Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(365,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.365");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 365.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.365 |
Dual form | 804.2.o.c.641.2 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.949490 | − | 0.548188i | −0.358873 | − | 0.207196i | 0.309713 | − | 0.950830i | \(-0.399767\pi\) |
−0.668586 | + | 0.743634i | \(0.733100\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.724745 | − | 1.25529i | 0.218519 | − | 0.378486i | −0.735837 | − | 0.677159i | \(-0.763211\pi\) |
0.954355 | + | 0.298674i | \(0.0965442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50000 | − | 2.59808i | 1.24808 | − | 0.720577i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | + | 2.82843i | −0.516398 | + | 0.730297i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.17423 | + | 2.98735i | −1.25494 | + | 0.724538i | −0.972086 | − | 0.234626i | \(-0.924613\pi\) |
−0.282851 | + | 0.959164i | \(0.591280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | − | 2.59808i | −0.344124 | − | 0.596040i | 0.641071 | − | 0.767482i | \(-0.278491\pi\) |
−0.985194 | + | 0.171442i | \(0.945157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72474 | + | 0.794593i | −0.376370 | + | 0.173394i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.825765 | + | 0.476756i | −0.172184 | + | 0.0994105i | −0.583615 | − | 0.812030i | \(-0.698362\pi\) |
0.411431 | + | 0.911441i | \(0.365029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.62372 | − | 2.66951i | −0.858604 | − | 0.495715i | 0.00494052 | − | 0.999988i | \(-0.498427\pi\) |
−0.863545 | + | 0.504273i | \(0.831761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.05051 | − | 2.28024i | −0.182870 | − | 0.396939i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.89898 | + | 1.09638i | 0.320986 | + | 0.185321i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.94949 | − | 8.57277i | −0.813691 | − | 1.40935i | −0.910264 | − | 0.414028i | \(-0.864121\pi\) |
0.0965729 | − | 0.995326i | \(-0.469212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.825765 | − | 8.96204i | 0.132228 | − | 1.43507i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.72474 | + | 2.98735i | −0.269360 | + | 0.466545i | −0.968697 | − | 0.248247i | \(-0.920145\pi\) |
0.699337 | + | 0.714792i | \(0.253479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.27135i | 0.193879i | 0.995290 | + | 0.0969395i | \(0.0309053\pi\) | ||||
−0.995290 | + | 0.0969395i | \(0.969095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | + | 5.65685i | 0.298142 | + | 0.843274i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.275255 | − | 0.158919i | −0.0401501 | − | 0.0231807i | 0.479791 | − | 0.877383i | \(-0.340713\pi\) |
−0.519941 | + | 0.854202i | \(0.674046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.89898 | − | 5.02118i | −0.414140 | − | 0.717311i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.949490 | + | 10.3048i | −0.132955 | + | 1.44296i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.44949 | + | 2.51059i | −0.195449 | + | 0.338528i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.17423 | − | 0.476756i | −0.685344 | − | 0.0631479i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.635674i | − | 0.0827578i | −0.999144 | − | 0.0413789i | \(-0.986825\pi\) | ||
0.999144 | − | 0.0413789i | \(-0.0131751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.39898 | − | 5.42650i | 1.20342 | − | 0.694793i | 0.242103 | − | 0.970251i | \(-0.422163\pi\) |
0.961313 | + | 0.275458i | \(0.0888295\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.601021 | + | 3.23375i | −0.0757215 | + | 0.407414i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00000 | + | 5.19615i | −1.11631 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | + | 1.73205i | 0.977356 | + | 0.211604i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.151531 | + | 1.64456i | −0.0182422 | + | 0.197982i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1742 | + | 6.45145i | 1.32614 | + | 0.765646i | 0.984700 | − | 0.174258i | \(-0.0557528\pi\) |
0.341438 | + | 0.939904i | \(0.389086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94949 | + | 5.10867i | 0.345212 | + | 0.597924i | 0.985392 | − | 0.170300i | \(-0.0544738\pi\) |
−0.640181 | + | 0.768224i | \(0.721140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | + | 1.41421i | −0.115470 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.37628 | + | 0.794593i | −0.156841 | + | 0.0905523i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.398979 | + | 0.230351i | 0.0448887 | + | 0.0259165i | 0.522276 | − | 0.852776i | \(-0.325083\pi\) |
−0.477388 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0732 | + | 5.81577i | −1.10568 | + | 0.638364i | −0.937707 | − | 0.347428i | \(-0.887055\pi\) |
−0.167972 | + | 0.985792i | \(0.553722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3485 | − | 5.97469i | 1.12245 | − | 0.648046i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.39898 | + | 3.86943i | −0.900465 | + | 0.414846i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.73545i | − | 0.501957i | −0.967993 | − | 0.250978i | \(-0.919248\pi\) | ||
0.967993 | − | 0.250978i | \(-0.0807523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.69694 | −0.597201 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.72474 | + | 1.25529i | −0.282543 | + | 0.130168i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8485 | − | 6.84072i | 1.20303 | − | 0.694570i | 0.241802 | − | 0.970326i | \(-0.422262\pi\) |
0.961228 | + | 0.275756i | \(0.0889282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.27526 | − | 0.794593i | −0.429679 | − | 0.0798596i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.72474 | − | 11.6476i | 0.669137 | − | 1.15898i | −0.309009 | − | 0.951059i | \(-0.599997\pi\) |
0.978146 | − | 0.207920i | \(-0.0666695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.94949 | − | 3.37662i | 0.192089 | − | 0.332708i | −0.753853 | − | 0.657043i | \(-0.771807\pi\) |
0.945942 | + | 0.324335i | \(0.105140\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.44949 | − | 1.58919i | 0.336636 | − | 0.155089i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.12096i | − | 0.881756i | −0.897567 | − | 0.440878i | \(-0.854667\pi\) | ||
0.897567 | − | 0.440878i | \(-0.145333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.02118i | 0.480942i | 0.970656 | + | 0.240471i | \(0.0773019\pi\) | ||||
−0.970656 | + | 0.240471i | \(0.922698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.0732 | − | 1.57313i | −1.62052 | − | 0.149315i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.27526 | − | 5.67291i | 0.308110 | − | 0.533662i | −0.669839 | − | 0.742507i | \(-0.733637\pi\) |
0.977949 | + | 0.208844i | \(0.0669702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.65153 | − | 0.953512i | 0.154006 | − | 0.0889154i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.8485 | − | 10.1298i | −1.09539 | − | 0.936505i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.55051 | 0.600484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.44949 | + | 7.70674i | 0.404499 | + | 0.700613i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.50000 | + | 5.42650i | 0.225417 | + | 0.489291i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.39898 | − | 7.61926i | 0.390346 | − | 0.676100i | −0.602149 | − | 0.798384i | \(-0.705689\pi\) |
0.992495 | + | 0.122284i | \(0.0390219\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.79796 | + | 1.27135i | 0.158301 | + | 0.111936i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.29253i | 0.549781i | 0.961476 | + | 0.274890i | \(0.0886416\pi\) | ||||
−0.961476 | + | 0.274890i | \(0.911358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.28913i | 0.285204i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0000 | + | 2.82843i | 0.860663 | + | 0.243432i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.10102 | 0.777553 | 0.388776 | − | 0.921332i | \(-0.372898\pi\) | ||||
0.388776 | + | 0.921332i | \(0.372898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.21393i | 0.611878i | 0.952051 | + | 0.305939i | \(0.0989703\pi\) | ||||
−0.952051 | + | 0.305939i | \(0.901030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.500000 | + | 0.230351i | −0.0421076 | + | 0.0193990i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.53177i | − | 0.629838i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.24745 | + | 5.33902i | 0.767959 | + | 0.443381i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.0000 | − | 0.921404i | −0.824786 | − | 0.0759961i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.7778i | − | 1.21065i | −0.795980 | − | 0.605323i | \(-0.793044\pi\) | ||
0.795980 | − | 0.605323i | \(-0.206956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.39898 | − | 7.61926i | −0.357984 | − | 0.620046i | 0.629640 | − | 0.776887i | \(-0.283202\pi\) |
−0.987624 | + | 0.156841i | \(0.949869\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.6237 | + | 11.6476i | 1.10141 | + | 0.941653i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | + | 1.73205i | 0.240966 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.94949 | + | 12.0369i | 0.554630 | + | 0.960647i | 0.997932 | + | 0.0642747i | \(0.0204734\pi\) |
−0.443303 | + | 0.896372i | \(0.646193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | − | 8.48528i | 0.475831 | − | 0.672927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.04541 | 0.0823897 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2980 | + | 19.5686i | −0.884924 | + | 1.53273i | −0.0391242 | + | 0.999234i | \(0.512457\pi\) |
−0.845800 | + | 0.533500i | \(0.820877\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.10102 | + | 4.56048i | 0.163564 | + | 0.355033i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.0732 | − | 12.7440i | −1.70808 | − | 0.986158i | −0.936941 | − | 0.349487i | \(-0.886356\pi\) |
−0.771136 | − | 0.636671i | \(-0.780311\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | − | 12.1244i | 0.538462 | − | 0.932643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.84847 | + | 6.84072i | −0.447244 | + | 0.523123i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6237 | − | 6.13361i | 0.807707 | − | 0.466330i | −0.0384521 | − | 0.999260i | \(-0.512243\pi\) |
0.846159 | + | 0.532931i | \(0.178909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.949490 | + | 0.548188i | 0.0717747 | + | 0.0414391i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.898979 | − | 0.635674i | −0.0675714 | − | 0.0477802i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5959 | −1.01621 | −0.508103 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508103 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.05051 | − | 1.81954i | 0.0780838 | − | 0.135245i | −0.824339 | − | 0.566096i | \(-0.808453\pi\) |
0.902423 | + | 0.430851i | \(0.141786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.72474 | − | 18.7187i | 0.127497 | − | 1.38372i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.89898 | + | 17.1455i | 0.727787 | + | 1.26056i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.66025i | 0.633300i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.97219 | + | 4.08372i | 0.288935 | + | 0.297047i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.72474 | − | 15.1117i | −0.631300 | − | 1.09344i | −0.987286 | − | 0.158953i | \(-0.949188\pi\) |
0.355986 | − | 0.934491i | \(-0.384145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8990 | −0.928489 | −0.464244 | − | 0.885707i | \(-0.653674\pi\) | ||||
−0.464244 | + | 0.885707i | \(0.653674\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.65153 | + | 17.9241i | −0.118269 | + | 1.28357i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.62372 | − | 2.81237i | 0.115686 | − | 0.200373i | −0.802368 | − | 0.596830i | \(-0.796427\pi\) |
0.918054 | + | 0.396456i | \(0.129760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50000 | + | 9.52628i | 0.389885 | + | 0.675300i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4495 | − | 9.58166i | 0.737050 | − | 0.675838i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.92679 | + | 5.06934i | 0.205420 | + | 0.355798i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.44949 | − | 5.97469i | 0.240923 | − | 0.417291i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.17423 | + | 1.85886i | 0.151120 | + | 0.129200i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.34847 | −0.300790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.94949 | + | 5.10867i | 0.203051 | + | 0.351695i | 0.949510 | − | 0.313737i | \(-0.101581\pi\) |
−0.746459 | + | 0.665432i | \(0.768248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.2980 | − | 9.35131i | 1.39079 | − | 0.640741i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.54270i | − | 0.173411i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.949490 | + | 1.64456i | 0.0644556 | + | 0.111640i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.1742 | + | 0.937458i | 0.687511 | + | 0.0633475i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5227 | + | 26.8861i | −1.04417 | + | 1.80856i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6969 | 1.38597 | 0.692985 | − | 0.720952i | \(-0.256295\pi\) | ||||
0.692985 | + | 0.720952i | \(0.256295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.4217 | + | 13.5225i | 1.55455 | + | 0.897521i | 0.997762 | + | 0.0668675i | \(0.0213005\pi\) |
0.556790 | + | 0.830653i | \(0.312033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.84847 | + | 5.10867i | −0.584723 | + | 0.337590i | −0.763008 | − | 0.646389i | \(-0.776278\pi\) |
0.178285 | + | 0.983979i | \(0.442945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.252551 | + | 2.74094i | −0.0166167 | + | 0.180341i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.27526 | − | 16.0652i | 0.607642 | − | 1.05247i | −0.383986 | − | 0.923339i | \(-0.625449\pi\) |
0.991628 | − | 0.129128i | \(-0.0412178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.550510 | + | 0.317837i | 0.0359113 | + | 0.0207334i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.724745 | − | 0.333891i | 0.0470772 | − | 0.0216886i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.62372 | + | 9.74058i | −0.363768 | + | 0.630066i | −0.988578 | − | 0.150712i | \(-0.951843\pi\) |
0.624809 | + | 0.780777i | \(0.285177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.79796 | + | 10.0424i | 0.370418 | + | 0.641583i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.5000 | − | 7.79423i | −0.858984 | − | 0.495935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.84847 | + | 20.0614i | −0.117142 | + | 1.27134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0732 | + | 17.4473i | 0.635816 | + | 1.10126i | 0.986342 | + | 0.164712i | \(0.0526695\pi\) |
−0.350526 | + | 0.936553i | \(0.613997\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.38211i | 0.0868922i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.89898 | − | 20.6096i | 0.118919 | − | 1.29063i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0732 | − | 7.54782i | −0.815485 | − | 0.470820i | 0.0333722 | − | 0.999443i | \(-0.489375\pi\) |
−0.848857 | + | 0.528623i | \(0.822709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.8530i | 0.674373i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.92679 | + | 15.7474i | −0.181163 | + | 0.974738i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.84961i | 0.484027i | 0.970273 | + | 0.242014i | \(0.0778079\pi\) | ||||
−0.970273 | + | 0.242014i | \(0.922192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.69694 | − | 4.73545i | −0.409846 | − | 0.289805i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00680i | 0.366241i | 0.983090 | + | 0.183121i | \(0.0586199\pi\) | ||||
−0.983090 | + | 0.183121i | \(0.941380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.75663i | − | 0.592673i | −0.955084 | − | 0.296337i | \(-0.904235\pi\) | ||
0.955084 | − | 0.296337i | \(-0.0957650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.69694 | + | 8.05669i | −0.344794 | + | 0.487613i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.724745 | + | 1.25529i | −0.0437038 | + | 0.0756971i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.7980 | 1.55005 | 0.775025 | − | 0.631931i | \(-0.217737\pi\) | ||||
0.775025 | + | 0.631931i | \(0.217737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.949490 | + | 5.10867i | −0.0568445 | + | 0.305848i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.72474 | + | 6.45145i | 0.222200 | + | 0.384861i | 0.955476 | − | 0.295070i | \(-0.0953430\pi\) |
−0.733276 | + | 0.679931i | \(0.762010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.79796 | −0.463541 | −0.231770 | − | 0.972771i | \(-0.574452\pi\) | ||||
−0.231770 | + | 0.972771i | \(0.574452\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3485 | + | 0.953512i | 0.612990 | + | 0.0564812i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.27526 | − | 1.89097i | 0.193332 | − | 0.111620i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.34847 | − | 16.1920i | 0.549910 | − | 0.952472i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.17423 | − | 23.5970i | 0.127456 | − | 1.38328i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 29.2699i | − | 1.70997i | −0.518657 | − | 0.854983i | \(-0.673568\pi\) | ||
0.518657 | − | 0.854983i | \(-0.326432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27135i | 0.0740208i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.39898 | + | 5.25153i | −0.313281 | + | 0.304725i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.47730 | + | 4.29080i | −0.143266 | + | 0.248144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.696938 | − | 1.20713i | 0.0401709 | − | 0.0695780i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.74745 | − | 21.1578i | −0.559976 | − | 1.21549i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.7980 | + | 10.8530i | −1.07637 | + | 0.621441i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.29796 | − | 7.44428i | −0.245297 | − | 0.424868i | 0.716918 | − | 0.697158i | \(-0.245552\pi\) |
−0.962215 | + | 0.272290i | \(0.912219\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82577 | − | 6.13361i | −0.160752 | − | 0.348929i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.2020 | −0.805324 | −0.402662 | − | 0.915349i | \(-0.631915\pi\) | ||||
−0.402662 | + | 0.915349i | \(0.631915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.6637i | − | 0.659269i | −0.944109 | − | 0.329634i | \(-0.893075\pi\) | ||
0.944109 | − | 0.329634i | \(-0.106925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.20204 | − | 6.46750i | 0.0677273 | − | 0.364402i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3207 | − | 9.42274i | 0.916660 | − | 0.529234i | 0.0340918 | − | 0.999419i | \(-0.489146\pi\) |
0.882568 | + | 0.470185i | \(0.155813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.70204 | + | 3.86943i | −0.375242 | + | 0.216646i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8990 | − | 9.12096i | −0.719951 | − | 0.509082i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.5227 | + | 8.96204i | 0.863706 | + | 0.498661i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.50000 | + | 2.59808i | −0.249615 | + | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.10102 | + | 5.02118i | 0.392687 | + | 0.277672i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.174235 | + | 0.301783i | 0.00960587 | + | 0.0166378i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0959 | − | 6.98358i | −0.664852 | − | 0.383852i | 0.129271 | − | 0.991609i | \(-0.458736\pi\) |
−0.794123 | + | 0.607757i | \(0.792070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.2980 | + | 22.5720i | −1.05752 | + | 1.23694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.0000 | − | 3.46410i | −0.874173 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9495 | + | 9.20844i | −0.868824 | + | 0.501616i | −0.866957 | − | 0.498382i | \(-0.833928\pi\) |
−0.00186678 | + | 0.999998i | \(0.500594\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.74745 | − | 10.3048i | −0.257846 | − | 0.559681i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.17423 | + | 1.25529i | −0.117741 | + | 0.0679780i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0314i | 0.757623i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.303062 | − | 3.28913i | 0.0163163 | − | 0.177081i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.07321 | − | 10.5191i | 0.326027 | − | 0.564696i | −0.655693 | − | 0.755028i | \(-0.727623\pi\) |
0.981720 | + | 0.190332i | \(0.0609566\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.20204 | 0.117873 | 0.0589363 | − | 0.998262i | \(-0.481229\pi\) | ||||
0.0589363 | + | 0.998262i | \(0.481229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.1742 | + | 6.62642i | −1.39708 | + | 0.353692i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.17423 | − | 5.49794i | −0.168947 | − | 0.292626i | 0.769103 | − | 0.639125i | \(-0.220703\pi\) |
−0.938050 | + | 0.346500i | \(0.887370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.3485 | − | 12.9029i | −1.18613 | − | 0.684815i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.55051 | − | 9.26382i | 0.346690 | − | 0.490293i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.5065i | − | 0.712844i | −0.934325 | − | 0.356422i | \(-0.883997\pi\) | ||
0.934325 | − | 0.356422i | \(-0.116003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3485 | + | 1.41421i | 0.805586 | + | 0.0742270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.89898 | − | 10.2173i | −0.308767 | − | 0.534800i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5000 | + | 7.79423i | 0.704694 | + | 0.406855i | 0.809093 | − | 0.587680i | \(-0.199959\pi\) |
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.1742 | + | 1.89097i | 0.529649 | + | 0.0984399i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.69694 | − | 3.28913i | −0.295770 | − | 0.170763i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.398979 | + | 0.230351i | 0.0206584 | + | 0.0119271i | 0.510294 | − | 0.860000i | \(-0.329537\pi\) |
−0.489635 | + | 0.871927i | \(0.662870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | − | 16.9706i | 0.619677 | − | 0.876356i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.7423 | −1.42880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6010 | + | 11.8940i | −1.05820 | + | 0.610954i | −0.924935 | − | 0.380126i | \(-0.875881\pi\) |
−0.133269 | + | 0.991080i | \(0.542547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.37628 | − | 13.8404i | −0.326666 | − | 0.709063i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0732 | + | 20.9114i | 0.616912 | + | 1.06852i | 0.990046 | + | 0.140746i | \(0.0449501\pi\) |
−0.373133 | + | 0.927778i | \(0.621717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.75255 | − | 1.58919i | 0.140283 | − | 0.0809924i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.59592 | − | 1.27135i | 0.182791 | − | 0.0646263i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.97219 | − | 5.18010i | 0.454908 | − | 0.262641i | −0.254993 | − | 0.966943i | \(-0.582073\pi\) |
0.709901 | + | 0.704302i | \(0.248740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.84847 | − | 4.93369i | 0.144053 | − | 0.249508i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.89898 | + | 6.29253i | 0.448894 | + | 0.317416i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.797959 | − | 0.460702i | −0.0401497 | − | 0.0231804i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.6969 | −1.33988 | −0.669940 | − | 0.742415i | \(-0.733680\pi\) | ||||
−0.669940 | + | 0.742415i | \(0.733680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.65153 | + | 3.28913i | 0.232868 | + | 0.164662i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.10102 | −0.254733 | −0.127366 | − | 0.991856i | \(-0.540652\pi\) | ||||
−0.127366 | + | 0.991856i | \(0.540652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | −0.448322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0000 | − | 11.3137i | 0.695666 | − | 0.562183i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.3485 | −0.711227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5000 | − | 9.52628i | −0.815872 | − | 0.471044i | 0.0331186 | − | 0.999451i | \(-0.489456\pi\) |
−0.848991 | + | 0.528407i | \(0.822789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.10102 | − | 12.8708i | 0.448920 | − | 0.634869i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.348469 | + | 0.603566i | −0.0171470 | + | 0.0296996i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1464 | − | 11.6315i | 0.988949 | − | 0.570970i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.2020 | + | 7.21393i | 0.499596 | + | 0.353268i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.3207 | + | 12.8868i | −1.09044 | + | 0.629563i | −0.933692 | − | 0.358076i | \(-0.883433\pi\) |
−0.156743 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.50000 | − | 11.2583i | −0.316791 | − | 0.548697i | 0.663026 | − | 0.748596i | \(-0.269272\pi\) |
−0.979817 | + | 0.199899i | \(0.935939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.174235 | + | 0.937458i | −0.00847158 | + | 0.0455808i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.17423 | − | 2.98735i | 0.250987 | − | 0.144908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.8990 | −0.575832 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.6515 | − | 7.53177i | −0.514261 | − | 0.363637i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7702 | − | 16.0331i | −1.33764 | − | 0.772287i | −0.351184 | − | 0.936306i | \(-0.614221\pi\) |
−0.986457 | + | 0.164019i | \(0.947554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5000 | − | 7.79423i | −0.648769 | − | 0.374567i | 0.139216 | − | 0.990262i | \(-0.455542\pi\) |
−0.787984 | + | 0.615695i | \(0.788875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.7980 | − | 7.73885i | 0.805400 | − | 0.371049i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.47730 | + | 1.43027i | 0.118505 | + | 0.0684190i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.60102 | − | 7.96920i | −0.219595 | − | 0.380349i | 0.735089 | − | 0.677970i | \(-0.237140\pi\) |
−0.954684 | + | 0.297621i | \(0.903807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.3031 | + | 13.2207i | −0.538241 | + | 0.629559i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6237 | − | 28.7931i | 0.789817 | − | 1.36800i | −0.136262 | − | 0.990673i | \(-0.543509\pi\) |
0.926079 | − | 0.377330i | \(-0.123158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.47090i | 0.448964i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.8990 | − | 14.7778i | −0.988488 | − | 0.698966i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.1742 | − | 8.18350i | −0.668923 | − | 0.386203i | 0.126745 | − | 0.991935i | \(-0.459547\pi\) |
−0.795669 | + | 0.605732i | \(0.792880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.50000 | + | 4.33013i | 0.117720 | + | 0.203898i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.1742 | − | 1.39816i | −0.712948 | − | 0.0656913i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3939 | 0.534153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1969 | − | 31.5180i | 0.851217 | − | 1.47435i | −0.0288939 | − | 0.999582i | \(-0.509198\pi\) |
0.880111 | − | 0.474768i | \(-0.157468\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.0959 | − | 7.61926i | 1.40476 | − | 0.355636i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.1407i | 1.96269i | 0.192263 | + | 0.981344i | \(0.438417\pi\) | ||||
−0.192263 | + | 0.981344i | \(0.561583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.19694 | + | 4.15515i | −0.334470 | + | 0.193106i | −0.657824 | − | 0.753172i | \(-0.728523\pi\) |
0.323354 | + | 0.946278i | \(0.395190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.44949 | − | 2.51059i | 0.252714 | − | 0.116426i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.1742 | − | 20.3079i | 1.62767 | − | 0.939735i | 0.642883 | − | 0.765964i | \(-0.277738\pi\) |
0.984786 | − | 0.173771i | \(-0.0555954\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.64643 | − | 6.03007i | −0.306904 | − | 0.278443i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.9722 | + | 2.20881i | 1.10458 | + | 0.101776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.59592 | + | 0.921404i | 0.0733804 | + | 0.0423662i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.50000 | + | 2.59808i | 0.0688247 | + | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | − | 16.9706i | −0.274721 | − | 0.777029i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7247 | − | 10.2334i | 0.809864 | − | 0.467575i | −0.0370445 | − | 0.999314i | \(-0.511794\pi\) |
0.846909 | + | 0.531738i | \(0.178461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.5454 | − | 25.7183i | −2.03110 | − | 1.17265i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.04541 | − | 1.47843i | 0.0475677 | − | 0.0672709i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6969 | + | 13.6814i | −1.07602 | + | 0.621242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.60102 | + | 4.96580i | −0.389749 | + | 0.225022i | −0.682052 | − | 0.731304i | \(-0.738912\pi\) |
0.292302 | + | 0.956326i | \(0.405579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.3763 | + | 35.5464i | 0.740561 | + | 1.60746i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6637i | 0.526373i | 0.964745 | + | 0.263187i | \(0.0847735\pi\) | ||||
−0.964745 | + | 0.263187i | \(0.915226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.8990 | 1.43666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.55051 | + | 1.58919i | 0.384317 | + | 0.0714286i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.07321 | − | 12.2512i | −0.317277 | − | 0.549540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.39898 | + | 1.96240i | −0.152159 | + | 0.0878492i | −0.574147 | − | 0.818753i | \(-0.694666\pi\) |
0.421987 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.0959 | + | 18.4723i | −1.79135 | + | 0.825280i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.1742 | + | 38.4069i | −0.988700 | + | 1.71248i | −0.364528 | + | 0.931193i | \(0.618770\pi\) |
−0.624173 | + | 0.781287i | \(0.714564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4495 | + | 23.2952i | −0.598494 | + | 1.03662i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.1464 | − | 22.0239i | −0.450619 | − | 0.978114i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.82843i | − | 0.125368i | −0.998033 | − | 0.0626839i | \(-0.980034\pi\) | ||
0.998033 | − | 0.0626839i | \(-0.0199660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.46750i | − | 0.286105i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.82577 | + | 15.1117i | 0.168912 | + | 0.667198i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.89898 | + | 6.75323i | −0.171810 | + | 0.297583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.398979 | + | 0.230351i | −0.0175471 | + | 0.0101308i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.94949 | − | 21.1578i | 0.0855731 | − | 0.928725i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.2929 | 1.76526 | 0.882631 | − | 0.470066i | \(-0.155770\pi\) | ||||
0.882631 | + | 0.470066i | \(0.155770\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.6464 | + | 39.2248i | 0.990259 | + | 1.71518i | 0.615712 | + | 0.787971i | \(0.288869\pi\) |
0.374547 | + | 0.927208i | \(0.377798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.72474 | − | 0.794593i | 0.0752740 | − | 0.0346789i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3485 | 0.450786 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0454 | + | 19.1312i | −0.480235 | + | 0.831792i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.79796 | + | 0.635674i | −0.0780248 | + | 0.0275859i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.9241i | 0.776378i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2419i | 0.788667i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5959 | + | 19.2275i | −0.586707 | + | 0.829729i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.40408 | −0.361989 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.6766i | − | 1.66284i | −0.555648 | − | 0.831418i | \(-0.687530\pi\) | ||
0.555648 | − | 0.831418i | \(-0.312470\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.52270 | − | 3.30518i | −0.0653455 | − | 0.141839i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 10.0424i | − | 0.430167i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8485 | + | 10.3048i | 0.763145 | + | 0.440602i | 0.830424 | − | 0.557132i | \(-0.188098\pi\) |
−0.0672785 | + | 0.997734i | \(0.521432\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.7474 | − | 21.1578i | −1.05620 | − | 0.902994i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0171i | 0.682349i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.252551 | − | 0.437432i | −0.0107396 | − | 0.0186015i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.1464 | + | 3.14626i | 1.44944 | + | 0.133551i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.07321 | + | 4.08372i | 0.299702 | + | 0.173033i | 0.642309 | − | 0.766446i | \(-0.277977\pi\) |
−0.342607 | + | 0.939479i | \(0.611310\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.30306 | + | 5.72107i | 0.139705 | + | 0.241975i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.2474 | + | 8.66025i | 0.517088 | + | 0.365636i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.2929 | 1.78243 | 0.891216 | − | 0.453580i | \(-0.149853\pi\) | ||||
0.891216 | + | 0.453580i | \(0.149853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.55051 | + | 11.3458i | −0.275582 | + | 0.477322i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.74745 | − | 1.53381i | 0.409354 | − | 0.0644139i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.4217 | − | 13.5225i | −0.981888 | − | 0.566893i | −0.0790484 | − | 0.996871i | \(-0.525188\pi\) |
−0.902840 | + | 0.429977i | \(0.858522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8485 | + | 32.6465i | −0.788784 | + | 1.36621i | 0.137928 | + | 0.990442i | \(0.455956\pi\) |
−0.926712 | + | 0.375772i | \(0.877378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0959 | − | 2.77305i | −1.25728 | − | 0.115846i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.825765 | − | 0.476756i | 0.0344368 | − | 0.0198821i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8485 | − | 15.5010i | −1.11772 | − | 0.645314i | −0.176899 | − | 0.984229i | \(-0.556607\pi\) |
−0.940817 | + | 0.338915i | \(0.889940\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.8990 | + | 18.2419i | −0.536063 | + | 0.758108i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7526 | 0.529065 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.34847 | − | 7.53177i | 0.180095 | − | 0.311934i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.6969 | + | 20.2597i | 0.979748 | + | 0.837635i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.27526 | − | 14.3332i | −0.341556 | − | 0.591593i | 0.643166 | − | 0.765727i | \(-0.277621\pi\) |
−0.984722 | + | 0.174134i | \(0.944287\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.19615i | 0.214104i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.35357 | − | 5.10867i | −0.0968130 | − | 0.210142i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9722 | − | 20.7364i | −0.491639 | − | 0.851544i | 0.508315 | − | 0.861171i | \(-0.330269\pi\) |
−0.999954 | + | 0.00962762i | \(0.996935\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.1010 | −0.537089 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9722 | + | 1.74810i | 0.776480 | + | 0.0715452i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.17423 | − | 14.1582i | 0.333990 | − | 0.578488i | −0.649300 | − | 0.760532i | \(-0.724938\pi\) |
0.983290 | + | 0.182044i | \(0.0582714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.39898 | − | 2.42310i | −0.0570656 | − | 0.0988405i | 0.836081 | − | 0.548605i | \(-0.184841\pi\) |
−0.893147 | + | 0.449765i | \(0.851508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.10102 | − | 24.3595i | −0.126283 | − | 0.991994i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.89898 | − | 15.4135i | −0.361795 | − | 0.626647i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.84847 | + | 17.0580i | −0.399737 | + | 0.692365i | −0.993693 | − | 0.112133i | \(-0.964232\pi\) |
0.593956 | + | 0.804497i | \(0.297565\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0959 | + | 0.930242i | 0.409107 | + | 0.0376953i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.65153 | −0.0668138 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.1969 | + | 22.8578i | 0.533019 | + | 0.923217i | 0.999256 | + | 0.0385567i | \(0.0122760\pi\) |
−0.466237 | + | 0.884660i | \(0.654391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.00000 | − | 10.8530i | −0.201619 | − | 0.437635i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.7272i | 1.07600i | 0.842946 | + | 0.537998i | \(0.180819\pi\) | ||||
−0.842946 | + | 0.537998i | \(0.819181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.94949 | − | 5.10867i | −0.118550 | − | 0.205335i | 0.800643 | − | 0.599141i | \(-0.204491\pi\) |
−0.919193 | + | 0.393807i | \(0.871158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.80306 | − | 1.21597i | 0.192740 | − | 0.0487952i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.59592 | + | 4.49626i | −0.104003 | + | 0.180139i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.34847 | + | 6.14966i | −0.173661 | + | 0.245594i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.2196 | + | 29.5717i | 2.04226 | + | 1.17910i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5454 | − | 13.5939i | 0.937328 | − | 0.541167i | 0.0482062 | − | 0.998837i | \(-0.484650\pi\) |
0.889122 | + | 0.457671i | \(0.151316\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1742 | + | 0.937458i | 0.404390 | + | 0.0372606i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.79796 | + | 15.2385i | −0.349136 | + | 0.604722i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.0908 | − | 15.0635i | −1.03376 | − | 0.596839i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.07321 | − | 38.0570i | 0.279812 | − | 1.50551i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.5227 | + | 37.2784i | −0.850096 | + | 1.47241i | 0.0310256 | + | 0.999519i | \(0.490123\pi\) |
−0.881121 | + | 0.472890i | \(0.843211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1918 | 1.15121 | 0.575607 | − | 0.817727i | \(-0.304766\pi\) | ||||
0.575607 | + | 0.817727i | \(0.304766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.59592 | − | 2.54270i | −0.141589 | − | 0.100119i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.174235 | − | 0.301783i | −0.00684987 | − | 0.0118643i | 0.862580 | − | 0.505920i | \(-0.168847\pi\) |
−0.869430 | + | 0.494056i | \(0.835514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.797959 | − | 0.460702i | −0.0313226 | − | 0.0180841i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.27526 | + | 0.301783i | 0.128367 | + | 0.0118278i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.62372 | − | 16.6688i | −0.376605 | − | 0.652300i | 0.613960 | − | 0.789337i | \(-0.289575\pi\) |
−0.990566 | + | 0.137037i | \(0.956242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.5851i | − | 0.491739i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.5000 | − | 13.4511i | 0.448658 | − | 0.524777i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.72474 | − | 3.30518i | −0.223004 | − | 0.128752i | 0.384336 | − | 0.923193i | \(-0.374430\pi\) |
−0.607341 | + | 0.794442i | \(0.707764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.1195i | 1.44378i | 0.692007 | + | 0.721891i | \(0.256727\pi\) | ||||
−0.692007 | + | 0.721891i | \(0.743273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.5000 | + | 48.8385i | 0.873828 | + | 1.89673i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.57826i | − | 0.255094i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.09082 | 0.197117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.6969 | − | 29.2699i | 0.800190 | − | 1.13164i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.7313i | − | 0.607301i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.38551i | 0.169049i | 0.996421 | + | 0.0845244i | \(0.0269371\pi\) | ||||
−0.996421 | + | 0.0845244i | \(0.973063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | + | 1.41421i | 0.192450 | + | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2753 | + | 29.9216i | −0.663942 | + | 1.14998i | 0.315629 | + | 0.948883i | \(0.397784\pi\) |
−0.979571 | + | 0.201099i | \(0.935549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0000 | −0.575647 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.5454 | − | 19.6007i | 1.63034 | − | 0.751102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.1742 | − | 28.0146i | −0.618890 | − | 1.07195i | −0.989689 | − | 0.143235i | \(-0.954249\pi\) |
0.370799 | − | 0.928713i | \(-0.379084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2020 | −0.695464 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.62372 | + | 17.6223i | −0.0619489 | + | 0.672332i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.0000 | − | 15.5885i | 1.02862 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6464 | + | 23.6363i | −0.519135 | + | 0.899167i | 0.480618 | + | 0.876930i | \(0.340412\pi\) |
−0.999753 | + | 0.0222375i | \(0.992921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.62372 | + | 3.09810i | 0.137654 | + | 0.117687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 14.4279i | − | 0.547280i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.6096i | − | 0.780646i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4444 | − | 29.1824i | −0.508513 | − | 1.10378i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.82577 | − | 11.8226i | 0.257806 | − | 0.446532i | −0.707848 | − | 0.706365i | \(-0.750334\pi\) |
0.965654 | + | 0.259832i | \(0.0836673\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.8485 | + | 25.7183i | −0.560021 | + | 0.969984i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.00000 | − | 0.460702i | 0.0376622 | − | 0.0173510i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.7702 | + | 7.37285i | −0.480271 | + | 0.277285i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7474 | + | 22.0792i | 0.478740 | + | 0.829203i | 0.999703 | − | 0.0243768i | \(-0.00776015\pi\) |
−0.520962 | + | 0.853580i | \(0.674427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.252551 | − | 1.35884i | 0.00947141 | − | 0.0509603i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.65153 | 0.0618503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0635i | 0.563344i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.15153 | + | 17.6937i | 0.304424 | + | 0.660784i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.6691 | − | 8.46923i | 0.547066 | − | 0.315849i | −0.200872 | − | 0.979618i | \(-0.564377\pi\) |
0.747938 | + | 0.663769i | \(0.231044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.70204 | + | 2.13737i | −0.137871 | + | 0.0796000i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000 | − | 5.65685i | 0.148762 | − | 0.210381i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.62372 | + | 2.66951i | 0.171721 | + | 0.0991431i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.8939 | − | 26.4968i | 1.70211 | − | 0.982713i | 0.758488 | − | 0.651687i | \(-0.225938\pi\) |
0.943621 | − | 0.331027i | \(-0.107395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.79796 | − | 6.57826i | −0.140473 | − | 0.243306i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0505 | + | 8.11207i | 0.518967 | + | 0.299626i | 0.736512 | − | 0.676424i | \(-0.236471\pi\) |
−0.217545 | + | 0.976050i | \(0.569805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.0000 | + | 1.84281i | 0.737711 | + | 0.0679730i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.97219 | − | 8.78706i | 0.293660 | − | 0.323676i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.6464 | + | 21.1578i | −1.34806 | + | 0.778303i | −0.987975 | − | 0.154616i | \(-0.950586\pi\) |
−0.360086 | + | 0.932919i | \(0.617253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.5227 | + | 11.2977i | −0.900864 | + | 0.415030i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.27526 | − | 3.62302i | 0.230217 | − | 0.132916i | −0.380455 | − | 0.924799i | \(-0.624233\pi\) |
0.610672 | + | 0.791884i | \(0.290899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.5556i | 1.08283i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.5227 | + | 22.6756i | 0.970415 | + | 0.829656i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.00000 | + | 8.66025i | −0.182696 | + | 0.316439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3939 | 0.561731 | 0.280865 | − | 0.959747i | \(-0.409379\pi\) | ||||
0.280865 | + | 0.959747i | \(0.409379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.7474 | + | 3.20164i | 1.26627 | + | 0.116674i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.79796 | + | 15.2385i | 0.320191 | + | 0.554586i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0505 | − | 9.84412i | −0.619711 | − | 0.357791i | 0.157045 | − | 0.987591i | \(-0.449803\pi\) |
−0.776757 | + | 0.629801i | \(0.783136\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.95459 | + | 1.38211i | 0.0709472 | + | 0.0501673i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.9562i | − | 0.650911i | −0.945557 | − | 0.325456i | \(-0.894482\pi\) | ||
0.945557 | − | 0.325456i | \(-0.105518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.75255 | − | 4.76756i | 0.0996490 | − | 0.172597i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.2474 | − | 23.2952i | −0.985134 | − | 0.842240i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.65153 | − | 2.86054i | −0.0596333 | − | 0.103288i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7474 | − | 6.20504i | −0.387563 | − | 0.223760i | 0.293541 | − | 0.955947i | \(-0.405166\pi\) |
−0.681104 | + | 0.732187i | \(0.738500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.7474 | + | 10.9405i | −0.855243 | + | 0.394012i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.97219 | − | 1.71600i | −0.106902 | − | 0.0617201i | 0.445596 | − | 0.895234i | \(-0.352992\pi\) |
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | + | 0.866025i | 0.0538816 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.3485 | + | 10.8530i | 0.550623 | + | 0.389349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3485 | 0.370772 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.1969 | − | 9.35131i | 0.579572 | − | 0.334616i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.3434 | + | 19.8865i | 0.691276 | + | 0.710685i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.8990 | − | 24.0737i | −0.496076 | − | 0.859229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.6464 | − | 10.7655i | 0.664673 | − | 0.383749i | −0.129382 | − | 0.991595i | \(-0.541299\pi\) |
0.794055 | + | 0.607845i | \(0.207966\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.1010 | + | 7.84961i | 0.395207 | + | 0.279453i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.21964 | + | 3.59091i | −0.221145 | + | 0.127678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.1969 | − | 48.8385i | 1.00130 | − | 1.73431i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0000 | + | 16.9706i | −0.425596 | + | 0.601884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.1742 | − | 6.45145i | −0.395812 | − | 0.228522i | 0.288864 | − | 0.957370i | \(-0.406723\pi\) |
−0.684675 | + | 0.728848i | \(0.740056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.89898 | 0.0671811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.3939 | + | 4.73545i | −0.473249 | + | 0.167319i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.55051 | 0.301741 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.09082 | −0.0736916 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.49490 | + | 6.00680i | 0.299035 | + | 0.211449i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.2020 | −0.710266 | −0.355133 | − | 0.934816i | \(-0.615564\pi\) | ||||
−0.355133 | + | 0.934816i | \(0.615564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.8485 | − | 12.0369i | −0.732089 | − | 0.422672i | 0.0870971 | − | 0.996200i | \(-0.472241\pi\) |
−0.819186 | + | 0.573528i | \(0.805574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7980 | − | 9.75663i | −0.483916 | − | 0.342180i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.5959 | − | 39.1373i | 0.791500 | − | 1.37092i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.30306 | − | 1.90702i | 0.115559 | − | 0.0667183i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.69694 | + | 16.1134i | 0.199067 | + | 0.563047i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7247 | + | 8.50134i | −0.513897 | + | 0.296699i | −0.734434 | − | 0.678680i | \(-0.762552\pi\) |
0.220537 | + | 0.975379i | \(0.429219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3990 | + | 35.3321i | 0.711064 | + | 1.23160i | 0.964458 | + | 0.264235i | \(0.0851196\pi\) |
−0.253394 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.05051 | + | 2.28024i | 0.0365741 | + | 0.0793877i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.3207 | + | 21.5471i | −1.29777 | + | 0.749266i | −0.980018 | − | 0.198909i | \(-0.936260\pi\) |
−0.317749 | + | 0.948175i | \(0.602927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.3939 | 0.673577 | 0.336789 | − | 0.941580i | \(-0.390659\pi\) | ||||
0.336789 | + | 0.941580i | \(0.390659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.7980 | − | 36.4838i | 0.894921 | − | 1.26561i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.0000 | + | 17.3205i | 1.03944 | + | 0.600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.1464 | + | 25.4880i | 1.52775 | + | 0.882047i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.27526 | + | 6.45145i | 0.216905 | + | 0.222995i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.52270 | + | 5.49794i | 0.328760 | + | 0.189810i | 0.655291 | − | 0.755377i | \(-0.272546\pi\) |
−0.326530 | + | 0.945187i | \(0.605880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.247449 | − | 0.428594i | −0.00853271 | − | 0.0147791i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.8485 | + | 1.18386i | 0.442525 | + | 0.0407744i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.0000 | + | 24.2487i | −0.481615 | + | 0.834181i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.75663i | − | 0.335242i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.79796 | + | 11.0280i | −0.267625 | + | 0.378479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.17423 | + | 4.71940i | 0.280209 | + | 0.161779i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6464 | + | 37.4927i | 0.741160 | + | 1.28373i | 0.951968 | + | 0.306199i | \(0.0990572\pi\) |
−0.210808 | + | 0.977527i | \(0.567610\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.6969 | − | 13.6814i | 0.400027 | − | 0.467895i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.5959 | 0.464428 | 0.232214 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232214 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.84847 | + | 3.20164i | −0.0630690 | + | 0.109239i | −0.895836 | − | 0.444385i | \(-0.853422\pi\) |
0.832767 | + | 0.553624i | \(0.186755\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.601021 | − | 6.52288i | 0.0204827 | − | 0.222299i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.47848i | − | 0.0843685i | −0.999110 | − | 0.0421843i | \(-0.986568\pi\) | ||
0.999110 | − | 0.0421843i | \(-0.0134316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.2474 | + | 12.2672i | −0.722435 | + | 0.417098i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.5505 | − | 29.4128i | −0.460199 | − | 0.998910i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.578317 | − | 0.333891i | 0.0196180 | − | 0.0113265i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.5000 | − | 12.9904i | 1.37229 | − | 0.440162i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1969 | − | 26.6718i | −1.05586 | − | 0.902704i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3939 | − | 6.57826i | −0.385183 | − | 0.222386i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.6464 | − | 42.6889i | −0.832251 | − | 1.44150i | −0.896249 | − | 0.443551i | \(-0.853719\pi\) |
0.0639986 | − | 0.997950i | \(-0.479615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.3939 | − | 29.2699i | −1.39618 | − | 0.987249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.3207 | − | 16.3509i | 0.954147 | − | 0.550877i | 0.0597805 | − | 0.998212i | \(-0.480960\pi\) |
0.894367 | + | 0.447334i | \(0.147627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.54541 | − | 3.20164i | −0.186618 | − | 0.107744i | 0.403780 | − | 0.914856i | \(-0.367696\pi\) |
−0.590398 | + | 0.807112i | \(0.701029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.79796 | + | 1.27135i | 0.0604377 | + | 0.0427359i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7702 | + | 10.8370i | −0.630240 | + | 0.363869i | −0.780845 | − | 0.624725i | \(-0.785211\pi\) |
0.150605 | + | 0.988594i | \(0.451878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.35357 | + | 4.82294i | −0.280170 | + | 0.161756i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.02781 | + | 12.8868i | 0.0679341 | + | 0.431725i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.953512i | 0.0319081i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.1918 | 0.908923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.59082 | + | 7.79423i | 0.119894 | + | 0.260242i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.62372 | + | 8.00853i | 0.154210 | + | 0.267099i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.0454 | + | 17.9241i | −1.03427 | + | 0.597137i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.01021 | − | 2.19275i | −0.0336175 | − | 0.0729702i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.10102 | + | 3.63907i | −0.0698403 | + | 0.120967i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6010 | − | 30.4859i | 0.584432 | − | 1.01227i | −0.410514 | − | 0.911854i | \(-0.634651\pi\) |
0.994946 | − | 0.100412i | \(-0.0320161\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.6691 | − | 7.37285i | −1.31574 | − | 0.244542i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.1195i | − | 1.22982i | −0.788596 | − | 0.614912i | \(-0.789192\pi\) | ||
0.788596 | − | 0.614912i | \(-0.210808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.8598i | 0.557978i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.44949 | + | 37.4373i | −0.114037 | + | 1.23764i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.44949 | − | 5.97469i | 0.113912 | − | 0.197302i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.84847 | − | 1.64456i | 0.0939623 | − | 0.0542492i | −0.452283 | − | 0.891875i | \(-0.649390\pi\) |
0.546245 | + | 0.837626i | \(0.316057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.8258 | − | 1.36605i | −0.488526 | − | 0.0450129i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.0454 | 2.20683 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.94949 | + | 8.57277i | 0.162738 | + | 0.281871i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.5000 | − | 2.13737i | −0.377710 | − | 0.0702006i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.4949 | 1.59107 | 0.795533 | − | 0.605910i | \(-0.207191\pi\) | ||||
0.795533 | + | 0.605910i | \(0.207191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.69694 | + | 15.0635i | −0.285031 | + | 0.493688i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.2020 | + | 20.0847i | −0.464954 | + | 0.657544i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 17.3205i | − | 0.566441i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.3908i | 1.25417i | 0.778949 | + | 0.627087i | \(0.215753\pi\) | ||||
−0.778949 | + | 0.627087i | \(0.784247\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4949 | − | 11.6637i | −0.538291 | − | 0.380629i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.2929 | −1.31351 | −0.656755 | − | 0.754104i | \(-0.728071\pi\) | ||||
−0.656755 | + | 0.754104i | \(0.728071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.28913i | − | 0.107109i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.94439 | − | 8.16744i | −0.258431 | − | 0.265687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 36.8338i | − | 1.19694i | −0.801146 | − | 0.598468i | \(-0.795776\pi\) | ||
0.801146 | − | 0.598468i | \(-0.204224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.5454 | + | 15.3260i | 0.861700 | + | 0.497503i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.99490 | − | 32.5036i | 0.0971162 | − | 1.05400i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2351i | 0.396334i | 0.980168 | + | 0.198167i | \(0.0634989\pi\) | ||||
−0.980168 | + | 0.198167i | \(0.936501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4495 | + | 30.2234i | 0.564652 | + | 0.978006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.22985 | + | 13.3475i | −0.0397553 | + | 0.431465i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.64133 | − | 4.98907i | −0.279043 | − | 0.161106i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.7980 | + | 9.12096i | −0.831328 | + | 0.293919i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.7980 | 0.830466 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.84847 | − | 11.8619i | 0.220232 | − | 0.381453i | −0.734646 | − | 0.678450i | \(-0.762652\pi\) |
0.954878 | + | 0.296997i | \(0.0959852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.1969 | − | 12.9904i | 0.905816 | − | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.2196 | + | 17.4473i | 0.969794 | + | 0.559911i | 0.899174 | − | 0.437592i | \(-0.144169\pi\) |
0.0706209 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95459 | − | 6.84955i | 0.126778 | − | 0.219587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.825765 | + | 8.96204i | −0.0264457 | + | 0.287015i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.3207 | + | 12.8868i | −0.714101 | + | 0.412287i | −0.812578 | − | 0.582853i | \(-0.801936\pi\) |
0.0984765 | + | 0.995139i | \(0.468603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.94439 | − | 3.43199i | −0.189983 | − | 0.109687i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.2020 | − | 5.02118i | 0.453436 | − | 0.160314i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.5959 | −1.00775 | −0.503877 | − | 0.863776i | \(-0.668093\pi\) | ||||
−0.503877 | + | 0.863776i | \(0.668093\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.24745 | + | 5.62475i | −0.103472 | + | 0.179219i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.601021 | + | 0.0553782i | 0.0191307 | + | 0.00176271i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.606123 | − | 1.04984i | −0.0192736 | − | 0.0333828i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.5276i | − | 0.588550i | −0.955721 | − | 0.294275i | \(-0.904922\pi\) | ||
0.955721 | − | 0.294275i | \(-0.0950781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.9722 | + | 10.1226i | −0.697266 | + | 0.321232i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.0000 | − | 19.0526i | −0.348723 | − | 0.604007i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.2929 | −1.08607 | −0.543033 | − | 0.839711i | \(-0.682724\pi\) | ||||
−0.543033 | + | 0.839711i | \(0.682724\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.6237 | + | 49.8635i | 0.399397 | + | 1.57761i |
(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 | 804.2.o.c.365.1 | yes | 4 | |
3.2 | odd | 2 | 804.2.o.b.365.1 | ✓ | 4 | ||
67.38 | odd | 6 | 804.2.o.b.641.2 | yes | 4 | ||
201.38 | even | 6 | inner | 804.2.o.c.641.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.o.b.365.1 | ✓ | 4 | 3.2 | odd | 2 | ||
804.2.o.b.641.2 | yes | 4 | 67.38 | odd | 6 | ||
804.2.o.c.365.1 | yes | 4 | 1.1 | even | 1 | trivial | |
804.2.o.c.641.2 | yes | 4 | 201.38 | even | 6 | inner |