Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(569,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.c (of order \(2\), degree \(1\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1499238400.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 59x^{4} - 66x^{3} + 54x^{2} - 26x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 569.3 | ||
Root | \(0.500000 + 1.41267i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.f.569.5 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.500000 | + | 1.65831i | 0.288675 | + | 0.957427i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.91267 | − | 1.15831i | −0.855373 | − | 0.518013i | ||||
\(6\) | 1.65831 | − | 0.500000i | 0.677003 | − | 0.204124i | ||||
\(7\) | − | 3.21974i | − | 1.21695i | −0.793574 | − | 0.608474i | \(-0.791782\pi\) | ||
0.793574 | − | 0.608474i | \(-0.208218\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.50000 | + | 1.65831i | −0.833333 | + | 0.552771i | ||||
\(10\) | −1.15831 | + | 1.91267i | −0.366291 | + | 0.604840i | ||||
\(11\) | 4.31662i | 1.30151i | 0.759287 | + | 0.650756i | \(0.225548\pi\) | ||||
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(12\) | −0.500000 | − | 1.65831i | −0.144338 | − | 0.478714i | ||||
\(13\) | −3.31662 | −0.919866 | −0.459933 | − | 0.887954i | \(-0.652127\pi\) | ||||
−0.459933 | + | 0.887954i | \(0.652127\pi\) | |||||||
\(14\) | −3.21974 | −0.860513 | ||||||||
\(15\) | 0.964508 | − | 3.75096i | 0.249035 | − | 0.968495i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.21974 | −0.780903 | −0.390451 | − | 0.920624i | \(-0.627681\pi\) | ||||
−0.390451 | + | 0.920624i | \(0.627681\pi\) | |||||||
\(18\) | 1.65831 | + | 2.50000i | 0.390868 | + | 0.589256i | ||||
\(19\) | −4.31662 | − | 0.605599i | −0.990302 | − | 0.138934i | ||||
\(20\) | 1.91267 | + | 1.15831i | 0.427686 | + | 0.259007i | ||||
\(21\) | 5.33934 | − | 1.60987i | 1.16514 | − | 0.351303i | ||||
\(22\) | 4.31662 | 0.920307 | ||||||||
\(23\) | −7.04509 | −1.46900 | −0.734501 | − | 0.678608i | \(-0.762584\pi\) | ||||
−0.734501 | + | 0.678608i | \(0.762584\pi\) | |||||||
\(24\) | −1.65831 | + | 0.500000i | −0.338502 | + | 0.102062i | ||||
\(25\) | 2.31662 | + | 4.43094i | 0.463325 | + | 0.886188i | ||||
\(26\) | 3.31662i | 0.650444i | ||||||||
\(27\) | −4.00000 | − | 3.31662i | −0.769800 | − | 0.638285i | ||||
\(28\) | 3.21974i | 0.608474i | ||||||||
\(29\) | 8.25629 | 1.53315 | 0.766577 | − | 0.642153i | \(-0.221958\pi\) | ||||
0.766577 | + | 0.642153i | \(0.221958\pi\) | |||||||
\(30\) | −3.75096 | − | 0.964508i | −0.684829 | − | 0.176094i | ||||
\(31\) | − | 2.61414i | − | 0.469514i | −0.972054 | − | 0.234757i | \(-0.924571\pi\) | ||
0.972054 | − | 0.234757i | \(-0.0754295\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −7.15831 | + | 2.15831i | −1.24610 | + | 0.375714i | ||||
\(34\) | 3.21974i | 0.552182i | ||||||||
\(35\) | −3.72947 | + | 6.15831i | −0.630395 | + | 1.04094i | ||||
\(36\) | 2.50000 | − | 1.65831i | 0.416667 | − | 0.276385i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −0.605599 | + | 4.31662i | −0.0982412 | + | 0.700249i | ||||
\(39\) | −1.65831 | − | 5.50000i | −0.265543 | − | 0.880705i | ||||
\(40\) | 1.15831 | − | 1.91267i | 0.183145 | − | 0.302420i | ||||
\(41\) | −11.4760 | −1.79225 | −0.896127 | − | 0.443797i | \(-0.853631\pi\) | ||||
−0.896127 | + | 0.443797i | \(0.853631\pi\) | |||||||
\(42\) | −1.60987 | − | 5.33934i | −0.248409 | − | 0.823878i | ||||
\(43\) | − | 3.82534i | − | 0.583359i | −0.956516 | − | 0.291680i | \(-0.905786\pi\) | ||
0.956516 | − | 0.291680i | \(-0.0942141\pi\) | |||||||
\(44\) | − | 4.31662i | − | 0.650756i | ||||||
\(45\) | 6.70252 | − | 0.276026i | 0.999153 | − | 0.0411475i | ||||
\(46\) | 7.04509i | 1.03874i | ||||||||
\(47\) | −8.86188 | −1.29264 | −0.646319 | − | 0.763067i | \(-0.723693\pi\) | ||||
−0.646319 | + | 0.763067i | \(0.723693\pi\) | |||||||
\(48\) | 0.500000 | + | 1.65831i | 0.0721688 | + | 0.239357i | ||||
\(49\) | −3.36675 | −0.480964 | ||||||||
\(50\) | 4.43094 | − | 2.31662i | 0.626630 | − | 0.327620i | ||||
\(51\) | −1.60987 | − | 5.33934i | −0.225427 | − | 0.747657i | ||||
\(52\) | 3.31662 | 0.459933 | ||||||||
\(53\) | − | 1.00000i | − | 0.137361i | −0.997639 | − | 0.0686803i | \(-0.978121\pi\) | ||
0.997639 | − | 0.0686803i | \(-0.0218788\pi\) | |||||||
\(54\) | −3.31662 | + | 4.00000i | −0.451335 | + | 0.544331i | ||||
\(55\) | 5.00000 | − | 8.25629i | 0.674200 | − | 1.11328i | ||||
\(56\) | 3.21974 | 0.430256 | ||||||||
\(57\) | −1.15404 | − | 7.46111i | −0.152856 | − | 0.988248i | ||||
\(58\) | − | 8.25629i | − | 1.08410i | ||||||
\(59\) | −5.64214 | −0.734544 | −0.367272 | − | 0.930114i | \(-0.619708\pi\) | ||||
−0.367272 | + | 0.930114i | \(0.619708\pi\) | |||||||
\(60\) | −0.964508 | + | 3.75096i | −0.124517 | + | 0.484247i | ||||
\(61\) | −2.31662 | −0.296613 | −0.148307 | − | 0.988941i | \(-0.547382\pi\) | ||||
−0.148307 | + | 0.988941i | \(0.547382\pi\) | |||||||
\(62\) | −2.61414 | −0.331997 | ||||||||
\(63\) | 5.33934 | + | 8.04936i | 0.672694 | + | 1.01412i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.34361 | + | 3.84169i | 0.786828 | + | 0.476503i | ||||
\(66\) | 2.15831 | + | 7.15831i | 0.265670 | + | 0.881127i | ||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | 3.21974 | 0.390451 | ||||||||
\(69\) | −3.52254 | − | 11.6830i | −0.424064 | − | 1.40646i | ||||
\(70\) | 6.15831 | + | 3.72947i | 0.736059 | + | 0.445757i | ||||
\(71\) | 10.2648 | 1.21821 | 0.609106 | − | 0.793089i | \(-0.291529\pi\) | ||||
0.609106 | + | 0.793089i | \(0.291529\pi\) | |||||||
\(72\) | −1.65831 | − | 2.50000i | −0.195434 | − | 0.294628i | ||||
\(73\) | 1.81680i | 0.212640i | 0.994332 | + | 0.106320i | \(0.0339068\pi\) | ||||
−0.994332 | + | 0.106320i | \(0.966093\pi\) | |||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | −6.18957 | + | 6.05716i | −0.714710 | + | 0.699420i | ||||
\(76\) | 4.31662 | + | 0.605599i | 0.495151 | + | 0.0694670i | ||||
\(77\) | 13.8984 | 1.58387 | ||||||||
\(78\) | −5.50000 | + | 1.65831i | −0.622752 | + | 0.187767i | ||||
\(79\) | 15.3014i | 1.72154i | 0.508995 | + | 0.860769i | \(0.330017\pi\) | ||||
−0.508995 | + | 0.860769i | \(0.669983\pi\) | |||||||
\(80\) | −1.91267 | − | 1.15831i | −0.213843 | − | 0.129503i | ||||
\(81\) | 3.50000 | − | 8.29156i | 0.388889 | − | 0.921285i | ||||
\(82\) | 11.4760i | 1.26732i | ||||||||
\(83\) | 6.43949 | 0.706826 | 0.353413 | − | 0.935467i | \(-0.385021\pi\) | ||||
0.353413 | + | 0.935467i | \(0.385021\pi\) | |||||||
\(84\) | −5.33934 | + | 1.60987i | −0.582570 | + | 0.175651i | ||||
\(85\) | 6.15831 | + | 3.72947i | 0.667963 | + | 0.404518i | ||||
\(86\) | −3.82534 | −0.412497 | ||||||||
\(87\) | 4.12814 | + | 13.6915i | 0.442583 | + | 1.46788i | ||||
\(88\) | −4.31662 | −0.460154 | ||||||||
\(89\) | 2.61414 | 0.277099 | 0.138549 | − | 0.990356i | \(-0.455756\pi\) | ||||
0.138549 | + | 0.990356i | \(0.455756\pi\) | |||||||
\(90\) | −0.276026 | − | 6.70252i | −0.0290957 | − | 0.706508i | ||||
\(91\) | 10.6787i | 1.11943i | ||||||||
\(92\) | 7.04509 | 0.734501 | ||||||||
\(93\) | 4.33507 | − | 1.30707i | 0.449526 | − | 0.135537i | ||||
\(94\) | 8.86188i | 0.914034i | ||||||||
\(95\) | 7.55481 | + | 6.15831i | 0.775107 | + | 0.631830i | ||||
\(96\) | 1.65831 | − | 0.500000i | 0.169251 | − | 0.0510310i | ||||
\(97\) | 3.36675 | 0.341842 | 0.170921 | − | 0.985285i | \(-0.445326\pi\) | ||||
0.170921 | + | 0.985285i | \(0.445326\pi\) | |||||||
\(98\) | 3.36675i | 0.340093i | ||||||||
\(99\) | −7.15831 | − | 10.7916i | −0.719437 | − | 1.08459i | ||||
\(100\) | −2.31662 | − | 4.43094i | −0.231662 | − | 0.443094i | ||||
\(101\) | − | 14.3166i | − | 1.42456i | −0.701897 | − | 0.712279i | \(-0.747663\pi\) | ||
0.701897 | − | 0.712279i | \(-0.252337\pi\) | |||||||
\(102\) | −5.33934 | + | 1.60987i | −0.528674 | + | 0.159401i | ||||
\(103\) | 17.5831 | 1.73252 | 0.866258 | − | 0.499596i | \(-0.166518\pi\) | ||||
0.866258 | + | 0.499596i | \(0.166518\pi\) | |||||||
\(104\) | − | 3.31662i | − | 0.325222i | ||||||
\(105\) | −12.0771 | − | 3.10547i | −1.17861 | − | 0.303063i | ||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | − | 0.0501256i | − | 0.00484583i | −0.999997 | − | 0.00242291i | \(-0.999229\pi\) | ||
0.999997 | − | 0.00242291i | \(-0.000771238\pi\) | |||||||
\(108\) | 4.00000 | + | 3.31662i | 0.384900 | + | 0.319142i | ||||
\(109\) | − | 6.85334i | − | 0.656431i | −0.944603 | − | 0.328215i | \(-0.893553\pi\) | ||
0.944603 | − | 0.328215i | \(-0.106447\pi\) | |||||||
\(110\) | −8.25629 | − | 5.00000i | −0.787206 | − | 0.476731i | ||||
\(111\) | 1.00000 | + | 3.31662i | 0.0949158 | + | 0.314800i | ||||
\(112\) | − | 3.21974i | − | 0.304237i | ||||||
\(113\) | − | 1.68338i | − | 0.158359i | −0.996860 | − | 0.0791793i | \(-0.974770\pi\) | ||
0.996860 | − | 0.0791793i | \(-0.0252300\pi\) | |||||||
\(114\) | −7.46111 | + | 1.15404i | −0.698797 | + | 0.108086i | ||||
\(115\) | 13.4749 | + | 8.16041i | 1.25654 | + | 0.760962i | ||||
\(116\) | −8.25629 | −0.766577 | ||||||||
\(117\) | 8.29156 | − | 5.50000i | 0.766555 | − | 0.508475i | ||||
\(118\) | 5.64214i | 0.519401i | ||||||||
\(119\) | 10.3668i | 0.950318i | ||||||||
\(120\) | 3.75096 | + | 0.964508i | 0.342415 | + | 0.0880471i | ||||
\(121\) | −7.63325 | −0.693932 | ||||||||
\(122\) | 2.31662i | 0.209737i | ||||||||
\(123\) | −5.73801 | − | 19.0308i | −0.517379 | − | 1.71595i | ||||
\(124\) | 2.61414i | 0.234757i | ||||||||
\(125\) | 0.701473 | − | 11.1583i | 0.0627417 | − | 0.998030i | ||||
\(126\) | 8.04936 | − | 5.33934i | 0.717094 | − | 0.475666i | ||||
\(127\) | −16.6332 | −1.47596 | −0.737981 | − | 0.674821i | \(-0.764221\pi\) | ||||
−0.737981 | + | 0.674821i | \(0.764221\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.34361 | − | 1.91267i | 0.558524 | − | 0.168401i | ||||
\(130\) | 3.84169 | − | 6.34361i | 0.336938 | − | 0.556372i | ||||
\(131\) | − | 10.0000i | − | 0.873704i | −0.899533 | − | 0.436852i | \(-0.856093\pi\) | ||
0.899533 | − | 0.436852i | \(-0.143907\pi\) | |||||||
\(132\) | 7.15831 | − | 2.15831i | 0.623051 | − | 0.187857i | ||||
\(133\) | −1.94987 | + | 13.8984i | −0.169076 | + | 1.20515i | ||||
\(134\) | − | 7.00000i | − | 0.604708i | ||||||
\(135\) | 3.80900 | + | 10.9769i | 0.327826 | + | 0.944738i | ||||
\(136\) | − | 3.21974i | − | 0.276091i | ||||||
\(137\) | −3.21974 | −0.275081 | −0.137541 | − | 0.990496i | \(-0.543920\pi\) | ||||
−0.137541 | + | 0.990496i | \(0.543920\pi\) | |||||||
\(138\) | −11.6830 | + | 3.52254i | −0.994519 | + | 0.299859i | ||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 3.72947 | − | 6.15831i | 0.315198 | − | 0.520472i | ||||
\(141\) | −4.43094 | − | 14.6958i | −0.373153 | − | 1.23761i | ||||
\(142\) | − | 10.2648i | − | 0.861405i | ||||||
\(143\) | − | 14.3166i | − | 1.19722i | ||||||
\(144\) | −2.50000 | + | 1.65831i | −0.208333 | + | 0.138193i | ||||
\(145\) | −15.7916 | − | 9.56336i | −1.31142 | − | 0.794194i | ||||
\(146\) | 1.81680 | 0.150359 | ||||||||
\(147\) | −1.68338 | − | 5.58312i | −0.138842 | − | 0.460488i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 4.00000i | 0.327693i | 0.986486 | + | 0.163846i | \(0.0523901\pi\) | ||||
−0.986486 | + | 0.163846i | \(0.947610\pi\) | |||||||
\(150\) | 6.05716 | + | 6.18957i | 0.494565 | + | 0.505377i | ||||
\(151\) | 16.5126i | 1.34377i | 0.740654 | + | 0.671887i | \(0.234516\pi\) | ||||
−0.740654 | + | 0.671887i | \(0.765484\pi\) | |||||||
\(152\) | 0.605599 | − | 4.31662i | 0.0491206 | − | 0.350125i | ||||
\(153\) | 8.04936 | − | 5.33934i | 0.650752 | − | 0.431660i | ||||
\(154\) | − | 13.8984i | − | 1.11997i | ||||||
\(155\) | −3.02800 | + | 5.00000i | −0.243215 | + | 0.401610i | ||||
\(156\) | 1.65831 | + | 5.50000i | 0.132771 | + | 0.440352i | ||||
\(157\) | 7.65069i | 0.610591i | 0.952258 | + | 0.305296i | \(0.0987553\pi\) | ||||
−0.952258 | + | 0.305296i | \(0.901245\pi\) | |||||||
\(158\) | 15.3014 | 1.21731 | ||||||||
\(159\) | 1.65831 | − | 0.500000i | 0.131513 | − | 0.0396526i | ||||
\(160\) | −1.15831 | + | 1.91267i | −0.0915726 | + | 0.151210i | ||||
\(161\) | 22.6834i | 1.78770i | ||||||||
\(162\) | −8.29156 | − | 3.50000i | −0.651447 | − | 0.274986i | ||||
\(163\) | 1.40295i | 0.109887i | 0.998489 | + | 0.0549436i | \(0.0174979\pi\) | ||||
−0.998489 | + | 0.0549436i | \(0.982502\pi\) | |||||||
\(164\) | 11.4760 | 0.896127 | ||||||||
\(165\) | 16.1915 | + | 4.16342i | 1.26051 | + | 0.324122i | ||||
\(166\) | − | 6.43949i | − | 0.499801i | ||||||
\(167\) | 24.9499i | 1.93068i | 0.260997 | + | 0.965340i | \(0.415949\pi\) | ||||
−0.260997 | + | 0.965340i | \(0.584051\pi\) | |||||||
\(168\) | 1.60987 | + | 5.33934i | 0.124204 | + | 0.411939i | ||||
\(169\) | −2.00000 | −0.153846 | ||||||||
\(170\) | 3.72947 | − | 6.15831i | 0.286037 | − | 0.472321i | ||||
\(171\) | 11.7958 | − | 5.64431i | 0.902050 | − | 0.431632i | ||||
\(172\) | 3.82534i | 0.291680i | ||||||||
\(173\) | − | 13.2665i | − | 1.00863i | −0.863519 | − | 0.504317i | \(-0.831744\pi\) | ||
0.863519 | − | 0.504317i | \(-0.168256\pi\) | |||||||
\(174\) | 13.6915 | − | 4.12814i | 1.03795 | − | 0.312954i | ||||
\(175\) | 14.2665 | − | 7.45894i | 1.07845 | − | 0.563843i | ||||
\(176\) | 4.31662i | 0.325378i | ||||||||
\(177\) | −2.82107 | − | 9.35643i | −0.212045 | − | 0.703272i | ||||
\(178\) | − | 2.61414i | − | 0.195938i | ||||||
\(179\) | −16.5126 | −1.23421 | −0.617104 | − | 0.786882i | \(-0.711694\pi\) | ||||
−0.617104 | + | 0.786882i | \(0.711694\pi\) | |||||||
\(180\) | −6.70252 | + | 0.276026i | −0.499577 | + | 0.0205738i | ||||
\(181\) | − | 16.5126i | − | 1.22737i | −0.789551 | − | 0.613685i | \(-0.789687\pi\) | ||
0.789551 | − | 0.613685i | \(-0.210313\pi\) | |||||||
\(182\) | 10.6787 | 0.791557 | ||||||||
\(183\) | −1.15831 | − | 3.84169i | −0.0856249 | − | 0.283986i | ||||
\(184\) | − | 7.04509i | − | 0.519371i | ||||||
\(185\) | −3.82534 | − | 2.31662i | −0.281245 | − | 0.170322i | ||||
\(186\) | −1.30707 | − | 4.33507i | −0.0958392 | − | 0.317863i | ||||
\(187\) | − | 13.8984i | − | 1.01635i | ||||||
\(188\) | 8.86188 | 0.646319 | ||||||||
\(189\) | −10.6787 | + | 12.8790i | −0.776760 | + | 0.936808i | ||||
\(190\) | 6.15831 | − | 7.55481i | 0.446771 | − | 0.548084i | ||||
\(191\) | − | 5.00000i | − | 0.361787i | −0.983503 | − | 0.180894i | \(-0.942101\pi\) | ||
0.983503 | − | 0.180894i | \(-0.0578990\pi\) | |||||||
\(192\) | −0.500000 | − | 1.65831i | −0.0360844 | − | 0.119678i | ||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | − | 3.36675i | − | 0.241719i | ||||||
\(195\) | −3.19891 | + | 12.4405i | −0.229079 | + | 0.890885i | ||||
\(196\) | 3.36675 | 0.240482 | ||||||||
\(197\) | 5.03654 | 0.358839 | 0.179419 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179419 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(198\) | −10.7916 | + | 7.15831i | −0.766923 | + | 0.508719i | ||||
\(199\) | −25.2164 | −1.78754 | −0.893771 | − | 0.448524i | \(-0.851950\pi\) | ||||
−0.893771 | + | 0.448524i | \(0.851950\pi\) | |||||||
\(200\) | −4.43094 | + | 2.31662i | −0.313315 | + | 0.163810i | ||||
\(201\) | 3.50000 | + | 11.6082i | 0.246871 | + | 0.818778i | ||||
\(202\) | −14.3166 | −1.00731 | ||||||||
\(203\) | − | 26.5831i | − | 1.86577i | ||||||
\(204\) | 1.60987 | + | 5.33934i | 0.112714 | + | 0.373829i | ||||
\(205\) | 21.9499 | + | 13.2928i | 1.53305 | + | 0.928411i | ||||
\(206\) | − | 17.5831i | − | 1.22507i | ||||||
\(207\) | 17.6127 | − | 11.6830i | 1.22417 | − | 0.812022i | ||||
\(208\) | −3.31662 | −0.229967 | ||||||||
\(209\) | 2.61414 | − | 18.6332i | 0.180824 | − | 1.28889i | ||||
\(210\) | −3.10547 | + | 12.0771i | −0.214298 | + | 0.833402i | ||||
\(211\) | − | 3.02800i | − | 0.208456i | −0.994553 | − | 0.104228i | \(-0.966763\pi\) | ||
0.994553 | − | 0.104228i | \(-0.0332371\pi\) | |||||||
\(212\) | 1.00000i | 0.0686803i | ||||||||
\(213\) | 5.13242 | + | 17.0223i | 0.351667 | + | 1.16635i | ||||
\(214\) | −0.0501256 | −0.00342652 | ||||||||
\(215\) | −4.43094 | + | 7.31662i | −0.302188 | + | 0.498990i | ||||
\(216\) | 3.31662 | − | 4.00000i | 0.225668 | − | 0.272166i | ||||
\(217\) | −8.41688 | −0.571375 | ||||||||
\(218\) | −6.85334 | −0.464167 | ||||||||
\(219\) | −3.01282 | + | 0.908399i | −0.203587 | + | 0.0613839i | ||||
\(220\) | −5.00000 | + | 8.25629i | −0.337100 | + | 0.556639i | ||||
\(221\) | 10.6787 | 0.718326 | ||||||||
\(222\) | 3.31662 | − | 1.00000i | 0.222597 | − | 0.0671156i | ||||
\(223\) | 3.26650 | 0.218741 | 0.109370 | − | 0.994001i | \(-0.465117\pi\) | ||||
0.109370 | + | 0.994001i | \(0.465117\pi\) | |||||||
\(224\) | −3.21974 | −0.215128 | ||||||||
\(225\) | −13.1394 | − | 7.23567i | −0.875963 | − | 0.482378i | ||||
\(226\) | −1.68338 | −0.111976 | ||||||||
\(227\) | 19.9499i | 1.32412i | 0.749451 | + | 0.662060i | \(0.230318\pi\) | ||||
−0.749451 | + | 0.662060i | \(0.769682\pi\) | |||||||
\(228\) | 1.15404 | + | 7.46111i | 0.0764281 | + | 0.494124i | ||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 8.16041 | − | 13.4749i | 0.538082 | − | 0.888511i | ||||
\(231\) | 6.94921 | + | 23.0479i | 0.457225 | + | 1.51644i | ||||
\(232\) | 8.25629i | 0.542052i | ||||||||
\(233\) | −26.5857 | −1.74168 | −0.870842 | − | 0.491563i | \(-0.836426\pi\) | ||||
−0.870842 | + | 0.491563i | \(0.836426\pi\) | |||||||
\(234\) | −5.50000 | − | 8.29156i | −0.359546 | − | 0.542036i | ||||
\(235\) | 16.9499 | + | 10.2648i | 1.10569 | + | 0.669604i | ||||
\(236\) | 5.64214 | 0.367272 | ||||||||
\(237\) | −25.3745 | + | 7.65069i | −1.64825 | + | 0.496965i | ||||
\(238\) | 10.3668 | 0.671977 | ||||||||
\(239\) | − | 19.6332i | − | 1.26997i | −0.772525 | − | 0.634985i | \(-0.781006\pi\) | ||
0.772525 | − | 0.634985i | \(-0.218994\pi\) | |||||||
\(240\) | 0.964508 | − | 3.75096i | 0.0622587 | − | 0.242124i | ||||
\(241\) | − | 5.22829i | − | 0.336784i | −0.985720 | − | 0.168392i | \(-0.946143\pi\) | ||
0.985720 | − | 0.168392i | \(-0.0538574\pi\) | |||||||
\(242\) | 7.63325i | 0.490684i | ||||||||
\(243\) | 15.5000 | + | 1.65831i | 0.994325 | + | 0.106381i | ||||
\(244\) | 2.31662 | 0.148307 | ||||||||
\(245\) | 6.43949 | + | 3.89975i | 0.411404 | + | 0.249146i | ||||
\(246\) | −19.0308 | + | 5.73801i | −1.21336 | + | 0.365842i | ||||
\(247\) | 14.3166 | + | 2.00855i | 0.910945 | + | 0.127801i | ||||
\(248\) | 2.61414 | 0.165998 | ||||||||
\(249\) | 3.21974 | + | 10.6787i | 0.204043 | + | 0.676734i | ||||
\(250\) | −11.1583 | − | 0.701473i | −0.705714 | − | 0.0443651i | ||||
\(251\) | 31.5831i | 1.99351i | 0.0805007 | + | 0.996755i | \(0.474348\pi\) | ||||
−0.0805007 | + | 0.996755i | \(0.525652\pi\) | |||||||
\(252\) | −5.33934 | − | 8.04936i | −0.336347 | − | 0.507062i | ||||
\(253\) | − | 30.4110i | − | 1.91192i | ||||||
\(254\) | 16.6332i | 1.04366i | ||||||||
\(255\) | −3.10547 | + | 12.0771i | −0.194472 | + | 0.756300i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.94987i | 0.308765i | 0.988011 | + | 0.154382i | \(0.0493388\pi\) | ||||
−0.988011 | + | 0.154382i | \(0.950661\pi\) | |||||||
\(258\) | −1.91267 | − | 6.34361i | −0.119078 | − | 0.394936i | ||||
\(259\) | − | 6.43949i | − | 0.400130i | ||||||
\(260\) | −6.34361 | − | 3.84169i | −0.393414 | − | 0.238251i | ||||
\(261\) | −20.6407 | + | 13.6915i | −1.27763 | + | 0.847483i | ||||
\(262\) | −10.0000 | −0.617802 | ||||||||
\(263\) | −20.5297 | −1.26591 | −0.632957 | − | 0.774187i | \(-0.718159\pi\) | ||||
−0.632957 | + | 0.774187i | \(0.718159\pi\) | |||||||
\(264\) | −2.15831 | − | 7.15831i | −0.132835 | − | 0.440564i | ||||
\(265\) | −1.15831 | + | 1.91267i | −0.0711546 | + | 0.117494i | ||||
\(266\) | 13.8984 | + | 1.94987i | 0.852167 | + | 0.119554i | ||||
\(267\) | 1.30707 | + | 4.33507i | 0.0799915 | + | 0.265302i | ||||
\(268\) | −7.00000 | −0.427593 | ||||||||
\(269\) | −21.7409 | −1.32556 | −0.662782 | − | 0.748813i | \(-0.730624\pi\) | ||||
−0.662782 | + | 0.748813i | \(0.730624\pi\) | |||||||
\(270\) | 10.9769 | − | 3.80900i | 0.668031 | − | 0.231808i | ||||
\(271\) | 2.68338 | 0.163003 | 0.0815017 | − | 0.996673i | \(-0.474028\pi\) | ||||
0.0815017 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(272\) | −3.21974 | −0.195226 | ||||||||
\(273\) | −17.7086 | + | 5.33934i | −1.07177 | + | 0.323152i | ||||
\(274\) | 3.21974i | 0.194512i | ||||||||
\(275\) | −19.1267 | + | 10.0000i | −1.15338 | + | 0.603023i | ||||
\(276\) | 3.52254 | + | 11.6830i | 0.212032 | + | 0.703231i | ||||
\(277\) | − | 14.0902i | − | 0.846596i | −0.905990 | − | 0.423298i | \(-0.860872\pi\) | ||
0.905990 | − | 0.423298i | \(-0.139128\pi\) | |||||||
\(278\) | 10.0000i | 0.599760i | ||||||||
\(279\) | 4.33507 | + | 6.53536i | 0.259534 | + | 0.391262i | ||||
\(280\) | −6.15831 | − | 3.72947i | −0.368030 | − | 0.222878i | ||||
\(281\) | −6.24774 | −0.372709 | −0.186354 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186354 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(282\) | −14.6958 | + | 4.43094i | −0.875121 | + | 0.263859i | ||||
\(283\) | 26.5857i | 1.58035i | 0.612879 | + | 0.790177i | \(0.290011\pi\) | ||||
−0.612879 | + | 0.790177i | \(0.709989\pi\) | |||||||
\(284\) | −10.2648 | −0.609106 | ||||||||
\(285\) | −6.43500 | + | 15.6074i | −0.381176 | + | 0.924502i | ||||
\(286\) | −14.3166 | −0.846560 | ||||||||
\(287\) | 36.9499i | 2.18108i | ||||||||
\(288\) | 1.65831 | + | 2.50000i | 0.0977170 | + | 0.147314i | ||||
\(289\) | −6.63325 | −0.390191 | ||||||||
\(290\) | −9.56336 | + | 15.7916i | −0.561580 | + | 0.927312i | ||||
\(291\) | 1.68338 | + | 5.58312i | 0.0986812 | + | 0.327289i | ||||
\(292\) | − | 1.81680i | − | 0.106320i | ||||||
\(293\) | − | 18.2665i | − | 1.06714i | −0.845756 | − | 0.533570i | \(-0.820850\pi\) | ||
0.845756 | − | 0.533570i | \(-0.179150\pi\) | |||||||
\(294\) | −5.58312 | + | 1.68338i | −0.325614 | + | 0.0981764i | ||||
\(295\) | 10.7916 | + | 6.53536i | 0.628309 | + | 0.380503i | ||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 14.3166 | − | 17.2665i | 0.830735 | − | 1.00190i | ||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | 23.3659 | 1.35129 | ||||||||
\(300\) | 6.18957 | − | 6.05716i | 0.357355 | − | 0.349710i | ||||
\(301\) | −12.3166 | −0.709918 | ||||||||
\(302\) | 16.5126 | 0.950192 | ||||||||
\(303\) | 23.7414 | − | 7.15831i | 1.36391 | − | 0.411234i | ||||
\(304\) | −4.31662 | − | 0.605599i | −0.247575 | − | 0.0347335i | ||||
\(305\) | 4.43094 | + | 2.68338i | 0.253715 | + | 0.153650i | ||||
\(306\) | −5.33934 | − | 8.04936i | −0.305230 | − | 0.460151i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −13.8984 | −0.791936 | ||||||||
\(309\) | 8.79156 | + | 29.1583i | 0.500134 | + | 1.65876i | ||||
\(310\) | 5.00000 | + | 3.02800i | 0.283981 | + | 0.171979i | ||||
\(311\) | − | 20.8997i | − | 1.18512i | −0.805528 | − | 0.592558i | \(-0.798118\pi\) | ||
0.805528 | − | 0.592558i | \(-0.201882\pi\) | |||||||
\(312\) | 5.50000 | − | 1.65831i | 0.311376 | − | 0.0938835i | ||||
\(313\) | − | 20.7518i | − | 1.17296i | −0.809964 | − | 0.586480i | \(-0.800513\pi\) | ||
0.809964 | − | 0.586480i | \(-0.199487\pi\) | |||||||
\(314\) | 7.65069 | 0.431753 | ||||||||
\(315\) | −0.888733 | − | 21.5804i | −0.0500744 | − | 1.21592i | ||||
\(316\) | − | 15.3014i | − | 0.860769i | ||||||
\(317\) | 17.0000i | 0.954815i | 0.878682 | + | 0.477408i | \(0.158423\pi\) | ||||
−0.878682 | + | 0.477408i | \(0.841577\pi\) | |||||||
\(318\) | −0.500000 | − | 1.65831i | −0.0280386 | − | 0.0929935i | ||||
\(319\) | 35.6393i | 1.99542i | ||||||||
\(320\) | 1.91267 | + | 1.15831i | 0.106922 | + | 0.0647516i | ||||
\(321\) | 0.0831240 | − | 0.0250628i | 0.00463953 | − | 0.00139887i | ||||
\(322\) | 22.6834 | 1.26410 | ||||||||
\(323\) | 13.8984 | + | 1.94987i | 0.773329 | + | 0.108494i | ||||
\(324\) | −3.50000 | + | 8.29156i | −0.194444 | + | 0.460642i | ||||
\(325\) | −7.68338 | − | 14.6958i | −0.426197 | − | 0.815175i | ||||
\(326\) | 1.40295 | 0.0777020 | ||||||||
\(327\) | 11.3650 | − | 3.42667i | 0.628485 | − | 0.189495i | ||||
\(328\) | − | 11.4760i | − | 0.633658i | ||||||
\(329\) | 28.5330i | 1.57308i | ||||||||
\(330\) | 4.16342 | − | 16.1915i | 0.229189 | − | 0.891313i | ||||
\(331\) | 13.4846i | 0.741179i | 0.928797 | + | 0.370590i | \(0.120844\pi\) | ||||
−0.928797 | + | 0.370590i | \(0.879156\pi\) | |||||||
\(332\) | −6.43949 | −0.353413 | ||||||||
\(333\) | −5.00000 | + | 3.31662i | −0.273998 | + | 0.181750i | ||||
\(334\) | 24.9499 | 1.36520 | ||||||||
\(335\) | −13.3887 | − | 8.10819i | −0.731503 | − | 0.442998i | ||||
\(336\) | 5.33934 | − | 1.60987i | 0.291285 | − | 0.0878257i | ||||
\(337\) | −28.2164 | −1.53704 | −0.768522 | − | 0.639823i | \(-0.779007\pi\) | ||||
−0.768522 | + | 0.639823i | \(0.779007\pi\) | |||||||
\(338\) | 2.00000i | 0.108786i | ||||||||
\(339\) | 2.79156 | − | 0.841688i | 0.151617 | − | 0.0457142i | ||||
\(340\) | −6.15831 | − | 3.72947i | −0.333981 | − | 0.202259i | ||||
\(341\) | 11.2843 | 0.611078 | ||||||||
\(342\) | −5.64431 | − | 11.7958i | −0.305210 | − | 0.637846i | ||||
\(343\) | − | 11.6981i | − | 0.631640i | ||||||
\(344\) | 3.82534 | 0.206249 | ||||||||
\(345\) | −6.79504 | + | 26.4259i | −0.365833 | + | 1.42272i | ||||
\(346\) | −13.2665 | −0.713211 | ||||||||
\(347\) | −20.1462 | −1.08150 | −0.540751 | − | 0.841182i | \(-0.681860\pi\) | ||||
−0.540751 | + | 0.841182i | \(0.681860\pi\) | |||||||
\(348\) | −4.12814 | − | 13.6915i | −0.221292 | − | 0.733941i | ||||
\(349\) | 8.63325 | 0.462127 | 0.231064 | − | 0.972939i | \(-0.425779\pi\) | ||||
0.231064 | + | 0.972939i | \(0.425779\pi\) | |||||||
\(350\) | −7.45894 | − | 14.2665i | −0.398697 | − | 0.762576i | ||||
\(351\) | 13.2665 | + | 11.0000i | 0.708113 | + | 0.587137i | ||||
\(352\) | 4.31662 | 0.230077 | ||||||||
\(353\) | 23.3659 | 1.24364 | 0.621821 | − | 0.783159i | \(-0.286393\pi\) | ||||
0.621821 | + | 0.783159i | \(0.286393\pi\) | |||||||
\(354\) | −9.35643 | + | 2.82107i | −0.497289 | + | 0.149938i | ||||
\(355\) | −19.6332 | − | 11.8899i | −1.04202 | − | 0.631049i | ||||
\(356\) | −2.61414 | −0.138549 | ||||||||
\(357\) | −17.1913 | + | 5.18338i | −0.909861 | + | 0.274333i | ||||
\(358\) | 16.5126i | 0.872716i | ||||||||
\(359\) | 4.89975i | 0.258599i | 0.991606 | + | 0.129299i | \(0.0412728\pi\) | ||||
−0.991606 | + | 0.129299i | \(0.958727\pi\) | |||||||
\(360\) | 0.276026 | + | 6.70252i | 0.0145478 | + | 0.353254i | ||||
\(361\) | 18.2665 | + | 5.22829i | 0.961395 | + | 0.275173i | ||||
\(362\) | −16.5126 | −0.867881 | ||||||||
\(363\) | −3.81662 | − | 12.6583i | −0.200321 | − | 0.664389i | ||||
\(364\) | − | 10.6787i | − | 0.559715i | ||||||
\(365\) | 2.10442 | − | 3.47494i | 0.110150 | − | 0.181887i | ||||
\(366\) | −3.84169 | + | 1.15831i | −0.200808 | + | 0.0605460i | ||||
\(367\) | 7.65069i | 0.399363i | 0.979861 | + | 0.199681i | \(0.0639907\pi\) | ||||
−0.979861 | + | 0.199681i | \(0.936009\pi\) | |||||||
\(368\) | −7.04509 | −0.367251 | ||||||||
\(369\) | 28.6901 | − | 19.0308i | 1.49355 | − | 0.990706i | ||||
\(370\) | −2.31662 | + | 3.82534i | −0.120436 | + | 0.198870i | ||||
\(371\) | −3.21974 | −0.167161 | ||||||||
\(372\) | −4.33507 | + | 1.30707i | −0.224763 | + | 0.0677685i | ||||
\(373\) | −23.3166 | −1.20729 | −0.603645 | − | 0.797254i | \(-0.706285\pi\) | ||||
−0.603645 | + | 0.797254i | \(0.706285\pi\) | |||||||
\(374\) | −13.8984 | −0.718671 | ||||||||
\(375\) | 18.8547 | − | 4.41589i | 0.973653 | − | 0.228036i | ||||
\(376\) | − | 8.86188i | − | 0.457017i | ||||||
\(377\) | −27.3830 | −1.41030 | ||||||||
\(378\) | 12.8790 | + | 10.6787i | 0.662423 | + | 0.549252i | ||||
\(379\) | − | 36.4366i | − | 1.87162i | −0.352499 | − | 0.935812i | \(-0.614668\pi\) | ||
0.352499 | − | 0.935812i | \(-0.385332\pi\) | |||||||
\(380\) | −7.55481 | − | 6.15831i | −0.387554 | − | 0.315915i | ||||
\(381\) | −8.31662 | − | 27.5831i | −0.426074 | − | 1.41313i | ||||
\(382\) | −5.00000 | −0.255822 | ||||||||
\(383\) | − | 7.58312i | − | 0.387480i | −0.981053 | − | 0.193740i | \(-0.937938\pi\) | ||
0.981053 | − | 0.193740i | \(-0.0620617\pi\) | |||||||
\(384\) | −1.65831 | + | 0.500000i | −0.0846254 | + | 0.0255155i | ||||
\(385\) | −26.5831 | − | 16.0987i | −1.35480 | − | 0.820467i | ||||
\(386\) | − | 6.00000i | − | 0.305392i | ||||||
\(387\) | 6.34361 | + | 9.56336i | 0.322464 | + | 0.486133i | ||||
\(388\) | −3.36675 | −0.170921 | ||||||||
\(389\) | − | 16.2164i | − | 0.822203i | −0.911590 | − | 0.411101i | \(-0.865144\pi\) | ||
0.911590 | − | 0.411101i | \(-0.134856\pi\) | |||||||
\(390\) | 12.4405 | + | 3.19891i | 0.629951 | + | 0.161983i | ||||
\(391\) | 22.6834 | 1.14715 | ||||||||
\(392\) | − | 3.36675i | − | 0.170047i | ||||||
\(393\) | 16.5831 | − | 5.00000i | 0.836508 | − | 0.252217i | ||||
\(394\) | − | 5.03654i | − | 0.253737i | ||||||
\(395\) | 17.7238 | − | 29.2665i | 0.891780 | − | 1.47256i | ||||
\(396\) | 7.15831 | + | 10.7916i | 0.359719 | + | 0.542296i | ||||
\(397\) | 29.3915i | 1.47512i | 0.675282 | + | 0.737560i | \(0.264022\pi\) | ||||
−0.675282 | + | 0.737560i | \(0.735978\pi\) | |||||||
\(398\) | 25.2164i | 1.26398i | ||||||||
\(399\) | −24.0229 | + | 3.71571i | −1.20265 | + | 0.186018i | ||||
\(400\) | 2.31662 | + | 4.43094i | 0.115831 | + | 0.221547i | ||||
\(401\) | 21.5491 | 1.07611 | 0.538056 | − | 0.842909i | \(-0.319159\pi\) | ||||
0.538056 | + | 0.842909i | \(0.319159\pi\) | |||||||
\(402\) | 11.6082 | − | 3.50000i | 0.578964 | − | 0.174564i | ||||
\(403\) | 8.67014i | 0.431890i | ||||||||
\(404\) | 14.3166i | 0.712279i | ||||||||
\(405\) | −16.2986 | + | 11.8049i | −0.809882 | + | 0.586592i | ||||
\(406\) | −26.5831 | −1.31930 | ||||||||
\(407\) | 8.63325i | 0.427934i | ||||||||
\(408\) | 5.33934 | − | 1.60987i | 0.264337 | − | 0.0797005i | ||||
\(409\) | − | 3.82534i | − | 0.189151i | −0.995518 | − | 0.0945755i | \(-0.969851\pi\) | ||
0.995518 | − | 0.0945755i | \(-0.0301494\pi\) | |||||||
\(410\) | 13.2928 | − | 21.9499i | 0.656486 | − | 1.08403i | ||||
\(411\) | −1.60987 | − | 5.33934i | −0.0794091 | − | 0.263370i | ||||
\(412\) | −17.5831 | −0.866258 | ||||||||
\(413\) | 18.1662i | 0.893903i | ||||||||
\(414\) | −11.6830 | − | 17.6127i | −0.574186 | − | 0.865618i | ||||
\(415\) | −12.3166 | − | 7.45894i | −0.604599 | − | 0.366145i | ||||
\(416\) | 3.31662i | 0.162611i | ||||||||
\(417\) | −5.00000 | − | 16.5831i | −0.244851 | − | 0.812079i | ||||
\(418\) | −18.6332 | − | 2.61414i | −0.911382 | − | 0.127862i | ||||
\(419\) | − | 3.05013i | − | 0.149008i | −0.997221 | − | 0.0745042i | \(-0.976263\pi\) | ||
0.997221 | − | 0.0745042i | \(-0.0237374\pi\) | |||||||
\(420\) | 12.0771 | + | 3.10547i | 0.589304 | + | 0.151531i | ||||
\(421\) | − | 16.0987i | − | 0.784604i | −0.919837 | − | 0.392302i | \(-0.871679\pi\) | ||
0.919837 | − | 0.392302i | \(-0.128321\pi\) | |||||||
\(422\) | −3.02800 | −0.147401 | ||||||||
\(423\) | 22.1547 | − | 14.6958i | 1.07720 | − | 0.714533i | ||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −7.45894 | − | 14.2665i | −0.361812 | − | 0.692027i | ||||
\(426\) | 17.0223 | − | 5.13242i | 0.824733 | − | 0.248666i | ||||
\(427\) | 7.45894i | 0.360963i | ||||||||
\(428\) | 0.0501256i | 0.00242291i | ||||||||
\(429\) | 23.7414 | − | 7.15831i | 1.14625 | − | 0.345607i | ||||
\(430\) | 7.31662 | + | 4.43094i | 0.352839 | + | 0.213679i | ||||
\(431\) | −17.5320 | −0.844488 | −0.422244 | − | 0.906482i | \(-0.638757\pi\) | ||||
−0.422244 | + | 0.906482i | \(0.638757\pi\) | |||||||
\(432\) | −4.00000 | − | 3.31662i | −0.192450 | − | 0.159571i | ||||
\(433\) | 1.68338 | 0.0808978 | 0.0404489 | − | 0.999182i | \(-0.487121\pi\) | ||||
0.0404489 | + | 0.999182i | \(0.487121\pi\) | |||||||
\(434\) | 8.41688i | 0.404023i | ||||||||
\(435\) | 7.96325 | − | 30.9690i | 0.381809 | − | 1.48485i | ||||
\(436\) | 6.85334i | 0.328215i | ||||||||
\(437\) | 30.4110 | + | 4.26650i | 1.45476 | + | 0.204094i | ||||
\(438\) | 0.908399 | + | 3.01282i | 0.0434050 | + | 0.143958i | ||||
\(439\) | − | 3.82534i | − | 0.182574i | −0.995825 | − | 0.0912868i | \(-0.970902\pi\) | ||
0.995825 | − | 0.0912868i | \(-0.0290980\pi\) | |||||||
\(440\) | 8.25629 | + | 5.00000i | 0.393603 | + | 0.238366i | ||||
\(441\) | 8.41688 | − | 5.58312i | 0.400804 | − | 0.265863i | ||||
\(442\) | − | 10.6787i | − | 0.507933i | ||||||
\(443\) | −12.6872 | −0.602788 | −0.301394 | − | 0.953500i | \(-0.597452\pi\) | ||||
−0.301394 | + | 0.953500i | \(0.597452\pi\) | |||||||
\(444\) | −1.00000 | − | 3.31662i | −0.0474579 | − | 0.157400i | ||||
\(445\) | −5.00000 | − | 3.02800i | −0.237023 | − | 0.143541i | ||||
\(446\) | − | 3.26650i | − | 0.154673i | ||||||
\(447\) | −6.63325 | + | 2.00000i | −0.313742 | + | 0.0945968i | ||||
\(448\) | 3.21974i | 0.152119i | ||||||||
\(449\) | 26.9691 | 1.27275 | 0.636376 | − | 0.771379i | \(-0.280433\pi\) | ||||
0.636376 | + | 0.771379i | \(0.280433\pi\) | |||||||
\(450\) | −7.23567 | + | 13.1394i | −0.341093 | + | 0.619400i | ||||
\(451\) | − | 49.5377i | − | 2.33264i | ||||||
\(452\) | 1.68338i | 0.0791793i | ||||||||
\(453\) | −27.3830 | + | 8.25629i | −1.28657 | + | 0.387914i | ||||
\(454\) | 19.9499 | 0.936294 | ||||||||
\(455\) | 12.3693 | − | 20.4248i | 0.579879 | − | 0.957530i | ||||
\(456\) | 7.46111 | − | 1.15404i | 0.349399 | − | 0.0540429i | ||||
\(457\) | 27.1913i | 1.27195i | 0.771708 | + | 0.635977i | \(0.219403\pi\) | ||||
−0.771708 | + | 0.635977i | \(0.780597\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.8790 | + | 10.6787i | 0.601139 | + | 0.498438i | ||||
\(460\) | −13.4749 | − | 8.16041i | −0.628272 | − | 0.380481i | ||||
\(461\) | 21.5831i | 1.00523i | 0.864511 | + | 0.502613i | \(0.167628\pi\) | ||||
−0.864511 | + | 0.502613i | \(0.832372\pi\) | |||||||
\(462\) | 23.0479 | − | 6.94921i | 1.07229 | − | 0.323307i | ||||
\(463\) | 15.3014i | 0.711115i | 0.934654 | + | 0.355558i | \(0.115709\pi\) | ||||
−0.934654 | + | 0.355558i | \(0.884291\pi\) | |||||||
\(464\) | 8.25629 | 0.383288 | ||||||||
\(465\) | −9.80556 | − | 2.52136i | −0.454722 | − | 0.116925i | ||||
\(466\) | 26.5857i | 1.23156i | ||||||||
\(467\) | 26.7774 | 1.23911 | 0.619555 | − | 0.784953i | \(-0.287313\pi\) | ||||
0.619555 | + | 0.784953i | \(0.287313\pi\) | |||||||
\(468\) | −8.29156 | + | 5.50000i | −0.383278 | + | 0.254238i | ||||
\(469\) | − | 22.5382i | − | 1.04072i | ||||||
\(470\) | 10.2648 | − | 16.9499i | 0.473481 | − | 0.781839i | ||||
\(471\) | −12.6872 | + | 3.82534i | −0.584597 | + | 0.176263i | ||||
\(472\) | − | 5.64214i | − | 0.259701i | ||||||
\(473\) | 16.5126 | 0.759249 | ||||||||
\(474\) | 7.65069 | + | 25.3745i | 0.351408 | + | 1.16549i | ||||
\(475\) | −7.31662 | − | 20.5297i | −0.335710 | − | 0.941965i | ||||
\(476\) | − | 10.3668i | − | 0.475159i | ||||||
\(477\) | 1.65831 | + | 2.50000i | 0.0759289 | + | 0.114467i | ||||
\(478\) | −19.6332 | −0.898004 | ||||||||
\(479\) | 14.0000i | 0.639676i | 0.947472 | + | 0.319838i | \(0.103629\pi\) | ||||
−0.947472 | + | 0.319838i | \(0.896371\pi\) | |||||||
\(480\) | −3.75096 | − | 0.964508i | −0.171207 | − | 0.0440236i | ||||
\(481\) | −6.63325 | −0.302450 | ||||||||
\(482\) | −5.22829 | −0.238142 | ||||||||
\(483\) | −37.6161 | + | 11.3417i | −1.71159 | + | 0.516065i | ||||
\(484\) | 7.63325 | 0.346966 | ||||||||
\(485\) | −6.43949 | − | 3.89975i | −0.292402 | − | 0.177078i | ||||
\(486\) | 1.65831 | − | 15.5000i | 0.0752226 | − | 0.703094i | ||||
\(487\) | 36.5330 | 1.65547 | 0.827734 | − | 0.561121i | \(-0.189630\pi\) | ||||
0.827734 | + | 0.561121i | \(0.189630\pi\) | |||||||
\(488\) | − | 2.31662i | − | 0.104869i | ||||||
\(489\) | −2.32652 | + | 0.701473i | −0.105209 | + | 0.0317217i | ||||
\(490\) | 3.89975 | − | 6.43949i | 0.176173 | − | 0.290906i | ||||
\(491\) | 8.41688i | 0.379848i | 0.981799 | + | 0.189924i | \(0.0608242\pi\) | ||||
−0.981799 | + | 0.189924i | \(0.939176\pi\) | |||||||
\(492\) | 5.73801 | + | 19.0308i | 0.258690 | + | 0.857977i | ||||
\(493\) | −26.5831 | −1.19724 | ||||||||
\(494\) | 2.00855 | − | 14.3166i | 0.0903687 | − | 0.644135i | ||||
\(495\) | 1.19150 | + | 28.9323i | 0.0535540 | + | 1.30041i | ||||
\(496\) | − | 2.61414i | − | 0.117379i | ||||||
\(497\) | − | 33.0501i | − | 1.48250i | ||||||
\(498\) | 10.6787 | − | 3.21974i | 0.478523 | − | 0.144280i | ||||
\(499\) | 8.41688 | 0.376791 | 0.188396 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188396 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(500\) | −0.701473 | + | 11.1583i | −0.0313708 | + | 0.499015i | ||||
\(501\) | −41.3747 | + | 12.4749i | −1.84848 | + | 0.557339i | ||||
\(502\) | 31.5831 | 1.40962 | ||||||||
\(503\) | −18.3294 | −0.817266 | −0.408633 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408633 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(504\) | −8.04936 | + | 5.33934i | −0.358547 | + | 0.237833i | ||||
\(505\) | −16.5831 | + | 27.3830i | −0.737939 | + | 1.21853i | ||||
\(506\) | −30.4110 | −1.35193 | ||||||||
\(507\) | −1.00000 | − | 3.31662i | −0.0444116 | − | 0.147296i | ||||
\(508\) | 16.6332 | 0.737981 | ||||||||
\(509\) | −5.22829 | −0.231740 | −0.115870 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115870 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(510\) | 12.0771 | + | 3.10547i | 0.534785 | + | 0.137512i | ||||
\(511\) | 5.84962 | 0.258772 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 15.2580 | + | 16.7390i | 0.673655 | + | 0.739046i | ||||
\(514\) | 4.94987 | 0.218330 | ||||||||
\(515\) | −33.6307 | − | 20.3668i | −1.48195 | − | 0.897466i | ||||
\(516\) | −6.34361 | + | 1.91267i | −0.279262 | + | 0.0842007i | ||||
\(517\) | − | 38.2534i | − | 1.68238i | ||||||
\(518\) | −6.43949 | −0.282935 | ||||||||
\(519\) | 22.0000 | − | 6.63325i | 0.965693 | − | 0.291167i | ||||
\(520\) | −3.84169 | + | 6.34361i | −0.168469 | + | 0.278186i | ||||
\(521\) | −14.9179 | −0.653564 | −0.326782 | − | 0.945100i | \(-0.605964\pi\) | ||||
−0.326782 | + | 0.945100i | \(0.605964\pi\) | |||||||
\(522\) | 13.6915 | + | 20.6407i | 0.599261 | + | 0.903419i | ||||
\(523\) | −29.0000 | −1.26808 | −0.634041 | − | 0.773300i | \(-0.718605\pi\) | ||||
−0.634041 | + | 0.773300i | \(0.718605\pi\) | |||||||
\(524\) | 10.0000i | 0.436852i | ||||||||
\(525\) | 19.5025 | + | 19.9288i | 0.851159 | + | 0.869766i | ||||
\(526\) | 20.5297i | 0.895136i | ||||||||
\(527\) | 8.41688i | 0.366645i | ||||||||
\(528\) | −7.15831 | + | 2.15831i | −0.311526 | + | 0.0939285i | ||||
\(529\) | 26.6332 | 1.15797 | ||||||||
\(530\) | 1.91267 | + | 1.15831i | 0.0830811 | + | 0.0503139i | ||||
\(531\) | 14.1054 | − | 9.35643i | 0.612120 | − | 0.406035i | ||||
\(532\) | 1.94987 | − | 13.8984i | 0.0845378 | − | 0.602573i | ||||
\(533\) | 38.0617 | 1.64863 | ||||||||
\(534\) | 4.33507 | − | 1.30707i | 0.187597 | − | 0.0565626i | ||||
\(535\) | −0.0580611 | + | 0.0958739i | −0.00251020 | + | 0.00414499i | ||||
\(536\) | 7.00000i | 0.302354i | ||||||||
\(537\) | −8.25629 | − | 27.3830i | −0.356285 | − | 1.18166i | ||||
\(538\) | 21.7409i | 0.937315i | ||||||||
\(539\) | − | 14.5330i | − | 0.625981i | ||||||
\(540\) | −3.80900 | − | 10.9769i | −0.163913 | − | 0.472369i | ||||
\(541\) | 30.8496 | 1.32633 | 0.663164 | − | 0.748474i | \(-0.269213\pi\) | ||||
0.663164 | + | 0.748474i | \(0.269213\pi\) | |||||||
\(542\) | − | 2.68338i | − | 0.115261i | ||||||
\(543\) | 27.3830 | − | 8.25629i | 1.17512 | − | 0.354311i | ||||
\(544\) | 3.21974i | 0.138045i | ||||||||
\(545\) | −7.93831 | + | 13.1082i | −0.340040 | + | 0.561493i | ||||
\(546\) | 5.33934 | + | 17.7086i | 0.228503 | + | 0.757858i | ||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 3.21974 | 0.137541 | ||||||||
\(549\) | 5.79156 | − | 3.84169i | 0.247178 | − | 0.163959i | ||||
\(550\) | 10.0000 | + | 19.1267i | 0.426401 | + | 0.815566i | ||||
\(551\) | −35.6393 | − | 5.00000i | −1.51828 | − | 0.213007i | ||||
\(552\) | 11.6830 | − | 3.52254i | 0.497260 | − | 0.149929i | ||||
\(553\) | 49.2665 | 2.09502 | ||||||||
\(554\) | −14.0902 | −0.598634 | ||||||||
\(555\) | 1.92902 | − | 7.50193i | 0.0818822 | − | 0.318439i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | 13.7067 | 0.580771 | 0.290385 | − | 0.956910i | \(-0.406217\pi\) | ||||
0.290385 | + | 0.956910i | \(0.406217\pi\) | |||||||
\(558\) | 6.53536 | − | 4.33507i | 0.276664 | − | 0.183518i | ||||
\(559\) | 12.6872i | 0.536613i | ||||||||
\(560\) | −3.72947 | + | 6.15831i | −0.157599 | + | 0.260236i | ||||
\(561\) | 23.0479 | − | 6.94921i | 0.973084 | − | 0.293396i | ||||
\(562\) | 6.24774i | 0.263545i | ||||||||
\(563\) | 29.8997i | 1.26012i | 0.776545 | + | 0.630062i | \(0.216971\pi\) | ||||
−0.776545 | + | 0.630062i | \(0.783029\pi\) | |||||||
\(564\) | 4.43094 | + | 14.6958i | 0.186576 | + | 0.618804i | ||||
\(565\) | −1.94987 | + | 3.21974i | −0.0820318 | + | 0.135456i | ||||
\(566\) | 26.5857 | 1.11748 | ||||||||
\(567\) | −26.6967 | − | 11.2691i | −1.12116 | − | 0.473258i | ||||
\(568\) | 10.2648i | 0.430703i | ||||||||
\(569\) | −5.22829 | −0.219181 | −0.109591 | − | 0.993977i | \(-0.534954\pi\) | ||||
−0.109591 | + | 0.993977i | \(0.534954\pi\) | |||||||
\(570\) | 15.6074 | + | 6.43500i | 0.653722 | + | 0.269532i | ||||
\(571\) | −32.3166 | −1.35241 | −0.676204 | − | 0.736714i | \(-0.736376\pi\) | ||||
−0.676204 | + | 0.736714i | \(0.736376\pi\) | |||||||
\(572\) | 14.3166i | 0.598608i | ||||||||
\(573\) | 8.29156 | − | 2.50000i | 0.346385 | − | 0.104439i | ||||
\(574\) | 36.9499 | 1.54226 | ||||||||
\(575\) | −16.3208 | − | 31.2164i | −0.680625 | − | 1.30181i | ||||
\(576\) | 2.50000 | − | 1.65831i | 0.104167 | − | 0.0690963i | ||||
\(577\) | − | 17.1182i | − | 0.712639i | −0.934364 | − | 0.356319i | \(-0.884032\pi\) | ||
0.934364 | − | 0.356319i | \(-0.115968\pi\) | |||||||
\(578\) | 6.63325i | 0.275907i | ||||||||
\(579\) | 3.00000 | + | 9.94987i | 0.124676 | + | 0.413503i | ||||
\(580\) | 15.7916 | + | 9.56336i | 0.655709 | + | 0.397097i | ||||
\(581\) | − | 20.7335i | − | 0.860171i | ||||||
\(582\) | 5.58312 | − | 1.68338i | 0.231428 | − | 0.0697781i | ||||
\(583\) | 4.31662 | 0.178776 | ||||||||
\(584\) | −1.81680 | −0.0751796 | ||||||||
\(585\) | −22.2298 | + | 0.915474i | −0.919087 | + | 0.0378502i | ||||
\(586\) | −18.2665 | −0.754582 | ||||||||
\(587\) | 16.3208 | 0.673632 | 0.336816 | − | 0.941570i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941570i | \(0.390650\pi\) | |||||||
\(588\) | 1.68338 | + | 5.58312i | 0.0694212 | + | 0.230244i | ||||
\(589\) | −1.58312 | + | 11.2843i | −0.0652315 | + | 0.464961i | ||||
\(590\) | 6.53536 | − | 10.7916i | 0.269057 | − | 0.444282i | ||||
\(591\) | 2.51827 | + | 8.35216i | 0.103588 | + | 0.343562i | ||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −20.5297 | −0.843052 | −0.421526 | − | 0.906816i | \(-0.638505\pi\) | ||||
−0.421526 | + | 0.906816i | \(0.638505\pi\) | |||||||
\(594\) | −17.2665 | − | 14.3166i | −0.708453 | − | 0.587418i | ||||
\(595\) | 12.0079 | − | 19.8282i | 0.492277 | − | 0.812876i | ||||
\(596\) | − | 4.00000i | − | 0.163846i | ||||||
\(597\) | −12.6082 | − | 41.8166i | −0.516019 | − | 1.71144i | ||||
\(598\) | − | 23.3659i | − | 0.955503i | ||||||
\(599\) | −19.9544 | −0.815315 | −0.407658 | − | 0.913135i | \(-0.633654\pi\) | ||||
−0.407658 | + | 0.913135i | \(0.633654\pi\) | |||||||
\(600\) | −6.05716 | − | 6.18957i | −0.247282 | − | 0.252688i | ||||
\(601\) | 24.3550i | 0.993461i | 0.867905 | + | 0.496731i | \(0.165466\pi\) | ||||
−0.867905 | + | 0.496731i | \(0.834534\pi\) | |||||||
\(602\) | 12.3166i | 0.501988i | ||||||||
\(603\) | −17.5000 | + | 11.6082i | −0.712655 | + | 0.472722i | ||||
\(604\) | − | 16.5126i | − | 0.671887i | ||||||
\(605\) | 14.5999 | + | 8.84169i | 0.593570 | + | 0.359466i | ||||
\(606\) | −7.15831 | − | 23.7414i | −0.290787 | − | 0.964430i | ||||
\(607\) | −36.6332 | −1.48690 | −0.743449 | − | 0.668793i | \(-0.766811\pi\) | ||||
−0.743449 | + | 0.668793i | \(0.766811\pi\) | |||||||
\(608\) | −0.605599 | + | 4.31662i | −0.0245603 | + | 0.175062i | ||||
\(609\) | 44.0831 | − | 13.2916i | 1.78634 | − | 0.538601i | ||||
\(610\) | 2.68338 | − | 4.43094i | 0.108647 | − | 0.179404i | ||||
\(611\) | 29.3915 | 1.18905 | ||||||||
\(612\) | −8.04936 | + | 5.33934i | −0.325376 | + | 0.215830i | ||||
\(613\) | 17.9155i | 0.723601i | 0.932256 | + | 0.361800i | \(0.117838\pi\) | ||||
−0.932256 | + | 0.361800i | \(0.882162\pi\) | |||||||
\(614\) | − | 2.00000i | − | 0.0807134i | ||||||
\(615\) | −11.0687 | + | 43.0462i | −0.446334 | + | 1.73579i | ||||
\(616\) | 13.8984i | 0.559984i | ||||||||
\(617\) | 18.9350 | 0.762293 | 0.381147 | − | 0.924515i | \(-0.375529\pi\) | ||||
0.381147 | + | 0.924515i | \(0.375529\pi\) | |||||||
\(618\) | 29.1583 | − | 8.79156i | 1.17292 | − | 0.353648i | ||||
\(619\) | 1.58312 | 0.0636311 | 0.0318156 | − | 0.999494i | \(-0.489871\pi\) | ||||
0.0318156 | + | 0.999494i | \(0.489871\pi\) | |||||||
\(620\) | 3.02800 | − | 5.00000i | 0.121607 | − | 0.200805i | ||||
\(621\) | 28.1803 | + | 23.3659i | 1.13084 | + | 0.937642i | ||||
\(622\) | −20.8997 | −0.838004 | ||||||||
\(623\) | − | 8.41688i | − | 0.337215i | ||||||
\(624\) | −1.65831 | − | 5.50000i | −0.0663856 | − | 0.220176i | ||||
\(625\) | −14.2665 | + | 20.5297i | −0.570660 | + | 0.821186i | ||||
\(626\) | −20.7518 | −0.829407 | ||||||||
\(627\) | 32.2068 | − | 4.98156i | 1.28622 | − | 0.198944i | ||||
\(628\) | − | 7.65069i | − | 0.305296i | ||||||
\(629\) | −6.43949 | −0.256759 | ||||||||
\(630\) | −21.5804 | + | 0.888733i | −0.859784 | + | 0.0354080i | ||||
\(631\) | −23.8997 | −0.951434 | −0.475717 | − | 0.879598i | \(-0.657811\pi\) | ||||
−0.475717 | + | 0.879598i | \(0.657811\pi\) | |||||||
\(632\) | −15.3014 | −0.608656 | ||||||||
\(633\) | 5.02136 | − | 1.51400i | 0.199581 | − | 0.0601760i | ||||
\(634\) | 17.0000 | 0.675156 | ||||||||
\(635\) | 31.8139 | + | 19.2665i | 1.26250 | + | 0.764568i | ||||
\(636\) | −1.65831 | + | 0.500000i | −0.0657564 | + | 0.0198263i | ||||
\(637\) | 11.1662 | 0.442423 | ||||||||
\(638\) | 35.6393 | 1.41097 | ||||||||
\(639\) | −25.6621 | + | 17.0223i | −1.01518 | + | 0.673392i | ||||
\(640\) | 1.15831 | − | 1.91267i | 0.0457863 | − | 0.0756050i | ||||
\(641\) | −0.191748 | −0.00757358 | −0.00378679 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378679 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(642\) | −0.0250628 | − | 0.0831240i | −0.000989150 | − | 0.00328064i | ||||
\(643\) | − | 0.383495i | − | 0.0151236i | −0.999971 | − | 0.00756179i | \(-0.997593\pi\) | ||
0.999971 | − | 0.00756179i | \(-0.00240702\pi\) | |||||||
\(644\) | − | 22.6834i | − | 0.893850i | ||||||
\(645\) | −14.3487 | − | 3.68957i | −0.564980 | − | 0.145277i | ||||
\(646\) | 1.94987 | − | 13.8984i | 0.0767168 | − | 0.546826i | ||||
\(647\) | −0.605599 | −0.0238086 | −0.0119043 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119043 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(648\) | 8.29156 | + | 3.50000i | 0.325723 | + | 0.137493i | ||||
\(649\) | − | 24.3550i | − | 0.956018i | ||||||
\(650\) | −14.6958 | + | 7.68338i | −0.576416 | + | 0.301367i | ||||
\(651\) | −4.20844 | − | 13.9578i | −0.164942 | − | 0.547050i | ||||
\(652\) | − | 1.40295i | − | 0.0549436i | ||||||
\(653\) | 11.6678 | 0.456595 | 0.228298 | − | 0.973591i | \(-0.426684\pi\) | ||||
0.228298 | + | 0.973591i | \(0.426684\pi\) | |||||||
\(654\) | −3.42667 | − | 11.3650i | −0.133993 | − | 0.444406i | ||||
\(655\) | −11.5831 | + | 19.1267i | −0.452590 | + | 0.747343i | ||||
\(656\) | −11.4760 | −0.448064 | ||||||||
\(657\) | −3.01282 | − | 4.54199i | −0.117541 | − | 0.177200i | ||||
\(658\) | 28.5330 | 1.11233 | ||||||||
\(659\) | 22.1547 | 0.863025 | 0.431513 | − | 0.902107i | \(-0.357980\pi\) | ||||
0.431513 | + | 0.902107i | \(0.357980\pi\) | |||||||
\(660\) | −16.1915 | − | 4.16342i | −0.630253 | − | 0.162061i | ||||
\(661\) | 32.6113i | 1.26843i | 0.773156 | + | 0.634216i | \(0.218677\pi\) | ||||
−0.773156 | + | 0.634216i | \(0.781323\pi\) | |||||||
\(662\) | 13.4846 | 0.524093 | ||||||||
\(663\) | 5.33934 | + | 17.7086i | 0.207363 | + | 0.687745i | ||||
\(664\) | 6.43949i | 0.249901i | ||||||||
\(665\) | 19.8282 | − | 24.3246i | 0.768904 | − | 0.943266i | ||||
\(666\) | 3.31662 | + | 5.00000i | 0.128517 | + | 0.193746i | ||||
\(667\) | −58.1662 | −2.25221 | ||||||||
\(668\) | − | 24.9499i | − | 0.965340i | ||||||
\(669\) | 1.63325 | + | 5.41688i | 0.0631451 | + | 0.209429i | ||||
\(670\) | −8.10819 | + | 13.3887i | −0.313247 | + | 0.517251i | ||||
\(671\) | − | 10.0000i | − | 0.386046i | ||||||
\(672\) | −1.60987 | − | 5.33934i | −0.0621022 | − | 0.205970i | ||||
\(673\) | 13.2665 | 0.511386 | 0.255693 | − | 0.966758i | \(-0.417696\pi\) | ||||
0.255693 | + | 0.966758i | \(0.417696\pi\) | |||||||
\(674\) | 28.2164i | 1.08685i | ||||||||
\(675\) | 5.42927 | − | 25.4071i | 0.208973 | − | 0.977921i | ||||
\(676\) | 2.00000 | 0.0769231 | ||||||||
\(677\) | − | 46.1662i | − | 1.77431i | −0.461469 | − | 0.887157i | \(-0.652677\pi\) | ||
0.461469 | − | 0.887157i | \(-0.347323\pi\) | |||||||
\(678\) | −0.841688 | − | 2.79156i | −0.0323248 | − | 0.107209i | ||||
\(679\) | − | 10.8401i | − | 0.416004i | ||||||
\(680\) | −3.72947 | + | 6.15831i | −0.143019 | + | 0.236160i | ||||
\(681\) | −33.0831 | + | 9.97494i | −1.26775 | + | 0.382240i | ||||
\(682\) | − | 11.2843i | − | 0.432097i | ||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | −11.7958 | + | 5.64431i | −0.451025 | + | 0.215816i | ||||
\(685\) | 6.15831 | + | 3.72947i | 0.235297 | + | 0.142496i | ||||
\(686\) | −11.6981 | −0.446637 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 3.82534i | − | 0.145840i | ||||||
\(689\) | 3.31662i | 0.126353i | ||||||||
\(690\) | 26.4259 | + | 6.79504i | 1.00602 | + | 0.258683i | ||||
\(691\) | −13.8997 | −0.528771 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(692\) | 13.2665i | 0.504317i | ||||||||
\(693\) | −34.7461 | + | 23.0479i | −1.31989 | + | 0.875519i | ||||
\(694\) | 20.1462i | 0.764738i | ||||||||
\(695\) | 19.1267 | + | 11.5831i | 0.725518 | + | 0.439373i | ||||
\(696\) | −13.6915 | + | 4.12814i | −0.518975 | + | 0.156477i | ||||
\(697\) | 36.9499 | 1.39958 | ||||||||
\(698\) | − | 8.63325i | − | 0.326773i | ||||||
\(699\) | −13.2928 | − | 44.0873i | −0.502781 | − | 1.66754i | ||||
\(700\) | −14.2665 | + | 7.45894i | −0.539223 | + | 0.281921i | ||||
\(701\) | − | 37.2665i | − | 1.40754i | −0.710430 | − | 0.703768i | \(-0.751499\pi\) | ||
0.710430 | − | 0.703768i | \(-0.248501\pi\) | |||||||
\(702\) | 11.0000 | − | 13.2665i | 0.415168 | − | 0.500712i | ||||
\(703\) | −8.63325 | − | 1.21120i | −0.325609 | − | 0.0456812i | ||||
\(704\) | − | 4.31662i | − | 0.162689i | ||||||
\(705\) | −8.54736 | + | 33.2406i | −0.321912 | + | 1.25191i | ||||
\(706\) | − | 23.3659i | − | 0.879388i | ||||||
\(707\) | −46.0959 | −1.73361 | ||||||||
\(708\) | 2.82107 | + | 9.35643i | 0.106022 | + | 0.351636i | ||||
\(709\) | 28.6332 | 1.07534 | 0.537672 | − | 0.843154i | \(-0.319304\pi\) | ||||
0.537672 | + | 0.843154i | \(0.319304\pi\) | |||||||
\(710\) | −11.8899 | + | 19.6332i | −0.446219 | + | 0.736823i | ||||
\(711\) | −25.3745 | − | 38.2534i | −0.951616 | − | 1.43462i | ||||
\(712\) | 2.61414i | 0.0979692i | ||||||||
\(713\) | 18.4169i | 0.689717i | ||||||||
\(714\) | 5.18338 | + | 17.1913i | 0.193983 | + | 0.643369i | ||||
\(715\) | −16.5831 | + | 27.3830i | −0.620174 | + | 1.02407i | ||||
\(716\) | 16.5126 | 0.617104 | ||||||||
\(717\) | 32.5581 | − | 9.81662i | 1.21590 | − | 0.366609i | ||||
\(718\) | 4.89975 | 0.182857 | ||||||||
\(719\) | 34.8997i | 1.30154i | 0.759274 | + | 0.650771i | \(0.225554\pi\) | ||||
−0.759274 | + | 0.650771i | \(0.774446\pi\) | |||||||
\(720\) | 6.70252 | − | 0.276026i | 0.249788 | − | 0.0102869i | ||||
\(721\) | − | 56.6132i | − | 2.10838i | ||||||
\(722\) | 5.22829 | − | 18.2665i | 0.194577 | − | 0.679809i | ||||
\(723\) | 8.67014 | − | 2.61414i | 0.322446 | − | 0.0972211i | ||||
\(724\) | 16.5126i | 0.613685i | ||||||||
\(725\) | 19.1267 | + | 36.5831i | 0.710348 | + | 1.35866i | ||||
\(726\) | −12.6583 | + | 3.81662i | −0.469794 | + | 0.141648i | ||||
\(727\) | 13.2928i | 0.493004i | 0.969142 | + | 0.246502i | \(0.0792811\pi\) | ||||
−0.969142 | + | 0.246502i | \(0.920719\pi\) | |||||||
\(728\) | −10.6787 | −0.395778 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | −3.47494 | − | 2.10442i | −0.128613 | − | 0.0778881i | ||||
\(731\) | 12.3166i | 0.455547i | ||||||||
\(732\) | 1.15831 | + | 3.84169i | 0.0428125 | + | 0.141993i | ||||
\(733\) | − | 6.43949i | − | 0.237848i | −0.992903 | − | 0.118924i | \(-0.962056\pi\) | ||
0.992903 | − | 0.118924i | \(-0.0379445\pi\) | |||||||
\(734\) | 7.65069 | 0.282392 | ||||||||
\(735\) | −3.24726 | + | 12.6286i | −0.119777 | + | 0.465811i | ||||
\(736\) | 7.04509i | 0.259685i | ||||||||
\(737\) | 30.2164i | 1.11303i | ||||||||
\(738\) | −19.0308 | − | 28.6901i | −0.700535 | − | 1.05610i | ||||
\(739\) | −10.2164 | −0.375815 | −0.187908 | − | 0.982187i | \(-0.560171\pi\) | ||||
−0.187908 | + | 0.982187i | \(0.560171\pi\) | |||||||
\(740\) | 3.82534 | + | 2.31662i | 0.140622 | + | 0.0851608i | ||||
\(741\) | 3.82752 | + | 24.7457i | 0.140607 | + | 0.909056i | ||||
\(742\) | 3.21974i | 0.118201i | ||||||||
\(743\) | − | 44.8496i | − | 1.64537i | −0.568495 | − | 0.822687i | \(-0.692474\pi\) | ||
0.568495 | − | 0.822687i | \(-0.307526\pi\) | |||||||
\(744\) | 1.30707 | + | 4.33507i | 0.0479196 | + | 0.158931i | ||||
\(745\) | 4.63325 | − | 7.65069i | 0.169749 | − | 0.280299i | ||||
\(746\) | 23.3166i | 0.853682i | ||||||||
\(747\) | −16.0987 | + | 10.6787i | −0.589021 | + | 0.390713i | ||||
\(748\) | 13.8984i | 0.508177i | ||||||||
\(749\) | −0.161392 | −0.00589712 | ||||||||
\(750\) | −4.41589 | − | 18.8547i | −0.161246 | − | 0.688476i | ||||
\(751\) | 24.3550i | 0.888727i | 0.895847 | + | 0.444363i | \(0.146570\pi\) | ||||
−0.895847 | + | 0.444363i | \(0.853430\pi\) | |||||||
\(752\) | −8.86188 | −0.323160 | ||||||||
\(753\) | −52.3747 | + | 15.7916i | −1.90864 | + | 0.575477i | ||||
\(754\) | 27.3830i | 0.997230i | ||||||||
\(755\) | 19.1267 | − | 31.5831i | 0.696092 | − | 1.14943i | ||||
\(756\) | 10.6787 | − | 12.8790i | 0.388380 | − | 0.468404i | ||||
\(757\) | 12.8790i | 0.468094i | 0.972225 | + | 0.234047i | \(0.0751970\pi\) | ||||
−0.972225 | + | 0.234047i | \(0.924803\pi\) | |||||||
\(758\) | −36.4366 | −1.32344 | ||||||||
\(759\) | 50.4309 | − | 15.2055i | 1.83053 | − | 0.551925i | ||||
\(760\) | −6.15831 | + | 7.55481i | −0.223385 | + | 0.274042i | ||||
\(761\) | − | 10.6834i | − | 0.387272i | −0.981073 | − | 0.193636i | \(-0.937972\pi\) | ||
0.981073 | − | 0.193636i | \(-0.0620281\pi\) | |||||||
\(762\) | −27.5831 | + | 8.31662i | −0.999231 | + | 0.301280i | ||||
\(763\) | −22.0660 | −0.798843 | ||||||||
\(764\) | 5.00000i | 0.180894i | ||||||||
\(765\) | −21.5804 | + | 0.888733i | −0.780241 | + | 0.0321322i | ||||
\(766\) | −7.58312 | −0.273989 | ||||||||
\(767\) | 18.7129 | 0.675682 | ||||||||
\(768\) | 0.500000 | + | 1.65831i | 0.0180422 | + | 0.0598392i | ||||
\(769\) | −48.1662 | −1.73692 | −0.868460 | − | 0.495760i | \(-0.834890\pi\) | ||||
−0.868460 | + | 0.495760i | \(0.834890\pi\) | |||||||
\(770\) | −16.0987 | + | 26.5831i | −0.580158 | + | 0.957989i | ||||
\(771\) | −8.20844 | + | 2.47494i | −0.295620 | + | 0.0891327i | ||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | − | 24.1662i | − | 0.869200i | −0.900624 | − | 0.434600i | \(-0.856890\pi\) | ||
0.900624 | − | 0.434600i | \(-0.143110\pi\) | |||||||
\(774\) | 9.56336 | − | 6.34361i | 0.343748 | − | 0.228016i | ||||
\(775\) | 11.5831 | − | 6.05599i | 0.416078 | − | 0.217538i | ||||
\(776\) | 3.36675i | 0.120859i | ||||||||
\(777\) | 10.6787 | − | 3.21974i | 0.383096 | − | 0.115508i | ||||
\(778\) | −16.2164 | −0.581385 | ||||||||
\(779\) | 49.5377 | + | 6.94987i | 1.77487 | + | 0.249005i | ||||
\(780\) | 3.19891 | − | 12.4405i | 0.114539 | − | 0.445443i | ||||
\(781\) | 44.3094i | 1.58552i | ||||||||
\(782\) | − | 22.6834i | − | 0.811156i | ||||||
\(783\) | −33.0251 | − | 27.3830i | −1.18022 | − | 0.978589i | ||||
\(784\) | −3.36675 | −0.120241 | ||||||||
\(785\) | 8.86188 | − | 14.6332i | 0.316294 | − | 0.522283i | ||||
\(786\) | −5.00000 | − | 16.5831i | −0.178344 | − | 0.591500i | ||||
\(787\) | 8.36675 | 0.298242 | 0.149121 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149121 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(788\) | −5.03654 | −0.179419 | ||||||||
\(789\) | −10.2648 | − | 34.0446i | −0.365438 | − | 1.21202i | ||||
\(790\) | −29.2665 | − | 17.7238i | −1.04126 | − | 0.630583i | ||||
\(791\) | −5.42004 | −0.192714 | ||||||||
\(792\) | 10.7916 | − | 7.15831i | 0.383461 | − | 0.254360i | ||||
\(793\) | 7.68338 | 0.272845 | ||||||||
\(794\) | 29.3915 | 1.04307 | ||||||||
\(795\) | −3.75096 | − | 0.964508i | −0.133033 | − | 0.0342076i | ||||
\(796\) | 25.2164 | 0.893771 | ||||||||
\(797\) | − | 31.6332i | − | 1.12051i | −0.828321 | − | 0.560254i | \(-0.810704\pi\) | ||
0.828321 | − | 0.560254i | \(-0.189296\pi\) | |||||||
\(798\) | 3.71571 | + | 24.0229i | 0.131535 | + | 0.850400i | ||||
\(799\) | 28.5330 | 1.00942 | ||||||||
\(800\) | 4.43094 | − | 2.31662i | 0.156657 | − | 0.0819051i | ||||
\(801\) | −6.53536 | + | 4.33507i | −0.230916 | + | 0.153172i | ||||
\(802\) | − | 21.5491i | − | 0.760926i | ||||||
\(803\) | −7.84243 | −0.276753 | ||||||||
\(804\) | −3.50000 | − | 11.6082i | −0.123435 | − | 0.409389i | ||||
\(805\) | 26.2744 | − | 43.3858i | 0.926052 | − | 1.52915i | ||||
\(806\) | 8.67014 | 0.305393 | ||||||||
\(807\) | −10.8704 | − | 36.0531i | −0.382657 | − | 1.26913i | ||||
\(808\) | 14.3166 | 0.503657 | ||||||||
\(809\) | 1.94987i | 0.0685539i | 0.999412 | + | 0.0342770i | \(0.0109128\pi\) | ||||
−0.999412 | + | 0.0342770i | \(0.989087\pi\) | |||||||
\(810\) | 11.8049 | + | 16.2986i | 0.414783 | + | 0.572673i | ||||
\(811\) | − | 41.2814i | − | 1.44959i | −0.688966 | − | 0.724793i | \(-0.741935\pi\) | ||
0.688966 | − | 0.724793i | \(-0.258065\pi\) | |||||||
\(812\) | 26.5831i | 0.932885i | ||||||||
\(813\) | 1.34169 | + | 4.44987i | 0.0470550 | + | 0.156064i | ||||
\(814\) | 8.63325 | 0.302595 | ||||||||
\(815\) | 1.62505 | − | 2.68338i | 0.0569230 | − | 0.0939945i | ||||
\(816\) | −1.60987 | − | 5.33934i | −0.0563568 | − | 0.186914i | ||||
\(817\) | −2.31662 | + | 16.5126i | −0.0810484 | + | 0.577702i | ||||
\(818\) | −3.82534 | −0.133750 | ||||||||
\(819\) | −17.7086 | − | 26.6967i | −0.618788 | − | 0.932858i | ||||
\(820\) | −21.9499 | − | 13.2928i | −0.766523 | − | 0.464206i | ||||
\(821\) | − | 30.0000i | − | 1.04701i | −0.852023 | − | 0.523504i | \(-0.824625\pi\) | ||
0.852023 | − | 0.523504i | \(-0.175375\pi\) | |||||||
\(822\) | −5.33934 | + | 1.60987i | −0.186231 | + | 0.0561507i | ||||
\(823\) | − | 17.3099i | − | 0.603386i | −0.953405 | − | 0.301693i | \(-0.902448\pi\) | ||
0.953405 | − | 0.301693i | \(-0.0975517\pi\) | |||||||
\(824\) | 17.5831i | 0.612537i | ||||||||
\(825\) | −26.1465 | − | 26.7181i | −0.910304 | − | 0.930204i | ||||
\(826\) | 18.1662 | 0.632085 | ||||||||
\(827\) | 8.58312i | 0.298464i | 0.988802 | + | 0.149232i | \(0.0476802\pi\) | ||||
−0.988802 | + | 0.149232i | \(0.952320\pi\) | |||||||
\(828\) | −17.6127 | + | 11.6830i | −0.612084 | + | 0.406011i | ||||
\(829\) | 31.4001i | 1.09057i | 0.838251 | + | 0.545285i | \(0.183579\pi\) | ||||
−0.838251 | + | 0.545285i | \(0.816421\pi\) | |||||||
\(830\) | −7.45894 | + | 12.3166i | −0.258904 | + | 0.427516i | ||||
\(831\) | 23.3659 | − | 7.04509i | 0.810554 | − | 0.244391i | ||||
\(832\) | 3.31662 | 0.114983 | ||||||||
\(833\) | 10.8401 | 0.375586 | ||||||||
\(834\) | −16.5831 | + | 5.00000i | −0.574227 | + | 0.173136i | ||||
\(835\) | 28.8997 | − | 47.7209i | 1.00012 | − | 1.65145i | ||||
\(836\) | −2.61414 | + | 18.6332i | −0.0904121 | + | 0.644444i | ||||
\(837\) | −8.67014 | + | 10.4566i | −0.299684 | + | 0.361432i | ||||
\(838\) | −3.05013 | −0.105365 | ||||||||
\(839\) | 6.05599 | 0.209076 | 0.104538 | − | 0.994521i | \(-0.466664\pi\) | ||||
0.104538 | + | 0.994521i | \(0.466664\pi\) | |||||||
\(840\) | 3.10547 | − | 12.0771i | 0.107149 | − | 0.416701i | ||||
\(841\) | 39.1662 | 1.35056 | ||||||||
\(842\) | −16.0987 | −0.554799 | ||||||||
\(843\) | −3.12387 | − | 10.3607i | −0.107592 | − | 0.356842i | ||||
\(844\) | 3.02800i | 0.104228i | ||||||||
\(845\) | 3.82534 | + | 2.31662i | 0.131596 | + | 0.0796943i | ||||
\(846\) | −14.6958 | − | 22.1547i | −0.505251 | − | 0.761695i | ||||
\(847\) | 24.5771i | 0.844479i | ||||||||
\(848\) | − | 1.00000i | − | 0.0343401i | ||||||
\(849\) | −44.0873 | + | 13.2928i | −1.51307 | + | 0.456209i | ||||
\(850\) | −14.2665 | + | 7.45894i | −0.489337 | + | 0.255839i | ||||
\(851\) | −14.0902 | −0.483005 | ||||||||
\(852\) | −5.13242 | − | 17.0223i | −0.175834 | − | 0.583174i | ||||
\(853\) | − | 49.9212i | − | 1.70927i | −0.519230 | − | 0.854635i | \(-0.673781\pi\) | ||
0.519230 | − | 0.854635i | \(-0.326219\pi\) | |||||||
\(854\) | 7.45894 | 0.255240 | ||||||||
\(855\) | −29.0994 | − | 2.86754i | −0.995180 | − | 0.0980679i | ||||
\(856\) | 0.0501256 | 0.00171326 | ||||||||
\(857\) | 12.0000i | 0.409912i | 0.978771 | + | 0.204956i | \(0.0657052\pi\) | ||||
−0.978771 | + | 0.204956i | \(0.934295\pi\) | |||||||
\(858\) | −7.15831 | − | 23.7414i | −0.244381 | − | 0.810519i | ||||
\(859\) | 2.94987 | 0.100648 | 0.0503242 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503242 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(860\) | 4.43094 | − | 7.31662i | 0.151094 | − | 0.249495i | ||||
\(861\) | −61.2744 | + | 18.4749i | −2.08823 | + | 0.629624i | ||||
\(862\) | 17.5320i | 0.597143i | ||||||||
\(863\) | − | 11.6834i | − | 0.397707i | −0.980029 | − | 0.198853i | \(-0.936278\pi\) | ||
0.980029 | − | 0.198853i | \(-0.0637217\pi\) | |||||||
\(864\) | −3.31662 | + | 4.00000i | −0.112834 | + | 0.136083i | ||||
\(865\) | −15.3668 | + | 25.3745i | −0.522485 | + | 0.862757i | ||||
\(866\) | − | 1.68338i | − | 0.0572034i | ||||||
\(867\) | −3.31662 | − | 11.0000i | −0.112638 | − | 0.373580i | ||||
\(868\) | 8.41688 | 0.285687 | ||||||||
\(869\) | −66.0503 | −2.24060 | ||||||||
\(870\) | −30.9690 | − | 7.96325i | −1.04995 | − | 0.269980i | ||||
\(871\) | −23.2164 | −0.786657 | ||||||||
\(872\) | 6.85334 | 0.232083 | ||||||||
\(873\) | −8.41688 | + | 5.58312i | −0.284868 | + | 0.188960i | ||||
\(874\) | 4.26650 | − | 30.4110i | 0.144316 | − | 1.02867i | ||||
\(875\) | −35.9269 | − | 2.25856i | −1.21455 | − | 0.0763534i | ||||
\(876\) | 3.01282 | − | 0.908399i | 0.101794 | − | 0.0306920i | ||||
\(877\) | 19.9499 | 0.673659 | 0.336830 | − | 0.941566i | \(-0.390645\pi\) | ||||
0.336830 | + | 0.941566i | \(0.390645\pi\) | |||||||
\(878\) | −3.82534 | −0.129099 | ||||||||
\(879\) | 30.2916 | − | 9.13325i | 1.02171 | − | 0.308057i | ||||
\(880\) | 5.00000 | − | 8.25629i | 0.168550 | − | 0.278319i | ||||
\(881\) | 15.8997i | 0.535676i | 0.963464 | + | 0.267838i | \(0.0863092\pi\) | ||||
−0.963464 | + | 0.267838i | \(0.913691\pi\) | |||||||
\(882\) | −5.58312 | − | 8.41688i | −0.187994 | − | 0.283411i | ||||
\(883\) | − | 0.383495i | − | 0.0129056i | −0.999979 | − | 0.00645282i | \(-0.997946\pi\) | ||
0.999979 | − | 0.00645282i | \(-0.00205401\pi\) | |||||||
\(884\) | −10.6787 | −0.359163 | ||||||||
\(885\) | −5.44189 | + | 21.1635i | −0.182927 | + | 0.711402i | ||||
\(886\) | 12.6872i | 0.426236i | ||||||||
\(887\) | 33.5831i | 1.12761i | 0.825908 | + | 0.563805i | \(0.190663\pi\) | ||||
−0.825908 | + | 0.563805i | \(0.809337\pi\) | |||||||
\(888\) | −3.31662 | + | 1.00000i | −0.111299 | + | 0.0335578i | ||||
\(889\) | 53.5548i | 1.79617i | ||||||||
\(890\) | −3.02800 | + | 5.00000i | −0.101499 | + | 0.167600i | ||||
\(891\) | 35.7916 | + | 15.1082i | 1.19906 | + | 0.506143i | ||||
\(892\) | −3.26650 | −0.109370 | ||||||||
\(893\) | 38.2534 | + | 5.36675i | 1.28010 | + | 0.179591i | ||||
\(894\) | 2.00000 | + | 6.63325i | 0.0668900 | + | 0.221849i | ||||
\(895\) | 31.5831 | + | 19.1267i | 1.05571 | + | 0.639336i | ||||
\(896\) | 3.21974 | 0.107564 | ||||||||
\(897\) | 11.6830 | + | 38.7480i | 0.390083 | + | 1.29376i | ||||
\(898\) | − | 26.9691i | − | 0.899972i | ||||||
\(899\) | − | 21.5831i | − | 0.719837i | ||||||
\(900\) | 13.1394 | + | 7.23567i | 0.437982 | + | 0.241189i | ||||
\(901\) | 3.21974i | 0.107265i | ||||||||
\(902\) | −49.5377 | −1.64943 | ||||||||
\(903\) | −6.15831 | − | 20.4248i | −0.204936 | − | 0.679695i | ||||
\(904\) | 1.68338 | 0.0559882 | ||||||||
\(905\) | −19.1267 | + | 31.5831i | −0.635794 | + | 1.04986i | ||||
\(906\) | 8.25629 | + | 27.3830i | 0.274297 | + | 0.909739i | ||||
\(907\) | −6.16625 | −0.204747 | −0.102373 | − | 0.994746i | \(-0.532644\pi\) | ||||
−0.102373 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(908\) | − | 19.9499i | − | 0.662060i | ||||||
\(909\) | 23.7414 | + | 35.7916i | 0.787454 | + | 1.18713i | ||||
\(910\) | −20.4248 | − | 12.3693i | −0.677076 | − | 0.410037i | ||||
\(911\) | 24.1633 | 0.800564 | 0.400282 | − | 0.916392i | \(-0.368912\pi\) | ||||
0.400282 | + | 0.916392i | \(0.368912\pi\) | |||||||
\(912\) | −1.15404 | − | 7.46111i | −0.0382141 | − | 0.247062i | ||||
\(913\) | 27.7969i | 0.919942i | ||||||||
\(914\) | 27.1913 | 0.899407 | ||||||||
\(915\) | −2.23440 | + | 8.68957i | −0.0738671 | + | 0.287268i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.1974 | −1.06325 | ||||||||
\(918\) | 10.6787 | − | 12.8790i | 0.352449 | − | 0.425070i | ||||
\(919\) | −17.9499 | −0.592112 | −0.296056 | − | 0.955171i | \(-0.595671\pi\) | ||||
−0.296056 | + | 0.955171i | \(0.595671\pi\) | |||||||
\(920\) | −8.16041 | + | 13.4749i | −0.269041 | + | 0.444256i | ||||
\(921\) | 1.00000 | + | 3.31662i | 0.0329511 | + | 0.109287i | ||||
\(922\) | 21.5831 | 0.710802 | ||||||||
\(923\) | −34.0446 | −1.12059 | ||||||||
\(924\) | −6.94921 | − | 23.0479i | −0.228612 | − | 0.758221i | ||||
\(925\) | 4.63325 | + | 8.86188i | 0.152340 | + | 0.291377i | ||||
\(926\) | 15.3014 | 0.502834 | ||||||||
\(927\) | −43.9578 | + | 29.1583i | −1.44376 | + | 0.957685i | ||||
\(928\) | − | 8.25629i | − | 0.271026i | ||||||
\(929\) | − | 18.0501i | − | 0.592205i | −0.955156 | − | 0.296103i | \(-0.904313\pi\) | ||
0.955156 | − | 0.296103i | \(-0.0956871\pi\) | |||||||
\(930\) | −2.52136 | + | 9.80556i | −0.0826788 | + | 0.321537i | ||||
\(931\) | 14.5330 | + | 2.03890i | 0.476300 | + | 0.0668223i | ||||
\(932\) | 26.5857 | 0.870842 | ||||||||
\(933\) | 34.6583 | − | 10.4499i | 1.13466 | − | 0.342114i | ||||
\(934\) | − | 26.7774i | − | 0.876183i | ||||||
\(935\) | −16.0987 | + | 26.5831i | −0.526484 | + | 0.869361i | ||||
\(936\) | 5.50000 | + | 8.29156i | 0.179773 | + | 0.271018i | ||||
\(937\) | 15.0793i | 0.492618i | 0.969191 | + | 0.246309i | \(0.0792178\pi\) | ||||
−0.969191 | + | 0.246309i | \(0.920782\pi\) | |||||||
\(938\) | −22.5382 | −0.735899 | ||||||||
\(939\) | 34.4129 | − | 10.3759i | 1.12302 | − | 0.338604i | ||||
\(940\) | −16.9499 | − | 10.2648i | −0.552844 | − | 0.334802i | ||||
\(941\) | −5.83389 | −0.190179 | −0.0950897 | − | 0.995469i | \(-0.530314\pi\) | ||||
−0.0950897 | + | 0.995469i | \(0.530314\pi\) | |||||||
\(942\) | 3.82534 | + | 12.6872i | 0.124636 | + | 0.413372i | ||||
\(943\) | 80.8496 | 2.63283 | ||||||||
\(944\) | −5.64214 | −0.183636 | ||||||||
\(945\) | 35.3427 | − | 12.2640i | 1.14970 | − | 0.398948i | ||||
\(946\) | − | 16.5126i | − | 0.536870i | ||||||
\(947\) | 18.9350 | 0.615304 | 0.307652 | − | 0.951499i | \(-0.400457\pi\) | ||||
0.307652 | + | 0.951499i | \(0.400457\pi\) | |||||||
\(948\) | 25.3745 | − | 7.65069i | 0.824124 | − | 0.248483i | ||||
\(949\) | − | 6.02564i | − | 0.195600i | ||||||
\(950\) | −20.5297 | + | 7.31662i | −0.666070 | + | 0.237383i | ||||
\(951\) | −28.1913 | + | 8.50000i | −0.914166 | + | 0.275631i | ||||
\(952\) | −10.3668 | −0.335988 | ||||||||
\(953\) | 2.41688i | 0.0782903i | 0.999234 | + | 0.0391451i | \(0.0124635\pi\) | ||||
−0.999234 | + | 0.0391451i | \(0.987537\pi\) | |||||||
\(954\) | 2.50000 | − | 1.65831i | 0.0809405 | − | 0.0536898i | ||||
\(955\) | −5.79156 | + | 9.56336i | −0.187411 | + | 0.309463i | ||||
\(956\) | 19.6332i | 0.634985i | ||||||||
\(957\) | −59.1011 | + | 17.8196i | −1.91047 | + | 0.576027i | ||||
\(958\) | 14.0000 | 0.452319 | ||||||||
\(959\) | 10.3668i | 0.334760i | ||||||||
\(960\) | −0.964508 | + | 3.75096i | −0.0311294 | + | 0.121062i | ||||
\(961\) | 24.1662 | 0.779556 | ||||||||
\(962\) | 6.63325i | 0.213865i | ||||||||
\(963\) | 0.0831240 | + | 0.125314i | 0.00267863 | + | 0.00403819i | ||||
\(964\) | 5.22829i | 0.168392i | ||||||||
\(965\) | −11.4760 | − | 6.94987i | −0.369426 | − | 0.223724i | ||||
\(966\) | 11.3417 | + | 37.6161i | 0.364913 | + | 1.21028i | ||||
\(967\) | − | 35.8310i | − | 1.15225i | −0.817362 | − | 0.576124i | \(-0.804564\pi\) | ||
0.817362 | − | 0.576124i | \(-0.195436\pi\) | |||||||
\(968\) | − | 7.63325i | − | 0.245342i | ||||||
\(969\) | 3.71571 | + | 24.0229i | 0.119366 | + | 0.771726i | ||||
\(970\) | −3.89975 | + | 6.43949i | −0.125213 | + | 0.206759i | ||||
\(971\) | −8.03418 | −0.257829 | −0.128915 | − | 0.991656i | \(-0.541149\pi\) | ||||
−0.128915 | + | 0.991656i | \(0.541149\pi\) | |||||||
\(972\) | −15.5000 | − | 1.65831i | −0.497163 | − | 0.0531904i | ||||
\(973\) | 32.1974i | 1.03220i | ||||||||
\(974\) | − | 36.5330i | − | 1.17059i | ||||||
\(975\) | 20.5285 | − | 20.0893i | 0.657438 | − | 0.643373i | ||||
\(976\) | −2.31662 | −0.0741534 | ||||||||
\(977\) | − | 29.5831i | − | 0.946448i | −0.880942 | − | 0.473224i | \(-0.843090\pi\) | ||
0.880942 | − | 0.473224i | \(-0.156910\pi\) | |||||||
\(978\) | 0.701473 | + | 2.32652i | 0.0224306 | + | 0.0743940i | ||||
\(979\) | 11.2843i | 0.360647i | ||||||||
\(980\) | −6.43949 | − | 3.89975i | −0.205702 | − | 0.124573i | ||||
\(981\) | 11.3650 | + | 17.1333i | 0.362856 | + | 0.547026i | ||||
\(982\) | 8.41688 | 0.268593 | ||||||||
\(983\) | 27.1662i | 0.866469i | 0.901281 | + | 0.433234i | \(0.142628\pi\) | ||||
−0.901281 | + | 0.433234i | \(0.857372\pi\) | |||||||
\(984\) | 19.0308 | − | 5.73801i | 0.606681 | − | 0.182921i | ||||
\(985\) | −9.63325 | − | 5.83389i | −0.306941 | − | 0.185883i | ||||
\(986\) | 26.5831i | 0.846579i | ||||||||
\(987\) | −47.3166 | + | 14.2665i | −1.50610 | + | 0.454108i | ||||
\(988\) | −14.3166 | − | 2.00855i | −0.455473 | − | 0.0639003i | ||||
\(989\) | 26.9499i | 0.856956i | ||||||||
\(990\) | 28.9323 | − | 1.19150i | 0.919528 | − | 0.0378684i | ||||
\(991\) | 30.4110i | 0.966037i | 0.875610 | + | 0.483019i | \(0.160460\pi\) | ||||
−0.875610 | + | 0.483019i | \(0.839540\pi\) | |||||||
\(992\) | −2.61414 | −0.0829992 | ||||||||
\(993\) | −22.3616 | + | 6.74229i | −0.709625 | + | 0.213960i | ||||
\(994\) | −33.0501 | −1.04829 | ||||||||
\(995\) | 48.2306 | + | 29.2084i | 1.52901 | + | 0.925970i | ||||
\(996\) | −3.21974 | − | 10.6787i | −0.102021 | − | 0.338367i | ||||
\(997\) | − | 33.2169i | − | 1.05199i | −0.850488 | − | 0.525995i | \(-0.823693\pi\) | ||
0.850488 | − | 0.525995i | \(-0.176307\pi\) | |||||||
\(998\) | − | 8.41688i | − | 0.266432i | ||||||
\(999\) | −8.00000 | − | 6.63325i | −0.253109 | − | 0.209867i |
(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 | 570.2.c.f.569.3 | yes | 8 | |
3.2 | odd | 2 | inner | 570.2.c.f.569.6 | yes | 8 | |
5.4 | even | 2 | 570.2.c.c.569.6 | yes | 8 | ||
15.14 | odd | 2 | 570.2.c.c.569.3 | ✓ | 8 | ||
19.18 | odd | 2 | 570.2.c.c.569.5 | yes | 8 | ||
57.56 | even | 2 | 570.2.c.c.569.4 | yes | 8 | ||
95.94 | odd | 2 | inner | 570.2.c.f.569.4 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.f.569.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.c.569.3 | ✓ | 8 | 15.14 | odd | 2 | ||
570.2.c.c.569.4 | yes | 8 | 57.56 | even | 2 | ||
570.2.c.c.569.5 | yes | 8 | 19.18 | odd | 2 | ||
570.2.c.c.569.6 | yes | 8 | 5.4 | even | 2 | ||
570.2.c.f.569.3 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.c.f.569.4 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.f.569.5 | yes | 8 | 285.284 | even | 2 | inner | |
570.2.c.f.569.6 | yes | 8 | 3.2 | odd | 2 | inner |