Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.12 | ||
Root | \(0.437361i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.9 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437361i | 0.309261i | 0.987972 | + | 0.154630i | \(0.0494187\pi\) | ||||
−0.987972 | + | 0.154630i | \(0.950581\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.80872 | 0.904358 | ||||||||
\(5\) | 0.978157 | + | 2.01077i | 0.437445 | + | 0.899245i | ||||
\(6\) | −0.437361 | −0.178552 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 1.66578i | 0.588943i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.879433 | + | 0.427807i | −0.278101 | + | 0.135285i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.80872i | 0.522131i | ||||||||
\(13\) | − | 0.0257972i | − | 0.00715484i | −0.999994 | − | 0.00357742i | \(-0.998861\pi\) | ||
0.999994 | − | 0.00357742i | \(-0.00113873\pi\) | |||||||
\(14\) | 0.437361 | 0.116890 | ||||||||
\(15\) | −2.01077 | + | 0.978157i | −0.519179 | + | 0.252559i | ||||
\(16\) | 2.88888 | 0.722221 | ||||||||
\(17\) | 1.73932i | 0.421847i | 0.977503 | + | 0.210923i | \(0.0676471\pi\) | ||||
−0.977503 | + | 0.210923i | \(0.932353\pi\) | |||||||
\(18\) | − | 0.437361i | − | 0.103087i | ||||||
\(19\) | −2.62891 | −0.603112 | −0.301556 | − | 0.953448i | \(-0.597506\pi\) | ||||
−0.301556 | + | 0.953448i | \(0.597506\pi\) | |||||||
\(20\) | 1.76921 | + | 3.63692i | 0.395607 | + | 0.813239i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 0.437361i | − | 0.0932456i | ||||||
\(23\) | 8.28038i | 1.72658i | 0.504710 | + | 0.863289i | \(0.331600\pi\) | ||||
−0.504710 | + | 0.863289i | \(0.668400\pi\) | |||||||
\(24\) | −1.66578 | −0.340026 | ||||||||
\(25\) | −3.08642 | + | 3.93370i | −0.617284 | + | 0.786740i | ||||
\(26\) | 0.0112827 | 0.00221271 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 1.80872i | − | 0.341815i | ||||||
\(29\) | 4.93063 | 0.915596 | 0.457798 | − | 0.889056i | \(-0.348638\pi\) | ||||
0.457798 | + | 0.889056i | \(0.348638\pi\) | |||||||
\(30\) | −0.427807 | − | 0.879433i | −0.0781066 | − | 0.160562i | ||||
\(31\) | 1.90570 | 0.342273 | 0.171137 | − | 0.985247i | \(-0.445256\pi\) | ||||
0.171137 | + | 0.985247i | \(0.445256\pi\) | |||||||
\(32\) | 4.59505i | 0.812298i | ||||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | −0.760710 | −0.130461 | ||||||||
\(35\) | 2.01077 | − | 0.978157i | 0.339883 | − | 0.165339i | ||||
\(36\) | −1.80872 | −0.301453 | ||||||||
\(37\) | 3.18596i | 0.523768i | 0.965099 | + | 0.261884i | \(0.0843438\pi\) | ||||
−0.965099 | + | 0.261884i | \(0.915656\pi\) | |||||||
\(38\) | − | 1.14978i | − | 0.186519i | ||||||
\(39\) | 0.0257972 | 0.00413085 | ||||||||
\(40\) | −3.34951 | + | 1.62940i | −0.529604 | + | 0.257630i | ||||
\(41\) | −2.07074 | −0.323395 | −0.161698 | − | 0.986840i | \(-0.551697\pi\) | ||||
−0.161698 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(42\) | 0.437361i | 0.0674862i | ||||||||
\(43\) | − | 3.85880i | − | 0.588461i | −0.955734 | − | 0.294231i | \(-0.904937\pi\) | ||
0.955734 | − | 0.294231i | \(-0.0950634\pi\) | |||||||
\(44\) | −1.80872 | −0.272674 | ||||||||
\(45\) | −0.978157 | − | 2.01077i | −0.145815 | − | 0.299748i | ||||
\(46\) | −3.62151 | −0.533963 | ||||||||
\(47\) | − | 10.1019i | − | 1.47352i | −0.676155 | − | 0.736759i | \(-0.736355\pi\) | ||
0.676155 | − | 0.736759i | \(-0.263645\pi\) | |||||||
\(48\) | 2.88888i | 0.416974i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.72045 | − | 1.34988i | −0.243308 | − | 0.190902i | ||||
\(51\) | −1.73932 | −0.243553 | ||||||||
\(52\) | − | 0.0466597i | − | 0.00647054i | ||||||
\(53\) | 10.9173i | 1.49961i | 0.661658 | + | 0.749806i | \(0.269853\pi\) | ||||
−0.661658 | + | 0.749806i | \(0.730147\pi\) | |||||||
\(54\) | 0.437361 | 0.0595173 | ||||||||
\(55\) | −0.978157 | − | 2.01077i | −0.131895 | − | 0.271133i | ||||
\(56\) | 1.66578 | 0.222600 | ||||||||
\(57\) | − | 2.62891i | − | 0.348207i | ||||||
\(58\) | 2.15647i | 0.283158i | ||||||||
\(59\) | 7.00705 | 0.912240 | 0.456120 | − | 0.889918i | \(-0.349239\pi\) | ||||
0.456120 | + | 0.889918i | \(0.349239\pi\) | |||||||
\(60\) | −3.63692 | + | 1.76921i | −0.469524 | + | 0.228404i | ||||
\(61\) | −1.71290 | −0.219314 | −0.109657 | − | 0.993969i | \(-0.534975\pi\) | ||||
−0.109657 | + | 0.993969i | \(0.534975\pi\) | |||||||
\(62\) | 0.833477i | 0.105852i | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 3.76807 | 0.471009 | ||||||||
\(65\) | 0.0518722 | − | 0.0252337i | 0.00643396 | − | 0.00312985i | ||||
\(66\) | 0.437361 | 0.0538354 | ||||||||
\(67\) | − | 7.39906i | − | 0.903939i | −0.892033 | − | 0.451969i | \(-0.850722\pi\) | ||
0.892033 | − | 0.451969i | \(-0.149278\pi\) | |||||||
\(68\) | 3.14593i | 0.381501i | ||||||||
\(69\) | −8.28038 | −0.996840 | ||||||||
\(70\) | 0.427807 | + | 0.879433i | 0.0511327 | + | 0.105112i | ||||
\(71\) | 2.36851 | 0.281090 | 0.140545 | − | 0.990074i | \(-0.455115\pi\) | ||||
0.140545 | + | 0.990074i | \(0.455115\pi\) | |||||||
\(72\) | − | 1.66578i | − | 0.196314i | ||||||
\(73\) | − | 11.0792i | − | 1.29672i | −0.761335 | − | 0.648359i | \(-0.775456\pi\) | ||
0.761335 | − | 0.648359i | \(-0.224544\pi\) | |||||||
\(74\) | −1.39341 | −0.161981 | ||||||||
\(75\) | −3.93370 | − | 3.08642i | −0.454225 | − | 0.356389i | ||||
\(76\) | −4.75494 | −0.545429 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 0.0112827i | 0.00127751i | ||||||||
\(79\) | 8.85469 | 0.996231 | 0.498115 | − | 0.867111i | \(-0.334026\pi\) | ||||
0.498115 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(80\) | 2.82578 | + | 5.80889i | 0.315932 | + | 0.649454i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.905660i | − | 0.100013i | ||||||
\(83\) | − | 9.51268i | − | 1.04415i | −0.852899 | − | 0.522076i | \(-0.825158\pi\) | ||
0.852899 | − | 0.522076i | \(-0.174842\pi\) | |||||||
\(84\) | 1.80872 | 0.197347 | ||||||||
\(85\) | −3.49738 | + | 1.70133i | −0.379344 | + | 0.184535i | ||||
\(86\) | 1.68769 | 0.181988 | ||||||||
\(87\) | 4.93063i | 0.528619i | ||||||||
\(88\) | − | 1.66578i | − | 0.177573i | ||||||
\(89\) | −9.48265 | −1.00516 | −0.502580 | − | 0.864531i | \(-0.667616\pi\) | ||||
−0.502580 | + | 0.864531i | \(0.667616\pi\) | |||||||
\(90\) | 0.879433 | − | 0.427807i | 0.0927004 | − | 0.0450948i | ||||
\(91\) | −0.0257972 | −0.00270428 | ||||||||
\(92\) | 14.9769i | 1.56144i | ||||||||
\(93\) | 1.90570i | 0.197612i | ||||||||
\(94\) | 4.41819 | 0.455701 | ||||||||
\(95\) | −2.57148 | − | 5.28613i | −0.263828 | − | 0.542346i | ||||
\(96\) | −4.59505 | −0.468980 | ||||||||
\(97\) | 0.755716i | 0.0767314i | 0.999264 | + | 0.0383657i | \(0.0122152\pi\) | ||||
−0.999264 | + | 0.0383657i | \(0.987785\pi\) | |||||||
\(98\) | − | 0.437361i | − | 0.0441801i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −5.58246 | + | 7.11495i | −0.558246 | + | 0.711495i | ||||
\(101\) | 10.9386 | 1.08844 | 0.544218 | − | 0.838944i | \(-0.316827\pi\) | ||||
0.544218 | + | 0.838944i | \(0.316827\pi\) | |||||||
\(102\) | − | 0.760710i | − | 0.0753215i | ||||||
\(103\) | 9.47623i | 0.933721i | 0.884331 | + | 0.466860i | \(0.154615\pi\) | ||||
−0.884331 | + | 0.466860i | \(0.845385\pi\) | |||||||
\(104\) | 0.0429725 | 0.00421380 | ||||||||
\(105\) | 0.978157 | + | 2.01077i | 0.0954583 | + | 0.196231i | ||||
\(106\) | −4.77481 | −0.463771 | ||||||||
\(107\) | 5.34487i | 0.516708i | 0.966050 | + | 0.258354i | \(0.0831801\pi\) | ||||
−0.966050 | + | 0.258354i | \(0.916820\pi\) | |||||||
\(108\) | − | 1.80872i | − | 0.174044i | ||||||
\(109\) | −16.5202 | −1.58234 | −0.791172 | − | 0.611594i | \(-0.790529\pi\) | ||||
−0.791172 | + | 0.611594i | \(0.790529\pi\) | |||||||
\(110\) | 0.879433 | − | 0.427807i | 0.0838507 | − | 0.0407898i | ||||
\(111\) | −3.18596 | −0.302398 | ||||||||
\(112\) | − | 2.88888i | − | 0.272974i | ||||||
\(113\) | − | 5.05846i | − | 0.475860i | −0.971282 | − | 0.237930i | \(-0.923531\pi\) | ||
0.971282 | − | 0.237930i | \(-0.0764689\pi\) | |||||||
\(114\) | 1.14978 | 0.107687 | ||||||||
\(115\) | −16.6500 | + | 8.09951i | −1.55262 | + | 0.755283i | ||||
\(116\) | 8.91811 | 0.828026 | ||||||||
\(117\) | 0.0257972i | 0.00238495i | ||||||||
\(118\) | 3.06461i | 0.282120i | ||||||||
\(119\) | 1.73932 | 0.159443 | ||||||||
\(120\) | −1.62940 | − | 3.34951i | −0.148743 | − | 0.305767i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 0.749155i | − | 0.0678253i | ||||||
\(123\) | − | 2.07074i | − | 0.186712i | ||||||
\(124\) | 3.44686 | 0.309537 | ||||||||
\(125\) | −10.9288 | − | 2.35831i | −0.977500 | − | 0.210934i | ||||
\(126\) | −0.437361 | −0.0389632 | ||||||||
\(127\) | − | 9.34124i | − | 0.828901i | −0.910072 | − | 0.414450i | \(-0.863974\pi\) | ||
0.910072 | − | 0.414450i | \(-0.136026\pi\) | |||||||
\(128\) | 10.8381i | 0.957962i | ||||||||
\(129\) | 3.85880 | 0.339748 | ||||||||
\(130\) | 0.0110362 | + | 0.0226869i | 0.000967940 | + | 0.00198977i | ||||
\(131\) | 4.71375 | 0.411842 | 0.205921 | − | 0.978569i | \(-0.433981\pi\) | ||||
0.205921 | + | 0.978569i | \(0.433981\pi\) | |||||||
\(132\) | − | 1.80872i | − | 0.157428i | ||||||
\(133\) | 2.62891i | 0.227955i | ||||||||
\(134\) | 3.23606 | 0.279553 | ||||||||
\(135\) | 2.01077 | − | 0.978157i | 0.173060 | − | 0.0841863i | ||||
\(136\) | −2.89733 | −0.248444 | ||||||||
\(137\) | 1.06035i | 0.0905920i | 0.998974 | + | 0.0452960i | \(0.0144231\pi\) | ||||
−0.998974 | + | 0.0452960i | \(0.985577\pi\) | |||||||
\(138\) | − | 3.62151i | − | 0.308284i | ||||||
\(139\) | −14.8517 | −1.25970 | −0.629852 | − | 0.776716i | \(-0.716884\pi\) | ||||
−0.629852 | + | 0.776716i | \(0.716884\pi\) | |||||||
\(140\) | 3.63692 | − | 1.76921i | 0.307376 | − | 0.149525i | ||||
\(141\) | 10.1019 | 0.850736 | ||||||||
\(142\) | 1.03589i | 0.0869301i | ||||||||
\(143\) | 0.0257972i | 0.00215727i | ||||||||
\(144\) | −2.88888 | −0.240740 | ||||||||
\(145\) | 4.82293 | + | 9.91439i | 0.400523 | + | 0.823345i | ||||
\(146\) | 4.84559 | 0.401024 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 5.76249i | 0.473674i | ||||||||
\(149\) | 15.5241 | 1.27178 | 0.635892 | − | 0.771778i | \(-0.280632\pi\) | ||||
0.635892 | + | 0.771778i | \(0.280632\pi\) | |||||||
\(150\) | 1.34988 | − | 1.72045i | 0.110217 | − | 0.140474i | ||||
\(151\) | 16.5877 | 1.34989 | 0.674943 | − | 0.737870i | \(-0.264168\pi\) | ||||
0.674943 | + | 0.737870i | \(0.264168\pi\) | |||||||
\(152\) | − | 4.37919i | − | 0.355199i | ||||||
\(153\) | − | 1.73932i | − | 0.140616i | ||||||
\(154\) | −0.437361 | −0.0352435 | ||||||||
\(155\) | 1.86407 | + | 3.83192i | 0.149726 | + | 0.307788i | ||||
\(156\) | 0.0466597 | 0.00373577 | ||||||||
\(157\) | 0.0195881i | 0.00156330i | 1.00000 | 0.000781652i | \(0.000248807\pi\) | |||||
−1.00000 | 0.000781652i | \(0.999751\pi\) | ||||||||
\(158\) | 3.87270i | 0.308095i | ||||||||
\(159\) | −10.9173 | −0.865801 | ||||||||
\(160\) | −9.23960 | + | 4.49468i | −0.730455 | + | 0.355335i | ||||
\(161\) | 8.28038 | 0.652585 | ||||||||
\(162\) | 0.437361i | 0.0343623i | ||||||||
\(163\) | 0.512887i | 0.0401724i | 0.999798 | + | 0.0200862i | \(0.00639406\pi\) | ||||
−0.999798 | + | 0.0200862i | \(0.993606\pi\) | |||||||
\(164\) | −3.74538 | −0.292465 | ||||||||
\(165\) | 2.01077 | − | 0.978157i | 0.156538 | − | 0.0761494i | ||||
\(166\) | 4.16047 | 0.322915 | ||||||||
\(167\) | − | 16.7502i | − | 1.29617i | −0.761568 | − | 0.648085i | \(-0.775570\pi\) | ||
0.761568 | − | 0.648085i | \(-0.224430\pi\) | |||||||
\(168\) | 1.66578i | 0.128518i | ||||||||
\(169\) | 12.9993 | 0.999949 | ||||||||
\(170\) | −0.744094 | − | 1.52962i | −0.0570694 | − | 0.117316i | ||||
\(171\) | 2.62891 | 0.201037 | ||||||||
\(172\) | − | 6.97947i | − | 0.532179i | ||||||
\(173\) | 3.91073i | 0.297327i | 0.988888 | + | 0.148664i | \(0.0474972\pi\) | ||||
−0.988888 | + | 0.148664i | \(0.952503\pi\) | |||||||
\(174\) | −2.15647 | −0.163481 | ||||||||
\(175\) | 3.93370 | + | 3.08642i | 0.297360 | + | 0.233311i | ||||
\(176\) | −2.88888 | −0.217758 | ||||||||
\(177\) | 7.00705i | 0.526682i | ||||||||
\(178\) | − | 4.14734i | − | 0.310856i | ||||||
\(179\) | −3.41672 | −0.255377 | −0.127689 | − | 0.991814i | \(-0.540756\pi\) | ||||
−0.127689 | + | 0.991814i | \(0.540756\pi\) | |||||||
\(180\) | −1.76921 | − | 3.63692i | −0.131869 | − | 0.271080i | ||||
\(181\) | 2.93257 | 0.217977 | 0.108988 | − | 0.994043i | \(-0.465239\pi\) | ||||
0.108988 | + | 0.994043i | \(0.465239\pi\) | |||||||
\(182\) | − | 0.0112827i | − | 0.000836327i | ||||||
\(183\) | − | 1.71290i | − | 0.126621i | ||||||
\(184\) | −13.7933 | −1.01686 | ||||||||
\(185\) | −6.40624 | + | 3.11637i | −0.470996 | + | 0.229120i | ||||
\(186\) | −0.833477 | −0.0611135 | ||||||||
\(187\) | − | 1.73932i | − | 0.127192i | ||||||
\(188\) | − | 18.2715i | − | 1.33259i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 2.31195 | − | 1.12467i | 0.167726 | − | 0.0815918i | ||||
\(191\) | 11.6978 | 0.846426 | 0.423213 | − | 0.906030i | \(-0.360902\pi\) | ||||
0.423213 | + | 0.906030i | \(0.360902\pi\) | |||||||
\(192\) | 3.76807i | 0.271937i | ||||||||
\(193\) | − | 19.3725i | − | 1.39446i | −0.716846 | − | 0.697232i | \(-0.754415\pi\) | ||
0.716846 | − | 0.697232i | \(-0.245585\pi\) | |||||||
\(194\) | −0.330521 | −0.0237300 | ||||||||
\(195\) | 0.0252337 | + | 0.0518722i | 0.00180702 | + | 0.00371465i | ||||
\(196\) | −1.80872 | −0.129194 | ||||||||
\(197\) | 12.6669i | 0.902481i | 0.892402 | + | 0.451241i | \(0.149018\pi\) | ||||
−0.892402 | + | 0.451241i | \(0.850982\pi\) | |||||||
\(198\) | 0.437361i | 0.0310819i | ||||||||
\(199\) | −12.8379 | −0.910058 | −0.455029 | − | 0.890477i | \(-0.650371\pi\) | ||||
−0.455029 | + | 0.890477i | \(0.650371\pi\) | |||||||
\(200\) | −6.55269 | − | 5.14130i | −0.463345 | − | 0.363545i | ||||
\(201\) | 7.39906 | 0.521889 | ||||||||
\(202\) | 4.78413i | 0.336610i | ||||||||
\(203\) | − | 4.93063i | − | 0.346063i | ||||||
\(204\) | −3.14593 | −0.220259 | ||||||||
\(205\) | −2.02551 | − | 4.16379i | −0.141468 | − | 0.290812i | ||||
\(206\) | −4.14453 | −0.288763 | ||||||||
\(207\) | − | 8.28038i | − | 0.575526i | ||||||
\(208\) | − | 0.0745250i | − | 0.00516738i | ||||||
\(209\) | 2.62891 | 0.181845 | ||||||||
\(210\) | −0.879433 | + | 0.427807i | −0.0606867 | + | 0.0295215i | ||||
\(211\) | 7.36203 | 0.506823 | 0.253412 | − | 0.967359i | \(-0.418447\pi\) | ||||
0.253412 | + | 0.967359i | \(0.418447\pi\) | |||||||
\(212\) | 19.7464i | 1.35619i | ||||||||
\(213\) | 2.36851i | 0.162287i | ||||||||
\(214\) | −2.33764 | −0.159797 | ||||||||
\(215\) | 7.75917 | − | 3.77451i | 0.529171 | − | 0.257419i | ||||
\(216\) | 1.66578 | 0.113342 | ||||||||
\(217\) | − | 1.90570i | − | 0.129367i | ||||||
\(218\) | − | 7.22527i | − | 0.489357i | ||||||
\(219\) | 11.0792 | 0.748660 | ||||||||
\(220\) | −1.76921 | − | 3.63692i | −0.119280 | − | 0.245201i | ||||
\(221\) | 0.0448695 | 0.00301825 | ||||||||
\(222\) | − | 1.39341i | − | 0.0935197i | ||||||
\(223\) | − | 21.2820i | − | 1.42515i | −0.701598 | − | 0.712573i | \(-0.747530\pi\) | ||
0.701598 | − | 0.712573i | \(-0.252470\pi\) | |||||||
\(224\) | 4.59505 | 0.307020 | ||||||||
\(225\) | 3.08642 | − | 3.93370i | 0.205761 | − | 0.262247i | ||||
\(226\) | 2.21237 | 0.147165 | ||||||||
\(227\) | − | 10.4419i | − | 0.693051i | −0.938041 | − | 0.346525i | \(-0.887361\pi\) | ||
0.938041 | − | 0.346525i | \(-0.112639\pi\) | |||||||
\(228\) | − | 4.75494i | − | 0.314904i | ||||||
\(229\) | 13.9313 | 0.920606 | 0.460303 | − | 0.887762i | \(-0.347741\pi\) | ||||
0.460303 | + | 0.887762i | \(0.347741\pi\) | |||||||
\(230\) | −3.54241 | − | 7.28204i | −0.233579 | − | 0.480164i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 8.21336i | 0.539234i | ||||||||
\(233\) | − | 17.8902i | − | 1.17202i | −0.810302 | − | 0.586012i | \(-0.800697\pi\) | ||
0.810302 | − | 0.586012i | \(-0.199303\pi\) | |||||||
\(234\) | −0.0112827 | −0.000737571 | ||||||||
\(235\) | 20.3127 | − | 9.88127i | 1.32505 | − | 0.644583i | ||||
\(236\) | 12.6738 | 0.824991 | ||||||||
\(237\) | 8.85469i | 0.575174i | ||||||||
\(238\) | 0.760710i | 0.0493095i | ||||||||
\(239\) | −26.5267 | −1.71587 | −0.857935 | − | 0.513758i | \(-0.828253\pi\) | ||||
−0.857935 | + | 0.513758i | \(0.828253\pi\) | |||||||
\(240\) | −5.80889 | + | 2.82578i | −0.374962 | + | 0.182403i | ||||
\(241\) | 11.7385 | 0.756143 | 0.378072 | − | 0.925776i | \(-0.376587\pi\) | ||||
0.378072 | + | 0.925776i | \(0.376587\pi\) | |||||||
\(242\) | 0.437361i | 0.0281146i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −3.09815 | −0.198339 | ||||||||
\(245\) | −0.978157 | − | 2.01077i | −0.0624921 | − | 0.128464i | ||||
\(246\) | 0.905660 | 0.0577428 | ||||||||
\(247\) | 0.0678183i | 0.00431518i | ||||||||
\(248\) | 3.17448i | 0.201579i | ||||||||
\(249\) | 9.51268 | 0.602842 | ||||||||
\(250\) | 1.03143 | − | 4.77982i | 0.0652336 | − | 0.302302i | ||||
\(251\) | 18.3852 | 1.16046 | 0.580231 | − | 0.814452i | \(-0.302962\pi\) | ||||
0.580231 | + | 0.814452i | \(0.302962\pi\) | |||||||
\(252\) | 1.80872i | 0.113938i | ||||||||
\(253\) | − | 8.28038i | − | 0.520583i | ||||||
\(254\) | 4.08549 | 0.256346 | ||||||||
\(255\) | −1.70133 | − | 3.49738i | −0.106541 | − | 0.219014i | ||||
\(256\) | 2.79598 | 0.174749 | ||||||||
\(257\) | − | 1.53575i | − | 0.0957973i | −0.998852 | − | 0.0478986i | \(-0.984748\pi\) | ||
0.998852 | − | 0.0478986i | \(-0.0152524\pi\) | |||||||
\(258\) | 1.68769i | 0.105071i | ||||||||
\(259\) | 3.18596 | 0.197966 | ||||||||
\(260\) | 0.0938221 | − | 0.0456405i | 0.00581860 | − | 0.00283050i | ||||
\(261\) | −4.93063 | −0.305199 | ||||||||
\(262\) | 2.06161i | 0.127367i | ||||||||
\(263\) | 14.0623i | 0.867121i | 0.901125 | + | 0.433560i | \(0.142743\pi\) | ||||
−0.901125 | + | 0.433560i | \(0.857257\pi\) | |||||||
\(264\) | 1.66578 | 0.102522 | ||||||||
\(265\) | −21.9523 | + | 10.6789i | −1.34852 | + | 0.655997i | ||||
\(266\) | −1.14978 | −0.0704976 | ||||||||
\(267\) | − | 9.48265i | − | 0.580329i | ||||||
\(268\) | − | 13.3828i | − | 0.817484i | ||||||
\(269\) | −12.3826 | −0.754982 | −0.377491 | − | 0.926013i | \(-0.623213\pi\) | ||||
−0.377491 | + | 0.926013i | \(0.623213\pi\) | |||||||
\(270\) | 0.427807 | + | 0.879433i | 0.0260355 | + | 0.0535206i | ||||
\(271\) | 4.80521 | 0.291896 | 0.145948 | − | 0.989292i | \(-0.453377\pi\) | ||||
0.145948 | + | 0.989292i | \(0.453377\pi\) | |||||||
\(272\) | 5.02469i | 0.304667i | ||||||||
\(273\) | − | 0.0257972i | − | 0.00156132i | ||||||
\(274\) | −0.463756 | −0.0280166 | ||||||||
\(275\) | 3.08642 | − | 3.93370i | 0.186118 | − | 0.237211i | ||||
\(276\) | −14.9769 | −0.901500 | ||||||||
\(277\) | − | 19.8713i | − | 1.19395i | −0.802260 | − | 0.596974i | \(-0.796369\pi\) | ||
0.802260 | − | 0.596974i | \(-0.203631\pi\) | |||||||
\(278\) | − | 6.49554i | − | 0.389577i | ||||||
\(279\) | −1.90570 | −0.114091 | ||||||||
\(280\) | 1.62940 | + | 3.34951i | 0.0973750 | + | 0.200172i | ||||
\(281\) | 27.2198 | 1.62379 | 0.811897 | − | 0.583800i | \(-0.198435\pi\) | ||||
0.811897 | + | 0.583800i | \(0.198435\pi\) | |||||||
\(282\) | 4.41819i | 0.263099i | ||||||||
\(283\) | − | 17.3650i | − | 1.03224i | −0.856516 | − | 0.516121i | \(-0.827376\pi\) | ||
0.856516 | − | 0.516121i | \(-0.172624\pi\) | |||||||
\(284\) | 4.28395 | 0.254206 | ||||||||
\(285\) | 5.28613 | − | 2.57148i | 0.313124 | − | 0.152321i | ||||
\(286\) | −0.0112827 | −0.000667158 | ||||||||
\(287\) | 2.07074i | 0.122232i | ||||||||
\(288\) | − | 4.59505i | − | 0.270766i | ||||||
\(289\) | 13.9748 | 0.822045 | ||||||||
\(290\) | −4.33616 | + | 2.10936i | −0.254628 | + | 0.123866i | ||||
\(291\) | −0.755716 | −0.0443009 | ||||||||
\(292\) | − | 20.0390i | − | 1.17270i | ||||||
\(293\) | − | 5.96726i | − | 0.348611i | −0.984692 | − | 0.174306i | \(-0.944232\pi\) | ||
0.984692 | − | 0.174306i | \(-0.0557680\pi\) | |||||||
\(294\) | 0.437361 | 0.0255074 | ||||||||
\(295\) | 6.85399 | + | 14.0896i | 0.399055 | + | 0.820327i | ||||
\(296\) | −5.30711 | −0.308470 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 6.78963i | 0.393313i | ||||||||
\(299\) | 0.213610 | 0.0123534 | ||||||||
\(300\) | −7.11495 | − | 5.58246i | −0.410782 | − | 0.322303i | ||||
\(301\) | −3.85880 | −0.222417 | ||||||||
\(302\) | 7.25480i | 0.417467i | ||||||||
\(303\) | 10.9386i | 0.628408i | ||||||||
\(304\) | −7.59460 | −0.435580 | ||||||||
\(305\) | −1.67548 | − | 3.44425i | −0.0959380 | − | 0.197217i | ||||
\(306\) | 0.760710 | 0.0434869 | ||||||||
\(307\) | − | 7.18932i | − | 0.410316i | −0.978729 | − | 0.205158i | \(-0.934229\pi\) | ||
0.978729 | − | 0.205158i | \(-0.0657708\pi\) | |||||||
\(308\) | 1.80872i | 0.103061i | ||||||||
\(309\) | −9.47623 | −0.539084 | ||||||||
\(310\) | −1.67593 | + | 0.815271i | −0.0951866 | + | 0.0463043i | ||||
\(311\) | 10.9338 | 0.619999 | 0.309999 | − | 0.950737i | \(-0.399671\pi\) | ||||
0.309999 | + | 0.950737i | \(0.399671\pi\) | |||||||
\(312\) | 0.0429725i | 0.00243284i | ||||||||
\(313\) | 6.26466i | 0.354100i | 0.984202 | + | 0.177050i | \(0.0566554\pi\) | ||||
−0.984202 | + | 0.177050i | \(0.943345\pi\) | |||||||
\(314\) | −0.00856708 | −0.000483468 | ||||||||
\(315\) | −2.01077 | + | 0.978157i | −0.113294 | + | 0.0551129i | ||||
\(316\) | 16.0156 | 0.900949 | ||||||||
\(317\) | − | 3.52327i | − | 0.197887i | −0.995093 | − | 0.0989433i | \(-0.968454\pi\) | ||
0.995093 | − | 0.0989433i | \(-0.0315463\pi\) | |||||||
\(318\) | − | 4.77481i | − | 0.267758i | ||||||
\(319\) | −4.93063 | −0.276063 | ||||||||
\(320\) | 3.68576 | + | 7.57674i | 0.206041 | + | 0.423553i | ||||
\(321\) | −5.34487 | −0.298321 | ||||||||
\(322\) | 3.62151i | 0.201819i | ||||||||
\(323\) | − | 4.57251i | − | 0.254421i | ||||||
\(324\) | 1.80872 | 0.100484 | ||||||||
\(325\) | 0.101478 | + | 0.0796209i | 0.00562901 | + | 0.00441657i | ||||
\(326\) | −0.224316 | −0.0124237 | ||||||||
\(327\) | − | 16.5202i | − | 0.913566i | ||||||
\(328\) | − | 3.44940i | − | 0.190461i | ||||||
\(329\) | −10.1019 | −0.556937 | ||||||||
\(330\) | 0.427807 | + | 0.879433i | 0.0235500 | + | 0.0484112i | ||||
\(331\) | 17.0628 | 0.937856 | 0.468928 | − | 0.883236i | \(-0.344640\pi\) | ||||
0.468928 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(332\) | − | 17.2057i | − | 0.944287i | ||||||
\(333\) | − | 3.18596i | − | 0.174589i | ||||||
\(334\) | 7.32588 | 0.400854 | ||||||||
\(335\) | 14.8778 | − | 7.23744i | 0.812863 | − | 0.395423i | ||||
\(336\) | 2.88888 | 0.157602 | ||||||||
\(337\) | 8.61745i | 0.469423i | 0.972065 | + | 0.234711i | \(0.0754145\pi\) | ||||
−0.972065 | + | 0.234711i | \(0.924586\pi\) | |||||||
\(338\) | 5.68540i | 0.309245i | ||||||||
\(339\) | 5.05846 | 0.274738 | ||||||||
\(340\) | −6.32576 | + | 3.07722i | −0.343063 | + | 0.166885i | ||||
\(341\) | −1.90570 | −0.103199 | ||||||||
\(342\) | 1.14978i | 0.0621730i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 6.42792 | 0.346570 | ||||||||
\(345\) | −8.09951 | − | 16.6500i | −0.436063 | − | 0.896404i | ||||
\(346\) | −1.71040 | −0.0919516 | ||||||||
\(347\) | − | 7.64356i | − | 0.410328i | −0.978728 | − | 0.205164i | \(-0.934227\pi\) | ||
0.978728 | − | 0.205164i | \(-0.0657728\pi\) | |||||||
\(348\) | 8.91811i | 0.478061i | ||||||||
\(349\) | −6.84409 | −0.366356 | −0.183178 | − | 0.983080i | \(-0.558638\pi\) | ||||
−0.183178 | + | 0.983080i | \(0.558638\pi\) | |||||||
\(350\) | −1.34988 | + | 1.72045i | −0.0721541 | + | 0.0919618i | ||||
\(351\) | −0.0257972 | −0.00137695 | ||||||||
\(352\) | − | 4.59505i | − | 0.244917i | ||||||
\(353\) | 18.2214i | 0.969827i | 0.874562 | + | 0.484914i | \(0.161149\pi\) | ||||
−0.874562 | + | 0.484914i | \(0.838851\pi\) | |||||||
\(354\) | −3.06461 | −0.162882 | ||||||||
\(355\) | 2.31677 | + | 4.76253i | 0.122961 | + | 0.252769i | ||||
\(356\) | −17.1514 | −0.909024 | ||||||||
\(357\) | 1.73932i | 0.0920546i | ||||||||
\(358\) | − | 1.49434i | − | 0.0789782i | ||||||
\(359\) | 8.69863 | 0.459096 | 0.229548 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229548 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(360\) | 3.34951 | − | 1.62940i | 0.176535 | − | 0.0858767i | ||||
\(361\) | −12.0889 | −0.636255 | ||||||||
\(362\) | 1.28259i | 0.0674116i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −0.0466597 | −0.00244563 | ||||||||
\(365\) | 22.2777 | − | 10.8372i | 1.16607 | − | 0.567243i | ||||
\(366\) | 0.749155 | 0.0391590 | ||||||||
\(367\) | − | 13.4591i | − | 0.702557i | −0.936271 | − | 0.351278i | \(-0.885747\pi\) | ||
0.936271 | − | 0.351278i | \(-0.114253\pi\) | |||||||
\(368\) | 23.9210i | 1.24697i | ||||||||
\(369\) | 2.07074 | 0.107798 | ||||||||
\(370\) | −1.36298 | − | 2.80184i | −0.0708577 | − | 0.145661i | ||||
\(371\) | 10.9173 | 0.566800 | ||||||||
\(372\) | 3.44686i | 0.178712i | ||||||||
\(373\) | 15.3062i | 0.792525i | 0.918137 | + | 0.396263i | \(0.129693\pi\) | ||||
−0.918137 | + | 0.396263i | \(0.870307\pi\) | |||||||
\(374\) | 0.760710 | 0.0393354 | ||||||||
\(375\) | 2.35831 | − | 10.9288i | 0.121783 | − | 0.564360i | ||||
\(376\) | 16.8276 | 0.867818 | ||||||||
\(377\) | − | 0.127196i | − | 0.00655095i | ||||||
\(378\) | − | 0.437361i | − | 0.0224954i | ||||||
\(379\) | −2.21901 | −0.113983 | −0.0569916 | − | 0.998375i | \(-0.518151\pi\) | ||||
−0.0569916 | + | 0.998375i | \(0.518151\pi\) | |||||||
\(380\) | −4.65108 | − | 9.56111i | −0.238595 | − | 0.490475i | ||||
\(381\) | 9.34124 | 0.478566 | ||||||||
\(382\) | 5.11618i | 0.261766i | ||||||||
\(383\) | 29.2940i | 1.49686i | 0.663216 | + | 0.748428i | \(0.269191\pi\) | ||||
−0.663216 | + | 0.748428i | \(0.730809\pi\) | |||||||
\(384\) | −10.8381 | −0.553080 | ||||||||
\(385\) | −2.01077 | + | 0.978157i | −0.102479 | + | 0.0498515i | ||||
\(386\) | 8.47277 | 0.431253 | ||||||||
\(387\) | 3.85880i | 0.196154i | ||||||||
\(388\) | 1.36688i | 0.0693926i | ||||||||
\(389\) | −26.1981 | −1.32830 | −0.664148 | − | 0.747601i | \(-0.731205\pi\) | ||||
−0.664148 | + | 0.747601i | \(0.731205\pi\) | |||||||
\(390\) | −0.0226869 | + | 0.0110362i | −0.00114879 | + | 0.000558840i | ||||
\(391\) | −14.4022 | −0.728352 | ||||||||
\(392\) | − | 1.66578i | − | 0.0841347i | ||||||
\(393\) | 4.71375i | 0.237777i | ||||||||
\(394\) | −5.54002 | −0.279102 | ||||||||
\(395\) | 8.66128 | + | 17.8048i | 0.435796 | + | 0.895856i | ||||
\(396\) | 1.80872 | 0.0908914 | ||||||||
\(397\) | 30.3740i | 1.52443i | 0.647324 | + | 0.762215i | \(0.275888\pi\) | ||||
−0.647324 | + | 0.762215i | \(0.724112\pi\) | |||||||
\(398\) | − | 5.61481i | − | 0.281445i | ||||||
\(399\) | −2.62891 | −0.131610 | ||||||||
\(400\) | −8.91631 | + | 11.3640i | −0.445815 | + | 0.568200i | ||||
\(401\) | 18.2717 | 0.912444 | 0.456222 | − | 0.889866i | \(-0.349202\pi\) | ||||
0.456222 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(402\) | 3.23606i | 0.161400i | ||||||||
\(403\) | − | 0.0491616i | − | 0.00244891i | ||||||
\(404\) | 19.7849 | 0.984335 | ||||||||
\(405\) | 0.978157 | + | 2.01077i | 0.0486050 | + | 0.0999161i | ||||
\(406\) | 2.15647 | 0.107024 | ||||||||
\(407\) | − | 3.18596i | − | 0.157922i | ||||||
\(408\) | − | 2.89733i | − | 0.143439i | ||||||
\(409\) | −37.0325 | −1.83114 | −0.915570 | − | 0.402159i | \(-0.868260\pi\) | ||||
−0.915570 | + | 0.402159i | \(0.868260\pi\) | |||||||
\(410\) | 1.82108 | − | 0.885877i | 0.0899366 | − | 0.0437504i | ||||
\(411\) | −1.06035 | −0.0523033 | ||||||||
\(412\) | 17.1398i | 0.844418i | ||||||||
\(413\) | − | 7.00705i | − | 0.344794i | ||||||
\(414\) | 3.62151 | 0.177988 | ||||||||
\(415\) | 19.1278 | − | 9.30489i | 0.938949 | − | 0.456759i | ||||
\(416\) | 0.118539 | 0.00581186 | ||||||||
\(417\) | − | 14.8517i | − | 0.727290i | ||||||
\(418\) | 1.14978i | 0.0562376i | ||||||||
\(419\) | −39.7187 | −1.94039 | −0.970194 | − | 0.242330i | \(-0.922088\pi\) | ||||
−0.970194 | + | 0.242330i | \(0.922088\pi\) | |||||||
\(420\) | 1.76921 | + | 3.63692i | 0.0863285 | + | 0.177463i | ||||
\(421\) | 21.4636 | 1.04607 | 0.523037 | − | 0.852310i | \(-0.324799\pi\) | ||||
0.523037 | + | 0.852310i | \(0.324799\pi\) | |||||||
\(422\) | 3.21986i | 0.156741i | ||||||||
\(423\) | 10.1019i | 0.491173i | ||||||||
\(424\) | −18.1859 | −0.883186 | ||||||||
\(425\) | −6.84197 | − | 5.36827i | −0.331884 | − | 0.260399i | ||||
\(426\) | −1.03589 | −0.0501891 | ||||||||
\(427\) | 1.71290i | 0.0828931i | ||||||||
\(428\) | 9.66735i | 0.467289i | ||||||||
\(429\) | −0.0257972 | −0.00124550 | ||||||||
\(430\) | 1.65082 | + | 3.39356i | 0.0796097 | + | 0.163652i | ||||
\(431\) | −21.0475 | −1.01382 | −0.506911 | − | 0.861998i | \(-0.669213\pi\) | ||||
−0.506911 | + | 0.861998i | \(0.669213\pi\) | |||||||
\(432\) | − | 2.88888i | − | 0.138991i | ||||||
\(433\) | 6.40458i | 0.307784i | 0.988088 | + | 0.153892i | \(0.0491808\pi\) | ||||
−0.988088 | + | 0.153892i | \(0.950819\pi\) | |||||||
\(434\) | 0.833477 | 0.0400082 | ||||||||
\(435\) | −9.91439 | + | 4.82293i | −0.475359 | + | 0.231242i | ||||
\(436\) | −29.8803 | −1.43100 | ||||||||
\(437\) | − | 21.7683i | − | 1.04132i | ||||||
\(438\) | 4.84559i | 0.231531i | ||||||||
\(439\) | 30.1740 | 1.44013 | 0.720064 | − | 0.693907i | \(-0.244112\pi\) | ||||
0.720064 | + | 0.693907i | \(0.244112\pi\) | |||||||
\(440\) | 3.34951 | − | 1.62940i | 0.159682 | − | 0.0776784i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.0196242i | 0.000933426i | ||||||||
\(443\) | − | 23.9132i | − | 1.13615i | −0.822977 | − | 0.568075i | \(-0.807688\pi\) | ||
0.822977 | − | 0.568075i | \(-0.192312\pi\) | |||||||
\(444\) | −5.76249 | −0.273476 | ||||||||
\(445\) | −9.27552 | − | 19.0675i | −0.439702 | − | 0.903885i | ||||
\(446\) | 9.30790 | 0.440742 | ||||||||
\(447\) | 15.5241i | 0.734265i | ||||||||
\(448\) | − | 3.76807i | − | 0.178025i | ||||||
\(449\) | −37.1653 | −1.75394 | −0.876969 | − | 0.480548i | \(-0.840438\pi\) | ||||
−0.876969 | + | 0.480548i | \(0.840438\pi\) | |||||||
\(450\) | 1.72045 | + | 1.34988i | 0.0811026 | + | 0.0636339i | ||||
\(451\) | 2.07074 | 0.0975073 | ||||||||
\(452\) | − | 9.14932i | − | 0.430348i | ||||||
\(453\) | 16.5877i | 0.779357i | ||||||||
\(454\) | 4.56686 | 0.214333 | ||||||||
\(455\) | −0.0252337 | − | 0.0518722i | −0.00118297 | − | 0.00243181i | ||||
\(456\) | 4.37919 | 0.205074 | ||||||||
\(457\) | 33.7866i | 1.58047i | 0.612804 | + | 0.790235i | \(0.290042\pi\) | ||||
−0.612804 | + | 0.790235i | \(0.709958\pi\) | |||||||
\(458\) | 6.09300i | 0.284707i | ||||||||
\(459\) | 1.73932 | 0.0811845 | ||||||||
\(460\) | −30.1151 | + | 14.6497i | −1.40412 | + | 0.683046i | ||||
\(461\) | −39.8493 | −1.85597 | −0.927985 | − | 0.372619i | \(-0.878460\pi\) | ||||
−0.927985 | + | 0.372619i | \(0.878460\pi\) | |||||||
\(462\) | − | 0.437361i | − | 0.0203479i | ||||||
\(463\) | − | 21.5789i | − | 1.00285i | −0.865200 | − | 0.501427i | \(-0.832808\pi\) | ||
0.865200 | − | 0.501427i | \(-0.167192\pi\) | |||||||
\(464\) | 14.2440 | 0.661262 | ||||||||
\(465\) | −3.83192 | + | 1.86407i | −0.177701 | + | 0.0864442i | ||||
\(466\) | 7.82446 | 0.362461 | ||||||||
\(467\) | 13.6268i | 0.630571i | 0.948997 | + | 0.315286i | \(0.102100\pi\) | ||||
−0.948997 | + | 0.315286i | \(0.897900\pi\) | |||||||
\(468\) | 0.0466597i | 0.00215685i | ||||||||
\(469\) | −7.39906 | −0.341657 | ||||||||
\(470\) | 4.32168 | + | 8.88397i | 0.199344 | + | 0.409787i | ||||
\(471\) | −0.0195881 | −0.000902574 | ||||||||
\(472\) | 11.6722i | 0.537257i | ||||||||
\(473\) | 3.85880i | 0.177428i | ||||||||
\(474\) | −3.87270 | −0.177879 | ||||||||
\(475\) | 8.11391 | − | 10.3413i | 0.372292 | − | 0.474493i | ||||
\(476\) | 3.14593 | 0.144194 | ||||||||
\(477\) | − | 10.9173i | − | 0.499871i | ||||||
\(478\) | − | 11.6017i | − | 0.530651i | ||||||
\(479\) | 17.1083 | 0.781698 | 0.390849 | − | 0.920455i | \(-0.372181\pi\) | ||||
0.390849 | + | 0.920455i | \(0.372181\pi\) | |||||||
\(480\) | −4.49468 | − | 9.23960i | −0.205153 | − | 0.421728i | ||||
\(481\) | 0.0821887 | 0.00374748 | ||||||||
\(482\) | 5.13396i | 0.233845i | ||||||||
\(483\) | 8.28038i | 0.376770i | ||||||||
\(484\) | 1.80872 | 0.0822143 | ||||||||
\(485\) | −1.51957 | + | 0.739209i | −0.0690003 | + | 0.0335658i | ||||
\(486\) | −0.437361 | −0.0198391 | ||||||||
\(487\) | − | 32.9977i | − | 1.49527i | −0.664111 | − | 0.747634i | \(-0.731190\pi\) | ||
0.664111 | − | 0.747634i | \(-0.268810\pi\) | |||||||
\(488\) | − | 2.85332i | − | 0.129164i | ||||||
\(489\) | −0.512887 | −0.0231935 | ||||||||
\(490\) | 0.879433 | − | 0.427807i | 0.0397287 | − | 0.0193264i | ||||
\(491\) | 26.9846 | 1.21780 | 0.608898 | − | 0.793248i | \(-0.291612\pi\) | ||||
0.608898 | + | 0.793248i | \(0.291612\pi\) | |||||||
\(492\) | − | 3.74538i | − | 0.168855i | ||||||
\(493\) | 8.57595i | 0.386241i | ||||||||
\(494\) | −0.0296611 | −0.00133451 | ||||||||
\(495\) | 0.978157 | + | 2.01077i | 0.0439649 | + | 0.0903775i | ||||
\(496\) | 5.50534 | 0.247197 | ||||||||
\(497\) | − | 2.36851i | − | 0.106242i | ||||||
\(498\) | 4.16047i | 0.186435i | ||||||||
\(499\) | 23.6494 | 1.05869 | 0.529346 | − | 0.848406i | \(-0.322437\pi\) | ||||
0.529346 | + | 0.848406i | \(0.322437\pi\) | |||||||
\(500\) | −19.7671 | − | 4.26552i | −0.884010 | − | 0.190760i | ||||
\(501\) | 16.7502 | 0.748344 | ||||||||
\(502\) | 8.04096i | 0.358886i | ||||||||
\(503\) | 2.38267i | 0.106238i | 0.998588 | + | 0.0531189i | \(0.0169162\pi\) | ||||
−0.998588 | + | 0.0531189i | \(0.983084\pi\) | |||||||
\(504\) | −1.66578 | −0.0741999 | ||||||||
\(505\) | 10.6997 | + | 21.9951i | 0.476130 | + | 0.978770i | ||||
\(506\) | 3.62151 | 0.160996 | ||||||||
\(507\) | 12.9993i | 0.577321i | ||||||||
\(508\) | − | 16.8956i | − | 0.749623i | ||||||
\(509\) | 11.9399 | 0.529226 | 0.264613 | − | 0.964355i | \(-0.414756\pi\) | ||||
0.264613 | + | 0.964355i | \(0.414756\pi\) | |||||||
\(510\) | 1.52962 | − | 0.744094i | 0.0677325 | − | 0.0329490i | ||||
\(511\) | −11.0792 | −0.490113 | ||||||||
\(512\) | 22.8991i | 1.01201i | ||||||||
\(513\) | 2.62891i | 0.116069i | ||||||||
\(514\) | 0.671675 | 0.0296263 | ||||||||
\(515\) | −19.0545 | + | 9.26924i | −0.839644 | + | 0.408451i | ||||
\(516\) | 6.97947 | 0.307254 | ||||||||
\(517\) | 10.1019i | 0.444282i | ||||||||
\(518\) | 1.39341i | 0.0612230i | ||||||||
\(519\) | −3.91073 | −0.171662 | ||||||||
\(520\) | 0.0420338 | + | 0.0864079i | 0.00184330 | + | 0.00378924i | ||||
\(521\) | −35.5144 | −1.55592 | −0.777958 | − | 0.628316i | \(-0.783744\pi\) | ||||
−0.777958 | + | 0.628316i | \(0.783744\pi\) | |||||||
\(522\) | − | 2.15647i | − | 0.0943859i | ||||||
\(523\) | − | 2.23505i | − | 0.0977319i | −0.998805 | − | 0.0488660i | \(-0.984439\pi\) | ||
0.998805 | − | 0.0488660i | \(-0.0155607\pi\) | |||||||
\(524\) | 8.52583 | 0.372453 | ||||||||
\(525\) | −3.08642 | + | 3.93370i | −0.134702 | + | 0.171681i | ||||
\(526\) | −6.15031 | −0.268166 | ||||||||
\(527\) | 3.31462i | 0.144387i | ||||||||
\(528\) | − | 2.88888i | − | 0.125723i | ||||||
\(529\) | −45.5647 | −1.98107 | ||||||||
\(530\) | −4.67052 | − | 9.60107i | −0.202874 | − | 0.417044i | ||||
\(531\) | −7.00705 | −0.304080 | ||||||||
\(532\) | 4.75494i | 0.206153i | ||||||||
\(533\) | 0.0534192i | 0.00231384i | ||||||||
\(534\) | 4.14734 | 0.179473 | ||||||||
\(535\) | −10.7473 | + | 5.22812i | −0.464647 | + | 0.226031i | ||||
\(536\) | 12.3252 | 0.532368 | ||||||||
\(537\) | − | 3.41672i | − | 0.147442i | ||||||
\(538\) | − | 5.41568i | − | 0.233486i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 3.63692 | − | 1.76921i | 0.156508 | − | 0.0761345i | ||||
\(541\) | 37.4515 | 1.61017 | 0.805083 | − | 0.593163i | \(-0.202121\pi\) | ||||
0.805083 | + | 0.593163i | \(0.202121\pi\) | |||||||
\(542\) | 2.10161i | 0.0902719i | ||||||||
\(543\) | 2.93257i | 0.125849i | ||||||||
\(544\) | −7.99226 | −0.342665 | ||||||||
\(545\) | −16.1593 | − | 33.2183i | −0.692188 | − | 1.42291i | ||||
\(546\) | 0.0112827 | 0.000482853 | ||||||||
\(547\) | 14.1039i | 0.603038i | 0.953460 | + | 0.301519i | \(0.0974938\pi\) | ||||
−0.953460 | + | 0.301519i | \(0.902506\pi\) | |||||||
\(548\) | 1.91788i | 0.0819276i | ||||||||
\(549\) | 1.71290 | 0.0731048 | ||||||||
\(550\) | 1.72045 | + | 1.34988i | 0.0733601 | + | 0.0575590i | ||||
\(551\) | −12.9622 | −0.552207 | ||||||||
\(552\) | − | 13.7933i | − | 0.587082i | ||||||
\(553\) | − | 8.85469i | − | 0.376540i | ||||||
\(554\) | 8.69091 | 0.369242 | ||||||||
\(555\) | −3.11637 | − | 6.40624i | −0.132282 | − | 0.271930i | ||||
\(556\) | −26.8625 | −1.13922 | ||||||||
\(557\) | 35.1520i | 1.48944i | 0.667377 | + | 0.744720i | \(0.267417\pi\) | ||||
−0.667377 | + | 0.744720i | \(0.732583\pi\) | |||||||
\(558\) | − | 0.833477i | − | 0.0352839i | ||||||
\(559\) | −0.0995460 | −0.00421035 | ||||||||
\(560\) | 5.80889 | − | 2.82578i | 0.245470 | − | 0.119411i | ||||
\(561\) | 1.73932 | 0.0734341 | ||||||||
\(562\) | 11.9049i | 0.502176i | ||||||||
\(563\) | 0.837376i | 0.0352912i | 0.999844 | + | 0.0176456i | \(0.00561706\pi\) | ||||
−0.999844 | + | 0.0176456i | \(0.994383\pi\) | |||||||
\(564\) | 18.2715 | 0.769370 | ||||||||
\(565\) | 10.1714 | − | 4.94797i | 0.427915 | − | 0.208163i | ||||
\(566\) | 7.59477 | 0.319232 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 3.94542i | 0.165546i | ||||||||
\(569\) | −41.1209 | −1.72388 | −0.861939 | − | 0.507012i | \(-0.830750\pi\) | ||||
−0.861939 | + | 0.507012i | \(0.830750\pi\) | |||||||
\(570\) | 1.12467 | + | 2.31195i | 0.0471070 | + | 0.0968368i | ||||
\(571\) | −23.1499 | −0.968795 | −0.484398 | − | 0.874848i | \(-0.660961\pi\) | ||||
−0.484398 | + | 0.874848i | \(0.660961\pi\) | |||||||
\(572\) | 0.0466597i | 0.00195094i | ||||||||
\(573\) | 11.6978i | 0.488684i | ||||||||
\(574\) | −0.905660 | −0.0378015 | ||||||||
\(575\) | −32.5725 | − | 25.5567i | −1.35837 | − | 1.06579i | ||||
\(576\) | −3.76807 | −0.157003 | ||||||||
\(577\) | 41.6966i | 1.73585i | 0.496694 | + | 0.867926i | \(0.334547\pi\) | ||||
−0.496694 | + | 0.867926i | \(0.665453\pi\) | |||||||
\(578\) | 6.11201i | 0.254226i | ||||||||
\(579\) | 19.3725 | 0.805094 | ||||||||
\(580\) | 8.72331 | + | 17.9323i | 0.362216 | + | 0.744599i | ||||
\(581\) | −9.51268 | −0.394652 | ||||||||
\(582\) | − | 0.330521i | − | 0.0137005i | ||||||
\(583\) | − | 10.9173i | − | 0.452150i | ||||||
\(584\) | 18.4555 | 0.763693 | ||||||||
\(585\) | −0.0518722 | + | 0.0252337i | −0.00214465 | + | 0.00104328i | ||||
\(586\) | 2.60985 | 0.107812 | ||||||||
\(587\) | − | 34.7195i | − | 1.43303i | −0.697572 | − | 0.716514i | \(-0.745736\pi\) | ||
0.697572 | − | 0.716514i | \(-0.254264\pi\) | |||||||
\(588\) | − | 1.80872i | − | 0.0745902i | ||||||
\(589\) | −5.00990 | −0.206429 | ||||||||
\(590\) | −6.16223 | + | 2.99767i | −0.253695 | + | 0.123412i | ||||
\(591\) | −12.6669 | −0.521048 | ||||||||
\(592\) | 9.20386i | 0.378276i | ||||||||
\(593\) | 29.2291i | 1.20029i | 0.799889 | + | 0.600147i | \(0.204891\pi\) | ||||
−0.799889 | + | 0.600147i | \(0.795109\pi\) | |||||||
\(594\) | −0.437361 | −0.0179451 | ||||||||
\(595\) | 1.70133 | + | 3.49738i | 0.0697476 | + | 0.143378i | ||||
\(596\) | 28.0787 | 1.15015 | ||||||||
\(597\) | − | 12.8379i | − | 0.525422i | ||||||
\(598\) | 0.0934247i | 0.00382042i | ||||||||
\(599\) | −14.2643 | −0.582823 | −0.291412 | − | 0.956598i | \(-0.594125\pi\) | ||||
−0.291412 | + | 0.956598i | \(0.594125\pi\) | |||||||
\(600\) | 5.14130 | − | 6.55269i | 0.209893 | − | 0.267513i | ||||
\(601\) | −12.8690 | −0.524936 | −0.262468 | − | 0.964941i | \(-0.584536\pi\) | ||||
−0.262468 | + | 0.964941i | \(0.584536\pi\) | |||||||
\(602\) | − | 1.68769i | − | 0.0687850i | ||||||
\(603\) | 7.39906i | 0.301313i | ||||||||
\(604\) | 30.0024 | 1.22078 | ||||||||
\(605\) | 0.978157 | + | 2.01077i | 0.0397677 | + | 0.0817496i | ||||
\(606\) | −4.78413 | −0.194342 | ||||||||
\(607\) | − | 30.2146i | − | 1.22637i | −0.789938 | − | 0.613186i | \(-0.789888\pi\) | ||
0.789938 | − | 0.613186i | \(-0.210112\pi\) | |||||||
\(608\) | − | 12.0800i | − | 0.489907i | ||||||
\(609\) | 4.93063 | 0.199799 | ||||||||
\(610\) | 1.50638 | − | 0.732791i | 0.0609916 | − | 0.0296699i | ||||
\(611\) | −0.260601 | −0.0105428 | ||||||||
\(612\) | − | 3.14593i | − | 0.127167i | ||||||
\(613\) | 21.5477i | 0.870302i | 0.900357 | + | 0.435151i | \(0.143305\pi\) | ||||
−0.900357 | + | 0.435151i | \(0.856695\pi\) | |||||||
\(614\) | 3.14432 | 0.126895 | ||||||||
\(615\) | 4.16379 | − | 2.02551i | 0.167900 | − | 0.0816763i | ||||
\(616\) | −1.66578 | −0.0671163 | ||||||||
\(617\) | − | 36.2211i | − | 1.45821i | −0.684404 | − | 0.729103i | \(-0.739938\pi\) | ||
0.684404 | − | 0.729103i | \(-0.260062\pi\) | |||||||
\(618\) | − | 4.14453i | − | 0.166717i | ||||||
\(619\) | 34.2672 | 1.37732 | 0.688658 | − | 0.725086i | \(-0.258200\pi\) | ||||
0.688658 | + | 0.725086i | \(0.258200\pi\) | |||||||
\(620\) | 3.37157 | + | 6.93086i | 0.135406 | + | 0.278350i | ||||
\(621\) | 8.28038 | 0.332280 | ||||||||
\(622\) | 4.78201i | 0.191741i | ||||||||
\(623\) | 9.48265i | 0.379914i | ||||||||
\(624\) | 0.0745250 | 0.00298339 | ||||||||
\(625\) | −5.94803 | − | 24.2821i | −0.237921 | − | 0.971284i | ||||
\(626\) | −2.73992 | −0.109509 | ||||||||
\(627\) | 2.62891i | 0.104988i | ||||||||
\(628\) | 0.0354294i | 0.00141379i | ||||||||
\(629\) | −5.54140 | −0.220950 | ||||||||
\(630\) | −0.427807 | − | 0.879433i | −0.0170442 | − | 0.0350375i | ||||
\(631\) | 6.62987 | 0.263931 | 0.131966 | − | 0.991254i | \(-0.457871\pi\) | ||||
0.131966 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(632\) | 14.7500i | 0.586723i | ||||||||
\(633\) | 7.36203i | 0.292615i | ||||||||
\(634\) | 1.54094 | 0.0611986 | ||||||||
\(635\) | 18.7831 | − | 9.13719i | 0.745385 | − | 0.362598i | ||||
\(636\) | −19.7464 | −0.782994 | ||||||||
\(637\) | 0.0257972i | 0.00102212i | ||||||||
\(638\) | − | 2.15647i | − | 0.0853753i | ||||||
\(639\) | −2.36851 | −0.0936966 | ||||||||
\(640\) | −21.7930 | + | 10.6014i | −0.861443 | + | 0.419056i | ||||
\(641\) | 1.02086 | 0.0403217 | 0.0201609 | − | 0.999797i | \(-0.493582\pi\) | ||||
0.0201609 | + | 0.999797i | \(0.493582\pi\) | |||||||
\(642\) | − | 2.33764i | − | 0.0922591i | ||||||
\(643\) | − | 15.9759i | − | 0.630027i | −0.949087 | − | 0.315013i | \(-0.897991\pi\) | ||
0.949087 | − | 0.315013i | \(-0.102009\pi\) | |||||||
\(644\) | 14.9769 | 0.590171 | ||||||||
\(645\) | 3.77451 | + | 7.75917i | 0.148621 | + | 0.305517i | ||||
\(646\) | 1.99984 | 0.0786825 | ||||||||
\(647\) | 0.879073i | 0.0345599i | 0.999851 | + | 0.0172800i | \(0.00550066\pi\) | ||||
−0.999851 | + | 0.0172800i | \(0.994499\pi\) | |||||||
\(648\) | 1.66578i | 0.0654381i | ||||||||
\(649\) | −7.00705 | −0.275051 | ||||||||
\(650\) | −0.0348230 | + | 0.0443826i | −0.00136587 | + | 0.00174083i | ||||
\(651\) | 1.90570 | 0.0746902 | ||||||||
\(652\) | 0.927666i | 0.0363302i | ||||||||
\(653\) | 16.5372i | 0.647152i | 0.946202 | + | 0.323576i | \(0.104885\pi\) | ||||
−0.946202 | + | 0.323576i | \(0.895115\pi\) | |||||||
\(654\) | 7.22527 | 0.282530 | ||||||||
\(655\) | 4.61079 | + | 9.47829i | 0.180158 | + | 0.370347i | ||||
\(656\) | −5.98212 | −0.233563 | ||||||||
\(657\) | 11.0792i | 0.432239i | ||||||||
\(658\) | − | 4.41819i | − | 0.172239i | ||||||
\(659\) | 10.2423 | 0.398984 | 0.199492 | − | 0.979899i | \(-0.436071\pi\) | ||||
0.199492 | + | 0.979899i | \(0.436071\pi\) | |||||||
\(660\) | 3.63692 | − | 1.76921i | 0.141567 | − | 0.0688663i | ||||
\(661\) | 22.7201 | 0.883708 | 0.441854 | − | 0.897087i | \(-0.354321\pi\) | ||||
0.441854 | + | 0.897087i | \(0.354321\pi\) | |||||||
\(662\) | 7.46259i | 0.290042i | ||||||||
\(663\) | 0.0448695i | 0.00174259i | ||||||||
\(664\) | 15.8461 | 0.614946 | ||||||||
\(665\) | −5.28613 | + | 2.57148i | −0.204988 | + | 0.0997178i | ||||
\(666\) | 1.39341 | 0.0539937 | ||||||||
\(667\) | 40.8275i | 1.58085i | ||||||||
\(668\) | − | 30.2964i | − | 1.17220i | ||||||
\(669\) | 21.2820 | 0.822809 | ||||||||
\(670\) | 3.16537 | + | 6.50698i | 0.122289 | + | 0.251386i | ||||
\(671\) | 1.71290 | 0.0661258 | ||||||||
\(672\) | 4.59505i | 0.177258i | ||||||||
\(673\) | 15.0702i | 0.580912i | 0.956888 | + | 0.290456i | \(0.0938070\pi\) | ||||
−0.956888 | + | 0.290456i | \(0.906193\pi\) | |||||||
\(674\) | −3.76894 | −0.145174 | ||||||||
\(675\) | 3.93370 | + | 3.08642i | 0.151408 | + | 0.118796i | ||||
\(676\) | 23.5121 | 0.904312 | ||||||||
\(677\) | 27.9338i | 1.07358i | 0.843715 | + | 0.536791i | \(0.180364\pi\) | ||||
−0.843715 | + | 0.536791i | \(0.819636\pi\) | |||||||
\(678\) | 2.21237i | 0.0849657i | ||||||||
\(679\) | 0.755716 | 0.0290017 | ||||||||
\(680\) | −2.83404 | − | 5.82587i | −0.108680 | − | 0.223412i | ||||
\(681\) | 10.4419 | 0.400133 | ||||||||
\(682\) | − | 0.833477i | − | 0.0319155i | ||||||
\(683\) | 32.5701i | 1.24626i | 0.782118 | + | 0.623130i | \(0.214139\pi\) | ||||
−0.782118 | + | 0.623130i | \(0.785861\pi\) | |||||||
\(684\) | 4.75494 | 0.181810 | ||||||||
\(685\) | −2.13213 | + | 1.03719i | −0.0814644 | + | 0.0396290i | ||||
\(686\) | −0.437361 | −0.0166985 | ||||||||
\(687\) | 13.9313i | 0.531512i | ||||||||
\(688\) | − | 11.1476i | − | 0.424999i | ||||||
\(689\) | 0.281636 | 0.0107295 | ||||||||
\(690\) | 7.28204 | − | 3.54241i | 0.277223 | − | 0.134857i | ||||
\(691\) | −31.8400 | −1.21125 | −0.605626 | − | 0.795750i | \(-0.707077\pi\) | ||||
−0.605626 | + | 0.795750i | \(0.707077\pi\) | |||||||
\(692\) | 7.07340i | 0.268890i | ||||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | 3.34299 | 0.126898 | ||||||||
\(695\) | −14.5273 | − | 29.8634i | −0.551051 | − | 1.13278i | ||||
\(696\) | −8.21336 | −0.311327 | ||||||||
\(697\) | − | 3.60168i | − | 0.136423i | ||||||
\(698\) | − | 2.99334i | − | 0.113299i | ||||||
\(699\) | 17.8902 | 0.676669 | ||||||||
\(700\) | 7.11495 | + | 5.58246i | 0.268920 | + | 0.210997i | ||||
\(701\) | −23.3301 | −0.881167 | −0.440584 | − | 0.897712i | \(-0.645228\pi\) | ||||
−0.440584 | + | 0.897712i | \(0.645228\pi\) | |||||||
\(702\) | − | 0.0112827i | − | 0.000425837i | ||||||
\(703\) | − | 8.37558i | − | 0.315891i | ||||||
\(704\) | −3.76807 | −0.142015 | ||||||||
\(705\) | 9.88127 | + | 20.3127i | 0.372150 | + | 0.765020i | ||||
\(706\) | −7.96932 | −0.299929 | ||||||||
\(707\) | − | 10.9386i | − | 0.411390i | ||||||
\(708\) | 12.6738i | 0.476309i | ||||||||
\(709\) | 3.93346 | 0.147724 | 0.0738621 | − | 0.997268i | \(-0.476468\pi\) | ||||
0.0738621 | + | 0.997268i | \(0.476468\pi\) | |||||||
\(710\) | −2.08294 | + | 1.01326i | −0.0781715 | + | 0.0380271i | ||||
\(711\) | −8.85469 | −0.332077 | ||||||||
\(712\) | − | 15.7960i | − | 0.591982i | ||||||
\(713\) | 15.7799i | 0.590962i | ||||||||
\(714\) | −0.760710 | −0.0284689 | ||||||||
\(715\) | −0.0518722 | + | 0.0252337i | −0.00193991 | + | 0.000943685i | ||||
\(716\) | −6.17987 | −0.230953 | ||||||||
\(717\) | − | 26.5267i | − | 0.990658i | ||||||
\(718\) | 3.80444i | 0.141980i | ||||||||
\(719\) | −27.2732 | −1.01712 | −0.508560 | − | 0.861026i | \(-0.669822\pi\) | ||||
−0.508560 | + | 0.861026i | \(0.669822\pi\) | |||||||
\(720\) | −2.82578 | − | 5.80889i | −0.105311 | − | 0.216485i | ||||
\(721\) | 9.47623 | 0.352913 | ||||||||
\(722\) | − | 5.28719i | − | 0.196769i | ||||||
\(723\) | 11.7385i | 0.436560i | ||||||||
\(724\) | 5.30419 | 0.197129 | ||||||||
\(725\) | −15.2180 | + | 19.3956i | −0.565183 | + | 0.720336i | ||||
\(726\) | −0.437361 | −0.0162320 | ||||||||
\(727\) | 51.5190i | 1.91073i | 0.295422 | + | 0.955367i | \(0.404540\pi\) | ||||
−0.295422 | + | 0.955367i | \(0.595460\pi\) | |||||||
\(728\) | − | 0.0429725i | − | 0.00159267i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.73975 | + | 9.74338i | 0.175426 | + | 0.360619i | ||||
\(731\) | 6.71168 | 0.248241 | ||||||||
\(732\) | − | 3.09815i | − | 0.114511i | ||||||
\(733\) | − | 23.1428i | − | 0.854800i | −0.904063 | − | 0.427400i | \(-0.859430\pi\) | ||
0.904063 | − | 0.427400i | \(-0.140570\pi\) | |||||||
\(734\) | 5.88646 | 0.217273 | ||||||||
\(735\) | 2.01077 | − | 0.978157i | 0.0741685 | − | 0.0360798i | ||||
\(736\) | −38.0488 | −1.40250 | ||||||||
\(737\) | 7.39906i | 0.272548i | ||||||||
\(738\) | 0.905660i | 0.0333378i | ||||||||
\(739\) | 31.4244 | 1.15596 | 0.577982 | − | 0.816049i | \(-0.303840\pi\) | ||||
0.577982 | + | 0.816049i | \(0.303840\pi\) | |||||||
\(740\) | −11.5871 | + | 5.63662i | −0.425949 | + | 0.207206i | ||||
\(741\) | −0.0678183 | −0.00249137 | ||||||||
\(742\) | 4.77481i | 0.175289i | ||||||||
\(743\) | 29.8588i | 1.09541i | 0.836670 | + | 0.547707i | \(0.184499\pi\) | ||||
−0.836670 | + | 0.547707i | \(0.815501\pi\) | |||||||
\(744\) | −3.17448 | −0.116382 | ||||||||
\(745\) | 15.1850 | + | 31.2155i | 0.556335 | + | 1.14365i | ||||
\(746\) | −6.69433 | −0.245097 | ||||||||
\(747\) | 9.51268i | 0.348051i | ||||||||
\(748\) | − | 3.14593i | − | 0.115027i | ||||||
\(749\) | 5.34487 | 0.195297 | ||||||||
\(750\) | 4.77982 | + | 1.03143i | 0.174534 | + | 0.0376626i | ||||
\(751\) | −2.27149 | −0.0828879 | −0.0414439 | − | 0.999141i | \(-0.513196\pi\) | ||||
−0.0414439 | + | 0.999141i | \(0.513196\pi\) | |||||||
\(752\) | − | 29.1833i | − | 1.06421i | ||||||
\(753\) | 18.3852i | 0.669993i | ||||||||
\(754\) | 0.0556307 | 0.00202595 | ||||||||
\(755\) | 16.2253 | + | 33.3540i | 0.590501 | + | 1.21388i | ||||
\(756\) | −1.80872 | −0.0657824 | ||||||||
\(757\) | 21.5578i | 0.783533i | 0.920065 | + | 0.391766i | \(0.128136\pi\) | ||||
−0.920065 | + | 0.391766i | \(0.871864\pi\) | |||||||
\(758\) | − | 0.970510i | − | 0.0352505i | ||||||
\(759\) | 8.28038 | 0.300559 | ||||||||
\(760\) | 8.80555 | − | 4.28353i | 0.319411 | − | 0.155380i | ||||
\(761\) | −18.9626 | −0.687394 | −0.343697 | − | 0.939081i | \(-0.611679\pi\) | ||||
−0.343697 | + | 0.939081i | \(0.611679\pi\) | |||||||
\(762\) | 4.08549i | 0.148002i | ||||||||
\(763\) | 16.5202i | 0.598070i | ||||||||
\(764\) | 21.1581 | 0.765472 | ||||||||
\(765\) | 3.49738 | − | 1.70133i | 0.126448 | − | 0.0615116i | ||||
\(766\) | −12.8121 | −0.462919 | ||||||||
\(767\) | − | 0.180762i | − | 0.00652693i | ||||||
\(768\) | 2.79598i | 0.100891i | ||||||||
\(769\) | −27.0273 | −0.974631 | −0.487315 | − | 0.873226i | \(-0.662024\pi\) | ||||
−0.487315 | + | 0.873226i | \(0.662024\pi\) | |||||||
\(770\) | −0.427807 | − | 0.879433i | −0.0154171 | − | 0.0316926i | ||||
\(771\) | 1.53575 | 0.0553086 | ||||||||
\(772\) | − | 35.0394i | − | 1.26109i | ||||||
\(773\) | − | 45.5894i | − | 1.63974i | −0.572553 | − | 0.819868i | \(-0.694047\pi\) | ||
0.572553 | − | 0.819868i | \(-0.305953\pi\) | |||||||
\(774\) | −1.68769 | −0.0606626 | ||||||||
\(775\) | −5.88178 | + | 7.49644i | −0.211280 | + | 0.269280i | ||||
\(776\) | −1.25886 | −0.0451904 | ||||||||
\(777\) | 3.18596i | 0.114296i | ||||||||
\(778\) | − | 11.4580i | − | 0.410790i | ||||||
\(779\) | 5.44378 | 0.195044 | ||||||||
\(780\) | 0.0456405 | + | 0.0938221i | 0.00163419 | + | 0.00335937i | ||||
\(781\) | −2.36851 | −0.0847518 | ||||||||
\(782\) | − | 6.29897i | − | 0.225251i | ||||||
\(783\) | − | 4.93063i | − | 0.176206i | ||||||
\(784\) | −2.88888 | −0.103174 | ||||||||
\(785\) | −0.0393873 | + | 0.0191603i | −0.00140579 | + | 0.000683859i | ||||
\(786\) | −2.06161 | −0.0735352 | ||||||||
\(787\) | − | 28.1716i | − | 1.00421i | −0.864807 | − | 0.502105i | \(-0.832559\pi\) | ||
0.864807 | − | 0.502105i | \(-0.167441\pi\) | |||||||
\(788\) | 22.9109i | 0.816166i | ||||||||
\(789\) | −14.0623 | −0.500632 | ||||||||
\(790\) | −7.78711 | + | 3.78810i | −0.277053 | + | 0.134775i | ||||
\(791\) | −5.05846 | −0.179858 | ||||||||
\(792\) | 1.66578i | 0.0591910i | ||||||||
\(793\) | 0.0441880i | 0.00156916i | ||||||||
\(794\) | −13.2844 | −0.471446 | ||||||||
\(795\) | −10.6789 | − | 21.9523i | −0.378740 | − | 0.778568i | ||||
\(796\) | −23.2202 | −0.823018 | ||||||||
\(797\) | − | 38.3583i | − | 1.35872i | −0.733804 | − | 0.679361i | \(-0.762257\pi\) | ||
0.733804 | − | 0.679361i | \(-0.237743\pi\) | |||||||
\(798\) | − | 1.14978i | − | 0.0407018i | ||||||
\(799\) | 17.5705 | 0.621599 | ||||||||
\(800\) | −18.0756 | − | 14.1822i | −0.639067 | − | 0.501418i | ||||
\(801\) | 9.48265 | 0.335053 | ||||||||
\(802\) | 7.99132i | 0.282183i | ||||||||
\(803\) | 11.0792i | 0.390975i | ||||||||
\(804\) | 13.3828 | 0.471975 | ||||||||
\(805\) | 8.09951 | + | 16.6500i | 0.285470 | + | 0.586834i | ||||
\(806\) | 0.0215013 | 0.000757352 | ||||||||
\(807\) | − | 12.3826i | − | 0.435889i | ||||||
\(808\) | 18.2214i | 0.641026i | ||||||||
\(809\) | −52.4122 | −1.84271 | −0.921357 | − | 0.388717i | \(-0.872918\pi\) | ||||
−0.921357 | + | 0.388717i | \(0.872918\pi\) | |||||||
\(810\) | −0.879433 | + | 0.427807i | −0.0309001 | + | 0.0150316i | ||||
\(811\) | 29.2676 | 1.02773 | 0.513863 | − | 0.857872i | \(-0.328214\pi\) | ||||
0.513863 | + | 0.857872i | \(0.328214\pi\) | |||||||
\(812\) | − | 8.91811i | − | 0.312964i | ||||||
\(813\) | 4.80521i | 0.168526i | ||||||||
\(814\) | 1.39341 | 0.0488391 | ||||||||
\(815\) | −1.03130 | + | 0.501683i | −0.0361248 | + | 0.0175732i | ||||
\(816\) | −5.02469 | −0.175899 | ||||||||
\(817\) | 10.1444i | 0.354908i | ||||||||
\(818\) | − | 16.1966i | − | 0.566300i | ||||||
\(819\) | 0.0257972 | 0.000901426 | ||||||||
\(820\) | −3.66357 | − | 7.53111i | −0.127937 | − | 0.262998i | ||||
\(821\) | −41.1927 | −1.43764 | −0.718818 | − | 0.695199i | \(-0.755316\pi\) | ||||
−0.718818 | + | 0.695199i | \(0.755316\pi\) | |||||||
\(822\) | − | 0.463756i | − | 0.0161754i | ||||||
\(823\) | − | 21.4531i | − | 0.747809i | −0.927467 | − | 0.373905i | \(-0.878019\pi\) | ||
0.927467 | − | 0.373905i | \(-0.121981\pi\) | |||||||
\(824\) | −15.7853 | −0.549908 | ||||||||
\(825\) | 3.93370 | + | 3.08642i | 0.136954 | + | 0.107455i | ||||
\(826\) | 3.06461 | 0.106631 | ||||||||
\(827\) | − | 12.4824i | − | 0.434056i | −0.976165 | − | 0.217028i | \(-0.930364\pi\) | ||
0.976165 | − | 0.217028i | \(-0.0696363\pi\) | |||||||
\(828\) | − | 14.9769i | − | 0.520482i | ||||||
\(829\) | 46.2552 | 1.60651 | 0.803255 | − | 0.595635i | \(-0.203099\pi\) | ||||
0.803255 | + | 0.595635i | \(0.203099\pi\) | |||||||
\(830\) | 4.06959 | + | 8.36577i | 0.141258 | + | 0.290380i | ||||
\(831\) | 19.8713 | 0.689327 | ||||||||
\(832\) | − | 0.0972056i | − | 0.00337000i | ||||||
\(833\) | − | 1.73932i | − | 0.0602638i | ||||||
\(834\) | 6.49554 | 0.224922 | ||||||||
\(835\) | 33.6809 | − | 16.3843i | 1.16557 | − | 0.567003i | ||||
\(836\) | 4.75494 | 0.164453 | ||||||||
\(837\) | − | 1.90570i | − | 0.0658705i | ||||||
\(838\) | − | 17.3714i | − | 0.600086i | ||||||
\(839\) | −43.5378 | −1.50309 | −0.751547 | − | 0.659680i | \(-0.770692\pi\) | ||||
−0.751547 | + | 0.659680i | \(0.770692\pi\) | |||||||
\(840\) | −3.34951 | + | 1.62940i | −0.115569 | + | 0.0562195i | ||||
\(841\) | −4.68885 | −0.161684 | ||||||||
\(842\) | 9.38735i | 0.323509i | ||||||||
\(843\) | 27.2198i | 0.937498i | ||||||||
\(844\) | 13.3158 | 0.458350 | ||||||||
\(845\) | 12.7154 | + | 26.1387i | 0.437423 | + | 0.899199i | ||||
\(846\) | −4.41819 | −0.151900 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 31.5389i | 1.08305i | ||||||||
\(849\) | 17.3650 | 0.595965 | ||||||||
\(850\) | 2.34787 | − | 2.99241i | 0.0805313 | − | 0.102639i | ||||
\(851\) | −26.3809 | −0.904327 | ||||||||
\(852\) | 4.28395i | 0.146766i | ||||||||
\(853\) | − | 49.9931i | − | 1.71173i | −0.517200 | − | 0.855865i | \(-0.673026\pi\) | ||
0.517200 | − | 0.855865i | \(-0.326974\pi\) | |||||||
\(854\) | −0.749155 | −0.0256356 | ||||||||
\(855\) | 2.57148 | + | 5.28613i | 0.0879428 | + | 0.180782i | ||||
\(856\) | −8.90339 | −0.304312 | ||||||||
\(857\) | − | 10.7203i | − | 0.366199i | −0.983094 | − | 0.183099i | \(-0.941387\pi\) | ||
0.983094 | − | 0.183099i | \(-0.0586130\pi\) | |||||||
\(858\) | − | 0.0112827i | − | 0.000385184i | ||||||
\(859\) | −2.41919 | −0.0825418 | −0.0412709 | − | 0.999148i | \(-0.513141\pi\) | ||||
−0.0412709 | + | 0.999148i | \(0.513141\pi\) | |||||||
\(860\) | 14.0341 | − | 6.82701i | 0.478560 | − | 0.232799i | ||||
\(861\) | −2.07074 | −0.0705706 | ||||||||
\(862\) | − | 9.20535i | − | 0.313536i | ||||||
\(863\) | − | 10.1189i | − | 0.344451i | −0.985058 | − | 0.172226i | \(-0.944904\pi\) | ||
0.985058 | − | 0.172226i | \(-0.0550958\pi\) | |||||||
\(864\) | 4.59505 | 0.156327 | ||||||||
\(865\) | −7.86359 | + | 3.82531i | −0.267370 | + | 0.130064i | ||||
\(866\) | −2.80111 | −0.0951856 | ||||||||
\(867\) | 13.9748i | 0.474608i | ||||||||
\(868\) | − | 3.44686i | − | 0.116994i | ||||||
\(869\) | −8.85469 | −0.300375 | ||||||||
\(870\) | −2.10936 | − | 4.33616i | −0.0715140 | − | 0.147010i | ||||
\(871\) | −0.190875 | −0.00646754 | ||||||||
\(872\) | − | 27.5190i | − | 0.931910i | ||||||
\(873\) | − | 0.755716i | − | 0.0255771i | ||||||
\(874\) | 9.52062 | 0.322040 | ||||||||
\(875\) | −2.35831 | + | 10.9288i | −0.0797256 | + | 0.369460i | ||||
\(876\) | 20.0390 | 0.677057 | ||||||||
\(877\) | 38.2969i | 1.29320i | 0.762831 | + | 0.646598i | \(0.223809\pi\) | ||||
−0.762831 | + | 0.646598i | \(0.776191\pi\) | |||||||
\(878\) | 13.1969i | 0.445375i | ||||||||
\(879\) | 5.96726 | 0.201271 | ||||||||
\(880\) | −2.82578 | − | 5.80889i | −0.0952570 | − | 0.195818i | ||||
\(881\) | −30.1330 | −1.01521 | −0.507603 | − | 0.861591i | \(-0.669469\pi\) | ||||
−0.507603 | + | 0.861591i | \(0.669469\pi\) | |||||||
\(882\) | 0.437361i | 0.0147267i | ||||||||
\(883\) | − | 27.4676i | − | 0.924358i | −0.886787 | − | 0.462179i | \(-0.847068\pi\) | ||
0.886787 | − | 0.462179i | \(-0.152932\pi\) | |||||||
\(884\) | 0.0811562 | 0.00272958 | ||||||||
\(885\) | −14.0896 | + | 6.85399i | −0.473616 | + | 0.230394i | ||||
\(886\) | 10.4587 | 0.351366 | ||||||||
\(887\) | − | 40.2212i | − | 1.35049i | −0.737591 | − | 0.675247i | \(-0.764037\pi\) | ||
0.737591 | − | 0.675247i | \(-0.235963\pi\) | |||||||
\(888\) | − | 5.30711i | − | 0.178095i | ||||||
\(889\) | −9.34124 | −0.313295 | ||||||||
\(890\) | 8.33936 | − | 4.05675i | 0.279536 | − | 0.135982i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − | 38.4930i | − | 1.28884i | ||||||
\(893\) | 26.5570i | 0.888697i | ||||||||
\(894\) | −6.78963 | −0.227079 | ||||||||
\(895\) | −3.34208 | − | 6.87024i | −0.111714 | − | 0.229647i | ||||
\(896\) | 10.8381 | 0.362076 | ||||||||
\(897\) | 0.213610i | 0.00713224i | ||||||||
\(898\) | − | 16.2546i | − | 0.542424i | ||||||
\(899\) | 9.39629 | 0.313384 | ||||||||
\(900\) | 5.58246 | − | 7.11495i | 0.186082 | − | 0.237165i | ||||
\(901\) | −18.9887 | −0.632607 | ||||||||
\(902\) | 0.905660i | 0.0301552i | ||||||||
\(903\) | − | 3.85880i | − | 0.128413i | ||||||
\(904\) | 8.42630 | 0.280255 | ||||||||
\(905\) | 2.86852 | + | 5.89674i | 0.0953527 | + | 0.196014i | ||||
\(906\) | −7.25480 | −0.241024 | ||||||||
\(907\) | 36.0929i | 1.19845i | 0.800582 | + | 0.599223i | \(0.204524\pi\) | ||||
−0.800582 | + | 0.599223i | \(0.795476\pi\) | |||||||
\(908\) | − | 18.8864i | − | 0.626766i | ||||||
\(909\) | −10.9386 | −0.362812 | ||||||||
\(910\) | 0.0226869 | − | 0.0110362i | 0.000752063 | − | 0.000365847i | ||||
\(911\) | −32.8345 | −1.08786 | −0.543928 | − | 0.839132i | \(-0.683064\pi\) | ||||
−0.543928 | + | 0.839132i | \(0.683064\pi\) | |||||||
\(912\) | − | 7.59460i | − | 0.251482i | ||||||
\(913\) | 9.51268i | 0.314824i | ||||||||
\(914\) | −14.7769 | −0.488777 | ||||||||
\(915\) | 3.44425 | − | 1.67548i | 0.113864 | − | 0.0553898i | ||||
\(916\) | 25.1978 | 0.832557 | ||||||||
\(917\) | − | 4.71375i | − | 0.155662i | ||||||
\(918\) | 0.760710i | 0.0251072i | ||||||||
\(919\) | −47.5464 | −1.56841 | −0.784206 | − | 0.620500i | \(-0.786930\pi\) | ||||
−0.784206 | + | 0.620500i | \(0.786930\pi\) | |||||||
\(920\) | −13.4920 | − | 27.7352i | −0.444819 | − | 0.914403i | ||||
\(921\) | 7.18932 | 0.236896 | ||||||||
\(922\) | − | 17.4285i | − | 0.573978i | ||||||
\(923\) | − | 0.0611007i | − | 0.00201115i | ||||||
\(924\) | −1.80872 | −0.0595024 | ||||||||
\(925\) | −12.5326 | − | 9.83320i | −0.412070 | − | 0.323314i | ||||
\(926\) | 9.43775 | 0.310144 | ||||||||
\(927\) | − | 9.47623i | − | 0.311240i | ||||||
\(928\) | 22.6565i | 0.743736i | ||||||||
\(929\) | −40.5411 | −1.33011 | −0.665054 | − | 0.746795i | \(-0.731592\pi\) | ||||
−0.665054 | + | 0.746795i | \(0.731592\pi\) | |||||||
\(930\) | −0.815271 | − | 1.67593i | −0.0267338 | − | 0.0549560i | ||||
\(931\) | 2.62891 | 0.0861589 | ||||||||
\(932\) | − | 32.3582i | − | 1.05993i | ||||||
\(933\) | 10.9338i | 0.357957i | ||||||||
\(934\) | −5.95981 | −0.195011 | ||||||||
\(935\) | 3.49738 | − | 1.70133i | 0.114376 | − | 0.0556393i | ||||
\(936\) | −0.0429725 | −0.00140460 | ||||||||
\(937\) | 16.8775i | 0.551365i | 0.961249 | + | 0.275683i | \(0.0889039\pi\) | ||||
−0.961249 | + | 0.275683i | \(0.911096\pi\) | |||||||
\(938\) | − | 3.23606i | − | 0.105661i | ||||||
\(939\) | −6.26466 | −0.204439 | ||||||||
\(940\) | 36.7399 | − | 17.8724i | 1.19832 | − | 0.582934i | ||||
\(941\) | 10.2428 | 0.333906 | 0.166953 | − | 0.985965i | \(-0.446607\pi\) | ||||
0.166953 | + | 0.985965i | \(0.446607\pi\) | |||||||
\(942\) | − | 0.00856708i | − | 0.000279131i | ||||||
\(943\) | − | 17.1465i | − | 0.558367i | ||||||
\(944\) | 20.2425 | 0.658839 | ||||||||
\(945\) | −0.978157 | − | 2.01077i | −0.0318194 | − | 0.0654105i | ||||
\(946\) | −1.68769 | −0.0548714 | ||||||||
\(947\) | 43.8469i | 1.42483i | 0.701757 | + | 0.712416i | \(0.252399\pi\) | ||||
−0.701757 | + | 0.712416i | \(0.747601\pi\) | |||||||
\(948\) | 16.0156i | 0.520163i | ||||||||
\(949\) | −0.285811 | −0.00927781 | ||||||||
\(950\) | 4.52289 | + | 3.54870i | 0.146742 | + | 0.115135i | ||||
\(951\) | 3.52327 | 0.114250 | ||||||||
\(952\) | 2.89733i | 0.0939029i | ||||||||
\(953\) | − | 48.4706i | − | 1.57012i | −0.619422 | − | 0.785058i | \(-0.712633\pi\) | ||
0.619422 | − | 0.785058i | \(-0.287367\pi\) | |||||||
\(954\) | 4.77481 | 0.154590 | ||||||||
\(955\) | 11.4423 | + | 23.5217i | 0.370265 | + | 0.761144i | ||||
\(956\) | −47.9793 | −1.55176 | ||||||||
\(957\) | − | 4.93063i | − | 0.159385i | ||||||
\(958\) | 7.48250i | 0.241749i | ||||||||
\(959\) | 1.06035 | 0.0342406 | ||||||||
\(960\) | −7.57674 | + | 3.68576i | −0.244538 | + | 0.118958i | ||||
\(961\) | −27.3683 | −0.882849 | ||||||||
\(962\) | 0.0359461i | 0.00115895i | ||||||||
\(963\) | − | 5.34487i | − | 0.172236i | ||||||
\(964\) | 21.2316 | 0.683824 | ||||||||
\(965\) | 38.9537 | − | 18.9493i | 1.25396 | − | 0.610001i | ||||
\(966\) | −3.62151 | −0.116520 | ||||||||
\(967\) | 48.0624i | 1.54558i | 0.634661 | + | 0.772791i | \(0.281140\pi\) | ||||
−0.634661 | + | 0.772791i | \(0.718860\pi\) | |||||||
\(968\) | 1.66578i | 0.0535403i | ||||||||
\(969\) | 4.57251 | 0.146890 | ||||||||
\(970\) | −0.323301 | − | 0.664602i | −0.0103806 | − | 0.0213391i | ||||
\(971\) | −7.93304 | −0.254583 | −0.127292 | − | 0.991865i | \(-0.540628\pi\) | ||||
−0.127292 | + | 0.991865i | \(0.540628\pi\) | |||||||
\(972\) | 1.80872i | 0.0580146i | ||||||||
\(973\) | 14.8517i | 0.476123i | ||||||||
\(974\) | 14.4319 | 0.462428 | ||||||||
\(975\) | −0.0796209 | + | 0.101478i | −0.00254991 | + | 0.00324991i | ||||
\(976\) | −4.94837 | −0.158393 | ||||||||
\(977\) | − | 20.2929i | − | 0.649227i | −0.945847 | − | 0.324614i | \(-0.894766\pi\) | ||
0.945847 | − | 0.324614i | \(-0.105234\pi\) | |||||||
\(978\) | − | 0.224316i | − | 0.00717285i | ||||||
\(979\) | 9.48265 | 0.303067 | ||||||||
\(980\) | −1.76921 | − | 3.63692i | −0.0565152 | − | 0.116177i | ||||
\(981\) | 16.5202 | 0.527448 | ||||||||
\(982\) | 11.8020i | 0.376617i | ||||||||
\(983\) | − | 53.3231i | − | 1.70074i | −0.526184 | − | 0.850371i | \(-0.676378\pi\) | ||
0.526184 | − | 0.850371i | \(-0.323622\pi\) | |||||||
\(984\) | 3.44940 | 0.109963 | ||||||||
\(985\) | −25.4703 | + | 12.3902i | −0.811552 | + | 0.394786i | ||||
\(986\) | −3.75078 | −0.119449 | ||||||||
\(987\) | − | 10.1019i | − | 0.321548i | ||||||
\(988\) | 0.122664i | 0.00390246i | ||||||||
\(989\) | 31.9523 | 1.01602 | ||||||||
\(990\) | −0.879433 | + | 0.427807i | −0.0279502 | + | 0.0135966i | ||||
\(991\) | 36.9618 | 1.17413 | 0.587065 | − | 0.809540i | \(-0.300283\pi\) | ||||
0.587065 | + | 0.809540i | \(0.300283\pi\) | |||||||
\(992\) | 8.75677i | 0.278028i | ||||||||
\(993\) | 17.0628i | 0.541471i | ||||||||
\(994\) | 1.03589 | 0.0328565 | ||||||||
\(995\) | −12.5575 | − | 25.8142i | −0.398100 | − | 0.818365i | ||||
\(996\) | 17.2057 | 0.545184 | ||||||||
\(997\) | − | 29.4173i | − | 0.931654i | −0.884876 | − | 0.465827i | \(-0.845757\pi\) | ||
0.884876 | − | 0.465827i | \(-0.154243\pi\) | |||||||
\(998\) | 10.3433i | 0.327412i | ||||||||
\(999\) | 3.18596 | 0.100799 |
(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 | 1155.2.c.e.694.12 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cp.1.4 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cm.1.7 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.9 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.e.694.12 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cm.1.7 | 10 | 5.3 | odd | 4 | |||
5775.2.a.cp.1.4 | 10 | 5.2 | odd | 4 |