Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,3,Mod(91,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.c (of order \(2\), degree \(1\), 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: | \(4.90464475849\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 180.91 |
Dual form | 180.3.c.a.91.2 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | − | 1.90211i | −0.309017 | − | 0.951057i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.25731i | − | 0.751044i | −0.926813 | − | 0.375522i | \(-0.877463\pi\) | ||
0.926813 | − | 0.375522i | \(-0.122537\pi\) | |||||||
\(8\) | 6.47214 | + | 4.70228i | 0.809017 | + | 0.587785i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.38197 | − | 4.25325i | −0.138197 | − | 0.425325i | ||||
\(11\) | − | 19.9192i | − | 1.81084i | −0.424522 | − | 0.905418i | \(-0.639558\pi\) | ||
0.424522 | − | 0.905418i | \(-0.360442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.47214 | −0.651703 | −0.325851 | − | 0.945421i | \(-0.605651\pi\) | ||||
−0.325851 | + | 0.945421i | \(0.605651\pi\) | |||||||
\(14\) | −10.0000 | + | 3.24920i | −0.714286 | + | 0.232085i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(17\) | −11.8885 | −0.699326 | −0.349663 | − | 0.936876i | \(-0.613704\pi\) | ||||
−0.349663 | + | 0.936876i | \(0.613704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 15.2169i | − | 0.800890i | −0.916321 | − | 0.400445i | \(-0.868856\pi\) | ||
0.916321 | − | 0.400445i | \(-0.131144\pi\) | |||||||
\(20\) | −7.23607 | + | 5.25731i | −0.361803 | + | 0.262866i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −37.8885 | + | 12.3107i | −1.72221 | + | 0.559579i | ||||
\(23\) | 0.555029i | 0.0241317i | 0.999927 | + | 0.0120659i | \(0.00384077\pi\) | ||||
−0.999927 | + | 0.0120659i | \(0.996159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 5.23607 | + | 16.1150i | 0.201387 | + | 0.619806i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.3607 | + | 17.0130i | 0.441453 | + | 0.607608i | ||||
\(29\) | 10.9443 | 0.377389 | 0.188694 | − | 0.982036i | \(-0.439574\pi\) | ||||
0.188694 | + | 0.982036i | \(0.439574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.29451i | − | 0.267565i | −0.991011 | − | 0.133782i | \(-0.957288\pi\) | ||
0.991011 | − | 0.133782i | \(-0.0427123\pi\) | |||||||
\(32\) | −32.0000 | −1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.34752 | + | 22.6134i | 0.216104 | + | 0.665099i | ||||
\(35\) | − | 11.7557i | − | 0.335877i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.3607 | −0.496235 | −0.248117 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248117 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(38\) | −28.9443 | + | 9.40456i | −0.761691 | + | 0.247489i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.4721 | + | 10.5146i | 0.361803 | + | 0.262866i | ||||
\(41\) | 14.5836 | 0.355697 | 0.177849 | − | 0.984058i | \(-0.443086\pi\) | ||||
0.177849 | + | 0.984058i | \(0.443086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.2703i | 0.517915i | 0.965889 | + | 0.258957i | \(0.0833789\pi\) | ||||
−0.965889 | + | 0.258957i | \(0.916621\pi\) | |||||||
\(44\) | 46.8328 | + | 64.4598i | 1.06438 | + | 1.46500i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05573 | − | 0.343027i | 0.0229506 | − | 0.00745711i | ||||
\(47\) | − | 53.3902i | − | 1.13596i | −0.823042 | − | 0.567981i | \(-0.807725\pi\) | ||
0.823042 | − | 0.567981i | \(-0.192275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.3607 | 0.435932 | ||||||||
\(50\) | −3.09017 | − | 9.51057i | −0.0618034 | − | 0.190211i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 27.4164 | − | 19.9192i | 0.527239 | − | 0.383061i | ||||
\(53\) | 66.3607 | 1.25209 | 0.626044 | − | 0.779788i | \(-0.284673\pi\) | ||||
0.626044 | + | 0.779788i | \(0.284673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 44.5407i | − | 0.809830i | ||||||
\(56\) | 24.7214 | − | 34.0260i | 0.441453 | − | 0.607608i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.76393 | − | 20.8172i | −0.116620 | − | 0.358918i | ||||
\(59\) | − | 17.4370i | − | 0.295543i | −0.989022 | − | 0.147771i | \(-0.952790\pi\) | ||
0.989022 | − | 0.147771i | \(-0.0472100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 90.1378 | 1.47767 | 0.738834 | − | 0.673887i | \(-0.235377\pi\) | ||||
0.738834 | + | 0.673887i | \(0.235377\pi\) | |||||||
\(62\) | −15.7771 | + | 5.12629i | −0.254469 | + | 0.0826820i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19.7771 | + | 60.8676i | 0.309017 | + | 0.951057i | ||||
\(65\) | −18.9443 | −0.291450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50.2220i | 0.749582i | 0.927109 | + | 0.374791i | \(0.122285\pi\) | ||||
−0.927109 | + | 0.374791i | \(0.877715\pi\) | |||||||
\(68\) | 38.4721 | − | 27.9516i | 0.565767 | − | 0.411054i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −22.3607 | + | 7.26543i | −0.319438 | + | 0.103792i | ||||
\(71\) | 80.7868i | 1.13784i | 0.822392 | + | 0.568921i | \(0.192639\pi\) | ||||
−0.822392 | + | 0.568921i | \(0.807361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55418 | −0.0760846 | −0.0380423 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380423 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(74\) | 11.3475 | + | 34.9241i | 0.153345 | + | 0.471947i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 35.7771 | + | 49.2429i | 0.470751 | + | 0.647933i | ||||
\(77\) | −104.721 | −1.36002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.8448i | − | 0.175251i | −0.996154 | − | 0.0876253i | \(-0.972072\pi\) | ||
0.996154 | − | 0.0876253i | \(-0.0279278\pi\) | |||||||
\(80\) | 11.0557 | − | 34.0260i | 0.138197 | − | 0.425325i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.01316 | − | 27.7396i | −0.109917 | − | 0.338288i | ||||
\(83\) | 76.2155i | 0.918260i | 0.888369 | + | 0.459130i | \(0.151839\pi\) | ||||
−0.888369 | + | 0.459130i | \(0.848161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.5836 | −0.312748 | ||||||||
\(86\) | 42.3607 | − | 13.7638i | 0.492566 | − | 0.160044i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 93.6656 | − | 128.920i | 1.06438 | − | 1.46500i | ||||
\(89\) | 111.443 | 1.25217 | 0.626083 | − | 0.779757i | \(-0.284657\pi\) | ||||
0.626083 | + | 0.779757i | \(0.284657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44.5407i | 0.489458i | ||||||||
\(92\) | −1.30495 | − | 1.79611i | −0.0141843 | − | 0.0195230i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −101.554 | + | 32.9970i | −1.08036 | + | 0.351031i | ||||
\(95\) | − | 34.0260i | − | 0.358169i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −92.8328 | −0.957039 | −0.478520 | − | 0.878077i | \(-0.658826\pi\) | ||||
−0.478520 | + | 0.878077i | \(0.658826\pi\) | |||||||
\(98\) | −13.2016 | − | 40.6304i | −0.134710 | − | 0.414596i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.1803 | + | 11.7557i | −0.161803 | + | 0.117557i | ||||
\(101\) | −64.1115 | −0.634767 | −0.317383 | − | 0.948297i | \(-0.602804\pi\) | ||||
−0.317383 | + | 0.948297i | \(0.602804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 137.769i | 1.33757i | 0.743458 | + | 0.668783i | \(0.233184\pi\) | ||||
−0.743458 | + | 0.668783i | \(0.766816\pi\) | |||||||
\(104\) | −54.8328 | − | 39.8384i | −0.527239 | − | 0.383061i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −41.0132 | − | 126.226i | −0.386917 | − | 1.19081i | ||||
\(107\) | 51.3320i | 0.479739i | 0.970805 | + | 0.239869i | \(0.0771046\pi\) | ||||
−0.970805 | + | 0.239869i | \(0.922895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 133.469 | 1.22449 | 0.612243 | − | 0.790669i | \(-0.290267\pi\) | ||||
0.612243 | + | 0.790669i | \(0.290267\pi\) | |||||||
\(110\) | −84.7214 | + | 27.5276i | −0.770194 | + | 0.250251i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −80.0000 | − | 25.9936i | −0.714286 | − | 0.232085i | ||||
\(113\) | −170.721 | −1.51081 | −0.755404 | − | 0.655259i | \(-0.772559\pi\) | ||||
−0.755404 | + | 0.655259i | \(0.772559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.24108i | 0.0107920i | ||||||||
\(116\) | −35.4164 | + | 25.7315i | −0.305314 | + | 0.221824i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −33.1672 | + | 10.7767i | −0.281078 | + | 0.0913277i | ||||
\(119\) | 62.5018i | 0.525225i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −275.774 | −2.27912 | ||||||||
\(122\) | −55.7082 | − | 171.452i | −0.456625 | − | 1.40535i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.5016 | + | 26.8416i | 0.157271 | + | 0.216464i | ||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 198.637i | − | 1.56407i | −0.623235 | − | 0.782035i | \(-0.714182\pi\) | ||
0.623235 | − | 0.782035i | \(-0.285818\pi\) | |||||||
\(128\) | 103.554 | − | 75.2365i | 0.809017 | − | 0.587785i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.7082 | + | 36.0341i | 0.0900631 | + | 0.277186i | ||||
\(131\) | − | 7.77041i | − | 0.0593161i | −0.999560 | − | 0.0296580i | \(-0.990558\pi\) | ||
0.999560 | − | 0.0296580i | \(-0.00944183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.0000 | −0.601504 | ||||||||
\(134\) | 95.5279 | − | 31.0389i | 0.712895 | − | 0.231633i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −76.9443 | − | 55.9033i | −0.565767 | − | 0.411054i | ||||
\(137\) | −0.832816 | −0.00607895 | −0.00303947 | − | 0.999995i | \(-0.500967\pi\) | ||||
−0.00303947 | + | 0.999995i | \(0.500967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 237.658i | − | 1.70977i | −0.518817 | − | 0.854885i | \(-0.673627\pi\) | ||
0.518817 | − | 0.854885i | \(-0.326373\pi\) | |||||||
\(140\) | 27.6393 | + | 38.0423i | 0.197424 | + | 0.271730i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 153.666 | − | 49.9290i | 1.08215 | − | 0.351613i | ||||
\(143\) | 168.758i | 1.18013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.4721 | 0.168773 | ||||||||
\(146\) | 3.43267 | + | 10.5647i | 0.0235114 | + | 0.0723607i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 59.4164 | − | 43.1685i | 0.401462 | − | 0.291679i | ||||
\(149\) | 36.9706 | 0.248125 | 0.124062 | − | 0.992274i | \(-0.460408\pi\) | ||||
0.124062 | + | 0.992274i | \(0.460408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 282.723i | 1.87234i | 0.351552 | + | 0.936168i | \(0.385654\pi\) | ||||
−0.351552 | + | 0.936168i | \(0.614346\pi\) | |||||||
\(152\) | 71.5542 | − | 98.4859i | 0.470751 | − | 0.647933i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 64.7214 | + | 199.192i | 0.420269 | + | 1.29345i | ||||
\(155\) | − | 18.5471i | − | 0.119659i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 204.748 | 1.30413 | 0.652063 | − | 0.758165i | \(-0.273904\pi\) | ||||
0.652063 | + | 0.758165i | \(0.273904\pi\) | |||||||
\(158\) | −26.3344 | + | 8.55656i | −0.166673 | + | 0.0541554i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −71.5542 | −0.447214 | ||||||||
\(161\) | 2.91796 | 0.0181240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 107.235i | 0.657885i | 0.944350 | + | 0.328943i | \(0.106692\pi\) | ||||
−0.944350 | + | 0.328943i | \(0.893308\pi\) | |||||||
\(164\) | −47.1935 | + | 34.2881i | −0.287765 | + | 0.209074i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 144.971 | − | 47.1038i | 0.873317 | − | 0.283758i | ||||
\(167\) | − | 33.2090i | − | 0.198856i | −0.995045 | − | 0.0994280i | \(-0.968299\pi\) | ||
0.995045 | − | 0.0994280i | \(-0.0317013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −97.2229 | −0.575284 | ||||||||
\(170\) | 16.4296 | + | 50.5650i | 0.0966445 | + | 0.297441i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −52.3607 | − | 72.0683i | −0.304423 | − | 0.419002i | ||||
\(173\) | 226.361 | 1.30844 | 0.654222 | − | 0.756303i | \(-0.272996\pi\) | ||||
0.654222 | + | 0.756303i | \(0.272996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 26.2866i | − | 0.150209i | ||||||
\(176\) | −303.108 | − | 98.4859i | −1.72221 | − | 0.559579i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −68.8754 | − | 211.977i | −0.386940 | − | 1.19088i | ||||
\(179\) | − | 224.337i | − | 1.25328i | −0.779308 | − | 0.626641i | \(-0.784429\pi\) | ||
0.779308 | − | 0.626641i | \(-0.215571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 86.2229 | 0.476370 | 0.238185 | − | 0.971220i | \(-0.423448\pi\) | ||||
0.238185 | + | 0.971220i | \(0.423448\pi\) | |||||||
\(182\) | 84.7214 | − | 27.5276i | 0.465502 | − | 0.151251i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.60990 | + | 3.59222i | −0.0141843 | + | 0.0195230i | ||||
\(185\) | −41.0557 | −0.221923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 236.810i | 1.26636i | ||||||||
\(188\) | 125.528 | + | 172.774i | 0.667701 | + | 0.919012i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −64.7214 | + | 21.0292i | −0.340639 | + | 0.110680i | ||||
\(191\) | 31.0198i | 0.162407i | 0.996698 | + | 0.0812036i | \(0.0258764\pi\) | ||||
−0.996698 | + | 0.0812036i | \(0.974124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.223 | 0.571103 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(194\) | 57.3738 | + | 176.579i | 0.295741 | + | 0.910198i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −69.1246 | + | 50.2220i | −0.352677 | + | 0.256235i | ||||
\(197\) | 172.525 | 0.875760 | 0.437880 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437880 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 272.208i | − | 1.36788i | −0.729538 | − | 0.683940i | \(-0.760265\pi\) | ||
0.729538 | − | 0.683940i | \(-0.239735\pi\) | |||||||
\(200\) | 32.3607 | + | 23.5114i | 0.161803 | + | 0.117557i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.6231 | + | 121.947i | 0.196154 | + | 0.603699i | ||||
\(203\) | − | 57.5374i | − | 0.283436i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.6099 | 0.159073 | ||||||||
\(206\) | 262.053 | − | 85.1461i | 1.27210 | − | 0.413330i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −41.8885 | + | 128.920i | −0.201387 | + | 0.619806i | ||||
\(209\) | −303.108 | −1.45028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 205.266i | − | 0.972826i | −0.873729 | − | 0.486413i | \(-0.838305\pi\) | ||
0.873729 | − | 0.486413i | \(-0.161695\pi\) | |||||||
\(212\) | −214.748 | + | 156.023i | −1.01296 | + | 0.735959i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 97.6393 | − | 31.7249i | 0.456259 | − | 0.148247i | ||||
\(215\) | 49.7980i | 0.231618i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −43.6068 | −0.200953 | ||||||||
\(218\) | −82.4884 | − | 253.873i | −0.378387 | − | 1.16456i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 104.721 | + | 144.137i | 0.476006 | + | 0.655166i | ||||
\(221\) | 100.721 | 0.455753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 235.731i | 1.05709i | 0.848905 | + | 0.528545i | \(0.177262\pi\) | ||||
−0.848905 | + | 0.528545i | \(0.822738\pi\) | |||||||
\(224\) | 168.234i | 0.751044i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 105.512 | + | 324.731i | 0.466865 | + | 1.43686i | ||||
\(227\) | 58.5165i | 0.257782i | 0.991659 | + | 0.128891i | \(0.0411417\pi\) | ||||
−0.991659 | + | 0.128891i | \(0.958858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 162.721 | 0.710574 | 0.355287 | − | 0.934757i | \(-0.384383\pi\) | ||||
0.355287 | + | 0.934757i | \(0.384383\pi\) | |||||||
\(230\) | 2.36068 | − | 0.767031i | 0.0102638 | − | 0.00333492i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 70.8328 | + | 51.4631i | 0.305314 | + | 0.221824i | ||||
\(233\) | −319.050 | −1.36931 | −0.684656 | − | 0.728867i | \(-0.740047\pi\) | ||||
−0.684656 | + | 0.728867i | \(0.740047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 119.384i | − | 0.508017i | ||||||
\(236\) | 40.9969 | + | 56.4274i | 0.173716 | + | 0.239099i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 118.885 | − | 38.6282i | 0.499519 | − | 0.162303i | ||||
\(239\) | − | 236.810i | − | 0.990837i | −0.868654 | − | 0.495419i | \(-0.835015\pi\) | ||
0.868654 | − | 0.495419i | \(-0.164985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.917961 | −0.00380897 | −0.00190448 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190448 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(242\) | 170.438 | + | 524.553i | 0.704288 | + | 2.16758i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −291.692 | + | 211.927i | −1.19546 | + | 0.868552i | ||||
\(245\) | 47.7639 | 0.194955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 128.920i | 0.521942i | ||||||||
\(248\) | 39.0031 | − | 53.6832i | 0.157271 | − | 0.216464i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.90983 | − | 21.2663i | −0.0276393 | − | 0.0850651i | ||||
\(251\) | 136.690i | 0.544582i | 0.962215 | + | 0.272291i | \(0.0877813\pi\) | ||||
−0.962215 | + | 0.272291i | \(0.912219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0557 | 0.0436985 | ||||||||
\(254\) | −377.830 | + | 122.764i | −1.48752 | + | 0.483324i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −207.108 | − | 150.473i | −0.809017 | − | 0.587785i | ||||
\(257\) | 274.944 | 1.06982 | 0.534911 | − | 0.844908i | \(-0.320345\pi\) | ||||
0.534911 | + | 0.844908i | \(0.320345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96.5278i | 0.372694i | ||||||||
\(260\) | 61.3050 | − | 44.5407i | 0.235788 | − | 0.171310i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.7802 | + | 4.80238i | −0.0564130 | + | 0.0183297i | ||||
\(263\) | − | 406.385i | − | 1.54519i | −0.634899 | − | 0.772596i | \(-0.718958\pi\) | ||
0.634899 | − | 0.772596i | \(-0.281042\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 148.387 | 0.559951 | ||||||||
\(266\) | 49.4427 | + | 152.169i | 0.185875 | + | 0.572064i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −118.079 | − | 162.522i | −0.440593 | − | 0.606424i | ||||
\(269\) | 348.525 | 1.29563 | 0.647816 | − | 0.761797i | \(-0.275683\pi\) | ||||
0.647816 | + | 0.761797i | \(0.275683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 247.849i | − | 0.914571i | −0.889320 | − | 0.457286i | \(-0.848822\pi\) | ||
0.889320 | − | 0.457286i | \(-0.151178\pi\) | |||||||
\(272\) | −58.7802 | + | 180.907i | −0.216104 | + | 0.665099i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.514708 | + | 1.58411i | 0.00187850 | + | 0.00578142i | ||||
\(275\) | − | 99.5959i | − | 0.362167i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −54.7539 | −0.197667 | −0.0988337 | − | 0.995104i | \(-0.531511\pi\) | ||||
−0.0988337 | + | 0.995104i | \(0.531511\pi\) | |||||||
\(278\) | −452.053 | + | 146.881i | −1.62609 | + | 0.528348i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 55.2786 | − | 76.0845i | 0.197424 | − | 0.271730i | ||||
\(281\) | 50.3607 | 0.179220 | 0.0896098 | − | 0.995977i | \(-0.471438\pi\) | ||||
0.0896098 | + | 0.995977i | \(0.471438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 147.336i | − | 0.520621i | −0.965525 | − | 0.260310i | \(-0.916175\pi\) | ||
0.965525 | − | 0.260310i | \(-0.0838249\pi\) | |||||||
\(284\) | −189.941 | − | 261.432i | −0.668807 | − | 0.920534i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 320.997 | − | 104.298i | 1.12237 | − | 0.364679i | ||||
\(287\) | − | 76.6705i | − | 0.267145i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −147.663 | −0.510943 | ||||||||
\(290\) | −15.1246 | − | 46.5488i | −0.0521538 | − | 0.160513i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.9737 | − | 13.0586i | 0.0615537 | − | 0.0447214i | ||||
\(293\) | −178.859 | −0.610441 | −0.305220 | − | 0.952282i | \(-0.598730\pi\) | ||||
−0.305220 | + | 0.952282i | \(0.598730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 38.9904i | − | 0.132171i | ||||||
\(296\) | −118.833 | − | 86.3371i | −0.401462 | − | 0.291679i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.8491 | − | 70.3222i | −0.0766748 | − | 0.235981i | ||||
\(299\) | − | 4.70228i | − | 0.0157267i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 117.082 | 0.388977 | ||||||||
\(302\) | 537.771 | − | 174.732i | 1.78070 | − | 0.578584i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −231.554 | − | 75.2365i | −0.761691 | − | 0.247489i | ||||
\(305\) | 201.554 | 0.660833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 284.550i | − | 0.926873i | −0.886130 | − | 0.463436i | \(-0.846616\pi\) | ||
0.886130 | − | 0.463436i | \(-0.153384\pi\) | |||||||
\(308\) | 338.885 | − | 246.215i | 1.10028 | − | 0.799398i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.2786 | + | 11.4627i | −0.113802 | + | 0.0369765i | ||||
\(311\) | − | 282.199i | − | 0.907392i | −0.891157 | − | 0.453696i | \(-0.850105\pi\) | ||
0.891157 | − | 0.453696i | \(-0.149895\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −567.548 | −1.81325 | −0.906626 | − | 0.421935i | \(-0.861351\pi\) | ||||
−0.906626 | + | 0.421935i | \(0.861351\pi\) | |||||||
\(314\) | −126.541 | − | 389.453i | −0.402997 | − | 1.24030i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.5511 | + | 44.8027i | 0.103010 | + | 0.141781i | ||||
\(317\) | −161.141 | −0.508331 | −0.254165 | − | 0.967161i | \(-0.581801\pi\) | ||||
−0.254165 | + | 0.967161i | \(0.581801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 218.001i | − | 0.683389i | ||||||
\(320\) | 44.2229 | + | 136.104i | 0.138197 | + | 0.425325i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.80340 | − | 5.55029i | −0.00560062 | − | 0.0172369i | ||||
\(323\) | 180.907i | 0.560083i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.3607 | −0.130341 | ||||||||
\(326\) | 203.974 | − | 66.2751i | 0.625686 | − | 0.203298i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 94.3870 | + | 68.5762i | 0.287765 | + | 0.209074i | ||||
\(329\) | −280.689 | −0.853158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 331.966i | 1.00292i | 0.865181 | + | 0.501459i | \(0.167203\pi\) | ||||
−0.865181 | + | 0.501459i | \(0.832797\pi\) | |||||||
\(332\) | −179.193 | − | 246.639i | −0.539739 | − | 0.742888i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −63.1672 | + | 20.5243i | −0.189123 | + | 0.0614499i | ||||
\(335\) | 112.300i | 0.335223i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −269.108 | −0.798541 | −0.399271 | − | 0.916833i | \(-0.630737\pi\) | ||||
−0.399271 | + | 0.916833i | \(0.630737\pi\) | |||||||
\(338\) | 60.0871 | + | 184.929i | 0.177772 | + | 0.547127i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 86.0263 | − | 62.5018i | 0.253019 | − | 0.183829i | ||||
\(341\) | −165.220 | −0.484516 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 369.908i | − | 1.07845i | ||||||
\(344\) | −104.721 | + | 144.137i | −0.304423 | + | 0.419002i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −139.899 | − | 430.564i | −0.404331 | − | 1.24440i | ||||
\(347\) | 503.075i | 1.44978i | 0.688863 | + | 0.724892i | \(0.258110\pi\) | ||||
−0.688863 | + | 0.724892i | \(0.741890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.504658 | −0.00144601 | −0.000723006 | − | 1.00000i | \(-0.500230\pi\) | ||||
−0.000723006 | 1.00000i | \(0.500230\pi\) | ||||||||
\(350\) | −50.0000 | + | 16.2460i | −0.142857 | + | 0.0464171i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 637.414i | 1.81084i | ||||||||
\(353\) | 335.994 | 0.951824 | 0.475912 | − | 0.879493i | \(-0.342118\pi\) | ||||
0.475912 | + | 0.879493i | \(0.342118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 180.645i | 0.508859i | ||||||||
\(356\) | −360.636 | + | 262.018i | −1.01302 | + | 0.736004i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −426.715 | + | 138.648i | −1.19194 | + | 0.387285i | ||||
\(359\) | − | 98.4859i | − | 0.274334i | −0.990548 | − | 0.137167i | \(-0.956200\pi\) | ||
0.990548 | − | 0.137167i | \(-0.0437997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129.446 | 0.358576 | ||||||||
\(362\) | −53.2887 | − | 164.006i | −0.147206 | − | 0.453054i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −104.721 | − | 144.137i | −0.287696 | − | 0.395980i | ||||
\(365\) | −12.4195 | −0.0340261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 498.473i | 1.35824i | 0.734029 | + | 0.679118i | \(0.237638\pi\) | ||||
−0.734029 | + | 0.679118i | \(0.762362\pi\) | |||||||
\(368\) | 8.44582 | + | 2.74421i | 0.0229506 | + | 0.00745711i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.3738 | + | 78.0926i | 0.0685779 | + | 0.211061i | ||||
\(371\) | − | 348.879i | − | 0.940374i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 600.354 | 1.60953 | 0.804765 | − | 0.593594i | \(-0.202291\pi\) | ||||
0.804765 | + | 0.593594i | \(0.202291\pi\) | |||||||
\(374\) | 450.440 | − | 146.357i | 1.20438 | − | 0.391328i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 251.056 | − | 345.549i | 0.667701 | − | 0.919012i | ||||
\(377\) | −92.7214 | −0.245945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 303.490i | 0.800765i | 0.916348 | + | 0.400383i | \(0.131123\pi\) | ||||
−0.916348 | + | 0.400383i | \(0.868877\pi\) | |||||||
\(380\) | 80.0000 | + | 110.111i | 0.210526 | + | 0.289765i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 59.0031 | − | 19.1713i | 0.154458 | − | 0.0501866i | ||||
\(383\) | 332.583i | 0.868362i | 0.900826 | + | 0.434181i | \(0.142962\pi\) | ||||
−0.900826 | + | 0.434181i | \(0.857038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −234.164 | −0.608218 | ||||||||
\(386\) | −68.1215 | − | 209.656i | −0.176481 | − | 0.543151i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 300.413 | − | 218.263i | 0.774261 | − | 0.562534i | ||||
\(389\) | −392.354 | −1.00862 | −0.504312 | − | 0.863522i | \(-0.668254\pi\) | ||||
−0.504312 | + | 0.863522i | \(0.668254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.59849i | − | 0.0168759i | ||||||
\(392\) | 138.249 | + | 100.444i | 0.352677 | + | 0.256235i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −106.626 | − | 328.162i | −0.270625 | − | 0.832897i | ||||
\(395\) | − | 30.9579i | − | 0.0783744i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 334.190 | 0.841789 | 0.420895 | − | 0.907110i | \(-0.361716\pi\) | ||||
0.420895 | + | 0.907110i | \(0.361716\pi\) | |||||||
\(398\) | −517.771 | + | 168.234i | −1.30093 | + | 0.422698i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.7214 | − | 76.0845i | 0.0618034 | − | 0.190211i | ||||
\(401\) | −121.003 | −0.301753 | −0.150877 | − | 0.988553i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988553i | \(0.548210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 70.2722i | 0.174373i | ||||||||
\(404\) | 207.469 | − | 150.735i | 0.513537 | − | 0.373107i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −109.443 | + | 35.5601i | −0.269563 | + | 0.0875864i | ||||
\(407\) | 365.730i | 0.898599i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −607.410 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(410\) | −20.1540 | − | 62.0277i | −0.0491562 | − | 0.151287i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −323.915 | − | 445.831i | −0.786201 | − | 1.08211i | ||||
\(413\) | −91.6718 | −0.221966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.423i | 0.410658i | ||||||||
\(416\) | 271.108 | 0.651703 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 187.331 | + | 576.546i | 0.448161 | + | 1.37930i | ||||
\(419\) | 466.760i | 1.11398i | 0.830518 | + | 0.556992i | \(0.188045\pi\) | ||||
−0.830518 | + | 0.556992i | \(0.811955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −73.0883 | −0.173606 | −0.0868031 | − | 0.996225i | \(-0.527665\pi\) | ||||
−0.0868031 | + | 0.996225i | \(0.527665\pi\) | |||||||
\(422\) | −390.440 | + | 126.862i | −0.925212 | + | 0.300620i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 429.495 | + | 312.047i | 1.01296 | + | 0.735959i | ||||
\(425\) | −59.4427 | −0.139865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 473.882i | − | 1.10979i | ||||||
\(428\) | −120.689 | − | 166.114i | −0.281983 | − | 0.388117i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 94.7214 | − | 30.7768i | 0.220282 | − | 0.0715740i | ||||
\(431\) | 463.630i | 1.07571i | 0.843038 | + | 0.537853i | \(0.180765\pi\) | ||||
−0.843038 | + | 0.537853i | \(0.819235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −99.8359 | −0.230568 | −0.115284 | − | 0.993333i | \(-0.536778\pi\) | ||||
−0.115284 | + | 0.993333i | \(0.536778\pi\) | |||||||
\(434\) | 26.9505 | + | 82.9451i | 0.0620979 | + | 0.191118i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −431.915 | + | 313.805i | −0.990630 | + | 0.719735i | ||||
\(437\) | 8.44582 | 0.0193268 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 374.086i | 0.852133i | 0.904692 | + | 0.426066i | \(0.140101\pi\) | ||||
−0.904692 | + | 0.426066i | \(0.859899\pi\) | |||||||
\(440\) | 209.443 | − | 288.273i | 0.476006 | − | 0.655166i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −62.2492 | − | 191.583i | −0.140835 | − | 0.433447i | ||||
\(443\) | 290.100i | 0.654854i | 0.944877 | + | 0.327427i | \(0.106182\pi\) | ||||
−0.944877 | + | 0.327427i | \(0.893818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 249.193 | 0.559985 | ||||||||
\(446\) | 448.387 | − | 145.690i | 1.00535 | − | 0.326659i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 320.000 | − | 103.974i | 0.714286 | − | 0.232085i | ||||
\(449\) | −299.921 | −0.667976 | −0.333988 | − | 0.942577i | \(-0.608394\pi\) | ||||
−0.333988 | + | 0.942577i | \(0.608394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 290.493i | − | 0.644109i | ||||||
\(452\) | 552.466 | − | 401.390i | 1.22227 | − | 0.888031i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 111.305 | − | 36.1652i | 0.245165 | − | 0.0796590i | ||||
\(455\) | 99.5959i | 0.218892i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 822.328 | 1.79941 | 0.899703 | − | 0.436503i | \(-0.143783\pi\) | ||||
0.899703 | + | 0.436503i | \(0.143783\pi\) | |||||||
\(458\) | −100.567 | − | 309.514i | −0.219579 | − | 0.675796i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.91796 | − | 4.01623i | −0.00634339 | − | 0.00873093i | ||||
\(461\) | 456.885 | 0.991075 | 0.495537 | − | 0.868587i | \(-0.334971\pi\) | ||||
0.495537 | + | 0.868587i | \(0.334971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 400.249i | 0.864469i | 0.901761 | + | 0.432234i | \(0.142275\pi\) | ||||
−0.901761 | + | 0.432234i | \(0.857725\pi\) | |||||||
\(464\) | 54.1115 | − | 166.538i | 0.116620 | − | 0.358918i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 197.183 | + | 606.868i | 0.423140 | + | 1.30229i | ||||
\(467\) | − | 913.145i | − | 1.95534i | −0.210139 | − | 0.977672i | \(-0.567392\pi\) | ||
0.210139 | − | 0.977672i | \(-0.432608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 264.033 | 0.562969 | ||||||||
\(470\) | −227.082 | + | 73.7834i | −0.483153 | + | 0.156986i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 81.9938 | − | 112.855i | 0.173716 | − | 0.239099i | ||||
\(473\) | 443.607 | 0.937858 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 76.0845i | − | 0.160178i | ||||||
\(476\) | −146.950 | − | 202.260i | −0.308720 | − | 0.424916i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −450.440 | + | 146.357i | −0.942342 | + | 0.306186i | ||||
\(479\) | 526.131i | 1.09840i | 0.835692 | + | 0.549198i | \(0.185067\pi\) | ||||
−0.835692 | + | 0.549198i | \(0.814933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 155.554 | 0.323397 | ||||||||
\(482\) | 0.567331 | + | 1.74606i | 0.00117704 | + | 0.00362254i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 892.423 | − | 648.384i | 1.84385 | − | 1.33964i | ||||
\(485\) | −207.580 | −0.428001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 443.541i | 0.910762i | 0.890297 | + | 0.455381i | \(0.150497\pi\) | ||||
−0.890297 | + | 0.455381i | \(0.849503\pi\) | |||||||
\(488\) | 583.384 | + | 423.853i | 1.19546 | + | 0.868552i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29.5197 | − | 90.8524i | −0.0602444 | − | 0.185413i | ||||
\(491\) | 287.163i | 0.584854i | 0.956288 | + | 0.292427i | \(0.0944628\pi\) | ||||
−0.956288 | + | 0.292427i | \(0.905537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −130.111 | −0.263918 | ||||||||
\(494\) | 245.220 | − | 79.6767i | 0.496396 | − | 0.161289i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −126.217 | − | 41.0103i | −0.254469 | − | 0.0826820i | ||||
\(497\) | 424.721 | 0.854570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 810.936i | 1.62512i | 0.582876 | + | 0.812561i | \(0.301927\pi\) | ||||
−0.582876 | + | 0.812561i | \(0.698073\pi\) | |||||||
\(500\) | −36.1803 | + | 26.2866i | −0.0723607 | + | 0.0525731i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 260.000 | − | 84.4791i | 0.517928 | − | 0.168285i | ||||
\(503\) | − | 642.471i | − | 1.27728i | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||
0.769506 | − | 0.638639i | \(-0.220502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −143.358 | −0.283876 | ||||||||
\(506\) | −6.83282 | − | 21.0292i | −0.0135036 | − | 0.0415598i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 467.023 | + | 642.802i | 0.919337 | + | 1.26536i | ||||
\(509\) | 915.050 | 1.79774 | 0.898870 | − | 0.438216i | \(-0.144389\pi\) | ||||
0.898870 | + | 0.438216i | \(0.144389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.2000i | 0.0571429i | ||||||||
\(512\) | −158.217 | + | 486.941i | −0.309017 | + | 0.951057i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −169.925 | − | 522.975i | −0.330593 | − | 1.01746i | ||||
\(515\) | 308.061i | 0.598177i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1063.49 | −2.05704 | ||||||||
\(518\) | 183.607 | − | 59.6575i | 0.354453 | − | 0.115169i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −122.610 | − | 89.0813i | −0.235788 | − | 0.171310i | ||||
\(521\) | −1006.98 | −1.93279 | −0.966396 | − | 0.257058i | \(-0.917247\pi\) | ||||
−0.966396 | + | 0.257058i | \(0.917247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 774.173i | − | 1.48025i | −0.672467 | − | 0.740127i | \(-0.734765\pi\) | ||
0.672467 | − | 0.740127i | \(-0.265235\pi\) | |||||||
\(524\) | 18.2693 | + | 25.1456i | 0.0348651 | + | 0.0479877i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −772.991 | + | 251.160i | −1.46956 | + | 0.477490i | ||||
\(527\) | 98.6096i | 0.187115i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.692 | 0.999418 | ||||||||
\(530\) | −91.7082 | − | 282.249i | −0.173034 | − | 0.532545i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 258.885 | − | 188.091i | 0.486627 | − | 0.353555i | ||||
\(533\) | −123.554 | −0.231809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 114.782i | 0.214546i | ||||||||
\(536\) | −236.158 | + | 325.043i | −0.440593 | + | 0.606424i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −215.400 | − | 662.933i | −0.400372 | − | 1.23222i | ||||
\(539\) | − | 425.487i | − | 0.789401i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −259.115 | −0.478955 | −0.239477 | − | 0.970902i | \(-0.576976\pi\) | ||||
−0.239477 | + | 0.970902i | \(0.576976\pi\) | |||||||
\(542\) | −471.437 | + | 153.179i | −0.869809 | + | 0.282618i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 380.433 | 0.699326 | ||||||||
\(545\) | 298.446 | 0.547607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 149.818i | − | 0.273890i | −0.990579 | − | 0.136945i | \(-0.956272\pi\) | ||
0.990579 | − | 0.136945i | \(-0.0437284\pi\) | |||||||
\(548\) | 2.69505 | − | 1.95807i | 0.00491797 | − | 0.00357312i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −189.443 | + | 61.5537i | −0.344441 | + | 0.111916i | ||||
\(551\) | − | 166.538i | − | 0.302247i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −72.7864 | −0.131621 | ||||||||
\(554\) | 33.8398 | + | 104.148i | 0.0610826 | + | 0.187993i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 558.768 | + | 769.078i | 1.00498 | + | 1.38323i | ||||
\(557\) | −511.698 | −0.918668 | −0.459334 | − | 0.888264i | \(-0.651912\pi\) | ||||
−0.459334 | + | 0.888264i | \(0.651912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 188.677i | − | 0.337526i | ||||||
\(560\) | −178.885 | − | 58.1234i | −0.319438 | − | 0.103792i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.1246 | − | 95.7917i | −0.0553819 | − | 0.170448i | ||||
\(563\) | − | 490.726i | − | 0.871627i | −0.900037 | − | 0.435814i | \(-0.856461\pi\) | ||
0.900037 | − | 0.435814i | \(-0.143539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −381.745 | −0.675654 | ||||||||
\(566\) | −280.249 | + | 91.0585i | −0.495140 | + | 0.160881i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −379.882 | + | 522.863i | −0.668807 | + | 0.920534i | ||||
\(569\) | 232.748 | 0.409047 | 0.204523 | − | 0.978862i | \(-0.434436\pi\) | ||||
0.204523 | + | 0.978862i | \(0.434436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 210.755i | − | 0.369098i | −0.982823 | − | 0.184549i | \(-0.940918\pi\) | ||
0.982823 | − | 0.184549i | \(-0.0590824\pi\) | |||||||
\(572\) | −396.774 | − | 546.113i | −0.693661 | − | 0.954742i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −145.836 | + | 47.3850i | −0.254070 | + | 0.0825522i | ||||
\(575\) | 2.77515i | 0.00482634i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 341.712 | 0.592222 | 0.296111 | − | 0.955154i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955154i | \(0.404310\pi\) | |||||||
\(578\) | 91.2605 | + | 280.871i | 0.157890 | + | 0.485936i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −79.1935 | + | 57.5374i | −0.136541 | + | 0.0992025i | ||||
\(581\) | 400.689 | 0.689654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1321.85i | − | 2.26733i | ||||||
\(584\) | −35.9474 | − | 26.1173i | −0.0615537 | − | 0.0447214i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 110.541 | + | 340.210i | 0.188637 | + | 0.580564i | ||||
\(587\) | − | 618.412i | − | 1.05351i | −0.850016 | − | 0.526756i | \(-0.823408\pi\) | ||
0.850016 | − | 0.526756i | \(-0.176592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −126.217 | −0.214290 | ||||||||
\(590\) | −74.1641 | + | 24.0974i | −0.125702 | + | 0.0408430i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −90.7802 | + | 279.393i | −0.153345 | + | 0.471947i | ||||
\(593\) | −120.663 | −0.203478 | −0.101739 | − | 0.994811i | \(-0.532441\pi\) | ||||
−0.101739 | + | 0.994811i | \(0.532441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 139.758i | 0.234888i | ||||||||
\(596\) | −119.639 | + | 86.9231i | −0.200737 | + | 0.145844i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.94427 | + | 2.90617i | −0.0149570 | + | 0.00485982i | ||||
\(599\) | 849.927i | 1.41891i | 0.704751 | + | 0.709455i | \(0.251059\pi\) | ||||
−0.704751 | + | 0.709455i | \(0.748941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3576 | −0.0188978 | −0.00944890 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944890 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(602\) | −72.3607 | − | 222.703i | −0.120200 | − | 0.369939i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −664.721 | − | 914.910i | −1.10053 | − | 1.51475i | ||||
\(605\) | −616.649 | −1.01926 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1115.12i | − | 1.83710i | −0.395305 | − | 0.918550i | \(-0.629361\pi\) | ||
0.395305 | − | 0.918550i | \(-0.370639\pi\) | |||||||
\(608\) | 486.941i | 0.800890i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −124.567 | − | 383.379i | −0.204209 | − | 0.628490i | ||||
\(611\) | 452.329i | 0.740309i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 499.475 | 0.814805 | 0.407402 | − | 0.913249i | \(-0.366435\pi\) | ||||
0.407402 | + | 0.913249i | \(0.366435\pi\) | |||||||
\(614\) | −541.246 | + | 175.862i | −0.881508 | + | 0.286419i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −677.771 | − | 492.429i | −1.10028 | − | 0.799398i | ||||
\(617\) | −545.935 | −0.884822 | −0.442411 | − | 0.896813i | \(-0.645877\pi\) | ||||
−0.442411 | + | 0.896813i | \(0.645877\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 455.011i | 0.735075i | 0.930009 | + | 0.367537i | \(0.119799\pi\) | ||||
−0.930009 | + | 0.367537i | \(0.880201\pi\) | |||||||
\(620\) | 43.6068 | + | 60.0196i | 0.0703335 | + | 0.0968058i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −536.774 | + | 174.408i | −0.862981 | + | 0.280399i | ||||
\(623\) | − | 585.889i | − | 0.940432i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 350.764 | + | 1079.54i | 0.560326 | + | 1.72451i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −662.577 | + | 481.391i | −1.05506 | + | 0.766546i | ||||
\(629\) | 218.282 | 0.347030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 267.706i | 0.424257i | 0.977242 | + | 0.212128i | \(0.0680395\pi\) | ||||
−0.977242 | + | 0.212128i | \(0.931960\pi\) | |||||||
\(632\) | 65.1021 | − | 89.6054i | 0.103010 | − | 0.141781i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 99.5905 | + | 306.508i | 0.157083 | + | 0.483451i | ||||
\(635\) | − | 444.165i | − | 0.699473i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −180.971 | −0.284098 | ||||||||
\(638\) | −414.663 | + | 134.732i | −0.649941 | + | 0.211179i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 231.554 | − | 168.234i | 0.361803 | − | 0.262866i | ||||
\(641\) | 418.571 | 0.652997 | 0.326499 | − | 0.945198i | \(-0.394131\pi\) | ||||
0.326499 | + | 0.945198i | \(0.394131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 439.339i | 0.683265i | 0.939834 | + | 0.341633i | \(0.110980\pi\) | ||||
−0.939834 | + | 0.341633i | \(0.889020\pi\) | |||||||
\(644\) | −9.44272 | + | 6.86054i | −0.0146626 | + | 0.0106530i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 344.105 | − | 111.807i | 0.532671 | − | 0.173075i | ||||
\(647\) | − | 419.644i | − | 0.648600i | −0.945954 | − | 0.324300i | \(-0.894871\pi\) | ||
0.945954 | − | 0.324300i | \(-0.105129\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −347.331 | −0.535179 | ||||||||
\(650\) | 26.1803 | + | 80.5748i | 0.0402774 | + | 0.123961i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −252.125 | − | 347.021i | −0.386695 | − | 0.532240i | ||||
\(653\) | 370.085 | 0.566746 | 0.283373 | − | 0.959010i | \(-0.408547\pi\) | ||||
0.283373 | + | 0.959010i | \(0.408547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.3752i | − | 0.0265270i | ||||||
\(656\) | 72.1052 | − | 221.917i | 0.109917 | − | 0.338288i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 173.475 | + | 533.902i | 0.263640 | + | 0.811401i | ||||
\(659\) | 322.823i | 0.489868i | 0.969540 | + | 0.244934i | \(0.0787664\pi\) | ||||
−0.969540 | + | 0.244934i | \(0.921234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −812.735 | −1.22955 | −0.614777 | − | 0.788701i | \(-0.710754\pi\) | ||||
−0.614777 | + | 0.788701i | \(0.710754\pi\) | |||||||
\(662\) | 631.437 | − | 205.166i | 0.953832 | − | 0.309919i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −358.387 | + | 493.277i | −0.539739 | + | 0.742888i | ||||
\(665\) | −178.885 | −0.269001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.07439i | 0.00910703i | ||||||||
\(668\) | 78.0789 | + | 107.466i | 0.116885 | + | 0.160878i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 213.607 | − | 69.4051i | 0.318816 | − | 0.103590i | ||||
\(671\) | − | 1795.47i | − | 2.67581i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 467.378 | 0.694469 | 0.347235 | − | 0.937778i | \(-0.387121\pi\) | ||||
0.347235 | + | 0.937778i | \(0.387121\pi\) | |||||||
\(674\) | 166.318 | + | 511.875i | 0.246763 | + | 0.759458i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 314.620 | − | 228.585i | 0.465414 | − | 0.338143i | ||||
\(677\) | −548.237 | −0.809803 | −0.404902 | − | 0.914360i | \(-0.632694\pi\) | ||||
−0.404902 | + | 0.914360i | \(0.632694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 488.051i | 0.718779i | ||||||||
\(680\) | −172.053 | − | 125.004i | −0.253019 | − | 0.183829i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 102.111 | + | 314.267i | 0.149724 | + | 0.460802i | ||||
\(683\) | − | 23.9663i | − | 0.0350898i | −0.999846 | − | 0.0175449i | \(-0.994415\pi\) | ||
0.999846 | − | 0.0175449i | \(-0.00558500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.86223 | −0.00271859 | ||||||||
\(686\) | −703.607 | + | 228.616i | −1.02567 | + | 0.333259i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 338.885 | + | 110.111i | 0.492566 | + | 0.160044i | ||||
\(689\) | −562.217 | −0.815989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 186.981i | − | 0.270595i | −0.990805 | − | 0.135298i | \(-0.956801\pi\) | ||
0.990805 | − | 0.135298i | \(-0.0431990\pi\) | |||||||
\(692\) | −732.519 | + | 532.206i | −1.05855 | + | 0.769084i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 956.906 | − | 310.917i | 1.37883 | − | 0.448008i | ||||
\(695\) | − | 531.420i | − | 0.764633i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −173.378 | −0.248748 | ||||||||
\(698\) | 0.311896 | + | 0.959917i | 0.000446842 | + | 0.00137524i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 61.8034 | + | 85.0651i | 0.0882906 | + | 0.121522i | ||||
\(701\) | 706.636 | 1.00804 | 0.504020 | − | 0.863692i | \(-0.331854\pi\) | ||||
0.504020 | + | 0.863692i | \(0.331854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.393i | 0.397429i | ||||||||
\(704\) | 1212.43 | − | 393.943i | 1.72221 | − | 0.559579i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −207.656 | − | 639.098i | −0.294130 | − | 0.905238i | ||||
\(707\) | 337.054i | 0.476738i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −188.597 | −0.266005 | −0.133002 | − | 0.991116i | \(-0.542462\pi\) | ||||
−0.133002 | + | 0.991116i | \(0.542462\pi\) | |||||||
\(710\) | 343.607 | − | 111.645i | 0.483953 | − | 0.157246i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 721.272 | + | 524.035i | 1.01302 | + | 0.736004i | ||||
\(713\) | 4.60369 | 0.00645679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 377.354i | 0.527769i | ||||||||
\(716\) | 527.449 | + | 725.971i | 0.736661 | + | 1.01393i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −187.331 | + | 60.8676i | −0.260907 | + | 0.0847738i | ||||
\(719\) | − | 156.085i | − | 0.217086i | −0.994092 | − | 0.108543i | \(-0.965381\pi\) | ||
0.994092 | − | 0.108543i | \(-0.0346186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 724.296 | 1.00457 | ||||||||
\(722\) | −80.0019 | − | 246.221i | −0.110806 | − | 0.341026i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −279.023 | + | 202.722i | −0.385391 | + | 0.280003i | ||||
\(725\) | 54.7214 | 0.0754777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 715.164i | − | 0.983719i | −0.870675 | − | 0.491859i | \(-0.836317\pi\) | ||
0.870675 | − | 0.491859i | \(-0.163683\pi\) | |||||||
\(728\) | −209.443 | + | 288.273i | −0.287696 | + | 0.395980i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.67568 | + | 23.6233i | 0.0105146 | + | 0.0323607i | ||||
\(731\) | − | 264.762i | − | 0.362191i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1233.29 | 1.68252 | 0.841259 | − | 0.540632i | \(-0.181815\pi\) | ||||
0.841259 | + | 0.540632i | \(0.181815\pi\) | |||||||
\(734\) | 948.152 | − | 308.073i | 1.29176 | − | 0.419718i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 17.7609i | − | 0.0241317i | ||||||
\(737\) | 1000.38 | 1.35737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.55656i | 0.0115786i | 0.999983 | + | 0.00578928i | \(0.00184280\pi\) | ||||
−0.999983 | + | 0.00578928i | \(0.998157\pi\) | |||||||
\(740\) | 132.859 | − | 96.5278i | 0.179539 | − | 0.130443i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −663.607 | + | 215.619i | −0.894349 | + | 0.290592i | ||||
\(743\) | 1010.56i | 1.36011i | 0.733163 | + | 0.680053i | \(0.238043\pi\) | ||||
−0.733163 | + | 0.680053i | \(0.761957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 82.6687 | 0.110965 | ||||||||
\(746\) | −371.039 | − | 1141.94i | −0.497372 | − | 1.53075i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −556.774 | − | 766.334i | −0.744350 | − | 1.02451i | ||||
\(749\) | 269.868 | 0.360305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1104.31i | − | 1.47046i | −0.677820 | − | 0.735228i | \(-0.737075\pi\) | ||
0.677820 | − | 0.735228i | \(-0.262925\pi\) | |||||||
\(752\) | −812.433 | − | 263.976i | −1.08036 | − | 0.351031i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 57.3050 | + | 176.367i | 0.0760013 | + | 0.233908i | ||||
\(755\) | 632.188i | 0.837335i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −875.633 | −1.15671 | −0.578357 | − | 0.815783i | \(-0.696306\pi\) | ||||
−0.578357 | + | 0.815783i | \(0.696306\pi\) | |||||||
\(758\) | 577.272 | − | 187.567i | 0.761573 | − | 0.247450i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 160.000 | − | 220.221i | 0.210526 | − | 0.289765i | ||||
\(761\) | 647.207 | 0.850470 | 0.425235 | − | 0.905083i | \(-0.360192\pi\) | ||||
0.425235 | + | 0.905083i | \(0.360192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 701.688i | − | 0.919644i | ||||||
\(764\) | −72.9318 | − | 100.382i | −0.0954605 | − | 0.131390i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 632.610 | − | 205.547i | 0.825861 | − | 0.268339i | ||||
\(767\) | 147.729i | 0.192606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 631.430 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(770\) | 144.721 | + | 445.407i | 0.187950 | + | 0.578450i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −356.689 | + | 259.150i | −0.462032 | + | 0.335686i | ||||
\(773\) | 421.522 | 0.545306 | 0.272653 | − | 0.962112i | \(-0.412099\pi\) | ||||
0.272653 | + | 0.962112i | \(0.412099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 41.4725i | − | 0.0535129i | ||||||
\(776\) | −600.827 | − | 436.526i | −0.774261 | − | 0.562534i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 242.488 | + | 746.303i | 0.311682 | + | 0.959258i | ||||
\(779\) | − | 221.917i | − | 0.284874i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1609.21 | 2.06044 | ||||||||
\(782\) | −12.5511 | + | 4.07809i | −0.0160500 | + | 0.00521495i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 105.613 | − | 325.043i | 0.134710 | − | 0.414596i | ||||
\(785\) | 457.830 | 0.583223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 838.633i | 1.06561i | 0.846239 | + | 0.532804i | \(0.178862\pi\) | ||||
−0.846239 | + | 0.532804i | \(0.821138\pi\) | |||||||
\(788\) | −558.302 | + | 405.630i | −0.708505 | + | 0.514759i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −58.8854 | + | 19.1330i | −0.0745385 | + | 0.0242190i | ||||
\(791\) | 897.535i | 1.13468i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −763.659 | −0.963001 | ||||||||
\(794\) | −206.541 | − | 635.668i | −0.260127 | − | 0.800589i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 640.000 | + | 880.884i | 0.804020 | + | 1.10664i | ||||
\(797\) | −1213.57 | −1.52268 | −0.761339 | − | 0.648354i | \(-0.775458\pi\) | ||||
−0.761339 | + | 0.648354i | \(0.775458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 634.732i | 0.794408i | ||||||||
\(800\) | −160.000 | −0.200000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 74.7840 | + | 230.162i | 0.0932469 | + | 0.286985i | ||||
\(803\) | 110.635i | 0.137777i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.52476 | 0.00810529 | ||||||||
\(806\) | 133.666 | − | 43.4306i | 0.165838 | − | 0.0538841i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −414.938 | − | 301.470i | −0.513537 | − | 0.373107i | ||||
\(809\) | 229.214 | 0.283330 | 0.141665 | − | 0.989915i | \(-0.454754\pi\) | ||||
0.141665 | + | 0.989915i | \(0.454754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 454.225i | 0.560080i | 0.959988 | + | 0.280040i | \(0.0903478\pi\) | ||||
−0.959988 | + | 0.280040i | \(0.909652\pi\) | |||||||
\(812\) | 135.279 | + | 186.195i | 0.166599 | + | 0.229304i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 695.659 | − | 226.033i | 0.854618 | − | 0.277682i | ||||
\(815\) | 239.785i | 0.294215i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 338.885 | 0.414792 | ||||||||
\(818\) | 375.400 | + | 1155.36i | 0.458924 | + | 1.41242i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −105.528 | + | 76.6705i | −0.128693 | + | 0.0935006i | ||||
\(821\) | −1130.90 | −1.37747 | −0.688733 | − | 0.725015i | \(-0.741833\pi\) | ||||
−0.688733 | + | 0.725015i | \(0.741833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 780.148i | 0.947931i | 0.880543 | + | 0.473966i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473966i | \(0.842822\pi\) | |||||||
\(824\) | −647.830 | + | 891.661i | −0.786201 | + | 1.08211i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 56.6563 | + | 174.370i | 0.0685912 | + | 0.211102i | ||||
\(827\) | − | 209.175i | − | 0.252932i | −0.991971 | − | 0.126466i | \(-0.959636\pi\) | ||
0.991971 | − | 0.126466i | \(-0.0403635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −508.525 | −0.613419 | −0.306710 | − | 0.951803i | \(-0.599228\pi\) | ||||
−0.306710 | + | 0.951803i | \(0.599228\pi\) | |||||||
\(830\) | 324.164 | − | 105.327i | 0.390559 | − | 0.126900i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −167.554 | − | 515.679i | −0.201387 | − | 0.619806i | ||||
\(833\) | −253.947 | −0.304859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 74.2575i | − | 0.0889311i | ||||||
\(836\) | 980.879 | − | 712.650i | 1.17330 | − | 0.852453i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 887.830 | − | 288.473i | 1.05946 | − | 0.344240i | ||||
\(839\) | 274.028i | 0.326613i | 0.986575 | + | 0.163306i | \(0.0522159\pi\) | ||||
−0.986575 | + | 0.163306i | \(0.947784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −721.223 | −0.857578 | ||||||||
\(842\) | 45.1710 | + | 139.022i | 0.0536473 | + | 0.165109i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 482.610 | + | 664.256i | 0.571813 | + | 0.787033i | ||||
\(845\) | −217.397 | −0.257275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1449.83i | 1.71172i | ||||||||
\(848\) | 328.105 | − | 1009.80i | 0.386917 | − | 1.19081i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 36.7376 | + | 113.067i | 0.0432207 | + | 0.133020i | ||||
\(851\) | − | 10.1907i | − | 0.0119750i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1583.28 | −1.85613 | −0.928066 | − | 0.372416i | \(-0.878529\pi\) | ||||
−0.928066 | + | 0.372416i | \(0.878529\pi\) | |||||||
\(854\) | −901.378 | + | 292.875i | −1.05548 | + | 0.342945i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −241.378 | + | 332.228i | −0.281983 | + | 0.388117i | ||||
\(857\) | 1007.38 | 1.17547 | 0.587735 | − | 0.809054i | \(-0.300020\pi\) | ||||
0.587735 | + | 0.809054i | \(0.300020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 76.6086i | − | 0.0891835i | −0.999005 | − | 0.0445917i | \(-0.985801\pi\) | ||
0.999005 | − | 0.0445917i | \(-0.0141987\pi\) | |||||||
\(860\) | −117.082 | − | 161.150i | −0.136142 | − | 0.187383i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 881.876 | − | 286.539i | 1.02306 | − | 0.332412i | ||||
\(863\) | 255.450i | 0.296002i | 0.988987 | + | 0.148001i | \(0.0472839\pi\) | ||||
−0.988987 | + | 0.148001i | \(0.952716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 506.158 | 0.585154 | ||||||||
\(866\) | 61.7020 | + | 189.899i | 0.0712494 | + | 0.219283i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 141.115 | − | 102.526i | 0.162574 | − | 0.118117i | ||||
\(869\) | −275.777 | −0.317350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 425.487i | − | 0.488504i | ||||||
\(872\) | 863.830 | + | 627.609i | 0.990630 | + | 0.719735i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.21981 | − | 16.0649i | −0.00597232 | − | 0.0183809i | ||||
\(875\) | − | 58.7785i | − | 0.0671755i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 601.522 | 0.685886 | 0.342943 | − | 0.939356i | \(-0.388576\pi\) | ||||
0.342943 | + | 0.939356i | \(0.388576\pi\) | |||||||
\(878\) | 711.554 | − | 231.198i | 0.810426 | − | 0.263323i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −677.771 | − | 220.221i | −0.770194 | − | 0.250251i | ||||
\(881\) | −237.850 | −0.269977 | −0.134989 | − | 0.990847i | \(-0.543100\pi\) | ||||
−0.134989 | + | 0.990847i | \(0.543100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.30294i | − | 0.00147559i | −1.00000 | 0.000737794i | \(-0.999765\pi\) | |||
1.00000 | 0.000737794i | \(-0.000234847\pi\) | ||||||||
\(884\) | −325.941 | + | 236.810i | −0.368712 | + | 0.267885i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 551.803 | − | 179.292i | 0.622803 | − | 0.202361i | ||||
\(887\) | 536.353i | 0.604682i | 0.953200 | + | 0.302341i | \(0.0977682\pi\) | ||||
−0.953200 | + | 0.302341i | \(0.902232\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1044.30 | −1.17469 | ||||||||
\(890\) | −154.010 | − | 473.994i | −0.173045 | − | 0.532578i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −554.237 | − | 762.842i | −0.621342 | − | 0.855203i | ||||
\(893\) | −812.433 | −0.909780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 501.634i | − | 0.560485i | ||||||
\(896\) | −395.542 | − | 544.417i | −0.441453 | − | 0.607608i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 185.361 | + | 570.484i | 0.206416 | + | 0.635283i | ||||
\(899\) | − | 90.7773i | − | 0.100976i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −788.932 | −0.875618 | ||||||||
\(902\) | −552.551 | + | 179.535i | −0.612584 | + | 0.199041i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1104.93 | − | 802.780i | −1.22227 | − | 0.888031i | ||||
\(905\) | 192.800 | 0.213039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 332.159i | 0.366217i | 0.983093 | + | 0.183108i | \(0.0586159\pi\) | ||||
−0.983093 | + | 0.183108i | \(0.941384\pi\) | |||||||
\(908\) | −137.580 | − | 189.363i | −0.151520 | − | 0.208550i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 189.443 | − | 61.5537i | 0.208179 | − | 0.0676414i | ||||
\(911\) | 1450.06i | 1.59172i | 0.605478 | + | 0.795862i | \(0.292982\pi\) | ||||
−0.605478 | + | 0.795862i | \(0.707018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1518.15 | 1.66282 | ||||||||
\(914\) | −508.227 | − | 1564.16i | −0.556047 | − | 1.71134i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −526.577 | + | 382.581i | −0.574866 | + | 0.417665i | ||||
\(917\) | −40.8514 | −0.0445490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 814.405i | 0.886186i | 0.896476 | + | 0.443093i | \(0.146119\pi\) | ||||
−0.896476 | + | 0.443093i | \(0.853881\pi\) | |||||||
\(920\) | −5.83592 | + | 8.03246i | −0.00634339 | + | 0.00873093i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −282.371 | − | 869.048i | −0.306259 | − | 0.942568i | ||||
\(923\) | − | 684.437i | − | 0.741535i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −91.8034 | −0.0992469 | ||||||||
\(926\) | 761.319 | − | 247.367i | 0.822159 | − | 0.267136i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −350.217 | −0.377389 | ||||||||
\(929\) | −400.039 | −0.430612 | −0.215306 | − | 0.976547i | \(-0.569075\pi\) | ||||
−0.215306 | + | 0.976547i | \(0.569075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 325.043i | − | 0.349134i | ||||||
\(932\) | 1032.47 | − | 750.130i | 1.10780 | − | 0.804861i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1736.91 | + | 564.355i | −1.85964 | + | 0.604234i | ||||
\(935\) | 529.524i | 0.566335i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 249.279 | 0.266039 | 0.133020 | − | 0.991113i | \(-0.457533\pi\) | ||||
0.133020 | + | 0.991113i | \(0.457533\pi\) | |||||||
\(938\) | −163.181 | − | 502.220i | −0.173967 | − | 0.535415i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 280.689 | + | 386.335i | 0.298605 | + | 0.410995i | ||||
\(941\) | −724.229 | −0.769638 | −0.384819 | − | 0.922992i | \(-0.625736\pi\) | ||||
−0.384819 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.09432i | 0.00858358i | ||||||||
\(944\) | −265.337 | − | 86.2134i | −0.281078 | − | 0.0913277i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −274.164 | − | 843.790i | −0.289814 | − | 0.891956i | ||||
\(947\) | 1141.54i | 1.20542i | 0.797959 | + | 0.602712i | \(0.205913\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.0557 | 0.0495845 | ||||||||
\(950\) | −144.721 | + | 47.0228i | −0.152338 | + | 0.0494977i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −293.901 | + | 404.520i | −0.308720 | + | 0.424916i | ||||
\(953\) | −1295.33 | −1.35921 | −0.679604 | − | 0.733579i | \(-0.737848\pi\) | ||||
−0.679604 | + | 0.733579i | \(0.737848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.3623i | 0.0726307i | ||||||||
\(956\) | 556.774 | + | 766.334i | 0.582400 | + | 0.801604i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1000.76 | − | 325.167i | 1.04464 | − | 0.339423i | ||||
\(959\) | 4.37837i | 0.00456556i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 892.201 | 0.928409 | ||||||||
\(962\) | −96.1378 | − | 295.882i | −0.0999353 | − | 0.307569i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.97058 | − | 2.15825i | 0.00308152 | − | 0.00223885i | ||||
\(965\) | 246.466 | 0.255405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 398.477i | − | 0.412075i | −0.978544 | − | 0.206037i | \(-0.933943\pi\) | ||
0.978544 | − | 0.206037i | \(-0.0660569\pi\) | |||||||
\(968\) | −1784.85 | − | 1296.77i | −1.84385 | − | 1.33964i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 128.292 | + | 394.842i | 0.132260 | + | 0.407053i | ||||
\(971\) | 928.093i | 0.955811i | 0.878411 | + | 0.477906i | \(0.158604\pi\) | ||||
−0.878411 | + | 0.477906i | \(0.841396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1249.44 | −1.28411 | ||||||||
\(974\) | 843.666 | − | 274.124i | 0.866186 | − | 0.281441i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 445.666 | − | 1371.62i | 0.456625 | − | 1.40535i | ||||
\(977\) | 1378.05 | 1.41049 | 0.705247 | − | 0.708962i | \(-0.250836\pi\) | ||||
0.705247 | + | 0.708962i | \(0.250836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2219.85i | − | 2.26747i | ||||||
\(980\) | −154.567 | + | 112.300i | −0.157722 | + | 0.114592i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 546.217 | − | 177.477i | 0.556229 | − | 0.180730i | ||||
\(983\) | − | 311.291i | − | 0.316675i | −0.987385 | − | 0.158337i | \(-0.949387\pi\) | ||
0.987385 | − | 0.158337i | \(-0.0506134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 385.777 | 0.391652 | ||||||||
\(986\) | 80.4133 | + | 247.487i | 0.0815551 | + | 0.251001i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −303.108 | − | 417.193i | −0.306790 | − | 0.422260i | ||||
\(989\) | −12.3607 | −0.0124982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 961.147i | 0.969876i | 0.874549 | + | 0.484938i | \(0.161158\pi\) | ||||
−0.874549 | + | 0.484938i | \(0.838842\pi\) | |||||||
\(992\) | 265.424i | 0.267565i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −262.492 | − | 807.868i | −0.264077 | − | 0.812745i | ||||
\(995\) | − | 608.676i | − | 0.611735i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1089.68 | −1.09296 | −0.546479 | − | 0.837473i | \(-0.684032\pi\) | ||||
−0.546479 | + | 0.837473i | \(0.684032\pi\) | |||||||
\(998\) | 1542.49 | − | 501.186i | 1.54558 | − | 0.502190i | ||||
\(999\) | 0 | 0 |
(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 | 180.3.c.a.91.1 | 4 | ||
3.2 | odd | 2 | 20.3.b.a.11.4 | yes | 4 | ||
4.3 | odd | 2 | inner | 180.3.c.a.91.2 | 4 | ||
5.2 | odd | 4 | 900.3.f.e.199.7 | 8 | |||
5.3 | odd | 4 | 900.3.f.e.199.2 | 8 | |||
5.4 | even | 2 | 900.3.c.k.451.4 | 4 | |||
8.3 | odd | 2 | 2880.3.e.e.2431.2 | 4 | |||
8.5 | even | 2 | 2880.3.e.e.2431.1 | 4 | |||
12.11 | even | 2 | 20.3.b.a.11.3 | ✓ | 4 | ||
15.2 | even | 4 | 100.3.d.b.99.2 | 8 | |||
15.8 | even | 4 | 100.3.d.b.99.7 | 8 | |||
15.14 | odd | 2 | 100.3.b.f.51.1 | 4 | |||
20.3 | even | 4 | 900.3.f.e.199.8 | 8 | |||
20.7 | even | 4 | 900.3.f.e.199.1 | 8 | |||
20.19 | odd | 2 | 900.3.c.k.451.3 | 4 | |||
24.5 | odd | 2 | 320.3.b.c.191.3 | 4 | |||
24.11 | even | 2 | 320.3.b.c.191.2 | 4 | |||
48.5 | odd | 4 | 1280.3.g.e.1151.3 | 8 | |||
48.11 | even | 4 | 1280.3.g.e.1151.5 | 8 | |||
48.29 | odd | 4 | 1280.3.g.e.1151.6 | 8 | |||
48.35 | even | 4 | 1280.3.g.e.1151.4 | 8 | |||
60.23 | odd | 4 | 100.3.d.b.99.1 | 8 | |||
60.47 | odd | 4 | 100.3.d.b.99.8 | 8 | |||
60.59 | even | 2 | 100.3.b.f.51.2 | 4 | |||
120.29 | odd | 2 | 1600.3.b.s.1151.2 | 4 | |||
120.53 | even | 4 | 1600.3.h.n.1599.3 | 8 | |||
120.59 | even | 2 | 1600.3.b.s.1151.3 | 4 | |||
120.77 | even | 4 | 1600.3.h.n.1599.5 | 8 | |||
120.83 | odd | 4 | 1600.3.h.n.1599.6 | 8 | |||
120.107 | odd | 4 | 1600.3.h.n.1599.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.b.a.11.3 | ✓ | 4 | 12.11 | even | 2 | ||
20.3.b.a.11.4 | yes | 4 | 3.2 | odd | 2 | ||
100.3.b.f.51.1 | 4 | 15.14 | odd | 2 | |||
100.3.b.f.51.2 | 4 | 60.59 | even | 2 | |||
100.3.d.b.99.1 | 8 | 60.23 | odd | 4 | |||
100.3.d.b.99.2 | 8 | 15.2 | even | 4 | |||
100.3.d.b.99.7 | 8 | 15.8 | even | 4 | |||
100.3.d.b.99.8 | 8 | 60.47 | odd | 4 | |||
180.3.c.a.91.1 | 4 | 1.1 | even | 1 | trivial | ||
180.3.c.a.91.2 | 4 | 4.3 | odd | 2 | inner | ||
320.3.b.c.191.2 | 4 | 24.11 | even | 2 | |||
320.3.b.c.191.3 | 4 | 24.5 | odd | 2 | |||
900.3.c.k.451.3 | 4 | 20.19 | odd | 2 | |||
900.3.c.k.451.4 | 4 | 5.4 | even | 2 | |||
900.3.f.e.199.1 | 8 | 20.7 | even | 4 | |||
900.3.f.e.199.2 | 8 | 5.3 | odd | 4 | |||
900.3.f.e.199.7 | 8 | 5.2 | odd | 4 | |||
900.3.f.e.199.8 | 8 | 20.3 | even | 4 | |||
1280.3.g.e.1151.3 | 8 | 48.5 | odd | 4 | |||
1280.3.g.e.1151.4 | 8 | 48.35 | even | 4 | |||
1280.3.g.e.1151.5 | 8 | 48.11 | even | 4 | |||
1280.3.g.e.1151.6 | 8 | 48.29 | odd | 4 | |||
1600.3.b.s.1151.2 | 4 | 120.29 | odd | 2 | |||
1600.3.b.s.1151.3 | 4 | 120.59 | even | 2 | |||
1600.3.h.n.1599.3 | 8 | 120.53 | even | 4 | |||
1600.3.h.n.1599.4 | 8 | 120.107 | odd | 4 | |||
1600.3.h.n.1599.5 | 8 | 120.77 | even | 4 | |||
1600.3.h.n.1599.6 | 8 | 120.83 | odd | 4 | |||
2880.3.e.e.2431.1 | 4 | 8.5 | even | 2 | |||
2880.3.e.e.2431.2 | 4 | 8.3 | odd | 2 |