Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(23,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.67 |
Dual form | 154.2.e.e.23.2 |
$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.20711 | − | 2.09077i | 0.696923 | − | 1.20711i | −0.272605 | − | 0.962126i | \(-0.587885\pi\) |
0.969528 | − | 0.244981i | \(-0.0787816\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.292893 | + | 0.507306i | 0.130986 | + | 0.226874i | 0.924057 | − | 0.382255i | \(-0.124852\pi\) |
−0.793071 | + | 0.609129i | \(0.791519\pi\) | |||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 1.62132 | − | 2.09077i | 0.612801 | − | 0.790237i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0.292893 | − | 0.507306i | 0.0926210 | − | 0.160424i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 1.20711 | + | 2.09077i | 0.348462 | + | 0.603553i | ||||
\(13\) | −3.82843 | −1.06181 | −0.530907 | − | 0.847430i | \(-0.678149\pi\) | ||||
−0.530907 | + | 0.847430i | \(0.678149\pi\) | |||||||
\(14\) | −2.62132 | − | 0.358719i | −0.700577 | − | 0.0958718i | ||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.82843 | + | 3.16693i | −0.443459 | + | 0.768093i | −0.997943 | − | 0.0641009i | \(-0.979582\pi\) |
0.554485 | + | 0.832194i | \(0.312915\pi\) | |||||||
\(18\) | −1.41421 | + | 2.44949i | −0.333333 | + | 0.577350i | ||||
\(19\) | 0.292893 | + | 0.507306i | 0.0671943 | + | 0.116384i | 0.897665 | − | 0.440678i | \(-0.145262\pi\) |
−0.830471 | + | 0.557062i | \(0.811929\pi\) | |||||||
\(20\) | −0.585786 | −0.130986 | ||||||||
\(21\) | −2.41421 | − | 5.91359i | −0.526825 | − | 1.29045i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.12132 | + | 5.40629i | 0.650840 | + | 1.12729i | 0.982919 | + | 0.184037i | \(0.0589166\pi\) |
−0.332079 | + | 0.943252i | \(0.607750\pi\) | |||||||
\(24\) | 1.20711 | − | 2.09077i | 0.246400 | − | 0.426777i | ||||
\(25\) | 2.32843 | − | 4.03295i | 0.465685 | − | 0.806591i | ||||
\(26\) | 1.91421 | + | 3.31552i | 0.375408 | + | 0.650226i | ||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 1.00000 | + | 2.44949i | 0.188982 | + | 0.462910i | ||||
\(29\) | 2.65685 | 0.493365 | 0.246683 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246683 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(30\) | −0.707107 | − | 1.22474i | −0.129099 | − | 0.223607i | ||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.20711 | + | 2.09077i | 0.210130 | + | 0.363956i | ||||
\(34\) | 3.65685 | 0.627145 | ||||||||
\(35\) | 1.53553 | + | 0.210133i | 0.259553 | + | 0.0355190i | ||||
\(36\) | 2.82843 | 0.471405 | ||||||||
\(37\) | 4.70711 | + | 8.15295i | 0.773844 | + | 1.34034i | 0.935442 | + | 0.353480i | \(0.115002\pi\) |
−0.161599 | + | 0.986857i | \(0.551665\pi\) | |||||||
\(38\) | 0.292893 | − | 0.507306i | 0.0475136 | − | 0.0822959i | ||||
\(39\) | −4.62132 | + | 8.00436i | −0.740003 | + | 1.28172i | ||||
\(40\) | 0.292893 | + | 0.507306i | 0.0463105 | + | 0.0802121i | ||||
\(41\) | −5.41421 | −0.845558 | −0.422779 | − | 0.906233i | \(-0.638945\pi\) | ||||
−0.422779 | + | 0.906233i | \(0.638945\pi\) | |||||||
\(42\) | −3.91421 | + | 5.04757i | −0.603976 | + | 0.778856i | ||||
\(43\) | −5.65685 | −0.862662 | −0.431331 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 0.828427 | − | 1.43488i | 0.123495 | − | 0.213899i | ||||
\(46\) | 3.12132 | − | 5.40629i | 0.460214 | − | 0.797113i | ||||
\(47\) | 5.24264 | + | 9.08052i | 0.764718 | + | 1.32453i | 0.940396 | + | 0.340082i | \(0.110455\pi\) |
−0.175678 | + | 0.984448i | \(0.556212\pi\) | |||||||
\(48\) | −2.41421 | −0.348462 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | −4.65685 | −0.658579 | ||||||||
\(51\) | 4.41421 | + | 7.64564i | 0.618114 | + | 1.07060i | ||||
\(52\) | 1.91421 | − | 3.31552i | 0.265454 | − | 0.459779i | ||||
\(53\) | −3.94975 | + | 6.84116i | −0.542540 | + | 0.939706i | 0.456218 | + | 0.889868i | \(0.349204\pi\) |
−0.998757 | + | 0.0498379i | \(0.984130\pi\) | |||||||
\(54\) | −0.207107 | − | 0.358719i | −0.0281837 | − | 0.0488155i | ||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | 1.62132 | − | 2.09077i | 0.216658 | − | 0.279391i | ||||
\(57\) | 1.41421 | 0.187317 | ||||||||
\(58\) | −1.32843 | − | 2.30090i | −0.174431 | − | 0.302123i | ||||
\(59\) | 2.79289 | − | 4.83743i | 0.363604 | − | 0.629780i | −0.624947 | − | 0.780667i | \(-0.714880\pi\) |
0.988551 | + | 0.150887i | \(0.0482129\pi\) | |||||||
\(60\) | −0.707107 | + | 1.22474i | −0.0912871 | + | 0.158114i | ||||
\(61\) | −5.91421 | − | 10.2437i | −0.757237 | − | 1.31157i | −0.944254 | − | 0.329217i | \(-0.893215\pi\) |
0.187017 | − | 0.982357i | \(-0.440118\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | −7.41421 | − | 1.01461i | −0.934103 | − | 0.127829i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.12132 | − | 1.94218i | −0.139083 | − | 0.240898i | ||||
\(66\) | 1.20711 | − | 2.09077i | 0.148585 | − | 0.257356i | ||||
\(67\) | −1.37868 | + | 2.38794i | −0.168433 | + | 0.291734i | −0.937869 | − | 0.346990i | \(-0.887204\pi\) |
0.769436 | + | 0.638723i | \(0.220537\pi\) | |||||||
\(68\) | −1.82843 | − | 3.16693i | −0.221729 | − | 0.384047i | ||||
\(69\) | 15.0711 | 1.81434 | ||||||||
\(70\) | −0.585786 | − | 1.43488i | −0.0700149 | − | 0.171501i | ||||
\(71\) | −11.0711 | −1.31389 | −0.656947 | − | 0.753937i | \(-0.728152\pi\) | ||||
−0.656947 | + | 0.753937i | \(0.728152\pi\) | |||||||
\(72\) | −1.41421 | − | 2.44949i | −0.166667 | − | 0.288675i | ||||
\(73\) | 4.70711 | − | 8.15295i | 0.550925 | − | 0.954230i | −0.447283 | − | 0.894393i | \(-0.647608\pi\) |
0.998208 | − | 0.0598379i | \(-0.0190584\pi\) | |||||||
\(74\) | 4.70711 | − | 8.15295i | 0.547190 | − | 0.947761i | ||||
\(75\) | −5.62132 | − | 9.73641i | −0.649094 | − | 1.12426i | ||||
\(76\) | −0.585786 | −0.0671943 | ||||||||
\(77\) | 1.00000 | + | 2.44949i | 0.113961 | + | 0.279145i | ||||
\(78\) | 9.24264 | 1.04652 | ||||||||
\(79\) | 6.62132 | + | 11.4685i | 0.744957 | + | 1.29030i | 0.950215 | + | 0.311595i | \(0.100863\pi\) |
−0.205258 | + | 0.978708i | \(0.565803\pi\) | |||||||
\(80\) | 0.292893 | − | 0.507306i | 0.0327465 | − | 0.0567185i | ||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 2.70711 | + | 4.68885i | 0.298950 | + | 0.517796i | ||||
\(83\) | −12.1421 | −1.33277 | −0.666386 | − | 0.745607i | \(-0.732160\pi\) | ||||
−0.666386 | + | 0.745607i | \(0.732160\pi\) | |||||||
\(84\) | 6.32843 | + | 0.866025i | 0.690488 | + | 0.0944911i | ||||
\(85\) | −2.14214 | −0.232347 | ||||||||
\(86\) | 2.82843 | + | 4.89898i | 0.304997 | + | 0.528271i | ||||
\(87\) | 3.20711 | − | 5.55487i | 0.343838 | − | 0.595545i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −6.24264 | − | 10.8126i | −0.661719 | − | 1.14613i | −0.980164 | − | 0.198189i | \(-0.936494\pi\) |
0.318445 | − | 0.947941i | \(-0.396839\pi\) | |||||||
\(90\) | −1.65685 | −0.174648 | ||||||||
\(91\) | −6.20711 | + | 8.00436i | −0.650682 | + | 0.839085i | ||||
\(92\) | −6.24264 | −0.650840 | ||||||||
\(93\) | −4.82843 | − | 8.36308i | −0.500685 | − | 0.867211i | ||||
\(94\) | 5.24264 | − | 9.08052i | 0.540737 | − | 0.936584i | ||||
\(95\) | −0.171573 | + | 0.297173i | −0.0176030 | + | 0.0304893i | ||||
\(96\) | 1.20711 | + | 2.09077i | 0.123200 | + | 0.213388i | ||||
\(97\) | −3.82843 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(98\) | −5.00000 | + | 4.89898i | −0.505076 | + | 0.494872i | ||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 2.32843 | + | 4.03295i | 0.232843 | + | 0.403295i | ||||
\(101\) | −3.08579 | + | 5.34474i | −0.307047 | + | 0.531821i | −0.977715 | − | 0.209936i | \(-0.932674\pi\) |
0.670668 | + | 0.741758i | \(0.266008\pi\) | |||||||
\(102\) | 4.41421 | − | 7.64564i | 0.437072 | − | 0.757031i | ||||
\(103\) | −6.70711 | − | 11.6170i | −0.660871 | − | 1.14466i | −0.980387 | − | 0.197081i | \(-0.936854\pi\) |
0.319516 | − | 0.947581i | \(-0.396480\pi\) | |||||||
\(104\) | −3.82843 | −0.375408 | ||||||||
\(105\) | 2.29289 | − | 2.95680i | 0.223763 | − | 0.288554i | ||||
\(106\) | 7.89949 | 0.767267 | ||||||||
\(107\) | 1.53553 | + | 2.65962i | 0.148446 | + | 0.257115i | 0.930653 | − | 0.365903i | \(-0.119240\pi\) |
−0.782207 | + | 0.623018i | \(0.785906\pi\) | |||||||
\(108\) | −0.207107 | + | 0.358719i | −0.0199289 | + | 0.0345178i | ||||
\(109\) | −8.24264 | + | 14.2767i | −0.789502 | + | 1.36746i | 0.136771 | + | 0.990603i | \(0.456328\pi\) |
−0.926272 | + | 0.376854i | \(0.877006\pi\) | |||||||
\(110\) | 0.292893 | + | 0.507306i | 0.0279263 | + | 0.0483697i | ||||
\(111\) | 22.7279 | 2.15724 | ||||||||
\(112\) | −2.62132 | − | 0.358719i | −0.247691 | − | 0.0338958i | ||||
\(113\) | −8.17157 | −0.768717 | −0.384358 | − | 0.923184i | \(-0.625577\pi\) | ||||
−0.384358 | + | 0.923184i | \(0.625577\pi\) | |||||||
\(114\) | −0.707107 | − | 1.22474i | −0.0662266 | − | 0.114708i | ||||
\(115\) | −1.82843 | + | 3.16693i | −0.170502 | + | 0.295318i | ||||
\(116\) | −1.32843 | + | 2.30090i | −0.123341 | + | 0.213634i | ||||
\(117\) | 5.41421 | + | 9.37769i | 0.500544 | + | 0.866968i | ||||
\(118\) | −5.58579 | −0.514213 | ||||||||
\(119\) | 3.65685 | + | 8.95743i | 0.335223 | + | 0.821126i | ||||
\(120\) | 1.41421 | 0.129099 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −5.91421 | + | 10.2437i | −0.535448 | + | 0.927423i | ||||
\(123\) | −6.53553 | + | 11.3199i | −0.589289 | + | 1.02068i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 2.82843 | + | 6.92820i | 0.251976 | + | 0.617213i | ||||
\(127\) | 15.7279 | 1.39563 | 0.697814 | − | 0.716279i | \(-0.254156\pi\) | ||||
0.697814 | + | 0.716279i | \(0.254156\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.82843 | + | 11.8272i | −0.601209 | + | 1.04133i | ||||
\(130\) | −1.12132 | + | 1.94218i | −0.0983463 | + | 0.170341i | ||||
\(131\) | 0.292893 | + | 0.507306i | 0.0255902 | + | 0.0443235i | 0.878537 | − | 0.477674i | \(-0.158520\pi\) |
−0.852947 | + | 0.521998i | \(0.825187\pi\) | |||||||
\(132\) | −2.41421 | −0.210130 | ||||||||
\(133\) | 1.53553 | + | 0.210133i | 0.133148 | + | 0.0182208i | ||||
\(134\) | 2.75736 | 0.238200 | ||||||||
\(135\) | 0.121320 | + | 0.210133i | 0.0104416 | + | 0.0180854i | ||||
\(136\) | −1.82843 | + | 3.16693i | −0.156786 | + | 0.271562i | ||||
\(137\) | 8.32843 | − | 14.4253i | 0.711546 | − | 1.23243i | −0.252731 | − | 0.967537i | \(-0.581329\pi\) |
0.964277 | − | 0.264897i | \(-0.0853378\pi\) | |||||||
\(138\) | −7.53553 | − | 13.0519i | −0.641467 | − | 1.11105i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −0.949747 | + | 1.22474i | −0.0802683 | + | 0.103510i | ||||
\(141\) | 25.3137 | 2.13180 | ||||||||
\(142\) | 5.53553 | + | 9.58783i | 0.464532 | + | 0.804592i | ||||
\(143\) | 1.91421 | − | 3.31552i | 0.160075 | − | 0.277257i | ||||
\(144\) | −1.41421 | + | 2.44949i | −0.117851 | + | 0.204124i | ||||
\(145\) | 0.778175 | + | 1.34784i | 0.0646239 | + | 0.111932i | ||||
\(146\) | −9.41421 | −0.779126 | ||||||||
\(147\) | −16.2782 | − | 4.54026i | −1.34260 | − | 0.374474i | ||||
\(148\) | −9.41421 | −0.773844 | ||||||||
\(149\) | −8.82843 | − | 15.2913i | −0.723253 | − | 1.25271i | −0.959689 | − | 0.281064i | \(-0.909313\pi\) |
0.236436 | − | 0.971647i | \(-0.424021\pi\) | |||||||
\(150\) | −5.62132 | + | 9.73641i | −0.458979 | + | 0.794975i | ||||
\(151\) | 7.86396 | − | 13.6208i | 0.639960 | − | 1.10844i | −0.345481 | − | 0.938426i | \(-0.612284\pi\) |
0.985441 | − | 0.170018i | \(-0.0543825\pi\) | |||||||
\(152\) | 0.292893 | + | 0.507306i | 0.0237568 | + | 0.0411479i | ||||
\(153\) | 10.3431 | 0.836194 | ||||||||
\(154\) | 1.62132 | − | 2.09077i | 0.130650 | − | 0.168479i | ||||
\(155\) | 2.34315 | 0.188206 | ||||||||
\(156\) | −4.62132 | − | 8.00436i | −0.370002 | − | 0.640862i | ||||
\(157\) | −8.82843 | + | 15.2913i | −0.704585 | + | 1.22038i | 0.262256 | + | 0.964998i | \(0.415534\pi\) |
−0.966841 | + | 0.255379i | \(0.917800\pi\) | |||||||
\(158\) | 6.62132 | − | 11.4685i | 0.526764 | − | 0.912382i | ||||
\(159\) | 9.53553 | + | 16.5160i | 0.756217 | + | 1.30981i | ||||
\(160\) | −0.585786 | −0.0463105 | ||||||||
\(161\) | 16.3640 | + | 2.23936i | 1.28966 | + | 0.176486i | ||||
\(162\) | −9.48528 | −0.745234 | ||||||||
\(163\) | −4.86396 | − | 8.42463i | −0.380975 | − | 0.659868i | 0.610227 | − | 0.792227i | \(-0.291078\pi\) |
−0.991202 | + | 0.132359i | \(0.957745\pi\) | |||||||
\(164\) | 2.70711 | − | 4.68885i | 0.211390 | − | 0.366137i | ||||
\(165\) | −0.707107 | + | 1.22474i | −0.0550482 | + | 0.0953463i | ||||
\(166\) | 6.07107 | + | 10.5154i | 0.471206 | + | 0.816153i | ||||
\(167\) | 13.7279 | 1.06230 | 0.531149 | − | 0.847278i | \(-0.321760\pi\) | ||||
0.531149 | + | 0.847278i | \(0.321760\pi\) | |||||||
\(168\) | −2.41421 | − | 5.91359i | −0.186261 | − | 0.456243i | ||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 1.07107 | + | 1.85514i | 0.0821472 | + | 0.142283i | ||||
\(171\) | 0.828427 | − | 1.43488i | 0.0633514 | − | 0.109728i | ||||
\(172\) | 2.82843 | − | 4.89898i | 0.215666 | − | 0.373544i | ||||
\(173\) | 4.91421 | + | 8.51167i | 0.373621 | + | 0.647130i | 0.990120 | − | 0.140226i | \(-0.0447828\pi\) |
−0.616499 | + | 0.787356i | \(0.711449\pi\) | |||||||
\(174\) | −6.41421 | −0.486260 | ||||||||
\(175\) | −4.65685 | − | 11.4069i | −0.352025 | − | 0.862282i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −6.74264 | − | 11.6786i | −0.506808 | − | 0.877817i | ||||
\(178\) | −6.24264 | + | 10.8126i | −0.467906 | + | 0.810436i | ||||
\(179\) | −0.449747 | + | 0.778985i | −0.0336157 | + | 0.0582241i | −0.882344 | − | 0.470605i | \(-0.844036\pi\) |
0.848728 | + | 0.528829i | \(0.177369\pi\) | |||||||
\(180\) | 0.828427 | + | 1.43488i | 0.0617473 | + | 0.106949i | ||||
\(181\) | −7.65685 | −0.569129 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(182\) | 10.0355 | + | 1.37333i | 0.743883 | + | 0.101798i | ||||
\(183\) | −28.5563 | −2.11095 | ||||||||
\(184\) | 3.12132 | + | 5.40629i | 0.230107 | + | 0.398557i | ||||
\(185\) | −2.75736 | + | 4.77589i | −0.202725 | + | 0.351130i | ||||
\(186\) | −4.82843 | + | 8.36308i | −0.354037 | + | 0.613211i | ||||
\(187\) | −1.82843 | − | 3.16693i | −0.133708 | − | 0.231589i | ||||
\(188\) | −10.4853 | −0.764718 | ||||||||
\(189\) | 0.671573 | − | 0.866025i | 0.0488497 | − | 0.0629941i | ||||
\(190\) | 0.343146 | 0.0248944 | ||||||||
\(191\) | 3.58579 | + | 6.21076i | 0.259458 | + | 0.449395i | 0.966097 | − | 0.258180i | \(-0.0831226\pi\) |
−0.706639 | + | 0.707575i | \(0.749789\pi\) | |||||||
\(192\) | 1.20711 | − | 2.09077i | 0.0871154 | − | 0.150888i | ||||
\(193\) | −10.9497 | + | 18.9655i | −0.788180 | + | 1.36517i | 0.138901 | + | 0.990306i | \(0.455643\pi\) |
−0.927081 | + | 0.374862i | \(0.877690\pi\) | |||||||
\(194\) | 1.91421 | + | 3.31552i | 0.137433 | + | 0.238040i | ||||
\(195\) | −5.41421 | −0.387720 | ||||||||
\(196\) | 6.74264 | + | 1.88064i | 0.481617 | + | 0.134331i | ||||
\(197\) | −0.514719 | −0.0366722 | −0.0183361 | − | 0.999832i | \(-0.505837\pi\) | ||||
−0.0183361 | + | 0.999832i | \(0.505837\pi\) | |||||||
\(198\) | −1.41421 | − | 2.44949i | −0.100504 | − | 0.174078i | ||||
\(199\) | −0.0502525 | + | 0.0870399i | −0.00356231 | + | 0.00617010i | −0.867801 | − | 0.496912i | \(-0.834467\pi\) |
0.864239 | + | 0.503082i | \(0.167801\pi\) | |||||||
\(200\) | 2.32843 | − | 4.03295i | 0.164645 | − | 0.285173i | ||||
\(201\) | 3.32843 | + | 5.76500i | 0.234769 | + | 0.406632i | ||||
\(202\) | 6.17157 | 0.434230 | ||||||||
\(203\) | 4.30761 | − | 5.55487i | 0.302335 | − | 0.389876i | ||||
\(204\) | −8.82843 | −0.618114 | ||||||||
\(205\) | −1.58579 | − | 2.74666i | −0.110756 | − | 0.191835i | ||||
\(206\) | −6.70711 | + | 11.6170i | −0.467306 | + | 0.809398i | ||||
\(207\) | 8.82843 | − | 15.2913i | 0.613618 | − | 1.06282i | ||||
\(208\) | 1.91421 | + | 3.31552i | 0.132727 | + | 0.229890i | ||||
\(209\) | −0.585786 | −0.0405197 | ||||||||
\(210\) | −3.70711 | − | 0.507306i | −0.255815 | − | 0.0350074i | ||||
\(211\) | 7.41421 | 0.510416 | 0.255208 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255208 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(212\) | −3.94975 | − | 6.84116i | −0.271270 | − | 0.469853i | ||||
\(213\) | −13.3640 | + | 23.1471i | −0.915684 | + | 1.58601i | ||||
\(214\) | 1.53553 | − | 2.65962i | 0.104967 | − | 0.181808i | ||||
\(215\) | −1.65685 | − | 2.86976i | −0.112997 | − | 0.195716i | ||||
\(216\) | 0.414214 | 0.0281837 | ||||||||
\(217\) | −4.00000 | − | 9.79796i | −0.271538 | − | 0.665129i | ||||
\(218\) | 16.4853 | 1.11652 | ||||||||
\(219\) | −11.3640 | − | 19.6830i | −0.767905 | − | 1.33005i | ||||
\(220\) | 0.292893 | − | 0.507306i | 0.0197469 | − | 0.0342026i | ||||
\(221\) | 7.00000 | − | 12.1244i | 0.470871 | − | 0.815572i | ||||
\(222\) | −11.3640 | − | 19.6830i | −0.762699 | − | 1.32103i | ||||
\(223\) | 8.58579 | 0.574947 | 0.287473 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287473 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(224\) | 1.00000 | + | 2.44949i | 0.0668153 | + | 0.163663i | ||||
\(225\) | −13.1716 | −0.878105 | ||||||||
\(226\) | 4.08579 | + | 7.07679i | 0.271782 | + | 0.470741i | ||||
\(227\) | 14.4142 | − | 24.9662i | 0.956705 | − | 1.65706i | 0.226288 | − | 0.974061i | \(-0.427341\pi\) |
0.730417 | − | 0.683001i | \(-0.239326\pi\) | |||||||
\(228\) | −0.707107 | + | 1.22474i | −0.0468293 | + | 0.0811107i | ||||
\(229\) | −11.6569 | − | 20.1903i | −0.770307 | − | 1.33421i | −0.937395 | − | 0.348268i | \(-0.886770\pi\) |
0.167088 | − | 0.985942i | \(-0.446564\pi\) | |||||||
\(230\) | 3.65685 | 0.241126 | ||||||||
\(231\) | 6.32843 | + | 0.866025i | 0.416380 | + | 0.0569803i | ||||
\(232\) | 2.65685 | 0.174431 | ||||||||
\(233\) | −0.707107 | − | 1.22474i | −0.0463241 | − | 0.0802357i | 0.841934 | − | 0.539581i | \(-0.181417\pi\) |
−0.888258 | + | 0.459345i | \(0.848084\pi\) | |||||||
\(234\) | 5.41421 | − | 9.37769i | 0.353938 | − | 0.613039i | ||||
\(235\) | −3.07107 | + | 5.31925i | −0.200334 | + | 0.346989i | ||||
\(236\) | 2.79289 | + | 4.83743i | 0.181802 | + | 0.314890i | ||||
\(237\) | 31.9706 | 2.07671 | ||||||||
\(238\) | 5.92893 | − | 7.64564i | 0.384316 | − | 0.495593i | ||||
\(239\) | 20.2132 | 1.30748 | 0.653742 | − | 0.756718i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756718i | \(0.273198\pi\) | |||||||
\(240\) | −0.707107 | − | 1.22474i | −0.0456435 | − | 0.0790569i | ||||
\(241\) | −6.12132 | + | 10.6024i | −0.394309 | + | 0.682963i | −0.993013 | − | 0.118007i | \(-0.962349\pi\) |
0.598704 | + | 0.800971i | \(0.295683\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | −10.8284 | − | 18.7554i | −0.694644 | − | 1.20316i | ||||
\(244\) | 11.8284 | 0.757237 | ||||||||
\(245\) | 2.92893 | − | 2.86976i | 0.187123 | − | 0.183342i | ||||
\(246\) | 13.0711 | 0.833381 | ||||||||
\(247\) | −1.12132 | − | 1.94218i | −0.0713479 | − | 0.123578i | ||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | −14.6569 | + | 25.3864i | −0.928840 | + | 1.60880i | ||||
\(250\) | −2.82843 | − | 4.89898i | −0.178885 | − | 0.309839i | ||||
\(251\) | −26.1421 | −1.65008 | −0.825038 | − | 0.565077i | \(-0.808847\pi\) | ||||
−0.825038 | + | 0.565077i | \(0.808847\pi\) | |||||||
\(252\) | 4.58579 | − | 5.91359i | 0.288877 | − | 0.372521i | ||||
\(253\) | −6.24264 | −0.392471 | ||||||||
\(254\) | −7.86396 | − | 13.6208i | −0.493429 | − | 0.854644i | ||||
\(255\) | −2.58579 | + | 4.47871i | −0.161928 | + | 0.280468i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 12.5711 | + | 21.7737i | 0.784162 | + | 1.35821i | 0.929499 | + | 0.368826i | \(0.120240\pi\) |
−0.145337 | + | 0.989382i | \(0.546427\pi\) | |||||||
\(258\) | 13.6569 | 0.850239 | ||||||||
\(259\) | 24.6777 | + | 3.37706i | 1.53340 | + | 0.209840i | ||||
\(260\) | 2.24264 | 0.139083 | ||||||||
\(261\) | −3.75736 | − | 6.50794i | −0.232575 | − | 0.402831i | ||||
\(262\) | 0.292893 | − | 0.507306i | 0.0180950 | − | 0.0313415i | ||||
\(263\) | 8.52082 | − | 14.7585i | 0.525416 | − | 0.910047i | −0.474146 | − | 0.880446i | \(-0.657243\pi\) |
0.999562 | − | 0.0296008i | \(-0.00942362\pi\) | |||||||
\(264\) | 1.20711 | + | 2.09077i | 0.0742923 | + | 0.128678i | ||||
\(265\) | −4.62742 | −0.284260 | ||||||||
\(266\) | −0.585786 | − | 1.43488i | −0.0359169 | − | 0.0879780i | ||||
\(267\) | −30.1421 | −1.84467 | ||||||||
\(268\) | −1.37868 | − | 2.38794i | −0.0842163 | − | 0.145867i | ||||
\(269\) | −1.17157 | + | 2.02922i | −0.0714321 | + | 0.123724i | −0.899529 | − | 0.436861i | \(-0.856090\pi\) |
0.828097 | + | 0.560585i | \(0.189424\pi\) | |||||||
\(270\) | 0.121320 | − | 0.210133i | 0.00738332 | − | 0.0127883i | ||||
\(271\) | −2.27817 | − | 3.94591i | −0.138389 | − | 0.239697i | 0.788498 | − | 0.615038i | \(-0.210859\pi\) |
−0.926887 | + | 0.375340i | \(0.877526\pi\) | |||||||
\(272\) | 3.65685 | 0.221729 | ||||||||
\(273\) | 9.24264 | + | 22.6398i | 0.559390 | + | 1.37022i | ||||
\(274\) | −16.6569 | −1.00628 | ||||||||
\(275\) | 2.32843 | + | 4.03295i | 0.140409 | + | 0.243196i | ||||
\(276\) | −7.53553 | + | 13.0519i | −0.453586 | + | 0.785634i | ||||
\(277\) | −0.914214 | + | 1.58346i | −0.0549298 | + | 0.0951412i | −0.892183 | − | 0.451675i | \(-0.850827\pi\) |
0.837253 | + | 0.546816i | \(0.184160\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3137 | −0.677334 | ||||||||
\(280\) | 1.53553 | + | 0.210133i | 0.0917657 | + | 0.0125578i | ||||
\(281\) | 8.72792 | 0.520664 | 0.260332 | − | 0.965519i | \(-0.416168\pi\) | ||||
0.260332 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(282\) | −12.6569 | − | 21.9223i | −0.753705 | − | 1.30545i | ||||
\(283\) | 11.7071 | − | 20.2773i | 0.695915 | − | 1.20536i | −0.273956 | − | 0.961742i | \(-0.588332\pi\) |
0.969871 | − | 0.243618i | \(-0.0783344\pi\) | |||||||
\(284\) | 5.53553 | − | 9.58783i | 0.328474 | − | 0.568933i | ||||
\(285\) | 0.414214 | + | 0.717439i | 0.0245359 | + | 0.0424974i | ||||
\(286\) | −3.82843 | −0.226380 | ||||||||
\(287\) | −8.77817 | + | 11.3199i | −0.518159 | + | 0.668191i | ||||
\(288\) | 2.82843 | 0.166667 | ||||||||
\(289\) | 1.81371 | + | 3.14144i | 0.106689 | + | 0.184790i | ||||
\(290\) | 0.778175 | − | 1.34784i | 0.0456960 | − | 0.0791478i | ||||
\(291\) | −4.62132 | + | 8.00436i | −0.270907 | + | 0.469224i | ||||
\(292\) | 4.70711 | + | 8.15295i | 0.275463 | + | 0.477115i | ||||
\(293\) | −10.8284 | −0.632603 | −0.316302 | − | 0.948659i | \(-0.602441\pi\) | ||||
−0.316302 | + | 0.948659i | \(0.602441\pi\) | |||||||
\(294\) | 4.20711 | + | 16.3674i | 0.245363 | + | 0.954569i | ||||
\(295\) | 3.27208 | 0.190508 | ||||||||
\(296\) | 4.70711 | + | 8.15295i | 0.273595 | + | 0.473880i | ||||
\(297\) | −0.207107 | + | 0.358719i | −0.0120176 | + | 0.0208150i | ||||
\(298\) | −8.82843 | + | 15.2913i | −0.511417 | + | 0.885800i | ||||
\(299\) | −11.9497 | − | 20.6976i | −0.691072 | − | 1.19697i | ||||
\(300\) | 11.2426 | 0.649094 | ||||||||
\(301\) | −9.17157 | + | 11.8272i | −0.528641 | + | 0.681707i | ||||
\(302\) | −15.7279 | −0.905040 | ||||||||
\(303\) | 7.44975 | + | 12.9033i | 0.427977 | + | 0.741278i | ||||
\(304\) | 0.292893 | − | 0.507306i | 0.0167986 | − | 0.0290960i | ||||
\(305\) | 3.46447 | − | 6.00063i | 0.198375 | − | 0.343595i | ||||
\(306\) | −5.17157 | − | 8.95743i | −0.295639 | − | 0.512062i | ||||
\(307\) | 9.89949 | 0.564994 | 0.282497 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282497 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(308\) | −2.62132 | − | 0.358719i | −0.149364 | − | 0.0204399i | ||||
\(309\) | −32.3848 | −1.84231 | ||||||||
\(310\) | −1.17157 | − | 2.02922i | −0.0665409 | − | 0.115252i | ||||
\(311\) | −8.36396 | + | 14.4868i | −0.474277 | + | 0.821471i | −0.999566 | − | 0.0294522i | \(-0.990624\pi\) |
0.525289 | + | 0.850924i | \(0.323957\pi\) | |||||||
\(312\) | −4.62132 | + | 8.00436i | −0.261631 | + | 0.453158i | ||||
\(313\) | 10.3284 | + | 17.8894i | 0.583797 | + | 1.01117i | 0.995024 | + | 0.0996335i | \(0.0317670\pi\) |
−0.411227 | + | 0.911533i | \(0.634900\pi\) | |||||||
\(314\) | 17.6569 | 0.996434 | ||||||||
\(315\) | −1.65685 | − | 4.05845i | −0.0933532 | − | 0.228668i | ||||
\(316\) | −13.2426 | −0.744957 | ||||||||
\(317\) | −4.34315 | − | 7.52255i | −0.243935 | − | 0.422508i | 0.717896 | − | 0.696150i | \(-0.245105\pi\) |
−0.961832 | + | 0.273642i | \(0.911772\pi\) | |||||||
\(318\) | 9.53553 | − | 16.5160i | 0.534726 | − | 0.926173i | ||||
\(319\) | −1.32843 | + | 2.30090i | −0.0743776 | + | 0.128826i | ||||
\(320\) | 0.292893 | + | 0.507306i | 0.0163732 | + | 0.0283593i | ||||
\(321\) | 7.41421 | 0.413821 | ||||||||
\(322\) | −6.24264 | − | 15.2913i | −0.347889 | − | 0.852150i | ||||
\(323\) | −2.14214 | −0.119192 | ||||||||
\(324\) | 4.74264 | + | 8.21449i | 0.263480 | + | 0.456361i | ||||
\(325\) | −8.91421 | + | 15.4399i | −0.494472 | + | 0.856450i | ||||
\(326\) | −4.86396 | + | 8.42463i | −0.269390 | + | 0.466597i | ||||
\(327\) | 19.8995 | + | 34.4669i | 1.10044 | + | 1.90603i | ||||
\(328\) | −5.41421 | −0.298950 | ||||||||
\(329\) | 27.4853 | + | 3.76127i | 1.51531 | + | 0.207366i | ||||
\(330\) | 1.41421 | 0.0778499 | ||||||||
\(331\) | 12.0355 | + | 20.8462i | 0.661533 | + | 1.14581i | 0.980213 | + | 0.197946i | \(0.0634271\pi\) |
−0.318680 | + | 0.947862i | \(0.603240\pi\) | |||||||
\(332\) | 6.07107 | − | 10.5154i | 0.333193 | − | 0.577107i | ||||
\(333\) | 13.3137 | − | 23.0600i | 0.729587 | − | 1.26368i | ||||
\(334\) | −6.86396 | − | 11.8887i | −0.375579 | − | 0.650522i | ||||
\(335\) | −1.61522 | −0.0882491 | ||||||||
\(336\) | −3.91421 | + | 5.04757i | −0.213538 | + | 0.275367i | ||||
\(337\) | −28.2426 | −1.53847 | −0.769237 | − | 0.638963i | \(-0.779364\pi\) | ||||
−0.769237 | + | 0.638963i | \(0.779364\pi\) | |||||||
\(338\) | −0.828427 | − | 1.43488i | −0.0450605 | − | 0.0780471i | ||||
\(339\) | −9.86396 | + | 17.0849i | −0.535737 | + | 0.927923i | ||||
\(340\) | 1.07107 | − | 1.85514i | 0.0580868 | − | 0.100609i | ||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | −1.65685 | −0.0895924 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | −5.65685 | −0.304997 | ||||||||
\(345\) | 4.41421 | + | 7.64564i | 0.237653 | + | 0.411628i | ||||
\(346\) | 4.91421 | − | 8.51167i | 0.264190 | − | 0.457590i | ||||
\(347\) | −8.70711 | + | 15.0812i | −0.467422 | + | 0.809599i | −0.999307 | − | 0.0372179i | \(-0.988150\pi\) |
0.531885 | + | 0.846816i | \(0.321484\pi\) | |||||||
\(348\) | 3.20711 | + | 5.55487i | 0.171919 | + | 0.297772i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −7.55025 | + | 9.73641i | −0.403578 | + | 0.520433i | ||||
\(351\) | −1.58579 | −0.0846430 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 1.34315 | − | 2.32640i | 0.0714884 | − | 0.123822i | −0.828065 | − | 0.560632i | \(-0.810558\pi\) |
0.899554 | + | 0.436810i | \(0.143892\pi\) | |||||||
\(354\) | −6.74264 | + | 11.6786i | −0.358367 | + | 0.620710i | ||||
\(355\) | −3.24264 | − | 5.61642i | −0.172101 | − | 0.298089i | ||||
\(356\) | 12.4853 | 0.661719 | ||||||||
\(357\) | 23.1421 | + | 3.16693i | 1.22481 | + | 0.167612i | ||||
\(358\) | 0.899495 | 0.0475398 | ||||||||
\(359\) | −9.62132 | − | 16.6646i | −0.507794 | − | 0.879525i | −0.999959 | − | 0.00902308i | \(-0.997128\pi\) |
0.492165 | − | 0.870502i | \(-0.336206\pi\) | |||||||
\(360\) | 0.828427 | − | 1.43488i | 0.0436619 | − | 0.0756247i | ||||
\(361\) | 9.32843 | − | 16.1573i | 0.490970 | − | 0.850385i | ||||
\(362\) | 3.82843 | + | 6.63103i | 0.201218 | + | 0.348519i | ||||
\(363\) | −2.41421 | −0.126713 | ||||||||
\(364\) | −3.82843 | − | 9.37769i | −0.200664 | − | 0.491525i | ||||
\(365\) | 5.51472 | 0.288654 | ||||||||
\(366\) | 14.2782 | + | 24.7305i | 0.746332 | + | 1.29269i | ||||
\(367\) | 5.36396 | − | 9.29065i | 0.279996 | − | 0.484968i | −0.691387 | − | 0.722485i | \(-0.743000\pi\) |
0.971384 | + | 0.237516i | \(0.0763334\pi\) | |||||||
\(368\) | 3.12132 | − | 5.40629i | 0.162710 | − | 0.281822i | ||||
\(369\) | 7.65685 | + | 13.2621i | 0.398600 | + | 0.690395i | ||||
\(370\) | 5.51472 | 0.286697 | ||||||||
\(371\) | 7.89949 | + | 19.3497i | 0.410121 | + | 1.00459i | ||||
\(372\) | 9.65685 | 0.500685 | ||||||||
\(373\) | 9.98528 | + | 17.2950i | 0.517018 | + | 0.895502i | 0.999805 | + | 0.0197638i | \(0.00629142\pi\) |
−0.482786 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(374\) | −1.82843 | + | 3.16693i | −0.0945457 | + | 0.163758i | ||||
\(375\) | 6.82843 | − | 11.8272i | 0.352618 | − | 0.610753i | ||||
\(376\) | 5.24264 | + | 9.08052i | 0.270369 | + | 0.468292i | ||||
\(377\) | −10.1716 | −0.523863 | ||||||||
\(378\) | −1.08579 | − | 0.148586i | −0.0558468 | − | 0.00764246i | ||||
\(379\) | 27.8701 | 1.43159 | 0.715794 | − | 0.698311i | \(-0.246065\pi\) | ||||
0.715794 | + | 0.698311i | \(0.246065\pi\) | |||||||
\(380\) | −0.171573 | − | 0.297173i | −0.00880150 | − | 0.0152447i | ||||
\(381\) | 18.9853 | − | 32.8835i | 0.972645 | − | 1.68467i | ||||
\(382\) | 3.58579 | − | 6.21076i | 0.183465 | − | 0.317770i | ||||
\(383\) | 3.19239 | + | 5.52938i | 0.163123 | + | 0.282538i | 0.935987 | − | 0.352034i | \(-0.114510\pi\) |
−0.772864 | + | 0.634572i | \(0.781176\pi\) | |||||||
\(384\) | −2.41421 | −0.123200 | ||||||||
\(385\) | −0.949747 | + | 1.22474i | −0.0484036 | + | 0.0624188i | ||||
\(386\) | 21.8995 | 1.11465 | ||||||||
\(387\) | 8.00000 | + | 13.8564i | 0.406663 | + | 0.704361i | ||||
\(388\) | 1.91421 | − | 3.31552i | 0.0971795 | − | 0.168320i | ||||
\(389\) | 11.3640 | − | 19.6830i | 0.576176 | − | 0.997966i | −0.419737 | − | 0.907646i | \(-0.637878\pi\) |
0.995913 | − | 0.0903199i | \(-0.0287889\pi\) | |||||||
\(390\) | 2.70711 | + | 4.68885i | 0.137080 | + | 0.237429i | ||||
\(391\) | −22.8284 | −1.15448 | ||||||||
\(392\) | −1.74264 | − | 6.77962i | −0.0880166 | − | 0.342422i | ||||
\(393\) | 1.41421 | 0.0713376 | ||||||||
\(394\) | 0.257359 | + | 0.445759i | 0.0129656 | + | 0.0224570i | ||||
\(395\) | −3.87868 | + | 6.71807i | −0.195158 | + | 0.338023i | ||||
\(396\) | −1.41421 | + | 2.44949i | −0.0710669 | + | 0.123091i | ||||
\(397\) | −11.0000 | − | 19.0526i | −0.552074 | − | 0.956221i | −0.998125 | − | 0.0612128i | \(-0.980503\pi\) |
0.446051 | − | 0.895008i | \(-0.352830\pi\) | |||||||
\(398\) | 0.100505 | 0.00503786 | ||||||||
\(399\) | 2.29289 | − | 2.95680i | 0.114788 | − | 0.148025i | ||||
\(400\) | −4.65685 | −0.232843 | ||||||||
\(401\) | −9.15685 | − | 15.8601i | −0.457271 | − | 0.792017i | 0.541544 | − | 0.840672i | \(-0.317840\pi\) |
−0.998816 | + | 0.0486549i | \(0.984507\pi\) | |||||||
\(402\) | 3.32843 | − | 5.76500i | 0.166007 | − | 0.287532i | ||||
\(403\) | −7.65685 | + | 13.2621i | −0.381415 | + | 0.660630i | ||||
\(404\) | −3.08579 | − | 5.34474i | −0.153524 | − | 0.265911i | ||||
\(405\) | 5.55635 | 0.276097 | ||||||||
\(406\) | −6.96447 | − | 0.953065i | −0.345641 | − | 0.0472998i | ||||
\(407\) | −9.41421 | −0.466645 | ||||||||
\(408\) | 4.41421 | + | 7.64564i | 0.218536 | + | 0.378516i | ||||
\(409\) | −1.36396 | + | 2.36245i | −0.0674435 | + | 0.116816i | −0.897775 | − | 0.440454i | \(-0.854818\pi\) |
0.830332 | + | 0.557269i | \(0.188151\pi\) | |||||||
\(410\) | −1.58579 | + | 2.74666i | −0.0783164 | + | 0.135648i | ||||
\(411\) | −20.1066 | − | 34.8257i | −0.991786 | − | 1.71782i | ||||
\(412\) | 13.4142 | 0.660871 | ||||||||
\(413\) | −5.58579 | − | 13.6823i | −0.274859 | − | 0.673263i | ||||
\(414\) | −17.6569 | −0.867787 | ||||||||
\(415\) | −3.55635 | − | 6.15978i | −0.174574 | − | 0.302372i | ||||
\(416\) | 1.91421 | − | 3.31552i | 0.0938520 | − | 0.162557i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.292893 | + | 0.507306i | 0.0143259 | + | 0.0248131i | ||||
\(419\) | −26.1421 | −1.27713 | −0.638563 | − | 0.769569i | \(-0.720471\pi\) | ||||
−0.638563 | + | 0.769569i | \(0.720471\pi\) | |||||||
\(420\) | 1.41421 | + | 3.46410i | 0.0690066 | + | 0.169031i | ||||
\(421\) | 0.686292 | 0.0334478 | 0.0167239 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167239 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(422\) | −3.70711 | − | 6.42090i | −0.180459 | − | 0.312564i | ||||
\(423\) | 14.8284 | − | 25.6836i | 0.720983 | − | 1.24878i | ||||
\(424\) | −3.94975 | + | 6.84116i | −0.191817 | + | 0.332236i | ||||
\(425\) | 8.51472 | + | 14.7479i | 0.413025 | + | 0.715379i | ||||
\(426\) | 26.7279 | 1.29497 | ||||||||
\(427\) | −31.0061 | − | 4.24309i | −1.50049 | − | 0.205337i | ||||
\(428\) | −3.07107 | −0.148446 | ||||||||
\(429\) | −4.62132 | − | 8.00436i | −0.223119 | − | 0.386454i | ||||
\(430\) | −1.65685 | + | 2.86976i | −0.0799006 | + | 0.138392i | ||||
\(431\) | 8.79289 | − | 15.2297i | 0.423539 | − | 0.733591i | −0.572744 | − | 0.819734i | \(-0.694121\pi\) |
0.996283 | + | 0.0861437i | \(0.0274544\pi\) | |||||||
\(432\) | −0.207107 | − | 0.358719i | −0.00996443 | − | 0.0172589i | ||||
\(433\) | 26.1421 | 1.25631 | 0.628155 | − | 0.778088i | \(-0.283810\pi\) | ||||
0.628155 | + | 0.778088i | \(0.283810\pi\) | |||||||
\(434\) | −6.48528 | + | 8.36308i | −0.311303 | + | 0.401441i | ||||
\(435\) | 3.75736 | 0.180152 | ||||||||
\(436\) | −8.24264 | − | 14.2767i | −0.394751 | − | 0.683729i | ||||
\(437\) | −1.82843 | + | 3.16693i | −0.0874655 | + | 0.151495i | ||||
\(438\) | −11.3640 | + | 19.6830i | −0.542991 | + | 0.940488i | ||||
\(439\) | 13.6924 | + | 23.7159i | 0.653502 | + | 1.13190i | 0.982267 | + | 0.187487i | \(0.0600342\pi\) |
−0.328765 | + | 0.944412i | \(0.606632\pi\) | |||||||
\(440\) | −0.585786 | −0.0279263 | ||||||||
\(441\) | −14.1421 | + | 13.8564i | −0.673435 | + | 0.659829i | ||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | −6.31371 | − | 10.9357i | −0.299973 | − | 0.519569i | 0.676156 | − | 0.736758i | \(-0.263644\pi\) |
−0.976130 | + | 0.217189i | \(0.930311\pi\) | |||||||
\(444\) | −11.3640 | + | 19.6830i | −0.539310 | + | 0.934112i | ||||
\(445\) | 3.65685 | − | 6.33386i | 0.173352 | − | 0.300254i | ||||
\(446\) | −4.29289 | − | 7.43551i | −0.203274 | − | 0.352082i | ||||
\(447\) | −42.6274 | −2.01621 | ||||||||
\(448\) | 1.62132 | − | 2.09077i | 0.0766002 | − | 0.0987796i | ||||
\(449\) | 22.3431 | 1.05444 | 0.527219 | − | 0.849729i | \(-0.323235\pi\) | ||||
0.527219 | + | 0.849729i | \(0.323235\pi\) | |||||||
\(450\) | 6.58579 | + | 11.4069i | 0.310457 | + | 0.537727i | ||||
\(451\) | 2.70711 | − | 4.68885i | 0.127473 | − | 0.220789i | ||||
\(452\) | 4.08579 | − | 7.07679i | 0.192179 | − | 0.332864i | ||||
\(453\) | −18.9853 | − | 32.8835i | −0.892006 | − | 1.54500i | ||||
\(454\) | −28.8284 | −1.35299 | ||||||||
\(455\) | −5.87868 | − | 0.804479i | −0.275597 | − | 0.0377146i | ||||
\(456\) | 1.41421 | 0.0662266 | ||||||||
\(457\) | 5.82843 | + | 10.0951i | 0.272642 | + | 0.472230i | 0.969538 | − | 0.244943i | \(-0.0787691\pi\) |
−0.696895 | + | 0.717173i | \(0.745436\pi\) | |||||||
\(458\) | −11.6569 | + | 20.1903i | −0.544689 | + | 0.943429i | ||||
\(459\) | −0.757359 | + | 1.31178i | −0.0353505 | + | 0.0612289i | ||||
\(460\) | −1.82843 | − | 3.16693i | −0.0852509 | − | 0.147659i | ||||
\(461\) | −8.31371 | −0.387208 | −0.193604 | − | 0.981080i | \(-0.562018\pi\) | ||||
−0.193604 | + | 0.981080i | \(0.562018\pi\) | |||||||
\(462\) | −2.41421 | − | 5.91359i | −0.112319 | − | 0.275125i | ||||
\(463\) | 12.8284 | 0.596188 | 0.298094 | − | 0.954537i | \(-0.403649\pi\) | ||||
0.298094 | + | 0.954537i | \(0.403649\pi\) | |||||||
\(464\) | −1.32843 | − | 2.30090i | −0.0616707 | − | 0.106817i | ||||
\(465\) | 2.82843 | − | 4.89898i | 0.131165 | − | 0.227185i | ||||
\(466\) | −0.707107 | + | 1.22474i | −0.0327561 | + | 0.0567352i | ||||
\(467\) | 17.0000 | + | 29.4449i | 0.786666 | + | 1.36255i | 0.927999 | + | 0.372584i | \(0.121528\pi\) |
−0.141332 | + | 0.989962i | \(0.545139\pi\) | |||||||
\(468\) | −10.8284 | −0.500544 | ||||||||
\(469\) | 2.75736 | + | 6.75412i | 0.127323 | + | 0.311876i | ||||
\(470\) | 6.14214 | 0.283316 | ||||||||
\(471\) | 21.3137 | + | 36.9164i | 0.982084 | + | 1.70102i | ||||
\(472\) | 2.79289 | − | 4.83743i | 0.128553 | − | 0.222661i | ||||
\(473\) | 2.82843 | − | 4.89898i | 0.130051 | − | 0.225255i | ||||
\(474\) | −15.9853 | − | 27.6873i | −0.734228 | − | 1.27172i | ||||
\(475\) | 2.72792 | 0.125166 | ||||||||
\(476\) | −9.58579 | − | 1.31178i | −0.439364 | − | 0.0601256i | ||||
\(477\) | 22.3431 | 1.02302 | ||||||||
\(478\) | −10.1066 | − | 17.5051i | −0.462265 | − | 0.800667i | ||||
\(479\) | 5.96447 | − | 10.3308i | 0.272523 | − | 0.472024i | −0.696984 | − | 0.717087i | \(-0.745475\pi\) |
0.969507 | + | 0.245062i | \(0.0788084\pi\) | |||||||
\(480\) | −0.707107 | + | 1.22474i | −0.0322749 | + | 0.0559017i | ||||
\(481\) | −18.0208 | − | 31.2130i | −0.821678 | − | 1.42319i | ||||
\(482\) | 12.2426 | 0.557637 | ||||||||
\(483\) | 24.4350 | − | 31.5101i | 1.11183 | − | 1.43376i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −1.12132 | − | 1.94218i | −0.0509165 | − | 0.0881900i | ||||
\(486\) | −10.8284 | + | 18.7554i | −0.491187 | + | 0.850762i | ||||
\(487\) | 4.82843 | − | 8.36308i | 0.218797 | − | 0.378967i | −0.735644 | − | 0.677369i | \(-0.763120\pi\) |
0.954440 | + | 0.298402i | \(0.0964534\pi\) | |||||||
\(488\) | −5.91421 | − | 10.2437i | −0.267724 | − | 0.463711i | ||||
\(489\) | −23.4853 | −1.06204 | ||||||||
\(490\) | −3.94975 | − | 1.10165i | −0.178431 | − | 0.0497676i | ||||
\(491\) | 19.1716 | 0.865201 | 0.432600 | − | 0.901586i | \(-0.357596\pi\) | ||||
0.432600 | + | 0.901586i | \(0.357596\pi\) | |||||||
\(492\) | −6.53553 | − | 11.3199i | −0.294645 | − | 0.510339i | ||||
\(493\) | −4.85786 | + | 8.41407i | −0.218787 | + | 0.378951i | ||||
\(494\) | −1.12132 | + | 1.94218i | −0.0504506 | + | 0.0873830i | ||||
\(495\) | 0.828427 | + | 1.43488i | 0.0372350 | + | 0.0644930i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −17.9497 | + | 23.1471i | −0.805156 | + | 1.03829i | ||||
\(498\) | 29.3137 | 1.31358 | ||||||||
\(499\) | −11.0711 | − | 19.1757i | −0.495609 | − | 0.858420i | 0.504378 | − | 0.863483i | \(-0.331722\pi\) |
−0.999987 | + | 0.00506282i | \(0.998388\pi\) | |||||||
\(500\) | −2.82843 | + | 4.89898i | −0.126491 | + | 0.219089i | ||||
\(501\) | 16.5711 | − | 28.7019i | 0.740341 | − | 1.28231i | ||||
\(502\) | 13.0711 | + | 22.6398i | 0.583390 | + | 1.01046i | ||||
\(503\) | 4.21320 | 0.187857 | 0.0939287 | − | 0.995579i | \(-0.470057\pi\) | ||||
0.0939287 | + | 0.995579i | \(0.470057\pi\) | |||||||
\(504\) | −7.41421 | − | 1.01461i | −0.330255 | − | 0.0451944i | ||||
\(505\) | −3.61522 | −0.160875 | ||||||||
\(506\) | 3.12132 | + | 5.40629i | 0.138760 | + | 0.240339i | ||||
\(507\) | 2.00000 | − | 3.46410i | 0.0888231 | − | 0.153846i | ||||
\(508\) | −7.86396 | + | 13.6208i | −0.348907 | + | 0.604324i | ||||
\(509\) | −4.65685 | − | 8.06591i | −0.206411 | − | 0.357515i | 0.744170 | − | 0.667990i | \(-0.232845\pi\) |
−0.950582 | + | 0.310475i | \(0.899512\pi\) | |||||||
\(510\) | 5.17157 | 0.229001 | ||||||||
\(511\) | −9.41421 | − | 23.0600i | −0.416460 | − | 1.02012i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.121320 | + | 0.210133i | 0.00535642 | + | 0.00927760i | ||||
\(514\) | 12.5711 | − | 21.7737i | 0.554486 | − | 0.960398i | ||||
\(515\) | 3.92893 | − | 6.80511i | 0.173129 | − | 0.299869i | ||||
\(516\) | −6.82843 | − | 11.8272i | −0.300605 | − | 0.520663i | ||||
\(517\) | −10.4853 | −0.461142 | ||||||||
\(518\) | −9.41421 | − | 23.0600i | −0.413637 | − | 1.01320i | ||||
\(519\) | 23.7279 | 1.04154 | ||||||||
\(520\) | −1.12132 | − | 1.94218i | −0.0491731 | − | 0.0851704i | ||||
\(521\) | 14.1421 | − | 24.4949i | 0.619578 | − | 1.07314i | −0.369984 | − | 0.929038i | \(-0.620637\pi\) |
0.989563 | − | 0.144103i | \(-0.0460297\pi\) | |||||||
\(522\) | −3.75736 | + | 6.50794i | −0.164455 | + | 0.284845i | ||||
\(523\) | 6.36396 | + | 11.0227i | 0.278277 | + | 0.481989i | 0.970957 | − | 0.239256i | \(-0.0769035\pi\) |
−0.692680 | + | 0.721245i | \(0.743570\pi\) | |||||||
\(524\) | −0.585786 | −0.0255902 | ||||||||
\(525\) | −29.4706 | − | 4.03295i | −1.28620 | − | 0.176013i | ||||
\(526\) | −17.0416 | −0.743050 | ||||||||
\(527\) | 7.31371 | + | 12.6677i | 0.318590 | + | 0.551814i | ||||
\(528\) | 1.20711 | − | 2.09077i | 0.0525326 | − | 0.0909891i | ||||
\(529\) | −7.98528 | + | 13.8309i | −0.347186 | + | 0.601344i | ||||
\(530\) | 2.31371 | + | 4.00746i | 0.100501 | + | 0.174073i | ||||
\(531\) | −15.7990 | −0.685618 | ||||||||
\(532\) | −0.949747 | + | 1.22474i | −0.0411768 | + | 0.0530994i | ||||
\(533\) | 20.7279 | 0.897826 | ||||||||
\(534\) | 15.0711 | + | 26.1039i | 0.652189 | + | 1.12962i | ||||
\(535\) | −0.899495 | + | 1.55797i | −0.0388886 | + | 0.0673570i | ||||
\(536\) | −1.37868 | + | 2.38794i | −0.0595499 | + | 0.103143i | ||||
\(537\) | 1.08579 | + | 1.88064i | 0.0468551 | + | 0.0811555i | ||||
\(538\) | 2.34315 | 0.101020 | ||||||||
\(539\) | 6.74264 | + | 1.88064i | 0.290426 | + | 0.0810048i | ||||
\(540\) | −0.242641 | −0.0104416 | ||||||||
\(541\) | 6.42893 | + | 11.1352i | 0.276401 | + | 0.478741i | 0.970488 | − | 0.241151i | \(-0.0775248\pi\) |
−0.694086 | + | 0.719892i | \(0.744191\pi\) | |||||||
\(542\) | −2.27817 | + | 3.94591i | −0.0978560 | + | 0.169492i | ||||
\(543\) | −9.24264 | + | 16.0087i | −0.396640 | + | 0.687000i | ||||
\(544\) | −1.82843 | − | 3.16693i | −0.0783932 | − | 0.135781i | ||||
\(545\) | −9.65685 | −0.413654 | ||||||||
\(546\) | 14.9853 | − | 19.3242i | 0.641311 | − | 0.827001i | ||||
\(547\) | 34.8701 | 1.49094 | 0.745468 | − | 0.666541i | \(-0.232226\pi\) | ||||
0.745468 | + | 0.666541i | \(0.232226\pi\) | |||||||
\(548\) | 8.32843 | + | 14.4253i | 0.355773 | + | 0.616217i | ||||
\(549\) | −16.7279 | + | 28.9736i | −0.713930 | + | 1.23656i | ||||
\(550\) | 2.32843 | − | 4.03295i | 0.0992845 | − | 0.171966i | ||||
\(551\) | 0.778175 | + | 1.34784i | 0.0331514 | + | 0.0574198i | ||||
\(552\) | 15.0711 | 0.641467 | ||||||||
\(553\) | 34.7132 | + | 4.75039i | 1.47616 | + | 0.202007i | ||||
\(554\) | 1.82843 | 0.0776824 | ||||||||
\(555\) | 6.65685 | + | 11.5300i | 0.282568 | + | 0.489422i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.75736 | + | 6.50794i | −0.159204 | + | 0.275750i | −0.934582 | − | 0.355748i | \(-0.884226\pi\) |
0.775378 | + | 0.631498i | \(0.217560\pi\) | |||||||
\(558\) | 5.65685 | + | 9.79796i | 0.239474 | + | 0.414781i | ||||
\(559\) | 21.6569 | 0.915987 | ||||||||
\(560\) | −0.585786 | − | 1.43488i | −0.0247540 | − | 0.0606347i | ||||
\(561\) | −8.82843 | −0.372736 | ||||||||
\(562\) | −4.36396 | − | 7.55860i | −0.184083 | − | 0.318840i | ||||
\(563\) | −4.53553 | + | 7.85578i | −0.191150 | + | 0.331081i | −0.945632 | − | 0.325240i | \(-0.894555\pi\) |
0.754482 | + | 0.656321i | \(0.227888\pi\) | |||||||
\(564\) | −12.6569 | + | 21.9223i | −0.532950 | + | 0.923096i | ||||
\(565\) | −2.39340 | − | 4.14549i | −0.100691 | − | 0.174402i | ||||
\(566\) | −23.4142 | −0.984173 | ||||||||
\(567\) | −9.48528 | − | 23.2341i | −0.398344 | − | 0.975740i | ||||
\(568\) | −11.0711 | −0.464532 | ||||||||
\(569\) | 2.00000 | + | 3.46410i | 0.0838444 | + | 0.145223i | 0.904898 | − | 0.425628i | \(-0.139947\pi\) |
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(570\) | 0.414214 | − | 0.717439i | 0.0173495 | − | 0.0300502i | ||||
\(571\) | −13.1924 | + | 22.8499i | −0.552084 | + | 0.956238i | 0.446040 | + | 0.895013i | \(0.352834\pi\) |
−0.998124 | + | 0.0612248i | \(0.980499\pi\) | |||||||
\(572\) | 1.91421 | + | 3.31552i | 0.0800373 | + | 0.138629i | ||||
\(573\) | 17.3137 | 0.723291 | ||||||||
\(574\) | 14.1924 | + | 1.94218i | 0.592379 | + | 0.0810652i | ||||
\(575\) | 29.0711 | 1.21235 | ||||||||
\(576\) | −1.41421 | − | 2.44949i | −0.0589256 | − | 0.102062i | ||||
\(577\) | 4.84315 | − | 8.38857i | 0.201623 | − | 0.349221i | −0.747429 | − | 0.664342i | \(-0.768712\pi\) |
0.949051 | + | 0.315121i | \(0.102045\pi\) | |||||||
\(578\) | 1.81371 | − | 3.14144i | 0.0754403 | − | 0.130666i | ||||
\(579\) | 26.4350 | + | 45.7868i | 1.09860 | + | 1.90284i | ||||
\(580\) | −1.55635 | −0.0646239 | ||||||||
\(581\) | −19.6863 | + | 25.3864i | −0.816725 | + | 1.05321i | ||||
\(582\) | 9.24264 | 0.383120 | ||||||||
\(583\) | −3.94975 | − | 6.84116i | −0.163582 | − | 0.283332i | ||||
\(584\) | 4.70711 | − | 8.15295i | 0.194781 | − | 0.337371i | ||||
\(585\) | −3.17157 | + | 5.49333i | −0.131128 | + | 0.227121i | ||||
\(586\) | 5.41421 | + | 9.37769i | 0.223659 | + | 0.387389i | ||||
\(587\) | −25.1005 | −1.03601 | −0.518004 | − | 0.855378i | \(-0.673325\pi\) | ||||
−0.518004 | + | 0.855378i | \(0.673325\pi\) | |||||||
\(588\) | 12.0711 | − | 11.8272i | 0.497802 | − | 0.487745i | ||||
\(589\) | 2.34315 | 0.0965476 | ||||||||
\(590\) | −1.63604 | − | 2.83370i | −0.0673547 | − | 0.116662i | ||||
\(591\) | −0.621320 | + | 1.07616i | −0.0255577 | + | 0.0442672i | ||||
\(592\) | 4.70711 | − | 8.15295i | 0.193461 | − | 0.335084i | ||||
\(593\) | −11.8492 | − | 20.5235i | −0.486590 | − | 0.842799i | 0.513291 | − | 0.858215i | \(-0.328426\pi\) |
−0.999881 | + | 0.0154159i | \(0.995093\pi\) | |||||||
\(594\) | 0.414214 | 0.0169954 | ||||||||
\(595\) | −3.47309 | + | 4.47871i | −0.142383 | + | 0.183609i | ||||
\(596\) | 17.6569 | 0.723253 | ||||||||
\(597\) | 0.121320 | + | 0.210133i | 0.00496531 | + | 0.00860017i | ||||
\(598\) | −11.9497 | + | 20.6976i | −0.488662 | + | 0.846387i | ||||
\(599\) | −21.3137 | + | 36.9164i | −0.870855 | + | 1.50836i | −0.00974040 | + | 0.999953i | \(0.503101\pi\) |
−0.861114 | + | 0.508412i | \(0.830233\pi\) | |||||||
\(600\) | −5.62132 | − | 9.73641i | −0.229489 | − | 0.397487i | ||||
\(601\) | 31.9411 | 1.30291 | 0.651453 | − | 0.758689i | \(-0.274160\pi\) | ||||
0.651453 | + | 0.758689i | \(0.274160\pi\) | |||||||
\(602\) | 14.8284 | + | 2.02922i | 0.604362 | + | 0.0827050i | ||||
\(603\) | 7.79899 | 0.317599 | ||||||||
\(604\) | 7.86396 | + | 13.6208i | 0.319980 | + | 0.554222i | ||||
\(605\) | 0.292893 | − | 0.507306i | 0.0119078 | − | 0.0206249i | ||||
\(606\) | 7.44975 | − | 12.9033i | 0.302625 | − | 0.524162i | ||||
\(607\) | 21.4853 | + | 37.2136i | 0.872061 | + | 1.51045i | 0.859861 | + | 0.510528i | \(0.170550\pi\) |
0.0121994 | + | 0.999926i | \(0.496117\pi\) | |||||||
\(608\) | −0.585786 | −0.0237568 | ||||||||
\(609\) | −6.41421 | − | 15.7116i | −0.259917 | − | 0.636664i | ||||
\(610\) | −6.92893 | −0.280544 | ||||||||
\(611\) | −20.0711 | − | 34.7641i | −0.811988 | − | 1.40641i | ||||
\(612\) | −5.17157 | + | 8.95743i | −0.209048 | + | 0.362083i | ||||
\(613\) | −14.3137 | + | 24.7921i | −0.578125 | + | 1.00134i | 0.417569 | + | 0.908645i | \(0.362882\pi\) |
−0.995694 | + | 0.0926971i | \(0.970451\pi\) | |||||||
\(614\) | −4.94975 | − | 8.57321i | −0.199756 | − | 0.345987i | ||||
\(615\) | −7.65685 | −0.308754 | ||||||||
\(616\) | 1.00000 | + | 2.44949i | 0.0402911 | + | 0.0986928i | ||||
\(617\) | −41.9706 | −1.68967 | −0.844836 | − | 0.535026i | \(-0.820302\pi\) | ||||
−0.844836 | + | 0.535026i | \(0.820302\pi\) | |||||||
\(618\) | 16.1924 | + | 28.0460i | 0.651353 | + | 1.12818i | ||||
\(619\) | 10.9706 | − | 19.0016i | 0.440944 | − | 0.763738i | −0.556816 | − | 0.830636i | \(-0.687977\pi\) |
0.997760 | + | 0.0668984i | \(0.0213104\pi\) | |||||||
\(620\) | −1.17157 | + | 2.02922i | −0.0470515 | + | 0.0814956i | ||||
\(621\) | 1.29289 | + | 2.23936i | 0.0518820 | + | 0.0898623i | ||||
\(622\) | 16.7279 | 0.670729 | ||||||||
\(623\) | −32.7279 | − | 4.47871i | −1.31122 | − | 0.179436i | ||||
\(624\) | 9.24264 | 0.370002 | ||||||||
\(625\) | −9.98528 | − | 17.2950i | −0.399411 | − | 0.691801i | ||||
\(626\) | 10.3284 | − | 17.8894i | 0.412807 | − | 0.715003i | ||||
\(627\) | −0.707107 | + | 1.22474i | −0.0282391 | + | 0.0489116i | ||||
\(628\) | −8.82843 | − | 15.2913i | −0.352293 | − | 0.610189i | ||||
\(629\) | −34.4264 | −1.37267 | ||||||||
\(630\) | −2.68629 | + | 3.46410i | −0.107024 | + | 0.138013i | ||||
\(631\) | 23.2721 | 0.926447 | 0.463223 | − | 0.886242i | \(-0.346693\pi\) | ||||
0.463223 | + | 0.886242i | \(0.346693\pi\) | |||||||
\(632\) | 6.62132 | + | 11.4685i | 0.263382 | + | 0.456191i | ||||
\(633\) | 8.94975 | − | 15.5014i | 0.355721 | − | 0.616126i | ||||
\(634\) | −4.34315 | + | 7.52255i | −0.172488 | + | 0.298759i | ||||
\(635\) | 4.60660 | + | 7.97887i | 0.182807 | + | 0.316632i | ||||
\(636\) | −19.0711 | −0.756217 | ||||||||
\(637\) | 6.67157 | + | 25.9553i | 0.264337 | + | 1.02839i | ||||
\(638\) | 2.65685 | 0.105186 | ||||||||
\(639\) | 15.6569 | + | 27.1185i | 0.619376 | + | 1.07279i | ||||
\(640\) | 0.292893 | − | 0.507306i | 0.0115776 | − | 0.0200530i | ||||
\(641\) | −7.64214 | + | 13.2366i | −0.301846 | + | 0.522813i | −0.976554 | − | 0.215272i | \(-0.930936\pi\) |
0.674708 | + | 0.738085i | \(0.264270\pi\) | |||||||
\(642\) | −3.70711 | − | 6.42090i | −0.146308 | − | 0.253413i | ||||
\(643\) | 1.58579 | 0.0625373 | 0.0312687 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312687 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(644\) | −10.1213 | + | 13.0519i | −0.398836 | + | 0.514318i | ||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 1.07107 | + | 1.85514i | 0.0421406 | + | 0.0729897i | ||||
\(647\) | −15.0919 | + | 26.1399i | −0.593323 | + | 1.02767i | 0.400458 | + | 0.916315i | \(0.368851\pi\) |
−0.993781 | + | 0.111351i | \(0.964482\pi\) | |||||||
\(648\) | 4.74264 | − | 8.21449i | 0.186309 | − | 0.322696i | ||||
\(649\) | 2.79289 | + | 4.83743i | 0.109631 | + | 0.189886i | ||||
\(650\) | 17.8284 | 0.699288 | ||||||||
\(651\) | −25.3137 | − | 3.46410i | −0.992122 | − | 0.135769i | ||||
\(652\) | 9.72792 | 0.380975 | ||||||||
\(653\) | 9.19239 | + | 15.9217i | 0.359726 | + | 0.623064i | 0.987915 | − | 0.154997i | \(-0.0495369\pi\) |
−0.628189 | + | 0.778061i | \(0.716204\pi\) | |||||||
\(654\) | 19.8995 | − | 34.4669i | 0.778132 | − | 1.34776i | ||||
\(655\) | −0.171573 | + | 0.297173i | −0.00670391 | + | 0.0116115i | ||||
\(656\) | 2.70711 | + | 4.68885i | 0.105695 | + | 0.183069i | ||||
\(657\) | −26.6274 | −1.03883 | ||||||||
\(658\) | −10.4853 | − | 25.6836i | −0.408759 | − | 1.00125i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | −0.707107 | − | 1.22474i | −0.0275241 | − | 0.0476731i | ||||
\(661\) | −9.48528 | + | 16.4290i | −0.368935 | + | 0.639014i | −0.989399 | − | 0.145221i | \(-0.953611\pi\) |
0.620465 | + | 0.784234i | \(0.286944\pi\) | |||||||
\(662\) | 12.0355 | − | 20.8462i | 0.467774 | − | 0.810209i | ||||
\(663\) | −16.8995 | − | 29.2708i | −0.656322 | − | 1.13678i | ||||
\(664\) | −12.1421 | −0.471206 | ||||||||
\(665\) | 0.343146 | + | 0.840532i | 0.0133066 | + | 0.0325944i | ||||
\(666\) | −26.6274 | −1.03179 | ||||||||
\(667\) | 8.29289 | + | 14.3637i | 0.321102 | + | 0.556165i | ||||
\(668\) | −6.86396 | + | 11.8887i | −0.265575 | + | 0.459989i | ||||
\(669\) | 10.3640 | − | 17.9509i | 0.400694 | − | 0.694022i | ||||
\(670\) | 0.807612 | + | 1.39882i | 0.0312008 | + | 0.0540413i | ||||
\(671\) | 11.8284 | 0.456631 | ||||||||
\(672\) | 6.32843 | + | 0.866025i | 0.244124 | + | 0.0334077i | ||||
\(673\) | 5.55635 | 0.214182 | 0.107091 | − | 0.994249i | \(-0.465846\pi\) | ||||
0.107091 | + | 0.994249i | \(0.465846\pi\) | |||||||
\(674\) | 14.1213 | + | 24.4588i | 0.543933 | + | 0.942119i | ||||
\(675\) | 0.964466 | − | 1.67050i | 0.0371223 | − | 0.0642977i | ||||
\(676\) | −0.828427 | + | 1.43488i | −0.0318626 | + | 0.0551876i | ||||
\(677\) | 17.6569 | + | 30.5826i | 0.678608 | + | 1.17538i | 0.975400 | + | 0.220441i | \(0.0707498\pi\) |
−0.296792 | + | 0.954942i | \(0.595917\pi\) | |||||||
\(678\) | 19.7279 | 0.757646 | ||||||||
\(679\) | −6.20711 | + | 8.00436i | −0.238207 | + | 0.307179i | ||||
\(680\) | −2.14214 | −0.0821472 | ||||||||
\(681\) | −34.7990 | − | 60.2736i | −1.33350 | − | 2.30969i | ||||
\(682\) | 2.00000 | − | 3.46410i | 0.0765840 | − | 0.132647i | ||||
\(683\) | −6.79289 | + | 11.7656i | −0.259923 | + | 0.450200i | −0.966221 | − | 0.257715i | \(-0.917030\pi\) |
0.706298 | + | 0.707914i | \(0.250364\pi\) | |||||||
\(684\) | 0.828427 | + | 1.43488i | 0.0316757 | + | 0.0548639i | ||||
\(685\) | 9.75736 | 0.372810 | ||||||||
\(686\) | 2.13604 | + | 18.3967i | 0.0815543 | + | 0.702388i | ||||
\(687\) | −56.2843 | −2.14738 | ||||||||
\(688\) | 2.82843 | + | 4.89898i | 0.107833 | + | 0.186772i | ||||
\(689\) | 15.1213 | − | 26.1909i | 0.576076 | − | 0.997794i | ||||
\(690\) | 4.41421 | − | 7.64564i | 0.168046 | − | 0.291065i | ||||
\(691\) | −14.0355 | − | 24.3103i | −0.533937 | − | 0.924806i | −0.999214 | − | 0.0396407i | \(-0.987379\pi\) |
0.465277 | − | 0.885165i | \(-0.345955\pi\) | |||||||
\(692\) | −9.82843 | −0.373621 | ||||||||
\(693\) | 4.58579 | − | 5.91359i | 0.174200 | − | 0.224639i | ||||
\(694\) | 17.4142 | 0.661035 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.20711 | − | 5.55487i | 0.121565 | − | 0.210557i | ||||
\(697\) | 9.89949 | − | 17.1464i | 0.374970 | − | 0.649467i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.41421 | −0.129137 | ||||||||
\(700\) | 12.2071 | + | 1.67050i | 0.461385 | + | 0.0631391i | ||||
\(701\) | −26.1127 | −0.986263 | −0.493132 | − | 0.869955i | \(-0.664148\pi\) | ||||
−0.493132 | + | 0.869955i | \(0.664148\pi\) | |||||||
\(702\) | 0.792893 | + | 1.37333i | 0.0299258 | + | 0.0518331i | ||||
\(703\) | −2.75736 | + | 4.77589i | −0.103996 | + | 0.180126i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 7.41421 | + | 12.8418i | 0.279235 | + | 0.483650i | ||||
\(706\) | −2.68629 | −0.101100 | ||||||||
\(707\) | 6.17157 | + | 15.1172i | 0.232106 | + | 0.568541i | ||||
\(708\) | 13.4853 | 0.506808 | ||||||||
\(709\) | 6.02082 | + | 10.4284i | 0.226116 | + | 0.391645i | 0.956654 | − | 0.291228i | \(-0.0940637\pi\) |
−0.730537 | + | 0.682873i | \(0.760730\pi\) | |||||||
\(710\) | −3.24264 | + | 5.61642i | −0.121694 | + | 0.210780i | ||||
\(711\) | 18.7279 | − | 32.4377i | 0.702352 | − | 1.21651i | ||||
\(712\) | −6.24264 | − | 10.8126i | −0.233953 | − | 0.405218i | ||||
\(713\) | 24.9706 | 0.935155 | ||||||||
\(714\) | −8.82843 | − | 21.6251i | −0.330396 | − | 0.809301i | ||||
\(715\) | 2.24264 | 0.0838700 | ||||||||
\(716\) | −0.449747 | − | 0.778985i | −0.0168079 | − | 0.0291121i | ||||
\(717\) | 24.3995 | − | 42.2612i | 0.911216 | − | 1.57827i | ||||
\(718\) | −9.62132 | + | 16.6646i | −0.359064 | + | 0.621918i | ||||
\(719\) | 0.757359 | + | 1.31178i | 0.0282447 | + | 0.0489213i | 0.879802 | − | 0.475340i | \(-0.157675\pi\) |
−0.851558 | + | 0.524261i | \(0.824342\pi\) | |||||||
\(720\) | −1.65685 | −0.0617473 | ||||||||
\(721\) | −35.1630 | − | 4.81194i | −1.30954 | − | 0.179206i | ||||
\(722\) | −18.6569 | −0.694336 | ||||||||
\(723\) | 14.7782 | + | 25.5965i | 0.549606 | + | 0.951946i | ||||
\(724\) | 3.82843 | − | 6.63103i | 0.142282 | − | 0.246440i | ||||
\(725\) | 6.18629 | − | 10.7150i | 0.229753 | − | 0.397944i | ||||
\(726\) | 1.20711 | + | 2.09077i | 0.0447999 | + | 0.0775958i | ||||
\(727\) | 36.4264 | 1.35098 | 0.675490 | − | 0.737369i | \(-0.263932\pi\) | ||||
0.675490 | + | 0.737369i | \(0.263932\pi\) | |||||||
\(728\) | −6.20711 | + | 8.00436i | −0.230051 | + | 0.296661i | ||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | −2.75736 | − | 4.77589i | −0.102054 | − | 0.176763i | ||||
\(731\) | 10.3431 | − | 17.9149i | 0.382555 | − | 0.662605i | ||||
\(732\) | 14.2782 | − | 24.7305i | 0.527737 | − | 0.914066i | ||||
\(733\) | 6.50000 | + | 11.2583i | 0.240083 | + | 0.415836i | 0.960738 | − | 0.277458i | \(-0.0894920\pi\) |
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(734\) | −10.7279 | −0.395975 | ||||||||
\(735\) | −2.46447 | − | 9.58783i | −0.0909032 | − | 0.353652i | ||||
\(736\) | −6.24264 | −0.230107 | ||||||||
\(737\) | −1.37868 | − | 2.38794i | −0.0507843 | − | 0.0879610i | ||||
\(738\) | 7.65685 | − | 13.2621i | 0.281853 | − | 0.488183i | ||||
\(739\) | 26.2132 | − | 45.4026i | 0.964268 | − | 1.67016i | 0.252700 | − | 0.967545i | \(-0.418681\pi\) |
0.711568 | − | 0.702617i | \(-0.247985\pi\) | |||||||
\(740\) | −2.75736 | − | 4.77589i | −0.101363 | − | 0.175565i | ||||
\(741\) | −5.41421 | −0.198896 | ||||||||
\(742\) | 12.8076 | − | 16.5160i | 0.470182 | − | 0.606323i | ||||
\(743\) | −13.3137 | −0.488433 | −0.244216 | − | 0.969721i | \(-0.578531\pi\) | ||||
−0.244216 | + | 0.969721i | \(0.578531\pi\) | |||||||
\(744\) | −4.82843 | − | 8.36308i | −0.177019 | − | 0.306605i | ||||
\(745\) | 5.17157 | − | 8.95743i | 0.189472 | − | 0.328175i | ||||
\(746\) | 9.98528 | − | 17.2950i | 0.365587 | − | 0.633215i | ||||
\(747\) | 17.1716 | + | 29.7420i | 0.628275 | + | 1.08820i | ||||
\(748\) | 3.65685 | 0.133708 | ||||||||
\(749\) | 8.05025 | + | 1.10165i | 0.294150 | + | 0.0402535i | ||||
\(750\) | −13.6569 | −0.498678 | ||||||||
\(751\) | −22.8284 | − | 39.5400i | −0.833021 | − | 1.44283i | −0.895631 | − | 0.444797i | \(-0.853276\pi\) |
0.0626103 | − | 0.998038i | \(-0.480057\pi\) | |||||||
\(752\) | 5.24264 | − | 9.08052i | 0.191179 | − | 0.331132i | ||||
\(753\) | −31.5563 | + | 54.6572i | −1.14998 | + | 1.99182i | ||||
\(754\) | 5.08579 | + | 8.80884i | 0.185213 | + | 0.320799i | ||||
\(755\) | 9.21320 | 0.335303 | ||||||||
\(756\) | 0.414214 | + | 1.01461i | 0.0150648 | + | 0.0369011i | ||||
\(757\) | 8.34315 | 0.303237 | 0.151618 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151618 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(758\) | −13.9350 | − | 24.1362i | −0.506143 | − | 0.876665i | ||||
\(759\) | −7.53553 | + | 13.0519i | −0.273523 | + | 0.473755i | ||||
\(760\) | −0.171573 | + | 0.297173i | −0.00622360 | + | 0.0107796i | ||||
\(761\) | −15.4853 | − | 26.8213i | −0.561341 | − | 0.972271i | −0.997380 | − | 0.0723433i | \(-0.976952\pi\) |
0.436039 | − | 0.899928i | \(-0.356381\pi\) | |||||||
\(762\) | −37.9706 | −1.37553 | ||||||||
\(763\) | 16.4853 | + | 40.3805i | 0.596807 | + | 1.46187i | ||||
\(764\) | −7.17157 | −0.259458 | ||||||||
\(765\) | 3.02944 | + | 5.24714i | 0.109530 | + | 0.189711i | ||||
\(766\) | 3.19239 | − | 5.52938i | 0.115346 | − | 0.199785i | ||||
\(767\) | −10.6924 | + | 18.5198i | −0.386080 | + | 0.668710i | ||||
\(768\) | 1.20711 | + | 2.09077i | 0.0435577 | + | 0.0754442i | ||||
\(769\) | 22.9706 | 0.828340 | 0.414170 | − | 0.910200i | \(-0.364072\pi\) | ||||
0.414170 | + | 0.910200i | \(0.364072\pi\) | |||||||
\(770\) | 1.53553 | + | 0.210133i | 0.0553368 | + | 0.00757267i | ||||
\(771\) | 60.6985 | 2.18600 | ||||||||
\(772\) | −10.9497 | − | 18.9655i | −0.394090 | − | 0.682584i | ||||
\(773\) | 10.9706 | − | 19.0016i | 0.394584 | − | 0.683439i | −0.598464 | − | 0.801150i | \(-0.704222\pi\) |
0.993048 | + | 0.117710i | \(0.0375555\pi\) | |||||||
\(774\) | 8.00000 | − | 13.8564i | 0.287554 | − | 0.498058i | ||||
\(775\) | −9.31371 | − | 16.1318i | −0.334558 | − | 0.579472i | ||||
\(776\) | −3.82843 | −0.137433 | ||||||||
\(777\) | 36.8492 | − | 47.5189i | 1.32196 | − | 1.70473i | ||||
\(778\) | −22.7279 | −0.814835 | ||||||||
\(779\) | −1.58579 | − | 2.74666i | −0.0568167 | − | 0.0984094i | ||||
\(780\) | 2.70711 | − | 4.68885i | 0.0969300 | − | 0.167888i | ||||
\(781\) | 5.53553 | − | 9.58783i | 0.198077 | − | 0.343079i | ||||
\(782\) | 11.4142 | + | 19.7700i | 0.408171 | + | 0.706974i | ||||
\(783\) | 1.10051 | 0.0393288 | ||||||||
\(784\) | −5.00000 | + | 4.89898i | −0.178571 | + | 0.174964i | ||||
\(785\) | −10.3431 | −0.369163 | ||||||||
\(786\) | −0.707107 | − | 1.22474i | −0.0252217 | − | 0.0436852i | ||||
\(787\) | −6.77817 | + | 11.7401i | −0.241616 | + | 0.418491i | −0.961175 | − | 0.275941i | \(-0.911011\pi\) |
0.719559 | + | 0.694431i | \(0.244344\pi\) | |||||||
\(788\) | 0.257359 | − | 0.445759i | 0.00916805 | − | 0.0158795i | ||||
\(789\) | −20.5711 | − | 35.6301i | −0.732349 | − | 1.26847i | ||||
\(790\) | 7.75736 | 0.275994 | ||||||||
\(791\) | −13.2487 | + | 17.0849i | −0.471071 | + | 0.607468i | ||||
\(792\) | 2.82843 | 0.100504 | ||||||||
\(793\) | 22.6421 | + | 39.2173i | 0.804046 | + | 1.39265i | ||||
\(794\) | −11.0000 | + | 19.0526i | −0.390375 | + | 0.676150i | ||||
\(795\) | −5.58579 | + | 9.67487i | −0.198107 | + | 0.343132i | ||||
\(796\) | −0.0502525 | − | 0.0870399i | −0.00178115 | − | 0.00308505i | ||||
\(797\) | −7.65685 | −0.271220 | −0.135610 | − | 0.990762i | \(-0.543299\pi\) | ||||
−0.135610 | + | 0.990762i | \(0.543299\pi\) | |||||||
\(798\) | −3.70711 | − | 0.507306i | −0.131230 | − | 0.0179584i | ||||
\(799\) | −38.3431 | −1.35648 | ||||||||
\(800\) | 2.32843 | + | 4.03295i | 0.0823223 | + | 0.142586i | ||||
\(801\) | −17.6569 | + | 30.5826i | −0.623874 | + | 1.08058i | ||||
\(802\) | −9.15685 | + | 15.8601i | −0.323340 | + | 0.560041i | ||||
\(803\) | 4.70711 | + | 8.15295i | 0.166110 | + | 0.287711i | ||||
\(804\) | −6.65685 | −0.234769 | ||||||||
\(805\) | 3.65685 | + | 8.95743i | 0.128887 | + | 0.315708i | ||||
\(806\) | 15.3137 | 0.539402 | ||||||||
\(807\) | 2.82843 | + | 4.89898i | 0.0995654 | + | 0.172452i | ||||
\(808\) | −3.08579 | + | 5.34474i | −0.108558 | + | 0.188027i | ||||
\(809\) | 23.3137 | − | 40.3805i | 0.819666 | − | 1.41970i | −0.0862619 | − | 0.996272i | \(-0.527492\pi\) |
0.905928 | − | 0.423431i | \(-0.139174\pi\) | |||||||
\(810\) | −2.77817 | − | 4.81194i | −0.0976151 | − | 0.169074i | ||||
\(811\) | −24.2843 | −0.852736 | −0.426368 | − | 0.904550i | \(-0.640207\pi\) | ||||
−0.426368 | + | 0.904550i | \(0.640207\pi\) | |||||||
\(812\) | 2.65685 | + | 6.50794i | 0.0932373 | + | 0.228384i | ||||
\(813\) | −11.0000 | −0.385787 | ||||||||
\(814\) | 4.70711 | + | 8.15295i | 0.164984 | + | 0.285761i | ||||
\(815\) | 2.84924 | − | 4.93503i | 0.0998046 | − | 0.172867i | ||||
\(816\) | 4.41421 | − | 7.64564i | 0.154528 | − | 0.267651i | ||||
\(817\) | −1.65685 | − | 2.86976i | −0.0579660 | − | 0.100400i | ||||
\(818\) | 2.72792 | 0.0953796 | ||||||||
\(819\) | 28.3848 | + | 3.88437i | 0.991844 | + | 0.135731i | ||||
\(820\) | 3.17157 | 0.110756 | ||||||||
\(821\) | 14.7426 | + | 25.5350i | 0.514522 | + | 0.891178i | 0.999858 | + | 0.0168502i | \(0.00536384\pi\) |
−0.485336 | + | 0.874328i | \(0.661303\pi\) | |||||||
\(822\) | −20.1066 | + | 34.8257i | −0.701298 | + | 1.21468i | ||||
\(823\) | 21.7279 | − | 37.6339i | 0.757388 | − | 1.31183i | −0.186791 | − | 0.982400i | \(-0.559809\pi\) |
0.944178 | − | 0.329434i | \(-0.106858\pi\) | |||||||
\(824\) | −6.70711 | − | 11.6170i | −0.233653 | − | 0.404699i | ||||
\(825\) | 11.2426 | 0.391419 | ||||||||
\(826\) | −9.05635 | + | 11.6786i | −0.315111 | + | 0.406350i | ||||
\(827\) | −21.3553 | −0.742598 | −0.371299 | − | 0.928513i | \(-0.621087\pi\) | ||||
−0.371299 | + | 0.928513i | \(0.621087\pi\) | |||||||
\(828\) | 8.82843 | + | 15.2913i | 0.306809 | + | 0.531409i | ||||
\(829\) | −10.8787 | + | 18.8424i | −0.377832 | + | 0.654425i | −0.990747 | − | 0.135725i | \(-0.956664\pi\) |
0.612914 | + | 0.790149i | \(0.289997\pi\) | |||||||
\(830\) | −3.55635 | + | 6.15978i | −0.123443 | + | 0.213809i | ||||
\(831\) | 2.20711 | + | 3.82282i | 0.0765637 | + | 0.132612i | ||||
\(832\) | −3.82843 | −0.132727 | ||||||||
\(833\) | 24.6569 | + | 6.87722i | 0.854309 | + | 0.238281i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.02082 | + | 6.96426i | 0.139146 | + | 0.241008i | ||||
\(836\) | 0.292893 | − | 0.507306i | 0.0101299 | − | 0.0175455i | ||||
\(837\) | 0.828427 | − | 1.43488i | 0.0286346 | − | 0.0495966i | ||||
\(838\) | 13.0711 | + | 22.6398i | 0.451533 | + | 0.782077i | ||||
\(839\) | −18.4853 | −0.638183 | −0.319091 | − | 0.947724i | \(-0.603378\pi\) | ||||
−0.319091 | + | 0.947724i | \(0.603378\pi\) | |||||||
\(840\) | 2.29289 | − | 2.95680i | 0.0791123 | − | 0.102019i | ||||
\(841\) | −21.9411 | −0.756591 | ||||||||
\(842\) | −0.343146 | − | 0.594346i | −0.0118256 | − | 0.0204825i | ||||
\(843\) | 10.5355 | − | 18.2481i | 0.362863 | − | 0.628497i | ||||
\(844\) | −3.70711 | + | 6.42090i | −0.127604 | + | 0.221016i | ||||
\(845\) | 0.485281 | + | 0.840532i | 0.0166942 | + | 0.0289152i | ||||
\(846\) | −29.6569 | −1.01962 | ||||||||
\(847\) | −2.62132 | − | 0.358719i | −0.0900696 | − | 0.0123257i | ||||
\(848\) | 7.89949 | 0.271270 | ||||||||
\(849\) | −28.2635 | − | 48.9537i | −0.969999 | − | 1.68009i | ||||
\(850\) | 8.51472 | − | 14.7479i | 0.292052 | − | 0.505850i | ||||
\(851\) | −29.3848 | + | 50.8959i | −1.00730 | + | 1.74469i | ||||
\(852\) | −13.3640 | − | 23.1471i | −0.457842 | − | 0.793005i | ||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 11.8284 | + | 28.9736i | 0.404760 | + | 0.991457i | ||||
\(855\) | 0.970563 | 0.0331925 | ||||||||
\(856\) | 1.53553 | + | 2.65962i | 0.0524835 | + | 0.0909040i | ||||
\(857\) | 17.3137 | − | 29.9882i | 0.591425 | − | 1.02438i | −0.402616 | − | 0.915369i | \(-0.631899\pi\) |
0.994041 | − | 0.109009i | \(-0.0347678\pi\) | |||||||
\(858\) | −4.62132 | + | 8.00436i | −0.157769 | + | 0.273264i | ||||
\(859\) | 2.86396 | + | 4.96053i | 0.0977171 | + | 0.169251i | 0.910739 | − | 0.412982i | \(-0.135513\pi\) |
−0.813022 | + | 0.582233i | \(0.802179\pi\) | |||||||
\(860\) | 3.31371 | 0.112997 | ||||||||
\(861\) | 13.0711 | + | 32.0174i | 0.445461 | + | 1.09115i | ||||
\(862\) | −17.5858 | −0.598974 | ||||||||
\(863\) | −17.6066 | − | 30.4955i | −0.599336 | − | 1.03808i | −0.992919 | − | 0.118791i | \(-0.962098\pi\) |
0.393584 | − | 0.919289i | \(-0.371235\pi\) | |||||||
\(864\) | −0.207107 | + | 0.358719i | −0.00704592 | + | 0.0122039i | ||||
\(865\) | −2.87868 | + | 4.98602i | −0.0978780 | + | 0.169530i | ||||
\(866\) | −13.0711 | − | 22.6398i | −0.444173 | − | 0.769330i | ||||
\(867\) | 8.75736 | 0.297416 | ||||||||
\(868\) | 10.4853 | + | 1.43488i | 0.355894 | + | 0.0487029i | ||||
\(869\) | −13.2426 | −0.449226 | ||||||||
\(870\) | −1.87868 | − | 3.25397i | −0.0636932 | − | 0.110320i | ||||
\(871\) | 5.27817 | − | 9.14207i | 0.178844 | − | 0.309767i | ||||
\(872\) | −8.24264 | + | 14.2767i | −0.279131 | + | 0.483469i | ||||
\(873\) | 5.41421 | + | 9.37769i | 0.183243 | + | 0.317387i | ||||
\(874\) | 3.65685 | 0.123695 | ||||||||
\(875\) | 9.17157 | − | 11.8272i | 0.310056 | − | 0.399832i | ||||
\(876\) | 22.7279 | 0.767905 | ||||||||
\(877\) | −9.81371 | − | 16.9978i | −0.331385 | − | 0.573976i | 0.651398 | − | 0.758736i | \(-0.274183\pi\) |
−0.982784 | + | 0.184760i | \(0.940849\pi\) | |||||||
\(878\) | 13.6924 | − | 23.7159i | 0.462096 | − | 0.800373i | ||||
\(879\) | −13.0711 | + | 22.6398i | −0.440876 | + | 0.763620i | ||||
\(880\) | 0.292893 | + | 0.507306i | 0.00987343 | + | 0.0171013i | ||||
\(881\) | 6.45584 | 0.217503 | 0.108751 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108751 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(882\) | 19.0711 | + | 5.31925i | 0.642156 | + | 0.179108i | ||||
\(883\) | 15.7279 | 0.529287 | 0.264643 | − | 0.964346i | \(-0.414746\pi\) | ||||
0.264643 | + | 0.964346i | \(0.414746\pi\) | |||||||
\(884\) | 7.00000 | + | 12.1244i | 0.235435 | + | 0.407786i | ||||
\(885\) | 3.94975 | − | 6.84116i | 0.132769 | − | 0.229963i | ||||
\(886\) | −6.31371 | + | 10.9357i | −0.212113 | + | 0.367391i | ||||
\(887\) | 1.55025 | + | 2.68512i | 0.0520524 | + | 0.0901574i | 0.890878 | − | 0.454243i | \(-0.150090\pi\) |
−0.838825 | + | 0.544401i | \(0.816757\pi\) | |||||||
\(888\) | 22.7279 | 0.762699 | ||||||||
\(889\) | 25.5000 | − | 32.8835i | 0.855243 | − | 1.10288i | ||||
\(890\) | −7.31371 | −0.245156 | ||||||||
\(891\) | 4.74264 | + | 8.21449i | 0.158884 | + | 0.275196i | ||||
\(892\) | −4.29289 | + | 7.43551i | −0.143737 | + | 0.248959i | ||||
\(893\) | −3.07107 | + | 5.31925i | −0.102769 | + | 0.178002i | ||||
\(894\) | 21.3137 | + | 36.9164i | 0.712837 | + | 1.23467i | ||||
\(895\) | −0.526912 | −0.0176127 | ||||||||
\(896\) | −2.62132 | − | 0.358719i | −0.0875722 | − | 0.0119840i | ||||
\(897\) | −57.6985 | −1.92650 | ||||||||
\(898\) | −11.1716 | − | 19.3497i | −0.372800 | − | 0.645709i | ||||
\(899\) | 5.31371 | − | 9.20361i | 0.177222 | − | 0.306958i | ||||
\(900\) | 6.58579 | − | 11.4069i | 0.219526 | − | 0.380231i | ||||
\(901\) | −14.4437 | − | 25.0171i | −0.481188 | − | 0.833442i | ||||
\(902\) | −5.41421 | −0.180274 | ||||||||
\(903\) | 13.6569 | + | 33.4523i | 0.454472 | + | 1.11322i | ||||
\(904\) | −8.17157 | −0.271782 | ||||||||
\(905\) | −2.24264 | − | 3.88437i | −0.0745479 | − | 0.129121i | ||||
\(906\) | −18.9853 | + | 32.8835i | −0.630744 | + | 1.09248i | ||||
\(907\) | −5.34315 | + | 9.25460i | −0.177416 | + | 0.307294i | −0.940995 | − | 0.338421i | \(-0.890107\pi\) |
0.763579 | + | 0.645715i | \(0.223441\pi\) | |||||||
\(908\) | 14.4142 | + | 24.9662i | 0.478352 | + | 0.828531i | ||||
\(909\) | 17.4558 | 0.578974 | ||||||||
\(910\) | 2.24264 | + | 5.49333i | 0.0743428 | + | 0.182102i | ||||
\(911\) | −30.4853 | −1.01002 | −0.505011 | − | 0.863113i | \(-0.668512\pi\) | ||||
−0.505011 | + | 0.863113i | \(0.668512\pi\) | |||||||
\(912\) | −0.707107 | − | 1.22474i | −0.0234146 | − | 0.0405554i | ||||
\(913\) | 6.07107 | − | 10.5154i | 0.200923 | − | 0.348009i | ||||
\(914\) | 5.82843 | − | 10.0951i | 0.192787 | − | 0.333917i | ||||
\(915\) | −8.36396 | − | 14.4868i | −0.276504 | − | 0.478919i | ||||
\(916\) | 23.3137 | 0.770307 | ||||||||
\(917\) | 1.53553 | + | 0.210133i | 0.0507078 | + | 0.00693920i | ||||
\(918\) | 1.51472 | 0.0499932 | ||||||||
\(919\) | −11.0711 | − | 19.1757i | −0.365201 | − | 0.632546i | 0.623608 | − | 0.781738i | \(-0.285666\pi\) |
−0.988808 | + | 0.149191i | \(0.952333\pi\) | |||||||
\(920\) | −1.82843 | + | 3.16693i | −0.0602815 | + | 0.104411i | ||||
\(921\) | 11.9497 | − | 20.6976i | 0.393758 | − | 0.682008i | ||||
\(922\) | 4.15685 | + | 7.19988i | 0.136899 | + | 0.237116i | ||||
\(923\) | 42.3848 | 1.39511 | ||||||||
\(924\) | −3.91421 | + | 5.04757i | −0.128768 | + | 0.166053i | ||||
\(925\) | 43.8406 | 1.44147 | ||||||||
\(926\) | −6.41421 | − | 11.1097i | −0.210784 | − | 0.365089i | ||||
\(927\) | −18.9706 | + | 32.8580i | −0.623075 | + | 1.07920i | ||||
\(928\) | −1.32843 | + | 2.30090i | −0.0436078 | + | 0.0755309i | ||||
\(929\) | 20.2279 | + | 35.0358i | 0.663657 | + | 1.14949i | 0.979648 | + | 0.200725i | \(0.0643297\pi\) |
−0.315991 | + | 0.948762i | \(0.602337\pi\) | |||||||
\(930\) | −5.65685 | −0.185496 | ||||||||
\(931\) | 2.92893 | − | 2.86976i | 0.0959919 | − | 0.0940524i | ||||
\(932\) | 1.41421 | 0.0463241 | ||||||||
\(933\) | 20.1924 | + | 34.9742i | 0.661069 | + | 1.14501i | ||||
\(934\) | 17.0000 | − | 29.4449i | 0.556257 | − | 0.963465i | ||||
\(935\) | 1.07107 | − | 1.85514i | 0.0350277 | − | 0.0606697i | ||||
\(936\) | 5.41421 | + | 9.37769i | 0.176969 | + | 0.306519i | ||||
\(937\) | −19.4142 | −0.634235 | −0.317117 | − | 0.948386i | \(-0.602715\pi\) | ||||
−0.317117 | + | 0.948386i | \(0.602715\pi\) | |||||||
\(938\) | 4.47056 | − | 5.76500i | 0.145969 | − | 0.188234i | ||||
\(939\) | 49.8701 | 1.62745 | ||||||||
\(940\) | −3.07107 | − | 5.31925i | −0.100167 | − | 0.173495i | ||||
\(941\) | −12.3284 | + | 21.3535i | −0.401895 | + | 0.696103i | −0.993955 | − | 0.109791i | \(-0.964982\pi\) |
0.592059 | + | 0.805894i | \(0.298315\pi\) | |||||||
\(942\) | 21.3137 | − | 36.9164i | 0.694438 | − | 1.20280i | ||||
\(943\) | −16.8995 | − | 29.2708i | −0.550323 | − | 0.953188i | ||||
\(944\) | −5.58579 | −0.181802 | ||||||||
\(945\) | 0.636039 | + | 0.0870399i | 0.0206903 | + | 0.00283141i | ||||
\(946\) | −5.65685 | −0.183920 | ||||||||
\(947\) | −17.4142 | − | 30.1623i | −0.565886 | − | 0.980143i | −0.996967 | − | 0.0778298i | \(-0.975201\pi\) |
0.431081 | − | 0.902313i | \(-0.358132\pi\) | |||||||
\(948\) | −15.9853 | + | 27.6873i | −0.519178 | + | 0.899242i | ||||
\(949\) | −18.0208 | + | 31.2130i | −0.584980 | + | 1.01322i | ||||
\(950\) | −1.36396 | − | 2.36245i | −0.0442527 | − | 0.0766480i | ||||
\(951\) | −20.9706 | −0.680017 | ||||||||
\(952\) | 3.65685 | + | 8.95743i | 0.118519 | + | 0.290312i | ||||
\(953\) | 5.55635 | 0.179988 | 0.0899939 | − | 0.995942i | \(-0.471315\pi\) | ||||
0.0899939 | + | 0.995942i | \(0.471315\pi\) | |||||||
\(954\) | −11.1716 | − | 19.3497i | −0.361693 | − | 0.626471i | ||||
\(955\) | −2.10051 | + | 3.63818i | −0.0679707 | + | 0.117729i | ||||
\(956\) | −10.1066 | + | 17.5051i | −0.326871 | + | 0.566157i | ||||
\(957\) | 3.20711 | + | 5.55487i | 0.103671 | + | 0.179564i | ||||
\(958\) | −11.9289 | −0.385406 | ||||||||
\(959\) | −16.6569 | − | 40.8008i | −0.537878 | − | 1.31753i | ||||
\(960\) | 1.41421 | 0.0456435 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | −18.0208 | + | 31.2130i | −0.581014 | + | 1.00635i | ||||
\(963\) | 4.34315 | − | 7.52255i | 0.139956 | − | 0.242411i | ||||
\(964\) | −6.12132 | − | 10.6024i | −0.197154 | − | 0.341482i | ||||
\(965\) | −12.8284 | −0.412962 | ||||||||
\(966\) | −39.5061 | − | 5.40629i | −1.27109 | − | 0.173944i | ||||
\(967\) | −36.2843 | −1.16682 | −0.583412 | − | 0.812177i | \(-0.698283\pi\) | ||||
−0.583412 | + | 0.812177i | \(0.698283\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | −2.58579 | + | 4.47871i | −0.0830674 | + | 0.143877i | ||||
\(970\) | −1.12132 | + | 1.94218i | −0.0360034 | + | 0.0623598i | ||||
\(971\) | −11.1360 | − | 19.2882i | −0.357372 | − | 0.618987i | 0.630149 | − | 0.776475i | \(-0.282994\pi\) |
−0.987521 | + | 0.157487i | \(0.949661\pi\) | |||||||
\(972\) | 21.6569 | 0.694644 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.65685 | −0.309426 | ||||||||
\(975\) | 21.5208 | + | 37.2751i | 0.689218 | + | 1.19376i | ||||
\(976\) | −5.91421 | + | 10.2437i | −0.189309 | + | 0.327893i | ||||
\(977\) | −20.0000 | + | 34.6410i | −0.639857 | + | 1.10826i | 0.345607 | + | 0.938379i | \(0.387673\pi\) |
−0.985464 | + | 0.169885i | \(0.945660\pi\) | |||||||
\(978\) | 11.7426 | + | 20.3389i | 0.375488 | + | 0.650365i | ||||
\(979\) | 12.4853 | 0.399031 | ||||||||
\(980\) | 1.02082 | + | 3.97141i | 0.0326087 | + | 0.126862i | ||||
\(981\) | 46.6274 | 1.48870 | ||||||||
\(982\) | −9.58579 | − | 16.6031i | −0.305895 | − | 0.529825i | ||||
\(983\) | −16.2132 | + | 28.0821i | −0.517121 | + | 0.895680i | 0.482681 | + | 0.875796i | \(0.339663\pi\) |
−0.999802 | + | 0.0198836i | \(0.993670\pi\) | |||||||
\(984\) | −6.53553 | + | 11.3199i | −0.208345 | + | 0.360864i | ||||
\(985\) | −0.150758 | − | 0.261120i | −0.00480354 | − | 0.00831997i | ||||
\(986\) | 9.71573 | 0.309412 | ||||||||
\(987\) | 41.0416 | − | 52.9251i | 1.30637 | − | 1.68463i | ||||
\(988\) | 2.24264 | 0.0713479 | ||||||||
\(989\) | −17.6569 | − | 30.5826i | −0.561455 | − | 0.972469i | ||||
\(990\) | 0.828427 | − | 1.43488i | 0.0263291 | − | 0.0456034i | ||||
\(991\) | 0.807612 | − | 1.39882i | 0.0256546 | − | 0.0444351i | −0.852913 | − | 0.522053i | \(-0.825166\pi\) |
0.878568 | + | 0.477618i | \(0.158500\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | 58.1127 | 1.84415 | ||||||||
\(994\) | 29.0208 | + | 3.97141i | 0.920484 | + | 0.125965i | ||||
\(995\) | −0.0588745 | −0.00186645 | ||||||||
\(996\) | −14.6569 | − | 25.3864i | −0.464420 | − | 0.804399i | ||||
\(997\) | −6.58579 | + | 11.4069i | −0.208574 | + | 0.361261i | −0.951266 | − | 0.308373i | \(-0.900216\pi\) |
0.742692 | + | 0.669634i | \(0.233549\pi\) | |||||||
\(998\) | −11.0711 | + | 19.1757i | −0.350449 | + | 0.606995i | ||||
\(999\) | 1.94975 | + | 3.37706i | 0.0616873 | + | 0.106846i |
(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 | 154.2.e.e.67.2 | yes | 4 | |
3.2 | odd | 2 | 1386.2.k.t.991.2 | 4 | |||
4.3 | odd | 2 | 1232.2.q.f.529.1 | 4 | |||
7.2 | even | 3 | inner | 154.2.e.e.23.2 | ✓ | 4 | |
7.3 | odd | 6 | 1078.2.a.x.1.2 | 2 | |||
7.4 | even | 3 | 1078.2.a.t.1.1 | 2 | |||
7.5 | odd | 6 | 1078.2.e.m.177.1 | 4 | |||
7.6 | odd | 2 | 1078.2.e.m.67.1 | 4 | |||
21.2 | odd | 6 | 1386.2.k.t.793.2 | 4 | |||
21.11 | odd | 6 | 9702.2.a.cx.1.1 | 2 | |||
21.17 | even | 6 | 9702.2.a.ch.1.2 | 2 | |||
28.3 | even | 6 | 8624.2.a.bh.1.1 | 2 | |||
28.11 | odd | 6 | 8624.2.a.cc.1.2 | 2 | |||
28.23 | odd | 6 | 1232.2.q.f.177.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.e.23.2 | ✓ | 4 | 7.2 | even | 3 | inner | |
154.2.e.e.67.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1078.2.a.t.1.1 | 2 | 7.4 | even | 3 | |||
1078.2.a.x.1.2 | 2 | 7.3 | odd | 6 | |||
1078.2.e.m.67.1 | 4 | 7.6 | odd | 2 | |||
1078.2.e.m.177.1 | 4 | 7.5 | odd | 6 | |||
1232.2.q.f.177.1 | 4 | 28.23 | odd | 6 | |||
1232.2.q.f.529.1 | 4 | 4.3 | odd | 2 | |||
1386.2.k.t.793.2 | 4 | 21.2 | odd | 6 | |||
1386.2.k.t.991.2 | 4 | 3.2 | odd | 2 | |||
8624.2.a.bh.1.1 | 2 | 28.3 | even | 6 | |||
8624.2.a.cc.1.2 | 2 | 28.11 | odd | 6 | |||
9702.2.a.ch.1.2 | 2 | 21.17 | even | 6 | |||
9702.2.a.cx.1.1 | 2 | 21.11 | odd | 6 |