Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.j.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62132 | − | 2.09077i | −0.612801 | − | 0.790237i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12132 | − | 3.67423i | 0.639602 | − | 1.10782i | −0.345918 | − | 0.938265i | \(-0.612432\pi\) |
0.985520 | − | 0.169559i | \(-0.0542342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.12132 | + | 3.67423i | −0.514496 | + | 0.891133i | 0.485363 | + | 0.874313i | \(0.338688\pi\) |
−0.999859 | + | 0.0168199i | \(0.994646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62132 | − | 2.80821i | −0.371956 | − | 0.644247i | 0.617910 | − | 0.786249i | \(-0.287980\pi\) |
−0.989866 | + | 0.142001i | \(0.954646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.62132 | + | 0.358719i | −0.572019 | + | 0.0782790i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.48528 | −1.57568 | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||||
−0.787839 | + | 0.615882i | \(0.788800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.12132 | − | 3.67423i | −0.369274 | − | 0.639602i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | + | 4.33013i | 0.410997 | + | 0.711868i | 0.994999 | − | 0.0998840i | \(-0.0318472\pi\) |
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.50000 | + | 4.33013i | −0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.75736 | −0.274453 | −0.137227 | − | 0.990540i | \(-0.543819\pi\) | ||||
−0.137227 | + | 0.990540i | \(0.543819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.48528 | −0.683999 | −0.341999 | − | 0.939700i | \(-0.611104\pi\) | ||||
−0.341999 | + | 0.939700i | \(0.611104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.878680 | + | 1.52192i | 0.128169 | + | 0.221995i | 0.922967 | − | 0.384879i | \(-0.125757\pi\) |
−0.794798 | + | 0.606873i | \(0.792423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12132 | + | 3.67423i | 0.297044 | + | 0.514496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.12132 | + | 3.67423i | −0.291386 | + | 0.504695i | −0.974138 | − | 0.225955i | \(-0.927450\pi\) |
0.682752 | + | 0.730650i | \(0.260783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.24264 | −0.429498 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.878680 | + | 1.52192i | −0.114394 | + | 0.198137i | −0.917537 | − | 0.397649i | \(-0.869826\pi\) |
0.803143 | + | 0.595786i | \(0.203159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | + | 2.44949i | −0.125988 | + | 0.308607i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.86396 | + | 11.8887i | −0.838566 | + | 1.45244i | 0.0525271 | + | 0.998619i | \(0.483272\pi\) |
−0.891093 | + | 0.453820i | \(0.850061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528 | 1.00702 | 0.503509 | − | 0.863990i | \(-0.332042\pi\) | ||||
0.503509 | + | 0.863990i | \(0.332042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.74264 | − | 11.6786i | 0.789166 | − | 1.36688i | −0.137312 | − | 0.990528i | \(-0.543846\pi\) |
0.926478 | − | 0.376348i | \(-0.122820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.1213 | + | 1.52192i | −1.26739 | + | 0.173439i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.378680 | − | 0.655892i | −0.0426048 | − | 0.0737937i | 0.843937 | − | 0.536443i | \(-0.180232\pi\) |
−0.886541 | + | 0.462649i | \(0.846899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2426 | −1.12428 | −0.562138 | − | 0.827043i | \(-0.690021\pi\) | ||||
−0.562138 | + | 0.827043i | \(0.690021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24264 | + | 7.34847i | −0.454859 | + | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.12132 | − | 14.0665i | −0.860858 | − | 1.49105i | −0.871102 | − | 0.491103i | \(-0.836594\pi\) |
0.0102435 | − | 0.999948i | \(-0.496739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.10660 | + | 10.4539i | 0.849803 | + | 1.09586i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9706 | −1.62156 | −0.810782 | − | 0.585348i | \(-0.800958\pi\) | ||||
−0.810782 | + | 0.585348i | \(0.800958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24264 | −0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.36396 | − | 16.2189i | 0.931749 | − | 1.61384i | 0.151418 | − | 0.988470i | \(-0.451616\pi\) |
0.780331 | − | 0.625367i | \(-0.215051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.62132 | + | 8.00436i | 0.455352 | + | 0.788693i | 0.998708 | − | 0.0508091i | \(-0.0161800\pi\) |
−0.543356 | + | 0.839502i | \(0.682847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.36396 | − | 16.2189i | −0.905248 | − | 1.56794i | −0.820584 | − | 0.571527i | \(-0.806351\pi\) |
−0.0846647 | − | 0.996409i | \(-0.526982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.74264 | + | 16.8747i | −0.933176 | + | 1.61631i | −0.155321 | + | 0.987864i | \(0.549641\pi\) |
−0.777855 | + | 0.628444i | \(0.783692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | 0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.50000 | + | 4.33013i | 0.231125 | + | 0.400320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1213 | − | 1.52192i | 1.01949 | − | 0.139514i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.878680 | + | 1.52192i | −0.0792279 | + | 0.137227i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.24264 | −0.820152 | −0.410076 | − | 0.912051i | \(-0.634498\pi\) | ||||
−0.410076 | + | 0.912051i | \(0.634498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.24264 | + | 3.88437i | −0.197454 | + | 0.341999i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.24264 | + | 7.94282i | −0.281173 | + | 0.688729i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.24264 | − | 12.5446i | 0.618781 | − | 1.07176i | −0.370928 | − | 0.928662i | \(-0.620960\pi\) |
0.989709 | − | 0.143098i | \(-0.0457063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7279 | −1.16439 | −0.582194 | − | 0.813050i | \(-0.697805\pi\) | ||||
−0.582194 | + | 0.813050i | \(0.697805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.75736 | 0.147996 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.6066 | + | 18.3712i | −0.886969 | + | 1.53627i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | + | 4.89898i | 0.412393 | + | 0.404061i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.87868 | + | 11.9142i | 0.563523 | + | 0.976051i | 0.997185 | + | 0.0749755i | \(0.0238879\pi\) |
−0.433662 | + | 0.901076i | \(0.642779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.86396 | + | 10.1567i | −0.477202 | + | 0.826539i | −0.999659 | − | 0.0261273i | \(-0.991682\pi\) |
0.522456 | + | 0.852666i | \(0.325016\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24264 | 0.342997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.742641 | − | 1.28629i | 0.0592692 | − | 0.102657i | −0.834868 | − | 0.550450i | \(-0.814456\pi\) |
0.894138 | + | 0.447792i | \(0.147790\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.12132 | + | 3.67423i | 0.168232 | + | 0.291386i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 14.6969i | 0.472866 | − | 1.15828i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.37868 | − | 7.58410i | −0.342965 | − | 0.594032i | 0.642017 | − | 0.766690i | \(-0.278098\pi\) |
−0.984982 | + | 0.172658i | \(0.944764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.75736 | 0.135989 | 0.0679943 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679943 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.62132 | + | 2.80821i | −0.123985 | + | 0.214749i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.878680 | + | 1.52192i | 0.0660456 | + | 0.114394i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.75736 | + | 3.04384i | −0.131351 | + | 0.227507i | −0.924198 | − | 0.381914i | \(-0.875265\pi\) |
0.792846 | + | 0.609421i | \(0.208598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.48528 | 0.333388 | 0.166694 | − | 0.986009i | \(-0.446691\pi\) | ||||
0.166694 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | + | 15.5885i | 0.658145 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.62132 | + | 2.09077i | 0.117934 | + | 0.152081i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.12132 | − | 14.0665i | −0.587638 | − | 1.01782i | −0.994541 | − | 0.104348i | \(-0.966725\pi\) |
0.406903 | − | 0.913471i | \(-0.366609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.24264 | − | 3.88437i | 0.161429 | − | 0.279603i | −0.773953 | − | 0.633244i | \(-0.781723\pi\) |
0.935381 | + | 0.353641i | \(0.115056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | −0.604551 | −0.302276 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302276 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.62132 | − | 14.9326i | 0.611149 | − | 1.05854i | −0.379898 | − | 0.925028i | \(-0.624041\pi\) |
0.991047 | − | 0.133513i | \(-0.0426258\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.86396 | + | 11.8887i | 0.484146 | + | 0.838566i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.7574 | + | 17.7408i | 0.965577 | + | 1.24516i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.7574 | −0.951616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7574 | 0.878253 | 0.439126 | − | 0.898425i | \(-0.355288\pi\) | ||||
0.439126 | + | 0.898425i | \(0.355288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.24264 | − | 7.34847i | 0.290701 | − | 0.503509i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4853 | + | 1.43488i | −0.711787 | + | 0.0974059i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.74264 | − | 11.6786i | −0.455625 | − | 0.789166i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6066 | − | 18.3712i | 0.713477 | − | 1.23578i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.24264 | −0.618933 | −0.309466 | − | 0.950910i | \(-0.600150\pi\) | ||||
−0.309466 | + | 0.950910i | \(0.600150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.75736 | + | 3.04384i | −0.116640 | + | 0.202026i | −0.918434 | − | 0.395574i | \(-0.870546\pi\) |
0.801794 | + | 0.597600i | \(0.203879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.98528 | + | 5.17066i | 0.197273 | + | 0.341687i | 0.947643 | − | 0.319331i | \(-0.103458\pi\) |
−0.750370 | + | 0.661018i | \(0.770125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.24264 | + | 10.3923i | −0.279145 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.12132 | − | 8.87039i | −0.335509 | − | 0.581118i | 0.648074 | − | 0.761578i | \(-0.275575\pi\) |
−0.983582 | + | 0.180459i | \(0.942242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.757359 | −0.0491958 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.9706 | 1.87395 | 0.936975 | − | 0.349397i | \(-0.113613\pi\) | ||||
0.936975 | + | 0.349397i | \(0.113613\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9853 | + | 24.2232i | −0.900871 | + | 1.56035i | −0.0745056 | + | 0.997221i | \(0.523738\pi\) |
−0.826366 | + | 0.563134i | \(0.809595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.10660 | + | 14.0410i | 0.515811 | + | 0.893410i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.12132 | + | 8.87039i | −0.324550 | + | 0.562138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.75736 | −0.489640 | −0.244820 | − | 0.969569i | \(-0.578729\pi\) | ||||
−0.244820 | + | 0.969569i | \(0.578729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4558 | 1.60040 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.87868 | − | 11.9142i | −0.429080 | − | 0.743189i | 0.567712 | − | 0.823228i | \(-0.307829\pi\) |
−0.996792 | + | 0.0800388i | \(0.974496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 12.2474i | 0.310685 | − | 0.761019i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.24264 | + | 7.34847i | 0.262613 | + | 0.454859i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.48528 | + | 4.30463i | −0.153249 | + | 0.265435i | −0.932420 | − | 0.361376i | \(-0.882307\pi\) |
0.779171 | + | 0.626811i | \(0.215640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.2426 | −0.994033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.36396 | + | 5.82655i | −0.205104 | + | 0.355251i | −0.950166 | − | 0.311745i | \(-0.899087\pi\) |
0.745062 | + | 0.666996i | \(0.232420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.1066 | − | 1.79360i | 0.793248 | − | 0.108553i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7426 | − | 27.2671i | 0.945884 | − | 1.63832i | 0.191911 | − | 0.981412i | \(-0.438531\pi\) |
0.753972 | − | 0.656906i | \(-0.228135\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.7574 | −1.17863 | −0.589313 | − | 0.807905i | \(-0.700601\pi\) | ||||
−0.589313 | + | 0.807905i | \(0.700601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.62132 | + | 9.73641i | −0.334153 | + | 0.578770i | −0.983322 | − | 0.181875i | \(-0.941783\pi\) |
0.649169 | + | 0.760644i | \(0.275117\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.84924 | + | 3.67423i | 0.168185 | + | 0.216883i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.98528 | + | 13.8309i | −0.468105 | + | 0.810782i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.4853 | −1.19676 | −0.598381 | − | 0.801211i | \(-0.704189\pi\) | ||||
−0.598381 | + | 0.801211i | \(0.704189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.12132 | + | 3.67423i | −0.123091 | + | 0.213201i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0000 | − | 25.9808i | −0.867472 | − | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.27208 | + | 9.37769i | 0.419156 | + | 0.540521i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.36396 | − | 16.2189i | −0.537946 | − | 0.931749i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4853 | 0.712573 | 0.356286 | − | 0.934377i | \(-0.384043\pi\) | ||||
0.356286 | + | 0.934377i | \(0.384043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.24264 | 0.525795 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24264 | − | 2.15232i | 0.0704637 | − | 0.122047i | −0.828641 | − | 0.559781i | \(-0.810885\pi\) |
0.899105 | + | 0.437734i | \(0.144219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4853 | − | 28.5533i | −0.931803 | − | 1.61393i | −0.780238 | − | 0.625483i | \(-0.784902\pi\) |
−0.151566 | − | 0.988447i | \(-0.548431\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | + | 31.1769i | −1.00781 | + | 1.74557i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7279 | −1.04529 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.7574 | 0.765480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.74264 | + | 16.8747i | 0.538769 | + | 0.933176i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.75736 | − | 4.30463i | 0.0968864 | − | 0.237322i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.37868 | + | 7.58410i | 0.240674 | + | 0.416860i | 0.960906 | − | 0.276873i | \(-0.0892982\pi\) |
−0.720232 | + | 0.693733i | \(0.755965\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.50000 | − | 4.33013i | 0.136999 | − | 0.237289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.97056 | 0.488658 | 0.244329 | − | 0.969692i | \(-0.421432\pi\) | ||||
0.244329 | + | 0.969692i | \(0.421432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | − | 14.6969i | −0.459504 | − | 0.795884i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3640 | − | 26.6112i | 0.824781 | − | 1.42856i | −0.0773062 | − | 0.997007i | \(-0.524632\pi\) |
0.902087 | − | 0.431555i | \(-0.142035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.36396 | − | 5.82655i | 0.179046 | − | 0.310116i | −0.762508 | − | 0.646978i | \(-0.776032\pi\) |
0.941554 | + | 0.336862i | \(0.109366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.24264 | − | 10.3923i | 0.224544 | − | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.3640 | − | 26.6112i | −0.810879 | − | 1.40448i | −0.912250 | − | 0.409635i | \(-0.865656\pi\) |
0.101371 | − | 0.994849i | \(-0.467677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.24264 | − | 7.34847i | 0.223297 | − | 0.386762i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | − | 12.1244i | 0.365397 | − | 0.632886i | −0.623443 | − | 0.781869i | \(-0.714267\pi\) |
0.988840 | + | 0.148983i | \(0.0475999\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.878680 | + | 1.52192i | 0.0457422 | + | 0.0792279i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1213 | − | 1.52192i | 0.577390 | − | 0.0790140i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.74264 | − | 13.4106i | −0.400899 | − | 0.694377i | 0.592936 | − | 0.805250i | \(-0.297969\pi\) |
−0.993835 | + | 0.110873i | \(0.964635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.4264 | 2.18507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7279 | 0.602423 | 0.301211 | − | 0.953557i | \(-0.402609\pi\) | ||||
0.301211 | + | 0.953557i | \(0.402609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.62132 | + | 8.00436i | −0.236757 | + | 0.410076i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.72792 | + | 16.8493i | 0.497074 | + | 0.860957i | 0.999994 | − | 0.00337583i | \(-0.00107456\pi\) |
−0.502921 | + | 0.864333i | \(0.667741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.24264 | + | 3.88437i | 0.114000 | + | 0.197454i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.63604 | + | 4.56575i | −0.133652 | + | 0.231493i | −0.925082 | − | 0.379768i | \(-0.876004\pi\) |
0.791429 | + | 0.611261i | \(0.209337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.4558 | −1.28736 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | + | 17.3205i | 0.501886 | + | 0.869291i | 0.999998 | + | 0.00217869i | \(0.000693499\pi\) |
−0.498112 | + | 0.867113i | \(0.665973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.25736 | + | 6.77962i | 0.263197 | + | 0.339405i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.60660 | − | 13.1750i | −0.379856 | − | 0.657929i | 0.611185 | − | 0.791487i | \(-0.290693\pi\) |
−0.991041 | + | 0.133558i | \(0.957360\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2132 | 1.05150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.173064 | − | 0.299755i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.939490 | + | 0.342578i | \(0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.24264 | − | 12.5446i | −0.357253 | − | 0.618781i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.60660 | − | 0.630399i | 0.226676 | − | 0.0310199i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.86396 | + | 11.8887i | −0.336130 | + | 0.582194i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.7279 | 0.621800 | 0.310900 | − | 0.950443i | \(-0.399370\pi\) | ||||
0.310900 | + | 0.950443i | \(0.399370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.878680 | − | 1.52192i | 0.0427229 | − | 0.0739982i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | − | 2.44949i | 0.0483934 | − | 0.118539i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.6066 | + | 18.3712i | 0.512092 | + | 0.886969i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2426 | + | 22.9369i | −0.637876 | + | 1.10483i | 0.348023 | + | 0.937486i | \(0.386853\pi\) |
−0.985898 | + | 0.167347i | \(0.946480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.97056 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.72792 | − | 16.8493i | 0.465350 | − | 0.806009i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8640 | − | 30.9413i | −0.852600 | − | 1.47675i | −0.878853 | − | 0.477092i | \(-0.841691\pi\) |
0.0262531 | − | 0.999655i | \(-0.491642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.74264 | − | 1.88064i | 0.321078 | − | 0.0895542i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7279 | + | 27.2416i | 0.747256 | + | 1.29429i | 0.949133 | + | 0.314875i | \(0.101963\pi\) |
−0.201877 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.7574 | 0.650701 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.7279 | 1.73330 | 0.866649 | − | 0.498919i | \(-0.166269\pi\) | ||||
0.866649 | + | 0.498919i | \(0.166269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72792 | + | 6.45695i | −0.175541 | + | 0.304046i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.86396 | + | 10.1567i | 0.275513 | + | 0.477202i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.74264 | + | 6.48244i | 0.175073 | + | 0.303236i | 0.940187 | − | 0.340660i | \(-0.110650\pi\) |
−0.765113 | + | 0.643896i | \(0.777317\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.12132 | − | 3.67423i | 0.0990148 | − | 0.171499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4853 | −1.23354 | −0.616771 | − | 0.787142i | \(-0.711560\pi\) | ||||
−0.616771 | + | 0.787142i | \(0.711560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.75736 | 0.128145 | 0.0640727 | − | 0.997945i | \(-0.479591\pi\) | ||||
0.0640727 | + | 0.997945i | \(0.479591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.7279 | − | 27.2416i | −0.727801 | − | 1.26059i | −0.957810 | − | 0.287401i | \(-0.907209\pi\) |
0.230009 | − | 0.973188i | \(-0.426124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.9853 | − | 4.92447i | 1.66165 | − | 0.227391i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.742641 | − | 1.28629i | −0.0342191 | − | 0.0592692i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.51472 | + | 16.4800i | −0.437487 | + | 0.757750i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.24264 | 0.194257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6066 | − | 23.5673i | 0.621702 | − | 1.07682i | −0.367467 | − | 0.930036i | \(-0.619775\pi\) |
0.989169 | − | 0.146782i | \(-0.0468916\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5000 | − | 21.6506i | −0.569951 | − | 0.987184i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.72792 | − | 12.5446i | −0.442636 | − | 0.570800i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.75736 | − | 9.97204i | 0.260891 | − | 0.451876i | −0.705588 | − | 0.708622i | \(-0.749317\pi\) |
0.966479 | + | 0.256746i | \(0.0826504\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.75736 | −0.396021 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.5147 | 0.970946 | 0.485473 | − | 0.874252i | \(-0.338647\pi\) | ||||
0.485473 | + | 0.874252i | \(0.338647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | − | 31.1769i | 0.810679 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.7574 | − | 17.7408i | −0.617102 | − | 0.795782i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.62132 | + | 4.54026i | 0.117346 | + | 0.203250i | 0.918715 | − | 0.394921i | \(-0.129228\pi\) |
−0.801369 | + | 0.598170i | \(0.795895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.878680 | − | 1.52192i | 0.0392565 | − | 0.0679943i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4558 | 1.13502 | 0.567510 | − | 0.823367i | \(-0.307907\pi\) | ||||
0.567510 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.2426 | − | 38.5254i | −0.985888 | − | 1.70761i | −0.637923 | − | 0.770100i | \(-0.720206\pi\) |
−0.347964 | − | 0.937508i | \(-0.613127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.3492 | + | 4.83743i | −1.56376 | + | 0.213995i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.62132 | + | 2.80821i | 0.0715830 | + | 0.123985i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.45584 | 0.327908 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7279 | − | 37.6339i | 0.951918 | − | 1.64877i | 0.210648 | − | 0.977562i | \(-0.432443\pi\) |
0.741269 | − | 0.671208i | \(-0.234224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.75736 | − | 6.50794i | −0.164298 | − | 0.284572i | 0.772108 | − | 0.635492i | \(-0.219202\pi\) |
−0.936406 | + | 0.350919i | \(0.885869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.48528 | + | 14.6969i | 0.369625 | + | 0.640209i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.75736 | 0.0762629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.78680 | 0.380598 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.75736 | + | 3.04384i | 0.0758357 | + | 0.131351i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.2132 | + | 20.7846i | 0.913717 | + | 0.895257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.74264 | + | 13.4106i | 0.332882 | + | 0.576569i | 0.983076 | − | 0.183200i | \(-0.0586455\pi\) |
−0.650194 | + | 0.759769i | \(0.725312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.24264 | − | 3.88437i | 0.0962409 | − | 0.166694i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0000 | −1.11168 | −0.555840 | − | 0.831289i | \(-0.687603\pi\) | ||||
−0.555840 | + | 0.831289i | \(0.687603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.500000 | − | 0.866025i | 0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.7574 | + | 23.8284i | 0.586083 | + | 1.01513i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.757359 | + | 1.85514i | −0.0322062 | + | 0.0788887i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.2426 | − | 38.5254i | 0.942451 | − | 1.63237i | 0.181675 | − | 0.983359i | \(-0.441848\pi\) |
0.760776 | − | 0.649014i | \(-0.224818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.4264 | 0.948536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | 0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.1213 | − | 24.4588i | 0.595143 | − | 1.03082i | −0.398384 | − | 0.917219i | \(-0.630429\pi\) |
0.993527 | − | 0.113599i | \(-0.0362378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.62132 | − | 0.358719i | 0.110085 | − | 0.0150648i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.63604 | − | 4.56575i | −0.110509 | − | 0.191406i | 0.805467 | − | 0.592641i | \(-0.201915\pi\) |
−0.915975 | + | 0.401234i | \(0.868581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6213 | + | 39.1813i | −0.946673 | + | 1.63969i | −0.194306 | + | 0.980941i | \(0.562245\pi\) |
−0.752367 | + | 0.658744i | \(0.771088\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.2426 | −0.678546 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.48528 | + | 12.9649i | −0.311616 | + | 0.539735i | −0.978712 | − | 0.205236i | \(-0.934204\pi\) |
0.667096 | + | 0.744972i | \(0.267537\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.24264 | − | 3.88437i | −0.0932010 | − | 0.161429i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.6066 | + | 21.4150i | 0.688958 | + | 0.888444i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.9706 | −0.452804 | −0.226402 | − | 0.974034i | \(-0.572696\pi\) | ||||
−0.226402 | + | 0.974034i | \(0.572696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.9706 | −0.534443 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.24264 | + | 7.34847i | −0.174519 | + | 0.302276i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.4853 | − | 30.2854i | −0.718034 | − | 1.24367i | −0.961777 | − | 0.273832i | \(-0.911709\pi\) |
0.243743 | − | 0.969840i | \(-0.421625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.62132 | − | 14.9326i | −0.352847 | − | 0.611149i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8492 | + | 30.9158i | −0.729300 | + | 1.26319i | 0.227879 | + | 0.973689i | \(0.426821\pi\) |
−0.957179 | + | 0.289496i | \(0.906512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.48528 | 0.305331 | 0.152665 | − | 0.988278i | \(-0.451214\pi\) | ||||
0.152665 | + | 0.988278i | \(0.451214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7279 | 0.559044 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5919 | + | 37.3982i | 0.876388 | + | 1.51795i | 0.855277 | + | 0.518171i | \(0.173387\pi\) |
0.0211102 | + | 0.999777i | \(0.493280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.2426 | − | 3.04384i | 0.901317 | − | 0.123342i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.39340 | − | 7.60959i | −0.177738 | − | 0.307851i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.00000 | + | 13.8564i | −0.323117 | + | 0.559655i | −0.981129 | − | 0.193352i | \(-0.938064\pi\) |
0.658012 | + | 0.753007i | \(0.271397\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.4558 | 1.50792 | 0.753958 | − | 0.656923i | \(-0.228142\pi\) | ||||
0.753958 | + | 0.656923i | \(0.228142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.24264 | + | 14.2767i | −0.331300 | + | 0.573828i | −0.982767 | − | 0.184849i | \(-0.940820\pi\) |
0.651467 | + | 0.758677i | \(0.274154\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.2426 | + | 39.7862i | −0.650748 | + | 1.59400i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.87868 | + | 11.9142i | −0.274708 | + | 0.475808i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2132 | −0.845826 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.2132 | −0.645437 | −0.322719 | − | 0.946495i | \(-0.604597\pi\) | ||||
−0.322719 | + | 0.946495i | \(0.604597\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.37868 | − | 11.0482i | 0.253530 | − | 0.439126i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.71320 | − | 33.8981i | 0.345230 | − | 1.34309i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.24264 | − | 7.34847i | −0.167836 | − | 0.290701i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | + | 20.7846i | −0.473972 | + | 0.820943i | −0.999556 | − | 0.0297987i | \(-0.990513\pi\) |
0.525584 | + | 0.850741i | \(0.323847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.7279 | −0.935738 | −0.467869 | − | 0.883798i | \(-0.654978\pi\) | ||||
−0.467869 | + | 0.883798i | \(0.654978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.1213 | + | 34.8511i | −0.791051 | + | 1.37014i | 0.134266 | + | 0.990945i | \(0.457132\pi\) |
−0.925317 | + | 0.379195i | \(0.876201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.72792 | + | 6.45695i | 0.146334 | + | 0.253457i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | + | 9.79796i | −0.156772 | + | 0.384012i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.1213 | − | 19.2627i | −0.435211 | − | 0.753807i | 0.562102 | − | 0.827068i | \(-0.309993\pi\) |
−0.997313 | + | 0.0732606i | \(0.976660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.4853 | −0.526111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.2721 | 0.906551 | 0.453276 | − | 0.891370i | \(-0.350255\pi\) | ||||
0.453276 | + | 0.891370i | \(0.350255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0147186 | + | 0.0254934i | −0.000572488 | + | 0.000991579i | −0.866312 | − | 0.499504i | \(-0.833516\pi\) |
0.865739 | + | 0.500496i | \(0.166849\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.6066 | − | 18.3712i | −0.411926 | − | 0.713477i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.4558 | − | 44.0908i | −0.985654 | − | 1.70720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.62132 | + | 8.00436i | −0.178671 | + | 0.309466i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.24264 | 0.163785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4853 | 0.828197 | 0.414098 | − | 0.910232i | \(-0.364097\pi\) | ||||
0.414098 | + | 0.910232i | \(0.364097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.72792 | + | 16.8493i | 0.373874 | + | 0.647569i | 0.990158 | − | 0.139955i | \(-0.0446958\pi\) |
−0.616283 | + | 0.787524i | \(0.711362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.8934 | + | 33.3908i | 0.993697 | + | 1.28142i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.75736 | + | 3.04384i | 0.0673422 | + | 0.116640i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3640 | + | 21.4150i | −0.473094 | + | 0.819423i | −0.999526 | − | 0.0307948i | \(-0.990196\pi\) |
0.526432 | + | 0.850217i | \(0.323530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.97056 | 0.227791 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.6066 | − | 18.3712i | 0.404079 | − | 0.699886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3492 | + | 26.5857i | 0.583913 | + | 1.01137i | 0.995010 | + | 0.0997750i | \(0.0318123\pi\) |
−0.411097 | + | 0.911591i | \(0.634854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.87868 | + | 8.87039i | 0.261299 | + | 0.336958i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.72792 | − | 6.45695i | 0.141205 | − | 0.244574i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2426 | −0.387412 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7279 | −1.38719 | −0.693597 | − | 0.720363i | \(-0.743975\pi\) | ||||
−0.693597 | + | 0.720363i | \(0.743975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.10660 | − | 14.0410i | 0.305746 | − | 0.529568i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.0919 | + | 6.71807i | −1.84629 | + | 0.252659i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.74264 | + | 8.21449i | 0.178114 | + | 0.308502i | 0.941234 | − | 0.337754i | \(-0.109667\pi\) |
−0.763121 | + | 0.646256i | \(0.776334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.378680 | + | 0.655892i | −0.0142016 | + | 0.0245979i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.4853 | − | 25.0892i | 0.540963 | − | 0.936975i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.0919 | + | 22.6758i | 0.488245 | + | 0.845665i | 0.999909 | − | 0.0135209i | \(-0.00430397\pi\) |
−0.511664 | + | 0.859186i | \(0.670971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.24264 | − | 22.6398i | 0.344214 | − | 0.843148i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.9853 | + | 24.2232i | 0.520118 | + | 0.900871i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.2426 | 1.75213 | 0.876066 | − | 0.482191i | \(-0.160159\pi\) | ||||
0.876066 | + | 0.482191i | \(0.160159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.51472 | − | 16.4800i | 0.351915 | − | 0.609534i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.25736 | + | 7.37396i | 0.157249 | + | 0.272364i | 0.933876 | − | 0.357598i | \(-0.116404\pi\) |
−0.776627 | + | 0.629961i | \(0.783071\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.1213 | + | 50.4396i | 1.07270 | + | 1.85797i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.8345 | − | 36.0865i | 0.766410 | − | 1.32746i | −0.173087 | − | 0.984906i | \(-0.555374\pi\) |
0.939498 | − | 0.342555i | \(-0.111292\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.2132 | 0.595607 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.9706 | 0.842708 | 0.421354 | − | 0.906896i | \(-0.361555\pi\) | ||||
0.421354 | + | 0.906896i | \(0.361555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.12132 | + | 8.87039i | 0.187379 | + | 0.324550i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.7279 | + | 45.8739i | −0.684303 | + | 1.67619i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.86396 | + | 6.69258i | 0.140998 | + | 0.244216i | 0.927873 | − | 0.372897i | \(-0.121636\pi\) |
−0.786875 | + | 0.617113i | \(0.788302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.87868 | + | 6.71807i | −0.141347 | + | 0.244820i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.4558 | −1.32501 | −0.662505 | − | 0.749057i | \(-0.730507\pi\) | ||||
−0.662505 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7279 | − | 22.0454i | 0.461994 | − | 0.800198i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.8787 | − | 27.5027i | −0.575602 | − | 0.996971i | −0.995976 | − | 0.0896206i | \(-0.971435\pi\) |
0.420374 | − | 0.907351i | \(-0.361899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.0772 | − | 6.98975i | 1.84912 | − | 0.253046i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.39340 | − | 7.60959i | 0.158636 | − | 0.274766i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.4853 | −1.74842 | −0.874212 | − | 0.485544i | \(-0.838621\pi\) | ||||
−0.874212 | + | 0.485544i | \(0.838621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7574 | −0.495459 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.10660 | − | 10.4539i | −0.290823 | − | 0.375030i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.84924 | + | 4.93503i | 0.102085 | + | 0.176816i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.48528 | 0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.86396 | + | 6.69258i | −0.137735 | + | 0.238565i | −0.926639 | − | 0.375952i | \(-0.877316\pi\) |
0.788904 | + | 0.614517i | \(0.210649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.48528 | + | 4.30463i | 0.0884784 | + | 0.153249i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.72792 | − | 12.5446i | −0.345885 | − | 0.446035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | − | 4.33013i | −0.0887776 | − | 0.153767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.4264 | −1.29029 | −0.645145 | − | 0.764060i | \(-0.723203\pi\) | ||||
−0.645145 | + | 0.764060i | \(0.723203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.45584 | −0.263769 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.12132 | + | 14.0665i | −0.286953 | + | 0.497017i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.6066 | − | 49.5481i | −1.00951 | − | 1.74851i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.36396 | + | 5.82655i | 0.118417 | + | 0.205104i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.27208 | + | 3.93535i | −0.0798820 | + | 0.138360i | −0.903199 | − | 0.429222i | \(-0.858788\pi\) |
0.823317 | + | 0.567582i | \(0.192121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.2426 | 0.745930 | 0.372965 | − | 0.927845i | \(-0.378341\pi\) | ||||
0.372965 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.00000 | −0.0701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.27208 | + | 12.5956i | 0.254418 | + | 0.440665i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00000 | − | 12.2474i | 0.174714 | − | 0.427960i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.878680 | + | 1.52192i | 0.0306661 | + | 0.0531153i | 0.880951 | − | 0.473207i | \(-0.156904\pi\) |
−0.850285 | + | 0.526322i | \(0.823570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.3492 | + | 26.5857i | −0.535041 | + | 0.926718i | 0.464120 | + | 0.885772i | \(0.346370\pi\) |
−0.999161 | + | 0.0409460i | \(0.986963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.9411 | −0.762968 | −0.381484 | − | 0.924376i | \(-0.624587\pi\) | ||||
−0.381484 | + | 0.924376i | \(0.624587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7426 | − | 39.3914i | 0.789885 | − | 1.36812i | −0.136153 | − | 0.990688i | \(-0.543474\pi\) |
0.926037 | − | 0.377432i | \(-0.123193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.7426 | − | 27.2671i | −0.546106 | − | 0.945884i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.2132 | − | 20.7846i | −0.734994 | − | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | + | 3.46410i | −0.0691301 | + | 0.119737i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9706 | 1.62160 | 0.810802 | − | 0.585321i | \(-0.199031\pi\) | ||||
0.810802 | + | 0.585321i | \(0.199031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.87868 | + | 17.1104i | −0.340240 | + | 0.589313i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | + | 17.1464i | −0.240523 | + | 0.589158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.62132 | + | 9.73641i | 0.192923 | + | 0.334153i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.0000 | + | 25.9808i | −0.514193 | + | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.4853 | + | 19.8931i | −0.392330 | + | 0.679535i | −0.992756 | − | 0.120145i | \(-0.961664\pi\) |
0.600427 | + | 0.799680i | \(0.294997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.4558 | − | 40.6267i | −0.800303 | − | 1.38617i | −0.919417 | − | 0.393285i | \(-0.871339\pi\) |
0.119114 | − | 0.992881i | \(-0.461995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.60660 | − | 0.630399i | 0.156993 | − | 0.0214839i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.36396 | + | 16.2189i | 0.318753 | + | 0.552096i | 0.980228 | − | 0.197871i | \(-0.0634026\pi\) |
−0.661475 | + | 0.749967i | \(0.730069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.21320 | −0.109000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.3198 | − | 59.4436i | 1.16288 | − | 2.01417i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.98528 | + | 13.8309i | 0.270261 | + | 0.468105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9853 | − | 25.9553i | −0.506017 | − | 0.876447i | −0.999976 | − | 0.00696182i | \(-0.997784\pi\) |
0.493959 | − | 0.869485i | \(-0.335549\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.2426 | + | 17.7408i | −0.345476 | + | 0.598381i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4853 | 1.09446 | 0.547228 | − | 0.836983i | \(-0.315683\pi\) | ||||
0.547228 | + | 0.836983i | \(0.315683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.6985 | −1.57153 | −0.785765 | − | 0.618526i | \(-0.787730\pi\) | ||||
−0.785765 | + | 0.618526i | \(0.787730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.7574 | − | 18.6323i | −0.361197 | − | 0.625611i | 0.626961 | − | 0.779050i | \(-0.284298\pi\) |
−0.988158 | + | 0.153439i | \(0.950965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.9853 | + | 19.3242i | 0.502590 | + | 0.648114i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.12132 | + | 3.67423i | 0.0710669 | + | 0.123091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.84924 | − | 4.93503i | 0.0953463 | − | 0.165145i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.0000 | −1.00167 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9706 | + | 29.3939i | −0.566000 | + | 0.980341i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.7574 | − | 1.60896i | 0.391260 | − | 0.0535428i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.10660 | − | 7.11284i | 0.136357 | − | 0.236178i | −0.789758 | − | 0.613419i | \(-0.789794\pi\) |
0.926115 | + | 0.377241i | \(0.123127\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.7279 | −0.621166 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.7279 | + | 37.6339i | −0.719089 | + | 1.24550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | + | 14.6969i | −0.198137 | + | 0.485336i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.4853 | − | 42.4098i | −0.807695 | − | 1.39897i | −0.914457 | − | 0.404684i | \(-0.867382\pi\) |
0.106762 | − | 0.994285i | \(-0.465952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.24264 | − | 10.8126i | 0.205702 | − | 0.356286i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.4264 | −1.39648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.62132 | − | 8.00436i | 0.151784 | − | 0.262898i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.0919 | − | 27.8720i | −0.527958 | − | 0.914449i | −0.999469 | − | 0.0325893i | \(-0.989625\pi\) |
0.471511 | − | 0.881860i | \(-0.343709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.8640 | − | 6.09823i | 0.716562 | − | 0.199861i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.24264 | − | 2.15232i | −0.0406822 | − | 0.0704637i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.4558 | −0.700932 | −0.350466 | − | 0.936575i | \(-0.613977\pi\) | ||||
−0.350466 | + | 0.936575i | \(0.613977\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.9706 | −1.07595 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.4558 | + | 49.2870i | −0.927634 | + | 1.60671i | −0.140365 | + | 0.990100i | \(0.544828\pi\) |
−0.787269 | + | 0.616609i | \(0.788506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.27208 | − | 9.13151i | −0.171682 | − | 0.297363i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7279 | − | 27.2416i | −0.511089 | − | 0.885232i | −0.999917 | − | 0.0128519i | \(-0.995909\pi\) |
0.488829 | − | 0.872380i | \(-0.337424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.7132 | + | 58.3930i | −1.09438 | + | 1.89552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.2426 | −0.331792 | −0.165896 | − | 0.986143i | \(-0.553052\pi\) | ||||
−0.165896 | + | 0.986143i | \(0.553052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0000 | + | 31.1769i | 0.581857 | + | 1.00781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.9706 | + | 5.19615i | −1.22613 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.36396 | + | 16.2189i | −0.301749 | + | 0.522645i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.24264 | −0.297223 | −0.148612 | − | 0.988896i | \(-0.547480\pi\) | ||||
−0.148612 | + | 0.988896i | \(0.547480\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.87868 | − | 11.9142i | 0.220975 | − | 0.382740i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3640 | + | 42.1996i | 0.781877 | + | 1.35425i | 0.930847 | + | 0.365409i | \(0.119071\pi\) |
−0.148971 | + | 0.988842i | \(0.547596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.2574 | + | 28.7019i | 0.713538 | + | 0.920142i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.150758 | − | 0.261120i | 0.00482316 | − | 0.00835396i | −0.863604 | − | 0.504171i | \(-0.831798\pi\) |
0.868427 | + | 0.495817i | \(0.165131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.9117 | −2.20243 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.4853 | 0.622117 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.8787 | + | 22.3065i | −0.410766 | + | 0.711468i | −0.994974 | − | 0.100137i | \(-0.968072\pi\) |
0.584208 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.84924 | − | 3.67423i | −0.0906924 | − | 0.116952i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4558 | − | 23.3062i | −0.427871 | − | 0.741094i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.48528 | − | 12.9649i | 0.237778 | − | 0.411843i | −0.722299 | − | 0.691581i | \(-0.756914\pi\) |
0.960076 | + | 0.279738i | \(0.0902477\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.75736 | 0.277906 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2279 | + | 17.7153i | −0.323922 | + | 0.561049i | −0.981294 | − | 0.192518i | \(-0.938335\pi\) |
0.657372 | + | 0.753566i | \(0.271668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50000 | − | 4.33013i | −0.0790965 | − | 0.136999i |
(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 | 2100.2.q.j.1201.1 | yes | 4 | |
5.2 | odd | 4 | 2100.2.bc.g.949.2 | 8 | |||
5.3 | odd | 4 | 2100.2.bc.g.949.3 | 8 | |||
5.4 | even | 2 | 2100.2.q.f.1201.2 | ✓ | 4 | ||
7.2 | even | 3 | inner | 2100.2.q.j.1801.1 | yes | 4 | |
35.2 | odd | 12 | 2100.2.bc.g.1549.3 | 8 | |||
35.9 | even | 6 | 2100.2.q.f.1801.2 | yes | 4 | ||
35.23 | odd | 12 | 2100.2.bc.g.1549.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.f.1201.2 | ✓ | 4 | 5.4 | even | 2 | ||
2100.2.q.f.1801.2 | yes | 4 | 35.9 | even | 6 | ||
2100.2.q.j.1201.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2100.2.q.j.1801.1 | yes | 4 | 7.2 | even | 3 | inner | |
2100.2.bc.g.949.2 | 8 | 5.2 | odd | 4 | |||
2100.2.bc.g.949.3 | 8 | 5.3 | odd | 4 | |||
2100.2.bc.g.1549.2 | 8 | 35.23 | odd | 12 | |||
2100.2.bc.g.1549.3 | 8 | 35.2 | odd | 12 |