Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 76.2 | ||
Root | \(-1.08982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.76 |
Dual form | 375.2.g.d.301.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.881682 | − | 0.640580i | −0.623444 | − | 0.452958i | 0.230679 | − | 0.973030i | \(-0.425905\pi\) |
−0.854123 | + | 0.520072i | \(0.825905\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | −0.251013 | − | 0.772537i | −0.125506 | − | 0.386269i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.336773 | + | 1.03648i | −0.137487 | + | 0.423141i | ||||
\(7\) | −3.08724 | −1.16687 | −0.583434 | − | 0.812160i | \(-0.698291\pi\) | ||||
−0.583434 | + | 0.812160i | \(0.698291\pi\) | |||||||
\(8\) | −0.947104 | + | 2.91489i | −0.334852 | + | 1.03057i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.929002 | + | 0.674959i | 0.280105 | + | 0.203508i | 0.718963 | − | 0.695048i | \(-0.244617\pi\) |
−0.438858 | + | 0.898556i | \(0.644617\pi\) | |||||||
\(12\) | −0.657159 | + | 0.477454i | −0.189706 | + | 0.137829i | ||||
\(13\) | −3.30042 | + | 2.39789i | −0.915372 | + | 0.665056i | −0.942368 | − | 0.334579i | \(-0.891406\pi\) |
0.0269961 | + | 0.999636i | \(0.491406\pi\) | |||||||
\(14\) | 2.72197 | + | 1.97763i | 0.727477 | + | 0.528543i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.38794 | − | 1.00840i | 0.346986 | − | 0.252100i | ||||
\(17\) | 1.43000 | − | 4.40109i | 0.346826 | − | 1.06742i | −0.613773 | − | 0.789482i | \(-0.710349\pi\) |
0.960599 | − | 0.277938i | \(-0.0896510\pi\) | |||||||
\(18\) | 1.08982 | 0.256873 | ||||||||
\(19\) | −1.84452 | + | 5.67685i | −0.423162 | + | 1.30236i | 0.481582 | + | 0.876401i | \(0.340062\pi\) |
−0.904744 | + | 0.425957i | \(0.859938\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.954011 | + | 2.93614i | 0.208182 | + | 0.640719i | ||||
\(22\) | −0.386719 | − | 1.19020i | −0.0824488 | − | 0.253751i | ||||
\(23\) | 1.88152 | + | 1.36700i | 0.392324 | + | 0.285040i | 0.766407 | − | 0.642355i | \(-0.222043\pi\) |
−0.374083 | + | 0.927395i | \(0.622043\pi\) | |||||||
\(24\) | 3.06489 | 0.625619 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.44596 | 0.871925 | ||||||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | 0.774937 | + | 2.38501i | 0.146449 | + | 0.450725i | ||||
\(29\) | −1.63290 | − | 5.02554i | −0.303221 | − | 0.933220i | −0.980335 | − | 0.197341i | \(-0.936769\pi\) |
0.677113 | − | 0.735879i | \(-0.263231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.182097 | + | 0.560438i | −0.0327056 | + | 0.100658i | −0.966077 | − | 0.258255i | \(-0.916852\pi\) |
0.933371 | + | 0.358913i | \(0.116852\pi\) | |||||||
\(32\) | 4.26010 | 0.753086 | ||||||||
\(33\) | 0.354847 | − | 1.09211i | 0.0617709 | − | 0.190111i | ||||
\(34\) | −4.08005 | + | 2.96433i | −0.699723 | + | 0.508379i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.657159 | + | 0.477454i | 0.109527 | + | 0.0795757i | ||||
\(37\) | −9.22252 | + | 6.70056i | −1.51617 | + | 1.10156i | −0.552830 | + | 0.833294i | \(0.686452\pi\) |
−0.963344 | + | 0.268271i | \(0.913548\pi\) | |||||||
\(38\) | 5.26275 | − | 3.82361i | 0.853731 | − | 0.620272i | ||||
\(39\) | 3.30042 | + | 2.39789i | 0.528490 | + | 0.383970i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.67919 | + | 5.57926i | −1.19929 | + | 0.871334i | −0.994215 | − | 0.107413i | \(-0.965743\pi\) |
−0.205073 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(42\) | 1.03970 | − | 3.19987i | 0.160429 | − | 0.493750i | ||||
\(43\) | 2.42954 | 0.370501 | 0.185250 | − | 0.982691i | \(-0.440690\pi\) | ||||
0.185250 | + | 0.982691i | \(0.440690\pi\) | |||||||
\(44\) | 0.288240 | − | 0.887112i | 0.0434538 | − | 0.133737i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.783227 | − | 2.41052i | −0.115481 | − | 0.355412i | ||||
\(47\) | 1.86955 | + | 5.75387i | 0.272701 | + | 0.839289i | 0.989818 | + | 0.142336i | \(0.0454613\pi\) |
−0.717117 | + | 0.696953i | \(0.754539\pi\) | |||||||
\(48\) | −1.38794 | − | 1.00840i | −0.200332 | − | 0.145550i | ||||
\(49\) | 2.53108 | 0.361583 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.62758 | −0.647990 | ||||||||
\(52\) | 2.68091 | + | 1.94779i | 0.371775 | + | 0.270111i | ||||
\(53\) | −1.00239 | − | 3.08503i | −0.137689 | − | 0.423762i | 0.858310 | − | 0.513132i | \(-0.171515\pi\) |
−0.995999 | + | 0.0893696i | \(0.971515\pi\) | |||||||
\(54\) | −0.336773 | − | 1.03648i | −0.0458290 | − | 0.141047i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.92394 | − | 8.99897i | 0.390728 | − | 1.20254i | ||||
\(57\) | 5.96899 | 0.790612 | ||||||||
\(58\) | −1.77956 | + | 5.47693i | −0.233668 | + | 0.719157i | ||||
\(59\) | −2.57785 | + | 1.87292i | −0.335607 | + | 0.243833i | −0.742806 | − | 0.669507i | \(-0.766506\pi\) |
0.407199 | + | 0.913340i | \(0.366506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1201 | − | 8.07922i | −1.42378 | − | 1.03444i | −0.991133 | − | 0.132876i | \(-0.957579\pi\) |
−0.432650 | − | 0.901562i | \(-0.642421\pi\) | |||||||
\(62\) | 0.519557 | − | 0.377480i | 0.0659838 | − | 0.0479400i | ||||
\(63\) | 2.49763 | − | 1.81464i | 0.314672 | − | 0.228623i | ||||
\(64\) | −6.53194 | − | 4.74573i | −0.816493 | − | 0.593217i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.01244 | + | 0.735584i | −0.124623 | + | 0.0905441i | ||||
\(67\) | 0.976103 | − | 3.00414i | 0.119250 | − | 0.367014i | −0.873560 | − | 0.486717i | \(-0.838194\pi\) |
0.992810 | + | 0.119703i | \(0.0381943\pi\) | |||||||
\(68\) | −3.75895 | −0.455840 | ||||||||
\(69\) | 0.718676 | − | 2.21186i | 0.0865184 | − | 0.266276i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.99795 | + | 6.14907i | 0.237113 | + | 0.729760i | 0.996834 | + | 0.0795103i | \(0.0253357\pi\) |
−0.759721 | + | 0.650250i | \(0.774664\pi\) | |||||||
\(72\) | −0.947104 | − | 2.91489i | −0.111617 | − | 0.343523i | ||||
\(73\) | −5.83300 | − | 4.23792i | −0.682701 | − | 0.496011i | 0.191552 | − | 0.981482i | \(-0.438648\pi\) |
−0.874252 | + | 0.485472i | \(0.838648\pi\) | |||||||
\(74\) | 12.4236 | 1.44421 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.84857 | 0.556169 | ||||||||
\(77\) | −2.86806 | − | 2.08376i | −0.326845 | − | 0.237467i | ||||
\(78\) | −1.37388 | − | 4.22836i | −0.155561 | − | 0.478768i | ||||
\(79\) | −3.81246 | − | 11.7336i | −0.428936 | − | 1.32013i | −0.899175 | − | 0.437590i | \(-0.855832\pi\) |
0.470239 | − | 0.882539i | \(-0.344168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 10.3446 | 1.14237 | ||||||||
\(83\) | 3.82999 | − | 11.7875i | 0.420396 | − | 1.29384i | −0.486939 | − | 0.873436i | \(-0.661887\pi\) |
0.907335 | − | 0.420409i | \(-0.138113\pi\) | |||||||
\(84\) | 2.02881 | − | 1.47402i | 0.221361 | − | 0.160829i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.14208 | − | 1.55631i | −0.230986 | − | 0.167821i | ||||
\(87\) | −4.27498 | + | 3.10596i | −0.458326 | + | 0.332993i | ||||
\(88\) | −2.84729 | + | 2.06868i | −0.303522 | + | 0.220522i | ||||
\(89\) | −0.877003 | − | 0.637180i | −0.0929621 | − | 0.0675409i | 0.540333 | − | 0.841451i | \(-0.318298\pi\) |
−0.633295 | + | 0.773910i | \(0.718298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.1892 | − | 7.40289i | 1.06812 | − | 0.776034i | ||||
\(92\) | 0.583776 | − | 1.79668i | 0.0608628 | − | 0.187317i | ||||
\(93\) | 0.589279 | 0.0611054 | ||||||||
\(94\) | 2.03747 | − | 6.27068i | 0.210149 | − | 0.646772i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.31644 | − | 4.05159i | −0.134359 | − | 0.413514i | ||||
\(97\) | 1.39717 | + | 4.30003i | 0.141861 | + | 0.436602i | 0.996594 | − | 0.0824653i | \(-0.0262794\pi\) |
−0.854733 | + | 0.519067i | \(0.826279\pi\) | |||||||
\(98\) | −2.23161 | − | 1.62136i | −0.225426 | − | 0.163782i | ||||
\(99\) | −1.14831 | −0.115409 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.61332 | −0.658050 | −0.329025 | − | 0.944321i | \(-0.606720\pi\) | ||||
−0.329025 | + | 0.944321i | \(0.606720\pi\) | |||||||
\(102\) | 4.08005 | + | 2.96433i | 0.403985 | + | 0.293513i | ||||
\(103\) | 1.29983 | + | 4.00047i | 0.128076 | + | 0.394178i | 0.994449 | − | 0.105220i | \(-0.0335547\pi\) |
−0.866373 | + | 0.499398i | \(0.833555\pi\) | |||||||
\(104\) | −3.86375 | − | 11.8914i | −0.378872 | − | 1.16605i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.09242 | + | 3.36213i | −0.106105 | + | 0.326559i | ||||
\(107\) | −4.01195 | −0.387849 | −0.193925 | − | 0.981016i | \(-0.562122\pi\) | ||||
−0.193925 | + | 0.981016i | \(0.562122\pi\) | |||||||
\(108\) | 0.251013 | − | 0.772537i | 0.0241537 | − | 0.0743374i | ||||
\(109\) | −7.35691 | + | 5.34511i | −0.704664 | + | 0.511969i | −0.881448 | − | 0.472281i | \(-0.843431\pi\) |
0.176784 | + | 0.984250i | \(0.443431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.22252 | + | 6.70056i | 0.875363 | + | 0.635989i | ||||
\(112\) | −4.28492 | + | 3.11318i | −0.404887 | + | 0.294168i | ||||
\(113\) | −3.03758 | + | 2.20693i | −0.285751 | + | 0.207610i | −0.721422 | − | 0.692496i | \(-0.756511\pi\) |
0.435671 | + | 0.900106i | \(0.356511\pi\) | |||||||
\(114\) | −5.26275 | − | 3.82361i | −0.492902 | − | 0.358114i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.47254 | + | 2.52295i | −0.322417 | + | 0.234250i | ||||
\(117\) | 1.26065 | − | 3.87988i | 0.116547 | − | 0.358695i | ||||
\(118\) | 3.47260 | 0.319678 | ||||||||
\(119\) | −4.41476 | + | 13.5872i | −0.404700 | + | 1.24554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.99171 | − | 9.20755i | −0.271974 | − | 0.837050i | ||||
\(122\) | 4.62901 | + | 14.2466i | 0.419091 | + | 1.28983i | ||||
\(123\) | 7.67919 | + | 5.57926i | 0.692409 | + | 0.503065i | ||||
\(124\) | 0.478668 | 0.0429856 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.36454 | −0.299737 | ||||||||
\(127\) | −9.18904 | − | 6.67623i | −0.815395 | − | 0.592419i | 0.0999946 | − | 0.994988i | \(-0.468117\pi\) |
−0.915390 | + | 0.402569i | \(0.868117\pi\) | |||||||
\(128\) | 0.0861909 | + | 0.265268i | 0.00761827 | + | 0.0234466i | ||||
\(129\) | −0.750768 | − | 2.31063i | −0.0661014 | − | 0.203439i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.642289 | + | 1.97676i | −0.0561170 | + | 0.172711i | −0.975186 | − | 0.221385i | \(-0.928942\pi\) |
0.919069 | + | 0.394096i | \(0.128942\pi\) | |||||||
\(132\) | −0.932764 | −0.0811867 | ||||||||
\(133\) | 5.69448 | − | 17.5258i | 0.493774 | − | 1.51968i | ||||
\(134\) | −2.78500 | + | 2.02342i | −0.240587 | + | 0.174797i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.4743 | + | 8.33657i | 0.983914 | + | 0.714855i | ||||
\(137\) | 15.6975 | − | 11.4049i | 1.34113 | − | 0.974387i | 0.341726 | − | 0.939800i | \(-0.388988\pi\) |
0.999402 | − | 0.0345870i | \(-0.0110116\pi\) | |||||||
\(138\) | −2.05051 | + | 1.48979i | −0.174551 | + | 0.126819i | ||||
\(139\) | 13.8830 | + | 10.0866i | 1.17754 | + | 0.855531i | 0.991892 | − | 0.127086i | \(-0.0405624\pi\) |
0.185646 | + | 0.982617i | \(0.440562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.89454 | − | 3.55609i | 0.412194 | − | 0.299477i | ||||
\(142\) | 2.17741 | − | 6.70137i | 0.182724 | − | 0.562367i | ||||
\(143\) | −4.68458 | −0.391744 | ||||||||
\(144\) | −0.530147 | + | 1.63162i | −0.0441789 | + | 0.135969i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.42812 | + | 7.47300i | 0.200953 | + | 0.618470i | ||||
\(147\) | −0.782147 | − | 2.40720i | −0.0645104 | − | 0.198542i | ||||
\(148\) | 7.49140 | + | 5.44282i | 0.615789 | + | 0.447397i | ||||
\(149\) | 0.210127 | 0.0172143 | 0.00860714 | − | 0.999963i | \(-0.497260\pi\) | ||||
0.00860714 | + | 0.999963i | \(0.497260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.05924 | −0.330336 | −0.165168 | − | 0.986265i | \(-0.552817\pi\) | ||||
−0.165168 | + | 0.986265i | \(0.552817\pi\) | |||||||
\(152\) | −14.8004 | − | 10.7531i | −1.20047 | − | 0.872194i | ||||
\(153\) | 1.43000 | + | 4.40109i | 0.115609 | + | 0.355807i | ||||
\(154\) | 1.19390 | + | 3.67444i | 0.0962070 | + | 0.296095i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.02402 | − | 3.15160i | 0.0819869 | − | 0.252330i | ||||
\(157\) | 0.440336 | 0.0351426 | 0.0175713 | − | 0.999846i | \(-0.494407\pi\) | ||||
0.0175713 | + | 0.999846i | \(0.494407\pi\) | |||||||
\(158\) | −4.15490 | + | 12.7875i | −0.330546 | + | 1.01732i | ||||
\(159\) | −2.62429 | + | 1.90666i | −0.208119 | + | 0.151208i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.80871 | − | 4.22027i | −0.457790 | − | 0.332604i | ||||
\(162\) | −0.881682 | + | 0.640580i | −0.0692715 | + | 0.0503287i | ||||
\(163\) | −2.62210 | + | 1.90506i | −0.205378 | + | 0.149216i | −0.685720 | − | 0.727865i | \(-0.740513\pi\) |
0.480342 | + | 0.877081i | \(0.340513\pi\) | |||||||
\(164\) | 6.23776 | + | 4.53200i | 0.487087 | + | 0.353889i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.9277 | + | 7.93941i | −0.848151 | + | 0.616218i | ||||
\(167\) | −4.93207 | + | 15.1793i | −0.381655 | + | 1.17461i | 0.557223 | + | 0.830363i | \(0.311867\pi\) |
−0.938878 | + | 0.344250i | \(0.888133\pi\) | |||||||
\(168\) | −9.46207 | −0.730015 | ||||||||
\(169\) | 1.12565 | − | 3.46438i | 0.0865882 | − | 0.266491i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.84452 | − | 5.67685i | −0.141054 | − | 0.434119i | ||||
\(172\) | −0.609844 | − | 1.87691i | −0.0465002 | − | 0.143113i | ||||
\(173\) | −0.454497 | − | 0.330212i | −0.0345548 | − | 0.0251055i | 0.570374 | − | 0.821385i | \(-0.306798\pi\) |
−0.604929 | + | 0.796280i | \(0.706798\pi\) | |||||||
\(174\) | 5.75879 | 0.436573 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.97003 | 0.148497 | ||||||||
\(177\) | 2.57785 | + | 1.87292i | 0.193763 | + | 0.140777i | ||||
\(178\) | 0.365073 | + | 1.12358i | 0.0273634 | + | 0.0842159i | ||||
\(179\) | 4.92532 | + | 15.1586i | 0.368136 | + | 1.13301i | 0.947994 | + | 0.318288i | \(0.103108\pi\) |
−0.579858 | + | 0.814718i | \(0.696892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.64001 | + | 20.4358i | −0.493548 | + | 1.51898i | 0.325660 | + | 0.945487i | \(0.394414\pi\) |
−0.819208 | + | 0.573497i | \(0.805586\pi\) | |||||||
\(182\) | −13.7258 | −1.01742 | ||||||||
\(183\) | −4.24750 | + | 13.0725i | −0.313984 | + | 0.966344i | ||||
\(184\) | −5.76665 | + | 4.18972i | −0.425123 | + | 0.308870i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.519557 | − | 0.377480i | −0.0380958 | − | 0.0276782i | ||||
\(187\) | 4.29903 | − | 3.12343i | 0.314376 | − | 0.228408i | ||||
\(188\) | 3.97580 | − | 2.88859i | 0.289965 | − | 0.210672i | ||||
\(189\) | −2.49763 | − | 1.81464i | −0.181676 | − | 0.131995i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8810 | − | 10.8117i | 1.07675 | − | 0.782304i | 0.0996355 | − | 0.995024i | \(-0.468232\pi\) |
0.977113 | + | 0.212720i | \(0.0682323\pi\) | |||||||
\(192\) | −2.49498 | + | 7.67876i | −0.180060 | + | 0.554167i | ||||
\(193\) | −2.02523 | −0.145780 | −0.0728898 | − | 0.997340i | \(-0.523222\pi\) | ||||
−0.0728898 | + | 0.997340i | \(0.523222\pi\) | |||||||
\(194\) | 1.52266 | − | 4.68626i | 0.109320 | − | 0.336454i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.635333 | − | 1.95535i | −0.0453809 | − | 0.139668i | ||||
\(197\) | 3.56774 | + | 10.9804i | 0.254191 | + | 0.782319i | 0.993988 | + | 0.109489i | \(0.0349214\pi\) |
−0.739797 | + | 0.672830i | \(0.765079\pi\) | |||||||
\(198\) | 1.01244 | + | 0.735584i | 0.0719513 | + | 0.0522757i | ||||
\(199\) | 22.9779 | 1.62886 | 0.814431 | − | 0.580260i | \(-0.197049\pi\) | ||||
0.814431 | + | 0.580260i | \(0.197049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.15873 | −0.222800 | ||||||||
\(202\) | 5.83085 | + | 4.23636i | 0.410257 | + | 0.298069i | ||||
\(203\) | 5.04115 | + | 15.5151i | 0.353820 | + | 1.08894i | ||||
\(204\) | 1.16158 | + | 3.57497i | 0.0813268 | + | 0.250298i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.41658 | − | 4.35979i | 0.0986978 | − | 0.303761i | ||||
\(207\) | −2.32568 | −0.161646 | ||||||||
\(208\) | −2.16276 | + | 6.65628i | −0.149960 | + | 0.461530i | ||||
\(209\) | −5.54520 | + | 4.02882i | −0.383570 | + | 0.278680i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.56717 | + | 4.04479i | 0.383260 | + | 0.278455i | 0.762688 | − | 0.646767i | \(-0.223879\pi\) |
−0.379428 | + | 0.925221i | \(0.623879\pi\) | |||||||
\(212\) | −2.13169 | + | 1.54876i | −0.146405 | + | 0.106370i | ||||
\(213\) | 5.23071 | − | 3.80033i | 0.358402 | − | 0.260394i | ||||
\(214\) | 3.53726 | + | 2.56997i | 0.241802 | + | 0.175680i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.47955 | + | 1.80150i | −0.168712 | + | 0.122576i | ||||
\(217\) | 0.562179 | − | 1.73021i | 0.0381632 | − | 0.117454i | ||||
\(218\) | 9.91043 | 0.671219 | ||||||||
\(219\) | −2.22801 | + | 6.85710i | −0.150555 | + | 0.463360i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.83375 | + | 17.9544i | 0.392420 | + | 1.20775i | ||||
\(222\) | −3.83910 | − | 11.8155i | −0.257663 | − | 0.793006i | ||||
\(223\) | −6.57432 | − | 4.77652i | −0.440249 | − | 0.319860i | 0.345485 | − | 0.938424i | \(-0.387714\pi\) |
−0.785734 | + | 0.618565i | \(0.787714\pi\) | |||||||
\(224\) | −13.1520 | −0.878753 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.09189 | 0.272188 | ||||||||
\(227\) | −20.7351 | − | 15.0649i | −1.37624 | − | 0.999895i | −0.997221 | − | 0.0745050i | \(-0.976262\pi\) |
−0.379017 | − | 0.925390i | \(-0.623738\pi\) | |||||||
\(228\) | −1.49829 | − | 4.61127i | −0.0992268 | − | 0.305389i | ||||
\(229\) | 0.381062 | + | 1.17279i | 0.0251813 | + | 0.0775001i | 0.962857 | − | 0.270010i | \(-0.0870271\pi\) |
−0.937676 | + | 0.347510i | \(0.887027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.09550 | + | 3.37160i | −0.0720786 | + | 0.221835i | ||||
\(232\) | 16.1954 | 1.06328 | ||||||||
\(233\) | −0.927012 | + | 2.85305i | −0.0607306 | + | 0.186909i | −0.976819 | − | 0.214067i | \(-0.931329\pi\) |
0.916088 | + | 0.400976i | \(0.131329\pi\) | |||||||
\(234\) | −3.59686 | + | 2.61327i | −0.235134 | + | 0.170835i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.09397 | + | 1.52136i | 0.136306 | + | 0.0990320i | ||||
\(237\) | −9.98116 | + | 7.25174i | −0.648346 | + | 0.471051i | ||||
\(238\) | 12.5961 | − | 9.15162i | 0.816485 | − | 0.593211i | ||||
\(239\) | −17.9069 | − | 13.0101i | −1.15830 | − | 0.841554i | −0.168738 | − | 0.985661i | \(-0.553969\pi\) |
−0.989562 | + | 0.144107i | \(0.953969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8734 | − | 7.89999i | 0.700418 | − | 0.508883i | −0.179651 | − | 0.983730i | \(-0.557497\pi\) |
0.880068 | + | 0.474847i | \(0.157497\pi\) | |||||||
\(242\) | −3.26043 | + | 10.0346i | −0.209588 | + | 0.645046i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.45022 | + | 10.6187i | −0.220877 | + | 0.679791i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.19665 | − | 9.83827i | −0.203811 | − | 0.627265i | ||||
\(247\) | −7.52479 | − | 23.1589i | −0.478791 | − | 1.47357i | ||||
\(248\) | −1.46115 | − | 1.06159i | −0.0927829 | − | 0.0674107i | ||||
\(249\) | −12.3941 | −0.785444 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8799 | 1.19169 | 0.595843 | − | 0.803101i | \(-0.296818\pi\) | ||||
0.595843 | + | 0.803101i | \(0.296818\pi\) | |||||||
\(252\) | −2.02881 | − | 1.47402i | −0.127803 | − | 0.0928544i | ||||
\(253\) | 0.825262 | + | 2.53990i | 0.0518838 | + | 0.159682i | ||||
\(254\) | 3.82516 | + | 11.7726i | 0.240012 | + | 0.738680i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.89603 | + | 15.0684i | −0.306002 | + | 0.941776i | ||||
\(257\) | 7.06320 | 0.440590 | 0.220295 | − | 0.975433i | \(-0.429298\pi\) | ||||
0.220295 | + | 0.975433i | \(0.429298\pi\) | |||||||
\(258\) | −0.818201 | + | 2.51816i | −0.0509390 | + | 0.156774i | ||||
\(259\) | 28.4722 | − | 20.6863i | 1.76918 | − | 1.28538i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.27498 | + | 3.10596i | 0.264615 | + | 0.192254i | ||||
\(262\) | 1.83257 | − | 1.33144i | 0.113216 | − | 0.0822566i | ||||
\(263\) | −16.5328 | + | 12.0118i | −1.01945 | + | 0.740677i | −0.966171 | − | 0.257903i | \(-0.916969\pi\) |
−0.0532829 | + | 0.998579i | \(0.516969\pi\) | |||||||
\(264\) | 2.84729 | + | 2.06868i | 0.175239 | + | 0.127318i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −16.2474 | + | 11.8044i | −0.996192 | + | 0.723776i | ||||
\(267\) | −0.334985 | + | 1.03098i | −0.0205008 | + | 0.0630949i | ||||
\(268\) | −2.56582 | −0.156732 | ||||||||
\(269\) | 6.54880 | − | 20.1551i | 0.399287 | − | 1.22888i | −0.526285 | − | 0.850308i | \(-0.676416\pi\) |
0.925572 | − | 0.378571i | \(-0.123584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.07570 | + | 9.46603i | 0.186835 | + | 0.575020i | 0.999975 | − | 0.00704817i | \(-0.00224352\pi\) |
−0.813140 | + | 0.582069i | \(0.802244\pi\) | |||||||
\(272\) | −2.45330 | − | 7.55047i | −0.148753 | − | 0.457814i | ||||
\(273\) | −10.1892 | − | 7.40289i | −0.616679 | − | 0.448043i | ||||
\(274\) | −21.1460 | −1.27747 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.88914 | −0.113713 | ||||||||
\(277\) | 15.1569 | + | 11.0121i | 0.910689 | + | 0.661654i | 0.941189 | − | 0.337880i | \(-0.109710\pi\) |
−0.0304998 | + | 0.999535i | \(0.509710\pi\) | |||||||
\(278\) | −5.77912 | − | 17.7863i | −0.346608 | − | 1.06675i | ||||
\(279\) | −0.182097 | − | 0.560438i | −0.0109019 | − | 0.0335525i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.98981 | − | 27.6678i | 0.536287 | − | 1.65052i | −0.204565 | − | 0.978853i | \(-0.565578\pi\) |
0.740852 | − | 0.671668i | \(-0.234422\pi\) | |||||||
\(282\) | −6.59339 | −0.392630 | ||||||||
\(283\) | 2.21876 | − | 6.82865i | 0.131892 | − | 0.405921i | −0.863202 | − | 0.504859i | \(-0.831545\pi\) |
0.995094 | + | 0.0989379i | \(0.0315445\pi\) | |||||||
\(284\) | 4.24887 | − | 3.08699i | 0.252124 | − | 0.183179i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.13031 | + | 3.00084i | 0.244230 | + | 0.177444i | ||||
\(287\) | 23.7075 | − | 17.2245i | 1.39941 | − | 1.01673i | ||||
\(288\) | −3.44649 | + | 2.50402i | −0.203087 | + | 0.147551i | ||||
\(289\) | −3.57138 | − | 2.59476i | −0.210081 | − | 0.152633i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.65783 | − | 2.65757i | 0.214426 | − | 0.155789i | ||||
\(292\) | −1.80980 | + | 5.56998i | −0.105910 | + | 0.325958i | ||||
\(293\) | −1.79825 | −0.105055 | −0.0525276 | − | 0.998619i | \(-0.516728\pi\) | ||||
−0.0525276 | + | 0.998619i | \(0.516728\pi\) | |||||||
\(294\) | −0.852398 | + | 2.62341i | −0.0497129 | + | 0.153001i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.7967 | − | 33.2287i | −0.627544 | − | 1.93138i | ||||
\(297\) | 0.354847 | + | 1.09211i | 0.0205903 | + | 0.0633705i | ||||
\(298\) | −0.185265 | − | 0.134603i | −0.0107321 | − | 0.00779735i | ||||
\(299\) | −9.48773 | −0.548689 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.50057 | −0.432326 | ||||||||
\(302\) | 3.57896 | + | 2.60027i | 0.205946 | + | 0.149629i | ||||
\(303\) | 2.04363 | + | 6.28965i | 0.117403 | + | 0.361331i | ||||
\(304\) | 3.16444 | + | 9.73915i | 0.181493 | + | 0.558579i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.55844 | − | 4.79639i | 0.0890902 | − | 0.274191i | ||||
\(307\) | −5.98864 | −0.341790 | −0.170895 | − | 0.985289i | \(-0.554666\pi\) | ||||
−0.170895 | + | 0.985289i | \(0.554666\pi\) | |||||||
\(308\) | −0.889867 | + | 2.73873i | −0.0507049 | + | 0.156054i | ||||
\(309\) | 3.40300 | − | 2.47242i | 0.193590 | − | 0.140651i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.3099 | − | 14.0295i | −1.09497 | − | 0.795539i | −0.114735 | − | 0.993396i | \(-0.536602\pi\) |
−0.980231 | + | 0.197857i | \(0.936602\pi\) | |||||||
\(312\) | −10.1154 | + | 7.34929i | −0.572673 | + | 0.416072i | ||||
\(313\) | 4.65924 | − | 3.38513i | 0.263356 | − | 0.191339i | −0.448269 | − | 0.893898i | \(-0.647959\pi\) |
0.711625 | + | 0.702559i | \(0.247959\pi\) | |||||||
\(314\) | −0.388236 | − | 0.282070i | −0.0219094 | − | 0.0159181i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.10763 | + | 5.89054i | −0.456090 | + | 0.331369i | ||||
\(317\) | 3.78487 | − | 11.6486i | 0.212580 | − | 0.654253i | −0.786737 | − | 0.617288i | \(-0.788231\pi\) |
0.999317 | − | 0.0369645i | \(-0.0117688\pi\) | |||||||
\(318\) | 3.53515 | 0.198242 | ||||||||
\(319\) | 1.87507 | − | 5.77088i | 0.104984 | − | 0.323107i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.23976 | + | 3.81559i | 0.0691966 | + | 0.212965i | ||||
\(322\) | 2.41801 | + | 7.44188i | 0.134751 | + | 0.414720i | ||||
\(323\) | 22.3466 | + | 16.2358i | 1.24340 | + | 0.903383i | ||||
\(324\) | −0.812294 | −0.0451274 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.53220 | 0.195631 | ||||||||
\(327\) | 7.35691 | + | 5.34511i | 0.406838 | + | 0.295585i | ||||
\(328\) | −8.98991 | − | 27.6681i | −0.496385 | − | 1.52772i | ||||
\(329\) | −5.77175 | − | 17.7636i | −0.318207 | − | 0.979340i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.86306 | + | 5.73391i | −0.102403 | + | 0.315164i | −0.989112 | − | 0.147163i | \(-0.952986\pi\) |
0.886709 | + | 0.462328i | \(0.152986\pi\) | |||||||
\(332\) | −10.0676 | −0.552534 | ||||||||
\(333\) | 3.52269 | − | 10.8417i | 0.193042 | − | 0.594123i | ||||
\(334\) | 14.0721 | − | 10.2240i | 0.769991 | − | 0.559431i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.28492 | + | 3.11318i | 0.233762 | + | 0.169838i | ||||
\(337\) | 4.47454 | − | 3.25094i | 0.243744 | − | 0.177090i | −0.459206 | − | 0.888330i | \(-0.651866\pi\) |
0.702949 | + | 0.711240i | \(0.251866\pi\) | |||||||
\(338\) | −3.21168 | + | 2.33342i | −0.174692 | + | 0.126921i | ||||
\(339\) | 3.03758 | + | 2.20693i | 0.164978 | + | 0.119864i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.547441 | + | 0.397739i | −0.0296456 | + | 0.0215388i | ||||
\(342\) | −2.01019 | + | 6.18674i | −0.108699 | + | 0.334540i | ||||
\(343\) | 13.7967 | 0.744949 | ||||||||
\(344\) | −2.30102 | + | 7.08182i | −0.124063 | + | 0.381826i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.189195 | + | 0.582283i | 0.0101712 | + | 0.0313038i | ||||
\(347\) | 8.01729 | + | 24.6747i | 0.430391 | + | 1.32461i | 0.897737 | + | 0.440532i | \(0.145210\pi\) |
−0.467346 | + | 0.884075i | \(0.654790\pi\) | |||||||
\(348\) | 3.47254 | + | 2.52295i | 0.186148 | + | 0.135244i | ||||
\(349\) | −19.0025 | −1.01718 | −0.508591 | − | 0.861008i | \(-0.669833\pi\) | ||||
−0.508591 | + | 0.861008i | \(0.669833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.07954 | −0.217750 | ||||||||
\(352\) | 3.95764 | + | 2.87539i | 0.210943 | + | 0.153259i | ||||
\(353\) | −2.53126 | − | 7.79043i | −0.134726 | − | 0.414642i | 0.860822 | − | 0.508907i | \(-0.169950\pi\) |
−0.995547 | + | 0.0942642i | \(0.969950\pi\) | |||||||
\(354\) | −1.07309 | − | 3.30263i | −0.0570341 | − | 0.175533i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.272106 | + | 0.837457i | −0.0144216 | + | 0.0443852i | ||||
\(357\) | 14.2865 | 0.756120 | ||||||||
\(358\) | 5.36771 | − | 16.5201i | 0.283692 | − | 0.873116i | ||||
\(359\) | 21.6701 | − | 15.7442i | 1.14370 | − | 0.830948i | 0.156071 | − | 0.987746i | \(-0.450117\pi\) |
0.987631 | + | 0.156797i | \(0.0501170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4530 | − | 9.77419i | −0.708053 | − | 0.514431i | ||||
\(362\) | 18.9452 | − | 13.7645i | 0.995736 | − | 0.723444i | ||||
\(363\) | −7.83241 | + | 5.69058i | −0.411095 | + | 0.298678i | ||||
\(364\) | −8.27662 | − | 6.01332i | −0.433813 | − | 0.315184i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.1189 | − | 8.80489i | 0.633465 | − | 0.460239i | ||||
\(367\) | −5.82600 | + | 17.9306i | −0.304114 | + | 0.935968i | 0.675892 | + | 0.737001i | \(0.263759\pi\) |
−0.980006 | + | 0.198967i | \(0.936241\pi\) | |||||||
\(368\) | 3.98992 | 0.207989 | ||||||||
\(369\) | 2.93319 | − | 9.02743i | 0.152696 | − | 0.469949i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.09462 | + | 9.52426i | 0.160665 | + | 0.494475i | ||||
\(372\) | −0.147916 | − | 0.455240i | −0.00766911 | − | 0.0236031i | ||||
\(373\) | −14.4391 | − | 10.4906i | −0.747627 | − | 0.543183i | 0.147464 | − | 0.989067i | \(-0.452889\pi\) |
−0.895090 | + | 0.445885i | \(0.852889\pi\) | |||||||
\(374\) | −5.79118 | −0.299455 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.5425 | −0.956259 | ||||||||
\(377\) | 17.4400 | + | 12.6709i | 0.898204 | + | 0.652583i | ||||
\(378\) | 1.03970 | + | 3.19987i | 0.0534764 | + | 0.164583i | ||||
\(379\) | 3.88290 | + | 11.9503i | 0.199451 | + | 0.613848i | 0.999896 | + | 0.0144408i | \(0.00459680\pi\) |
−0.800445 | + | 0.599407i | \(0.795403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50990 | + | 10.8024i | −0.179818 | + | 0.553422i | ||||
\(382\) | −20.0460 | −1.02564 | ||||||||
\(383\) | −2.32918 | + | 7.16849i | −0.119016 | + | 0.366292i | −0.992763 | − | 0.120087i | \(-0.961683\pi\) |
0.873748 | + | 0.486379i | \(0.161683\pi\) | |||||||
\(384\) | 0.225651 | − | 0.163945i | 0.0115152 | − | 0.00836628i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.78561 | + | 1.29732i | 0.0908854 | + | 0.0660321i | ||||
\(387\) | −1.96554 | + | 1.42805i | −0.0999138 | + | 0.0725916i | ||||
\(388\) | 2.97123 | − | 2.15872i | 0.150841 | − | 0.109593i | ||||
\(389\) | 11.1103 | + | 8.07211i | 0.563315 | + | 0.409272i | 0.832671 | − | 0.553768i | \(-0.186811\pi\) |
−0.269356 | + | 0.963041i | \(0.586811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.70687 | − | 6.32591i | 0.440325 | − | 0.319915i | ||||
\(392\) | −2.39719 | + | 7.37781i | −0.121077 | + | 0.372636i | ||||
\(393\) | 2.07849 | 0.104846 | ||||||||
\(394\) | 3.88819 | − | 11.9666i | 0.195884 | − | 0.602869i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.288240 | + | 0.887112i | 0.0144846 | + | 0.0445790i | ||||
\(397\) | −4.01790 | − | 12.3658i | −0.201653 | − | 0.620623i | −0.999834 | − | 0.0182061i | \(-0.994204\pi\) |
0.798182 | − | 0.602417i | \(-0.205796\pi\) | |||||||
\(398\) | −20.2592 | − | 14.7192i | −1.01550 | − | 0.737807i | ||||
\(399\) | −18.4277 | −0.922540 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.47047 | −0.323120 | −0.161560 | − | 0.986863i | \(-0.551653\pi\) | ||||
−0.161560 | + | 0.986863i | \(0.551653\pi\) | |||||||
\(402\) | 2.78500 | + | 2.02342i | 0.138903 | + | 0.100919i | ||||
\(403\) | −0.742874 | − | 2.28633i | −0.0370052 | − | 0.113890i | ||||
\(404\) | 1.66003 | + | 5.10904i | 0.0825894 | + | 0.254184i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.49395 | − | 16.9086i | 0.272660 | − | 0.839161i | ||||
\(407\) | −13.0903 | −0.648864 | ||||||||
\(408\) | 4.38280 | − | 13.4889i | 0.216981 | − | 0.667798i | ||||
\(409\) | 0.899629 | − | 0.653619i | 0.0444838 | − | 0.0323194i | −0.565321 | − | 0.824871i | \(-0.691248\pi\) |
0.609805 | + | 0.792552i | \(0.291248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.6975 | − | 11.4049i | −0.774301 | − | 0.562562i | ||||
\(412\) | 2.76424 | − | 2.00833i | 0.136184 | − | 0.0989435i | ||||
\(413\) | 7.95845 | − | 5.78215i | 0.391610 | − | 0.284521i | ||||
\(414\) | 2.05051 | + | 1.48979i | 0.100777 | + | 0.0732190i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.0601 | + | 10.2153i | −0.689354 | + | 0.500845i | ||||
\(417\) | 5.30282 | − | 16.3204i | 0.259680 | − | 0.799213i | ||||
\(418\) | 7.46989 | 0.365364 | ||||||||
\(419\) | 3.64430 | − | 11.2160i | 0.178036 | − | 0.547938i | −0.821723 | − | 0.569887i | \(-0.806987\pi\) |
0.999759 | + | 0.0219489i | \(0.00698712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.12900 | − | 9.63007i | −0.152498 | − | 0.469341i | 0.845401 | − | 0.534133i | \(-0.179362\pi\) |
−0.997899 | + | 0.0647918i | \(0.979362\pi\) | |||||||
\(422\) | −2.31747 | − | 7.13244i | −0.112813 | − | 0.347202i | ||||
\(423\) | −4.89454 | − | 3.55609i | −0.237981 | − | 0.172903i | ||||
\(424\) | 9.94189 | 0.482821 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.04624 | −0.341391 | ||||||||
\(427\) | 34.3305 | + | 24.9425i | 1.66137 | + | 1.20705i | ||||
\(428\) | 1.00705 | + | 3.09938i | 0.0486775 | + | 0.149814i | ||||
\(429\) | 1.44761 | + | 4.45530i | 0.0698914 | + | 0.215104i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.75911 | + | 5.41397i | −0.0847332 | + | 0.260782i | −0.984442 | − | 0.175708i | \(-0.943779\pi\) |
0.899709 | + | 0.436490i | \(0.143779\pi\) | |||||||
\(432\) | 1.71559 | 0.0825415 | ||||||||
\(433\) | −10.2126 | + | 31.4313i | −0.490788 | + | 1.51049i | 0.332631 | + | 0.943057i | \(0.392064\pi\) |
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(434\) | −1.60400 | + | 1.16537i | −0.0769945 | + | 0.0559397i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.97597 | + | 4.34180i | 0.286197 | + | 0.207934i | ||||
\(437\) | −11.2308 | + | 8.15963i | −0.537240 | + | 0.390328i | ||||
\(438\) | 6.35691 | − | 4.61857i | 0.303745 | − | 0.220684i | ||||
\(439\) | −9.27430 | − | 6.73818i | −0.442638 | − | 0.321596i | 0.344044 | − | 0.938954i | \(-0.388203\pi\) |
−0.786682 | + | 0.617358i | \(0.788203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.04769 | + | 1.48773i | −0.0975089 | + | 0.0708443i | ||||
\(442\) | 6.35773 | − | 19.5671i | 0.302406 | − | 0.930711i | ||||
\(443\) | 17.8993 | 0.850422 | 0.425211 | − | 0.905094i | \(-0.360200\pi\) | ||||
0.425211 | + | 0.905094i | \(0.360200\pi\) | |||||||
\(444\) | 2.86146 | − | 8.80667i | 0.135799 | − | 0.417946i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.73672 | + | 8.42275i | 0.129587 | + | 0.398829i | ||||
\(447\) | −0.0649328 | − | 0.199843i | −0.00307122 | − | 0.00945223i | ||||
\(448\) | 20.1657 | + | 14.6512i | 0.952740 | + | 0.692206i | ||||
\(449\) | −6.82040 | −0.321874 | −0.160937 | − | 0.986965i | \(-0.551452\pi\) | ||||
−0.160937 | + | 0.986965i | \(0.551452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8998 | −0.513249 | ||||||||
\(452\) | 2.46740 | + | 1.79267i | 0.116057 | + | 0.0843203i | ||||
\(453\) | 1.25437 | + | 3.86057i | 0.0589356 | + | 0.181385i | ||||
\(454\) | 8.63148 | + | 26.5650i | 0.405096 | + | 1.24676i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.65325 | + | 17.3989i | −0.264738 | + | 0.814779i | ||||
\(457\) | 2.76381 | 0.129286 | 0.0646429 | − | 0.997908i | \(-0.479409\pi\) | ||||
0.0646429 | + | 0.997908i | \(0.479409\pi\) | |||||||
\(458\) | 0.415289 | − | 1.27813i | 0.0194052 | − | 0.0597230i | ||||
\(459\) | 3.74379 | − | 2.72002i | 0.174745 | − | 0.126960i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.25254 | + | 5.26928i | 0.337784 | + | 0.245415i | 0.743726 | − | 0.668484i | \(-0.233057\pi\) |
−0.405942 | + | 0.913899i | \(0.633057\pi\) | |||||||
\(462\) | 3.12566 | − | 2.27093i | 0.145419 | − | 0.105653i | ||||
\(463\) | −10.6480 | + | 7.73623i | −0.494855 | + | 0.359533i | −0.807048 | − | 0.590485i | \(-0.798936\pi\) |
0.312193 | + | 0.950019i | \(0.398936\pi\) | |||||||
\(464\) | −7.33412 | − | 5.32855i | −0.340478 | − | 0.247372i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.64494 | − | 1.92166i | 0.122524 | − | 0.0890191i | ||||
\(467\) | −6.73671 | + | 20.7335i | −0.311738 | + | 0.959430i | 0.665339 | + | 0.746542i | \(0.268287\pi\) |
−0.977076 | + | 0.212889i | \(0.931713\pi\) | |||||||
\(468\) | −3.31379 | −0.153180 | ||||||||
\(469\) | −3.01347 | + | 9.27450i | −0.139149 | + | 0.428257i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.136071 | − | 0.418784i | −0.00626983 | − | 0.0192966i | ||||
\(472\) | −3.01785 | − | 9.28798i | −0.138908 | − | 0.427514i | ||||
\(473\) | 2.25704 | + | 1.63984i | 0.103779 | + | 0.0753998i | ||||
\(474\) | 13.4455 | 0.617574 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.6048 | 0.531905 | ||||||||
\(477\) | 2.62429 | + | 1.90666i | 0.120158 | + | 0.0872998i | ||||
\(478\) | 7.45417 | + | 22.9416i | 0.340946 | + | 1.04932i | ||||
\(479\) | 13.2102 | + | 40.6567i | 0.603588 | + | 1.85765i | 0.506221 | + | 0.862404i | \(0.331042\pi\) |
0.0973673 | + | 0.995249i | \(0.468958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3710 | − | 44.2293i | 0.655260 | − | 2.01668i | ||||
\(482\) | −14.6475 | −0.667174 | ||||||||
\(483\) | −2.21873 | + | 6.82854i | −0.100956 | + | 0.310709i | ||||
\(484\) | −6.36221 | + | 4.62242i | −0.289192 | + | 0.210110i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.881682 | + | 0.640580i | 0.0399939 | + | 0.0290573i | ||||
\(487\) | −9.18213 | + | 6.67121i | −0.416082 | + | 0.302301i | −0.776059 | − | 0.630660i | \(-0.782784\pi\) |
0.359978 | + | 0.932961i | \(0.382784\pi\) | |||||||
\(488\) | 34.0819 | − | 24.7619i | 1.54281 | − | 1.12092i | ||||
\(489\) | 2.62210 | + | 1.90506i | 0.118575 | + | 0.0861500i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4739 | + | 9.78936i | −0.608068 | + | 0.441788i | −0.848734 | − | 0.528821i | \(-0.822634\pi\) |
0.240665 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(492\) | 2.38261 | − | 7.33292i | 0.107416 | − | 0.330594i | ||||
\(493\) | −24.4529 | −1.10130 | ||||||||
\(494\) | −8.20067 | + | 25.2391i | −0.368965 | + | 1.13556i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.312405 | + | 0.961483i | 0.0140274 | + | 0.0431718i | ||||
\(497\) | −6.16817 | − | 18.9837i | −0.276680 | − | 0.851534i | ||||
\(498\) | 10.9277 | + | 7.93941i | 0.489680 | + | 0.355773i | ||||
\(499\) | −12.2321 | −0.547584 | −0.273792 | − | 0.961789i | \(-0.588278\pi\) | ||||
−0.273792 | + | 0.961789i | \(0.588278\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.9605 | 0.713063 | ||||||||
\(502\) | −16.6460 | − | 12.0941i | −0.742949 | − | 0.539784i | ||||
\(503\) | 0.404709 | + | 1.24557i | 0.0180451 | + | 0.0555371i | 0.959674 | − | 0.281117i | \(-0.0907048\pi\) |
−0.941629 | + | 0.336654i | \(0.890705\pi\) | |||||||
\(504\) | 2.92394 | + | 8.99897i | 0.130243 | + | 0.400846i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.899387 | − | 2.76803i | 0.0399826 | − | 0.123054i | ||||
\(507\) | −3.64267 | −0.161777 | ||||||||
\(508\) | −2.85107 | + | 8.77469i | −0.126496 | + | 0.389314i | ||||
\(509\) | −14.3453 | + | 10.4225i | −0.635844 | + | 0.461968i | −0.858420 | − | 0.512948i | \(-0.828553\pi\) |
0.222576 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0079 | + | 13.0835i | 0.796622 | + | 0.578780i | ||||
\(512\) | 14.4206 | − | 10.4772i | 0.637305 | − | 0.463029i | ||||
\(513\) | −4.82901 | + | 3.50848i | −0.213206 | + | 0.154903i | ||||
\(514\) | −6.22750 | − | 4.52454i | −0.274683 | − | 0.199569i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.59659 | + | 1.15999i | −0.0702860 | + | 0.0510658i | ||||
\(517\) | −2.14682 | + | 6.60723i | −0.0944170 | + | 0.290586i | ||||
\(518\) | −38.3546 | −1.68521 | ||||||||
\(519\) | −0.173602 | + | 0.534294i | −0.00762030 | + | 0.0234529i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.11527 | + | 24.9762i | 0.355536 | + | 1.09423i | 0.955698 | + | 0.294349i | \(0.0951030\pi\) |
−0.600162 | + | 0.799879i | \(0.704897\pi\) | |||||||
\(522\) | −1.77956 | − | 5.47693i | −0.0778894 | − | 0.239719i | ||||
\(523\) | −2.06844 | − | 1.50281i | −0.0904467 | − | 0.0657134i | 0.541643 | − | 0.840609i | \(-0.317803\pi\) |
−0.632090 | + | 0.774895i | \(0.717803\pi\) | |||||||
\(524\) | 1.68834 | 0.0737557 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2711 | 0.971068 | ||||||||
\(527\) | 2.20614 | + | 1.60285i | 0.0961008 | + | 0.0698213i | ||||
\(528\) | −0.608773 | − | 1.87361i | −0.0264934 | − | 0.0815384i | ||||
\(529\) | −5.43598 | − | 16.7302i | −0.236347 | − | 0.727401i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.984650 | − | 3.03044i | 0.0427302 | − | 0.131510i | ||||
\(532\) | −14.9687 | −0.648977 | ||||||||
\(533\) | 11.9661 | − | 36.8278i | 0.518308 | − | 1.59519i | ||||
\(534\) | 0.955775 | − | 0.694411i | 0.0413604 | − | 0.0300501i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.83224 | + | 5.69046i | 0.338301 | + | 0.245790i | ||||
\(537\) | 12.8947 | − | 9.36852i | 0.556446 | − | 0.404282i | ||||
\(538\) | −18.6849 | + | 13.5754i | −0.805564 | + | 0.585277i | ||||
\(539\) | 2.35138 | + | 1.70838i | 0.101281 | + | 0.0735849i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.59599 | + | 5.51881i | −0.326577 | + | 0.237272i | −0.738977 | − | 0.673731i | \(-0.764691\pi\) |
0.412400 | + | 0.911003i | \(0.364691\pi\) | |||||||
\(542\) | 3.35196 | − | 10.3163i | 0.143979 | − | 0.443121i | ||||
\(543\) | 21.4875 | 0.922118 | ||||||||
\(544\) | 6.09194 | − | 18.7491i | 0.261190 | − | 0.803860i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.24150 | + | 13.0540i | 0.181519 | + | 0.558659i | ||||
\(547\) | −10.7708 | − | 33.1490i | −0.460524 | − | 1.41735i | −0.864525 | − | 0.502590i | \(-0.832381\pi\) |
0.404000 | − | 0.914759i | \(-0.367619\pi\) | |||||||
\(548\) | −12.7510 | − | 9.26413i | −0.544695 | − | 0.395744i | ||||
\(549\) | 13.7452 | 0.586631 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.5411 | 1.34370 | ||||||||
\(552\) | 5.76665 | + | 4.18972i | 0.245445 | + | 0.178326i | ||||
\(553\) | 11.7700 | + | 36.2244i | 0.500512 | + | 1.54042i | ||||
\(554\) | −6.30942 | − | 19.4184i | −0.268062 | − | 0.825009i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.30745 | − | 13.2570i | 0.182676 | − | 0.562220i | ||||
\(557\) | −14.1466 | −0.599411 | −0.299705 | − | 0.954032i | \(-0.596888\pi\) | ||||
−0.299705 | + | 0.954032i | \(0.596888\pi\) | |||||||
\(558\) | −0.198453 | + | 0.610776i | −0.00840119 | + | 0.0258562i | ||||
\(559\) | −8.01849 | + | 5.82577i | −0.339146 | + | 0.246404i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.29903 | − | 3.12343i | −0.181505 | − | 0.131871i | ||||
\(562\) | −25.6496 | + | 18.6355i | −1.08196 | + | 0.786091i | ||||
\(563\) | −30.8926 | + | 22.4448i | −1.30197 | + | 0.945936i | −0.999973 | − | 0.00737325i | \(-0.997653\pi\) |
−0.301996 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(564\) | −3.97580 | − | 2.88859i | −0.167411 | − | 0.121632i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.33054 | + | 4.59941i | −0.266092 | + | 0.193327i | ||||
\(567\) | −0.954011 | + | 2.93614i | −0.0400647 | + | 0.123306i | ||||
\(568\) | −19.8161 | −0.831465 | ||||||||
\(569\) | 9.15622 | − | 28.1799i | 0.383849 | − | 1.18136i | −0.553463 | − | 0.832873i | \(-0.686694\pi\) |
0.937312 | − | 0.348491i | \(-0.113306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0895 | + | 31.0524i | 0.422234 | + | 1.29950i | 0.905618 | + | 0.424093i | \(0.139407\pi\) |
−0.483385 | + | 0.875408i | \(0.660593\pi\) | |||||||
\(572\) | 1.17589 | + | 3.61901i | 0.0491663 | + | 0.151318i | ||||
\(573\) | −14.8810 | − | 10.8117i | −0.621661 | − | 0.451663i | ||||
\(574\) | −31.9362 | −1.33299 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.07392 | 0.336413 | ||||||||
\(577\) | −18.3188 | − | 13.3094i | −0.762622 | − | 0.554077i | 0.137091 | − | 0.990558i | \(-0.456225\pi\) |
−0.899713 | + | 0.436481i | \(0.856225\pi\) | |||||||
\(578\) | 1.48667 | + | 4.57551i | 0.0618374 | + | 0.190316i | ||||
\(579\) | 0.625832 | + | 1.92611i | 0.0260087 | + | 0.0800465i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8241 | + | 36.3909i | −0.490547 | + | 1.50975i | ||||
\(582\) | −4.92742 | −0.204248 | ||||||||
\(583\) | 1.15105 | − | 3.54257i | 0.0476717 | − | 0.146718i | ||||
\(584\) | 17.8775 | − | 12.9888i | 0.739776 | − | 0.537479i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.58549 | + | 1.15193i | 0.0654960 | + | 0.0475856i | ||||
\(587\) | −33.6281 | + | 24.4323i | −1.38798 | + | 1.00843i | −0.391899 | + | 0.920008i | \(0.628182\pi\) |
−0.996083 | + | 0.0884196i | \(0.971818\pi\) | |||||||
\(588\) | −1.66332 | + | 1.20847i | −0.0685943 | + | 0.0498366i | ||||
\(589\) | −2.84564 | − | 2.06748i | −0.117252 | − | 0.0851889i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.34046 | − | 6.78624i | 0.384215 | − | 0.279149i | ||||
\(592\) | −6.04350 | + | 18.6000i | −0.248386 | + | 0.764454i | ||||
\(593\) | 2.09050 | 0.0858465 | 0.0429233 | − | 0.999078i | \(-0.486333\pi\) | ||||
0.0429233 | + | 0.999078i | \(0.486333\pi\) | |||||||
\(594\) | 0.386719 | − | 1.19020i | 0.0158673 | − | 0.0488345i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0527445 | − | 0.162331i | −0.00216050 | − | 0.00664933i | ||||
\(597\) | −7.10057 | − | 21.8533i | −0.290607 | − | 0.894397i | ||||
\(598\) | 8.36516 | + | 6.07765i | 0.342077 | + | 0.248533i | ||||
\(599\) | 17.9768 | 0.734511 | 0.367255 | − | 0.930120i | \(-0.380298\pi\) | ||||
0.367255 | + | 0.930120i | \(0.380298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.11000 | −0.0452778 | −0.0226389 | − | 0.999744i | \(-0.507207\pi\) | ||||
−0.0226389 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(602\) | 6.61312 | + | 4.80471i | 0.269531 | + | 0.195826i | ||||
\(603\) | 0.976103 | + | 3.00414i | 0.0397500 | + | 0.122338i | ||||
\(604\) | 1.01892 | + | 3.13591i | 0.0414593 | + | 0.127599i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.22719 | − | 6.85458i | 0.0904733 | − | 0.278448i | ||||
\(607\) | −12.2310 | −0.496441 | −0.248220 | − | 0.968704i | \(-0.579846\pi\) | ||||
−0.248220 | + | 0.968704i | \(0.579846\pi\) | |||||||
\(608\) | −7.85783 | + | 24.1839i | −0.318677 | + | 0.980788i | ||||
\(609\) | 13.1979 | − | 9.58884i | 0.534806 | − | 0.388560i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.9675 | − | 14.5072i | −0.807798 | − | 0.586899i | ||||
\(612\) | 3.04106 | − | 2.20946i | 0.122927 | − | 0.0893120i | ||||
\(613\) | 10.4991 | − | 7.62804i | 0.424055 | − | 0.308094i | −0.355213 | − | 0.934786i | \(-0.615591\pi\) |
0.779267 | + | 0.626692i | \(0.215591\pi\) | |||||||
\(614\) | 5.28008 | + | 3.83620i | 0.213087 | + | 0.154817i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.79028 | − | 6.38651i | 0.354171 | − | 0.257320i | ||||
\(617\) | 6.33241 | − | 19.4891i | 0.254933 | − | 0.784603i | −0.738910 | − | 0.673804i | \(-0.764659\pi\) |
0.993843 | − | 0.110799i | \(-0.0353410\pi\) | |||||||
\(618\) | −4.58415 | −0.184402 | ||||||||
\(619\) | −12.6838 | + | 39.0367i | −0.509804 | + | 1.56902i | 0.282737 | + | 0.959198i | \(0.408758\pi\) |
−0.792541 | + | 0.609819i | \(0.791242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.718676 | + | 2.21186i | 0.0288395 | + | 0.0887588i | ||||
\(622\) | 8.03822 | + | 24.7391i | 0.322303 | + | 0.991948i | ||||
\(623\) | 2.70752 | + | 1.96713i | 0.108475 | + | 0.0788114i | ||||
\(624\) | 6.99883 | 0.280177 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.27641 | −0.250856 | ||||||||
\(627\) | 5.54520 | + | 4.02882i | 0.221454 | + | 0.160896i | ||||
\(628\) | −0.110530 | − | 0.340176i | −0.00441062 | − | 0.0135745i | ||||
\(629\) | 16.3015 | + | 50.1709i | 0.649984 | + | 2.00045i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.35319 | − | 13.3977i | 0.173298 | − | 0.533356i | −0.826254 | − | 0.563298i | \(-0.809532\pi\) |
0.999552 | + | 0.0299421i | \(0.00953228\pi\) | |||||||
\(632\) | 37.8128 | 1.50411 | ||||||||
\(633\) | 2.12647 | − | 6.54460i | 0.0845196 | − | 0.260125i | ||||
\(634\) | −10.7989 | + | 7.84589i | −0.428881 | + | 0.311600i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.13169 | + | 1.54876i | 0.0845271 | + | 0.0614125i | ||||
\(637\) | −8.35362 | + | 6.06926i | −0.330983 | + | 0.240473i | ||||
\(638\) | −5.34992 | + | 3.88695i | −0.211806 | + | 0.153886i | ||||
\(639\) | −5.23071 | − | 3.80033i | −0.206924 | − | 0.150339i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.0050 | − | 16.7141i | 0.908644 | − | 0.660168i | −0.0320278 | − | 0.999487i | \(-0.510197\pi\) |
0.940671 | + | 0.339319i | \(0.110197\pi\) | |||||||
\(642\) | 1.35111 | − | 4.15830i | 0.0533242 | − | 0.164115i | ||||
\(643\) | −10.8408 | −0.427521 | −0.213761 | − | 0.976886i | \(-0.568571\pi\) | ||||
−0.213761 | + | 0.976886i | \(0.568571\pi\) | |||||||
\(644\) | −1.80226 | + | 5.54678i | −0.0710189 | + | 0.218574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.30232 | − | 28.6296i | −0.365995 | − | 1.12642i | ||||
\(647\) | −10.7040 | − | 32.9435i | −0.420817 | − | 1.29514i | −0.906943 | − | 0.421253i | \(-0.861590\pi\) |
0.486126 | − | 0.873889i | \(-0.338410\pi\) | |||||||
\(648\) | 2.47955 | + | 1.80150i | 0.0974059 | + | 0.0707695i | ||||
\(649\) | −3.65897 | −0.143627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.81925 | −0.0713020 | ||||||||
\(652\) | 2.12991 | + | 1.54747i | 0.0834138 | + | 0.0606037i | ||||
\(653\) | −1.28398 | − | 3.95170i | −0.0502462 | − | 0.154642i | 0.922785 | − | 0.385315i | \(-0.125907\pi\) |
−0.973031 | + | 0.230673i | \(0.925907\pi\) | |||||||
\(654\) | −3.06249 | − | 9.42538i | −0.119753 | − | 0.368561i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.03216 | + | 15.4874i | −0.196473 | + | 0.604681i | ||||
\(657\) | 7.20998 | 0.281288 | ||||||||
\(658\) | −6.29016 | + | 19.3591i | −0.245216 | + | 0.754698i | ||||
\(659\) | 3.24759 | − | 2.35951i | 0.126508 | − | 0.0919135i | −0.522732 | − | 0.852497i | \(-0.675087\pi\) |
0.649240 | + | 0.760584i | \(0.275087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9107 | − | 11.5598i | −0.618853 | − | 0.449623i | 0.233668 | − | 0.972316i | \(-0.424927\pi\) |
−0.852521 | + | 0.522694i | \(0.824927\pi\) | |||||||
\(662\) | 5.31566 | − | 3.86205i | 0.206599 | − | 0.150103i | ||||
\(663\) | 15.2729 | − | 11.0964i | 0.593152 | − | 0.430950i | ||||
\(664\) | 30.7318 | + | 22.3279i | 1.19262 | + | 0.866492i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0509 | + | 7.30240i | −0.389464 | + | 0.282962i | ||||
\(667\) | 3.79760 | − | 11.6878i | 0.147044 | − | 0.452554i | ||||
\(668\) | 12.9646 | 0.501616 | ||||||||
\(669\) | −2.51117 | + | 7.72858i | −0.0970873 | + | 0.298804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.87744 | − | 15.0112i | −0.188292 | − | 0.579502i | ||||
\(672\) | 4.06418 | + | 12.5083i | 0.156779 | + | 0.482517i | ||||
\(673\) | 33.5308 | + | 24.3615i | 1.29252 | + | 0.939068i | 0.999853 | − | 0.0171473i | \(-0.00545843\pi\) |
0.292663 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(674\) | −6.02761 | −0.232175 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.95892 | −0.113804 | ||||||||
\(677\) | −14.7109 | − | 10.6881i | −0.565386 | − | 0.410777i | 0.268040 | − | 0.963408i | \(-0.413624\pi\) |
−0.833426 | + | 0.552631i | \(0.813624\pi\) | |||||||
\(678\) | −1.26446 | − | 3.89162i | −0.0485614 | − | 0.149457i | ||||
\(679\) | −4.31339 | − | 13.2753i | −0.165533 | − | 0.509457i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.92011 | + | 24.3756i | −0.303499 | + | 0.934074i | ||||
\(682\) | 0.737453 | 0.0282385 | ||||||||
\(683\) | 8.79224 | − | 27.0597i | 0.336426 | − | 1.03541i | −0.629590 | − | 0.776928i | \(-0.716777\pi\) |
0.966015 | − | 0.258484i | \(-0.0832231\pi\) | |||||||
\(684\) | −3.92258 | + | 2.84992i | −0.149983 | + | 0.108969i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.1643 | − | 8.83786i | −0.464434 | − | 0.337431i | ||||
\(687\) | 0.997634 | − | 0.724824i | 0.0380621 | − | 0.0276537i | ||||
\(688\) | 3.37206 | − | 2.44994i | 0.128558 | − | 0.0934032i | ||||
\(689\) | 10.7059 | + | 7.77828i | 0.407862 | + | 0.296329i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7541 | + | 14.3522i | −0.751483 | + | 0.545984i | −0.896286 | − | 0.443476i | \(-0.853745\pi\) |
0.144803 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(692\) | −0.141016 | + | 0.434003i | −0.00536063 | + | 0.0164983i | ||||
\(693\) | 3.54511 | 0.134668 | ||||||||
\(694\) | 8.73740 | − | 26.8910i | 0.331667 | − | 1.02077i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.00465 | − | 15.4027i | −0.189701 | − | 0.583840i | ||||
\(697\) | 13.5736 | + | 41.7751i | 0.514135 | + | 1.58235i | ||||
\(698\) | 16.7542 | + | 12.1726i | 0.634155 | + | 0.460741i | ||||
\(699\) | 2.99987 | 0.113466 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0371 | −0.945638 | −0.472819 | − | 0.881159i | \(-0.656764\pi\) | ||||
−0.472819 | + | 0.881159i | \(0.656764\pi\) | |||||||
\(702\) | 3.59686 | + | 2.61327i | 0.135755 | + | 0.0986316i | ||||
\(703\) | −21.0269 | − | 64.7142i | −0.793045 | − | 2.44074i | ||||
\(704\) | −2.86501 | − | 8.81759i | −0.107979 | − | 0.332325i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.75862 | + | 8.49016i | −0.103822 | + | 0.319531i | ||||
\(707\) | 20.4170 | 0.767858 | ||||||||
\(708\) | 0.799825 | − | 2.46161i | 0.0300593 | − | 0.0925129i | ||||
\(709\) | −29.5804 | + | 21.4914i | −1.11091 | + | 0.807126i | −0.982807 | − | 0.184634i | \(-0.940890\pi\) |
−0.128107 | + | 0.991760i | \(0.540890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.98116 | + | 7.25174i | 0.374323 | + | 0.271961i | ||||
\(712\) | 2.68792 | − | 1.95289i | 0.100734 | − | 0.0731876i | ||||
\(713\) | −1.10874 | + | 0.805546i | −0.0415226 | + | 0.0301679i | ||||
\(714\) | −12.5961 | − | 9.15162i | −0.471398 | − | 0.342491i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.4743 | − | 7.60999i | 0.391441 | − | 0.284399i | ||||
\(717\) | −6.83982 | + | 21.0508i | −0.255438 | + | 0.786157i | ||||
\(718\) | −29.1915 | −1.08942 | ||||||||
\(719\) | −2.23596 | + | 6.88157i | −0.0833872 | + | 0.256639i | −0.984054 | − | 0.177872i | \(-0.943079\pi\) |
0.900667 | + | 0.434511i | \(0.143079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.01289 | − | 12.3504i | −0.149448 | − | 0.459954i | ||||
\(722\) | 5.60014 | + | 17.2355i | 0.208416 | + | 0.641437i | ||||
\(723\) | −10.8734 | − | 7.89999i | −0.404386 | − | 0.293804i | ||||
\(724\) | 17.4542 | 0.648679 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.5510 | 0.391583 | ||||||||
\(727\) | −10.7680 | − | 7.82337i | −0.399361 | − | 0.290153i | 0.369920 | − | 0.929064i | \(-0.379385\pi\) |
−0.769281 | + | 0.638911i | \(0.779385\pi\) | |||||||
\(728\) | 11.9283 | + | 36.7117i | 0.442094 | + | 1.36062i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.47424 | − | 10.6926i | 0.128499 | − | 0.395480i | ||||
\(732\) | 11.1651 | 0.412675 | ||||||||
\(733\) | −8.89333 | + | 27.3709i | −0.328483 | + | 1.01097i | 0.641361 | + | 0.767239i | \(0.278370\pi\) |
−0.969844 | + | 0.243727i | \(0.921630\pi\) | |||||||
\(734\) | 16.6226 | − | 12.0771i | 0.613553 | − | 0.445772i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.01545 | + | 5.82357i | 0.295454 | + | 0.214660i | ||||
\(737\) | 2.93447 | − | 2.13202i | 0.108093 | − | 0.0785339i | ||||
\(738\) | −8.36893 | + | 6.08038i | −0.308065 | + | 0.223822i | ||||
\(739\) | −32.6202 | − | 23.7000i | −1.19995 | − | 0.871818i | −0.205674 | − | 0.978621i | \(-0.565939\pi\) |
−0.994280 | + | 0.106803i | \(0.965939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.7002 | + | 14.3130i | −0.723704 | + | 0.525802i | ||||
\(742\) | 3.37258 | − | 10.3797i | 0.123811 | − | 0.381051i | ||||
\(743\) | 27.8114 | 1.02030 | 0.510151 | − | 0.860085i | \(-0.329589\pi\) | ||||
0.510151 | + | 0.860085i | \(0.329589\pi\) | |||||||
\(744\) | −0.558109 | + | 1.71768i | −0.0204613 | + | 0.0629733i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.01061 | + | 18.4988i | 0.220064 | + | 0.677288i | ||||
\(747\) | 3.82999 | + | 11.7875i | 0.140132 | + | 0.431282i | ||||
\(748\) | −3.49207 | − | 2.53714i | −0.127683 | − | 0.0927670i | ||||
\(749\) | 12.3859 | 0.452569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4124 | −0.416443 | −0.208221 | − | 0.978082i | \(-0.566767\pi\) | ||||
−0.208221 | + | 0.978082i | \(0.566767\pi\) | |||||||
\(752\) | 8.39703 | + | 6.10080i | 0.306208 | + | 0.222473i | ||||
\(753\) | −5.83420 | − | 17.9558i | −0.212610 | − | 0.654346i | ||||
\(754\) | −7.25980 | − | 22.3434i | −0.264386 | − | 0.813698i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.774937 | + | 2.38501i | −0.0281842 | + | 0.0867420i | ||||
\(757\) | 13.7637 | 0.500251 | 0.250126 | − | 0.968213i | \(-0.419528\pi\) | ||||
0.250126 | + | 0.968213i | \(0.419528\pi\) | |||||||
\(758\) | 4.23166 | − | 13.0237i | 0.153701 | − | 0.473042i | ||||
\(759\) | 2.16056 | − | 1.56974i | 0.0784235 | − | 0.0569780i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.9257 | + | 8.66451i | 0.432305 | + | 0.314088i | 0.782570 | − | 0.622562i | \(-0.213908\pi\) |
−0.350265 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(762\) | 10.0144 | − | 7.27588i | 0.362783 | − | 0.263577i | ||||
\(763\) | 22.7126 | − | 16.5017i | 0.822251 | − | 0.597400i | ||||
\(764\) | −12.0877 | − | 8.78224i | −0.437318 | − | 0.317730i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.64559 | − | 4.82830i | 0.240115 | − | 0.174454i | ||||
\(767\) | 4.01692 | − | 12.3628i | 0.145043 | − | 0.446395i | ||||
\(768\) | 15.8439 | 0.571717 | ||||||||
\(769\) | −0.753239 | + | 2.31823i | −0.0271625 | + | 0.0835976i | −0.963719 | − | 0.266920i | \(-0.913994\pi\) |
0.936556 | + | 0.350517i | \(0.113994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.18265 | − | 6.71750i | −0.0786061 | − | 0.241925i | ||||
\(772\) | 0.508359 | + | 1.56457i | 0.0182963 | + | 0.0563101i | ||||
\(773\) | −20.4957 | − | 14.8910i | −0.737180 | − | 0.535592i | 0.154647 | − | 0.987970i | \(-0.450576\pi\) |
−0.891827 | + | 0.452377i | \(0.850576\pi\) | |||||||
\(774\) | 2.64776 | 0.0951716 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.8574 | −0.497450 | ||||||||
\(777\) | −28.4722 | − | 20.6863i | −1.02143 | − | 0.742115i | ||||
\(778\) | −4.62493 | − | 14.2341i | −0.165812 | − | 0.510317i | ||||
\(779\) | −17.5082 | − | 53.8846i | −0.627296 | − | 1.93062i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.29427 | + | 7.06103i | −0.0820953 | + | 0.252664i | ||||
\(782\) | −11.7289 | −0.419426 | ||||||||
\(783\) | 1.63290 | − | 5.02554i | 0.0583550 | − | 0.179598i | ||||
\(784\) | 3.51299 | − | 2.55234i | 0.125464 | − | 0.0911550i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.83257 | − | 1.33144i | −0.0653656 | − | 0.0474909i | ||||
\(787\) | 31.2669 | − | 22.7167i | 1.11454 | − | 0.809763i | 0.131170 | − | 0.991360i | \(-0.458127\pi\) |
0.983373 | + | 0.181597i | \(0.0581266\pi\) | |||||||
\(788\) | 7.58719 | − | 5.51242i | 0.270283 | − | 0.196372i | ||||
\(789\) | 16.5328 | + | 12.0118i | 0.588582 | + | 0.427630i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.37774 | − | 6.81333i | 0.333434 | − | 0.242254i | ||||
\(792\) | 1.08757 | − | 3.34719i | 0.0386450 | − | 0.118937i | ||||
\(793\) | 56.0741 | 1.99125 | ||||||||
\(794\) | −4.37879 | + | 13.4765i | −0.155397 | + | 0.478264i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.76775 | − | 17.7513i | −0.204432 | − | 0.629178i | ||||
\(797\) | 16.1004 | + | 49.5519i | 0.570306 | + | 1.75522i | 0.651635 | + | 0.758533i | \(0.274083\pi\) |
−0.0813294 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(798\) | 16.2474 | + | 11.8044i | 0.575152 | + | 0.417872i | ||||
\(799\) | 27.9968 | 0.990454 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.08404 | 0.0383025 | ||||||||
\(802\) | 5.70490 | + | 4.14485i | 0.201447 | + | 0.146360i | ||||
\(803\) | −2.55844 | − | 7.87407i | −0.0902854 | − | 0.277870i | ||||
\(804\) | 0.792882 | + | 2.44024i | 0.0279628 | + | 0.0860606i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.809598 | + | 2.49169i | −0.0285169 | + | 0.0877659i | ||||
\(807\) | −21.1923 | −0.746006 | ||||||||
\(808\) | 6.26350 | − | 19.2771i | 0.220349 | − | 0.678166i | ||||
\(809\) | −25.7217 | + | 18.6879i | −0.904328 | + | 0.657033i | −0.939574 | − | 0.342346i | \(-0.888778\pi\) |
0.0352461 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.1777 | + | 18.2927i | 0.884108 | + | 0.642342i | 0.934335 | − | 0.356395i | \(-0.115994\pi\) |
−0.0502268 | + | 0.998738i | \(0.515994\pi\) | |||||||
\(812\) | 10.7206 | − | 7.78896i | 0.376219 | − | 0.273339i | ||||
\(813\) | 8.05229 | − | 5.85033i | 0.282406 | − | 0.205180i | ||||
\(814\) | 11.5415 | + | 8.38541i | 0.404530 | + | 0.293908i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.42281 | + | 4.66645i | −0.224843 | + | 0.163358i | ||||
\(817\) | −4.48133 | + | 13.7921i | −0.156782 | + | 0.482525i | ||||
\(818\) | −1.21188 | −0.0423725 | ||||||||
\(819\) | −3.89193 | + | 11.9781i | −0.135995 | + | 0.418550i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5319 | − | 44.7247i | −0.507168 | − | 1.56090i | −0.797095 | − | 0.603854i | \(-0.793631\pi\) |
0.289927 | − | 0.957049i | \(-0.406369\pi\) | |||||||
\(822\) | 6.53446 | + | 20.1110i | 0.227916 | + | 0.701452i | ||||
\(823\) | −22.9296 | − | 16.6593i | −0.799276 | − | 0.580708i | 0.111426 | − | 0.993773i | \(-0.464458\pi\) |
−0.910702 | + | 0.413065i | \(0.864458\pi\) | |||||||
\(824\) | −12.8920 | −0.449113 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.7208 | −0.373023 | ||||||||
\(827\) | 11.4622 | + | 8.32775i | 0.398579 | + | 0.289584i | 0.768962 | − | 0.639295i | \(-0.220774\pi\) |
−0.370383 | + | 0.928879i | \(0.620774\pi\) | |||||||
\(828\) | 0.583776 | + | 1.79668i | 0.0202876 | + | 0.0624389i | ||||
\(829\) | 0.468647 | + | 1.44235i | 0.0162768 | + | 0.0500948i | 0.958865 | − | 0.283862i | \(-0.0916159\pi\) |
−0.942588 | + | 0.333957i | \(0.891616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.78942 | − | 17.8180i | 0.200833 | − | 0.618099i | ||||
\(832\) | 32.9379 | 1.14192 | ||||||||
\(833\) | 3.61944 | − | 11.1395i | 0.125406 | − | 0.385961i | ||||
\(834\) | −15.1299 | + | 10.9925i | −0.523906 | + | 0.380640i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.50433 | + | 3.27259i | 0.155786 | + | 0.113185i | ||||
\(837\) | −0.476737 | + | 0.346370i | −0.0164784 | + | 0.0119723i | ||||
\(838\) | −10.3979 | + | 7.55449i | −0.359188 | + | 0.260965i | ||||
\(839\) | −8.48811 | − | 6.16697i | −0.293042 | − | 0.212908i | 0.431544 | − | 0.902092i | \(-0.357969\pi\) |
−0.724586 | + | 0.689184i | \(0.757969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.871777 | − | 0.633383i | 0.0300613 | − | 0.0218408i | ||||
\(842\) | −3.41004 | + | 10.4950i | −0.117518 | + | 0.361683i | ||||
\(843\) | −29.0916 | −1.00197 | ||||||||
\(844\) | 1.72732 | − | 5.31614i | 0.0594568 | − | 0.182989i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.03747 | + | 6.27068i | 0.0700496 | + | 0.215591i | ||||
\(847\) | 9.23615 | + | 28.4259i | 0.317358 | + | 0.976727i | ||||
\(848\) | −4.50221 | − | 3.27104i | −0.154606 | − | 0.112328i | ||||
\(849\) | −7.18007 | −0.246419 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.5120 | −0.908820 | ||||||||
\(852\) | −4.24887 | − | 3.08699i | −0.145564 | − | 0.105758i | ||||
\(853\) | 4.59110 | + | 14.1300i | 0.157196 | + | 0.483801i | 0.998377 | − | 0.0569538i | \(-0.0181388\pi\) |
−0.841180 | + | 0.540755i | \(0.818139\pi\) | |||||||
\(854\) | −14.2909 | − | 43.9828i | −0.489024 | − | 1.50506i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.79973 | − | 11.6944i | 0.129872 | − | 0.399705i | ||||
\(857\) | 26.4088 | 0.902109 | 0.451054 | − | 0.892496i | \(-0.351048\pi\) | ||||
0.451054 | + | 0.892496i | \(0.351048\pi\) | |||||||
\(858\) | 1.57764 | − | 4.85547i | 0.0538597 | − | 0.165763i | ||||
\(859\) | 7.38643 | − | 5.36656i | 0.252022 | − | 0.183105i | −0.454601 | − | 0.890695i | \(-0.650218\pi\) |
0.706622 | + | 0.707591i | \(0.250218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.7075 | − | 17.2245i | −0.807951 | − | 0.587011i | ||||
\(862\) | 5.01906 | − | 3.64656i | 0.170950 | − | 0.124202i | ||||
\(863\) | 10.0962 | − | 7.33532i | 0.343679 | − | 0.249697i | −0.402534 | − | 0.915405i | \(-0.631870\pi\) |
0.746212 | + | 0.665708i | \(0.231870\pi\) | |||||||
\(864\) | 3.44649 | + | 2.50402i | 0.117252 | + | 0.0851886i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.1386 | − | 21.1704i | 0.990168 | − | 0.719399i | ||||
\(867\) | −1.36415 | + | 4.19841i | −0.0463288 | + | 0.142585i | ||||
\(868\) | −1.47776 | −0.0501586 | ||||||||
\(869\) | 4.37789 | − | 13.4738i | 0.148510 | − | 0.457066i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.98205 | + | 12.2555i | 0.134927 | + | 0.415262i | ||||
\(872\) | −8.61262 | − | 26.5069i | −0.291660 | − | 0.897638i | ||||
\(873\) | −3.65783 | − | 2.65757i | −0.123799 | − | 0.0899450i | ||||
\(874\) | 15.1289 | 0.511741 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.85662 | 0.197877 | ||||||||
\(877\) | −33.0177 | − | 23.9888i | −1.11493 | − | 0.810043i | −0.131496 | − | 0.991317i | \(-0.541978\pi\) |
−0.983433 | + | 0.181273i | \(0.941978\pi\) | |||||||
\(878\) | 3.86065 | + | 11.8819i | 0.130291 | + | 0.400993i | ||||
\(879\) | 0.555691 | + | 1.71024i | 0.0187430 | + | 0.0576850i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.12544 | + | 3.46374i | −0.0379170 | + | 0.116696i | −0.968223 | − | 0.250087i | \(-0.919541\pi\) |
0.930306 | + | 0.366783i | \(0.119541\pi\) | |||||||
\(882\) | 2.75842 | 0.0928808 | ||||||||
\(883\) | 0.102858 | − | 0.316564i | 0.00346144 | − | 0.0106532i | −0.949311 | − | 0.314339i | \(-0.898217\pi\) |
0.952772 | + | 0.303686i | \(0.0982172\pi\) | |||||||
\(884\) | 12.4061 | − | 9.01357i | 0.417263 | − | 0.303159i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.7815 | − | 11.4659i | −0.530190 | − | 0.385206i | ||||
\(887\) | 0.924496 | − | 0.671685i | 0.0310415 | − | 0.0225530i | −0.572156 | − | 0.820145i | \(-0.693893\pi\) |
0.603198 | + | 0.797592i | \(0.293893\pi\) | |||||||
\(888\) | −28.2660 | + | 20.5365i | −0.948546 | + | 0.689159i | ||||
\(889\) | 28.3688 | + | 20.6111i | 0.951459 | + | 0.691276i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.929002 | − | 0.674959i | 0.0311227 | − | 0.0226120i | ||||
\(892\) | −2.03980 | + | 6.27787i | −0.0682977 | + | 0.210199i | ||||
\(893\) | −36.1123 | −1.20845 | ||||||||
\(894\) | −0.0707650 | + | 0.217792i | −0.00236674 | + | 0.00728407i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.266092 | − | 0.818948i | −0.00888953 | − | 0.0273591i | ||||
\(897\) | 2.93187 | + | 9.02336i | 0.0978923 | + | 0.301281i | ||||
\(898\) | 6.01342 | + | 4.36901i | 0.200671 | + | 0.145796i | ||||
\(899\) | 3.11385 | 0.103853 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0109 | −0.500086 | ||||||||
\(902\) | 9.61012 | + | 6.98216i | 0.319982 | + | 0.232481i | ||||
\(903\) | 2.31780 | + | 7.13347i | 0.0771317 | + | 0.237387i | ||||
\(904\) | −3.55604 | − | 10.9444i | −0.118272 | − | 0.364004i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.36704 | − | 4.20732i | 0.0454169 | − | 0.139779i | ||||
\(907\) | −18.4202 | −0.611632 | −0.305816 | − | 0.952091i | \(-0.598929\pi\) | ||||
−0.305816 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(908\) | −6.43345 | + | 19.8001i | −0.213502 | + | 0.657090i | ||||
\(909\) | 5.35029 | − | 3.88721i | 0.177458 | − | 0.128931i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7651 | − | 10.7274i | −0.489188 | − | 0.355416i | 0.315684 | − | 0.948864i | \(-0.397766\pi\) |
−0.804872 | + | 0.593449i | \(0.797766\pi\) | |||||||
\(912\) | 8.28462 | − | 6.01913i | 0.274331 | − | 0.199313i | ||||
\(913\) | 11.5141 | − | 8.36551i | 0.381062 | − | 0.276858i | ||||
\(914\) | −2.43681 | − | 1.77044i | −0.0806024 | − | 0.0585611i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.810372 | − | 0.588770i | 0.0267754 | − | 0.0194535i | ||||
\(917\) | 1.98290 | − | 6.10275i | 0.0654812 | − | 0.201531i | ||||
\(918\) | −5.04322 | −0.166451 | ||||||||
\(919\) | 3.34919 | − | 10.3078i | 0.110480 | − | 0.340022i | −0.880498 | − | 0.474050i | \(-0.842791\pi\) |
0.990977 | + | 0.134029i | \(0.0427914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.85059 | + | 5.69554i | 0.0609791 | + | 0.187674i | ||||
\(922\) | −3.01904 | − | 9.29166i | −0.0994269 | − | 0.306005i | ||||
\(923\) | −21.3389 | − | 15.5036i | −0.702378 | − | 0.510308i | ||||
\(924\) | 2.87967 | 0.0947342 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.3438 | 0.471368 | ||||||||
\(927\) | −3.40300 | − | 2.47242i | −0.111769 | − | 0.0812051i | ||||
\(928\) | −6.95631 | − | 21.4093i | −0.228352 | − | 0.702795i | ||||
\(929\) | −16.1768 | − | 49.7870i | −0.530743 | − | 1.63346i | −0.752673 | − | 0.658395i | \(-0.771236\pi\) |
0.221930 | − | 0.975063i | \(-0.428764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.66862 | + | 14.3685i | −0.153008 | + | 0.470910i | ||||
\(932\) | 2.43678 | 0.0798193 | ||||||||
\(933\) | −7.37574 | + | 22.7002i | −0.241471 | + | 0.743171i | ||||
\(934\) | 19.2211 | − | 13.9649i | 0.628933 | − | 0.456947i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.1154 | + | 7.34929i | 0.330633 | + | 0.240219i | ||||
\(937\) | 0.00106163 | 0.000771322i | 3.46821e−5 | 2.51980e-5i | −0.587768 | − | 0.809030i | \(-0.699993\pi\) | ||
0.587803 | + | 0.809004i | \(0.299993\pi\) | |||||||
\(938\) | 8.59798 | − | 6.24680i | 0.280734 | − | 0.203965i | ||||
\(939\) | −4.65924 | − | 3.38513i | −0.152048 | − | 0.110470i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.5737 | − | 12.7680i | 0.572885 | − | 0.416225i | −0.263267 | − | 0.964723i | \(-0.584800\pi\) |
0.836152 | + | 0.548498i | \(0.184800\pi\) | |||||||
\(942\) | −0.148293 | + | 0.456399i | −0.00483165 | + | 0.0148703i | ||||
\(943\) | −22.0754 | −0.718874 | ||||||||
\(944\) | −1.68926 | + | 5.19900i | −0.0549807 | + | 0.169213i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.939548 | − | 2.89163i | −0.0305473 | − | 0.0940151i | ||||
\(947\) | −10.4839 | − | 32.2661i | −0.340681 | − | 1.04851i | −0.963855 | − | 0.266426i | \(-0.914157\pi\) |
0.623174 | − | 0.782083i | \(-0.285843\pi\) | |||||||
\(948\) | 8.10763 | + | 5.89054i | 0.263324 | + | 0.191316i | ||||
\(949\) | 29.4134 | 0.954800 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2481 | −0.397172 | ||||||||
\(952\) | −35.4240 | − | 25.7370i | −1.14810 | − | 0.834142i | ||||
\(953\) | −2.56579 | − | 7.89670i | −0.0831142 | − | 0.255799i | 0.900860 | − | 0.434109i | \(-0.142937\pi\) |
−0.983974 | + | 0.178310i | \(0.942937\pi\) | |||||||
\(954\) | −1.09242 | − | 3.36213i | −0.0353685 | − | 0.108853i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.55594 | + | 17.0994i | −0.179692 | + | 0.553035i | ||||
\(957\) | −6.06786 | −0.196146 | ||||||||
\(958\) | 14.3967 | − | 44.3085i | 0.465136 | − | 1.43154i | ||||
\(959\) | −48.4620 | + | 35.2097i | −1.56492 | + | 1.13698i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.7986 | + | 18.0172i | 0.799955 | + | 0.581201i | ||||
\(962\) | −41.0030 | + | 29.7904i | −1.32199 | + | 0.960482i | ||||
\(963\) | 3.24573 | − | 2.35816i | 0.104592 | − | 0.0759907i | ||||
\(964\) | −8.83240 | − | 6.41711i | −0.284472 | − | 0.206681i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.33044 | − | 4.59933i | 0.203679 | − | 0.147981i | ||||
\(967\) | 8.58804 | − | 26.4313i | 0.276173 | − | 0.849972i | −0.712734 | − | 0.701434i | \(-0.752543\pi\) |
0.988907 | − | 0.148538i | \(-0.0474567\pi\) | |||||||
\(968\) | 29.6724 | 0.953707 | ||||||||
\(969\) | 8.53565 | − | 26.2700i | 0.274205 | − | 0.843915i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.59377 | − | 29.5266i | −0.307879 | − | 0.947554i | −0.978587 | − | 0.205833i | \(-0.934010\pi\) |
0.670708 | − | 0.741721i | \(-0.265990\pi\) | |||||||
\(972\) | 0.251013 | + | 0.772537i | 0.00805123 | + | 0.0247791i | ||||
\(973\) | −42.8601 | − | 31.1397i | −1.37403 | − | 0.998292i | ||||
\(974\) | 12.3692 | 0.396333 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.5811 | −0.754814 | ||||||||
\(977\) | −35.9137 | − | 26.0928i | −1.14898 | − | 0.834783i | −0.160635 | − | 0.987014i | \(-0.551354\pi\) |
−0.988345 | + | 0.152231i | \(0.951354\pi\) | |||||||
\(978\) | −1.09151 | − | 3.35932i | −0.0349027 | − | 0.107419i | ||||
\(979\) | −0.384667 | − | 1.18388i | −0.0122940 | − | 0.0378370i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.81009 | − | 8.64857i | 0.0897193 | − | 0.276127i | ||||
\(982\) | 18.1506 | 0.579208 | ||||||||
\(983\) | −13.5305 | + | 41.6427i | −0.431557 | + | 1.32820i | 0.465017 | + | 0.885302i | \(0.346048\pi\) |
−0.896574 | + | 0.442894i | \(0.853952\pi\) | |||||||
\(984\) | −23.5359 | + | 17.0998i | −0.750297 | + | 0.545123i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.5597 | + | 15.6640i | 0.686600 | + | 0.498844i | ||||
\(987\) | −15.1106 | + | 10.9785i | −0.480977 | + | 0.349450i | ||||
\(988\) | −16.0023 | + | 11.6264i | −0.509102 | + | 0.369884i | ||||
\(989\) | 4.57121 | + | 3.32118i | 0.145356 | + | 0.105607i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.8586 | + | 20.2404i | −0.884957 | + | 0.642959i | −0.934558 | − | 0.355810i | \(-0.884205\pi\) |
0.0496015 | + | 0.998769i | \(0.484205\pi\) | |||||||
\(992\) | −0.775752 | + | 2.38752i | −0.0246302 | + | 0.0758039i | ||||
\(993\) | 6.02899 | 0.191324 | ||||||||
\(994\) | −6.72219 | + | 20.6888i | −0.213215 | + | 0.656208i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.11107 | + | 9.57490i | 0.0985781 | + | 0.303392i | ||||
\(997\) | 5.99154 | + | 18.4401i | 0.189754 | + | 0.584002i | 0.999998 | − | 0.00209042i | \(-0.000665403\pi\) |
−0.810244 | + | 0.586093i | \(0.800665\pi\) | |||||||
\(998\) | 10.7848 | + | 7.83564i | 0.341388 | + | 0.248033i | ||||
\(999\) | −11.3997 | −0.360670 |
(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 | 375.2.g.d.76.2 | 16 | ||
5.2 | odd | 4 | 375.2.i.c.49.3 | 16 | |||
5.3 | odd | 4 | 75.2.i.a.34.2 | ✓ | 16 | ||
5.4 | even | 2 | 375.2.g.e.76.3 | 16 | |||
15.8 | even | 4 | 225.2.m.b.109.3 | 16 | |||
25.2 | odd | 20 | 75.2.i.a.64.2 | yes | 16 | ||
25.6 | even | 5 | 1875.2.a.p.1.5 | 8 | |||
25.8 | odd | 20 | 1875.2.b.h.1249.6 | 16 | |||
25.11 | even | 5 | inner | 375.2.g.d.301.2 | 16 | ||
25.14 | even | 10 | 375.2.g.e.301.3 | 16 | |||
25.17 | odd | 20 | 1875.2.b.h.1249.11 | 16 | |||
25.19 | even | 10 | 1875.2.a.m.1.4 | 8 | |||
25.23 | odd | 20 | 375.2.i.c.199.3 | 16 | |||
75.2 | even | 20 | 225.2.m.b.64.3 | 16 | |||
75.44 | odd | 10 | 5625.2.a.bd.1.5 | 8 | |||
75.56 | odd | 10 | 5625.2.a.t.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.2 | ✓ | 16 | 5.3 | odd | 4 | ||
75.2.i.a.64.2 | yes | 16 | 25.2 | odd | 20 | ||
225.2.m.b.64.3 | 16 | 75.2 | even | 20 | |||
225.2.m.b.109.3 | 16 | 15.8 | even | 4 | |||
375.2.g.d.76.2 | 16 | 1.1 | even | 1 | trivial | ||
375.2.g.d.301.2 | 16 | 25.11 | even | 5 | inner | ||
375.2.g.e.76.3 | 16 | 5.4 | even | 2 | |||
375.2.g.e.301.3 | 16 | 25.14 | even | 10 | |||
375.2.i.c.49.3 | 16 | 5.2 | odd | 4 | |||
375.2.i.c.199.3 | 16 | 25.23 | odd | 20 | |||
1875.2.a.m.1.4 | 8 | 25.19 | even | 10 | |||
1875.2.a.p.1.5 | 8 | 25.6 | even | 5 | |||
1875.2.b.h.1249.6 | 16 | 25.8 | odd | 20 | |||
1875.2.b.h.1249.11 | 16 | 25.17 | odd | 20 | |||
5625.2.a.t.1.4 | 8 | 75.56 | odd | 10 | |||
5625.2.a.bd.1.5 | 8 | 75.44 | odd | 10 |