Properties

Label 1280.2.l.a.321.4
Level $1280$
Weight $2$
Character 1280.321
Analytic conductor $10.221$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1280,2,Mod(321,1280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1280.321");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.2208514587\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 321.4
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1280.321
Dual form 1280.2.l.a.961.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.07313 + 1.07313i) q^{3} +(-0.707107 + 0.707107i) q^{5} -0.103425i q^{7} -0.696775i q^{9} +O(q^{10})\) \(q+(1.07313 + 1.07313i) q^{3} +(-0.707107 + 0.707107i) q^{5} -0.103425i q^{7} -0.696775i q^{9} +(2.21441 - 2.21441i) q^{11} +(0.931852 + 0.931852i) q^{13} -1.51764 q^{15} +2.54587 q^{17} +(2.94646 + 2.94646i) q^{19} +(0.110988 - 0.110988i) q^{21} -1.07812i q^{23} -1.00000i q^{25} +(3.96713 - 3.96713i) q^{27} +(6.32780 + 6.32780i) q^{29} -0.635674 q^{31} +4.75272 q^{33} +(0.0731322 + 0.0731322i) q^{35} +(-3.76733 + 3.76733i) q^{37} +2.00000i q^{39} +5.23143i q^{41} +(5.85872 - 5.85872i) q^{43} +(0.492694 + 0.492694i) q^{45} -9.86005 q^{47} +6.98930 q^{49} +(2.73205 + 2.73205i) q^{51} +(6.04284 - 6.04284i) q^{53} +3.13165i q^{55} +6.32389i q^{57} +(-6.78094 + 6.78094i) q^{59} +(5.58114 + 5.58114i) q^{61} -0.0720636 q^{63} -1.31784 q^{65} +(-0.187769 - 0.187769i) q^{67} +(1.15696 - 1.15696i) q^{69} -2.42883i q^{71} +14.1662i q^{73} +(1.07313 - 1.07313i) q^{75} +(-0.229025 - 0.229025i) q^{77} -10.9647 q^{79} +6.42418 q^{81} +(1.03029 + 1.03029i) q^{83} +(-1.80020 + 1.80020i) q^{85} +13.5811i q^{87} -6.75787i q^{89} +(0.0963763 - 0.0963763i) q^{91} +(-0.682163 - 0.682163i) q^{93} -4.16693 q^{95} -17.9734 q^{97} +(-1.54295 - 1.54295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 8 q^{11} - 8 q^{13} - 8 q^{15} - 8 q^{17} - 16 q^{21} + 8 q^{27} - 8 q^{29} + 24 q^{33} - 12 q^{35} - 8 q^{37} + 44 q^{43} + 8 q^{45} - 8 q^{47} + 8 q^{51} + 16 q^{53} - 16 q^{59} + 8 q^{61} + 48 q^{63} - 8 q^{65} - 12 q^{67} + 40 q^{69} - 4 q^{75} + 16 q^{77} - 96 q^{79} - 16 q^{81} + 28 q^{83} - 16 q^{85} - 8 q^{91} - 8 q^{93} - 8 q^{95} - 24 q^{97} - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 1.07313 + 1.07313i 0.619573 + 0.619573i 0.945422 0.325849i \(-0.105650\pi\)
−0.325849 + 0.945422i \(0.605650\pi\)
\(4\) 0 0
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 0.103425i 0.0390908i −0.999809 0.0195454i \(-0.993778\pi\)
0.999809 0.0195454i \(-0.00622189\pi\)
\(8\) 0 0
\(9\) 0.696775i 0.232258i
\(10\) 0 0
\(11\) 2.21441 2.21441i 0.667671 0.667671i −0.289506 0.957176i \(-0.593491\pi\)
0.957176 + 0.289506i \(0.0934909\pi\)
\(12\) 0 0
\(13\) 0.931852 + 0.931852i 0.258449 + 0.258449i 0.824423 0.565974i \(-0.191500\pi\)
−0.565974 + 0.824423i \(0.691500\pi\)
\(14\) 0 0
\(15\) −1.51764 −0.391852
\(16\) 0 0
\(17\) 2.54587 0.617463 0.308732 0.951149i \(-0.400096\pi\)
0.308732 + 0.951149i \(0.400096\pi\)
\(18\) 0 0
\(19\) 2.94646 + 2.94646i 0.675965 + 0.675965i 0.959085 0.283120i \(-0.0913693\pi\)
−0.283120 + 0.959085i \(0.591369\pi\)
\(20\) 0 0
\(21\) 0.110988 0.110988i 0.0242196 0.0242196i
\(22\) 0 0
\(23\) 1.07812i 0.224803i −0.993663 0.112401i \(-0.964146\pi\)
0.993663 0.112401i \(-0.0358542\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 0 0
\(27\) 3.96713 3.96713i 0.763474 0.763474i
\(28\) 0 0
\(29\) 6.32780 + 6.32780i 1.17504 + 1.17504i 0.980991 + 0.194053i \(0.0621633\pi\)
0.194053 + 0.980991i \(0.437837\pi\)
\(30\) 0 0
\(31\) −0.635674 −0.114171 −0.0570853 0.998369i \(-0.518181\pi\)
−0.0570853 + 0.998369i \(0.518181\pi\)
\(32\) 0 0
\(33\) 4.75272 0.827342
\(34\) 0 0
\(35\) 0.0731322 + 0.0731322i 0.0123616 + 0.0123616i
\(36\) 0 0
\(37\) −3.76733 + 3.76733i −0.619345 + 0.619345i −0.945363 0.326019i \(-0.894293\pi\)
0.326019 + 0.945363i \(0.394293\pi\)
\(38\) 0 0
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 5.23143i 0.817012i 0.912756 + 0.408506i \(0.133950\pi\)
−0.912756 + 0.408506i \(0.866050\pi\)
\(42\) 0 0
\(43\) 5.85872 5.85872i 0.893446 0.893446i −0.101399 0.994846i \(-0.532332\pi\)
0.994846 + 0.101399i \(0.0323320\pi\)
\(44\) 0 0
\(45\) 0.492694 + 0.492694i 0.0734465 + 0.0734465i
\(46\) 0 0
\(47\) −9.86005 −1.43824 −0.719118 0.694888i \(-0.755454\pi\)
−0.719118 + 0.694888i \(0.755454\pi\)
\(48\) 0 0
\(49\) 6.98930 0.998472
\(50\) 0 0
\(51\) 2.73205 + 2.73205i 0.382564 + 0.382564i
\(52\) 0 0
\(53\) 6.04284 6.04284i 0.830048 0.830048i −0.157475 0.987523i \(-0.550335\pi\)
0.987523 + 0.157475i \(0.0503354\pi\)
\(54\) 0 0
\(55\) 3.13165i 0.422272i
\(56\) 0 0
\(57\) 6.32389i 0.837620i
\(58\) 0 0
\(59\) −6.78094 + 6.78094i −0.882804 + 0.882804i −0.993819 0.111015i \(-0.964590\pi\)
0.111015 + 0.993819i \(0.464590\pi\)
\(60\) 0 0
\(61\) 5.58114 + 5.58114i 0.714592 + 0.714592i 0.967492 0.252900i \(-0.0813845\pi\)
−0.252900 + 0.967492i \(0.581384\pi\)
\(62\) 0 0
\(63\) −0.0720636 −0.00907916
\(64\) 0 0
\(65\) −1.31784 −0.163458
\(66\) 0 0
\(67\) −0.187769 0.187769i −0.0229396 0.0229396i 0.695544 0.718484i \(-0.255163\pi\)
−0.718484 + 0.695544i \(0.755163\pi\)
\(68\) 0 0
\(69\) 1.15696 1.15696i 0.139282 0.139282i
\(70\) 0 0
\(71\) 2.42883i 0.288249i −0.989560 0.144124i \(-0.953963\pi\)
0.989560 0.144124i \(-0.0460365\pi\)
\(72\) 0 0
\(73\) 14.1662i 1.65803i 0.559228 + 0.829014i \(0.311098\pi\)
−0.559228 + 0.829014i \(0.688902\pi\)
\(74\) 0 0
\(75\) 1.07313 1.07313i 0.123915 0.123915i
\(76\) 0 0
\(77\) −0.229025 0.229025i −0.0260998 0.0260998i
\(78\) 0 0
\(79\) −10.9647 −1.23363 −0.616814 0.787109i \(-0.711577\pi\)
−0.616814 + 0.787109i \(0.711577\pi\)
\(80\) 0 0
\(81\) 6.42418 0.713798
\(82\) 0 0
\(83\) 1.03029 + 1.03029i 0.113089 + 0.113089i 0.761387 0.648298i \(-0.224519\pi\)
−0.648298 + 0.761387i \(0.724519\pi\)
\(84\) 0 0
\(85\) −1.80020 + 1.80020i −0.195259 + 0.195259i
\(86\) 0 0
\(87\) 13.5811i 1.45605i
\(88\) 0 0
\(89\) 6.75787i 0.716333i −0.933658 0.358167i \(-0.883402\pi\)
0.933658 0.358167i \(-0.116598\pi\)
\(90\) 0 0
\(91\) 0.0963763 0.0963763i 0.0101030 0.0101030i
\(92\) 0 0
\(93\) −0.682163 0.682163i −0.0707370 0.0707370i
\(94\) 0 0
\(95\) −4.16693 −0.427518
\(96\) 0 0
\(97\) −17.9734 −1.82493 −0.912464 0.409158i \(-0.865822\pi\)
−0.912464 + 0.409158i \(0.865822\pi\)
\(98\) 0 0
\(99\) −1.54295 1.54295i −0.155072 0.155072i
\(100\) 0 0
\(101\) 6.86370 6.86370i 0.682964 0.682964i −0.277703 0.960667i \(-0.589573\pi\)
0.960667 + 0.277703i \(0.0895731\pi\)
\(102\) 0 0
\(103\) 17.3706i 1.71158i −0.517323 0.855790i \(-0.673071\pi\)
0.517323 0.855790i \(-0.326929\pi\)
\(104\) 0 0
\(105\) 0.156961i 0.0153178i
\(106\) 0 0
\(107\) 12.1184 12.1184i 1.17153 1.17153i 0.189682 0.981846i \(-0.439254\pi\)
0.981846 0.189682i \(-0.0607457\pi\)
\(108\) 0 0
\(109\) 9.08516 + 9.08516i 0.870201 + 0.870201i 0.992494 0.122293i \(-0.0390248\pi\)
−0.122293 + 0.992494i \(0.539025\pi\)
\(110\) 0 0
\(111\) −8.08568 −0.767459
\(112\) 0 0
\(113\) 6.39230 0.601337 0.300669 0.953729i \(-0.402790\pi\)
0.300669 + 0.953729i \(0.402790\pi\)
\(114\) 0 0
\(115\) 0.762343 + 0.762343i 0.0710889 + 0.0710889i
\(116\) 0 0
\(117\) 0.649291 0.649291i 0.0600269 0.0600269i
\(118\) 0 0
\(119\) 0.263305i 0.0241371i
\(120\) 0 0
\(121\) 1.19275i 0.108432i
\(122\) 0 0
\(123\) −5.61401 + 5.61401i −0.506199 + 0.506199i
\(124\) 0 0
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) −3.19000 −0.283066 −0.141533 0.989934i \(-0.545203\pi\)
−0.141533 + 0.989934i \(0.545203\pi\)
\(128\) 0 0
\(129\) 12.5744 1.10711
\(130\) 0 0
\(131\) −5.62863 5.62863i −0.491775 0.491775i 0.417090 0.908865i \(-0.363050\pi\)
−0.908865 + 0.417090i \(0.863050\pi\)
\(132\) 0 0
\(133\) 0.304737 0.304737i 0.0264240 0.0264240i
\(134\) 0 0
\(135\) 5.61037i 0.482863i
\(136\) 0 0
\(137\) 0.277401i 0.0237000i −0.999930 0.0118500i \(-0.996228\pi\)
0.999930 0.0118500i \(-0.00377206\pi\)
\(138\) 0 0
\(139\) −12.1586 + 12.1586i −1.03128 + 1.03128i −0.0317874 + 0.999495i \(0.510120\pi\)
−0.999495 + 0.0317874i \(0.989880\pi\)
\(140\) 0 0
\(141\) −10.5811 10.5811i −0.891093 0.891093i
\(142\) 0 0
\(143\) 4.12701 0.345118
\(144\) 0 0
\(145\) −8.94887 −0.743163
\(146\) 0 0
\(147\) 7.50045 + 7.50045i 0.618626 + 0.618626i
\(148\) 0 0
\(149\) 5.81722 5.81722i 0.476565 0.476565i −0.427466 0.904031i \(-0.640594\pi\)
0.904031 + 0.427466i \(0.140594\pi\)
\(150\) 0 0
\(151\) 6.01994i 0.489895i −0.969536 0.244948i \(-0.921229\pi\)
0.969536 0.244948i \(-0.0787708\pi\)
\(152\) 0 0
\(153\) 1.77389i 0.143411i
\(154\) 0 0
\(155\) 0.449490 0.449490i 0.0361039 0.0361039i
\(156\) 0 0
\(157\) −9.18494 9.18494i −0.733038 0.733038i 0.238182 0.971220i \(-0.423448\pi\)
−0.971220 + 0.238182i \(0.923448\pi\)
\(158\) 0 0
\(159\) 12.9695 1.02855
\(160\) 0 0
\(161\) −0.111504 −0.00878772
\(162\) 0 0
\(163\) −2.74408 2.74408i −0.214933 0.214933i 0.591426 0.806359i \(-0.298565\pi\)
−0.806359 + 0.591426i \(0.798565\pi\)
\(164\) 0 0
\(165\) −3.36068 + 3.36068i −0.261628 + 0.261628i
\(166\) 0 0
\(167\) 6.66923i 0.516080i 0.966134 + 0.258040i \(0.0830767\pi\)
−0.966134 + 0.258040i \(0.916923\pi\)
\(168\) 0 0
\(169\) 11.2633i 0.866408i
\(170\) 0 0
\(171\) 2.05302 2.05302i 0.156998 0.156998i
\(172\) 0 0
\(173\) 0.732051 + 0.732051i 0.0556568 + 0.0556568i 0.734387 0.678731i \(-0.237470\pi\)
−0.678731 + 0.734387i \(0.737470\pi\)
\(174\) 0 0
\(175\) −0.103425 −0.00781816
\(176\) 0 0
\(177\) −14.5537 −1.09392
\(178\) 0 0
\(179\) 0.619174 + 0.619174i 0.0462792 + 0.0462792i 0.729868 0.683588i \(-0.239582\pi\)
−0.683588 + 0.729868i \(0.739582\pi\)
\(180\) 0 0
\(181\) −7.55583 + 7.55583i −0.561621 + 0.561621i −0.929768 0.368147i \(-0.879992\pi\)
0.368147 + 0.929768i \(0.379992\pi\)
\(182\) 0 0
\(183\) 11.9786i 0.885484i
\(184\) 0 0
\(185\) 5.32780i 0.391708i
\(186\) 0 0
\(187\) 5.63760 5.63760i 0.412262 0.412262i
\(188\) 0 0
\(189\) −0.410298 0.410298i −0.0298448 0.0298448i
\(190\) 0 0
\(191\) 24.2268 1.75299 0.876494 0.481412i \(-0.159876\pi\)
0.876494 + 0.481412i \(0.159876\pi\)
\(192\) 0 0
\(193\) 3.78318 0.272319 0.136160 0.990687i \(-0.456524\pi\)
0.136160 + 0.990687i \(0.456524\pi\)
\(194\) 0 0
\(195\) −1.41421 1.41421i −0.101274 0.101274i
\(196\) 0 0
\(197\) −14.5322 + 14.5322i −1.03538 + 1.03538i −0.0360292 + 0.999351i \(0.511471\pi\)
−0.999351 + 0.0360292i \(0.988529\pi\)
\(198\) 0 0
\(199\) 24.5851i 1.74279i −0.490583 0.871394i \(-0.663216\pi\)
0.490583 0.871394i \(-0.336784\pi\)
\(200\) 0 0
\(201\) 0.403001i 0.0284255i
\(202\) 0 0
\(203\) 0.654450 0.654450i 0.0459334 0.0459334i
\(204\) 0 0
\(205\) −3.69918 3.69918i −0.258362 0.258362i
\(206\) 0 0
\(207\) −0.751204 −0.0522123
\(208\) 0 0
\(209\) 13.0494 0.902644
\(210\) 0 0
\(211\) 11.8214 + 11.8214i 0.813817 + 0.813817i 0.985204 0.171387i \(-0.0548247\pi\)
−0.171387 + 0.985204i \(0.554825\pi\)
\(212\) 0 0
\(213\) 2.60645 2.60645i 0.178591 0.178591i
\(214\) 0 0
\(215\) 8.28548i 0.565065i
\(216\) 0 0
\(217\) 0.0657443i 0.00446302i
\(218\) 0 0
\(219\) −15.2022 + 15.2022i −1.02727 + 1.02727i
\(220\) 0 0
\(221\) 2.37237 + 2.37237i 0.159583 + 0.159583i
\(222\) 0 0
\(223\) 20.3129 1.36026 0.680128 0.733094i \(-0.261924\pi\)
0.680128 + 0.733094i \(0.261924\pi\)
\(224\) 0 0
\(225\) −0.696775 −0.0464516
\(226\) 0 0
\(227\) −19.0831 19.0831i −1.26659 1.26659i −0.947838 0.318752i \(-0.896736\pi\)
−0.318752 0.947838i \(-0.603264\pi\)
\(228\) 0 0
\(229\) −1.26330 + 1.26330i −0.0834815 + 0.0834815i −0.747614 0.664133i \(-0.768801\pi\)
0.664133 + 0.747614i \(0.268801\pi\)
\(230\) 0 0
\(231\) 0.491547i 0.0323414i
\(232\) 0 0
\(233\) 22.7727i 1.49189i −0.666010 0.745943i \(-0.731999\pi\)
0.666010 0.745943i \(-0.268001\pi\)
\(234\) 0 0
\(235\) 6.97211 6.97211i 0.454810 0.454810i
\(236\) 0 0
\(237\) −11.7666 11.7666i −0.764323 0.764323i
\(238\) 0 0
\(239\) 22.0126 1.42388 0.711940 0.702241i \(-0.247817\pi\)
0.711940 + 0.702241i \(0.247817\pi\)
\(240\) 0 0
\(241\) −19.5653 −1.26031 −0.630155 0.776469i \(-0.717009\pi\)
−0.630155 + 0.776469i \(0.717009\pi\)
\(242\) 0 0
\(243\) −5.00739 5.00739i −0.321224 0.321224i
\(244\) 0 0
\(245\) −4.94218 + 4.94218i −0.315745 + 0.315745i
\(246\) 0 0
\(247\) 5.49133i 0.349405i
\(248\) 0 0
\(249\) 2.21128i 0.140134i
\(250\) 0 0
\(251\) −3.92188 + 3.92188i −0.247547 + 0.247547i −0.819963 0.572416i \(-0.806006\pi\)
0.572416 + 0.819963i \(0.306006\pi\)
\(252\) 0 0
\(253\) −2.38739 2.38739i −0.150094 0.150094i
\(254\) 0 0
\(255\) −3.86370 −0.241954
\(256\) 0 0
\(257\) −14.4064 −0.898647 −0.449323 0.893369i \(-0.648335\pi\)
−0.449323 + 0.893369i \(0.648335\pi\)
\(258\) 0 0
\(259\) 0.389634 + 0.389634i 0.0242107 + 0.0242107i
\(260\) 0 0
\(261\) 4.40905 4.40905i 0.272914 0.272914i
\(262\) 0 0
\(263\) 16.0095i 0.987187i −0.869693 0.493594i \(-0.835683\pi\)
0.869693 0.493594i \(-0.164317\pi\)
\(264\) 0 0
\(265\) 8.54587i 0.524968i
\(266\) 0 0
\(267\) 7.25209 7.25209i 0.443821 0.443821i
\(268\) 0 0
\(269\) 2.24604 + 2.24604i 0.136944 + 0.136944i 0.772256 0.635312i \(-0.219129\pi\)
−0.635312 + 0.772256i \(0.719129\pi\)
\(270\) 0 0
\(271\) −2.97202 −0.180537 −0.0902687 0.995917i \(-0.528773\pi\)
−0.0902687 + 0.995917i \(0.528773\pi\)
\(272\) 0 0
\(273\) 0.206849 0.0125191
\(274\) 0 0
\(275\) −2.21441 2.21441i −0.133534 0.133534i
\(276\) 0 0
\(277\) −20.1163 + 20.1163i −1.20867 + 1.20867i −0.237215 + 0.971457i \(0.576235\pi\)
−0.971457 + 0.237215i \(0.923765\pi\)
\(278\) 0 0
\(279\) 0.442922i 0.0265170i
\(280\) 0 0
\(281\) 18.5865i 1.10878i −0.832258 0.554388i \(-0.812952\pi\)
0.832258 0.554388i \(-0.187048\pi\)
\(282\) 0 0
\(283\) −20.7499 + 20.7499i −1.23345 + 1.23345i −0.270827 + 0.962628i \(0.587297\pi\)
−0.962628 + 0.270827i \(0.912703\pi\)
\(284\) 0 0
\(285\) −4.47167 4.47167i −0.264879 0.264879i
\(286\) 0 0
\(287\) 0.541058 0.0319376
\(288\) 0 0
\(289\) −10.5186 −0.618739
\(290\) 0 0
\(291\) −19.2879 19.2879i −1.13068 1.13068i
\(292\) 0 0
\(293\) 6.59059 6.59059i 0.385027 0.385027i −0.487883 0.872909i \(-0.662231\pi\)
0.872909 + 0.487883i \(0.162231\pi\)
\(294\) 0 0
\(295\) 9.58970i 0.558334i
\(296\) 0 0
\(297\) 17.5697i 1.01950i
\(298\) 0 0
\(299\) 1.00464 1.00464i 0.0581001 0.0581001i
\(300\) 0 0
\(301\) −0.605935 0.605935i −0.0349255 0.0349255i
\(302\) 0 0
\(303\) 14.7313 0.846292
\(304\) 0 0
\(305\) −7.89293 −0.451948
\(306\) 0 0
\(307\) −0.494394 0.494394i −0.0282166 0.0282166i 0.692858 0.721074i \(-0.256351\pi\)
−0.721074 + 0.692858i \(0.756351\pi\)
\(308\) 0 0
\(309\) 18.6410 18.6410i 1.06045 1.06045i
\(310\) 0 0
\(311\) 10.2409i 0.580707i 0.956919 + 0.290354i \(0.0937729\pi\)
−0.956919 + 0.290354i \(0.906227\pi\)
\(312\) 0 0
\(313\) 10.0058i 0.565563i 0.959184 + 0.282782i \(0.0912572\pi\)
−0.959184 + 0.282782i \(0.908743\pi\)
\(314\) 0 0
\(315\) 0.0509567 0.0509567i 0.00287108 0.00287108i
\(316\) 0 0
\(317\) −19.3441 19.3441i −1.08647 1.08647i −0.995889 0.0905836i \(-0.971127\pi\)
−0.0905836 0.995889i \(-0.528873\pi\)
\(318\) 0 0
\(319\) 28.0247 1.56908
\(320\) 0 0
\(321\) 26.0092 1.45169
\(322\) 0 0
\(323\) 7.50130 + 7.50130i 0.417384 + 0.417384i
\(324\) 0 0
\(325\) 0.931852 0.931852i 0.0516898 0.0516898i
\(326\) 0 0
\(327\) 19.4992i 1.07831i
\(328\) 0 0
\(329\) 1.01977i 0.0562218i
\(330\) 0 0
\(331\) −22.2691 + 22.2691i −1.22402 + 1.22402i −0.257831 + 0.966190i \(0.583008\pi\)
−0.966190 + 0.257831i \(0.916992\pi\)
\(332\) 0 0
\(333\) 2.62498 + 2.62498i 0.143848 + 0.143848i
\(334\) 0 0
\(335\) 0.265545 0.0145083
\(336\) 0 0
\(337\) −17.4689 −0.951592 −0.475796 0.879556i \(-0.657840\pi\)
−0.475796 + 0.879556i \(0.657840\pi\)
\(338\) 0 0
\(339\) 6.85979 + 6.85979i 0.372573 + 0.372573i
\(340\) 0 0
\(341\) −1.40765 + 1.40765i −0.0762283 + 0.0762283i
\(342\) 0 0
\(343\) 1.44684i 0.0781219i
\(344\) 0 0
\(345\) 1.63619i 0.0880895i
\(346\) 0 0
\(347\) 7.12078 7.12078i 0.382264 0.382264i −0.489654 0.871917i \(-0.662877\pi\)
0.871917 + 0.489654i \(0.162877\pi\)
\(348\) 0 0
\(349\) −9.33386 9.33386i −0.499630 0.499630i 0.411693 0.911323i \(-0.364938\pi\)
−0.911323 + 0.411693i \(0.864938\pi\)
\(350\) 0 0
\(351\) 7.39355 0.394638
\(352\) 0 0
\(353\) −10.8922 −0.579732 −0.289866 0.957067i \(-0.593611\pi\)
−0.289866 + 0.957067i \(0.593611\pi\)
\(354\) 0 0
\(355\) 1.71744 + 1.71744i 0.0911522 + 0.0911522i
\(356\) 0 0
\(357\) 0.282561 0.282561i 0.0149547 0.0149547i
\(358\) 0 0
\(359\) 14.9262i 0.787775i −0.919159 0.393888i \(-0.871130\pi\)
0.919159 0.393888i \(-0.128870\pi\)
\(360\) 0 0
\(361\) 1.63671i 0.0861424i
\(362\) 0 0
\(363\) −1.27998 + 1.27998i −0.0671816 + 0.0671816i
\(364\) 0 0
\(365\) −10.0170 10.0170i −0.524315 0.524315i
\(366\) 0 0
\(367\) −35.9265 −1.87535 −0.937673 0.347518i \(-0.887025\pi\)
−0.937673 + 0.347518i \(0.887025\pi\)
\(368\) 0 0
\(369\) 3.64513 0.189758
\(370\) 0 0
\(371\) −0.624978 0.624978i −0.0324472 0.0324472i
\(372\) 0 0
\(373\) −6.04576 + 6.04576i −0.313038 + 0.313038i −0.846085 0.533048i \(-0.821047\pi\)
0.533048 + 0.846085i \(0.321047\pi\)
\(374\) 0 0
\(375\) 1.51764i 0.0783705i
\(376\) 0 0
\(377\) 11.7932i 0.607378i
\(378\) 0 0
\(379\) −10.9598 + 10.9598i −0.562969 + 0.562969i −0.930150 0.367181i \(-0.880323\pi\)
0.367181 + 0.930150i \(0.380323\pi\)
\(380\) 0 0
\(381\) −3.42329 3.42329i −0.175380 0.175380i
\(382\) 0 0
\(383\) −28.3120 −1.44667 −0.723337 0.690495i \(-0.757393\pi\)
−0.723337 + 0.690495i \(0.757393\pi\)
\(384\) 0 0
\(385\) 0.323890 0.0165069
\(386\) 0 0
\(387\) −4.08221 4.08221i −0.207510 0.207510i
\(388\) 0 0
\(389\) 20.1249 20.1249i 1.02037 1.02037i 0.0205833 0.999788i \(-0.493448\pi\)
0.999788 0.0205833i \(-0.00655234\pi\)
\(390\) 0 0
\(391\) 2.74474i 0.138807i
\(392\) 0 0
\(393\) 12.0805i 0.609382i
\(394\) 0 0
\(395\) 7.75323 7.75323i 0.390107 0.390107i
\(396\) 0 0
\(397\) 4.43247 + 4.43247i 0.222459 + 0.222459i 0.809533 0.587074i \(-0.199720\pi\)
−0.587074 + 0.809533i \(0.699720\pi\)
\(398\) 0 0
\(399\) 0.654045 0.0327432
\(400\) 0 0
\(401\) −18.4044 −0.919072 −0.459536 0.888159i \(-0.651984\pi\)
−0.459536 + 0.888159i \(0.651984\pi\)
\(402\) 0 0
\(403\) −0.592354 0.592354i −0.0295073 0.0295073i
\(404\) 0 0
\(405\) −4.54258 + 4.54258i −0.225723 + 0.225723i
\(406\) 0 0
\(407\) 16.6848i 0.827036i
\(408\) 0 0
\(409\) 26.1503i 1.29305i 0.762892 + 0.646526i \(0.223779\pi\)
−0.762892 + 0.646526i \(0.776221\pi\)
\(410\) 0 0
\(411\) 0.297688 0.297688i 0.0146839 0.0146839i
\(412\) 0 0
\(413\) 0.701316 + 0.701316i 0.0345095 + 0.0345095i
\(414\) 0 0
\(415\) −1.45705 −0.0715239
\(416\) 0 0
\(417\) −26.0956 −1.27791
\(418\) 0 0
\(419\) −16.3655 16.3655i −0.799506 0.799506i 0.183511 0.983018i \(-0.441254\pi\)
−0.983018 + 0.183511i \(0.941254\pi\)
\(420\) 0 0
\(421\) 3.77589 3.77589i 0.184025 0.184025i −0.609082 0.793107i \(-0.708462\pi\)
0.793107 + 0.609082i \(0.208462\pi\)
\(422\) 0 0
\(423\) 6.87024i 0.334042i
\(424\) 0 0
\(425\) 2.54587i 0.123493i
\(426\) 0 0
\(427\) 0.577227 0.577227i 0.0279340 0.0279340i
\(428\) 0 0
\(429\) 4.42883 + 4.42883i 0.213826 + 0.213826i
\(430\) 0 0
\(431\) −12.9282 −0.622730 −0.311365 0.950290i \(-0.600786\pi\)
−0.311365 + 0.950290i \(0.600786\pi\)
\(432\) 0 0
\(433\) −0.716195 −0.0344181 −0.0172091 0.999852i \(-0.505478\pi\)
−0.0172091 + 0.999852i \(0.505478\pi\)
\(434\) 0 0
\(435\) −9.60332 9.60332i −0.460444 0.460444i
\(436\) 0 0
\(437\) 3.17663 3.17663i 0.151959 0.151959i
\(438\) 0 0
\(439\) 33.9527i 1.62048i −0.586101 0.810238i \(-0.699338\pi\)
0.586101 0.810238i \(-0.300662\pi\)
\(440\) 0 0
\(441\) 4.86997i 0.231903i
\(442\) 0 0
\(443\) −21.3464 + 21.3464i −1.01420 + 1.01420i −0.0143006 + 0.999898i \(0.504552\pi\)
−0.999898 + 0.0143006i \(0.995448\pi\)
\(444\) 0 0
\(445\) 4.77854 + 4.77854i 0.226524 + 0.226524i
\(446\) 0 0
\(447\) 12.4853 0.590534
\(448\) 0 0
\(449\) 30.5066 1.43970 0.719848 0.694131i \(-0.244211\pi\)
0.719848 + 0.694131i \(0.244211\pi\)
\(450\) 0 0
\(451\) 11.5845 + 11.5845i 0.545495 + 0.545495i
\(452\) 0 0
\(453\) 6.46019 6.46019i 0.303526 0.303526i
\(454\) 0 0
\(455\) 0.136297i 0.00638969i
\(456\) 0 0
\(457\) 13.8063i 0.645831i 0.946428 + 0.322915i \(0.104663\pi\)
−0.946428 + 0.322915i \(0.895337\pi\)
\(458\) 0 0
\(459\) 10.0998 10.0998i 0.471417 0.471417i
\(460\) 0 0
\(461\) 10.8637 + 10.8637i 0.505973 + 0.505973i 0.913288 0.407315i \(-0.133535\pi\)
−0.407315 + 0.913288i \(0.633535\pi\)
\(462\) 0 0
\(463\) 0.401792 0.0186729 0.00933643 0.999956i \(-0.497028\pi\)
0.00933643 + 0.999956i \(0.497028\pi\)
\(464\) 0 0
\(465\) 0.964724 0.0447380
\(466\) 0 0
\(467\) −0.822963 0.822963i −0.0380822 0.0380822i 0.687809 0.725891i \(-0.258573\pi\)
−0.725891 + 0.687809i \(0.758573\pi\)
\(468\) 0 0
\(469\) −0.0194199 + 0.0194199i −0.000896728 + 0.000896728i
\(470\) 0 0
\(471\) 19.7133i 0.908341i
\(472\) 0 0
\(473\) 25.9472i 1.19306i
\(474\) 0 0
\(475\) 2.94646 2.94646i 0.135193 0.135193i
\(476\) 0 0
\(477\) −4.21050 4.21050i −0.192785 0.192785i
\(478\) 0 0
\(479\) −9.24996 −0.422641 −0.211321 0.977417i \(-0.567776\pi\)
−0.211321 + 0.977417i \(0.567776\pi\)
\(480\) 0 0
\(481\) −7.02118 −0.320138
\(482\) 0 0
\(483\) −0.119658 0.119658i −0.00544463 0.00544463i
\(484\) 0 0
\(485\) 12.7091 12.7091i 0.577093 0.577093i
\(486\) 0 0
\(487\) 6.23242i 0.282418i −0.989980 0.141209i \(-0.954901\pi\)
0.989980 0.141209i \(-0.0450990\pi\)
\(488\) 0 0
\(489\) 5.88953i 0.266334i
\(490\) 0 0
\(491\) 2.91407 2.91407i 0.131510 0.131510i −0.638288 0.769798i \(-0.720357\pi\)
0.769798 + 0.638288i \(0.220357\pi\)
\(492\) 0 0
\(493\) 16.1097 + 16.1097i 0.725546 + 0.725546i
\(494\) 0 0
\(495\) 2.18206 0.0980761
\(496\) 0 0
\(497\) −0.251200 −0.0112679
\(498\) 0 0
\(499\) 2.33145 + 2.33145i 0.104370 + 0.104370i 0.757364 0.652993i \(-0.226487\pi\)
−0.652993 + 0.757364i \(0.726487\pi\)
\(500\) 0 0
\(501\) −7.15696 + 7.15696i −0.319749 + 0.319749i
\(502\) 0 0
\(503\) 30.9063i 1.37805i 0.724740 + 0.689023i \(0.241960\pi\)
−0.724740 + 0.689023i \(0.758040\pi\)
\(504\) 0 0
\(505\) 9.70674i 0.431944i
\(506\) 0 0
\(507\) 12.0870 12.0870i 0.536803 0.536803i
\(508\) 0 0
\(509\) −7.41473 7.41473i −0.328652 0.328652i 0.523422 0.852074i \(-0.324655\pi\)
−0.852074 + 0.523422i \(0.824655\pi\)
\(510\) 0 0
\(511\) 1.46513 0.0648136
\(512\) 0 0
\(513\) 23.3780 1.03216
\(514\) 0 0
\(515\) 12.2829 + 12.2829i 0.541249 + 0.541249i
\(516\) 0 0
\(517\) −21.8342 + 21.8342i −0.960268 + 0.960268i
\(518\) 0 0
\(519\) 1.57117i 0.0689669i
\(520\) 0 0
\(521\) 39.7156i 1.73997i 0.493075 + 0.869987i \(0.335873\pi\)
−0.493075 + 0.869987i \(0.664127\pi\)
\(522\) 0 0
\(523\) −0.451554 + 0.451554i −0.0197451 + 0.0197451i −0.716910 0.697165i \(-0.754444\pi\)
0.697165 + 0.716910i \(0.254444\pi\)
\(524\) 0 0
\(525\) −0.110988 0.110988i −0.00484392 0.00484392i
\(526\) 0 0
\(527\) −1.61834 −0.0704961
\(528\) 0 0
\(529\) 21.8377 0.949464
\(530\) 0 0
\(531\) 4.72479 + 4.72479i 0.205038 + 0.205038i
\(532\) 0 0
\(533\) −4.87492 + 4.87492i −0.211156 + 0.211156i
\(534\) 0 0
\(535\) 17.1380i 0.740939i
\(536\) 0 0
\(537\) 1.32891i 0.0573468i
\(538\) 0 0
\(539\) 15.4772 15.4772i 0.666650 0.666650i
\(540\) 0 0
\(541\) 10.4792 + 10.4792i 0.450537 + 0.450537i 0.895533 0.444996i \(-0.146795\pi\)
−0.444996 + 0.895533i \(0.646795\pi\)
\(542\) 0 0
\(543\) −16.2168 −0.695930
\(544\) 0 0
\(545\) −12.8484 −0.550363
\(546\) 0 0
\(547\) 16.6370 + 16.6370i 0.711347 + 0.711347i 0.966817 0.255470i \(-0.0822302\pi\)
−0.255470 + 0.966817i \(0.582230\pi\)
\(548\) 0 0
\(549\) 3.88880 3.88880i 0.165970 0.165970i
\(550\) 0 0
\(551\) 37.2893i 1.58858i
\(552\) 0 0
\(553\) 1.13402i 0.0482235i
\(554\) 0 0
\(555\) 5.71744 5.71744i 0.242692 0.242692i
\(556\) 0 0
\(557\) 15.2321 + 15.2321i 0.645405 + 0.645405i 0.951879 0.306474i \(-0.0991492\pi\)
−0.306474 + 0.951879i \(0.599149\pi\)
\(558\) 0 0
\(559\) 10.9189 0.461821
\(560\) 0 0
\(561\) 12.0998 0.510853
\(562\) 0 0
\(563\) −5.12478 5.12478i −0.215984 0.215984i 0.590820 0.806804i \(-0.298804\pi\)
−0.806804 + 0.590820i \(0.798804\pi\)
\(564\) 0 0
\(565\) −4.52004 + 4.52004i −0.190160 + 0.190160i
\(566\) 0 0
\(567\) 0.664418i 0.0279029i
\(568\) 0 0
\(569\) 14.3617i 0.602073i 0.953613 + 0.301036i \(0.0973325\pi\)
−0.953613 + 0.301036i \(0.902667\pi\)
\(570\) 0 0
\(571\) 16.7503 16.7503i 0.700979 0.700979i −0.263642 0.964621i \(-0.584924\pi\)
0.964621 + 0.263642i \(0.0849237\pi\)
\(572\) 0 0
\(573\) 25.9985 + 25.9985i 1.08610 + 1.08610i
\(574\) 0 0
\(575\) −1.07812 −0.0449605
\(576\) 0 0
\(577\) 19.0222 0.791905 0.395952 0.918271i \(-0.370414\pi\)
0.395952 + 0.918271i \(0.370414\pi\)
\(578\) 0 0
\(579\) 4.05986 + 4.05986i 0.168722 + 0.168722i
\(580\) 0 0
\(581\) 0.106557 0.106557i 0.00442075 0.00442075i
\(582\) 0 0
\(583\) 26.7627i 1.10840i
\(584\) 0 0
\(585\) 0.918236i 0.0379644i
\(586\) 0 0
\(587\) 6.13612 6.13612i 0.253265 0.253265i −0.569043 0.822308i \(-0.692686\pi\)
0.822308 + 0.569043i \(0.192686\pi\)
\(588\) 0 0
\(589\) −1.87299 1.87299i −0.0771753 0.0771753i
\(590\) 0 0
\(591\) −31.1901 −1.28299
\(592\) 0 0
\(593\) 28.0963 1.15378 0.576889 0.816823i \(-0.304267\pi\)
0.576889 + 0.816823i \(0.304267\pi\)
\(594\) 0 0
\(595\) 0.186185 + 0.186185i 0.00763283 + 0.00763283i
\(596\) 0 0
\(597\) 26.3830 26.3830i 1.07978 1.07978i
\(598\) 0 0
\(599\) 2.27156i 0.0928135i −0.998923 0.0464068i \(-0.985223\pi\)
0.998923 0.0464068i \(-0.0147770\pi\)
\(600\) 0 0
\(601\) 21.4534i 0.875103i −0.899193 0.437551i \(-0.855846\pi\)
0.899193 0.437551i \(-0.144154\pi\)
\(602\) 0 0
\(603\) −0.130833 + 0.130833i −0.00532791 + 0.00532791i
\(604\) 0 0
\(605\) −0.843403 0.843403i −0.0342892 0.0342892i
\(606\) 0 0
\(607\) −6.63203 −0.269186 −0.134593 0.990901i \(-0.542973\pi\)
−0.134593 + 0.990901i \(0.542973\pi\)
\(608\) 0 0
\(609\) 1.40462 0.0569182
\(610\) 0 0
\(611\) −9.18811 9.18811i −0.371711 0.371711i
\(612\) 0 0
\(613\) −24.1766 + 24.1766i −0.976486 + 0.976486i −0.999730 0.0232442i \(-0.992600\pi\)
0.0232442 + 0.999730i \(0.492600\pi\)
\(614\) 0 0
\(615\) 7.93942i 0.320148i
\(616\) 0 0
\(617\) 15.0311i 0.605131i −0.953129 0.302566i \(-0.902157\pi\)
0.953129 0.302566i \(-0.0978431\pi\)
\(618\) 0 0
\(619\) −1.08276 + 1.08276i −0.0435198 + 0.0435198i −0.728532 0.685012i \(-0.759797\pi\)
0.685012 + 0.728532i \(0.259797\pi\)
\(620\) 0 0
\(621\) −4.27702 4.27702i −0.171631 0.171631i
\(622\) 0 0
\(623\) −0.698930 −0.0280020
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 14.0037 + 14.0037i 0.559254 + 0.559254i
\(628\) 0 0
\(629\) −9.59111 + 9.59111i −0.382423 + 0.382423i
\(630\) 0 0
\(631\) 16.1104i 0.641346i −0.947190 0.320673i \(-0.896091\pi\)
0.947190 0.320673i \(-0.103909\pi\)
\(632\) 0 0
\(633\) 25.3718i 1.00844i
\(634\) 0 0
\(635\) 2.25567 2.25567i 0.0895135 0.0895135i
\(636\) 0 0
\(637\) 6.51299 + 6.51299i 0.258054 + 0.258054i
\(638\) 0 0
\(639\) −1.69234 −0.0669481
\(640\) 0 0
\(641\) 33.5492 1.32511 0.662557 0.749012i \(-0.269471\pi\)
0.662557 + 0.749012i \(0.269471\pi\)
\(642\) 0 0
\(643\) 25.6497 + 25.6497i 1.01153 + 1.01153i 0.999933 + 0.0115939i \(0.00369055\pi\)
0.0115939 + 0.999933i \(0.496309\pi\)
\(644\) 0 0
\(645\) −8.89142 + 8.89142i −0.350099 + 0.350099i
\(646\) 0 0
\(647\) 36.6300i 1.44008i 0.693935 + 0.720038i \(0.255875\pi\)
−0.693935 + 0.720038i \(0.744125\pi\)
\(648\) 0 0
\(649\) 30.0316i 1.17884i
\(650\) 0 0
\(651\) −0.0705524 + 0.0705524i −0.00276517 + 0.00276517i
\(652\) 0 0
\(653\) −11.7702 11.7702i −0.460605 0.460605i 0.438249 0.898854i \(-0.355599\pi\)
−0.898854 + 0.438249i \(0.855599\pi\)
\(654\) 0 0
\(655\) 7.96008 0.311026
\(656\) 0 0
\(657\) 9.87065 0.385091
\(658\) 0 0
\(659\) 0.496974 + 0.496974i 0.0193593 + 0.0193593i 0.716720 0.697361i \(-0.245642\pi\)
−0.697361 + 0.716720i \(0.745642\pi\)
\(660\) 0 0
\(661\) −0.919644 + 0.919644i −0.0357700 + 0.0357700i −0.724766 0.688996i \(-0.758052\pi\)
0.688996 + 0.724766i \(0.258052\pi\)
\(662\) 0 0
\(663\) 5.09173i 0.197746i
\(664\) 0 0
\(665\) 0.430963i 0.0167120i
\(666\) 0 0
\(667\) 6.82211 6.82211i 0.264153 0.264153i
\(668\) 0 0
\(669\) 21.7985 + 21.7985i 0.842778 + 0.842778i
\(670\) 0 0
\(671\) 24.7179 0.954224
\(672\) 0 0
\(673\) −19.6303 −0.756693 −0.378346 0.925664i \(-0.623507\pi\)
−0.378346 + 0.925664i \(0.623507\pi\)
\(674\) 0 0
\(675\) −3.96713 3.96713i −0.152695 0.152695i
\(676\) 0 0
\(677\) −0.644131 + 0.644131i −0.0247560 + 0.0247560i −0.719376 0.694620i \(-0.755572\pi\)
0.694620 + 0.719376i \(0.255572\pi\)
\(678\) 0 0
\(679\) 1.85890i 0.0713379i
\(680\) 0 0
\(681\) 40.9574i 1.56949i
\(682\) 0 0
\(683\) 29.6404 29.6404i 1.13416 1.13416i 0.144682 0.989478i \(-0.453784\pi\)
0.989478 0.144682i \(-0.0462159\pi\)
\(684\) 0 0
\(685\) 0.196152 + 0.196152i 0.00749460 + 0.00749460i
\(686\) 0 0
\(687\) −2.71139 −0.103446
\(688\) 0 0
\(689\) 11.2621 0.429050
\(690\) 0 0
\(691\) 25.0761 + 25.0761i 0.953941 + 0.953941i 0.998985 0.0450436i \(-0.0143427\pi\)
−0.0450436 + 0.998985i \(0.514343\pi\)
\(692\) 0 0
\(693\) −0.159579 + 0.159579i −0.00606189 + 0.00606189i
\(694\) 0 0
\(695\) 17.1949i 0.652240i
\(696\) 0 0
\(697\) 13.3185i 0.504475i
\(698\) 0 0
\(699\) 24.4381 24.4381i 0.924332 0.924332i
\(700\) 0 0
\(701\) 15.5904 + 15.5904i 0.588841 + 0.588841i 0.937317 0.348477i \(-0.113301\pi\)
−0.348477 + 0.937317i \(0.613301\pi\)
\(702\) 0 0
\(703\) −22.2006 −0.837311
\(704\) 0 0
\(705\) 14.9640 0.563577
\(706\) 0 0
\(707\) −0.709875 0.709875i −0.0266976 0.0266976i
\(708\) 0 0
\(709\) −8.59111 + 8.59111i −0.322646 + 0.322646i −0.849781 0.527135i \(-0.823266\pi\)
0.527135 + 0.849781i \(0.323266\pi\)
\(710\) 0 0
\(711\) 7.63994i 0.286520i
\(712\) 0 0
\(713\) 0.685331i 0.0256658i
\(714\) 0 0
\(715\) −2.91824 + 2.91824i −0.109136 + 0.109136i
\(716\) 0 0
\(717\) 23.6225 + 23.6225i 0.882197 + 0.882197i
\(718\) 0 0
\(719\) −27.1112 −1.01108 −0.505538 0.862804i \(-0.668706\pi\)
−0.505538 + 0.862804i \(0.668706\pi\)
\(720\) 0 0
\(721\) −1.79655 −0.0669070
\(722\) 0 0
\(723\) −20.9961 20.9961i −0.780855 0.780855i
\(724\) 0 0
\(725\) 6.32780 6.32780i 0.235009 0.235009i
\(726\) 0 0
\(727\) 40.9979i 1.52053i −0.649614 0.760264i \(-0.725069\pi\)
0.649614 0.760264i \(-0.274931\pi\)
\(728\) 0 0
\(729\) 30.0197i 1.11184i
\(730\) 0 0
\(731\) 14.9155 14.9155i 0.551670 0.551670i
\(732\) 0 0
\(733\) 7.49473 + 7.49473i 0.276824 + 0.276824i 0.831840 0.555016i \(-0.187288\pi\)
−0.555016 + 0.831840i \(0.687288\pi\)
\(734\) 0 0
\(735\) −10.6072 −0.391254
\(736\) 0 0
\(737\) −0.831595 −0.0306322
\(738\) 0 0
\(739\) 24.3947 + 24.3947i 0.897374 + 0.897374i 0.995203 0.0978293i \(-0.0311899\pi\)
−0.0978293 + 0.995203i \(0.531190\pi\)
\(740\) 0 0
\(741\) −5.89293 + 5.89293i −0.216482 + 0.216482i
\(742\) 0 0
\(743\) 13.5703i 0.497848i −0.968523 0.248924i \(-0.919923\pi\)
0.968523 0.248924i \(-0.0800769\pi\)
\(744\) 0 0
\(745\) 8.22678i 0.301406i
\(746\) 0 0
\(747\) 0.717882 0.717882i 0.0262659 0.0262659i
\(748\) 0 0
\(749\) −1.25334 1.25334i −0.0457959 0.0457959i
\(750\) 0 0
\(751\) −22.3407 −0.815225 −0.407612 0.913155i \(-0.633639\pi\)
−0.407612 + 0.913155i \(0.633639\pi\)
\(752\) 0 0
\(753\) −8.41740 −0.306747
\(754\) 0 0
\(755\) 4.25674 + 4.25674i 0.154919 + 0.154919i
\(756\) 0 0
\(757\) −4.33046 + 4.33046i −0.157393 + 0.157393i −0.781410 0.624017i \(-0.785499\pi\)
0.624017 + 0.781410i \(0.285499\pi\)
\(758\) 0 0
\(759\) 5.12398i 0.185989i
\(760\) 0 0
\(761\) 16.6770i 0.604541i 0.953222 + 0.302270i \(0.0977446\pi\)
−0.953222 + 0.302270i \(0.902255\pi\)
\(762\) 0 0
\(763\) 0.939629 0.939629i 0.0340168 0.0340168i
\(764\) 0 0
\(765\) 1.25433 + 1.25433i 0.0453505 + 0.0453505i
\(766\) 0 0
\(767\) −12.6377 −0.456320
\(768\) 0 0
\(769\) −6.38199 −0.230140 −0.115070 0.993357i \(-0.536709\pi\)
−0.115070 + 0.993357i \(0.536709\pi\)
\(770\) 0 0
\(771\) −15.4600 15.4600i −0.556777 0.556777i
\(772\) 0 0
\(773\) 32.7136 32.7136i 1.17663 1.17663i 0.196027 0.980598i \(-0.437196\pi\)
0.980598 0.196027i \(-0.0628041\pi\)
\(774\) 0 0
\(775\) 0.635674i 0.0228341i
\(776\) 0 0
\(777\) 0.836258i 0.0300006i
\(778\) 0 0
\(779\) −15.4142 + 15.4142i −0.552272 + 0.552272i
\(780\) 0 0
\(781\) −5.37842 5.37842i −0.192455 0.192455i
\(782\) 0 0
\(783\) 50.2064 1.79423
\(784\) 0 0
\(785\) 12.9895 0.463614
\(786\) 0 0
\(787\) −1.23233 1.23233i −0.0439279 0.0439279i 0.684802 0.728730i \(-0.259889\pi\)
−0.728730 + 0.684802i \(0.759889\pi\)
\(788\) 0 0
\(789\) 17.1803 17.1803i 0.611635 0.611635i
\(790\) 0 0
\(791\) 0.661121i 0.0235068i
\(792\) 0 0
\(793\) 10.4016i 0.369371i
\(794\) 0 0
\(795\) −9.17084 + 9.17084i −0.325256 + 0.325256i
\(796\) 0 0
\(797\) −2.62007 2.62007i −0.0928075 0.0928075i 0.659179 0.751986i \(-0.270904\pi\)
−0.751986 + 0.659179i \(0.770904\pi\)
\(798\) 0 0
\(799\) −25.1024 −0.888058
\(800\) 0 0
\(801\) −4.70872 −0.166374
\(802\) 0 0
\(803\) 31.3698 + 31.3698i 1.10702 + 1.10702i
\(804\) 0 0
\(805\) 0.0788450 0.0788450i 0.00277892 0.00277892i
\(806\) 0 0
\(807\) 4.82060i 0.169693i
\(808\) 0 0
\(809\) 3.63795i 0.127904i −0.997953 0.0639518i \(-0.979630\pi\)
0.997953 0.0639518i \(-0.0203704\pi\)
\(810\) 0 0
\(811\) −25.1436 + 25.1436i −0.882913 + 0.882913i −0.993830 0.110917i \(-0.964621\pi\)
0.110917 + 0.993830i \(0.464621\pi\)
\(812\) 0 0
\(813\) −3.18937 3.18937i −0.111856 0.111856i
\(814\) 0 0
\(815\) 3.88072 0.135936
\(816\) 0 0
\(817\) 34.5250 1.20788
\(818\) 0 0
\(819\) −0.0671526 0.0671526i −0.00234650 0.00234650i
\(820\) 0 0
\(821\) 8.04790 8.04790i 0.280874 0.280874i −0.552584 0.833457i \(-0.686358\pi\)
0.833457 + 0.552584i \(0.186358\pi\)
\(822\) 0 0
\(823\) 45.1452i 1.57366i 0.617168 + 0.786832i \(0.288280\pi\)
−0.617168 + 0.786832i \(0.711720\pi\)
\(824\) 0 0
\(825\) 4.75272i 0.165468i
\(826\) 0 0
\(827\) −8.20254 + 8.20254i −0.285230 + 0.285230i −0.835191 0.549960i \(-0.814643\pi\)
0.549960 + 0.835191i \(0.314643\pi\)
\(828\) 0 0
\(829\) 5.74467 + 5.74467i 0.199521 + 0.199521i 0.799795 0.600274i \(-0.204942\pi\)
−0.600274 + 0.799795i \(0.704942\pi\)
\(830\) 0 0
\(831\) −43.1749 −1.49772
\(832\) 0 0
\(833\) 17.7938 0.616520
\(834\) 0 0
\(835\) −4.71585 4.71585i −0.163199 0.163199i
\(836\) 0 0
\(837\) −2.52180 + 2.52180i −0.0871662 + 0.0871662i
\(838\) 0 0
\(839\) 29.7201i 1.02605i 0.858373 + 0.513026i \(0.171476\pi\)
−0.858373 + 0.513026i \(0.828524\pi\)
\(840\) 0 0
\(841\) 51.0822i 1.76146i
\(842\) 0 0
\(843\) 19.9457 19.9457i 0.686968 0.686968i
\(844\) 0 0
\(845\) 7.96436 + 7.96436i 0.273982 + 0.273982i
\(846\) 0 0
\(847\) 0.123360 0.00423870
\(848\) 0 0
\(849\) −44.5348 −1.52843
\(850\) 0 0
\(851\) 4.06162 + 4.06162i 0.139230 + 0.139230i
\(852\) 0 0
\(853\) 5.09538 5.09538i 0.174463 0.174463i −0.614474 0.788937i \(-0.710632\pi\)
0.788937 + 0.614474i \(0.210632\pi\)
\(854\) 0 0
\(855\) 2.90341i 0.0992945i
\(856\) 0 0
\(857\) 0.735948i 0.0251395i −0.999921 0.0125698i \(-0.995999\pi\)
0.999921 0.0125698i \(-0.00400118\pi\)
\(858\) 0 0
\(859\) 9.39668 9.39668i 0.320611 0.320611i −0.528391 0.849001i \(-0.677204\pi\)
0.849001 + 0.528391i \(0.177204\pi\)
\(860\) 0 0
\(861\) 0.580627 + 0.580627i 0.0197877 + 0.0197877i
\(862\) 0 0
\(863\) −47.0950 −1.60313 −0.801565 0.597907i \(-0.795999\pi\)
−0.801565 + 0.597907i \(0.795999\pi\)
\(864\) 0 0
\(865\) −1.03528 −0.0352004
\(866\) 0 0
\(867\) −11.2878 11.2878i −0.383354 0.383354i
\(868\) 0 0
\(869\) −24.2804 + 24.2804i −0.823657 + 0.823657i
\(870\) 0 0
\(871\) 0.349945i 0.0118574i
\(872\) 0 0
\(873\) 12.5234i 0.423854i
\(874\) 0 0
\(875\) 0.0731322 0.0731322i 0.00247232 0.00247232i
\(876\) 0 0
\(877\) −38.7479 38.7479i −1.30842 1.30842i −0.922554 0.385868i \(-0.873902\pi\)
−0.385868 0.922554i \(-0.626098\pi\)
\(878\) 0 0
\(879\) 14.1452 0.477104
\(880\) 0 0
\(881\) −1.67684 −0.0564942 −0.0282471 0.999601i \(-0.508993\pi\)
−0.0282471 + 0.999601i \(0.508993\pi\)
\(882\) 0 0
\(883\) −31.4734 31.4734i −1.05916 1.05916i −0.998136 0.0610287i \(-0.980562\pi\)
−0.0610287 0.998136i \(-0.519438\pi\)
\(884\) 0 0
\(885\) 10.2910 10.2910i 0.345929 0.345929i
\(886\) 0 0
\(887\) 29.4396i 0.988484i −0.869324 0.494242i \(-0.835446\pi\)
0.869324 0.494242i \(-0.164554\pi\)
\(888\) 0 0
\(889\) 0.329924i 0.0110653i
\(890\) 0 0
\(891\) 14.2258 14.2258i 0.476582 0.476582i
\(892\) 0 0
\(893\) −29.0523 29.0523i −0.972198 0.972198i
\(894\) 0 0
\(895\) −0.875644 −0.0292696
\(896\) 0 0
\(897\) 2.15623 0.0719945
\(898\) 0 0
\(899\) −4.02242 4.02242i −0.134155 0.134155i
\(900\) 0 0
\(901\) 15.3843 15.3843i 0.512524 0.512524i
\(902\) 0 0
\(903\) 1.30050i 0.0432778i
\(904\) 0 0
\(905\) 10.6856i 0.355200i
\(906\) 0 0
\(907\) −35.4520 + 35.4520i −1.17716 + 1.17716i −0.196702 + 0.980463i \(0.563023\pi\)
−0.980463 + 0.196702i \(0.936977\pi\)
\(908\) 0 0
\(909\) −4.78245 4.78245i −0.158624 0.158624i
\(910\) 0 0
\(911\) 43.9590 1.45643 0.728213 0.685351i \(-0.240351\pi\)
0.728213 + 0.685351i \(0.240351\pi\)
\(912\) 0 0
\(913\) 4.56298 0.151013
\(914\) 0 0
\(915\) −8.47015 8.47015i −0.280015 0.280015i
\(916\) 0 0
\(917\) −0.582138 + 0.582138i −0.0192239 + 0.0192239i
\(918\) 0 0
\(919\) 46.6638i 1.53930i 0.638469 + 0.769648i \(0.279568\pi\)
−0.638469 + 0.769648i \(0.720432\pi\)
\(920\) 0 0
\(921\) 1.06110i 0.0349644i
\(922\) 0 0
\(923\) 2.26330 2.26330i 0.0744976 0.0744976i
\(924\) 0 0
\(925\) 3.76733 + 3.76733i 0.123869 + 0.123869i
\(926\) 0 0
\(927\) −12.1034 −0.397529
\(928\) 0 0
\(929\) −44.3630 −1.45550 −0.727752 0.685840i \(-0.759435\pi\)
−0.727752 + 0.685840i \(0.759435\pi\)
\(930\) 0 0
\(931\) 20.5937 + 20.5937i 0.674932 + 0.674932i
\(932\) 0 0
\(933\) −10.9898 + 10.9898i −0.359791 + 0.359791i
\(934\) 0 0
\(935\) 7.97277i 0.260737i
\(936\) 0 0
\(937\) 1.00338i 0.0327790i −0.999866 0.0163895i \(-0.994783\pi\)
0.999866 0.0163895i \(-0.00521718\pi\)
\(938\) 0 0
\(939\) −10.7376 + 10.7376i −0.350408 + 0.350408i
\(940\) 0 0
\(941\) 10.0597 + 10.0597i 0.327937 + 0.327937i 0.851801 0.523865i \(-0.175510\pi\)
−0.523865 + 0.851801i \(0.675510\pi\)
\(942\) 0 0
\(943\) 5.64009 0.183667
\(944\) 0 0
\(945\) 0.580249 0.0188755
\(946\) 0 0
\(947\) −18.3749 18.3749i −0.597103 0.597103i 0.342438 0.939541i \(-0.388747\pi\)
−0.939541 + 0.342438i \(0.888747\pi\)
\(948\) 0 0
\(949\) −13.2008 + 13.2008i −0.428516 + 0.428516i
\(950\) 0 0
\(951\) 41.5175i 1.34630i
\(952\) 0 0
\(953\) 16.2842i 0.527497i −0.964591 0.263749i \(-0.915041\pi\)
0.964591 0.263749i \(-0.0849589\pi\)
\(954\) 0 0
\(955\) −17.1309 + 17.1309i −0.554344 + 0.554344i
\(956\) 0 0
\(957\) 30.0743 + 30.0743i 0.972163 + 0.972163i
\(958\) 0 0
\(959\) −0.0286901 −0.000926452
\(960\) 0 0
\(961\) −30.5959 −0.986965
\(962\) 0 0
\(963\) −8.44378 8.44378i −0.272097 0.272097i
\(964\) 0 0
\(965\) −2.67511 + 2.67511i −0.0861150 + 0.0861150i
\(966\) 0 0
\(967\) 29.5190i 0.949269i −0.880183 0.474634i \(-0.842580\pi\)
0.880183 0.474634i \(-0.157420\pi\)
\(968\) 0 0
\(969\) 16.0998i 0.517199i
\(970\) 0 0
\(971\) −12.0000 + 12.0000i −0.385099 + 0.385099i −0.872935 0.487836i \(-0.837786\pi\)
0.487836 + 0.872935i \(0.337786\pi\)
\(972\) 0 0
\(973\) 1.25750 + 1.25750i 0.0403136 + 0.0403136i
\(974\) 0 0
\(975\) 2.00000 0.0640513
\(976\) 0 0
\(977\) 48.0884 1.53848 0.769241 0.638958i \(-0.220634\pi\)
0.769241 + 0.638958i \(0.220634\pi\)
\(978\) 0 0
\(979\) −14.9647 14.9647i −0.478275 0.478275i
\(980\) 0 0
\(981\) 6.33031 6.33031i 0.202111 0.202111i
\(982\) 0 0
\(983\) 37.1975i 1.18642i −0.805050 0.593208i \(-0.797861\pi\)
0.805050 0.593208i \(-0.202139\pi\)
\(984\) 0 0
\(985\) 20.5517i 0.654832i
\(986\) 0 0
\(987\) −1.09435 + 1.09435i −0.0348335 + 0.0348335i
\(988\) 0 0
\(989\) −6.31638 6.31638i −0.200849 0.200849i
\(990\) 0 0
\(991\) 42.2588 1.34240 0.671198 0.741278i \(-0.265780\pi\)
0.671198 + 0.741278i \(0.265780\pi\)
\(992\) 0 0
\(993\) −47.7954 −1.51674
\(994\) 0 0
\(995\) 17.3843 + 17.3843i 0.551118 + 0.551118i
\(996\) 0 0
\(997\) 40.6128 40.6128i 1.28622 1.28622i 0.349154 0.937065i \(-0.386469\pi\)
0.937065 0.349154i \(-0.113531\pi\)
\(998\) 0 0
\(999\) 29.8909i 0.945707i
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 1280.2.l.a.321.4 8
4.3 odd 2 1280.2.l.f.321.1 yes 8
8.3 odd 2 1280.2.l.d.321.4 yes 8
8.5 even 2 1280.2.l.g.321.1 yes 8
16.3 odd 4 1280.2.l.d.961.4 yes 8
16.5 even 4 inner 1280.2.l.a.961.4 yes 8
16.11 odd 4 1280.2.l.f.961.1 yes 8
16.13 even 4 1280.2.l.g.961.1 yes 8
32.5 even 8 5120.2.a.a.1.2 4
32.11 odd 8 5120.2.a.b.1.2 4
32.21 even 8 5120.2.a.r.1.3 4
32.27 odd 8 5120.2.a.q.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1280.2.l.a.321.4 8 1.1 even 1 trivial
1280.2.l.a.961.4 yes 8 16.5 even 4 inner
1280.2.l.d.321.4 yes 8 8.3 odd 2
1280.2.l.d.961.4 yes 8 16.3 odd 4
1280.2.l.f.321.1 yes 8 4.3 odd 2
1280.2.l.f.961.1 yes 8 16.11 odd 4
1280.2.l.g.321.1 yes 8 8.5 even 2
1280.2.l.g.961.1 yes 8 16.13 even 4
5120.2.a.a.1.2 4 32.5 even 8
5120.2.a.b.1.2 4 32.11 odd 8
5120.2.a.q.1.3 4 32.27 odd 8
5120.2.a.r.1.3 4 32.21 even 8