Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,2,Mod(19,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.h (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.19775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 139.1 | ||
Root | \(-0.587785 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.139 |
Dual form | 150.2.h.a.109.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.587785 | − | 0.809017i | −0.415627 | − | 0.572061i | ||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | 0.530249 | − | 2.17229i | 0.237134 | − | 0.971477i | ||||
\(6\) | −0.309017 | − | 0.951057i | −0.126156 | − | 0.388267i | ||||
\(7\) | − | 0.273457i | − | 0.103357i | −0.998664 | − | 0.0516786i | \(-0.983543\pi\) | ||
0.998664 | − | 0.0516786i | \(-0.0164571\pi\) | |||||||
\(8\) | 0.951057 | − | 0.309017i | 0.336249 | − | 0.109254i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | −2.06909 | + | 0.847859i | −0.654304 | + | 0.268116i | ||||
\(11\) | 3.87811 | − | 2.81761i | 1.16929 | − | 0.849541i | 0.178369 | − | 0.983964i | \(-0.442918\pi\) |
0.990924 | + | 0.134422i | \(0.0429178\pi\) | |||||||
\(12\) | −0.587785 | + | 0.809017i | −0.169679 | + | 0.233543i | ||||
\(13\) | −1.01869 | + | 1.40211i | −0.282535 | + | 0.388876i | −0.926572 | − | 0.376119i | \(-0.877259\pi\) |
0.644036 | + | 0.764995i | \(0.277259\pi\) | |||||||
\(14\) | −0.221232 | + | 0.160734i | −0.0591267 | + | 0.0429580i | ||||
\(15\) | 1.17557 | − | 1.90211i | 0.303531 | − | 0.491123i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.79892 | + | 0.584503i | −0.436301 | + | 0.141763i | −0.518928 | − | 0.854818i | \(-0.673669\pi\) |
0.0826274 | + | 0.996581i | \(0.473669\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 0.930333 | + | 2.86327i | 0.213433 | + | 0.656879i | 0.999261 | + | 0.0384344i | \(0.0122371\pi\) |
−0.785828 | + | 0.618445i | \(0.787763\pi\) | |||||||
\(20\) | 1.90211 | + | 1.17557i | 0.425325 | + | 0.262866i | ||||
\(21\) | 0.0845030 | − | 0.260074i | 0.0184401 | − | 0.0567527i | ||||
\(22\) | −4.55899 | − | 1.48131i | −0.971980 | − | 0.315815i | ||||
\(23\) | −2.73076 | − | 3.75856i | −0.569402 | − | 0.783715i | 0.423081 | − | 0.906092i | \(-0.360948\pi\) |
−0.992484 | + | 0.122377i | \(0.960948\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.43767 | − | 2.30371i | −0.887535 | − | 0.460741i | ||||
\(26\) | 1.73311 | 0.339890 | ||||||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | 0.260074 | + | 0.0845030i | 0.0491493 | + | 0.0159696i | ||||
\(29\) | −2.80808 | + | 8.64240i | −0.521448 | + | 1.60485i | 0.249786 | + | 0.968301i | \(0.419640\pi\) |
−0.771234 | + | 0.636552i | \(0.780360\pi\) | |||||||
\(30\) | −2.22982 | + | 0.166977i | −0.407108 | + | 0.0304858i | ||||
\(31\) | 1.18474 | + | 3.64625i | 0.212786 | + | 0.654887i | 0.999303 | + | 0.0373190i | \(0.0118818\pi\) |
−0.786518 | + | 0.617568i | \(0.788118\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.55899 | − | 1.48131i | 0.793618 | − | 0.257862i | ||||
\(34\) | 1.53025 | + | 1.11179i | 0.262435 | + | 0.190671i | ||||
\(35\) | −0.594028 | − | 0.145000i | −0.100409 | − | 0.0245096i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | −5.29563 | + | 7.28881i | −0.870597 | + | 1.19827i | 0.108341 | + | 0.994114i | \(0.465446\pi\) |
−0.978938 | + | 0.204160i | \(0.934554\pi\) | |||||||
\(38\) | 1.76960 | − | 2.43564i | 0.287067 | − | 0.395114i | ||||
\(39\) | −1.40211 | + | 1.01869i | −0.224518 | + | 0.163122i | ||||
\(40\) | −0.166977 | − | 2.22982i | −0.0264015 | − | 0.352566i | ||||
\(41\) | 6.13287 | + | 4.45579i | 0.957793 | + | 0.695878i | 0.952637 | − | 0.304109i | \(-0.0983587\pi\) |
0.00515619 | + | 0.999987i | \(0.498359\pi\) | |||||||
\(42\) | −0.260074 | + | 0.0845030i | −0.0401302 | + | 0.0130391i | ||||
\(43\) | 2.88963i | 0.440664i | 0.975425 | + | 0.220332i | \(0.0707141\pi\) | ||||
−0.975425 | + | 0.220332i | \(0.929286\pi\) | |||||||
\(44\) | 1.48131 | + | 4.55899i | 0.223315 | + | 0.687293i | ||||
\(45\) | 1.70582 | − | 1.44575i | 0.254289 | − | 0.215519i | ||||
\(46\) | −1.43564 | + | 4.41846i | −0.211674 | + | 0.651466i | ||||
\(47\) | −1.12991 | − | 0.367130i | −0.164814 | − | 0.0535514i | 0.225448 | − | 0.974255i | \(-0.427616\pi\) |
−0.390262 | + | 0.920704i | \(0.627616\pi\) | |||||||
\(48\) | −0.587785 | − | 0.809017i | −0.0848395 | − | 0.116772i | ||||
\(49\) | 6.92522 | 0.989317 | ||||||||
\(50\) | 0.744661 | + | 4.94424i | 0.105311 | + | 0.699221i | ||||
\(51\) | −1.89149 | −0.264862 | ||||||||
\(52\) | −1.01869 | − | 1.40211i | −0.141268 | − | 0.194438i | ||||
\(53\) | −11.0465 | − | 3.58924i | −1.51736 | − | 0.493020i | −0.572334 | − | 0.820020i | \(-0.693962\pi\) |
−0.945024 | + | 0.327001i | \(0.893962\pi\) | |||||||
\(54\) | 0.309017 | − | 0.951057i | 0.0420519 | − | 0.129422i | ||||
\(55\) | −4.06430 | − | 9.91840i | −0.548030 | − | 1.33740i | ||||
\(56\) | −0.0845030 | − | 0.260074i | −0.0112922 | − | 0.0347538i | ||||
\(57\) | 3.01062i | 0.398767i | ||||||||
\(58\) | 8.64240 | − | 2.80808i | 1.13480 | − | 0.368720i | ||||
\(59\) | −11.5604 | − | 8.39915i | −1.50504 | − | 1.09348i | −0.968319 | − | 0.249718i | \(-0.919662\pi\) |
−0.536723 | − | 0.843759i | \(-0.680338\pi\) | |||||||
\(60\) | 1.44575 | + | 1.70582i | 0.186645 | + | 0.220220i | ||||
\(61\) | 4.16750 | − | 3.02786i | 0.533593 | − | 0.387678i | −0.288107 | − | 0.957598i | \(-0.593026\pi\) |
0.821700 | + | 0.569920i | \(0.193026\pi\) | |||||||
\(62\) | 2.25351 | − | 3.10169i | 0.286196 | − | 0.393915i | ||||
\(63\) | 0.160734 | − | 0.221232i | 0.0202506 | − | 0.0278726i | ||||
\(64\) | 0.809017 | − | 0.587785i | 0.101127 | − | 0.0734732i | ||||
\(65\) | 2.50563 | + | 2.95637i | 0.310785 | + | 0.366692i | ||||
\(66\) | −3.87811 | − | 2.81761i | −0.477362 | − | 0.346824i | ||||
\(67\) | 5.98215 | − | 1.94372i | 0.730836 | − | 0.237463i | 0.0801208 | − | 0.996785i | \(-0.474469\pi\) |
0.650715 | + | 0.759322i | \(0.274469\pi\) | |||||||
\(68\) | − | 1.89149i | − | 0.229377i | ||||||
\(69\) | −1.43564 | − | 4.41846i | −0.172831 | − | 0.531920i | ||||
\(70\) | 0.231853 | + | 0.565808i | 0.0277118 | + | 0.0676270i | ||||
\(71\) | −0.433294 | + | 1.33354i | −0.0514226 | + | 0.158262i | −0.973470 | − | 0.228814i | \(-0.926515\pi\) |
0.922048 | + | 0.387077i | \(0.126515\pi\) | |||||||
\(72\) | 0.951057 | + | 0.309017i | 0.112083 | + | 0.0364180i | ||||
\(73\) | −1.04691 | − | 1.44095i | −0.122532 | − | 0.168651i | 0.743344 | − | 0.668909i | \(-0.233238\pi\) |
−0.865876 | + | 0.500258i | \(0.833238\pi\) | |||||||
\(74\) | 9.00947 | 1.04733 | ||||||||
\(75\) | −3.50859 | − | 3.56227i | −0.405137 | − | 0.411336i | ||||
\(76\) | −3.01062 | −0.345342 | ||||||||
\(77\) | −0.770497 | − | 1.06050i | −0.0878062 | − | 0.120855i | ||||
\(78\) | 1.64828 | + | 0.535560i | 0.186631 | + | 0.0606402i | ||||
\(79\) | 4.96261 | − | 15.2733i | 0.558337 | − | 1.71839i | −0.128626 | − | 0.991693i | \(-0.541057\pi\) |
0.686963 | − | 0.726692i | \(-0.258943\pi\) | |||||||
\(80\) | −1.70582 | + | 1.44575i | −0.190716 | + | 0.161639i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | − | 7.58064i | − | 0.837142i | ||||||
\(83\) | 14.3983 | − | 4.67828i | 1.58041 | − | 0.513508i | 0.618250 | − | 0.785981i | \(-0.287842\pi\) |
0.962163 | + | 0.272474i | \(0.0878417\pi\) | |||||||
\(84\) | 0.221232 | + | 0.160734i | 0.0241384 | + | 0.0175375i | ||||
\(85\) | 0.315836 | + | 4.21769i | 0.0342573 | + | 0.457473i | ||||
\(86\) | 2.33776 | − | 1.69848i | 0.252087 | − | 0.183152i | ||||
\(87\) | −5.34129 | + | 7.35166i | −0.572647 | + | 0.788181i | ||||
\(88\) | 2.81761 | − | 3.87811i | 0.300358 | − | 0.413408i | ||||
\(89\) | −11.9956 | + | 8.71529i | −1.27153 | + | 0.923819i | −0.999262 | − | 0.0384036i | \(-0.987773\pi\) |
−0.272265 | + | 0.962222i | \(0.587773\pi\) | |||||||
\(90\) | −2.17229 | − | 0.530249i | −0.228979 | − | 0.0558931i | ||||
\(91\) | 0.383418 | + | 0.278570i | 0.0401932 | + | 0.0292020i | ||||
\(92\) | 4.41846 | − | 1.43564i | 0.460656 | − | 0.149676i | ||||
\(93\) | 3.83390i | 0.397557i | ||||||||
\(94\) | 0.367130 | + | 1.12991i | 0.0378665 | + | 0.116541i | ||||
\(95\) | 6.71316 | − | 0.502706i | 0.688756 | − | 0.0515765i | ||||
\(96\) | −0.309017 | + | 0.951057i | −0.0315389 | + | 0.0970668i | ||||
\(97\) | 5.59789 | + | 1.81886i | 0.568379 | + | 0.184678i | 0.579088 | − | 0.815265i | \(-0.303409\pi\) |
−0.0107087 | + | 0.999943i | \(0.503409\pi\) | |||||||
\(98\) | −4.07054 | − | 5.60262i | −0.411187 | − | 0.565950i | ||||
\(99\) | 4.79360 | 0.481775 | ||||||||
\(100\) | 3.56227 | − | 3.50859i | 0.356227 | − | 0.350859i | ||||
\(101\) | 4.83576 | 0.481176 | 0.240588 | − | 0.970627i | \(-0.422660\pi\) | ||||
0.240588 | + | 0.970627i | \(0.422660\pi\) | |||||||
\(102\) | 1.11179 | + | 1.53025i | 0.110084 | + | 0.151517i | ||||
\(103\) | −0.0694118 | − | 0.0225533i | −0.00683935 | − | 0.00222224i | 0.305595 | − | 0.952161i | \(-0.401145\pi\) |
−0.312435 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(104\) | −0.535560 | + | 1.64828i | −0.0525159 | + | 0.161627i | ||||
\(105\) | −0.520147 | − | 0.321469i | −0.0507612 | − | 0.0313721i | ||||
\(106\) | 3.58924 | + | 11.0465i | 0.348618 | + | 1.07293i | ||||
\(107\) | − | 5.84754i | − | 0.565303i | −0.959223 | − | 0.282651i | \(-0.908786\pi\) | ||
0.959223 | − | 0.282651i | \(-0.0912140\pi\) | |||||||
\(108\) | −0.951057 | + | 0.309017i | −0.0915155 | + | 0.0297352i | ||||
\(109\) | −7.93329 | − | 5.76388i | −0.759872 | − | 0.552079i | 0.138999 | − | 0.990292i | \(-0.455611\pi\) |
−0.898871 | + | 0.438213i | \(0.855611\pi\) | |||||||
\(110\) | −5.63522 | + | 9.11798i | −0.537297 | + | 0.869365i | ||||
\(111\) | −7.28881 | + | 5.29563i | −0.691824 | + | 0.502639i | ||||
\(112\) | −0.160734 | + | 0.221232i | −0.0151880 | + | 0.0209044i | ||||
\(113\) | −10.1858 | + | 14.0196i | −0.958201 | + | 1.31885i | −0.0104140 | + | 0.999946i | \(0.503315\pi\) |
−0.947787 | + | 0.318905i | \(0.896685\pi\) | |||||||
\(114\) | 2.43564 | − | 1.76960i | 0.228119 | − | 0.165738i | ||||
\(115\) | −9.61267 | + | 3.93902i | −0.896386 | + | 0.367315i | ||||
\(116\) | −7.35166 | − | 5.34129i | −0.682585 | − | 0.495927i | ||||
\(117\) | −1.64828 | + | 0.535560i | −0.152384 | + | 0.0495125i | ||||
\(118\) | 14.2895i | 1.31545i | ||||||||
\(119\) | 0.159837 | + | 0.491927i | 0.0146522 | + | 0.0450949i | ||||
\(120\) | 0.530249 | − | 2.17229i | 0.0484049 | − | 0.198302i | ||||
\(121\) | 3.70160 | − | 11.3924i | 0.336510 | − | 1.03567i | ||||
\(122\) | −4.89919 | − | 1.59184i | −0.443552 | − | 0.144119i | ||||
\(123\) | 4.45579 | + | 6.13287i | 0.401765 | + | 0.552982i | ||||
\(124\) | −3.83390 | −0.344294 | ||||||||
\(125\) | −7.35738 | + | 8.41837i | −0.658064 | + | 0.752962i | ||||
\(126\) | −0.273457 | −0.0243615 | ||||||||
\(127\) | 10.7963 | + | 14.8598i | 0.958013 | + | 1.31859i | 0.947875 | + | 0.318643i | \(0.103227\pi\) |
0.0101377 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(128\) | −0.951057 | − | 0.309017i | −0.0840623 | − | 0.0273135i | ||||
\(129\) | −0.892944 | + | 2.74820i | −0.0786193 | + | 0.241965i | ||||
\(130\) | 0.918978 | − | 3.76481i | 0.0805997 | − | 0.330196i | ||||
\(131\) | −2.34036 | − | 7.20289i | −0.204478 | − | 0.629320i | −0.999734 | − | 0.0230460i | \(-0.992664\pi\) |
0.795256 | − | 0.606274i | \(-0.207336\pi\) | |||||||
\(132\) | 4.79360i | 0.417230i | ||||||||
\(133\) | 0.782983 | − | 0.254407i | 0.0678932 | − | 0.0220598i | ||||
\(134\) | −5.08872 | − | 3.69717i | −0.439598 | − | 0.319387i | ||||
\(135\) | 2.06909 | − | 0.847859i | 0.178079 | − | 0.0729721i | ||||
\(136\) | −1.53025 | + | 1.11179i | −0.131218 | + | 0.0953353i | ||||
\(137\) | 11.5262 | − | 15.8644i | 0.984747 | − | 1.35539i | 0.0505148 | − | 0.998723i | \(-0.483914\pi\) |
0.934232 | − | 0.356665i | \(-0.116086\pi\) | |||||||
\(138\) | −2.73076 | + | 3.75856i | −0.232457 | + | 0.319950i | ||||
\(139\) | 7.73836 | − | 5.62225i | 0.656359 | − | 0.476873i | −0.209072 | − | 0.977900i | \(-0.567044\pi\) |
0.865431 | + | 0.501027i | \(0.167044\pi\) | |||||||
\(140\) | 0.321469 | − | 0.520147i | 0.0271691 | − | 0.0439604i | ||||
\(141\) | −0.961158 | − | 0.698322i | −0.0809441 | − | 0.0588093i | ||||
\(142\) | 1.33354 | − | 0.433294i | 0.111908 | − | 0.0363612i | ||||
\(143\) | 8.30783i | 0.694736i | ||||||||
\(144\) | −0.309017 | − | 0.951057i | −0.0257514 | − | 0.0792547i | ||||
\(145\) | 17.2848 | + | 10.6826i | 1.43542 | + | 0.887141i | ||||
\(146\) | −0.550396 | + | 1.69394i | −0.0455511 | + | 0.140192i | ||||
\(147\) | 6.58628 | + | 2.14001i | 0.543227 | + | 0.176505i | ||||
\(148\) | −5.29563 | − | 7.28881i | −0.435298 | − | 0.599137i | ||||
\(149\) | 4.64398 | 0.380449 | 0.190225 | − | 0.981741i | \(-0.439078\pi\) | ||||
0.190225 | + | 0.981741i | \(0.439078\pi\) | |||||||
\(150\) | −0.819639 | + | 4.93236i | −0.0669232 | + | 0.402726i | ||||
\(151\) | −16.7881 | −1.36619 | −0.683097 | − | 0.730327i | \(-0.739368\pi\) | ||||
−0.683097 | + | 0.730327i | \(0.739368\pi\) | |||||||
\(152\) | 1.76960 | + | 2.43564i | 0.143533 | + | 0.197557i | ||||
\(153\) | −1.79892 | − | 0.584503i | −0.145434 | − | 0.0472543i | ||||
\(154\) | −0.405074 | + | 1.24669i | −0.0326418 | + | 0.100461i | ||||
\(155\) | 8.54892 | − | 0.640175i | 0.686666 | − | 0.0514201i | ||||
\(156\) | −0.535560 | − | 1.64828i | −0.0428791 | − | 0.131968i | ||||
\(157\) | − | 5.57763i | − | 0.445143i | −0.974916 | − | 0.222572i | \(-0.928555\pi\) | ||
0.974916 | − | 0.222572i | \(-0.0714451\pi\) | |||||||
\(158\) | −15.2733 | + | 4.96261i | −1.21508 | + | 0.394804i | ||||
\(159\) | −9.39675 | − | 6.82714i | −0.745210 | − | 0.541427i | ||||
\(160\) | 2.17229 | + | 0.530249i | 0.171734 | + | 0.0419198i | ||||
\(161\) | −1.02781 | + | 0.746746i | −0.0810026 | + | 0.0588518i | ||||
\(162\) | 0.587785 | − | 0.809017i | 0.0461808 | − | 0.0635624i | ||||
\(163\) | −10.8007 | + | 14.8659i | −0.845978 | + | 1.16439i | 0.138757 | + | 0.990327i | \(0.455689\pi\) |
−0.984735 | + | 0.174062i | \(0.944311\pi\) | |||||||
\(164\) | −6.13287 | + | 4.45579i | −0.478897 | + | 0.347939i | ||||
\(165\) | −0.800424 | − | 10.6889i | −0.0623129 | − | 0.832130i | ||||
\(166\) | −12.2479 | − | 8.89861i | −0.950620 | − | 0.690666i | ||||
\(167\) | 8.50651 | − | 2.76393i | 0.658253 | − | 0.213879i | 0.0392036 | − | 0.999231i | \(-0.487518\pi\) |
0.619050 | + | 0.785352i | \(0.287518\pi\) | |||||||
\(168\) | − | 0.273457i | − | 0.0210977i | ||||||
\(169\) | 3.08904 | + | 9.50708i | 0.237618 | + | 0.731314i | ||||
\(170\) | 3.22654 | − | 2.73462i | 0.247465 | − | 0.209735i | ||||
\(171\) | −0.930333 | + | 2.86327i | −0.0711444 | + | 0.218960i | ||||
\(172\) | −2.74820 | − | 0.892944i | −0.209548 | − | 0.0680863i | ||||
\(173\) | −7.00354 | − | 9.63954i | −0.532469 | − | 0.732881i | 0.455035 | − | 0.890473i | \(-0.349627\pi\) |
−0.987504 | + | 0.157593i | \(0.949627\pi\) | |||||||
\(174\) | 9.08715 | 0.688895 | ||||||||
\(175\) | −0.629966 | + | 1.21351i | −0.0476209 | + | 0.0917331i | ||||
\(176\) | −4.79360 | −0.361332 | ||||||||
\(177\) | −8.39915 | − | 11.5604i | −0.631319 | − | 0.868936i | ||||
\(178\) | 14.1016 | + | 4.58190i | 1.05696 | + | 0.343428i | ||||
\(179\) | 1.16073 | − | 3.57237i | 0.0867574 | − | 0.267012i | −0.898261 | − | 0.439463i | \(-0.855169\pi\) |
0.985018 | + | 0.172451i | \(0.0551688\pi\) | |||||||
\(180\) | 0.847859 | + | 2.06909i | 0.0631957 | + | 0.154221i | ||||
\(181\) | −5.58164 | − | 17.1785i | −0.414880 | − | 1.27687i | −0.912358 | − | 0.409393i | \(-0.865740\pi\) |
0.497478 | − | 0.867477i | \(-0.334260\pi\) | |||||||
\(182\) | − | 0.473931i | − | 0.0351301i | ||||||
\(183\) | 4.89919 | − | 1.59184i | 0.362158 | − | 0.117672i | ||||
\(184\) | −3.75856 | − | 2.73076i | −0.277085 | − | 0.201314i | ||||
\(185\) | 13.0254 | + | 15.3685i | 0.957647 | + | 1.12992i | ||||
\(186\) | 3.10169 | − | 2.25351i | 0.227427 | − | 0.165235i | ||||
\(187\) | −5.32949 | + | 7.33541i | −0.389731 | + | 0.536418i | ||||
\(188\) | 0.698322 | − | 0.961158i | 0.0509304 | − | 0.0700997i | ||||
\(189\) | 0.221232 | − | 0.160734i | 0.0160922 | − | 0.0116917i | ||||
\(190\) | −4.35259 | − | 5.13558i | −0.315770 | − | 0.372574i | ||||
\(191\) | 13.4303 | + | 9.75767i | 0.971781 | + | 0.706040i | 0.955857 | − | 0.293833i | \(-0.0949310\pi\) |
0.0159240 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(192\) | 0.951057 | − | 0.309017i | 0.0686366 | − | 0.0223014i | ||||
\(193\) | 3.84858i | 0.277027i | 0.990361 | + | 0.138513i | \(0.0442324\pi\) | ||||
−0.990361 | + | 0.138513i | \(0.955768\pi\) | |||||||
\(194\) | −1.81886 | − | 5.59789i | −0.130587 | − | 0.401905i | ||||
\(195\) | 1.46943 | + | 3.58596i | 0.105228 | + | 0.256796i | ||||
\(196\) | −2.14001 | + | 6.58628i | −0.152858 | + | 0.470448i | ||||
\(197\) | −10.2174 | − | 3.31984i | −0.727960 | − | 0.236529i | −0.0784892 | − | 0.996915i | \(-0.525010\pi\) |
−0.649471 | + | 0.760386i | \(0.725010\pi\) | |||||||
\(198\) | −2.81761 | − | 3.87811i | −0.200239 | − | 0.275605i | ||||
\(199\) | −2.49808 | −0.177084 | −0.0885421 | − | 0.996072i | \(-0.528221\pi\) | ||||
−0.0885421 | + | 0.996072i | \(0.528221\pi\) | |||||||
\(200\) | −4.93236 | − | 0.819639i | −0.348771 | − | 0.0579572i | ||||
\(201\) | 6.29000 | 0.443662 | ||||||||
\(202\) | −2.84239 | − | 3.91221i | −0.199990 | − | 0.275262i | ||||
\(203\) | 2.36333 | + | 0.767892i | 0.165873 | + | 0.0538954i | ||||
\(204\) | 0.584503 | − | 1.79892i | 0.0409234 | − | 0.125949i | ||||
\(205\) | 12.9312 | − | 10.9597i | 0.903155 | − | 0.765458i | ||||
\(206\) | 0.0225533 | + | 0.0694118i | 0.00157136 | + | 0.00483615i | ||||
\(207\) | − | 4.64584i | − | 0.322908i | ||||||
\(208\) | 1.64828 | − | 0.535560i | 0.114288 | − | 0.0371344i | ||||
\(209\) | 11.6755 | + | 8.48276i | 0.807612 | + | 0.586765i | ||||
\(210\) | 0.0456612 | + | 0.609762i | 0.00315092 | + | 0.0420776i | ||||
\(211\) | −19.6381 | + | 14.2679i | −1.35194 | + | 0.982245i | −0.353032 | + | 0.935611i | \(0.614849\pi\) |
−0.998912 | + | 0.0466338i | \(0.985151\pi\) | |||||||
\(212\) | 6.82714 | − | 9.39675i | 0.468890 | − | 0.645371i | ||||
\(213\) | −0.824175 | + | 1.13438i | −0.0564715 | + | 0.0777264i | ||||
\(214\) | −4.73076 | + | 3.43710i | −0.323388 | + | 0.234955i | ||||
\(215\) | 6.27710 | + | 1.53222i | 0.428095 | + | 0.104497i | ||||
\(216\) | 0.809017 | + | 0.587785i | 0.0550466 | + | 0.0399937i | ||||
\(217\) | 0.997095 | − | 0.323976i | 0.0676872 | − | 0.0219929i | ||||
\(218\) | 9.80609i | 0.664152i | ||||||||
\(219\) | −0.550396 | − | 1.69394i | −0.0371923 | − | 0.114466i | ||||
\(220\) | 10.6889 | − | 0.800424i | 0.720645 | − | 0.0539646i | ||||
\(221\) | 1.01301 | − | 3.11771i | 0.0681422 | − | 0.209720i | ||||
\(222\) | 8.56851 | + | 2.78408i | 0.575081 | + | 0.186855i | ||||
\(223\) | −7.67291 | − | 10.5609i | −0.513816 | − | 0.707207i | 0.470741 | − | 0.882271i | \(-0.343987\pi\) |
−0.984557 | + | 0.175064i | \(0.943987\pi\) | |||||||
\(224\) | 0.273457 | 0.0182711 | ||||||||
\(225\) | −2.23607 | − | 4.47214i | −0.149071 | − | 0.298142i | ||||
\(226\) | 17.3291 | 1.15272 | ||||||||
\(227\) | 4.15067 | + | 5.71290i | 0.275489 | + | 0.379179i | 0.924233 | − | 0.381828i | \(-0.124705\pi\) |
−0.648744 | + | 0.761007i | \(0.724705\pi\) | |||||||
\(228\) | −2.86327 | − | 0.930333i | −0.189625 | − | 0.0616128i | ||||
\(229\) | 3.88654 | − | 11.9615i | 0.256830 | − | 0.790441i | −0.736634 | − | 0.676292i | \(-0.763586\pi\) |
0.993464 | − | 0.114149i | \(-0.0364143\pi\) | |||||||
\(230\) | 8.83692 | + | 5.46151i | 0.582689 | + | 0.360122i | ||||
\(231\) | −0.405074 | − | 1.24669i | −0.0266519 | − | 0.0820262i | ||||
\(232\) | 9.08715i | 0.596601i | ||||||||
\(233\) | 9.32536 | − | 3.02999i | 0.610925 | − | 0.198501i | 0.0128179 | − | 0.999918i | \(-0.495920\pi\) |
0.598107 | + | 0.801416i | \(0.295920\pi\) | |||||||
\(234\) | 1.40211 | + | 1.01869i | 0.0916590 | + | 0.0665942i | ||||
\(235\) | −1.39664 | + | 2.25982i | −0.0911071 | + | 0.147414i | ||||
\(236\) | 11.5604 | − | 8.39915i | 0.752521 | − | 0.546738i | ||||
\(237\) | 9.43945 | − | 12.9923i | 0.613158 | − | 0.843939i | ||||
\(238\) | 0.304027 | − | 0.418458i | 0.0197072 | − | 0.0271246i | ||||
\(239\) | 4.07768 | − | 2.96261i | 0.263763 | − | 0.191635i | −0.448041 | − | 0.894013i | \(-0.647878\pi\) |
0.711805 | + | 0.702378i | \(0.247878\pi\) | |||||||
\(240\) | −2.06909 | + | 0.847859i | −0.133559 | + | 0.0547290i | ||||
\(241\) | −5.53446 | − | 4.02102i | −0.356506 | − | 0.259017i | 0.395087 | − | 0.918644i | \(-0.370714\pi\) |
−0.751593 | + | 0.659627i | \(0.770714\pi\) | |||||||
\(242\) | −11.3924 | + | 3.70160i | −0.732329 | + | 0.237948i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 1.59184 | + | 4.89919i | 0.101907 | + | 0.313638i | ||||
\(245\) | 3.67209 | − | 15.0436i | 0.234601 | − | 0.961099i | ||||
\(246\) | 2.34255 | − | 7.20962i | 0.149355 | − | 0.459669i | ||||
\(247\) | −4.96236 | − | 1.61237i | −0.315747 | − | 0.102592i | ||||
\(248\) | 2.25351 | + | 3.10169i | 0.143098 | + | 0.196957i | ||||
\(249\) | 15.1392 | 0.959409 | ||||||||
\(250\) | 11.1352 | + | 1.00406i | 0.704250 | + | 0.0635021i | ||||
\(251\) | −7.07549 | −0.446601 | −0.223301 | − | 0.974750i | \(-0.571683\pi\) | ||||
−0.223301 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(252\) | 0.160734 | + | 0.221232i | 0.0101253 | + | 0.0139363i | ||||
\(253\) | −21.1803 | − | 6.88191i | −1.33160 | − | 0.432662i | ||||
\(254\) | 5.67593 | − | 17.4687i | 0.356139 | − | 1.09608i | ||||
\(255\) | −1.00296 | + | 4.10886i | −0.0628079 | + | 0.257307i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | − | 4.47318i | − | 0.279029i | −0.990220 | − | 0.139515i | \(-0.955446\pi\) | ||
0.990220 | − | 0.139515i | \(-0.0445542\pi\) | |||||||
\(258\) | 2.74820 | − | 0.892944i | 0.171095 | − | 0.0555922i | ||||
\(259\) | 1.99318 | + | 1.44813i | 0.123850 | + | 0.0899824i | ||||
\(260\) | −3.58596 | + | 1.46943i | −0.222392 | + | 0.0911302i | ||||
\(261\) | −7.35166 | + | 5.34129i | −0.455056 | + | 0.330618i | ||||
\(262\) | −4.45163 | + | 6.12715i | −0.275023 | + | 0.378536i | ||||
\(263\) | 1.47083 | − | 2.02442i | 0.0906950 | − | 0.124831i | −0.761258 | − | 0.648449i | \(-0.775418\pi\) |
0.851953 | + | 0.523618i | \(0.175418\pi\) | |||||||
\(264\) | 3.87811 | − | 2.81761i | 0.238681 | − | 0.173412i | ||||
\(265\) | −13.6543 | + | 22.0931i | −0.838775 | + | 1.35717i | ||||
\(266\) | −0.666045 | − | 0.483910i | −0.0408378 | − | 0.0296704i | ||||
\(267\) | −14.1016 | + | 4.58190i | −0.863006 | + | 0.280408i | ||||
\(268\) | 6.29000i | 0.384223i | ||||||||
\(269\) | −1.91241 | − | 5.88580i | −0.116602 | − | 0.358864i | 0.875676 | − | 0.482899i | \(-0.160416\pi\) |
−0.992278 | + | 0.124036i | \(0.960416\pi\) | |||||||
\(270\) | −1.90211 | − | 1.17557i | −0.115759 | − | 0.0715429i | ||||
\(271\) | 4.06941 | − | 12.5244i | 0.247199 | − | 0.760801i | −0.748068 | − | 0.663622i | \(-0.769018\pi\) |
0.995267 | − | 0.0971785i | \(-0.0309818\pi\) | |||||||
\(272\) | 1.79892 | + | 0.584503i | 0.109075 | + | 0.0354407i | ||||
\(273\) | 0.278570 | + | 0.383418i | 0.0168598 | + | 0.0232055i | ||||
\(274\) | −19.6095 | −1.18465 | ||||||||
\(275\) | −23.7007 | + | 3.56961i | −1.42921 | + | 0.215256i | ||||
\(276\) | 4.64584 | 0.279647 | ||||||||
\(277\) | −3.03717 | − | 4.18031i | −0.182486 | − | 0.251170i | 0.707967 | − | 0.706245i | \(-0.249612\pi\) |
−0.890453 | + | 0.455075i | \(0.849612\pi\) | |||||||
\(278\) | −9.09699 | − | 2.95579i | −0.545601 | − | 0.177277i | ||||
\(279\) | −1.18474 | + | 3.64625i | −0.0709285 | + | 0.218296i | ||||
\(280\) | −0.609762 | + | 0.0456612i | −0.0364403 | + | 0.00272878i | ||||
\(281\) | −0.0145149 | − | 0.0446724i | −0.000865889 | − | 0.00266493i | 0.950623 | − | 0.310349i | \(-0.100446\pi\) |
−0.951489 | + | 0.307684i | \(0.900446\pi\) | |||||||
\(282\) | 1.18806i | 0.0707478i | ||||||||
\(283\) | 20.8007 | − | 6.75856i | 1.23647 | − | 0.401755i | 0.383419 | − | 0.923575i | \(-0.374747\pi\) |
0.853056 | + | 0.521820i | \(0.174747\pi\) | |||||||
\(284\) | −1.13438 | − | 0.824175i | −0.0673130 | − | 0.0489058i | ||||
\(285\) | 6.53994 | + | 1.59638i | 0.387392 | + | 0.0945613i | ||||
\(286\) | 6.72118 | − | 4.88322i | 0.397431 | − | 0.288751i | ||||
\(287\) | 1.21847 | − | 1.67708i | 0.0719240 | − | 0.0989949i | ||||
\(288\) | −0.587785 | + | 0.809017i | −0.0346356 | + | 0.0476718i | ||||
\(289\) | −10.8588 | + | 7.88941i | −0.638755 | + | 0.464083i | ||||
\(290\) | −1.51735 | − | 20.2628i | −0.0891018 | − | 1.18987i | ||||
\(291\) | 4.76185 | + | 3.45968i | 0.279144 | + | 0.202810i | ||||
\(292\) | 1.69394 | − | 0.550396i | 0.0991306 | − | 0.0322095i | ||||
\(293\) | 8.35289i | 0.487981i | 0.969778 | + | 0.243991i | \(0.0784566\pi\) | ||||
−0.969778 | + | 0.243991i | \(0.921543\pi\) | |||||||
\(294\) | −2.14001 | − | 6.58628i | −0.124808 | − | 0.384119i | ||||
\(295\) | −24.3753 | + | 20.6590i | −1.41918 | + | 1.20281i | ||||
\(296\) | −2.78408 | + | 8.56851i | −0.161821 | + | 0.498035i | ||||
\(297\) | 4.55899 | + | 1.48131i | 0.264539 | + | 0.0859540i | ||||
\(298\) | −2.72966 | − | 3.75706i | −0.158125 | − | 0.217640i | ||||
\(299\) | 8.05174 | 0.465644 | ||||||||
\(300\) | 4.47214 | − | 2.23607i | 0.258199 | − | 0.129099i | ||||
\(301\) | 0.790190 | 0.0455458 | ||||||||
\(302\) | 9.86779 | + | 13.5818i | 0.567827 | + | 0.781547i | ||||
\(303\) | 4.59908 | + | 1.49433i | 0.264210 | + | 0.0858472i | ||||
\(304\) | 0.930333 | − | 2.86327i | 0.0533583 | − | 0.164220i | ||||
\(305\) | −4.36758 | − | 10.6585i | −0.250087 | − | 0.610305i | ||||
\(306\) | 0.584503 | + | 1.79892i | 0.0334138 | + | 0.102837i | ||||
\(307\) | 2.28918i | 0.130650i | 0.997864 | + | 0.0653251i | \(0.0208084\pi\) | ||||
−0.997864 | + | 0.0653251i | \(0.979192\pi\) | |||||||
\(308\) | 1.24669 | − | 0.405074i | 0.0710367 | − | 0.0230812i | ||||
\(309\) | −0.0590452 | − | 0.0428988i | −0.00335896 | − | 0.00244043i | ||||
\(310\) | −5.54284 | − | 6.53994i | −0.314812 | − | 0.371444i | ||||
\(311\) | −20.7653 | + | 15.0869i | −1.17749 | + | 0.855497i | −0.991886 | − | 0.127128i | \(-0.959424\pi\) |
−0.185604 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(312\) | −1.01869 | + | 1.40211i | −0.0576722 | + | 0.0793790i | ||||
\(313\) | 17.7576 | − | 24.4412i | 1.00372 | − | 1.38150i | 0.0807005 | − | 0.996738i | \(-0.474284\pi\) |
0.923017 | − | 0.384760i | \(-0.125716\pi\) | |||||||
\(314\) | −4.51240 | + | 3.27845i | −0.254649 | + | 0.185013i | ||||
\(315\) | −0.395350 | − | 0.466469i | −0.0222754 | − | 0.0262826i | ||||
\(316\) | 12.9923 | + | 9.43945i | 0.730873 | + | 0.531010i | ||||
\(317\) | −24.5955 | + | 7.99157i | −1.38142 | + | 0.448851i | −0.903137 | − | 0.429353i | \(-0.858742\pi\) |
−0.478286 | + | 0.878204i | \(0.658742\pi\) | |||||||
\(318\) | 11.6150i | 0.651338i | ||||||||
\(319\) | 13.4608 | + | 41.4282i | 0.753663 | + | 2.31954i | ||||
\(320\) | −0.847859 | − | 2.06909i | −0.0473967 | − | 0.115666i | ||||
\(321\) | 1.80699 | − | 5.56134i | 0.100856 | − | 0.310404i | ||||
\(322\) | 1.20826 | + | 0.392588i | 0.0673337 | + | 0.0218781i | ||||
\(323\) | −3.34718 | − | 4.60700i | −0.186242 | − | 0.256340i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 7.75069 | − | 3.87535i | 0.429931 | − | 0.214965i | ||||
\(326\) | 18.3753 | 1.01771 | ||||||||
\(327\) | −5.76388 | − | 7.93329i | −0.318743 | − | 0.438712i | ||||
\(328\) | 7.20962 | + | 2.34255i | 0.398085 | + | 0.129346i | ||||
\(329\) | −0.100394 | + | 0.308982i | −0.00553492 | + | 0.0170347i | ||||
\(330\) | −8.17702 | + | 6.93033i | −0.450130 | + | 0.381502i | ||||
\(331\) | 4.48366 | + | 13.7993i | 0.246444 | + | 0.758477i | 0.995396 | + | 0.0958519i | \(0.0305575\pi\) |
−0.748952 | + | 0.662625i | \(0.769442\pi\) | |||||||
\(332\) | 15.1392i | 0.830873i | ||||||||
\(333\) | −8.56851 | + | 2.78408i | −0.469552 | + | 0.152567i | ||||
\(334\) | −7.23607 | − | 5.25731i | −0.395940 | − | 0.287667i | ||||
\(335\) | −1.05029 | − | 14.0256i | −0.0573834 | − | 0.766300i | ||||
\(336\) | −0.221232 | + | 0.160734i | −0.0120692 | + | 0.00876877i | ||||
\(337\) | −6.50536 | + | 8.95385i | −0.354369 | + | 0.487747i | −0.948569 | − | 0.316570i | \(-0.897469\pi\) |
0.594200 | + | 0.804317i | \(0.297469\pi\) | |||||||
\(338\) | 5.87570 | − | 8.08721i | 0.319596 | − | 0.439886i | ||||
\(339\) | −14.0196 | + | 10.1858i | −0.761439 | + | 0.553217i | ||||
\(340\) | −4.10886 | − | 1.00296i | −0.222834 | − | 0.0543932i | ||||
\(341\) | 14.8683 | + | 10.8024i | 0.805162 | + | 0.584984i | ||||
\(342\) | 2.86327 | − | 0.930333i | 0.154828 | − | 0.0503067i | ||||
\(343\) | − | 3.80796i | − | 0.205610i | ||||||
\(344\) | 0.892944 | + | 2.74820i | 0.0481443 | + | 0.148173i | ||||
\(345\) | −10.3594 | + | 0.775751i | −0.557732 | + | 0.0417650i | ||||
\(346\) | −3.68198 | + | 11.3320i | −0.197944 | + | 0.609210i | ||||
\(347\) | −0.961158 | − | 0.312299i | −0.0515977 | − | 0.0167651i | 0.283104 | − | 0.959089i | \(-0.408636\pi\) |
−0.334702 | + | 0.942324i | \(0.608636\pi\) | |||||||
\(348\) | −5.34129 | − | 7.35166i | −0.286323 | − | 0.394090i | ||||
\(349\) | −30.4268 | −1.62871 | −0.814356 | − | 0.580366i | \(-0.802910\pi\) | ||||
−0.814356 | + | 0.580366i | \(0.802910\pi\) | |||||||
\(350\) | 1.35204 | − | 0.203633i | 0.0722695 | − | 0.0108846i | ||||
\(351\) | −1.73311 | −0.0925064 | ||||||||
\(352\) | 2.81761 | + | 3.87811i | 0.150179 | + | 0.206704i | ||||
\(353\) | 14.8932 | + | 4.83911i | 0.792687 | + | 0.257560i | 0.677248 | − | 0.735755i | \(-0.263172\pi\) |
0.115439 | + | 0.993315i | \(0.463172\pi\) | |||||||
\(354\) | −4.41570 | + | 13.5901i | −0.234692 | + | 0.722306i | ||||
\(355\) | 2.66708 | + | 1.64835i | 0.141554 | + | 0.0874853i | ||||
\(356\) | −4.58190 | − | 14.1016i | −0.242840 | − | 0.747385i | ||||
\(357\) | 0.517242i | 0.0273754i | ||||||||
\(358\) | −3.57237 | + | 1.16073i | −0.188806 | + | 0.0613467i | ||||
\(359\) | 3.53800 | + | 2.57051i | 0.186729 | + | 0.135666i | 0.677222 | − | 0.735778i | \(-0.263184\pi\) |
−0.490494 | + | 0.871445i | \(0.663184\pi\) | |||||||
\(360\) | 1.17557 | − | 1.90211i | 0.0619580 | − | 0.100250i | ||||
\(361\) | 8.03852 | − | 5.84033i | 0.423080 | − | 0.307386i | ||||
\(362\) | −10.6169 | + | 14.6129i | −0.558013 | + | 0.768039i | ||||
\(363\) | 7.04087 | − | 9.69093i | 0.369550 | − | 0.508642i | ||||
\(364\) | −0.383418 | + | 0.278570i | −0.0200966 | + | 0.0146010i | ||||
\(365\) | −3.68529 | + | 1.51014i | −0.192897 | + | 0.0790442i | ||||
\(366\) | −4.16750 | − | 3.02786i | −0.217839 | − | 0.158269i | ||||
\(367\) | 20.7648 | − | 6.74689i | 1.08391 | − | 0.352185i | 0.288022 | − | 0.957624i | \(-0.407003\pi\) |
0.795892 | + | 0.605439i | \(0.207003\pi\) | |||||||
\(368\) | 4.64584i | 0.242181i | ||||||||
\(369\) | 2.34255 | + | 7.20962i | 0.121948 | + | 0.375318i | ||||
\(370\) | 4.77726 | − | 19.5712i | 0.248358 | − | 1.01746i | ||||
\(371\) | −0.981504 | + | 3.02076i | −0.0509571 | + | 0.156830i | ||||
\(372\) | −3.64625 | − | 1.18474i | −0.189049 | − | 0.0614259i | ||||
\(373\) | 0.833899 | + | 1.14776i | 0.0431776 | + | 0.0594289i | 0.830060 | − | 0.557674i | \(-0.188306\pi\) |
−0.786882 | + | 0.617103i | \(0.788306\pi\) | |||||||
\(374\) | 9.06706 | 0.468847 | ||||||||
\(375\) | −9.59871 | + | 5.73279i | −0.495675 | + | 0.296040i | ||||
\(376\) | −1.18806 | −0.0612694 | ||||||||
\(377\) | −9.25703 | − | 12.7412i | −0.476762 | − | 0.656206i | ||||
\(378\) | −0.260074 | − | 0.0845030i | −0.0133767 | − | 0.00434637i | ||||
\(379\) | 8.05934 | − | 24.8041i | 0.413981 | − | 1.27410i | −0.499179 | − | 0.866499i | \(-0.666365\pi\) |
0.913159 | − | 0.407603i | \(-0.133635\pi\) | |||||||
\(380\) | −1.59638 | + | 6.53994i | −0.0818925 | + | 0.335492i | ||||
\(381\) | 5.67593 | + | 17.4687i | 0.290787 | + | 0.894949i | ||||
\(382\) | − | 16.6007i | − | 0.849367i | ||||||
\(383\) | 31.1609 | − | 10.1248i | 1.59225 | − | 0.517353i | 0.627074 | − | 0.778960i | \(-0.284252\pi\) |
0.965175 | + | 0.261607i | \(0.0842523\pi\) | |||||||
\(384\) | −0.809017 | − | 0.587785i | −0.0412850 | − | 0.0299953i | ||||
\(385\) | −2.71226 | + | 1.11141i | −0.138230 | + | 0.0566429i | ||||
\(386\) | 3.11356 | − | 2.26214i | 0.158476 | − | 0.115140i | ||||
\(387\) | −1.69848 | + | 2.33776i | −0.0863386 | + | 0.118835i | ||||
\(388\) | −3.45968 | + | 4.76185i | −0.175639 | + | 0.241746i | ||||
\(389\) | −3.60929 | + | 2.62231i | −0.182998 | + | 0.132956i | −0.675513 | − | 0.737348i | \(-0.736078\pi\) |
0.492515 | + | 0.870304i | \(0.336078\pi\) | |||||||
\(390\) | 2.03739 | − | 3.29657i | 0.103167 | − | 0.166928i | ||||
\(391\) | 7.10929 | + | 5.16520i | 0.359532 | + | 0.261216i | ||||
\(392\) | 6.58628 | − | 2.14001i | 0.332657 | − | 0.108087i | ||||
\(393\) | − | 7.57357i | − | 0.382036i | ||||||
\(394\) | 3.31984 | + | 10.2174i | 0.167251 | + | 0.514746i | ||||
\(395\) | −30.5467 | − | 18.8789i | −1.53697 | − | 0.949900i | ||||
\(396\) | −1.48131 | + | 4.55899i | −0.0744384 | + | 0.229098i | ||||
\(397\) | 2.01364 | + | 0.654271i | 0.101062 | + | 0.0328369i | 0.359111 | − | 0.933295i | \(-0.383080\pi\) |
−0.258050 | + | 0.966132i | \(0.583080\pi\) | |||||||
\(398\) | 1.46833 | + | 2.02099i | 0.0736009 | + | 0.101303i | ||||
\(399\) | 0.823277 | 0.0412154 | ||||||||
\(400\) | 2.23607 | + | 4.47214i | 0.111803 | + | 0.223607i | ||||
\(401\) | −28.6530 | −1.43086 | −0.715431 | − | 0.698683i | \(-0.753770\pi\) | ||||
−0.715431 | + | 0.698683i | \(0.753770\pi\) | |||||||
\(402\) | −3.69717 | − | 5.08872i | −0.184398 | − | 0.253802i | ||||
\(403\) | −6.31935 | − | 2.05328i | −0.314789 | − | 0.102281i | ||||
\(404\) | −1.49433 | + | 4.59908i | −0.0743458 | + | 0.228813i | ||||
\(405\) | 2.22982 | − | 0.166977i | 0.110801 | − | 0.00829718i | ||||
\(406\) | −0.767892 | − | 2.36333i | −0.0381098 | − | 0.117290i | ||||
\(407\) | 43.1878i | 2.14074i | ||||||||
\(408\) | −1.79892 | + | 0.584503i | −0.0890596 | + | 0.0289372i | ||||
\(409\) | 31.8385 | + | 23.1320i | 1.57431 | + | 1.14381i | 0.922872 | + | 0.385107i | \(0.125835\pi\) |
0.651442 | + | 0.758699i | \(0.274165\pi\) | |||||||
\(410\) | −16.4673 | − | 4.01963i | −0.813264 | − | 0.198515i | ||||
\(411\) | 15.8644 | − | 11.5262i | 0.782534 | − | 0.568544i | ||||
\(412\) | 0.0428988 | − | 0.0590452i | 0.00211347 | − | 0.00290895i | ||||
\(413\) | −2.29681 | + | 3.16129i | −0.113019 | + | 0.155557i | ||||
\(414\) | −3.75856 | + | 2.73076i | −0.184723 | + | 0.134209i | ||||
\(415\) | −2.52791 | − | 33.7578i | −0.124090 | − | 1.65711i | ||||
\(416\) | −1.40211 | − | 1.01869i | −0.0687442 | − | 0.0499456i | ||||
\(417\) | 9.09699 | − | 2.95579i | 0.445481 | − | 0.144746i | ||||
\(418\) | − | 14.4317i | − | 0.705879i | ||||||
\(419\) | −4.35926 | − | 13.4164i | −0.212964 | − | 0.655434i | −0.999292 | − | 0.0376256i | \(-0.988021\pi\) |
0.786328 | − | 0.617809i | \(-0.211979\pi\) | |||||||
\(420\) | 0.466469 | − | 0.395350i | 0.0227614 | − | 0.0192911i | ||||
\(421\) | 5.03839 | − | 15.5066i | 0.245556 | − | 0.755744i | −0.749988 | − | 0.661451i | \(-0.769941\pi\) |
0.995545 | − | 0.0942928i | \(-0.0300590\pi\) | |||||||
\(422\) | 23.0860 | + | 7.50110i | 1.12381 | + | 0.365148i | ||||
\(423\) | −0.698322 | − | 0.961158i | −0.0339536 | − | 0.0467331i | ||||
\(424\) | −11.6150 | −0.564075 | ||||||||
\(425\) | 9.32952 | + | 1.55034i | 0.452548 | + | 0.0752025i | ||||
\(426\) | 1.40217 | 0.0679353 | ||||||||
\(427\) | −0.827992 | − | 1.13963i | −0.0400693 | − | 0.0551507i | ||||
\(428\) | 5.56134 | + | 1.80699i | 0.268817 | + | 0.0873441i | ||||
\(429\) | −2.56726 | + | 7.90122i | −0.123949 | + | 0.381474i | ||||
\(430\) | −2.45000 | − | 5.97890i | −0.118149 | − | 0.288328i | ||||
\(431\) | −0.612525 | − | 1.88516i | −0.0295043 | − | 0.0908048i | 0.935220 | − | 0.354067i | \(-0.115202\pi\) |
−0.964724 | + | 0.263262i | \(0.915202\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 4.26971 | − | 1.38731i | 0.205189 | − | 0.0666699i | −0.204619 | − | 0.978842i | \(-0.565596\pi\) |
0.409808 | + | 0.912172i | \(0.365596\pi\) | |||||||
\(434\) | −0.848180 | − | 0.616239i | −0.0407139 | − | 0.0295804i | ||||
\(435\) | 13.1377 | + | 15.5010i | 0.629905 | + | 0.743218i | ||||
\(436\) | 7.93329 | − | 5.76388i | 0.379936 | − | 0.276040i | ||||
\(437\) | 8.22128 | − | 11.3156i | 0.393277 | − | 0.541299i | ||||
\(438\) | −1.04691 | + | 1.44095i | −0.0500235 | + | 0.0688515i | ||||
\(439\) | 20.8045 | − | 15.1154i | 0.992946 | − | 0.721417i | 0.0323816 | − | 0.999476i | \(-0.489691\pi\) |
0.960564 | + | 0.278058i | \(0.0896908\pi\) | |||||||
\(440\) | −6.93033 | − | 8.17702i | −0.330391 | − | 0.389824i | ||||
\(441\) | 5.60262 | + | 4.07054i | 0.266791 | + | 0.193835i | ||||
\(442\) | −3.11771 | + | 1.01301i | −0.148294 | + | 0.0481838i | ||||
\(443\) | − | 29.1477i | − | 1.38485i | −0.721491 | − | 0.692423i | \(-0.756543\pi\) | ||
0.721491 | − | 0.692423i | \(-0.243457\pi\) | |||||||
\(444\) | −2.78408 | − | 8.56851i | −0.132127 | − | 0.406644i | ||||
\(445\) | 12.5715 | + | 30.6791i | 0.595946 | + | 1.45433i | ||||
\(446\) | −4.03389 | + | 12.4150i | −0.191010 | + | 0.587869i | ||||
\(447\) | 4.41668 | + | 1.43507i | 0.208902 | + | 0.0678764i | ||||
\(448\) | −0.160734 | − | 0.221232i | −0.00759398 | − | 0.0104522i | ||||
\(449\) | 5.14037 | 0.242589 | 0.121295 | − | 0.992617i | \(-0.461295\pi\) | ||||
0.121295 | + | 0.992617i | \(0.461295\pi\) | |||||||
\(450\) | −2.30371 | + | 4.43767i | −0.108598 | + | 0.209194i | ||||
\(451\) | 36.3386 | 1.71112 | ||||||||
\(452\) | −10.1858 | − | 14.0196i | −0.479100 | − | 0.659425i | ||||
\(453\) | −15.9664 | − | 5.18780i | −0.750168 | − | 0.243744i | ||||
\(454\) | 2.18213 | − | 6.71592i | 0.102413 | − | 0.315194i | ||||
\(455\) | 0.808441 | − | 0.685184i | 0.0379003 | − | 0.0321219i | ||||
\(456\) | 0.930333 | + | 2.86327i | 0.0435668 | + | 0.134085i | ||||
\(457\) | − | 20.8445i | − | 0.975066i | −0.873105 | − | 0.487533i | \(-0.837897\pi\) | ||
0.873105 | − | 0.487533i | \(-0.162103\pi\) | |||||||
\(458\) | −11.9615 | + | 3.88654i | −0.558926 | + | 0.181606i | ||||
\(459\) | −1.53025 | − | 1.11179i | −0.0714259 | − | 0.0518939i | ||||
\(460\) | −0.775751 | − | 10.3594i | −0.0361696 | − | 0.483010i | ||||
\(461\) | 4.02072 | − | 2.92123i | 0.187264 | − | 0.136055i | −0.490204 | − | 0.871608i | \(-0.663078\pi\) |
0.677467 | + | 0.735553i | \(0.263078\pi\) | |||||||
\(462\) | −0.770497 | + | 1.06050i | −0.0358467 | + | 0.0493388i | ||||
\(463\) | 4.17718 | − | 5.74940i | 0.194130 | − | 0.267197i | −0.700845 | − | 0.713314i | \(-0.747193\pi\) |
0.894975 | + | 0.446117i | \(0.147193\pi\) | |||||||
\(464\) | 7.35166 | − | 5.34129i | 0.341292 | − | 0.247963i | ||||
\(465\) | 8.32833 | + | 2.03292i | 0.386217 | + | 0.0942744i | ||||
\(466\) | −7.93263 | − | 5.76339i | −0.367472 | − | 0.266984i | ||||
\(467\) | −28.7049 | + | 9.32679i | −1.32831 | + | 0.431592i | −0.885339 | − | 0.464946i | \(-0.846074\pi\) |
−0.442966 | + | 0.896538i | \(0.646074\pi\) | |||||||
\(468\) | − | 1.73311i | − | 0.0801129i | ||||||
\(469\) | −0.531524 | − | 1.63586i | −0.0245435 | − | 0.0755371i | ||||
\(470\) | 2.64916 | − | 0.198379i | 0.122197 | − | 0.00915053i | ||||
\(471\) | 1.72358 | − | 5.30464i | 0.0794184 | − | 0.244425i | ||||
\(472\) | −13.5901 | − | 4.41570i | −0.625536 | − | 0.203249i | ||||
\(473\) | 8.14184 | + | 11.2063i | 0.374362 | + | 0.515265i | ||||
\(474\) | −16.0593 | −0.737630 | ||||||||
\(475\) | 2.46762 | − | 14.8495i | 0.113222 | − | 0.681341i | ||||
\(476\) | −0.517242 | −0.0237078 | ||||||||
\(477\) | −6.82714 | − | 9.39675i | −0.312593 | − | 0.430247i | ||||
\(478\) | −4.79360 | − | 1.55754i | −0.219254 | − | 0.0712401i | ||||
\(479\) | −8.60350 | + | 26.4788i | −0.393104 | + | 1.20985i | 0.537325 | + | 0.843376i | \(0.319435\pi\) |
−0.930428 | + | 0.366474i | \(0.880565\pi\) | |||||||
\(480\) | 1.90211 | + | 1.17557i | 0.0868192 | + | 0.0536572i | ||||
\(481\) | −4.82511 | − | 14.8502i | −0.220006 | − | 0.677109i | ||||
\(482\) | 6.84097i | 0.311598i | ||||||||
\(483\) | −1.20826 | + | 0.392588i | −0.0549777 | + | 0.0178634i | ||||
\(484\) | 9.69093 | + | 7.04087i | 0.440497 | + | 0.320040i | ||||
\(485\) | 6.91937 | − | 11.1958i | 0.314192 | − | 0.508374i | ||||
\(486\) | 0.809017 | − | 0.587785i | 0.0366978 | − | 0.0266625i | ||||
\(487\) | 0.763835 | − | 1.05133i | 0.0346127 | − | 0.0476402i | −0.791360 | − | 0.611351i | \(-0.790627\pi\) |
0.825973 | + | 0.563710i | \(0.190627\pi\) | |||||||
\(488\) | 3.02786 | − | 4.16750i | 0.137065 | − | 0.188654i | ||||
\(489\) | −14.8659 | + | 10.8007i | −0.672260 | + | 0.488426i | ||||
\(490\) | −14.3289 | + | 5.87161i | −0.647314 | + | 0.265252i | ||||
\(491\) | −15.5048 | − | 11.2649i | −0.699723 | − | 0.508379i | 0.180119 | − | 0.983645i | \(-0.442352\pi\) |
−0.879842 | + | 0.475266i | \(0.842352\pi\) | |||||||
\(492\) | −7.20962 | + | 2.34255i | −0.325035 | + | 0.105610i | ||||
\(493\) | − | 17.1883i | − | 0.774121i | ||||||
\(494\) | 1.61237 | + | 4.96236i | 0.0725438 | + | 0.223267i | ||||
\(495\) | 2.54180 | − | 10.4131i | 0.114246 | − | 0.468034i | ||||
\(496\) | 1.18474 | − | 3.64625i | 0.0531964 | − | 0.163722i | ||||
\(497\) | 0.364667 | + | 0.118488i | 0.0163576 | + | 0.00531489i | ||||
\(498\) | −8.89861 | − | 12.2479i | −0.398756 | − | 0.548841i | ||||
\(499\) | −6.41339 | −0.287103 | −0.143551 | − | 0.989643i | \(-0.545852\pi\) | ||||
−0.143551 | + | 0.989643i | \(0.545852\pi\) | |||||||
\(500\) | −5.73279 | − | 9.59871i | −0.256378 | − | 0.429267i | ||||
\(501\) | 8.94427 | 0.399601 | ||||||||
\(502\) | 4.15887 | + | 5.72419i | 0.185619 | + | 0.255483i | ||||
\(503\) | 34.0189 | + | 11.0534i | 1.51683 | + | 0.492848i | 0.944873 | − | 0.327436i | \(-0.106185\pi\) |
0.571956 | + | 0.820284i | \(0.306185\pi\) | |||||||
\(504\) | 0.0845030 | − | 0.260074i | 0.00376406 | − | 0.0115846i | ||||
\(505\) | 2.56416 | − | 10.5047i | 0.114104 | − | 0.467452i | ||||
\(506\) | 6.88191 | + | 21.1803i | 0.305938 | + | 0.941581i | ||||
\(507\) | 9.99634i | 0.443953i | ||||||||
\(508\) | −17.4687 | + | 5.67593i | −0.775049 | + | 0.251829i | ||||
\(509\) | 9.75570 | + | 7.08793i | 0.432414 | + | 0.314167i | 0.782613 | − | 0.622508i | \(-0.213886\pi\) |
−0.350200 | + | 0.936675i | \(0.613886\pi\) | |||||||
\(510\) | 3.91367 | − | 1.60372i | 0.173300 | − | 0.0710138i | ||||
\(511\) | −0.394040 | + | 0.286287i | −0.0174313 | + | 0.0126646i | ||||
\(512\) | 0.587785 | − | 0.809017i | 0.0259767 | − | 0.0357538i | ||||
\(513\) | −1.76960 | + | 2.43564i | −0.0781297 | + | 0.107536i | ||||
\(514\) | −3.61888 | + | 2.62927i | −0.159622 | + | 0.115972i | ||||
\(515\) | −0.0857977 | + | 0.138824i | −0.00378070 | + | 0.00611730i | ||||
\(516\) | −2.33776 | − | 1.69848i | −0.102914 | − | 0.0747714i | ||||
\(517\) | −5.41634 | + | 1.75987i | −0.238210 | + | 0.0773992i | ||||
\(518\) | − | 2.46371i | − | 0.108249i | ||||||
\(519\) | −3.68198 | − | 11.3320i | −0.161621 | − | 0.497418i | ||||
\(520\) | 3.29657 | + | 2.03739i | 0.144564 | + | 0.0893454i | ||||
\(521\) | 1.08563 | − | 3.34124i | 0.0475625 | − | 0.146382i | −0.924455 | − | 0.381292i | \(-0.875479\pi\) |
0.972017 | + | 0.234909i | \(0.0754794\pi\) | |||||||
\(522\) | 8.64240 | + | 2.80808i | 0.378267 | + | 0.122907i | ||||
\(523\) | 14.3695 | + | 19.7779i | 0.628333 | + | 0.864826i | 0.997926 | − | 0.0643677i | \(-0.0205030\pi\) |
−0.369593 | + | 0.929194i | \(0.620503\pi\) | |||||||
\(524\) | 7.57357 | 0.330853 | ||||||||
\(525\) | −0.974130 | + | 0.959451i | −0.0425145 | + | 0.0418739i | ||||
\(526\) | −2.50232 | −0.109106 | ||||||||
\(527\) | −4.26249 | − | 5.86682i | −0.185677 | − | 0.255563i | ||||
\(528\) | −4.55899 | − | 1.48131i | −0.198405 | − | 0.0644655i | ||||
\(529\) | 0.437616 | − | 1.34684i | 0.0190268 | − | 0.0585584i | ||||
\(530\) | 25.8995 | − | 1.93945i | 1.12500 | − | 0.0842442i | ||||
\(531\) | −4.41570 | − | 13.5901i | −0.191625 | − | 0.589761i | ||||
\(532\) | 0.823277i | 0.0356936i | ||||||||
\(533\) | −12.4950 | + | 4.05989i | −0.541220 | + | 0.175853i | ||||
\(534\) | 11.9956 | + | 8.71529i | 0.519099 | + | 0.377147i | ||||
\(535\) | −12.7025 | − | 3.10065i | −0.549179 | − | 0.134053i | ||||
\(536\) | 5.08872 | − | 3.69717i | 0.219799 | − | 0.159693i | ||||
\(537\) | 2.20785 | − | 3.03884i | 0.0952757 | − | 0.131136i | ||||
\(538\) | −3.63763 | + | 5.00676i | −0.156829 | + | 0.215857i | ||||
\(539\) | 26.8568 | − | 19.5126i | 1.15680 | − | 0.840466i | ||||
\(540\) | 0.166977 | + | 2.22982i | 0.00718557 | + | 0.0959564i | ||||
\(541\) | 31.3407 | + | 22.7703i | 1.34744 | + | 0.978974i | 0.999135 | + | 0.0415933i | \(0.0132434\pi\) |
0.348307 | + | 0.937380i | \(0.386757\pi\) | |||||||
\(542\) | −12.5244 | + | 4.06941i | −0.537967 | + | 0.174796i | ||||
\(543\) | − | 18.0626i | − | 0.775139i | ||||||
\(544\) | −0.584503 | − | 1.79892i | −0.0250604 | − | 0.0771279i | ||||
\(545\) | −16.7274 | + | 14.1771i | −0.716524 | + | 0.607281i | ||||
\(546\) | 0.146453 | − | 0.450735i | 0.00626760 | − | 0.0192897i | ||||
\(547\) | −28.8377 | − | 9.36994i | −1.23301 | − | 0.400630i | −0.381207 | − | 0.924490i | \(-0.624491\pi\) |
−0.851804 | + | 0.523860i | \(0.824491\pi\) | |||||||
\(548\) | 11.5262 | + | 15.8644i | 0.492374 | + | 0.677694i | ||||
\(549\) | 5.15131 | 0.219853 | ||||||||
\(550\) | 16.8188 | + | 17.0761i | 0.717156 | + | 0.728128i | ||||
\(551\) | −27.3580 | −1.16549 | ||||||||
\(552\) | −2.73076 | − | 3.75856i | −0.116229 | − | 0.159975i | ||||
\(553\) | −4.17661 | − | 1.35706i | −0.177608 | − | 0.0577082i | ||||
\(554\) | −1.59673 | + | 4.91424i | −0.0678387 | + | 0.208786i | ||||
\(555\) | 7.63876 | + | 18.6414i | 0.324247 | + | 0.791284i | ||||
\(556\) | 2.95579 | + | 9.09699i | 0.125353 | + | 0.385798i | ||||
\(557\) | 25.7254i | 1.09002i | 0.838430 | + | 0.545010i | \(0.183474\pi\) | ||||
−0.838430 | + | 0.545010i | \(0.816526\pi\) | |||||||
\(558\) | 3.64625 | − | 1.18474i | 0.154358 | − | 0.0501540i | ||||
\(559\) | −4.05158 | − | 2.94365i | −0.171364 | − | 0.124503i | ||||
\(560\) | 0.395350 | + | 0.466469i | 0.0167066 | + | 0.0197119i | ||||
\(561\) | −7.33541 | + | 5.32949i | −0.309701 | + | 0.225011i | ||||
\(562\) | −0.0276091 | + | 0.0380006i | −0.00116462 | + | 0.00160296i | ||||
\(563\) | −18.0058 | + | 24.7829i | −0.758854 | + | 1.04447i | 0.238454 | + | 0.971154i | \(0.423359\pi\) |
−0.997308 | + | 0.0733197i | \(0.976641\pi\) | |||||||
\(564\) | 0.961158 | − | 0.698322i | 0.0404721 | − | 0.0294047i | ||||
\(565\) | 25.0535 | + | 29.5604i | 1.05401 | + | 1.24361i | ||||
\(566\) | −17.6942 | − | 12.8556i | −0.743741 | − | 0.540359i | ||||
\(567\) | 0.260074 | − | 0.0845030i | 0.0109221 | − | 0.00354879i | ||||
\(568\) | 1.40217i | 0.0588337i | ||||||||
\(569\) | −3.85826 | − | 11.8745i | −0.161747 | − | 0.497805i | 0.837035 | − | 0.547149i | \(-0.184287\pi\) |
−0.998782 | + | 0.0493440i | \(0.984287\pi\) | |||||||
\(570\) | −2.55258 | − | 6.22925i | −0.106916 | − | 0.260915i | ||||
\(571\) | −7.52655 | + | 23.1644i | −0.314976 | + | 0.969398i | 0.660788 | + | 0.750573i | \(0.270222\pi\) |
−0.975764 | + | 0.218825i | \(0.929778\pi\) | |||||||
\(572\) | −7.90122 | − | 2.56726i | −0.330366 | − | 0.107343i | ||||
\(573\) | 9.75767 | + | 13.4303i | 0.407632 | + | 0.561058i | ||||
\(574\) | −2.07298 | −0.0865247 | ||||||||
\(575\) | 3.45958 | + | 22.9701i | 0.144274 | + | 0.957921i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.88827 | − | 2.59898i | −0.0786098 | − | 0.108197i | 0.767901 | − | 0.640568i | \(-0.221301\pi\) |
−0.846511 | + | 0.532371i | \(0.821301\pi\) | |||||||
\(578\) | 12.7653 | + | 4.14771i | 0.530968 | + | 0.172522i | ||||
\(579\) | −1.18928 | + | 3.66021i | −0.0494246 | + | 0.152113i | ||||
\(580\) | −15.5010 | + | 13.1377i | −0.643646 | + | 0.545514i | ||||
\(581\) | −1.27931 | − | 3.93731i | −0.0530747 | − | 0.163347i | ||||
\(582\) | − | 5.88597i | − | 0.243981i | ||||||
\(583\) | −52.9527 | + | 17.2054i | −2.19308 | + | 0.712574i | ||||
\(584\) | −1.44095 | − | 1.04691i | −0.0596271 | − | 0.0433216i | ||||
\(585\) | 0.289390 | + | 3.86452i | 0.0119648 | + | 0.159778i | ||||
\(586\) | 6.75763 | − | 4.90971i | 0.279155 | − | 0.202818i | ||||
\(587\) | −8.92797 | + | 12.2883i | −0.368497 | + | 0.507192i | −0.952491 | − | 0.304565i | \(-0.901489\pi\) |
0.583995 | + | 0.811757i | \(0.301489\pi\) | |||||||
\(588\) | −4.07054 | + | 5.60262i | −0.167866 | + | 0.231048i | ||||
\(589\) | −9.33801 | + | 6.78446i | −0.384766 | + | 0.279549i | ||||
\(590\) | 31.0409 | + | 7.57698i | 1.27793 | + | 0.311940i | ||||
\(591\) | −8.69145 | − | 6.31471i | −0.357518 | − | 0.259752i | ||||
\(592\) | 8.56851 | − | 2.78408i | 0.352164 | − | 0.114425i | ||||
\(593\) | 4.96989i | 0.204089i | 0.994780 | + | 0.102044i | \(0.0325384\pi\) | ||||
−0.994780 | + | 0.102044i | \(0.967462\pi\) | |||||||
\(594\) | −1.48131 | − | 4.55899i | −0.0607787 | − | 0.187058i | ||||
\(595\) | 1.15336 | − | 0.0863678i | 0.0472832 | − | 0.00354074i | ||||
\(596\) | −1.43507 | + | 4.41668i | −0.0587827 | + | 0.180914i | ||||
\(597\) | −2.37581 | − | 0.771949i | −0.0972356 | − | 0.0315938i | ||||
\(598\) | −4.73269 | − | 6.51400i | −0.193534 | − | 0.266377i | ||||
\(599\) | 3.23524 | 0.132188 | 0.0660942 | − | 0.997813i | \(-0.478946\pi\) | ||||
0.0660942 | + | 0.997813i | \(0.478946\pi\) | |||||||
\(600\) | −4.43767 | − | 2.30371i | −0.181167 | − | 0.0940484i | ||||
\(601\) | −8.78152 | −0.358205 | −0.179103 | − | 0.983830i | \(-0.557319\pi\) | ||||
−0.179103 | + | 0.983830i | \(0.557319\pi\) | |||||||
\(602\) | −0.464462 | − | 0.639277i | −0.0189301 | − | 0.0260550i | ||||
\(603\) | 5.98215 | + | 1.94372i | 0.243612 | + | 0.0791543i | ||||
\(604\) | 5.18780 | − | 15.9664i | 0.211089 | − | 0.649664i | ||||
\(605\) | −22.7847 | − | 14.0817i | −0.926331 | − | 0.572504i | ||||
\(606\) | −1.49433 | − | 4.59908i | −0.0607031 | − | 0.186825i | ||||
\(607\) | − | 39.5692i | − | 1.60606i | −0.595937 | − | 0.803031i | \(-0.703219\pi\) | ||
0.595937 | − | 0.803031i | \(-0.296781\pi\) | |||||||
\(608\) | −2.86327 | + | 0.930333i | −0.116121 | + | 0.0377300i | ||||
\(609\) | 2.01037 | + | 1.46062i | 0.0814642 | + | 0.0591872i | ||||
\(610\) | −6.05573 | + | 9.79837i | −0.245189 | + | 0.396725i | ||||
\(611\) | 1.66579 | − | 1.21027i | 0.0673907 | − | 0.0489622i | ||||
\(612\) | 1.11179 | − | 1.53025i | 0.0449415 | − | 0.0618566i | ||||
\(613\) | −27.5582 | + | 37.9307i | −1.11307 | + | 1.53201i | −0.296248 | + | 0.955111i | \(0.595736\pi\) |
−0.816819 | + | 0.576894i | \(0.804264\pi\) | |||||||
\(614\) | 1.85198 | − | 1.34554i | 0.0747399 | − | 0.0543017i | ||||
\(615\) | 15.6850 | − | 6.42732i | 0.632482 | − | 0.259174i | ||||
\(616\) | −1.06050 | − | 0.770497i | −0.0427287 | − | 0.0310442i | ||||
\(617\) | 13.4594 | − | 4.37322i | 0.541854 | − | 0.176059i | −0.0252863 | − | 0.999680i | \(-0.508050\pi\) |
0.567140 | + | 0.823621i | \(0.308050\pi\) | |||||||
\(618\) | 0.0729839i | 0.00293584i | ||||||||
\(619\) | 2.02304 | + | 6.22627i | 0.0813128 | + | 0.250255i | 0.983446 | − | 0.181203i | \(-0.0579992\pi\) |
−0.902133 | + | 0.431458i | \(0.857999\pi\) | |||||||
\(620\) | −2.03292 | + | 8.32833i | −0.0816440 | + | 0.334474i | ||||
\(621\) | 1.43564 | − | 4.41846i | 0.0576104 | − | 0.177307i | ||||
\(622\) | 24.4110 | + | 7.93163i | 0.978794 | + | 0.318029i | ||||
\(623\) | 2.38326 | + | 3.28028i | 0.0954833 | + | 0.131422i | ||||
\(624\) | 1.73311 | 0.0693798 | ||||||||
\(625\) | 14.3859 | + | 20.4462i | 0.575435 | + | 0.817848i | ||||
\(626\) | −30.2110 | −1.20747 | ||||||||
\(627\) | 8.48276 | + | 11.6755i | 0.338769 | + | 0.466275i | ||||
\(628\) | 5.30464 | + | 1.72358i | 0.211678 | + | 0.0687784i | ||||
\(629\) | 5.26606 | − | 16.2073i | 0.209972 | − | 0.646226i | ||||
\(630\) | −0.145000 | + | 0.594028i | −0.00577696 | + | 0.0236667i | ||||
\(631\) | 1.86919 | + | 5.75279i | 0.0744114 | + | 0.229015i | 0.981344 | − | 0.192262i | \(-0.0615822\pi\) |
−0.906932 | + | 0.421276i | \(0.861582\pi\) | |||||||
\(632\) | − | 16.0593i | − | 0.638806i | ||||||
\(633\) | −23.0860 | + | 7.50110i | −0.917586 | + | 0.298142i | ||||
\(634\) | 20.9222 | + | 15.2009i | 0.830927 | + | 0.603704i | ||||
\(635\) | 38.0044 | − | 15.5732i | 1.50816 | − | 0.618004i | ||||
\(636\) | 9.39675 | − | 6.82714i | 0.372605 | − | 0.270714i | ||||
\(637\) | −7.05469 | + | 9.70994i | −0.279517 | + | 0.384722i | ||||
\(638\) | 25.6041 | − | 35.2410i | 1.01367 | − | 1.39520i | ||||
\(639\) | −1.13438 | + | 0.824175i | −0.0448753 | + | 0.0326038i | ||||
\(640\) | −1.17557 | + | 1.90211i | −0.0464685 | + | 0.0751876i | ||||
\(641\) | −26.1185 | − | 18.9762i | −1.03162 | − | 0.749515i | −0.0629869 | − | 0.998014i | \(-0.520063\pi\) |
−0.968632 | + | 0.248499i | \(0.920063\pi\) | |||||||
\(642\) | −5.56134 | + | 1.80699i | −0.219489 | + | 0.0713161i | ||||
\(643\) | − | 12.1187i | − | 0.477914i | −0.971030 | − | 0.238957i | \(-0.923194\pi\) | ||
0.971030 | − | 0.238957i | \(-0.0768056\pi\) | |||||||
\(644\) | −0.392588 | − | 1.20826i | −0.0154701 | − | 0.0476121i | ||||
\(645\) | 5.49640 | + | 3.39696i | 0.216420 | + | 0.133755i | ||||
\(646\) | −1.75972 | + | 5.41585i | −0.0692352 | + | 0.213084i | ||||
\(647\) | 19.2386 | + | 6.25100i | 0.756348 | + | 0.245752i | 0.661710 | − | 0.749760i | \(-0.269831\pi\) |
0.0946373 | + | 0.995512i | \(0.469831\pi\) | |||||||
\(648\) | 0.587785 | + | 0.809017i | 0.0230904 | + | 0.0317812i | ||||
\(649\) | −68.4982 | −2.68879 | ||||||||
\(650\) | −7.69096 | − | 3.99257i | −0.301664 | − | 0.156601i | ||||
\(651\) | 1.04841 | 0.0410904 | ||||||||
\(652\) | −10.8007 | − | 14.8659i | −0.422989 | − | 0.582194i | ||||
\(653\) | −31.7499 | − | 10.3162i | −1.24247 | − | 0.403702i | −0.387252 | − | 0.921974i | \(-0.626576\pi\) |
−0.855216 | + | 0.518271i | \(0.826576\pi\) | |||||||
\(654\) | −3.03025 | + | 9.32615i | −0.118492 | + | 0.364681i | ||||
\(655\) | −16.8877 | + | 1.26462i | −0.659858 | + | 0.0494126i | ||||
\(656\) | −2.34255 | − | 7.20962i | −0.0914611 | − | 0.281488i | ||||
\(657\) | − | 1.78112i | − | 0.0694880i | ||||||
\(658\) | 0.308982 | − | 0.100394i | 0.0120454 | − | 0.00391378i | ||||
\(659\) | −24.5894 | − | 17.8653i | −0.957869 | − | 0.695932i | −0.00521401 | − | 0.999986i | \(-0.501660\pi\) |
−0.952655 | + | 0.304054i | \(0.901660\pi\) | |||||||
\(660\) | 10.4131 | + | 2.54180i | 0.405329 | + | 0.0989395i | ||||
\(661\) | −20.1744 | + | 14.6576i | −0.784694 | + | 0.570114i | −0.906384 | − | 0.422455i | \(-0.861169\pi\) |
0.121690 | + | 0.992568i | \(0.461169\pi\) | |||||||
\(662\) | 8.52842 | − | 11.7384i | 0.331466 | − | 0.456224i | ||||
\(663\) | 1.92685 | − | 2.65208i | 0.0748327 | − | 0.102998i | ||||
\(664\) | 12.2479 | − | 8.89861i | 0.475310 | − | 0.345333i | ||||
\(665\) | −0.137469 | − | 1.83576i | −0.00533081 | − | 0.0711879i | ||||
\(666\) | 7.28881 | + | 5.29563i | 0.282436 | + | 0.205202i | ||||
\(667\) | 40.1512 | − | 13.0459i | 1.55466 | − | 0.505140i | ||||
\(668\) | 8.94427i | 0.346064i | ||||||||
\(669\) | −4.03389 | − | 12.4150i | −0.155959 | − | 0.479993i | ||||
\(670\) | −10.7296 | + | 9.09374i | −0.414521 | + | 0.351322i | ||||
\(671\) | 7.63066 | − | 23.4848i | 0.294578 | − | 0.906619i | ||||
\(672\) | 0.260074 | + | 0.0845030i | 0.0100326 | + | 0.00325977i | ||||
\(673\) | 27.0791 | + | 37.2711i | 1.04382 | + | 1.43670i | 0.894045 | + | 0.447977i | \(0.147855\pi\) |
0.149777 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(674\) | 11.0676 | 0.426307 | ||||||||
\(675\) | −0.744661 | − | 4.94424i | −0.0286620 | − | 0.190304i | ||||
\(676\) | −9.99634 | −0.384475 | ||||||||
\(677\) | 16.8060 | + | 23.1315i | 0.645908 | + | 0.889016i | 0.998913 | − | 0.0466053i | \(-0.0148403\pi\) |
−0.353006 | + | 0.935621i | \(0.614840\pi\) | |||||||
\(678\) | 16.4810 | + | 5.35500i | 0.632949 | + | 0.205658i | ||||
\(679\) | 0.497382 | − | 1.53078i | 0.0190878 | − | 0.0587461i | ||||
\(680\) | 1.60372 | + | 3.91367i | 0.0614998 | + | 0.150082i | ||||
\(681\) | 2.18213 | + | 6.71592i | 0.0836196 | + | 0.257355i | ||||
\(682\) | − | 18.3782i | − | 0.703737i | ||||||
\(683\) | −8.49047 | + | 2.75872i | −0.324879 | + | 0.105560i | −0.466916 | − | 0.884302i | \(-0.654635\pi\) |
0.142037 | + | 0.989861i | \(0.454635\pi\) | |||||||
\(684\) | −2.43564 | − | 1.76960i | −0.0931292 | − | 0.0676623i | ||||
\(685\) | −28.3503 | − | 33.4502i | −1.08321 | − | 1.27807i | ||||
\(686\) | −3.08070 | + | 2.23826i | −0.117622 | + | 0.0854572i | ||||
\(687\) | 7.39264 | − | 10.1751i | 0.282047 | − | 0.388204i | ||||
\(688\) | 1.69848 | − | 2.33776i | 0.0647539 | − | 0.0891262i | ||||
\(689\) | 16.2856 | − | 11.8322i | 0.620431 | − | 0.450769i | ||||
\(690\) | 6.71671 | + | 7.92497i | 0.255701 | + | 0.301698i | ||||
\(691\) | 1.06206 | + | 0.771634i | 0.0404028 | + | 0.0293543i | 0.607803 | − | 0.794088i | \(-0.292051\pi\) |
−0.567401 | + | 0.823442i | \(0.692051\pi\) | |||||||
\(692\) | 11.3320 | − | 3.68198i | 0.430777 | − | 0.139968i | ||||
\(693\) | − | 1.31085i | − | 0.0497950i | ||||||
\(694\) | 0.312299 | + | 0.961158i | 0.0118547 | + | 0.0364851i | ||||
\(695\) | −8.10989 | − | 19.7911i | −0.307626 | − | 0.750721i | ||||
\(696\) | −2.80808 | + | 8.64240i | −0.106440 | + | 0.327589i | ||||
\(697\) | −13.6369 | − | 4.43091i | −0.516536 | − | 0.167833i | ||||
\(698\) | 17.8845 | + | 24.6158i | 0.676936 | + | 0.931723i | ||||
\(699\) | 9.80527 | 0.370869 | ||||||||
\(700\) | −0.959451 | − | 0.974130i | −0.0362638 | − | 0.0368186i | ||||
\(701\) | 22.5267 | 0.850822 | 0.425411 | − | 0.905000i | \(-0.360130\pi\) | ||||
0.425411 | + | 0.905000i | \(0.360130\pi\) | |||||||
\(702\) | 1.01869 | + | 1.40211i | 0.0384482 | + | 0.0529193i | ||||
\(703\) | −25.7966 | − | 8.38181i | −0.972935 | − | 0.316126i | ||||
\(704\) | 1.48131 | − | 4.55899i | 0.0558288 | − | 0.171823i | ||||
\(705\) | −2.02661 | + | 1.71763i | −0.0763266 | + | 0.0646896i | ||||
\(706\) | −4.83911 | − | 14.8932i | −0.182122 | − | 0.560515i | ||||
\(707\) | − | 1.32238i | − | 0.0497331i | ||||||
\(708\) | 13.5901 | − | 4.41570i | 0.510748 | − | 0.165952i | ||||
\(709\) | −5.57914 | − | 4.05348i | −0.209529 | − | 0.152232i | 0.478072 | − | 0.878321i | \(-0.341336\pi\) |
−0.687600 | + | 0.726089i | \(0.741336\pi\) | |||||||
\(710\) | −0.234131 | − | 3.12659i | −0.00878677 | − | 0.117339i | ||||
\(711\) | 12.9923 | − | 9.43945i | 0.487249 | − | 0.354007i | ||||
\(712\) | −8.71529 | + | 11.9956i | −0.326619 | + | 0.449553i | ||||
\(713\) | 10.4694 | − | 14.4100i | 0.392084 | − | 0.539657i | ||||
\(714\) | 0.418458 | − | 0.304027i | 0.0156604 | − | 0.0113779i | ||||
\(715\) | 18.0470 | + | 4.40522i | 0.674920 | + | 0.164746i | ||||
\(716\) | 3.03884 | + | 2.20785i | 0.113567 | + | 0.0825111i | ||||
\(717\) | 4.79360 | − | 1.55754i | 0.179020 | − | 0.0581673i | ||||
\(718\) | − | 4.37321i | − | 0.163207i | ||||||
\(719\) | −8.75827 | − | 26.9552i | −0.326628 | − | 1.00526i | −0.970700 | − | 0.240293i | \(-0.922756\pi\) |
0.644072 | − | 0.764965i | \(-0.277244\pi\) | |||||||
\(720\) | −2.22982 | + | 0.166977i | −0.0831007 | + | 0.00622288i | ||||
\(721\) | −0.00616736 | + | 0.0189812i | −0.000229684 | + | 0.000706896i | ||||
\(722\) | −9.44985 | − | 3.07044i | −0.351687 | − | 0.114270i | ||||
\(723\) | −4.02102 | − | 5.53446i | −0.149543 | − | 0.205829i | ||||
\(724\) | 18.0626 | 0.671290 | ||||||||
\(725\) | 32.3709 | − | 31.8831i | 1.20223 | − | 1.18411i | ||||
\(726\) | −11.9786 | −0.444569 | ||||||||
\(727\) | 10.0395 | + | 13.8182i | 0.372344 | + | 0.512487i | 0.953536 | − | 0.301279i | \(-0.0974135\pi\) |
−0.581192 | + | 0.813766i | \(0.697414\pi\) | |||||||
\(728\) | 0.450735 | + | 0.146453i | 0.0167054 | + | 0.00542790i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 3.38789 | + | 2.09383i | 0.125391 | + | 0.0774961i | ||||
\(731\) | −1.68900 | − | 5.19819i | −0.0624698 | − | 0.192262i | ||||
\(732\) | 5.15131i | 0.190398i | ||||||||
\(733\) | 11.3102 | − | 3.67491i | 0.417753 | − | 0.135736i | −0.0925958 | − | 0.995704i | \(-0.529516\pi\) |
0.510348 | + | 0.859968i | \(0.329516\pi\) | |||||||
\(734\) | −17.6636 | − | 12.8333i | −0.651975 | − | 0.473687i | ||||
\(735\) | 8.14109 | − | 13.1726i | 0.300288 | − | 0.485877i | ||||
\(736\) | 3.75856 | − | 2.73076i | 0.138543 | − | 0.100657i | ||||
\(737\) | 17.7228 | − | 24.3933i | 0.652827 | − | 0.898539i | ||||
\(738\) | 4.45579 | − | 6.13287i | 0.164020 | − | 0.225754i | ||||
\(739\) | 9.27173 | − | 6.73631i | 0.341066 | − | 0.247799i | −0.404045 | − | 0.914739i | \(-0.632396\pi\) |
0.745112 | + | 0.666940i | \(0.232396\pi\) | |||||||
\(740\) | −18.6414 | + | 7.63876i | −0.685272 | + | 0.280806i | ||||
\(741\) | −4.22123 | − | 3.06690i | −0.155071 | − | 0.112666i | ||||
\(742\) | 3.02076 | − | 0.981504i | 0.110896 | − | 0.0360321i | ||||
\(743\) | 8.64114i | 0.317013i | 0.987358 | + | 0.158506i | \(0.0506678\pi\) | ||||
−0.987358 | + | 0.158506i | \(0.949332\pi\) | |||||||
\(744\) | 1.18474 | + | 3.64625i | 0.0434347 | + | 0.133678i | ||||
\(745\) | 2.46246 | − | 10.0881i | 0.0902177 | − | 0.369598i | ||||
\(746\) | 0.438406 | − | 1.34928i | 0.0160512 | − | 0.0494005i | ||||
\(747\) | 14.3983 | + | 4.67828i | 0.526805 | + | 0.171169i | ||||
\(748\) | −5.32949 | − | 7.33541i | −0.194865 | − | 0.268209i | ||||
\(749\) | −1.59905 | −0.0584281 | ||||||||
\(750\) | 10.2799 | + | 4.39587i | 0.375369 | + | 0.160514i | ||||
\(751\) | −8.45998 | −0.308709 | −0.154354 | − | 0.988016i | \(-0.549330\pi\) | ||||
−0.154354 | + | 0.988016i | \(0.549330\pi\) | |||||||
\(752\) | 0.698322 | + | 0.961158i | 0.0254652 | + | 0.0350498i | ||||
\(753\) | −6.72919 | − | 2.18645i | −0.245225 | − | 0.0796786i | ||||
\(754\) | −4.86671 | + | 14.9782i | −0.177235 | + | 0.545474i | ||||
\(755\) | −8.90186 | + | 36.4685i | −0.323972 | + | 1.32723i | ||||
\(756\) | 0.0845030 | + | 0.260074i | 0.00307334 | + | 0.00945878i | ||||
\(757\) | 53.6675i | 1.95058i | 0.220932 | + | 0.975289i | \(0.429090\pi\) | ||||
−0.220932 | + | 0.975289i | \(0.570910\pi\) | |||||||
\(758\) | −24.8041 | + | 8.05934i | −0.900926 | + | 0.292729i | ||||
\(759\) | −18.0171 | − | 13.0902i | −0.653978 | − | 0.475143i | ||||
\(760\) | 6.22925 | − | 2.55258i | 0.225959 | − | 0.0925919i | ||||
\(761\) | −9.52327 | + | 6.91906i | −0.345218 | + | 0.250816i | −0.746860 | − | 0.664981i | \(-0.768440\pi\) |
0.401642 | + | 0.915797i | \(0.368440\pi\) | |||||||
\(762\) | 10.7963 | − | 14.8598i | 0.391107 | − | 0.538313i | ||||
\(763\) | −1.57617 | + | 2.16942i | −0.0570614 | + | 0.0785382i | ||||
\(764\) | −13.4303 | + | 9.75767i | −0.485890 | + | 0.353020i | ||||
\(765\) | −2.22358 | + | 3.59783i | −0.0803938 | + | 0.130080i | ||||
\(766\) | −26.5071 | − | 19.2585i | −0.957739 | − | 0.695838i | ||||
\(767\) | 23.5531 | − | 7.65287i | 0.850454 | − | 0.276329i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −1.57472 | − | 4.84650i | −0.0567859 | − | 0.174769i | 0.918641 | − | 0.395094i | \(-0.129288\pi\) |
−0.975426 | + | 0.220325i | \(0.929288\pi\) | |||||||
\(770\) | 2.49338 | + | 1.54099i | 0.0898551 | + | 0.0555335i | ||||
\(771\) | 1.38229 | − | 4.25424i | 0.0497819 | − | 0.153213i | ||||
\(772\) | −3.66021 | − | 1.18928i | −0.131734 | − | 0.0428030i | ||||
\(773\) | 7.41916 | + | 10.2116i | 0.266849 | + | 0.367285i | 0.921323 | − | 0.388799i | \(-0.127110\pi\) |
−0.654474 | + | 0.756084i | \(0.727110\pi\) | |||||||
\(774\) | 2.88963 | 0.103865 | ||||||||
\(775\) | 3.14241 | − | 18.9102i | 0.112879 | − | 0.679274i | ||||
\(776\) | 5.88597 | 0.211294 | ||||||||
\(777\) | 1.44813 | + | 1.99318i | 0.0519514 | + | 0.0715050i | ||||
\(778\) | 4.24298 | + | 1.37863i | 0.152118 | + | 0.0494262i | ||||
\(779\) | −7.05253 | + | 21.7054i | −0.252683 | + | 0.777678i | ||||
\(780\) | −3.86452 | + | 0.289390i | −0.138372 | + | 0.0103618i | ||||
\(781\) | 2.07704 | + | 6.39247i | 0.0743224 | + | 0.228741i | ||||
\(782\) | − | 8.78757i | − | 0.314243i | ||||||
\(783\) | −8.64240 | + | 2.80808i | −0.308854 | + | 0.100353i | ||||
\(784\) | −5.60262 | − | 4.07054i | −0.200094 | − | 0.145377i | ||||
\(785\) | −12.1162 | − | 2.95753i | −0.432446 | − | 0.105559i | ||||
\(786\) | −6.12715 | + | 4.45163i | −0.218548 | + | 0.158784i | ||||
\(787\) | 25.9859 | − | 35.7665i | 0.926296 | − | 1.27494i | −0.0349910 | − | 0.999388i | \(-0.511140\pi\) |
0.961287 | − | 0.275549i | \(-0.0888597\pi\) | |||||||
\(788\) | 6.31471 | − | 8.69145i | 0.224952 | − | 0.309620i | ||||
\(789\) | 2.02442 | − | 1.47083i | 0.0720712 | − | 0.0523628i | ||||
\(790\) | 2.68155 | + | 35.8095i | 0.0954052 | + | 1.27405i | ||||
\(791\) | 3.83376 | + | 2.78539i | 0.136313 | + | 0.0990370i | ||||
\(792\) | 4.55899 | − | 1.48131i | 0.161997 | − | 0.0526359i | ||||
\(793\) | 8.92777i | 0.317034i | ||||||||
\(794\) | −0.654271 | − | 2.01364i | −0.0232192 | − | 0.0714614i | ||||
\(795\) | −19.8131 | + | 16.7924i | −0.702699 | + | 0.595564i | ||||
\(796\) | 0.771949 | − | 2.37581i | 0.0273610 | − | 0.0842085i | ||||
\(797\) | 44.0719 | + | 14.3198i | 1.56111 | + | 0.507235i | 0.957103 | − | 0.289746i | \(-0.0935710\pi\) |
0.604004 | + | 0.796981i | \(0.293571\pi\) | |||||||
\(798\) | −0.483910 | − | 0.666045i | −0.0171302 | − | 0.0235777i | ||||
\(799\) | 2.24720 | 0.0795002 | ||||||||
\(800\) | 2.30371 | − | 4.43767i | 0.0814483 | − | 0.156895i | ||||
\(801\) | −14.8273 | −0.523898 | ||||||||
\(802\) | 16.8418 | + | 23.1808i | 0.594705 | + | 0.818541i | ||||
\(803\) | −8.12010 | − | 2.63838i | −0.286552 | − | 0.0931064i | ||||
\(804\) | −1.94372 | + | 5.98215i | −0.0685496 | + | 0.210974i | ||||
\(805\) | 1.07715 | + | 2.62866i | 0.0379647 | + | 0.0926479i | ||||
\(806\) | 2.05328 | + | 6.31935i | 0.0723237 | + | 0.222590i | ||||
\(807\) | − | 6.18870i | − | 0.217853i | ||||||
\(808\) | 4.59908 | − | 1.49433i | 0.161795 | − | 0.0525705i | ||||
\(809\) | 40.0393 | + | 29.0902i | 1.40771 | + | 1.02276i | 0.993651 | + | 0.112507i | \(0.0358881\pi\) |
0.414056 | + | 0.910252i | \(0.364112\pi\) | |||||||
\(810\) | −1.44575 | − | 1.70582i | −0.0507983 | − | 0.0599364i | ||||
\(811\) | 2.27136 | − | 1.65024i | 0.0797583 | − | 0.0579478i | −0.547192 | − | 0.837007i | \(-0.684303\pi\) |
0.626950 | + | 0.779060i | \(0.284303\pi\) | |||||||
\(812\) | −1.46062 | + | 2.01037i | −0.0512576 | + | 0.0705500i | ||||
\(813\) | 7.74048 | − | 10.6539i | 0.271471 | − | 0.373647i | ||||
\(814\) | 34.9397 | − | 25.3852i | 1.22464 | − | 0.889750i | ||||
\(815\) | 26.5660 | + | 31.3449i | 0.930566 | + | 1.09796i | ||||
\(816\) | 1.53025 | + | 1.11179i | 0.0535694 | + | 0.0389205i | ||||
\(817\) | −8.27378 | + | 2.68832i | −0.289463 | + | 0.0940523i | ||||
\(818\) | − | 39.3546i | − | 1.37600i | ||||||
\(819\) | 0.146453 | + | 0.450735i | 0.00511747 | + | 0.0157500i | ||||
\(820\) | 6.42732 | + | 15.6850i | 0.224452 | + | 0.547745i | ||||
\(821\) | −11.5462 | + | 35.5356i | −0.402965 | + | 1.24020i | 0.519617 | + | 0.854399i | \(0.326075\pi\) |
−0.922582 | + | 0.385800i | \(0.873925\pi\) | |||||||
\(822\) | −18.6497 | − | 6.05967i | −0.650484 | − | 0.211355i | ||||
\(823\) | 13.4238 | + | 18.4763i | 0.467925 | + | 0.644044i | 0.976129 | − | 0.217193i | \(-0.0696902\pi\) |
−0.508203 | + | 0.861237i | \(0.669690\pi\) | |||||||
\(824\) | −0.0729839 | −0.00254251 | ||||||||
\(825\) | −23.6438 | − | 3.92902i | −0.823171 | − | 0.136791i | ||||
\(826\) | 3.90757 | 0.135962 | ||||||||
\(827\) | 6.29560 | + | 8.66515i | 0.218919 | + | 0.301317i | 0.904325 | − | 0.426845i | \(-0.140375\pi\) |
−0.685405 | + | 0.728162i | \(0.740375\pi\) | |||||||
\(828\) | 4.41846 | + | 1.43564i | 0.153552 | + | 0.0498921i | ||||
\(829\) | 8.52760 | − | 26.2453i | 0.296176 | − | 0.911536i | −0.686648 | − | 0.726990i | \(-0.740919\pi\) |
0.982824 | − | 0.184546i | \(-0.0590814\pi\) | |||||||
\(830\) | −25.8248 | + | 21.8875i | −0.896391 | + | 0.759725i | ||||
\(831\) | −1.59673 | − | 4.91424i | −0.0553901 | − | 0.170473i | ||||
\(832\) | 1.73311i | 0.0600847i | ||||||||
\(833\) | −12.4579 | + | 4.04781i | −0.431640 | + | 0.140248i | ||||
\(834\) | −7.73836 | − | 5.62225i | −0.267958 | − | 0.194683i | ||||
\(835\) | −1.49349 | − | 19.9442i | −0.0516844 | − | 0.690196i | ||||
\(836\) | −11.6755 | + | 8.48276i | −0.403806 | + | 0.293382i | ||||
\(837\) | −2.25351 | + | 3.10169i | −0.0778927 | + | 0.107210i | ||||
\(838\) | −8.29180 | + | 11.4127i | −0.286435 | + | 0.394244i | ||||
\(839\) | −8.03884 | + | 5.84056i | −0.277532 | + | 0.201639i | −0.717840 | − | 0.696208i | \(-0.754869\pi\) |
0.440308 | + | 0.897847i | \(0.354869\pi\) | |||||||
\(840\) | −0.594028 | − | 0.145000i | −0.0204959 | − | 0.00500299i | ||||
\(841\) | −43.3442 | − | 31.4914i | −1.49463 | − | 1.08591i | ||||
\(842\) | −15.5066 | + | 5.03839i | −0.534392 | + | 0.173634i | ||||
\(843\) | − | 0.0469714i | − | 0.00161778i | ||||||
\(844\) | −7.50110 | − | 23.0860i | −0.258198 | − | 0.794653i | ||||
\(845\) | 22.2901 | − | 1.66916i | 0.766802 | − | 0.0574210i | ||||
\(846\) | −0.367130 | + | 1.12991i | −0.0126222 | + | 0.0388471i | ||||
\(847\) | −3.11533 | − | 1.01223i | −0.107044 | − | 0.0347807i | ||||
\(848\) | 6.82714 | + | 9.39675i | 0.234445 | + | 0.322686i | ||||
\(849\) | 21.8712 | 0.750617 | ||||||||
\(850\) | −4.22950 | − | 8.45901i | −0.145071 | − | 0.290142i | ||||
\(851\) | 41.8566 | 1.43482 | ||||||||
\(852\) | −0.824175 | − | 1.13438i | −0.0282358 | − | 0.0388632i | ||||
\(853\) | 42.8052 | + | 13.9083i | 1.46562 | + | 0.476210i | 0.929782 | − | 0.368110i | \(-0.119995\pi\) |
0.535840 | + | 0.844319i | \(0.319995\pi\) | |||||||
\(854\) | −0.435301 | + | 1.33972i | −0.0148957 | + | 0.0458442i | ||||
\(855\) | 5.72654 | + | 3.53920i | 0.195844 | + | 0.121038i | ||||
\(856\) | −1.80699 | − | 5.56134i | −0.0617616 | − | 0.190083i | ||||
\(857\) | − | 24.6986i | − | 0.843686i | −0.906669 | − | 0.421843i | \(-0.861383\pi\) | ||
0.906669 | − | 0.421843i | \(-0.138617\pi\) | |||||||
\(858\) | 7.90122 | − | 2.56726i | 0.269743 | − | 0.0876448i | ||||
\(859\) | −14.0283 | − | 10.1922i | −0.478641 | − | 0.347753i | 0.322159 | − | 0.946686i | \(-0.395592\pi\) |
−0.800799 | + | 0.598933i | \(0.795592\pi\) | |||||||
\(860\) | −3.39696 | + | 5.49640i | −0.115835 | + | 0.187426i | ||||
\(861\) | 1.67708 | − | 1.21847i | 0.0571547 | − | 0.0415253i | ||||
\(862\) | −1.16509 | + | 1.60361i | −0.0396832 | + | 0.0546192i | ||||
\(863\) | −15.2158 | + | 20.9428i | −0.517954 | + | 0.712902i | −0.985235 | − | 0.171207i | \(-0.945233\pi\) |
0.467282 | + | 0.884109i | \(0.345233\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | −24.6535 | + | 10.1023i | −0.838243 | + | 0.343490i | ||||
\(866\) | −3.63203 | − | 2.63882i | −0.123421 | − | 0.0896709i | ||||
\(867\) | −12.7653 | + | 4.14771i | −0.433533 | + | 0.140863i | ||||
\(868\) | 1.04841i | 0.0355853i | ||||||||
\(869\) | −23.7888 | − | 73.2144i | −0.806979 | − | 2.48363i | ||||
\(870\) | 4.81845 | − | 19.7399i | 0.163361 | − | 0.669246i | ||||
\(871\) | −3.36867 | + | 10.3677i | −0.114143 | + | 0.351296i | ||||
\(872\) | −9.32615 | − | 3.03025i | −0.315823 | − | 0.102617i | ||||
\(873\) | 3.45968 | + | 4.76185i | 0.117093 | + | 0.161164i | ||||
\(874\) | −13.9869 | −0.473113 | ||||||||
\(875\) | 2.30207 | + | 2.01193i | 0.0778240 | + | 0.0680157i | ||||
\(876\) | 1.78112 | 0.0601784 | ||||||||
\(877\) | 11.8673 | + | 16.3339i | 0.400729 | + | 0.551557i | 0.960927 | − | 0.276802i | \(-0.0892748\pi\) |
−0.560198 | + | 0.828359i | \(0.689275\pi\) | |||||||
\(878\) | −24.4572 | − | 7.94662i | −0.825390 | − | 0.268185i | ||||
\(879\) | −2.58119 | + | 7.94407i | −0.0870612 | + | 0.267947i | ||||
\(880\) | −2.54180 | + | 10.4131i | −0.0856842 | + | 0.351025i | ||||
\(881\) | 7.34633 | + | 22.6097i | 0.247504 | + | 0.761739i | 0.995215 | + | 0.0977143i | \(0.0311531\pi\) |
−0.747710 | + | 0.664025i | \(0.768847\pi\) | |||||||
\(882\) | − | 6.92522i | − | 0.233184i | ||||||
\(883\) | −30.9842 | + | 10.0674i | −1.04270 | + | 0.338794i | −0.779800 | − | 0.626029i | \(-0.784679\pi\) |
−0.262900 | + | 0.964823i | \(0.584679\pi\) | |||||||
\(884\) | 2.65208 | + | 1.92685i | 0.0891993 | + | 0.0648071i | ||||
\(885\) | −29.5663 | + | 12.1155i | −0.993859 | + | 0.407257i | ||||
\(886\) | −23.5809 | + | 17.1326i | −0.792217 | + | 0.575580i | ||||
\(887\) | −33.1027 | + | 45.5619i | −1.11148 | + | 1.52982i | −0.292261 | + | 0.956339i | \(0.594408\pi\) |
−0.819218 | + | 0.573482i | \(0.805592\pi\) | |||||||
\(888\) | −5.29563 | + | 7.28881i | −0.177710 | + | 0.244597i | ||||
\(889\) | 4.06351 | − | 2.95232i | 0.136286 | − | 0.0990175i | ||||
\(890\) | 17.4306 | − | 28.2033i | 0.584274 | − | 0.945376i | ||||
\(891\) | 3.87811 | + | 2.81761i | 0.129921 | + | 0.0943935i | ||||
\(892\) | 12.4150 | − | 4.03389i | 0.415686 | − | 0.135065i | ||||
\(893\) | − | 3.57679i | − | 0.119693i | ||||||
\(894\) | −1.43507 | − | 4.41668i | −0.0479958 | − | 0.147716i | ||||
\(895\) | −7.14475 | − | 4.41570i | −0.238823 | − | 0.147600i | ||||
\(896\) | −0.0845030 | + | 0.260074i | −0.00282305 | + | 0.00868845i | ||||
\(897\) | 7.65766 | + | 2.48812i | 0.255682 | + | 0.0830761i | ||||
\(898\) | −3.02144 | − | 4.15865i | −0.100827 | − | 0.138776i | ||||
\(899\) | −34.8392 | −1.16195 | ||||||||
\(900\) | 4.94424 | − | 0.744661i | 0.164808 | − | 0.0248220i | ||||
\(901\) | 21.9697 | 0.731917 | ||||||||
\(902\) | −21.3593 | − | 29.3986i | −0.711187 | − | 0.978865i | ||||
\(903\) | 0.751515 | + | 0.244182i | 0.0250089 | + | 0.00812587i | ||||
\(904\) | −5.35500 | + | 16.4810i | −0.178105 | + | 0.548150i | ||||
\(905\) | −40.2764 | + | 3.01604i | −1.33883 | + | 0.100257i | ||||
\(906\) | 5.18780 | + | 15.9664i | 0.172353 | + | 0.530449i | ||||
\(907\) | − | 46.7617i | − | 1.55270i | −0.630304 | − | 0.776349i | \(-0.717070\pi\) | ||
0.630304 | − | 0.776349i | \(-0.282930\pi\) | |||||||
\(908\) | −6.71592 | + | 2.18213i | −0.222876 | + | 0.0724167i | ||||
\(909\) | 3.91221 | + | 2.84239i | 0.129760 | + | 0.0942761i | ||||
\(910\) | −1.02951 | − | 0.251301i | −0.0341281 | − | 0.00833056i | ||||
\(911\) | 13.5487 | − | 9.84374i | 0.448890 | − | 0.326138i | −0.340268 | − | 0.940329i | \(-0.610518\pi\) |
0.789157 | + | 0.614191i | \(0.210518\pi\) | |||||||
\(912\) | 1.76960 | − | 2.43564i | 0.0585973 | − | 0.0806522i | ||||
\(913\) | 42.6564 | − | 58.7115i | 1.41172 | − | 1.94307i | ||||
\(914\) | −16.8636 | + | 12.2521i | −0.557797 | + | 0.405263i | ||||
\(915\) | −0.860153 | − | 11.4865i | −0.0284358 | − | 0.379733i | ||||
\(916\) | 10.1751 | + | 7.39264i | 0.336195 | + | 0.244260i | ||||
\(917\) | −1.96968 | + | 0.639989i | −0.0650447 | + | 0.0211343i | ||||
\(918\) | 1.89149i | 0.0624285i | ||||||||
\(919\) | 1.58373 | + | 4.87423i | 0.0522426 | + | 0.160786i | 0.973774 | − | 0.227518i | \(-0.0730610\pi\) |
−0.921531 | + | 0.388304i | \(0.873061\pi\) | |||||||
\(920\) | −7.92497 | + | 6.71671i | −0.261278 | + | 0.221443i | ||||
\(921\) | −0.707394 | + | 2.17714i | −0.0233094 | + | 0.0717391i | ||||
\(922\) | −4.72664 | − | 1.53578i | −0.155664 | − | 0.0505782i | ||||
\(923\) | −1.42838 | − | 1.96600i | −0.0470158 | − | 0.0647117i | ||||
\(924\) | 1.31085 | 0.0431237 | ||||||||
\(925\) | 40.2916 | − | 20.1458i | 1.32478 | − | 0.662389i | ||||
\(926\) | −7.10664 | −0.233539 | ||||||||
\(927\) | −0.0428988 | − | 0.0590452i | −0.00140898 | − | 0.00193930i | ||||
\(928\) | −8.64240 | − | 2.80808i | −0.283701 | − | 0.0921799i | ||||
\(929\) | −14.0119 | + | 43.1241i | −0.459715 | + | 1.41486i | 0.405795 | + | 0.913964i | \(0.366995\pi\) |
−0.865510 | + | 0.500892i | \(0.833005\pi\) | |||||||
\(930\) | −3.25060 | − | 7.93268i | −0.106592 | − | 0.260123i | ||||
\(931\) | 6.44276 | + | 19.8288i | 0.211153 | + | 0.649862i | ||||
\(932\) | 9.80527i | 0.321182i | ||||||||
\(933\) | −24.4110 | + | 7.93163i | −0.799182 | + | 0.259670i | ||||
\(934\) | 24.4179 | + | 17.7406i | 0.798977 | + | 0.580491i | ||||
\(935\) | 13.1087 | + | 15.4668i | 0.428699 | + | 0.505817i | ||||
\(936\) | −1.40211 | + | 1.01869i | −0.0458295 | + | 0.0332971i | ||||
\(937\) | −18.2283 | + | 25.0891i | −0.595493 | + | 0.819626i | −0.995286 | − | 0.0969794i | \(-0.969082\pi\) |
0.399793 | + | 0.916605i | \(0.369082\pi\) | |||||||
\(938\) | −1.01102 | + | 1.39155i | −0.0330109 | + | 0.0454356i | ||||
\(939\) | 24.4412 | − | 17.7576i | 0.797608 | − | 0.579496i | ||||
\(940\) | −1.71763 | − | 2.02661i | −0.0560229 | − | 0.0661007i | ||||
\(941\) | 39.0847 | + | 28.3967i | 1.27412 | + | 0.925705i | 0.999359 | − | 0.0358067i | \(-0.0114001\pi\) |
0.274765 | + | 0.961512i | \(0.411400\pi\) | |||||||
\(942\) | −5.30464 | + | 1.72358i | −0.172834 | + | 0.0561573i | ||||
\(943\) | − | 35.2185i | − | 1.14687i | ||||||
\(944\) | 4.41570 | + | 13.5901i | 0.143719 | + | 0.442321i | ||||
\(945\) | −0.231853 | − | 0.565808i | −0.00754219 | − | 0.0184057i | ||||
\(946\) | 4.28042 | − | 13.1738i | 0.139168 | − | 0.428316i | ||||
\(947\) | −31.7532 | − | 10.3172i | −1.03184 | − | 0.335265i | −0.256322 | − | 0.966591i | \(-0.582511\pi\) |
−0.775517 | + | 0.631327i | \(0.782511\pi\) | |||||||
\(948\) | 9.43945 | + | 12.9923i | 0.306579 | + | 0.421970i | ||||
\(949\) | 3.08687 | 0.100204 | ||||||||
\(950\) | −13.4639 | + | 6.73195i | −0.436827 | + | 0.218413i | ||||
\(951\) | −25.8613 | −0.838609 | ||||||||
\(952\) | 0.304027 | + | 0.418458i | 0.00985359 | + | 0.0135623i | ||||
\(953\) | 20.7830 | + | 6.75280i | 0.673226 | + | 0.218745i | 0.625627 | − | 0.780122i | \(-0.284843\pi\) |
0.0475990 | + | 0.998867i | \(0.484843\pi\) | |||||||
\(954\) | −3.58924 | + | 11.0465i | −0.116206 | + | 0.357645i | ||||
\(955\) | 28.3179 | − | 24.0004i | 0.916344 | − | 0.776636i | ||||
\(956\) | 1.55754 | + | 4.79360i | 0.0503743 | + | 0.155036i | ||||
\(957\) | 43.5602i | 1.40810i | ||||||||
\(958\) | 26.4788 | − | 8.60350i | 0.855493 | − | 0.277966i | ||||
\(959\) | −4.33824 | − | 3.15192i | −0.140089 | − | 0.101781i | ||||
\(960\) | −0.166977 | − | 2.22982i | −0.00538917 | − | 0.0719673i | ||||
\(961\) | 13.1880 | − | 9.58162i | 0.425418 | − | 0.309084i | ||||
\(962\) | −9.17790 | + | 12.6323i | −0.295907 | + | 0.407282i | ||||
\(963\) | 3.43710 | − | 4.73076i | 0.110759 | − | 0.152447i | ||||
\(964\) | 5.53446 | − | 4.02102i | 0.178253 | − | 0.129508i | ||||
\(965\) | 8.36022 | + | 2.04070i | 0.269125 | + | 0.0656926i | ||||
\(966\) | 1.02781 | + | 0.746746i | 0.0330692 | + | 0.0240262i | ||||
\(967\) | −30.6435 | + | 9.95669i | −0.985430 | + | 0.320186i | −0.757029 | − | 0.653382i | \(-0.773350\pi\) |
−0.228401 | + | 0.973567i | \(0.573350\pi\) | |||||||
\(968\) | − | 11.9786i | − | 0.385008i | ||||||
\(969\) | −1.75972 | − | 5.41585i | −0.0565303 | − | 0.173982i | ||||
\(970\) | −13.1247 | + | 0.982824i | −0.421408 | + | 0.0315566i | ||||
\(971\) | 11.0045 | − | 33.8684i | 0.353152 | − | 1.08689i | −0.603922 | − | 0.797044i | \(-0.706396\pi\) |
0.957073 | − | 0.289845i | \(-0.0936039\pi\) | |||||||
\(972\) | −0.951057 | − | 0.309017i | −0.0305052 | − | 0.00991172i | ||||
\(973\) | −1.53745 | − | 2.11611i | −0.0492883 | − | 0.0678395i | ||||
\(974\) | −1.29951 | −0.0416391 | ||||||||
\(975\) | 8.56889 | − | 1.29058i | 0.274424 | − | 0.0413315i | ||||
\(976\) | −5.15131 | −0.164889 | ||||||||
\(977\) | −5.79486 | − | 7.97594i | −0.185394 | − | 0.255173i | 0.706196 | − | 0.708016i | \(-0.250410\pi\) |
−0.891590 | + | 0.452843i | \(0.850410\pi\) | |||||||
\(978\) | 17.4759 | + | 5.67828i | 0.558819 | + | 0.181571i | ||||
\(979\) | −21.9638 | + | 67.5976i | −0.701966 | + | 2.16043i | ||||
\(980\) | 13.1726 | + | 8.14109i | 0.420782 | + | 0.260057i | ||||
\(981\) | −3.03025 | − | 9.32615i | −0.0967484 | − | 0.297761i | ||||
\(982\) | 19.1650i | 0.611580i | ||||||||
\(983\) | −28.9244 | + | 9.39810i | −0.922544 | + | 0.299753i | −0.731510 | − | 0.681831i | \(-0.761184\pi\) |
−0.191034 | + | 0.981583i | \(0.561184\pi\) | |||||||
\(984\) | 6.13287 | + | 4.45579i | 0.195509 | + | 0.142045i | ||||
\(985\) | −12.6294 | + | 20.4348i | −0.402406 | + | 0.651107i | ||||
\(986\) | −13.9056 | + | 10.1030i | −0.442845 | + | 0.321745i | ||||
\(987\) | −0.190961 | + | 0.262836i | −0.00607837 | + | 0.00836616i | ||||
\(988\) | 3.06690 | − | 4.22123i | 0.0975712 | − | 0.134295i | ||||
\(989\) | 10.8608 | − | 7.89087i | 0.345355 | − | 0.250915i | ||||
\(990\) | −9.91840 | + | 4.06430i | −0.315227 | + | 0.129172i | ||||
\(991\) | 33.1759 | + | 24.1037i | 1.05387 | + | 0.765680i | 0.972944 | − | 0.231040i | \(-0.0742128\pi\) |
0.0809242 | + | 0.996720i | \(0.474213\pi\) | |||||||
\(992\) | −3.64625 | + | 1.18474i | −0.115769 | + | 0.0376155i | ||||
\(993\) | 14.5094i | 0.460442i | ||||||||
\(994\) | −0.118488 | − | 0.364667i | −0.00375820 | − | 0.0115665i | ||||
\(995\) | −1.32460 | + | 5.42655i | −0.0419927 | + | 0.172033i | ||||
\(996\) | −4.67828 | + | 14.3983i | −0.148237 | + | 0.456226i | ||||
\(997\) | −7.61617 | − | 2.47464i | −0.241206 | − | 0.0783727i | 0.185919 | − | 0.982565i | \(-0.440474\pi\) |
−0.427126 | + | 0.904192i | \(0.640474\pi\) | |||||||
\(998\) | 3.76970 | + | 5.18854i | 0.119328 | + | 0.164240i | ||||
\(999\) | −9.00947 | −0.285047 |
(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 | 150.2.h.a.139.1 | yes | 8 | |
3.2 | odd | 2 | 450.2.l.a.289.2 | 8 | |||
5.2 | odd | 4 | 750.2.g.e.301.1 | 8 | |||
5.3 | odd | 4 | 750.2.g.c.301.2 | 8 | |||
5.4 | even | 2 | 750.2.h.c.199.2 | 8 | |||
25.3 | odd | 20 | 3750.2.a.o.1.3 | 4 | |||
25.4 | even | 10 | 3750.2.c.e.1249.2 | 8 | |||
25.9 | even | 10 | inner | 150.2.h.a.109.1 | ✓ | 8 | |
25.12 | odd | 20 | 750.2.g.e.451.1 | 8 | |||
25.13 | odd | 20 | 750.2.g.c.451.2 | 8 | |||
25.16 | even | 5 | 750.2.h.c.49.2 | 8 | |||
25.21 | even | 5 | 3750.2.c.e.1249.7 | 8 | |||
25.22 | odd | 20 | 3750.2.a.m.1.2 | 4 | |||
75.59 | odd | 10 | 450.2.l.a.109.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.a.109.1 | ✓ | 8 | 25.9 | even | 10 | inner | |
150.2.h.a.139.1 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.l.a.109.2 | 8 | 75.59 | odd | 10 | |||
450.2.l.a.289.2 | 8 | 3.2 | odd | 2 | |||
750.2.g.c.301.2 | 8 | 5.3 | odd | 4 | |||
750.2.g.c.451.2 | 8 | 25.13 | odd | 20 | |||
750.2.g.e.301.1 | 8 | 5.2 | odd | 4 | |||
750.2.g.e.451.1 | 8 | 25.12 | odd | 20 | |||
750.2.h.c.49.2 | 8 | 25.16 | even | 5 | |||
750.2.h.c.199.2 | 8 | 5.4 | even | 2 | |||
3750.2.a.m.1.2 | 4 | 25.22 | odd | 20 | |||
3750.2.a.o.1.3 | 4 | 25.3 | odd | 20 | |||
3750.2.c.e.1249.2 | 8 | 25.4 | even | 10 | |||
3750.2.c.e.1249.7 | 8 | 25.21 | even | 5 |