Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(121,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("370.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.e (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 10x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(-1.58114 - 2.73861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.121 |
Dual form | 370.2.e.e.211.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.58114 | − | 4.47066i | −0.975579 | − | 1.68975i | −0.678012 | − | 0.735051i | \(-0.737158\pi\) |
−0.297567 | − | 0.954701i | \(-0.596175\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.16228 | −0.350440 | −0.175220 | − | 0.984529i | \(-0.556064\pi\) | ||||
−0.175220 | + | 0.984529i | \(0.556064\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 2.08114 | + | 3.60464i | 0.577204 | + | 0.999747i | 0.995798 | + | 0.0915734i | \(0.0291896\pi\) |
−0.418594 | + | 0.908173i | \(0.637477\pi\) | |||||||
\(14\) | −5.16228 | −1.37968 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.581139 | + | 1.00656i | −0.140947 | + | 0.244127i | −0.927853 | − | 0.372945i | \(-0.878348\pi\) |
0.786907 | + | 0.617072i | \(0.211681\pi\) | |||||||
\(18\) | −1.00000 | − | 1.73205i | −0.235702 | − | 0.408248i | ||||
\(19\) | −4.16228 | − | 7.20928i | −0.954892 | − | 1.65392i | −0.734615 | − | 0.678484i | \(-0.762637\pi\) |
−0.220277 | − | 0.975437i | \(-0.570696\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 2.58114 | − | 4.47066i | 0.563251 | − | 0.975579i | ||||
\(22\) | −0.581139 | + | 1.00656i | −0.123899 | + | 0.214600i | ||||
\(23\) | 3.16228 | 0.659380 | 0.329690 | − | 0.944089i | \(-0.393056\pi\) | ||||
0.329690 | + | 0.944089i | \(0.393056\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 4.16228 | 0.816290 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −2.58114 | + | 4.47066i | −0.487789 | + | 0.844876i | ||||
\(29\) | 8.32456 | 1.54583 | 0.772916 | − | 0.634509i | \(-0.218798\pi\) | ||||
0.772916 | + | 0.634509i | \(0.218798\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | 4.16228 | 0.747567 | 0.373784 | − | 0.927516i | \(-0.378060\pi\) | ||||
0.373784 | + | 0.927516i | \(0.378060\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.581139 | − | 1.00656i | −0.101163 | − | 0.175220i | ||||
\(34\) | 0.581139 | + | 1.00656i | 0.0996645 | + | 0.172624i | ||||
\(35\) | −2.58114 | + | 4.47066i | −0.436292 | + | 0.755680i | ||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −6.08114 | − | 0.140537i | −0.999733 | − | 0.0231041i | ||||
\(38\) | −8.32456 | −1.35042 | ||||||||
\(39\) | −2.08114 | + | 3.60464i | −0.333249 | + | 0.577204i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −2.66228 | − | 4.61120i | −0.415778 | − | 0.720148i | 0.579732 | − | 0.814807i | \(-0.303157\pi\) |
−0.995510 | + | 0.0946588i | \(0.969824\pi\) | |||||||
\(42\) | −2.58114 | − | 4.47066i | −0.398278 | − | 0.689838i | ||||
\(43\) | 7.32456 | 1.11698 | 0.558492 | − | 0.829510i | \(-0.311380\pi\) | ||||
0.558492 | + | 0.829510i | \(0.311380\pi\) | |||||||
\(44\) | 0.581139 | + | 1.00656i | 0.0876100 | + | 0.151745i | ||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 1.58114 | − | 2.73861i | 0.233126 | − | 0.403786i | ||||
\(47\) | 5.16228 | 0.752996 | 0.376498 | − | 0.926418i | \(-0.377128\pi\) | ||||
0.376498 | + | 0.926418i | \(0.377128\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −9.82456 | + | 17.0166i | −1.40351 | + | 2.43095i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | −1.16228 | −0.162751 | ||||||||
\(52\) | 2.08114 | − | 3.60464i | 0.288602 | − | 0.499873i | ||||
\(53\) | −7.08114 | + | 12.2649i | −0.972669 | + | 1.68471i | −0.285248 | + | 0.958454i | \(0.592076\pi\) |
−0.687422 | + | 0.726259i | \(0.741257\pi\) | |||||||
\(54\) | 2.50000 | − | 4.33013i | 0.340207 | − | 0.589256i | ||||
\(55\) | 0.581139 | + | 1.00656i | 0.0783607 | + | 0.135725i | ||||
\(56\) | 2.58114 | + | 4.47066i | 0.344919 | + | 0.597418i | ||||
\(57\) | 4.16228 | − | 7.20928i | 0.551307 | − | 0.954892i | ||||
\(58\) | 4.16228 | − | 7.20928i | 0.546534 | − | 0.946624i | ||||
\(59\) | 0.581139 | − | 1.00656i | 0.0756578 | − | 0.131043i | −0.825714 | − | 0.564089i | \(-0.809228\pi\) |
0.901372 | + | 0.433045i | \(0.142561\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 4.16228 | + | 7.20928i | 0.532925 | + | 0.923053i | 0.999261 | + | 0.0384454i | \(0.0122406\pi\) |
−0.466336 | + | 0.884608i | \(0.654426\pi\) | |||||||
\(62\) | 2.08114 | − | 3.60464i | 0.264305 | − | 0.457790i | ||||
\(63\) | −10.3246 | −1.30077 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.08114 | − | 3.60464i | 0.258134 | − | 0.447100i | ||||
\(66\) | −1.16228 | −0.143066 | ||||||||
\(67\) | 4.16228 | + | 7.20928i | 0.508503 | + | 0.880753i | 0.999952 | + | 0.00984658i | \(0.00313431\pi\) |
−0.491448 | + | 0.870907i | \(0.663532\pi\) | |||||||
\(68\) | 1.16228 | 0.140947 | ||||||||
\(69\) | 1.58114 | + | 2.73861i | 0.190347 | + | 0.329690i | ||||
\(70\) | 2.58114 | + | 4.47066i | 0.308505 | + | 0.534347i | ||||
\(71\) | −3.16228 | − | 5.47723i | −0.375293 | − | 0.650027i | 0.615078 | − | 0.788467i | \(-0.289125\pi\) |
−0.990371 | + | 0.138440i | \(0.955791\pi\) | |||||||
\(72\) | −1.00000 | + | 1.73205i | −0.117851 | + | 0.204124i | ||||
\(73\) | 3.48683 | 0.408103 | 0.204051 | − | 0.978960i | \(-0.434589\pi\) | ||||
0.204051 | + | 0.978960i | \(0.434589\pi\) | |||||||
\(74\) | −3.16228 | + | 5.19615i | −0.367607 | + | 0.604040i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −4.16228 | + | 7.20928i | −0.477446 | + | 0.826961i | ||||
\(77\) | 3.00000 | + | 5.19615i | 0.341882 | + | 0.592157i | ||||
\(78\) | 2.08114 | + | 3.60464i | 0.235643 | + | 0.408145i | ||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.32456 | −0.587999 | ||||||||
\(83\) | 2.00000 | − | 3.46410i | 0.219529 | − | 0.380235i | −0.735135 | − | 0.677920i | \(-0.762881\pi\) |
0.954664 | + | 0.297686i | \(0.0962148\pi\) | |||||||
\(84\) | −5.16228 | −0.563251 | ||||||||
\(85\) | 1.16228 | 0.126067 | ||||||||
\(86\) | 3.66228 | − | 6.34325i | 0.394914 | − | 0.684010i | ||||
\(87\) | 4.16228 | + | 7.20928i | 0.446243 | + | 0.772916i | ||||
\(88\) | 1.16228 | 0.123899 | ||||||||
\(89\) | 8.32456 | − | 14.4186i | 0.882401 | − | 1.52836i | 0.0337374 | − | 0.999431i | \(-0.489259\pi\) |
0.848664 | − | 0.528933i | \(-0.177408\pi\) | |||||||
\(90\) | −1.00000 | + | 1.73205i | −0.105409 | + | 0.182574i | ||||
\(91\) | 10.7434 | − | 18.6081i | 1.12622 | − | 1.95066i | ||||
\(92\) | −1.58114 | − | 2.73861i | −0.164845 | − | 0.285520i | ||||
\(93\) | 2.08114 | + | 3.60464i | 0.215804 | + | 0.373784i | ||||
\(94\) | 2.58114 | − | 4.47066i | 0.266224 | − | 0.461114i | ||||
\(95\) | −4.16228 | + | 7.20928i | −0.427041 | + | 0.739656i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −12.3246 | −1.25137 | −0.625684 | − | 0.780076i | \(-0.715180\pi\) | ||||
−0.625684 | + | 0.780076i | \(0.715180\pi\) | |||||||
\(98\) | 9.82456 | + | 17.0166i | 0.992430 | + | 1.71894i | ||||
\(99\) | −1.16228 | + | 2.01312i | −0.116813 | + | 0.202327i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.8377 | 1.27740 | 0.638701 | − | 0.769455i | \(-0.279472\pi\) | ||||
0.638701 | + | 0.769455i | \(0.279472\pi\) | |||||||
\(102\) | −0.581139 | + | 1.00656i | −0.0575413 | + | 0.0996645i | ||||
\(103\) | −13.4868 | −1.32890 | −0.664449 | − | 0.747334i | \(-0.731334\pi\) | ||||
−0.664449 | + | 0.747334i | \(0.731334\pi\) | |||||||
\(104\) | −2.08114 | − | 3.60464i | −0.204072 | − | 0.353464i | ||||
\(105\) | −5.16228 | −0.503787 | ||||||||
\(106\) | 7.08114 | + | 12.2649i | 0.687781 | + | 1.19127i | ||||
\(107\) | 3.50000 | + | 6.06218i | 0.338358 | + | 0.586053i | 0.984124 | − | 0.177482i | \(-0.0567953\pi\) |
−0.645766 | + | 0.763535i | \(0.723462\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | −1.83772 | + | 3.18303i | −0.176022 | + | 0.304879i | −0.940514 | − | 0.339754i | \(-0.889656\pi\) |
0.764493 | + | 0.644633i | \(0.222990\pi\) | |||||||
\(110\) | 1.16228 | 0.110819 | ||||||||
\(111\) | −2.91886 | − | 5.33669i | −0.277046 | − | 0.506536i | ||||
\(112\) | 5.16228 | 0.487789 | ||||||||
\(113\) | 3.16228 | − | 5.47723i | 0.297482 | − | 0.515254i | −0.678077 | − | 0.734991i | \(-0.737186\pi\) |
0.975559 | + | 0.219737i | \(0.0705198\pi\) | |||||||
\(114\) | −4.16228 | − | 7.20928i | −0.389833 | − | 0.675211i | ||||
\(115\) | −1.58114 | − | 2.73861i | −0.147442 | − | 0.255377i | ||||
\(116\) | −4.16228 | − | 7.20928i | −0.386458 | − | 0.669365i | ||||
\(117\) | 8.32456 | 0.769605 | ||||||||
\(118\) | −0.581139 | − | 1.00656i | −0.0534982 | − | 0.0926615i | ||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | −0.500000 | + | 0.866025i | −0.0456435 | + | 0.0790569i | ||||
\(121\) | −9.64911 | −0.877192 | ||||||||
\(122\) | 8.32456 | 0.753670 | ||||||||
\(123\) | 2.66228 | − | 4.61120i | 0.240049 | − | 0.415778i | ||||
\(124\) | −2.08114 | − | 3.60464i | −0.186892 | − | 0.323706i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.16228 | + | 8.94133i | −0.459892 | + | 0.796557i | ||||
\(127\) | −2.83772 | + | 4.91508i | −0.251807 | + | 0.436143i | −0.964023 | − | 0.265817i | \(-0.914358\pi\) |
0.712216 | + | 0.701960i | \(0.247692\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.66228 | + | 6.34325i | 0.322446 | + | 0.558492i | ||||
\(130\) | −2.08114 | − | 3.60464i | −0.182528 | − | 0.316148i | ||||
\(131\) | 9.00000 | − | 15.5885i | 0.786334 | − | 1.36197i | −0.141865 | − | 0.989886i | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | −0.581139 | + | 1.00656i | −0.0505816 | + | 0.0876100i | ||||
\(133\) | −21.4868 | + | 37.2163i | −1.86314 | + | 3.22706i | ||||
\(134\) | 8.32456 | 0.719132 | ||||||||
\(135\) | −2.50000 | − | 4.33013i | −0.215166 | − | 0.372678i | ||||
\(136\) | 0.581139 | − | 1.00656i | 0.0498322 | − | 0.0863120i | ||||
\(137\) | 11.4868 | 0.981386 | 0.490693 | − | 0.871332i | \(-0.336744\pi\) | ||||
0.490693 | + | 0.871332i | \(0.336744\pi\) | |||||||
\(138\) | 3.16228 | 0.269191 | ||||||||
\(139\) | 7.74342 | − | 13.4120i | 0.656788 | − | 1.13759i | −0.324654 | − | 0.945833i | \(-0.605248\pi\) |
0.981442 | − | 0.191757i | \(-0.0614187\pi\) | |||||||
\(140\) | 5.16228 | 0.436292 | ||||||||
\(141\) | 2.58114 | + | 4.47066i | 0.217371 | + | 0.376498i | ||||
\(142\) | −6.32456 | −0.530745 | ||||||||
\(143\) | −2.41886 | − | 4.18959i | −0.202275 | − | 0.350351i | ||||
\(144\) | 1.00000 | + | 1.73205i | 0.0833333 | + | 0.144338i | ||||
\(145\) | −4.16228 | − | 7.20928i | −0.345658 | − | 0.598698i | ||||
\(146\) | 1.74342 | − | 3.01969i | 0.144286 | − | 0.249911i | ||||
\(147\) | −19.6491 | −1.62063 | ||||||||
\(148\) | 2.91886 | + | 5.33669i | 0.239929 | + | 0.438673i | ||||
\(149\) | 12.0000 | 0.983078 | 0.491539 | − | 0.870855i | \(-0.336434\pi\) | ||||
0.491539 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −1.75658 | − | 3.04249i | −0.142949 | − | 0.247594i | 0.785657 | − | 0.618662i | \(-0.212325\pi\) |
−0.928606 | + | 0.371068i | \(0.878992\pi\) | |||||||
\(152\) | 4.16228 | + | 7.20928i | 0.337605 | + | 0.584750i | ||||
\(153\) | 1.16228 | + | 2.01312i | 0.0939646 | + | 0.162751i | ||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | −2.08114 | − | 3.60464i | −0.167161 | − | 0.289532i | ||||
\(156\) | 4.16228 | 0.333249 | ||||||||
\(157\) | 5.08114 | − | 8.80079i | 0.405519 | − | 0.702380i | −0.588863 | − | 0.808233i | \(-0.700424\pi\) |
0.994382 | + | 0.105854i | \(0.0337575\pi\) | |||||||
\(158\) | 2.00000 | 0.159111 | ||||||||
\(159\) | −14.1623 | −1.12314 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −8.16228 | − | 14.1375i | −0.643278 | − | 1.11419i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.82456 | + | 4.89227i | −0.221236 | + | 0.383192i | −0.955184 | − | 0.296014i | \(-0.904343\pi\) |
0.733947 | + | 0.679206i | \(0.237676\pi\) | |||||||
\(164\) | −2.66228 | + | 4.61120i | −0.207889 | + | 0.360074i | ||||
\(165\) | −0.581139 | + | 1.00656i | −0.0452416 | + | 0.0783607i | ||||
\(166\) | −2.00000 | − | 3.46410i | −0.155230 | − | 0.268866i | ||||
\(167\) | 4.16228 | + | 7.20928i | 0.322087 | + | 0.557871i | 0.980918 | − | 0.194420i | \(-0.0622824\pi\) |
−0.658832 | + | 0.752290i | \(0.728949\pi\) | |||||||
\(168\) | −2.58114 | + | 4.47066i | −0.199139 | + | 0.344919i | ||||
\(169\) | −2.16228 | + | 3.74517i | −0.166329 | + | 0.288090i | ||||
\(170\) | 0.581139 | − | 1.00656i | 0.0445713 | − | 0.0771998i | ||||
\(171\) | −16.6491 | −1.27319 | ||||||||
\(172\) | −3.66228 | − | 6.34325i | −0.279246 | − | 0.483668i | ||||
\(173\) | −1.16228 | + | 2.01312i | −0.0883663 | + | 0.153055i | −0.906821 | − | 0.421517i | \(-0.861498\pi\) |
0.818454 | + | 0.574572i | \(0.194831\pi\) | |||||||
\(174\) | 8.32456 | 0.631083 | ||||||||
\(175\) | 5.16228 | 0.390232 | ||||||||
\(176\) | 0.581139 | − | 1.00656i | 0.0438050 | − | 0.0758725i | ||||
\(177\) | 1.16228 | 0.0873621 | ||||||||
\(178\) | −8.32456 | − | 14.4186i | −0.623952 | − | 1.08072i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 1.00000 | + | 1.73205i | 0.0745356 | + | 0.129099i | ||||
\(181\) | −2.25658 | − | 3.90852i | −0.167731 | − | 0.290518i | 0.769891 | − | 0.638175i | \(-0.220311\pi\) |
−0.937622 | + | 0.347658i | \(0.886977\pi\) | |||||||
\(182\) | −10.7434 | − | 18.6081i | −0.796355 | − | 1.37933i | ||||
\(183\) | −4.16228 | + | 7.20928i | −0.307684 | + | 0.532925i | ||||
\(184\) | −3.16228 | −0.233126 | ||||||||
\(185\) | 2.91886 | + | 5.33669i | 0.214599 | + | 0.392361i | ||||
\(186\) | 4.16228 | 0.305193 | ||||||||
\(187\) | 0.675445 | − | 1.16990i | 0.0493934 | − | 0.0855519i | ||||
\(188\) | −2.58114 | − | 4.47066i | −0.188249 | − | 0.326057i | ||||
\(189\) | −12.9057 | − | 22.3533i | −0.938751 | − | 1.62596i | ||||
\(190\) | 4.16228 | + | 7.20928i | 0.301963 | + | 0.523016i | ||||
\(191\) | −8.81139 | −0.637570 | −0.318785 | − | 0.947827i | \(-0.603275\pi\) | ||||
−0.318785 | + | 0.947827i | \(0.603275\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −0.513167 | −0.0369386 | −0.0184693 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184693 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(194\) | −6.16228 | + | 10.6734i | −0.442426 | + | 0.766304i | ||||
\(195\) | 4.16228 | 0.298067 | ||||||||
\(196\) | 19.6491 | 1.40351 | ||||||||
\(197\) | −6.91886 | + | 11.9838i | −0.492948 | + | 0.853812i | −0.999967 | − | 0.00812338i | \(-0.997414\pi\) |
0.507019 | + | 0.861935i | \(0.330748\pi\) | |||||||
\(198\) | 1.16228 | + | 2.01312i | 0.0825995 | + | 0.143066i | ||||
\(199\) | −5.83772 | −0.413825 | −0.206913 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206913 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −4.16228 | + | 7.20928i | −0.293584 | + | 0.508503i | ||||
\(202\) | 6.41886 | − | 11.1178i | 0.451629 | − | 0.782245i | ||||
\(203\) | −21.4868 | − | 37.2163i | −1.50808 | − | 2.61207i | ||||
\(204\) | 0.581139 | + | 1.00656i | 0.0406879 | + | 0.0704734i | ||||
\(205\) | −2.66228 | + | 4.61120i | −0.185942 | + | 0.322060i | ||||
\(206\) | −6.74342 | + | 11.6799i | −0.469836 | + | 0.813780i | ||||
\(207\) | 3.16228 | − | 5.47723i | 0.219793 | − | 0.380693i | ||||
\(208\) | −4.16228 | −0.288602 | ||||||||
\(209\) | 4.83772 | + | 8.37918i | 0.334632 | + | 0.579600i | ||||
\(210\) | −2.58114 | + | 4.47066i | −0.178116 | + | 0.308505i | ||||
\(211\) | −8.32456 | −0.573086 | −0.286543 | − | 0.958067i | \(-0.592506\pi\) | ||||
−0.286543 | + | 0.958067i | \(0.592506\pi\) | |||||||
\(212\) | 14.1623 | 0.972669 | ||||||||
\(213\) | 3.16228 | − | 5.47723i | 0.216676 | − | 0.375293i | ||||
\(214\) | 7.00000 | 0.478510 | ||||||||
\(215\) | −3.66228 | − | 6.34325i | −0.249765 | − | 0.432606i | ||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −10.7434 | − | 18.6081i | −0.729311 | − | 1.26320i | ||||
\(218\) | 1.83772 | + | 3.18303i | 0.124466 | + | 0.215582i | ||||
\(219\) | 1.74342 | + | 3.01969i | 0.117809 | + | 0.204051i | ||||
\(220\) | 0.581139 | − | 1.00656i | 0.0391804 | − | 0.0678624i | ||||
\(221\) | −4.83772 | −0.325420 | ||||||||
\(222\) | −6.08114 | − | 0.140537i | −0.408139 | − | 0.00943220i | ||||
\(223\) | 0.837722 | 0.0560980 | 0.0280490 | − | 0.999607i | \(-0.491071\pi\) | ||||
0.0280490 | + | 0.999607i | \(0.491071\pi\) | |||||||
\(224\) | 2.58114 | − | 4.47066i | 0.172460 | − | 0.298709i | ||||
\(225\) | 1.00000 | + | 1.73205i | 0.0666667 | + | 0.115470i | ||||
\(226\) | −3.16228 | − | 5.47723i | −0.210352 | − | 0.364340i | ||||
\(227\) | 1.33772 | + | 2.31700i | 0.0887878 | + | 0.153785i | 0.906999 | − | 0.421133i | \(-0.138367\pi\) |
−0.818211 | + | 0.574918i | \(0.805034\pi\) | |||||||
\(228\) | −8.32456 | −0.551307 | ||||||||
\(229\) | 5.41886 | + | 9.38574i | 0.358088 | + | 0.620227i | 0.987641 | − | 0.156730i | \(-0.0500953\pi\) |
−0.629553 | + | 0.776958i | \(0.716762\pi\) | |||||||
\(230\) | −3.16228 | −0.208514 | ||||||||
\(231\) | −3.00000 | + | 5.19615i | −0.197386 | + | 0.341882i | ||||
\(232\) | −8.32456 | −0.546534 | ||||||||
\(233\) | 13.4868 | 0.883552 | 0.441776 | − | 0.897125i | \(-0.354349\pi\) | ||||
0.441776 | + | 0.897125i | \(0.354349\pi\) | |||||||
\(234\) | 4.16228 | − | 7.20928i | 0.272097 | − | 0.471285i | ||||
\(235\) | −2.58114 | − | 4.47066i | −0.168375 | − | 0.291634i | ||||
\(236\) | −1.16228 | −0.0756578 | ||||||||
\(237\) | −1.00000 | + | 1.73205i | −0.0649570 | + | 0.112509i | ||||
\(238\) | 3.00000 | − | 5.19615i | 0.194461 | − | 0.336817i | ||||
\(239\) | −5.32456 | + | 9.22240i | −0.344417 | + | 0.596547i | −0.985248 | − | 0.171135i | \(-0.945257\pi\) |
0.640831 | + | 0.767682i | \(0.278590\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | 5.32456 | + | 9.22240i | 0.342985 | + | 0.594067i | 0.984986 | − | 0.172637i | \(-0.0552287\pi\) |
−0.642001 | + | 0.766704i | \(0.721895\pi\) | |||||||
\(242\) | −4.82456 | + | 8.35637i | −0.310134 | + | 0.537168i | ||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 4.16228 | − | 7.20928i | 0.266463 | − | 0.461527i | ||||
\(245\) | 19.6491 | 1.25534 | ||||||||
\(246\) | −2.66228 | − | 4.61120i | −0.169741 | − | 0.293999i | ||||
\(247\) | 17.3246 | − | 30.0070i | 1.10234 | − | 1.90930i | ||||
\(248\) | −4.16228 | −0.264305 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 5.16228 | + | 8.94133i | 0.325193 | + | 0.563251i | ||||
\(253\) | −3.67544 | −0.231073 | ||||||||
\(254\) | 2.83772 | + | 4.91508i | 0.178055 | + | 0.308400i | ||||
\(255\) | 0.581139 | + | 1.00656i | 0.0363923 | + | 0.0630334i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −8.74342 | + | 15.1440i | −0.545399 | + | 0.944659i | 0.453182 | + | 0.891418i | \(0.350289\pi\) |
−0.998582 | + | 0.0532415i | \(0.983045\pi\) | |||||||
\(258\) | 7.32456 | 0.456007 | ||||||||
\(259\) | 15.0680 | + | 27.5495i | 0.936278 | + | 1.71184i | ||||
\(260\) | −4.16228 | −0.258134 | ||||||||
\(261\) | 8.32456 | − | 14.4186i | 0.515277 | − | 0.892486i | ||||
\(262\) | −9.00000 | − | 15.5885i | −0.556022 | − | 0.963058i | ||||
\(263\) | 3.74342 | + | 6.48379i | 0.230829 | + | 0.399807i | 0.958052 | − | 0.286593i | \(-0.0925229\pi\) |
−0.727223 | + | 0.686401i | \(0.759190\pi\) | |||||||
\(264\) | 0.581139 | + | 1.00656i | 0.0357666 | + | 0.0619496i | ||||
\(265\) | 14.1623 | 0.869982 | ||||||||
\(266\) | 21.4868 | + | 37.2163i | 1.31744 | + | 2.28188i | ||||
\(267\) | 16.6491 | 1.01891 | ||||||||
\(268\) | 4.16228 | − | 7.20928i | 0.254252 | − | 0.440377i | ||||
\(269\) | 27.1623 | 1.65611 | 0.828057 | − | 0.560644i | \(-0.189447\pi\) | ||||
0.828057 | + | 0.560644i | \(0.189447\pi\) | |||||||
\(270\) | −5.00000 | −0.304290 | ||||||||
\(271\) | −13.2434 | + | 22.9383i | −0.804480 | + | 1.39340i | 0.112161 | + | 0.993690i | \(0.464223\pi\) |
−0.916641 | + | 0.399711i | \(0.869111\pi\) | |||||||
\(272\) | −0.581139 | − | 1.00656i | −0.0352367 | − | 0.0610318i | ||||
\(273\) | 21.4868 | 1.30044 | ||||||||
\(274\) | 5.74342 | − | 9.94789i | 0.346972 | − | 0.600974i | ||||
\(275\) | 0.581139 | − | 1.00656i | 0.0350440 | − | 0.0606980i | ||||
\(276\) | 1.58114 | − | 2.73861i | 0.0951734 | − | 0.164845i | ||||
\(277\) | 4.24342 | + | 7.34981i | 0.254962 | + | 0.441607i | 0.964885 | − | 0.262672i | \(-0.0846036\pi\) |
−0.709923 | + | 0.704279i | \(0.751270\pi\) | |||||||
\(278\) | −7.74342 | − | 13.4120i | −0.464419 | − | 0.804398i | ||||
\(279\) | 4.16228 | − | 7.20928i | 0.249189 | − | 0.431608i | ||||
\(280\) | 2.58114 | − | 4.47066i | 0.154253 | − | 0.267173i | ||||
\(281\) | 0.824555 | − | 1.42817i | 0.0491888 | − | 0.0851976i | −0.840383 | − | 0.541994i | \(-0.817670\pi\) |
0.889571 | + | 0.456796i | \(0.151003\pi\) | |||||||
\(282\) | 5.16228 | 0.307409 | ||||||||
\(283\) | −15.3114 | − | 26.5201i | −0.910168 | − | 1.57646i | −0.813826 | − | 0.581108i | \(-0.802619\pi\) |
−0.0963412 | − | 0.995348i | \(-0.530714\pi\) | |||||||
\(284\) | −3.16228 | + | 5.47723i | −0.187647 | + | 0.325014i | ||||
\(285\) | −8.32456 | −0.493104 | ||||||||
\(286\) | −4.83772 | −0.286061 | ||||||||
\(287\) | −13.7434 | + | 23.8043i | −0.811248 | + | 1.40512i | ||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | 7.82456 | + | 13.5525i | 0.460268 | + | 0.797207i | ||||
\(290\) | −8.32456 | −0.488835 | ||||||||
\(291\) | −6.16228 | − | 10.6734i | −0.361239 | − | 0.625684i | ||||
\(292\) | −1.74342 | − | 3.01969i | −0.102026 | − | 0.176714i | ||||
\(293\) | −0.243416 | − | 0.421610i | −0.0142205 | − | 0.0246307i | 0.858828 | − | 0.512265i | \(-0.171193\pi\) |
−0.873048 | + | 0.487634i | \(0.837860\pi\) | |||||||
\(294\) | −9.82456 | + | 17.0166i | −0.572980 | + | 0.992430i | ||||
\(295\) | −1.16228 | −0.0676704 | ||||||||
\(296\) | 6.08114 | + | 0.140537i | 0.353459 | + | 0.00816852i | ||||
\(297\) | −5.81139 | −0.337211 | ||||||||
\(298\) | 6.00000 | − | 10.3923i | 0.347571 | − | 0.602010i | ||||
\(299\) | 6.58114 | + | 11.3989i | 0.380597 | + | 0.659213i | ||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | −18.9057 | − | 32.7456i | −1.08971 | − | 1.88743i | ||||
\(302\) | −3.51317 | −0.202160 | ||||||||
\(303\) | 6.41886 | + | 11.1178i | 0.368754 | + | 0.638701i | ||||
\(304\) | 8.32456 | 0.477446 | ||||||||
\(305\) | 4.16228 | − | 7.20928i | 0.238331 | − | 0.412802i | ||||
\(306\) | 2.32456 | 0.132886 | ||||||||
\(307\) | −26.2982 | −1.50092 | −0.750459 | − | 0.660917i | \(-0.770168\pi\) | ||||
−0.750459 | + | 0.660917i | \(0.770168\pi\) | |||||||
\(308\) | 3.00000 | − | 5.19615i | 0.170941 | − | 0.296078i | ||||
\(309\) | −6.74342 | − | 11.6799i | −0.383620 | − | 0.664449i | ||||
\(310\) | −4.16228 | −0.236401 | ||||||||
\(311\) | −4.08114 | + | 7.06874i | −0.231420 | + | 0.400831i | −0.958226 | − | 0.286011i | \(-0.907671\pi\) |
0.726806 | + | 0.686843i | \(0.241004\pi\) | |||||||
\(312\) | 2.08114 | − | 3.60464i | 0.117821 | − | 0.204072i | ||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | −5.08114 | − | 8.80079i | −0.286745 | − | 0.496657i | ||||
\(315\) | 5.16228 | + | 8.94133i | 0.290861 | + | 0.503787i | ||||
\(316\) | 1.00000 | − | 1.73205i | 0.0562544 | − | 0.0974355i | ||||
\(317\) | 3.24342 | − | 5.61776i | 0.182168 | − | 0.315525i | −0.760450 | − | 0.649396i | \(-0.775022\pi\) |
0.942619 | + | 0.333871i | \(0.108355\pi\) | |||||||
\(318\) | −7.08114 | + | 12.2649i | −0.397091 | + | 0.687781i | ||||
\(319\) | −9.67544 | −0.541721 | ||||||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −3.50000 | + | 6.06218i | −0.195351 | + | 0.338358i | ||||
\(322\) | −16.3246 | −0.909732 | ||||||||
\(323\) | 9.67544 | 0.538356 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −4.16228 | −0.230882 | ||||||||
\(326\) | 2.82456 | + | 4.89227i | 0.156438 | + | 0.270958i | ||||
\(327\) | −3.67544 | −0.203253 | ||||||||
\(328\) | 2.66228 | + | 4.61120i | 0.147000 | + | 0.254611i | ||||
\(329\) | −13.3246 | − | 23.0788i | −0.734607 | − | 1.27238i | ||||
\(330\) | 0.581139 | + | 1.00656i | 0.0319906 | + | 0.0554094i | ||||
\(331\) | −7.25658 | + | 12.5688i | −0.398858 | + | 0.690842i | −0.993585 | − | 0.113085i | \(-0.963927\pi\) |
0.594727 | + | 0.803927i | \(0.297260\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | −6.32456 | + | 10.3923i | −0.346583 | + | 0.569495i | ||||
\(334\) | 8.32456 | 0.455499 | ||||||||
\(335\) | 4.16228 | − | 7.20928i | 0.227410 | − | 0.393885i | ||||
\(336\) | 2.58114 | + | 4.47066i | 0.140813 | + | 0.243895i | ||||
\(337\) | 13.6491 | + | 23.6410i | 0.743514 | + | 1.28780i | 0.950886 | + | 0.309542i | \(0.100176\pi\) |
−0.207371 | + | 0.978262i | \(0.566491\pi\) | |||||||
\(338\) | 2.16228 | + | 3.74517i | 0.117612 | + | 0.203711i | ||||
\(339\) | 6.32456 | 0.343503 | ||||||||
\(340\) | −0.581139 | − | 1.00656i | −0.0315167 | − | 0.0545885i | ||||
\(341\) | −4.83772 | −0.261977 | ||||||||
\(342\) | −8.32456 | + | 14.4186i | −0.450140 | + | 0.779666i | ||||
\(343\) | 65.2982 | 3.52577 | ||||||||
\(344\) | −7.32456 | −0.394914 | ||||||||
\(345\) | 1.58114 | − | 2.73861i | 0.0851257 | − | 0.147442i | ||||
\(346\) | 1.16228 | + | 2.01312i | 0.0624844 | + | 0.108226i | ||||
\(347\) | −7.67544 | −0.412039 | −0.206020 | − | 0.978548i | \(-0.566051\pi\) | ||||
−0.206020 | + | 0.978548i | \(0.566051\pi\) | |||||||
\(348\) | 4.16228 | − | 7.20928i | 0.223122 | − | 0.386458i | ||||
\(349\) | −1.00000 | + | 1.73205i | −0.0535288 | + | 0.0927146i | −0.891548 | − | 0.452926i | \(-0.850380\pi\) |
0.838019 | + | 0.545640i | \(0.183714\pi\) | |||||||
\(350\) | 2.58114 | − | 4.47066i | 0.137968 | − | 0.238967i | ||||
\(351\) | 10.4057 | + | 18.0232i | 0.555415 | + | 0.962007i | ||||
\(352\) | −0.581139 | − | 1.00656i | −0.0309748 | − | 0.0536499i | ||||
\(353\) | −7.90569 | + | 13.6931i | −0.420778 | + | 0.728808i | −0.996016 | − | 0.0891778i | \(-0.971576\pi\) |
0.575238 | + | 0.817986i | \(0.304909\pi\) | |||||||
\(354\) | 0.581139 | − | 1.00656i | 0.0308872 | − | 0.0534982i | ||||
\(355\) | −3.16228 | + | 5.47723i | −0.167836 | + | 0.290701i | ||||
\(356\) | −16.6491 | −0.882401 | ||||||||
\(357\) | 3.00000 | + | 5.19615i | 0.158777 | + | 0.275010i | ||||
\(358\) | −6.00000 | + | 10.3923i | −0.317110 | + | 0.549250i | ||||
\(359\) | 4.48683 | 0.236806 | 0.118403 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118403 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | −25.1491 | + | 43.5595i | −1.32364 | + | 2.29261i | ||||
\(362\) | −4.51317 | −0.237207 | ||||||||
\(363\) | −4.82456 | − | 8.35637i | −0.253223 | − | 0.438596i | ||||
\(364\) | −21.4868 | −1.12622 | ||||||||
\(365\) | −1.74342 | − | 3.01969i | −0.0912546 | − | 0.158058i | ||||
\(366\) | 4.16228 | + | 7.20928i | 0.217566 | + | 0.376835i | ||||
\(367\) | 3.32456 | + | 5.75830i | 0.173540 | + | 0.300581i | 0.939655 | − | 0.342123i | \(-0.111146\pi\) |
−0.766115 | + | 0.642704i | \(0.777813\pi\) | |||||||
\(368\) | −1.58114 | + | 2.73861i | −0.0824226 | + | 0.142760i | ||||
\(369\) | −10.6491 | −0.554371 | ||||||||
\(370\) | 6.08114 | + | 0.140537i | 0.316143 | + | 0.00730615i | ||||
\(371\) | 73.1096 | 3.79566 | ||||||||
\(372\) | 2.08114 | − | 3.60464i | 0.107902 | − | 0.186892i | ||||
\(373\) | −5.24342 | − | 9.08186i | −0.271494 | − | 0.470241i | 0.697751 | − | 0.716341i | \(-0.254184\pi\) |
−0.969245 | + | 0.246100i | \(0.920851\pi\) | |||||||
\(374\) | −0.675445 | − | 1.16990i | −0.0349264 | − | 0.0604943i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −5.16228 | −0.266224 | ||||||||
\(377\) | 17.3246 | + | 30.0070i | 0.892260 | + | 1.54544i | ||||
\(378\) | −25.8114 | −1.32759 | ||||||||
\(379\) | −15.7434 | + | 27.2684i | −0.808685 | + | 1.40068i | 0.105090 | + | 0.994463i | \(0.466487\pi\) |
−0.913775 | + | 0.406221i | \(0.866846\pi\) | |||||||
\(380\) | 8.32456 | 0.427041 | ||||||||
\(381\) | −5.67544 | −0.290762 | ||||||||
\(382\) | −4.40569 | + | 7.63089i | −0.225415 | + | 0.390430i | ||||
\(383\) | 0.581139 | + | 1.00656i | 0.0296948 | + | 0.0514329i | 0.880491 | − | 0.474063i | \(-0.157213\pi\) |
−0.850796 | + | 0.525496i | \(0.823880\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 3.00000 | − | 5.19615i | 0.152894 | − | 0.264820i | ||||
\(386\) | −0.256584 | + | 0.444416i | −0.0130598 | + | 0.0226202i | ||||
\(387\) | 7.32456 | − | 12.6865i | 0.372328 | − | 0.644891i | ||||
\(388\) | 6.16228 | + | 10.6734i | 0.312842 | + | 0.541859i | ||||
\(389\) | −14.3246 | − | 24.8109i | −0.726284 | − | 1.25796i | −0.958443 | − | 0.285283i | \(-0.907913\pi\) |
0.232160 | − | 0.972678i | \(-0.425421\pi\) | |||||||
\(390\) | 2.08114 | − | 3.60464i | 0.105383 | − | 0.182528i | ||||
\(391\) | −1.83772 | + | 3.18303i | −0.0929376 | + | 0.160973i | ||||
\(392\) | 9.82456 | − | 17.0166i | 0.496215 | − | 0.859470i | ||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 6.91886 | + | 11.9838i | 0.348567 | + | 0.603736i | ||||
\(395\) | 1.00000 | − | 1.73205i | 0.0503155 | − | 0.0871489i | ||||
\(396\) | 2.32456 | 0.116813 | ||||||||
\(397\) | 4.16228 | 0.208899 | 0.104449 | − | 0.994530i | \(-0.466692\pi\) | ||||
0.104449 | + | 0.994530i | \(0.466692\pi\) | |||||||
\(398\) | −2.91886 | + | 5.05562i | −0.146309 | + | 0.253415i | ||||
\(399\) | −42.9737 | −2.15137 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −8.00000 | −0.399501 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(402\) | 4.16228 | + | 7.20928i | 0.207596 | + | 0.359566i | ||||
\(403\) | 8.66228 | + | 15.0035i | 0.431499 | + | 0.747378i | ||||
\(404\) | −6.41886 | − | 11.1178i | −0.319350 | − | 0.553131i | ||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | −42.9737 | −2.13275 | ||||||||
\(407\) | 7.06797 | + | 0.163343i | 0.350346 | + | 0.00809659i | ||||
\(408\) | 1.16228 | 0.0575413 | ||||||||
\(409\) | 9.82456 | − | 17.0166i | 0.485793 | − | 0.841418i | −0.514074 | − | 0.857746i | \(-0.671864\pi\) |
0.999867 | + | 0.0163279i | \(0.00519755\pi\) | |||||||
\(410\) | 2.66228 | + | 4.61120i | 0.131481 | + | 0.227731i | ||||
\(411\) | 5.74342 | + | 9.94789i | 0.283302 | + | 0.490693i | ||||
\(412\) | 6.74342 | + | 11.6799i | 0.332224 | + | 0.575429i | ||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | −3.16228 | − | 5.47723i | −0.155417 | − | 0.269191i | ||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | −2.08114 | + | 3.60464i | −0.102036 | + | 0.176732i | ||||
\(417\) | 15.4868 | 0.758393 | ||||||||
\(418\) | 9.67544 | 0.473241 | ||||||||
\(419\) | 8.90569 | − | 15.4251i | 0.435072 | − | 0.753566i | −0.562230 | − | 0.826981i | \(-0.690056\pi\) |
0.997301 | + | 0.0734148i | \(0.0233897\pi\) | |||||||
\(420\) | 2.58114 | + | 4.47066i | 0.125947 | + | 0.218146i | ||||
\(421\) | −11.4868 | −0.559834 | −0.279917 | − | 0.960024i | \(-0.590307\pi\) | ||||
−0.279917 | + | 0.960024i | \(0.590307\pi\) | |||||||
\(422\) | −4.16228 | + | 7.20928i | −0.202617 | + | 0.350942i | ||||
\(423\) | 5.16228 | − | 8.94133i | 0.250999 | − | 0.434742i | ||||
\(424\) | 7.08114 | − | 12.2649i | 0.343891 | − | 0.595636i | ||||
\(425\) | −0.581139 | − | 1.00656i | −0.0281894 | − | 0.0488254i | ||||
\(426\) | −3.16228 | − | 5.47723i | −0.153213 | − | 0.265372i | ||||
\(427\) | 21.4868 | − | 37.2163i | 1.03982 | − | 1.80102i | ||||
\(428\) | 3.50000 | − | 6.06218i | 0.169179 | − | 0.293026i | ||||
\(429\) | 2.41886 | − | 4.18959i | 0.116784 | − | 0.202275i | ||||
\(430\) | −7.32456 | −0.353221 | ||||||||
\(431\) | 13.5680 | + | 23.5004i | 0.653546 | + | 1.13198i | 0.982256 | + | 0.187544i | \(0.0600528\pi\) |
−0.328710 | + | 0.944431i | \(0.606614\pi\) | |||||||
\(432\) | −2.50000 | + | 4.33013i | −0.120281 | + | 0.208333i | ||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | −21.4868 | −1.03140 | ||||||||
\(435\) | 4.16228 | − | 7.20928i | 0.199566 | − | 0.345658i | ||||
\(436\) | 3.67544 | 0.176022 | ||||||||
\(437\) | −13.1623 | − | 22.7977i | −0.629637 | − | 1.09056i | ||||
\(438\) | 3.48683 | 0.166607 | ||||||||
\(439\) | 2.40569 | + | 4.16678i | 0.114818 | + | 0.198870i | 0.917707 | − | 0.397258i | \(-0.130038\pi\) |
−0.802889 | + | 0.596128i | \(0.796705\pi\) | |||||||
\(440\) | −0.581139 | − | 1.00656i | −0.0277047 | − | 0.0479860i | ||||
\(441\) | 19.6491 | + | 34.0333i | 0.935672 | + | 1.62063i | ||||
\(442\) | −2.41886 | + | 4.18959i | −0.115053 | + | 0.199278i | ||||
\(443\) | 37.3246 | 1.77334 | 0.886672 | − | 0.462400i | \(-0.153011\pi\) | ||||
0.886672 | + | 0.462400i | \(0.153011\pi\) | |||||||
\(444\) | −3.16228 | + | 5.19615i | −0.150075 | + | 0.246598i | ||||
\(445\) | −16.6491 | −0.789244 | ||||||||
\(446\) | 0.418861 | − | 0.725489i | 0.0198337 | − | 0.0343529i | ||||
\(447\) | 6.00000 | + | 10.3923i | 0.283790 | + | 0.491539i | ||||
\(448\) | −2.58114 | − | 4.47066i | −0.121947 | − | 0.211219i | ||||
\(449\) | −3.17544 | − | 5.50003i | −0.149858 | − | 0.259563i | 0.781317 | − | 0.624135i | \(-0.214548\pi\) |
−0.931175 | + | 0.364572i | \(0.881215\pi\) | |||||||
\(450\) | 2.00000 | 0.0942809 | ||||||||
\(451\) | 3.09431 | + | 5.35949i | 0.145705 | + | 0.252369i | ||||
\(452\) | −6.32456 | −0.297482 | ||||||||
\(453\) | 1.75658 | − | 3.04249i | 0.0825315 | − | 0.142949i | ||||
\(454\) | 2.67544 | 0.125565 | ||||||||
\(455\) | −21.4868 | −1.00732 | ||||||||
\(456\) | −4.16228 | + | 7.20928i | −0.194917 | + | 0.337605i | ||||
\(457\) | −3.48683 | − | 6.03937i | −0.163107 | − | 0.282510i | 0.772874 | − | 0.634559i | \(-0.218818\pi\) |
−0.935981 | + | 0.352049i | \(0.885485\pi\) | |||||||
\(458\) | 10.8377 | 0.506414 | ||||||||
\(459\) | −2.90569 | + | 5.03281i | −0.135626 | + | 0.234911i | ||||
\(460\) | −1.58114 | + | 2.73861i | −0.0737210 | + | 0.127688i | ||||
\(461\) | 3.83772 | − | 6.64713i | 0.178741 | − | 0.309588i | −0.762709 | − | 0.646742i | \(-0.776131\pi\) |
0.941449 | + | 0.337154i | \(0.109464\pi\) | |||||||
\(462\) | 3.00000 | + | 5.19615i | 0.139573 | + | 0.241747i | ||||
\(463\) | −9.48683 | − | 16.4317i | −0.440891 | − | 0.763645i | 0.556865 | − | 0.830603i | \(-0.312004\pi\) |
−0.997756 | + | 0.0669581i | \(0.978671\pi\) | |||||||
\(464\) | −4.16228 | + | 7.20928i | −0.193229 | + | 0.334682i | ||||
\(465\) | 2.08114 | − | 3.60464i | 0.0965105 | − | 0.167161i | ||||
\(466\) | 6.74342 | − | 11.6799i | 0.312383 | − | 0.541063i | ||||
\(467\) | −41.6491 | −1.92729 | −0.963645 | − | 0.267184i | \(-0.913907\pi\) | ||||
−0.963645 | + | 0.267184i | \(0.913907\pi\) | |||||||
\(468\) | −4.16228 | − | 7.20928i | −0.192401 | − | 0.333249i | ||||
\(469\) | 21.4868 | − | 37.2163i | 0.992170 | − | 1.71849i | ||||
\(470\) | −5.16228 | −0.238118 | ||||||||
\(471\) | 10.1623 | 0.468253 | ||||||||
\(472\) | −0.581139 | + | 1.00656i | −0.0267491 | + | 0.0463308i | ||||
\(473\) | −8.51317 | −0.391436 | ||||||||
\(474\) | 1.00000 | + | 1.73205i | 0.0459315 | + | 0.0795557i | ||||
\(475\) | 8.32456 | 0.381957 | ||||||||
\(476\) | −3.00000 | − | 5.19615i | −0.137505 | − | 0.238165i | ||||
\(477\) | 14.1623 | + | 24.5298i | 0.648446 | + | 1.12314i | ||||
\(478\) | 5.32456 | + | 9.22240i | 0.243539 | + | 0.421823i | ||||
\(479\) | −16.0811 | + | 27.8533i | −0.734766 | + | 1.27265i | 0.220060 | + | 0.975486i | \(0.429375\pi\) |
−0.954826 | + | 0.297166i | \(0.903959\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −12.1491 | − | 22.2128i | −0.553952 | − | 1.01282i | ||||
\(482\) | 10.6491 | 0.485054 | ||||||||
\(483\) | 8.16228 | − | 14.1375i | 0.371396 | − | 0.643278i | ||||
\(484\) | 4.82456 | + | 8.35637i | 0.219298 | + | 0.379835i | ||||
\(485\) | 6.16228 | + | 10.6734i | 0.279815 | + | 0.484653i | ||||
\(486\) | −8.00000 | − | 13.8564i | −0.362887 | − | 0.628539i | ||||
\(487\) | −23.2982 | −1.05574 | −0.527872 | − | 0.849324i | \(-0.677010\pi\) | ||||
−0.527872 | + | 0.849324i | \(0.677010\pi\) | |||||||
\(488\) | −4.16228 | − | 7.20928i | −0.188417 | − | 0.326349i | ||||
\(489\) | −5.64911 | −0.255462 | ||||||||
\(490\) | 9.82456 | − | 17.0166i | 0.443828 | − | 0.768733i | ||||
\(491\) | 12.5132 | 0.564711 | 0.282356 | − | 0.959310i | \(-0.408884\pi\) | ||||
0.282356 | + | 0.959310i | \(0.408884\pi\) | |||||||
\(492\) | −5.32456 | −0.240049 | ||||||||
\(493\) | −4.83772 | + | 8.37918i | −0.217880 | + | 0.377379i | ||||
\(494\) | −17.3246 | − | 30.0070i | −0.779469 | − | 1.35008i | ||||
\(495\) | 2.32456 | 0.104481 | ||||||||
\(496\) | −2.08114 | + | 3.60464i | −0.0934459 | + | 0.161853i | ||||
\(497\) | −16.3246 | + | 28.2750i | −0.732256 | + | 1.26831i | ||||
\(498\) | 2.00000 | − | 3.46410i | 0.0896221 | − | 0.155230i | ||||
\(499\) | 5.67544 | + | 9.83016i | 0.254068 | + | 0.440058i | 0.964642 | − | 0.263564i | \(-0.0848980\pi\) |
−0.710574 | + | 0.703622i | \(0.751565\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −4.16228 | + | 7.20928i | −0.185957 | + | 0.322087i | ||||
\(502\) | 3.00000 | − | 5.19615i | 0.133897 | − | 0.231916i | ||||
\(503\) | 1.74342 | − | 3.01969i | 0.0777351 | − | 0.134641i | −0.824537 | − | 0.565808i | \(-0.808564\pi\) |
0.902272 | + | 0.431166i | \(0.141898\pi\) | |||||||
\(504\) | 10.3246 | 0.459892 | ||||||||
\(505\) | −6.41886 | − | 11.1178i | −0.285636 | − | 0.494735i | ||||
\(506\) | −1.83772 | + | 3.18303i | −0.0816967 | + | 0.141503i | ||||
\(507\) | −4.32456 | −0.192060 | ||||||||
\(508\) | 5.67544 | 0.251807 | ||||||||
\(509\) | −18.3925 | + | 31.8568i | −0.815234 | + | 1.41203i | 0.0939250 | + | 0.995579i | \(0.470059\pi\) |
−0.909159 | + | 0.416448i | \(0.863275\pi\) | |||||||
\(510\) | 1.16228 | 0.0514665 | ||||||||
\(511\) | −9.00000 | − | 15.5885i | −0.398137 | − | 0.689593i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −20.8114 | − | 36.0464i | −0.918845 | − | 1.59149i | ||||
\(514\) | 8.74342 | + | 15.1440i | 0.385656 | + | 0.667975i | ||||
\(515\) | 6.74342 | + | 11.6799i | 0.297150 | + | 0.514680i | ||||
\(516\) | 3.66228 | − | 6.34325i | 0.161223 | − | 0.279246i | ||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 31.3925 | + | 0.725489i | 1.37931 | + | 0.0318761i | ||||
\(519\) | −2.32456 | −0.102037 | ||||||||
\(520\) | −2.08114 | + | 3.60464i | −0.0912640 | + | 0.158074i | ||||
\(521\) | −11.8246 | − | 20.4807i | −0.518043 | − | 0.897277i | −0.999780 | − | 0.0209613i | \(-0.993327\pi\) |
0.481737 | − | 0.876316i | \(-0.340006\pi\) | |||||||
\(522\) | −8.32456 | − | 14.4186i | −0.364356 | − | 0.631083i | ||||
\(523\) | 11.9868 | + | 20.7618i | 0.524148 | + | 0.907850i | 0.999605 | + | 0.0281114i | \(0.00894932\pi\) |
−0.475457 | + | 0.879739i | \(0.657717\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 2.58114 | + | 4.47066i | 0.112650 | + | 0.195116i | ||||
\(526\) | 7.48683 | 0.326441 | ||||||||
\(527\) | −2.41886 | + | 4.18959i | −0.105367 | + | 0.182501i | ||||
\(528\) | 1.16228 | 0.0505816 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 7.08114 | − | 12.2649i | 0.307585 | − | 0.532753i | ||||
\(531\) | −1.16228 | − | 2.01312i | −0.0504386 | − | 0.0873621i | ||||
\(532\) | 42.9737 | 1.86314 | ||||||||
\(533\) | 11.0811 | − | 19.1931i | 0.479977 | − | 0.831345i | ||||
\(534\) | 8.32456 | − | 14.4186i | 0.360239 | − | 0.623952i | ||||
\(535\) | 3.50000 | − | 6.06218i | 0.151318 | − | 0.262091i | ||||
\(536\) | −4.16228 | − | 7.20928i | −0.179783 | − | 0.311393i | ||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | 13.5811 | − | 23.5232i | 0.585524 | − | 1.01416i | ||||
\(539\) | 11.4189 | − | 19.7780i | 0.491845 | − | 0.851901i | ||||
\(540\) | −2.50000 | + | 4.33013i | −0.107583 | + | 0.186339i | ||||
\(541\) | 33.6228 | 1.44556 | 0.722778 | − | 0.691080i | \(-0.242865\pi\) | ||||
0.722778 | + | 0.691080i | \(0.242865\pi\) | |||||||
\(542\) | 13.2434 | + | 22.9383i | 0.568853 | + | 0.985283i | ||||
\(543\) | 2.25658 | − | 3.90852i | 0.0968393 | − | 0.167731i | ||||
\(544\) | −1.16228 | −0.0498322 | ||||||||
\(545\) | 3.67544 | 0.157439 | ||||||||
\(546\) | 10.7434 | − | 18.6081i | 0.459776 | − | 0.796355i | ||||
\(547\) | 23.9737 | 1.02504 | 0.512520 | − | 0.858675i | \(-0.328712\pi\) | ||||
0.512520 | + | 0.858675i | \(0.328712\pi\) | |||||||
\(548\) | −5.74342 | − | 9.94789i | −0.245347 | − | 0.424953i | ||||
\(549\) | 16.6491 | 0.710567 | ||||||||
\(550\) | −0.581139 | − | 1.00656i | −0.0247798 | − | 0.0429199i | ||||
\(551\) | −34.6491 | − | 60.0140i | −1.47610 | − | 2.55668i | ||||
\(552\) | −1.58114 | − | 2.73861i | −0.0672977 | − | 0.116563i | ||||
\(553\) | 5.16228 | − | 8.94133i | 0.219522 | − | 0.380224i | ||||
\(554\) | 8.48683 | 0.360571 | ||||||||
\(555\) | −3.16228 | + | 5.19615i | −0.134231 | + | 0.220564i | ||||
\(556\) | −15.4868 | −0.656788 | ||||||||
\(557\) | 3.59431 | − | 6.22552i | 0.152296 | − | 0.263784i | −0.779775 | − | 0.626059i | \(-0.784667\pi\) |
0.932071 | + | 0.362276i | \(0.118000\pi\) | |||||||
\(558\) | −4.16228 | − | 7.20928i | −0.176203 | − | 0.305193i | ||||
\(559\) | 15.2434 | + | 26.4024i | 0.644728 | + | 1.11670i | ||||
\(560\) | −2.58114 | − | 4.47066i | −0.109073 | − | 0.188920i | ||||
\(561\) | 1.35089 | 0.0570346 | ||||||||
\(562\) | −0.824555 | − | 1.42817i | −0.0347818 | − | 0.0602438i | ||||
\(563\) | −11.2982 | −0.476163 | −0.238082 | − | 0.971245i | \(-0.576519\pi\) | ||||
−0.238082 | + | 0.971245i | \(0.576519\pi\) | |||||||
\(564\) | 2.58114 | − | 4.47066i | 0.108686 | − | 0.188249i | ||||
\(565\) | −6.32456 | −0.266076 | ||||||||
\(566\) | −30.6228 | −1.28717 | ||||||||
\(567\) | −2.58114 | + | 4.47066i | −0.108398 | + | 0.187750i | ||||
\(568\) | 3.16228 | + | 5.47723i | 0.132686 | + | 0.229819i | ||||
\(569\) | 27.3246 | 1.14550 | 0.572752 | − | 0.819728i | \(-0.305876\pi\) | ||||
0.572752 | + | 0.819728i | \(0.305876\pi\) | |||||||
\(570\) | −4.16228 | + | 7.20928i | −0.174339 | + | 0.301963i | ||||
\(571\) | −11.1623 | + | 19.3336i | −0.467127 | + | 0.809087i | −0.999295 | − | 0.0375515i | \(-0.988044\pi\) |
0.532168 | + | 0.846639i | \(0.321378\pi\) | |||||||
\(572\) | −2.41886 | + | 4.18959i | −0.101138 | + | 0.175176i | ||||
\(573\) | −4.40569 | − | 7.63089i | −0.184051 | − | 0.318785i | ||||
\(574\) | 13.7434 | + | 23.8043i | 0.573639 | + | 0.993572i | ||||
\(575\) | −1.58114 | + | 2.73861i | −0.0659380 | + | 0.114208i | ||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | 21.5811 | − | 37.3796i | 0.898435 | − | 1.55613i | 0.0689391 | − | 0.997621i | \(-0.478039\pi\) |
0.829495 | − | 0.558513i | \(-0.188628\pi\) | |||||||
\(578\) | 15.6491 | 0.650917 | ||||||||
\(579\) | −0.256584 | − | 0.444416i | −0.0106632 | − | 0.0184693i | ||||
\(580\) | −4.16228 | + | 7.20928i | −0.172829 | + | 0.299349i | ||||
\(581\) | −20.6491 | −0.856669 | ||||||||
\(582\) | −12.3246 | −0.510869 | ||||||||
\(583\) | 8.23025 | − | 14.2552i | 0.340862 | − | 0.590390i | ||||
\(584\) | −3.48683 | −0.144286 | ||||||||
\(585\) | −4.16228 | − | 7.20928i | −0.172089 | − | 0.298067i | ||||
\(586\) | −0.486833 | −0.0201109 | ||||||||
\(587\) | 9.31139 | + | 16.1278i | 0.384322 | + | 0.665665i | 0.991675 | − | 0.128767i | \(-0.0411019\pi\) |
−0.607353 | + | 0.794432i | \(0.707769\pi\) | |||||||
\(588\) | 9.82456 | + | 17.0166i | 0.405158 | + | 0.701754i | ||||
\(589\) | −17.3246 | − | 30.0070i | −0.713846 | − | 1.23642i | ||||
\(590\) | −0.581139 | + | 1.00656i | −0.0239251 | + | 0.0414395i | ||||
\(591\) | −13.8377 | −0.569208 | ||||||||
\(592\) | 3.16228 | − | 5.19615i | 0.129969 | − | 0.213561i | ||||
\(593\) | −44.1359 | −1.81245 | −0.906223 | − | 0.422800i | \(-0.861047\pi\) | ||||
−0.906223 | + | 0.422800i | \(0.861047\pi\) | |||||||
\(594\) | −2.90569 | + | 5.03281i | −0.119222 | + | 0.206499i | ||||
\(595\) | −3.00000 | − | 5.19615i | −0.122988 | − | 0.213021i | ||||
\(596\) | −6.00000 | − | 10.3923i | −0.245770 | − | 0.425685i | ||||
\(597\) | −2.91886 | − | 5.05562i | −0.119461 | − | 0.206913i | ||||
\(598\) | 13.1623 | 0.538246 | ||||||||
\(599\) | 21.7302 | + | 37.6379i | 0.887874 | + | 1.53784i | 0.842384 | + | 0.538878i | \(0.181152\pi\) |
0.0454901 | + | 0.998965i | \(0.485515\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −3.82456 | + | 6.62432i | −0.156007 | + | 0.270212i | −0.933425 | − | 0.358772i | \(-0.883196\pi\) |
0.777418 | + | 0.628984i | \(0.216529\pi\) | |||||||
\(602\) | −37.8114 | −1.54108 | ||||||||
\(603\) | 16.6491 | 0.678004 | ||||||||
\(604\) | −1.75658 | + | 3.04249i | −0.0714744 | + | 0.123797i | ||||
\(605\) | 4.82456 | + | 8.35637i | 0.196146 | + | 0.339735i | ||||
\(606\) | 12.8377 | 0.521497 | ||||||||
\(607\) | 8.25658 | − | 14.3008i | 0.335124 | − | 0.580452i | −0.648384 | − | 0.761313i | \(-0.724555\pi\) |
0.983509 | + | 0.180861i | \(0.0578883\pi\) | |||||||
\(608\) | 4.16228 | − | 7.20928i | 0.168803 | − | 0.292375i | ||||
\(609\) | 21.4868 | − | 37.2163i | 0.870690 | − | 1.50808i | ||||
\(610\) | −4.16228 | − | 7.20928i | −0.168526 | − | 0.291895i | ||||
\(611\) | 10.7434 | + | 18.6081i | 0.434632 | + | 0.752805i | ||||
\(612\) | 1.16228 | − | 2.01312i | 0.0469823 | − | 0.0813757i | ||||
\(613\) | 12.1623 | − | 21.0657i | 0.491230 | − | 0.850835i | −0.508719 | − | 0.860932i | \(-0.669881\pi\) |
0.999949 | + | 0.0100976i | \(0.00321421\pi\) | |||||||
\(614\) | −13.1491 | + | 22.7749i | −0.530655 | + | 0.919121i | ||||
\(615\) | −5.32456 | −0.214707 | ||||||||
\(616\) | −3.00000 | − | 5.19615i | −0.120873 | − | 0.209359i | ||||
\(617\) | −0.486833 | + | 0.843219i | −0.0195992 | + | 0.0339467i | −0.875659 | − | 0.482931i | \(-0.839572\pi\) |
0.856059 | + | 0.516877i | \(0.172906\pi\) | |||||||
\(618\) | −13.4868 | −0.542520 | ||||||||
\(619\) | −34.0000 | −1.36658 | −0.683288 | − | 0.730149i | \(-0.739451\pi\) | ||||
−0.683288 | + | 0.730149i | \(0.739451\pi\) | |||||||
\(620\) | −2.08114 | + | 3.60464i | −0.0835805 | + | 0.144766i | ||||
\(621\) | 15.8114 | 0.634489 | ||||||||
\(622\) | 4.08114 | + | 7.06874i | 0.163639 | + | 0.283431i | ||||
\(623\) | −85.9473 | −3.44341 | ||||||||
\(624\) | −2.08114 | − | 3.60464i | −0.0833122 | − | 0.144301i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | −4.83772 | + | 8.37918i | −0.193200 | + | 0.334632i | ||||
\(628\) | −10.1623 | −0.405519 | ||||||||
\(629\) | 3.67544 | − | 6.03937i | 0.146550 | − | 0.240806i | ||||
\(630\) | 10.3246 | 0.411340 | ||||||||
\(631\) | −5.91886 | + | 10.2518i | −0.235626 | + | 0.408116i | −0.959454 | − | 0.281864i | \(-0.909047\pi\) |
0.723828 | + | 0.689980i | \(0.242381\pi\) | |||||||
\(632\) | −1.00000 | − | 1.73205i | −0.0397779 | − | 0.0688973i | ||||
\(633\) | −4.16228 | − | 7.20928i | −0.165436 | − | 0.286543i | ||||
\(634\) | −3.24342 | − | 5.61776i | −0.128813 | − | 0.223110i | ||||
\(635\) | 5.67544 | 0.225223 | ||||||||
\(636\) | 7.08114 | + | 12.2649i | 0.280785 | + | 0.486335i | ||||
\(637\) | −81.7851 | −3.24044 | ||||||||
\(638\) | −4.83772 | + | 8.37918i | −0.191527 | + | 0.331735i | ||||
\(639\) | −12.6491 | −0.500391 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −9.33772 | + | 16.1734i | −0.368818 | + | 0.638811i | −0.989381 | − | 0.145345i | \(-0.953571\pi\) |
0.620563 | + | 0.784156i | \(0.286904\pi\) | |||||||
\(642\) | 3.50000 | + | 6.06218i | 0.138134 | + | 0.239255i | ||||
\(643\) | 10.0263 | 0.395400 | 0.197700 | − | 0.980263i | \(-0.436653\pi\) | ||||
0.197700 | + | 0.980263i | \(0.436653\pi\) | |||||||
\(644\) | −8.16228 | + | 14.1375i | −0.321639 | + | 0.557095i | ||||
\(645\) | 3.66228 | − | 6.34325i | 0.144202 | − | 0.249765i | ||||
\(646\) | 4.83772 | − | 8.37918i | 0.190338 | − | 0.329674i | ||||
\(647\) | −13.1623 | − | 22.7977i | −0.517463 | − | 0.896271i | −0.999794 | − | 0.0202828i | \(-0.993543\pi\) |
0.482332 | − | 0.875989i | \(-0.339790\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −0.675445 | + | 1.16990i | −0.0265135 | + | 0.0459228i | ||||
\(650\) | −2.08114 | + | 3.60464i | −0.0816290 | + | 0.141386i | ||||
\(651\) | 10.7434 | − | 18.6081i | 0.421068 | − | 0.729311i | ||||
\(652\) | 5.64911 | 0.221236 | ||||||||
\(653\) | 9.73025 | + | 16.8533i | 0.380774 | + | 0.659520i | 0.991173 | − | 0.132574i | \(-0.0423242\pi\) |
−0.610399 | + | 0.792094i | \(0.708991\pi\) | |||||||
\(654\) | −1.83772 | + | 3.18303i | −0.0718606 | + | 0.124466i | ||||
\(655\) | −18.0000 | −0.703318 | ||||||||
\(656\) | 5.32456 | 0.207889 | ||||||||
\(657\) | 3.48683 | − | 6.03937i | 0.136034 | − | 0.235618i | ||||
\(658\) | −26.6491 | −1.03889 | ||||||||
\(659\) | −21.4868 | − | 37.2163i | −0.837008 | − | 1.44974i | −0.892385 | − | 0.451275i | \(-0.850969\pi\) |
0.0553767 | − | 0.998466i | \(-0.482364\pi\) | |||||||
\(660\) | 1.16228 | 0.0452416 | ||||||||
\(661\) | −1.09431 | − | 1.89539i | −0.0425636 | − | 0.0737223i | 0.843959 | − | 0.536408i | \(-0.180219\pi\) |
−0.886522 | + | 0.462686i | \(0.846886\pi\) | |||||||
\(662\) | 7.25658 | + | 12.5688i | 0.282035 | + | 0.488499i | ||||
\(663\) | −2.41886 | − | 4.18959i | −0.0939408 | − | 0.162710i | ||||
\(664\) | −2.00000 | + | 3.46410i | −0.0776151 | + | 0.134433i | ||||
\(665\) | 42.9737 | 1.66645 | ||||||||
\(666\) | 5.83772 | + | 10.6734i | 0.226207 | + | 0.413585i | ||||
\(667\) | 26.3246 | 1.01929 | ||||||||
\(668\) | 4.16228 | − | 7.20928i | 0.161043 | − | 0.278935i | ||||
\(669\) | 0.418861 | + | 0.725489i | 0.0161941 | + | 0.0280490i | ||||
\(670\) | −4.16228 | − | 7.20928i | −0.160803 | − | 0.278519i | ||||
\(671\) | −4.83772 | − | 8.37918i | −0.186758 | − | 0.323475i | ||||
\(672\) | 5.16228 | 0.199139 | ||||||||
\(673\) | 7.90569 | + | 13.6931i | 0.304742 | + | 0.527829i | 0.977204 | − | 0.212303i | \(-0.0680964\pi\) |
−0.672462 | + | 0.740132i | \(0.734763\pi\) | |||||||
\(674\) | 27.2982 | 1.05149 | ||||||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | 4.32456 | 0.166329 | ||||||||
\(677\) | 21.6228 | 0.831031 | 0.415515 | − | 0.909586i | \(-0.363601\pi\) | ||||
0.415515 | + | 0.909586i | \(0.363601\pi\) | |||||||
\(678\) | 3.16228 | − | 5.47723i | 0.121447 | − | 0.210352i | ||||
\(679\) | 31.8114 | + | 55.0989i | 1.22081 | + | 2.11450i | ||||
\(680\) | −1.16228 | −0.0445713 | ||||||||
\(681\) | −1.33772 | + | 2.31700i | −0.0512616 | + | 0.0887878i | ||||
\(682\) | −2.41886 | + | 4.18959i | −0.0926230 | + | 0.160428i | ||||
\(683\) | −13.8246 | + | 23.9448i | −0.528982 | + | 0.916224i | 0.470447 | + | 0.882428i | \(0.344093\pi\) |
−0.999429 | + | 0.0337952i | \(0.989241\pi\) | |||||||
\(684\) | 8.32456 | + | 14.4186i | 0.318297 | + | 0.551307i | ||||
\(685\) | −5.74342 | − | 9.94789i | −0.219445 | − | 0.380089i | ||||
\(686\) | 32.6491 | − | 56.5499i | 1.24655 | − | 2.15909i | ||||
\(687\) | −5.41886 | + | 9.38574i | −0.206742 | + | 0.358088i | ||||
\(688\) | −3.66228 | + | 6.34325i | −0.139623 | + | 0.241834i | ||||
\(689\) | −58.9473 | −2.24571 | ||||||||
\(690\) | −1.58114 | − | 2.73861i | −0.0601929 | − | 0.104257i | ||||
\(691\) | 1.90569 | − | 3.30076i | 0.0724960 | − | 0.125567i | −0.827499 | − | 0.561468i | \(-0.810237\pi\) |
0.899995 | + | 0.435901i | \(0.143570\pi\) | |||||||
\(692\) | 2.32456 | 0.0883663 | ||||||||
\(693\) | 12.0000 | 0.455842 | ||||||||
\(694\) | −3.83772 | + | 6.64713i | −0.145678 | + | 0.252322i | ||||
\(695\) | −15.4868 | −0.587449 | ||||||||
\(696\) | −4.16228 | − | 7.20928i | −0.157771 | − | 0.273267i | ||||
\(697\) | 6.18861 | 0.234410 | ||||||||
\(698\) | 1.00000 | + | 1.73205i | 0.0378506 | + | 0.0655591i | ||||
\(699\) | 6.74342 | + | 11.6799i | 0.255059 | + | 0.441776i | ||||
\(700\) | −2.58114 | − | 4.47066i | −0.0975579 | − | 0.168975i | ||||
\(701\) | −4.48683 | + | 7.77142i | −0.169465 | + | 0.293523i | −0.938232 | − | 0.346007i | \(-0.887537\pi\) |
0.768767 | + | 0.639529i | \(0.220871\pi\) | |||||||
\(702\) | 20.8114 | 0.785475 | ||||||||
\(703\) | 24.2982 | + | 44.4256i | 0.916425 | + | 1.67554i | ||||
\(704\) | −1.16228 | −0.0438050 | ||||||||
\(705\) | 2.58114 | − | 4.47066i | 0.0972113 | − | 0.168375i | ||||
\(706\) | 7.90569 | + | 13.6931i | 0.297535 | + | 0.515345i | ||||
\(707\) | −33.1359 | − | 57.3931i | −1.24621 | − | 2.15849i | ||||
\(708\) | −0.581139 | − | 1.00656i | −0.0218405 | − | 0.0378289i | ||||
\(709\) | 3.35089 | 0.125845 | 0.0629226 | − | 0.998018i | \(-0.479958\pi\) | ||||
0.0629226 | + | 0.998018i | \(0.479958\pi\) | |||||||
\(710\) | 3.16228 | + | 5.47723i | 0.118678 | + | 0.205557i | ||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | −8.32456 | + | 14.4186i | −0.311976 | + | 0.540358i | ||||
\(713\) | 13.1623 | 0.492931 | ||||||||
\(714\) | 6.00000 | 0.224544 | ||||||||
\(715\) | −2.41886 | + | 4.18959i | −0.0904603 | + | 0.156682i | ||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | −10.6491 | −0.397698 | ||||||||
\(718\) | 2.24342 | − | 3.88571i | 0.0837236 | − | 0.145013i | ||||
\(719\) | 2.56797 | − | 4.44786i | 0.0957692 | − | 0.165877i | −0.814160 | − | 0.580640i | \(-0.802802\pi\) |
0.909929 | + | 0.414763i | \(0.136136\pi\) | |||||||
\(720\) | 1.00000 | − | 1.73205i | 0.0372678 | − | 0.0645497i | ||||
\(721\) | 34.8114 | + | 60.2951i | 1.29644 | + | 2.24551i | ||||
\(722\) | 25.1491 | + | 43.5595i | 0.935953 | + | 1.62112i | ||||
\(723\) | −5.32456 | + | 9.22240i | −0.198022 | + | 0.342985i | ||||
\(724\) | −2.25658 | + | 3.90852i | −0.0838653 | + | 0.145259i | ||||
\(725\) | −4.16228 | + | 7.20928i | −0.154583 | + | 0.267746i | ||||
\(726\) | −9.64911 | −0.358112 | ||||||||
\(727\) | −0.837722 | − | 1.45098i | −0.0310694 | − | 0.0538138i | 0.850073 | − | 0.526666i | \(-0.176558\pi\) |
−0.881142 | + | 0.472852i | \(0.843225\pi\) | |||||||
\(728\) | −10.7434 | + | 18.6081i | −0.398178 | + | 0.689664i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −3.48683 | −0.129053 | ||||||||
\(731\) | −4.25658 | + | 7.37262i | −0.157435 | + | 0.272686i | ||||
\(732\) | 8.32456 | 0.307684 | ||||||||
\(733\) | 3.32456 | + | 5.75830i | 0.122795 | + | 0.212688i | 0.920869 | − | 0.389872i | \(-0.127481\pi\) |
−0.798074 | + | 0.602560i | \(0.794147\pi\) | |||||||
\(734\) | 6.64911 | 0.245423 | ||||||||
\(735\) | 9.82456 | + | 17.0166i | 0.362384 | + | 0.627668i | ||||
\(736\) | 1.58114 | + | 2.73861i | 0.0582816 | + | 0.100947i | ||||
\(737\) | −4.83772 | − | 8.37918i | −0.178200 | − | 0.308651i | ||||
\(738\) | −5.32456 | + | 9.22240i | −0.196000 | + | 0.339481i | ||||
\(739\) | 15.4868 | 0.569692 | 0.284846 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284846 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(740\) | 3.16228 | − | 5.19615i | 0.116248 | − | 0.191014i | ||||
\(741\) | 34.6491 | 1.27287 | ||||||||
\(742\) | 36.5548 | − | 63.3148i | 1.34197 | − | 2.32436i | ||||
\(743\) | 2.41886 | + | 4.18959i | 0.0887394 | + | 0.153701i | 0.906979 | − | 0.421177i | \(-0.138383\pi\) |
−0.818239 | + | 0.574878i | \(0.805049\pi\) | |||||||
\(744\) | −2.08114 | − | 3.60464i | −0.0762983 | − | 0.132152i | ||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | −10.4868 | −0.383950 | ||||||||
\(747\) | −4.00000 | − | 6.92820i | −0.146352 | − | 0.253490i | ||||
\(748\) | −1.35089 | −0.0493934 | ||||||||
\(749\) | 18.0680 | − | 31.2946i | 0.660189 | − | 1.14348i | ||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 14.4868 | 0.528632 | 0.264316 | − | 0.964436i | \(-0.414854\pi\) | ||||
0.264316 | + | 0.964436i | \(0.414854\pi\) | |||||||
\(752\) | −2.58114 | + | 4.47066i | −0.0941244 | + | 0.163028i | ||||
\(753\) | 3.00000 | + | 5.19615i | 0.109326 | + | 0.189358i | ||||
\(754\) | 34.6491 | 1.26185 | ||||||||
\(755\) | −1.75658 | + | 3.04249i | −0.0639286 | + | 0.110728i | ||||
\(756\) | −12.9057 | + | 22.3533i | −0.469376 | + | 0.812982i | ||||
\(757\) | −11.2434 | + | 19.4742i | −0.408649 | + | 0.707801i | −0.994739 | − | 0.102445i | \(-0.967333\pi\) |
0.586090 | + | 0.810246i | \(0.300667\pi\) | |||||||
\(758\) | 15.7434 | + | 27.2684i | 0.571827 | + | 0.990433i | ||||
\(759\) | −1.83772 | − | 3.18303i | −0.0667051 | − | 0.115537i | ||||
\(760\) | 4.16228 | − | 7.20928i | 0.150982 | − | 0.261508i | ||||
\(761\) | −7.16228 | + | 12.4054i | −0.259632 | + | 0.449696i | −0.966143 | − | 0.258006i | \(-0.916935\pi\) |
0.706511 | + | 0.707702i | \(0.250268\pi\) | |||||||
\(762\) | −2.83772 | + | 4.91508i | −0.102800 | + | 0.178055i | ||||
\(763\) | 18.9737 | 0.686893 | ||||||||
\(764\) | 4.40569 | + | 7.63089i | 0.159392 | + | 0.276076i | ||||
\(765\) | 1.16228 | − | 2.01312i | 0.0420222 | − | 0.0727847i | ||||
\(766\) | 1.16228 | 0.0419948 | ||||||||
\(767\) | 4.83772 | 0.174680 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 14.9737 | 0.539964 | 0.269982 | − | 0.962865i | \(-0.412982\pi\) | ||||
0.269982 | + | 0.962865i | \(0.412982\pi\) | |||||||
\(770\) | −3.00000 | − | 5.19615i | −0.108112 | − | 0.187256i | ||||
\(771\) | −17.4868 | −0.629773 | ||||||||
\(772\) | 0.256584 | + | 0.444416i | 0.00923464 | + | 0.0159949i | ||||
\(773\) | 14.8925 | + | 25.7946i | 0.535647 | + | 0.927768i | 0.999132 | + | 0.0416629i | \(0.0132655\pi\) |
−0.463485 | + | 0.886105i | \(0.653401\pi\) | |||||||
\(774\) | −7.32456 | − | 12.6865i | −0.263276 | − | 0.456007i | ||||
\(775\) | −2.08114 | + | 3.60464i | −0.0747567 | + | 0.129482i | ||||
\(776\) | 12.3246 | 0.442426 | ||||||||
\(777\) | −16.3246 | + | 26.8240i | −0.585640 | + | 0.962305i | ||||
\(778\) | −28.6491 | −1.02712 | ||||||||
\(779\) | −22.1623 | + | 38.3862i | −0.794046 | + | 1.37533i | ||||
\(780\) | −2.08114 | − | 3.60464i | −0.0745167 | − | 0.129067i | ||||
\(781\) | 3.67544 | + | 6.36606i | 0.131518 | + | 0.227795i | ||||
\(782\) | 1.83772 | + | 3.18303i | 0.0657168 | + | 0.113825i | ||||
\(783\) | 41.6228 | 1.48748 | ||||||||
\(784\) | −9.82456 | − | 17.0166i | −0.350877 | − | 0.607737i | ||||
\(785\) | −10.1623 | −0.362707 | ||||||||
\(786\) | 9.00000 | − | 15.5885i | 0.321019 | − | 0.556022i | ||||
\(787\) | −7.97367 | −0.284230 | −0.142115 | − | 0.989850i | \(-0.545390\pi\) | ||||
−0.142115 | + | 0.989850i | \(0.545390\pi\) | |||||||
\(788\) | 13.8377 | 0.492948 | ||||||||
\(789\) | −3.74342 | + | 6.48379i | −0.133269 | + | 0.230829i | ||||
\(790\) | −1.00000 | − | 1.73205i | −0.0355784 | − | 0.0616236i | ||||
\(791\) | −32.6491 | −1.16087 | ||||||||
\(792\) | 1.16228 | − | 2.01312i | 0.0412997 | − | 0.0715332i | ||||
\(793\) | −17.3246 | + | 30.0070i | −0.615213 | + | 1.06558i | ||||
\(794\) | 2.08114 | − | 3.60464i | 0.0738569 | − | 0.127924i | ||||
\(795\) | 7.08114 | + | 12.2649i | 0.251142 | + | 0.434991i | ||||
\(796\) | 2.91886 | + | 5.05562i | 0.103456 | + | 0.179192i | ||||
\(797\) | 18.0811 | − | 31.3175i | 0.640467 | − | 1.10932i | −0.344862 | − | 0.938653i | \(-0.612074\pi\) |
0.985329 | − | 0.170668i | \(-0.0545924\pi\) | |||||||
\(798\) | −21.4868 | + | 37.2163i | −0.760626 | + | 1.31744i | ||||
\(799\) | −3.00000 | + | 5.19615i | −0.106132 | + | 0.183827i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −16.6491 | − | 28.8371i | −0.588267 | − | 1.01891i | ||||
\(802\) | −4.00000 | + | 6.92820i | −0.141245 | + | 0.244643i | ||||
\(803\) | −4.05267 | −0.143016 | ||||||||
\(804\) | 8.32456 | 0.293584 | ||||||||
\(805\) | −8.16228 | + | 14.1375i | −0.287682 | + | 0.498281i | ||||
\(806\) | 17.3246 | 0.610231 | ||||||||
\(807\) | 13.5811 | + | 23.5232i | 0.478079 | + | 0.828057i | ||||
\(808\) | −12.8377 | −0.451629 | ||||||||
\(809\) | −20.1491 | − | 34.8993i | −0.708405 | − | 1.22699i | −0.965449 | − | 0.260594i | \(-0.916082\pi\) |
0.257044 | − | 0.966400i | \(-0.417252\pi\) | |||||||
\(810\) | 0.500000 | + | 0.866025i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | −16.9737 | − | 29.3993i | −0.596026 | − | 1.03235i | −0.993401 | − | 0.114691i | \(-0.963412\pi\) |
0.397375 | − | 0.917656i | \(-0.369921\pi\) | |||||||
\(812\) | −21.4868 | + | 37.2163i | −0.754040 | + | 1.30604i | ||||
\(813\) | −26.4868 | −0.928934 | ||||||||
\(814\) | 3.67544 | − | 6.03937i | 0.128824 | − | 0.211680i | ||||
\(815\) | 5.64911 | 0.197880 | ||||||||
\(816\) | 0.581139 | − | 1.00656i | 0.0203439 | − | 0.0352367i | ||||
\(817\) | −30.4868 | − | 52.8047i | −1.06660 | − | 1.84740i | ||||
\(818\) | −9.82456 | − | 17.0166i | −0.343508 | − | 0.594972i | ||||
\(819\) | −21.4868 | − | 37.2163i | −0.750811 | − | 1.30044i | ||||
\(820\) | 5.32456 | 0.185942 | ||||||||
\(821\) | 15.8377 | + | 27.4317i | 0.552740 | + | 0.957374i | 0.998076 | + | 0.0620104i | \(0.0197512\pi\) |
−0.445335 | + | 0.895364i | \(0.646915\pi\) | |||||||
\(822\) | 11.4868 | 0.400649 | ||||||||
\(823\) | −1.93203 | + | 3.34637i | −0.0673463 | + | 0.116647i | −0.897732 | − | 0.440541i | \(-0.854787\pi\) |
0.830386 | + | 0.557188i | \(0.188120\pi\) | |||||||
\(824\) | 13.4868 | 0.469836 | ||||||||
\(825\) | 1.16228 | 0.0404653 | ||||||||
\(826\) | −3.00000 | + | 5.19615i | −0.104383 | + | 0.180797i | ||||
\(827\) | 14.1623 | + | 24.5298i | 0.492471 | + | 0.852984i | 0.999962 | − | 0.00867244i | \(-0.00276056\pi\) |
−0.507492 | + | 0.861657i | \(0.669427\pi\) | |||||||
\(828\) | −6.32456 | −0.219793 | ||||||||
\(829\) | −19.5548 | + | 33.8699i | −0.679166 | + | 1.17635i | 0.296066 | + | 0.955168i | \(0.404325\pi\) |
−0.975232 | + | 0.221183i | \(0.929008\pi\) | |||||||
\(830\) | −2.00000 | + | 3.46410i | −0.0694210 | + | 0.120241i | ||||
\(831\) | −4.24342 | + | 7.34981i | −0.147202 | + | 0.254962i | ||||
\(832\) | 2.08114 | + | 3.60464i | 0.0721505 | + | 0.124968i | ||||
\(833\) | −11.4189 | − | 19.7780i | −0.395640 | − | 0.685269i | ||||
\(834\) | 7.74342 | − | 13.4120i | 0.268133 | − | 0.464419i | ||||
\(835\) | 4.16228 | − | 7.20928i | 0.144042 | − | 0.249487i | ||||
\(836\) | 4.83772 | − | 8.37918i | 0.167316 | − | 0.289800i | ||||
\(837\) | 20.8114 | 0.719347 | ||||||||
\(838\) | −8.90569 | − | 15.4251i | −0.307642 | − | 0.532852i | ||||
\(839\) | 8.75658 | − | 15.1668i | 0.302311 | − | 0.523618i | −0.674348 | − | 0.738414i | \(-0.735575\pi\) |
0.976659 | + | 0.214796i | \(0.0689086\pi\) | |||||||
\(840\) | 5.16228 | 0.178116 | ||||||||
\(841\) | 40.2982 | 1.38959 | ||||||||
\(842\) | −5.74342 | + | 9.94789i | −0.197931 | + | 0.342827i | ||||
\(843\) | 1.64911 | 0.0567984 | ||||||||
\(844\) | 4.16228 | + | 7.20928i | 0.143272 | + | 0.248154i | ||||
\(845\) | 4.32456 | 0.148769 | ||||||||
\(846\) | −5.16228 | − | 8.94133i | −0.177483 | − | 0.307409i | ||||
\(847\) | 24.9057 | + | 43.1379i | 0.855770 | + | 1.48224i | ||||
\(848\) | −7.08114 | − | 12.2649i | −0.243167 | − | 0.421178i | ||||
\(849\) | 15.3114 | − | 26.5201i | 0.525485 | − | 0.910168i | ||||
\(850\) | −1.16228 | −0.0398658 | ||||||||
\(851\) | −19.2302 | − | 0.444416i | −0.659204 | − | 0.0152344i | ||||
\(852\) | −6.32456 | −0.216676 | ||||||||
\(853\) | −22.5680 | + | 39.0889i | −0.772713 | + | 1.33838i | 0.163359 | + | 0.986567i | \(0.447767\pi\) |
−0.936071 | + | 0.351811i | \(0.885566\pi\) | |||||||
\(854\) | −21.4868 | − | 37.2163i | −0.735264 | − | 1.27352i | ||||
\(855\) | 8.32456 | + | 14.4186i | 0.284694 | + | 0.493104i | ||||
\(856\) | −3.50000 | − | 6.06218i | −0.119628 | − | 0.207201i | ||||
\(857\) | 8.51317 | 0.290804 | 0.145402 | − | 0.989373i | \(-0.453552\pi\) | ||||
0.145402 | + | 0.989373i | \(0.453552\pi\) | |||||||
\(858\) | −2.41886 | − | 4.18959i | −0.0825786 | − | 0.143030i | ||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | −3.66228 | + | 6.34325i | −0.124883 | + | 0.216303i | ||||
\(861\) | −27.4868 | −0.936749 | ||||||||
\(862\) | 27.1359 | 0.924254 | ||||||||
\(863\) | −18.9737 | + | 32.8634i | −0.645871 | + | 1.11868i | 0.338228 | + | 0.941064i | \(0.390172\pi\) |
−0.984100 | + | 0.177618i | \(0.943161\pi\) | |||||||
\(864\) | 2.50000 | + | 4.33013i | 0.0850517 | + | 0.147314i | ||||
\(865\) | 2.32456 | 0.0790373 | ||||||||
\(866\) | −8.00000 | + | 13.8564i | −0.271851 | + | 0.470860i | ||||
\(867\) | −7.82456 | + | 13.5525i | −0.265736 | + | 0.460268i | ||||
\(868\) | −10.7434 | + | 18.6081i | −0.364655 | + | 0.631602i | ||||
\(869\) | −1.16228 | − | 2.01312i | −0.0394276 | − | 0.0682906i | ||||
\(870\) | −4.16228 | − | 7.20928i | −0.141114 | − | 0.244417i | ||||
\(871\) | −17.3246 | + | 30.0070i | −0.587020 | + | 1.01675i | ||||
\(872\) | 1.83772 | − | 3.18303i | 0.0622331 | − | 0.107791i | ||||
\(873\) | −12.3246 | + | 21.3468i | −0.417123 | + | 0.722478i | ||||
\(874\) | −26.3246 | −0.890441 | ||||||||
\(875\) | −2.58114 | − | 4.47066i | −0.0872584 | − | 0.151136i | ||||
\(876\) | 1.74342 | − | 3.01969i | 0.0589046 | − | 0.102026i | ||||
\(877\) | 33.8377 | 1.14262 | 0.571309 | − | 0.820735i | \(-0.306436\pi\) | ||||
0.571309 | + | 0.820735i | \(0.306436\pi\) | |||||||
\(878\) | 4.81139 | 0.162376 | ||||||||
\(879\) | 0.243416 | − | 0.421610i | 0.00821023 | − | 0.0142205i | ||||
\(880\) | −1.16228 | −0.0391804 | ||||||||
\(881\) | −8.51317 | − | 14.7452i | −0.286816 | − | 0.496780i | 0.686232 | − | 0.727383i | \(-0.259263\pi\) |
−0.973048 | + | 0.230603i | \(0.925930\pi\) | |||||||
\(882\) | 39.2982 | 1.32324 | ||||||||
\(883\) | 3.50000 | + | 6.06218i | 0.117784 | + | 0.204009i | 0.918889 | − | 0.394515i | \(-0.129088\pi\) |
−0.801105 | + | 0.598524i | \(0.795754\pi\) | |||||||
\(884\) | 2.41886 | + | 4.18959i | 0.0813551 | + | 0.140911i | ||||
\(885\) | −0.581139 | − | 1.00656i | −0.0195348 | − | 0.0338352i | ||||
\(886\) | 18.6623 | − | 32.3240i | 0.626971 | − | 1.08595i | ||||
\(887\) | −12.9737 | −0.435613 | −0.217807 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217807 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(888\) | 2.91886 | + | 5.33669i | 0.0979506 | + | 0.179088i | ||||
\(889\) | 29.2982 | 0.982631 | ||||||||
\(890\) | −8.32456 | + | 14.4186i | −0.279040 | + | 0.483311i | ||||
\(891\) | 0.581139 | + | 1.00656i | 0.0194689 | + | 0.0337211i | ||||
\(892\) | −0.418861 | − | 0.725489i | −0.0140245 | − | 0.0242912i | ||||
\(893\) | −21.4868 | − | 37.2163i | −0.719029 | − | 1.24540i | ||||
\(894\) | 12.0000 | 0.401340 | ||||||||
\(895\) | 6.00000 | + | 10.3923i | 0.200558 | + | 0.347376i | ||||
\(896\) | −5.16228 | −0.172460 | ||||||||
\(897\) | −6.58114 | + | 11.3989i | −0.219738 | + | 0.380597i | ||||
\(898\) | −6.35089 | −0.211932 | ||||||||
\(899\) | 34.6491 | 1.15561 | ||||||||
\(900\) | 1.00000 | − | 1.73205i | 0.0333333 | − | 0.0577350i | ||||
\(901\) | −8.23025 | − | 14.2552i | −0.274189 | − | 0.474910i | ||||
\(902\) | 6.18861 | 0.206058 | ||||||||
\(903\) | 18.9057 | − | 32.7456i | 0.629142 | − | 1.08971i | ||||
\(904\) | −3.16228 | + | 5.47723i | −0.105176 | + | 0.182170i | ||||
\(905\) | −2.25658 | + | 3.90852i | −0.0750114 | + | 0.129924i | ||||
\(906\) | −1.75658 | − | 3.04249i | −0.0583586 | − | 0.101080i | ||||
\(907\) | −24.4868 | − | 42.4124i | −0.813072 | − | 1.40828i | −0.910704 | − | 0.413059i | \(-0.864460\pi\) |
0.0976322 | − | 0.995223i | \(-0.468873\pi\) | |||||||
\(908\) | 1.33772 | − | 2.31700i | 0.0443939 | − | 0.0768924i | ||||
\(909\) | 12.8377 | − | 22.2356i | 0.425800 | − | 0.737508i | ||||
\(910\) | −10.7434 | + | 18.6081i | −0.356141 | + | 0.616854i | ||||
\(911\) | 28.1623 | 0.933058 | 0.466529 | − | 0.884506i | \(-0.345504\pi\) | ||||
0.466529 | + | 0.884506i | \(0.345504\pi\) | |||||||
\(912\) | 4.16228 | + | 7.20928i | 0.137827 | + | 0.238723i | ||||
\(913\) | −2.32456 | + | 4.02625i | −0.0769316 | + | 0.133249i | ||||
\(914\) | −6.97367 | −0.230668 | ||||||||
\(915\) | 8.32456 | 0.275201 | ||||||||
\(916\) | 5.41886 | − | 9.38574i | 0.179044 | − | 0.310114i | ||||
\(917\) | −92.9210 | −3.06852 | ||||||||
\(918\) | 2.90569 | + | 5.03281i | 0.0959022 | + | 0.166107i | ||||
\(919\) | 22.3246 | 0.736419 | 0.368210 | − | 0.929743i | \(-0.379971\pi\) | ||||
0.368210 | + | 0.929743i | \(0.379971\pi\) | |||||||
\(920\) | 1.58114 | + | 2.73861i | 0.0521286 | + | 0.0902894i | ||||
\(921\) | −13.1491 | − | 22.7749i | −0.433278 | − | 0.750459i | ||||
\(922\) | −3.83772 | − | 6.64713i | −0.126389 | − | 0.218912i | ||||
\(923\) | 13.1623 | − | 22.7977i | 0.433242 | − | 0.750397i | ||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | 3.16228 | − | 5.19615i | 0.103975 | − | 0.170848i | ||||
\(926\) | −18.9737 | −0.623513 | ||||||||
\(927\) | −13.4868 | + | 23.3599i | −0.442966 | + | 0.767239i | ||||
\(928\) | 4.16228 | + | 7.20928i | 0.136633 | + | 0.236656i | ||||
\(929\) | 9.82456 | + | 17.0166i | 0.322333 | + | 0.558297i | 0.980969 | − | 0.194164i | \(-0.0621995\pi\) |
−0.658636 | + | 0.752462i | \(0.728866\pi\) | |||||||
\(930\) | −2.08114 | − | 3.60464i | −0.0682432 | − | 0.118201i | ||||
\(931\) | 163.570 | 5.36079 | ||||||||
\(932\) | −6.74342 | − | 11.6799i | −0.220888 | − | 0.382589i | ||||
\(933\) | −8.16228 | −0.267221 | ||||||||
\(934\) | −20.8246 | + | 36.0692i | −0.681400 | + | 1.18022i | ||||
\(935\) | −1.35089 | −0.0441788 | ||||||||
\(936\) | −8.32456 | −0.272097 | ||||||||
\(937\) | 22.2982 | − | 38.6217i | 0.728451 | − | 1.26171i | −0.229086 | − | 0.973406i | \(-0.573574\pi\) |
0.957538 | − | 0.288308i | \(-0.0930928\pi\) | |||||||
\(938\) | −21.4868 | − | 37.2163i | −0.701570 | − | 1.21515i | ||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −2.58114 | + | 4.47066i | −0.0841875 | + | 0.145817i | ||||
\(941\) | 14.2302 | − | 24.6475i | 0.463893 | − | 0.803486i | −0.535258 | − | 0.844689i | \(-0.679786\pi\) |
0.999151 | + | 0.0412026i | \(0.0131189\pi\) | |||||||
\(942\) | 5.08114 | − | 8.80079i | 0.165552 | − | 0.286745i | ||||
\(943\) | −8.41886 | − | 14.5819i | −0.274156 | − | 0.474852i | ||||
\(944\) | 0.581139 | + | 1.00656i | 0.0189145 | + | 0.0327608i | ||||
\(945\) | −12.9057 | + | 22.3533i | −0.419822 | + | 0.727153i | ||||
\(946\) | −4.25658 | + | 7.37262i | −0.138393 | + | 0.239705i | ||||
\(947\) | 18.3377 | − | 31.7619i | 0.595896 | − | 1.03212i | −0.397524 | − | 0.917592i | \(-0.630130\pi\) |
0.993420 | − | 0.114530i | \(-0.0365363\pi\) | |||||||
\(948\) | 2.00000 | 0.0649570 | ||||||||
\(949\) | 7.25658 | + | 12.5688i | 0.235559 | + | 0.408000i | ||||
\(950\) | 4.16228 | − | 7.20928i | 0.135042 | − | 0.233900i | ||||
\(951\) | 6.48683 | 0.210350 | ||||||||
\(952\) | −6.00000 | −0.194461 | ||||||||
\(953\) | −18.5811 | + | 32.1835i | −0.601902 | + | 1.04253i | 0.390631 | + | 0.920547i | \(0.372257\pi\) |
−0.992533 | + | 0.121978i | \(0.961076\pi\) | |||||||
\(954\) | 28.3246 | 0.917041 | ||||||||
\(955\) | 4.40569 | + | 7.63089i | 0.142565 | + | 0.246930i | ||||
\(956\) | 10.6491 | 0.344417 | ||||||||
\(957\) | −4.83772 | − | 8.37918i | −0.156381 | − | 0.270860i | ||||
\(958\) | 16.0811 | + | 27.8533i | 0.519558 | + | 0.899901i | ||||
\(959\) | −29.6491 | − | 51.3538i | −0.957420 | − | 1.65830i | ||||
\(960\) | 0.500000 | − | 0.866025i | 0.0161374 | − | 0.0279508i | ||||
\(961\) | −13.6754 | −0.441143 | ||||||||
\(962\) | −25.3114 | − | 0.584952i | −0.816072 | − | 0.0188596i | ||||
\(963\) | 14.0000 | 0.451144 | ||||||||
\(964\) | 5.32456 | − | 9.22240i | 0.171492 | − | 0.297034i | ||||
\(965\) | 0.256584 | + | 0.444416i | 0.00825972 | + | 0.0143062i | ||||
\(966\) | −8.16228 | − | 14.1375i | −0.262617 | − | 0.454866i | ||||
\(967\) | −2.32456 | − | 4.02625i | −0.0747527 | − | 0.129475i | 0.826226 | − | 0.563339i | \(-0.190483\pi\) |
−0.900979 | + | 0.433863i | \(0.857150\pi\) | |||||||
\(968\) | 9.64911 | 0.310134 | ||||||||
\(969\) | 4.83772 | + | 8.37918i | 0.155410 | + | 0.269178i | ||||
\(970\) | 12.3246 | 0.395718 | ||||||||
\(971\) | 1.93203 | − | 3.34637i | 0.0620017 | − | 0.107390i | −0.833358 | − | 0.552733i | \(-0.813585\pi\) |
0.895360 | + | 0.445343i | \(0.146918\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | −79.9473 | −2.56299 | ||||||||
\(974\) | −11.6491 | + | 20.1769i | −0.373262 | + | 0.646508i | ||||
\(975\) | −2.08114 | − | 3.60464i | −0.0666498 | − | 0.115441i | ||||
\(976\) | −8.32456 | −0.266463 | ||||||||
\(977\) | 23.9737 | − | 41.5236i | 0.766986 | − | 1.32846i | −0.172205 | − | 0.985061i | \(-0.555089\pi\) |
0.939190 | − | 0.343397i | \(-0.111578\pi\) | |||||||
\(978\) | −2.82456 | + | 4.89227i | −0.0903193 | + | 0.156438i | ||||
\(979\) | −9.67544 | + | 16.7584i | −0.309229 | + | 0.535600i | ||||
\(980\) | −9.82456 | − | 17.0166i | −0.313834 | − | 0.543576i | ||||
\(981\) | 3.67544 | + | 6.36606i | 0.117348 | + | 0.203253i | ||||
\(982\) | 6.25658 | − | 10.8367i | 0.199656 | − | 0.345814i | ||||
\(983\) | −6.48683 | + | 11.2355i | −0.206898 | + | 0.358358i | −0.950736 | − | 0.310002i | \(-0.899670\pi\) |
0.743838 | + | 0.668360i | \(0.233003\pi\) | |||||||
\(984\) | −2.66228 | + | 4.61120i | −0.0848703 | + | 0.147000i | ||||
\(985\) | 13.8377 | 0.440906 | ||||||||
\(986\) | 4.83772 | + | 8.37918i | 0.154064 | + | 0.266847i | ||||
\(987\) | 13.3246 | − | 23.0788i | 0.424125 | − | 0.734607i | ||||
\(988\) | −34.6491 | −1.10234 | ||||||||
\(989\) | 23.1623 | 0.736518 | ||||||||
\(990\) | 1.16228 | − | 2.01312i | 0.0369396 | − | 0.0639813i | ||||
\(991\) | −10.1623 | −0.322815 | −0.161408 | − | 0.986888i | \(-0.551603\pi\) | ||||
−0.161408 | + | 0.986888i | \(0.551603\pi\) | |||||||
\(992\) | 2.08114 | + | 3.60464i | 0.0660762 | + | 0.114447i | ||||
\(993\) | −14.5132 | −0.460561 | ||||||||
\(994\) | 16.3246 | + | 28.2750i | 0.517783 | + | 0.896827i | ||||
\(995\) | 2.91886 | + | 5.05562i | 0.0925341 | + | 0.160274i | ||||
\(996\) | −2.00000 | − | 3.46410i | −0.0633724 | − | 0.109764i | ||||
\(997\) | 21.7302 | − | 37.6379i | 0.688204 | − | 1.19200i | −0.284214 | − | 0.958761i | \(-0.591733\pi\) |
0.972418 | − | 0.233243i | \(-0.0749339\pi\) | |||||||
\(998\) | 11.3509 | 0.359306 | ||||||||
\(999\) | −30.4057 | − | 0.702683i | −0.961994 | − | 0.0222319i |
(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 | 370.2.e.e.121.1 | ✓ | 4 | |
37.26 | even | 3 | inner | 370.2.e.e.211.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.e.e.121.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
370.2.e.e.211.1 | yes | 4 | 37.26 | even | 3 | inner |