Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(49,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.h (of order \(10\), 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.587785 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.49 |
Dual form | 750.2.h.b.199.2 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587785 | − | 0.809017i | 0.415627 | − | 0.572061i | ||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | ||||
\(4\) | −0.309017 | − | 0.951057i | −0.154508 | − | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | 2.61803i | 0.989524i | 0.869029 | + | 0.494762i | \(0.164745\pi\) | ||||
−0.869029 | + | 0.494762i | \(0.835255\pi\) | |||||||
\(8\) | −0.951057 | − | 0.309017i | −0.336249 | − | 0.109254i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.92705 | − | 2.12663i | −0.882539 | − | 0.641202i | 0.0513829 | − | 0.998679i | \(-0.483637\pi\) |
−0.933922 | + | 0.357477i | \(0.883637\pi\) | |||||||
\(12\) | 0.587785 | + | 0.809017i | 0.169679 | + | 0.233543i | ||||
\(13\) | −3.80423 | − | 5.23607i | −1.05510 | − | 1.45222i | −0.884300 | − | 0.466919i | \(-0.845364\pi\) |
−0.170802 | − | 0.985305i | \(-0.554636\pi\) | |||||||
\(14\) | 2.11803 | + | 1.53884i | 0.566068 | + | 0.411273i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 1.17557 | + | 0.381966i | 0.285118 | + | 0.0926404i | 0.448085 | − | 0.893991i | \(-0.352106\pi\) |
−0.162967 | + | 0.986632i | \(0.552106\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.76393 | − | 5.42882i | 0.404674 | − | 1.24546i | −0.516494 | − | 0.856291i | \(-0.672763\pi\) |
0.921167 | − | 0.389167i | \(-0.127237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.809017 | − | 2.48990i | −0.176542 | − | 0.543340i | ||||
\(22\) | −3.44095 | + | 1.11803i | −0.733614 | + | 0.238366i | ||||
\(23\) | −2.62866 | + | 3.61803i | −0.548113 | + | 0.754412i | −0.989755 | − | 0.142779i | \(-0.954396\pi\) |
0.441642 | + | 0.897191i | \(0.354396\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.47214 | −1.26929 | ||||||||
\(27\) | −0.587785 | + | 0.809017i | −0.113119 | + | 0.155695i | ||||
\(28\) | 2.48990 | − | 0.809017i | 0.470547 | − | 0.152890i | ||||
\(29\) | −2.61803 | − | 8.05748i | −0.486157 | − | 1.49624i | −0.830299 | − | 0.557319i | \(-0.811830\pi\) |
0.344142 | − | 0.938918i | \(-0.388170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04508 | − | 6.29412i | 0.367308 | − | 1.13046i | −0.581215 | − | 0.813750i | \(-0.697422\pi\) |
0.948523 | − | 0.316708i | \(-0.102578\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.44095 | + | 1.11803i | 0.598993 | + | 0.194625i | ||||
\(34\) | 1.00000 | − | 0.726543i | 0.171499 | − | 0.124601i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | −4.70228 | − | 6.47214i | −0.773050 | − | 1.06401i | −0.996015 | − | 0.0891861i | \(-0.971573\pi\) |
0.222965 | − | 0.974827i | \(-0.428427\pi\) | |||||||
\(38\) | −3.35520 | − | 4.61803i | −0.544285 | − | 0.749144i | ||||
\(39\) | 5.23607 | + | 3.80423i | 0.838442 | + | 0.609164i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.61803 | + | 3.35520i | −0.721216 | + | 0.523994i | −0.886772 | − | 0.462206i | \(-0.847058\pi\) |
0.165557 | + | 0.986200i | \(0.447058\pi\) | |||||||
\(42\) | −2.48990 | − | 0.809017i | −0.384200 | − | 0.124834i | ||||
\(43\) | 7.70820i | 1.17549i | 0.809046 | + | 0.587745i | \(0.199984\pi\) | ||||
−0.809046 | + | 0.587745i | \(0.800016\pi\) | |||||||
\(44\) | −1.11803 | + | 3.44095i | −0.168550 | + | 0.518743i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.38197 | + | 4.25325i | 0.203760 | + | 0.627108i | ||||
\(47\) | −1.62460 | + | 0.527864i | −0.236972 | + | 0.0769969i | −0.425096 | − | 0.905149i | \(-0.639759\pi\) |
0.188123 | + | 0.982145i | \(0.439759\pi\) | |||||||
\(48\) | 0.587785 | − | 0.809017i | 0.0848395 | − | 0.116772i | ||||
\(49\) | 0.145898 | 0.0208426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | −3.80423 | + | 5.23607i | −0.527551 | + | 0.726112i | ||||
\(53\) | −1.98787 | + | 0.645898i | −0.273055 | + | 0.0887209i | −0.442344 | − | 0.896846i | \(-0.645853\pi\) |
0.169289 | + | 0.985566i | \(0.445853\pi\) | |||||||
\(54\) | 0.309017 | + | 0.951057i | 0.0420519 | + | 0.129422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.809017 | − | 2.48990i | 0.108109 | − | 0.332727i | ||||
\(57\) | 5.70820i | 0.756070i | ||||||||
\(58\) | −8.05748 | − | 2.61803i | −1.05800 | − | 0.343765i | ||||
\(59\) | −2.92705 | + | 2.12663i | −0.381070 | + | 0.276863i | −0.761786 | − | 0.647829i | \(-0.775677\pi\) |
0.380717 | + | 0.924692i | \(0.375677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.23607 | − | 1.62460i | −0.286299 | − | 0.208009i | 0.435361 | − | 0.900256i | \(-0.356621\pi\) |
−0.721660 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(62\) | −3.88998 | − | 5.35410i | −0.494028 | − | 0.679972i | ||||
\(63\) | 1.53884 | + | 2.11803i | 0.193876 | + | 0.266847i | ||||
\(64\) | 0.809017 | + | 0.587785i | 0.101127 | + | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.92705 | − | 2.12663i | 0.360295 | − | 0.261770i | ||||
\(67\) | −1.45309 | − | 0.472136i | −0.177523 | − | 0.0576806i | 0.218907 | − | 0.975746i | \(-0.429751\pi\) |
−0.396430 | + | 0.918065i | \(0.629751\pi\) | |||||||
\(68\) | − | 1.23607i | − | 0.149895i | ||||||
\(69\) | 1.38197 | − | 4.25325i | 0.166369 | − | 0.512032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70820 | + | 5.25731i | 0.202727 | + | 0.623928i | 0.999799 | + | 0.0200445i | \(0.00638080\pi\) |
−0.797073 | + | 0.603884i | \(0.793619\pi\) | |||||||
\(72\) | −0.951057 | + | 0.309017i | −0.112083 | + | 0.0364180i | ||||
\(73\) | −2.07363 | + | 2.85410i | −0.242700 | + | 0.334047i | −0.912938 | − | 0.408099i | \(-0.866192\pi\) |
0.670238 | + | 0.742146i | \(0.266192\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.70820 | −0.654776 | ||||||||
\(77\) | 5.56758 | − | 7.66312i | 0.634485 | − | 0.873293i | ||||
\(78\) | 6.15537 | − | 2.00000i | 0.696958 | − | 0.226455i | ||||
\(79\) | 1.73607 | + | 5.34307i | 0.195323 | + | 0.601142i | 0.999973 | + | 0.00739236i | \(0.00235308\pi\) |
−0.804650 | + | 0.593750i | \(0.797647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 5.70820i | 0.630366i | ||||||||
\(83\) | −2.04087 | − | 0.663119i | −0.224015 | − | 0.0727868i | 0.194859 | − | 0.980831i | \(-0.437575\pi\) |
−0.418874 | + | 0.908044i | \(0.637575\pi\) | |||||||
\(84\) | −2.11803 | + | 1.53884i | −0.231096 | + | 0.167901i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.23607 | + | 4.53077i | 0.672453 | + | 0.488565i | ||||
\(87\) | 4.97980 | + | 6.85410i | 0.533890 | + | 0.734837i | ||||
\(88\) | 2.12663 | + | 2.92705i | 0.226699 | + | 0.312025i | ||||
\(89\) | 2.85410 | + | 2.07363i | 0.302534 | + | 0.219804i | 0.728686 | − | 0.684848i | \(-0.240131\pi\) |
−0.426152 | + | 0.904651i | \(0.640131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7082 | − | 9.95959i | 1.43701 | − | 1.04405i | ||||
\(92\) | 4.25325 | + | 1.38197i | 0.443432 | + | 0.144080i | ||||
\(93\) | 6.61803i | 0.686258i | ||||||||
\(94\) | −0.527864 | + | 1.62460i | −0.0544450 | + | 0.167565i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.309017 | − | 0.951057i | −0.0315389 | − | 0.0970668i | ||||
\(97\) | 3.21644 | − | 1.04508i | 0.326580 | − | 0.106112i | −0.141138 | − | 0.989990i | \(-0.545076\pi\) |
0.467718 | + | 0.883878i | \(0.345076\pi\) | |||||||
\(98\) | 0.0857567 | − | 0.118034i | 0.00866274 | − | 0.0119232i | ||||
\(99\) | −3.61803 | −0.363626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38197 | 0.436022 | 0.218011 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218011 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(102\) | −0.726543 | + | 1.00000i | −0.0719384 | + | 0.0990148i | ||||
\(103\) | 13.6251 | − | 4.42705i | 1.34252 | − | 0.436210i | 0.452348 | − | 0.891841i | \(-0.350586\pi\) |
0.890169 | + | 0.455631i | \(0.150586\pi\) | |||||||
\(104\) | 2.00000 | + | 6.15537i | 0.196116 | + | 0.603583i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.645898 | + | 1.98787i | −0.0627352 | + | 0.193079i | ||||
\(107\) | − | 11.6180i | − | 1.12316i | −0.827423 | − | 0.561579i | \(-0.810194\pi\) | ||
0.827423 | − | 0.561579i | \(-0.189806\pi\) | |||||||
\(108\) | 0.951057 | + | 0.309017i | 0.0915155 | + | 0.0297352i | ||||
\(109\) | 13.9443 | − | 10.1311i | 1.33562 | − | 0.970384i | 0.336026 | − | 0.941853i | \(-0.390917\pi\) |
0.999593 | − | 0.0285313i | \(-0.00908304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.47214 | + | 4.70228i | 0.614308 | + | 0.446321i | ||||
\(112\) | −1.53884 | − | 2.11803i | −0.145407 | − | 0.200135i | ||||
\(113\) | −11.3067 | − | 15.5623i | −1.06364 | − | 1.46398i | −0.876350 | − | 0.481674i | \(-0.840029\pi\) |
−0.187292 | − | 0.982304i | \(-0.559971\pi\) | |||||||
\(114\) | 4.61803 | + | 3.35520i | 0.432519 | + | 0.314243i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.85410 | + | 4.97980i | −0.636387 | + | 0.462363i | ||||
\(117\) | −6.15537 | − | 2.00000i | −0.569064 | − | 0.184900i | ||||
\(118\) | 3.61803i | 0.333067i | ||||||||
\(119\) | −1.00000 | + | 3.07768i | −0.0916698 | + | 0.282131i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.645898 | + | 1.98787i | 0.0587180 | + | 0.180715i | ||||
\(122\) | −2.62866 | + | 0.854102i | −0.237987 | + | 0.0773268i | ||||
\(123\) | 3.35520 | − | 4.61803i | 0.302528 | − | 0.416394i | ||||
\(124\) | −6.61803 | −0.594317 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | 8.00448 | − | 11.0172i | 0.710283 | − | 0.977620i | −0.289508 | − | 0.957176i | \(-0.593492\pi\) |
0.999791 | − | 0.0204448i | \(-0.00650822\pi\) | |||||||
\(128\) | 0.951057 | − | 0.309017i | 0.0840623 | − | 0.0273135i | ||||
\(129\) | −2.38197 | − | 7.33094i | −0.209720 | − | 0.645453i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.52786 | + | 17.0130i | −0.482972 | + | 1.48643i | 0.351925 | + | 0.936028i | \(0.385527\pi\) |
−0.834897 | + | 0.550406i | \(0.814473\pi\) | |||||||
\(132\) | − | 3.61803i | − | 0.314909i | ||||||
\(133\) | 14.2128 | + | 4.61803i | 1.23241 | + | 0.400434i | ||||
\(134\) | −1.23607 | + | 0.898056i | −0.106780 | + | 0.0775802i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 0.726543i | −0.0857493 | − | 0.0623005i | ||||
\(137\) | 7.15942 | + | 9.85410i | 0.611671 | + | 0.841893i | 0.996714 | − | 0.0810060i | \(-0.0258133\pi\) |
−0.385043 | + | 0.922899i | \(0.625813\pi\) | |||||||
\(138\) | −2.62866 | − | 3.61803i | −0.223766 | − | 0.307988i | ||||
\(139\) | 8.47214 | + | 6.15537i | 0.718597 | + | 0.522091i | 0.885936 | − | 0.463808i | \(-0.153517\pi\) |
−0.167339 | + | 0.985899i | \(0.553517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.38197 | − | 1.00406i | 0.116383 | − | 0.0845569i | ||||
\(142\) | 5.25731 | + | 1.70820i | 0.441184 | + | 0.143349i | ||||
\(143\) | 23.4164i | 1.95818i | ||||||||
\(144\) | −0.309017 | + | 0.951057i | −0.0257514 | + | 0.0792547i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.09017 | + | 3.35520i | 0.0902231 | + | 0.277678i | ||||
\(147\) | −0.138757 | + | 0.0450850i | −0.0114445 | + | 0.00371855i | ||||
\(148\) | −4.70228 | + | 6.47214i | −0.386525 | + | 0.532006i | ||||
\(149\) | −22.0902 | −1.80970 | −0.904849 | − | 0.425733i | \(-0.860016\pi\) | ||||
−0.904849 | + | 0.425733i | \(0.860016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3262 | 1.49137 | 0.745684 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745684 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(152\) | −3.35520 | + | 4.61803i | −0.272143 | + | 0.374572i | ||||
\(153\) | 1.17557 | − | 0.381966i | 0.0950392 | − | 0.0308801i | ||||
\(154\) | −2.92705 | − | 9.00854i | −0.235868 | − | 0.725929i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 6.15537i | 0.160128 | − | 0.492824i | ||||
\(157\) | 8.65248i | 0.690543i | 0.938503 | + | 0.345271i | \(0.112213\pi\) | ||||
−0.938503 | + | 0.345271i | \(0.887787\pi\) | |||||||
\(158\) | 5.34307 | + | 1.73607i | 0.425072 | + | 0.138114i | ||||
\(159\) | 1.69098 | − | 1.22857i | 0.134104 | − | 0.0974320i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.47214 | − | 6.88191i | −0.746509 | − | 0.542370i | ||||
\(162\) | −0.587785 | − | 0.809017i | −0.0461808 | − | 0.0635624i | ||||
\(163\) | −0.277515 | − | 0.381966i | −0.0217366 | − | 0.0299179i | 0.798010 | − | 0.602644i | \(-0.205886\pi\) |
−0.819747 | + | 0.572726i | \(0.805886\pi\) | |||||||
\(164\) | 4.61803 | + | 3.35520i | 0.360608 | + | 0.261997i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.73607 | + | 1.26133i | −0.134745 | + | 0.0978980i | ||||
\(167\) | 11.1352 | + | 3.61803i | 0.861665 | + | 0.279972i | 0.706324 | − | 0.707889i | \(-0.250352\pi\) |
0.155341 | + | 0.987861i | \(0.450352\pi\) | |||||||
\(168\) | 2.61803i | 0.201986i | ||||||||
\(169\) | −8.92705 | + | 27.4746i | −0.686696 | + | 2.11343i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.76393 | − | 5.42882i | −0.134891 | − | 0.415153i | ||||
\(172\) | 7.33094 | − | 2.38197i | 0.558979 | − | 0.181623i | ||||
\(173\) | −2.99193 | + | 4.11803i | −0.227472 | + | 0.313088i | −0.907463 | − | 0.420132i | \(-0.861984\pi\) |
0.679991 | + | 0.733221i | \(0.261984\pi\) | |||||||
\(174\) | 8.47214 | 0.642271 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.61803 | 0.272720 | ||||||||
\(177\) | 2.12663 | − | 2.92705i | 0.159847 | − | 0.220011i | ||||
\(178\) | 3.35520 | − | 1.09017i | 0.251483 | − | 0.0817117i | ||||
\(179\) | −3.04508 | − | 9.37181i | −0.227600 | − | 0.700482i | −0.998017 | − | 0.0629414i | \(-0.979952\pi\) |
0.770417 | − | 0.637540i | \(-0.220048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.05573 | + | 6.32688i | −0.152801 | + | 0.470273i | −0.997931 | − | 0.0642869i | \(-0.979523\pi\) |
0.845130 | + | 0.534560i | \(0.179523\pi\) | |||||||
\(182\) | − | 16.9443i | − | 1.25599i | ||||||
\(183\) | 2.62866 | + | 0.854102i | 0.194316 | + | 0.0631370i | ||||
\(184\) | 3.61803 | − | 2.62866i | 0.266725 | − | 0.193787i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.35410 | + | 3.88998i | 0.392582 | + | 0.285227i | ||||
\(187\) | −2.62866 | − | 3.61803i | −0.192226 | − | 0.264577i | ||||
\(188\) | 1.00406 | + | 1.38197i | 0.0732284 | + | 0.100790i | ||||
\(189\) | −2.11803 | − | 1.53884i | −0.154064 | − | 0.111934i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.47214 | + | 2.52265i | −0.251235 | + | 0.182533i | −0.706274 | − | 0.707939i | \(-0.749625\pi\) |
0.455039 | + | 0.890472i | \(0.349625\pi\) | |||||||
\(192\) | −0.951057 | − | 0.309017i | −0.0686366 | − | 0.0223014i | ||||
\(193\) | − | 17.8541i | − | 1.28517i | −0.766216 | − | 0.642583i | \(-0.777863\pi\) | ||
0.766216 | − | 0.642583i | \(-0.222137\pi\) | |||||||
\(194\) | 1.04508 | − | 3.21644i | 0.0750327 | − | 0.230927i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0450850 | − | 0.138757i | −0.00322036 | − | 0.00991123i | ||||
\(197\) | 16.2537 | − | 5.28115i | 1.15803 | − | 0.376267i | 0.333867 | − | 0.942620i | \(-0.391646\pi\) |
0.824162 | + | 0.566354i | \(0.191646\pi\) | |||||||
\(198\) | −2.12663 | + | 2.92705i | −0.151133 | + | 0.208016i | ||||
\(199\) | −19.5066 | −1.38278 | −0.691392 | − | 0.722480i | \(-0.743002\pi\) | ||||
−0.691392 | + | 0.722480i | \(0.743002\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52786 | 0.107767 | ||||||||
\(202\) | 2.57565 | − | 3.54508i | 0.181222 | − | 0.249431i | ||||
\(203\) | 21.0948 | − | 6.85410i | 1.48056 | − | 0.481064i | ||||
\(204\) | 0.381966 | + | 1.17557i | 0.0267430 | + | 0.0823064i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.42705 | − | 13.6251i | 0.308447 | − | 0.949303i | ||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | 6.15537 | + | 2.00000i | 0.426798 | + | 0.138675i | ||||
\(209\) | −16.7082 | + | 12.1392i | −1.15573 | + | 0.839687i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.76393 | + | 2.00811i | 0.190277 | + | 0.138244i | 0.678845 | − | 0.734281i | \(-0.262481\pi\) |
−0.488568 | + | 0.872526i | \(0.662481\pi\) | |||||||
\(212\) | 1.22857 | + | 1.69098i | 0.0843786 | + | 0.116137i | ||||
\(213\) | −3.24920 | − | 4.47214i | −0.222631 | − | 0.306426i | ||||
\(214\) | −9.39919 | − | 6.82891i | −0.642515 | − | 0.466815i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.809017 | − | 0.587785i | 0.0550466 | − | 0.0399937i | ||||
\(217\) | 16.4782 | + | 5.35410i | 1.11862 | + | 0.363460i | ||||
\(218\) | − | 17.2361i | − | 1.16737i | ||||||
\(219\) | 1.09017 | − | 3.35520i | 0.0736669 | − | 0.226723i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | − | 7.60845i | −0.166294 | − | 0.511800i | ||||
\(222\) | 7.60845 | − | 2.47214i | 0.510646 | − | 0.165919i | ||||
\(223\) | 4.75528 | − | 6.54508i | 0.318437 | − | 0.438291i | −0.619552 | − | 0.784956i | \(-0.712686\pi\) |
0.937989 | + | 0.346664i | \(0.112686\pi\) | |||||||
\(224\) | −2.61803 | −0.174925 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.2361 | −1.27956 | ||||||||
\(227\) | −13.0903 | + | 18.0172i | −0.868832 | + | 1.19584i | 0.110558 | + | 0.993870i | \(0.464736\pi\) |
−0.979391 | + | 0.201975i | \(0.935264\pi\) | |||||||
\(228\) | 5.42882 | − | 1.76393i | 0.359533 | − | 0.116819i | ||||
\(229\) | 1.70820 | + | 5.25731i | 0.112881 | + | 0.347413i | 0.991499 | − | 0.130113i | \(-0.0415339\pi\) |
−0.878618 | + | 0.477525i | \(0.841534\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92705 | + | 9.00854i | −0.192586 | + | 0.592718i | ||||
\(232\) | 8.47214i | 0.556223i | ||||||||
\(233\) | −17.7396 | − | 5.76393i | −1.16216 | − | 0.377608i | −0.336447 | − | 0.941702i | \(-0.609225\pi\) |
−0.825710 | + | 0.564095i | \(0.809225\pi\) | |||||||
\(234\) | −5.23607 | + | 3.80423i | −0.342292 | + | 0.248690i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.92705 | + | 2.12663i | 0.190535 | + | 0.138432i | ||||
\(237\) | −3.30220 | − | 4.54508i | −0.214501 | − | 0.295235i | ||||
\(238\) | 1.90211 | + | 2.61803i | 0.123296 | + | 0.169702i | ||||
\(239\) | 9.94427 | + | 7.22494i | 0.643241 | + | 0.467342i | 0.860962 | − | 0.508669i | \(-0.169862\pi\) |
−0.217721 | + | 0.976011i | \(0.569862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.73607 | + | 5.62058i | −0.498324 | + | 0.362054i | −0.808376 | − | 0.588666i | \(-0.799653\pi\) |
0.310052 | + | 0.950719i | \(0.399653\pi\) | |||||||
\(242\) | 1.98787 | + | 0.645898i | 0.127785 | + | 0.0415199i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.854102 | + | 2.62866i | −0.0546783 | + | 0.168282i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.76393 | − | 5.42882i | −0.112464 | − | 0.346129i | ||||
\(247\) | −35.1361 | + | 11.4164i | −2.23566 | + | 0.726409i | ||||
\(248\) | −3.88998 | + | 5.35410i | −0.247014 | + | 0.339986i | ||||
\(249\) | 2.14590 | 0.135991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5623 | 0.856045 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(252\) | 1.53884 | − | 2.11803i | 0.0969379 | − | 0.133424i | ||||
\(253\) | 15.3884 | − | 5.00000i | 0.967462 | − | 0.314347i | ||||
\(254\) | −4.20820 | − | 12.9515i | −0.264046 | − | 0.812651i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | − | 22.0000i | − | 1.37232i | −0.727450 | − | 0.686161i | \(-0.759294\pi\) | ||
0.727450 | − | 0.686161i | \(-0.240706\pi\) | |||||||
\(258\) | −7.33094 | − | 2.38197i | −0.456404 | − | 0.148295i | ||||
\(259\) | 16.9443 | − | 12.3107i | 1.05287 | − | 0.764952i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.85410 | − | 4.97980i | −0.424258 | − | 0.308242i | ||||
\(262\) | 10.5146 | + | 14.4721i | 0.649596 | + | 0.894092i | ||||
\(263\) | −6.88191 | − | 9.47214i | −0.424357 | − | 0.584077i | 0.542290 | − | 0.840192i | \(-0.317558\pi\) |
−0.966646 | + | 0.256115i | \(0.917558\pi\) | |||||||
\(264\) | −2.92705 | − | 2.12663i | −0.180148 | − | 0.130885i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.0902 | − | 8.78402i | 0.741296 | − | 0.538583i | ||||
\(267\) | −3.35520 | − | 1.09017i | −0.205335 | − | 0.0667173i | ||||
\(268\) | 1.52786i | 0.0933292i | ||||||||
\(269\) | 2.80902 | − | 8.64527i | 0.171269 | − | 0.527111i | −0.828175 | − | 0.560470i | \(-0.810620\pi\) |
0.999443 | + | 0.0333590i | \(0.0106205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57295 | − | 17.1518i | −0.338533 | − | 1.04190i | −0.964956 | − | 0.262413i | \(-0.915482\pi\) |
0.626423 | − | 0.779483i | \(-0.284518\pi\) | |||||||
\(272\) | −1.17557 | + | 0.381966i | −0.0712794 | + | 0.0231601i | ||||
\(273\) | −9.95959 | + | 13.7082i | −0.602782 | + | 0.829658i | ||||
\(274\) | 12.1803 | 0.735841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | 9.95959 | − | 13.7082i | 0.598414 | − | 0.823646i | −0.397148 | − | 0.917755i | \(-0.630000\pi\) |
0.995562 | + | 0.0941084i | \(0.0300000\pi\) | |||||||
\(278\) | 9.95959 | − | 3.23607i | 0.597337 | − | 0.194086i | ||||
\(279\) | −2.04508 | − | 6.29412i | −0.122436 | − | 0.376819i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81966 | − | 5.60034i | 0.108552 | − | 0.334088i | −0.881996 | − | 0.471257i | \(-0.843800\pi\) |
0.990548 | + | 0.137169i | \(0.0438004\pi\) | |||||||
\(282\) | − | 1.70820i | − | 0.101722i | ||||||
\(283\) | −4.35926 | − | 1.41641i | −0.259131 | − | 0.0841967i | 0.176571 | − | 0.984288i | \(-0.443500\pi\) |
−0.435701 | + | 0.900091i | \(0.643500\pi\) | |||||||
\(284\) | 4.47214 | − | 3.24920i | 0.265372 | − | 0.192804i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.9443 | + | 13.7638i | 1.12020 | + | 0.813872i | ||||
\(287\) | −8.78402 | − | 12.0902i | −0.518504 | − | 0.713660i | ||||
\(288\) | 0.587785 | + | 0.809017i | 0.0346356 | + | 0.0476718i | ||||
\(289\) | −12.5172 | − | 9.09429i | −0.736307 | − | 0.534958i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.73607 | + | 1.98787i | −0.160391 | + | 0.116531i | ||||
\(292\) | 3.35520 | + | 1.09017i | 0.196348 | + | 0.0637974i | ||||
\(293\) | 22.0902i | 1.29052i | 0.763962 | + | 0.645261i | \(0.223251\pi\) | ||||
−0.763962 | + | 0.645261i | \(0.776749\pi\) | |||||||
\(294\) | −0.0450850 | + | 0.138757i | −0.00262941 | + | 0.00809249i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.47214 | + | 7.60845i | 0.143690 | + | 0.442232i | ||||
\(297\) | 3.44095 | − | 1.11803i | 0.199664 | − | 0.0648749i | ||||
\(298\) | −12.9843 | + | 17.8713i | −0.752159 | + | 1.03526i | ||||
\(299\) | 28.9443 | 1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1803 | −1.16318 | ||||||||
\(302\) | 10.7719 | − | 14.8262i | 0.619853 | − | 0.853154i | ||||
\(303\) | −4.16750 | + | 1.35410i | −0.239416 | + | 0.0777911i | ||||
\(304\) | 1.76393 | + | 5.42882i | 0.101168 | + | 0.311364i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.381966 | − | 1.17557i | 0.0218355 | − | 0.0672029i | ||||
\(307\) | 10.0000i | 0.570730i | 0.958419 | + | 0.285365i | \(0.0921148\pi\) | ||||
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(308\) | −9.00854 | − | 2.92705i | −0.513309 | − | 0.166784i | ||||
\(309\) | −11.5902 | + | 8.42075i | −0.659342 | + | 0.479040i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.854102 | + | 0.620541i | 0.0484317 | + | 0.0351877i | 0.611738 | − | 0.791061i | \(-0.290471\pi\) |
−0.563306 | + | 0.826248i | \(0.690471\pi\) | |||||||
\(312\) | −3.80423 | − | 5.23607i | −0.215372 | − | 0.296434i | ||||
\(313\) | −9.56357 | − | 13.1631i | −0.540565 | − | 0.744023i | 0.448130 | − | 0.893969i | \(-0.352090\pi\) |
−0.988694 | + | 0.149945i | \(0.952090\pi\) | |||||||
\(314\) | 7.00000 | + | 5.08580i | 0.395033 | + | 0.287008i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.54508 | − | 3.30220i | 0.255681 | − | 0.185763i | ||||
\(317\) | −19.5559 | − | 6.35410i | −1.09837 | − | 0.356882i | −0.296895 | − | 0.954910i | \(-0.595951\pi\) |
−0.801475 | + | 0.598028i | \(0.795951\pi\) | |||||||
\(318\) | − | 2.09017i | − | 0.117211i | ||||||
\(319\) | −9.47214 | + | 29.1522i | −0.530338 | + | 1.63221i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.59017 | + | 11.0494i | 0.200384 | + | 0.616718i | ||||
\(322\) | −11.1352 | + | 3.61803i | −0.620538 | + | 0.201625i | ||||
\(323\) | 4.14725 | − | 5.70820i | 0.230759 | − | 0.317613i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.472136 | −0.0261492 | ||||||||
\(327\) | −10.1311 | + | 13.9443i | −0.560251 | + | 0.771120i | ||||
\(328\) | 5.42882 | − | 1.76393i | 0.299757 | − | 0.0973969i | ||||
\(329\) | −1.38197 | − | 4.25325i | −0.0761903 | − | 0.234489i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56231 | + | 17.1190i | −0.305732 | + | 0.940946i | 0.673671 | + | 0.739031i | \(0.264716\pi\) |
−0.979403 | + | 0.201915i | \(0.935284\pi\) | |||||||
\(332\) | 2.14590i | 0.117771i | ||||||||
\(333\) | −7.60845 | − | 2.47214i | −0.416941 | − | 0.135472i | ||||
\(334\) | 9.47214 | − | 6.88191i | 0.518292 | − | 0.376561i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.11803 | + | 1.53884i | 0.115548 | + | 0.0839507i | ||||
\(337\) | −0.534785 | − | 0.736068i | −0.0291316 | − | 0.0400962i | 0.794203 | − | 0.607653i | \(-0.207889\pi\) |
−0.823334 | + | 0.567557i | \(0.807889\pi\) | |||||||
\(338\) | 16.9803 | + | 23.3713i | 0.923604 | + | 1.27123i | ||||
\(339\) | 15.5623 | + | 11.3067i | 0.845228 | + | 0.614094i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3713 | + | 14.0741i | −1.04902 | + | 0.762155i | ||||
\(342\) | −5.42882 | − | 1.76393i | −0.293557 | − | 0.0953825i | ||||
\(343\) | 18.7082i | 1.01015i | ||||||||
\(344\) | 2.38197 | − | 7.33094i | 0.128427 | − | 0.395258i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.57295 | + | 4.84104i | 0.0845623 | + | 0.260256i | ||||
\(347\) | −19.5559 | + | 6.35410i | −1.04982 | + | 0.341106i | −0.782596 | − | 0.622529i | \(-0.786105\pi\) |
−0.267220 | + | 0.963636i | \(0.586105\pi\) | |||||||
\(348\) | 4.97980 | − | 6.85410i | 0.266945 | − | 0.367418i | ||||
\(349\) | 27.8885 | 1.49284 | 0.746420 | − | 0.665475i | \(-0.231771\pi\) | ||||
0.746420 | + | 0.665475i | \(0.231771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.47214 | 0.345457 | ||||||||
\(352\) | 2.12663 | − | 2.92705i | 0.113350 | − | 0.156012i | ||||
\(353\) | −12.5882 | + | 4.09017i | −0.670005 | + | 0.217698i | −0.624214 | − | 0.781253i | \(-0.714581\pi\) |
−0.0457907 | + | 0.998951i | \(0.514581\pi\) | |||||||
\(354\) | −1.11803 | − | 3.44095i | −0.0594228 | − | 0.182885i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.09017 | − | 3.35520i | 0.0577789 | − | 0.177825i | ||||
\(357\) | − | 3.23607i | − | 0.171271i | ||||||
\(358\) | −9.37181 | − | 3.04508i | −0.495315 | − | 0.160938i | ||||
\(359\) | 17.9443 | − | 13.0373i | 0.947062 | − | 0.688081i | −0.00304782 | − | 0.999995i | \(-0.500970\pi\) |
0.950110 | + | 0.311914i | \(0.100970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.9894 | − | 7.98424i | −0.578387 | − | 0.420223i | ||||
\(362\) | 3.91023 | + | 5.38197i | 0.205517 | + | 0.282870i | ||||
\(363\) | −1.22857 | − | 1.69098i | −0.0644833 | − | 0.0887536i | ||||
\(364\) | −13.7082 | − | 9.95959i | −0.718505 | − | 0.522025i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.23607 | − | 1.62460i | 0.116881 | − | 0.0849191i | ||||
\(367\) | −29.1195 | − | 9.46149i | −1.52002 | − | 0.493886i | −0.574242 | − | 0.818686i | \(-0.694703\pi\) |
−0.945783 | + | 0.324800i | \(0.894703\pi\) | |||||||
\(368\) | − | 4.47214i | − | 0.233126i | ||||||
\(369\) | −1.76393 | + | 5.42882i | −0.0918266 | + | 0.282613i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.69098 | − | 5.20431i | −0.0877915 | − | 0.270194i | ||||
\(372\) | 6.29412 | − | 2.04508i | 0.326335 | − | 0.106033i | ||||
\(373\) | 6.77591 | − | 9.32624i | 0.350843 | − | 0.482894i | −0.596726 | − | 0.802445i | \(-0.703532\pi\) |
0.947569 | + | 0.319551i | \(0.103532\pi\) | |||||||
\(374\) | −4.47214 | −0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.70820 | 0.0880939 | ||||||||
\(377\) | −32.2299 | + | 44.3607i | −1.65993 | + | 2.28469i | ||||
\(378\) | −2.48990 | + | 0.809017i | −0.128067 | + | 0.0416113i | ||||
\(379\) | 6.23607 | + | 19.1926i | 0.320325 | + | 0.985860i | 0.973507 | + | 0.228658i | \(0.0734339\pi\) |
−0.653181 | + | 0.757201i | \(0.726566\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.20820 | + | 12.9515i | −0.215593 | + | 0.663526i | ||||
\(382\) | 4.29180i | 0.219587i | ||||||||
\(383\) | 19.0211 | + | 6.18034i | 0.971934 | + | 0.315801i | 0.751597 | − | 0.659623i | \(-0.229284\pi\) |
0.220338 | + | 0.975424i | \(0.429284\pi\) | |||||||
\(384\) | −0.809017 | + | 0.587785i | −0.0412850 | + | 0.0299953i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.4443 | − | 10.4944i | −0.735194 | − | 0.534150i | ||||
\(387\) | 4.53077 | + | 6.23607i | 0.230312 | + | 0.316997i | ||||
\(388\) | −1.98787 | − | 2.73607i | −0.100919 | − | 0.138903i | ||||
\(389\) | −10.0172 | − | 7.27794i | −0.507893 | − | 0.369006i | 0.304131 | − | 0.952630i | \(-0.401634\pi\) |
−0.812024 | + | 0.583624i | \(0.801634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.47214 | + | 3.24920i | −0.226166 | + | 0.164319i | ||||
\(392\) | −0.138757 | − | 0.0450850i | −0.00700830 | − | 0.00227713i | ||||
\(393\) | − | 17.8885i | − | 0.902358i | ||||||
\(394\) | 5.28115 | − | 16.2537i | 0.266061 | − | 0.818850i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.11803 | + | 3.44095i | 0.0561833 | + | 0.172914i | ||||
\(397\) | 29.2582 | − | 9.50658i | 1.46843 | − | 0.477121i | 0.537796 | − | 0.843075i | \(-0.319257\pi\) |
0.930633 | + | 0.365954i | \(0.119257\pi\) | |||||||
\(398\) | −11.4657 | + | 15.7812i | −0.574723 | + | 0.791038i | ||||
\(399\) | −14.9443 | −0.748149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.7082 | 1.28381 | 0.641903 | − | 0.766786i | \(-0.278145\pi\) | ||||
0.641903 | + | 0.766786i | \(0.278145\pi\) | |||||||
\(402\) | 0.898056 | − | 1.23607i | 0.0447910 | − | 0.0616495i | ||||
\(403\) | −40.7364 | + | 13.2361i | −2.02923 | + | 0.659336i | ||||
\(404\) | −1.35410 | − | 4.16750i | −0.0673691 | − | 0.207341i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.85410 | − | 21.0948i | 0.340163 | − | 1.04692i | ||||
\(407\) | 28.9443i | 1.43471i | ||||||||
\(408\) | 1.17557 | + | 0.381966i | 0.0581994 | + | 0.0189101i | ||||
\(409\) | 4.69098 | − | 3.40820i | 0.231954 | − | 0.168525i | −0.465737 | − | 0.884923i | \(-0.654211\pi\) |
0.697691 | + | 0.716399i | \(0.254211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.85410 | − | 7.15942i | −0.486067 | − | 0.353148i | ||||
\(412\) | −8.42075 | − | 11.5902i | −0.414861 | − | 0.571007i | ||||
\(413\) | −5.56758 | − | 7.66312i | −0.273963 | − | 0.377077i | ||||
\(414\) | 3.61803 | + | 2.62866i | 0.177817 | + | 0.129191i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.23607 | − | 3.80423i | 0.256719 | − | 0.186518i | ||||
\(417\) | −9.95959 | − | 3.23607i | −0.487723 | − | 0.158471i | ||||
\(418\) | 20.6525i | 1.01015i | ||||||||
\(419\) | 0.954915 | − | 2.93893i | 0.0466507 | − | 0.143576i | −0.925018 | − | 0.379923i | \(-0.875950\pi\) |
0.971669 | + | 0.236347i | \(0.0759504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.03444 | − | 21.6498i | −0.342838 | − | 1.05515i | −0.962731 | − | 0.270460i | \(-0.912824\pi\) |
0.619893 | − | 0.784686i | \(-0.287176\pi\) | |||||||
\(422\) | 3.24920 | − | 1.05573i | 0.158168 | − | 0.0513920i | ||||
\(423\) | −1.00406 | + | 1.38197i | −0.0488189 | + | 0.0671935i | ||||
\(424\) | 2.09017 | 0.101508 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.52786 | −0.267826 | ||||||||
\(427\) | 4.25325 | − | 5.85410i | 0.205829 | − | 0.283300i | ||||
\(428\) | −11.0494 | + | 3.59017i | −0.534093 | + | 0.173537i | ||||
\(429\) | −7.23607 | − | 22.2703i | −0.349361 | − | 1.07522i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.20163 | − | 16.0090i | 0.250554 | − | 0.771124i | −0.744120 | − | 0.668046i | \(-0.767131\pi\) |
0.994673 | − | 0.103078i | \(-0.0328692\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −14.7476 | − | 4.79180i | −0.708726 | − | 0.230279i | −0.0675976 | − | 0.997713i | \(-0.521533\pi\) |
−0.641128 | + | 0.767434i | \(0.721533\pi\) | |||||||
\(434\) | 14.0172 | − | 10.1841i | 0.672848 | − | 0.488853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9443 | − | 10.1311i | −0.667810 | − | 0.485192i | ||||
\(437\) | 15.0049 | + | 20.6525i | 0.717782 | + | 0.987942i | ||||
\(438\) | −2.07363 | − | 2.85410i | −0.0990817 | − | 0.136374i | ||||
\(439\) | −19.0172 | − | 13.8168i | −0.907642 | − | 0.659441i | 0.0327751 | − | 0.999463i | \(-0.489566\pi\) |
−0.940418 | + | 0.340022i | \(0.889566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.118034 | − | 0.0857567i | 0.00562067 | − | 0.00408365i | ||||
\(442\) | −7.60845 | − | 2.47214i | −0.361897 | − | 0.117588i | ||||
\(443\) | − | 16.6180i | − | 0.789547i | −0.918779 | − | 0.394773i | \(-0.870823\pi\) | ||
0.918779 | − | 0.394773i | \(-0.129177\pi\) | |||||||
\(444\) | 2.47214 | − | 7.60845i | 0.117322 | − | 0.361081i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.50000 | − | 7.69421i | −0.118378 | − | 0.364331i | ||||
\(447\) | 21.0090 | − | 6.82624i | 0.993692 | − | 0.322870i | ||||
\(448\) | −1.53884 | + | 2.11803i | −0.0727034 | + | 0.100068i | ||||
\(449\) | 27.7082 | 1.30763 | 0.653815 | − | 0.756654i | \(-0.273167\pi\) | ||||
0.653815 | + | 0.756654i | \(0.273167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6525 | 0.972487 | ||||||||
\(452\) | −11.3067 | + | 15.5623i | −0.531821 | + | 0.731989i | ||||
\(453\) | −17.4293 | + | 5.66312i | −0.818899 | + | 0.266077i | ||||
\(454\) | 6.88197 | + | 21.1805i | 0.322987 | + | 0.994051i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.76393 | − | 5.42882i | 0.0826037 | − | 0.254228i | ||||
\(457\) | − | 4.09017i | − | 0.191330i | −0.995414 | − | 0.0956650i | \(-0.969502\pi\) | ||
0.995414 | − | 0.0956650i | \(-0.0304978\pi\) | |||||||
\(458\) | 5.25731 | + | 1.70820i | 0.245658 | + | 0.0798191i | ||||
\(459\) | −1.00000 | + | 0.726543i | −0.0466760 | + | 0.0339121i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.11803 | − | 4.44501i | −0.284945 | − | 0.207025i | 0.436126 | − | 0.899885i | \(-0.356350\pi\) |
−0.721072 | + | 0.692861i | \(0.756350\pi\) | |||||||
\(462\) | 5.56758 | + | 7.66312i | 0.259027 | + | 0.356521i | ||||
\(463\) | −13.4208 | − | 18.4721i | −0.623717 | − | 0.858473i | 0.373900 | − | 0.927469i | \(-0.378020\pi\) |
−0.997617 | + | 0.0689961i | \(0.978020\pi\) | |||||||
\(464\) | 6.85410 | + | 4.97980i | 0.318194 | + | 0.231181i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0902 | + | 10.9637i | −0.699039 | + | 0.507881i | ||||
\(467\) | 10.1514 | + | 3.29837i | 0.469749 | + | 0.152631i | 0.534320 | − | 0.845283i | \(-0.320568\pi\) |
−0.0645710 | + | 0.997913i | \(0.520568\pi\) | |||||||
\(468\) | 6.47214i | 0.299175i | ||||||||
\(469\) | 1.23607 | − | 3.80423i | 0.0570763 | − | 0.175663i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.67376 | − | 8.22899i | −0.123200 | − | 0.379172i | ||||
\(472\) | 3.44095 | − | 1.11803i | 0.158383 | − | 0.0514617i | ||||
\(473\) | 16.3925 | − | 22.5623i | 0.753727 | − | 1.03742i | ||||
\(474\) | −5.61803 | −0.258045 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.23607 | 0.148325 | ||||||||
\(477\) | −1.22857 | + | 1.69098i | −0.0562524 | + | 0.0774248i | ||||
\(478\) | 11.6902 | − | 3.79837i | 0.534697 | − | 0.173734i | ||||
\(479\) | 9.00000 | + | 27.6992i | 0.411220 | + | 1.26561i | 0.915588 | + | 0.402117i | \(0.131726\pi\) |
−0.504368 | + | 0.863489i | \(0.668274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | + | 49.2429i | −0.729537 | + | 2.24528i | ||||
\(482\) | 9.56231i | 0.435551i | ||||||||
\(483\) | 11.1352 | + | 3.61803i | 0.506667 | + | 0.164626i | ||||
\(484\) | 1.69098 | − | 1.22857i | 0.0768629 | − | 0.0558441i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | −10.4616 | − | 14.3992i | −0.474061 | − | 0.652489i | 0.503289 | − | 0.864118i | \(-0.332123\pi\) |
−0.977350 | + | 0.211629i | \(0.932123\pi\) | |||||||
\(488\) | 1.62460 | + | 2.23607i | 0.0735421 | + | 0.101222i | ||||
\(489\) | 0.381966 | + | 0.277515i | 0.0172731 | + | 0.0125496i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.4443 | − | 14.8536i | 0.922637 | − | 0.670335i | −0.0215419 | − | 0.999768i | \(-0.506858\pi\) |
0.944179 | + | 0.329433i | \(0.106858\pi\) | |||||||
\(492\) | −5.42882 | − | 1.76393i | −0.244750 | − | 0.0795242i | ||||
\(493\) | − | 10.4721i | − | 0.471641i | ||||||
\(494\) | −11.4164 | + | 35.1361i | −0.513648 | + | 1.58085i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.04508 | + | 6.29412i | 0.0918270 | + | 0.282615i | ||||
\(497\) | −13.7638 | + | 4.47214i | −0.617392 | + | 0.200603i | ||||
\(498\) | 1.26133 | − | 1.73607i | 0.0565214 | − | 0.0777951i | ||||
\(499\) | −35.5967 | −1.59353 | −0.796765 | − | 0.604290i | \(-0.793457\pi\) | ||||
−0.796765 | + | 0.604290i | \(0.793457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7082 | −0.523084 | ||||||||
\(502\) | 7.97172 | − | 10.9721i | 0.355795 | − | 0.489710i | ||||
\(503\) | 22.7194 | − | 7.38197i | 1.01301 | − | 0.329146i | 0.244955 | − | 0.969534i | \(-0.421227\pi\) |
0.768051 | + | 0.640389i | \(0.221227\pi\) | |||||||
\(504\) | −0.809017 | − | 2.48990i | −0.0360365 | − | 0.110909i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.00000 | − | 15.3884i | 0.222277 | − | 0.684099i | ||||
\(507\) | − | 28.8885i | − | 1.28299i | ||||||
\(508\) | −12.9515 | − | 4.20820i | −0.574631 | − | 0.186709i | ||||
\(509\) | −14.1631 | + | 10.2901i | −0.627769 | + | 0.456101i | −0.855627 | − | 0.517593i | \(-0.826828\pi\) |
0.227857 | + | 0.973694i | \(0.426828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.47214 | − | 5.42882i | −0.330548 | − | 0.240157i | ||||
\(512\) | −0.587785 | − | 0.809017i | −0.0259767 | − | 0.0357538i | ||||
\(513\) | 3.35520 | + | 4.61803i | 0.148136 | + | 0.203891i | ||||
\(514\) | −17.7984 | − | 12.9313i | −0.785053 | − | 0.570374i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.23607 | + | 4.53077i | −0.274528 | + | 0.199456i | ||||
\(517\) | 5.87785 | + | 1.90983i | 0.258508 | + | 0.0839942i | ||||
\(518\) | − | 20.9443i | − | 0.920238i | ||||||
\(519\) | 1.57295 | − | 4.84104i | 0.0690448 | − | 0.212498i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.38197 | + | 13.4863i | 0.191977 | + | 0.590846i | 0.999999 | + | 0.00169226i | \(0.000538663\pi\) |
−0.808021 | + | 0.589153i | \(0.799461\pi\) | |||||||
\(522\) | −8.05748 | + | 2.61803i | −0.352666 | + | 0.114588i | ||||
\(523\) | −6.49839 | + | 8.94427i | −0.284155 | + | 0.391106i | −0.927105 | − | 0.374803i | \(-0.877710\pi\) |
0.642950 | + | 0.765908i | \(0.277710\pi\) | |||||||
\(524\) | 17.8885 | 0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.7082 | −0.510502 | ||||||||
\(527\) | 4.80828 | − | 6.61803i | 0.209452 | − | 0.288286i | ||||
\(528\) | −3.44095 | + | 1.11803i | −0.149748 | + | 0.0486562i | ||||
\(529\) | 0.927051 | + | 2.85317i | 0.0403066 | + | 0.124051i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11803 | + | 3.44095i | −0.0485185 | + | 0.149325i | ||||
\(532\) | − | 14.9443i | − | 0.647916i | ||||||
\(533\) | 35.1361 | + | 11.4164i | 1.52191 | + | 0.494500i | ||||
\(534\) | −2.85410 | + | 2.07363i | −0.123509 | + | 0.0897346i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.23607 | + | 0.898056i | 0.0533900 | + | 0.0387901i | ||||
\(537\) | 5.79210 | + | 7.97214i | 0.249947 | + | 0.344023i | ||||
\(538\) | −5.34307 | − | 7.35410i | −0.230356 | − | 0.317058i | ||||
\(539\) | −0.427051 | − | 0.310271i | −0.0183944 | − | 0.0133643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1803 | − | 15.3884i | 0.910614 | − | 0.661600i | −0.0305561 | − | 0.999533i | \(-0.509728\pi\) |
0.941170 | + | 0.337933i | \(0.109728\pi\) | |||||||
\(542\) | −17.1518 | − | 5.57295i | −0.736732 | − | 0.239379i | ||||
\(543\) | − | 6.65248i | − | 0.285485i | ||||||
\(544\) | −0.381966 | + | 1.17557i | −0.0163767 | + | 0.0504022i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.23607 | + | 16.1150i | 0.224083 | + | 0.689657i | ||||
\(547\) | −9.23305 | + | 3.00000i | −0.394777 | + | 0.128271i | −0.499677 | − | 0.866212i | \(-0.666548\pi\) |
0.104900 | + | 0.994483i | \(0.466548\pi\) | |||||||
\(548\) | 7.15942 | − | 9.85410i | 0.305835 | − | 0.420946i | ||||
\(549\) | −2.76393 | −0.117962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.3607 | −2.06023 | ||||||||
\(552\) | −2.62866 | + | 3.61803i | −0.111883 | + | 0.153994i | ||||
\(553\) | −13.9883 | + | 4.54508i | −0.594844 | + | 0.193277i | ||||
\(554\) | −5.23607 | − | 16.1150i | −0.222459 | − | 0.684659i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.23607 | − | 9.95959i | 0.137240 | − | 0.422381i | ||||
\(557\) | − | 18.3262i | − | 0.776508i | −0.921552 | − | 0.388254i | \(-0.873078\pi\) | ||
0.921552 | − | 0.388254i | \(-0.126922\pi\) | |||||||
\(558\) | −6.29412 | − | 2.04508i | −0.266452 | − | 0.0865754i | ||||
\(559\) | 40.3607 | − | 29.3238i | 1.70707 | − | 1.24026i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.61803 | + | 2.62866i | 0.152754 | + | 0.110982i | ||||
\(562\) | −3.46120 | − | 4.76393i | −0.146002 | − | 0.200954i | ||||
\(563\) | 12.5025 | + | 17.2082i | 0.526917 | + | 0.725239i | 0.986657 | − | 0.162815i | \(-0.0520572\pi\) |
−0.459739 | + | 0.888054i | \(0.652057\pi\) | |||||||
\(564\) | −1.38197 | − | 1.00406i | −0.0581913 | − | 0.0422784i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.70820 | + | 2.69417i | −0.155867 | + | 0.113244i | ||||
\(567\) | 2.48990 | + | 0.809017i | 0.104566 | + | 0.0339755i | ||||
\(568\) | − | 5.52786i | − | 0.231944i | ||||||
\(569\) | 8.58359 | − | 26.4176i | 0.359843 | − | 1.10748i | −0.593305 | − | 0.804978i | \(-0.702177\pi\) |
0.953148 | − | 0.302505i | \(-0.0978228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.43769 | + | 7.50245i | 0.102014 | + | 0.313968i | 0.989018 | − | 0.147794i | \(-0.0472174\pi\) |
−0.887004 | + | 0.461762i | \(0.847217\pi\) | |||||||
\(572\) | 22.2703 | − | 7.23607i | 0.931169 | − | 0.302555i | ||||
\(573\) | 2.52265 | − | 3.47214i | 0.105385 | − | 0.145051i | ||||
\(574\) | −14.9443 | −0.623762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.27756 | − | 7.26393i | 0.219708 | − | 0.302401i | −0.684908 | − | 0.728629i | \(-0.740158\pi\) |
0.904616 | + | 0.426228i | \(0.140158\pi\) | |||||||
\(578\) | −14.7149 | + | 4.78115i | −0.612058 | + | 0.198870i | ||||
\(579\) | 5.51722 | + | 16.9803i | 0.229288 | + | 0.705676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73607 | − | 5.34307i | 0.0720242 | − | 0.221668i | ||||
\(582\) | 3.38197i | 0.140187i | ||||||||
\(583\) | 7.19218 | + | 2.33688i | 0.297870 | + | 0.0967837i | ||||
\(584\) | 2.85410 | − | 2.07363i | 0.118104 | − | 0.0858073i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.8713 | + | 12.9843i | 0.738258 | + | 0.536376i | ||||
\(587\) | 0.567541 | + | 0.781153i | 0.0234249 | + | 0.0322416i | 0.820569 | − | 0.571548i | \(-0.193657\pi\) |
−0.797144 | + | 0.603789i | \(0.793657\pi\) | |||||||
\(588\) | 0.0857567 | + | 0.118034i | 0.00353655 | + | 0.00486764i | ||||
\(589\) | −30.5623 | − | 22.2048i | −1.25930 | − | 0.914933i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.8262 | + | 10.0453i | −0.568735 | + | 0.413210i | ||||
\(592\) | 7.60845 | + | 2.47214i | 0.312705 | + | 0.101604i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 1.11803 | − | 3.44095i | 0.0458735 | − | 0.141184i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.82624 | + | 21.0090i | 0.279614 | + | 0.860562i | ||||
\(597\) | 18.5519 | − | 6.02786i | 0.759277 | − | 0.246704i | ||||
\(598\) | 17.0130 | − | 23.4164i | 0.695714 | − | 0.957568i | ||||
\(599\) | −0.472136 | −0.0192910 | −0.00964548 | − | 0.999953i | \(-0.503070\pi\) | ||||
−0.00964548 | + | 0.999953i | \(0.503070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.72949 | −0.315292 | −0.157646 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157646 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(602\) | −11.8617 | + | 16.3262i | −0.483447 | + | 0.665408i | ||||
\(603\) | −1.45309 | + | 0.472136i | −0.0591742 | + | 0.0192269i | ||||
\(604\) | −5.66312 | − | 17.4293i | −0.230429 | − | 0.709188i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.35410 | + | 4.16750i | −0.0550066 | + | 0.169293i | ||||
\(607\) | 6.56231i | 0.266356i | 0.991092 | + | 0.133178i | \(0.0425182\pi\) | ||||
−0.991092 | + | 0.133178i | \(0.957482\pi\) | |||||||
\(608\) | 5.42882 | + | 1.76393i | 0.220168 | + | 0.0715369i | ||||
\(609\) | −17.9443 | + | 13.0373i | −0.727139 | + | 0.528297i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.94427 | + | 6.49839i | 0.361847 | + | 0.262897i | ||||
\(612\) | −0.726543 | − | 1.00000i | −0.0293687 | − | 0.0404226i | ||||
\(613\) | 28.3602 | + | 39.0344i | 1.14546 | + | 1.57659i | 0.754669 | + | 0.656105i | \(0.227797\pi\) |
0.390788 | + | 0.920481i | \(0.372203\pi\) | |||||||
\(614\) | 8.09017 | + | 5.87785i | 0.326493 | + | 0.237211i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.66312 | + | 5.56758i | −0.308756 | + | 0.224324i | ||||
\(617\) | 2.00811 | + | 0.652476i | 0.0808436 | + | 0.0262677i | 0.349160 | − | 0.937063i | \(-0.386467\pi\) |
−0.268316 | + | 0.963331i | \(0.586467\pi\) | |||||||
\(618\) | 14.3262i | 0.576286i | ||||||||
\(619\) | 2.90983 | − | 8.95554i | 0.116956 | − | 0.359953i | −0.875394 | − | 0.483410i | \(-0.839398\pi\) |
0.992350 | + | 0.123457i | \(0.0393980\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38197 | − | 4.25325i | −0.0554564 | − | 0.170677i | ||||
\(622\) | 1.00406 | − | 0.326238i | 0.0402590 | − | 0.0130809i | ||||
\(623\) | −5.42882 | + | 7.47214i | −0.217501 | + | 0.299365i | ||||
\(624\) | −6.47214 | −0.259093 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2705 | −0.650300 | ||||||||
\(627\) | 12.1392 | − | 16.7082i | 0.484794 | − | 0.667261i | ||||
\(628\) | 8.22899 | − | 2.67376i | 0.328373 | − | 0.106695i | ||||
\(629\) | −3.05573 | − | 9.40456i | −0.121840 | − | 0.374985i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3607 | − | 44.1976i | 0.571690 | − | 1.75948i | −0.0754947 | − | 0.997146i | \(-0.524054\pi\) |
0.647184 | − | 0.762334i | \(-0.275946\pi\) | |||||||
\(632\) | − | 5.61803i | − | 0.223473i | ||||||
\(633\) | −3.24920 | − | 1.05573i | −0.129144 | − | 0.0419614i | ||||
\(634\) | −16.6353 | + | 12.0862i | −0.660670 | + | 0.480005i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.69098 | − | 1.22857i | −0.0670518 | − | 0.0487160i | ||||
\(637\) | −0.555029 | − | 0.763932i | −0.0219911 | − | 0.0302681i | ||||
\(638\) | 18.0171 | + | 24.7984i | 0.713303 | + | 0.981777i | ||||
\(639\) | 4.47214 | + | 3.24920i | 0.176915 | + | 0.128536i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1803 | − | 8.12299i | 0.441597 | − | 0.320839i | −0.344672 | − | 0.938723i | \(-0.612010\pi\) |
0.786269 | + | 0.617884i | \(0.212010\pi\) | |||||||
\(642\) | 11.0494 | + | 3.59017i | 0.436085 | + | 0.141693i | ||||
\(643\) | − | 21.8885i | − | 0.863200i | −0.902065 | − | 0.431600i | \(-0.857949\pi\) | ||
0.902065 | − | 0.431600i | \(-0.142051\pi\) | |||||||
\(644\) | −3.61803 | + | 11.1352i | −0.142571 | + | 0.438787i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.18034 | − | 6.71040i | −0.0857843 | − | 0.264017i | ||||
\(647\) | 21.8213 | − | 7.09017i | 0.857884 | − | 0.278743i | 0.153139 | − | 0.988205i | \(-0.451062\pi\) |
0.704744 | + | 0.709461i | \(0.251062\pi\) | |||||||
\(648\) | −0.587785 | + | 0.809017i | −0.0230904 | + | 0.0317812i | ||||
\(649\) | 13.0902 | 0.513834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3262 | −0.679069 | ||||||||
\(652\) | −0.277515 | + | 0.381966i | −0.0108683 | + | 0.0149589i | ||||
\(653\) | −3.66547 | + | 1.19098i | −0.143441 | + | 0.0466068i | −0.379858 | − | 0.925045i | \(-0.624027\pi\) |
0.236417 | + | 0.971652i | \(0.424027\pi\) | |||||||
\(654\) | 5.32624 | + | 16.3925i | 0.208272 | + | 0.640996i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.76393 | − | 5.42882i | 0.0688700 | − | 0.211960i | ||||
\(657\) | 3.52786i | 0.137635i | ||||||||
\(658\) | −4.25325 | − | 1.38197i | −0.165809 | − | 0.0538746i | ||||
\(659\) | −16.6803 | + | 12.1190i | −0.649774 | + | 0.472088i | −0.863194 | − | 0.504872i | \(-0.831540\pi\) |
0.213420 | + | 0.976960i | \(0.431540\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6525 | + | 17.9111i | 0.958870 | + | 0.696660i | 0.952888 | − | 0.303322i | \(-0.0980958\pi\) |
0.00598211 | + | 0.999982i | \(0.498096\pi\) | |||||||
\(662\) | 10.5801 | + | 14.5623i | 0.411209 | + | 0.565980i | ||||
\(663\) | 4.70228 | + | 6.47214i | 0.182622 | + | 0.251357i | ||||
\(664\) | 1.73607 | + | 1.26133i | 0.0673725 | + | 0.0489490i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.47214 | + | 4.70228i | −0.250790 | + | 0.182210i | ||||
\(667\) | 36.0341 | + | 11.7082i | 1.39525 | + | 0.453343i | ||||
\(668\) | − | 11.7082i | − | 0.453004i | ||||||
\(669\) | −2.50000 | + | 7.69421i | −0.0966556 | + | 0.297475i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.09017 | + | 9.51057i | 0.119295 | + | 0.367151i | ||||
\(672\) | 2.48990 | − | 0.809017i | 0.0960499 | − | 0.0312085i | ||||
\(673\) | 18.4863 | − | 25.4443i | 0.712596 | − | 0.980805i | −0.287141 | − | 0.957888i | \(-0.592705\pi\) |
0.999737 | − | 0.0229163i | \(-0.00729513\pi\) | |||||||
\(674\) | −0.909830 | −0.0350453 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | 17.0988 | − | 23.5344i | 0.657159 | − | 0.904502i | −0.342224 | − | 0.939618i | \(-0.611180\pi\) |
0.999383 | + | 0.0351163i | \(0.0111802\pi\) | |||||||
\(678\) | 18.2946 | − | 5.94427i | 0.702599 | − | 0.228288i | ||||
\(679\) | 2.73607 | + | 8.42075i | 0.105001 | + | 0.323159i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.88197 | − | 21.1805i | 0.263718 | − | 0.811639i | ||||
\(682\) | 23.9443i | 0.916874i | ||||||||
\(683\) | −31.8666 | − | 10.3541i | −1.21934 | − | 0.396189i | −0.372501 | − | 0.928032i | \(-0.621500\pi\) |
−0.846843 | + | 0.531843i | \(0.821500\pi\) | |||||||
\(684\) | −4.61803 | + | 3.35520i | −0.176575 | + | 0.128289i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.1353 | + | 10.9964i | 0.577867 | + | 0.419845i | ||||
\(687\) | −3.24920 | − | 4.47214i | −0.123965 | − | 0.170623i | ||||
\(688\) | −4.53077 | − | 6.23607i | −0.172734 | − | 0.237748i | ||||
\(689\) | 10.9443 | + | 7.95148i | 0.416944 | + | 0.302927i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.09017 | + | 6.60440i | −0.345806 | + | 0.251243i | −0.747108 | − | 0.664703i | \(-0.768558\pi\) |
0.401301 | + | 0.915946i | \(0.368558\pi\) | |||||||
\(692\) | 4.84104 | + | 1.57295i | 0.184029 | + | 0.0597945i | ||||
\(693\) | − | 9.47214i | − | 0.359817i | ||||||
\(694\) | −6.35410 | + | 19.5559i | −0.241198 | + | 0.742332i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.61803 | − | 8.05748i | −0.0992363 | − | 0.305418i | ||||
\(697\) | −6.71040 | + | 2.18034i | −0.254174 | + | 0.0825863i | ||||
\(698\) | 16.3925 | − | 22.5623i | 0.620464 | − | 0.853996i | ||||
\(699\) | 18.6525 | 0.705501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8328 | 1.54223 | 0.771117 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771117 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(702\) | 3.80423 | − | 5.23607i | 0.143581 | − | 0.197623i | ||||
\(703\) | −43.4306 | + | 14.1115i | −1.63802 | + | 0.532224i | ||||
\(704\) | −1.11803 | − | 3.44095i | −0.0421375 | − | 0.129686i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.09017 | + | 12.5882i | −0.153936 | + | 0.473765i | ||||
\(707\) | 11.4721i | 0.431454i | ||||||||
\(708\) | −3.44095 | − | 1.11803i | −0.129319 | − | 0.0420183i | ||||
\(709\) | −35.3607 | + | 25.6910i | −1.32800 | + | 0.964847i | −0.328203 | + | 0.944607i | \(0.606443\pi\) |
−0.999795 | + | 0.0202400i | \(0.993557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.54508 | + | 3.30220i | 0.170454 | + | 0.123842i | ||||
\(712\) | −2.07363 | − | 2.85410i | −0.0777124 | − | 0.106962i | ||||
\(713\) | 17.3965 | + | 23.9443i | 0.651505 | + | 0.896720i | ||||
\(714\) | −2.61803 | − | 1.90211i | −0.0979775 | − | 0.0711848i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.97214 | + | 5.79210i | −0.297933 | + | 0.216461i | ||||
\(717\) | −11.6902 | − | 3.79837i | −0.436578 | − | 0.141853i | ||||
\(718\) | − | 22.1803i | − | 0.827763i | ||||||
\(719\) | 5.12461 | − | 15.7719i | 0.191116 | − | 0.588194i | −0.808884 | − | 0.587968i | \(-0.799928\pi\) |
1.00000 | 0.000225882i | \(-7.19006e-5\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5902 | + | 35.6709i | 0.431640 | + | 1.32845i | ||||
\(722\) | −12.9188 | + | 4.19756i | −0.480787 | + | 0.156217i | ||||
\(723\) | 5.62058 | − | 7.73607i | 0.209032 | − | 0.287707i | ||||
\(724\) | 6.65248 | 0.247237 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.09017 | −0.0775735 | ||||||||
\(727\) | −5.04531 | + | 6.94427i | −0.187120 | + | 0.257549i | −0.892263 | − | 0.451517i | \(-0.850883\pi\) |
0.705142 | + | 0.709066i | \(0.250883\pi\) | |||||||
\(728\) | −16.1150 | + | 5.23607i | −0.597260 | + | 0.194062i | ||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.94427 | + | 9.06154i | −0.108898 | + | 0.335153i | ||||
\(732\) | − | 2.76393i | − | 0.102158i | ||||||
\(733\) | 34.1320 | + | 11.0902i | 1.26070 | + | 0.409625i | 0.861742 | − | 0.507346i | \(-0.169374\pi\) |
0.398953 | + | 0.916971i | \(0.369374\pi\) | |||||||
\(734\) | −24.7705 | + | 17.9968i | −0.914296 | + | 0.664275i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.61803 | − | 2.62866i | −0.133363 | − | 0.0968935i | ||||
\(737\) | 3.24920 | + | 4.47214i | 0.119686 | + | 0.164733i | ||||
\(738\) | 3.35520 | + | 4.61803i | 0.123507 | + | 0.169992i | ||||
\(739\) | −38.9787 | − | 28.3197i | −1.43386 | − | 1.04176i | −0.989283 | − | 0.146014i | \(-0.953356\pi\) |
−0.444573 | − | 0.895743i | \(-0.646644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.8885 | − | 21.7153i | 1.09798 | − | 0.797731i | ||||
\(742\) | −5.20431 | − | 1.69098i | −0.191056 | − | 0.0620779i | ||||
\(743\) | 39.0132i | 1.43125i | 0.698483 | + | 0.715627i | \(0.253859\pi\) | ||||
−0.698483 | + | 0.715627i | \(0.746141\pi\) | |||||||
\(744\) | 2.04508 | − | 6.29412i | 0.0749765 | − | 0.230754i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.56231 | − | 10.9637i | −0.130425 | − | 0.401408i | ||||
\(747\) | −2.04087 | + | 0.663119i | −0.0746715 | + | 0.0242623i | ||||
\(748\) | −2.62866 | + | 3.61803i | −0.0961132 | + | 0.132288i | ||||
\(749\) | 30.4164 | 1.11139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7984 | 0.904906 | 0.452453 | − | 0.891788i | \(-0.350549\pi\) | ||||
0.452453 | + | 0.891788i | \(0.350549\pi\) | |||||||
\(752\) | 1.00406 | − | 1.38197i | 0.0366142 | − | 0.0503951i | ||||
\(753\) | −12.8985 | + | 4.19098i | −0.470048 | + | 0.152728i | ||||
\(754\) | 16.9443 | + | 52.1491i | 0.617074 | + | 1.89916i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.809017 | + | 2.48990i | −0.0294237 | + | 0.0905567i | ||||
\(757\) | − | 17.1246i | − | 0.622405i | −0.950344 | − | 0.311202i | \(-0.899268\pi\) | ||
0.950344 | − | 0.311202i | \(-0.100732\pi\) | |||||||
\(758\) | 19.1926 | + | 6.23607i | 0.697108 | + | 0.226504i | ||||
\(759\) | −13.0902 | + | 9.51057i | −0.475143 | + | 0.345212i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.14590 | − | 0.832544i | −0.0415388 | − | 0.0301797i | 0.566822 | − | 0.823840i | \(-0.308173\pi\) |
−0.608361 | + | 0.793661i | \(0.708173\pi\) | |||||||
\(762\) | 8.00448 | + | 11.0172i | 0.289972 | + | 0.399112i | ||||
\(763\) | 26.5236 | + | 36.5066i | 0.960218 | + | 1.32163i | ||||
\(764\) | 3.47214 | + | 2.52265i | 0.125617 | + | 0.0912664i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.1803 | − | 11.7557i | 0.584619 | − | 0.424751i | ||||
\(767\) | 22.2703 | + | 7.23607i | 0.804135 | + | 0.261279i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −7.62868 | + | 23.4787i | −0.275097 | + | 0.846662i | 0.714097 | + | 0.700047i | \(0.246838\pi\) |
−0.989194 | + | 0.146615i | \(0.953162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.79837 | + | 20.9232i | 0.244837 | + | 0.753532i | ||||
\(772\) | −16.9803 | + | 5.51722i | −0.611133 | + | 0.198569i | ||||
\(773\) | 0.673542 | − | 0.927051i | 0.0242256 | − | 0.0333437i | −0.796732 | − | 0.604332i | \(-0.793440\pi\) |
0.820958 | + | 0.570989i | \(0.193440\pi\) | |||||||
\(774\) | 7.70820 | 0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.38197 | −0.121406 | ||||||||
\(777\) | −12.3107 | + | 16.9443i | −0.441645 | + | 0.607872i | ||||
\(778\) | −11.7759 | + | 3.82624i | −0.422188 | + | 0.137177i | ||||
\(779\) | 10.0689 | + | 30.9888i | 0.360755 | + | 1.11029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.18034 | − | 19.0211i | 0.221150 | − | 0.680630i | ||||
\(782\) | 5.52786i | 0.197676i | ||||||||
\(783\) | 8.05748 | + | 2.61803i | 0.287951 | + | 0.0935609i | ||||
\(784\) | −0.118034 | + | 0.0857567i | −0.00421550 | + | 0.00306274i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.4721 | − | 10.5146i | −0.516204 | − | 0.375044i | ||||
\(787\) | −16.4985 | − | 22.7082i | −0.588107 | − | 0.809460i | 0.406448 | − | 0.913674i | \(-0.366767\pi\) |
−0.994555 | + | 0.104214i | \(0.966767\pi\) | |||||||
\(788\) | −10.0453 | − | 13.8262i | −0.357851 | − | 0.492539i | ||||
\(789\) | 9.47214 | + | 6.88191i | 0.337217 | + | 0.245002i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.7426 | − | 29.6013i | 1.44864 | − | 1.05250i | ||||
\(792\) | 3.44095 | + | 1.11803i | 0.122269 | + | 0.0397276i | ||||
\(793\) | 17.8885i | 0.635241i | ||||||||
\(794\) | 9.50658 | − | 29.2582i | 0.337376 | − | 1.03834i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.02786 | + | 18.5519i | 0.213652 | + | 0.657553i | ||||
\(797\) | −1.43284 | + | 0.465558i | −0.0507538 | + | 0.0164909i | −0.334284 | − | 0.942472i | \(-0.608494\pi\) |
0.283530 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(798\) | −8.78402 | + | 12.0902i | −0.310951 | + | 0.427987i | ||||
\(799\) | −2.11146 | −0.0746979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.52786 | 0.124651 | ||||||||
\(802\) | 15.1109 | − | 20.7984i | 0.533585 | − | 0.734416i | ||||
\(803\) | 12.1392 | − | 3.94427i | 0.428384 | − | 0.139190i | ||||
\(804\) | −0.472136 | − | 1.45309i | −0.0166510 | − | 0.0512464i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2361 | + | 40.7364i | −0.466221 | + | 1.43488i | ||||
\(807\) | 9.09017i | 0.319989i | ||||||||
\(808\) | −4.16750 | − | 1.35410i | −0.146612 | − | 0.0476371i | ||||
\(809\) | −24.9443 | + | 18.1231i | −0.876994 | + | 0.637173i | −0.932454 | − | 0.361288i | \(-0.882337\pi\) |
0.0554606 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.61803 | + | 3.35520i | 0.162161 | + | 0.117817i | 0.665906 | − | 0.746035i | \(-0.268045\pi\) |
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(812\) | −13.0373 | − | 17.9443i | −0.457519 | − | 0.629720i | ||||
\(813\) | 10.6004 | + | 14.5902i | 0.371772 | + | 0.511700i | ||||
\(814\) | 23.4164 | + | 17.0130i | 0.820745 | + | 0.596306i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | − | 0.726543i | 0.0350070 | − | 0.0254341i | ||||
\(817\) | 41.8465 | + | 13.5967i | 1.46402 | + | 0.475690i | ||||
\(818\) | − | 5.79837i | − | 0.202735i | ||||||
\(819\) | 5.23607 | − | 16.1150i | 0.182963 | − | 0.563102i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9336 | − | 42.8833i | −0.486287 | − | 1.49664i | −0.830108 | − | 0.557602i | \(-0.811721\pi\) |
0.343821 | − | 0.939035i | \(-0.388279\pi\) | |||||||
\(822\) | −11.5842 | + | 3.76393i | −0.404045 | + | 0.131282i | ||||
\(823\) | −1.74311 | + | 2.39919i | −0.0607610 | + | 0.0836304i | −0.838316 | − | 0.545184i | \(-0.816460\pi\) |
0.777555 | + | 0.628815i | \(0.216460\pi\) | |||||||
\(824\) | −14.3262 | −0.499078 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.47214 | −0.329578 | ||||||||
\(827\) | 25.9233 | − | 35.6803i | 0.901441 | − | 1.24073i | −0.0685652 | − | 0.997647i | \(-0.521842\pi\) |
0.970006 | − | 0.243080i | \(-0.0781579\pi\) | |||||||
\(828\) | 4.25325 | − | 1.38197i | 0.147811 | − | 0.0480266i | ||||
\(829\) | −8.00000 | − | 24.6215i | −0.277851 | − | 0.855139i | −0.988451 | − | 0.151542i | \(-0.951576\pi\) |
0.710599 | − | 0.703597i | \(-0.248424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.23607 | + | 16.1150i | −0.181637 | + | 0.559022i | ||||
\(832\) | − | 6.47214i | − | 0.224381i | ||||||
\(833\) | 0.171513 | + | 0.0557281i | 0.00594259 | + | 0.00193086i | ||||
\(834\) | −8.47214 | + | 6.15537i | −0.293366 | + | 0.213143i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.7082 | + | 12.1392i | 0.577865 | + | 0.419844i | ||||
\(837\) | 3.88998 | + | 5.35410i | 0.134457 | + | 0.185065i | ||||
\(838\) | −1.81636 | − | 2.50000i | −0.0627450 | − | 0.0863611i | ||||
\(839\) | 5.14590 | + | 3.73871i | 0.177656 | + | 0.129075i | 0.673060 | − | 0.739588i | \(-0.264980\pi\) |
−0.495403 | + | 0.868663i | \(0.664980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.6074 | + | 25.1437i | −1.19336 | + | 0.867026i | ||||
\(842\) | −21.6498 | − | 7.03444i | −0.746101 | − | 0.242423i | ||||
\(843\) | 5.88854i | 0.202812i | ||||||||
\(844\) | 1.05573 | − | 3.24920i | 0.0363397 | − | 0.111842i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.527864 | + | 1.62460i | 0.0181483 | + | 0.0558548i | ||||
\(847\) | −5.20431 | + | 1.69098i | −0.178822 | + | 0.0581029i | ||||
\(848\) | 1.22857 | − | 1.69098i | 0.0421893 | − | 0.0580686i | ||||
\(849\) | 4.58359 | 0.157308 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7771 | 1.22642 | ||||||||
\(852\) | −3.24920 | + | 4.47214i | −0.111316 | + | 0.153213i | ||||
\(853\) | −41.4630 | + | 13.4721i | −1.41967 | + | 0.461277i | −0.915496 | − | 0.402328i | \(-0.868201\pi\) |
−0.504169 | + | 0.863605i | \(0.668201\pi\) | |||||||
\(854\) | −2.23607 | − | 6.88191i | −0.0765167 | − | 0.235494i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.59017 | + | 11.0494i | −0.122709 | + | 0.377661i | ||||
\(857\) | − | 16.0689i | − | 0.548903i | −0.961601 | − | 0.274451i | \(-0.911504\pi\) | ||
0.961601 | − | 0.274451i | \(-0.0884962\pi\) | |||||||
\(858\) | −22.2703 | − | 7.23607i | −0.760296 | − | 0.247035i | ||||
\(859\) | −1.85410 | + | 1.34708i | −0.0632611 | + | 0.0459619i | −0.618966 | − | 0.785417i | \(-0.712448\pi\) |
0.555705 | + | 0.831379i | \(0.312448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0902 | + | 8.78402i | 0.412032 | + | 0.299359i | ||||
\(862\) | −9.89408 | − | 13.6180i | −0.336994 | − | 0.463832i | ||||
\(863\) | −5.98385 | − | 8.23607i | −0.203693 | − | 0.280359i | 0.694934 | − | 0.719074i | \(-0.255434\pi\) |
−0.898626 | + | 0.438715i | \(0.855434\pi\) | |||||||
\(864\) | −0.809017 | − | 0.587785i | −0.0275233 | − | 0.0199969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.5451 | + | 9.11454i | −0.426299 | + | 0.309725i | ||||
\(867\) | 14.7149 | + | 4.78115i | 0.499743 | + | 0.162376i | ||||
\(868\) | − | 17.3262i | − | 0.588091i | ||||||
\(869\) | 6.28115 | − | 19.3314i | 0.213074 | − | 0.655773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.05573 | + | 9.40456i | 0.103539 | + | 0.318661i | ||||
\(872\) | −16.3925 | + | 5.32624i | −0.555119 | + | 0.180369i | ||||
\(873\) | 1.98787 | − | 2.73607i | 0.0672792 | − | 0.0926019i | ||||
\(874\) | 25.5279 | 0.863493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.52786 | −0.119195 | ||||||||
\(877\) | −21.8213 | + | 30.0344i | −0.736853 | + | 1.01419i | 0.261941 | + | 0.965084i | \(0.415638\pi\) |
−0.998794 | + | 0.0491070i | \(0.984362\pi\) | |||||||
\(878\) | −22.3561 | + | 7.26393i | −0.754481 | + | 0.245146i | ||||
\(879\) | −6.82624 | − | 21.0090i | −0.230243 | − | 0.708616i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.29180 | + | 22.4418i | −0.245667 | + | 0.756085i | 0.749859 | + | 0.661597i | \(0.230121\pi\) |
−0.995526 | + | 0.0944874i | \(0.969879\pi\) | |||||||
\(882\) | − | 0.145898i | − | 0.00491264i | ||||||
\(883\) | 28.5972 | + | 9.29180i | 0.962373 | + | 0.312694i | 0.747733 | − | 0.663999i | \(-0.231142\pi\) |
0.214640 | + | 0.976693i | \(0.431142\pi\) | |||||||
\(884\) | −6.47214 | + | 4.70228i | −0.217681 | + | 0.158155i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.4443 | − | 9.76784i | −0.451669 | − | 0.328157i | ||||
\(887\) | −13.7638 | − | 18.9443i | −0.462144 | − | 0.636086i | 0.512808 | − | 0.858503i | \(-0.328605\pi\) |
−0.974952 | + | 0.222417i | \(0.928605\pi\) | |||||||
\(888\) | −4.70228 | − | 6.47214i | −0.157798 | − | 0.217191i | ||||
\(889\) | 28.8435 | + | 20.9560i | 0.967379 | + | 0.702842i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.92705 | + | 2.12663i | −0.0980599 | + | 0.0712447i | ||||
\(892\) | −7.69421 | − | 2.50000i | −0.257621 | − | 0.0837062i | ||||
\(893\) | 9.75078i | 0.326297i | ||||||||
\(894\) | 6.82624 | − | 21.0090i | 0.228304 | − | 0.702646i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.809017 | + | 2.48990i | 0.0270274 | + | 0.0831817i | ||||
\(897\) | −27.5276 | + | 8.94427i | −0.919121 | + | 0.298641i | ||||
\(898\) | 16.2865 | − | 22.4164i | 0.543487 | − | 0.748045i | ||||
\(899\) | −56.0689 | −1.87000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.58359 | −0.0860719 | ||||||||
\(902\) | 12.1392 | − | 16.7082i | 0.404192 | − | 0.556322i | ||||
\(903\) | 19.1926 | − | 6.23607i | 0.638691 | − | 0.207523i | ||||
\(904\) | 5.94427 | + | 18.2946i | 0.197704 | + | 0.608469i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.66312 | + | 17.4293i | −0.188145 | + | 0.579049i | ||||
\(907\) | 30.4721i | 1.01181i | 0.862589 | + | 0.505905i | \(0.168841\pi\) | ||||
−0.862589 | + | 0.505905i | \(0.831159\pi\) | |||||||
\(908\) | 21.1805 | + | 6.88197i | 0.702900 | + | 0.228386i | ||||
\(909\) | 3.54508 | − | 2.57565i | 0.117583 | − | 0.0854291i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7082 | − | 10.6861i | −0.487305 | − | 0.354047i | 0.316842 | − | 0.948478i | \(-0.397377\pi\) |
−0.804147 | + | 0.594431i | \(0.797377\pi\) | |||||||
\(912\) | −3.35520 | − | 4.61803i | −0.111102 | − | 0.152918i | ||||
\(913\) | 4.56352 | + | 6.28115i | 0.151031 | + | 0.207876i | ||||
\(914\) | −3.30902 | − | 2.40414i | −0.109453 | − | 0.0795219i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.47214 | − | 3.24920i | 0.147764 | − | 0.107356i | ||||
\(917\) | −44.5407 | − | 14.4721i | −1.47086 | − | 0.477912i | ||||
\(918\) | 1.23607i | 0.0407963i | ||||||||
\(919\) | 12.5836 | − | 38.7283i | 0.415094 | − | 1.27753i | −0.497072 | − | 0.867709i | \(-0.665592\pi\) |
0.912166 | − | 0.409820i | \(-0.134408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.09017 | − | 9.51057i | −0.101825 | − | 0.313384i | ||||
\(922\) | −7.19218 | + | 2.33688i | −0.236862 | + | 0.0769611i | ||||
\(923\) | 21.0292 | − | 28.9443i | 0.692186 | − | 0.952712i | ||||
\(924\) | 9.47214 | 0.311610 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.8328 | −0.750333 | ||||||||
\(927\) | 8.42075 | − | 11.5902i | 0.276574 | − | 0.380671i | ||||
\(928\) | 8.05748 | − | 2.61803i | 0.264500 | − | 0.0859412i | ||||
\(929\) | 5.87539 | + | 18.0826i | 0.192765 | + | 0.593270i | 0.999995 | + | 0.00303360i | \(0.000965627\pi\) |
−0.807230 | + | 0.590237i | \(0.799034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.257354 | − | 0.792055i | 0.00843444 | − | 0.0259585i | ||||
\(932\) | 18.6525i | 0.610982i | ||||||||
\(933\) | −1.00406 | − | 0.326238i | −0.0328714 | − | 0.0106806i | ||||
\(934\) | 8.63525 | − | 6.27388i | 0.282554 | − | 0.205288i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.23607 | + | 3.80423i | 0.171146 | + | 0.124345i | ||||
\(937\) | 5.10604 | + | 7.02786i | 0.166807 | + | 0.229590i | 0.884235 | − | 0.467043i | \(-0.154681\pi\) |
−0.717428 | + | 0.696633i | \(0.754681\pi\) | |||||||
\(938\) | −2.35114 | − | 3.23607i | −0.0767675 | − | 0.105661i | ||||
\(939\) | 13.1631 | + | 9.56357i | 0.429562 | + | 0.312095i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.59017 | − | 2.60841i | 0.117036 | − | 0.0850318i | −0.527728 | − | 0.849414i | \(-0.676956\pi\) |
0.644764 | + | 0.764382i | \(0.276956\pi\) | |||||||
\(942\) | −8.22899 | − | 2.67376i | −0.268115 | − | 0.0871159i | ||||
\(943\) | − | 25.5279i | − | 0.831302i | ||||||
\(944\) | 1.11803 | − | 3.44095i | 0.0363889 | − | 0.111994i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.61803 | − | 26.5236i | −0.280196 | − | 0.862356i | ||||
\(947\) | 31.9196 | − | 10.3713i | 1.03725 | − | 0.337023i | 0.259597 | − | 0.965717i | \(-0.416410\pi\) |
0.777652 | + | 0.628694i | \(0.216410\pi\) | |||||||
\(948\) | −3.30220 | + | 4.54508i | −0.107250 | + | 0.147617i | ||||
\(949\) | 22.8328 | 0.741185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | 1.90211 | − | 2.61803i | 0.0616478 | − | 0.0848510i | ||||
\(953\) | 5.04531 | − | 1.63932i | 0.163434 | − | 0.0531028i | −0.226157 | − | 0.974091i | \(-0.572616\pi\) |
0.389591 | + | 0.920988i | \(0.372616\pi\) | |||||||
\(954\) | 0.645898 | + | 1.98787i | 0.0209117 | + | 0.0643597i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.79837 | − | 11.6902i | 0.122848 | − | 0.378088i | ||||
\(957\) | − | 30.6525i | − | 0.990854i | ||||||
\(958\) | 27.6992 | + | 9.00000i | 0.894919 | + | 0.290777i | ||||
\(959\) | −25.7984 | + | 18.7436i | −0.833073 | + | 0.605263i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3541 | − | 7.52270i | −0.334003 | − | 0.242668i | ||||
\(962\) | 30.4338 | + | 41.8885i | 0.981225 | + | 1.35054i | ||||
\(963\) | −6.82891 | − | 9.39919i | −0.220059 | − | 0.302885i | ||||
\(964\) | 7.73607 | + | 5.62058i | 0.249162 | + | 0.181027i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.47214 | − | 6.88191i | 0.304761 | − | 0.221422i | ||||
\(967\) | 10.3759 | + | 3.37132i | 0.333665 | + | 0.108414i | 0.471058 | − | 0.882102i | \(-0.343872\pi\) |
−0.137393 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(968\) | − | 2.09017i | − | 0.0671806i | ||||||
\(969\) | −2.18034 | + | 6.71040i | −0.0700426 | + | 0.215569i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.39261 | − | 13.5191i | −0.140966 | − | 0.433847i | 0.855505 | − | 0.517795i | \(-0.173247\pi\) |
−0.996470 | + | 0.0839479i | \(0.973247\pi\) | |||||||
\(972\) | 0.951057 | − | 0.309017i | 0.0305052 | − | 0.00991172i | ||||
\(973\) | −16.1150 | + | 22.1803i | −0.516622 | + | 0.711069i | ||||
\(974\) | −17.7984 | −0.570297 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76393 | 0.0884713 | ||||||||
\(977\) | −0.449028 | + | 0.618034i | −0.0143657 | + | 0.0197727i | −0.816139 | − | 0.577855i | \(-0.803890\pi\) |
0.801774 | + | 0.597628i | \(0.203890\pi\) | |||||||
\(978\) | 0.449028 | − | 0.145898i | 0.0143583 | − | 0.00466530i | ||||
\(979\) | −3.94427 | − | 12.1392i | −0.126059 | − | 0.387971i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.32624 | − | 16.3925i | 0.170054 | − | 0.523371i | ||||
\(982\) | − | 25.2705i | − | 0.806414i | ||||||
\(983\) | −38.2138 | − | 12.4164i | −1.21883 | − | 0.396022i | −0.372174 | − | 0.928163i | \(-0.621388\pi\) |
−0.846656 | + | 0.532141i | \(0.821388\pi\) | |||||||
\(984\) | −4.61803 | + | 3.35520i | −0.147218 | + | 0.106960i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.47214 | − | 6.15537i | −0.269808 | − | 0.196027i | ||||
\(987\) | 2.62866 | + | 3.61803i | 0.0836710 | + | 0.115163i | ||||
\(988\) | 21.7153 | + | 29.8885i | 0.690856 | + | 0.950881i | ||||
\(989\) | −27.8885 | − | 20.2622i | −0.886804 | − | 0.644301i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8262 | + | 17.3108i | −0.756865 | + | 0.549895i | −0.897947 | − | 0.440103i | \(-0.854942\pi\) |
0.141082 | + | 0.989998i | \(0.454942\pi\) | |||||||
\(992\) | 6.29412 | + | 2.04508i | 0.199839 | + | 0.0649315i | ||||
\(993\) | − | 18.0000i | − | 0.571213i | ||||||
\(994\) | −4.47214 | + | 13.7638i | −0.141848 | + | 0.436562i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.663119 | − | 2.04087i | −0.0210117 | − | 0.0646675i | ||||
\(997\) | 5.32282 | − | 1.72949i | 0.168576 | − | 0.0547735i | −0.223513 | − | 0.974701i | \(-0.571753\pi\) |
0.392089 | + | 0.919927i | \(0.371753\pi\) | |||||||
\(998\) | −20.9232 | + | 28.7984i | −0.662314 | + | 0.911597i | ||||
\(999\) | 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 | 750.2.h.b.49.2 | 8 | ||
5.2 | odd | 4 | 750.2.g.b.451.1 | 4 | |||
5.3 | odd | 4 | 150.2.g.a.91.1 | yes | 4 | ||
5.4 | even | 2 | inner | 750.2.h.b.49.1 | 8 | ||
15.8 | even | 4 | 450.2.h.c.91.1 | 4 | |||
25.2 | odd | 20 | 750.2.g.b.301.1 | 4 | |||
25.6 | even | 5 | 3750.2.c.b.1249.4 | 4 | |||
25.8 | odd | 20 | 3750.2.a.f.1.2 | 2 | |||
25.11 | even | 5 | inner | 750.2.h.b.199.1 | 8 | ||
25.14 | even | 10 | inner | 750.2.h.b.199.2 | 8 | ||
25.17 | odd | 20 | 3750.2.a.d.1.1 | 2 | |||
25.19 | even | 10 | 3750.2.c.b.1249.1 | 4 | |||
25.23 | odd | 20 | 150.2.g.a.61.1 | ✓ | 4 | ||
75.23 | even | 20 | 450.2.h.c.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.61.1 | ✓ | 4 | 25.23 | odd | 20 | ||
150.2.g.a.91.1 | yes | 4 | 5.3 | odd | 4 | ||
450.2.h.c.91.1 | 4 | 15.8 | even | 4 | |||
450.2.h.c.361.1 | 4 | 75.23 | even | 20 | |||
750.2.g.b.301.1 | 4 | 25.2 | odd | 20 | |||
750.2.g.b.451.1 | 4 | 5.2 | odd | 4 | |||
750.2.h.b.49.1 | 8 | 5.4 | even | 2 | inner | ||
750.2.h.b.49.2 | 8 | 1.1 | even | 1 | trivial | ||
750.2.h.b.199.1 | 8 | 25.11 | even | 5 | inner | ||
750.2.h.b.199.2 | 8 | 25.14 | even | 10 | inner | ||
3750.2.a.d.1.1 | 2 | 25.17 | odd | 20 | |||
3750.2.a.f.1.2 | 2 | 25.8 | odd | 20 | |||
3750.2.c.b.1249.1 | 4 | 25.19 | even | 10 | |||
3750.2.c.b.1249.4 | 4 | 25.6 | even | 5 |