Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(459,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.o (of order \(6\), degree \(2\), not 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: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.4 | ||
Root | \(0.500000 - 1.73154i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.459 |
Dual form | 1274.2.o.e.569.1 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.432757 | − | 0.749558i | −0.249853 | − | 0.432757i | 0.713632 | − | 0.700521i | \(-0.247049\pi\) |
−0.963485 | + | 0.267763i | \(0.913716\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.21409 | − | 1.85566i | 1.43739 | − | 0.829875i | 0.439718 | − | 0.898136i | \(-0.355078\pi\) |
0.997667 | + | 0.0682612i | \(0.0217451\pi\) | |||||||
\(6\) | 0.749558 | − | 0.432757i | 0.306006 | − | 0.176673i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.12544 | − | 1.94932i | 0.375147 | − | 0.649774i | ||||
\(10\) | 1.85566 | + | 3.21409i | 0.586810 | + | 1.01638i | ||||
\(11\) | 5.00118 | − | 2.88743i | 1.50791 | − | 0.870594i | 0.507955 | − | 0.861384i | \(-0.330402\pi\) |
0.999958 | − | 0.00920984i | \(-0.00293162\pi\) | |||||||
\(12\) | 0.432757 | + | 0.749558i | 0.124926 | + | 0.216379i | ||||
\(13\) | −2.87757 | + | 2.17246i | −0.798095 | + | 0.602531i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.78184 | − | 1.60610i | −0.718269 | − | 0.414693i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.212197 | −0.0514653 | −0.0257327 | − | 0.999669i | \(-0.508192\pi\) | ||||
−0.0257327 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(18\) | 1.94932 | + | 1.12544i | 0.459460 | + | 0.265269i | ||||
\(19\) | 1.85081 | + | 1.06857i | 0.424606 | + | 0.245146i | 0.697046 | − | 0.717026i | \(-0.254497\pi\) |
−0.272440 | + | 0.962173i | \(0.587831\pi\) | |||||||
\(20\) | −3.21409 | + | 1.85566i | −0.718693 | + | 0.414937i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.88743 | + | 5.00118i | 0.615603 | + | 1.06626i | ||||
\(23\) | −2.47940 | −0.516990 | −0.258495 | − | 0.966013i | \(-0.583227\pi\) | ||||
−0.258495 | + | 0.966013i | \(0.583227\pi\) | |||||||
\(24\) | −0.749558 | + | 0.432757i | −0.153003 | + | 0.0883363i | ||||
\(25\) | 4.38692 | − | 7.59837i | 0.877384 | − | 1.51967i | ||||
\(26\) | −2.17246 | − | 2.87757i | −0.426054 | − | 0.564339i | ||||
\(27\) | −4.54472 | −0.874632 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0492830 | − | 0.0853606i | 0.00915162 | − | 0.0158511i | −0.861413 | − | 0.507905i | \(-0.830420\pi\) |
0.870565 | + | 0.492054i | \(0.163754\pi\) | |||||||
\(30\) | 1.60610 | − | 2.78184i | 0.293232 | − | 0.507893i | ||||
\(31\) | 2.00118 | + | 1.15538i | 0.359422 | + | 0.207513i | 0.668827 | − | 0.743418i | \(-0.266797\pi\) |
−0.309405 | + | 0.950930i | \(0.600130\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −4.32860 | − | 2.49912i | −0.753512 | − | 0.435040i | ||||
\(34\) | − | 0.212197i | − | 0.0363915i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.12544 | + | 1.94932i | −0.187574 | + | 0.324887i | ||||
\(37\) | − | 7.87343i | − | 1.29438i | −0.762327 | − | 0.647192i | \(-0.775943\pi\) | ||
0.762327 | − | 0.647192i | \(-0.224057\pi\) | |||||||
\(38\) | −1.06857 | + | 1.85081i | −0.173345 | + | 0.300242i | ||||
\(39\) | 2.87367 | + | 1.21676i | 0.460156 | + | 0.194838i | ||||
\(40\) | −1.85566 | − | 3.21409i | −0.293405 | − | 0.508192i | ||||
\(41\) | −6.51354 | − | 3.76060i | −1.01724 | − | 0.587306i | −0.103940 | − | 0.994584i | \(-0.533145\pi\) |
−0.913305 | + | 0.407277i | \(0.866478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28987 | + | 3.96617i | 0.349201 | + | 0.604835i | 0.986108 | − | 0.166107i | \(-0.0531196\pi\) |
−0.636906 | + | 0.770941i | \(0.719786\pi\) | |||||||
\(44\) | −5.00118 | + | 2.88743i | −0.753956 | + | 0.435297i | ||||
\(45\) | − | 8.35373i | − | 1.24530i | ||||||
\(46\) | − | 2.47940i | − | 0.365567i | ||||||
\(47\) | −7.92907 | + | 4.57785i | −1.15657 | + | 0.667748i | −0.950480 | − | 0.310785i | \(-0.899408\pi\) |
−0.206093 | + | 0.978532i | \(0.566075\pi\) | |||||||
\(48\) | −0.432757 | − | 0.749558i | −0.0624632 | − | 0.108189i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.59837 | + | 4.38692i | 1.07457 | + | 0.620404i | ||||
\(51\) | 0.0918298 | + | 0.159054i | 0.0128587 | + | 0.0222720i | ||||
\(52\) | 2.87757 | − | 2.17246i | 0.399048 | − | 0.301266i | ||||
\(53\) | −6.04740 | + | 10.4744i | −0.830674 | + | 1.43877i | 0.0668303 | + | 0.997764i | \(0.478711\pi\) |
−0.897504 | + | 0.441005i | \(0.854622\pi\) | |||||||
\(54\) | − | 4.54472i | − | 0.618458i | ||||||
\(55\) | 10.7162 | − | 18.5609i | 1.44497 | − | 2.50276i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.84972i | − | 0.245002i | ||||||
\(58\) | 0.0853606 | + | 0.0492830i | 0.0112084 | + | 0.00647117i | ||||
\(59\) | 0.231914i | 0.0301926i | 0.999886 | + | 0.0150963i | \(0.00480549\pi\) | ||||
−0.999886 | + | 0.0150963i | \(0.995195\pi\) | |||||||
\(60\) | 2.78184 | + | 1.60610i | 0.359135 | + | 0.207346i | ||||
\(61\) | 4.01605 | − | 6.95601i | 0.514203 | − | 0.890626i | −0.485661 | − | 0.874147i | \(-0.661421\pi\) |
0.999864 | − | 0.0164787i | \(-0.00524558\pi\) | |||||||
\(62\) | −1.15538 | + | 2.00118i | −0.146734 | + | 0.254150i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.21745 | + | 12.3223i | −0.647145 | + | 1.52839i | ||||
\(66\) | 2.49912 | − | 4.32860i | 0.307620 | − | 0.532813i | ||||
\(67\) | 11.2323 | − | 6.48500i | 1.37225 | − | 0.792269i | 0.381039 | − | 0.924559i | \(-0.375567\pi\) |
0.991211 | + | 0.132291i | \(0.0422332\pi\) | |||||||
\(68\) | 0.212197 | 0.0257327 | ||||||||
\(69\) | 1.07298 | + | 1.85845i | 0.129171 | + | 0.223731i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.37721 | − | 3.68188i | 0.756836 | − | 0.436959i | −0.0713229 | − | 0.997453i | \(-0.522722\pi\) |
0.828158 | + | 0.560494i | \(0.189389\pi\) | |||||||
\(72\) | −1.94932 | − | 1.12544i | −0.229730 | − | 0.132635i | ||||
\(73\) | 4.85333 | + | 2.80207i | 0.568039 | + | 0.327958i | 0.756366 | − | 0.654149i | \(-0.226973\pi\) |
−0.188327 | + | 0.982106i | \(0.560306\pi\) | |||||||
\(74\) | 7.87343 | 0.915268 | ||||||||
\(75\) | −7.59389 | −0.876867 | ||||||||
\(76\) | −1.85081 | − | 1.06857i | −0.212303 | − | 0.122573i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.21676 | + | 2.87367i | −0.137771 | + | 0.325380i | ||||
\(79\) | 4.59875 | + | 7.96526i | 0.517399 | + | 0.896162i | 0.999796 | + | 0.0202088i | \(0.00643311\pi\) |
−0.482397 | + | 0.875953i | \(0.660234\pi\) | |||||||
\(80\) | 3.21409 | − | 1.85566i | 0.359346 | − | 0.207469i | ||||
\(81\) | −1.40956 | − | 2.44144i | −0.156618 | − | 0.271271i | ||||
\(82\) | 3.76060 | − | 6.51354i | 0.415288 | − | 0.719301i | ||||
\(83\) | − | 3.17186i | − | 0.348157i | −0.984732 | − | 0.174078i | \(-0.944305\pi\) | ||
0.984732 | − | 0.174078i | \(-0.0556946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.682021 | + | 0.393765i | −0.0739755 | + | 0.0427098i | ||||
\(86\) | −3.96617 | + | 2.28987i | −0.427683 | + | 0.246923i | ||||
\(87\) | −0.0853103 | −0.00914623 | ||||||||
\(88\) | −2.88743 | − | 5.00118i | −0.307801 | − | 0.533128i | ||||
\(89\) | − | 11.8167i | − | 1.25256i | −0.779597 | − | 0.626282i | \(-0.784576\pi\) | ||
0.779597 | − | 0.626282i | \(-0.215424\pi\) | |||||||
\(90\) | 8.35373 | 0.880561 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.47940 | 0.258495 | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | −4.57785 | − | 7.92907i | −0.472169 | − | 0.817821i | ||||
\(95\) | 7.93158 | 0.813763 | ||||||||
\(96\) | 0.749558 | − | 0.432757i | 0.0765014 | − | 0.0441681i | ||||
\(97\) | −12.1952 | + | 7.04093i | −1.23824 | + | 0.714898i | −0.968734 | − | 0.248101i | \(-0.920194\pi\) |
−0.269506 | + | 0.962999i | \(0.586860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 12.9985i | − | 1.30640i | ||||||
\(100\) | −4.38692 | + | 7.59837i | −0.438692 | + | 0.759837i | ||||
\(101\) | 3.07622 | + | 5.32816i | 0.306095 | + | 0.530172i | 0.977505 | − | 0.210914i | \(-0.0676441\pi\) |
−0.671410 | + | 0.741087i | \(0.734311\pi\) | |||||||
\(102\) | −0.159054 | + | 0.0918298i | −0.0157487 | + | 0.00909251i | ||||
\(103\) | 9.67453 | + | 16.7568i | 0.953260 | + | 1.65109i | 0.738301 | + | 0.674471i | \(0.235628\pi\) |
0.214959 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(104\) | 2.17246 | + | 2.87757i | 0.213027 | + | 0.282169i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4744 | − | 6.04740i | −1.01736 | − | 0.587375i | ||||
\(107\) | 11.6501 | 1.12626 | 0.563130 | − | 0.826368i | \(-0.309597\pi\) | ||||
0.563130 | + | 0.826368i | \(0.309597\pi\) | |||||||
\(108\) | 4.54472 | 0.437316 | ||||||||
\(109\) | 4.96499 | + | 2.86654i | 0.475559 | + | 0.274564i | 0.718564 | − | 0.695461i | \(-0.244800\pi\) |
−0.243005 | + | 0.970025i | \(0.578133\pi\) | |||||||
\(110\) | 18.5609 | + | 10.7162i | 1.76972 | + | 1.02175i | ||||
\(111\) | −5.90159 | + | 3.40729i | −0.560154 | + | 0.323405i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.25971 | − | 14.3062i | −0.777008 | − | 1.34582i | −0.933659 | − | 0.358164i | \(-0.883403\pi\) |
0.156650 | − | 0.987654i | \(-0.449930\pi\) | |||||||
\(114\) | 1.84972 | 0.173243 | ||||||||
\(115\) | −7.96901 | + | 4.60091i | −0.743114 | + | 0.429037i | ||||
\(116\) | −0.0492830 | + | 0.0853606i | −0.00457581 | + | 0.00792554i | ||||
\(117\) | 0.996277 | + | 8.05429i | 0.0921059 | + | 0.744620i | ||||
\(118\) | −0.231914 | −0.0213494 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.60610 | + | 2.78184i | −0.146616 | + | 0.253946i | ||||
\(121\) | 11.1745 | − | 19.3549i | 1.01587 | − | 1.75953i | ||||
\(122\) | 6.95601 | + | 4.01605i | 0.629768 | + | 0.363597i | ||||
\(123\) | 6.50970i | 0.586960i | ||||||||
\(124\) | −2.00118 | − | 1.15538i | −0.179711 | − | 0.103756i | ||||
\(125\) | − | 14.0059i | − | 1.25273i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.89420 | + | 10.2090i | −0.523025 | + | 0.905907i | 0.476616 | + | 0.879112i | \(0.341863\pi\) |
−0.999641 | + | 0.0267947i | \(0.991470\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.98191 | − | 3.43278i | 0.174498 | − | 0.302239i | ||||
\(130\) | −12.3223 | − | 5.21745i | −1.08073 | − | 0.457601i | ||||
\(131\) | −2.56429 | − | 4.44149i | −0.224043 | − | 0.388055i | 0.731989 | − | 0.681317i | \(-0.238592\pi\) |
−0.956032 | + | 0.293262i | \(0.905259\pi\) | |||||||
\(132\) | 4.32860 | + | 2.49912i | 0.376756 | + | 0.217520i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.48500 | + | 11.2323i | 0.560219 | + | 0.970327i | ||||
\(135\) | −14.6071 | + | 8.43344i | −1.25718 | + | 0.725835i | ||||
\(136\) | 0.212197i | 0.0181957i | ||||||||
\(137\) | − | 9.39328i | − | 0.802522i | −0.915964 | − | 0.401261i | \(-0.868572\pi\) | ||
0.915964 | − | 0.401261i | \(-0.131428\pi\) | |||||||
\(138\) | −1.85845 | + | 1.07298i | −0.158202 | + | 0.0913380i | ||||
\(139\) | 7.57063 | + | 13.1127i | 0.642133 | + | 1.11221i | 0.984956 | + | 0.172806i | \(0.0552835\pi\) |
−0.342823 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.86273 | + | 3.96220i | 0.577946 | + | 0.333677i | ||||
\(142\) | 3.68188 | + | 6.37721i | 0.308977 | + | 0.535164i | ||||
\(143\) | −8.11844 | + | 19.1736i | −0.678898 | + | 1.60338i | ||||
\(144\) | 1.12544 | − | 1.94932i | 0.0937868 | − | 0.162444i | ||||
\(145\) | − | 0.365809i | − | 0.0303788i | ||||||
\(146\) | −2.80207 | + | 4.85333i | −0.231901 | + | 0.401664i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.87343i | 0.647192i | ||||||||
\(149\) | 17.8425 | + | 10.3013i | 1.46171 | + | 0.843919i | 0.999091 | − | 0.0426374i | \(-0.0135760\pi\) |
0.462620 | + | 0.886557i | \(0.346909\pi\) | |||||||
\(150\) | − | 7.59389i | − | 0.620039i | ||||||
\(151\) | −10.3410 | − | 5.97036i | −0.841535 | − | 0.485861i | 0.0162505 | − | 0.999868i | \(-0.494827\pi\) |
−0.857786 | + | 0.514007i | \(0.828160\pi\) | |||||||
\(152\) | 1.06857 | − | 1.85081i | 0.0866723 | − | 0.150121i | ||||
\(153\) | −0.238815 | + | 0.413640i | −0.0193071 | + | 0.0334408i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.57596 | 0.688838 | ||||||||
\(156\) | −2.87367 | − | 1.21676i | −0.230078 | − | 0.0974189i | ||||
\(157\) | 4.67011 | − | 8.08887i | 0.372715 | − | 0.645562i | −0.617267 | − | 0.786754i | \(-0.711760\pi\) |
0.989982 | + | 0.141192i | \(0.0450934\pi\) | |||||||
\(158\) | −7.96526 | + | 4.59875i | −0.633682 | + | 0.365857i | ||||
\(159\) | 10.4682 | 0.830185 | ||||||||
\(160\) | 1.85566 | + | 3.21409i | 0.146703 | + | 0.254096i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.44144 | − | 1.40956i | 0.191817 | − | 0.110746i | ||||
\(163\) | −3.87746 | − | 2.23865i | −0.303706 | − | 0.175345i | 0.340401 | − | 0.940280i | \(-0.389437\pi\) |
−0.644106 | + | 0.764936i | \(0.722771\pi\) | |||||||
\(164\) | 6.51354 | + | 3.76060i | 0.508622 | + | 0.293653i | ||||
\(165\) | −18.5500 | −1.44412 | ||||||||
\(166\) | 3.17186 | 0.246184 | ||||||||
\(167\) | −12.7365 | − | 7.35342i | −0.985579 | − | 0.569025i | −0.0816295 | − | 0.996663i | \(-0.526012\pi\) |
−0.903950 | + | 0.427638i | \(0.859346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.56086 | − | 12.5028i | 0.273912 | − | 0.961755i | ||||
\(170\) | −0.393765 | − | 0.682021i | −0.0302004 | − | 0.0523086i | ||||
\(171\) | 4.16597 | − | 2.40522i | 0.318580 | − | 0.183932i | ||||
\(172\) | −2.28987 | − | 3.96617i | −0.174601 | − | 0.302417i | ||||
\(173\) | −6.88286 | + | 11.9215i | −0.523294 | + | 0.906372i | 0.476339 | + | 0.879262i | \(0.341964\pi\) |
−0.999632 | + | 0.0271097i | \(0.991370\pi\) | |||||||
\(174\) | − | 0.0853103i | − | 0.00646736i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00118 | − | 2.88743i | 0.376978 | − | 0.217648i | ||||
\(177\) | 0.173833 | − | 0.100363i | 0.0130661 | − | 0.00754371i | ||||
\(178\) | 11.8167 | 0.885696 | ||||||||
\(179\) | 7.63936 | + | 13.2318i | 0.570992 | + | 0.988988i | 0.996464 | + | 0.0840164i | \(0.0267748\pi\) |
−0.425472 | + | 0.904972i | \(0.639892\pi\) | |||||||
\(180\) | 8.35373i | 0.622651i | ||||||||
\(181\) | 1.66748 | 0.123943 | 0.0619713 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619713 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.95191 | −0.513900 | ||||||||
\(184\) | 2.47940i | 0.182784i | ||||||||
\(185\) | −14.6104 | − | 25.3059i | −1.07418 | − | 1.86053i | ||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | −1.06124 | + | 0.612704i | −0.0776052 | + | 0.0448054i | ||||
\(188\) | 7.92907 | − | 4.57785i | 0.578287 | − | 0.333874i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.93158i | 0.575418i | ||||||||
\(191\) | −0.0604880 | + | 0.104768i | −0.00437676 | + | 0.00758076i | −0.868205 | − | 0.496205i | \(-0.834727\pi\) |
0.863829 | + | 0.503786i | \(0.168060\pi\) | |||||||
\(192\) | 0.432757 | + | 0.749558i | 0.0312316 | + | 0.0540947i | ||||
\(193\) | 2.38633 | − | 1.37775i | 0.171772 | − | 0.0991725i | −0.411649 | − | 0.911342i | \(-0.635047\pi\) |
0.583421 | + | 0.812170i | \(0.301714\pi\) | |||||||
\(194\) | −7.04093 | − | 12.1952i | −0.505509 | − | 0.875568i | ||||
\(195\) | 11.4941 | − | 1.42177i | 0.823113 | − | 0.101815i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0989 | − | 7.56267i | −0.933260 | − | 0.538818i | −0.0454187 | − | 0.998968i | \(-0.514462\pi\) |
−0.887841 | + | 0.460150i | \(0.847796\pi\) | |||||||
\(198\) | 12.9985 | 0.923767 | ||||||||
\(199\) | 5.30640 | 0.376161 | 0.188080 | − | 0.982154i | \(-0.439773\pi\) | ||||
0.188080 | + | 0.982154i | \(0.439773\pi\) | |||||||
\(200\) | −7.59837 | − | 4.38692i | −0.537286 | − | 0.310202i | ||||
\(201\) | −9.72176 | − | 5.61286i | −0.685720 | − | 0.395901i | ||||
\(202\) | −5.32816 | + | 3.07622i | −0.374888 | + | 0.216442i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0918298 | − | 0.159054i | −0.00642937 | − | 0.0111360i | ||||
\(205\) | −27.9135 | −1.94956 | ||||||||
\(206\) | −16.7568 | + | 9.67453i | −1.16750 | + | 0.674056i | ||||
\(207\) | −2.79042 | + | 4.83315i | −0.193948 | + | 0.335927i | ||||
\(208\) | −2.87757 | + | 2.17246i | −0.199524 | + | 0.150633i | ||||
\(209\) | 12.3417 | 0.853691 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.94910 | + | 15.5003i | −0.616081 | + | 1.06708i | 0.374112 | + | 0.927383i | \(0.377947\pi\) |
−0.990194 | + | 0.139701i | \(0.955386\pi\) | |||||||
\(212\) | 6.04740 | − | 10.4744i | 0.415337 | − | 0.719385i | ||||
\(213\) | −5.51957 | − | 3.18673i | −0.378195 | − | 0.218351i | ||||
\(214\) | 11.6501i | 0.796386i | ||||||||
\(215\) | 14.7197 | + | 8.49841i | 1.00387 | + | 0.579587i | ||||
\(216\) | 4.54472i | 0.309229i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.86654 | + | 4.96499i | −0.194146 | + | 0.336271i | ||||
\(219\) | − | 4.85047i | − | 0.327764i | ||||||
\(220\) | −10.7162 | + | 18.5609i | −0.722484 | + | 1.25138i | ||||
\(221\) | 0.610613 | − | 0.460989i | 0.0410742 | − | 0.0310095i | ||||
\(222\) | −3.40729 | − | 5.90159i | −0.228682 | − | 0.396089i | ||||
\(223\) | 14.2362 | + | 8.21925i | 0.953324 | + | 0.550402i | 0.894112 | − | 0.447844i | \(-0.147808\pi\) |
0.0592118 | + | 0.998245i | \(0.481141\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.87445 | − | 17.1031i | −0.658297 | − | 1.14020i | ||||
\(226\) | 14.3062 | − | 8.25971i | 0.951637 | − | 0.549428i | ||||
\(227\) | 5.63095i | 0.373739i | 0.982385 | + | 0.186870i | \(0.0598342\pi\) | ||||
−0.982385 | + | 0.186870i | \(0.940166\pi\) | |||||||
\(228\) | 1.84972i | 0.122501i | ||||||||
\(229\) | −24.0084 | + | 13.8613i | −1.58652 | + | 0.915978i | −0.592646 | + | 0.805463i | \(0.701917\pi\) |
−0.993874 | + | 0.110515i | \(0.964750\pi\) | |||||||
\(230\) | −4.60091 | − | 7.96901i | −0.303375 | − | 0.525461i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0853606 | − | 0.0492830i | −0.00560420 | − | 0.00323559i | ||||
\(233\) | 10.0552 | + | 17.4161i | 0.658737 | + | 1.14097i | 0.980943 | + | 0.194296i | \(0.0622422\pi\) |
−0.322206 | + | 0.946669i | \(0.604425\pi\) | |||||||
\(234\) | −8.05429 | + | 0.996277i | −0.526526 | + | 0.0651287i | ||||
\(235\) | −16.9898 | + | 29.4272i | −1.10829 | + | 1.91962i | ||||
\(236\) | − | 0.231914i | − | 0.0150963i | ||||||
\(237\) | 3.98028 | − | 6.89405i | 0.258547 | − | 0.447817i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.62968i | 0.428838i | 0.976742 | + | 0.214419i | \(0.0687858\pi\) | ||||
−0.976742 | + | 0.214419i | \(0.931214\pi\) | |||||||
\(240\) | −2.78184 | − | 1.60610i | −0.179567 | − | 0.103673i | ||||
\(241\) | − | 1.61687i | − | 0.104151i | −0.998643 | − | 0.0520757i | \(-0.983416\pi\) | ||
0.998643 | − | 0.0520757i | \(-0.0165837\pi\) | |||||||
\(242\) | 19.3549 | + | 11.1745i | 1.24418 | + | 0.718326i | ||||
\(243\) | −8.03708 | + | 13.9206i | −0.515579 | + | 0.893009i | ||||
\(244\) | −4.01605 | + | 6.95601i | −0.257102 | + | 0.445313i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.50970 | −0.415044 | ||||||||
\(247\) | −7.64727 | + | 0.945931i | −0.486584 | + | 0.0601881i | ||||
\(248\) | 1.15538 | − | 2.00118i | 0.0733668 | − | 0.127075i | ||||
\(249\) | −2.37749 | + | 1.37265i | −0.150667 | + | 0.0869879i | ||||
\(250\) | 14.0059 | 0.885812 | ||||||||
\(251\) | −0.253506 | − | 0.439085i | −0.0160011 | − | 0.0277148i | 0.857914 | − | 0.513793i | \(-0.171760\pi\) |
−0.873915 | + | 0.486079i | \(0.838427\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3999 | + | 7.15910i | −0.779576 | + | 0.450089i | ||||
\(254\) | −10.2090 | − | 5.89420i | −0.640573 | − | 0.369835i | ||||
\(255\) | 0.590299 | + | 0.340809i | 0.0369660 | + | 0.0213423i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.64063 | −0.601366 | −0.300683 | − | 0.953724i | \(-0.597215\pi\) | ||||
−0.300683 | + | 0.953724i | \(0.597215\pi\) | |||||||
\(258\) | 3.43278 | + | 1.98191i | 0.213715 | + | 0.123389i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.21745 | − | 12.3223i | 0.323573 | − | 0.764194i | ||||
\(261\) | −0.110930 | − | 0.192137i | −0.00686641 | − | 0.0118930i | ||||
\(262\) | 4.44149 | − | 2.56429i | 0.274396 | − | 0.158423i | ||||
\(263\) | 3.67309 | + | 6.36197i | 0.226492 | + | 0.392296i | 0.956766 | − | 0.290858i | \(-0.0939409\pi\) |
−0.730274 | + | 0.683155i | \(0.760608\pi\) | |||||||
\(264\) | −2.49912 | + | 4.32860i | −0.153810 | + | 0.266407i | ||||
\(265\) | 44.8876i | 2.75742i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.85727 | + | 5.11375i | −0.542056 | + | 0.312956i | ||||
\(268\) | −11.2323 | + | 6.48500i | −0.686125 | + | 0.396134i | ||||
\(269\) | −22.3541 | −1.36295 | −0.681476 | − | 0.731841i | \(-0.738662\pi\) | ||||
−0.681476 | + | 0.731841i | \(0.738662\pi\) | |||||||
\(270\) | −8.43344 | − | 14.6071i | −0.513243 | − | 0.888962i | ||||
\(271\) | − | 9.61740i | − | 0.584215i | −0.956385 | − | 0.292108i | \(-0.905643\pi\) | ||
0.956385 | − | 0.292108i | \(-0.0943566\pi\) | |||||||
\(272\) | −0.212197 | −0.0128663 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.39328 | 0.567469 | ||||||||
\(275\) | − | 50.6678i | − | 3.05538i | ||||||
\(276\) | −1.07298 | − | 1.85845i | −0.0645857 | − | 0.111866i | ||||
\(277\) | −10.1789 | −0.611590 | −0.305795 | − | 0.952097i | \(-0.598922\pi\) | ||||
−0.305795 | + | 0.952097i | \(0.598922\pi\) | |||||||
\(278\) | −13.1127 | + | 7.57063i | −0.786449 | + | 0.454056i | ||||
\(279\) | 4.50442 | − | 2.60063i | 0.269673 | − | 0.155696i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1692i | 0.845265i | 0.906301 | + | 0.422633i | \(0.138894\pi\) | ||||
−0.906301 | + | 0.422633i | \(0.861106\pi\) | |||||||
\(282\) | −3.96220 | + | 6.86273i | −0.235945 | + | 0.408669i | ||||
\(283\) | −9.46631 | − | 16.3961i | −0.562714 | − | 0.974649i | −0.997258 | − | 0.0739986i | \(-0.976424\pi\) |
0.434545 | − | 0.900650i | \(-0.356909\pi\) | |||||||
\(284\) | −6.37721 | + | 3.68188i | −0.378418 | + | 0.218480i | ||||
\(285\) | −3.43245 | − | 5.94518i | −0.203321 | − | 0.352162i | ||||
\(286\) | −19.1736 | − | 8.11844i | −1.13376 | − | 0.480053i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.94932 | + | 1.12544i | 0.114865 | + | 0.0663173i | ||||
\(289\) | −16.9550 | −0.997351 | ||||||||
\(290\) | 0.365809 | 0.0214811 | ||||||||
\(291\) | 10.5552 | + | 6.09403i | 0.618755 | + | 0.357238i | ||||
\(292\) | −4.85333 | − | 2.80207i | −0.284020 | − | 0.163979i | ||||
\(293\) | −3.16950 | + | 1.82991i | −0.185164 | + | 0.106905i | −0.589717 | − | 0.807610i | \(-0.700761\pi\) |
0.404553 | + | 0.914515i | \(0.367427\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.430353 | + | 0.745393i | 0.0250561 | + | 0.0433985i | ||||
\(296\) | −7.87343 | −0.457634 | ||||||||
\(297\) | −22.7290 | + | 13.1226i | −1.31887 | + | 0.761449i | ||||
\(298\) | −10.3013 | + | 17.8425i | −0.596741 | + | 1.03359i | ||||
\(299\) | 7.13465 | − | 5.38639i | 0.412608 | − | 0.311503i | ||||
\(300\) | 7.59389 | 0.438434 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.97036 | − | 10.3410i | 0.343555 | − | 0.595055i | ||||
\(303\) | 2.66251 | − | 4.61161i | 0.152957 | − | 0.264930i | ||||
\(304\) | 1.85081 | + | 1.06857i | 0.106151 | + | 0.0612866i | ||||
\(305\) | − | 29.8097i | − | 1.70690i | ||||||
\(306\) | −0.413640 | − | 0.238815i | −0.0236462 | − | 0.0136522i | ||||
\(307\) | 19.6987i | 1.12426i | 0.827048 | + | 0.562132i | \(0.190019\pi\) | ||||
−0.827048 | + | 0.562132i | \(0.809981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.37345 | − | 14.5032i | 0.476349 | − | 0.825061i | ||||
\(310\) | 8.57596i | 0.487082i | ||||||||
\(311\) | 8.48425 | − | 14.6952i | 0.481098 | − | 0.833286i | −0.518667 | − | 0.854976i | \(-0.673572\pi\) |
0.999765 | + | 0.0216906i | \(0.00690488\pi\) | |||||||
\(312\) | 1.21676 | − | 2.87367i | 0.0688855 | − | 0.162690i | ||||
\(313\) | −2.26897 | − | 3.92997i | −0.128250 | − | 0.222135i | 0.794749 | − | 0.606939i | \(-0.207603\pi\) |
−0.922999 | + | 0.384803i | \(0.874269\pi\) | |||||||
\(314\) | 8.08887 | + | 4.67011i | 0.456481 | + | 0.263550i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.59875 | − | 7.96526i | −0.258700 | − | 0.448081i | ||||
\(317\) | 25.2763 | − | 14.5933i | 1.41966 | − | 0.819641i | 0.423392 | − | 0.905947i | \(-0.360839\pi\) |
0.996269 | + | 0.0863056i | \(0.0275061\pi\) | |||||||
\(318\) | 10.4682i | 0.587029i | ||||||||
\(319\) | − | 0.569205i | − | 0.0318694i | ||||||
\(320\) | −3.21409 | + | 1.85566i | −0.179673 | + | 0.103734i | ||||
\(321\) | −5.04168 | − | 8.73244i | −0.281399 | − | 0.487397i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.392737 | − | 0.226747i | −0.0218525 | − | 0.0126165i | ||||
\(324\) | 1.40956 | + | 2.44144i | 0.0783091 | + | 0.135635i | ||||
\(325\) | 3.88344 | + | 31.3953i | 0.215415 | + | 1.74150i | ||||
\(326\) | 2.23865 | − | 3.87746i | 0.123987 | − | 0.214752i | ||||
\(327\) | − | 4.96206i | − | 0.274403i | ||||||
\(328\) | −3.76060 | + | 6.51354i | −0.207644 | + | 0.359650i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 18.5500i | − | 1.02114i | ||||||
\(331\) | −4.16161 | − | 2.40271i | −0.228743 | − | 0.132065i | 0.381249 | − | 0.924472i | \(-0.375494\pi\) |
−0.609992 | + | 0.792408i | \(0.708827\pi\) | |||||||
\(332\) | 3.17186i | 0.174078i | ||||||||
\(333\) | −15.3479 | − | 8.86109i | −0.841057 | − | 0.485585i | ||||
\(334\) | 7.35342 | − | 12.7365i | 0.402361 | − | 0.696910i | ||||
\(335\) | 24.0679 | − | 41.6868i | 1.31497 | − | 2.27759i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7312 | 0.965883 | 0.482941 | − | 0.875653i | \(-0.339568\pi\) | ||||
0.482941 | + | 0.875653i | \(0.339568\pi\) | |||||||
\(338\) | 12.5028 | + | 3.56086i | 0.680063 | + | 0.193685i | ||||
\(339\) | −7.14890 | + | 12.3823i | −0.388275 | + | 0.672512i | ||||
\(340\) | 0.682021 | − | 0.393765i | 0.0369878 | − | 0.0213549i | ||||
\(341\) | 13.3443 | 0.722637 | ||||||||
\(342\) | 2.40522 | + | 4.16597i | 0.130060 | + | 0.225270i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.96617 | − | 2.28987i | 0.213841 | − | 0.123461i | ||||
\(345\) | 6.89730 | + | 3.98216i | 0.371338 | + | 0.214392i | ||||
\(346\) | −11.9215 | − | 6.88286i | −0.640902 | − | 0.370025i | ||||
\(347\) | −16.7048 | −0.896760 | −0.448380 | − | 0.893843i | \(-0.647999\pi\) | ||||
−0.448380 | + | 0.893843i | \(0.647999\pi\) | |||||||
\(348\) | 0.0853103 | 0.00457311 | ||||||||
\(349\) | −0.0173616 | − | 0.0100237i | −0.000929347 | − | 0.000536559i | 0.499535 | − | 0.866294i | \(-0.333504\pi\) |
−0.500465 | + | 0.865757i | \(0.666837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.0778 | − | 9.87321i | 0.698039 | − | 0.526993i | ||||
\(352\) | 2.88743 | + | 5.00118i | 0.153901 | + | 0.266564i | ||||
\(353\) | 25.8299 | − | 14.9129i | 1.37479 | − | 0.793734i | 0.383262 | − | 0.923640i | \(-0.374801\pi\) |
0.991526 | + | 0.129905i | \(0.0414674\pi\) | |||||||
\(354\) | 0.100363 | + | 0.173833i | 0.00533421 | + | 0.00923912i | ||||
\(355\) | 13.6646 | − | 23.6678i | 0.725243 | − | 1.25616i | ||||
\(356\) | 11.8167i | 0.626282i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.2318 | + | 7.63936i | −0.699320 | + | 0.403753i | ||||
\(359\) | −15.8786 | + | 9.16753i | −0.838042 | + | 0.483844i | −0.856598 | − | 0.515984i | \(-0.827426\pi\) |
0.0185563 | + | 0.999828i | \(0.494093\pi\) | |||||||
\(360\) | −8.35373 | −0.440280 | ||||||||
\(361\) | −7.21632 | − | 12.4990i | −0.379806 | − | 0.657844i | ||||
\(362\) | 1.66748i | 0.0876407i | ||||||||
\(363\) | −19.3434 | −1.01527 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.7987 | 1.08866 | ||||||||
\(366\) | − | 6.95191i | − | 0.363382i | ||||||
\(367\) | 0.672426 | + | 1.16468i | 0.0351004 | + | 0.0607956i | 0.883042 | − | 0.469294i | \(-0.155492\pi\) |
−0.847942 | + | 0.530090i | \(0.822158\pi\) | |||||||
\(368\) | −2.47940 | −0.129248 | ||||||||
\(369\) | −14.6612 | + | 8.46466i | −0.763233 | + | 0.440653i | ||||
\(370\) | 25.3059 | − | 14.6104i | 1.31559 | − | 0.759558i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | 5.53575 | − | 9.58821i | 0.286630 | − | 0.496458i | −0.686373 | − | 0.727250i | \(-0.740798\pi\) |
0.973003 | + | 0.230791i | \(0.0741315\pi\) | |||||||
\(374\) | −0.612704 | − | 1.06124i | −0.0316822 | − | 0.0548752i | ||||
\(375\) | −10.4982 | + | 6.06116i | −0.542127 | + | 0.312997i | ||||
\(376\) | 4.57785 | + | 7.92907i | 0.236085 | + | 0.408910i | ||||
\(377\) | 0.0436269 | + | 0.352697i | 0.00224690 | + | 0.0181648i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5583 | + | 8.40523i | 0.747808 | + | 0.431747i | 0.824902 | − | 0.565276i | \(-0.191231\pi\) |
−0.0770930 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(380\) | −7.93158 | −0.406882 | ||||||||
\(381\) | 10.2030 | 0.522717 | ||||||||
\(382\) | −0.104768 | − | 0.0604880i | −0.00536041 | − | 0.00309483i | ||||
\(383\) | 14.3562 | + | 8.28855i | 0.733567 | + | 0.423525i | 0.819726 | − | 0.572756i | \(-0.194126\pi\) |
−0.0861585 | + | 0.996281i | \(0.527459\pi\) | |||||||
\(384\) | −0.749558 | + | 0.432757i | −0.0382507 | + | 0.0220841i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.37775 | + | 2.38633i | 0.0701256 | + | 0.121461i | ||||
\(387\) | 10.3084 | 0.524008 | ||||||||
\(388\) | 12.1952 | − | 7.04093i | 0.619120 | − | 0.357449i | ||||
\(389\) | 0.585065 | − | 1.01336i | 0.0296640 | − | 0.0513795i | −0.850812 | − | 0.525470i | \(-0.823890\pi\) |
0.880476 | + | 0.474090i | \(0.157223\pi\) | |||||||
\(390\) | 1.42177 | + | 11.4941i | 0.0719941 | + | 0.582028i | ||||
\(391\) | 0.526121 | 0.0266071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.21944 | + | 3.84418i | −0.111956 | + | 0.193913i | ||||
\(394\) | 7.56267 | − | 13.0989i | 0.381002 | − | 0.659914i | ||||
\(395\) | 29.5616 | + | 17.0674i | 1.48740 | + | 0.858753i | ||||
\(396\) | 12.9985i | 0.653202i | ||||||||
\(397\) | 22.6877 | + | 13.0987i | 1.13866 | + | 0.657406i | 0.946099 | − | 0.323878i | \(-0.104987\pi\) |
0.192562 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(398\) | 5.30640i | 0.265986i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.38692 | − | 7.59837i | 0.219346 | − | 0.379919i | ||||
\(401\) | 11.3687i | 0.567726i | 0.958865 | + | 0.283863i | \(0.0916162\pi\) | ||||
−0.958865 | + | 0.283863i | \(0.908384\pi\) | |||||||
\(402\) | 5.61286 | − | 9.72176i | 0.279944 | − | 0.484878i | ||||
\(403\) | −8.26856 | + | 1.02278i | −0.411886 | + | 0.0509483i | ||||
\(404\) | −3.07622 | − | 5.32816i | −0.153048 | − | 0.265086i | ||||
\(405\) | −9.06094 | − | 5.23134i | −0.450242 | − | 0.259947i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.7340 | − | 39.3764i | −1.12688 | − | 1.95182i | ||||
\(408\) | 0.159054 | − | 0.0918298i | 0.00787434 | − | 0.00454625i | ||||
\(409\) | 23.3314i | 1.15366i | 0.816863 | + | 0.576832i | \(0.195711\pi\) | ||||
−0.816863 | + | 0.576832i | \(0.804289\pi\) | |||||||
\(410\) | − | 27.9135i | − | 1.37855i | ||||||
\(411\) | −7.04081 | + | 4.06501i | −0.347298 | + | 0.200512i | ||||
\(412\) | −9.67453 | − | 16.7568i | −0.476630 | − | 0.825547i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.83315 | − | 2.79042i | −0.237536 | − | 0.137142i | ||||
\(415\) | −5.88588 | − | 10.1946i | −0.288926 | − | 0.500435i | ||||
\(416\) | −2.17246 | − | 2.87757i | −0.106513 | − | 0.141085i | ||||
\(417\) | 6.55250 | − | 11.3493i | 0.320877 | − | 0.555775i | ||||
\(418\) | 12.3417i | 0.603651i | ||||||||
\(419\) | −6.33402 | + | 10.9709i | −0.309437 | + | 0.535961i | −0.978239 | − | 0.207479i | \(-0.933474\pi\) |
0.668802 | + | 0.743441i | \(0.266807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6625i | 1.34819i | 0.738646 | + | 0.674094i | \(0.235466\pi\) | ||||
−0.738646 | + | 0.674094i | \(0.764534\pi\) | |||||||
\(422\) | −15.5003 | − | 8.94910i | −0.754543 | − | 0.435635i | ||||
\(423\) | 20.6084i | 1.00202i | ||||||||
\(424\) | 10.4744 | + | 6.04740i | 0.508682 | + | 0.293688i | ||||
\(425\) | −0.930892 | + | 1.61235i | −0.0451549 | + | 0.0782105i | ||||
\(426\) | 3.18673 | − | 5.51957i | 0.154397 | − | 0.267424i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.6501 | −0.563130 | ||||||||
\(429\) | 17.8851 | − | 2.21230i | 0.863500 | − | 0.106811i | ||||
\(430\) | −8.49841 | + | 14.7197i | −0.409830 | + | 0.709846i | ||||
\(431\) | −5.55462 | + | 3.20696i | −0.267557 | + | 0.154474i | −0.627777 | − | 0.778393i | \(-0.716035\pi\) |
0.360220 | + | 0.932867i | \(0.382702\pi\) | |||||||
\(432\) | −4.54472 | −0.218658 | ||||||||
\(433\) | 0.0325135 | + | 0.0563150i | 0.00156250 | + | 0.00270633i | 0.866806 | − | 0.498646i | \(-0.166169\pi\) |
−0.865243 | + | 0.501353i | \(0.832836\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.274195 | + | 0.158307i | −0.0131467 | + | 0.00759022i | ||||
\(436\) | −4.96499 | − | 2.86654i | −0.237780 | − | 0.137282i | ||||
\(437\) | −4.58891 | − | 2.64941i | −0.219517 | − | 0.126738i | ||||
\(438\) | 4.85047 | 0.231764 | ||||||||
\(439\) | 36.7778 | 1.75531 | 0.877655 | − | 0.479294i | \(-0.159107\pi\) | ||||
0.877655 | + | 0.479294i | \(0.159107\pi\) | |||||||
\(440\) | −18.5609 | − | 10.7162i | −0.884858 | − | 0.510873i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.460989 | + | 0.610613i | 0.0219270 | + | 0.0290439i | ||||
\(443\) | 4.23191 | + | 7.32989i | 0.201064 | + | 0.348254i | 0.948872 | − | 0.315662i | \(-0.102227\pi\) |
−0.747807 | + | 0.663916i | \(0.768893\pi\) | |||||||
\(444\) | 5.90159 | − | 3.40729i | 0.280077 | − | 0.161703i | ||||
\(445\) | −21.9277 | − | 37.9798i | −1.03947 | − | 1.80042i | ||||
\(446\) | −8.21925 | + | 14.2362i | −0.389193 | + | 0.674102i | ||||
\(447\) | − | 17.8319i | − | 0.843422i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5984 | + | 11.3152i | −0.924907 | + | 0.533995i | −0.885197 | − | 0.465216i | \(-0.845977\pi\) |
−0.0397096 | + | 0.999211i | \(0.512643\pi\) | |||||||
\(450\) | 17.1031 | − | 9.87445i | 0.806246 | − | 0.465486i | ||||
\(451\) | −43.4339 | −2.04522 | ||||||||
\(452\) | 8.25971 | + | 14.3062i | 0.388504 | + | 0.672909i | ||||
\(453\) | 10.3349i | 0.485574i | ||||||||
\(454\) | −5.63095 | −0.264274 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.84972 | −0.0866213 | ||||||||
\(457\) | 16.3170i | 0.763278i | 0.924311 | + | 0.381639i | \(0.124640\pi\) | ||||
−0.924311 | + | 0.381639i | \(0.875360\pi\) | |||||||
\(458\) | −13.8613 | − | 24.0084i | −0.647694 | − | 1.12184i | ||||
\(459\) | 0.964376 | 0.0450132 | ||||||||
\(460\) | 7.96901 | − | 4.60091i | 0.371557 | − | 0.214519i | ||||
\(461\) | −16.6951 | + | 9.63892i | −0.777568 | + | 0.448929i | −0.835568 | − | 0.549387i | \(-0.814861\pi\) |
0.0579996 | + | 0.998317i | \(0.481528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.70218i | − | 0.125581i | −0.998027 | − | 0.0627904i | \(-0.980000\pi\) | ||
0.998027 | − | 0.0627904i | \(-0.0200000\pi\) | |||||||
\(464\) | 0.0492830 | − | 0.0853606i | 0.00228791 | − | 0.00396277i | ||||
\(465\) | −3.71131 | − | 6.42818i | −0.172108 | − | 0.298100i | ||||
\(466\) | −17.4161 | + | 10.0552i | −0.806784 | + | 0.465797i | ||||
\(467\) | −9.19528 | − | 15.9267i | −0.425507 | − | 0.736999i | 0.570961 | − | 0.820977i | \(-0.306571\pi\) |
−0.996468 | + | 0.0839779i | \(0.973237\pi\) | |||||||
\(468\) | −0.996277 | − | 8.05429i | −0.0460529 | − | 0.372310i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −29.4272 | − | 16.9898i | −1.35738 | − | 0.783682i | ||||
\(471\) | −8.08410 | −0.372496 | ||||||||
\(472\) | 0.231914 | 0.0106747 | ||||||||
\(473\) | 22.9041 | + | 13.2237i | 1.05313 | + | 0.608025i | ||||
\(474\) | 6.89405 | + | 3.98028i | 0.316654 | + | 0.182820i | ||||
\(475\) | 16.2388 | − | 9.37545i | 0.745085 | − | 0.430175i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.6120 | + | 23.5767i | 0.623250 | + | 1.07950i | ||||
\(478\) | −6.62968 | −0.303234 | ||||||||
\(479\) | 35.3951 | − | 20.4354i | 1.61725 | − | 0.933717i | 0.629617 | − | 0.776906i | \(-0.283212\pi\) |
0.987629 | − | 0.156811i | \(-0.0501213\pi\) | |||||||
\(480\) | 1.60610 | − | 2.78184i | 0.0733080 | − | 0.126973i | ||||
\(481\) | 17.1047 | + | 22.6564i | 0.779907 | + | 1.03304i | ||||
\(482\) | 1.61687 | 0.0736462 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.1745 | + | 19.3549i | −0.507933 | + | 0.879766i | ||||
\(485\) | −26.1311 | + | 45.2604i | −1.18655 | + | 2.05517i | ||||
\(486\) | −13.9206 | − | 8.03708i | −0.631452 | − | 0.364569i | ||||
\(487\) | 17.6293i | 0.798861i | 0.916764 | + | 0.399430i | \(0.130792\pi\) | ||||
−0.916764 | + | 0.399430i | \(0.869208\pi\) | |||||||
\(488\) | −6.95601 | − | 4.01605i | −0.314884 | − | 0.181798i | ||||
\(489\) | 3.87517i | 0.175241i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.42997 | + | 16.3332i | −0.425569 | + | 0.737106i | −0.996473 | − | 0.0839098i | \(-0.973259\pi\) |
0.570905 | + | 0.821016i | \(0.306593\pi\) | |||||||
\(492\) | − | 6.50970i | − | 0.293480i | ||||||
\(493\) | −0.0104577 | + | 0.0181133i | −0.000470991 | + | 0.000815781i | ||||
\(494\) | −0.945931 | − | 7.64727i | −0.0425594 | − | 0.344067i | ||||
\(495\) | −24.1208 | − | 41.7785i | −1.08415 | − | 1.87780i | ||||
\(496\) | 2.00118 | + | 1.15538i | 0.0898556 | + | 0.0518782i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.37265 | − | 2.37749i | −0.0615097 | − | 0.106538i | ||||
\(499\) | 1.82508 | − | 1.05371i | 0.0817017 | − | 0.0471705i | −0.458593 | − | 0.888647i | \(-0.651646\pi\) |
0.540294 | + | 0.841476i | \(0.318313\pi\) | |||||||
\(500\) | 14.0059i | 0.626364i | ||||||||
\(501\) | 12.7290i | 0.568689i | ||||||||
\(502\) | 0.439085 | − | 0.253506i | 0.0195973 | − | 0.0113145i | ||||
\(503\) | 10.8942 | + | 18.8693i | 0.485749 | + | 0.841342i | 0.999866 | − | 0.0163784i | \(-0.00521363\pi\) |
−0.514117 | + | 0.857720i | \(0.671880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.7745 | + | 11.4168i | 0.879953 | + | 0.508041i | ||||
\(506\) | −7.15910 | − | 12.3999i | −0.318261 | − | 0.551244i | ||||
\(507\) | −10.9126 | + | 2.74161i | −0.484644 | + | 0.121759i | ||||
\(508\) | 5.89420 | − | 10.2090i | 0.261513 | − | 0.452953i | ||||
\(509\) | − | 12.1977i | − | 0.540655i | −0.962768 | − | 0.270328i | \(-0.912868\pi\) | ||
0.962768 | − | 0.270328i | \(-0.0871321\pi\) | |||||||
\(510\) | −0.340809 | + | 0.590299i | −0.0150913 | + | 0.0261389i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −8.41143 | − | 4.85634i | −0.371374 | − | 0.214413i | ||||
\(514\) | − | 9.64063i | − | 0.425230i | ||||||
\(515\) | 62.1896 | + | 35.9052i | 2.74040 | + | 1.58217i | ||||
\(516\) | −1.98191 | + | 3.43278i | −0.0872489 | + | 0.151120i | ||||
\(517\) | −26.4365 | + | 45.7893i | −1.16267 | + | 2.01381i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9144 | 0.522986 | ||||||||
\(520\) | 12.3223 | + | 5.21745i | 0.540367 | + | 0.228800i | ||||
\(521\) | −13.4883 | + | 23.3624i | −0.590932 | + | 1.02352i | 0.403175 | + | 0.915123i | \(0.367906\pi\) |
−0.994107 | + | 0.108401i | \(0.965427\pi\) | |||||||
\(522\) | 0.192137 | − | 0.110930i | 0.00840960 | − | 0.00485529i | ||||
\(523\) | 3.75365 | 0.164136 | 0.0820679 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820679 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(524\) | 2.56429 | + | 4.44149i | 0.112022 | + | 0.194027i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.36197 | + | 3.67309i | −0.277395 | + | 0.160154i | ||||
\(527\) | −0.424644 | − | 0.245168i | −0.0184978 | − | 0.0106797i | ||||
\(528\) | −4.32860 | − | 2.49912i | −0.188378 | − | 0.108760i | ||||
\(529\) | −16.8526 | −0.732721 | ||||||||
\(530\) | −44.8876 | −1.94979 | ||||||||
\(531\) | 0.452075 | + | 0.261006i | 0.0196184 | + | 0.0113267i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.9129 | − | 3.32900i | 1.16573 | − | 0.144195i | ||||
\(534\) | −5.11375 | − | 8.85727i | −0.221293 | − | 0.383292i | ||||
\(535\) | 37.4445 | − | 21.6186i | 1.61887 | − | 0.934654i | ||||
\(536\) | −6.48500 | − | 11.2323i | −0.280109 | − | 0.485163i | ||||
\(537\) | 6.61198 | − | 11.4523i | 0.285328 | − | 0.494203i | ||||
\(538\) | − | 22.3541i | − | 0.963752i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.6071 | − | 8.43344i | 0.628591 | − | 0.362917i | ||||
\(541\) | −0.0117524 | + | 0.00678524i | −0.000505274 | + | 0.000291720i | −0.500253 | − | 0.865880i | \(-0.666760\pi\) |
0.499747 | + | 0.866171i | \(0.333426\pi\) | |||||||
\(542\) | 9.61740 | 0.413103 | ||||||||
\(543\) | −0.721614 | − | 1.24987i | −0.0309674 | − | 0.0536371i | ||||
\(544\) | − | 0.212197i | − | 0.00909787i | ||||||
\(545\) | 21.2772 | 0.911416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.66115 | −0.413081 | −0.206540 | − | 0.978438i | \(-0.566220\pi\) | ||||
−0.206540 | + | 0.978438i | \(0.566220\pi\) | |||||||
\(548\) | 9.39328i | 0.401261i | ||||||||
\(549\) | −9.03967 | − | 15.6572i | −0.385804 | − | 0.668232i | ||||
\(550\) | 50.6678 | 2.16048 | ||||||||
\(551\) | 0.182427 | − | 0.105324i | 0.00777167 | − | 0.00448697i | ||||
\(552\) | 1.85845 | − | 1.07298i | 0.0791010 | − | 0.0456690i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 10.1789i | − | 0.432460i | ||||||
\(555\) | −12.6455 | + | 21.9027i | −0.536772 | + | 0.929716i | ||||
\(556\) | −7.57063 | − | 13.1127i | −0.321066 | − | 0.556103i | ||||
\(557\) | 21.6145 | − | 12.4791i | 0.915834 | − | 0.528757i | 0.0335307 | − | 0.999438i | \(-0.489325\pi\) |
0.882304 | + | 0.470680i | \(0.155992\pi\) | |||||||
\(558\) | 2.60063 | + | 4.50442i | 0.110093 | + | 0.190687i | ||||
\(559\) | −15.2056 | − | 6.43830i | −0.643128 | − | 0.272311i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.918515 | + | 0.530305i | 0.0387797 | + | 0.0223895i | ||||
\(562\) | −14.1692 | −0.597693 | ||||||||
\(563\) | 15.8994 | 0.670080 | 0.335040 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335040 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(564\) | −6.86273 | − | 3.96220i | −0.288973 | − | 0.166839i | ||||
\(565\) | −53.0949 | − | 30.6544i | −2.23372 | − | 1.28964i | ||||
\(566\) | 16.3961 | − | 9.46631i | 0.689181 | − | 0.397899i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.68188 | − | 6.37721i | −0.154488 | − | 0.267582i | ||||
\(569\) | 17.9093 | 0.750797 | 0.375398 | − | 0.926864i | \(-0.377506\pi\) | ||||
0.375398 | + | 0.926864i | \(0.377506\pi\) | |||||||
\(570\) | 5.94518 | − | 3.43245i | 0.249016 | − | 0.143770i | ||||
\(571\) | 6.25615 | − | 10.8360i | 0.261812 | − | 0.453471i | −0.704912 | − | 0.709295i | \(-0.749013\pi\) |
0.966723 | + | 0.255824i | \(0.0823467\pi\) | |||||||
\(572\) | 8.11844 | − | 19.1736i | 0.339449 | − | 0.801690i | ||||
\(573\) | 0.104707 | 0.00437418 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8769 | + | 18.8394i | −0.453599 | + | 0.785657i | ||||
\(576\) | −1.12544 | + | 1.94932i | −0.0468934 | + | 0.0812218i | ||||
\(577\) | 19.1314 | + | 11.0455i | 0.796450 | + | 0.459831i | 0.842228 | − | 0.539121i | \(-0.181243\pi\) |
−0.0457781 | + | 0.998952i | \(0.514577\pi\) | |||||||
\(578\) | − | 16.9550i | − | 0.705234i | ||||||
\(579\) | −2.06540 | − | 1.19246i | −0.0858353 | − | 0.0495570i | ||||
\(580\) | 0.365809i | 0.0151894i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.09403 | + | 10.5552i | −0.252606 | + | 0.437526i | ||||
\(583\) | 69.8458i | 2.89272i | ||||||||
\(584\) | 2.80207 | − | 4.85333i | 0.115951 | − | 0.200832i | ||||
\(585\) | 18.1481 | + | 24.0385i | 0.750333 | + | 0.993869i | ||||
\(586\) | −1.82991 | − | 3.16950i | −0.0755929 | − | 0.130931i | ||||
\(587\) | 18.3007 | + | 10.5659i | 0.755352 | + | 0.436102i | 0.827624 | − | 0.561282i | \(-0.189692\pi\) |
−0.0722727 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.46921 | + | 4.27679i | 0.101742 | + | 0.176222i | ||||
\(590\) | −0.745393 | + | 0.430353i | −0.0306873 | + | 0.0177173i | ||||
\(591\) | 13.0912i | 0.538500i | ||||||||
\(592\) | − | 7.87343i | − | 0.323596i | ||||||
\(593\) | 7.75520 | − | 4.47747i | 0.318468 | − | 0.183867i | −0.332242 | − | 0.943194i | \(-0.607805\pi\) |
0.650709 | + | 0.759327i | \(0.274472\pi\) | |||||||
\(594\) | −13.1226 | − | 22.7290i | −0.538425 | − | 0.932580i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.8425 | − | 10.3013i | −0.730855 | − | 0.421960i | ||||
\(597\) | −2.29639 | − | 3.97746i | −0.0939848 | − | 0.162786i | ||||
\(598\) | 5.38639 | + | 7.13465i | 0.220266 | + | 0.291758i | ||||
\(599\) | −20.8998 | + | 36.1995i | −0.853942 | + | 1.47907i | 0.0236813 | + | 0.999720i | \(0.492461\pi\) |
−0.877623 | + | 0.479351i | \(0.840872\pi\) | |||||||
\(600\) | 7.59389i | 0.310019i | ||||||||
\(601\) | 7.64481 | − | 13.2412i | 0.311838 | − | 0.540120i | −0.666922 | − | 0.745127i | \(-0.732389\pi\) |
0.978760 | + | 0.205008i | \(0.0657220\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 29.1940i | − | 1.18887i | ||||||
\(604\) | 10.3410 | + | 5.97036i | 0.420768 | + | 0.242930i | ||||
\(605\) | − | 82.9444i | − | 3.37217i | ||||||
\(606\) | 4.61161 | + | 2.66251i | 0.187334 | + | 0.108157i | ||||
\(607\) | 7.30434 | − | 12.6515i | 0.296474 | − | 0.513508i | −0.678853 | − | 0.734275i | \(-0.737522\pi\) |
0.975327 | + | 0.220766i | \(0.0708558\pi\) | |||||||
\(608\) | −1.06857 | + | 1.85081i | −0.0433362 | + | 0.0750604i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.8097 | 1.20696 | ||||||||
\(611\) | 12.8713 | − | 30.3987i | 0.520717 | − | 1.22980i | ||||
\(612\) | 0.238815 | − | 0.413640i | 0.00965354 | − | 0.0167204i | ||||
\(613\) | 33.9623 | − | 19.6081i | 1.37172 | − | 0.791965i | 0.380579 | − | 0.924748i | \(-0.375725\pi\) |
0.991145 | + | 0.132783i | \(0.0423914\pi\) | |||||||
\(614\) | −19.6987 | −0.794975 | ||||||||
\(615\) | 12.0798 | + | 20.9228i | 0.487104 | + | 0.843688i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.10486 | − | 4.67934i | 0.326289 | − | 0.188383i | −0.327903 | − | 0.944711i | \(-0.606342\pi\) |
0.654192 | + | 0.756328i | \(0.273009\pi\) | |||||||
\(618\) | 14.5032 | + | 8.37345i | 0.583406 | + | 0.336830i | ||||
\(619\) | 37.8518 | + | 21.8537i | 1.52139 | + | 0.878376i | 0.999681 | + | 0.0252541i | \(0.00803947\pi\) |
0.521711 | + | 0.853122i | \(0.325294\pi\) | |||||||
\(620\) | −8.57596 | −0.344419 | ||||||||
\(621\) | 11.2682 | 0.452176 | ||||||||
\(622\) | 14.6952 | + | 8.48425i | 0.589222 | + | 0.340187i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.87367 | + | 1.21676i | 0.115039 | + | 0.0487094i | ||||
\(625\) | −4.05556 | − | 7.02443i | −0.162222 | − | 0.280977i | ||||
\(626\) | 3.92997 | − | 2.26897i | 0.157073 | − | 0.0906863i | ||||
\(627\) | −5.34095 | − | 9.25080i | −0.213297 | − | 0.369441i | ||||
\(628\) | −4.67011 | + | 8.08887i | −0.186358 | + | 0.322781i | ||||
\(629\) | 1.67072i | 0.0666159i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0096 | + | 10.3978i | −0.716951 | + | 0.413932i | −0.813629 | − | 0.581384i | \(-0.802511\pi\) |
0.0966785 | + | 0.995316i | \(0.469178\pi\) | |||||||
\(632\) | 7.96526 | − | 4.59875i | 0.316841 | − | 0.182928i | ||||
\(633\) | 15.4912 | 0.615718 | ||||||||
\(634\) | 14.5933 | + | 25.2763i | 0.579574 | + | 1.00385i | ||||
\(635\) | 43.7504i | 1.73618i | ||||||||
\(636\) | −10.4682 | −0.415092 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.569205 | 0.0225350 | ||||||||
\(639\) | − | 16.5750i | − | 0.655696i | ||||||
\(640\) | −1.85566 | − | 3.21409i | −0.0733513 | − | 0.127048i | ||||
\(641\) | 7.23795 | 0.285882 | 0.142941 | − | 0.989731i | \(-0.454344\pi\) | ||||
0.142941 | + | 0.989731i | \(0.454344\pi\) | |||||||
\(642\) | 8.73244 | − | 5.04168i | 0.344642 | − | 0.198979i | ||||
\(643\) | −34.7898 | + | 20.0859i | −1.37198 | + | 0.792111i | −0.991177 | − | 0.132547i | \(-0.957685\pi\) |
−0.380800 | + | 0.924658i | \(0.624351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 14.7110i | − | 0.579245i | ||||||
\(646\) | 0.226747 | − | 0.392737i | 0.00892124 | − | 0.0154520i | ||||
\(647\) | −7.27561 | − | 12.6017i | −0.286034 | − | 0.495425i | 0.686826 | − | 0.726822i | \(-0.259004\pi\) |
−0.972859 | + | 0.231397i | \(0.925670\pi\) | |||||||
\(648\) | −2.44144 | + | 1.40956i | −0.0959087 | + | 0.0553729i | ||||
\(649\) | 0.669636 | + | 1.15984i | 0.0262855 | + | 0.0455278i | ||||
\(650\) | −31.3953 | + | 3.88344i | −1.23142 | + | 0.152321i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.87746 | + | 2.23865i | 0.151853 | + | 0.0876723i | ||||
\(653\) | −49.7267 | −1.94596 | −0.972978 | − | 0.230896i | \(-0.925834\pi\) | ||||
−0.972978 | + | 0.230896i | \(0.925834\pi\) | |||||||
\(654\) | 4.96206 | 0.194032 | ||||||||
\(655\) | −16.4838 | − | 9.51690i | −0.644074 | − | 0.371856i | ||||
\(656\) | −6.51354 | − | 3.76060i | −0.254311 | − | 0.146827i | ||||
\(657\) | 10.9243 | − | 6.30714i | 0.426197 | − | 0.246065i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.7988 | + | 27.3644i | 0.615436 | + | 1.06597i | 0.990308 | + | 0.138889i | \(0.0443532\pi\) |
−0.374872 | + | 0.927076i | \(0.622313\pi\) | |||||||
\(660\) | 18.5500 | 0.722058 | ||||||||
\(661\) | −21.5391 | + | 12.4356i | −0.837775 | + | 0.483689i | −0.856507 | − | 0.516135i | \(-0.827370\pi\) |
0.0187325 | + | 0.999825i | \(0.494037\pi\) | |||||||
\(662\) | 2.40271 | − | 4.16161i | 0.0933839 | − | 0.161746i | ||||
\(663\) | −0.609785 | − | 0.258193i | −0.0236821 | − | 0.0100274i | ||||
\(664\) | −3.17186 | −0.123092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.86109 | − | 15.3479i | 0.343360 | − | 0.594717i | ||||
\(667\) | −0.122192 | + | 0.211643i | −0.00473130 | + | 0.00819485i | ||||
\(668\) | 12.7365 | + | 7.35342i | 0.492790 | + | 0.284512i | ||||
\(669\) | − | 14.2278i | − | 0.550077i | ||||||
\(670\) | 41.6868 | + | 24.0679i | 1.61050 | + | 0.929822i | ||||
\(671\) | − | 46.3843i | − | 1.79065i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8245 | + | 18.7486i | −0.417254 | + | 0.722705i | −0.995662 | − | 0.0930423i | \(-0.970341\pi\) |
0.578408 | + | 0.815748i | \(0.303674\pi\) | |||||||
\(674\) | 17.7312i | 0.682982i | ||||||||
\(675\) | −19.9373 | + | 34.5325i | −0.767388 | + | 1.32916i | ||||
\(676\) | −3.56086 | + | 12.5028i | −0.136956 | + | 0.480877i | ||||
\(677\) | 7.19675 | + | 12.4651i | 0.276594 | + | 0.479074i | 0.970536 | − | 0.240956i | \(-0.0774611\pi\) |
−0.693942 | + | 0.720031i | \(0.744128\pi\) | |||||||
\(678\) | −12.3823 | − | 7.14890i | −0.475538 | − | 0.274552i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.393765 | + | 0.682021i | 0.0151002 | + | 0.0261543i | ||||
\(681\) | 4.22072 | − | 2.43684i | 0.161738 | − | 0.0933797i | ||||
\(682\) | 13.3443i | 0.510981i | ||||||||
\(683\) | − | 42.3738i | − | 1.62139i | −0.585471 | − | 0.810694i | \(-0.699090\pi\) | ||
0.585471 | − | 0.810694i | \(-0.300910\pi\) | |||||||
\(684\) | −4.16597 | + | 2.40522i | −0.159290 | + | 0.0919660i | ||||
\(685\) | −17.4307 | − | 30.1909i | −0.665993 | − | 1.15353i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.7796 | + | 11.9971i | 0.792793 | + | 0.457719i | ||||
\(688\) | 2.28987 | + | 3.96617i | 0.0873003 | + | 0.151209i | ||||
\(689\) | −5.35335 | − | 43.2786i | −0.203946 | − | 1.64878i | ||||
\(690\) | −3.98216 | + | 6.89730i | −0.151598 | + | 0.262576i | ||||
\(691\) | − | 22.9382i | − | 0.872610i | −0.899799 | − | 0.436305i | \(-0.856287\pi\) | ||
0.899799 | − | 0.436305i | \(-0.143713\pi\) | |||||||
\(692\) | 6.88286 | − | 11.9215i | 0.261647 | − | 0.453186i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 16.7048i | − | 0.634105i | ||||||
\(695\) | 48.6654 | + | 28.0970i | 1.84598 | + | 1.06578i | ||||
\(696\) | 0.0853103i | 0.00323368i | ||||||||
\(697\) | 1.38215 | + | 0.797987i | 0.0523528 | + | 0.0302259i | ||||
\(698\) | 0.0100237 | − | 0.0173616i | 0.000379404 | − | 0.000657147i | ||||
\(699\) | 8.70291 | − | 15.0739i | 0.329174 | − | 0.570146i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.70699 | 0.0644723 | 0.0322361 | − | 0.999480i | \(-0.489737\pi\) | ||||
0.0322361 | + | 0.999480i | \(0.489737\pi\) | |||||||
\(702\) | 9.87321 | + | 13.0778i | 0.372640 | + | 0.493588i | ||||
\(703\) | 8.41330 | − | 14.5723i | 0.317314 | − | 0.549603i | ||||
\(704\) | −5.00118 | + | 2.88743i | −0.188489 | + | 0.108824i | ||||
\(705\) | 29.4099 | 1.10764 | ||||||||
\(706\) | 14.9129 | + | 25.8299i | 0.561255 | + | 0.972122i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.173833 | + | 0.100363i | −0.00653304 | + | 0.00377186i | ||||
\(709\) | 15.7730 | + | 9.10657i | 0.592369 | + | 0.342005i | 0.766034 | − | 0.642800i | \(-0.222228\pi\) |
−0.173665 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(710\) | 23.6678 | + | 13.6646i | 0.888237 | + | 0.512824i | ||||
\(711\) | 20.7025 | 0.776404 | ||||||||
\(712\) | −11.8167 | −0.442848 | ||||||||
\(713\) | −4.96172 | − | 2.86465i | −0.185818 | − | 0.107282i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.48629 | + | 76.6909i | 0.354767 | + | 2.86808i | ||||
\(716\) | −7.63936 | − | 13.2318i | −0.285496 | − | 0.494494i | ||||
\(717\) | 4.96933 | − | 2.86904i | 0.185583 | − | 0.107146i | ||||
\(718\) | −9.16753 | − | 15.8786i | −0.342129 | − | 0.592585i | ||||
\(719\) | −1.79107 | + | 3.10222i | −0.0667956 | + | 0.115693i | −0.897489 | − | 0.441037i | \(-0.854611\pi\) |
0.830694 | + | 0.556730i | \(0.187944\pi\) | |||||||
\(720\) | − | 8.35373i | − | 0.311325i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.4990 | − | 7.21632i | 0.465166 | − | 0.268564i | ||||
\(723\) | −1.21193 | + | 0.699710i | −0.0450723 | + | 0.0260225i | ||||
\(724\) | −1.66748 | −0.0619713 | ||||||||
\(725\) | −0.432401 | − | 0.748941i | −0.0160590 | − | 0.0278150i | ||||
\(726\) | − | 19.3434i | − | 0.717903i | ||||||
\(727\) | −3.21747 | −0.119329 | −0.0596647 | − | 0.998218i | \(-0.519003\pi\) | ||||
−0.0596647 | + | 0.998218i | \(0.519003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.45503 | 0.202038 | ||||||||
\(730\) | 20.7987i | 0.769796i | ||||||||
\(731\) | −0.485903 | − | 0.841608i | −0.0179718 | − | 0.0311280i | ||||
\(732\) | 6.95191 | 0.256950 | ||||||||
\(733\) | 4.15028 | − | 2.39616i | 0.153294 | − | 0.0885043i | −0.421391 | − | 0.906879i | \(-0.638458\pi\) |
0.574685 | + | 0.818375i | \(0.305125\pi\) | |||||||
\(734\) | −1.16468 | + | 0.672426i | −0.0429890 | + | 0.0248197i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.47940i | − | 0.0913919i | ||||||
\(737\) | 37.4500 | − | 64.8653i | 1.37949 | − | 2.38934i | ||||
\(738\) | −8.46466 | − | 14.6612i | −0.311589 | − | 0.539687i | ||||
\(739\) | −9.69853 | + | 5.59945i | −0.356766 | + | 0.205979i | −0.667661 | − | 0.744465i | \(-0.732705\pi\) |
0.310895 | + | 0.950444i | \(0.399371\pi\) | |||||||
\(740\) | 14.6104 | + | 25.3059i | 0.537088 | + | 0.930264i | ||||
\(741\) | 4.01845 | + | 5.32272i | 0.147621 | + | 0.195535i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.1315 | − | 19.1285i | −1.21548 | − | 0.701757i | −0.251531 | − | 0.967849i | \(-0.580934\pi\) |
−0.963947 | + | 0.266093i | \(0.914267\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 76.4630 | 2.80139 | ||||||||
\(746\) | 9.58821 | + | 5.53575i | 0.351049 | + | 0.202678i | ||||
\(747\) | −6.18297 | − | 3.56974i | −0.226223 | − | 0.130610i | ||||
\(748\) | 1.06124 | − | 0.612704i | 0.0388026 | − | 0.0224027i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.06116 | − | 10.4982i | −0.221322 | − | 0.383342i | ||||
\(751\) | 1.84025 | 0.0671517 | 0.0335758 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335758 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(752\) | −7.92907 | + | 4.57785i | −0.289143 | + | 0.166937i | ||||
\(753\) | −0.219413 | + | 0.380034i | −0.00799585 | + | 0.0138492i | ||||
\(754\) | −0.352697 | + | 0.0436269i | −0.0128445 | + | 0.00158880i | ||||
\(755\) | −44.3157 | −1.61281 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5961 | − | 18.3529i | 0.385120 | − | 0.667048i | −0.606666 | − | 0.794957i | \(-0.707493\pi\) |
0.991786 | + | 0.127909i | \(0.0408266\pi\) | |||||||
\(758\) | −8.40523 | + | 14.5583i | −0.305292 | + | 0.528780i | ||||
\(759\) | 10.7323 | + | 6.19631i | 0.389558 | + | 0.224912i | ||||
\(760\) | − | 7.93158i | − | 0.287709i | ||||||
\(761\) | −12.2381 | − | 7.06566i | −0.443630 | − | 0.256130i | 0.261506 | − | 0.965202i | \(-0.415781\pi\) |
−0.705136 | + | 0.709072i | \(0.749114\pi\) | |||||||
\(762\) | 10.2030i | 0.369617i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.0604880 | − | 0.104768i | 0.00218838 | − | 0.00379038i | ||||
\(765\) | 1.77264i | 0.0640898i | ||||||||
\(766\) | −8.28855 | + | 14.3562i | −0.299478 | + | 0.518710i | ||||
\(767\) | −0.503823 | − | 0.667350i | −0.0181920 | − | 0.0240966i | ||||
\(768\) | −0.432757 | − | 0.749558i | −0.0156158 | − | 0.0270473i | ||||
\(769\) | 26.5219 | + | 15.3124i | 0.956405 | + | 0.552181i | 0.895065 | − | 0.445936i | \(-0.147129\pi\) |
0.0613401 | + | 0.998117i | \(0.480463\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.17206 | + | 7.22621i | 0.150253 | + | 0.260246i | ||||
\(772\) | −2.38633 | + | 1.37775i | −0.0858859 | + | 0.0495863i | ||||
\(773\) | 9.79479i | 0.352294i | 0.984364 | + | 0.176147i | \(0.0563634\pi\) | ||||
−0.984364 | + | 0.176147i | \(0.943637\pi\) | |||||||
\(774\) | 10.3084i | 0.370529i | ||||||||
\(775\) | 17.5580 | − | 10.1371i | 0.630703 | − | 0.364137i | ||||
\(776\) | 7.04093 | + | 12.1952i | 0.252755 | + | 0.437784i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.01336 | + | 0.585065i | 0.0363308 | + | 0.0209756i | ||||
\(779\) | −8.03691 | − | 13.9203i | −0.287952 | − | 0.498748i | ||||
\(780\) | −11.4941 | + | 1.42177i | −0.411556 | + | 0.0509075i | ||||
\(781\) | 21.2624 | − | 36.8275i | 0.760828 | − | 1.31779i | ||||
\(782\) | 0.526121i | 0.0188140i | ||||||||
\(783\) | −0.223977 | + | 0.387940i | −0.00800430 | + | 0.0138638i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 34.6645i | − | 1.23723i | ||||||
\(786\) | −3.84418 | − | 2.21944i | −0.137117 | − | 0.0791647i | ||||
\(787\) | − | 20.6305i | − | 0.735397i | −0.929945 | − | 0.367699i | \(-0.880146\pi\) | ||
0.929945 | − | 0.367699i | \(-0.119854\pi\) | |||||||
\(788\) | 13.0989 | + | 7.56267i | 0.466630 | + | 0.269409i | ||||
\(789\) | 3.17911 | − | 5.50638i | 0.113179 | − | 0.196032i | ||||
\(790\) | −17.0674 | + | 29.5616i | −0.607230 | + | 1.05175i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.9985 | −0.461883 | ||||||||
\(793\) | 3.55514 | + | 28.7411i | 0.126247 | + | 1.02063i | ||||
\(794\) | −13.0987 | + | 22.6877i | −0.464856 | + | 0.805155i | ||||
\(795\) | 33.6458 | − | 19.4254i | 1.19330 | − | 0.688949i | ||||
\(796\) | −5.30640 | −0.188080 | ||||||||
\(797\) | −3.88584 | − | 6.73047i | −0.137643 | − | 0.238405i | 0.788961 | − | 0.614444i | \(-0.210619\pi\) |
−0.926604 | + | 0.376038i | \(0.877286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.68252 | − | 0.971406i | 0.0595234 | − | 0.0343659i | ||||
\(800\) | 7.59837 | + | 4.38692i | 0.268643 | + | 0.155101i | ||||
\(801\) | −23.0345 | − | 13.2990i | −0.813883 | − | 0.469896i | ||||
\(802\) | −11.3687 | −0.401443 | ||||||||
\(803\) | 32.3632 | 1.14207 | ||||||||
\(804\) | 9.72176 | + | 5.61286i | 0.342860 | + | 0.197950i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.02278 | − | 8.26856i | −0.0360259 | − | 0.291248i | ||||
\(807\) | 9.67389 | + | 16.7557i | 0.340537 | + | 0.589828i | ||||
\(808\) | 5.32816 | − | 3.07622i | 0.187444 | − | 0.108221i | ||||
\(809\) | −21.2715 | − | 36.8433i | −0.747866 | − | 1.29534i | −0.948844 | − | 0.315746i | \(-0.897745\pi\) |
0.200977 | − | 0.979596i | \(-0.435588\pi\) | |||||||
\(810\) | 5.23134 | − | 9.06094i | 0.183810 | − | 0.318369i | ||||
\(811\) | − | 22.1131i | − | 0.776494i | −0.921555 | − | 0.388247i | \(-0.873081\pi\) | ||
0.921555 | − | 0.388247i | \(-0.126919\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.20880 | + | 4.16200i | −0.252824 | + | 0.145968i | ||||
\(814\) | 39.3764 | − | 22.7340i | 1.38014 | − | 0.796826i | ||||
\(815\) | −16.6167 | −0.582056 | ||||||||
\(816\) | 0.0918298 | + | 0.159054i | 0.00321469 | + | 0.00556800i | ||||
\(817\) | 9.78752i | 0.342422i | ||||||||
\(818\) | −23.3314 | −0.815763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.9135 | 0.974782 | ||||||||
\(821\) | − | 24.3549i | − | 0.849992i | −0.905195 | − | 0.424996i | \(-0.860275\pi\) | ||
0.905195 | − | 0.424996i | \(-0.139725\pi\) | |||||||
\(822\) | −4.06501 | − | 7.04081i | −0.141784 | − | 0.245576i | ||||
\(823\) | 4.75914 | 0.165893 | 0.0829465 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829465 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(824\) | 16.7568 | − | 9.67453i | 0.583750 | − | 0.337028i | ||||
\(825\) | −37.9784 | + | 21.9269i | −1.32224 | + | 0.763395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.00333i | − | 0.243530i | −0.992559 | − | 0.121765i | \(-0.961145\pi\) | ||
0.992559 | − | 0.121765i | \(-0.0388554\pi\) | |||||||
\(828\) | 2.79042 | − | 4.83315i | 0.0969738 | − | 0.167964i | ||||
\(829\) | 2.87619 | + | 4.98170i | 0.0998941 | + | 0.173022i | 0.911641 | − | 0.410988i | \(-0.134816\pi\) |
−0.811747 | + | 0.584010i | \(0.801483\pi\) | |||||||
\(830\) | 10.1946 | − | 5.88588i | 0.353861 | − | 0.204302i | ||||
\(831\) | 4.40499 | + | 7.62967i | 0.152807 | + | 0.264670i | ||||
\(832\) | 2.87757 | − | 2.17246i | 0.0997619 | − | 0.0753164i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.3493 | + | 6.55250i | 0.392993 | + | 0.226894i | ||||
\(835\) | −54.5817 | −1.88888 | ||||||||
\(836\) | −12.3417 | −0.426846 | ||||||||
\(837\) | −9.09480 | − | 5.25088i | −0.314362 | − | 0.181497i | ||||
\(838\) | −10.9709 | − | 6.33402i | −0.378982 | − | 0.218805i | ||||
\(839\) | 35.6863 | − | 20.6035i | 1.23203 | − | 0.711311i | 0.264575 | − | 0.964365i | \(-0.414768\pi\) |
0.967452 | + | 0.253054i | \(0.0814350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4951 | + | 25.1063i | 0.499832 | + | 0.865735i | ||||
\(842\) | −27.6625 | −0.953312 | ||||||||
\(843\) | 10.6207 | − | 6.13184i | 0.365795 | − | 0.211192i | ||||
\(844\) | 8.94910 | − | 15.5003i | 0.308041 | − | 0.533542i | ||||
\(845\) | −11.7560 | − | 46.7929i | −0.404418 | − | 1.60973i | ||||
\(846\) | −20.6084 | −0.708532 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.04740 | + | 10.4744i | −0.207669 | + | 0.359692i | ||||
\(849\) | −8.19323 | + | 14.1911i | −0.281191 | + | 0.487037i | ||||
\(850\) | −1.61235 | − | 0.930892i | −0.0553032 | − | 0.0319293i | ||||
\(851\) | 19.5214i | 0.669184i | ||||||||
\(852\) | 5.51957 | + | 3.18673i | 0.189097 | + | 0.109175i | ||||
\(853\) | − | 2.38939i | − | 0.0818113i | −0.999163 | − | 0.0409056i | \(-0.986976\pi\) | ||
0.999163 | − | 0.0409056i | \(-0.0130243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.92654 | − | 15.4612i | 0.305281 | − | 0.528762i | ||||
\(856\) | − | 11.6501i | − | 0.398193i | ||||||
\(857\) | −6.90186 | + | 11.9544i | −0.235763 | + | 0.408353i | −0.959494 | − | 0.281729i | \(-0.909092\pi\) |
0.723731 | + | 0.690082i | \(0.242426\pi\) | |||||||
\(858\) | 2.21230 | + | 17.8851i | 0.0755266 | + | 0.610586i | ||||
\(859\) | −18.8638 | − | 32.6730i | −0.643624 | − | 1.11479i | −0.984617 | − | 0.174724i | \(-0.944097\pi\) |
0.340994 | − | 0.940066i | \(-0.389237\pi\) | |||||||
\(860\) | −14.7197 | − | 8.49841i | −0.501937 | − | 0.289793i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.20696 | − | 5.55462i | −0.109230 | − | 0.189191i | ||||
\(863\) | −22.0992 | + | 12.7590i | −0.752267 | + | 0.434322i | −0.826513 | − | 0.562918i | \(-0.809679\pi\) |
0.0742453 | + | 0.997240i | \(0.476345\pi\) | |||||||
\(864\) | − | 4.54472i | − | 0.154614i | ||||||
\(865\) | 51.0889i | 1.73707i | ||||||||
\(866\) | −0.0563150 | + | 0.0325135i | −0.00191366 | + | 0.00110485i | ||||
\(867\) | 7.33739 | + | 12.7087i | 0.249191 | + | 0.431611i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.9983 | + | 26.5571i | 1.56039 | + | 0.900889i | ||||
\(870\) | −0.158307 | − | 0.274195i | −0.00536710 | − | 0.00929609i | ||||
\(871\) | −18.2335 | + | 43.0628i | −0.617819 | + | 1.45913i | ||||
\(872\) | 2.86654 | − | 4.96499i | 0.0970732 | − | 0.168136i | ||||
\(873\) | 31.6966i | 1.07277i | ||||||||
\(874\) | 2.64941 | − | 4.58891i | 0.0896175 | − | 0.155222i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.85047i | 0.163882i | ||||||||
\(877\) | −10.7726 | − | 6.21955i | −0.363764 | − | 0.210019i | 0.306966 | − | 0.951720i | \(-0.400686\pi\) |
−0.670731 | + | 0.741701i | \(0.734019\pi\) | |||||||
\(878\) | 36.7778i | 1.24119i | ||||||||
\(879\) | 2.74325 | + | 1.58382i | 0.0925275 | + | 0.0534208i | ||||
\(880\) | 10.7162 | − | 18.5609i | 0.361242 | − | 0.625689i | ||||
\(881\) | 11.2710 | − | 19.5219i | 0.379728 | − | 0.657709i | −0.611294 | − | 0.791404i | \(-0.709351\pi\) |
0.991023 | + | 0.133694i | \(0.0426841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.1548 | −0.509998 | −0.254999 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254999 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(884\) | −0.610613 | + | 0.460989i | −0.0205371 | + | 0.0155047i | ||||
\(885\) | 0.372477 | − | 0.645149i | 0.0125207 | − | 0.0216864i | ||||
\(886\) | −7.32989 | + | 4.23191i | −0.246252 | + | 0.142174i | ||||
\(887\) | −41.7749 | −1.40266 | −0.701332 | − | 0.712835i | \(-0.747411\pi\) | ||||
−0.701332 | + | 0.712835i | \(0.747411\pi\) | |||||||
\(888\) | 3.40729 | + | 5.90159i | 0.114341 | + | 0.198044i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 37.9798 | − | 21.9277i | 1.27309 | − | 0.735017i | ||||
\(891\) | −14.0990 | − | 8.14004i | −0.472333 | − | 0.272702i | ||||
\(892\) | −14.2362 | − | 8.21925i | −0.476662 | − | 0.275201i | ||||
\(893\) | −19.5670 | −0.654784 | ||||||||
\(894\) | 17.8319 | 0.596389 | ||||||||
\(895\) | 49.1072 | + | 28.3521i | 1.64147 | + | 0.947705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.12498 | − | 3.01684i | −0.237896 | − | 0.100729i | ||||
\(898\) | −11.3152 | − | 19.5984i | −0.377592 | − | 0.654008i | ||||
\(899\) | 0.197248 | − | 0.113881i | 0.00657860 | − | 0.00379815i | ||||
\(900\) | 9.87445 | + | 17.1031i | 0.329148 | + | 0.570102i | ||||
\(901\) | 1.28324 | − | 2.22264i | 0.0427509 | − | 0.0740468i | ||||
\(902\) | − | 43.4339i | − | 1.44619i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.3062 | + | 8.25971i | −0.475818 | + | 0.274714i | ||||
\(905\) | 5.35943 | − | 3.09427i | 0.178153 | − | 0.102857i | ||||
\(906\) | −10.3349 | −0.343353 | ||||||||
\(907\) | 2.14376 | + | 3.71310i | 0.0711823 | + | 0.123291i | 0.899420 | − | 0.437086i | \(-0.143989\pi\) |
−0.828237 | + | 0.560377i | \(0.810656\pi\) | |||||||
\(908\) | − | 5.63095i | − | 0.186870i | ||||||
\(909\) | 13.8484 | 0.459323 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87618 | −0.128423 | −0.0642117 | − | 0.997936i | \(-0.520453\pi\) | ||||
−0.0642117 | + | 0.997936i | \(0.520453\pi\) | |||||||
\(912\) | − | 1.84972i | − | 0.0612505i | ||||||
\(913\) | −9.15853 | − | 15.8630i | −0.303103 | − | 0.524990i | ||||
\(914\) | −16.3170 | −0.539719 | ||||||||
\(915\) | −22.3441 | + | 12.9004i | −0.738672 | + | 0.426473i | ||||
\(916\) | 24.0084 | − | 13.8613i | 0.793260 | − | 0.457989i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.964376i | 0.0318291i | ||||||||
\(919\) | −22.9524 | + | 39.7547i | −0.757129 | + | 1.31139i | 0.187180 | + | 0.982326i | \(0.440065\pi\) |
−0.944309 | + | 0.329060i | \(0.893268\pi\) | |||||||
\(920\) | 4.60091 | + | 7.96901i | 0.151688 | + | 0.262731i | ||||
\(921\) | 14.7653 | − | 8.52476i | 0.486534 | − | 0.280900i | ||||
\(922\) | −9.63892 | − | 16.6951i | −0.317441 | − | 0.549824i | ||||
\(923\) | −10.3522 | + | 24.4491i | −0.340745 | + | 0.804752i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.8253 | − | 34.5401i | −1.96704 | − | 1.13567i | ||||
\(926\) | 2.70218 | 0.0887990 | ||||||||
\(927\) | 43.5525 | 1.43045 | ||||||||
\(928\) | 0.0853606 | + | 0.0492830i | 0.00280210 | + | 0.00161779i | ||||
\(929\) | 8.51833 | + | 4.91806i | 0.279477 | + | 0.161356i | 0.633187 | − | 0.773999i | \(-0.281746\pi\) |
−0.353709 | + | 0.935355i | \(0.615080\pi\) | |||||||
\(930\) | 6.42818 | − | 3.71131i | 0.210788 | − | 0.121699i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.0552 | − | 17.4161i | −0.329368 | − | 0.570483i | ||||
\(933\) | −14.6865 | −0.480814 | ||||||||
\(934\) | 15.9267 | − | 9.19528i | 0.521137 | − | 0.300879i | ||||
\(935\) | −2.27394 | + | 3.93858i | −0.0743657 | + | 0.128805i | ||||
\(936\) | 8.05429 | − | 0.996277i | 0.263263 | − | 0.0325643i | ||||
\(937\) | −21.5135 | −0.702815 | −0.351407 | − | 0.936223i | \(-0.614297\pi\) | ||||
−0.351407 | + | 0.936223i | \(0.614297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.96383 | + | 3.40145i | −0.0640871 | + | 0.111002i | ||||
\(940\) | 16.9898 | − | 29.4272i | 0.554147 | − | 0.959811i | ||||
\(941\) | −5.55854 | − | 3.20923i | −0.181203 | − | 0.104618i | 0.406655 | − | 0.913582i | \(-0.366695\pi\) |
−0.587858 | + | 0.808964i | \(0.700029\pi\) | |||||||
\(942\) | − | 8.08410i | − | 0.263394i | ||||||
\(943\) | 16.1497 | + | 9.32402i | 0.525906 | + | 0.303632i | ||||
\(944\) | 0.231914i | 0.00754816i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.2237 | + | 22.9041i | −0.429939 | + | 0.744675i | ||||
\(947\) | − | 7.57266i | − | 0.246078i | −0.992402 | − | 0.123039i | \(-0.960736\pi\) | ||
0.992402 | − | 0.123039i | \(-0.0392641\pi\) | |||||||
\(948\) | −3.98028 | + | 6.89405i | −0.129274 | + | 0.223908i | ||||
\(949\) | −20.0532 | + | 2.48048i | −0.650954 | + | 0.0805199i | ||||
\(950\) | 9.37545 | + | 16.2388i | 0.304180 | + | 0.526855i | ||||
\(951\) | −21.8770 | − | 12.6307i | −0.709412 | − | 0.409579i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.9022 | − | 31.0075i | −0.579909 | − | 1.00443i | −0.995489 | − | 0.0948754i | \(-0.969755\pi\) |
0.415580 | − | 0.909557i | \(-0.363579\pi\) | |||||||
\(954\) | −23.5767 | + | 13.6120i | −0.763323 | + | 0.440705i | ||||
\(955\) | 0.448980i | 0.0145286i | ||||||||
\(956\) | − | 6.62968i | − | 0.214419i | ||||||
\(957\) | −0.426652 | + | 0.246328i | −0.0137917 | + | 0.00796265i | ||||
\(958\) | 20.4354 | + | 35.3951i | 0.660238 | + | 1.14357i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.78184 | + | 1.60610i | 0.0897836 | + | 0.0518366i | ||||
\(961\) | −12.8302 | − | 22.2225i | −0.413877 | − | 0.716856i | ||||
\(962\) | −22.6564 | + | 17.1047i | −0.730471 | + | 0.551477i | ||||
\(963\) | 13.1115 | − | 22.7098i | 0.422513 | − | 0.731814i | ||||
\(964\) | 1.61687i | 0.0520757i | ||||||||
\(965\) | 5.11326 | − | 8.85642i | 0.164602 | − | 0.285098i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3876i | 1.04152i | 0.853704 | + | 0.520758i | \(0.174351\pi\) | ||||
−0.853704 | + | 0.520758i | \(0.825649\pi\) | |||||||
\(968\) | −19.3549 | − | 11.1745i | −0.622089 | − | 0.359163i | ||||
\(969\) | 0.392506i | 0.0126091i | ||||||||
\(970\) | −45.2604 | − | 26.1311i | −1.45322 | − | 0.839019i | ||||
\(971\) | 17.2033 | − | 29.7969i | 0.552079 | − | 0.956229i | −0.446045 | − | 0.895010i | \(-0.647168\pi\) |
0.998124 | − | 0.0612186i | \(-0.0194987\pi\) | |||||||
\(972\) | 8.03708 | − | 13.9206i | 0.257789 | − | 0.446504i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.6293 | −0.564880 | ||||||||
\(975\) | 21.8520 | − | 16.4974i | 0.699824 | − | 0.528340i | ||||
\(976\) | 4.01605 | − | 6.95601i | 0.128551 | − | 0.222656i | ||||
\(977\) | −20.0471 | + | 11.5742i | −0.641364 | + | 0.370291i | −0.785140 | − | 0.619319i | \(-0.787409\pi\) |
0.143776 | + | 0.989610i | \(0.454076\pi\) | |||||||
\(978\) | −3.87517 | −0.123914 | ||||||||
\(979\) | −34.1198 | − | 59.0972i | −1.09047 | − | 1.88876i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.1756 | − | 6.45224i | 0.356810 | − | 0.206004i | ||||
\(982\) | −16.3332 | − | 9.42997i | −0.521213 | − | 0.300922i | ||||
\(983\) | −40.7534 | − | 23.5290i | −1.29983 | − | 0.750458i | −0.319456 | − | 0.947601i | \(-0.603500\pi\) |
−0.980375 | + | 0.197143i | \(0.936834\pi\) | |||||||
\(984\) | 6.50970 | 0.207522 | ||||||||
\(985\) | −56.1349 | −1.78861 | ||||||||
\(986\) | −0.0181133 | − | 0.0104577i | −0.000576844 | − | 0.000333041i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.64727 | − | 0.945931i | 0.243292 | − | 0.0300941i | ||||
\(989\) | −5.67749 | − | 9.83371i | −0.180534 | − | 0.312694i | ||||
\(990\) | 41.7785 | − | 24.1208i | 1.32781 | − | 0.766611i | ||||
\(991\) | 5.95052 | + | 10.3066i | 0.189025 | + | 0.327400i | 0.944925 | − | 0.327286i | \(-0.106134\pi\) |
−0.755901 | + | 0.654686i | \(0.772801\pi\) | |||||||
\(992\) | −1.15538 | + | 2.00118i | −0.0366834 | + | 0.0635375i | ||||
\(993\) | 4.15916i | 0.131987i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0553 | − | 9.84686i | 0.540688 | − | 0.312167i | ||||
\(996\) | 2.37749 | − | 1.37265i | 0.0753337 | − | 0.0434939i | ||||
\(997\) | −13.0143 | −0.412166 | −0.206083 | − | 0.978534i | \(-0.566072\pi\) | ||||
−0.206083 | + | 0.978534i | \(0.566072\pi\) | |||||||
\(998\) | 1.05371 | + | 1.82508i | 0.0333546 | + | 0.0577718i | ||||
\(999\) | 35.7825i | 1.13211i |
(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 | 1274.2.o.e.459.4 | 12 | ||
7.2 | even | 3 | 1274.2.v.d.667.6 | 12 | |||
7.3 | odd | 6 | 182.2.m.b.43.3 | ✓ | 12 | ||
7.4 | even | 3 | 1274.2.m.c.589.1 | 12 | |||
7.5 | odd | 6 | 1274.2.v.e.667.4 | 12 | |||
7.6 | odd | 2 | 1274.2.o.d.459.6 | 12 | |||
13.10 | even | 6 | 1274.2.v.d.361.6 | 12 | |||
21.17 | even | 6 | 1638.2.bj.g.1135.6 | 12 | |||
28.3 | even | 6 | 1456.2.cc.d.225.2 | 12 | |||
91.10 | odd | 6 | 182.2.m.b.127.3 | yes | 12 | ||
91.17 | odd | 6 | 2366.2.d.r.337.2 | 12 | |||
91.23 | even | 6 | inner | 1274.2.o.e.569.1 | 12 | ||
91.45 | even | 12 | 2366.2.a.bh.1.2 | 6 | |||
91.59 | even | 12 | 2366.2.a.bf.1.2 | 6 | |||
91.62 | odd | 6 | 1274.2.v.e.361.4 | 12 | |||
91.75 | odd | 6 | 1274.2.o.d.569.3 | 12 | |||
91.87 | odd | 6 | 2366.2.d.r.337.8 | 12 | |||
91.88 | even | 6 | 1274.2.m.c.491.1 | 12 | |||
273.101 | even | 6 | 1638.2.bj.g.127.4 | 12 | |||
364.283 | even | 6 | 1456.2.cc.d.673.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.3 | ✓ | 12 | 7.3 | odd | 6 | ||
182.2.m.b.127.3 | yes | 12 | 91.10 | odd | 6 | ||
1274.2.m.c.491.1 | 12 | 91.88 | even | 6 | |||
1274.2.m.c.589.1 | 12 | 7.4 | even | 3 | |||
1274.2.o.d.459.6 | 12 | 7.6 | odd | 2 | |||
1274.2.o.d.569.3 | 12 | 91.75 | odd | 6 | |||
1274.2.o.e.459.4 | 12 | 1.1 | even | 1 | trivial | ||
1274.2.o.e.569.1 | 12 | 91.23 | even | 6 | inner | ||
1274.2.v.d.361.6 | 12 | 13.10 | even | 6 | |||
1274.2.v.d.667.6 | 12 | 7.2 | even | 3 | |||
1274.2.v.e.361.4 | 12 | 91.62 | odd | 6 | |||
1274.2.v.e.667.4 | 12 | 7.5 | odd | 6 | |||
1456.2.cc.d.225.2 | 12 | 28.3 | even | 6 | |||
1456.2.cc.d.673.2 | 12 | 364.283 | even | 6 | |||
1638.2.bj.g.127.4 | 12 | 273.101 | even | 6 | |||
1638.2.bj.g.1135.6 | 12 | 21.17 | even | 6 | |||
2366.2.a.bf.1.2 | 6 | 91.59 | even | 12 | |||
2366.2.a.bh.1.2 | 6 | 91.45 | even | 12 | |||
2366.2.d.r.337.2 | 12 | 91.17 | odd | 6 | |||
2366.2.d.r.337.8 | 12 | 91.87 | odd | 6 |