Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Character | \(\chi\) | \(=\) | 950.293 |
Dual form | 950.2.q.g.107.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | 0.186170 | + | 0.694795i | 0.107485 | + | 0.401140i | 0.998615 | − | 0.0526080i | \(-0.0167534\pi\) |
−0.891130 | + | 0.453748i | \(0.850087\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.359652 | − | 0.622936i | −0.146827 | − | 0.254312i | ||||
\(7\) | −1.01416 | + | 1.01416i | −0.383315 | + | 0.383315i | −0.872295 | − | 0.488980i | \(-0.837369\pi\) |
0.488980 | + | 0.872295i | \(0.337369\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.15000 | − | 1.24130i | 0.716665 | − | 0.413767i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.38827 | 0.720089 | 0.360045 | − | 0.932935i | \(-0.382761\pi\) | ||||
0.360045 | + | 0.932935i | \(0.382761\pi\) | |||||||
\(12\) | 0.508625 | + | 0.508625i | 0.146827 | + | 0.146827i | ||||
\(13\) | 2.90425 | + | 0.778192i | 0.805494 | + | 0.215831i | 0.637995 | − | 0.770041i | \(-0.279764\pi\) |
0.167499 | + | 0.985872i | \(0.446431\pi\) | |||||||
\(14\) | 0.717117 | − | 1.24208i | 0.191658 | − | 0.331961i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −1.22959 | − | 4.58888i | −0.298219 | − | 1.11297i | −0.938627 | − | 0.344933i | \(-0.887902\pi\) |
0.640408 | − | 0.768035i | \(-0.278765\pi\) | |||||||
\(18\) | −1.75546 | + | 1.75546i | −0.413767 | + | 0.413767i | ||||
\(19\) | −3.35250 | + | 2.78581i | −0.769117 | + | 0.639108i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.893436 | − | 0.515825i | −0.194964 | − | 0.112562i | ||||
\(22\) | −2.30689 | + | 0.618129i | −0.491830 | + | 0.131785i | ||||
\(23\) | 1.35931 | − | 5.07300i | 0.283435 | − | 1.05779i | −0.666541 | − | 0.745469i | \(-0.732226\pi\) |
0.949975 | − | 0.312325i | \(-0.101108\pi\) | |||||||
\(24\) | −0.622936 | − | 0.359652i | −0.127156 | − | 0.0734137i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00670 | −0.589663 | ||||||||
\(27\) | 2.78859 | + | 2.78859i | 0.536664 | + | 0.536664i | ||||
\(28\) | −0.371207 | + | 1.38536i | −0.0701516 | + | 0.261809i | ||||
\(29\) | 4.88449 | + | 8.46019i | 0.907027 | + | 1.57102i | 0.818172 | + | 0.574973i | \(0.194988\pi\) |
0.0888552 | + | 0.996045i | \(0.471679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.0965i | − | 1.81339i | −0.421791 | − | 0.906693i | \(-0.638598\pi\) | ||
0.421791 | − | 0.906693i | \(-0.361402\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 0.444623 | + | 1.65935i | 0.0773988 | + | 0.288856i | ||||
\(34\) | 2.37538 | + | 4.11428i | 0.407374 | + | 0.705593i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.24130 | − | 2.15000i | 0.206883 | − | 0.358333i | ||||
\(37\) | 2.87570 | + | 2.87570i | 0.472762 | + | 0.472762i | 0.902807 | − | 0.430046i | \(-0.141503\pi\) |
−0.430046 | + | 0.902807i | \(0.641503\pi\) | |||||||
\(38\) | 2.51725 | − | 3.55857i | 0.408352 | − | 0.577277i | ||||
\(39\) | 2.16273i | 0.346314i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.97985 | + | 4.02982i | 1.09007 | + | 0.629352i | 0.933595 | − | 0.358330i | \(-0.116654\pi\) |
0.156475 | + | 0.987682i | \(0.449987\pi\) | |||||||
\(42\) | 0.996498 | + | 0.267011i | 0.153763 | + | 0.0412007i | ||||
\(43\) | −1.76075 | + | 0.471793i | −0.268513 | + | 0.0719477i | −0.390563 | − | 0.920576i | \(-0.627720\pi\) |
0.122051 | + | 0.992524i | \(0.461053\pi\) | |||||||
\(44\) | 2.06830 | − | 1.19413i | 0.311808 | − | 0.180022i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.25195i | 0.774358i | ||||||||
\(47\) | 0.349235 | + | 0.0935773i | 0.0509412 | + | 0.0136496i | 0.284200 | − | 0.958765i | \(-0.408272\pi\) |
−0.233258 | + | 0.972415i | \(0.574939\pi\) | |||||||
\(48\) | 0.694795 | + | 0.186170i | 0.100285 | + | 0.0268713i | ||||
\(49\) | 4.94297i | 0.706139i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.95942 | − | 1.70862i | 0.414402 | − | 0.239255i | ||||
\(52\) | 2.90425 | − | 0.778192i | 0.402747 | − | 0.107916i | ||||
\(53\) | 7.08396 | + | 1.89814i | 0.973056 | + | 0.260730i | 0.710118 | − | 0.704083i | \(-0.248642\pi\) |
0.262939 | + | 0.964813i | \(0.415308\pi\) | |||||||
\(54\) | −3.41531 | − | 1.97183i | −0.464765 | − | 0.268332i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.43423i | − | 0.191658i | ||||||
\(57\) | −2.55970 | − | 1.81067i | −0.339040 | − | 0.239829i | ||||
\(58\) | −6.90772 | − | 6.90772i | −0.907027 | − | 0.907027i | ||||
\(59\) | 1.29825 | − | 2.24864i | 0.169018 | − | 0.292748i | −0.769057 | − | 0.639180i | \(-0.779274\pi\) |
0.938075 | + | 0.346433i | \(0.112607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.310205 | − | 0.537291i | −0.0397177 | − | 0.0687931i | 0.845483 | − | 0.534002i | \(-0.179313\pi\) |
−0.885201 | + | 0.465209i | \(0.845979\pi\) | |||||||
\(62\) | 2.61317 | + | 9.75248i | 0.331873 | + | 1.23857i | ||||
\(63\) | −0.921559 | + | 3.43931i | −0.116106 | + | 0.433312i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.858945 | − | 1.48774i | −0.105729 | − | 0.183128i | ||||
\(67\) | 0.368486 | − | 1.37521i | 0.0450177 | − | 0.168008i | −0.939757 | − | 0.341843i | \(-0.888949\pi\) |
0.984775 | + | 0.173834i | \(0.0556157\pi\) | |||||||
\(68\) | −3.35930 | − | 3.35930i | −0.407374 | − | 0.407374i | ||||
\(69\) | 3.77775 | 0.454788 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.38910 | − | 3.11140i | −0.639568 | − | 0.369255i | 0.144880 | − | 0.989449i | \(-0.453720\pi\) |
−0.784448 | + | 0.620194i | \(0.787054\pi\) | |||||||
\(72\) | −0.642545 | + | 2.39801i | −0.0757246 | + | 0.282608i | ||||
\(73\) | −3.21735 | + | 0.862086i | −0.376562 | + | 0.100900i | −0.442136 | − | 0.896948i | \(-0.645779\pi\) |
0.0655734 | + | 0.997848i | \(0.479112\pi\) | |||||||
\(74\) | −3.52199 | − | 2.03342i | −0.409424 | − | 0.236381i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.51045 | + | 4.08883i | −0.173261 | + | 0.469021i | ||||
\(77\) | −2.42208 | + | 2.42208i | −0.276021 | + | 0.276021i | ||||
\(78\) | −0.559756 | − | 2.08904i | −0.0633799 | − | 0.236537i | ||||
\(79\) | −0.0163335 | + | 0.0282904i | −0.00183766 | + | 0.00318292i | −0.866943 | − | 0.498408i | \(-0.833918\pi\) |
0.865105 | + | 0.501591i | \(0.167252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.30556 | − | 3.99334i | 0.256173 | − | 0.443705i | ||||
\(82\) | −7.78501 | − | 2.08599i | −0.859711 | − | 0.230359i | ||||
\(83\) | 12.0016 | + | 12.0016i | 1.31735 | + | 1.31735i | 0.915865 | + | 0.401485i | \(0.131506\pi\) |
0.401485 | + | 0.915865i | \(0.368494\pi\) | |||||||
\(84\) | −1.03165 | −0.112562 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.57865 | − | 0.911434i | 0.170230 | − | 0.0982824i | ||||
\(87\) | −4.96875 | + | 4.96875i | −0.532706 | + | 0.532706i | ||||
\(88\) | −1.68876 | + | 1.68876i | −0.180022 | + | 0.180022i | ||||
\(89\) | 1.11103 | + | 1.92436i | 0.117769 | + | 0.203981i | 0.918883 | − | 0.394530i | \(-0.129093\pi\) |
−0.801114 | + | 0.598511i | \(0.795759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.73457 | + | 2.15616i | −0.391490 | + | 0.226027i | ||||
\(92\) | −1.35931 | − | 5.07300i | −0.141717 | − | 0.528897i | ||||
\(93\) | 7.01500 | − | 1.87966i | 0.727421 | − | 0.194912i | ||||
\(94\) | −0.361555 | −0.0372915 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.719304 | −0.0734137 | ||||||||
\(97\) | 9.85916 | − | 2.64175i | 1.00105 | − | 0.268229i | 0.279162 | − | 0.960244i | \(-0.409943\pi\) |
0.721883 | + | 0.692015i | \(0.243277\pi\) | |||||||
\(98\) | −1.27934 | − | 4.77454i | −0.129232 | − | 0.482302i | ||||
\(99\) | 5.13476 | − | 2.96456i | 0.516063 | − | 0.297949i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.56678 | + | 14.8381i | 0.852427 | + | 1.47645i | 0.879012 | + | 0.476800i | \(0.158203\pi\) |
−0.0265848 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(102\) | −2.41636 | + | 2.41636i | −0.239255 | + | 0.239255i | ||||
\(103\) | −1.78051 | + | 1.78051i | −0.175438 | + | 0.175438i | −0.789364 | − | 0.613926i | \(-0.789590\pi\) |
0.613926 | + | 0.789364i | \(0.289590\pi\) | |||||||
\(104\) | −2.60388 | + | 1.50335i | −0.255331 | + | 0.147416i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.33385 | −0.712327 | ||||||||
\(107\) | 4.96199 | + | 4.96199i | 0.479694 | + | 0.479694i | 0.905034 | − | 0.425340i | \(-0.139845\pi\) |
−0.425340 | + | 0.905034i | \(0.639845\pi\) | |||||||
\(108\) | 3.80928 | + | 1.02069i | 0.366548 | + | 0.0982163i | ||||
\(109\) | 4.61026 | − | 7.98521i | 0.441583 | − | 0.764844i | −0.556224 | − | 0.831032i | \(-0.687750\pi\) |
0.997807 | + | 0.0661882i | \(0.0210838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.46265 | + | 2.53339i | −0.138829 | + | 0.240458i | ||||
\(112\) | 0.371207 | + | 1.38536i | 0.0350758 | + | 0.130905i | ||||
\(113\) | 0.471659 | − | 0.471659i | 0.0443699 | − | 0.0443699i | −0.684574 | − | 0.728944i | \(-0.740012\pi\) |
0.728944 | + | 0.684574i | \(0.240012\pi\) | |||||||
\(114\) | 2.94111 | + | 1.08647i | 0.275461 | + | 0.101758i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.46019 | + | 4.88449i | 0.785509 | + | 0.453514i | ||||
\(117\) | 7.21010 | − | 1.93194i | 0.666574 | − | 0.178608i | ||||
\(118\) | −0.672024 | + | 2.50803i | −0.0618648 | + | 0.230883i | ||||
\(119\) | 5.90084 | + | 3.40685i | 0.540929 | + | 0.312306i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.29619 | −0.481472 | ||||||||
\(122\) | 0.438696 | + | 0.438696i | 0.0397177 | + | 0.0397177i | ||||
\(123\) | −1.50046 | + | 5.59979i | −0.135292 | + | 0.504916i | ||||
\(124\) | −5.04825 | − | 8.74383i | −0.453347 | − | 0.785219i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 3.56063i | − | 0.317206i | ||||||
\(127\) | −2.58532 | + | 9.64853i | −0.229410 | + | 0.856169i | 0.751180 | + | 0.660097i | \(0.229485\pi\) |
−0.980590 | + | 0.196071i | \(0.937182\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −0.655598 | − | 1.13553i | −0.0577222 | − | 0.0999778i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.29085 | + | 5.69992i | −0.287523 | + | 0.498004i | −0.973218 | − | 0.229885i | \(-0.926165\pi\) |
0.685695 | + | 0.727889i | \(0.259498\pi\) | |||||||
\(132\) | 1.21473 | + | 1.21473i | 0.105729 | + | 0.105729i | ||||
\(133\) | 0.574720 | − | 6.22521i | 0.0498345 | − | 0.539794i | ||||
\(134\) | 1.42372i | 0.122991i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.11428 | + | 2.37538i | 0.352797 | + | 0.203687i | ||||
\(137\) | −8.71025 | − | 2.33391i | −0.744167 | − | 0.199399i | −0.133238 | − | 0.991084i | \(-0.542537\pi\) |
−0.610929 | + | 0.791685i | \(0.709204\pi\) | |||||||
\(138\) | −3.64903 | + | 0.977755i | −0.310626 | + | 0.0832320i | ||||
\(139\) | −4.69540 | + | 2.71089i | −0.398259 | + | 0.229935i | −0.685732 | − | 0.727854i | \(-0.740518\pi\) |
0.287474 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.260068i | 0.0219017i | ||||||||
\(142\) | 6.01076 | + | 1.61058i | 0.504412 | + | 0.135157i | ||||
\(143\) | 6.93612 | + | 1.85853i | 0.580028 | + | 0.155418i | ||||
\(144\) | − | 2.48260i | − | 0.206883i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.88460 | − | 1.66542i | 0.238731 | − | 0.137831i | ||||
\(147\) | −3.43435 | + | 0.920231i | −0.283260 | + | 0.0758994i | ||||
\(148\) | 3.92827 | + | 1.05258i | 0.322902 | + | 0.0865214i | ||||
\(149\) | −5.72771 | − | 3.30689i | −0.469232 | − | 0.270911i | 0.246686 | − | 0.969095i | \(-0.420658\pi\) |
−0.715918 | + | 0.698184i | \(0.753992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.2548i | − | 1.40418i | −0.712091 | − | 0.702088i | \(-0.752251\pi\) | ||
0.712091 | − | 0.702088i | \(-0.247749\pi\) | |||||||
\(152\) | 0.400715 | − | 4.34044i | 0.0325023 | − | 0.352056i | ||||
\(153\) | −8.33979 | − | 8.33979i | −0.674232 | − | 0.674232i | ||||
\(154\) | 1.71267 | − | 2.96642i | 0.138011 | − | 0.239041i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.08137 | + | 1.87298i | 0.0865786 | + | 0.149959i | ||||
\(157\) | −0.838326 | − | 3.12868i | −0.0669057 | − | 0.249696i | 0.924371 | − | 0.381496i | \(-0.124591\pi\) |
−0.991276 | + | 0.131800i | \(0.957924\pi\) | |||||||
\(158\) | 0.00845484 | − | 0.0315539i | 0.000672631 | − | 0.00251029i | ||||
\(159\) | 5.27527i | 0.418356i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.76627 | + | 6.52336i | 0.296823 | + | 0.514113i | ||||
\(162\) | −1.19344 | + | 4.45399i | −0.0937658 | + | 0.349939i | ||||
\(163\) | −13.0605 | − | 13.0605i | −1.02297 | − | 1.02297i | −0.999730 | − | 0.0232448i | \(-0.992600\pi\) |
−0.0232448 | − | 0.999730i | \(-0.507400\pi\) | |||||||
\(164\) | 8.05964 | 0.629352 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6989 | − | 8.48644i | −1.14086 | − | 0.658675i | ||||
\(167\) | 5.62051 | − | 20.9760i | 0.434928 | − | 1.62317i | −0.306309 | − | 0.951932i | \(-0.599094\pi\) |
0.741238 | − | 0.671243i | \(-0.234239\pi\) | |||||||
\(168\) | 0.996498 | − | 0.267011i | 0.0768815 | − | 0.0206003i | ||||
\(169\) | −3.42924 | − | 1.97987i | −0.263788 | − | 0.152298i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.74985 | + | 10.1509i | −0.286758 | + | 0.776262i | ||||
\(172\) | −1.28896 | + | 1.28896i | −0.0982824 | + | 0.0982824i | ||||
\(173\) | 1.72920 | + | 6.45347i | 0.131469 | + | 0.490649i | 0.999987 | − | 0.00500806i | \(-0.00159412\pi\) |
−0.868519 | + | 0.495657i | \(0.834927\pi\) | |||||||
\(174\) | 3.51344 | − | 6.08545i | 0.266353 | − | 0.461337i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.19413 | − | 2.06830i | 0.0900111 | − | 0.155904i | ||||
\(177\) | 1.80404 | + | 0.483390i | 0.135600 | + | 0.0363338i | ||||
\(178\) | −1.57123 | − | 1.57123i | −0.117769 | − | 0.117769i | ||||
\(179\) | −11.9857 | −0.895851 | −0.447925 | − | 0.894071i | \(-0.647837\pi\) | ||||
−0.447925 | + | 0.894071i | \(0.647837\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.6699 | + | 11.9338i | −1.53638 | + | 0.887031i | −0.537337 | + | 0.843368i | \(0.680570\pi\) |
−0.999046 | + | 0.0436636i | \(0.986097\pi\) | |||||||
\(182\) | 3.04927 | − | 3.04927i | 0.226027 | − | 0.226027i | ||||
\(183\) | 0.315556 | − | 0.315556i | 0.0233266 | − | 0.0233266i | ||||
\(184\) | 2.62598 | + | 4.54833i | 0.193590 | + | 0.335307i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.28948 | + | 3.63123i | −0.461167 | + | 0.266255i | ||||
\(187\) | −2.93658 | − | 10.9595i | −0.214744 | − | 0.801436i | ||||
\(188\) | 0.349235 | − | 0.0935773i | 0.0254706 | − | 0.00682482i | ||||
\(189\) | −5.65613 | −0.411423 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5623 | 1.19840 | 0.599201 | − | 0.800598i | \(-0.295485\pi\) | ||||
0.599201 | + | 0.800598i | \(0.295485\pi\) | |||||||
\(192\) | 0.694795 | − | 0.186170i | 0.0501425 | − | 0.0134356i | ||||
\(193\) | −2.74324 | − | 10.2379i | −0.197463 | − | 0.736941i | −0.991616 | − | 0.129223i | \(-0.958752\pi\) |
0.794153 | − | 0.607718i | \(-0.207915\pi\) | |||||||
\(194\) | −8.83948 | + | 5.10347i | −0.634637 | + | 0.366408i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.47149 | + | 4.28074i | 0.176535 | + | 0.305767i | ||||
\(197\) | 17.3356 | − | 17.3356i | 1.23511 | − | 1.23511i | 0.273139 | − | 0.961975i | \(-0.411938\pi\) |
0.961975 | − | 0.273139i | \(-0.0880618\pi\) | |||||||
\(198\) | −4.19251 | + | 4.19251i | −0.297949 | + | 0.297949i | ||||
\(199\) | −9.91254 | + | 5.72301i | −0.702682 | + | 0.405693i | −0.808345 | − | 0.588709i | \(-0.799637\pi\) |
0.105664 | + | 0.994402i | \(0.466303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.02409 | 0.0722336 | ||||||||
\(202\) | −12.1153 | − | 12.1153i | −0.852427 | − | 0.852427i | ||||
\(203\) | −13.5336 | − | 3.62632i | −0.949872 | − | 0.254518i | ||||
\(204\) | 1.70862 | − | 2.95942i | 0.119627 | − | 0.207201i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.25901 | − | 2.18067i | 0.0877192 | − | 0.151934i | ||||
\(207\) | −3.37461 | − | 12.5942i | −0.234552 | − | 0.875360i | ||||
\(208\) | 2.12606 | − | 2.12606i | 0.147416 | − | 0.147416i | ||||
\(209\) | −8.00667 | + | 6.65325i | −0.553833 | + | 0.460215i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.74675 | − | 3.89524i | −0.464465 | − | 0.268159i | 0.249455 | − | 0.968387i | \(-0.419749\pi\) |
−0.713920 | + | 0.700227i | \(0.753082\pi\) | |||||||
\(212\) | 7.08396 | − | 1.89814i | 0.486528 | − | 0.130365i | ||||
\(213\) | 1.15850 | − | 4.32356i | 0.0793788 | − | 0.296246i | ||||
\(214\) | −6.07718 | − | 3.50866i | −0.415427 | − | 0.239847i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.94366 | −0.268332 | ||||||||
\(217\) | 10.2394 | + | 10.2394i | 0.695099 | + | 0.695099i | ||||
\(218\) | −2.38645 | + | 8.90634i | −0.161631 | + | 0.603213i | ||||
\(219\) | −1.19795 | − | 2.07490i | −0.0809497 | − | 0.140209i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.2841i | − | 0.960854i | ||||||
\(222\) | 0.757124 | − | 2.82562i | 0.0508148 | − | 0.189643i | ||||
\(223\) | 3.10249 | + | 11.5787i | 0.207758 | + | 0.775365i | 0.988591 | + | 0.150625i | \(0.0481285\pi\) |
−0.780833 | + | 0.624740i | \(0.785205\pi\) | |||||||
\(224\) | −0.717117 | − | 1.24208i | −0.0479144 | − | 0.0829902i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.333513 | + | 0.577661i | −0.0221850 | + | 0.0384255i | ||||
\(227\) | −15.2621 | − | 15.2621i | −1.01298 | − | 1.01298i | −0.999915 | − | 0.0130664i | \(-0.995841\pi\) |
−0.0130664 | − | 0.999915i | \(-0.504159\pi\) | |||||||
\(228\) | −3.12210 | − | 0.288236i | −0.206766 | − | 0.0190889i | ||||
\(229\) | − | 14.2432i | − | 0.941219i | −0.882342 | − | 0.470609i | \(-0.844034\pi\) | ||
0.882342 | − | 0.470609i | \(-0.155966\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.13376 | − | 1.23193i | −0.140391 | − | 0.0810549i | ||||
\(232\) | −9.43611 | − | 2.52840i | −0.619511 | − | 0.165998i | ||||
\(233\) | −15.7624 | + | 4.22353i | −1.03263 | + | 0.276693i | −0.735056 | − | 0.678006i | \(-0.762844\pi\) |
−0.297575 | + | 0.954699i | \(0.596178\pi\) | |||||||
\(234\) | −6.46440 | + | 3.73222i | −0.422591 | + | 0.243983i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 2.59650i | − | 0.169018i | ||||||
\(237\) | −0.0226968 | − | 0.00608160i | −0.00147432 | − | 0.000395042i | ||||
\(238\) | −6.58153 | − | 1.76352i | −0.426617 | − | 0.114312i | ||||
\(239\) | − | 11.7603i | − | 0.760711i | −0.924840 | − | 0.380355i | \(-0.875802\pi\) | ||
0.924840 | − | 0.380355i | \(-0.124198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5318 | − | 6.65790i | 0.742829 | − | 0.428873i | −0.0802677 | − | 0.996773i | \(-0.525578\pi\) |
0.823097 | + | 0.567901i | \(0.192244\pi\) | |||||||
\(242\) | 5.11572 | − | 1.37075i | 0.328851 | − | 0.0881154i | ||||
\(243\) | 14.6316 | + | 3.92053i | 0.938619 | + | 0.251502i | ||||
\(244\) | −0.537291 | − | 0.310205i | −0.0343965 | − | 0.0198589i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 5.79733i | − | 0.369624i | ||||||
\(247\) | −11.9044 | + | 5.48179i | −0.757459 | + | 0.348798i | ||||
\(248\) | 7.13931 | + | 7.13931i | 0.453347 | + | 0.453347i | ||||
\(249\) | −6.10433 | + | 10.5730i | −0.386846 | + | 0.670037i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9058 | − | 22.3535i | −0.814606 | − | 1.41094i | −0.909610 | − | 0.415463i | \(-0.863620\pi\) |
0.0950040 | − | 0.995477i | \(-0.469714\pi\) | |||||||
\(252\) | 0.921559 | + | 3.43931i | 0.0580528 | + | 0.216656i | ||||
\(253\) | 3.24638 | − | 12.1157i | 0.204098 | − | 0.761706i | ||||
\(254\) | − | 9.98889i | − | 0.626759i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.83587 | + | 6.85158i | −0.114519 | + | 0.427390i | −0.999250 | − | 0.0387109i | \(-0.987675\pi\) |
0.884732 | + | 0.466101i | \(0.154342\pi\) | |||||||
\(258\) | 0.927156 | + | 0.927156i | 0.0577222 | + | 0.0577222i | ||||
\(259\) | −5.83281 | −0.362433 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.0033 | + | 12.1262i | 1.30007 | + | 0.750596i | ||||
\(262\) | 1.70347 | − | 6.35743i | 0.105241 | − | 0.392764i | ||||
\(263\) | 20.1313 | − | 5.39416i | 1.24135 | − | 0.332618i | 0.422359 | − | 0.906429i | \(-0.361202\pi\) |
0.818988 | + | 0.573811i | \(0.194535\pi\) | |||||||
\(264\) | −1.48774 | − | 0.858945i | −0.0915638 | − | 0.0528644i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.05607 | + | 6.16184i | 0.0647516 | + | 0.377807i | ||||
\(267\) | −1.13019 | + | 1.13019i | −0.0691667 | + | 0.0691667i | ||||
\(268\) | −0.368486 | − | 1.37521i | −0.0225088 | − | 0.0840042i | ||||
\(269\) | 10.3374 | − | 17.9049i | 0.630282 | − | 1.09168i | −0.357212 | − | 0.934023i | \(-0.616272\pi\) |
0.987494 | − | 0.157657i | \(-0.0503942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5983 | + | 21.8210i | −0.765295 | + | 1.32553i | 0.174796 | + | 0.984605i | \(0.444073\pi\) |
−0.940091 | + | 0.340925i | \(0.889260\pi\) | |||||||
\(272\) | −4.58888 | − | 1.22959i | −0.278242 | − | 0.0745547i | ||||
\(273\) | −2.19335 | − | 2.19335i | −0.132748 | − | 0.132748i | ||||
\(274\) | 9.01752 | 0.544768 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.27163 | − | 1.88888i | 0.196929 | − | 0.113697i | ||||
\(277\) | −16.2232 | + | 16.2232i | −0.974760 | + | 0.974760i | −0.999689 | − | 0.0249288i | \(-0.992064\pi\) |
0.0249288 | + | 0.999689i | \(0.492064\pi\) | |||||||
\(278\) | 3.83378 | − | 3.83378i | 0.229935 | − | 0.229935i | ||||
\(279\) | −12.5328 | − | 21.7074i | −0.750319 | − | 1.29959i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.62150 | + | 2.66822i | −0.275695 | + | 0.159173i | −0.631473 | − | 0.775398i | \(-0.717549\pi\) |
0.355778 | + | 0.934571i | \(0.384216\pi\) | |||||||
\(282\) | −0.0673105 | − | 0.251206i | −0.00400828 | − | 0.0149591i | ||||
\(283\) | −31.6725 | + | 8.48662i | −1.88274 | + | 0.504477i | −0.883377 | + | 0.468664i | \(0.844736\pi\) |
−0.999358 | + | 0.0358135i | \(0.988598\pi\) | |||||||
\(284\) | −6.22280 | −0.369255 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.18080 | −0.424610 | ||||||||
\(287\) | −11.1655 | + | 2.99179i | −0.659080 | + | 0.176600i | ||||
\(288\) | 0.642545 | + | 2.39801i | 0.0378623 | + | 0.141304i | ||||
\(289\) | −4.82354 | + | 2.78487i | −0.283737 | + | 0.163816i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.67095 | + | 6.35827i | 0.215195 | + | 0.372729i | ||||
\(292\) | −2.35526 | + | 2.35526i | −0.137831 | + | 0.137831i | ||||
\(293\) | −13.1650 | + | 13.1650i | −0.769106 | + | 0.769106i | −0.977949 | − | 0.208844i | \(-0.933030\pi\) |
0.208844 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(294\) | 3.07915 | − | 1.77775i | 0.179580 | − | 0.103681i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.06685 | −0.236381 | ||||||||
\(297\) | 6.65989 | + | 6.65989i | 0.386446 | + | 0.386446i | ||||
\(298\) | 6.38843 | + | 1.71177i | 0.370072 | + | 0.0991604i | ||||
\(299\) | 7.89553 | − | 13.6755i | 0.456610 | − | 0.790872i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.30721 | − | 2.26415i | 0.0753463 | − | 0.130504i | ||||
\(302\) | 4.46587 | + | 16.6669i | 0.256982 | + | 0.959070i | ||||
\(303\) | −8.71456 | + | 8.71456i | −0.500638 | + | 0.500638i | ||||
\(304\) | 0.736327 | + | 4.29626i | 0.0422313 | + | 0.246407i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.2141 | + | 5.89712i | 0.583902 | + | 0.337116i | ||||
\(307\) | −18.1679 | + | 4.86806i | −1.03689 | + | 0.277835i | −0.736826 | − | 0.676083i | \(-0.763676\pi\) |
−0.300069 | + | 0.953918i | \(0.597010\pi\) | |||||||
\(308\) | −0.886541 | + | 3.30862i | −0.0505154 | + | 0.188526i | ||||
\(309\) | −1.56856 | − | 0.905610i | −0.0892324 | − | 0.0515183i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.47649 | −0.253838 | −0.126919 | − | 0.991913i | \(-0.540509\pi\) | ||||
−0.126919 | + | 0.991913i | \(0.540509\pi\) | |||||||
\(312\) | −1.52928 | − | 1.52928i | −0.0865786 | − | 0.0865786i | ||||
\(313\) | −3.22806 | + | 12.0473i | −0.182461 | + | 0.680953i | 0.812699 | + | 0.582684i | \(0.197997\pi\) |
−0.995160 | + | 0.0982696i | \(0.968669\pi\) | |||||||
\(314\) | 1.61952 | + | 2.80509i | 0.0913949 | + | 0.158301i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0326670i | 0.00183766i | ||||||||
\(317\) | 1.46541 | − | 5.46899i | 0.0823058 | − | 0.307169i | −0.912485 | − | 0.409111i | \(-0.865839\pi\) |
0.994790 | + | 0.101942i | \(0.0325055\pi\) | |||||||
\(318\) | −1.36534 | − | 5.09552i | −0.0765645 | − | 0.285743i | ||||
\(319\) | 11.6655 | + | 20.2052i | 0.653141 | + | 1.13127i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.52379 | + | 4.37134i | −0.140864 | + | 0.243984i | ||||
\(322\) | −5.32631 | − | 5.32631i | −0.296823 | − | 0.296823i | ||||
\(323\) | 16.9059 | + | 11.9589i | 0.940672 | + | 0.665409i | ||||
\(324\) | − | 4.61111i | − | 0.256173i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.9957 | + | 9.23514i | 0.885922 | + | 0.511487i | ||||
\(327\) | 6.40637 | + | 1.71658i | 0.354273 | + | 0.0949272i | ||||
\(328\) | −7.78501 | + | 2.08599i | −0.429855 | + | 0.115179i | ||||
\(329\) | −0.449081 | + | 0.259277i | −0.0247586 | + | 0.0142944i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.4811i | 0.740988i | 0.928835 | + | 0.370494i | \(0.120812\pi\) | ||||
−0.928835 | + | 0.370494i | \(0.879188\pi\) | |||||||
\(332\) | 16.3945 | + | 4.39290i | 0.899767 | + | 0.241092i | ||||
\(333\) | 9.75234 | + | 2.61313i | 0.534425 | + | 0.143199i | ||||
\(334\) | 21.7160i | 1.18825i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.893436 | + | 0.515825i | −0.0487409 | + | 0.0281406i | ||||
\(337\) | 30.9819 | − | 8.30158i | 1.68769 | − | 0.452216i | 0.717900 | − | 0.696147i | \(-0.245104\pi\) |
0.969793 | + | 0.243931i | \(0.0784370\pi\) | |||||||
\(338\) | 3.82482 | + | 1.02486i | 0.208043 | + | 0.0557449i | ||||
\(339\) | 0.415514 | + | 0.239897i | 0.0225676 | + | 0.0130294i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 24.1131i | − | 1.30580i | ||||||
\(342\) | 0.994816 | − | 10.7756i | 0.0537935 | − | 0.582677i | ||||
\(343\) | −12.1120 | − | 12.1120i | −0.653989 | − | 0.653989i | ||||
\(344\) | 0.911434 | − | 1.57865i | 0.0491412 | − | 0.0851151i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.34056 | − | 5.78603i | −0.179590 | − | 0.311059i | ||||
\(347\) | −0.973759 | − | 3.63412i | −0.0522741 | − | 0.195090i | 0.934851 | − | 0.355041i | \(-0.115533\pi\) |
−0.987125 | + | 0.159951i | \(0.948866\pi\) | |||||||
\(348\) | −1.81869 | + | 6.78744i | −0.0974919 | + | 0.363845i | ||||
\(349\) | − | 31.2369i | − | 1.67207i | −0.548673 | − | 0.836037i | \(-0.684867\pi\) | ||
0.548673 | − | 0.836037i | \(-0.315133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.92870 | + | 10.2688i | 0.316451 | + | 0.548109i | ||||
\(352\) | −0.618129 | + | 2.30689i | −0.0329464 | + | 0.122958i | ||||
\(353\) | −17.2688 | − | 17.2688i | −0.919124 | − | 0.919124i | 0.0778415 | − | 0.996966i | \(-0.475197\pi\) |
−0.996966 | + | 0.0778415i | \(0.975197\pi\) | |||||||
\(354\) | −1.86767 | −0.0992658 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.92436 | + | 1.11103i | 0.101991 | + | 0.0588843i | ||||
\(357\) | −1.26851 | + | 4.73413i | −0.0671364 | + | 0.250556i | ||||
\(358\) | 11.5773 | − | 3.10212i | 0.611878 | − | 0.163952i | ||||
\(359\) | 11.6435 | + | 6.72238i | 0.614521 | + | 0.354794i | 0.774733 | − | 0.632289i | \(-0.217884\pi\) |
−0.160212 | + | 0.987083i | \(0.551218\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.47856 | − | 18.6789i | 0.183082 | − | 0.983098i | ||||
\(362\) | 16.8769 | − | 16.8769i | 0.887031 | − | 0.887031i | ||||
\(363\) | −0.985989 | − | 3.67976i | −0.0517510 | − | 0.193137i | ||||
\(364\) | −2.15616 | + | 3.73457i | −0.113013 | + | 0.195745i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.223132 | + | 0.386476i | −0.0116633 | + | 0.0202014i | ||||
\(367\) | 1.20298 | + | 0.322337i | 0.0627950 | + | 0.0168259i | 0.290080 | − | 0.957002i | \(-0.406318\pi\) |
−0.227285 | + | 0.973828i | \(0.572985\pi\) | |||||||
\(368\) | −3.71369 | − | 3.71369i | −0.193590 | − | 0.193590i | ||||
\(369\) | 20.0089 | 1.04162 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.10926 | + | 5.25923i | −0.472929 | + | 0.273046i | ||||
\(372\) | 5.13534 | − | 5.13534i | 0.266255 | − | 0.266255i | ||||
\(373\) | 20.2015 | − | 20.2015i | 1.04599 | − | 1.04599i | 0.0471036 | − | 0.998890i | \(-0.485001\pi\) |
0.998890 | − | 0.0471036i | \(-0.0149991\pi\) | |||||||
\(374\) | 5.67304 | + | 9.82599i | 0.293346 | + | 0.508090i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.313116 | + | 0.180777i | −0.0161477 | + | 0.00932288i | ||||
\(377\) | 7.60214 | + | 28.3716i | 0.391530 | + | 1.46121i | ||||
\(378\) | 5.46340 | − | 1.46391i | 0.281007 | − | 0.0752956i | ||||
\(379\) | −6.67007 | −0.342618 | −0.171309 | − | 0.985217i | \(-0.554800\pi\) | ||||
−0.171309 | + | 0.985217i | \(0.554800\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.18505 | −0.368101 | ||||||||
\(382\) | −15.9979 | + | 4.28663i | −0.818524 | + | 0.219323i | ||||
\(383\) | 6.20447 | + | 23.1554i | 0.317033 | + | 1.18319i | 0.922081 | + | 0.386996i | \(0.126487\pi\) |
−0.605048 | + | 0.796189i | \(0.706846\pi\) | |||||||
\(384\) | −0.622936 | + | 0.359652i | −0.0317891 | + | 0.0183534i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.29953 | + | 9.17906i | 0.269739 | + | 0.467202i | ||||
\(387\) | −3.19998 | + | 3.19998i | −0.162664 | + | 0.162664i | ||||
\(388\) | 7.21740 | − | 7.21740i | 0.366408 | − | 0.366408i | ||||
\(389\) | −0.912264 | + | 0.526696i | −0.0462536 | + | 0.0267045i | −0.522948 | − | 0.852364i | \(-0.675168\pi\) |
0.476695 | + | 0.879069i | \(0.341835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.9508 | −1.26182 | ||||||||
\(392\) | −3.49521 | − | 3.49521i | −0.176535 | − | 0.176535i | ||||
\(393\) | −4.57293 | − | 1.22531i | −0.230674 | − | 0.0618089i | ||||
\(394\) | −12.2582 | + | 21.2317i | −0.617557 | + | 1.06964i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.96456 | − | 5.13476i | 0.148975 | − | 0.258031i | ||||
\(397\) | −3.38776 | − | 12.6433i | −0.170027 | − | 0.634548i | −0.997345 | − | 0.0728155i | \(-0.976802\pi\) |
0.827319 | − | 0.561733i | \(-0.189865\pi\) | |||||||
\(398\) | 8.09356 | − | 8.09356i | 0.405693 | − | 0.405693i | ||||
\(399\) | 4.43224 | − | 0.759633i | 0.221889 | − | 0.0380292i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.812592 | + | 0.469150i | 0.0405789 | + | 0.0234282i | 0.520152 | − | 0.854074i | \(-0.325875\pi\) |
−0.479573 | + | 0.877502i | \(0.659209\pi\) | |||||||
\(402\) | −0.989193 | + | 0.265053i | −0.0493364 | + | 0.0132197i | ||||
\(403\) | 7.85702 | − | 29.3228i | 0.391386 | − | 1.46067i | ||||
\(404\) | 14.8381 | + | 8.56678i | 0.738223 | + | 0.426213i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.0110 | 0.695355 | ||||||||
\(407\) | 6.86793 | + | 6.86793i | 0.340430 | + | 0.340430i | ||||
\(408\) | −0.884448 | + | 3.30080i | −0.0437867 | + | 0.163414i | ||||
\(409\) | 6.72826 | + | 11.6537i | 0.332691 | + | 0.576238i | 0.983039 | − | 0.183399i | \(-0.0587100\pi\) |
−0.650347 | + | 0.759637i | \(0.725377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.48634i | − | 0.319947i | ||||||
\(412\) | −0.651710 | + | 2.43222i | −0.0321075 | + | 0.119827i | ||||
\(413\) | 0.963840 | + | 3.59710i | 0.0474275 | + | 0.177002i | ||||
\(414\) | 6.51926 | + | 11.2917i | 0.320404 | + | 0.554956i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.50335 | + | 2.60388i | −0.0737078 | + | 0.127666i | ||||
\(417\) | −2.75765 | − | 2.75765i | −0.135043 | − | 0.135043i | ||||
\(418\) | 6.01186 | − | 8.49882i | 0.294050 | − | 0.415691i | ||||
\(419\) | 31.4227i | 1.53510i | 0.640989 | + | 0.767550i | \(0.278524\pi\) | ||||
−0.640989 | + | 0.767550i | \(0.721476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8219 | − | 7.98005i | −0.673636 | − | 0.388924i | 0.123817 | − | 0.992305i | \(-0.460486\pi\) |
−0.797453 | + | 0.603381i | \(0.793820\pi\) | |||||||
\(422\) | 7.52502 | + | 2.01632i | 0.366312 | + | 0.0981531i | ||||
\(423\) | 0.867011 | − | 0.232315i | 0.0421555 | − | 0.0112955i | ||||
\(424\) | −6.35130 | + | 3.66693i | −0.308447 | + | 0.178082i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.47608i | 0.216867i | ||||||||
\(427\) | 0.859494 | + | 0.230301i | 0.0415938 | + | 0.0111450i | ||||
\(428\) | 6.77821 | + | 1.81622i | 0.327637 | + | 0.0877901i | ||||
\(429\) | 5.16518i | 0.249377i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0614 | − | 9.27303i | 0.773648 | − | 0.446666i | −0.0605263 | − | 0.998167i | \(-0.519278\pi\) |
0.834174 | + | 0.551501i | \(0.185945\pi\) | |||||||
\(432\) | 3.80928 | − | 1.02069i | 0.183274 | − | 0.0491082i | ||||
\(433\) | −4.93514 | − | 1.32237i | −0.237168 | − | 0.0635489i | 0.138277 | − | 0.990394i | \(-0.455843\pi\) |
−0.375445 | + | 0.926845i | \(0.622510\pi\) | |||||||
\(434\) | −12.5407 | − | 7.24038i | −0.601973 | − | 0.347549i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 9.22052i | − | 0.441583i | ||||||
\(437\) | 9.57532 | + | 20.7940i | 0.458049 | + | 0.994712i | ||||
\(438\) | 1.69415 | + | 1.69415i | 0.0809497 | + | 0.0809497i | ||||
\(439\) | −6.25946 | + | 10.8417i | −0.298748 | + | 0.517446i | −0.975850 | − | 0.218443i | \(-0.929902\pi\) |
0.677102 | + | 0.735889i | \(0.263236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.13572 | + | 10.6274i | 0.292177 | + | 0.506065i | ||||
\(442\) | 3.69700 | + | 13.7974i | 0.175848 | + | 0.656276i | ||||
\(443\) | −10.0467 | + | 37.4948i | −0.477333 | + | 1.78143i | 0.135017 | + | 0.990843i | \(0.456891\pi\) |
−0.612350 | + | 0.790587i | \(0.709776\pi\) | |||||||
\(444\) | 2.92530i | 0.138829i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.99356 | − | 10.3811i | −0.283803 | − | 0.491562i | ||||
\(447\) | 1.23129 | − | 4.59522i | 0.0582379 | − | 0.217347i | ||||
\(448\) | 1.01416 | + | 1.01416i | 0.0479144 | + | 0.0479144i | ||||
\(449\) | −10.8951 | −0.514169 | −0.257085 | − | 0.966389i | \(-0.582762\pi\) | ||||
−0.257085 | + | 0.966389i | \(0.582762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6697 | + | 9.62428i | 0.784947 | + | 0.453189i | ||||
\(452\) | 0.172639 | − | 0.644298i | 0.00812026 | − | 0.0303052i | ||||
\(453\) | 11.9885 | − | 3.21232i | 0.563271 | − | 0.150928i | ||||
\(454\) | 18.6922 | + | 10.7919i | 0.877267 | + | 0.506491i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.09032 | − | 0.529643i | 0.144717 | − | 0.0248028i | ||||
\(457\) | −10.9672 | + | 10.9672i | −0.513025 | + | 0.513025i | −0.915452 | − | 0.402427i | \(-0.868167\pi\) |
0.402427 | + | 0.915452i | \(0.368167\pi\) | |||||||
\(458\) | 3.68642 | + | 13.7579i | 0.172255 | + | 0.642864i | ||||
\(459\) | 9.36769 | − | 16.2253i | 0.437246 | − | 0.757333i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.58025 | − | 2.73707i | 0.0735995 | − | 0.127478i | −0.826877 | − | 0.562383i | \(-0.809885\pi\) |
0.900476 | + | 0.434905i | \(0.143218\pi\) | |||||||
\(462\) | 2.37990 | + | 0.637693i | 0.110723 | + | 0.0296682i | ||||
\(463\) | −25.6630 | − | 25.6630i | −1.19266 | − | 1.19266i | −0.976317 | − | 0.216344i | \(-0.930587\pi\) |
−0.216344 | − | 0.976317i | \(-0.569413\pi\) | |||||||
\(464\) | 9.76898 | 0.453514 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.1322 | − | 8.15923i | 0.654662 | − | 0.377969i | ||||
\(467\) | −15.1541 | + | 15.1541i | −0.701248 | + | 0.701248i | −0.964678 | − | 0.263431i | \(-0.915146\pi\) |
0.263431 | + | 0.964678i | \(0.415146\pi\) | |||||||
\(468\) | 5.27816 | − | 5.27816i | 0.243983 | − | 0.243983i | ||||
\(469\) | 1.02097 | + | 1.76838i | 0.0471442 | + | 0.0816561i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.01772 | − | 1.16493i | 0.0929715 | − | 0.0536771i | ||||
\(472\) | 0.672024 | + | 2.50803i | 0.0309324 | + | 0.115441i | ||||
\(473\) | −4.20515 | + | 1.12677i | −0.193353 | + | 0.0518088i | ||||
\(474\) | 0.0234975 | 0.00107928 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.81371 | 0.312306 | ||||||||
\(477\) | 17.5866 | − | 4.71233i | 0.805237 | − | 0.215763i | ||||
\(478\) | 3.04379 | + | 11.3596i | 0.139220 | + | 0.519575i | ||||
\(479\) | 8.65416 | − | 4.99648i | 0.395418 | − | 0.228295i | −0.289087 | − | 0.957303i | \(-0.593352\pi\) |
0.684505 | + | 0.729008i | \(0.260018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.11390 | + | 10.5896i | 0.278770 | + | 0.482843i | ||||
\(482\) | −9.41569 | + | 9.41569i | −0.428873 | + | 0.428873i | ||||
\(483\) | −3.83123 | + | 3.83123i | −0.174327 | + | 0.174327i | ||||
\(484\) | −4.58663 | + | 2.64809i | −0.208483 | + | 0.120368i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.1478 | −0.687117 | ||||||||
\(487\) | 3.95427 | + | 3.95427i | 0.179185 | + | 0.179185i | 0.791001 | − | 0.611815i | \(-0.209560\pi\) |
−0.611815 | + | 0.791001i | \(0.709560\pi\) | |||||||
\(488\) | 0.599271 | + | 0.160574i | 0.0271277 | + | 0.00726885i | ||||
\(489\) | 6.64288 | − | 11.5058i | 0.300401 | − | 0.520310i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2803 | − | 26.4663i | 0.689592 | − | 1.19441i | −0.282378 | − | 0.959303i | \(-0.591123\pi\) |
0.971970 | − | 0.235105i | \(-0.0755435\pi\) | |||||||
\(492\) | 1.50046 | + | 5.59979i | 0.0676459 | + | 0.252458i | ||||
\(493\) | 32.8169 | − | 32.8169i | 1.47800 | − | 1.47800i | ||||
\(494\) | 10.0800 | − | 8.37609i | 0.453520 | − | 0.376858i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.74383 | − | 5.04825i | −0.392610 | − | 0.226673i | ||||
\(497\) | 8.62084 | − | 2.30995i | 0.386697 | − | 0.103615i | ||||
\(498\) | 3.15983 | − | 11.7927i | 0.141596 | − | 0.528442i | ||||
\(499\) | 23.2626 | + | 13.4307i | 1.04138 | + | 0.601239i | 0.920223 | − | 0.391394i | \(-0.128007\pi\) |
0.121154 | + | 0.992634i | \(0.461340\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.6204 | 0.697868 | ||||||||
\(502\) | 18.2515 | + | 18.2515i | 0.814606 | + | 0.814606i | ||||
\(503\) | 6.03190 | − | 22.5113i | 0.268949 | − | 1.00373i | −0.690840 | − | 0.723008i | \(-0.742759\pi\) |
0.959789 | − | 0.280723i | \(-0.0905744\pi\) | |||||||
\(504\) | −1.78032 | − | 3.08360i | −0.0793016 | − | 0.137354i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.5431i | 0.557607i | ||||||||
\(507\) | 0.737185 | − | 2.75121i | 0.0327395 | − | 0.122186i | ||||
\(508\) | 2.58532 | + | 9.64853i | 0.114705 | + | 0.428084i | ||||
\(509\) | 4.75131 | + | 8.22951i | 0.210598 | + | 0.364767i | 0.951902 | − | 0.306403i | \(-0.0991255\pi\) |
−0.741304 | + | 0.671170i | \(0.765792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.38861 | − | 4.13719i | 0.105666 | − | 0.183018i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −17.1172 | − | 1.58028i | −0.755744 | − | 0.0697713i | ||||
\(514\) | − | 7.09327i | − | 0.312871i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.13553 | − | 0.655598i | −0.0499889 | − | 0.0288611i | ||||
\(517\) | 0.834066 | + | 0.223487i | 0.0366822 | + | 0.00982896i | ||||
\(518\) | 5.63406 | − | 1.50964i | 0.247547 | − | 0.0663299i | ||||
\(519\) | −4.16191 | + | 2.40288i | −0.182688 | + | 0.105475i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.0578i | 1.01018i | 0.863067 | + | 0.505090i | \(0.168541\pi\) | ||||
−0.863067 | + | 0.505090i | \(0.831459\pi\) | |||||||
\(522\) | −23.4261 | − | 6.27701i | −1.02533 | − | 0.274737i | ||||
\(523\) | 32.3420 | + | 8.66602i | 1.41422 | + | 0.378939i | 0.883429 | − | 0.468565i | \(-0.155229\pi\) |
0.530789 | + | 0.847504i | \(0.321896\pi\) | |||||||
\(524\) | 6.58170i | 0.287523i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0492 | + | 10.4207i | −0.786983 | + | 0.454365i | ||||
\(527\) | −46.3317 | + | 12.4145i | −2.01824 | + | 0.540786i | ||||
\(528\) | 1.65935 | + | 0.444623i | 0.0722141 | + | 0.0193497i | ||||
\(529\) | −3.96902 | − | 2.29151i | −0.172566 | − | 0.0996311i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.44608i | − | 0.279736i | ||||||
\(532\) | −2.61488 | − | 5.67855i | −0.113370 | − | 0.246196i | ||||
\(533\) | 17.1353 | + | 17.1353i | 0.742211 | + | 0.742211i | ||||
\(534\) | 0.799167 | − | 1.38420i | 0.0345833 | − | 0.0599001i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.711860 | + | 1.23298i | 0.0307477 | + | 0.0532565i | ||||
\(537\) | −2.23137 | − | 8.32758i | −0.0962906 | − | 0.359361i | ||||
\(538\) | −5.35103 | + | 19.9703i | −0.230699 | + | 0.860982i | ||||
\(539\) | 11.8051i | 0.508483i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.15206 | + | 10.6557i | 0.264498 | + | 0.458124i | 0.967432 | − | 0.253131i | \(-0.0814605\pi\) |
−0.702934 | + | 0.711255i | \(0.748127\pi\) | |||||||
\(542\) | 6.52138 | − | 24.3381i | 0.280117 | − | 1.04541i | ||||
\(543\) | −12.1396 | − | 12.1396i | −0.520962 | − | 0.520962i | ||||
\(544\) | 4.75076 | 0.203687 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.68629 | + | 1.55093i | 0.114963 | + | 0.0663738i | ||||
\(547\) | −9.47712 | + | 35.3691i | −0.405212 | + | 1.51227i | 0.398451 | + | 0.917189i | \(0.369548\pi\) |
−0.803664 | + | 0.595084i | \(0.797119\pi\) | |||||||
\(548\) | −8.71025 | + | 2.33391i | −0.372084 | + | 0.0996995i | ||||
\(549\) | −1.33388 | − | 0.770116i | −0.0569286 | − | 0.0328677i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.9437 | − | 14.7556i | −1.70166 | − | 0.628608i | ||||
\(552\) | −2.67127 | + | 2.67127i | −0.113697 | + | 0.113697i | ||||
\(553\) | −0.0121262 | − | 0.0452557i | −0.000515659 | − | 0.00192447i | ||||
\(554\) | 11.4716 | − | 19.8693i | 0.487380 | − | 0.844167i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.71089 | + | 4.69540i | −0.114967 | + | 0.199129i | ||||
\(557\) | 15.9320 | + | 4.26897i | 0.675061 | + | 0.180882i | 0.580033 | − | 0.814593i | \(-0.303040\pi\) |
0.0950272 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(558\) | 17.7241 | + | 17.7241i | 0.750319 | + | 0.750319i | ||||
\(559\) | −5.48082 | −0.231814 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.06788 | − | 4.08064i | 0.298406 | − | 0.172285i | ||||
\(562\) | 3.77344 | − | 3.77344i | 0.159173 | − | 0.159173i | ||||
\(563\) | −3.10059 | + | 3.10059i | −0.130674 | + | 0.130674i | −0.769419 | − | 0.638745i | \(-0.779454\pi\) |
0.638745 | + | 0.769419i | \(0.279454\pi\) | |||||||
\(564\) | 0.130034 | + | 0.225225i | 0.00547542 | + | 0.00948370i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.3968 | − | 16.3949i | 1.19361 | − | 0.689129i | ||||
\(567\) | 1.71168 | + | 6.38807i | 0.0718837 | + | 0.268274i | ||||
\(568\) | 6.01076 | − | 1.61058i | 0.252206 | − | 0.0675784i | ||||
\(569\) | −16.6846 | −0.699455 | −0.349727 | − | 0.936851i | \(-0.613726\pi\) | ||||
−0.349727 | + | 0.936851i | \(0.613726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.93391 | −0.332024 | −0.166012 | − | 0.986124i | \(-0.553089\pi\) | ||||
−0.166012 | + | 0.986124i | \(0.553089\pi\) | |||||||
\(572\) | 6.93612 | − | 1.85853i | 0.290014 | − | 0.0777090i | ||||
\(573\) | 3.08339 | + | 11.5074i | 0.128810 | + | 0.480727i | ||||
\(574\) | 10.0107 | − | 5.77970i | 0.417840 | − | 0.241240i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.24130 | − | 2.15000i | −0.0517209 | − | 0.0895832i | ||||
\(577\) | −12.2981 | + | 12.2981i | −0.511976 | + | 0.511976i | −0.915131 | − | 0.403156i | \(-0.867913\pi\) |
0.403156 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(578\) | 3.93840 | − | 3.93840i | 0.163816 | − | 0.163816i | ||||
\(579\) | 6.60254 | − | 3.81198i | 0.274392 | − | 0.158420i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.3431 | −1.00992 | ||||||||
\(582\) | −5.19151 | − | 5.19151i | −0.215195 | − | 0.215195i | ||||
\(583\) | 16.9184 | + | 4.53326i | 0.700687 | + | 0.187749i | ||||
\(584\) | 1.66542 | − | 2.88460i | 0.0689157 | − | 0.119365i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.30904 | − | 16.1237i | 0.384553 | − | 0.666065i | ||||
\(587\) | −0.106964 | − | 0.399196i | −0.00441488 | − | 0.0164766i | 0.963683 | − | 0.267048i | \(-0.0860482\pi\) |
−0.968098 | + | 0.250571i | \(0.919382\pi\) | |||||||
\(588\) | −2.51412 | + | 2.51412i | −0.103681 | + | 0.103681i | ||||
\(589\) | 28.1269 | + | 33.8486i | 1.15895 | + | 1.39471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.2721 | + | 8.81734i | 0.628209 | + | 0.362697i | ||||
\(592\) | 3.92827 | − | 1.05258i | 0.161451 | − | 0.0432607i | ||||
\(593\) | −0.915527 | + | 3.41679i | −0.0375962 | + | 0.140311i | −0.982173 | − | 0.187980i | \(-0.939806\pi\) |
0.944577 | + | 0.328291i | \(0.106473\pi\) | |||||||
\(594\) | −8.15666 | − | 4.70925i | −0.334672 | − | 0.193223i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.61379 | −0.270911 | ||||||||
\(597\) | −5.82173 | − | 5.82173i | −0.238268 | − | 0.238268i | ||||
\(598\) | −4.08703 | + | 15.2530i | −0.167131 | + | 0.623741i | ||||
\(599\) | −6.17905 | − | 10.7024i | −0.252469 | − | 0.437290i | 0.711736 | − | 0.702447i | \(-0.247909\pi\) |
−0.964205 | + | 0.265158i | \(0.914576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5516i | 0.797528i | 0.917054 | + | 0.398764i | \(0.130561\pi\) | ||||
−0.917054 | + | 0.398764i | \(0.869439\pi\) | |||||||
\(602\) | −0.676661 | + | 2.52533i | −0.0275787 | + | 0.102925i | ||||
\(603\) | −0.914803 | − | 3.41409i | −0.0372537 | − | 0.139033i | ||||
\(604\) | −8.62740 | − | 14.9431i | −0.351044 | − | 0.608026i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.16212 | − | 10.6731i | 0.250319 | − | 0.433566i | ||||
\(607\) | −11.0587 | − | 11.0587i | −0.448860 | − | 0.448860i | 0.446115 | − | 0.894975i | \(-0.352807\pi\) |
−0.894975 | + | 0.446115i | \(0.852807\pi\) | |||||||
\(608\) | −1.82319 | − | 3.95929i | −0.0739402 | − | 0.160570i | ||||
\(609\) | − | 10.0782i | − | 0.408388i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.941445 | + | 0.543544i | 0.0380868 | + | 0.0219894i | ||||
\(612\) | −11.3924 | − | 3.05258i | −0.460509 | − | 0.123393i | ||||
\(613\) | 3.06788 | − | 0.822036i | 0.123911 | − | 0.0332017i | −0.196331 | − | 0.980538i | \(-0.562903\pi\) |
0.320241 | + | 0.947336i | \(0.396236\pi\) | |||||||
\(614\) | 16.2889 | − | 9.40438i | 0.657365 | − | 0.379530i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 3.42533i | − | 0.138011i | ||||||
\(617\) | 35.6742 | + | 9.55886i | 1.43619 | + | 0.384825i | 0.891197 | − | 0.453617i | \(-0.149867\pi\) |
0.544990 | + | 0.838442i | \(0.316533\pi\) | |||||||
\(618\) | 1.74950 | + | 0.468778i | 0.0703753 | + | 0.0188570i | ||||
\(619\) | 18.5959i | 0.747433i | 0.927543 | + | 0.373716i | \(0.121917\pi\) | ||||
−0.927543 | + | 0.373716i | \(0.878083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.9370 | − | 10.3560i | 0.719789 | − | 0.415570i | ||||
\(622\) | 4.32396 | − | 1.15860i | 0.173375 | − | 0.0464556i | ||||
\(623\) | −3.07835 | − | 0.824843i | −0.123332 | − | 0.0330466i | ||||
\(624\) | 1.87298 | + | 1.08137i | 0.0749793 | + | 0.0432893i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 12.4723i | − | 0.498492i | ||||||
\(627\) | −6.11324 | − | 4.32436i | −0.244139 | − | 0.172698i | ||||
\(628\) | −2.29035 | − | 2.29035i | −0.0913949 | − | 0.0913949i | ||||
\(629\) | 9.66032 | − | 16.7322i | 0.385182 | − | 0.667155i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8281 | − | 32.6113i | −0.749536 | − | 1.29823i | −0.948045 | − | 0.318136i | \(-0.896943\pi\) |
0.198509 | − | 0.980099i | \(-0.436390\pi\) | |||||||
\(632\) | −0.00845484 | − | 0.0315539i | −0.000336315 | − | 0.00125515i | ||||
\(633\) | 1.45035 | − | 5.41278i | 0.0576462 | − | 0.215139i | ||||
\(634\) | 5.66192i | 0.224864i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.63764 | + | 4.56852i | 0.104589 | + | 0.181154i | ||||
\(637\) | −3.84658 | + | 14.3556i | −0.152407 | + | 0.568791i | ||||
\(638\) | −16.4975 | − | 16.4975i | −0.653141 | − | 0.653141i | ||||
\(639\) | −15.4487 | −0.611142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.8628 | + | 17.2413i | 1.17951 | + | 0.680990i | 0.955901 | − | 0.293689i | \(-0.0948829\pi\) |
0.223609 | + | 0.974679i | \(0.428216\pi\) | |||||||
\(642\) | 1.30641 | − | 4.87560i | 0.0515600 | − | 0.192424i | ||||
\(643\) | −29.4620 | + | 7.89433i | −1.16187 | + | 0.311322i | −0.787712 | − | 0.616044i | \(-0.788734\pi\) |
−0.374157 | + | 0.927365i | \(0.622068\pi\) | |||||||
\(644\) | 6.52336 | + | 3.76627i | 0.257057 | + | 0.148412i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.4251 | − | 7.17579i | −0.764269 | − | 0.282328i | ||||
\(647\) | −9.95134 | + | 9.95134i | −0.391227 | + | 0.391227i | −0.875125 | − | 0.483897i | \(-0.839221\pi\) |
0.483897 | + | 0.875125i | \(0.339221\pi\) | |||||||
\(648\) | 1.19344 | + | 4.45399i | 0.0468829 | + | 0.174969i | ||||
\(649\) | 3.10057 | − | 5.37034i | 0.121708 | − | 0.210804i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.20803 | + | 9.02058i | −0.204119 | + | 0.353544i | ||||
\(652\) | −17.8409 | − | 4.78046i | −0.698705 | − | 0.187217i | ||||
\(653\) | −25.1527 | − | 25.1527i | −0.984302 | − | 0.984302i | 0.0155764 | − | 0.999879i | \(-0.495042\pi\) |
−0.999879 | + | 0.0155764i | \(0.995042\pi\) | |||||||
\(654\) | −6.63236 | −0.259346 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.97985 | − | 4.02982i | 0.272517 | − | 0.157338i | ||||
\(657\) | −5.84718 | + | 5.84718i | −0.228120 | + | 0.228120i | ||||
\(658\) | 0.366673 | − | 0.366673i | 0.0142944 | − | 0.0142944i | ||||
\(659\) | −5.83576 | − | 10.1078i | −0.227329 | − | 0.393745i | 0.729687 | − | 0.683782i | \(-0.239666\pi\) |
−0.957016 | + | 0.290036i | \(0.906333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.70480 | + | 2.13897i | −0.144100 | + | 0.0831963i | −0.570317 | − | 0.821425i | \(-0.693180\pi\) |
0.426217 | + | 0.904621i | \(0.359846\pi\) | |||||||
\(662\) | −3.48916 | − | 13.0217i | −0.135610 | − | 0.506104i | ||||
\(663\) | 9.92453 | − | 2.65927i | 0.385437 | − | 0.103277i | ||||
\(664\) | −16.9729 | −0.658675 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0964 | −0.391226 | ||||||||
\(667\) | 49.5580 | − | 13.2790i | 1.91890 | − | 0.514166i | ||||
\(668\) | −5.62051 | − | 20.9760i | −0.217464 | − | 0.811587i | ||||
\(669\) | −7.46721 | + | 4.31119i | −0.288699 | + | 0.166680i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.740853 | − | 1.28319i | −0.0286003 | − | 0.0495372i | ||||
\(672\) | 0.729487 | − | 0.729487i | 0.0281406 | − | 0.0281406i | ||||
\(673\) | −28.2136 | + | 28.2136i | −1.08756 | + | 1.08756i | −0.0917757 | + | 0.995780i | \(0.529254\pi\) |
−0.995780 | + | 0.0917757i | \(0.970746\pi\) | |||||||
\(674\) | −27.7776 | + | 16.0374i | −1.06995 | + | 0.617738i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.95975 | −0.152298 | ||||||||
\(677\) | −28.7454 | − | 28.7454i | −1.10477 | − | 1.10477i | −0.993826 | − | 0.110948i | \(-0.964611\pi\) |
−0.110948 | − | 0.993826i | \(-0.535389\pi\) | |||||||
\(678\) | −0.463446 | − | 0.124180i | −0.0177985 | − | 0.00476910i | ||||
\(679\) | −7.31958 | + | 12.6779i | −0.280900 | + | 0.486532i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.76268 | − | 13.4454i | 0.297467 | − | 0.515227i | ||||
\(682\) | 6.24094 | + | 23.2915i | 0.238978 | + | 0.891878i | ||||
\(683\) | 26.4931 | − | 26.4931i | 1.01373 | − | 1.01373i | 0.0138253 | − | 0.999904i | \(-0.495599\pi\) |
0.999904 | − | 0.0138253i | \(-0.00440088\pi\) | |||||||
\(684\) | 1.82801 | + | 10.6659i | 0.0698956 | + | 0.407821i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.8342 | + | 8.56451i | 0.566371 | + | 0.326994i | ||||
\(687\) | 9.89611 | − | 2.65166i | 0.377560 | − | 0.101167i | ||||
\(688\) | −0.471793 | + | 1.76075i | −0.0179869 | + | 0.0671281i | ||||
\(689\) | 19.0965 | + | 11.0254i | 0.727518 | + | 0.420032i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6142 | 0.555951 | 0.277975 | − | 0.960588i | \(-0.410337\pi\) | ||||
0.277975 | + | 0.960588i | \(0.410337\pi\) | |||||||
\(692\) | 4.72427 | + | 4.72427i | 0.179590 | + | 0.179590i | ||||
\(693\) | −2.20093 | + | 8.21398i | −0.0836064 | + | 0.312023i | ||||
\(694\) | 1.88116 | + | 3.25826i | 0.0714078 | + | 0.123682i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 7.02687i | − | 0.266353i | ||||||
\(697\) | 9.91003 | − | 36.9847i | 0.375369 | − | 1.40090i | ||||
\(698\) | 8.08471 | + | 30.1725i | 0.306011 | + | 1.14205i | ||||
\(699\) | −5.86897 | − | 10.1654i | −0.221985 | − | 0.384489i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.12955 | + | 14.0808i | −0.307049 | + | 0.531824i | −0.977715 | − | 0.209935i | \(-0.932675\pi\) |
0.670666 | + | 0.741759i | \(0.266008\pi\) | |||||||
\(702\) | −8.38445 | − | 8.38445i | −0.316451 | − | 0.316451i | ||||
\(703\) | −17.6519 | − | 1.62965i | −0.665755 | − | 0.0614634i | ||||
\(704\) | − | 2.38827i | − | 0.0900111i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.1498 | + | 12.2109i | 0.795985 | + | 0.459562i | ||||
\(707\) | −23.7362 | − | 6.36010i | −0.892693 | − | 0.239196i | ||||
\(708\) | 1.80404 | − | 0.483390i | 0.0677998 | − | 0.0181669i | ||||
\(709\) | 5.92229 | − | 3.41924i | 0.222416 | − | 0.128412i | −0.384652 | − | 0.923062i | \(-0.625679\pi\) |
0.607069 | + | 0.794649i | \(0.292345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0810991i | 0.00304145i | ||||||||
\(712\) | −2.14634 | − | 0.575110i | −0.0804375 | − | 0.0215532i | ||||
\(713\) | −51.2196 | − | 13.7242i | −1.91819 | − | 0.513977i | ||||
\(714\) | − | 4.90113i | − | 0.183420i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.3799 | + | 5.99283i | −0.387915 | + | 0.223963i | ||||
\(717\) | 8.17099 | − | 2.18941i | 0.305151 | − | 0.0817651i | ||||
\(718\) | −12.9866 | − | 3.47976i | −0.484657 | − | 0.129864i | ||||
\(719\) | −38.3648 | − | 22.1499i | −1.43077 | − | 0.826054i | −0.433588 | − | 0.901111i | \(-0.642752\pi\) |
−0.997179 | + | 0.0750579i | \(0.976086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.61142i | − | 0.134496i | ||||||
\(722\) | 1.47441 | + | 18.9427i | 0.0548719 | + | 0.704975i | ||||
\(723\) | 6.77274 | + | 6.77274i | 0.251881 | + | 0.251881i | ||||
\(724\) | −11.9338 | + | 20.6699i | −0.443516 | + | 0.768192i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.90479 | + | 3.29918i | 0.0706932 | + | 0.122444i | ||||
\(727\) | 2.48623 | + | 9.27872i | 0.0922090 | + | 0.344129i | 0.996582 | − | 0.0826152i | \(-0.0263272\pi\) |
−0.904373 | + | 0.426744i | \(0.859661\pi\) | |||||||
\(728\) | 1.11611 | − | 4.16538i | 0.0413657 | − | 0.154379i | ||||
\(729\) | − | 2.93749i | − | 0.108796i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.33000 | + | 7.49979i | 0.160151 | + | 0.277390i | ||||
\(732\) | 0.115502 | − | 0.431058i | 0.00426906 | − | 0.0159324i | ||||
\(733\) | 13.8225 | + | 13.8225i | 0.510547 | + | 0.510547i | 0.914694 | − | 0.404147i | \(-0.132432\pi\) |
−0.404147 | + | 0.914694i | \(0.632432\pi\) | |||||||
\(734\) | −1.24542 | −0.0459691 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.54833 | + | 2.62598i | 0.167654 | + | 0.0967948i | ||||
\(737\) | 0.880042 | − | 3.28436i | 0.0324168 | − | 0.120981i | ||||
\(738\) | −19.3271 | + | 5.17868i | −0.711440 | + | 0.190630i | ||||
\(739\) | 2.25750 | + | 1.30337i | 0.0830433 | + | 0.0479451i | 0.540947 | − | 0.841057i | \(-0.318066\pi\) |
−0.457903 | + | 0.889002i | \(0.651399\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.02496 | − | 7.25057i | −0.221332 | − | 0.266356i | ||||
\(742\) | 7.43768 | − | 7.43768i | 0.273046 | − | 0.273046i | ||||
\(743\) | 7.64152 | + | 28.5185i | 0.280340 | + | 1.04624i | 0.952178 | + | 0.305545i | \(0.0988386\pi\) |
−0.671838 | + | 0.740698i | \(0.734495\pi\) | |||||||
\(744\) | −3.63123 | + | 6.28948i | −0.133127 | + | 0.230583i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.2846 | + | 24.7417i | −0.522997 | + | 0.905857i | ||||
\(747\) | 40.7011 | + | 10.9058i | 1.48918 | + | 0.399023i | ||||
\(748\) | −8.02289 | − | 8.02289i | −0.293346 | − | 0.293346i | ||||
\(749\) | −10.0645 | −0.367748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6406 | − | 13.6489i | 0.862659 | − | 0.498056i | −0.00224314 | − | 0.999997i | \(-0.500714\pi\) |
0.864902 | + | 0.501941i | \(0.167381\pi\) | |||||||
\(752\) | 0.255658 | − | 0.255658i | 0.00932288 | − | 0.00932288i | ||||
\(753\) | 13.1284 | − | 13.1284i | 0.478426 | − | 0.478426i | ||||
\(754\) | −14.6862 | − | 25.4373i | −0.534840 | − | 0.926370i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.89835 | + | 2.82806i | −0.178151 | + | 0.102856i | ||||
\(757\) | −9.93389 | − | 37.0738i | −0.361053 | − | 1.34747i | −0.872693 | − | 0.488270i | \(-0.837628\pi\) |
0.511639 | − | 0.859200i | \(-0.329038\pi\) | |||||||
\(758\) | 6.44279 | − | 1.72634i | 0.234013 | − | 0.0627035i | ||||
\(759\) | 9.02228 | 0.327488 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.8413 | −1.37175 | −0.685873 | − | 0.727721i | \(-0.740580\pi\) | ||||
−0.685873 | + | 0.727721i | \(0.740580\pi\) | |||||||
\(762\) | 6.94023 | − | 1.85963i | 0.251418 | − | 0.0673672i | ||||
\(763\) | 3.42272 | + | 12.7738i | 0.123911 | + | 0.462442i | ||||
\(764\) | 14.3433 | − | 8.28113i | 0.518924 | − | 0.299601i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.9861 | − | 20.7606i | −0.433076 | − | 0.750109i | ||||
\(767\) | 5.52032 | − | 5.52032i | 0.199327 | − | 0.199327i | ||||
\(768\) | 0.508625 | − | 0.508625i | 0.0183534 | − | 0.0183534i | ||||
\(769\) | 3.75568 | − | 2.16834i | 0.135433 | − | 0.0781925i | −0.430752 | − | 0.902470i | \(-0.641752\pi\) |
0.566186 | + | 0.824278i | \(0.308418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.10222 | −0.183752 | ||||||||
\(772\) | −7.49467 | − | 7.49467i | −0.269739 | − | 0.269739i | ||||
\(773\) | 15.7765 | + | 4.22729i | 0.567440 | + | 0.152045i | 0.531122 | − | 0.847295i | \(-0.321770\pi\) |
0.0363177 | + | 0.999340i | \(0.488437\pi\) | |||||||
\(774\) | 2.26273 | − | 3.91916i | 0.0813320 | − | 0.140871i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.10347 | + | 8.83948i | −0.183204 | + | 0.317319i | ||||
\(777\) | −1.08589 | − | 4.05261i | −0.0389562 | − | 0.145386i | ||||
\(778\) | 0.744860 | − | 0.744860i | 0.0267045 | − | 0.0267045i | ||||
\(779\) | −34.6263 | + | 5.93453i | −1.24061 | + | 0.212627i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8706 | − | 7.43084i | −0.460546 | − | 0.265897i | ||||
\(782\) | 24.1006 | − | 6.45774i | 0.861836 | − | 0.230928i | ||||
\(783\) | −9.97114 | + | 37.2128i | −0.356340 | + | 1.32988i | ||||
\(784\) | 4.28074 | + | 2.47149i | 0.152884 | + | 0.0882674i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.73425 | 0.168865 | ||||||||
\(787\) | −20.1032 | − | 20.1032i | −0.716600 | − | 0.716600i | 0.251307 | − | 0.967907i | \(-0.419140\pi\) |
−0.967907 | + | 0.251307i | \(0.919140\pi\) | |||||||
\(788\) | 6.34529 | − | 23.6809i | 0.226041 | − | 0.843598i | ||||
\(789\) | 7.49566 | + | 12.9829i | 0.266853 | + | 0.462202i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.956671i | 0.0340153i | ||||||||
\(792\) | −1.53457 | + | 5.72708i | −0.0545285 | + | 0.203503i | ||||
\(793\) | −0.482798 | − | 1.80183i | −0.0171447 | − | 0.0639848i | ||||
\(794\) | 6.54465 | + | 11.3357i | 0.232261 | + | 0.402287i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.72301 | + | 9.91254i | −0.202847 | + | 0.351341i | ||||
\(797\) | −15.3795 | − | 15.3795i | −0.544770 | − | 0.544770i | 0.380154 | − | 0.924923i | \(-0.375871\pi\) |
−0.924923 | + | 0.380154i | \(0.875871\pi\) | |||||||
\(798\) | −4.08460 | + | 1.88090i | −0.144593 | + | 0.0665830i | ||||
\(799\) | − | 1.71766i | − | 0.0607665i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.77741 | + | 2.75824i | 0.168801 | + | 0.0974576i | ||||
\(802\) | −0.906329 | − | 0.242850i | −0.0320036 | − | 0.00857533i | ||||
\(803\) | −7.68389 | + | 2.05889i | −0.271158 | + | 0.0726567i | ||||
\(804\) | 0.886886 | − | 0.512044i | 0.0312780 | − | 0.0180584i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.3572i | 1.06929i | ||||||||
\(807\) | 14.3647 | + | 3.84902i | 0.505663 | + | 0.135492i | ||||
\(808\) | −16.5498 | − | 4.43449i | −0.582218 | − | 0.156005i | ||||
\(809\) | − | 33.7129i | − | 1.18528i | −0.805466 | − | 0.592642i | \(-0.798085\pi\) | ||
0.805466 | − | 0.592642i | \(-0.201915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.19078 | + | 1.84220i | −0.112043 | + | 0.0646883i | −0.554974 | − | 0.831867i | \(-0.687272\pi\) |
0.442931 | + | 0.896556i | \(0.353939\pi\) | |||||||
\(812\) | −13.5336 | + | 3.62632i | −0.474936 | + | 0.127259i | ||||
\(813\) | −17.5065 | − | 4.69086i | −0.613980 | − | 0.164516i | ||||
\(814\) | −8.41146 | − | 4.85636i | −0.294821 | − | 0.170215i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 3.41724i | − | 0.119627i | ||||||
\(817\) | 4.58861 | − | 6.48681i | 0.160535 | − | 0.226945i | ||||
\(818\) | −9.51520 | − | 9.51520i | −0.332691 | − | 0.332691i | ||||
\(819\) | −5.35288 | + | 9.27146i | −0.187045 | + | 0.323971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9004 | + | 18.8801i | 0.380427 | + | 0.658919i | 0.991123 | − | 0.132946i | \(-0.0424437\pi\) |
−0.610696 | + | 0.791865i | \(0.709110\pi\) | |||||||
\(822\) | 1.67879 | + | 6.26532i | 0.0585545 | + | 0.218528i | ||||
\(823\) | −12.7952 | + | 47.7524i | −0.446014 | + | 1.66455i | 0.267232 | + | 0.963632i | \(0.413891\pi\) |
−0.713246 | + | 0.700914i | \(0.752776\pi\) | |||||||
\(824\) | − | 2.51802i | − | 0.0877192i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.86200 | − | 3.22507i | −0.0647871 | − | 0.112215i | ||||
\(827\) | −0.389735 | + | 1.45451i | −0.0135524 | + | 0.0505783i | −0.972371 | − | 0.233441i | \(-0.925001\pi\) |
0.958819 | + | 0.284019i | \(0.0916680\pi\) | |||||||
\(828\) | −9.21962 | − | 9.21962i | −0.320404 | − | 0.320404i | ||||
\(829\) | 14.5438 | 0.505127 | 0.252563 | − | 0.967580i | \(-0.418726\pi\) | ||||
0.252563 | + | 0.967580i | \(0.418726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2921 | − | 8.25155i | −0.495787 | − | 0.286243i | ||||
\(832\) | 0.778192 | − | 2.90425i | 0.0269789 | − | 0.100687i | ||||
\(833\) | 22.6827 | − | 6.07782i | 0.785910 | − | 0.210584i | ||||
\(834\) | 3.37742 | + | 1.94996i | 0.116951 | + | 0.0675215i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.60736 | + | 9.76521i | −0.124763 | + | 0.337737i | ||||
\(837\) | 28.1550 | − | 28.1550i | 0.973179 | − | 0.973179i | ||||
\(838\) | −8.13280 | − | 30.3520i | −0.280943 | − | 1.04849i | ||||
\(839\) | −27.6955 | + | 47.9700i | −0.956155 | + | 1.65611i | −0.224454 | + | 0.974485i | \(0.572060\pi\) |
−0.731702 | + | 0.681625i | \(0.761274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.2165 | + | 57.5327i | −1.14540 | + | 1.98389i | ||||
\(842\) | 15.4163 | + | 4.13078i | 0.531280 | + | 0.142356i | ||||
\(843\) | −2.71425 | − | 2.71425i | −0.0934837 | − | 0.0934837i | ||||
\(844\) | −7.79048 | −0.268159 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.777341 | + | 0.448798i | −0.0267255 | + | 0.0154300i | ||||
\(847\) | 5.37116 | − | 5.37116i | 0.184555 | − | 0.184555i | ||||
\(848\) | 5.18582 | − | 5.18582i | 0.178082 | − | 0.178082i | ||||
\(849\) | −11.7929 | − | 20.4259i | −0.404732 | − | 0.701016i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4974 | − | 10.6795i | 0.634081 | − | 0.366087i | ||||
\(852\) | −1.15850 | − | 4.32356i | −0.0396894 | − | 0.148123i | ||||
\(853\) | −3.24887 | + | 0.870532i | −0.111239 | + | 0.0298064i | −0.314009 | − | 0.949420i | \(-0.601672\pi\) |
0.202770 | + | 0.979226i | \(0.435006\pi\) | |||||||
\(854\) | −0.889814 | −0.0304488 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.01732 | −0.239847 | ||||||||
\(857\) | −54.1712 | + | 14.5151i | −1.85045 | + | 0.495827i | −0.999564 | − | 0.0295186i | \(-0.990603\pi\) |
−0.850889 | + | 0.525346i | \(0.823936\pi\) | |||||||
\(858\) | −1.33685 | − | 4.98918i | −0.0456392 | − | 0.170328i | ||||
\(859\) | −9.38131 | + | 5.41630i | −0.320086 | + | 0.184802i | −0.651431 | − | 0.758708i | \(-0.725831\pi\) |
0.331345 | + | 0.943510i | \(0.392498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.15737 | − | 7.20077i | −0.141683 | − | 0.245402i | ||||
\(862\) | −13.1140 | + | 13.1140i | −0.446666 | + | 0.446666i | ||||
\(863\) | 14.3014 | − | 14.3014i | 0.486824 | − | 0.486824i | −0.420479 | − | 0.907302i | \(-0.638138\pi\) |
0.907302 | + | 0.420479i | \(0.138138\pi\) | |||||||
\(864\) | −3.41531 | + | 1.97183i | −0.116191 | + | 0.0670830i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.10923 | 0.173619 | ||||||||
\(867\) | −2.83291 | − | 2.83291i | −0.0962106 | − | 0.0962106i | ||||
\(868\) | 13.9873 | + | 3.74790i | 0.474761 | + | 0.127212i | ||||
\(869\) | −0.0390087 | + | 0.0675651i | −0.00132328 | + | 0.00229199i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.14035 | − | 3.70719i | 0.0725230 | − | 0.125613i | ||||
\(872\) | 2.38645 | + | 8.90634i | 0.0808153 | + | 0.301607i | ||||
\(873\) | 17.9179 | − | 17.9179i | 0.606430 | − | 0.606430i | ||||
\(874\) | −14.6309 | − | 17.6072i | −0.494899 | − | 0.595572i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.07490 | − | 1.19795i | −0.0701045 | − | 0.0404748i | ||||
\(877\) | −38.7696 | + | 10.3883i | −1.30916 | + | 0.350787i | −0.844905 | − | 0.534917i | \(-0.820343\pi\) |
−0.464251 | + | 0.885704i | \(0.653676\pi\) | |||||||
\(878\) | 3.24013 | − | 12.0923i | 0.109349 | − | 0.408097i | ||||
\(879\) | −11.5979 | − | 6.69603i | −0.391186 | − | 0.225851i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6745 | 0.763922 | 0.381961 | − | 0.924178i | \(-0.375249\pi\) | ||||
0.381961 | + | 0.924178i | \(0.375249\pi\) | |||||||
\(882\) | −8.67721 | − | 8.67721i | −0.292177 | − | 0.292177i | ||||
\(883\) | 2.64511 | − | 9.87168i | 0.0890150 | − | 0.332209i | −0.907029 | − | 0.421068i | \(-0.861655\pi\) |
0.996044 | + | 0.0888592i | \(0.0283221\pi\) | |||||||
\(884\) | −7.14206 | − | 12.3704i | −0.240214 | − | 0.416062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 38.8174i | − | 1.30410i | ||||||
\(887\) | 8.93508 | − | 33.3462i | 0.300011 | − | 1.11966i | −0.637145 | − | 0.770744i | \(-0.719885\pi\) |
0.937156 | − | 0.348911i | \(-0.113449\pi\) | |||||||
\(888\) | −0.757124 | − | 2.82562i | −0.0254074 | − | 0.0948217i | ||||
\(889\) | −7.16321 | − | 12.4070i | −0.240246 | − | 0.416119i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.50628 | − | 9.53716i | 0.184467 | − | 0.319507i | ||||
\(892\) | 8.47617 | + | 8.47617i | 0.283803 | + | 0.283803i | ||||
\(893\) | −1.43150 | + | 0.659183i | −0.0479033 | + | 0.0220587i | ||||
\(894\) | 4.75733i | 0.159109i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.24208 | − | 0.717117i | −0.0414951 | − | 0.0239572i | ||||
\(897\) | 10.9715 | + | 2.93982i | 0.366329 | + | 0.0981576i | ||||
\(898\) | 10.5238 | − | 2.81985i | 0.351184 | − | 0.0940995i | ||||
\(899\) | 85.4184 | − | 49.3163i | 2.84886 | − | 1.64479i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 34.8414i | − | 1.16074i | ||||||
\(902\) | −18.5927 | − | 4.98189i | −0.619068 | − | 0.165879i | ||||
\(903\) | 1.81648 | + | 0.486725i | 0.0604488 | + | 0.0161972i | ||||
\(904\) | 0.667026i | 0.0221850i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.7486 | + | 6.20572i | −0.357099 | + | 0.206171i | ||||
\(907\) | 17.7271 | − | 4.74996i | 0.588618 | − | 0.157720i | 0.0477964 | − | 0.998857i | \(-0.484780\pi\) |
0.540821 | + | 0.841137i | \(0.318113\pi\) | |||||||
\(908\) | −20.8484 | − | 5.58632i | −0.691879 | − | 0.185388i | ||||
\(909\) | 36.8371 | + | 21.2679i | 1.22181 | + | 0.705412i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9694i | 0.595351i | 0.954667 | + | 0.297676i | \(0.0962114\pi\) | ||||
−0.954667 | + | 0.297676i | \(0.903789\pi\) | |||||||
\(912\) | −2.84793 | + | 1.31143i | −0.0943045 | + | 0.0434257i | ||||
\(913\) | 28.6631 | + | 28.6631i | 0.948610 | + | 0.948610i | ||||
\(914\) | 7.75500 | − | 13.4321i | 0.256513 | − | 0.444293i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.12161 | − | 12.3350i | −0.235305 | − | 0.407560i | ||||
\(917\) | −2.44317 | − | 9.11805i | −0.0806807 | − | 0.301105i | ||||
\(918\) | −4.84907 | + | 18.0970i | −0.160043 | + | 0.597290i | ||||
\(919\) | − | 37.9480i | − | 1.25179i | −0.779908 | − | 0.625895i | \(-0.784734\pi\) | ||
0.779908 | − | 0.625895i | \(-0.215266\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76461 | − | 11.7166i | −0.222901 | − | 0.386077i | ||||
\(922\) | −0.817997 | + | 3.05281i | −0.0269393 | + | 0.100539i | ||||
\(923\) | −13.2300 | − | 13.2300i | −0.435472 | − | 0.435472i | ||||
\(924\) | −2.46386 | −0.0810549 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.4306 | + | 18.1465i | 1.03287 | + | 0.596331i | ||||
\(927\) | −1.61794 | + | 6.03822i | −0.0531400 | + | 0.198321i | ||||
\(928\) | −9.43611 | + | 2.52840i | −0.309756 | + | 0.0829988i | ||||
\(929\) | −48.7534 | − | 28.1478i | −1.59955 | − | 0.923498i | −0.991574 | − | 0.129540i | \(-0.958650\pi\) |
−0.607972 | − | 0.793958i | \(-0.708017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.7702 | − | 16.5713i | −0.451299 | − | 0.543104i | ||||
\(932\) | −11.5389 | + | 11.5389i | −0.377969 | + | 0.377969i | ||||
\(933\) | −0.833386 | − | 3.11024i | −0.0272838 | − | 0.101825i | ||||
\(934\) | 10.7156 | − | 18.5599i | 0.350624 | − | 0.607298i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.73222 | + | 6.46440i | −0.121991 | + | 0.211295i | ||||
\(937\) | 38.7515 | + | 10.3834i | 1.26596 | + | 0.339212i | 0.828481 | − | 0.560017i | \(-0.189206\pi\) |
0.437477 | + | 0.899230i | \(0.355872\pi\) | |||||||
\(938\) | −1.44387 | − | 1.44387i | −0.0471442 | − | 0.0471442i | ||||
\(939\) | −8.97136 | −0.292769 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.03359 | − | 3.48349i | 0.196689 | − | 0.113559i | −0.398421 | − | 0.917203i | \(-0.630442\pi\) |
0.595110 | + | 0.803644i | \(0.297108\pi\) | |||||||
\(942\) | −1.64746 | + | 1.64746i | −0.0536771 | + | 0.0536771i | ||||
\(943\) | 29.9310 | − | 29.9310i | 0.974688 | − | 0.974688i | ||||
\(944\) | −1.29825 | − | 2.24864i | −0.0422545 | − | 0.0731869i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.77023 | − | 2.17675i | 0.122581 | − | 0.0707721i | ||||
\(947\) | 4.33802 | + | 16.1897i | 0.140967 | + | 0.526095i | 0.999902 | + | 0.0140106i | \(0.00445985\pi\) |
−0.858935 | + | 0.512084i | \(0.828873\pi\) | |||||||
\(948\) | −0.0226968 | + | 0.00608160i | −0.000737159 | + | 0.000197521i | ||||
\(949\) | −10.0149 | −0.325096 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.07264 | 0.132064 | ||||||||
\(952\) | −6.58153 | + | 1.76352i | −0.213309 | + | 0.0571559i | ||||
\(953\) | 6.50740 | + | 24.2860i | 0.210795 | + | 0.786699i | 0.987604 | + | 0.156963i | \(0.0501704\pi\) |
−0.776809 | + | 0.629736i | \(0.783163\pi\) | |||||||
\(954\) | −15.7678 | + | 9.10352i | −0.510500 | + | 0.294737i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.88015 | − | 10.1847i | −0.190178 | − | 0.329397i | ||||
\(957\) | −11.8667 | + | 11.8667i | −0.383596 | + | 0.383596i | ||||
\(958\) | −7.06609 | + | 7.06609i | −0.228295 | + | 0.228295i | ||||
\(959\) | 11.2005 | − | 6.46662i | 0.361683 | − | 0.208818i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −70.9395 | −2.28837 | ||||||||
\(962\) | −8.64636 | − | 8.64636i | −0.278770 | − | 0.278770i | ||||
\(963\) | 16.8276 | + | 4.50894i | 0.542262 | + | 0.145299i | ||||
\(964\) | 6.65790 | − | 11.5318i | 0.214436 | − | 0.371415i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.70909 | − | 4.69228i | 0.0871636 | − | 0.150972i | ||||
\(967\) | −6.83495 | − | 25.5084i | −0.219797 | − | 0.820295i | −0.984422 | − | 0.175819i | \(-0.943743\pi\) |
0.764625 | − | 0.644475i | \(-0.222924\pi\) | |||||||
\(968\) | 3.74497 | − | 3.74497i | 0.120368 | − | 0.120368i | ||||
\(969\) | −5.16158 | + | 13.9725i | −0.165814 | + | 0.448862i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.03518 | − | 3.48441i | −0.193678 | − | 0.111820i | 0.400025 | − | 0.916504i | \(-0.369001\pi\) |
−0.593703 | + | 0.804684i | \(0.702335\pi\) | |||||||
\(972\) | 14.6316 | − | 3.92053i | 0.469309 | − | 0.125751i | ||||
\(973\) | 2.01260 | − | 7.51114i | 0.0645211 | − | 0.240796i | ||||
\(974\) | −4.84298 | − | 2.79609i | −0.155179 | − | 0.0895926i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.620411 | −0.0198589 | ||||||||
\(977\) | −8.36612 | − | 8.36612i | −0.267656 | − | 0.267656i | 0.560499 | − | 0.828155i | \(-0.310609\pi\) |
−0.828155 | + | 0.560499i | \(0.810609\pi\) | |||||||
\(978\) | −3.43861 | + | 12.8331i | −0.109955 | + | 0.410356i | ||||
\(979\) | 2.65343 | + | 4.59587i | 0.0848039 | + | 0.146885i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 22.8909i | − | 0.730850i | ||||||
\(982\) | −7.90969 | + | 29.5194i | −0.252408 | + | 0.942000i | ||||
\(983\) | 1.60946 | + | 6.00658i | 0.0513338 | + | 0.191580i | 0.986831 | − | 0.161753i | \(-0.0517148\pi\) |
−0.935497 | + | 0.353333i | \(0.885048\pi\) | |||||||
\(984\) | −2.89867 | − | 5.02064i | −0.0924061 | − | 0.160052i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −23.2051 | + | 40.1923i | −0.739000 | + | 1.27999i | ||||
\(987\) | −0.263750 | − | 0.263750i | −0.00839524 | − | 0.00839524i | ||||
\(988\) | −7.56862 | + | 10.6996i | −0.240790 | + | 0.340399i | ||||
\(989\) | 9.57362i | 0.304423i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.1901 | + | 26.0905i | 1.43551 | + | 0.828793i | 0.997533 | − | 0.0701930i | \(-0.0223615\pi\) |
0.437978 | + | 0.898986i | \(0.355695\pi\) | |||||||
\(992\) | 9.75248 | + | 2.61317i | 0.309641 | + | 0.0829682i | ||||
\(993\) | −9.36659 | + | 2.50977i | −0.297240 | + | 0.0796451i | ||||
\(994\) | −7.72923 | + | 4.46247i | −0.245156 | + | 0.141541i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.2087i | 0.386846i | ||||||||
\(997\) | −27.0771 | − | 7.25528i | −0.857539 | − | 0.229777i | −0.196847 | − | 0.980434i | \(-0.563070\pi\) |
−0.660692 | + | 0.750657i | \(0.729737\pi\) | |||||||
\(998\) | −25.9461 | − | 6.95223i | −0.821308 | − | 0.220069i | ||||
\(999\) | 16.0383i | 0.507428i |
(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 | 950.2.q.g.293.2 | 32 | ||
5.2 | odd | 4 | inner | 950.2.q.g.407.2 | 32 | ||
5.3 | odd | 4 | 190.2.m.b.27.7 | ✓ | 32 | ||
5.4 | even | 2 | 190.2.m.b.103.7 | yes | 32 | ||
19.12 | odd | 6 | inner | 950.2.q.g.943.2 | 32 | ||
95.12 | even | 12 | inner | 950.2.q.g.107.2 | 32 | ||
95.69 | odd | 6 | 190.2.m.b.183.7 | yes | 32 | ||
95.88 | even | 12 | 190.2.m.b.107.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.m.b.27.7 | ✓ | 32 | 5.3 | odd | 4 | ||
190.2.m.b.103.7 | yes | 32 | 5.4 | even | 2 | ||
190.2.m.b.107.7 | yes | 32 | 95.88 | even | 12 | ||
190.2.m.b.183.7 | yes | 32 | 95.69 | odd | 6 | ||
950.2.q.g.107.2 | 32 | 95.12 | even | 12 | inner | ||
950.2.q.g.293.2 | 32 | 1.1 | even | 1 | trivial | ||
950.2.q.g.407.2 | 32 | 5.2 | odd | 4 | inner | ||
950.2.q.g.943.2 | 32 | 19.12 | odd | 6 | inner |