\) | 0.600595 | + | 0.346754i | 0.0345033 | + | 0.0199205i | ||||
\(304\) | 10.6742 | + | 18.4882i | 0.612205 | + | 1.06037i | ||||
\(305\) | −14.8754 | − | 25.7649i | −0.851763 | − | 1.47530i | ||||
\(306\) | −3.81015 | + | 10.4050i | −0.217812 | + | 0.594815i | ||||
\(307\) | 6.79127 | 0.387598 | 0.193799 | − | 0.981041i | \(-0.437919\pi\) | ||||
0.193799 | + | 0.981041i | \(0.437919\pi\) | |||||||
\(308\) | −3.45858 | + | 9.54090i | −0.197071 | + | 0.543643i | ||||
\(309\) | − | 3.06746i | − | 0.174502i | ||||||
\(310\) | 13.7263 | − | 23.7746i | 0.779601 | − | 1.35031i | ||||
\(311\) | −16.7970 | + | 9.69776i | −0.952471 | + | 0.549910i | −0.893848 | − | 0.448371i | \(-0.852005\pi\) |
−0.0586236 | + | 0.998280i | \(0.518671\pi\) | |||||||
\(312\) | −49.8108 | + | 28.7583i | −2.81998 | + | 1.62812i | ||||
\(313\) | −9.84706 | − | 5.68520i | −0.556589 | − | 0.321347i | 0.195187 | − | 0.980766i | \(-0.437469\pi\) |
−0.751775 | + | 0.659420i | \(0.770802\pi\) | |||||||
\(314\) | 38.2659 | 2.15947 | ||||||||
\(315\) | −5.86880 | − | 6.97575i | −0.330670 | − | 0.393039i | ||||
\(316\) | − | 60.7161i | − | 3.41555i | ||||||
\(317\) | −17.2322 | − | 9.94901i | −0.967856 | − | 0.558792i | −0.0692744 | − | 0.997598i | \(-0.522068\pi\) |
−0.898582 | + | 0.438805i | \(0.855402\pi\) | |||||||
\(318\) | 1.17926 | − | 0.680844i | 0.0661294 | − | 0.0381798i | ||||
\(319\) | −1.60467 | − | 2.77936i | −0.0898440 | − | 0.155614i | ||||
\(320\) | 61.0250 | + | 35.2328i | 3.41140 | + | 1.96957i | ||||
\(321\) | −0.0610327 | −0.00340651 | ||||||||
\(322\) | −21.5999 | − | 25.6739i | −1.20371 | − | 1.43075i | ||||
\(323\) | 6.75918 | − | 1.17822i | 0.376091 | − | 0.0655577i | ||||
\(324\) | −2.61122 | + | 4.52277i | −0.145068 | + | 0.251265i | ||||
\(325\) | 22.8201 | + | 39.5256i | 1.26583 | + | 2.19249i | ||||
\(326\) | −20.6679 | + | 11.9326i | −1.14469 | + | 0.660886i | ||||
\(327\) | 0.643932 | − | 1.11532i | 0.0356095 | − | 0.0616775i | ||||
\(328\) | 62.4779i | 3.44976i | ||||||||
\(329\) | −14.1751 | − | 5.13846i | −0.781496 | − | 0.283293i | ||||
\(330\) | − | 6.80111i | − | 0.374389i | ||||||
\(331\) | −2.56433 | + | 4.44156i | −0.140949 | + | 0.244130i | −0.927854 | − | 0.372943i | \(-0.878349\pi\) |
0.786906 | + | 0.617073i | \(0.211682\pi\) | |||||||
\(332\) | −9.15802 | − | 15.8622i | −0.502612 | − | 0.870549i | ||||
\(333\) | −0.711530 | + | 0.410802i | −0.0389916 | + | 0.0225118i | ||||
\(334\) | −35.7502 | − | 20.6404i | −1.95616 | − | 1.12939i | ||||
\(335\) | 7.26299i | 0.396820i | ||||||||
\(336\) | −33.4191 | + | 5.93744i | −1.82316 | + | 0.323914i | ||||
\(337\) | − | 18.2287i | − | 0.992980i | −0.868042 | − | 0.496490i | \(-0.834622\pi\) | ||
0.868042 | − | 0.496490i | \(-0.165378\pi\) | |||||||
\(338\) | −41.8025 | + | 72.4041i | −2.27376 | + | 3.93826i | ||||
\(339\) | 4.95047 | + | 8.57446i | 0.268872 | + | 0.465701i | ||||
\(340\) | 56.9278 | − | 47.5789i | 3.08734 | − | 2.58033i | ||||
\(341\) | −1.08874 | + | 1.88576i | −0.0589587 | + | 0.102119i | ||||
\(342\) | 4.47210 | 0.241824 | ||||||||
\(343\) | 9.32254 | + | 16.0028i | 0.503370 | + | 0.864071i | ||||
\(344\) | 27.3360 | 1.47386 | ||||||||
\(345\) | 14.0804 | + | 8.12930i | 0.758061 | + | 0.437667i | ||||
\(346\) | 36.2811 | − | 20.9469i | 1.95048 | − | 1.12611i | ||||
\(347\) | −8.51554 | + | 4.91645i | −0.457138 | + | 0.263929i | −0.710840 | − | 0.703354i | \(-0.751685\pi\) |
0.253702 | + | 0.967282i | \(0.418352\pi\) | |||||||
\(348\) | 11.4099 | − | 19.7626i | 0.611636 | − | 1.05938i | ||||
\(349\) | −17.5158 | −0.937600 | −0.468800 | − | 0.883304i | \(-0.655314\pi\) | ||||
−0.468800 | + | 0.883304i | \(0.655314\pi\) | |||||||
\(350\) | 8.54733 | + | 48.1089i | 0.456874 | + | 2.57153i | ||||
\(351\) | 6.64148i | 0.354496i | ||||||||
\(352\) | −10.9132 | − | 6.30072i | −0.581674 | − | 0.335830i | ||||
\(353\) | −10.3760 | − | 17.9718i | −0.552261 | − | 0.956544i | −0.998111 | − | 0.0614363i | \(-0.980432\pi\) |
0.445850 | − | 0.895108i | \(-0.352901\pi\) | |||||||
\(354\) | 25.4316 | − | 14.6829i | 1.35167 | − | 0.780390i | ||||
\(355\) | −23.8430 | + | 41.2973i | −1.26546 | + | 2.19183i | ||||
\(356\) | −9.11000 | −0.482829 | ||||||||
\(357\) | −1.90131 | + | 10.7417i | −0.100628 | + | 0.568513i | ||||
\(358\) | 13.4696 | 0.711890 | ||||||||
\(359\) | −0.556750 | + | 0.964319i | −0.0293841 | + | 0.0508948i | −0.880344 | − | 0.474337i | \(-0.842688\pi\) |
0.850959 | + | 0.525232i | \(0.176021\pi\) | |||||||
\(360\) | 25.8416 | − | 14.9197i | 1.36197 | − | 0.786336i | ||||
\(361\) | 8.11545 | + | 14.0564i | 0.427129 | + | 0.739809i | ||||
\(362\) | 19.9870 | + | 11.5395i | 1.05049 | + | 0.606504i | ||||
\(363\) | − | 10.4605i | − | 0.549036i | ||||||
\(364\) | −70.2212 | + | 59.0781i | −3.68059 | + | 3.09653i | ||||
\(365\) | 7.39708 | 0.387181 | ||||||||
\(366\) | −11.6024 | + | 20.0960i | −0.606469 | + | 1.05043i | ||||
\(367\) | 24.7549 | − | 14.2922i | 1.29219 | − | 0.746048i | 0.313150 | − | 0.949704i | \(-0.398616\pi\) |
0.979043 | + | 0.203656i | \(0.0652823\pi\) | |||||||
\(368\) | 52.4259 | − | 30.2681i | 2.73289 | − | 1.57783i | ||||
\(369\) | 6.24783 | + | 3.60719i | 0.325249 | + | 0.187783i | ||||
\(370\) | 7.60792 | 0.395517 | ||||||||
\(371\) | 1.02580 | − | 0.863025i | 0.0532571 | − | 0.0448060i | ||||
\(372\) | −15.4829 | −0.802752 | ||||||||
\(373\) | 12.7175 | − | 22.0274i | 0.658489 | − | 1.14054i | −0.322517 | − | 0.946564i | \(-0.604529\pi\) |
0.981007 | − | 0.193974i | \(-0.0621376\pi\) | |||||||
\(374\) | −6.24463 | + | 5.21911i | −0.322902 | + | 0.269874i | ||||
\(375\) | −3.22505 | − | 5.58594i | −0.166541 | − | 0.288457i | ||||
\(376\) | 24.6764 | − | 42.7409i | 1.27259 | − | 2.20419i | ||||
\(377\) | − | 29.0204i | − | 1.49463i | ||||||
\(378\) | −2.42320 | + | 6.68470i | −0.124636 | + | 0.343824i | ||||
\(379\) | − | 30.0748i | − | 1.54484i | −0.635113 | − | 0.772419i | \(-0.719047\pi\) | ||
0.635113 | − | 0.772419i | \(-0.280953\pi\) | |||||||
\(380\) | −25.9320 | − | 14.9718i | −1.33028 | − | 0.768039i | ||||
\(381\) | 10.3718 | − | 5.98818i | 0.531365 | − | 0.306784i | ||||
\(382\) | 17.2762 | + | 29.9232i | 0.883927 | + | 1.53101i | ||||
\(383\) | 7.69774 | − | 13.3329i | 0.393336 | − | 0.681278i | −0.599551 | − | 0.800336i | \(-0.704654\pi\) |
0.992887 | + | 0.119058i | \(0.0379875\pi\) | |||||||
\(384\) | − | 20.6471i | − | 1.05364i | ||||||
\(385\) | −1.17123 | − | 6.59232i | −0.0596915 | − | 0.335976i | ||||
\(386\) | 41.5145i | 2.11303i | ||||||||
\(387\) | 1.57826 | − | 2.73362i | 0.0802272 | − | 0.138958i | ||||
\(388\) | −56.7478 | + | 32.7634i | −2.88093 | + | 1.66331i | ||||
\(389\) | 13.7754 | + | 23.8598i | 0.698443 | + | 1.20974i | 0.969006 | + | 0.247037i | \(0.0794568\pi\) |
−0.270563 | + | 0.962702i | \(0.587210\pi\) | |||||||
\(390\) | 30.7496 | − | 53.2598i | 1.55706 | − | 2.69692i | ||||
\(391\) | −3.34100 | − | 19.1666i | −0.168962 | − | 0.969299i | ||||
\(392\) | −56.9114 | + | 20.8816i | −2.87446 | + | 1.05468i | ||||
\(393\) | 16.9965 | 0.857361 | ||||||||
\(394\) | −50.3186 | − | 29.0515i | −2.53502 | − | 1.46359i | ||||
\(395\) | 20.0291 | + | 34.6915i | 1.00778 | + | 1.74552i | ||||
\(396\) | −3.32185 | + | 1.91787i | −0.166929 | + | 0.0963767i | ||||
\(397\) | 27.4754 | + | 15.8629i | 1.37895 | + | 0.796138i | 0.992033 | − | 0.125976i | \(-0.0402062\pi\) |
0.386918 | + | 0.922114i | \(0.373539\pi\) | |||||||
\(398\) | 3.25225i | 0.163021i | ||||||||
\(399\) | 4.33481 | − | 0.770150i | 0.217012 | − | 0.0385557i | ||||
\(400\) | −88.1610 | −4.40805 | ||||||||
\(401\) | 29.7121 | + | 17.1543i | 1.48375 | + | 0.856644i | 0.999829 | − | 0.0184679i | \(-0.00587885\pi\) |
0.483921 | + | 0.875112i | \(0.339212\pi\) | |||||||
\(402\) | 4.90599 | − | 2.83247i | 0.244688 | − | 0.141271i | ||||
\(403\) | −17.0520 | + | 9.84497i | −0.849420 | + | 0.490413i | ||||
\(404\) | −1.81090 | + | 3.13658i | −0.0900958 | + | 0.156050i | ||||
\(405\) | − | 3.44558i | − | 0.171212i | ||||||
\(406\) | 10.5884 | − | 29.2093i | 0.525492 | − | 1.44963i | ||||
\(407\) | −0.603445 | −0.0299117 | ||||||||
\(408\) | −33.5296 | − | 12.2780i | −1.65996 | − | 0.607851i | ||||
\(409\) | −10.6787 | − | 18.4960i | −0.528025 | − | 0.914567i | −0.999466 | − | 0.0326691i | \(-0.989599\pi\) |
0.471441 | − | 0.881898i | \(-0.343734\pi\) | |||||||
\(410\) | −33.4020 | − | 57.8540i | −1.64961 | − | 2.85721i | ||||
\(411\) | 6.13517 | + | 3.54214i | 0.302626 | + | 0.174721i | ||||
\(412\) | 16.0196 | 0.789231 | ||||||||
\(413\) | 22.1223 | − | 18.6118i | 1.08857 | − | 0.915828i | ||||
\(414\) | − | 12.6813i | − | 0.623251i | ||||||
\(415\) | 10.4653 | + | 6.04212i | 0.513720 | + | 0.296596i | ||||
\(416\) | −56.9744 | − | 98.6825i | −2.79340 | − | 4.83831i | ||||
\(417\) | 2.99253 | + | 5.18322i | 0.146545 | + | 0.253823i | ||||
\(418\) | 2.84458 | + | 1.64232i | 0.139133 | + | 0.0803284i | ||||
\(419\) | 13.2879i | 0.649157i | 0.945859 | + | 0.324578i | \(0.105222\pi\) | ||||
−0.945859 | + | 0.324578i | \(0.894778\pi\) | |||||||
\(420\) | 36.4305 | − | 30.6495i | 1.77762 | − | 1.49554i | ||||
\(421\) | −10.8694 | −0.529743 | −0.264872 | − | 0.964284i | \(-0.585330\pi\) | ||||
−0.264872 | + | 0.964284i | \(0.585330\pi\) | |||||||
\(422\) | −19.2475 | − | 11.1125i | −0.936954 | − | 0.540950i | ||||
\(423\) | −2.84941 | − | 4.93533i | −0.138543 | − | 0.239964i | ||||
\(424\) | 2.19398 | + | 3.80009i | 0.106549 | + | 0.184549i | ||||
\(425\) | −9.74278 | + | 26.6062i | −0.472594 | + | 1.29059i | ||||
\(426\) | 37.1939 | 1.80205 | ||||||||
\(427\) | −7.78547 | + | 21.4771i | −0.376765 | + | 1.03935i | ||||
\(428\) | − | 0.318740i | − | 0.0154069i | ||||||
\(429\) | −2.43899 | + | 4.22446i | −0.117756 | + | 0.203959i | ||||
\(430\) | −25.3129 | + | 14.6144i | −1.22070 | + | 0.704769i | ||||
\(431\) | −14.9419 | + | 8.62668i | −0.719724 | + | 0.415533i | −0.814651 | − | 0.579952i | \(-0.803071\pi\) |
0.0949273 | + | 0.995484i | \(0.469738\pi\) | |||||||
\(432\) | −11.1103 | − | 6.41451i | −0.534543 | − | 0.308618i | ||||
\(433\) | 5.29663 | 0.254540 | 0.127270 | − | 0.991868i | \(-0.459379\pi\) | ||||
0.127270 | + | 0.991868i | \(0.459379\pi\) | |||||||
\(434\) | −20.7550 | + | 3.68746i | −0.996270 | + | 0.177004i | ||||
\(435\) | 15.0557i | 0.721865i | ||||||||
\(436\) | 5.82471 | + | 3.36290i | 0.278953 | + | 0.161054i | ||||
\(437\) | −6.80020 | + | 3.92610i | −0.325298 | + | 0.187811i | ||||
\(438\) | −2.88477 | − | 4.99656i | −0.137840 | − | 0.238745i | ||||
\(439\) | −9.61354 | − | 5.55038i | −0.458829 | − | 0.264905i | 0.252723 | − | 0.967539i | \(-0.418674\pi\) |
−0.711552 | + | 0.702634i | \(0.752007\pi\) | |||||||
\(440\) | 21.9162 | 1.04481 | ||||||||
\(441\) | −1.19763 | + | 6.89679i | −0.0570299 | + | 0.328418i | ||||
\(442\) | −72.4990 | + | 12.6375i | −3.44842 | + | 0.601106i | ||||
\(443\) | 5.63408 | − | 9.75851i | 0.267683 | − | 0.463641i | −0.700580 | − | 0.713574i | \(-0.747075\pi\) |
0.968263 | + | 0.249933i | \(0.0804086\pi\) | |||||||
\(444\) | −2.14539 | − | 3.71592i | −0.101816 | − | 0.176350i | ||||
\(445\) | 5.20519 | − | 3.00522i | 0.246750 | − | 0.142461i | ||||
\(446\) | 10.4662 | − | 18.1280i | 0.495590 | − | 0.858388i | ||||
\(447\) | − | 12.2978i | − | 0.581667i | ||||||
\(448\) | −9.46501 | − | 53.2741i | −0.447180 | − | 2.51696i | ||||
\(449\) | − | 21.5839i | − | 1.01861i | −0.860587 | − | 0.509303i | \(-0.829903\pi\) | ||
0.860587 | − | 0.509303i | \(-0.170097\pi\) | |||||||
\(450\) | −9.23410 | + | 15.9939i | −0.435300 | + | 0.753961i | ||||
\(451\) | 2.64938 | + | 4.58886i | 0.124755 | + | 0.216081i | ||||
\(452\) | −44.7796 | + | 25.8535i | −2.10626 | + | 1.21605i | ||||
\(453\) | 15.3236 | + | 8.84711i | 0.719968 | + | 0.415674i | ||||
\(454\) | 59.7510i | 2.80425i | ||||||||
\(455\) | 20.6336 | − | 56.9202i | 0.967318 | − | 2.66846i | ||||
\(456\) | 14.4111i | 0.674861i | ||||||||
\(457\) | −3.68744 | + | 6.38683i | −0.172491 | + | 0.298763i | −0.939290 | − | 0.343124i | \(-0.888515\pi\) |
0.766799 | + | 0.641887i | \(0.221848\pi\) | |||||||
\(458\) | 24.4170 | + | 42.2915i | 1.14093 | + | 1.97615i | ||||
\(459\) | −3.16365 | + | 2.64411i | −0.147667 | + | 0.123416i | ||||
\(460\) | −42.4548 | + | 73.5339i | −1.97947 | + | 3.42853i | ||||
\(461\) | −17.2157 | −0.801816 | −0.400908 | − | 0.916118i | \(-0.631305\pi\) | ||||
−0.400908 | + | 0.916118i | \(0.631305\pi\) | |||||||
\(462\) | −3.99620 | + | 3.36206i | −0.185920 | + | 0.156417i | ||||
\(463\) | −26.5827 | −1.23540 | −0.617701 | − | 0.786413i | \(-0.711936\pi\) | ||||
−0.617701 | + | 0.786413i | \(0.711936\pi\) | |||||||
\(464\) | 48.5471 | + | 28.0287i | 2.25374 | + | 1.30120i | ||||
\(465\) | 8.84651 | − | 5.10753i | 0.410247 | − | 0.236856i | ||||
\(466\) | −6.02054 | + | 3.47596i | −0.278896 | + | 0.161021i | ||||
\(467\) | −20.8691 | + | 36.1463i | −0.965706 | + | 1.67265i | −0.258000 | + | 0.966145i | \(0.583063\pi\) |
−0.707706 | + | 0.706507i | \(0.750270\pi\) | |||||||
\(468\) | −34.6848 | −1.60330 | ||||||||
\(469\) | 4.26759 | − | 3.59039i | 0.197059 | − | 0.165789i | ||||
\(470\) | 52.7702i | 2.43411i | ||||||||
\(471\) | 12.3311 | + | 7.11934i | 0.568185 | + | 0.328042i | ||||
\(472\) | 47.3150 | + | 81.9519i | 2.17785 | + | 3.77214i | ||||
\(473\) | 2.00777 | − | 1.15919i | 0.0923173 | − | 0.0532994i | ||||
\(474\) | 15.6222 | − | 27.0585i | 0.717552 | − | 1.24284i | ||||
\(475\) | 11.4354 | 0.524693 | ||||||||
\(476\) | −56.0981 | − | 9.92951i | −2.57125 | − | 0.455118i | ||||
\(477\) | 0.506682 | 0.0231994 | ||||||||
\(478\) | 29.5659 | − | 51.2097i | 1.35231 | − | 2.34228i | ||||
\(479\) | −13.1849 | + | 7.61233i | −0.602436 | + | 0.347816i | −0.769999 | − | 0.638045i | \(-0.779743\pi\) |
0.167564 | + | 0.985861i | \(0.446410\pi\) | |||||||
\(480\) | 29.5581 | + | 51.1961i | 1.34914 | + | 2.33677i | ||||
\(481\) | −4.72561 | − | 2.72833i | −0.215469 | − | 0.124401i | ||||
\(482\) | − | 57.0600i | − | 2.59901i | ||||||
\(483\) | −2.18387 | − | 12.2920i | −0.0993696 | − | 0.559305i | ||||
\(484\) | 54.6296 | 2.48316 | ||||||||
\(485\) | 21.6161 | − | 37.4401i | 0.981534 | − | 1.70007i | ||||
\(486\) | −2.32741 | + | 1.34373i | −0.105573 | + | 0.0609528i | ||||
\(487\) | 5.61774 | − | 3.24340i | 0.254564 | − | 0.146973i | −0.367288 | − | 0.930107i | \(-0.619714\pi\) |
0.621852 | + | 0.783135i | \(0.286380\pi\) | |||||||
\(488\) | −64.7582 | − | 37.3882i | −2.93147 | − | 1.69248i | ||||
\(489\) | −8.88021 | −0.401577 | ||||||||
\(490\) | 41.5357 | − | 49.7622i | 1.87639 | − | 2.24803i | ||||
\(491\) | −32.0196 | −1.44503 | −0.722513 | − | 0.691357i | \(-0.757013\pi\) | ||||
−0.722513 | + | 0.691357i | \(0.757013\pi\) | |||||||
\(492\) | −18.8383 | + | 32.6290i | −0.849298 | + | 1.47103i | ||||
\(493\) | 13.8238 | − | 11.5536i | 0.622593 | − | 0.520348i | ||||
\(494\) | 14.8507 | + | 25.7222i | 0.668164 | + | 1.15729i | ||||
\(495\) | 1.26534 | − | 2.19163i | 0.0568728 | − | 0.0985066i | ||||
\(496\) | − | 38.0341i | − | 1.70778i | ||||||
\(497\) | 36.0521 | − | 6.40523i | 1.61716 | − | 0.287314i | ||||
\(498\) | − | 9.42540i | − | 0.422362i | ||||||
\(499\) | 18.6848 | + | 10.7877i | 0.836447 | + | 0.482923i | 0.856055 | − | 0.516885i | \(-0.172908\pi\) |
−0.0196078 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(500\) | 29.1723 | − | 16.8426i | 1.30462 | − | 0.753225i | ||||
\(501\) | −7.68026 | − | 13.3026i | −0.343129 | − | 0.594316i | ||||
\(502\) | 11.8902 | − | 20.5944i | 0.530684 | − | 0.919171i | ||||
\(503\) | − | 9.46993i | − | 0.422243i | −0.977460 | − | 0.211122i | \(-0.932288\pi\) | ||
0.977460 | − | 0.211122i | \(-0.0677116\pi\) | |||||||
\(504\) | −21.5411 | − | 7.80864i | −0.959515 | − | 0.347824i | ||||
\(505\) | − | 2.38953i | − | 0.106333i | ||||||
\(506\) | 4.65703 | − | 8.06621i | 0.207030 | − | 0.358587i | ||||
\(507\) | −26.9414 | + | 15.5547i | −1.19651 | + | 0.690806i | ||||
\(508\) | 31.2730 | + | 54.1663i | 1.38751 | + | 2.40324i | ||||
\(509\) | −0.920031 | + | 1.59354i | −0.0407797 | + | 0.0706325i | −0.885695 | − | 0.464268i | \(-0.846318\pi\) |
0.844915 | + | 0.534900i | \(0.179651\pi\) | |||||||
\(510\) | 37.6122 | − | 6.55631i | 1.66550 | − | 0.290318i | ||||
\(511\) | −3.65668 | − | 4.34638i | −0.161762 | − | 0.192273i | ||||
\(512\) | −2.09435 | −0.0925583 | ||||||||
\(513\) | 1.44112 | + | 0.832031i | 0.0636270 | + | 0.0367351i | ||||
\(514\) | −20.8214 | − | 36.0637i | −0.918392 | − | 1.59070i | ||||
\(515\) | −9.15317 | + | 5.28459i | −0.403337 | + | 0.232867i | ||||
\(516\) | 14.2762 | + | 8.24235i | 0.628473 | + | 0.362849i | ||||
\(517\) | − | 4.18563i | − | 0.184084i | ||||||
\(518\) | −3.76090 | − | 4.47027i | −0.165245 | − | 0.196412i | ||||
\(519\) | 15.5886 | 0.684265 | ||||||||
\(520\) | 171.627 | + | 99.0887i | 7.52633 | + | 4.34533i | ||||
\(521\) | −29.4120 | + | 16.9810i | −1.28856 | + | 0.743951i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) |
−0.310164 | + | 0.950683i | \(0.600384\pi\) | |||||||
\(522\) | 10.1698 | − | 5.87152i | 0.445119 | − | 0.256990i | ||||
\(523\) | 13.1172 | − | 22.7197i | 0.573576 | − | 0.993462i | −0.422619 | − | 0.906307i | \(-0.638889\pi\) |
0.996195 | − | 0.0871549i | \(-0.0277775\pi\) | |||||||
\(524\) | 88.7634i | 3.87765i | ||||||||
\(525\) | −6.19628 | + | 17.0932i | −0.270428 | + | 0.746007i | ||||
\(526\) | 21.7903 | 0.950104 | ||||||||
\(527\) | −11.4784 | − | 4.20319i | −0.500005 | − | 0.183094i | ||||
\(528\) | −4.71129 | − | 8.16019i | −0.205032 | − | 0.355127i | ||||
\(529\) | −0.366990 | − | 0.635645i | −0.0159561 | − | 0.0276367i | ||||
\(530\) | −4.06322 | − | 2.34590i | −0.176495 | − | 0.101899i | ||||
\(531\) | 10.9270 | 0.474192 | ||||||||
\(532\) | 4.02206 | + | 22.6383i | 0.174379 | + | 0.981495i | ||||
\(533\) | 47.9142i | 2.07539i | ||||||||
\(534\) | −4.05992 | − | 2.34399i | −0.175690 | − | 0.101435i | ||||
\(535\) | 0.105146 | + | 0.182119i | 0.00454587 | + | 0.00787368i | ||||
\(536\) | 9.12748 | + | 15.8093i | 0.394247 | + | 0.682856i | ||||
\(537\) | 4.34053 | + | 2.50601i | 0.187308 | + | 0.108142i | ||||
\(538\) | 1.36292i | 0.0587596i | ||||||||
\(539\) | −3.29453 | + | 3.94704i | −0.141905 | + | 0.170011i | ||||
\(540\) | 17.9943 | 0.774352 | ||||||||
\(541\) | −32.3222 | − | 18.6612i | −1.38964 | − | 0.802308i | −0.396365 | − | 0.918093i | \(-0.629728\pi\) |
−0.993274 | + | 0.115785i | \(0.963062\pi\) | |||||||
\(542\) | 0.239032 | + | 0.414016i | 0.0102673 | + | 0.0177835i | ||||
\(543\) | 4.29384 | + | 7.43714i | 0.184266 | + | 0.319158i | ||||
\(544\) | 24.3245 | − | 66.4271i | 1.04291 | − | 2.84804i | ||||
\(545\) | −4.43743 | −0.190079 | ||||||||
\(546\) | −46.4952 | + | 8.26062i | −1.98981 | + | 0.353522i | ||||
\(547\) | 31.9948i | 1.36800i | 0.729482 | + | 0.684000i | \(0.239761\pi\) | ||||
−0.729482 | + | 0.684000i | \(0.760239\pi\) | |||||||
\(548\) | −18.4986 | + | 32.0406i | −0.790223 | + | 1.36871i | ||||
\(549\) | −7.47769 | + | 4.31725i | −0.319140 | + | 0.184256i | ||||
\(550\) | −11.7471 | + | 6.78220i | −0.500898 | + | 0.289194i | ||||
\(551\) | −6.29708 | − | 3.63562i | −0.268265 | − | 0.154883i | ||||
\(552\) | 40.8647 | 1.73932 | ||||||||
\(553\) | 10.4828 | − | 28.9181i | 0.445775 | − | 1.22972i | ||||
\(554\) | − | 77.8209i | − | 3.30629i | ||||||
\(555\) | 2.45163 | + | 1.41545i | 0.104066 | + | 0.0600825i | ||||
\(556\) | −27.0691 | + | 15.6283i | −1.14798 | + | 0.662789i | ||||
\(557\) | 17.5217 | + | 30.3484i | 0.742418 | + | 1.28591i | 0.951392 | + | 0.307984i | \(0.0996543\pi\) |
−0.208974 | + | 0.977921i | \(0.567012\pi\) | |||||||
\(558\) | −6.90005 | − | 3.98374i | −0.292102 | − | 0.168645i | ||||
\(559\) | 20.9639 | 0.886679 | ||||||||
\(560\) | 75.2910 | + | 89.4921i | 3.18163 | + | 3.78173i | ||||
\(561\) | −2.98332 | + | 0.520033i | −0.125956 | + | 0.0219558i | ||||
\(562\) | 5.20585 | − | 9.01680i | 0.219596 | − | 0.380351i | ||||
\(563\) | 2.52380 | + | 4.37136i | 0.106366 | + | 0.184231i | 0.914295 | − | 0.405048i | \(-0.132745\pi\) |
−0.807930 | + | 0.589279i | \(0.799412\pi\) | |||||||
\(564\) | 25.7745 | − | 14.8809i | 1.08530 | − | 0.626599i | ||||
\(565\) | 17.0572 | − | 29.5439i | 0.717602 | − | 1.24292i | ||||
\(566\) | − | 2.46867i | − | 0.103766i | ||||||
\(567\) | −2.02455 | + | 1.70329i | −0.0850232 | + | 0.0715313i | ||||
\(568\) | 119.855i | 5.02901i | ||||||||
\(569\) | −2.11760 | + | 3.66780i | −0.0887746 | + | 0.153762i | −0.906993 | − | 0.421145i | \(-0.861628\pi\) |
0.818219 | + | 0.574907i | \(0.194962\pi\) | |||||||
\(570\) | −7.70448 | − | 13.3446i | −0.322705 | − | 0.558942i | ||||
\(571\) | 14.6099 | − | 8.43501i | 0.611404 | − | 0.352994i | −0.162111 | − | 0.986773i | \(-0.551830\pi\) |
0.773515 | + | 0.633778i | \(0.218497\pi\) | |||||||
\(572\) | −22.0620 | − | 12.7375i | −0.922459 | − | 0.532582i | ||||
\(573\) | 12.8569i | 0.537104i | ||||||||
\(574\) | −17.4819 | + | 48.2259i | −0.729681 | + | 2.01291i | ||||
\(575\) | − | 32.4268i | − | 1.35229i | ||||||
\(576\) | 10.2255 | − | 17.7111i | 0.426063 | − | 0.737963i | ||||
\(577\) | 18.1321 | + | 31.4058i | 0.754850 | + | 1.30744i | 0.945449 | + | 0.325771i | \(0.105624\pi\) |
−0.190599 | + | 0.981668i | \(0.561043\pi\) | |||||||
\(578\) | −34.8831 | − | 29.5034i | −1.45095 | − | 1.22718i | ||||
\(579\) | −7.72374 | + | 13.3779i | −0.320988 | + | 0.555967i | ||||
\(580\) | −78.6275 | −3.26483 | ||||||||
\(581\) | −1.62317 | − | 9.13605i | −0.0673404 | − | 0.379027i | ||||
\(582\) | −33.7199 | −1.39774 | ||||||||
\(583\) | 0.322286 | + | 0.186072i | 0.0133477 | + | 0.00770632i | ||||
\(584\) | 16.1011 | − | 9.29600i | 0.666270 | − | 0.384671i | ||||
\(585\) | 19.8179 | − | 11.4419i | 0.819369 | − | 0.473063i | ||||
\(586\) | −25.3861 | + | 43.9701i | −1.04869 | + | 1.81639i | ||||
\(587\) | −27.2283 | −1.12383 | −0.561916 | − | 0.827195i | \(-0.689935\pi\) | ||||
−0.561916 | + | 0.827195i | \(0.689935\pi\) | |||||||
\(588\) | −36.0181 | − | 6.25455i | −1.48536 | − | 0.257933i | ||||
\(589\) | 4.93343i | 0.203278i | ||||||||
\(590\) | −87.6265 | − | 50.5912i | −3.60753 | − | 2.08281i | ||||
\(591\) | −10.8100 | − | 18.7235i | −0.444665 | − | 0.770182i | ||||
\(592\) | 9.12823 | − | 5.27019i | 0.375168 | − | 0.216603i | ||||
\(593\) | 9.23837 | − | 16.0013i | 0.379374 | − | 0.657096i | −0.611597 | − | 0.791169i | \(-0.709473\pi\) |
0.990971 | + | 0.134074i | \(0.0428059\pi\) | |||||||
\(594\) | −1.97387 | −0.0809887 | ||||||||
\(595\) | 35.3284 | − | 12.8323i | 1.44833 | − | 0.526073i | ||||
\(596\) | 64.2247 | 2.63074 | ||||||||
\(597\) | −0.605080 | + | 1.04803i | −0.0247643 | + | 0.0428930i | ||||
\(598\) | 72.9389 | − | 42.1113i | 2.98269 | − | 1.72206i | ||||
\(599\) | −13.3034 | − | 23.0421i | −0.543561 | − | 0.941475i | −0.998696 | − | 0.0510528i | \(-0.983742\pi\) |
0.455135 | − | 0.890422i | \(-0.349591\pi\) | |||||||
\(600\) | −51.5396 | − | 29.7564i | −2.10409 | − | 1.21480i | ||||
\(601\) | 39.2187i | 1.59976i | 0.600157 | + | 0.799882i | \(0.295105\pi\) | ||||
−0.600157 | + | 0.799882i | \(0.704895\pi\) | |||||||
\(602\) | 21.1003 | + | 7.64887i | 0.859985 | + | 0.311745i | ||||
\(603\) | 2.10792 | 0.0858411 | ||||||||
\(604\) | −46.2035 | + | 80.0269i | −1.88000 | + | 3.25625i | ||||
\(605\) | −31.2138 | + | 18.0213i | −1.26902 | + | 0.732670i | ||||
\(606\) | −1.61408 | + | 0.931888i | −0.0655674 | + | 0.0378553i | ||||
\(607\) | 1.00085 | + | 0.577840i | 0.0406232 | + | 0.0234538i | 0.520174 | − | 0.854060i | \(-0.325867\pi\) |
−0.479551 | + | 0.877514i | \(0.659200\pi\) | |||||||
\(608\) | −28.5505 | −1.15788 | ||||||||
\(609\) | 8.84643 | − | 7.44263i | 0.358475 | − | 0.301591i | ||||
\(610\) | 79.9541 | 3.23725 | ||||||||
\(611\) | 18.9243 | − | 32.7779i | 0.765596 | − | 1.32605i | ||||
\(612\) | −13.8087 | − | 16.5220i | −0.558183 | − | 0.667862i | ||||
\(613\) | 3.73593 | + | 6.47083i | 0.150893 | + | 0.261354i | 0.931556 | − | 0.363598i | \(-0.118452\pi\) |
−0.780663 | + | 0.624952i | \(0.785118\pi\) | |||||||
\(614\) | −9.12563 | + | 15.8061i | −0.368280 | + | 0.637880i | ||||
\(615\) | − | 24.8577i | − | 1.00236i | ||||||
\(616\) | −10.8340 | − | 12.8775i | −0.436516 | − | 0.518850i | ||||
\(617\) | 16.1698i | 0.650971i | 0.945547 | + | 0.325485i | \(0.105528\pi\) | ||||
−0.945547 | + | 0.325485i | \(0.894472\pi\) | |||||||
\(618\) | 7.13924 | + | 4.12184i | 0.287182 | + | 0.165805i | ||||
\(619\) | −6.24959 | + | 3.60821i | −0.251192 | + | 0.145026i | −0.620310 | − | 0.784357i | \(-0.712993\pi\) |
0.369118 | + | 0.929383i | \(0.379660\pi\) | |||||||
\(620\) | 26.6738 | + | 46.2004i | 1.07125 | + | 1.85545i | ||||
\(621\) | 2.35934 | − | 4.08650i | 0.0946772 | − | 0.163986i | ||||
\(622\) | − | 52.1247i | − | 2.09001i | ||||||
\(623\) | −4.33894 | − | 1.57287i | −0.173836 | − | 0.0630157i | ||||
\(624\) | − | 85.2038i | − | 3.41088i | ||||||
\(625\) | 6.06784 | − | 10.5098i | 0.242714 | − | 0.420392i | ||||
\(626\) | 26.4636 | − | 15.2788i | 1.05770 | − | 0.610662i | ||||
\(627\) | 0.611104 | + | 1.05846i | 0.0244052 | + | 0.0422710i | ||||
\(628\) | −37.1804 | + | 64.3983i | −1.48366 | + | 2.56977i | ||||
\(629\) | −0.581725 | − | 3.33724i | −0.0231949 | − | 0.133064i | ||||
\(630\) | 24.1215 | − | 4.28558i | 0.961024 | − | 0.170742i | ||||
\(631\) | −17.5995 | −0.700625 | −0.350313 | − | 0.936633i | \(-0.613925\pi\) | ||||
−0.350313 | + | 0.936633i | \(0.613925\pi\) | |||||||
\(632\) | 87.1944 | + | 50.3417i | 3.46841 | + | 2.00249i | ||||
\(633\) | −4.13496 | − | 7.16197i | −0.164350 | − | 0.284663i | ||||
\(634\) | 46.3108 | − | 26.7376i | 1.83924 | − | 1.06188i | ||||
\(635\) | −35.7370 | − | 20.6327i | −1.41818 | − | 0.818785i | ||||
\(636\) | 2.64612i | 0.104925i | ||||||||
\(637\) | −43.6452 | + | 16.0141i | −1.72929 | + | 0.634500i | ||||
\(638\) | 8.62495 | 0.341465 | ||||||||
\(639\) | 11.9856 | + | 6.91989i | 0.474143 | + | 0.273747i | ||||
\(640\) | −61.6101 | + | 35.5706i | −2.43535 | + | 1.40605i | ||||
\(641\) | 27.2757 | − | 15.7476i | 1.07733 | − | 0.621995i | 0.147153 | − | 0.989114i | \(-0.452989\pi\) |
0.930174 | + | 0.367119i | \(0.119656\pi\) | |||||||
\(642\) | 0.0820115 | − | 0.142048i | 0.00323673 | − | 0.00560619i | ||||
\(643\) | 32.3288i | 1.27492i | 0.770483 | + | 0.637461i | \(0.220015\pi\) | ||||
−0.770483 | + | 0.637461i | \(0.779985\pi\) | |||||||
\(644\) | 64.1942 | − | 11.4051i | 2.52961 | − | 0.449426i | ||||
\(645\) | −10.8760 | −0.428242 | ||||||||
\(646\) | −6.34033 | + | 17.3146i | −0.249457 | + | 0.681234i | ||||
\(647\) | −8.68766 | − | 15.0475i | −0.341547 | − | 0.591577i | 0.643173 | − | 0.765721i | \(-0.277618\pi\) |
−0.984720 | + | 0.174144i | \(0.944284\pi\) | |||||||
\(648\) | −4.33009 | − | 7.49994i | −0.170102 | − | 0.294626i | ||||
\(649\) | 6.95036 | + | 4.01279i | 0.272826 | + | 0.157516i | ||||
\(650\) | −122.656 | −4.81098 | ||||||||
\(651\) | −7.37427 | − | 2.67318i | −0.289020 | − | 0.104770i | ||||
\(652\) | − | 46.3764i | − | 1.81624i | ||||||
\(653\) | 31.6791 | + | 18.2899i | 1.23970 | + | 0.715740i | 0.969033 | − | 0.246933i | \(-0.0794227\pi\) |
0.270666 | + | 0.962673i | \(0.412756\pi\) | |||||||
\(654\) | 1.73054 | + | 2.99739i | 0.0676696 | + | 0.117207i | ||||
\(655\) | −29.2814 | − | 50.7169i | −1.14412 | − | 1.98167i | ||||
\(656\) | −80.1536 | − | 46.2767i | −3.12947 | − | 1.80680i | ||||
\(657\) | − | 2.14684i | − | 0.0837560i | ||||||
\(658\) | 31.0068 | − | 26.0865i | 1.20877 | − | 1.01696i | ||||
\(659\) | −44.2263 | −1.72281 | −0.861407 | − | 0.507915i | \(-0.830416\pi\) | ||||
−0.861407 | + | 0.507915i | \(0.830416\pi\) | |||||||
\(660\) | 11.4457 | + | 6.60817i | 0.445523 | + | 0.257223i | ||||
\(661\) | −17.3426 | − | 30.0383i | −0.674550 | − | 1.16836i | −0.976600 | − | 0.215063i | \(-0.931004\pi\) |
0.302050 | − | 0.953292i | \(-0.402329\pi\) | |||||||
\(662\) | −6.89155 | − | 11.9365i | −0.267848 | − | 0.463926i | ||||
\(663\) | −25.7138 | − | 9.41597i | −0.998640 | − | 0.365686i | ||||
\(664\) | 30.3728 | 1.17869 | ||||||||
\(665\) | −9.76606 | − | 11.6081i | −0.378711 | − | 0.450142i | ||||
\(666\) | − | 2.20803i | − | 0.0855593i | ||||||
\(667\) | −10.3093 | + | 17.8563i | −0.399178 | + | 0.691397i | ||||
\(668\) | 69.4721 | − | 40.1097i | 2.68795 | − | 1.55189i | ||||
\(669\) | 6.74542 | − | 3.89447i | 0.260793 | − | 0.150569i | ||||
\(670\) | −16.9040 | − | 9.75950i | −0.653057 | − | 0.377042i | ||||
\(671\) | −6.34180 | −0.244822 | ||||||||
\(672\) | 15.4701 | − | 42.6761i | 0.596771 | − | 1.64626i | ||||
\(673\) | − | 22.6579i | − | 0.873396i | −0.899608 | − | 0.436698i | \(-0.856148\pi\) | ||
0.899608 | − | 0.436698i | \(-0.143852\pi\) | |||||||
\(674\) | 42.4256 | + | 24.4944i | 1.63417 | + | 0.943491i | ||||
\(675\) | −5.95132 | + | 3.43600i | −0.229066 | + | 0.132252i | ||||
\(676\) | −81.2333 | − | 140.700i | −3.12436 | − | 5.41155i | ||||
\(677\) | 10.9284 | + | 6.30950i | 0.420012 | + | 0.242494i | 0.695082 | − | 0.718930i | \(-0.255368\pi\) |
−0.275071 | + | 0.961424i | \(0.588701\pi\) | |||||||
\(678\) | −26.6084 | −1.02189 | ||||||||
\(679\) | −32.6848 | + | 5.80698i | −1.25433 | + | 0.222851i | ||||
\(680\) | 21.1273 | + | 121.203i | 0.810196 | + | 4.64793i | ||||
\(681\) | −11.1166 | + | 19.2546i | −0.425990 | + | 0.737837i | ||||
\(682\) | −2.92595 | − | 5.06790i | −0.112040 | − | 0.194060i | ||||
\(683\) | 13.0266 | − | 7.52091i | 0.498449 | − | 0.287780i | −0.229624 | − | 0.973279i | \(-0.573750\pi\) |
0.728073 | + | 0.685500i | \(0.240416\pi\) | |||||||
\(684\) | −4.34524 | + | 7.52617i | −0.166144 | + | 0.287770i | ||||
\(685\) | − | 24.4095i | − | 0.932637i | ||||||
\(686\) | −49.7721 | + | 0.193905i | −1.90031 | + | 0.00740331i | ||||
\(687\) | 18.1710i | 0.693269i | ||||||||
\(688\) | −20.2475 | + | 35.0697i | −0.771928 | + | 1.33702i | ||||
\(689\) | 1.68256 | + | 2.91428i | 0.0641004 | + | 0.111025i | ||||
\(690\) | −37.8404 | + | 21.8472i | −1.44056 | + | 0.831708i | ||||
\(691\) | 24.7520 | + | 14.2906i | 0.941610 | + | 0.543639i | 0.890465 | − | 0.455053i | \(-0.150380\pi\) |
0.0511453 | + | 0.998691i | \(0.483713\pi\) | |||||||
\(692\) | 81.4107i | 3.09477i | ||||||||
\(693\) | −1.91327 | + | 0.339924i | −0.0726791 | + | 0.0129126i | ||||
\(694\) | − | 26.4255i | − | 1.00310i | ||||||
\(695\) | 10.3110 | − | 17.8592i | 0.391119 | − | 0.677437i | ||||
\(696\) | 18.9207 | + | 32.7715i | 0.717185 | + | 1.24220i | ||||
\(697\) | −22.8238 | + | 19.0756i | −0.864513 | + | 0.722539i | ||||
\(698\) | 23.5365 | − | 40.7665i | 0.890871 | − | 1.54303i | ||||
\(699\) | −2.58680 | −0.0978417 | ||||||||
\(700\) | −89.2681 | − | 32.3597i | −3.37402 | − | 1.22308i | ||||
\(701\) | −5.30427 | −0.200339 | −0.100170 | − | 0.994970i | \(-0.531939\pi\) | ||||
−0.100170 | + | 0.994970i | \(0.531939\pi\) | |||||||
\(702\) | −15.4574 | − | 8.92436i | −0.583404 | − | 0.336828i | ||||
\(703\) | −1.18403 | + | 0.683600i | −0.0446565 | + | 0.0257825i | ||||
\(704\) | 13.0083 | − | 7.51037i | 0.490270 | − | 0.283058i | ||||
\(705\) | −9.81786 | + | 17.0050i | −0.369762 | + | 0.640447i | ||||
\(706\) | 55.7704 | 2.09895 | ||||||||
\(707\) | −1.40404 | + | 1.18124i | −0.0528045 | + | 0.0444252i | ||||
\(708\) | 57.0657i | 2.14466i | ||||||||
\(709\) | −16.9648 | − | 9.79460i | −0.637125 | − | 0.367844i | 0.146381 | − | 0.989228i | \(-0.453237\pi\) |
−0.783506 | + | 0.621384i | \(0.786571\pi\) | |||||||
\(710\) | −64.0772 | − | 110.985i | −2.40477 | − | 4.16519i | ||||
\(711\) | 10.0684 | − | 5.81300i | 0.377595 | − | 0.218005i | ||||
\(712\) | 7.55339 | − | 13.0829i | 0.283075 | − | 0.490301i | ||||
\(713\) | 13.9895 | 0.523909 | ||||||||
\(714\) | −22.4456 | − | 18.8591i | −0.840004 | − | 0.705785i | ||||
\(715\) | 16.8075 | 0.628564 | ||||||||
\(716\) | −13.0875 | + | 22.6682i | −0.489102 | + | 0.847150i | ||||
\(717\) | 19.0551 | − | 11.0014i | 0.711624 | − | 0.410856i | ||||
\(718\) | −1.49624 | − | 2.59157i | −0.0558393 | − | 0.0967165i | ||||
\(719\) | −12.9412 | − | 7.47159i | −0.482624 | − | 0.278643i | 0.238885 | − | 0.971048i | \(-0.423218\pi\) |
−0.721510 | + | 0.692405i | \(0.756551\pi\) | |||||||
\(720\) | 44.2034i | 1.64736i | ||||||||
\(721\) | 7.62990 | + | 2.76584i | 0.284152 | + | 0.103005i | ||||
\(722\) | −43.6199 | −1.62336 | ||||||||
\(723\) | 10.6160 | − | 18.3874i | 0.394812 | − | 0.683835i | ||||
\(724\) | −38.8401 | + | 22.4243i | −1.44348 | + | 0.833393i | ||||
\(725\) | 26.0047 | − | 15.0138i | 0.965791 | − | 0.557600i | ||||
\(726\) | 24.3460 | + | 14.0562i | 0.903564 | + | 0.521673i | ||||
\(727\) | 50.3145 | 1.86606 | 0.933030 | − | 0.359799i | \(-0.117155\pi\) | ||||
0.933030 | + | 0.359799i | \(0.117155\pi\) | |||||||
\(728\) | −26.6194 | − | 149.828i | −0.986580 | − | 5.55300i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −9.93968 | + | 17.2160i | −0.367884 | + | 0.637194i | ||||
\(731\) | 8.34615 | + | 9.98611i | 0.308693 | + | 0.369349i | ||||
\(732\) | −22.5466 | − | 39.0518i | −0.833345 | − | 1.44340i | ||||
\(733\) | 15.7899 | − | 27.3489i | 0.583213 | − | 1.01015i | −0.411883 | − | 0.911237i | \(-0.635129\pi\) |
0.995096 | − | 0.0989173i | \(-0.0315379\pi\) | |||||||
\(734\) | 76.8196i | 2.83546i | ||||||||
\(735\) | 22.6430 | − | 8.30803i | 0.835199 | − | 0.306446i | ||||
\(736\) | 80.9591i | 2.98419i | ||||||||
\(737\) | 1.34079 | + | 0.774104i | 0.0493886 | + | 0.0285145i | ||||
\(738\) | −16.7908 | + | 9.69418i | −0.618078 | + | 0.356848i | ||||
\(739\) | 6.67523 | + | 11.5618i | 0.245552 | + | 0.425309i | 0.962287 | − | 0.272037i | \(-0.0876974\pi\) |
−0.716734 | + | 0.697346i | \(0.754364\pi\) | |||||||
\(740\) | −7.39210 | + | 12.8035i | −0.271739 | + | 0.470666i | ||||
\(741\) | 11.0518i | 0.406000i | ||||||||
\(742\) | 0.630207 | + | 3.54714i | 0.0231356 | + | 0.130220i | ||||
\(743\) | 14.5369i | 0.533308i | 0.963792 | + | 0.266654i | \(0.0859180\pi\) | ||||
−0.963792 | + | 0.266654i | \(0.914082\pi\) | |||||||
\(744\) | 12.8374 | − | 22.2350i | 0.470642 | − | 0.815175i | ||||
\(745\) | −36.6962 | + | 21.1865i | −1.34444 | + | 0.776215i | ||||
\(746\) | 34.1779 | + | 59.1978i | 1.25134 | + | 2.16739i | ||||
\(747\) | 1.75359 | − | 3.03731i | 0.0641605 | − | 0.111129i | ||||
\(748\) | −2.71584 | − | 15.5802i | −0.0993011 | − | 0.569670i | ||||
\(749\) | 0.0550314 | − | 0.151811i | 0.00201080 | − | 0.00554704i | ||||
\(750\) | 17.3344 | 0.632962 | ||||||||
\(751\) | 32.5004 | + | 18.7641i | 1.18596 | + | 0.684713i | 0.957385 | − | 0.288814i | \(-0.0932608\pi\) |
0.228573 | + | 0.973527i | \(0.426594\pi\) | |||||||
\(752\) | 36.5552 | + | 63.3154i | 1.33303 | + | 2.30888i | ||||
\(753\) | 7.66313 | − | 4.42431i | 0.279260 | − | 0.161231i | ||||
\(754\) | 67.5424 | + | 38.9956i | 2.45975 | + | 1.42014i | ||||
\(755\) | − | 60.9668i | − | 2.21881i | ||||||
\(756\) | −8.89532 | − | 10.5731i | −0.323520 | − | 0.384540i | ||||
\(757\) | −5.81812 | −0.211463 | −0.105732 | − | 0.994395i | \(-0.533718\pi\) | ||||
−0.105732 | + | 0.994395i | \(0.533718\pi\) | |||||||
\(758\) | 69.9963 | + | 40.4124i | 2.54238 | + | 1.46784i | ||||
\(759\) | 3.00143 | − | 1.73287i | 0.108945 | − | 0.0628993i | ||||
\(760\) | 43.0021 | − | 24.8273i | 1.55985 | − | 0.900579i | ||||
\(761\) | −2.67536 | + | 4.63385i | −0.0969816 | + | 0.167977i | −0.910434 | − | 0.413655i | \(-0.864252\pi\) |
0.813452 | + | 0.581632i | \(0.197585\pi\) | |||||||
\(762\) | 32.1860i | 1.16598i | ||||||||
\(763\) | 2.19360 | + | 2.60735i | 0.0794137 | + | 0.0943924i | ||||
\(764\) | −67.1444 | −2.42920 | ||||||||
\(765\) | 13.3402 | + | 4.88497i | 0.482316 | + | 0.176616i | ||||
\(766\) | 20.6874 | + | 35.8316i | 0.747465 | + | 1.29465i | ||||
\(767\) | 36.2858 | + | 62.8488i | 1.31020 | + | 2.26934i | ||||
\(768\) | 12.6320 | + | 7.29311i | 0.455819 | + | 0.263167i | ||||
\(769\) | 4.98467 | 0.179752 | 0.0898759 | − | 0.995953i | \(-0.471353\pi\) | ||||
0.0898759 | + | 0.995953i | \(0.471353\pi\) | |||||||
\(770\) | 16.9168 | + | 6.13236i | 0.609641 | + | 0.220995i | ||||
\(771\) | − | 15.4952i | − | 0.558047i | ||||||
\(772\) | −69.8653 | − | 40.3368i | −2.51451 | − | 1.45175i | ||||
\(773\) | 3.38408 | + | 5.86140i | 0.121717 | + | 0.210820i | 0.920445 | − | 0.390872i | \(-0.127827\pi\) |
−0.798728 | + | 0.601692i | \(0.794493\pi\) | |||||||
\(774\) | 4.24150 | + | 7.34649i | 0.152458 | + | 0.264064i | ||||
\(775\) | −17.6438 | − | 10.1867i | −0.633785 | − | 0.365916i | ||||
\(776\) | − | 108.661i | − | 3.90069i | ||||||
\(777\) | −0.380249 | − | 2.14024i | −0.0136414 | − | 0.0767808i | ||||
\(778\) | −74.0419 | −2.65453 | ||||||||
\(779\) | 10.3968 | + | 6.00259i | 0.372504 | + | 0.215065i | ||||
\(780\) | 59.7545 | + | 103.498i | 2.13955 | + | 3.70582i | ||||
\(781\) | 5.08247 | + | 8.80310i | 0.181865 | + | 0.315000i | ||||
\(782\) | 49.0980 | + | 17.9789i | 1.75574 | + | 0.642925i | ||||
\(783\) | 4.36957 | 0.156156 | ||||||||
\(784\) | 15.3644 | − | 88.4791i | 0.548729 | − | 3.15997i | ||||
\(785\) | − | 49.0605i | − | 1.75104i | ||||||
\(786\) | −22.8387 | + | 39.5579i | −0.814631 | + | 1.41098i | ||||
\(787\) | −15.4922 | + | 8.94444i | −0.552238 | + | 0.318835i | −0.750024 | − | 0.661410i | \(-0.769958\pi\) |
0.197786 | + | 0.980245i | \(0.436625\pi\) | |||||||
\(788\) | 97.7824 | − | 56.4547i | 3.48335 | − | 2.01111i | ||||
\(789\) | 7.02187 | + | 4.05408i | 0.249985 | + | 0.144329i | ||||
\(790\) | −107.655 | −3.83019 | ||||||||
\(791\) | −25.7915 | + | 4.58228i | −0.917040 | + | 0.162927i | ||||
\(792\) | − | 6.36067i | − | 0.226017i | ||||||
\(793\) | −49.6630 | − | 28.6729i | −1.76358 | − | 1.01821i | ||||
\(794\) | −73.8391 | + | 42.6310i | −2.62045 | + | 1.51292i | ||||
\(795\) | −0.872906 | − | 1.51192i | −0.0309588 | − | 0.0536222i | ||||
\(796\) | −5.47327 | − | 3.15999i | −0.193995 | − | 0.112003i | ||||
\(797\) | 39.7704 | 1.40874 | 0.704369 | − | 0.709834i | \(-0.251230\pi\) | ||||
0.704369 | + | 0.709834i | \(0.251230\pi\) | |||||||
\(798\) | −4.03236 | + | 11.1238i | −0.142744 | + | 0.393777i | ||||
\(799\) | 23.1478 | − | 4.03497i | 0.818911 | − | 0.142747i | ||||
\(800\) | 58.9518 | − | 102.108i | 2.08426 | − | 3.61005i | ||||
\(801\) | −0.872197 | − | 1.51069i | −0.0308176 | − | 0.0533776i | ||||
\(802\) | −79.8500 | + | 46.1014i | −2.81960 | + | 1.62790i | ||||
\(803\) | 0.788396 | − | 1.36554i | 0.0278219 | − | 0.0481889i | ||||
\(804\) | 11.0085i | 0.388239i | ||||||||
\(805\) | −32.9164 | + | 27.6931i | −1.16015 | + | 0.976052i | ||||
\(806\) | − | 52.9159i | − | 1.86388i | ||||||
\(807\) | −0.253570 | + | 0.439196i | −0.00892609 | + | 0.0154604i | ||||
\(808\) | −3.00295 | − | 5.20127i | −0.105644 | − | 0.182980i | ||||
\(809\) | −18.1506 | + | 10.4793i | −0.638142 | + | 0.368431i | −0.783898 | − | 0.620889i | \(-0.786772\pi\) |
0.145757 | + | 0.989320i | \(0.453438\pi\) | |||||||
\(810\) | 8.01926 | + | 4.62992i | 0.281768 | + | 0.162679i | ||||
\(811\) | − | 5.99034i | − | 0.210349i | −0.994454 | − | 0.105175i | \(-0.966460\pi\) | ||
0.994454 | − | 0.105175i | \(-0.0335401\pi\) | |||||||
\(812\) | 38.8687 | + | 46.2000i | 1.36402 | + | 1.62130i | ||||
\(813\) | 0.177887i | 0.00623877i | ||||||||
\(814\) | 0.810868 | − | 1.40446i | 0.0284209 | − | 0.0492265i | ||||
\(815\) | 15.2987 | + | 26.4982i | 0.535891 | + | 0.928190i | ||||
\(816\) | 40.5866 | − | 33.9213i | 1.42082 | − | 1.18748i | ||||
\(817\) | 2.62632 | − | 4.54891i | 0.0918832 | − | 0.159146i | ||||
\(818\) | 57.3969 | 2.00684 | ||||||||
\(819\) | −16.5198 | − | 5.98843i | −0.577249 | − | 0.209253i | ||||
\(820\) | 129.818 | 4.53344 | ||||||||
\(821\) | −0.182498 | − | 0.105365i | −0.00636923 | − | 0.00367728i | 0.496812 | − | 0.867858i | \(-0.334504\pi\) |
−0.503181 | + | 0.864181i | \(0.667837\pi\) | |||||||
\(822\) | −16.4880 | + | 9.51937i | −0.575086 | + | 0.332026i | ||||
\(823\) | −15.5360 | + | 8.96969i | −0.541550 | + | 0.312664i | −0.745707 | − | 0.666274i | \(-0.767888\pi\) |
0.204157 | + | 0.978938i | \(0.434555\pi\) | |||||||
\(824\) | −13.2824 | + | 23.0058i | −0.462714 | + | 0.801445i | ||||
\(825\) | −5.04729 | −0.175724 | ||||||||
\(826\) | 13.5909 | + | 76.4969i | 0.472889 | + | 2.66167i | ||||
\(827\) | 19.3366i | 0.672399i | 0.941791 | + | 0.336199i | \(0.109142\pi\) | ||||
−0.941791 | + | 0.336199i | \(0.890858\pi\) | |||||||
\(828\) | 21.3415 | + | 12.3215i | 0.741670 | + | 0.428203i | ||||
\(829\) | −21.4942 | − | 37.2290i | −0.746524 | − | 1.29302i | −0.949479 | − | 0.313829i | \(-0.898388\pi\) |
0.202955 | − | 0.979188i | \(-0.434945\pi\) | |||||||
\(830\) | −28.1250 | + | 16.2380i | −0.976233 | + | 0.563628i | ||||
\(831\) | 14.4785 | − | 25.0775i | 0.502254 | − | 0.869930i | ||||
\(832\) | 135.825 | 4.70889 | ||||||||
\(833\) | −25.0043 | − | 14.4148i | −0.866347 | − | 0.499443i | ||||
\(834\) | −16.0846 | −0.556965 | ||||||||
\(835\) | −26.4629 | + | 45.8351i | −0.915787 | + | 1.58619i | ||||
\(836\) | −5.52777 | + | 3.19146i | −0.191182 | + | 0.110379i | ||||
\(837\) | −1.48235 | − | 2.56750i | −0.0512373 | − | 0.0887457i | ||||
\(838\) | −30.9264 | − | 17.8554i | −1.06833 | − | 0.616803i | ||||
\(839\) | − | 54.7774i | − | 1.89113i | −0.325438 | − | 0.945563i | \(-0.605512\pi\) | ||
0.325438 | − | 0.945563i | \(-0.394488\pi\) | |||||||
\(840\) | 13.8100 | + | 77.7302i | 0.476492 | + | 2.68195i | ||||
\(841\) | 9.90686 | 0.341616 | ||||||||
\(842\) | 14.6056 | − | 25.2976i | 0.503341 | − | 0.871813i | ||||
\(843\) | 3.35514 | − | 1.93709i | 0.115557 | − | 0.0667169i | ||||
\(844\) | 37.4030 | − | 21.5946i | 1.28746 | − | 0.743317i | ||||
\(845\) | 92.8288 | + | 53.5947i | 3.19341 | + | 1.84371i | ||||
\(846\) | 15.3154 | 0.526553 | ||||||||
\(847\) | 26.0192 | + | 9.43197i | 0.894031 | + | 0.324086i | ||||
\(848\) | −6.50024 | −0.223219 | ||||||||
\(849\) | 0.459295 | − | 0.795522i | 0.0157630 | − | 0.0273022i | ||||
\(850\) | −48.8319 | − | 58.4270i | −1.67492 | − | 2.00403i | ||||
\(851\) | 1.93845 | + | 3.35749i | 0.0664491 | + | 0.115093i | ||||
\(852\) | −36.1387 | + | 62.5941i | −1.23809 | + | 2.14444i | ||||
\(853\) | − | 1.08867i | − | 0.0372754i | −0.999826 | − | 0.0186377i | \(-0.994067\pi\) | ||
0.999826 | − | 0.0186377i | \(-0.00593291\pi\) | |||||||
\(854\) | −39.5245 | − | 46.9795i | −1.35250 | − | 1.60760i | ||||
\(855\) | − | 5.73365i | − | 0.196087i | ||||||
\(856\) | 0.457742 | + | 0.264277i | 0.0156453 | + | 0.00903281i | ||||
\(857\) | 0.762520 | − | 0.440241i | 0.0260472 | − | 0.0150384i | −0.486920 | − | 0.873447i | \(-0.661880\pi\) |
0.512967 | + | 0.858408i | \(0.328546\pi\) | |||||||
\(858\) | −6.55470 | − | 11.3531i | −0.223774 | − | 0.387588i | ||||
\(859\) | 17.6373 | − | 30.5487i | 0.601777 | − | 1.04231i | −0.390776 | − | 0.920486i | \(-0.627793\pi\) |
0.992552 | − | 0.121821i | \(-0.0388735\pi\) | |||||||
\(860\) | − | 56.7993i | − | 1.93684i | ||||||
\(861\) | −14.6059 | + | 12.2882i | −0.497767 | + | 0.418779i | ||||
\(862\) | − | 46.3677i | − | 1.57929i | ||||||
\(863\) | −8.21302 | + | 14.2254i | −0.279574 | + | 0.484237i | −0.971279 | − | 0.237943i | \(-0.923527\pi\) |
0.691705 | + | 0.722181i | \(0.256860\pi\) | |||||||
\(864\) | 14.8585 | − | 8.57856i | 0.505497 | − | 0.291849i | ||||
\(865\) | −26.8559 | − | 46.5158i | −0.913128 | − | 1.58158i | ||||
\(866\) | −7.11724 | + | 12.3274i | −0.241854 | + | 0.418903i | ||||
\(867\) | −5.75188 | − | 15.9974i | −0.195344 | − | 0.543299i | ||||
\(868\) | 13.9605 | − | 38.5117i | 0.473850 | − | 1.30717i | ||||
\(869\) | 8.53898 | 0.289665 | ||||||||
\(870\) | −35.0407 | − | 20.2308i | −1.18799 | − | 0.685888i | ||||
\(871\) | 6.99985 | + | 12.1241i | 0.237181 | + | 0.410809i | ||||
\(872\) | −9.65891 | + | 5.57657i | −0.327092 | + | 0.188847i | ||||
\(873\) | −10.8661 | − | 6.27357i | −0.367763 | − | 0.212328i | ||||
\(874\) | − | 21.1025i | − | 0.713801i | ||||||
\(875\) | 16.8022 | − | 2.98519i | 0.568019 | − | 0.100918i | ||||
\(876\) | 11.2117 | 0.378809 | ||||||||
\(877\) | −37.6791 | − | 21.7540i | −1.27233 | − | 0.734582i | −0.296907 | − | 0.954907i | \(-0.595955\pi\) |
−0.975427 | + | 0.220325i | \(0.929288\pi\) | |||||||
\(878\) | 25.8360 | − | 14.9164i | 0.871923 | − | 0.503405i | ||||
\(879\) | −16.3612 | + | 9.44614i | −0.551849 | + | 0.318610i | ||||
\(880\) | −16.2331 | + | 28.1165i | −0.547217 | + | 0.947808i | ||||
\(881\) | − | 36.7445i | − | 1.23795i | −0.785410 | − | 0.618976i | \(-0.787548\pi\) | ||
0.785410 | − | 0.618976i | \(-0.212452\pi\) | |||||||
\(882\) | −14.4424 | − | 12.0548i | −0.486299 | − | 0.405906i | ||||
\(883\) | 41.9518 | 1.41179 | 0.705895 | − | 0.708317i | \(-0.250545\pi\) | ||||
0.705895 | + | 0.708317i | \(0.250545\pi\) | |||||||
\(884\) | 49.1744 | − | 134.289i | 1.65391 | − | 4.51662i | ||||
\(885\) | −18.8249 | − | 32.6057i | −0.632793 | − | 1.09603i | ||||
\(886\) | 15.1414 | + | 26.2256i | 0.508684 | + | 0.881067i | ||||
\(887\) | 37.6524 | + | 21.7386i | 1.26424 | + | 0.729911i | 0.973893 | − | 0.227009i | \(-0.0728946\pi\) |
0.290351 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(888\) | 7.11524 | 0.238772 | ||||||||
\(889\) | 5.54282 | + | 31.1979i | 0.185900 | + | 1.04634i | ||||
\(890\) | 16.1528i | 0.541444i | ||||||||
\(891\) | −0.636072 | − | 0.367236i | −0.0213092 | − | 0.0123029i | ||||
\(892\) | 20.3386 | + | 35.2276i | 0.680988 | + | 1.17951i | ||||
\(893\) | −4.74160 | − | 8.21269i | −0.158672 | − | 0.274827i | ||||
\(894\) | 28.6221 | + | 16.5250i | 0.957265 | + | 0.552677i | ||||
\(895\) | − | 17.2693i | − | 0.577248i | ||||||
\(896\) | 51.3569 | + | 18.6169i | 1.71571 | + | 0.621947i | ||||
\(897\) | 31.3391 | 1.04638 | ||||||||
\(898\) | 50.2345 | + | 29.0029i | 1.67635 | + | 0.967840i | ||||
\(899\) | 6.47721 | + | 11.2189i | 0.216027 | + | 0.374170i | ||||
\(900\) | −17.9443 | − | 31.0804i | −0.598143 | − | 1.03601i | ||||
\(901\) | −0.718349 | + | 1.96172i | −0.0239317 | + | 0.0653542i | ||||
\(902\) | −14.2402 | −0.474147 | ||||||||
\(903\) | 5.37644 | + | 6.39052i | 0.178917 | + | 0.212663i | ||||
\(904\) | − | 85.7439i | − | 2.85180i | ||||||
\(905\) | 14.7947 | − | 25.6252i | 0.491794 | − | 0.851812i | ||||
\(906\) | −41.1817 | + | 23.7763i | −1.36817 | + | 0.789913i | ||||
\(907\) | −10.5810 | + | 6.10893i | −0.351336 | + | 0.202844i | −0.665273 | − | 0.746600i | \(-0.731685\pi\) |
0.313938 | + | 0.949444i | \(0.398352\pi\) | |||||||
\(908\) | −100.556 | − | 58.0560i | −3.33706 | − | 1.92666i | ||||
\(909\) | −0.693508 | −0.0230022 | ||||||||
\(910\) | 104.751 | + | 124.508i | 3.47245 | + | 4.12741i | ||||
\(911\) | − | 41.7422i | − | 1.38298i | −0.722386 | − | 0.691490i | \(-0.756955\pi\) | ||
0.722386 | − | 0.691490i | \(-0.243045\pi\) | |||||||
\(912\) | −18.4882 | − | 10.6742i | −0.612205 | − | 0.353457i | ||||
\(913\) | 2.23082 | − | 1.28796i | 0.0738293 | − | 0.0426254i | ||||
\(914\) | −9.90985 | − | 17.1644i | −0.327789 | − | 0.567747i | ||||
\(915\) | 25.7649 | + | 14.8754i | 0.851763 | + | 0.491766i | ||||
\(916\) | −94.8973 | −3.13549 | ||||||||
\(917\) | −15.3253 | + | 42.2766i | −0.506085 | + | 1.39610i | ||||
\(918\) | −1.90282 | − | 10.9161i | −0.0628024 | − | 0.360284i | ||||
\(919\) | −12.4550 | + | 21.5726i | −0.410852 | + | 0.711616i | −0.994983 | − | 0.100043i | \(-0.968102\pi\) |
0.584132 | + | 0.811659i | \(0.301435\pi\) | |||||||
\(920\) | −70.4013 | − | 121.939i | −2.32106 | − | 4.02020i | ||||
\(921\) | −5.88141 | + | 3.39563i | −0.193799 | + | 0.111890i | ||||
\(922\) | 23.1333 | − | 40.0680i | 0.761854 | − | 1.31957i | ||||
\(923\) | 91.9167i | 3.02548i | ||||||||
\(924\) | −1.77523 | − | 9.99195i | −0.0584008 | − | 0.328711i | ||||
\(925\) | − | 5.64605i | − | 0.185641i | ||||||
\(926\) | 35.7200 | − | 61.8688i | 1.17383 | − | 2.03313i | ||||
\(927\) | 1.53373 | + | 2.65650i | 0.0503743 | + | 0.0872509i | ||||
\(928\) | −64.9253 | + | 37.4846i | −2.13128 | + | 1.23049i | ||||
\(929\) | 10.4166 | + | 6.01403i | 0.341758 | + | 0.197314i | 0.661049 | − | 0.750343i | \(-0.270112\pi\) |
−0.319291 | + | 0.947657i | \(0.603445\pi\) | |||||||
\(930\) | 27.4526i | 0.900206i | ||||||||
\(931\) | −1.99293 | + | 11.4767i | −0.0653156 | + | 0.376133i | ||||
\(932\) | − | 13.5094i | − | 0.442515i | ||||||
\(933\) | 9.69776 | − | 16.7970i | 0.317490 | − | 0.549910i | ||||
\(934\) | −56.0848 | − | 97.1418i | −1.83515 | − | 3.17858i | ||||
\(935\) | 6.69139 | + | 8.00620i | 0.218832 | + | 0.261831i | ||||
\(936\) | 28.7583 | − | 49.8108i | 0.939993 | − | 1.62812i | ||||
\(937\) | −42.1980 | −1.37855 | −0.689274 | − | 0.724501i | \(-0.742070\pi\) | ||||
−0.689274 | + | 0.724501i | \(0.742070\pi\) | |||||||
\(938\) | 2.62181 | + | 14.7569i | 0.0856052 | + | 0.481831i | ||||
\(939\) | 11.3704 | 0.371059 | ||||||||
\(940\) | −88.8079 | − | 51.2732i | −2.89659 | − | 1.67235i | ||||
\(941\) | 8.83666 | − | 5.10185i | 0.288067 | − | 0.166315i | −0.349003 | − | 0.937122i | \(-0.613480\pi\) |
0.637070 | + | 0.770806i | \(0.280146\pi\) | |||||||
\(942\) | −33.1392 | + | 19.1329i | −1.07973 | + | 0.623385i | ||||
\(943\) | 17.0212 | − | 29.4816i | 0.554287 | − | 0.960052i | ||||
\(944\) | −140.183 | −4.56256 | ||||||||
\(945\) | 8.57041 | + | 3.10678i | 0.278795 | + | 0.101063i | ||||
\(946\) | 6.23053i | 0.202572i | ||||||||
\(947\) | 11.0487 | + | 6.37898i | 0.359035 | + | 0.207289i | 0.668657 | − | 0.743571i | \(-0.266869\pi\) |
−0.309622 | + | 0.950860i | \(0.600203\pi\) | |||||||
\(948\) | 30.3581 | + | 52.5817i | 0.985984 | + | 1.70778i | ||||
\(949\) | 12.3479 | − | 7.12909i | 0.400831 | − | 0.231420i | ||||
\(950\) | −15.3661 | + | 26.6149i | −0.498543 | + | 0.863502i | ||||
\(951\) | 19.8980 | 0.645238 | ||||||||
\(952\) | 60.7725 | − | 72.3296i | 1.96965 | − | 2.34422i | ||||
\(953\) | −40.4442 | −1.31012 | −0.655058 | − | 0.755579i | \(-0.727356\pi\) | ||||
−0.655058 | + | 0.755579i | \(0.727356\pi\) | |||||||
\(954\) | −0.680844 | + | 1.17926i | −0.0220431 | + | 0.0381798i | ||||
\(955\) | 38.3644 | − | 22.1497i | 1.24144 | − | 0.716747i | ||||
\(956\) | 57.4544 | + | 99.5140i | 1.85821 | + | 3.21851i | ||||
\(957\) | 2.77936 | + | 1.60467i | 0.0898440 | + | 0.0518715i | ||||
\(958\) | − | 40.9157i | − | 1.32193i | ||||||
\(959\) | −14.3425 | + | 12.0666i | −0.463144 | + | 0.389650i | ||||
\(960\) | −70.4656 | −2.27427 | ||||||||
\(961\) | −11.1053 | + | 19.2350i | −0.358236 | + | 0.620482i | ||||
\(962\) | 12.6999 | − | 7.33229i | 0.409461 | − | 0.236402i | ||||
\(963\) | 0.0528559 | − | 0.0305163i | 0.00170326 | − | 0.000983375i | ||||
\(964\) | 96.0272 | + | 55.4413i | 3.09283 | + | 1.78564i | ||||
\(965\) | 53.2254 | 1.71339 | ||||||||
\(966\) | 31.5430 | + | 11.4343i | 1.01488 | + | 0.367894i | ||||
\(967\) | 48.1460 | 1.54827 | 0.774135 | − | 0.633020i | \(-0.218185\pi\) | ||||
0.774135 | + | 0.633020i | \(0.218185\pi\) | |||||||
\(968\) | −45.2952 | + | 78.4535i | −1.45584 | + | 2.52159i | ||||
\(969\) | −5.26452 | + | 4.39996i | −0.169121 | + | 0.141347i | ||||
\(970\) | 58.0923 | + | 100.619i | 1.86523 | + | 3.23067i | ||||
\(971\) | −11.9858 | + | 20.7600i | −0.384642 | + | 0.666220i | −0.991719 | − | 0.128423i | \(-0.959008\pi\) |
0.607077 | + | 0.794643i | \(0.292342\pi\) | |||||||
\(972\) | − | 5.22244i | − | 0.167510i | ||||||
\(973\) | −15.5908 | + | 2.76997i | −0.499820 | + | 0.0888011i | ||||
\(974\) | 17.4330i | 0.558590i | ||||||||
\(975\) | −39.5256 | − | 22.8201i | −1.26583 | − | 0.730828i | ||||
\(976\) | 95.9315 | − | 55.3861i | 3.07069 | − | 1.77287i | ||||
\(977\) | −9.23058 | − | 15.9878i | −0.295312 | − | 0.511496i | 0.679745 | − | 0.733448i | \(-0.262090\pi\) |
−0.975058 | + | 0.221952i | \(0.928757\pi\) | |||||||
\(978\) | 11.9326 | − | 20.6679i | 0.381563 | − | 0.660886i | ||||
\(979\) | − | 1.28121i | − | 0.0409476i | ||||||
\(980\) | 43.3882 | + | 118.252i | 1.38599 | + | 3.77741i | ||||
\(981\) | 1.28786i | 0.0411183i | ||||||||
\(982\) | 43.0258 | − | 74.5228i | 1.37301 | − | 2.37812i | ||||
\(983\) | −9.54106 | + | 5.50854i | −0.304313 | + | 0.175695i | −0.644379 | − | 0.764707i | \(-0.722884\pi\) |
0.340066 | + | 0.940402i | \(0.389551\pi\) | |||||||
\(984\) | −31.2389 | − | 54.1074i | −0.995861 | − | 1.72488i | ||||
\(985\) | −37.2467 | + | 64.5132i | −1.18678 | + | 2.05556i | ||||
\(986\) | 8.31450 | + | 47.6986i | 0.264788 | + | 1.51903i | ||||
\(987\) | 14.8452 | − | 2.63749i | 0.472528 | − | 0.0839522i | ||||
\(988\) | −57.7176 | −1.83624 | ||||||||
\(989\) | −12.8991 | − | 7.44730i | −0.410167 | − | 0.236810i | ||||
\(990\) | 3.40055 | + | 5.88993i | 0.108077 | + | 0.187194i | ||||
\(991\) | 46.0523 | − | 26.5883i | 1.46290 | − | 0.844606i | 0.463756 | − | 0.885963i | \(-0.346501\pi\) |
0.999144 | + | 0.0413565i | \(0.0131679\pi\) | |||||||
\(992\) | 44.0509 | + | 25.4328i | 1.39862 | + | 0.807492i | ||||
\(993\) | − | 5.12867i | − | 0.162753i | ||||||
\(994\) | −33.5366 | + | 92.5148i | −1.06372 | + | 2.93439i | ||||
\(995\) | 4.16969 | 0.132188 | ||||||||
\(996\) | 15.8622 | + | 9.15802i | 0.502612 | + | 0.290183i | ||||
\(997\) | −25.6469 | + | 14.8073i | −0.812246 | + | 0.468950i | −0.847735 | − | 0.530420i | \(-0.822034\pi\) |
0.0354892 | + | 0.999370i | \(0.488701\pi\) | |||||||
\(998\) | −50.2147 | + | 28.9915i | −1.58952 | + | 0.917709i | ||||
\(999\) | 0.410802 | − | 0.711530i | 0.0129972 | − | 0.0225118i |
(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 | 357.2.p.a.16.1 | ✓ | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.2 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.2 | yes | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.16.2 | yes | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.67.1 | yes | 48 | 119.67 | even | 6 | inner | |
357.2.p.a.67.2 | yes | 48 | 7.4 | even | 3 | inner |