Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(-2.09082 - 2.09082i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.e.117.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.09082 | + | 2.09082i | −1.20713 | + | 1.20713i | −0.235183 | + | 0.971951i | \(0.575569\pi\) |
−0.971951 | + | 0.235183i | \(0.924431\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.81614 | − | 1.30447i | −0.812201 | − | 0.583378i | ||||
\(6\) | 2.09082 | − | 2.09082i | 0.853573 | − | 0.853573i | ||||
\(7\) | −0.643605 | + | 0.643605i | −0.243260 | + | 0.243260i | −0.818197 | − | 0.574937i | \(-0.805026\pi\) |
0.574937 | + | 0.818197i | \(0.305026\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 5.74304i | − | 1.91435i | ||||||
\(10\) | 1.81614 | + | 1.30447i | 0.574313 | + | 0.412510i | ||||
\(11\) | − | 1.88405i | − | 0.568061i | −0.958815 | − | 0.284030i | \(-0.908328\pi\) | ||
0.958815 | − | 0.284030i | \(-0.0916717\pi\) | |||||||
\(12\) | −2.09082 | + | 2.09082i | −0.603567 | + | 0.603567i | ||||
\(13\) | −0.536082 | −0.148683 | −0.0743413 | − | 0.997233i | \(-0.523685\pi\) | ||||
−0.0743413 | + | 0.997233i | \(0.523685\pi\) | |||||||
\(14\) | 0.643605 | − | 0.643605i | 0.172011 | − | 0.172011i | ||||
\(15\) | 6.52462 | − | 1.06980i | 1.68465 | − | 0.276220i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.334703i | − | 0.0811774i | −0.999176 | − | 0.0405887i | \(-0.987077\pi\) | ||
0.999176 | − | 0.0405887i | \(-0.0129233\pi\) | |||||||
\(18\) | 5.74304i | 1.35365i | ||||||||
\(19\) | 1.08518 | + | 1.08518i | 0.248958 | + | 0.248958i | 0.820543 | − | 0.571585i | \(-0.193671\pi\) |
−0.571585 | + | 0.820543i | \(0.693671\pi\) | |||||||
\(20\) | −1.81614 | − | 1.30447i | −0.406101 | − | 0.291689i | ||||
\(21\) | − | 2.69132i | − | 0.587295i | ||||||
\(22\) | 1.88405i | 0.401680i | ||||||||
\(23\) | 4.65098 | 0.969797 | 0.484899 | − | 0.874570i | \(-0.338856\pi\) | ||||
0.484899 | + | 0.874570i | \(0.338856\pi\) | |||||||
\(24\) | 2.09082 | − | 2.09082i | 0.426786 | − | 0.426786i | ||||
\(25\) | 1.59670 | + | 4.73820i | 0.319341 | + | 0.947640i | ||||
\(26\) | 0.536082 | 0.105134 | ||||||||
\(27\) | 5.73519 | + | 5.73519i | 1.10374 | + | 1.10374i | ||||
\(28\) | −0.643605 | + | 0.643605i | −0.121630 | + | 0.121630i | ||||
\(29\) | 3.33033 | − | 3.33033i | 0.618427 | − | 0.618427i | −0.326701 | − | 0.945128i | \(-0.605937\pi\) |
0.945128 | + | 0.326701i | \(0.105937\pi\) | |||||||
\(30\) | −6.52462 | + | 1.06980i | −1.19123 | + | 0.195317i | ||||
\(31\) | 4.90948 | + | 4.90948i | 0.881769 | + | 0.881769i | 0.993714 | − | 0.111945i | \(-0.0357081\pi\) |
−0.111945 | + | 0.993714i | \(0.535708\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.93919 | + | 3.93919i | 0.685726 | + | 0.685726i | ||||
\(34\) | 0.334703i | 0.0574011i | ||||||||
\(35\) | 2.00844 | − | 0.329310i | 0.339488 | − | 0.0556635i | ||||
\(36\) | − | 5.74304i | − | 0.957173i | ||||||
\(37\) | −0.819646 | − | 6.02729i | −0.134749 | − | 0.990880i | ||||
\(38\) | −1.08518 | − | 1.08518i | −0.176040 | − | 0.176040i | ||||
\(39\) | 1.12085 | − | 1.12085i | 0.179480 | − | 0.179480i | ||||
\(40\) | 1.81614 | + | 1.30447i | 0.287156 | + | 0.206255i | ||||
\(41\) | − | 8.26486i | − | 1.29075i | −0.763864 | − | 0.645377i | \(-0.776700\pi\) | ||
0.763864 | − | 0.645377i | \(-0.223300\pi\) | |||||||
\(42\) | 2.69132i | 0.415280i | ||||||||
\(43\) | 11.9117 | 1.81652 | 0.908259 | − | 0.418409i | \(-0.137412\pi\) | ||||
0.908259 | + | 0.418409i | \(0.137412\pi\) | |||||||
\(44\) | − | 1.88405i | − | 0.284030i | ||||||
\(45\) | −7.49163 | + | 10.4301i | −1.11679 | + | 1.55483i | ||||
\(46\) | −4.65098 | −0.685750 | ||||||||
\(47\) | −0.141535 | + | 0.141535i | −0.0206450 | + | 0.0206450i | −0.717354 | − | 0.696709i | \(-0.754647\pi\) |
0.696709 | + | 0.717354i | \(0.254647\pi\) | |||||||
\(48\) | −2.09082 | + | 2.09082i | −0.301784 | + | 0.301784i | ||||
\(49\) | 6.17154i | 0.881649i | ||||||||
\(50\) | −1.59670 | − | 4.73820i | −0.225808 | − | 0.670083i | ||||
\(51\) | 0.699803 | + | 0.699803i | 0.0979920 | + | 0.0979920i | ||||
\(52\) | −0.536082 | −0.0743413 | ||||||||
\(53\) | −5.03296 | − | 5.03296i | −0.691330 | − | 0.691330i | 0.271194 | − | 0.962525i | \(-0.412581\pi\) |
−0.962525 | + | 0.271194i | \(0.912581\pi\) | |||||||
\(54\) | −5.73519 | − | 5.73519i | −0.780460 | − | 0.780460i | ||||
\(55\) | −2.45768 | + | 3.42168i | −0.331394 | + | 0.461380i | ||||
\(56\) | 0.643605 | − | 0.643605i | 0.0860054 | − | 0.0860054i | ||||
\(57\) | −4.53784 | −0.601051 | ||||||||
\(58\) | −3.33033 | + | 3.33033i | −0.437294 | + | 0.437294i | ||||
\(59\) | −4.10789 | − | 4.10789i | −0.534802 | − | 0.534802i | 0.387195 | − | 0.921998i | \(-0.373444\pi\) |
−0.921998 | + | 0.387195i | \(0.873444\pi\) | |||||||
\(60\) | 6.52462 | − | 1.06980i | 0.842325 | − | 0.138110i | ||||
\(61\) | −8.90180 | − | 8.90180i | −1.13976 | − | 1.13976i | −0.988493 | − | 0.151265i | \(-0.951665\pi\) |
−0.151265 | − | 0.988493i | \(-0.548335\pi\) | |||||||
\(62\) | −4.90948 | − | 4.90948i | −0.623505 | − | 0.623505i | ||||
\(63\) | 3.69625 | + | 3.69625i | 0.465683 | + | 0.465683i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.973599 | + | 0.699305i | 0.120760 | + | 0.0867381i | ||||
\(66\) | −3.93919 | − | 3.93919i | −0.484881 | − | 0.484881i | ||||
\(67\) | −3.61956 | − | 3.61956i | −0.442199 | − | 0.442199i | 0.450551 | − | 0.892751i | \(-0.351227\pi\) |
−0.892751 | + | 0.450551i | \(0.851227\pi\) | |||||||
\(68\) | − | 0.334703i | − | 0.0405887i | ||||||
\(69\) | −9.72436 | + | 9.72436i | −1.17068 | + | 1.17068i | ||||
\(70\) | −2.00844 | + | 0.329310i | −0.240054 | + | 0.0393601i | ||||
\(71\) | 15.5121 | 1.84095 | 0.920477 | − | 0.390798i | \(-0.127801\pi\) | ||||
0.920477 | + | 0.390798i | \(0.127801\pi\) | |||||||
\(72\) | 5.74304i | 0.676823i | ||||||||
\(73\) | 6.82739 | − | 6.82739i | 0.799086 | − | 0.799086i | −0.183866 | − | 0.982951i | \(-0.558861\pi\) |
0.982951 | + | 0.183866i | \(0.0588611\pi\) | |||||||
\(74\) | 0.819646 | + | 6.02729i | 0.0952819 | + | 0.700658i | ||||
\(75\) | −13.2451 | − | 6.56829i | −1.52942 | − | 0.758441i | ||||
\(76\) | 1.08518 | + | 1.08518i | 0.124479 | + | 0.124479i | ||||
\(77\) | 1.21258 | + | 1.21258i | 0.138186 | + | 0.138186i | ||||
\(78\) | −1.12085 | + | 1.12085i | −0.126911 | + | 0.126911i | ||||
\(79\) | −5.73637 | − | 5.73637i | −0.645392 | − | 0.645392i | 0.306484 | − | 0.951876i | \(-0.400847\pi\) |
−0.951876 | + | 0.306484i | \(0.900847\pi\) | |||||||
\(80\) | −1.81614 | − | 1.30447i | −0.203050 | − | 0.145844i | ||||
\(81\) | −6.75336 | −0.750373 | ||||||||
\(82\) | 8.26486i | 0.912701i | ||||||||
\(83\) | −7.90475 | − | 7.90475i | −0.867659 | − | 0.867659i | 0.124554 | − | 0.992213i | \(-0.460250\pi\) |
−0.992213 | + | 0.124554i | \(0.960250\pi\) | |||||||
\(84\) | − | 2.69132i | − | 0.293647i | ||||||
\(85\) | −0.436611 | + | 0.607866i | −0.0473571 | + | 0.0659323i | ||||
\(86\) | −11.9117 | −1.28447 | ||||||||
\(87\) | 13.9262i | 1.49305i | ||||||||
\(88\) | 1.88405i | 0.200840i | ||||||||
\(89\) | 1.21521 | − | 1.21521i | 0.128812 | − | 0.128812i | −0.639761 | − | 0.768574i | \(-0.720967\pi\) |
0.768574 | + | 0.639761i | \(0.220967\pi\) | |||||||
\(90\) | 7.49163 | − | 10.4301i | 0.789687 | − | 1.09943i | ||||
\(91\) | 0.345025 | − | 0.345025i | 0.0361685 | − | 0.0361685i | ||||
\(92\) | 4.65098 | 0.484899 | ||||||||
\(93\) | −20.5297 | −2.12883 | ||||||||
\(94\) | 0.141535 | − | 0.141535i | 0.0145982 | − | 0.0145982i | ||||
\(95\) | −0.555249 | − | 3.38643i | −0.0569674 | − | 0.347440i | ||||
\(96\) | 2.09082 | − | 2.09082i | 0.213393 | − | 0.213393i | ||||
\(97\) | 17.1767i | 1.74403i | 0.489477 | + | 0.872016i | \(0.337188\pi\) | ||||
−0.489477 | + | 0.872016i | \(0.662812\pi\) | |||||||
\(98\) | − | 6.17154i | − | 0.623420i | ||||||
\(99\) | −10.8201 | −1.08746 | ||||||||
\(100\) | 1.59670 | + | 4.73820i | 0.159670 | + | 0.473820i | ||||
\(101\) | 13.4676i | 1.34008i | 0.742324 | + | 0.670041i | \(0.233723\pi\) | ||||
−0.742324 | + | 0.670041i | \(0.766277\pi\) | |||||||
\(102\) | −0.699803 | − | 0.699803i | −0.0692908 | − | 0.0692908i | ||||
\(103\) | − | 12.6201i | − | 1.24350i | −0.783216 | − | 0.621749i | \(-0.786422\pi\) | ||
0.783216 | − | 0.621749i | \(-0.213578\pi\) | |||||||
\(104\) | 0.536082 | 0.0525672 | ||||||||
\(105\) | −3.51075 | + | 4.88781i | −0.342615 | + | 0.477001i | ||||
\(106\) | 5.03296 | + | 5.03296i | 0.488844 | + | 0.488844i | ||||
\(107\) | −1.64796 | + | 1.64796i | −0.159314 | + | 0.159314i | −0.782263 | − | 0.622949i | \(-0.785935\pi\) |
0.622949 | + | 0.782263i | \(0.285935\pi\) | |||||||
\(108\) | 5.73519 | + | 5.73519i | 0.551869 | + | 0.551869i | ||||
\(109\) | 7.06206 | + | 7.06206i | 0.676422 | + | 0.676422i | 0.959189 | − | 0.282766i | \(-0.0912521\pi\) |
−0.282766 | + | 0.959189i | \(0.591252\pi\) | |||||||
\(110\) | 2.45768 | − | 3.42168i | 0.234331 | − | 0.326245i | ||||
\(111\) | 14.3157 | + | 10.8882i | 1.35878 | + | 1.03346i | ||||
\(112\) | −0.643605 | + | 0.643605i | −0.0608150 | + | 0.0608150i | ||||
\(113\) | − | 15.1701i | − | 1.42709i | −0.700612 | − | 0.713543i | \(-0.747089\pi\) | ||
0.700612 | − | 0.713543i | \(-0.252911\pi\) | |||||||
\(114\) | 4.53784 | 0.425007 | ||||||||
\(115\) | −8.44682 | − | 6.06708i | −0.787670 | − | 0.565758i | ||||
\(116\) | 3.33033 | − | 3.33033i | 0.309213 | − | 0.309213i | ||||
\(117\) | 3.07874i | 0.284630i | ||||||||
\(118\) | 4.10789 | + | 4.10789i | 0.378162 | + | 0.378162i | ||||
\(119\) | 0.215416 | + | 0.215416i | 0.0197472 | + | 0.0197472i | ||||
\(120\) | −6.52462 | + | 1.06980i | −0.595614 | + | 0.0976587i | ||||
\(121\) | 7.45037 | 0.677307 | ||||||||
\(122\) | 8.90180 | + | 8.90180i | 0.805931 | + | 0.805931i | ||||
\(123\) | 17.2803 | + | 17.2803i | 1.55811 | + | 1.55811i | ||||
\(124\) | 4.90948 | + | 4.90948i | 0.440885 | + | 0.440885i | ||||
\(125\) | 3.28101 | − | 10.6881i | 0.293463 | − | 0.955970i | ||||
\(126\) | −3.69625 | − | 3.69625i | −0.329288 | − | 0.329288i | ||||
\(127\) | −3.59805 | + | 3.59805i | −0.319275 | + | 0.319275i | −0.848489 | − | 0.529213i | \(-0.822487\pi\) |
0.529213 | + | 0.848489i | \(0.322487\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −24.9052 | + | 24.9052i | −2.19278 | + | 2.19278i | ||||
\(130\) | −0.973599 | − | 0.699305i | −0.0853903 | − | 0.0613331i | ||||
\(131\) | 7.63639 | + | 7.63639i | 0.667194 | + | 0.667194i | 0.957066 | − | 0.289871i | \(-0.0936126\pi\) |
−0.289871 | + | 0.957066i | \(0.593613\pi\) | |||||||
\(132\) | 3.93919 | + | 3.93919i | 0.342863 | + | 0.342863i | ||||
\(133\) | −1.39686 | −0.121123 | ||||||||
\(134\) | 3.61956 | + | 3.61956i | 0.312682 | + | 0.312682i | ||||
\(135\) | −2.93449 | − | 17.8973i | −0.252561 | − | 1.54035i | ||||
\(136\) | 0.334703i | 0.0287005i | ||||||||
\(137\) | 5.48037 | − | 5.48037i | 0.468220 | − | 0.468220i | −0.433118 | − | 0.901337i | \(-0.642587\pi\) |
0.901337 | + | 0.433118i | \(0.142587\pi\) | |||||||
\(138\) | 9.72436 | − | 9.72436i | 0.827793 | − | 0.827793i | ||||
\(139\) | 4.24414 | 0.359983 | 0.179991 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179991 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(140\) | 2.00844 | − | 0.329310i | 0.169744 | − | 0.0278318i | ||||
\(141\) | − | 0.591849i | − | 0.0498427i | ||||||
\(142\) | −15.5121 | −1.30175 | ||||||||
\(143\) | 1.01000i | 0.0844607i | ||||||||
\(144\) | − | 5.74304i | − | 0.478586i | ||||||
\(145\) | −10.3927 | + | 1.70401i | −0.863063 | + | 0.141510i | ||||
\(146\) | −6.82739 | + | 6.82739i | −0.565039 | + | 0.565039i | ||||
\(147\) | −12.9036 | − | 12.9036i | −1.06427 | − | 1.06427i | ||||
\(148\) | −0.819646 | − | 6.02729i | −0.0673745 | − | 0.495440i | ||||
\(149\) | − | 20.3080i | − | 1.66370i | −0.555002 | − | 0.831849i | \(-0.687282\pi\) | ||
0.555002 | − | 0.831849i | \(-0.312718\pi\) | |||||||
\(150\) | 13.2451 | + | 6.56829i | 1.08146 | + | 0.536299i | ||||
\(151\) | − | 13.8362i | − | 1.12597i | −0.826466 | − | 0.562987i | \(-0.809652\pi\) | ||
0.826466 | − | 0.562987i | \(-0.190348\pi\) | |||||||
\(152\) | −1.08518 | − | 1.08518i | −0.0880199 | − | 0.0880199i | ||||
\(153\) | −1.92221 | −0.155402 | ||||||||
\(154\) | −1.21258 | − | 1.21258i | −0.0977126 | − | 0.0977126i | ||||
\(155\) | −2.51201 | − | 15.3206i | −0.201769 | − | 1.23058i | ||||
\(156\) | 1.12085 | − | 1.12085i | 0.0897399 | − | 0.0897399i | ||||
\(157\) | 13.2682 | − | 13.2682i | 1.05892 | − | 1.05892i | 0.0607691 | − | 0.998152i | \(-0.480645\pi\) |
0.998152 | − | 0.0607691i | \(-0.0193553\pi\) | |||||||
\(158\) | 5.73637 | + | 5.73637i | 0.456361 | + | 0.456361i | ||||
\(159\) | 21.0460 | 1.66906 | ||||||||
\(160\) | 1.81614 | + | 1.30447i | 0.143578 | + | 0.103128i | ||||
\(161\) | −2.99340 | + | 2.99340i | −0.235913 | + | 0.235913i | ||||
\(162\) | 6.75336 | 0.530594 | ||||||||
\(163\) | 1.48487i | 0.116304i | 0.998308 | + | 0.0581520i | \(0.0185208\pi\) | ||||
−0.998308 | + | 0.0581520i | \(0.981479\pi\) | |||||||
\(164\) | − | 8.26486i | − | 0.645377i | ||||||
\(165\) | −2.01555 | − | 12.2927i | −0.156910 | − | 0.956984i | ||||
\(166\) | 7.90475 | + | 7.90475i | 0.613527 | + | 0.613527i | ||||
\(167\) | 4.69210i | 0.363086i | 0.983383 | + | 0.181543i | \(0.0581091\pi\) | ||||
−0.983383 | + | 0.181543i | \(0.941891\pi\) | |||||||
\(168\) | 2.69132i | 0.207640i | ||||||||
\(169\) | −12.7126 | −0.977894 | ||||||||
\(170\) | 0.436611 | − | 0.607866i | 0.0334865 | − | 0.0466212i | ||||
\(171\) | 6.23224 | − | 6.23224i | 0.476591 | − | 0.476591i | ||||
\(172\) | 11.9117 | 0.908259 | ||||||||
\(173\) | −1.68127 | + | 1.68127i | −0.127825 | + | 0.127825i | −0.768125 | − | 0.640300i | \(-0.778810\pi\) |
0.640300 | + | 0.768125i | \(0.278810\pi\) | |||||||
\(174\) | − | 13.9262i | − | 1.05574i | ||||||
\(175\) | −4.07718 | − | 2.02188i | −0.308206 | − | 0.152840i | ||||
\(176\) | − | 1.88405i | − | 0.142015i | ||||||
\(177\) | 17.1777 | 1.29116 | ||||||||
\(178\) | −1.21521 | + | 1.21521i | −0.0910840 | + | 0.0910840i | ||||
\(179\) | −13.0168 | + | 13.0168i | −0.972921 | + | 0.972921i | −0.999643 | − | 0.0267216i | \(-0.991493\pi\) |
0.0267216 | + | 0.999643i | \(0.491493\pi\) | |||||||
\(180\) | −7.49163 | + | 10.4301i | −0.558393 | + | 0.777417i | ||||
\(181\) | 5.91911 | 0.439964 | 0.219982 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219982 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(182\) | −0.345025 | + | 0.345025i | −0.0255750 | + | 0.0255750i | ||||
\(183\) | 37.2241 | 2.75168 | ||||||||
\(184\) | −4.65098 | −0.342875 | ||||||||
\(185\) | −6.37384 | + | 12.0156i | −0.468614 | + | 0.883403i | ||||
\(186\) | 20.5297 | 1.50531 | ||||||||
\(187\) | −0.630595 | −0.0461137 | ||||||||
\(188\) | −0.141535 | + | 0.141535i | −0.0103225 | + | 0.0103225i | ||||
\(189\) | −7.38239 | −0.536990 | ||||||||
\(190\) | 0.555249 | + | 3.38643i | 0.0402820 | + | 0.245677i | ||||
\(191\) | −8.14150 | + | 8.14150i | −0.589099 | + | 0.589099i | −0.937387 | − | 0.348289i | \(-0.886763\pi\) |
0.348289 | + | 0.937387i | \(0.386763\pi\) | |||||||
\(192\) | −2.09082 | + | 2.09082i | −0.150892 | + | 0.150892i | ||||
\(193\) | 15.8717 | 1.14247 | 0.571235 | − | 0.820787i | \(-0.306465\pi\) | ||||
0.571235 | + | 0.820787i | \(0.306465\pi\) | |||||||
\(194\) | − | 17.1767i | − | 1.23322i | ||||||
\(195\) | −3.49774 | + | 0.573499i | −0.250478 | + | 0.0410691i | ||||
\(196\) | 6.17154i | 0.440825i | ||||||||
\(197\) | 3.60225 | − | 3.60225i | 0.256650 | − | 0.256650i | −0.567040 | − | 0.823690i | \(-0.691912\pi\) |
0.823690 | + | 0.567040i | \(0.191912\pi\) | |||||||
\(198\) | 10.8201 | 0.768954 | ||||||||
\(199\) | −1.14697 | + | 1.14697i | −0.0813064 | + | 0.0813064i | −0.746590 | − | 0.665284i | \(-0.768310\pi\) |
0.665284 | + | 0.746590i | \(0.268310\pi\) | |||||||
\(200\) | −1.59670 | − | 4.73820i | −0.112904 | − | 0.335041i | ||||
\(201\) | 15.1357 | 1.06759 | ||||||||
\(202\) | − | 13.4676i | − | 0.947581i | ||||||
\(203\) | 4.28683i | 0.300877i | ||||||||
\(204\) | 0.699803 | + | 0.699803i | 0.0489960 | + | 0.0489960i | ||||
\(205\) | −10.7813 | + | 15.0101i | −0.752997 | + | 1.04835i | ||||
\(206\) | 12.6201i | 0.879286i | ||||||||
\(207\) | − | 26.7108i | − | 1.85653i | ||||||
\(208\) | −0.536082 | −0.0371706 | ||||||||
\(209\) | 2.04453 | − | 2.04453i | 0.141423 | − | 0.141423i | ||||
\(210\) | 3.51075 | − | 4.88781i | 0.242265 | − | 0.337291i | ||||
\(211\) | 3.19579 | 0.220008 | 0.110004 | − | 0.993931i | \(-0.464914\pi\) | ||||
0.110004 | + | 0.993931i | \(0.464914\pi\) | |||||||
\(212\) | −5.03296 | − | 5.03296i | −0.345665 | − | 0.345665i | ||||
\(213\) | −32.4331 | + | 32.4331i | −2.22228 | + | 2.22228i | ||||
\(214\) | 1.64796 | − | 1.64796i | 0.112652 | − | 0.112652i | ||||
\(215\) | −21.6333 | − | 15.5385i | −1.47538 | − | 1.05972i | ||||
\(216\) | −5.73519 | − | 5.73519i | −0.390230 | − | 0.390230i | ||||
\(217\) | −6.31954 | −0.428998 | ||||||||
\(218\) | −7.06206 | − | 7.06206i | −0.478303 | − | 0.478303i | ||||
\(219\) | 28.5497i | 1.92921i | ||||||||
\(220\) | −2.45768 | + | 3.42168i | −0.165697 | + | 0.230690i | ||||
\(221\) | 0.179428i | 0.0120697i | ||||||||
\(222\) | −14.3157 | − | 10.8882i | −0.960806 | − | 0.730770i | ||||
\(223\) | −7.29909 | − | 7.29909i | −0.488783 | − | 0.488783i | 0.419139 | − | 0.907922i | \(-0.362332\pi\) |
−0.907922 | + | 0.419139i | \(0.862332\pi\) | |||||||
\(224\) | 0.643605 | − | 0.643605i | 0.0430027 | − | 0.0430027i | ||||
\(225\) | 27.2117 | − | 9.16993i | 1.81411 | − | 0.611329i | ||||
\(226\) | 15.1701i | 1.00910i | ||||||||
\(227\) | 19.6620i | 1.30501i | 0.757783 | + | 0.652507i | \(0.226283\pi\) | ||||
−0.757783 | + | 0.652507i | \(0.773717\pi\) | |||||||
\(228\) | −4.53784 | −0.300526 | ||||||||
\(229\) | − | 13.4975i | − | 0.891940i | −0.895048 | − | 0.445970i | \(-0.852859\pi\) | ||
0.895048 | − | 0.445970i | \(-0.147141\pi\) | |||||||
\(230\) | 8.44682 | + | 6.06708i | 0.556967 | + | 0.400051i | ||||
\(231\) | −5.07057 | −0.333619 | ||||||||
\(232\) | −3.33033 | + | 3.33033i | −0.218647 | + | 0.218647i | ||||
\(233\) | −1.10924 | + | 1.10924i | −0.0726687 | + | 0.0726687i | −0.742507 | − | 0.669838i | \(-0.766363\pi\) |
0.669838 | + | 0.742507i | \(0.266363\pi\) | |||||||
\(234\) | − | 3.07874i | − | 0.201264i | ||||||
\(235\) | 0.441676 | − | 0.0724186i | 0.0288118 | − | 0.00472407i | ||||
\(236\) | −4.10789 | − | 4.10789i | −0.267401 | − | 0.267401i | ||||
\(237\) | 23.9874 | 1.55815 | ||||||||
\(238\) | −0.215416 | − | 0.215416i | −0.0139634 | − | 0.0139634i | ||||
\(239\) | 10.5161 | + | 10.5161i | 0.680230 | + | 0.680230i | 0.960052 | − | 0.279822i | \(-0.0902754\pi\) |
−0.279822 | + | 0.960052i | \(0.590275\pi\) | |||||||
\(240\) | 6.52462 | − | 1.06980i | 0.421163 | − | 0.0690551i | ||||
\(241\) | −18.7617 | + | 18.7617i | −1.20855 | + | 1.20855i | −0.237047 | + | 0.971498i | \(0.576180\pi\) |
−0.971498 | + | 0.237047i | \(0.923820\pi\) | |||||||
\(242\) | −7.45037 | −0.478928 | ||||||||
\(243\) | −3.08553 | + | 3.08553i | −0.197937 | + | 0.197937i | ||||
\(244\) | −8.90180 | − | 8.90180i | −0.569879 | − | 0.569879i | ||||
\(245\) | 8.05061 | − | 11.2084i | 0.514334 | − | 0.716076i | ||||
\(246\) | −17.2803 | − | 17.2803i | −1.10175 | − | 1.10175i | ||||
\(247\) | −0.581747 | − | 0.581747i | −0.0370157 | − | 0.0370157i | ||||
\(248\) | −4.90948 | − | 4.90948i | −0.311752 | − | 0.311752i | ||||
\(249\) | 33.0548 | 2.09476 | ||||||||
\(250\) | −3.28101 | + | 10.6881i | −0.207510 | + | 0.675973i | ||||
\(251\) | 9.09164 | + | 9.09164i | 0.573859 | + | 0.573859i | 0.933205 | − | 0.359346i | \(-0.117000\pi\) |
−0.359346 | + | 0.933205i | \(0.617000\pi\) | |||||||
\(252\) | 3.69625 | + | 3.69625i | 0.232842 | + | 0.232842i | ||||
\(253\) | − | 8.76267i | − | 0.550904i | ||||||
\(254\) | 3.59805 | − | 3.59805i | 0.225762 | − | 0.225762i | ||||
\(255\) | −0.358064 | − | 2.18381i | −0.0224228 | − | 0.136756i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.08454i | 0.130030i | 0.997884 | + | 0.0650151i | \(0.0207096\pi\) | ||||
−0.997884 | + | 0.0650151i | \(0.979290\pi\) | |||||||
\(258\) | 24.9052 | − | 24.9052i | 1.55053 | − | 1.55053i | ||||
\(259\) | 4.40672 | + | 3.35166i | 0.273820 | + | 0.208262i | ||||
\(260\) | 0.973599 | + | 0.699305i | 0.0603800 | + | 0.0433690i | ||||
\(261\) | −19.1262 | − | 19.1262i | −1.18388 | − | 1.18388i | ||||
\(262\) | −7.63639 | − | 7.63639i | −0.471778 | − | 0.471778i | ||||
\(263\) | −6.41417 | + | 6.41417i | −0.395515 | + | 0.395515i | −0.876648 | − | 0.481133i | \(-0.840225\pi\) |
0.481133 | + | 0.876648i | \(0.340225\pi\) | |||||||
\(264\) | −3.93919 | − | 3.93919i | −0.242441 | − | 0.242441i | ||||
\(265\) | 2.57519 | + | 15.7059i | 0.158192 | + | 0.964806i | ||||
\(266\) | 1.39686 | 0.0856469 | ||||||||
\(267\) | 5.08157i | 0.310987i | ||||||||
\(268\) | −3.61956 | − | 3.61956i | −0.221100 | − | 0.221100i | ||||
\(269\) | 10.5529i | 0.643424i | 0.946838 | + | 0.321712i | \(0.104258\pi\) | ||||
−0.946838 | + | 0.321712i | \(0.895742\pi\) | |||||||
\(270\) | 2.93449 | + | 17.8973i | 0.178588 | + | 1.08919i | ||||
\(271\) | 19.2734 | 1.17078 | 0.585389 | − | 0.810753i | \(-0.300942\pi\) | ||||
0.585389 | + | 0.810753i | \(0.300942\pi\) | |||||||
\(272\) | − | 0.334703i | − | 0.0202943i | ||||||
\(273\) | 1.44277i | 0.0873204i | ||||||||
\(274\) | −5.48037 | + | 5.48037i | −0.331081 | + | 0.331081i | ||||
\(275\) | 8.92698 | − | 3.00826i | 0.538317 | − | 0.181405i | ||||
\(276\) | −9.72436 | + | 9.72436i | −0.585338 | + | 0.585338i | ||||
\(277\) | 7.82056 | 0.469892 | 0.234946 | − | 0.972008i | \(-0.424509\pi\) | ||||
0.234946 | + | 0.972008i | \(0.424509\pi\) | |||||||
\(278\) | −4.24414 | −0.254546 | ||||||||
\(279\) | 28.1953 | − | 28.1953i | 1.68801 | − | 1.68801i | ||||
\(280\) | −2.00844 | + | 0.329310i | −0.120027 | + | 0.0196800i | ||||
\(281\) | −10.4788 | + | 10.4788i | −0.625110 | + | 0.625110i | −0.946834 | − | 0.321723i | \(-0.895738\pi\) |
0.321723 | + | 0.946834i | \(0.395738\pi\) | |||||||
\(282\) | 0.591849i | 0.0352441i | ||||||||
\(283\) | 26.3960i | 1.56908i | 0.620079 | + | 0.784539i | \(0.287100\pi\) | ||||
−0.620079 | + | 0.784539i | \(0.712900\pi\) | |||||||
\(284\) | 15.5121 | 0.920477 | ||||||||
\(285\) | 8.24133 | + | 5.91948i | 0.488174 | + | 0.350640i | ||||
\(286\) | − | 1.01000i | − | 0.0597228i | ||||||
\(287\) | 5.31930 | + | 5.31930i | 0.313989 | + | 0.313989i | ||||
\(288\) | 5.74304i | 0.338412i | ||||||||
\(289\) | 16.8880 | 0.993410 | ||||||||
\(290\) | 10.3927 | − | 1.70401i | 0.610278 | − | 0.100063i | ||||
\(291\) | −35.9134 | − | 35.9134i | −2.10528 | − | 2.10528i | ||||
\(292\) | 6.82739 | − | 6.82739i | 0.399543 | − | 0.399543i | ||||
\(293\) | −22.4956 | − | 22.4956i | −1.31421 | − | 1.31421i | −0.918281 | − | 0.395928i | \(-0.870423\pi\) |
−0.395928 | − | 0.918281i | \(-0.629577\pi\) | |||||||
\(294\) | 12.9036 | + | 12.9036i | 0.752552 | + | 0.752552i | ||||
\(295\) | 2.10186 | + | 12.8191i | 0.122375 | + | 0.746359i | ||||
\(296\) | 0.819646 | + | 6.02729i | 0.0476410 | + | 0.350329i | ||||
\(297\) | 10.8054 | − | 10.8054i | 0.626990 | − | 0.626990i | ||||
\(298\) | 20.3080i | 1.17641i | ||||||||
\(299\) | −2.49331 | −0.144192 | ||||||||
\(300\) | −13.2451 | − | 6.56829i | −0.764708 | − | 0.379221i | ||||
\(301\) | −7.66643 | + | 7.66643i | −0.441886 | + | 0.441886i | ||||
\(302\) | 13.8362i | 0.796183i | ||||||||
\(303\) | −28.1584 | − | 28.1584i | −1.61766 | − | 1.61766i | ||||
\(304\) | 1.08518 | + | 1.08518i | 0.0622395 | + | 0.0622395i | ||||
\(305\) | 4.55473 | + | 27.7790i | 0.260803 | + | 1.59062i | ||||
\(306\) | 1.92221 | 0.109885 | ||||||||
\(307\) | −17.4358 | − | 17.4358i | −0.995111 | − | 0.995111i | 0.00487690 | − | 0.999988i | \(-0.498448\pi\) |
−0.999988 | + | 0.00487690i | \(0.998448\pi\) | |||||||
\(308\) | 1.21258 | + | 1.21258i | 0.0690932 | + | 0.0690932i | ||||
\(309\) | 26.3864 | + | 26.3864i | 1.50107 | + | 1.50107i | ||||
\(310\) | 2.51201 | + | 15.3206i | 0.142672 | + | 0.870150i | ||||
\(311\) | −3.97519 | − | 3.97519i | −0.225412 | − | 0.225412i | 0.585361 | − | 0.810773i | \(-0.300953\pi\) |
−0.810773 | + | 0.585361i | \(0.800953\pi\) | |||||||
\(312\) | −1.12085 | + | 1.12085i | −0.0634557 | + | 0.0634557i | ||||
\(313\) | 15.8472 | 0.895735 | 0.447867 | − | 0.894100i | \(-0.352184\pi\) | ||||
0.447867 | + | 0.894100i | \(0.352184\pi\) | |||||||
\(314\) | −13.2682 | + | 13.2682i | −0.748770 | + | 0.748770i | ||||
\(315\) | −1.89124 | − | 11.5345i | −0.106559 | − | 0.649898i | ||||
\(316\) | −5.73637 | − | 5.73637i | −0.322696 | − | 0.322696i | ||||
\(317\) | 0.950144 | + | 0.950144i | 0.0533654 | + | 0.0533654i | 0.733286 | − | 0.679920i | \(-0.237986\pi\) |
−0.679920 | + | 0.733286i | \(0.737986\pi\) | |||||||
\(318\) | −21.0460 | −1.18020 | ||||||||
\(319\) | −6.27449 | − | 6.27449i | −0.351304 | − | 0.351304i | ||||
\(320\) | −1.81614 | − | 1.30447i | −0.101525 | − | 0.0729222i | ||||
\(321\) | − | 6.89116i | − | 0.384627i | ||||||
\(322\) | 2.99340 | − | 2.99340i | 0.166816 | − | 0.166816i | ||||
\(323\) | 0.363214 | − | 0.363214i | 0.0202097 | − | 0.0202097i | ||||
\(324\) | −6.75336 | −0.375186 | ||||||||
\(325\) | −0.855965 | − | 2.54007i | −0.0474804 | − | 0.140897i | ||||
\(326\) | − | 1.48487i | − | 0.0822394i | ||||||
\(327\) | −29.5309 | −1.63306 | ||||||||
\(328\) | 8.26486i | 0.456350i | ||||||||
\(329\) | − | 0.182186i | − | 0.0100442i | ||||||
\(330\) | 2.01555 | + | 12.2927i | 0.110952 | + | 0.676690i | ||||
\(331\) | −19.3735 | + | 19.3735i | −1.06486 | + | 1.06486i | −0.0671177 | + | 0.997745i | \(0.521380\pi\) |
−0.997745 | + | 0.0671177i | \(0.978620\pi\) | |||||||
\(332\) | −7.90475 | − | 7.90475i | −0.433829 | − | 0.433829i | ||||
\(333\) | −34.6149 | + | 4.70726i | −1.89689 | + | 0.257956i | ||||
\(334\) | − | 4.69210i | − | 0.256740i | ||||||
\(335\) | 1.85200 | + | 11.2952i | 0.101186 | + | 0.617124i | ||||
\(336\) | − | 2.69132i | − | 0.146824i | ||||||
\(337\) | −3.21128 | − | 3.21128i | −0.174929 | − | 0.174929i | 0.614212 | − | 0.789141i | \(-0.289474\pi\) |
−0.789141 | + | 0.614212i | \(0.789474\pi\) | |||||||
\(338\) | 12.7126 | 0.691475 | ||||||||
\(339\) | 31.7180 | + | 31.7180i | 1.72268 | + | 1.72268i | ||||
\(340\) | −0.436611 | + | 0.607866i | −0.0236785 | + | 0.0329662i | ||||
\(341\) | 9.24969 | − | 9.24969i | 0.500899 | − | 0.500899i | ||||
\(342\) | −6.23224 | + | 6.23224i | −0.337001 | + | 0.337001i | ||||
\(343\) | −8.47727 | − | 8.47727i | −0.457730 | − | 0.457730i | ||||
\(344\) | −11.9117 | −0.642236 | ||||||||
\(345\) | 30.3459 | − | 4.97561i | 1.63377 | − | 0.267878i | ||||
\(346\) | 1.68127 | − | 1.68127i | 0.0903856 | − | 0.0903856i | ||||
\(347\) | −18.4401 | −0.989915 | −0.494957 | − | 0.868917i | \(-0.664816\pi\) | ||||
−0.494957 | + | 0.868917i | \(0.664816\pi\) | |||||||
\(348\) | 13.9262i | 0.746524i | ||||||||
\(349\) | − | 21.3314i | − | 1.14184i | −0.821005 | − | 0.570921i | \(-0.806586\pi\) | ||
0.821005 | − | 0.570921i | \(-0.193414\pi\) | |||||||
\(350\) | 4.07718 | + | 2.02188i | 0.217934 | + | 0.108074i | ||||
\(351\) | −3.07453 | − | 3.07453i | −0.164106 | − | 0.164106i | ||||
\(352\) | 1.88405i | 0.100420i | ||||||||
\(353\) | − | 11.9150i | − | 0.634173i | −0.948397 | − | 0.317086i | \(-0.897296\pi\) | ||
0.948397 | − | 0.317086i | \(-0.102704\pi\) | |||||||
\(354\) | −17.1777 | −0.912985 | ||||||||
\(355\) | −28.1722 | − | 20.2352i | −1.49522 | − | 1.07397i | ||||
\(356\) | 1.21521 | − | 1.21521i | 0.0644061 | − | 0.0644061i | ||||
\(357\) | −0.900793 | −0.0476750 | ||||||||
\(358\) | 13.0168 | − | 13.0168i | 0.687959 | − | 0.687959i | ||||
\(359\) | − | 24.9976i | − | 1.31932i | −0.751562 | − | 0.659662i | \(-0.770699\pi\) | ||
0.751562 | − | 0.659662i | \(-0.229301\pi\) | |||||||
\(360\) | 7.49163 | − | 10.4301i | 0.394844 | − | 0.549717i | ||||
\(361\) | − | 16.6448i | − | 0.876040i | ||||||
\(362\) | −5.91911 | −0.311101 | ||||||||
\(363\) | −15.5774 | + | 15.5774i | −0.817600 | + | 0.817600i | ||||
\(364\) | 0.345025 | − | 0.345025i | 0.0180842 | − | 0.0180842i | ||||
\(365\) | −21.3056 | + | 3.49333i | −1.11519 | + | 0.182849i | ||||
\(366\) | −37.2241 | −1.94573 | ||||||||
\(367\) | 0.228241 | − | 0.228241i | 0.0119141 | − | 0.0119141i | −0.701125 | − | 0.713039i | \(-0.747318\pi\) |
0.713039 | + | 0.701125i | \(0.247318\pi\) | |||||||
\(368\) | 4.65098 | 0.242449 | ||||||||
\(369\) | −47.4654 | −2.47095 | ||||||||
\(370\) | 6.37384 | − | 12.0156i | 0.331360 | − | 0.624660i | ||||
\(371\) | 6.47848 | 0.336346 | ||||||||
\(372\) | −20.5297 | −1.06441 | ||||||||
\(373\) | 5.32431 | − | 5.32431i | 0.275682 | − | 0.275682i | −0.555700 | − | 0.831383i | \(-0.687550\pi\) |
0.831383 | + | 0.555700i | \(0.187550\pi\) | |||||||
\(374\) | 0.630595 | 0.0326073 | ||||||||
\(375\) | 15.4868 | + | 29.2068i | 0.799735 | + | 1.50823i | ||||
\(376\) | 0.141535 | − | 0.141535i | 0.00729912 | − | 0.00729912i | ||||
\(377\) | −1.78533 | + | 1.78533i | −0.0919492 | + | 0.0919492i | ||||
\(378\) | 7.38239 | 0.379709 | ||||||||
\(379\) | − | 7.62224i | − | 0.391528i | −0.980651 | − | 0.195764i | \(-0.937281\pi\) | ||
0.980651 | − | 0.195764i | \(-0.0627187\pi\) | |||||||
\(380\) | −0.555249 | − | 3.38643i | −0.0284837 | − | 0.173720i | ||||
\(381\) | − | 15.0457i | − | 0.770816i | ||||||
\(382\) | 8.14150 | − | 8.14150i | 0.416556 | − | 0.416556i | ||||
\(383\) | 9.60774 | 0.490933 | 0.245466 | − | 0.969405i | \(-0.421059\pi\) | ||||
0.245466 | + | 0.969405i | \(0.421059\pi\) | |||||||
\(384\) | 2.09082 | − | 2.09082i | 0.106697 | − | 0.106697i | ||||
\(385\) | −0.620435 | − | 3.78399i | −0.0316203 | − | 0.192850i | ||||
\(386\) | −15.8717 | −0.807848 | ||||||||
\(387\) | − | 68.4093i | − | 3.47744i | ||||||
\(388\) | 17.1767i | 0.872016i | ||||||||
\(389\) | −12.3615 | − | 12.3615i | −0.626751 | − | 0.626751i | 0.320498 | − | 0.947249i | \(-0.396150\pi\) |
−0.947249 | + | 0.320498i | \(0.896150\pi\) | |||||||
\(390\) | 3.49774 | − | 0.573499i | 0.177115 | − | 0.0290403i | ||||
\(391\) | − | 1.55670i | − | 0.0787256i | ||||||
\(392\) | − | 6.17154i | − | 0.311710i | ||||||
\(393\) | −31.9326 | −1.61079 | ||||||||
\(394\) | −3.60225 | + | 3.60225i | −0.181479 | + | 0.181479i | ||||
\(395\) | 2.93510 | + | 17.9010i | 0.147681 | + | 0.900695i | ||||
\(396\) | −10.8201 | −0.543732 | ||||||||
\(397\) | 22.1034 | + | 22.1034i | 1.10934 | + | 1.10934i | 0.993238 | + | 0.116100i | \(0.0370394\pi\) |
0.116100 | + | 0.993238i | \(0.462961\pi\) | |||||||
\(398\) | 1.14697 | − | 1.14697i | 0.0574923 | − | 0.0574923i | ||||
\(399\) | 2.92058 | − | 2.92058i | 0.146212 | − | 0.146212i | ||||
\(400\) | 1.59670 | + | 4.73820i | 0.0798352 | + | 0.236910i | ||||
\(401\) | 11.3365 | + | 11.3365i | 0.566118 | + | 0.566118i | 0.931039 | − | 0.364921i | \(-0.118904\pi\) |
−0.364921 | + | 0.931039i | \(0.618904\pi\) | |||||||
\(402\) | −15.1357 | −0.754899 | ||||||||
\(403\) | −2.63189 | − | 2.63189i | −0.131104 | − | 0.131104i | ||||
\(404\) | 13.4676i | 0.670041i | ||||||||
\(405\) | 12.2650 | + | 8.80956i | 0.609454 | + | 0.437751i | ||||
\(406\) | − | 4.28683i | − | 0.212752i | ||||||
\(407\) | −11.3557 | + | 1.54425i | −0.562880 | + | 0.0765456i | ||||
\(408\) | −0.699803 | − | 0.699803i | −0.0346454 | − | 0.0346454i | ||||
\(409\) | −10.2703 | + | 10.2703i | −0.507834 | + | 0.507834i | −0.913861 | − | 0.406027i | \(-0.866914\pi\) |
0.406027 | + | 0.913861i | \(0.366914\pi\) | |||||||
\(410\) | 10.7813 | − | 15.0101i | 0.532449 | − | 0.741297i | ||||
\(411\) | 22.9169i | 1.13041i | ||||||||
\(412\) | − | 12.6201i | − | 0.621749i | ||||||
\(413\) | 5.28772 | 0.260192 | ||||||||
\(414\) | 26.7108i | 1.31276i | ||||||||
\(415\) | 4.04458 | + | 24.6676i | 0.198541 | + | 1.21089i | ||||
\(416\) | 0.536082 | 0.0262836 | ||||||||
\(417\) | −8.87372 | + | 8.87372i | −0.434548 | + | 0.434548i | ||||
\(418\) | −2.04453 | + | 2.04453i | −0.100001 | + | 0.100001i | ||||
\(419\) | 13.8549i | 0.676854i | 0.940993 | + | 0.338427i | \(0.109895\pi\) | ||||
−0.940993 | + | 0.338427i | \(0.890105\pi\) | |||||||
\(420\) | −3.51075 | + | 4.88781i | −0.171307 | + | 0.238501i | ||||
\(421\) | −25.5907 | − | 25.5907i | −1.24722 | − | 1.24722i | −0.956944 | − | 0.290273i | \(-0.906254\pi\) |
−0.290273 | − | 0.956944i | \(-0.593746\pi\) | |||||||
\(422\) | −3.19579 | −0.155569 | ||||||||
\(423\) | 0.812842 | + | 0.812842i | 0.0395217 | + | 0.0395217i | ||||
\(424\) | 5.03296 | + | 5.03296i | 0.244422 | + | 0.244422i | ||||
\(425\) | 1.58589 | − | 0.534422i | 0.0769269 | − | 0.0259233i | ||||
\(426\) | 32.4331 | − | 32.4331i | 1.57139 | − | 1.57139i | ||||
\(427\) | 11.4585 | 0.554515 | ||||||||
\(428\) | −1.64796 | + | 1.64796i | −0.0796571 | + | 0.0796571i | ||||
\(429\) | −2.11173 | − | 2.11173i | −0.101955 | − | 0.101955i | ||||
\(430\) | 21.6333 | + | 15.5385i | 1.04325 | + | 0.749332i | ||||
\(431\) | 16.4247 | + | 16.4247i | 0.791148 | + | 0.791148i | 0.981681 | − | 0.190533i | \(-0.0610215\pi\) |
−0.190533 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(432\) | 5.73519 | + | 5.73519i | 0.275934 | + | 0.275934i | ||||
\(433\) | 7.66855 | + | 7.66855i | 0.368527 | + | 0.368527i | 0.866940 | − | 0.498413i | \(-0.166084\pi\) |
−0.498413 | + | 0.866940i | \(0.666084\pi\) | |||||||
\(434\) | 6.31954 | 0.303347 | ||||||||
\(435\) | 18.1664 | − | 25.2919i | 0.871011 | − | 1.21265i | ||||
\(436\) | 7.06206 | + | 7.06206i | 0.338211 | + | 0.338211i | ||||
\(437\) | 5.04717 | + | 5.04717i | 0.241439 | + | 0.241439i | ||||
\(438\) | − | 28.5497i | − | 1.36416i | ||||||
\(439\) | 22.6564 | − | 22.6564i | 1.08133 | − | 1.08133i | 0.0849471 | − | 0.996385i | \(-0.472928\pi\) |
0.996385 | − | 0.0849471i | \(-0.0270721\pi\) | |||||||
\(440\) | 2.45768 | − | 3.42168i | 0.117166 | − | 0.163122i | ||||
\(441\) | 35.4434 | 1.68778 | ||||||||
\(442\) | − | 0.179428i | − | 0.00853453i | ||||||
\(443\) | 10.4105 | − | 10.4105i | 0.494616 | − | 0.494616i | −0.415141 | − | 0.909757i | \(-0.636268\pi\) |
0.909757 | + | 0.415141i | \(0.136268\pi\) | |||||||
\(444\) | 14.3157 | + | 10.8882i | 0.679392 | + | 0.516732i | ||||
\(445\) | −3.79220 | + | 0.621781i | −0.179768 | + | 0.0294753i | ||||
\(446\) | 7.29909 | + | 7.29909i | 0.345622 | + | 0.345622i | ||||
\(447\) | 42.4604 | + | 42.4604i | 2.00831 | + | 2.00831i | ||||
\(448\) | −0.643605 | + | 0.643605i | −0.0304075 | + | 0.0304075i | ||||
\(449\) | −16.6573 | − | 16.6573i | −0.786107 | − | 0.786107i | 0.194746 | − | 0.980854i | \(-0.437612\pi\) |
−0.980854 | + | 0.194746i | \(0.937612\pi\) | |||||||
\(450\) | −27.2117 | + | 9.16993i | −1.28277 | + | 0.432275i | ||||
\(451\) | −15.5714 | −0.733227 | ||||||||
\(452\) | − | 15.1701i | − | 0.713543i | ||||||
\(453\) | 28.9290 | + | 28.9290i | 1.35920 | + | 1.35920i | ||||
\(454\) | − | 19.6620i | − | 0.922784i | ||||||
\(455\) | −1.07669 | + | 0.176537i | −0.0504760 | + | 0.00827619i | ||||
\(456\) | 4.53784 | 0.212504 | ||||||||
\(457\) | − | 39.7899i | − | 1.86129i | −0.365919 | − | 0.930647i | \(-0.619245\pi\) | ||
0.365919 | − | 0.930647i | \(-0.380755\pi\) | |||||||
\(458\) | 13.4975i | 0.630697i | ||||||||
\(459\) | 1.91958 | − | 1.91958i | 0.0895985 | − | 0.0895985i | ||||
\(460\) | −8.44682 | − | 6.06708i | −0.393835 | − | 0.282879i | ||||
\(461\) | 7.71541 | − | 7.71541i | 0.359342 | − | 0.359342i | −0.504228 | − | 0.863570i | \(-0.668223\pi\) |
0.863570 | + | 0.504228i | \(0.168223\pi\) | |||||||
\(462\) | 5.07057 | 0.235904 | ||||||||
\(463\) | 14.7430 | 0.685164 | 0.342582 | − | 0.939488i | \(-0.388698\pi\) | ||||
0.342582 | + | 0.939488i | \(0.388698\pi\) | |||||||
\(464\) | 3.33033 | − | 3.33033i | 0.154607 | − | 0.154607i | ||||
\(465\) | 37.2847 | + | 26.7804i | 1.72904 | + | 1.24191i | ||||
\(466\) | 1.10924 | − | 1.10924i | 0.0513845 | − | 0.0513845i | ||||
\(467\) | 28.4840i | 1.31808i | 0.752107 | + | 0.659041i | \(0.229038\pi\) | ||||
−0.752107 | + | 0.659041i | \(0.770962\pi\) | |||||||
\(468\) | 3.07874i | 0.142315i | ||||||||
\(469\) | 4.65913 | 0.215139 | ||||||||
\(470\) | −0.441676 | + | 0.0724186i | −0.0203730 | + | 0.00334042i | ||||
\(471\) | 55.4829i | 2.55652i | ||||||||
\(472\) | 4.10789 | + | 4.10789i | 0.189081 | + | 0.189081i | ||||
\(473\) | − | 22.4422i | − | 1.03189i | ||||||
\(474\) | −23.9874 | −1.10178 | ||||||||
\(475\) | −3.40909 | + | 6.87453i | −0.156420 | + | 0.315425i | ||||
\(476\) | 0.215416 | + | 0.215416i | 0.00987360 | + | 0.00987360i | ||||
\(477\) | −28.9045 | + | 28.9045i | −1.32344 | + | 1.32344i | ||||
\(478\) | −10.5161 | − | 10.5161i | −0.480995 | − | 0.480995i | ||||
\(479\) | 2.09957 | + | 2.09957i | 0.0959318 | + | 0.0959318i | 0.753444 | − | 0.657512i | \(-0.228391\pi\) |
−0.657512 | + | 0.753444i | \(0.728391\pi\) | |||||||
\(480\) | −6.52462 | + | 1.06980i | −0.297807 | + | 0.0488293i | ||||
\(481\) | 0.439398 | + | 3.23112i | 0.0200348 | + | 0.147326i | ||||
\(482\) | 18.7617 | − | 18.7617i | 0.854571 | − | 0.854571i | ||||
\(483\) | − | 12.5173i | − | 0.569557i | ||||||
\(484\) | 7.45037 | 0.338653 | ||||||||
\(485\) | 22.4066 | − | 31.1953i | 1.01743 | − | 1.41651i | ||||
\(486\) | 3.08553 | − | 3.08553i | 0.139962 | − | 0.139962i | ||||
\(487\) | − | 17.7878i | − | 0.806044i | −0.915190 | − | 0.403022i | \(-0.867960\pi\) | ||
0.915190 | − | 0.403022i | \(-0.132040\pi\) | |||||||
\(488\) | 8.90180 | + | 8.90180i | 0.402965 | + | 0.402965i | ||||
\(489\) | −3.10459 | − | 3.10459i | −0.140395 | − | 0.140395i | ||||
\(490\) | −8.05061 | + | 11.2084i | −0.363689 | + | 0.506342i | ||||
\(491\) | 11.1728 | 0.504221 | 0.252110 | − | 0.967698i | \(-0.418875\pi\) | ||||
0.252110 | + | 0.967698i | \(0.418875\pi\) | |||||||
\(492\) | 17.2803 | + | 17.2803i | 0.779056 | + | 0.779056i | ||||
\(493\) | −1.11467 | − | 1.11467i | −0.0502022 | − | 0.0502022i | ||||
\(494\) | 0.581747 | + | 0.581747i | 0.0261740 | + | 0.0261740i | ||||
\(495\) | 19.6509 | + | 14.1146i | 0.883240 | + | 0.634403i | ||||
\(496\) | 4.90948 | + | 4.90948i | 0.220442 | + | 0.220442i | ||||
\(497\) | −9.98370 | + | 9.98370i | −0.447830 | + | 0.447830i | ||||
\(498\) | −33.0548 | −1.48122 | ||||||||
\(499\) | 9.60201 | − | 9.60201i | 0.429845 | − | 0.429845i | −0.458730 | − | 0.888576i | \(-0.651696\pi\) |
0.888576 | + | 0.458730i | \(0.151696\pi\) | |||||||
\(500\) | 3.28101 | − | 10.6881i | 0.146731 | − | 0.477985i | ||||
\(501\) | −9.81033 | − | 9.81033i | −0.438293 | − | 0.438293i | ||||
\(502\) | −9.09164 | − | 9.09164i | −0.405780 | − | 0.405780i | ||||
\(503\) | −14.7806 | −0.659035 | −0.329518 | − | 0.944149i | \(-0.606886\pi\) | ||||
−0.329518 | + | 0.944149i | \(0.606886\pi\) | |||||||
\(504\) | −3.69625 | − | 3.69625i | −0.164644 | − | 0.164644i | ||||
\(505\) | 17.5682 | − | 24.4591i | 0.781773 | − | 1.08842i | ||||
\(506\) | 8.76267i | 0.389548i | ||||||||
\(507\) | 26.5798 | − | 26.5798i | 1.18045 | − | 1.18045i | ||||
\(508\) | −3.59805 | + | 3.59805i | −0.159638 | + | 0.159638i | ||||
\(509\) | 4.49759 | 0.199352 | 0.0996760 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996760 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(510\) | 0.358064 | + | 2.18381i | 0.0158553 | + | 0.0967007i | ||||
\(511\) | 8.78829i | 0.388771i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.4475i | 0.549568i | ||||||||
\(514\) | − | 2.08454i | − | 0.0919453i | ||||||
\(515\) | −16.4626 | + | 22.9199i | −0.725429 | + | 1.00997i | ||||
\(516\) | −24.9052 | + | 24.9052i | −1.09639 | + | 1.09639i | ||||
\(517\) | 0.266659 | + | 0.266659i | 0.0117276 | + | 0.0117276i | ||||
\(518\) | −4.40672 | − | 3.35166i | −0.193620 | − | 0.147264i | ||||
\(519\) | − | 7.03045i | − | 0.308603i | ||||||
\(520\) | −0.973599 | − | 0.699305i | −0.0426951 | − | 0.0306665i | ||||
\(521\) | − | 14.5173i | − | 0.636014i | −0.948088 | − | 0.318007i | \(-0.896986\pi\) | ||
0.948088 | − | 0.318007i | \(-0.103014\pi\) | |||||||
\(522\) | 19.1262 | + | 19.1262i | 0.837131 | + | 0.837131i | ||||
\(523\) | 27.3756 | 1.19705 | 0.598526 | − | 0.801103i | \(-0.295753\pi\) | ||||
0.598526 | + | 0.801103i | \(0.295753\pi\) | |||||||
\(524\) | 7.63639 | + | 7.63639i | 0.333597 | + | 0.333597i | ||||
\(525\) | 12.7520 | − | 4.29725i | 0.556544 | − | 0.187547i | ||||
\(526\) | 6.41417 | − | 6.41417i | 0.279671 | − | 0.279671i | ||||
\(527\) | 1.64322 | − | 1.64322i | 0.0715797 | − | 0.0715797i | ||||
\(528\) | 3.93919 | + | 3.93919i | 0.171431 | + | 0.171431i | ||||
\(529\) | −1.36834 | −0.0594930 | ||||||||
\(530\) | −2.57519 | − | 15.7059i | −0.111859 | − | 0.682221i | ||||
\(531\) | −23.5918 | + | 23.5918i | −1.02380 | + | 1.02380i | ||||
\(532\) | −1.39686 | −0.0605615 | ||||||||
\(533\) | 4.43064i | 0.191913i | ||||||||
\(534\) | − | 5.08157i | − | 0.219901i | ||||||
\(535\) | 5.14264 | − | 0.843202i | 0.222336 | − | 0.0364548i | ||||
\(536\) | 3.61956 | + | 3.61956i | 0.156341 | + | 0.156341i | ||||
\(537\) | − | 54.4315i | − | 2.34889i | ||||||
\(538\) | − | 10.5529i | − | 0.454970i | ||||||
\(539\) | 11.6275 | 0.500831 | ||||||||
\(540\) | −2.93449 | − | 17.8973i | −0.126280 | − | 0.770176i | ||||
\(541\) | 15.0886 | − | 15.0886i | 0.648708 | − | 0.648708i | −0.303973 | − | 0.952681i | \(-0.598313\pi\) |
0.952681 | + | 0.303973i | \(0.0983133\pi\) | |||||||
\(542\) | −19.2734 | −0.827865 | ||||||||
\(543\) | −12.3758 | + | 12.3758i | −0.531095 | + | 0.531095i | ||||
\(544\) | 0.334703i | 0.0143503i | ||||||||
\(545\) | −3.61340 | − | 22.0379i | −0.154781 | − | 0.944001i | ||||
\(546\) | − | 1.44277i | − | 0.0617449i | ||||||
\(547\) | −24.9954 | −1.06873 | −0.534363 | − | 0.845255i | \(-0.679448\pi\) | ||||
−0.534363 | + | 0.845255i | \(0.679448\pi\) | |||||||
\(548\) | 5.48037 | − | 5.48037i | 0.234110 | − | 0.234110i | ||||
\(549\) | −51.1233 | + | 51.1233i | −2.18189 | + | 2.18189i | ||||
\(550\) | −8.92698 | + | 3.00826i | −0.380648 | + | 0.128273i | ||||
\(551\) | 7.22803 | 0.307924 | ||||||||
\(552\) | 9.72436 | − | 9.72436i | 0.413896 | − | 0.413896i | ||||
\(553\) | 7.38391 | 0.313996 | ||||||||
\(554\) | −7.82056 | −0.332264 | ||||||||
\(555\) | −11.7959 | − | 38.4489i | −0.500706 | − | 1.63207i | ||||
\(556\) | 4.24414 | 0.179991 | ||||||||
\(557\) | 12.4355 | 0.526909 | 0.263455 | − | 0.964672i | \(-0.415138\pi\) | ||||
0.263455 | + | 0.964672i | \(0.415138\pi\) | |||||||
\(558\) | −28.1953 | + | 28.1953i | −1.19360 | + | 1.19360i | ||||
\(559\) | −6.38565 | −0.270084 | ||||||||
\(560\) | 2.00844 | − | 0.329310i | 0.0848721 | − | 0.0139159i | ||||
\(561\) | 1.31846 | − | 1.31846i | 0.0556654 | − | 0.0556654i | ||||
\(562\) | 10.4788 | − | 10.4788i | 0.442020 | − | 0.442020i | ||||
\(563\) | 9.73552 | 0.410303 | 0.205152 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205152 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(564\) | − | 0.591849i | − | 0.0249213i | ||||||
\(565\) | −19.7890 | + | 27.5510i | −0.832530 | + | 1.15908i | ||||
\(566\) | − | 26.3960i | − | 1.10951i | ||||||
\(567\) | 4.34649 | − | 4.34649i | 0.182536 | − | 0.182536i | ||||
\(568\) | −15.5121 | −0.650875 | ||||||||
\(569\) | −10.5582 | + | 10.5582i | −0.442624 | + | 0.442624i | −0.892893 | − | 0.450269i | \(-0.851328\pi\) |
0.450269 | + | 0.892893i | \(0.351328\pi\) | |||||||
\(570\) | −8.24133 | − | 5.91948i | −0.345191 | − | 0.247940i | ||||
\(571\) | 13.3170 | 0.557301 | 0.278650 | − | 0.960393i | \(-0.410113\pi\) | ||||
0.278650 | + | 0.960393i | \(0.410113\pi\) | |||||||
\(572\) | 1.01000i | 0.0422304i | ||||||||
\(573\) | − | 34.0448i | − | 1.42224i | ||||||
\(574\) | −5.31930 | − | 5.31930i | −0.222023 | − | 0.222023i | ||||
\(575\) | 7.42625 | + | 22.0373i | 0.309696 | + | 0.919019i | ||||
\(576\) | − | 5.74304i | − | 0.239293i | ||||||
\(577\) | 4.76082i | 0.198195i | 0.995078 | + | 0.0990977i | \(0.0315956\pi\) | ||||
−0.995078 | + | 0.0990977i | \(0.968404\pi\) | |||||||
\(578\) | −16.8880 | −0.702447 | ||||||||
\(579\) | −33.1848 | + | 33.1848i | −1.37911 | + | 1.37911i | ||||
\(580\) | −10.3927 | + | 1.70401i | −0.431532 | + | 0.0707552i | ||||
\(581\) | 10.1751 | 0.422133 | ||||||||
\(582\) | 35.9134 | + | 35.9134i | 1.48866 | + | 1.48866i | ||||
\(583\) | −9.48232 | + | 9.48232i | −0.392718 | + | 0.392718i | ||||
\(584\) | −6.82739 | + | 6.82739i | −0.282519 | + | 0.282519i | ||||
\(585\) | 4.01613 | − | 5.59141i | 0.166047 | − | 0.231177i | ||||
\(586\) | 22.4956 | + | 22.4956i | 0.929287 | + | 0.929287i | ||||
\(587\) | −2.41574 | −0.0997081 | −0.0498540 | − | 0.998757i | \(-0.515876\pi\) | ||||
−0.0498540 | + | 0.998757i | \(0.515876\pi\) | |||||||
\(588\) | −12.9036 | − | 12.9036i | −0.532134 | − | 0.532134i | ||||
\(589\) | 10.6554i | 0.439047i | ||||||||
\(590\) | −2.10186 | − | 12.8191i | −0.0865324 | − | 0.527755i | ||||
\(591\) | 15.0633i | 0.619621i | ||||||||
\(592\) | −0.819646 | − | 6.02729i | −0.0336872 | − | 0.247720i | ||||
\(593\) | 1.14068 | + | 1.14068i | 0.0468420 | + | 0.0468420i | 0.730140 | − | 0.683298i | \(-0.239455\pi\) |
−0.683298 | + | 0.730140i | \(0.739455\pi\) | |||||||
\(594\) | −10.8054 | + | 10.8054i | −0.443349 | + | 0.443349i | ||||
\(595\) | −0.110221 | − | 0.672231i | −0.00451862 | − | 0.0275588i | ||||
\(596\) | − | 20.3080i | − | 0.831849i | ||||||
\(597\) | − | 4.79620i | − | 0.196295i | ||||||
\(598\) | 2.49331 | 0.101959 | ||||||||
\(599\) | 40.0185i | 1.63511i | 0.575851 | + | 0.817555i | \(0.304671\pi\) | ||||
−0.575851 | + | 0.817555i | \(0.695329\pi\) | |||||||
\(600\) | 13.2451 | + | 6.56829i | 0.540730 | + | 0.268149i | ||||
\(601\) | −11.7034 | −0.477393 | −0.238696 | − | 0.971094i | \(-0.576720\pi\) | ||||
−0.238696 | + | 0.971094i | \(0.576720\pi\) | |||||||
\(602\) | 7.66643 | − | 7.66643i | 0.312460 | − | 0.312460i | ||||
\(603\) | −20.7873 | + | 20.7873i | −0.846522 | + | 0.846522i | ||||
\(604\) | − | 13.8362i | − | 0.562987i | ||||||
\(605\) | −13.5309 | − | 9.71881i | −0.550109 | − | 0.395126i | ||||
\(606\) | 28.1584 | + | 28.1584i | 1.14386 | + | 1.14386i | ||||
\(607\) | 24.3851 | 0.989761 | 0.494881 | − | 0.868961i | \(-0.335212\pi\) | ||||
0.494881 | + | 0.868961i | \(0.335212\pi\) | |||||||
\(608\) | −1.08518 | − | 1.08518i | −0.0440100 | − | 0.0440100i | ||||
\(609\) | −8.96299 | − | 8.96299i | −0.363199 | − | 0.363199i | ||||
\(610\) | −4.55473 | − | 27.7790i | −0.184416 | − | 1.12474i | ||||
\(611\) | 0.0758746 | − | 0.0758746i | 0.00306956 | − | 0.00306956i | ||||
\(612\) | −1.92221 | −0.0777008 | ||||||||
\(613\) | 18.3951 | − | 18.3951i | 0.742971 | − | 0.742971i | −0.230178 | − | 0.973149i | \(-0.573931\pi\) |
0.973149 | + | 0.230178i | \(0.0739308\pi\) | |||||||
\(614\) | 17.4358 | + | 17.4358i | 0.703650 | + | 0.703650i | ||||
\(615\) | −8.84172 | − | 53.9251i | −0.356533 | − | 2.17447i | ||||
\(616\) | −1.21258 | − | 1.21258i | −0.0488563 | − | 0.0488563i | ||||
\(617\) | 31.2896 | + | 31.2896i | 1.25967 | + | 1.25967i | 0.951250 | + | 0.308421i | \(0.0998006\pi\) |
0.308421 | + | 0.951250i | \(0.400199\pi\) | |||||||
\(618\) | −26.3864 | − | 26.3864i | −1.06142 | − | 1.06142i | ||||
\(619\) | −39.6915 | −1.59534 | −0.797669 | − | 0.603096i | \(-0.793934\pi\) | ||||
−0.797669 | + | 0.603096i | \(0.793934\pi\) | |||||||
\(620\) | −2.51201 | − | 15.3206i | −0.100885 | − | 0.615289i | ||||
\(621\) | 26.6743 | + | 26.6743i | 1.07040 | + | 1.07040i | ||||
\(622\) | 3.97519 | + | 3.97519i | 0.159391 | + | 0.159391i | ||||
\(623\) | 1.56423i | 0.0626697i | ||||||||
\(624\) | 1.12085 | − | 1.12085i | 0.0448699 | − | 0.0448699i | ||||
\(625\) | −19.9011 | + | 15.1310i | −0.796043 | + | 0.605240i | ||||
\(626\) | −15.8472 | −0.633380 | ||||||||
\(627\) | 8.54949i | 0.341434i | ||||||||
\(628\) | 13.2682 | − | 13.2682i | 0.529460 | − | 0.529460i | ||||
\(629\) | −2.01735 | + | 0.274338i | −0.0804370 | + | 0.0109386i | ||||
\(630\) | 1.89124 | + | 11.5345i | 0.0753488 | + | 0.459547i | ||||
\(631\) | −29.5138 | − | 29.5138i | −1.17493 | − | 1.17493i | −0.981020 | − | 0.193907i | \(-0.937884\pi\) |
−0.193907 | − | 0.981020i | \(-0.562116\pi\) | |||||||
\(632\) | 5.73637 | + | 5.73637i | 0.228181 | + | 0.228181i | ||||
\(633\) | −6.68182 | + | 6.68182i | −0.265579 | + | 0.265579i | ||||
\(634\) | −0.950144 | − | 0.950144i | −0.0377350 | − | 0.0377350i | ||||
\(635\) | 11.2281 | − | 1.84099i | 0.445574 | − | 0.0730576i | ||||
\(636\) | 21.0460 | 0.834528 | ||||||||
\(637\) | − | 3.30846i | − | 0.131086i | ||||||
\(638\) | 6.27449 | + | 6.27449i | 0.248409 | + | 0.248409i | ||||
\(639\) | − | 89.0868i | − | 3.52422i | ||||||
\(640\) | 1.81614 | + | 1.30447i | 0.0717891 | + | 0.0515638i | ||||
\(641\) | −36.0367 | −1.42336 | −0.711681 | − | 0.702503i | \(-0.752066\pi\) | ||||
−0.711681 | + | 0.702503i | \(0.752066\pi\) | |||||||
\(642\) | 6.89116i | 0.271973i | ||||||||
\(643\) | − | 36.2733i | − | 1.43048i | −0.698880 | − | 0.715239i | \(-0.746318\pi\) | ||
0.698880 | − | 0.715239i | \(-0.253682\pi\) | |||||||
\(644\) | −2.99340 | + | 2.99340i | −0.117956 | + | 0.117956i | ||||
\(645\) | 77.7194 | − | 12.7431i | 3.06020 | − | 0.501759i | ||||
\(646\) | −0.363214 | + | 0.363214i | −0.0142905 | + | 0.0142905i | ||||
\(647\) | 20.1761 | 0.793203 | 0.396602 | − | 0.917991i | \(-0.370189\pi\) | ||||
0.396602 | + | 0.917991i | \(0.370189\pi\) | |||||||
\(648\) | 6.75336 | 0.265297 | ||||||||
\(649\) | −7.73946 | + | 7.73946i | −0.303800 | + | 0.303800i | ||||
\(650\) | 0.855965 | + | 2.54007i | 0.0335737 | + | 0.0996296i | ||||
\(651\) | 13.2130 | − | 13.2130i | 0.517858 | − | 0.517858i | ||||
\(652\) | 1.48487i | 0.0581520i | ||||||||
\(653\) | 45.2272i | 1.76988i | 0.465706 | + | 0.884939i | \(0.345800\pi\) | ||||
−0.465706 | + | 0.884939i | \(0.654200\pi\) | |||||||
\(654\) | 29.5309 | 1.15475 | ||||||||
\(655\) | −3.90727 | − | 23.8302i | −0.152670 | − | 0.931122i | ||||
\(656\) | − | 8.26486i | − | 0.322688i | ||||||
\(657\) | −39.2100 | − | 39.2100i | −1.52973 | − | 1.52973i | ||||
\(658\) | 0.182186i | 0.00710234i | ||||||||
\(659\) | −3.64301 | −0.141911 | −0.0709557 | − | 0.997479i | \(-0.522605\pi\) | ||||
−0.0709557 | + | 0.997479i | \(0.522605\pi\) | |||||||
\(660\) | −2.01555 | − | 12.2927i | −0.0784550 | − | 0.478492i | ||||
\(661\) | 0.359733 | + | 0.359733i | 0.0139920 | + | 0.0139920i | 0.714068 | − | 0.700076i | \(-0.246851\pi\) |
−0.700076 | + | 0.714068i | \(0.746851\pi\) | |||||||
\(662\) | 19.3735 | − | 19.3735i | 0.752972 | − | 0.752972i | ||||
\(663\) | −0.375152 | − | 0.375152i | −0.0145697 | − | 0.0145697i | ||||
\(664\) | 7.90475 | + | 7.90475i | 0.306764 | + | 0.306764i | ||||
\(665\) | 2.53689 | + | 1.82216i | 0.0983762 | + | 0.0706604i | ||||
\(666\) | 34.6149 | − | 4.70726i | 1.34130 | − | 0.182402i | ||||
\(667\) | 15.4893 | − | 15.4893i | 0.599749 | − | 0.599749i | ||||
\(668\) | 4.69210i | 0.181543i | ||||||||
\(669\) | 30.5221 | 1.18005 | ||||||||
\(670\) | −1.85200 | − | 11.2952i | −0.0715490 | − | 0.436373i | ||||
\(671\) | −16.7714 | + | 16.7714i | −0.647452 | + | 0.647452i | ||||
\(672\) | 2.69132i | 0.103820i | ||||||||
\(673\) | 12.3228 | + | 12.3228i | 0.475011 | + | 0.475011i | 0.903532 | − | 0.428521i | \(-0.140965\pi\) |
−0.428521 | + | 0.903532i | \(0.640965\pi\) | |||||||
\(674\) | 3.21128 | + | 3.21128i | 0.123694 | + | 0.123694i | ||||
\(675\) | −18.0171 | + | 36.3319i | −0.693477 | + | 1.39841i | ||||
\(676\) | −12.7126 | −0.488947 | ||||||||
\(677\) | 13.3890 | + | 13.3890i | 0.514579 | + | 0.514579i | 0.915926 | − | 0.401347i | \(-0.131458\pi\) |
−0.401347 | + | 0.915926i | \(0.631458\pi\) | |||||||
\(678\) | −31.7180 | − | 31.7180i | −1.21812 | − | 1.21812i | ||||
\(679\) | −11.0550 | − | 11.0550i | −0.424253 | − | 0.424253i | ||||
\(680\) | 0.436611 | − | 0.607866i | 0.0167433 | − | 0.0233106i | ||||
\(681\) | −41.1097 | − | 41.1097i | −1.57533 | − | 1.57533i | ||||
\(682\) | −9.24969 | + | 9.24969i | −0.354189 | + | 0.354189i | ||||
\(683\) | 26.4505 | 1.01210 | 0.506050 | − | 0.862504i | \(-0.331105\pi\) | ||||
0.506050 | + | 0.862504i | \(0.331105\pi\) | |||||||
\(684\) | 6.23224 | − | 6.23224i | 0.238296 | − | 0.238296i | ||||
\(685\) | −17.1021 | + | 2.80411i | −0.653437 | + | 0.107140i | ||||
\(686\) | 8.47727 | + | 8.47727i | 0.323664 | + | 0.323664i | ||||
\(687\) | 28.2208 | + | 28.2208i | 1.07669 | + | 1.07669i | ||||
\(688\) | 11.9117 | 0.454129 | ||||||||
\(689\) | 2.69808 | + | 2.69808i | 0.102789 | + | 0.102789i | ||||
\(690\) | −30.3459 | + | 4.97561i | −1.15525 | + | 0.189418i | ||||
\(691\) | 8.34143i | 0.317323i | 0.987333 | + | 0.158661i | \(0.0507178\pi\) | ||||
−0.987333 | + | 0.158661i | \(0.949282\pi\) | |||||||
\(692\) | −1.68127 | + | 1.68127i | −0.0639123 | + | 0.0639123i | ||||
\(693\) | 6.96390 | − | 6.96390i | 0.264537 | − | 0.264537i | ||||
\(694\) | 18.4401 | 0.699976 | ||||||||
\(695\) | −7.70793 | − | 5.53636i | −0.292379 | − | 0.210006i | ||||
\(696\) | − | 13.9262i | − | 0.527872i | ||||||
\(697\) | −2.76627 | −0.104780 | ||||||||
\(698\) | 21.3314i | 0.807405i | ||||||||
\(699\) | − | 4.63843i | − | 0.175442i | ||||||
\(700\) | −4.07718 | − | 2.02188i | −0.154103 | − | 0.0764200i | ||||
\(701\) | 15.0534 | − | 15.0534i | 0.568560 | − | 0.568560i | −0.363165 | − | 0.931725i | \(-0.618304\pi\) |
0.931725 | + | 0.363165i | \(0.118304\pi\) | |||||||
\(702\) | 3.07453 | + | 3.07453i | 0.116041 | + | 0.116041i | ||||
\(703\) | 5.65124 | − | 7.43017i | 0.213141 | − | 0.280234i | ||||
\(704\) | − | 1.88405i | − | 0.0710076i | ||||||
\(705\) | −0.772050 | + | 1.07488i | −0.0290771 | + | 0.0404823i | ||||
\(706\) | 11.9150i | 0.448428i | ||||||||
\(707\) | −8.66785 | − | 8.66785i | −0.325988 | − | 0.325988i | ||||
\(708\) | 17.1777 | 0.645578 | ||||||||
\(709\) | 26.5041 | + | 26.5041i | 0.995384 | + | 0.995384i | 0.999989 | − | 0.00460560i | \(-0.00146601\pi\) |
−0.00460560 | + | 0.999989i | \(0.501466\pi\) | |||||||
\(710\) | 28.1722 | + | 20.2352i | 1.05728 | + | 0.759412i | ||||
\(711\) | −32.9442 | + | 32.9442i | −1.23550 | + | 1.23550i | ||||
\(712\) | −1.21521 | + | 1.21521i | −0.0455420 | + | 0.0455420i | ||||
\(713\) | 22.8339 | + | 22.8339i | 0.855137 | + | 0.855137i | ||||
\(714\) | 0.900793 | 0.0337113 | ||||||||
\(715\) | 1.31752 | − | 1.83430i | 0.0492725 | − | 0.0685991i | ||||
\(716\) | −13.0168 | + | 13.0168i | −0.486461 | + | 0.486461i | ||||
\(717\) | −43.9745 | −1.64226 | ||||||||
\(718\) | 24.9976i | 0.932903i | ||||||||
\(719\) | 17.0904i | 0.637364i | 0.947862 | + | 0.318682i | \(0.103240\pi\) | ||||
−0.947862 | + | 0.318682i | \(0.896760\pi\) | |||||||
\(720\) | −7.49163 | + | 10.4301i | −0.279197 | + | 0.388708i | ||||
\(721\) | 8.12238 | + | 8.12238i | 0.302493 | + | 0.302493i | ||||
\(722\) | 16.6448i | 0.619454i | ||||||||
\(723\) | − | 78.4545i | − | 2.91775i | ||||||
\(724\) | 5.91911 | 0.219982 | ||||||||
\(725\) | 21.0973 | + | 10.4622i | 0.783535 | + | 0.388557i | ||||
\(726\) | 15.5774 | − | 15.5774i | 0.578131 | − | 0.578131i | ||||
\(727\) | −49.5068 | −1.83611 | −0.918053 | − | 0.396457i | \(-0.870240\pi\) | ||||
−0.918053 | + | 0.396457i | \(0.870240\pi\) | |||||||
\(728\) | −0.345025 | + | 0.345025i | −0.0127875 | + | 0.0127875i | ||||
\(729\) | − | 33.1626i | − | 1.22825i | ||||||
\(730\) | 21.3056 | − | 3.49333i | 0.788556 | − | 0.129294i | ||||
\(731\) | − | 3.98688i | − | 0.147460i | ||||||
\(732\) | 37.2241 | 1.37584 | ||||||||
\(733\) | 8.80945 | − | 8.80945i | 0.325385 | − | 0.325385i | −0.525444 | − | 0.850828i | \(-0.676101\pi\) |
0.850828 | + | 0.525444i | \(0.176101\pi\) | |||||||
\(734\) | −0.228241 | + | 0.228241i | −0.00842451 | + | 0.00842451i | ||||
\(735\) | 6.60230 | + | 40.2670i | 0.243530 | + | 1.48527i | ||||
\(736\) | −4.65098 | −0.171438 | ||||||||
\(737\) | −6.81941 | + | 6.81941i | −0.251196 | + | 0.251196i | ||||
\(738\) | 47.4654 | 1.74722 | ||||||||
\(739\) | −44.3001 | −1.62961 | −0.814803 | − | 0.579738i | \(-0.803155\pi\) | ||||
−0.814803 | + | 0.579738i | \(0.803155\pi\) | |||||||
\(740\) | −6.37384 | + | 12.0156i | −0.234307 | + | 0.441702i | ||||
\(741\) | 2.43265 | 0.0893658 | ||||||||
\(742\) | −6.47848 | −0.237832 | ||||||||
\(743\) | −16.9715 | + | 16.9715i | −0.622623 | + | 0.622623i | −0.946201 | − | 0.323579i | \(-0.895114\pi\) |
0.323579 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(744\) | 20.5297 | 0.752654 | ||||||||
\(745\) | −26.4913 | + | 36.8822i | −0.970564 | + | 1.35126i | ||||
\(746\) | −5.32431 | + | 5.32431i | −0.194937 | + | 0.194937i | ||||
\(747\) | −45.3972 | + | 45.3972i | −1.66100 | + | 1.66100i | ||||
\(748\) | −0.630595 | −0.0230568 | ||||||||
\(749\) | − | 2.12127i | − | 0.0775095i | ||||||
\(750\) | −15.4868 | − | 29.2068i | −0.565498 | − | 1.06648i | ||||
\(751\) | − | 10.2040i | − | 0.372350i | −0.982517 | − | 0.186175i | \(-0.940391\pi\) | ||
0.982517 | − | 0.186175i | \(-0.0596091\pi\) | |||||||
\(752\) | −0.141535 | + | 0.141535i | −0.00516126 | + | 0.00516126i | ||||
\(753\) | −38.0179 | −1.38545 | ||||||||
\(754\) | 1.78533 | − | 1.78533i | 0.0650179 | − | 0.0650179i | ||||
\(755\) | −18.0489 | + | 25.1284i | −0.656868 | + | 0.914517i | ||||
\(756\) | −7.38239 | −0.268495 | ||||||||
\(757\) | − | 6.71387i | − | 0.244020i | −0.992529 | − | 0.122010i | \(-0.961066\pi\) | ||
0.992529 | − | 0.122010i | \(-0.0389340\pi\) | |||||||
\(758\) | 7.62224i | 0.276852i | ||||||||
\(759\) | 18.3211 | + | 18.3211i | 0.665015 | + | 0.665015i | ||||
\(760\) | 0.555249 | + | 3.38643i | 0.0201410 | + | 0.122839i | ||||
\(761\) | − | 1.33026i | − | 0.0482218i | −0.999709 | − | 0.0241109i | \(-0.992325\pi\) | ||
0.999709 | − | 0.0241109i | \(-0.00767549\pi\) | |||||||
\(762\) | 15.0457i | 0.545049i | ||||||||
\(763\) | −9.09035 | −0.329093 | ||||||||
\(764\) | −8.14150 | + | 8.14150i | −0.294549 | + | 0.294549i | ||||
\(765\) | 3.49100 | + | 2.50747i | 0.126217 | + | 0.0906578i | ||||
\(766\) | −9.60774 | −0.347142 | ||||||||
\(767\) | 2.20217 | + | 2.20217i | 0.0795157 | + | 0.0795157i | ||||
\(768\) | −2.09082 | + | 2.09082i | −0.0754459 | + | 0.0754459i | ||||
\(769\) | 18.1678 | − | 18.1678i | 0.655148 | − | 0.655148i | −0.299080 | − | 0.954228i | \(-0.596680\pi\) |
0.954228 | + | 0.299080i | \(0.0966797\pi\) | |||||||
\(770\) | 0.620435 | + | 3.78399i | 0.0223589 | + | 0.136366i | ||||
\(771\) | −4.35840 | − | 4.35840i | −0.156964 | − | 0.156964i | ||||
\(772\) | 15.8717 | 0.571235 | ||||||||
\(773\) | 19.9474 | + | 19.9474i | 0.717458 | + | 0.717458i | 0.968084 | − | 0.250626i | \(-0.0806365\pi\) |
−0.250626 | + | 0.968084i | \(0.580637\pi\) | |||||||
\(774\) | 68.4093i | 2.45892i | ||||||||
\(775\) | −15.4231 | + | 31.1011i | −0.554015 | + | 1.11718i | ||||
\(776\) | − | 17.1767i | − | 0.616609i | ||||||
\(777\) | −16.2214 | + | 2.20593i | −0.581938 | + | 0.0791373i | ||||
\(778\) | 12.3615 | + | 12.3615i | 0.443180 | + | 0.443180i | ||||
\(779\) | 8.96888 | − | 8.96888i | 0.321343 | − | 0.321343i | ||||
\(780\) | −3.49774 | + | 0.573499i | −0.125239 | + | 0.0205346i | ||||
\(781\) | − | 29.2256i | − | 1.04577i | ||||||
\(782\) | 1.55670i | 0.0556674i | ||||||||
\(783\) | 38.2001 | 1.36516 | ||||||||
\(784\) | 6.17154i | 0.220412i | ||||||||
\(785\) | −41.4050 | + | 6.78889i | −1.47781 | + | 0.242306i | ||||
\(786\) | 31.9326 | 1.13900 | ||||||||
\(787\) | 34.1482 | − | 34.1482i | 1.21725 | − | 1.21725i | 0.248663 | − | 0.968590i | \(-0.420009\pi\) |
0.968590 | − | 0.248663i | \(-0.0799912\pi\) | |||||||
\(788\) | 3.60225 | − | 3.60225i | 0.128325 | − | 0.128325i | ||||
\(789\) | − | 26.8217i | − | 0.954878i | ||||||
\(790\) | −2.93510 | − | 17.9010i | −0.104426 | − | 0.636888i | ||||
\(791\) | 9.76357 | + | 9.76357i | 0.347153 | + | 0.347153i | ||||
\(792\) | 10.8201 | 0.384477 | ||||||||
\(793\) | 4.77210 | + | 4.77210i | 0.169462 | + | 0.169462i | ||||
\(794\) | −22.1034 | − | 22.1034i | −0.784420 | − | 0.784420i | ||||
\(795\) | −38.2224 | − | 27.4539i | −1.35561 | − | 0.973690i | ||||
\(796\) | −1.14697 | + | 1.14697i | −0.0406532 | + | 0.0406532i | ||||
\(797\) | −48.5605 | −1.72010 | −0.860050 | − | 0.510209i | \(-0.829568\pi\) | ||||
−0.860050 | + | 0.510209i | \(0.829568\pi\) | |||||||
\(798\) | −2.92058 | + | 2.92058i | −0.103387 | + | 0.103387i | ||||
\(799\) | 0.0473723 | + | 0.0473723i | 0.00167591 | + | 0.00167591i | ||||
\(800\) | −1.59670 | − | 4.73820i | −0.0564520 | − | 0.167521i | ||||
\(801\) | −6.97901 | − | 6.97901i | −0.246591 | − | 0.246591i | ||||
\(802\) | −11.3365 | − | 11.3365i | −0.400306 | − | 0.400306i | ||||
\(803\) | −12.8631 | − | 12.8631i | −0.453929 | − | 0.453929i | ||||
\(804\) | 15.1357 | 0.533794 | ||||||||
\(805\) | 9.34122 | − | 1.53162i | 0.329235 | − | 0.0539824i | ||||
\(806\) | 2.63189 | + | 2.63189i | 0.0927043 | + | 0.0927043i | ||||
\(807\) | −22.0643 | − | 22.0643i | −0.776699 | − | 0.776699i | ||||
\(808\) | − | 13.4676i | − | 0.473790i | ||||||
\(809\) | 18.4675 | − | 18.4675i | 0.649284 | − | 0.649284i | −0.303536 | − | 0.952820i | \(-0.598167\pi\) |
0.952820 | + | 0.303536i | \(0.0981674\pi\) | |||||||
\(810\) | −12.2650 | − | 8.80956i | −0.430949 | − | 0.309537i | ||||
\(811\) | −41.1929 | −1.44648 | −0.723238 | − | 0.690598i | \(-0.757347\pi\) | ||||
−0.723238 | + | 0.690598i | \(0.757347\pi\) | |||||||
\(812\) | 4.28683i | 0.150438i | ||||||||
\(813\) | −40.2972 | + | 40.2972i | −1.41329 | + | 1.41329i | ||||
\(814\) | 11.3557 | − | 1.54425i | 0.398016 | − | 0.0541259i | ||||
\(815\) | 1.93697 | − | 2.69673i | 0.0678492 | − | 0.0944623i | ||||
\(816\) | 0.699803 | + | 0.699803i | 0.0244980 | + | 0.0244980i | ||||
\(817\) | 12.9264 | + | 12.9264i | 0.452236 | + | 0.452236i | ||||
\(818\) | 10.2703 | − | 10.2703i | 0.359093 | − | 0.359093i | ||||
\(819\) | −1.98149 | − | 1.98149i | −0.0692390 | − | 0.0692390i | ||||
\(820\) | −10.7813 | + | 15.0101i | −0.376498 | + | 0.524176i | ||||
\(821\) | 54.6337 | 1.90673 | 0.953364 | − | 0.301822i | \(-0.0975948\pi\) | ||||
0.953364 | + | 0.301822i | \(0.0975948\pi\) | |||||||
\(822\) | − | 22.9169i | − | 0.799319i | ||||||
\(823\) | 38.9987 | + | 38.9987i | 1.35941 | + | 1.35941i | 0.874643 | + | 0.484768i | \(0.161096\pi\) |
0.484768 | + | 0.874643i | \(0.338904\pi\) | |||||||
\(824\) | 12.6201i | 0.439643i | ||||||||
\(825\) | −12.3750 | + | 24.9544i | −0.430841 | + | 0.868801i | ||||
\(826\) | −5.28772 | −0.183983 | ||||||||
\(827\) | 1.62207i | 0.0564050i | 0.999602 | + | 0.0282025i | \(0.00897832\pi\) | ||||
−0.999602 | + | 0.0282025i | \(0.991022\pi\) | |||||||
\(828\) | − | 26.7108i | − | 0.928264i | ||||||
\(829\) | 28.1215 | − | 28.1215i | 0.976699 | − | 0.976699i | −0.0230357 | − | 0.999735i | \(-0.507333\pi\) |
0.999735 | + | 0.0230357i | \(0.00733314\pi\) | |||||||
\(830\) | −4.04458 | − | 24.6676i | −0.140389 | − | 0.856226i | ||||
\(831\) | −16.3514 | + | 16.3514i | −0.567222 | + | 0.567222i | ||||
\(832\) | −0.536082 | −0.0185853 | ||||||||
\(833\) | 2.06563 | 0.0715700 | ||||||||
\(834\) | 8.87372 | − | 8.87372i | 0.307272 | − | 0.307272i | ||||
\(835\) | 6.12071 | − | 8.52150i | 0.211816 | − | 0.294899i | ||||
\(836\) | 2.04453 | − | 2.04453i | 0.0707116 | − | 0.0707116i | ||||
\(837\) | 56.3136i | 1.94648i | ||||||||
\(838\) | − | 13.8549i | − | 0.478608i | ||||||
\(839\) | −35.3409 | −1.22010 | −0.610052 | − | 0.792361i | \(-0.708851\pi\) | ||||
−0.610052 | + | 0.792361i | \(0.708851\pi\) | |||||||
\(840\) | 3.51075 | − | 4.88781i | 0.121133 | − | 0.168645i | ||||
\(841\) | 6.81781i | 0.235097i | ||||||||
\(842\) | 25.5907 | + | 25.5907i | 0.881915 | + | 0.881915i | ||||
\(843\) | − | 43.8183i | − | 1.50918i | ||||||
\(844\) | 3.19579 | 0.110004 | ||||||||
\(845\) | 23.0878 | + | 16.5833i | 0.794246 | + | 0.570481i | ||||
\(846\) | −0.812842 | − | 0.812842i | −0.0279461 | − | 0.0279461i | ||||
\(847\) | −4.79510 | + | 4.79510i | −0.164762 | + | 0.164762i | ||||
\(848\) | −5.03296 | − | 5.03296i | −0.172833 | − | 0.172833i | ||||
\(849\) | −55.1892 | − | 55.1892i | −1.89409 | − | 1.89409i | ||||
\(850\) | −1.58589 | + | 0.534422i | −0.0543955 | + | 0.0183305i | ||||
\(851\) | −3.81216 | − | 28.0328i | −0.130679 | − | 0.960953i | ||||
\(852\) | −32.4331 | + | 32.4331i | −1.11114 | + | 1.11114i | ||||
\(853\) | 42.8331i | 1.46658i | 0.679917 | + | 0.733289i | \(0.262016\pi\) | ||||
−0.679917 | + | 0.733289i | \(0.737984\pi\) | |||||||
\(854\) | −11.4585 | −0.392101 | ||||||||
\(855\) | −19.4484 | + | 3.18882i | −0.665121 | + | 0.109055i | ||||
\(856\) | 1.64796 | − | 1.64796i | 0.0563261 | − | 0.0563261i | ||||
\(857\) | 9.21841i | 0.314895i | 0.987527 | + | 0.157447i | \(0.0503265\pi\) | ||||
−0.987527 | + | 0.157447i | \(0.949674\pi\) | |||||||
\(858\) | 2.11173 | + | 2.11173i | 0.0720934 | + | 0.0720934i | ||||
\(859\) | −26.7930 | − | 26.7930i | −0.914167 | − | 0.914167i | 0.0824302 | − | 0.996597i | \(-0.473732\pi\) |
−0.996597 | + | 0.0824302i | \(0.973732\pi\) | |||||||
\(860\) | −21.6333 | − | 15.5385i | −0.737689 | − | 0.529858i | ||||
\(861\) | −22.2434 | −0.758053 | ||||||||
\(862\) | −16.4247 | − | 16.4247i | −0.559426 | − | 0.559426i | ||||
\(863\) | −28.1937 | − | 28.1937i | −0.959726 | − | 0.959726i | 0.0394943 | − | 0.999220i | \(-0.487425\pi\) |
−0.999220 | + | 0.0394943i | \(0.987425\pi\) | |||||||
\(864\) | −5.73519 | − | 5.73519i | −0.195115 | − | 0.195115i | ||||
\(865\) | 5.24658 | − | 0.860246i | 0.178389 | − | 0.0292492i | ||||
\(866\) | −7.66855 | − | 7.66855i | −0.260588 | − | 0.260588i | ||||
\(867\) | −35.3097 | + | 35.3097i | −1.19918 | + | 1.19918i | ||||
\(868\) | −6.31954 | −0.214499 | ||||||||
\(869\) | −10.8076 | + | 10.8076i | −0.366622 | + | 0.366622i | ||||
\(870\) | −18.1664 | + | 25.2919i | −0.615898 | + | 0.857476i | ||||
\(871\) | 1.94038 | + | 1.94038i | 0.0657473 | + | 0.0657473i | ||||
\(872\) | −7.06206 | − | 7.06206i | −0.239151 | − | 0.239151i | ||||
\(873\) | 98.6466 | 3.33868 | ||||||||
\(874\) | −5.04717 | − | 5.04717i | −0.170723 | − | 0.170723i | ||||
\(875\) | 4.76722 | + | 8.99058i | 0.161162 | + | 0.303937i | ||||
\(876\) | 28.5497i | 0.964604i | ||||||||
\(877\) | 19.0689 | − | 19.0689i | 0.643910 | − | 0.643910i | −0.307604 | − | 0.951514i | \(-0.599527\pi\) |
0.951514 | + | 0.307604i | \(0.0995274\pi\) | |||||||
\(878\) | −22.6564 | + | 22.6564i | −0.764618 | + | 0.764618i | ||||
\(879\) | 94.0686 | 3.17285 | ||||||||
\(880\) | −2.45768 | + | 3.42168i | −0.0828485 | + | 0.115345i | ||||
\(881\) | 2.04078i | 0.0687555i | 0.999409 | + | 0.0343777i | \(0.0109449\pi\) | ||||
−0.999409 | + | 0.0343777i | \(0.989055\pi\) | |||||||
\(882\) | −35.4434 | −1.19344 | ||||||||
\(883\) | 46.2566i | 1.55666i | 0.627857 | + | 0.778329i | \(0.283932\pi\) | ||||
−0.627857 | + | 0.778329i | \(0.716068\pi\) | |||||||
\(884\) | 0.179428i | 0.00603483i | ||||||||
\(885\) | −31.1971 | − | 22.4078i | −1.04868 | − | 0.753232i | ||||
\(886\) | −10.4105 | + | 10.4105i | −0.349746 | + | 0.349746i | ||||
\(887\) | −31.6807 | − | 31.6807i | −1.06373 | − | 1.06373i | −0.997826 | − | 0.0659094i | \(-0.979005\pi\) |
−0.0659094 | − | 0.997826i | \(-0.520995\pi\) | |||||||
\(888\) | −14.3157 | − | 10.8882i | −0.480403 | − | 0.365385i | ||||
\(889\) | − | 4.63145i | − | 0.155334i | ||||||
\(890\) | 3.79220 | − | 0.621781i | 0.127115 | − | 0.0208421i | ||||
\(891\) | 12.7236i | 0.426258i | ||||||||
\(892\) | −7.29909 | − | 7.29909i | −0.244392 | − | 0.244392i | ||||
\(893\) | −0.307183 | −0.0102795 | ||||||||
\(894\) | −42.4604 | − | 42.4604i | −1.42009 | − | 1.42009i | ||||
\(895\) | 40.6203 | − | 6.66024i | 1.35779 | − | 0.222627i | ||||
\(896\) | 0.643605 | − | 0.643605i | 0.0215013 | − | 0.0215013i | ||||
\(897\) | 5.21306 | − | 5.21306i | 0.174059 | − | 0.174059i | ||||
\(898\) | 16.6573 | + | 16.6573i | 0.555862 | + | 0.555862i | ||||
\(899\) | 32.7004 | 1.09062 | ||||||||
\(900\) | 27.2117 | − | 9.16993i | 0.907055 | − | 0.305664i | ||||
\(901\) | −1.68455 | + | 1.68455i | −0.0561204 | + | 0.0561204i | ||||
\(902\) | 15.5714 | 0.518470 | ||||||||
\(903\) | − | 32.0582i | − | 1.06683i | ||||||
\(904\) | 15.1701i | 0.504551i | ||||||||
\(905\) | −10.7499 | − | 7.72131i | −0.357339 | − | 0.256665i | ||||
\(906\) | −28.9290 | − | 28.9290i | −0.961100 | − | 0.961100i | ||||
\(907\) | 36.2975i | 1.20524i | 0.798029 | + | 0.602620i | \(0.205876\pi\) | ||||
−0.798029 | + | 0.602620i | \(0.794124\pi\) | |||||||
\(908\) | 19.6620i | 0.652507i | ||||||||
\(909\) | 77.3452 | 2.56538 | ||||||||
\(910\) | 1.07669 | − | 0.176537i | 0.0356919 | − | 0.00585215i | ||||
\(911\) | −5.83123 | + | 5.83123i | −0.193197 | + | 0.193197i | −0.797076 | − | 0.603879i | \(-0.793621\pi\) |
0.603879 | + | 0.797076i | \(0.293621\pi\) | |||||||
\(912\) | −4.53784 | −0.150263 | ||||||||
\(913\) | −14.8929 | + | 14.8929i | −0.492883 | + | 0.492883i | ||||
\(914\) | 39.7899i | 1.31613i | ||||||||
\(915\) | −67.6040 | − | 48.5578i | −2.23492 | − | 1.60527i | ||||
\(916\) | − | 13.4975i | − | 0.445970i | ||||||
\(917\) | −9.82963 | −0.324603 | ||||||||
\(918\) | −1.91958 | + | 1.91958i | −0.0633557 | + | 0.0633557i | ||||
\(919\) | −10.4404 | + | 10.4404i | −0.344396 | + | 0.344396i | −0.858017 | − | 0.513621i | \(-0.828304\pi\) |
0.513621 | + | 0.858017i | \(0.328304\pi\) | |||||||
\(920\) | 8.44682 | + | 6.06708i | 0.278484 | + | 0.200026i | ||||
\(921\) | 72.9100 | 2.40247 | ||||||||
\(922\) | −7.71541 | + | 7.71541i | −0.254093 | + | 0.254093i | ||||
\(923\) | −8.31579 | −0.273718 | ||||||||
\(924\) | −5.07057 | −0.166810 | ||||||||
\(925\) | 27.2498 | − | 13.5074i | 0.895966 | − | 0.444122i | ||||
\(926\) | −14.7430 | −0.484484 | ||||||||
\(927\) | −72.4779 | −2.38049 | ||||||||
\(928\) | −3.33033 | + | 3.33033i | −0.109323 | + | 0.109323i | ||||
\(929\) | −24.9525 | −0.818666 | −0.409333 | − | 0.912385i | \(-0.634239\pi\) | ||||
−0.409333 | + | 0.912385i | \(0.634239\pi\) | |||||||
\(930\) | −37.2847 | − | 26.7804i | −1.22261 | − | 0.878163i | ||||
\(931\) | −6.69725 | + | 6.69725i | −0.219494 | + | 0.219494i | ||||
\(932\) | −1.10924 | + | 1.10924i | −0.0363343 | + | 0.0363343i | ||||
\(933\) | 16.6228 | 0.544206 | ||||||||
\(934\) | − | 28.4840i | − | 0.932025i | ||||||
\(935\) | 1.14525 | + | 0.822594i | 0.0374536 | + | 0.0269017i | ||||
\(936\) | − | 3.07874i | − | 0.100632i | ||||||
\(937\) | −27.8220 | + | 27.8220i | −0.908904 | + | 0.908904i | −0.996184 | − | 0.0872802i | \(-0.972182\pi\) |
0.0872802 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(938\) | −4.65913 | −0.152126 | ||||||||
\(939\) | −33.1335 | + | 33.1335i | −1.08127 | + | 1.08127i | ||||
\(940\) | 0.441676 | − | 0.0724186i | 0.0144059 | − | 0.00236203i | ||||
\(941\) | 29.9817 | 0.977374 | 0.488687 | − | 0.872459i | \(-0.337476\pi\) | ||||
0.488687 | + | 0.872459i | \(0.337476\pi\) | |||||||
\(942\) | − | 55.4829i | − | 1.80773i | ||||||
\(943\) | − | 38.4397i | − | 1.25177i | ||||||
\(944\) | −4.10789 | − | 4.10789i | −0.133701 | − | 0.133701i | ||||
\(945\) | 13.4074 | + | 9.63013i | 0.436144 | + | 0.313268i | ||||
\(946\) | 22.4422i | 0.729658i | ||||||||
\(947\) | 26.4941i | 0.860941i | 0.902605 | + | 0.430471i | \(0.141652\pi\) | ||||
−0.902605 | + | 0.430471i | \(0.858348\pi\) | |||||||
\(948\) | 23.9874 | 0.779075 | ||||||||
\(949\) | −3.66004 | + | 3.66004i | −0.118810 | + | 0.118810i | ||||
\(950\) | 3.40909 | − | 6.87453i | 0.110606 | − | 0.223039i | ||||
\(951\) | −3.97316 | −0.128838 | ||||||||
\(952\) | −0.215416 | − | 0.215416i | −0.00698169 | − | 0.00698169i | ||||
\(953\) | −16.5640 | + | 16.5640i | −0.536561 | + | 0.536561i | −0.922517 | − | 0.385956i | \(-0.873872\pi\) |
0.385956 | + | 0.922517i | \(0.373872\pi\) | |||||||
\(954\) | 28.9045 | − | 28.9045i | 0.935817 | − | 0.935817i | ||||
\(955\) | 25.4064 | − | 4.16572i | 0.822133 | − | 0.134800i | ||||
\(956\) | 10.5161 | + | 10.5161i | 0.340115 | + | 0.340115i | ||||
\(957\) | 26.2376 | 0.848142 | ||||||||
\(958\) | −2.09957 | − | 2.09957i | −0.0678340 | − | 0.0678340i | ||||
\(959\) | 7.05439i | 0.227798i | ||||||||
\(960\) | 6.52462 | − | 1.06980i | 0.210581 | − | 0.0345276i | ||||
\(961\) | 17.2060i | 0.555033i | ||||||||
\(962\) | −0.439398 | − | 3.23112i | −0.0141668 | − | 0.104176i | ||||
\(963\) | 9.46429 | + | 9.46429i | 0.304982 | + | 0.304982i | ||||
\(964\) | −18.7617 | + | 18.7617i | −0.604273 | + | 0.604273i | ||||
\(965\) | −28.8252 | − | 20.7042i | −0.927915 | − | 0.666491i | ||||
\(966\) | 12.5173i | 0.402737i | ||||||||
\(967\) | − | 4.61124i | − | 0.148288i | −0.997248 | − | 0.0741438i | \(-0.976378\pi\) | ||
0.997248 | − | 0.0741438i | \(-0.0236224\pi\) | |||||||
\(968\) | −7.45037 | −0.239464 | ||||||||
\(969\) | 1.51883i | 0.0487918i | ||||||||
\(970\) | −22.4066 | + | 31.1953i | −0.719432 | + | 1.00162i | ||||
\(971\) | −27.9365 | −0.896524 | −0.448262 | − | 0.893902i | \(-0.647957\pi\) | ||||
−0.448262 | + | 0.893902i | \(0.647957\pi\) | |||||||
\(972\) | −3.08553 | + | 3.08553i | −0.0989684 | + | 0.0989684i | ||||
\(973\) | −2.73155 | + | 2.73155i | −0.0875694 | + | 0.0875694i | ||||
\(974\) | 17.7878i | 0.569959i | ||||||||
\(975\) | 7.10048 | + | 3.52115i | 0.227397 | + | 0.112767i | ||||
\(976\) | −8.90180 | − | 8.90180i | −0.284940 | − | 0.284940i | ||||
\(977\) | 6.07748 | 0.194436 | 0.0972180 | − | 0.995263i | \(-0.469006\pi\) | ||||
0.0972180 | + | 0.995263i | \(0.469006\pi\) | |||||||
\(978\) | 3.10459 | + | 3.10459i | 0.0992739 | + | 0.0992739i | ||||
\(979\) | −2.28951 | − | 2.28951i | −0.0731732 | − | 0.0731732i | ||||
\(980\) | 8.05061 | − | 11.2084i | 0.257167 | − | 0.358038i | ||||
\(981\) | 40.5576 | − | 40.5576i | 1.29491 | − | 1.29491i | ||||
\(982\) | −11.1728 | −0.356538 | ||||||||
\(983\) | 18.5414 | − | 18.5414i | 0.591379 | − | 0.591379i | −0.346625 | − | 0.938004i | \(-0.612672\pi\) |
0.938004 | + | 0.346625i | \(0.112672\pi\) | |||||||
\(984\) | −17.2803 | − | 17.2803i | −0.550876 | − | 0.550876i | ||||
\(985\) | −11.2412 | + | 1.84314i | −0.358175 | + | 0.0587274i | ||||
\(986\) | 1.11467 | + | 1.11467i | 0.0354983 | + | 0.0354983i | ||||
\(987\) | 0.380917 | + | 0.380917i | 0.0121247 | + | 0.0121247i | ||||
\(988\) | −0.581747 | − | 0.581747i | −0.0185078 | − | 0.0185078i | ||||
\(989\) | 55.4011 | 1.76165 | ||||||||
\(990\) | −19.6509 | − | 14.1146i | −0.624545 | − | 0.448590i | ||||
\(991\) | −8.80348 | − | 8.80348i | −0.279652 | − | 0.279652i | 0.553318 | − | 0.832970i | \(-0.313361\pi\) |
−0.832970 | + | 0.553318i | \(0.813361\pi\) | |||||||
\(992\) | −4.90948 | − | 4.90948i | −0.155876 | − | 0.155876i | ||||
\(993\) | − | 81.0128i | − | 2.57086i | ||||||
\(994\) | 9.98370 | − | 9.98370i | 0.316664 | − | 0.316664i | ||||
\(995\) | 3.57924 | − | 0.586863i | 0.113469 | − | 0.0186048i | ||||
\(996\) | 33.0548 | 1.04738 | ||||||||
\(997\) | 31.7260i | 1.00477i | 0.864644 | + | 0.502386i | \(0.167544\pi\) | ||||
−0.864644 | + | 0.502386i | \(0.832456\pi\) | |||||||
\(998\) | −9.60201 | + | 9.60201i | −0.303946 | + | 0.303946i | ||||
\(999\) | 29.8668 | − | 39.2684i | 0.944944 | − | 1.24240i |
(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 | 370.2.h.e.253.1 | yes | 20 | |
5.2 | odd | 4 | 370.2.g.e.327.10 | yes | 20 | ||
37.6 | odd | 4 | 370.2.g.e.43.10 | ✓ | 20 | ||
185.117 | even | 4 | inner | 370.2.h.e.117.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.10 | ✓ | 20 | 37.6 | odd | 4 | ||
370.2.g.e.327.10 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.117.1 | yes | 20 | 185.117 | even | 4 | inner | |
370.2.h.e.253.1 | yes | 20 | 1.1 | even | 1 | trivial |