Properties

Label 5292.2.i.f.1549.2
Level $5292$
Weight $2$
Character 5292.1549
Analytic conductor $42.257$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5292,2,Mod(1549,5292)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5292.1549");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.i (of order \(3\), 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: \(42.2568327497\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1549.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 5292.1549
Dual form 5292.2.i.f.2125.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.119562 + 0.207087i) q^{5} +O(q^{10})\) \(q+(0.119562 + 0.207087i) q^{5} +(-2.56238 + 4.43818i) q^{11} +(2.44282 - 4.23109i) q^{13} +(1.85185 + 3.20750i) q^{17} +(-1.83009 + 3.16982i) q^{19} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(1.73229 + 3.00041i) q^{29} -0.717370 q^{31} +(-2.30150 + 3.98632i) q^{37} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} -4.33981 q^{47} +(-0.471410 - 0.816506i) q^{53} -1.22545 q^{55} -7.57893 q^{59} +5.50808 q^{61} +1.16827 q^{65} -0.660190 q^{67} -13.7414 q^{71} +(1.83009 + 3.16982i) q^{73} -6.22545 q^{79} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.74433 + 6.48536i) q^{89} -0.875237 q^{95} +(8.57442 + 14.8513i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{5} + 2 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} + 14 q^{23} + 6 q^{25} + q^{29} - 6 q^{31} + 3 q^{37} - 3 q^{43} - 42 q^{47} + 6 q^{53} + 12 q^{55} - 62 q^{59} + 12 q^{61} - 30 q^{65} + 12 q^{67} - 34 q^{71} + 3 q^{73} - 18 q^{79} + 20 q^{83} + 15 q^{85} + 12 q^{89} - 40 q^{95} + 9 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(2647\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.119562 + 0.207087i 0.0534696 + 0.0926120i 0.891521 0.452979i \(-0.149639\pi\)
−0.838052 + 0.545591i \(0.816305\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.56238 + 4.43818i −0.772587 + 1.33816i 0.163554 + 0.986534i \(0.447704\pi\)
−0.936141 + 0.351626i \(0.885629\pi\)
\(12\) 0 0
\(13\) 2.44282 4.23109i 0.677516 1.17349i −0.298210 0.954500i \(-0.596390\pi\)
0.975727 0.218993i \(-0.0702770\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.85185 + 3.20750i 0.449139 + 0.777932i 0.998330 0.0577649i \(-0.0183974\pi\)
−0.549191 + 0.835697i \(0.685064\pi\)
\(18\) 0 0
\(19\) −1.83009 + 3.16982i −0.419853 + 0.727206i −0.995924 0.0901932i \(-0.971252\pi\)
0.576072 + 0.817399i \(0.304585\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.71053 + 6.42683i 0.773700 + 1.34009i 0.935522 + 0.353267i \(0.114929\pi\)
−0.161823 + 0.986820i \(0.551737\pi\)
\(24\) 0 0
\(25\) 2.47141 4.28061i 0.494282 0.856122i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.73229 + 3.00041i 0.321678 + 0.557162i 0.980834 0.194844i \(-0.0624200\pi\)
−0.659157 + 0.752006i \(0.729087\pi\)
\(30\) 0 0
\(31\) −0.717370 −0.128843 −0.0644217 0.997923i \(-0.520520\pi\)
−0.0644217 + 0.997923i \(0.520520\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.30150 + 3.98632i −0.378365 + 0.655348i −0.990825 0.135154i \(-0.956847\pi\)
0.612459 + 0.790502i \(0.290180\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.80150 4.85235i 0.437522 0.757810i −0.559976 0.828509i \(-0.689190\pi\)
0.997498 + 0.0706992i \(0.0225230\pi\)
\(42\) 0 0
\(43\) −6.24433 10.8155i −0.952251 1.64935i −0.740538 0.672015i \(-0.765429\pi\)
−0.211713 0.977332i \(-0.567904\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.33981 −0.633026 −0.316513 0.948588i \(-0.602512\pi\)
−0.316513 + 0.948588i \(0.602512\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.471410 0.816506i −0.0647531 0.112156i 0.831831 0.555029i \(-0.187293\pi\)
−0.896584 + 0.442873i \(0.853959\pi\)
\(54\) 0 0
\(55\) −1.22545 −0.165240
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.57893 −0.986693 −0.493347 0.869833i \(-0.664227\pi\)
−0.493347 + 0.869833i \(0.664227\pi\)
\(60\) 0 0
\(61\) 5.50808 0.705237 0.352619 0.935767i \(-0.385291\pi\)
0.352619 + 0.935767i \(0.385291\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.16827 0.144906
\(66\) 0 0
\(67\) −0.660190 −0.0806550 −0.0403275 0.999187i \(-0.512840\pi\)
−0.0403275 + 0.999187i \(0.512840\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13.7414 −1.63081 −0.815405 0.578891i \(-0.803486\pi\)
−0.815405 + 0.578891i \(0.803486\pi\)
\(72\) 0 0
\(73\) 1.83009 + 3.16982i 0.214196 + 0.370999i 0.953024 0.302896i \(-0.0979534\pi\)
−0.738827 + 0.673895i \(0.764620\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.22545 −0.700418 −0.350209 0.936672i \(-0.613889\pi\)
−0.350209 + 0.936672i \(0.613889\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.85185 + 8.40365i 0.532560 + 0.922420i 0.999277 + 0.0380138i \(0.0121031\pi\)
−0.466718 + 0.884406i \(0.654564\pi\)
\(84\) 0 0
\(85\) −0.442820 + 0.766987i −0.0480306 + 0.0831914i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.74433 + 6.48536i −0.396898 + 0.687447i −0.993341 0.115208i \(-0.963247\pi\)
0.596444 + 0.802655i \(0.296580\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.875237 −0.0897974
\(96\) 0 0
\(97\) 8.57442 + 14.8513i 0.870600 + 1.50792i 0.861377 + 0.507967i \(0.169603\pi\)
0.00922376 + 0.999957i \(0.497064\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.59097 6.21975i 0.357315 0.618888i −0.630196 0.776436i \(-0.717026\pi\)
0.987511 + 0.157548i \(0.0503589\pi\)
\(102\) 0 0
\(103\) 6.41423 + 11.1098i 0.632013 + 1.09468i 0.987140 + 0.159860i \(0.0511044\pi\)
−0.355127 + 0.934818i \(0.615562\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.78263 6.55171i 0.365681 0.633377i −0.623204 0.782059i \(-0.714170\pi\)
0.988885 + 0.148681i \(0.0475029\pi\)
\(108\) 0 0
\(109\) 3.49028 + 6.04535i 0.334309 + 0.579040i 0.983352 0.181712i \(-0.0581639\pi\)
−0.649043 + 0.760752i \(0.724831\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.78495 + 16.9480i −0.920491 + 1.59434i −0.121834 + 0.992550i \(0.538878\pi\)
−0.798657 + 0.601787i \(0.794456\pi\)
\(114\) 0 0
\(115\) −0.887275 + 1.53681i −0.0827388 + 0.143308i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.63160 13.2183i −0.693782 1.20167i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.37756 0.212655
\(126\) 0 0
\(127\) −16.8090 −1.49156 −0.745780 0.666192i \(-0.767923\pi\)
−0.745780 + 0.666192i \(0.767923\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.44966 + 4.24293i 0.214027 + 0.370706i 0.952971 0.303061i \(-0.0980085\pi\)
−0.738944 + 0.673767i \(0.764675\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.72257 4.71563i 0.232605 0.402884i −0.725969 0.687727i \(-0.758608\pi\)
0.958574 + 0.284844i \(0.0919417\pi\)
\(138\) 0 0
\(139\) −2.83009 + 4.90187i −0.240046 + 0.415771i −0.960727 0.277495i \(-0.910496\pi\)
0.720681 + 0.693266i \(0.243829\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.5189 + 21.6833i 1.04688 + 1.81325i
\(144\) 0 0
\(145\) −0.414230 + 0.717468i −0.0343999 + 0.0595824i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.14132 + 1.97682i 0.0935002 + 0.161947i 0.908982 0.416836i \(-0.136861\pi\)
−0.815481 + 0.578783i \(0.803528\pi\)
\(150\) 0 0
\(151\) −5.63160 + 9.75422i −0.458293 + 0.793787i −0.998871 0.0475071i \(-0.984872\pi\)
0.540578 + 0.841294i \(0.318206\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.0857699 0.148558i −0.00688921 0.0119325i
\(156\) 0 0
\(157\) 5.54583 0.442605 0.221303 0.975205i \(-0.428969\pi\)
0.221303 + 0.975205i \(0.428969\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.33009 + 5.76789i −0.260833 + 0.451776i −0.966464 0.256804i \(-0.917331\pi\)
0.705630 + 0.708580i \(0.250664\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.20370 3.81691i 0.170527 0.295362i −0.768077 0.640357i \(-0.778786\pi\)
0.938604 + 0.344996i \(0.112120\pi\)
\(168\) 0 0
\(169\) −5.43474 9.41325i −0.418057 0.724096i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −25.3308 −1.92586 −0.962932 0.269745i \(-0.913061\pi\)
−0.962932 + 0.269745i \(0.913061\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.77292 + 8.26693i 0.356744 + 0.617899i 0.987415 0.158151i \(-0.0505534\pi\)
−0.630670 + 0.776051i \(0.717220\pi\)
\(180\) 0 0
\(181\) 12.3743 0.919774 0.459887 0.887978i \(-0.347890\pi\)
0.459887 + 0.887978i \(0.347890\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.10069 −0.0809241
\(186\) 0 0
\(187\) −18.9806 −1.38800
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.1683 −0.952823 −0.476411 0.879223i \(-0.658063\pi\)
−0.476411 + 0.879223i \(0.658063\pi\)
\(192\) 0 0
\(193\) 11.1488 0.802511 0.401256 0.915966i \(-0.368574\pi\)
0.401256 + 0.915966i \(0.368574\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.144194 0.0102734 0.00513669 0.999987i \(-0.498365\pi\)
0.00513669 + 0.999987i \(0.498365\pi\)
\(198\) 0 0
\(199\) 9.73461 + 16.8608i 0.690068 + 1.19523i 0.971815 + 0.235744i \(0.0757528\pi\)
−0.281747 + 0.959489i \(0.590914\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.33981 0.0935764
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.37880 16.2446i −0.648745 1.12366i
\(210\) 0 0
\(211\) 1.61436 2.79615i 0.111137 0.192495i −0.805092 0.593150i \(-0.797884\pi\)
0.916229 + 0.400655i \(0.131217\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.49316 2.58623i 0.101833 0.176380i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 18.0949 1.21720
\(222\) 0 0
\(223\) −10.3856 17.9885i −0.695474 1.20460i −0.970021 0.243022i \(-0.921861\pi\)
0.274547 0.961574i \(-0.411472\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.9714 19.0030i 0.728198 1.26128i −0.229446 0.973321i \(-0.573691\pi\)
0.957644 0.287955i \(-0.0929752\pi\)
\(228\) 0 0
\(229\) −11.3856 19.7205i −0.752384 1.30317i −0.946664 0.322222i \(-0.895570\pi\)
0.194280 0.980946i \(-0.437763\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.8908 + 22.3276i −0.844507 + 1.46273i 0.0415414 + 0.999137i \(0.486773\pi\)
−0.886049 + 0.463592i \(0.846560\pi\)
\(234\) 0 0
\(235\) −0.518875 0.898718i −0.0338477 0.0586259i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.6488 + 23.6405i −0.882870 + 1.52918i −0.0347345 + 0.999397i \(0.511059\pi\)
−0.848136 + 0.529779i \(0.822275\pi\)
\(240\) 0 0
\(241\) −5.01724 + 8.69011i −0.323189 + 0.559779i −0.981144 0.193277i \(-0.938088\pi\)
0.657955 + 0.753057i \(0.271422\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.94119 + 15.4866i 0.568914 + 0.985388i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 28.3171 1.78736 0.893680 0.448705i \(-0.148115\pi\)
0.893680 + 0.448705i \(0.148115\pi\)
\(252\) 0 0
\(253\) −38.0312 −2.39100
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.4315 + 24.9960i 0.900210 + 1.55921i 0.827221 + 0.561877i \(0.189921\pi\)
0.0729899 + 0.997333i \(0.476746\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.604645 + 1.04728i −0.0372840 + 0.0645778i −0.884065 0.467363i \(-0.845204\pi\)
0.846781 + 0.531941i \(0.178537\pi\)
\(264\) 0 0
\(265\) 0.112725 0.195246i 0.00692465 0.0119938i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.50684 + 7.80607i 0.274787 + 0.475944i 0.970081 0.242780i \(-0.0780594\pi\)
−0.695295 + 0.718725i \(0.744726\pi\)
\(270\) 0 0
\(271\) −8.80150 + 15.2447i −0.534653 + 0.926047i 0.464527 + 0.885559i \(0.346224\pi\)
−0.999180 + 0.0404876i \(0.987109\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.6654 + 21.9371i 0.763752 + 1.32286i
\(276\) 0 0
\(277\) −0.727085 + 1.25935i −0.0436863 + 0.0756669i −0.887042 0.461689i \(-0.847244\pi\)
0.843355 + 0.537356i \(0.180577\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.1482 17.5771i −0.605388 1.04856i −0.991990 0.126316i \(-0.959685\pi\)
0.386602 0.922247i \(-0.373649\pi\)
\(282\) 0 0
\(283\) −4.60301 −0.273621 −0.136810 0.990597i \(-0.543685\pi\)
−0.136810 + 0.990597i \(0.543685\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.64132 2.84284i 0.0965479 0.167226i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.53667 + 6.12569i −0.206614 + 0.357867i −0.950646 0.310278i \(-0.899578\pi\)
0.744031 + 0.668145i \(0.232911\pi\)
\(294\) 0 0
\(295\) −0.906150 1.56950i −0.0527581 0.0913797i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 36.2567 2.09678
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.658555 + 1.14065i 0.0377088 + 0.0653135i
\(306\) 0 0
\(307\) 15.7518 0.899006 0.449503 0.893279i \(-0.351601\pi\)
0.449503 + 0.893279i \(0.351601\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.6238 1.11276 0.556382 0.830926i \(-0.312189\pi\)
0.556382 + 0.830926i \(0.312189\pi\)
\(312\) 0 0
\(313\) −25.4854 −1.44052 −0.720259 0.693705i \(-0.755977\pi\)
−0.720259 + 0.693705i \(0.755977\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.28263 −0.465199 −0.232599 0.972573i \(-0.574723\pi\)
−0.232599 + 0.972573i \(0.574723\pi\)
\(318\) 0 0
\(319\) −17.7551 −0.994096
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −13.5562 −0.754289
\(324\) 0 0
\(325\) −12.0744 20.9135i −0.669768 1.16007i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.9806 −0.658512 −0.329256 0.944241i \(-0.606798\pi\)
−0.329256 + 0.944241i \(0.606798\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.0789334 0.136717i −0.00431259 0.00746963i
\(336\) 0 0
\(337\) 6.46006 11.1892i 0.351902 0.609512i −0.634681 0.772774i \(-0.718868\pi\)
0.986583 + 0.163262i \(0.0522017\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.83818 3.18381i 0.0995428 0.172413i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.1866 −0.868942 −0.434471 0.900686i \(-0.643065\pi\)
−0.434471 + 0.900686i \(0.643065\pi\)
\(348\) 0 0
\(349\) 9.05718 + 15.6875i 0.484820 + 0.839732i 0.999848 0.0174409i \(-0.00555188\pi\)
−0.515028 + 0.857173i \(0.672219\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.84897 + 10.1307i −0.311309 + 0.539203i −0.978646 0.205553i \(-0.934101\pi\)
0.667337 + 0.744756i \(0.267434\pi\)
\(354\) 0 0
\(355\) −1.64295 2.84567i −0.0871987 0.151033i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.8623 30.9383i 0.942734 1.63286i 0.182507 0.983205i \(-0.441579\pi\)
0.760227 0.649658i \(-0.225088\pi\)
\(360\) 0 0
\(361\) 2.80150 + 4.85235i 0.147448 + 0.255387i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.437618 + 0.757977i −0.0229060 + 0.0396743i
\(366\) 0 0
\(367\) −8.52696 + 14.7691i −0.445103 + 0.770942i −0.998059 0.0622687i \(-0.980166\pi\)
0.552956 + 0.833210i \(0.313500\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 12.9617 + 22.4503i 0.671131 + 1.16243i 0.977584 + 0.210547i \(0.0675246\pi\)
−0.306453 + 0.951886i \(0.599142\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 16.9267 0.871767
\(378\) 0 0
\(379\) 26.8446 1.37892 0.689458 0.724326i \(-0.257849\pi\)
0.689458 + 0.724326i \(0.257849\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.4263 + 21.5229i 0.634953 + 1.09977i 0.986525 + 0.163610i \(0.0523137\pi\)
−0.351573 + 0.936161i \(0.614353\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.12640 + 15.8074i −0.462727 + 0.801466i −0.999096 0.0425174i \(-0.986462\pi\)
0.536369 + 0.843984i \(0.319796\pi\)
\(390\) 0 0
\(391\) −13.7427 + 23.8030i −0.694998 + 1.20377i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.744325 1.28921i −0.0374511 0.0648671i
\(396\) 0 0
\(397\) −6.18715 + 10.7164i −0.310524 + 0.537843i −0.978476 0.206361i \(-0.933838\pi\)
0.667952 + 0.744204i \(0.267171\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.48113 9.49359i −0.273714 0.474087i 0.696096 0.717949i \(-0.254919\pi\)
−0.969810 + 0.243862i \(0.921586\pi\)
\(402\) 0 0
\(403\) −1.75241 + 3.03526i −0.0872935 + 0.151197i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.7947 20.4290i −0.584640 1.01263i
\(408\) 0 0
\(409\) −13.3204 −0.658650 −0.329325 0.944217i \(-0.606821\pi\)
−0.329325 + 0.944217i \(0.606821\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.16019 + 2.00951i −0.0569515 + 0.0986429i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.35705 4.08253i 0.115149 0.199445i −0.802690 0.596396i \(-0.796599\pi\)
0.917839 + 0.396952i \(0.129932\pi\)
\(420\) 0 0
\(421\) −9.65856 16.7291i −0.470729 0.815327i 0.528710 0.848802i \(-0.322676\pi\)
−0.999440 + 0.0334755i \(0.989342\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 18.3067 0.888006
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.1397 26.2227i −0.729253 1.26310i −0.957199 0.289429i \(-0.906535\pi\)
0.227947 0.973674i \(-0.426799\pi\)
\(432\) 0 0
\(433\) 34.2060 1.64384 0.821918 0.569606i \(-0.192904\pi\)
0.821918 + 0.569606i \(0.192904\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −27.1625 −1.29936
\(438\) 0 0
\(439\) −0.622440 −0.0297075 −0.0148537 0.999890i \(-0.504728\pi\)
−0.0148537 + 0.999890i \(0.504728\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.17867 0.246046 0.123023 0.992404i \(-0.460741\pi\)
0.123023 + 0.992404i \(0.460741\pi\)
\(444\) 0 0
\(445\) −1.79071 −0.0848878
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.4977 0.495416 0.247708 0.968835i \(-0.420323\pi\)
0.247708 + 0.968835i \(0.420323\pi\)
\(450\) 0 0
\(451\) 14.3571 + 24.8671i 0.676047 + 1.17095i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.20929 −0.150124 −0.0750621 0.997179i \(-0.523916\pi\)
−0.0750621 + 0.997179i \(0.523916\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −18.1150 31.3762i −0.843702 1.46133i −0.886744 0.462261i \(-0.847038\pi\)
0.0430418 0.999073i \(-0.486295\pi\)
\(462\) 0 0
\(463\) −14.5253 + 25.1586i −0.675049 + 1.16922i 0.301406 + 0.953496i \(0.402544\pi\)
−0.976455 + 0.215723i \(0.930789\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.7466 + 32.4701i −0.867491 + 1.50254i −0.00293952 + 0.999996i \(0.500936\pi\)
−0.864552 + 0.502544i \(0.832398\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 64.0014 2.94279
\(474\) 0 0
\(475\) 9.04583 + 15.6678i 0.415051 + 0.718890i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14.9549 25.9026i 0.683305 1.18352i −0.290661 0.956826i \(-0.593875\pi\)
0.973966 0.226693i \(-0.0727914\pi\)
\(480\) 0 0
\(481\) 11.2443 + 19.4757i 0.512697 + 0.888017i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.05034 + 3.55130i −0.0931013 + 0.161256i
\(486\) 0 0
\(487\) −10.6316 18.4145i −0.481764 0.834439i 0.518017 0.855370i \(-0.326670\pi\)
−0.999781 + 0.0209309i \(0.993337\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10.6985 + 18.5303i −0.482816 + 0.836262i −0.999805 0.0197296i \(-0.993719\pi\)
0.516989 + 0.855992i \(0.327053\pi\)
\(492\) 0 0
\(493\) −6.41586 + 11.1126i −0.288956 + 0.500487i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −7.28263 12.6139i −0.326015 0.564675i 0.655702 0.755020i \(-0.272373\pi\)
−0.981717 + 0.190345i \(0.939039\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.92339 −0.130348 −0.0651738 0.997874i \(-0.520760\pi\)
−0.0651738 + 0.997874i \(0.520760\pi\)
\(504\) 0 0
\(505\) 1.71737 0.0764220
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.62025 16.6628i −0.426410 0.738564i 0.570141 0.821547i \(-0.306889\pi\)
−0.996551 + 0.0829830i \(0.973555\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.53379 + 2.65661i −0.0675869 + 0.117064i
\(516\) 0 0
\(517\) 11.1202 19.2608i 0.489068 0.847091i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.8743 + 24.0310i 0.607844 + 1.05282i 0.991595 + 0.129380i \(0.0412986\pi\)
−0.383751 + 0.923436i \(0.625368\pi\)
\(522\) 0 0
\(523\) 1.36840 2.37014i 0.0598360 0.103639i −0.834556 0.550924i \(-0.814276\pi\)
0.894392 + 0.447285i \(0.147609\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.32846 2.30096i −0.0578686 0.100231i
\(528\) 0 0
\(529\) −16.0361 + 27.7754i −0.697222 + 1.20762i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13.6871 23.7068i −0.592856 1.02686i
\(534\) 0 0
\(535\) 1.80903 0.0782112
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 5.98865 10.3726i 0.257472 0.445955i −0.708092 0.706120i \(-0.750444\pi\)
0.965564 + 0.260165i \(0.0837771\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.834608 + 1.44558i −0.0357507 + 0.0619220i
\(546\) 0 0
\(547\) 10.7346 + 18.5929i 0.458979 + 0.794975i 0.998907 0.0467363i \(-0.0148821\pi\)
−0.539928 + 0.841711i \(0.681549\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12.6810 −0.540229
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.9246 27.5823i −0.674748 1.16870i −0.976542 0.215325i \(-0.930919\pi\)
0.301794 0.953373i \(-0.402415\pi\)
\(558\) 0 0
\(559\) −61.0150 −2.58066
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −35.5483 −1.49818 −0.749091 0.662467i \(-0.769510\pi\)
−0.749091 + 0.662467i \(0.769510\pi\)
\(564\) 0 0
\(565\) −4.67962 −0.196873
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −21.7486 −0.911748 −0.455874 0.890044i \(-0.650673\pi\)
−0.455874 + 0.890044i \(0.650673\pi\)
\(570\) 0 0
\(571\) −9.59974 −0.401737 −0.200868 0.979618i \(-0.564376\pi\)
−0.200868 + 0.979618i \(0.564376\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 36.6810 1.52970
\(576\) 0 0
\(577\) −6.50916 11.2742i −0.270980 0.469351i 0.698133 0.715968i \(-0.254014\pi\)
−0.969113 + 0.246617i \(0.920681\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.83173 0.200110
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.64364 + 14.9712i 0.356761 + 0.617928i 0.987418 0.158134i \(-0.0505477\pi\)
−0.630657 + 0.776062i \(0.717214\pi\)
\(588\) 0 0
\(589\) 1.31285 2.27393i 0.0540952 0.0936957i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.20765 10.7520i 0.254918 0.441531i −0.709955 0.704247i \(-0.751285\pi\)
0.964873 + 0.262716i \(0.0846182\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.88564 0.322199 0.161099 0.986938i \(-0.448496\pi\)
0.161099 + 0.986938i \(0.448496\pi\)
\(600\) 0 0
\(601\) −11.1413 19.2973i −0.454464 0.787154i 0.544193 0.838960i \(-0.316836\pi\)
−0.998657 + 0.0518055i \(0.983502\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.82489 3.16081i 0.0741925 0.128505i
\(606\) 0 0
\(607\) −11.0458 19.1319i −0.448336 0.776541i 0.549942 0.835203i \(-0.314650\pi\)
−0.998278 + 0.0586617i \(0.981317\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.6014 + 18.3621i −0.428886 + 0.742852i
\(612\) 0 0
\(613\) 14.7632 + 25.5706i 0.596280 + 1.03279i 0.993365 + 0.115005i \(0.0366885\pi\)
−0.397085 + 0.917782i \(0.629978\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.01655 + 8.68892i −0.201959 + 0.349803i −0.949159 0.314796i \(-0.898064\pi\)
0.747201 + 0.664598i \(0.231397\pi\)
\(618\) 0 0
\(619\) 19.1283 33.1312i 0.768833 1.33166i −0.169364 0.985554i \(-0.554171\pi\)
0.938196 0.346103i \(-0.112495\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.0728 20.9107i −0.482911 0.836427i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −17.0482 −0.679754
\(630\) 0 0
\(631\) −23.0377 −0.917118 −0.458559 0.888664i \(-0.651634\pi\)
−0.458559 + 0.888664i \(0.651634\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.00972 3.48093i −0.0797531 0.138136i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.68646 + 15.0454i −0.343094 + 0.594257i −0.985006 0.172522i \(-0.944808\pi\)
0.641911 + 0.766779i \(0.278142\pi\)
\(642\) 0 0
\(643\) 9.47949 16.4190i 0.373835 0.647501i −0.616317 0.787498i \(-0.711376\pi\)
0.990152 + 0.139997i \(0.0447094\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.50972 + 16.4713i 0.373865 + 0.647554i 0.990157 0.139964i \(-0.0446988\pi\)
−0.616291 + 0.787518i \(0.711366\pi\)
\(648\) 0 0
\(649\) 19.4201 33.6366i 0.762306 1.32035i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.59329 6.22377i −0.140616 0.243555i 0.787112 0.616810i \(-0.211575\pi\)
−0.927729 + 0.373255i \(0.878242\pi\)
\(654\) 0 0
\(655\) −0.585770 + 1.01458i −0.0228879 + 0.0396430i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12.7261 + 22.0423i 0.495740 + 0.858647i 0.999988 0.00491209i \(-0.00156357\pi\)
−0.504248 + 0.863559i \(0.668230\pi\)
\(660\) 0 0
\(661\) 8.28590 0.322284 0.161142 0.986931i \(-0.448482\pi\)
0.161142 + 0.986931i \(0.448482\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12.8554 + 22.2662i −0.497764 + 0.862152i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.1138 + 24.4458i −0.544857 + 0.943721i
\(672\) 0 0
\(673\) 5.91586 + 10.2466i 0.228040 + 0.394977i 0.957227 0.289338i \(-0.0934350\pi\)
−0.729187 + 0.684314i \(0.760102\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.6063 −0.522932 −0.261466 0.965213i \(-0.584206\pi\)
−0.261466 + 0.965213i \(0.584206\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.79071 + 3.10160i 0.0685196 + 0.118679i 0.898250 0.439485i \(-0.144839\pi\)
−0.829730 + 0.558165i \(0.811506\pi\)
\(684\) 0 0
\(685\) 1.30206 0.0497492
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.60628 −0.175485
\(690\) 0 0
\(691\) 11.7174 0.445750 0.222875 0.974847i \(-0.428456\pi\)
0.222875 + 0.974847i \(0.428456\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.35348 −0.0513405
\(696\) 0 0
\(697\) 20.7518 0.786032
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10.5926 0.400077 0.200039 0.979788i \(-0.435893\pi\)
0.200039 + 0.979788i \(0.435893\pi\)
\(702\) 0 0
\(703\) −8.42395 14.5907i −0.317715 0.550299i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 38.2977 1.43830 0.719150 0.694855i \(-0.244532\pi\)
0.719150 + 0.694855i \(0.244532\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.66182 4.61042i −0.0996861 0.172661i
\(714\) 0 0
\(715\) −2.99355 + 5.18499i −0.111953 + 0.193908i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.8376 36.0918i 0.777112 1.34600i −0.156488 0.987680i \(-0.550017\pi\)
0.933600 0.358318i \(-0.116650\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 17.1248 0.635998
\(726\) 0 0
\(727\) 16.4126 + 28.4274i 0.608709 + 1.05432i 0.991453 + 0.130461i \(0.0416458\pi\)
−0.382744 + 0.923854i \(0.625021\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 23.1271 40.0573i 0.855386 1.48157i
\(732\) 0 0
\(733\) −4.64884 8.05203i −0.171709 0.297408i 0.767309 0.641278i \(-0.221595\pi\)
−0.939017 + 0.343870i \(0.888262\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.69166 2.93004i 0.0623130 0.107929i
\(738\) 0 0
\(739\) −5.68878 9.85326i −0.209265 0.362458i 0.742218 0.670158i \(-0.233774\pi\)
−0.951483 + 0.307701i \(0.900441\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.16182 + 2.01234i −0.0426232 + 0.0738256i −0.886550 0.462633i \(-0.846905\pi\)
0.843927 + 0.536458i \(0.180238\pi\)
\(744\) 0 0
\(745\) −0.272915 + 0.472703i −0.00999883 + 0.0173185i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 5.56690 + 9.64215i 0.203139 + 0.351847i 0.949538 0.313652i \(-0.101552\pi\)
−0.746399 + 0.665498i \(0.768219\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.69329 −0.0980190
\(756\) 0 0
\(757\) 52.1639 1.89593 0.947964 0.318376i \(-0.103138\pi\)
0.947964 + 0.318376i \(0.103138\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −23.5127 40.7252i −0.852336 1.47629i −0.879095 0.476647i \(-0.841852\pi\)
0.0267592 0.999642i \(-0.491481\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.5140 + 32.0671i −0.668501 + 1.15788i
\(768\) 0 0
\(769\) 3.30314 5.72121i 0.119114 0.206312i −0.800303 0.599596i \(-0.795328\pi\)
0.919417 + 0.393284i \(0.128661\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.54351 + 16.5298i 0.343256 + 0.594537i 0.985035 0.172352i \(-0.0551368\pi\)
−0.641779 + 0.766889i \(0.721803\pi\)
\(774\) 0 0
\(775\) −1.77292 + 3.07078i −0.0636850 + 0.110306i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.2540 + 17.7605i 0.367389 + 0.636337i
\(780\) 0 0
\(781\) 35.2108 60.9869i 1.25994 2.18228i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.663069 + 1.14847i 0.0236659 + 0.0409906i
\(786\) 0 0
\(787\) 50.9007 1.81441 0.907207 0.420685i \(-0.138210\pi\)
0.907207 + 0.420685i \(0.138210\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 13.4552 23.3052i 0.477810 0.827591i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4.38727 7.59898i 0.155405 0.269170i −0.777801 0.628510i \(-0.783665\pi\)
0.933207 + 0.359341i \(0.116998\pi\)
\(798\) 0 0
\(799\) −8.03667 13.9199i −0.284317 0.492451i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −18.7576 −0.661942
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −4.75692 8.23923i −0.167244 0.289676i 0.770206 0.637796i \(-0.220154\pi\)
−0.937450 + 0.348120i \(0.886820\pi\)
\(810\) 0 0
\(811\) −25.0118 −0.878282 −0.439141 0.898418i \(-0.644717\pi\)
−0.439141 + 0.898418i \(0.644717\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.59261 −0.0557866
\(816\) 0 0
\(817\) 45.7108 1.59922
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 35.5940 1.24224 0.621119 0.783716i \(-0.286678\pi\)
0.621119 + 0.783716i \(0.286678\pi\)
\(822\) 0 0
\(823\) 16.0000 0.557725 0.278862 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.4531 0.885090 0.442545 0.896746i \(-0.354076\pi\)
0.442545 + 0.896746i \(0.354076\pi\)
\(828\) 0 0
\(829\) 8.77292 + 15.1951i 0.304696 + 0.527749i 0.977194 0.212350i \(-0.0681118\pi\)
−0.672498 + 0.740099i \(0.734778\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.05391 0.0364721
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12.0562 + 20.8820i 0.416227 + 0.720927i 0.995556 0.0941668i \(-0.0300187\pi\)
−0.579329 + 0.815094i \(0.696685\pi\)
\(840\) 0 0
\(841\) 8.49837 14.7196i 0.293047 0.507572i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.29957 2.25093i 0.0447067 0.0774342i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −34.1592 −1.17096
\(852\) 0 0
\(853\) −16.2616 28.1659i −0.556785 0.964381i −0.997762 0.0668621i \(-0.978701\pi\)
0.440977 0.897518i \(-0.354632\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −0.299870 + 0.519390i −0.0102434 + 0.0177420i −0.871102 0.491103i \(-0.836594\pi\)
0.860858 + 0.508845i \(0.169927\pi\)
\(858\) 0 0
\(859\) 13.2174 + 22.8932i 0.450971 + 0.781104i 0.998447 0.0557171i \(-0.0177445\pi\)
−0.547476 + 0.836822i \(0.684411\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 9.92270 17.1866i 0.337773 0.585039i −0.646241 0.763134i \(-0.723660\pi\)
0.984013 + 0.178094i \(0.0569932\pi\)
\(864\) 0 0
\(865\) −3.02859 5.24567i −0.102975 0.178358i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 15.9520 27.6296i 0.541134 0.937271i
\(870\) 0 0
\(871\) −1.61273 + 2.79332i −0.0546451 + 0.0946481i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −10.2352 17.7278i −0.345617 0.598626i 0.639849 0.768501i \(-0.278997\pi\)
−0.985466 + 0.169875i \(0.945664\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 31.1683 1.05009 0.525043 0.851076i \(-0.324049\pi\)
0.525043 + 0.851076i \(0.324049\pi\)
\(882\) 0 0
\(883\) −2.64187 −0.0889060 −0.0444530 0.999011i \(-0.514154\pi\)
−0.0444530 + 0.999011i \(0.514154\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −11.5825 20.0615i −0.388902 0.673599i 0.603400 0.797439i \(-0.293812\pi\)
−0.992302 + 0.123840i \(0.960479\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 7.94226 13.7564i 0.265778 0.460341i
\(894\) 0 0
\(895\) −1.14132 + 1.97682i −0.0381500 + 0.0660777i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.24269 2.15240i −0.0414460 0.0717866i
\(900\) 0 0
\(901\) 1.74596 3.02409i 0.0581664 0.100747i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.47949 + 2.56255i 0.0491799 + 0.0851821i
\(906\) 0 0
\(907\) 25.0264 43.3470i 0.830988 1.43931i −0.0662676 0.997802i \(-0.521109\pi\)
0.897256 0.441511i \(-0.145558\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.42231 9.39172i −0.179649 0.311161i 0.762111 0.647446i \(-0.224163\pi\)
−0.941760 + 0.336285i \(0.890830\pi\)
\(912\) 0 0
\(913\) −49.7292 −1.64579
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −5.59549 + 9.69166i −0.184578 + 0.319699i −0.943434 0.331560i \(-0.892425\pi\)
0.758856 + 0.651258i \(0.225759\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −33.5679 + 58.1413i −1.10490 + 1.91374i
\(924\) 0 0
\(925\) 11.3759 + 19.7037i 0.374038 + 0.647853i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −41.2955 −1.35486 −0.677431 0.735586i \(-0.736907\pi\)
−0.677431 + 0.735586i \(0.736907\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.26935 3.93063i −0.0742156 0.128545i
\(936\) 0 0
\(937\) −33.5620 −1.09642 −0.548211 0.836340i \(-0.684691\pi\)
−0.548211 + 0.836340i \(0.684691\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −50.4224 −1.64372 −0.821862 0.569686i \(-0.807065\pi\)
−0.821862 + 0.569686i \(0.807065\pi\)
\(942\) 0 0
\(943\) 41.5803 1.35404
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.2424 −0.657789 −0.328895 0.944367i \(-0.606676\pi\)
−0.328895 + 0.944367i \(0.606676\pi\)
\(948\) 0 0
\(949\) 17.8824 0.580486
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 29.3685 0.951340 0.475670 0.879624i \(-0.342206\pi\)
0.475670 + 0.879624i \(0.342206\pi\)
\(954\) 0 0
\(955\) −1.57442 2.72698i −0.0509470 0.0882429i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.4854 −0.983399
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.33297 + 2.30878i 0.0429099 + 0.0743222i
\(966\) 0 0
\(967\) 15.2157 26.3544i 0.489305 0.847501i −0.510619 0.859807i \(-0.670584\pi\)
0.999924 + 0.0123057i \(0.00391714\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.59329 6.22377i 0.115314 0.199730i −0.802591 0.596530i \(-0.796546\pi\)
0.917905 + 0.396799i \(0.129879\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −28.5426 −0.913157 −0.456579 0.889683i \(-0.650925\pi\)
−0.456579 + 0.889683i \(0.650925\pi\)
\(978\) 0 0
\(979\) −19.1888 33.2359i −0.613276 1.06223i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.20821 3.82473i 0.0704310 0.121990i −0.828659 0.559753i \(-0.810896\pi\)
0.899090 + 0.437763i \(0.144229\pi\)
\(984\) 0 0
\(985\) 0.0172400 + 0.0298606i 0.000549313 + 0.000951438i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 46.3396 80.2625i 1.47351 2.55220i
\(990\) 0 0
\(991\) 2.90671 + 5.03456i 0.0923345 + 0.159928i 0.908493 0.417900i \(-0.137234\pi\)
−0.816159 + 0.577828i \(0.803900\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.32777 + 4.03182i −0.0737953 + 0.127817i
\(996\) 0 0
\(997\) 26.3204 45.5882i 0.833575 1.44379i −0.0616108 0.998100i \(-0.519624\pi\)
0.895186 0.445694i \(-0.147043\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 5292.2.i.f.1549.2 6
3.2 odd 2 1764.2.i.g.373.2 6
7.2 even 3 756.2.j.b.253.2 6
7.3 odd 6 5292.2.l.f.361.2 6
7.4 even 3 5292.2.l.e.361.2 6
7.5 odd 6 5292.2.j.d.1765.2 6
7.6 odd 2 5292.2.i.e.1549.2 6
9.2 odd 6 1764.2.l.e.961.3 6
9.7 even 3 5292.2.l.e.3313.2 6
21.2 odd 6 252.2.j.a.85.1 6
21.5 even 6 1764.2.j.e.589.3 6
21.11 odd 6 1764.2.l.e.949.3 6
21.17 even 6 1764.2.l.f.949.1 6
21.20 even 2 1764.2.i.d.373.2 6
28.23 odd 6 3024.2.r.j.1009.2 6
63.2 odd 6 252.2.j.a.169.1 yes 6
63.11 odd 6 1764.2.i.g.1537.2 6
63.16 even 3 756.2.j.b.505.2 6
63.20 even 6 1764.2.l.f.961.1 6
63.23 odd 6 2268.2.a.i.1.2 3
63.25 even 3 inner 5292.2.i.f.2125.2 6
63.34 odd 6 5292.2.l.f.3313.2 6
63.38 even 6 1764.2.i.d.1537.2 6
63.47 even 6 1764.2.j.e.1177.3 6
63.52 odd 6 5292.2.i.e.2125.2 6
63.58 even 3 2268.2.a.h.1.2 3
63.61 odd 6 5292.2.j.d.3529.2 6
84.23 even 6 1008.2.r.j.337.3 6
252.23 even 6 9072.2.a.by.1.2 3
252.79 odd 6 3024.2.r.j.2017.2 6
252.191 even 6 1008.2.r.j.673.3 6
252.247 odd 6 9072.2.a.bv.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.a.85.1 6 21.2 odd 6
252.2.j.a.169.1 yes 6 63.2 odd 6
756.2.j.b.253.2 6 7.2 even 3
756.2.j.b.505.2 6 63.16 even 3
1008.2.r.j.337.3 6 84.23 even 6
1008.2.r.j.673.3 6 252.191 even 6
1764.2.i.d.373.2 6 21.20 even 2
1764.2.i.d.1537.2 6 63.38 even 6
1764.2.i.g.373.2 6 3.2 odd 2
1764.2.i.g.1537.2 6 63.11 odd 6
1764.2.j.e.589.3 6 21.5 even 6
1764.2.j.e.1177.3 6 63.47 even 6
1764.2.l.e.949.3 6 21.11 odd 6
1764.2.l.e.961.3 6 9.2 odd 6
1764.2.l.f.949.1 6 21.17 even 6
1764.2.l.f.961.1 6 63.20 even 6
2268.2.a.h.1.2 3 63.58 even 3
2268.2.a.i.1.2 3 63.23 odd 6
3024.2.r.j.1009.2 6 28.23 odd 6
3024.2.r.j.2017.2 6 252.79 odd 6
5292.2.i.e.1549.2 6 7.6 odd 2
5292.2.i.e.2125.2 6 63.52 odd 6
5292.2.i.f.1549.2 6 1.1 even 1 trivial
5292.2.i.f.2125.2 6 63.25 even 3 inner
5292.2.j.d.1765.2 6 7.5 odd 6
5292.2.j.d.3529.2 6 63.61 odd 6
5292.2.l.e.361.2 6 7.4 even 3
5292.2.l.e.3313.2 6 9.7 even 3
5292.2.l.f.361.2 6 7.3 odd 6
5292.2.l.f.3313.2 6 63.34 odd 6
9072.2.a.bv.1.2 3 252.247 odd 6
9072.2.a.by.1.2 3 252.23 even 6