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 | 1201.2 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.j.1801.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(7\) | 2.62132 | + | 0.358719i | 0.990766 | + | 0.135583i | ||||
\(8\) | 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 | \(0.387568\pi\) |
−0.985520 | + | 0.169559i | \(0.945766\pi\) | |||||||
\(12\) | 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 | \(-0.661312\pi\) |
0.999859 | − | 0.0168199i | \(-0.00535420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.62132 | + | 4.54026i | 0.601372 | + | 1.04161i | 0.992614 | + | 0.121319i | \(0.0387124\pi\) |
−0.391241 | + | 0.920288i | \(0.627954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.62132 | − | 2.09077i | 0.353801 | − | 0.456243i | ||||
\(22\) | 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 | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 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 | ||||||||
\(41\) | −10.2426 | −1.59963 | −0.799816 | − | 0.600245i | \(-0.795070\pi\) | ||||
−0.799816 | + | 0.600245i | \(0.795070\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.4853 | 1.90399 | 0.951994 | − | 0.306117i | \(-0.0990300\pi\) | ||||
0.951994 | + | 0.306117i | \(0.0990300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.12132 | + | 8.87039i | 0.747021 | + | 1.29388i | 0.949244 | + | 0.314539i | \(0.101850\pi\) |
−0.202223 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | + | 1.88064i | 0.963234 | + | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.12132 | − | 3.67423i | −0.297044 | − | 0.514496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.12132 | − | 3.67423i | 0.291386 | − | 0.504695i | −0.682752 | − | 0.730650i | \(-0.739217\pi\) |
0.974138 | + | 0.225955i | \(0.0725503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.24264 | 0.694405 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.12132 | + | 8.87039i | −0.666739 | + | 1.15483i | 0.312072 | + | 0.950059i | \(0.398977\pi\) |
−0.978811 | + | 0.204767i | \(0.934356\pi\) | |||||||
\(60\) | 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 | ||||||||
\(67\) | 5.86396 | − | 10.1567i | 0.716397 | − | 1.24084i | −0.246021 | − | 0.969264i | \(-0.579123\pi\) |
0.962418 | − | 0.271571i | \(-0.0875433\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | −1.00702 | −0.503509 | − | 0.863990i | \(-0.667958\pi\) | ||||
−0.503509 | + | 0.863990i | \(0.667958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.74264 | + | 3.01834i | −0.203961 | + | 0.353270i | −0.949801 | − | 0.312854i | \(-0.898715\pi\) |
0.745840 | + | 0.666125i | \(0.232048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.87868 | + | 8.87039i | −0.783898 | + | 1.01087i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.62132 | − | 8.00436i | −0.519939 | − | 0.900561i | −0.999731 | − | 0.0231789i | \(-0.992621\pi\) |
0.479792 | − | 0.877382i | \(-0.340712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.75736 | −0.192895 | −0.0964476 | − | 0.995338i | \(-0.530748\pi\) | ||||
−0.0964476 | + | 0.995338i | \(0.530748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24264 | − | 7.34847i | 0.454859 | − | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.87868 | − | 6.71807i | −0.411139 | − | 0.712114i | 0.583875 | − | 0.811843i | \(-0.301536\pi\) |
−0.995015 | + | 0.0997293i | \(0.968202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.1066 | − | 1.79360i | −1.37395 | − | 0.188020i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.9706 | 1.82463 | 0.912317 | − | 0.409484i | \(-0.134291\pi\) | ||||
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.36396 | + | 5.82655i | −0.334727 | + | 0.579764i | −0.983432 | − | 0.181276i | \(-0.941977\pi\) |
0.648706 | + | 0.761039i | \(0.275311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.378680 | + | 0.655892i | 0.0373124 | + | 0.0646270i | 0.884079 | − | 0.467338i | \(-0.154787\pi\) |
−0.846766 | + | 0.531965i | \(0.821454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.36396 | + | 5.82655i | 0.325206 | + | 0.563274i | 0.981554 | − | 0.191185i | \(-0.0612329\pi\) |
−0.656348 | + | 0.754459i | \(0.727900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.25736 | + | 2.17781i | −0.120433 | + | 0.208596i | −0.919939 | − | 0.392063i | \(-0.871762\pi\) |
0.799505 | + | 0.600659i | \(0.205095\pi\) | |||||||
\(110\) | 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 | ||||||||
\(119\) | 6.87868 | − | 8.87039i | 0.630568 | − | 0.813147i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.12132 | + | 8.87039i | −0.461774 | + | 0.799816i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.757359 | −0.0672048 | −0.0336024 | − | 0.999435i | \(-0.510698\pi\) | ||||
−0.0336024 | + | 0.999435i | \(0.510698\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.24264 | − | 10.8126i | 0.549634 | − | 0.951994i | ||||
\(130\) | 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 | ||||||||
\(133\) | 5.24264 | + | 12.8418i | 0.454595 | + | 1.11352i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.24264 | + | 2.15232i | −0.106166 | + | 0.183885i | −0.914214 | − | 0.405232i | \(-0.867191\pi\) |
0.808048 | + | 0.589117i | \(0.200524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7279 | 0.994749 | 0.497375 | − | 0.867536i | \(-0.334297\pi\) | ||||
0.497375 | + | 0.867536i | \(0.334297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2426 | 0.862586 | ||||||||
\(142\) | 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 | ||||||||
\(149\) | 11.1213 | + | 19.2627i | 0.911094 | + | 1.57806i | 0.812521 | + | 0.582931i | \(0.198094\pi\) |
0.0985727 | + | 0.995130i | \(0.468572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.86396 | − | 11.8887i | 0.558581 | − | 0.967491i | −0.439034 | − | 0.898470i | \(-0.644679\pi\) |
0.997615 | − | 0.0690206i | \(-0.0219874\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24264 | −0.342997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.74264 | + | 13.4106i | −0.617930 | + | 1.07029i | 0.371933 | + | 0.928260i | \(0.378695\pi\) |
−0.989863 | + | 0.142027i | \(0.954638\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −8.62132 | − | 14.9326i | −0.675274 | − | 1.16961i | −0.976389 | − | 0.216021i | \(-0.930692\pi\) |
0.301115 | − | 0.953588i | \(-0.402641\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2426 | 0.792599 | 0.396300 | − | 0.918121i | \(-0.370294\pi\) | ||||
0.396300 | + | 0.918121i | \(0.370294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.62132 | − | 4.54026i | 0.200457 | − | 0.347202i | ||||
\(172\) | 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 | ||||||||
\(177\) | 5.12132 | + | 8.87039i | 0.384942 | + | 0.666739i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2426 | + | 17.7408i | −0.765571 | + | 1.32601i | 0.174373 | + | 0.984680i | \(0.444210\pi\) |
−0.939944 | + | 0.341328i | \(0.889123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4853 | −0.928024 | −0.464012 | − | 0.885829i | \(-0.653590\pi\) | ||||
−0.464012 | + | 0.885829i | \(0.653590\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | −2.62132 | − | 0.358719i | −0.190673 | − | 0.0260930i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.87868 | − | 6.71807i | −0.280651 | − | 0.486103i | 0.690894 | − | 0.722956i | \(-0.257217\pi\) |
−0.971545 | + | 0.236854i | \(0.923884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.24264 | + | 10.8126i | −0.449355 | + | 0.778306i | −0.998344 | − | 0.0575237i | \(-0.981680\pi\) |
0.548989 | + | 0.835830i | \(0.315013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528 | 0.604551 | 0.302276 | − | 0.953221i | \(-0.402254\pi\) | ||||
0.302276 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37868 | − | 7.58410i | 0.310396 | − | 0.537622i | −0.668052 | − | 0.744115i | \(-0.732872\pi\) |
0.978448 | + | 0.206492i | \(0.0662049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.86396 | − | 10.1567i | −0.413612 | − | 0.716397i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.2426 | + | 3.04384i | 1.56113 | + | 0.213635i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.2426 | −1.53856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.2426 | 1.46240 | 0.731202 | − | 0.682161i | \(-0.238960\pi\) | ||||
0.731202 | + | 0.682161i | \(0.238960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.24264 | + | 7.34847i | −0.290701 | + | 0.503509i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.48528 | − | 8.36308i | 0.440250 | − | 0.567723i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.74264 | + | 3.01834i | 0.117757 | + | 0.203961i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.6066 | + | 18.3712i | −0.713477 | + | 1.23578i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.757359 | −0.0507165 | −0.0253583 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253583 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2426 | + | 17.7408i | −0.679828 | + | 1.17750i | 0.295205 | + | 0.955434i | \(0.404612\pi\) |
−0.975032 | + | 0.222062i | \(0.928721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.9853 | − | 24.2232i | −0.924173 | − | 1.60072i | −0.792885 | − | 0.609371i | \(-0.791422\pi\) |
−0.131288 | − | 0.991344i | \(-0.541911\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.24264 | + | 10.3923i | 0.279145 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.878680 | − | 1.52192i | −0.0575642 | − | 0.0997042i | 0.835807 | − | 0.549023i | \(-0.185000\pi\) |
−0.893371 | + | 0.449319i | \(0.851667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.24264 | −0.600374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.97056 | −0.321519 | −0.160759 | − | 0.986994i | \(-0.551394\pi\) | ||||
−0.160759 | + | 0.986994i | \(0.551394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.98528 | − | 5.17066i | 0.192299 | − | 0.333071i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
0.946012 | + | 0.324132i | \(0.105072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1066 | − | 22.7013i | −0.833953 | − | 1.44445i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.878680 | + | 1.52192i | −0.0556841 | + | 0.0964476i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.2426 | −1.02523 | −0.512613 | − | 0.858620i | \(-0.671323\pi\) | ||||
−0.512613 | + | 0.858620i | \(0.671323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.4558 | −1.60040 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1213 | − | 19.2627i | −0.693729 | − | 1.20157i | −0.970607 | − | 0.240669i | \(-0.922633\pi\) |
0.276878 | − | 0.960905i | \(-0.410700\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 14.4853 | − | 25.0892i | 0.893201 | − | 1.54707i | 0.0571849 | − | 0.998364i | \(-0.481788\pi\) |
0.836016 | − | 0.548705i | \(-0.184879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.75736 | −0.474743 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.36396 | − | 16.2189i | 0.570931 | − | 0.988881i | −0.425540 | − | 0.904940i | \(-0.639916\pi\) |
0.996471 | − | 0.0839415i | \(-0.0267509\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −8.10660 | + | 10.4539i | −0.490634 | + | 0.632696i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.25736 | − | 12.5701i | 0.436052 | − | 0.755265i | −0.561328 | − | 0.827593i | \(-0.689710\pi\) |
0.997381 | + | 0.0723281i | \(0.0230429\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.2426 | −1.68481 | −0.842407 | − | 0.538841i | \(-0.818862\pi\) | ||||
−0.842407 | + | 0.538841i | \(0.818862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.37868 | + | 2.38794i | −0.0819540 | + | 0.141948i | −0.904089 | − | 0.427344i | \(-0.859449\pi\) |
0.822135 | + | 0.569292i | \(0.192783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.8492 | − | 3.67423i | −1.58486 | − | 0.216883i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.98528 | − | 15.5630i | 0.526727 | − | 0.912317i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.51472 | −0.205332 | −0.102666 | − | 0.994716i | \(-0.532737\pi\) | ||||
−0.102666 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 32.7279 | + | 4.47871i | 1.88641 | + | 0.258149i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.36396 | + | 5.82655i | 0.193255 | + | 0.334727i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.48528 | −0.255989 | −0.127994 | − | 0.991775i | \(-0.540854\pi\) | ||||
−0.127994 | + | 0.991775i | \(0.540854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.757359 | 0.0430847 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.24264 | + | 12.5446i | −0.410692 | + | 0.711340i | −0.994966 | − | 0.100217i | \(-0.968046\pi\) |
0.584273 | + | 0.811557i | \(0.301380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.485281 | + | 0.840532i | 0.0274297 | + | 0.0475097i | 0.879414 | − | 0.476057i | \(-0.157934\pi\) |
−0.851985 | + | 0.523567i | \(0.824601\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 6.72792 | 0.375516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.2426 | 1.23761 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.25736 | + | 2.17781i | 0.0695321 | + | 0.120433i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.2426 | + | 25.0892i | 0.564695 | + | 1.38321i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.62132 | + | 14.9326i | 0.473871 | + | 0.820768i | 0.999552 | − | 0.0299132i | \(-0.00952310\pi\) |
−0.525682 | + | 0.850681i | \(0.676190\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.50000 | − | 4.33013i | 0.136999 | − | 0.237289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.9706 | −1.36023 | −0.680117 | − | 0.733104i | \(-0.738071\pi\) | ||||
−0.680117 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | 2.63604 | − | 4.56575i | 0.141510 | − | 0.245102i | −0.786555 | − | 0.617520i | \(-0.788138\pi\) |
0.928065 | + | 0.372417i | \(0.121471\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −9.36396 | + | 16.2189i | −0.498393 | + | 0.863243i | −0.999998 | − | 0.00185420i | \(-0.999410\pi\) |
0.501605 | + | 0.865097i | \(0.332743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.24264 | − | 10.3923i | −0.224544 | − | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.63604 | − | 4.56575i | −0.139125 | − | 0.240971i | 0.788041 | − | 0.615623i | \(-0.211096\pi\) |
−0.927166 | + | 0.374652i | \(0.877762\pi\) | |||||||
\(360\) | 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 | ||||||||
\(369\) | 5.12132 | + | 8.87039i | 0.266605 | + | 0.461774i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.87868 | − | 8.87039i | 0.357123 | − | 0.460528i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.742641 | + | 1.28629i | 0.0384525 | + | 0.0666016i | 0.884611 | − | 0.466329i | \(-0.154424\pi\) |
−0.846159 | + | 0.532931i | \(0.821091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.4264 | −2.18507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.7279 | −0.705156 | −0.352578 | − | 0.935782i | \(-0.614695\pi\) | ||||
−0.352578 | + | 0.935782i | \(0.614695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.378680 | + | 0.655892i | −0.0194003 | + | 0.0336024i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.7279 | − | 27.2416i | −0.803659 | − | 1.39198i | −0.917192 | − | 0.398444i | \(-0.869550\pi\) |
0.113533 | − | 0.993534i | \(-0.463783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.24264 | − | 10.8126i | −0.317331 | − | 0.549634i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.3640 | + | 26.6112i | −0.778984 | + | 1.34924i | 0.153544 | + | 0.988142i | \(0.450931\pi\) |
−0.932528 | + | 0.361098i | \(0.882402\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | 13.7426 | + | 1.88064i | 0.687993 | + | 0.0941496i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6066 | + | 23.5673i | 0.679481 | + | 1.17690i | 0.975137 | + | 0.221602i | \(0.0711284\pi\) |
−0.295656 | + | 0.955294i | \(0.595538\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 1.24264 | + | 2.15232i | 0.0612949 | + | 0.106166i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.6066 | + | 21.4150i | −0.817157 | + | 1.05376i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.86396 | − | 10.1567i | 0.287159 | − | 0.497375i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7279 | −0.621800 | −0.310900 | − | 0.950443i | \(-0.600630\pi\) | ||||
−0.310900 | + | 0.950443i | \(0.600630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.12132 | − | 8.87039i | 0.249007 | − | 0.431293i | ||||
\(424\) | 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 | ||||||||
\(431\) | −4.75736 | + | 8.23999i | −0.229154 | + | 0.396906i | −0.957558 | − | 0.288242i | \(-0.906929\pi\) |
0.728404 | + | 0.685148i | \(0.240263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.9706 | −1.20001 | −0.600004 | − | 0.799997i | \(-0.704834\pi\) | ||||
−0.600004 | + | 0.799997i | \(0.704834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.7279 | + | 27.2416i | −0.752369 | + | 1.30314i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.13604 | − | 8.89588i | −0.245130 | − | 0.424577i | 0.717038 | − | 0.697034i | \(-0.245497\pi\) |
−0.962168 | + | 0.272457i | \(0.912164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.74264 | − | 6.77962i | −0.0829829 | − | 0.322839i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.72792 | − | 16.8493i | −0.462188 | − | 0.800532i | 0.536882 | − | 0.843657i | \(-0.319602\pi\) |
−0.999070 | + | 0.0431250i | \(0.986269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.2426 | 1.05204 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2721 | 0.531962 | 0.265981 | − | 0.963978i | \(-0.414304\pi\) | ||||
0.265981 | + | 0.963978i | \(0.414304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.7279 | − | 37.6339i | 1.02313 | − | 1.77211i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.86396 | − | 11.8887i | −0.322497 | − | 0.558581i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.74264 | − | 8.21449i | −0.221851 | − | 0.384258i | 0.733519 | − | 0.679669i | \(-0.237877\pi\) |
−0.955370 | + | 0.295411i | \(0.904543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.12132 | + | 3.67423i | −0.0990148 | + | 0.171499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.51472 | −0.443145 | −0.221572 | − | 0.975144i | \(-0.571119\pi\) | ||||
−0.221572 | + | 0.975144i | \(0.571119\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2426 | 0.522490 | 0.261245 | − | 0.965273i | \(-0.415867\pi\) | ||||
0.261245 | + | 0.965273i | \(0.415867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.72792 | + | 16.8493i | 0.450155 | + | 0.779691i | 0.998395 | − | 0.0566301i | \(-0.0180356\pi\) |
−0.548241 | + | 0.836321i | \(0.684702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0147 | − | 24.5204i | 0.878018 | − | 1.13225i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.74264 | + | 13.4106i | 0.356762 | + | 0.617930i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.4853 | + | 45.8739i | −1.21779 | + | 2.10928i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24264 | −0.194257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.60660 | + | 13.1750i | −0.347555 | + | 0.601982i | −0.985814 | − | 0.167839i | \(-0.946321\pi\) |
0.638260 | + | 0.769821i | \(0.279655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5000 | − | 21.6506i | −0.569951 | − | 0.987184i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.7279 | + | 2.15232i | 0.715645 | + | 0.0979338i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.2426 | − | 24.6690i | 0.645396 | − | 1.11786i | −0.338814 | − | 0.940853i | \(-0.610026\pi\) |
0.984210 | − | 0.177005i | \(-0.0566408\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2426 | −0.779739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4853 | 1.73682 | 0.868408 | − | 0.495850i | \(-0.165143\pi\) | ||||
0.868408 | + | 0.495850i | \(0.165143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | − | 31.1769i | 0.810679 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.2426 | − | 3.04384i | −0.997719 | − | 0.136535i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.62132 | − | 2.80821i | −0.0725803 | − | 0.125713i | 0.827451 | − | 0.561538i | \(-0.189790\pi\) |
−0.900031 | + | 0.435825i | \(0.856457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.12132 | − | 8.87039i | 0.228804 | − | 0.396300i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | −1.13502 | −0.567510 | − | 0.823367i | \(-0.692093\pi\) | ||||
−0.567510 | + | 0.823367i | \(0.692093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.7574 | − | 23.8284i | −0.609784 | − | 1.05618i | −0.991276 | − | 0.131805i | \(-0.957923\pi\) |
0.381491 | − | 0.924372i | \(-0.375411\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.65076 | + | 7.28692i | −0.249975 | + | 0.322354i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.62132 | − | 4.54026i | −0.115734 | − | 0.200457i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.4558 | −1.91119 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.72792 | + | 6.45695i | −0.163323 | + | 0.282884i | −0.936059 | − | 0.351844i | \(-0.885555\pi\) |
0.772735 | + | 0.634728i | \(0.218888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2426 | − | 21.2049i | −0.535333 | − | 0.927224i | −0.999147 | − | 0.0412918i | \(-0.986853\pi\) |
0.463814 | − | 0.885933i | \(-0.346481\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 10.2426 | 0.444493 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.2132 | 2.21829 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.2426 | + | 17.7408i | 0.442003 | + | 0.765571i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.2132 | + | 20.7846i | −0.913717 | + | 0.895257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.742641 | − | 1.28629i | −0.0319286 | − | 0.0553020i | 0.849620 | − | 0.527396i | \(-0.176832\pi\) |
−0.881548 | + | 0.472094i | \(0.843498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.24264 | + | 10.8126i | −0.267897 | + | 0.464012i | ||||
\(544\) | 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 | ||||||||
\(551\) | 22.2426 | + | 38.5254i | 0.947568 | + | 1.64124i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.24264 | − | 22.6398i | −0.393037 | − | 0.962740i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7574 | − | 23.8284i | 0.582918 | − | 1.00964i | −0.412213 | − | 0.911087i | \(-0.635244\pi\) |
0.995131 | − | 0.0985563i | \(-0.0314225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.4264 | −2.64036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | 0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.87868 | − | 17.1104i | 0.416337 | − | 0.721116i | −0.579231 | − | 0.815163i | \(-0.696647\pi\) |
0.995568 | + | 0.0940471i | \(0.0299804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.62132 | + | 2.09077i | −0.0680891 | + | 0.0878041i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.3640 | − | 26.6112i | −0.644091 | − | 1.11560i | −0.984511 | − | 0.175324i | \(-0.943903\pi\) |
0.340420 | − | 0.940273i | \(-0.389431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3787 | + | 31.8328i | −0.769124 | + | 1.33216i | 0.168915 | + | 0.985631i | \(0.445974\pi\) |
−0.938039 | + | 0.346531i | \(0.887360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.75736 | −0.324068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.48528 | − | 16.4290i | 0.394877 | − | 0.683948i | −0.598208 | − | 0.801341i | \(-0.704120\pi\) |
0.993086 | + | 0.117393i | \(0.0374537\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.24264 | + | 10.8126i | 0.259435 | + | 0.449355i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.60660 | − | 0.630399i | −0.191114 | − | 0.0261534i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9706 | 0.948097 | 0.474048 | − | 0.880499i | \(-0.342792\pi\) | ||||
0.474048 | + | 0.880499i | \(0.342792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.9706 | 0.864077 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.24264 | − | 7.34847i | 0.174519 | − | 0.302276i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.514719 | − | 0.891519i | −0.0211370 | − | 0.0366103i | 0.855263 | − | 0.518193i | \(-0.173395\pi\) |
−0.876400 | + | 0.481583i | \(0.840062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.37868 | − | 7.58410i | −0.179207 | − | 0.310396i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8492 | − | 20.5235i | 0.484147 | − | 0.838567i | −0.515687 | − | 0.856777i | \(-0.672463\pi\) |
0.999834 | + | 0.0182098i | \(0.00579669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.48528 | −0.386913 | −0.193456 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7279 | −0.477598 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5919 | − | 28.7380i | −0.673444 | − | 1.16644i | −0.976921 | − | 0.213600i | \(-0.931481\pi\) |
0.303477 | − | 0.952839i | \(-0.401852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.7574 | − | 17.7408i | 0.557476 | − | 0.718892i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.6066 | − | 44.3519i | −1.03593 | − | 1.79429i | ||||
\(612\) | 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 | ||||||||
\(617\) | −13.4558 | −0.541712 | −0.270856 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270856 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.242641 | − | 0.420266i | 0.00975255 | − | 0.0168919i | −0.861108 | − | 0.508422i | \(-0.830229\pi\) |
0.870860 | + | 0.491530i | \(0.163562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.75736 | − | 19.0016i | −0.310792 | − | 0.761282i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.1213 | + | 19.2627i | −0.444143 | + | 0.769278i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.2132 | 0.845826 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2132 | 1.04353 | 0.521766 | − | 0.853089i | \(-0.325274\pi\) | ||||
0.521766 | + | 0.853089i | \(0.325274\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.6213 | − | 18.3967i | 0.422160 | − | 0.731202i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.7132 | − | 9.40319i | −1.33577 | − | 0.372568i | ||||
\(638\) | 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 | ||||||||
\(643\) | 1.72792 | 0.0681426 | 0.0340713 | − | 0.999419i | \(-0.489153\pi\) | ||||
0.0340713 | + | 0.999419i | \(0.489153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.8787 | + | 27.5027i | −0.624255 | + | 1.08124i | 0.364429 | + | 0.931231i | \(0.381264\pi\) |
−0.988684 | + | 0.150011i | \(0.952069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.7279 | − | 37.6339i | −0.852896 | − | 1.47726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | − | 9.79796i | −0.156772 | − | 0.384012i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.87868 | − | 11.9142i | −0.269184 | − | 0.466240i | 0.699468 | − | 0.714664i | \(-0.253420\pi\) |
−0.968651 | + | 0.248425i | \(0.920087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.48528 | 0.135974 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.7279 | 1.89817 | 0.949085 | − | 0.315020i | \(-0.102011\pi\) | ||||
0.949085 | + | 0.315020i | \(0.102011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9853 | + | 29.4194i | −0.660651 | + | 1.14428i | 0.319794 | + | 0.947487i | \(0.396386\pi\) |
−0.980445 | + | 0.196794i | \(0.936947\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | −0.378680 | + | 0.655892i | −0.0146406 | + | 0.0253583i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.24264 | −0.163785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.51472 | 0.174030 | 0.0870148 | − | 0.996207i | \(-0.472267\pi\) | ||||
0.0870148 | + | 0.996207i | \(0.472267\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.7279 | − | 27.2416i | −0.604473 | − | 1.04698i | −0.992135 | − | 0.125176i | \(-0.960050\pi\) |
0.387661 | − | 0.921802i | \(-0.373283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.1066 | + | 6.44639i | 1.80779 | + | 0.247390i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.2426 | + | 17.7408i | 0.392499 | + | 0.679828i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.363961 | − | 0.630399i | 0.0139266 | − | 0.0241215i | −0.858978 | − | 0.512012i | \(-0.828900\pi\) |
0.872905 | + | 0.487891i | \(0.162234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.9706 | −1.06714 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.6066 | + | 18.3712i | −0.404079 | + | 0.699886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3492 | − | 24.8536i | −0.545871 | − | 0.945476i | −0.998552 | − | 0.0538034i | \(-0.982866\pi\) |
0.452681 | − | 0.891673i | \(-0.350468\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.1213 | + | 1.52192i | 0.422464 | + | 0.0578129i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.7279 | + | 37.6339i | −0.823004 | + | 1.42548i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.75736 | −0.0664694 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.2721 | −0.425741 | −0.212870 | − | 0.977080i | \(-0.568281\pi\) | ||||
−0.212870 | + | 0.977080i | \(0.568281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.1066 | + | 22.7013i | −0.494325 | + | 0.856196i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9081 | + | 14.0665i | −0.410242 | + | 0.529027i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.74264 | − | 6.48244i | −0.140558 | − | 0.243453i | 0.787149 | − | 0.616763i | \(-0.211556\pi\) |
−0.927707 | + | 0.373310i | \(0.878223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.62132 | + | 8.00436i | −0.173313 | + | 0.300187i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.48528 | + | 4.30463i | −0.0928145 | + | 0.160759i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.0919 | − | 43.4604i | −0.935769 | − | 1.62080i | −0.773256 | − | 0.634094i | \(-0.781373\pi\) |
−0.162513 | − | 0.986706i | \(-0.551960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.757359 | + | 1.85514i | 0.0282055 | + | 0.0690892i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.98528 | − | 5.17066i | −0.111024 | − | 0.192299i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.7574 | 1.43743 | 0.718715 | − | 0.695304i | \(-0.244730\pi\) | ||||
0.718715 | + | 0.695304i | \(0.244730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.4853 | − | 45.8739i | 0.979594 | − | 1.69671i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7426 | + | 22.0709i | 0.470660 | + | 0.815207i | 0.999437 | − | 0.0335536i | \(-0.0106825\pi\) |
−0.528777 | + | 0.848761i | \(0.677349\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.8787 | + | 43.0911i | 0.916418 | + | 1.58728i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8345 | + | 44.7467i | −0.950338 | + | 1.64603i | −0.205646 | + | 0.978626i | \(0.565929\pi\) |
−0.744692 | + | 0.667408i | \(0.767404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.2132 | −0.962966 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.9706 | −0.402471 | −0.201235 | − | 0.979543i | \(-0.564496\pi\) | ||||
−0.201235 | + | 0.979543i | \(0.564496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.878680 | + | 1.52192i | 0.0321492 | + | 0.0556841i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.72792 | + | 16.4800i | 0.245833 | + | 0.602165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.86396 | − | 15.3528i | −0.323451 | − | 0.560233i | 0.657747 | − | 0.753239i | \(-0.271510\pi\) |
−0.981198 | + | 0.193006i | \(0.938176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.12132 | + | 14.0665i | −0.295957 | + | 0.512613i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4558 | 0.525407 | 0.262703 | − | 0.964877i | \(-0.415386\pi\) | ||||
0.262703 | + | 0.964877i | \(0.415386\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.7279 | + | 22.0454i | −0.461994 | + | 0.800198i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1213 | − | 34.8511i | −0.729397 | − | 1.26335i | −0.957138 | − | 0.289631i | \(-0.906467\pi\) |
0.227741 | − | 0.973722i | \(-0.426866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.07716 | + | 5.25770i | −0.147603 | + | 0.190341i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.6066 | − | 44.3519i | 0.924601 | − | 1.60146i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5147 | −1.13645 | −0.568225 | − | 0.822873i | \(-0.692370\pi\) | ||||
−0.568225 | + | 0.822873i | \(0.692370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.2426 | −0.801049 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 13.1066 | + | 1.79360i | 0.470197 | + | 0.0643449i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.8492 | − | 46.5043i | −0.961974 | − | 1.66619i | ||||
\(780\) | 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 | ||||||||
\(787\) | 8.86396 | − | 15.3528i | 0.315966 | − | 0.547269i | −0.663676 | − | 0.748020i | \(-0.731005\pi\) |
0.979642 | + | 0.200751i | \(0.0643381\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.4853 | − | 25.0892i | −0.515690 | − | 0.893201i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.7279 | + | 2.15232i | 0.559221 | + | 0.0765276i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.50000 | − | 4.33013i | −0.0887776 | − | 0.153767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.4264 | 1.71535 | 0.857676 | − | 0.514191i | \(-0.171908\pi\) | ||||
0.857676 | + | 0.514191i | \(0.171908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.4558 | 1.53736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.87868 | + | 6.71807i | −0.137046 | + | 0.237371i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.39340 | − | 12.8057i | −0.260907 | − | 0.451905i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.36396 | − | 16.2189i | −0.329627 | − | 0.570931i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.7279 | + | 48.0262i | −0.974862 | + | 1.68851i | −0.294472 | + | 0.955660i | \(0.595144\pi\) |
−0.680390 | + | 0.732850i | \(0.738190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.7574 | 0.447971 | 0.223986 | − | 0.974592i | \(-0.428093\pi\) | ||||
0.223986 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.00000 | −0.0701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.7279 | + | 56.6864i | 1.14501 | + | 1.98321i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00000 | + | 12.2474i | 0.174714 | + | 0.427960i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.12132 | + | 8.87039i | 0.178735 | + | 0.309579i | 0.941448 | − | 0.337159i | \(-0.109466\pi\) |
−0.762712 | + | 0.646738i | \(0.776133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.3492 | − | 24.8536i | 0.500183 | − | 0.866343i | −0.499817 | − | 0.866131i | \(-0.666599\pi\) |
1.00000 | 0.000211493i | \(-6.73203e-5\pi\) | ||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.9411 | 1.59753 | 0.798765 | − | 0.601644i | \(-0.205487\pi\) | ||||
0.798765 | + | 0.601644i | \(0.205487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.2574 | − | 24.6945i | 0.495179 | − | 0.857674i | −0.504806 | − | 0.863233i | \(-0.668436\pi\) |
0.999985 | + | 0.00555840i | \(0.00176930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.25736 | − | 12.5701i | −0.251755 | − | 0.436052i | ||||
\(832\) | 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 | ||||||||
\(839\) | 13.0294 | 0.449826 | 0.224913 | − | 0.974379i | \(-0.427790\pi\) | ||||
0.224913 | + | 0.974379i | \(0.427790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.1213 | + | 24.4588i | −0.486364 | + | 0.842407i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | − | 17.1464i | −0.240523 | − | 0.589158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37868 | + | 2.38794i | 0.0473162 | + | 0.0819540i | ||||
\(850\) | 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 | ||||||||
\(857\) | 5.48528 | − | 9.50079i | 0.187374 | − | 0.324541i | −0.757000 | − | 0.653415i | \(-0.773336\pi\) |
0.944374 | + | 0.328874i | \(0.106669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.4558 | + | 47.5549i | 0.936781 | + | 1.62255i | 0.771426 | + | 0.636319i | \(0.219544\pi\) |
0.165355 | + | 0.986234i | \(0.447123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.6066 | + | 21.4150i | −0.565951 | + | 0.729822i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.36396 | − | 5.82655i | −0.114511 | − | 0.198338i | 0.803073 | − | 0.595880i | \(-0.203197\pi\) |
−0.917584 | + | 0.397542i | \(0.869863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.2132 | 1.33022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.3198 | + | 50.7834i | −0.993464 | + | 1.72073i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.98528 | − | 15.5630i | −0.304106 | − | 0.526727i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.98528 | + | 3.43861i | 0.0670382 | + | 0.116114i | 0.897596 | − | 0.440818i | \(-0.145312\pi\) |
−0.830558 | + | 0.556932i | \(0.811978\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.75736 | + | 3.04384i | −0.0592743 | + | 0.102666i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.5147 | 0.522704 | 0.261352 | − | 0.965244i | \(-0.415832\pi\) | ||||
0.261352 | + | 0.965244i | \(0.415832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.6985 | 0.427338 | 0.213669 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213669 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.2426 | − | 33.3292i | −0.646105 | − | 1.11909i | −0.984045 | − | 0.177919i | \(-0.943064\pi\) |
0.337941 | − | 0.941167i | \(-0.390270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.98528 | − | 0.271680i | −0.0665842 | − | 0.00911184i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12132 | − | 3.67423i | −0.0710669 | − | 0.123091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.8492 | + | 46.5043i | −0.898476 | + | 1.55621i | ||||
\(894\) | 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 | ||||||||
\(903\) | 20.2426 | − | 26.1039i | 0.673633 | − | 0.868682i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1066 | + | 29.6295i | −0.568015 | + | 0.983832i | 0.428747 | + | 0.903425i | \(0.358955\pi\) |
−0.996762 | + | 0.0804068i | \(0.974378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.72792 | 0.223151 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.72792 | − | 6.45695i | 0.123376 | − | 0.213694i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | − | 14.6969i | −0.198137 | − | 0.485336i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.51472 | − | 13.0159i | −0.247888 | − | 0.429354i | 0.715052 | − | 0.699071i | \(-0.246403\pi\) |
−0.962940 | + | 0.269717i | \(0.913070\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.24264 | + | 3.88437i | −0.0738975 | + | 0.127994i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.4264 | 1.39648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.378680 | − | 0.655892i | 0.0124375 | − | 0.0215423i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.0919 | + | 38.2643i | 0.724811 | + | 1.25541i | 0.959052 | + | 0.283231i | \(0.0914063\pi\) |
−0.234241 | + | 0.972179i | \(0.575260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.13604 | + | 35.5431i | 0.299422 | + | 1.16488i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.24264 | + | 12.5446i | 0.237113 | + | 0.410692i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4558 | 0.962280 | 0.481140 | − | 0.876644i | \(-0.340223\pi\) | ||||
0.481140 | + | 0.876644i | \(0.340223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.970563 | 0.0316731 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.4558 | − | 38.8947i | 0.732040 | − | 1.26793i | −0.223970 | − | 0.974596i | \(-0.571902\pi\) |
0.956010 | − | 0.293334i | \(-0.0947647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.7279 | − | 53.2223i | −1.00064 | − | 1.73316i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.72792 | + | 16.8493i | 0.316115 | + | 0.547527i | 0.979674 | − | 0.200597i | \(-0.0642881\pi\) |
−0.663559 | + | 0.748124i | \(0.730955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.71320 | − | 15.0917i | 0.282843 | − | 0.489898i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.75736 | −0.0569265 | −0.0284632 | − | 0.999595i | \(-0.509061\pi\) | ||||
−0.0284632 | + | 0.999595i | \(0.509061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0000 | + | 31.1769i | 0.581857 | + | 1.00781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.02944 | + | 5.19615i | −0.130117 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.36396 | − | 5.82655i | 0.108402 | − | 0.187758i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.757359 | −0.0243550 | −0.0121775 | − | 0.999926i | \(-0.503876\pi\) | ||||
−0.0121775 | + | 0.999926i | \(0.503876\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.1213 | − | 19.2627i | 0.357268 | − | 0.618807i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.6360 | + | 20.1542i | 0.373418 | + | 0.646779i | 0.990089 | − | 0.140442i | \(-0.0448523\pi\) |
−0.616671 | + | 0.787221i | \(0.711519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.7426 | + | 4.20703i | 0.985564 | + | 0.134871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.8492 | − | 51.7004i | 0.954962 | − | 1.65404i | 0.220506 | − | 0.975386i | \(-0.429229\pi\) |
0.734455 | − | 0.678657i | \(-0.237438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.9117 | 1.05186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.51472 | 0.0802888 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1213 | + | 29.6550i | −0.546085 | + | 0.945848i | 0.452452 | + | 0.891789i | \(0.350549\pi\) |
−0.998538 | + | 0.0540590i | \(0.982784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.8492 | + | 3.67423i | 0.854621 | + | 0.116952i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.4558 | + | 64.8754i | 1.19103 | + | 2.06292i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.48528 | + | 16.4290i | −0.301310 | + | 0.521884i | −0.976433 | − | 0.215821i | \(-0.930757\pi\) |
0.675123 | + | 0.737705i | \(0.264091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2426 | 0.547179 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.2279 | − | 26.3755i | 0.482273 | − | 0.835322i | −0.517520 | − | 0.855671i | \(-0.673145\pi\) |
0.999793 | + | 0.0203497i | \(0.00647795\pi\) | |||||||
\(998\) | 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.1201.2 | yes | 4 | |
5.2 | odd | 4 | 2100.2.bc.g.949.1 | 8 | |||
5.3 | odd | 4 | 2100.2.bc.g.949.4 | 8 | |||
5.4 | even | 2 | 2100.2.q.f.1201.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 2100.2.q.j.1801.2 | yes | 4 | |
35.2 | odd | 12 | 2100.2.bc.g.1549.4 | 8 | |||
35.9 | even | 6 | 2100.2.q.f.1801.1 | yes | 4 | ||
35.23 | odd | 12 | 2100.2.bc.g.1549.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.q.f.1201.1 | ✓ | 4 | 5.4 | even | 2 | ||
2100.2.q.f.1801.1 | yes | 4 | 35.9 | even | 6 | ||
2100.2.q.j.1201.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2100.2.q.j.1801.2 | yes | 4 | 7.2 | even | 3 | inner | |
2100.2.bc.g.949.1 | 8 | 5.2 | odd | 4 | |||
2100.2.bc.g.949.4 | 8 | 5.3 | odd | 4 | |||
2100.2.bc.g.1549.1 | 8 | 35.23 | odd | 12 | |||
2100.2.bc.g.1549.4 | 8 | 35.2 | odd | 12 |