Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,2,Mod(31,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.g (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.19775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.61 |
Dual form | 150.2.g.a.91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.80902 | − | 1.31433i | 0.809017 | − | 0.587785i | ||||
\(6\) | −0.309017 | − | 0.951057i | −0.126156 | − | 0.388267i | ||||
\(7\) | 2.61803 | 0.989524 | 0.494762 | − | 0.869029i | \(-0.335255\pi\) | ||||
0.494762 | + | 0.869029i | \(0.335255\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −0.690983 | + | 2.12663i | −0.218508 | + | 0.672499i | ||||
\(11\) | −2.92705 | + | 2.12663i | −0.882539 | + | 0.641202i | −0.933922 | − | 0.357477i | \(-0.883637\pi\) |
0.0513829 | + | 0.998679i | \(0.483637\pi\) | |||||||
\(12\) | 0.809017 | + | 0.587785i | 0.233543 | + | 0.169679i | ||||
\(13\) | 5.23607 | + | 3.80423i | 1.45222 | + | 1.05510i | 0.985305 | + | 0.170802i | \(0.0546359\pi\) |
0.466919 | + | 0.884300i | \(0.345364\pi\) | |||||||
\(14\) | −2.11803 | + | 1.53884i | −0.566068 | + | 0.411273i | ||||
\(15\) | 0.690983 | + | 2.12663i | 0.178411 | + | 0.549093i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.381966 | + | 1.17557i | 0.0926404 | + | 0.285118i | 0.986632 | − | 0.162967i | \(-0.0521064\pi\) |
−0.893991 | + | 0.448085i | \(0.852106\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.76393 | − | 5.42882i | −0.404674 | − | 1.24546i | −0.921167 | − | 0.389167i | \(-0.872763\pi\) |
0.516494 | − | 0.856291i | \(-0.327237\pi\) | |||||||
\(20\) | −0.690983 | − | 2.12663i | −0.154508 | − | 0.475528i | ||||
\(21\) | −0.809017 | + | 2.48990i | −0.176542 | + | 0.543340i | ||||
\(22\) | 1.11803 | − | 3.44095i | 0.238366 | − | 0.733614i | ||||
\(23\) | −3.61803 | + | 2.62866i | −0.754412 | + | 0.548113i | −0.897191 | − | 0.441642i | \(-0.854396\pi\) |
0.142779 | + | 0.989755i | \(0.454396\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.54508 | − | 4.75528i | 0.309017 | − | 0.951057i | ||||
\(26\) | −6.47214 | −1.26929 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 0.809017 | − | 2.48990i | 0.152890 | − | 0.470547i | ||||
\(29\) | 2.61803 | − | 8.05748i | 0.486157 | − | 1.49624i | −0.344142 | − | 0.938918i | \(-0.611830\pi\) |
0.830299 | − | 0.557319i | \(-0.188170\pi\) | |||||||
\(30\) | −1.80902 | − | 1.31433i | −0.330280 | − | 0.239962i | ||||
\(31\) | 2.04508 | + | 6.29412i | 0.367308 | + | 1.13046i | 0.948523 | + | 0.316708i | \(0.102578\pi\) |
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.11803 | − | 3.44095i | −0.194625 | − | 0.598993i | ||||
\(34\) | −1.00000 | − | 0.726543i | −0.171499 | − | 0.124601i | ||||
\(35\) | 4.73607 | − | 3.44095i | 0.800542 | − | 0.581628i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | −6.47214 | − | 4.70228i | −1.06401 | − | 0.773050i | −0.0891861 | − | 0.996015i | \(-0.528427\pi\) |
−0.974827 | + | 0.222965i | \(0.928427\pi\) | |||||||
\(38\) | 4.61803 | + | 3.35520i | 0.749144 | + | 0.544285i | ||||
\(39\) | −5.23607 | + | 3.80423i | −0.838442 | + | 0.609164i | ||||
\(40\) | 1.80902 | + | 1.31433i | 0.286031 | + | 0.207813i | ||||
\(41\) | −4.61803 | − | 3.35520i | −0.721216 | − | 0.523994i | 0.165557 | − | 0.986200i | \(-0.447058\pi\) |
−0.886772 | + | 0.462206i | \(0.847058\pi\) | |||||||
\(42\) | −0.809017 | − | 2.48990i | −0.124834 | − | 0.384200i | ||||
\(43\) | −7.70820 | −1.17549 | −0.587745 | − | 0.809046i | \(-0.699984\pi\) | ||||
−0.587745 | + | 0.809046i | \(0.699984\pi\) | |||||||
\(44\) | 1.11803 | + | 3.44095i | 0.168550 | + | 0.518743i | ||||
\(45\) | −2.23607 | −0.333333 | ||||||||
\(46\) | 1.38197 | − | 4.25325i | 0.203760 | − | 0.627108i | ||||
\(47\) | 0.527864 | − | 1.62460i | 0.0769969 | − | 0.236972i | −0.905149 | − | 0.425096i | \(-0.860241\pi\) |
0.982145 | + | 0.188123i | \(0.0602405\pi\) | |||||||
\(48\) | 0.809017 | − | 0.587785i | 0.116772 | − | 0.0848395i | ||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | 1.54508 | + | 4.75528i | 0.218508 | + | 0.672499i | ||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | 5.23607 | − | 3.80423i | 0.726112 | − | 0.527551i | ||||
\(53\) | −0.645898 | + | 1.98787i | −0.0887209 | + | 0.273055i | −0.985566 | − | 0.169289i | \(-0.945853\pi\) |
0.896846 | + | 0.442344i | \(0.145853\pi\) | |||||||
\(54\) | −0.309017 | + | 0.951057i | −0.0420519 | + | 0.129422i | ||||
\(55\) | −2.50000 | + | 7.69421i | −0.337100 | + | 1.03749i | ||||
\(56\) | 0.809017 | + | 2.48990i | 0.108109 | + | 0.332727i | ||||
\(57\) | 5.70820 | 0.756070 | ||||||||
\(58\) | 2.61803 | + | 8.05748i | 0.343765 | + | 1.05800i | ||||
\(59\) | 2.92705 | + | 2.12663i | 0.381070 | + | 0.276863i | 0.761786 | − | 0.647829i | \(-0.224323\pi\) |
−0.380717 | + | 0.924692i | \(0.624323\pi\) | |||||||
\(60\) | 2.23607 | 0.288675 | ||||||||
\(61\) | −2.23607 | + | 1.62460i | −0.286299 | + | 0.208009i | −0.721660 | − | 0.692247i | \(-0.756621\pi\) |
0.435361 | + | 0.900256i | \(0.356621\pi\) | |||||||
\(62\) | −5.35410 | − | 3.88998i | −0.679972 | − | 0.494028i | ||||
\(63\) | −2.11803 | − | 1.53884i | −0.266847 | − | 0.193876i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 2.92705 | + | 2.12663i | 0.360295 | + | 0.261770i | ||||
\(67\) | −0.472136 | − | 1.45309i | −0.0576806 | − | 0.177523i | 0.918065 | − | 0.396430i | \(-0.129751\pi\) |
−0.975746 | + | 0.218907i | \(0.929751\pi\) | |||||||
\(68\) | 1.23607 | 0.149895 | ||||||||
\(69\) | −1.38197 | − | 4.25325i | −0.166369 | − | 0.512032i | ||||
\(70\) | −1.80902 | + | 5.56758i | −0.216219 | + | 0.665453i | ||||
\(71\) | 1.70820 | − | 5.25731i | 0.202727 | − | 0.623928i | −0.797073 | − | 0.603884i | \(-0.793619\pi\) |
0.999799 | − | 0.0200445i | \(-0.00638080\pi\) | |||||||
\(72\) | 0.309017 | − | 0.951057i | 0.0364180 | − | 0.112083i | ||||
\(73\) | −2.85410 | + | 2.07363i | −0.334047 | + | 0.242700i | −0.742146 | − | 0.670238i | \(-0.766192\pi\) |
0.408099 | + | 0.912938i | \(0.366192\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 4.04508 | + | 2.93893i | 0.467086 | + | 0.339358i | ||||
\(76\) | −5.70820 | −0.654776 | ||||||||
\(77\) | −7.66312 | + | 5.56758i | −0.873293 | + | 0.634485i | ||||
\(78\) | 2.00000 | − | 6.15537i | 0.226455 | − | 0.696958i | ||||
\(79\) | −1.73607 | + | 5.34307i | −0.195323 | + | 0.601142i | 0.804650 | + | 0.593750i | \(0.202353\pi\) |
−0.999973 | + | 0.00739236i | \(0.997647\pi\) | |||||||
\(80\) | −2.23607 | −0.250000 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 5.70820 | 0.630366 | ||||||||
\(83\) | 0.663119 | + | 2.04087i | 0.0727868 | + | 0.224015i | 0.980831 | − | 0.194859i | \(-0.0624250\pi\) |
−0.908044 | + | 0.418874i | \(0.862425\pi\) | |||||||
\(84\) | 2.11803 | + | 1.53884i | 0.231096 | + | 0.167901i | ||||
\(85\) | 2.23607 | + | 1.62460i | 0.242536 | + | 0.176212i | ||||
\(86\) | 6.23607 | − | 4.53077i | 0.672453 | − | 0.488565i | ||||
\(87\) | 6.85410 | + | 4.97980i | 0.734837 | + | 0.533890i | ||||
\(88\) | −2.92705 | − | 2.12663i | −0.312025 | − | 0.226699i | ||||
\(89\) | −2.85410 | + | 2.07363i | −0.302534 | + | 0.219804i | −0.728686 | − | 0.684848i | \(-0.759869\pi\) |
0.426152 | + | 0.904651i | \(0.359869\pi\) | |||||||
\(90\) | 1.80902 | − | 1.31433i | 0.190687 | − | 0.138542i | ||||
\(91\) | 13.7082 | + | 9.95959i | 1.43701 | + | 1.04405i | ||||
\(92\) | 1.38197 | + | 4.25325i | 0.144080 | + | 0.443432i | ||||
\(93\) | −6.61803 | −0.686258 | ||||||||
\(94\) | 0.527864 | + | 1.62460i | 0.0544450 | + | 0.167565i | ||||
\(95\) | −10.3262 | − | 7.50245i | −1.05945 | − | 0.769735i | ||||
\(96\) | −0.309017 | + | 0.951057i | −0.0315389 | + | 0.0970668i | ||||
\(97\) | −1.04508 | + | 3.21644i | −0.106112 | + | 0.326580i | −0.989990 | − | 0.141138i | \(-0.954924\pi\) |
0.883878 | + | 0.467718i | \(0.154924\pi\) | |||||||
\(98\) | 0.118034 | − | 0.0857567i | 0.0119232 | − | 0.00866274i | ||||
\(99\) | 3.61803 | 0.363626 | ||||||||
\(100\) | −4.04508 | − | 2.93893i | −0.404508 | − | 0.293893i | ||||
\(101\) | 4.38197 | 0.436022 | 0.218011 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218011 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(102\) | 1.00000 | − | 0.726543i | 0.0990148 | − | 0.0719384i | ||||
\(103\) | 4.42705 | − | 13.6251i | 0.436210 | − | 1.34252i | −0.455631 | − | 0.890169i | \(-0.650586\pi\) |
0.891841 | − | 0.452348i | \(-0.149414\pi\) | |||||||
\(104\) | −2.00000 | + | 6.15537i | −0.196116 | + | 0.603583i | ||||
\(105\) | 1.80902 | + | 5.56758i | 0.176542 | + | 0.543340i | ||||
\(106\) | −0.645898 | − | 1.98787i | −0.0627352 | − | 0.193079i | ||||
\(107\) | −11.6180 | −1.12316 | −0.561579 | − | 0.827423i | \(-0.689806\pi\) | ||||
−0.561579 | + | 0.827423i | \(0.689806\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | −13.9443 | − | 10.1311i | −1.33562 | − | 0.970384i | −0.999593 | − | 0.0285313i | \(-0.990917\pi\) |
−0.336026 | − | 0.941853i | \(-0.609083\pi\) | |||||||
\(110\) | −2.50000 | − | 7.69421i | −0.238366 | − | 0.733614i | ||||
\(111\) | 6.47214 | − | 4.70228i | 0.614308 | − | 0.446321i | ||||
\(112\) | −2.11803 | − | 1.53884i | −0.200135 | − | 0.145407i | ||||
\(113\) | 15.5623 | + | 11.3067i | 1.46398 | + | 1.06364i | 0.982304 | + | 0.187292i | \(0.0599712\pi\) |
0.481674 | + | 0.876350i | \(0.340029\pi\) | |||||||
\(114\) | −4.61803 | + | 3.35520i | −0.432519 | + | 0.314243i | ||||
\(115\) | −3.09017 | + | 9.51057i | −0.288160 | + | 0.886865i | ||||
\(116\) | −6.85410 | − | 4.97980i | −0.636387 | − | 0.462363i | ||||
\(117\) | −2.00000 | − | 6.15537i | −0.184900 | − | 0.569064i | ||||
\(118\) | −3.61803 | −0.333067 | ||||||||
\(119\) | 1.00000 | + | 3.07768i | 0.0916698 | + | 0.282131i | ||||
\(120\) | −1.80902 | + | 1.31433i | −0.165140 | + | 0.119981i | ||||
\(121\) | 0.645898 | − | 1.98787i | 0.0587180 | − | 0.180715i | ||||
\(122\) | 0.854102 | − | 2.62866i | 0.0773268 | − | 0.237987i | ||||
\(123\) | 4.61803 | − | 3.35520i | 0.416394 | − | 0.302528i | ||||
\(124\) | 6.61803 | 0.594317 | ||||||||
\(125\) | −3.45492 | − | 10.6331i | −0.309017 | − | 0.951057i | ||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | −11.0172 | + | 8.00448i | −0.977620 | + | 0.710283i | −0.957176 | − | 0.289508i | \(-0.906508\pi\) |
−0.0204448 | + | 0.999791i | \(0.506508\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 2.38197 | − | 7.33094i | 0.209720 | − | 0.645453i | ||||
\(130\) | −11.7082 | + | 8.50651i | −1.02688 | + | 0.746070i | ||||
\(131\) | −5.52786 | − | 17.0130i | −0.482972 | − | 1.48643i | −0.834897 | − | 0.550406i | \(-0.814473\pi\) |
0.351925 | − | 0.936028i | \(-0.385527\pi\) | |||||||
\(132\) | −3.61803 | −0.314909 | ||||||||
\(133\) | −4.61803 | − | 14.2128i | −0.400434 | − | 1.23241i | ||||
\(134\) | 1.23607 | + | 0.898056i | 0.106780 | + | 0.0775802i | ||||
\(135\) | 0.690983 | − | 2.12663i | 0.0594703 | − | 0.183031i | ||||
\(136\) | −1.00000 | + | 0.726543i | −0.0857493 | + | 0.0623005i | ||||
\(137\) | 9.85410 | + | 7.15942i | 0.841893 | + | 0.611671i | 0.922899 | − | 0.385043i | \(-0.125813\pi\) |
−0.0810060 | + | 0.996714i | \(0.525813\pi\) | |||||||
\(138\) | 3.61803 | + | 2.62866i | 0.307988 | + | 0.223766i | ||||
\(139\) | −8.47214 | + | 6.15537i | −0.718597 | + | 0.522091i | −0.885936 | − | 0.463808i | \(-0.846483\pi\) |
0.167339 | + | 0.985899i | \(0.446483\pi\) | |||||||
\(140\) | −1.80902 | − | 5.56758i | −0.152890 | − | 0.470547i | ||||
\(141\) | 1.38197 | + | 1.00406i | 0.116383 | + | 0.0845569i | ||||
\(142\) | 1.70820 | + | 5.25731i | 0.143349 | + | 0.441184i | ||||
\(143\) | −23.4164 | −1.95818 | ||||||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | −5.85410 | − | 18.0171i | −0.486157 | − | 1.49624i | ||||
\(146\) | 1.09017 | − | 3.35520i | 0.0902231 | − | 0.277678i | ||||
\(147\) | 0.0450850 | − | 0.138757i | 0.00371855 | − | 0.0114445i | ||||
\(148\) | −6.47214 | + | 4.70228i | −0.532006 | + | 0.386525i | ||||
\(149\) | 22.0902 | 1.80970 | 0.904849 | − | 0.425733i | \(-0.139984\pi\) | ||||
0.904849 | + | 0.425733i | \(0.139984\pi\) | |||||||
\(150\) | −5.00000 | −0.408248 | ||||||||
\(151\) | 18.3262 | 1.49137 | 0.745684 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745684 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(152\) | 4.61803 | − | 3.35520i | 0.374572 | − | 0.272143i | ||||
\(153\) | 0.381966 | − | 1.17557i | 0.0308801 | − | 0.0950392i | ||||
\(154\) | 2.92705 | − | 9.00854i | 0.235868 | − | 0.725929i | ||||
\(155\) | 11.9721 | + | 8.69827i | 0.961625 | + | 0.698662i | ||||
\(156\) | 2.00000 | + | 6.15537i | 0.160128 | + | 0.492824i | ||||
\(157\) | 8.65248 | 0.690543 | 0.345271 | − | 0.938503i | \(-0.387787\pi\) | ||||
0.345271 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(158\) | −1.73607 | − | 5.34307i | −0.138114 | − | 0.425072i | ||||
\(159\) | −1.69098 | − | 1.22857i | −0.134104 | − | 0.0974320i | ||||
\(160\) | 1.80902 | − | 1.31433i | 0.143015 | − | 0.103907i | ||||
\(161\) | −9.47214 | + | 6.88191i | −0.746509 | + | 0.542370i | ||||
\(162\) | −0.809017 | − | 0.587785i | −0.0635624 | − | 0.0461808i | ||||
\(163\) | 0.381966 | + | 0.277515i | 0.0299179 | + | 0.0217366i | 0.602644 | − | 0.798010i | \(-0.294114\pi\) |
−0.572726 | + | 0.819747i | \(0.694114\pi\) | |||||||
\(164\) | −4.61803 | + | 3.35520i | −0.360608 | + | 0.261997i | ||||
\(165\) | −6.54508 | − | 4.75528i | −0.509534 | − | 0.370198i | ||||
\(166\) | −1.73607 | − | 1.26133i | −0.134745 | − | 0.0978980i | ||||
\(167\) | 3.61803 | + | 11.1352i | 0.279972 | + | 0.861665i | 0.987861 | + | 0.155341i | \(0.0496477\pi\) |
−0.707889 | + | 0.706324i | \(0.750352\pi\) | |||||||
\(168\) | −2.61803 | −0.201986 | ||||||||
\(169\) | 8.92705 | + | 27.4746i | 0.686696 | + | 2.11343i | ||||
\(170\) | −2.76393 | −0.211984 | ||||||||
\(171\) | −1.76393 | + | 5.42882i | −0.134891 | + | 0.415153i | ||||
\(172\) | −2.38197 | + | 7.33094i | −0.181623 | + | 0.558979i | ||||
\(173\) | −4.11803 | + | 2.99193i | −0.313088 | + | 0.227472i | −0.733221 | − | 0.679991i | \(-0.761984\pi\) |
0.420132 | + | 0.907463i | \(0.361984\pi\) | |||||||
\(174\) | −8.47214 | −0.642271 | ||||||||
\(175\) | 4.04508 | − | 12.4495i | 0.305780 | − | 0.941093i | ||||
\(176\) | 3.61803 | 0.272720 | ||||||||
\(177\) | −2.92705 | + | 2.12663i | −0.220011 | + | 0.159847i | ||||
\(178\) | 1.09017 | − | 3.35520i | 0.0817117 | − | 0.251483i | ||||
\(179\) | 3.04508 | − | 9.37181i | 0.227600 | − | 0.700482i | −0.770417 | − | 0.637540i | \(-0.779952\pi\) |
0.998017 | − | 0.0629414i | \(-0.0200481\pi\) | |||||||
\(180\) | −0.690983 | + | 2.12663i | −0.0515028 | + | 0.158509i | ||||
\(181\) | −2.05573 | − | 6.32688i | −0.152801 | − | 0.470273i | 0.845130 | − | 0.534560i | \(-0.179523\pi\) |
−0.997931 | + | 0.0642869i | \(0.979523\pi\) | |||||||
\(182\) | −16.9443 | −1.25599 | ||||||||
\(183\) | −0.854102 | − | 2.62866i | −0.0631370 | − | 0.194316i | ||||
\(184\) | −3.61803 | − | 2.62866i | −0.266725 | − | 0.193787i | ||||
\(185\) | −17.8885 | −1.31519 | ||||||||
\(186\) | 5.35410 | − | 3.88998i | 0.392582 | − | 0.285227i | ||||
\(187\) | −3.61803 | − | 2.62866i | −0.264577 | − | 0.192226i | ||||
\(188\) | −1.38197 | − | 1.00406i | −0.100790 | − | 0.0732284i | ||||
\(189\) | 2.11803 | − | 1.53884i | 0.154064 | − | 0.111934i | ||||
\(190\) | 12.7639 | 0.925993 | ||||||||
\(191\) | −3.47214 | − | 2.52265i | −0.251235 | − | 0.182533i | 0.455039 | − | 0.890472i | \(-0.349625\pi\) |
−0.706274 | + | 0.707939i | \(0.749625\pi\) | |||||||
\(192\) | −0.309017 | − | 0.951057i | −0.0223014 | − | 0.0686366i | ||||
\(193\) | 17.8541 | 1.28517 | 0.642583 | − | 0.766216i | \(-0.277863\pi\) | ||||
0.642583 | + | 0.766216i | \(0.277863\pi\) | |||||||
\(194\) | −1.04508 | − | 3.21644i | −0.0750327 | − | 0.230927i | ||||
\(195\) | −4.47214 | + | 13.7638i | −0.320256 | + | 0.985648i | ||||
\(196\) | −0.0450850 | + | 0.138757i | −0.00322036 | + | 0.00991123i | ||||
\(197\) | −5.28115 | + | 16.2537i | −0.376267 | + | 1.15803i | 0.566354 | + | 0.824162i | \(0.308354\pi\) |
−0.942620 | + | 0.333867i | \(0.891646\pi\) | |||||||
\(198\) | −2.92705 | + | 2.12663i | −0.208016 | + | 0.151133i | ||||
\(199\) | 19.5066 | 1.38278 | 0.691392 | − | 0.722480i | \(-0.256998\pi\) | ||||
0.691392 | + | 0.722480i | \(0.256998\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 1.52786 | 0.107767 | ||||||||
\(202\) | −3.54508 | + | 2.57565i | −0.249431 | + | 0.181222i | ||||
\(203\) | 6.85410 | − | 21.0948i | 0.481064 | − | 1.48056i | ||||
\(204\) | −0.381966 | + | 1.17557i | −0.0267430 | + | 0.0823064i | ||||
\(205\) | −12.7639 | −0.891472 | ||||||||
\(206\) | 4.42705 | + | 13.6251i | 0.308447 | + | 0.949303i | ||||
\(207\) | 4.47214 | 0.310835 | ||||||||
\(208\) | −2.00000 | − | 6.15537i | −0.138675 | − | 0.426798i | ||||
\(209\) | 16.7082 | + | 12.1392i | 1.15573 | + | 0.839687i | ||||
\(210\) | −4.73607 | − | 3.44095i | −0.326820 | − | 0.237448i | ||||
\(211\) | 2.76393 | − | 2.00811i | 0.190277 | − | 0.138244i | −0.488568 | − | 0.872526i | \(-0.662481\pi\) |
0.678845 | + | 0.734281i | \(0.262481\pi\) | |||||||
\(212\) | 1.69098 | + | 1.22857i | 0.116137 | + | 0.0843786i | ||||
\(213\) | 4.47214 | + | 3.24920i | 0.306426 | + | 0.222631i | ||||
\(214\) | 9.39919 | − | 6.82891i | 0.642515 | − | 0.466815i | ||||
\(215\) | −13.9443 | + | 10.1311i | −0.950991 | + | 0.690936i | ||||
\(216\) | 0.809017 | + | 0.587785i | 0.0550466 | + | 0.0399937i | ||||
\(217\) | 5.35410 | + | 16.4782i | 0.363460 | + | 1.11862i | ||||
\(218\) | 17.2361 | 1.16737 | ||||||||
\(219\) | −1.09017 | − | 3.35520i | −0.0736669 | − | 0.226723i | ||||
\(220\) | 6.54508 | + | 4.75528i | 0.441270 | + | 0.320601i | ||||
\(221\) | −2.47214 | + | 7.60845i | −0.166294 | + | 0.511800i | ||||
\(222\) | −2.47214 | + | 7.60845i | −0.165919 | + | 0.510646i | ||||
\(223\) | 6.54508 | − | 4.75528i | 0.438291 | − | 0.318437i | −0.346664 | − | 0.937989i | \(-0.612686\pi\) |
0.784956 | + | 0.619552i | \(0.212686\pi\) | |||||||
\(224\) | 2.61803 | 0.174925 | ||||||||
\(225\) | −4.04508 | + | 2.93893i | −0.269672 | + | 0.195928i | ||||
\(226\) | −19.2361 | −1.27956 | ||||||||
\(227\) | 18.0172 | − | 13.0903i | 1.19584 | − | 0.868832i | 0.201975 | − | 0.979391i | \(-0.435264\pi\) |
0.993870 | + | 0.110558i | \(0.0352639\pi\) | |||||||
\(228\) | 1.76393 | − | 5.42882i | 0.116819 | − | 0.359533i | ||||
\(229\) | −1.70820 | + | 5.25731i | −0.112881 | + | 0.347413i | −0.991499 | − | 0.130113i | \(-0.958466\pi\) |
0.878618 | + | 0.477525i | \(0.158466\pi\) | |||||||
\(230\) | −3.09017 | − | 9.51057i | −0.203760 | − | 0.627108i | ||||
\(231\) | −2.92705 | − | 9.00854i | −0.192586 | − | 0.592718i | ||||
\(232\) | 8.47214 | 0.556223 | ||||||||
\(233\) | 5.76393 | + | 17.7396i | 0.377608 | + | 1.16216i | 0.941702 | + | 0.336447i | \(0.109225\pi\) |
−0.564095 | + | 0.825710i | \(0.690775\pi\) | |||||||
\(234\) | 5.23607 | + | 3.80423i | 0.342292 | + | 0.248690i | ||||
\(235\) | −1.18034 | − | 3.63271i | −0.0769969 | − | 0.236972i | ||||
\(236\) | 2.92705 | − | 2.12663i | 0.190535 | − | 0.138432i | ||||
\(237\) | −4.54508 | − | 3.30220i | −0.295235 | − | 0.214501i | ||||
\(238\) | −2.61803 | − | 1.90211i | −0.169702 | − | 0.123296i | ||||
\(239\) | −9.94427 | + | 7.22494i | −0.643241 | + | 0.467342i | −0.860962 | − | 0.508669i | \(-0.830138\pi\) |
0.217721 | + | 0.976011i | \(0.430138\pi\) | |||||||
\(240\) | 0.690983 | − | 2.12663i | 0.0446028 | − | 0.137273i | ||||
\(241\) | −7.73607 | − | 5.62058i | −0.498324 | − | 0.362054i | 0.310052 | − | 0.950719i | \(-0.399653\pi\) |
−0.808376 | + | 0.588666i | \(0.799653\pi\) | |||||||
\(242\) | 0.645898 | + | 1.98787i | 0.0415199 | + | 0.127785i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.854102 | + | 2.62866i | 0.0546783 | + | 0.168282i | ||||
\(245\) | −0.263932 | + | 0.191758i | −0.0168620 | + | 0.0122510i | ||||
\(246\) | −1.76393 | + | 5.42882i | −0.112464 | + | 0.346129i | ||||
\(247\) | 11.4164 | − | 35.1361i | 0.726409 | − | 2.23566i | ||||
\(248\) | −5.35410 | + | 3.88998i | −0.339986 | + | 0.247014i | ||||
\(249\) | −2.14590 | −0.135991 | ||||||||
\(250\) | 9.04508 | + | 6.57164i | 0.572061 | + | 0.415627i | ||||
\(251\) | 13.5623 | 0.856045 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(252\) | −2.11803 | + | 1.53884i | −0.133424 | + | 0.0969379i | ||||
\(253\) | 5.00000 | − | 15.3884i | 0.314347 | − | 0.967462i | ||||
\(254\) | 4.20820 | − | 12.9515i | 0.264046 | − | 0.812651i | ||||
\(255\) | −2.23607 | + | 1.62460i | −0.140028 | + | 0.101736i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −22.0000 | −1.37232 | −0.686161 | − | 0.727450i | \(-0.740706\pi\) | ||||
−0.686161 | + | 0.727450i | \(0.740706\pi\) | |||||||
\(258\) | 2.38197 | + | 7.33094i | 0.148295 | + | 0.456404i | ||||
\(259\) | −16.9443 | − | 12.3107i | −1.05287 | − | 0.764952i | ||||
\(260\) | 4.47214 | − | 13.7638i | 0.277350 | − | 0.853596i | ||||
\(261\) | −6.85410 | + | 4.97980i | −0.424258 | + | 0.308242i | ||||
\(262\) | 14.4721 | + | 10.5146i | 0.894092 | + | 0.649596i | ||||
\(263\) | 9.47214 | + | 6.88191i | 0.584077 | + | 0.424357i | 0.840192 | − | 0.542290i | \(-0.182442\pi\) |
−0.256115 | + | 0.966646i | \(0.582442\pi\) | |||||||
\(264\) | 2.92705 | − | 2.12663i | 0.180148 | − | 0.130885i | ||||
\(265\) | 1.44427 | + | 4.44501i | 0.0887209 | + | 0.273055i | ||||
\(266\) | 12.0902 | + | 8.78402i | 0.741296 | + | 0.538583i | ||||
\(267\) | −1.09017 | − | 3.35520i | −0.0667173 | − | 0.205335i | ||||
\(268\) | −1.52786 | −0.0933292 | ||||||||
\(269\) | −2.80902 | − | 8.64527i | −0.171269 | − | 0.527111i | 0.828175 | − | 0.560470i | \(-0.189380\pi\) |
−0.999443 | + | 0.0333590i | \(0.989380\pi\) | |||||||
\(270\) | 0.690983 | + | 2.12663i | 0.0420519 | + | 0.129422i | ||||
\(271\) | −5.57295 | + | 17.1518i | −0.338533 | + | 1.04190i | 0.626423 | + | 0.779483i | \(0.284518\pi\) |
−0.964956 | + | 0.262413i | \(0.915482\pi\) | |||||||
\(272\) | 0.381966 | − | 1.17557i | 0.0231601 | − | 0.0712794i | ||||
\(273\) | −13.7082 | + | 9.95959i | −0.829658 | + | 0.602782i | ||||
\(274\) | −12.1803 | −0.735841 | ||||||||
\(275\) | 5.59017 | + | 17.2048i | 0.337100 | + | 1.03749i | ||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | −13.7082 | + | 9.95959i | −0.823646 | + | 0.598414i | −0.917755 | − | 0.397148i | \(-0.870000\pi\) |
0.0941084 | + | 0.995562i | \(0.470000\pi\) | |||||||
\(278\) | 3.23607 | − | 9.95959i | 0.194086 | − | 0.597337i | ||||
\(279\) | 2.04508 | − | 6.29412i | 0.122436 | − | 0.376819i | ||||
\(280\) | 4.73607 | + | 3.44095i | 0.283034 | + | 0.205636i | ||||
\(281\) | 1.81966 | + | 5.60034i | 0.108552 | + | 0.334088i | 0.990548 | − | 0.137169i | \(-0.0438004\pi\) |
−0.881996 | + | 0.471257i | \(0.843800\pi\) | |||||||
\(282\) | −1.70820 | −0.101722 | ||||||||
\(283\) | 1.41641 | + | 4.35926i | 0.0841967 | + | 0.259131i | 0.984288 | − | 0.176571i | \(-0.0565004\pi\) |
−0.900091 | + | 0.435701i | \(0.856500\pi\) | |||||||
\(284\) | −4.47214 | − | 3.24920i | −0.265372 | − | 0.192804i | ||||
\(285\) | 10.3262 | − | 7.50245i | 0.611674 | − | 0.444407i | ||||
\(286\) | 18.9443 | − | 13.7638i | 1.12020 | − | 0.813872i | ||||
\(287\) | −12.0902 | − | 8.78402i | −0.713660 | − | 0.518504i | ||||
\(288\) | −0.809017 | − | 0.587785i | −0.0476718 | − | 0.0346356i | ||||
\(289\) | 12.5172 | − | 9.09429i | 0.736307 | − | 0.534958i | ||||
\(290\) | 15.3262 | + | 11.1352i | 0.899988 | + | 0.653879i | ||||
\(291\) | −2.73607 | − | 1.98787i | −0.160391 | − | 0.116531i | ||||
\(292\) | 1.09017 | + | 3.35520i | 0.0637974 | + | 0.196348i | ||||
\(293\) | −22.0902 | −1.29052 | −0.645261 | − | 0.763962i | \(-0.723251\pi\) | ||||
−0.645261 | + | 0.763962i | \(0.723251\pi\) | |||||||
\(294\) | 0.0450850 | + | 0.138757i | 0.00262941 | + | 0.00809249i | ||||
\(295\) | 8.09017 | 0.471028 | ||||||||
\(296\) | 2.47214 | − | 7.60845i | 0.143690 | − | 0.442232i | ||||
\(297\) | −1.11803 | + | 3.44095i | −0.0648749 | + | 0.199664i | ||||
\(298\) | −17.8713 | + | 12.9843i | −1.03526 | + | 0.752159i | ||||
\(299\) | −28.9443 | −1.67389 | ||||||||
\(300\) | 4.04508 | − | 2.93893i | 0.233543 | − | 0.169679i | ||||
\(301\) | −20.1803 | −1.16318 | ||||||||
\(302\) | −14.8262 | + | 10.7719i | −0.853154 | + | 0.619853i | ||||
\(303\) | −1.35410 | + | 4.16750i | −0.0777911 | + | 0.239416i | ||||
\(304\) | −1.76393 | + | 5.42882i | −0.101168 | + | 0.311364i | ||||
\(305\) | −1.90983 | + | 5.87785i | −0.109357 | + | 0.336565i | ||||
\(306\) | 0.381966 | + | 1.17557i | 0.0218355 | + | 0.0672029i | ||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | 2.92705 | + | 9.00854i | 0.166784 | + | 0.513309i | ||||
\(309\) | 11.5902 | + | 8.42075i | 0.659342 | + | 0.479040i | ||||
\(310\) | −14.7984 | −0.840491 | ||||||||
\(311\) | 0.854102 | − | 0.620541i | 0.0484317 | − | 0.0351877i | −0.563306 | − | 0.826248i | \(-0.690471\pi\) |
0.611738 | + | 0.791061i | \(0.290471\pi\) | |||||||
\(312\) | −5.23607 | − | 3.80423i | −0.296434 | − | 0.215372i | ||||
\(313\) | 13.1631 | + | 9.56357i | 0.744023 | + | 0.540565i | 0.893969 | − | 0.448130i | \(-0.147910\pi\) |
−0.149945 | + | 0.988694i | \(0.547910\pi\) | |||||||
\(314\) | −7.00000 | + | 5.08580i | −0.395033 | + | 0.287008i | ||||
\(315\) | −5.85410 | −0.329841 | ||||||||
\(316\) | 4.54508 | + | 3.30220i | 0.255681 | + | 0.185763i | ||||
\(317\) | −6.35410 | − | 19.5559i | −0.356882 | − | 1.09837i | −0.954910 | − | 0.296895i | \(-0.904049\pi\) |
0.598028 | − | 0.801475i | \(-0.295951\pi\) | |||||||
\(318\) | 2.09017 | 0.117211 | ||||||||
\(319\) | 9.47214 | + | 29.1522i | 0.530338 | + | 1.63221i | ||||
\(320\) | −0.690983 | + | 2.12663i | −0.0386271 | + | 0.118882i | ||||
\(321\) | 3.59017 | − | 11.0494i | 0.200384 | − | 0.616718i | ||||
\(322\) | 3.61803 | − | 11.1352i | 0.201625 | − | 0.620538i | ||||
\(323\) | 5.70820 | − | 4.14725i | 0.317613 | − | 0.230759i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 26.1803 | − | 19.0211i | 1.45222 | − | 1.05510i | ||||
\(326\) | −0.472136 | −0.0261492 | ||||||||
\(327\) | 13.9443 | − | 10.1311i | 0.771120 | − | 0.560251i | ||||
\(328\) | 1.76393 | − | 5.42882i | 0.0973969 | − | 0.299757i | ||||
\(329\) | 1.38197 | − | 4.25325i | 0.0761903 | − | 0.234489i | ||||
\(330\) | 8.09017 | 0.445349 | ||||||||
\(331\) | −5.56231 | − | 17.1190i | −0.305732 | − | 0.940946i | −0.979403 | − | 0.201915i | \(-0.935284\pi\) |
0.673671 | − | 0.739031i | \(-0.264716\pi\) | |||||||
\(332\) | 2.14590 | 0.117771 | ||||||||
\(333\) | 2.47214 | + | 7.60845i | 0.135472 | + | 0.416941i | ||||
\(334\) | −9.47214 | − | 6.88191i | −0.518292 | − | 0.376561i | ||||
\(335\) | −2.76393 | − | 2.00811i | −0.151010 | − | 0.109715i | ||||
\(336\) | 2.11803 | − | 1.53884i | 0.115548 | − | 0.0839507i | ||||
\(337\) | −0.736068 | − | 0.534785i | −0.0400962 | − | 0.0291316i | 0.567557 | − | 0.823334i | \(-0.307889\pi\) |
−0.607653 | + | 0.794203i | \(0.707889\pi\) | |||||||
\(338\) | −23.3713 | − | 16.9803i | −1.27123 | − | 0.923604i | ||||
\(339\) | −15.5623 | + | 11.3067i | −0.845228 | + | 0.614094i | ||||
\(340\) | 2.23607 | − | 1.62460i | 0.121268 | − | 0.0881062i | ||||
\(341\) | −19.3713 | − | 14.0741i | −1.04902 | − | 0.762155i | ||||
\(342\) | −1.76393 | − | 5.42882i | −0.0953825 | − | 0.293557i | ||||
\(343\) | −18.7082 | −1.01015 | ||||||||
\(344\) | −2.38197 | − | 7.33094i | −0.128427 | − | 0.395258i | ||||
\(345\) | −8.09017 | − | 5.87785i | −0.435560 | − | 0.316453i | ||||
\(346\) | 1.57295 | − | 4.84104i | 0.0845623 | − | 0.260256i | ||||
\(347\) | 6.35410 | − | 19.5559i | 0.341106 | − | 1.04982i | −0.622529 | − | 0.782596i | \(-0.713895\pi\) |
0.963636 | − | 0.267220i | \(-0.0861051\pi\) | |||||||
\(348\) | 6.85410 | − | 4.97980i | 0.367418 | − | 0.266945i | ||||
\(349\) | −27.8885 | −1.49284 | −0.746420 | − | 0.665475i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665475i | \(0.768229\pi\) | |||||||
\(350\) | 4.04508 | + | 12.4495i | 0.216219 | + | 0.665453i | ||||
\(351\) | 6.47214 | 0.345457 | ||||||||
\(352\) | −2.92705 | + | 2.12663i | −0.156012 | + | 0.113350i | ||||
\(353\) | −4.09017 | + | 12.5882i | −0.217698 | + | 0.670005i | 0.781253 | + | 0.624214i | \(0.214581\pi\) |
−0.998951 | + | 0.0457907i | \(0.985419\pi\) | |||||||
\(354\) | 1.11803 | − | 3.44095i | 0.0594228 | − | 0.182885i | ||||
\(355\) | −3.81966 | − | 11.7557i | −0.202727 | − | 0.623928i | ||||
\(356\) | 1.09017 | + | 3.35520i | 0.0577789 | + | 0.177825i | ||||
\(357\) | −3.23607 | −0.171271 | ||||||||
\(358\) | 3.04508 | + | 9.37181i | 0.160938 | + | 0.495315i | ||||
\(359\) | −17.9443 | − | 13.0373i | −0.947062 | − | 0.688081i | 0.00304782 | − | 0.999995i | \(-0.499030\pi\) |
−0.950110 | + | 0.311914i | \(0.899030\pi\) | |||||||
\(360\) | −0.690983 | − | 2.12663i | −0.0364180 | − | 0.112083i | ||||
\(361\) | −10.9894 | + | 7.98424i | −0.578387 | + | 0.420223i | ||||
\(362\) | 5.38197 | + | 3.91023i | 0.282870 | + | 0.205517i | ||||
\(363\) | 1.69098 | + | 1.22857i | 0.0887536 | + | 0.0644833i | ||||
\(364\) | 13.7082 | − | 9.95959i | 0.718505 | − | 0.522025i | ||||
\(365\) | −2.43769 | + | 7.50245i | −0.127595 | + | 0.392696i | ||||
\(366\) | 2.23607 | + | 1.62460i | 0.116881 | + | 0.0849191i | ||||
\(367\) | −9.46149 | − | 29.1195i | −0.493886 | − | 1.52002i | −0.818686 | − | 0.574242i | \(-0.805297\pi\) |
0.324800 | − | 0.945783i | \(-0.394703\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | 1.76393 | + | 5.42882i | 0.0918266 | + | 0.282613i | ||||
\(370\) | 14.4721 | − | 10.5146i | 0.752371 | − | 0.546629i | ||||
\(371\) | −1.69098 | + | 5.20431i | −0.0877915 | + | 0.270194i | ||||
\(372\) | −2.04508 | + | 6.29412i | −0.106033 | + | 0.326335i | ||||
\(373\) | 9.32624 | − | 6.77591i | 0.482894 | − | 0.350843i | −0.319551 | − | 0.947569i | \(-0.603532\pi\) |
0.802445 | + | 0.596726i | \(0.203532\pi\) | |||||||
\(374\) | 4.47214 | 0.231249 | ||||||||
\(375\) | 11.1803 | 0.577350 | ||||||||
\(376\) | 1.70820 | 0.0880939 | ||||||||
\(377\) | 44.3607 | − | 32.2299i | 2.28469 | − | 1.65993i | ||||
\(378\) | −0.809017 | + | 2.48990i | −0.0416113 | + | 0.128067i | ||||
\(379\) | −6.23607 | + | 19.1926i | −0.320325 | + | 0.985860i | 0.653181 | + | 0.757201i | \(0.273434\pi\) |
−0.973507 | + | 0.228658i | \(0.926566\pi\) | |||||||
\(380\) | −10.3262 | + | 7.50245i | −0.529725 | + | 0.384868i | ||||
\(381\) | −4.20820 | − | 12.9515i | −0.215593 | − | 0.663526i | ||||
\(382\) | 4.29180 | 0.219587 | ||||||||
\(383\) | −6.18034 | − | 19.0211i | −0.315801 | − | 0.971934i | −0.975424 | − | 0.220338i | \(-0.929284\pi\) |
0.659623 | − | 0.751597i | \(-0.270716\pi\) | |||||||
\(384\) | 0.809017 | + | 0.587785i | 0.0412850 | + | 0.0299953i | ||||
\(385\) | −6.54508 | + | 20.1437i | −0.333568 | + | 1.02662i | ||||
\(386\) | −14.4443 | + | 10.4944i | −0.735194 | + | 0.534150i | ||||
\(387\) | 6.23607 | + | 4.53077i | 0.316997 | + | 0.230312i | ||||
\(388\) | 2.73607 | + | 1.98787i | 0.138903 | + | 0.100919i | ||||
\(389\) | 10.0172 | − | 7.27794i | 0.507893 | − | 0.369006i | −0.304131 | − | 0.952630i | \(-0.598366\pi\) |
0.812024 | + | 0.583624i | \(0.198366\pi\) | |||||||
\(390\) | −4.47214 | − | 13.7638i | −0.226455 | − | 0.696958i | ||||
\(391\) | −4.47214 | − | 3.24920i | −0.226166 | − | 0.164319i | ||||
\(392\) | −0.0450850 | − | 0.138757i | −0.00227713 | − | 0.00700830i | ||||
\(393\) | 17.8885 | 0.902358 | ||||||||
\(394\) | −5.28115 | − | 16.2537i | −0.266061 | − | 0.818850i | ||||
\(395\) | 3.88197 | + | 11.9475i | 0.195323 | + | 0.601142i | ||||
\(396\) | 1.11803 | − | 3.44095i | 0.0561833 | − | 0.172914i | ||||
\(397\) | −9.50658 | + | 29.2582i | −0.477121 | + | 1.46843i | 0.365954 | + | 0.930633i | \(0.380743\pi\) |
−0.843075 | + | 0.537796i | \(0.819257\pi\) | |||||||
\(398\) | −15.7812 | + | 11.4657i | −0.791038 | + | 0.574723i | ||||
\(399\) | 14.9443 | 0.748149 | ||||||||
\(400\) | −4.04508 | + | 2.93893i | −0.202254 | + | 0.146946i | ||||
\(401\) | 25.7082 | 1.28381 | 0.641903 | − | 0.766786i | \(-0.278145\pi\) | ||||
0.641903 | + | 0.766786i | \(0.278145\pi\) | |||||||
\(402\) | −1.23607 | + | 0.898056i | −0.0616495 | + | 0.0447910i | ||||
\(403\) | −13.2361 | + | 40.7364i | −0.659336 | + | 2.02923i | ||||
\(404\) | 1.35410 | − | 4.16750i | 0.0673691 | − | 0.207341i | ||||
\(405\) | 1.80902 | + | 1.31433i | 0.0898908 | + | 0.0653095i | ||||
\(406\) | 6.85410 | + | 21.0948i | 0.340163 | + | 1.04692i | ||||
\(407\) | 28.9443 | 1.43471 | ||||||||
\(408\) | −0.381966 | − | 1.17557i | −0.0189101 | − | 0.0581994i | ||||
\(409\) | −4.69098 | − | 3.40820i | −0.231954 | − | 0.168525i | 0.465737 | − | 0.884923i | \(-0.345789\pi\) |
−0.697691 | + | 0.716399i | \(0.745789\pi\) | |||||||
\(410\) | 10.3262 | − | 7.50245i | 0.509977 | − | 0.370520i | ||||
\(411\) | −9.85410 | + | 7.15942i | −0.486067 | + | 0.353148i | ||||
\(412\) | −11.5902 | − | 8.42075i | −0.571007 | − | 0.414861i | ||||
\(413\) | 7.66312 | + | 5.56758i | 0.377077 | + | 0.273963i | ||||
\(414\) | −3.61803 | + | 2.62866i | −0.177817 | + | 0.129191i | ||||
\(415\) | 3.88197 | + | 2.82041i | 0.190558 | + | 0.138449i | ||||
\(416\) | 5.23607 | + | 3.80423i | 0.256719 | + | 0.186518i | ||||
\(417\) | −3.23607 | − | 9.95959i | −0.158471 | − | 0.487723i | ||||
\(418\) | −20.6525 | −1.01015 | ||||||||
\(419\) | −0.954915 | − | 2.93893i | −0.0466507 | − | 0.143576i | 0.925018 | − | 0.379923i | \(-0.124050\pi\) |
−0.971669 | + | 0.236347i | \(0.924050\pi\) | |||||||
\(420\) | 5.85410 | 0.285651 | ||||||||
\(421\) | −7.03444 | + | 21.6498i | −0.342838 | + | 1.05515i | 0.619893 | + | 0.784686i | \(0.287176\pi\) |
−0.962731 | + | 0.270460i | \(0.912824\pi\) | |||||||
\(422\) | −1.05573 | + | 3.24920i | −0.0513920 | + | 0.158168i | ||||
\(423\) | −1.38197 | + | 1.00406i | −0.0671935 | + | 0.0488189i | ||||
\(424\) | −2.09017 | −0.101508 | ||||||||
\(425\) | 6.18034 | 0.299791 | ||||||||
\(426\) | −5.52786 | −0.267826 | ||||||||
\(427\) | −5.85410 | + | 4.25325i | −0.283300 | + | 0.205829i | ||||
\(428\) | −3.59017 | + | 11.0494i | −0.173537 | + | 0.534093i | ||||
\(429\) | 7.23607 | − | 22.2703i | 0.349361 | − | 1.07522i | ||||
\(430\) | 5.32624 | − | 16.3925i | 0.256854 | − | 0.790515i | ||||
\(431\) | 5.20163 | + | 16.0090i | 0.250554 | + | 0.771124i | 0.994673 | + | 0.103078i | \(0.0328692\pi\) |
−0.744120 | + | 0.668046i | \(0.767131\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.79180 | + | 14.7476i | 0.230279 | + | 0.708726i | 0.997713 | + | 0.0675976i | \(0.0215334\pi\) |
−0.767434 | + | 0.641128i | \(0.778467\pi\) | |||||||
\(434\) | −14.0172 | − | 10.1841i | −0.672848 | − | 0.488853i | ||||
\(435\) | 18.9443 | 0.908308 | ||||||||
\(436\) | −13.9443 | + | 10.1311i | −0.667810 | + | 0.485192i | ||||
\(437\) | 20.6525 | + | 15.0049i | 0.987942 | + | 0.717782i | ||||
\(438\) | 2.85410 | + | 2.07363i | 0.136374 | + | 0.0990817i | ||||
\(439\) | 19.0172 | − | 13.8168i | 0.907642 | − | 0.659441i | −0.0327751 | − | 0.999463i | \(-0.510434\pi\) |
0.940418 | + | 0.340022i | \(0.110434\pi\) | |||||||
\(440\) | −8.09017 | −0.385684 | ||||||||
\(441\) | 0.118034 | + | 0.0857567i | 0.00562067 | + | 0.00408365i | ||||
\(442\) | −2.47214 | − | 7.60845i | −0.117588 | − | 0.361897i | ||||
\(443\) | 16.6180 | 0.789547 | 0.394773 | − | 0.918779i | \(-0.370823\pi\) | ||||
0.394773 | + | 0.918779i | \(0.370823\pi\) | |||||||
\(444\) | −2.47214 | − | 7.60845i | −0.117322 | − | 0.361081i | ||||
\(445\) | −2.43769 | + | 7.50245i | −0.115558 | + | 0.355650i | ||||
\(446\) | −2.50000 | + | 7.69421i | −0.118378 | + | 0.364331i | ||||
\(447\) | −6.82624 | + | 21.0090i | −0.322870 | + | 0.993692i | ||||
\(448\) | −2.11803 | + | 1.53884i | −0.100068 | + | 0.0727034i | ||||
\(449\) | −27.7082 | −1.30763 | −0.653815 | − | 0.756654i | \(-0.726833\pi\) | ||||
−0.653815 | + | 0.756654i | \(0.726833\pi\) | |||||||
\(450\) | 1.54508 | − | 4.75528i | 0.0728360 | − | 0.224166i | ||||
\(451\) | 20.6525 | 0.972487 | ||||||||
\(452\) | 15.5623 | − | 11.3067i | 0.731989 | − | 0.531821i | ||||
\(453\) | −5.66312 | + | 17.4293i | −0.266077 | + | 0.818899i | ||||
\(454\) | −6.88197 | + | 21.1805i | −0.322987 | + | 0.994051i | ||||
\(455\) | 37.8885 | 1.77624 | ||||||||
\(456\) | 1.76393 | + | 5.42882i | 0.0826037 | + | 0.254228i | ||||
\(457\) | −4.09017 | −0.191330 | −0.0956650 | − | 0.995414i | \(-0.530498\pi\) | ||||
−0.0956650 | + | 0.995414i | \(0.530498\pi\) | |||||||
\(458\) | −1.70820 | − | 5.25731i | −0.0798191 | − | 0.245658i | ||||
\(459\) | 1.00000 | + | 0.726543i | 0.0466760 | + | 0.0339121i | ||||
\(460\) | 8.09017 | + | 5.87785i | 0.377206 | + | 0.274056i | ||||
\(461\) | −6.11803 | + | 4.44501i | −0.284945 | + | 0.207025i | −0.721072 | − | 0.692861i | \(-0.756350\pi\) |
0.436126 | + | 0.899885i | \(0.356350\pi\) | |||||||
\(462\) | 7.66312 | + | 5.56758i | 0.356521 | + | 0.259027i | ||||
\(463\) | 18.4721 | + | 13.4208i | 0.858473 | + | 0.623717i | 0.927469 | − | 0.373900i | \(-0.121980\pi\) |
−0.0689961 | + | 0.997617i | \(0.521980\pi\) | |||||||
\(464\) | −6.85410 | + | 4.97980i | −0.318194 | + | 0.231181i | ||||
\(465\) | −11.9721 | + | 8.69827i | −0.555195 | + | 0.403372i | ||||
\(466\) | −15.0902 | − | 10.9637i | −0.699039 | − | 0.507881i | ||||
\(467\) | 3.29837 | + | 10.1514i | 0.152631 | + | 0.469749i | 0.997913 | − | 0.0645710i | \(-0.0205679\pi\) |
−0.845283 | + | 0.534320i | \(0.820568\pi\) | |||||||
\(468\) | −6.47214 | −0.299175 | ||||||||
\(469\) | −1.23607 | − | 3.80423i | −0.0570763 | − | 0.175663i | ||||
\(470\) | 3.09017 | + | 2.24514i | 0.142539 | + | 0.103561i | ||||
\(471\) | −2.67376 | + | 8.22899i | −0.123200 | + | 0.379172i | ||||
\(472\) | −1.11803 | + | 3.44095i | −0.0514617 | + | 0.158383i | ||||
\(473\) | 22.5623 | − | 16.3925i | 1.03742 | − | 0.753727i | ||||
\(474\) | 5.61803 | 0.258045 | ||||||||
\(475\) | −28.5410 | −1.30955 | ||||||||
\(476\) | 3.23607 | 0.148325 | ||||||||
\(477\) | 1.69098 | − | 1.22857i | 0.0774248 | − | 0.0562524i | ||||
\(478\) | 3.79837 | − | 11.6902i | 0.173734 | − | 0.534697i | ||||
\(479\) | −9.00000 | + | 27.6992i | −0.411220 | + | 1.26561i | 0.504368 | + | 0.863489i | \(0.331726\pi\) |
−0.915588 | + | 0.402117i | \(0.868274\pi\) | |||||||
\(480\) | 0.690983 | + | 2.12663i | 0.0315389 | + | 0.0970668i | ||||
\(481\) | −16.0000 | − | 49.2429i | −0.729537 | − | 2.24528i | ||||
\(482\) | 9.56231 | 0.435551 | ||||||||
\(483\) | −3.61803 | − | 11.1352i | −0.164626 | − | 0.506667i | ||||
\(484\) | −1.69098 | − | 1.22857i | −0.0768629 | − | 0.0558441i | ||||
\(485\) | 2.33688 | + | 7.19218i | 0.106112 | + | 0.326580i | ||||
\(486\) | 0.809017 | − | 0.587785i | 0.0366978 | − | 0.0266625i | ||||
\(487\) | −14.3992 | − | 10.4616i | −0.652489 | − | 0.474061i | 0.211629 | − | 0.977350i | \(-0.432123\pi\) |
−0.864118 | + | 0.503289i | \(0.832123\pi\) | |||||||
\(488\) | −2.23607 | − | 1.62460i | −0.101222 | − | 0.0735421i | ||||
\(489\) | −0.381966 | + | 0.277515i | −0.0172731 | + | 0.0125496i | ||||
\(490\) | 0.100813 | − | 0.310271i | 0.00455427 | − | 0.0140166i | ||||
\(491\) | 20.4443 | + | 14.8536i | 0.922637 | + | 0.670335i | 0.944179 | − | 0.329433i | \(-0.106858\pi\) |
−0.0215419 | + | 0.999768i | \(0.506858\pi\) | |||||||
\(492\) | −1.76393 | − | 5.42882i | −0.0795242 | − | 0.244750i | ||||
\(493\) | 10.4721 | 0.471641 | ||||||||
\(494\) | 11.4164 | + | 35.1361i | 0.513648 | + | 1.58085i | ||||
\(495\) | 6.54508 | − | 4.75528i | 0.294180 | − | 0.213734i | ||||
\(496\) | 2.04508 | − | 6.29412i | 0.0918270 | − | 0.282615i | ||||
\(497\) | 4.47214 | − | 13.7638i | 0.200603 | − | 0.617392i | ||||
\(498\) | 1.73607 | − | 1.26133i | 0.0777951 | − | 0.0565214i | ||||
\(499\) | 35.5967 | 1.59353 | 0.796765 | − | 0.604290i | \(-0.206543\pi\) | ||||
0.796765 | + | 0.604290i | \(0.206543\pi\) | |||||||
\(500\) | −11.1803 | −0.500000 | ||||||||
\(501\) | −11.7082 | −0.523084 | ||||||||
\(502\) | −10.9721 | + | 7.97172i | −0.489710 | + | 0.355795i | ||||
\(503\) | 7.38197 | − | 22.7194i | 0.329146 | − | 1.01301i | −0.640389 | − | 0.768051i | \(-0.721227\pi\) |
0.969534 | − | 0.244955i | \(-0.0787732\pi\) | |||||||
\(504\) | 0.809017 | − | 2.48990i | 0.0360365 | − | 0.110909i | ||||
\(505\) | 7.92705 | − | 5.75934i | 0.352749 | − | 0.256287i | ||||
\(506\) | 5.00000 | + | 15.3884i | 0.222277 | + | 0.684099i | ||||
\(507\) | −28.8885 | −1.28299 | ||||||||
\(508\) | 4.20820 | + | 12.9515i | 0.186709 | + | 0.574631i | ||||
\(509\) | 14.1631 | + | 10.2901i | 0.627769 | + | 0.456101i | 0.855627 | − | 0.517593i | \(-0.173172\pi\) |
−0.227857 | + | 0.973694i | \(0.573172\pi\) | |||||||
\(510\) | 0.854102 | − | 2.62866i | 0.0378203 | − | 0.116399i | ||||
\(511\) | −7.47214 | + | 5.42882i | −0.330548 | + | 0.240157i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −4.61803 | − | 3.35520i | −0.203891 | − | 0.148136i | ||||
\(514\) | 17.7984 | − | 12.9313i | 0.785053 | − | 0.570374i | ||||
\(515\) | −9.89919 | − | 30.4666i | −0.436210 | − | 1.34252i | ||||
\(516\) | −6.23607 | − | 4.53077i | −0.274528 | − | 0.199456i | ||||
\(517\) | 1.90983 | + | 5.87785i | 0.0839942 | + | 0.258508i | ||||
\(518\) | 20.9443 | 0.920238 | ||||||||
\(519\) | −1.57295 | − | 4.84104i | −0.0690448 | − | 0.212498i | ||||
\(520\) | 4.47214 | + | 13.7638i | 0.196116 | + | 0.603583i | ||||
\(521\) | 4.38197 | − | 13.4863i | 0.191977 | − | 0.590846i | −0.808021 | − | 0.589153i | \(-0.799461\pi\) |
0.999999 | − | 0.00169226i | \(-0.000538663\pi\) | |||||||
\(522\) | 2.61803 | − | 8.05748i | 0.114588 | − | 0.352666i | ||||
\(523\) | −8.94427 | + | 6.49839i | −0.391106 | + | 0.284155i | −0.765908 | − | 0.642950i | \(-0.777710\pi\) |
0.374803 | + | 0.927105i | \(0.377710\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | 10.5902 | + | 7.69421i | 0.462193 | + | 0.335803i | ||||
\(526\) | −11.7082 | −0.510502 | ||||||||
\(527\) | −6.61803 | + | 4.80828i | −0.288286 | + | 0.209452i | ||||
\(528\) | −1.11803 | + | 3.44095i | −0.0486562 | + | 0.149748i | ||||
\(529\) | −0.927051 | + | 2.85317i | −0.0403066 | + | 0.124051i | ||||
\(530\) | −3.78115 | − | 2.74717i | −0.164243 | − | 0.119329i | ||||
\(531\) | −1.11803 | − | 3.44095i | −0.0485185 | − | 0.149325i | ||||
\(532\) | −14.9443 | −0.647916 | ||||||||
\(533\) | −11.4164 | − | 35.1361i | −0.494500 | − | 1.52191i | ||||
\(534\) | 2.85410 | + | 2.07363i | 0.123509 | + | 0.0897346i | ||||
\(535\) | −21.0172 | + | 15.2699i | −0.908654 | + | 0.660176i | ||||
\(536\) | 1.23607 | − | 0.898056i | 0.0533900 | − | 0.0387901i | ||||
\(537\) | 7.97214 | + | 5.79210i | 0.344023 | + | 0.249947i | ||||
\(538\) | 7.35410 | + | 5.34307i | 0.317058 | + | 0.230356i | ||||
\(539\) | 0.427051 | − | 0.310271i | 0.0183944 | − | 0.0133643i | ||||
\(540\) | −1.80902 | − | 1.31433i | −0.0778477 | − | 0.0565597i | ||||
\(541\) | 21.1803 | + | 15.3884i | 0.910614 | + | 0.661600i | 0.941170 | − | 0.337933i | \(-0.109728\pi\) |
−0.0305561 | + | 0.999533i | \(0.509728\pi\) | |||||||
\(542\) | −5.57295 | − | 17.1518i | −0.239379 | − | 0.736732i | ||||
\(543\) | 6.65248 | 0.285485 | ||||||||
\(544\) | 0.381966 | + | 1.17557i | 0.0163767 | + | 0.0504022i | ||||
\(545\) | −38.5410 | −1.65092 | ||||||||
\(546\) | 5.23607 | − | 16.1150i | 0.224083 | − | 0.689657i | ||||
\(547\) | 3.00000 | − | 9.23305i | 0.128271 | − | 0.394777i | −0.866212 | − | 0.499677i | \(-0.833452\pi\) |
0.994483 | + | 0.104900i | \(0.0334522\pi\) | |||||||
\(548\) | 9.85410 | − | 7.15942i | 0.420946 | − | 0.305835i | ||||
\(549\) | 2.76393 | 0.117962 | ||||||||
\(550\) | −14.6353 | − | 10.6331i | −0.624049 | − | 0.453398i | ||||
\(551\) | −48.3607 | −2.06023 | ||||||||
\(552\) | 3.61803 | − | 2.62866i | 0.153994 | − | 0.111883i | ||||
\(553\) | −4.54508 | + | 13.9883i | −0.193277 | + | 0.594844i | ||||
\(554\) | 5.23607 | − | 16.1150i | 0.222459 | − | 0.684659i | ||||
\(555\) | 5.52786 | − | 17.0130i | 0.234645 | − | 0.722162i | ||||
\(556\) | 3.23607 | + | 9.95959i | 0.137240 | + | 0.422381i | ||||
\(557\) | −18.3262 | −0.776508 | −0.388254 | − | 0.921552i | \(-0.626922\pi\) | ||||
−0.388254 | + | 0.921552i | \(0.626922\pi\) | |||||||
\(558\) | 2.04508 | + | 6.29412i | 0.0865754 | + | 0.266452i | ||||
\(559\) | −40.3607 | − | 29.3238i | −1.70707 | − | 1.24026i | ||||
\(560\) | −5.85410 | −0.247381 | ||||||||
\(561\) | 3.61803 | − | 2.62866i | 0.152754 | − | 0.110982i | ||||
\(562\) | −4.76393 | − | 3.46120i | −0.200954 | − | 0.146002i | ||||
\(563\) | −17.2082 | − | 12.5025i | −0.725239 | − | 0.526917i | 0.162815 | − | 0.986657i | \(-0.447943\pi\) |
−0.888054 | + | 0.459739i | \(0.847943\pi\) | |||||||
\(564\) | 1.38197 | − | 1.00406i | 0.0581913 | − | 0.0422784i | ||||
\(565\) | 43.0132 | 1.80958 | ||||||||
\(566\) | −3.70820 | − | 2.69417i | −0.155867 | − | 0.113244i | ||||
\(567\) | 0.809017 | + | 2.48990i | 0.0339755 | + | 0.104566i | ||||
\(568\) | 5.52786 | 0.231944 | ||||||||
\(569\) | −8.58359 | − | 26.4176i | −0.359843 | − | 1.10748i | −0.953148 | − | 0.302505i | \(-0.902177\pi\) |
0.593305 | − | 0.804978i | \(-0.297823\pi\) | |||||||
\(570\) | −3.94427 | + | 12.1392i | −0.165207 | + | 0.508456i | ||||
\(571\) | 2.43769 | − | 7.50245i | 0.102014 | − | 0.313968i | −0.887004 | − | 0.461762i | \(-0.847217\pi\) |
0.989018 | + | 0.147794i | \(0.0472174\pi\) | |||||||
\(572\) | −7.23607 | + | 22.2703i | −0.302555 | + | 0.931169i | ||||
\(573\) | 3.47214 | − | 2.52265i | 0.145051 | − | 0.105385i | ||||
\(574\) | 14.9443 | 0.623762 | ||||||||
\(575\) | 6.90983 | + | 21.2663i | 0.288160 | + | 0.886865i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.26393 | + | 5.27756i | −0.302401 | + | 0.219708i | −0.728629 | − | 0.684908i | \(-0.759842\pi\) |
0.426228 | + | 0.904616i | \(0.359842\pi\) | |||||||
\(578\) | −4.78115 | + | 14.7149i | −0.198870 | + | 0.612058i | ||||
\(579\) | −5.51722 | + | 16.9803i | −0.229288 | + | 0.705676i | ||||
\(580\) | −18.9443 | −0.786618 | ||||||||
\(581\) | 1.73607 | + | 5.34307i | 0.0720242 | + | 0.221668i | ||||
\(582\) | 3.38197 | 0.140187 | ||||||||
\(583\) | −2.33688 | − | 7.19218i | −0.0967837 | − | 0.297870i | ||||
\(584\) | −2.85410 | − | 2.07363i | −0.118104 | − | 0.0858073i | ||||
\(585\) | −11.7082 | − | 8.50651i | −0.484075 | − | 0.351701i | ||||
\(586\) | 17.8713 | − | 12.9843i | 0.738258 | − | 0.536376i | ||||
\(587\) | 0.781153 | + | 0.567541i | 0.0322416 | + | 0.0234249i | 0.603789 | − | 0.797144i | \(-0.293657\pi\) |
−0.571548 | + | 0.820569i | \(0.693657\pi\) | |||||||
\(588\) | −0.118034 | − | 0.0857567i | −0.00486764 | − | 0.00353655i | ||||
\(589\) | 30.5623 | − | 22.2048i | 1.25930 | − | 0.914933i | ||||
\(590\) | −6.54508 | + | 4.75528i | −0.269457 | + | 0.195772i | ||||
\(591\) | −13.8262 | − | 10.0453i | −0.568735 | − | 0.413210i | ||||
\(592\) | 2.47214 | + | 7.60845i | 0.101604 | + | 0.312705i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −1.11803 | − | 3.44095i | −0.0458735 | − | 0.141184i | ||||
\(595\) | 5.85410 | + | 4.25325i | 0.239995 | + | 0.174366i | ||||
\(596\) | 6.82624 | − | 21.0090i | 0.279614 | − | 0.860562i | ||||
\(597\) | −6.02786 | + | 18.5519i | −0.246704 | + | 0.759277i | ||||
\(598\) | 23.4164 | − | 17.0130i | 0.957568 | − | 0.695714i | ||||
\(599\) | 0.472136 | 0.0192910 | 0.00964548 | − | 0.999953i | \(-0.496930\pi\) | ||||
0.00964548 | + | 0.999953i | \(0.496930\pi\) | |||||||
\(600\) | −1.54508 | + | 4.75528i | −0.0630778 | + | 0.194134i | ||||
\(601\) | −7.72949 | −0.315292 | −0.157646 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157646 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(602\) | 16.3262 | − | 11.8617i | 0.665408 | − | 0.483447i | ||||
\(603\) | −0.472136 | + | 1.45309i | −0.0192269 | + | 0.0591742i | ||||
\(604\) | 5.66312 | − | 17.4293i | 0.230429 | − | 0.709188i | ||||
\(605\) | −1.44427 | − | 4.44501i | −0.0587180 | − | 0.180715i | ||||
\(606\) | −1.35410 | − | 4.16750i | −0.0550066 | − | 0.169293i | ||||
\(607\) | 6.56231 | 0.266356 | 0.133178 | − | 0.991092i | \(-0.457482\pi\) | ||||
0.133178 | + | 0.991092i | \(0.457482\pi\) | |||||||
\(608\) | −1.76393 | − | 5.42882i | −0.0715369 | − | 0.220168i | ||||
\(609\) | 17.9443 | + | 13.0373i | 0.727139 | + | 0.528297i | ||||
\(610\) | −1.90983 | − | 5.87785i | −0.0773268 | − | 0.237987i | ||||
\(611\) | 8.94427 | − | 6.49839i | 0.361847 | − | 0.262897i | ||||
\(612\) | −1.00000 | − | 0.726543i | −0.0404226 | − | 0.0293687i | ||||
\(613\) | −39.0344 | − | 28.3602i | −1.57659 | − | 1.14546i | −0.920481 | − | 0.390788i | \(-0.872203\pi\) |
−0.656105 | − | 0.754669i | \(-0.727797\pi\) | |||||||
\(614\) | −8.09017 | + | 5.87785i | −0.326493 | + | 0.237211i | ||||
\(615\) | 3.94427 | − | 12.1392i | 0.159048 | − | 0.489501i | ||||
\(616\) | −7.66312 | − | 5.56758i | −0.308756 | − | 0.224324i | ||||
\(617\) | 0.652476 | + | 2.00811i | 0.0262677 | + | 0.0808436i | 0.963331 | − | 0.268316i | \(-0.0864671\pi\) |
−0.937063 | + | 0.349160i | \(0.886467\pi\) | |||||||
\(618\) | −14.3262 | −0.576286 | ||||||||
\(619\) | −2.90983 | − | 8.95554i | −0.116956 | − | 0.359953i | 0.875394 | − | 0.483410i | \(-0.160602\pi\) |
−0.992350 | + | 0.123457i | \(0.960602\pi\) | |||||||
\(620\) | 11.9721 | − | 8.69827i | 0.480813 | − | 0.349331i | ||||
\(621\) | −1.38197 | + | 4.25325i | −0.0554564 | + | 0.170677i | ||||
\(622\) | −0.326238 | + | 1.00406i | −0.0130809 | + | 0.0402590i | ||||
\(623\) | −7.47214 | + | 5.42882i | −0.299365 | + | 0.217501i | ||||
\(624\) | 6.47214 | 0.259093 | ||||||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | −16.2705 | −0.650300 | ||||||||
\(627\) | −16.7082 | + | 12.1392i | −0.667261 | + | 0.484794i | ||||
\(628\) | 2.67376 | − | 8.22899i | 0.106695 | − | 0.328373i | ||||
\(629\) | 3.05573 | − | 9.40456i | 0.121840 | − | 0.374985i | ||||
\(630\) | 4.73607 | − | 3.44095i | 0.188689 | − | 0.137091i | ||||
\(631\) | 14.3607 | + | 44.1976i | 0.571690 | + | 1.75948i | 0.647184 | + | 0.762334i | \(0.275946\pi\) |
−0.0754947 | + | 0.997146i | \(0.524054\pi\) | |||||||
\(632\) | −5.61803 | −0.223473 | ||||||||
\(633\) | 1.05573 | + | 3.24920i | 0.0419614 | + | 0.129144i | ||||
\(634\) | 16.6353 | + | 12.0862i | 0.660670 | + | 0.480005i | ||||
\(635\) | −9.40983 | + | 28.9605i | −0.373418 | + | 1.14926i | ||||
\(636\) | −1.69098 | + | 1.22857i | −0.0670518 | + | 0.0487160i | ||||
\(637\) | −0.763932 | − | 0.555029i | −0.0302681 | − | 0.0219911i | ||||
\(638\) | −24.7984 | − | 18.0171i | −0.981777 | − | 0.713303i | ||||
\(639\) | −4.47214 | + | 3.24920i | −0.176915 | + | 0.128536i | ||||
\(640\) | −0.690983 | − | 2.12663i | −0.0273135 | − | 0.0840623i | ||||
\(641\) | 11.1803 | + | 8.12299i | 0.441597 | + | 0.320839i | 0.786269 | − | 0.617884i | \(-0.212010\pi\) |
−0.344672 | + | 0.938723i | \(0.612010\pi\) | |||||||
\(642\) | 3.59017 | + | 11.0494i | 0.141693 | + | 0.436085i | ||||
\(643\) | 21.8885 | 0.863200 | 0.431600 | − | 0.902065i | \(-0.357949\pi\) | ||||
0.431600 | + | 0.902065i | \(0.357949\pi\) | |||||||
\(644\) | 3.61803 | + | 11.1352i | 0.142571 | + | 0.438787i | ||||
\(645\) | −5.32624 | − | 16.3925i | −0.209720 | − | 0.645453i | ||||
\(646\) | −2.18034 | + | 6.71040i | −0.0857843 | + | 0.264017i | ||||
\(647\) | −7.09017 | + | 21.8213i | −0.278743 | + | 0.857884i | 0.709461 | + | 0.704744i | \(0.248938\pi\) |
−0.988205 | + | 0.153139i | \(0.951062\pi\) | |||||||
\(648\) | −0.809017 | + | 0.587785i | −0.0317812 | + | 0.0230904i | ||||
\(649\) | −13.0902 | −0.513834 | ||||||||
\(650\) | −10.0000 | + | 30.7768i | −0.392232 | + | 1.20717i | ||||
\(651\) | −17.3262 | −0.679069 | ||||||||
\(652\) | 0.381966 | − | 0.277515i | 0.0149589 | − | 0.0108683i | ||||
\(653\) | −1.19098 | + | 3.66547i | −0.0466068 | + | 0.143441i | −0.971652 | − | 0.236417i | \(-0.924027\pi\) |
0.925045 | + | 0.379858i | \(0.124027\pi\) | |||||||
\(654\) | −5.32624 | + | 16.3925i | −0.208272 | + | 0.640996i | ||||
\(655\) | −32.3607 | − | 23.5114i | −1.26444 | − | 0.918667i | ||||
\(656\) | 1.76393 | + | 5.42882i | 0.0688700 | + | 0.211960i | ||||
\(657\) | 3.52786 | 0.137635 | ||||||||
\(658\) | 1.38197 | + | 4.25325i | 0.0538746 | + | 0.165809i | ||||
\(659\) | 16.6803 | + | 12.1190i | 0.649774 | + | 0.472088i | 0.863194 | − | 0.504872i | \(-0.168460\pi\) |
−0.213420 | + | 0.976960i | \(0.568460\pi\) | |||||||
\(660\) | −6.54508 | + | 4.75528i | −0.254767 | + | 0.185099i | ||||
\(661\) | 24.6525 | − | 17.9111i | 0.958870 | − | 0.696660i | 0.00598211 | − | 0.999982i | \(-0.498096\pi\) |
0.952888 | + | 0.303322i | \(0.0980958\pi\) | |||||||
\(662\) | 14.5623 | + | 10.5801i | 0.565980 | + | 0.411209i | ||||
\(663\) | −6.47214 | − | 4.70228i | −0.251357 | − | 0.182622i | ||||
\(664\) | −1.73607 | + | 1.26133i | −0.0673725 | + | 0.0489490i | ||||
\(665\) | −27.0344 | − | 19.6417i | −1.04835 | − | 0.761671i | ||||
\(666\) | −6.47214 | − | 4.70228i | −0.250790 | − | 0.182210i | ||||
\(667\) | 11.7082 | + | 36.0341i | 0.453343 | + | 1.39525i | ||||
\(668\) | 11.7082 | 0.453004 | ||||||||
\(669\) | 2.50000 | + | 7.69421i | 0.0966556 | + | 0.297475i | ||||
\(670\) | 3.41641 | 0.131987 | ||||||||
\(671\) | 3.09017 | − | 9.51057i | 0.119295 | − | 0.367151i | ||||
\(672\) | −0.809017 | + | 2.48990i | −0.0312085 | + | 0.0960499i | ||||
\(673\) | 25.4443 | − | 18.4863i | 0.980805 | − | 0.712596i | 0.0229163 | − | 0.999737i | \(-0.492705\pi\) |
0.957888 | + | 0.287141i | \(0.0927049\pi\) | |||||||
\(674\) | 0.909830 | 0.0350453 | ||||||||
\(675\) | −1.54508 | − | 4.75528i | −0.0594703 | − | 0.183031i | ||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | −23.5344 | + | 17.0988i | −0.904502 | + | 0.657159i | −0.939618 | − | 0.342224i | \(-0.888820\pi\) |
0.0351163 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(678\) | 5.94427 | − | 18.2946i | 0.228288 | − | 0.702599i | ||||
\(679\) | −2.73607 | + | 8.42075i | −0.105001 | + | 0.323159i | ||||
\(680\) | −0.854102 | + | 2.62866i | −0.0327533 | + | 0.100804i | ||||
\(681\) | 6.88197 | + | 21.1805i | 0.263718 | + | 0.811639i | ||||
\(682\) | 23.9443 | 0.916874 | ||||||||
\(683\) | 10.3541 | + | 31.8666i | 0.396189 | + | 1.21934i | 0.928032 | + | 0.372501i | \(0.121500\pi\) |
−0.531843 | + | 0.846843i | \(0.678500\pi\) | |||||||
\(684\) | 4.61803 | + | 3.35520i | 0.176575 | + | 0.128289i | ||||
\(685\) | 27.2361 | 1.04064 | ||||||||
\(686\) | 15.1353 | − | 10.9964i | 0.577867 | − | 0.419845i | ||||
\(687\) | −4.47214 | − | 3.24920i | −0.170623 | − | 0.123965i | ||||
\(688\) | 6.23607 | + | 4.53077i | 0.237748 | + | 0.172734i | ||||
\(689\) | −10.9443 | + | 7.95148i | −0.416944 | + | 0.302927i | ||||
\(690\) | 10.0000 | 0.380693 | ||||||||
\(691\) | −9.09017 | − | 6.60440i | −0.345806 | − | 0.251243i | 0.401301 | − | 0.915946i | \(-0.368558\pi\) |
−0.747108 | + | 0.664703i | \(0.768558\pi\) | |||||||
\(692\) | 1.57295 | + | 4.84104i | 0.0597945 | + | 0.184029i | ||||
\(693\) | 9.47214 | 0.359817 | ||||||||
\(694\) | 6.35410 | + | 19.5559i | 0.241198 | + | 0.742332i | ||||
\(695\) | −7.23607 | + | 22.2703i | −0.274480 | + | 0.844762i | ||||
\(696\) | −2.61803 | + | 8.05748i | −0.0992363 | + | 0.305418i | ||||
\(697\) | 2.18034 | − | 6.71040i | 0.0825863 | − | 0.254174i | ||||
\(698\) | 22.5623 | − | 16.3925i | 0.853996 | − | 0.620464i | ||||
\(699\) | −18.6525 | −0.705501 | ||||||||
\(700\) | −10.5902 | − | 7.69421i | −0.400271 | − | 0.290814i | ||||
\(701\) | 40.8328 | 1.54223 | 0.771117 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771117 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(702\) | −5.23607 | + | 3.80423i | −0.197623 | + | 0.143581i | ||||
\(703\) | −14.1115 | + | 43.4306i | −0.532224 | + | 1.63802i | ||||
\(704\) | 1.11803 | − | 3.44095i | 0.0421375 | − | 0.129686i | ||||
\(705\) | 3.81966 | 0.143857 | ||||||||
\(706\) | −4.09017 | − | 12.5882i | −0.153936 | − | 0.473765i | ||||
\(707\) | 11.4721 | 0.431454 | ||||||||
\(708\) | 1.11803 | + | 3.44095i | 0.0420183 | + | 0.129319i | ||||
\(709\) | 35.3607 | + | 25.6910i | 1.32800 | + | 0.964847i | 0.999795 | + | 0.0202400i | \(0.00644302\pi\) |
0.328203 | + | 0.944607i | \(0.393557\pi\) | |||||||
\(710\) | 10.0000 | + | 7.26543i | 0.375293 | + | 0.272667i | ||||
\(711\) | 4.54508 | − | 3.30220i | 0.170454 | − | 0.123842i | ||||
\(712\) | −2.85410 | − | 2.07363i | −0.106962 | − | 0.0777124i | ||||
\(713\) | −23.9443 | − | 17.3965i | −0.896720 | − | 0.651505i | ||||
\(714\) | 2.61803 | − | 1.90211i | 0.0979775 | − | 0.0711848i | ||||
\(715\) | −42.3607 | + | 30.7768i | −1.58420 | + | 1.15099i | ||||
\(716\) | −7.97214 | − | 5.79210i | −0.297933 | − | 0.216461i | ||||
\(717\) | −3.79837 | − | 11.6902i | −0.141853 | − | 0.436578i | ||||
\(718\) | 22.1803 | 0.827763 | ||||||||
\(719\) | −5.12461 | − | 15.7719i | −0.191116 | − | 0.588194i | −1.00000 | 0.000225882i | \(-0.999928\pi\) | |
0.808884 | − | 0.587968i | \(-0.200072\pi\) | |||||||
\(720\) | 1.80902 | + | 1.31433i | 0.0674181 | + | 0.0489821i | ||||
\(721\) | 11.5902 | − | 35.6709i | 0.431640 | − | 1.32845i | ||||
\(722\) | 4.19756 | − | 12.9188i | 0.156217 | − | 0.480787i | ||||
\(723\) | 7.73607 | − | 5.62058i | 0.287707 | − | 0.209032i | ||||
\(724\) | −6.65248 | −0.247237 | ||||||||
\(725\) | −34.2705 | − | 24.8990i | −1.27277 | − | 0.924725i | ||||
\(726\) | −2.09017 | −0.0775735 | ||||||||
\(727\) | 6.94427 | − | 5.04531i | 0.257549 | − | 0.187120i | −0.451517 | − | 0.892263i | \(-0.649117\pi\) |
0.709066 | + | 0.705142i | \(0.249117\pi\) | |||||||
\(728\) | −5.23607 | + | 16.1150i | −0.194062 | + | 0.597260i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −2.43769 | − | 7.50245i | −0.0902231 | − | 0.277678i | ||||
\(731\) | −2.94427 | − | 9.06154i | −0.108898 | − | 0.335153i | ||||
\(732\) | −2.76393 | −0.102158 | ||||||||
\(733\) | −11.0902 | − | 34.1320i | −0.409625 | − | 1.26070i | −0.916971 | − | 0.398953i | \(-0.869374\pi\) |
0.507346 | − | 0.861742i | \(-0.330626\pi\) | |||||||
\(734\) | 24.7705 | + | 17.9968i | 0.914296 | + | 0.664275i | ||||
\(735\) | −0.100813 | − | 0.310271i | −0.00371855 | − | 0.0114445i | ||||
\(736\) | −3.61803 | + | 2.62866i | −0.133363 | + | 0.0968935i | ||||
\(737\) | 4.47214 | + | 3.24920i | 0.164733 | + | 0.119686i | ||||
\(738\) | −4.61803 | − | 3.35520i | −0.169992 | − | 0.123507i | ||||
\(739\) | 38.9787 | − | 28.3197i | 1.43386 | − | 1.04176i | 0.444573 | − | 0.895743i | \(-0.353356\pi\) |
0.989283 | − | 0.146014i | \(-0.0466444\pi\) | |||||||
\(740\) | −5.52786 | + | 17.0130i | −0.203208 | + | 0.625411i | ||||
\(741\) | 29.8885 | + | 21.7153i | 1.09798 | + | 0.797731i | ||||
\(742\) | −1.69098 | − | 5.20431i | −0.0620779 | − | 0.191056i | ||||
\(743\) | −39.0132 | −1.43125 | −0.715627 | − | 0.698483i | \(-0.753859\pi\) | ||||
−0.715627 | + | 0.698483i | \(0.753859\pi\) | |||||||
\(744\) | −2.04508 | − | 6.29412i | −0.0749765 | − | 0.230754i | ||||
\(745\) | 39.9615 | − | 29.0337i | 1.46408 | − | 1.06371i | ||||
\(746\) | −3.56231 | + | 10.9637i | −0.130425 | + | 0.401408i | ||||
\(747\) | 0.663119 | − | 2.04087i | 0.0242623 | − | 0.0746715i | ||||
\(748\) | −3.61803 | + | 2.62866i | −0.132288 | + | 0.0961132i | ||||
\(749\) | −30.4164 | −1.11139 | ||||||||
\(750\) | −9.04508 | + | 6.57164i | −0.330280 | + | 0.239962i | ||||
\(751\) | 24.7984 | 0.904906 | 0.452453 | − | 0.891788i | \(-0.350549\pi\) | ||||
0.452453 | + | 0.891788i | \(0.350549\pi\) | |||||||
\(752\) | −1.38197 | + | 1.00406i | −0.0503951 | + | 0.0366142i | ||||
\(753\) | −4.19098 | + | 12.8985i | −0.152728 | + | 0.470048i | ||||
\(754\) | −16.9443 | + | 52.1491i | −0.617074 | + | 1.89916i | ||||
\(755\) | 33.1525 | − | 24.0867i | 1.20654 | − | 0.876604i | ||||
\(756\) | −0.809017 | − | 2.48990i | −0.0294237 | − | 0.0905567i | ||||
\(757\) | −17.1246 | −0.622405 | −0.311202 | − | 0.950344i | \(-0.600732\pi\) | ||||
−0.311202 | + | 0.950344i | \(0.600732\pi\) | |||||||
\(758\) | −6.23607 | − | 19.1926i | −0.226504 | − | 0.697108i | ||||
\(759\) | 13.0902 | + | 9.51057i | 0.475143 | + | 0.345212i | ||||
\(760\) | 3.94427 | − | 12.1392i | 0.143074 | − | 0.440336i | ||||
\(761\) | −1.14590 | + | 0.832544i | −0.0415388 | + | 0.0301797i | −0.608361 | − | 0.793661i | \(-0.708173\pi\) |
0.566822 | + | 0.823840i | \(0.308173\pi\) | |||||||
\(762\) | 11.0172 | + | 8.00448i | 0.399112 | + | 0.289972i | ||||
\(763\) | −36.5066 | − | 26.5236i | −1.32163 | − | 0.960218i | ||||
\(764\) | −3.47214 | + | 2.52265i | −0.125617 | + | 0.0912664i | ||||
\(765\) | −0.854102 | − | 2.62866i | −0.0308801 | − | 0.0950392i | ||||
\(766\) | 16.1803 | + | 11.7557i | 0.584619 | + | 0.424751i | ||||
\(767\) | 7.23607 | + | 22.2703i | 0.261279 | + | 0.804135i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 7.62868 | + | 23.4787i | 0.275097 | + | 0.846662i | 0.989194 | + | 0.146615i | \(0.0468377\pi\) |
−0.714097 | + | 0.700047i | \(0.753162\pi\) | |||||||
\(770\) | −6.54508 | − | 20.1437i | −0.235868 | − | 0.725929i | ||||
\(771\) | 6.79837 | − | 20.9232i | 0.244837 | − | 0.753532i | ||||
\(772\) | 5.51722 | − | 16.9803i | 0.198569 | − | 0.611133i | ||||
\(773\) | 0.927051 | − | 0.673542i | 0.0333437 | − | 0.0242256i | −0.570989 | − | 0.820958i | \(-0.693440\pi\) |
0.604332 | + | 0.796732i | \(0.293440\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 33.0902 | 1.18863 | ||||||||
\(776\) | −3.38197 | −0.121406 | ||||||||
\(777\) | 16.9443 | − | 12.3107i | 0.607872 | − | 0.441645i | ||||
\(778\) | −3.82624 | + | 11.7759i | −0.137177 | + | 0.422188i | ||||
\(779\) | −10.0689 | + | 30.9888i | −0.360755 | + | 1.11029i | ||||
\(780\) | 11.7082 | + | 8.50651i | 0.419221 | + | 0.304582i | ||||
\(781\) | 6.18034 | + | 19.0211i | 0.221150 | + | 0.680630i | ||||
\(782\) | 5.52786 | 0.197676 | ||||||||
\(783\) | −2.61803 | − | 8.05748i | −0.0935609 | − | 0.287951i | ||||
\(784\) | 0.118034 | + | 0.0857567i | 0.00421550 | + | 0.00306274i | ||||
\(785\) | 15.6525 | − | 11.3722i | 0.558661 | − | 0.405891i | ||||
\(786\) | −14.4721 | + | 10.5146i | −0.516204 | + | 0.375044i | ||||
\(787\) | −22.7082 | − | 16.4985i | −0.809460 | − | 0.588107i | 0.104214 | − | 0.994555i | \(-0.466767\pi\) |
−0.913674 | + | 0.406448i | \(0.866767\pi\) | |||||||
\(788\) | 13.8262 | + | 10.0453i | 0.492539 | + | 0.357851i | ||||
\(789\) | −9.47214 | + | 6.88191i | −0.337217 | + | 0.245002i | ||||
\(790\) | −10.1631 | − | 7.38394i | −0.361588 | − | 0.262709i | ||||
\(791\) | 40.7426 | + | 29.6013i | 1.44864 | + | 1.05250i | ||||
\(792\) | 1.11803 | + | 3.44095i | 0.0397276 | + | 0.122269i | ||||
\(793\) | −17.8885 | −0.635241 | ||||||||
\(794\) | −9.50658 | − | 29.2582i | −0.337376 | − | 1.03834i | ||||
\(795\) | −4.67376 | −0.165761 | ||||||||
\(796\) | 6.02786 | − | 18.5519i | 0.213652 | − | 0.657553i | ||||
\(797\) | 0.465558 | − | 1.43284i | 0.0164909 | − | 0.0507538i | −0.942472 | − | 0.334284i | \(-0.891506\pi\) |
0.958963 | + | 0.283530i | \(0.0915056\pi\) | |||||||
\(798\) | −12.0902 | + | 8.78402i | −0.427987 | + | 0.310951i | ||||
\(799\) | 2.11146 | 0.0746979 | ||||||||
\(800\) | 1.54508 | − | 4.75528i | 0.0546270 | − | 0.168125i | ||||
\(801\) | 3.52786 | 0.124651 | ||||||||
\(802\) | −20.7984 | + | 15.1109i | −0.734416 | + | 0.533585i | ||||
\(803\) | 3.94427 | − | 12.1392i | 0.139190 | − | 0.428384i | ||||
\(804\) | 0.472136 | − | 1.45309i | 0.0166510 | − | 0.0512464i | ||||
\(805\) | −8.09017 | + | 24.8990i | −0.285141 | + | 0.877574i | ||||
\(806\) | −13.2361 | − | 40.7364i | −0.466221 | − | 1.43488i | ||||
\(807\) | 9.09017 | 0.319989 | ||||||||
\(808\) | 1.35410 | + | 4.16750i | 0.0476371 | + | 0.146612i | ||||
\(809\) | 24.9443 | + | 18.1231i | 0.876994 | + | 0.637173i | 0.932454 | − | 0.361288i | \(-0.117663\pi\) |
−0.0554606 | + | 0.998461i | \(0.517663\pi\) | |||||||
\(810\) | −2.23607 | −0.0785674 | ||||||||
\(811\) | 4.61803 | − | 3.35520i | 0.162161 | − | 0.117817i | −0.503745 | − | 0.863852i | \(-0.668045\pi\) |
0.665906 | + | 0.746035i | \(0.268045\pi\) | |||||||
\(812\) | −17.9443 | − | 13.0373i | −0.629720 | − | 0.457519i | ||||
\(813\) | −14.5902 | − | 10.6004i | −0.511700 | − | 0.371772i | ||||
\(814\) | −23.4164 | + | 17.0130i | −0.820745 | + | 0.596306i | ||||
\(815\) | 1.05573 | 0.0369805 | ||||||||
\(816\) | 1.00000 | + | 0.726543i | 0.0350070 | + | 0.0254341i | ||||
\(817\) | 13.5967 | + | 41.8465i | 0.475690 | + | 1.46402i | ||||
\(818\) | 5.79837 | 0.202735 | ||||||||
\(819\) | −5.23607 | − | 16.1150i | −0.182963 | − | 0.563102i | ||||
\(820\) | −3.94427 | + | 12.1392i | −0.137740 | + | 0.423920i | ||||
\(821\) | −13.9336 | + | 42.8833i | −0.486287 | + | 1.49664i | 0.343821 | + | 0.939035i | \(0.388279\pi\) |
−0.830108 | + | 0.557602i | \(0.811721\pi\) | |||||||
\(822\) | 3.76393 | − | 11.5842i | 0.131282 | − | 0.404045i | ||||
\(823\) | −2.39919 | + | 1.74311i | −0.0836304 | + | 0.0607610i | −0.628815 | − | 0.777555i | \(-0.716460\pi\) |
0.545184 | + | 0.838316i | \(0.316460\pi\) | |||||||
\(824\) | 14.3262 | 0.499078 | ||||||||
\(825\) | −18.0902 | −0.629819 | ||||||||
\(826\) | −9.47214 | −0.329578 | ||||||||
\(827\) | −35.6803 | + | 25.9233i | −1.24073 | + | 0.901441i | −0.997647 | − | 0.0685652i | \(-0.978158\pi\) |
−0.243080 | + | 0.970006i | \(0.578158\pi\) | |||||||
\(828\) | 1.38197 | − | 4.25325i | 0.0480266 | − | 0.147811i | ||||
\(829\) | 8.00000 | − | 24.6215i | 0.277851 | − | 0.855139i | −0.710599 | − | 0.703597i | \(-0.751576\pi\) |
0.988451 | − | 0.151542i | \(-0.0484239\pi\) | |||||||
\(830\) | −4.79837 | −0.166554 | ||||||||
\(831\) | −5.23607 | − | 16.1150i | −0.181637 | − | 0.559022i | ||||
\(832\) | −6.47214 | −0.224381 | ||||||||
\(833\) | −0.0557281 | − | 0.171513i | −0.00193086 | − | 0.00594259i | ||||
\(834\) | 8.47214 | + | 6.15537i | 0.293366 | + | 0.213143i | ||||
\(835\) | 21.1803 | + | 15.3884i | 0.732976 | + | 0.532538i | ||||
\(836\) | 16.7082 | − | 12.1392i | 0.577865 | − | 0.419844i | ||||
\(837\) | 5.35410 | + | 3.88998i | 0.185065 | + | 0.134457i | ||||
\(838\) | 2.50000 | + | 1.81636i | 0.0863611 | + | 0.0627450i | ||||
\(839\) | −5.14590 | + | 3.73871i | −0.177656 | + | 0.129075i | −0.673060 | − | 0.739588i | \(-0.735020\pi\) |
0.495403 | + | 0.868663i | \(0.335020\pi\) | |||||||
\(840\) | −4.73607 | + | 3.44095i | −0.163410 | + | 0.118724i | ||||
\(841\) | −34.6074 | − | 25.1437i | −1.19336 | − | 0.867026i | ||||
\(842\) | −7.03444 | − | 21.6498i | −0.242423 | − | 0.746101i | ||||
\(843\) | −5.88854 | −0.202812 | ||||||||
\(844\) | −1.05573 | − | 3.24920i | −0.0363397 | − | 0.111842i | ||||
\(845\) | 52.2599 | + | 37.9690i | 1.79779 | + | 1.30617i | ||||
\(846\) | 0.527864 | − | 1.62460i | 0.0181483 | − | 0.0558548i | ||||
\(847\) | 1.69098 | − | 5.20431i | 0.0581029 | − | 0.178822i | ||||
\(848\) | 1.69098 | − | 1.22857i | 0.0580686 | − | 0.0421893i | ||||
\(849\) | −4.58359 | −0.157308 | ||||||||
\(850\) | −5.00000 | + | 3.63271i | −0.171499 | + | 0.124601i | ||||
\(851\) | 35.7771 | 1.22642 | ||||||||
\(852\) | 4.47214 | − | 3.24920i | 0.153213 | − | 0.111316i | ||||
\(853\) | −13.4721 | + | 41.4630i | −0.461277 | + | 1.41967i | 0.402328 | + | 0.915496i | \(0.368201\pi\) |
−0.863605 | + | 0.504169i | \(0.831799\pi\) | |||||||
\(854\) | 2.23607 | − | 6.88191i | 0.0765167 | − | 0.235494i | ||||
\(855\) | 3.94427 | + | 12.1392i | 0.134891 | + | 0.415153i | ||||
\(856\) | −3.59017 | − | 11.0494i | −0.122709 | − | 0.377661i | ||||
\(857\) | −16.0689 | −0.548903 | −0.274451 | − | 0.961601i | \(-0.588496\pi\) | ||||
−0.274451 | + | 0.961601i | \(0.588496\pi\) | |||||||
\(858\) | 7.23607 | + | 22.2703i | 0.247035 | + | 0.760296i | ||||
\(859\) | 1.85410 | + | 1.34708i | 0.0632611 | + | 0.0459619i | 0.618966 | − | 0.785417i | \(-0.287552\pi\) |
−0.555705 | + | 0.831379i | \(0.687552\pi\) | |||||||
\(860\) | 5.32624 | + | 16.3925i | 0.181623 | + | 0.558979i | ||||
\(861\) | 12.0902 | − | 8.78402i | 0.412032 | − | 0.299359i | ||||
\(862\) | −13.6180 | − | 9.89408i | −0.463832 | − | 0.336994i | ||||
\(863\) | 8.23607 | + | 5.98385i | 0.280359 | + | 0.203693i | 0.719074 | − | 0.694934i | \(-0.244566\pi\) |
−0.438715 | + | 0.898626i | \(0.644566\pi\) | |||||||
\(864\) | 0.809017 | − | 0.587785i | 0.0275233 | − | 0.0199969i | ||||
\(865\) | −3.51722 | + | 10.8249i | −0.119589 | + | 0.368057i | ||||
\(866\) | −12.5451 | − | 9.11454i | −0.426299 | − | 0.309725i | ||||
\(867\) | 4.78115 | + | 14.7149i | 0.162376 | + | 0.499743i | ||||
\(868\) | 17.3262 | 0.588091 | ||||||||
\(869\) | −6.28115 | − | 19.3314i | −0.213074 | − | 0.655773i | ||||
\(870\) | −15.3262 | + | 11.1352i | −0.519608 | + | 0.377517i | ||||
\(871\) | 3.05573 | − | 9.40456i | 0.103539 | − | 0.318661i | ||||
\(872\) | 5.32624 | − | 16.3925i | 0.180369 | − | 0.555119i | ||||
\(873\) | 2.73607 | − | 1.98787i | 0.0926019 | − | 0.0672792i | ||||
\(874\) | −25.5279 | −0.863493 | ||||||||
\(875\) | −9.04508 | − | 27.8379i | −0.305780 | − | 0.941093i | ||||
\(876\) | −3.52786 | −0.119195 | ||||||||
\(877\) | 30.0344 | − | 21.8213i | 1.01419 | − | 0.736853i | 0.0491070 | − | 0.998794i | \(-0.484362\pi\) |
0.965084 | + | 0.261941i | \(0.0843625\pi\) | |||||||
\(878\) | −7.26393 | + | 22.3561i | −0.245146 | + | 0.754481i | ||||
\(879\) | 6.82624 | − | 21.0090i | 0.230243 | − | 0.708616i | ||||
\(880\) | 6.54508 | − | 4.75528i | 0.220635 | − | 0.160301i | ||||
\(881\) | −7.29180 | − | 22.4418i | −0.245667 | − | 0.756085i | −0.995526 | − | 0.0944874i | \(-0.969879\pi\) |
0.749859 | − | 0.661597i | \(-0.230121\pi\) | |||||||
\(882\) | −0.145898 | −0.00491264 | ||||||||
\(883\) | −9.29180 | − | 28.5972i | −0.312694 | − | 0.962373i | −0.976693 | − | 0.214640i | \(-0.931142\pi\) |
0.663999 | − | 0.747733i | \(-0.268858\pi\) | |||||||
\(884\) | 6.47214 | + | 4.70228i | 0.217681 | + | 0.158155i | ||||
\(885\) | −2.50000 | + | 7.69421i | −0.0840366 | + | 0.258638i | ||||
\(886\) | −13.4443 | + | 9.76784i | −0.451669 | + | 0.328157i | ||||
\(887\) | −18.9443 | − | 13.7638i | −0.636086 | − | 0.462144i | 0.222417 | − | 0.974952i | \(-0.428605\pi\) |
−0.858503 | + | 0.512808i | \(0.828605\pi\) | |||||||
\(888\) | 6.47214 | + | 4.70228i | 0.217191 | + | 0.157798i | ||||
\(889\) | −28.8435 | + | 20.9560i | −0.967379 | + | 0.702842i | ||||
\(890\) | −2.43769 | − | 7.50245i | −0.0817117 | − | 0.251483i | ||||
\(891\) | −2.92705 | − | 2.12663i | −0.0980599 | − | 0.0712447i | ||||
\(892\) | −2.50000 | − | 7.69421i | −0.0837062 | − | 0.257621i | ||||
\(893\) | −9.75078 | −0.326297 | ||||||||
\(894\) | −6.82624 | − | 21.0090i | −0.228304 | − | 0.702646i | ||||
\(895\) | −6.80902 | − | 20.9560i | −0.227600 | − | 0.700482i | ||||
\(896\) | 0.809017 | − | 2.48990i | 0.0270274 | − | 0.0831817i | ||||
\(897\) | 8.94427 | − | 27.5276i | 0.298641 | − | 0.919121i | ||||
\(898\) | 22.4164 | − | 16.2865i | 0.748045 | − | 0.543487i | ||||
\(899\) | 56.0689 | 1.87000 | ||||||||
\(900\) | 1.54508 | + | 4.75528i | 0.0515028 | + | 0.158509i | ||||
\(901\) | −2.58359 | −0.0860719 | ||||||||
\(902\) | −16.7082 | + | 12.1392i | −0.556322 | + | 0.404192i | ||||
\(903\) | 6.23607 | − | 19.1926i | 0.207523 | − | 0.638691i | ||||
\(904\) | −5.94427 | + | 18.2946i | −0.197704 | + | 0.608469i | ||||
\(905\) | −12.0344 | − | 8.74353i | −0.400038 | − | 0.290645i | ||||
\(906\) | −5.66312 | − | 17.4293i | −0.188145 | − | 0.579049i | ||||
\(907\) | 30.4721 | 1.01181 | 0.505905 | − | 0.862589i | \(-0.331159\pi\) | ||||
0.505905 | + | 0.862589i | \(0.331159\pi\) | |||||||
\(908\) | −6.88197 | − | 21.1805i | −0.228386 | − | 0.702900i | ||||
\(909\) | −3.54508 | − | 2.57565i | −0.117583 | − | 0.0854291i | ||||
\(910\) | −30.6525 | + | 22.2703i | −1.01612 | + | 0.738254i | ||||
\(911\) | −14.7082 | + | 10.6861i | −0.487305 | + | 0.354047i | −0.804147 | − | 0.594431i | \(-0.797377\pi\) |
0.316842 | + | 0.948478i | \(0.397377\pi\) | |||||||
\(912\) | −4.61803 | − | 3.35520i | −0.152918 | − | 0.111102i | ||||
\(913\) | −6.28115 | − | 4.56352i | −0.207876 | − | 0.151031i | ||||
\(914\) | 3.30902 | − | 2.40414i | 0.109453 | − | 0.0795219i | ||||
\(915\) | −5.00000 | − | 3.63271i | −0.165295 | − | 0.120094i | ||||
\(916\) | 4.47214 | + | 3.24920i | 0.147764 | + | 0.107356i | ||||
\(917\) | −14.4721 | − | 44.5407i | −0.477912 | − | 1.47086i | ||||
\(918\) | −1.23607 | −0.0407963 | ||||||||
\(919\) | −12.5836 | − | 38.7283i | −0.415094 | − | 1.27753i | −0.912166 | − | 0.409820i | \(-0.865592\pi\) |
0.497072 | − | 0.867709i | \(-0.334408\pi\) | |||||||
\(920\) | −10.0000 | −0.329690 | ||||||||
\(921\) | −3.09017 | + | 9.51057i | −0.101825 | + | 0.313384i | ||||
\(922\) | 2.33688 | − | 7.19218i | 0.0769611 | − | 0.236862i | ||||
\(923\) | 28.9443 | − | 21.0292i | 0.952712 | − | 0.692186i | ||||
\(924\) | −9.47214 | −0.311610 | ||||||||
\(925\) | −32.3607 | + | 23.5114i | −1.06401 | + | 0.773050i | ||||
\(926\) | −22.8328 | −0.750333 | ||||||||
\(927\) | −11.5902 | + | 8.42075i | −0.380671 | + | 0.276574i | ||||
\(928\) | 2.61803 | − | 8.05748i | 0.0859412 | − | 0.264500i | ||||
\(929\) | −5.87539 | + | 18.0826i | −0.192765 | + | 0.593270i | 0.807230 | + | 0.590237i | \(0.200966\pi\) |
−0.999995 | + | 0.00303360i | \(0.999034\pi\) | |||||||
\(930\) | 4.57295 | − | 14.0741i | 0.149953 | − | 0.461508i | ||||
\(931\) | 0.257354 | + | 0.792055i | 0.00843444 | + | 0.0259585i | ||||
\(932\) | 18.6525 | 0.610982 | ||||||||
\(933\) | 0.326238 | + | 1.00406i | 0.0106806 | + | 0.0328714i | ||||
\(934\) | −8.63525 | − | 6.27388i | −0.282554 | − | 0.205288i | ||||
\(935\) | −10.0000 | −0.327035 | ||||||||
\(936\) | 5.23607 | − | 3.80423i | 0.171146 | − | 0.124345i | ||||
\(937\) | 7.02786 | + | 5.10604i | 0.229590 | + | 0.166807i | 0.696633 | − | 0.717428i | \(-0.254681\pi\) |
−0.467043 | + | 0.884235i | \(0.654681\pi\) | |||||||
\(938\) | 3.23607 | + | 2.35114i | 0.105661 | + | 0.0767675i | ||||
\(939\) | −13.1631 | + | 9.56357i | −0.429562 | + | 0.312095i | ||||
\(940\) | −3.81966 | −0.124584 | ||||||||
\(941\) | 3.59017 | + | 2.60841i | 0.117036 | + | 0.0850318i | 0.644764 | − | 0.764382i | \(-0.276956\pi\) |
−0.527728 | + | 0.849414i | \(0.676956\pi\) | |||||||
\(942\) | −2.67376 | − | 8.22899i | −0.0871159 | − | 0.268115i | ||||
\(943\) | 25.5279 | 0.831302 | ||||||||
\(944\) | −1.11803 | − | 3.44095i | −0.0363889 | − | 0.111994i | ||||
\(945\) | 1.80902 | − | 5.56758i | 0.0588473 | − | 0.181113i | ||||
\(946\) | −8.61803 | + | 26.5236i | −0.280196 | + | 0.862356i | ||||
\(947\) | −10.3713 | + | 31.9196i | −0.337023 | + | 1.03725i | 0.628694 | + | 0.777652i | \(0.283590\pi\) |
−0.965717 | + | 0.259597i | \(0.916410\pi\) | |||||||
\(948\) | −4.54508 | + | 3.30220i | −0.147617 | + | 0.107250i | ||||
\(949\) | −22.8328 | −0.741185 | ||||||||
\(950\) | 23.0902 | − | 16.7760i | 0.749144 | − | 0.544285i | ||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | −2.61803 | + | 1.90211i | −0.0848510 | + | 0.0616478i | ||||
\(953\) | 1.63932 | − | 5.04531i | 0.0531028 | − | 0.163434i | −0.920988 | − | 0.389591i | \(-0.872616\pi\) |
0.974091 | + | 0.226157i | \(0.0726164\pi\) | |||||||
\(954\) | −0.645898 | + | 1.98787i | −0.0209117 | + | 0.0643597i | ||||
\(955\) | −9.59675 | −0.310543 | ||||||||
\(956\) | 3.79837 | + | 11.6902i | 0.122848 | + | 0.378088i | ||||
\(957\) | −30.6525 | −0.990854 | ||||||||
\(958\) | −9.00000 | − | 27.6992i | −0.290777 | − | 0.894919i | ||||
\(959\) | 25.7984 | + | 18.7436i | 0.833073 | + | 0.605263i | ||||
\(960\) | −1.80902 | − | 1.31433i | −0.0583858 | − | 0.0424197i | ||||
\(961\) | −10.3541 | + | 7.52270i | −0.334003 | + | 0.242668i | ||||
\(962\) | 41.8885 | + | 30.4338i | 1.35054 | + | 0.981225i | ||||
\(963\) | 9.39919 | + | 6.82891i | 0.302885 | + | 0.220059i | ||||
\(964\) | −7.73607 | + | 5.62058i | −0.249162 | + | 0.181027i | ||||
\(965\) | 32.2984 | − | 23.4661i | 1.03972 | − | 0.755402i | ||||
\(966\) | 9.47214 | + | 6.88191i | 0.304761 | + | 0.221422i | ||||
\(967\) | 3.37132 | + | 10.3759i | 0.108414 | + | 0.333665i | 0.990517 | − | 0.137393i | \(-0.0438722\pi\) |
−0.882102 | + | 0.471058i | \(0.843872\pi\) | |||||||
\(968\) | 2.09017 | 0.0671806 | ||||||||
\(969\) | 2.18034 | + | 6.71040i | 0.0700426 | + | 0.215569i | ||||
\(970\) | −6.11803 | − | 4.44501i | −0.196438 | − | 0.142721i | ||||
\(971\) | −4.39261 | + | 13.5191i | −0.140966 | + | 0.433847i | −0.996470 | − | 0.0839479i | \(-0.973247\pi\) |
0.855505 | + | 0.517795i | \(0.173247\pi\) | |||||||
\(972\) | −0.309017 | + | 0.951057i | −0.00991172 | + | 0.0305052i | ||||
\(973\) | −22.1803 | + | 16.1150i | −0.711069 | + | 0.516622i | ||||
\(974\) | 17.7984 | 0.570297 | ||||||||
\(975\) | 10.0000 | + | 30.7768i | 0.320256 | + | 0.985648i | ||||
\(976\) | 2.76393 | 0.0884713 | ||||||||
\(977\) | 0.618034 | − | 0.449028i | 0.0197727 | − | 0.0143657i | −0.577855 | − | 0.816139i | \(-0.696110\pi\) |
0.597628 | + | 0.801774i | \(0.296110\pi\) | |||||||
\(978\) | 0.145898 | − | 0.449028i | 0.00466530 | − | 0.0143583i | ||||
\(979\) | 3.94427 | − | 12.1392i | 0.126059 | − | 0.387971i | ||||
\(980\) | 0.100813 | + | 0.310271i | 0.00322036 | + | 0.00991123i | ||||
\(981\) | 5.32624 | + | 16.3925i | 0.170054 | + | 0.523371i | ||||
\(982\) | −25.2705 | −0.806414 | ||||||||
\(983\) | 12.4164 | + | 38.2138i | 0.396022 | + | 1.21883i | 0.928163 | + | 0.372174i | \(0.121388\pi\) |
−0.532141 | + | 0.846656i | \(0.678612\pi\) | |||||||
\(984\) | 4.61803 | + | 3.35520i | 0.147218 | + | 0.106960i | ||||
\(985\) | 11.8090 | + | 36.3444i | 0.376267 | + | 1.15803i | ||||
\(986\) | −8.47214 | + | 6.15537i | −0.269808 | + | 0.196027i | ||||
\(987\) | 3.61803 | + | 2.62866i | 0.115163 | + | 0.0836710i | ||||
\(988\) | −29.8885 | − | 21.7153i | −0.950881 | − | 0.690856i | ||||
\(989\) | 27.8885 | − | 20.2622i | 0.886804 | − | 0.644301i | ||||
\(990\) | −2.50000 | + | 7.69421i | −0.0794552 | + | 0.244538i | ||||
\(991\) | −23.8262 | − | 17.3108i | −0.756865 | − | 0.549895i | 0.141082 | − | 0.989998i | \(-0.454942\pi\) |
−0.897947 | + | 0.440103i | \(0.854942\pi\) | |||||||
\(992\) | 2.04508 | + | 6.29412i | 0.0649315 | + | 0.199839i | ||||
\(993\) | 18.0000 | 0.571213 | ||||||||
\(994\) | 4.47214 | + | 13.7638i | 0.141848 | + | 0.436562i | ||||
\(995\) | 35.2877 | − | 25.6380i | 1.11870 | − | 0.812780i | ||||
\(996\) | −0.663119 | + | 2.04087i | −0.0210117 | + | 0.0646675i | ||||
\(997\) | −1.72949 | + | 5.32282i | −0.0547735 | + | 0.168576i | −0.974701 | − | 0.223513i | \(-0.928247\pi\) |
0.919927 | + | 0.392089i | \(0.128247\pi\) | |||||||
\(998\) | −28.7984 | + | 20.9232i | −0.911597 | + | 0.662314i | ||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 150.2.g.a.61.1 | ✓ | 4 | |
3.2 | odd | 2 | 450.2.h.c.361.1 | 4 | |||
5.2 | odd | 4 | 750.2.h.b.199.1 | 8 | |||
5.3 | odd | 4 | 750.2.h.b.199.2 | 8 | |||
5.4 | even | 2 | 750.2.g.b.301.1 | 4 | |||
25.3 | odd | 20 | 3750.2.c.b.1249.1 | 4 | |||
25.4 | even | 10 | 3750.2.a.d.1.1 | 2 | |||
25.9 | even | 10 | 750.2.g.b.451.1 | 4 | |||
25.12 | odd | 20 | 750.2.h.b.49.2 | 8 | |||
25.13 | odd | 20 | 750.2.h.b.49.1 | 8 | |||
25.16 | even | 5 | inner | 150.2.g.a.91.1 | yes | 4 | |
25.21 | even | 5 | 3750.2.a.f.1.2 | 2 | |||
25.22 | odd | 20 | 3750.2.c.b.1249.4 | 4 | |||
75.41 | odd | 10 | 450.2.h.c.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.61.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
150.2.g.a.91.1 | yes | 4 | 25.16 | even | 5 | inner | |
450.2.h.c.91.1 | 4 | 75.41 | odd | 10 | |||
450.2.h.c.361.1 | 4 | 3.2 | odd | 2 | |||
750.2.g.b.301.1 | 4 | 5.4 | even | 2 | |||
750.2.g.b.451.1 | 4 | 25.9 | even | 10 | |||
750.2.h.b.49.1 | 8 | 25.13 | odd | 20 | |||
750.2.h.b.49.2 | 8 | 25.12 | odd | 20 | |||
750.2.h.b.199.1 | 8 | 5.2 | odd | 4 | |||
750.2.h.b.199.2 | 8 | 5.3 | odd | 4 | |||
3750.2.a.d.1.1 | 2 | 25.4 | even | 10 | |||
3750.2.a.f.1.2 | 2 | 25.21 | even | 5 | |||
3750.2.c.b.1249.1 | 4 | 25.3 | odd | 20 | |||
3750.2.c.b.1249.4 | 4 | 25.22 | odd | 20 |