Properties

Label 1120.2.bq.b.719.7
Level $1120$
Weight $2$
Character 1120.719
Analytic conductor $8.943$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1120,2,Mod(719,1120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1120.719");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.bq (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: \(8.94324502638\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 719.7
Character \(\chi\) \(=\) 1120.719
Dual form 1120.2.bq.b.1039.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13535 - 1.96648i) q^{3} +(0.406539 - 2.19880i) q^{5} +(-0.551936 + 2.58754i) q^{7} +(-1.07804 + 1.86722i) q^{9} +O(q^{10})\) \(q+(-1.13535 - 1.96648i) q^{3} +(0.406539 - 2.19880i) q^{5} +(-0.551936 + 2.58754i) q^{7} +(-1.07804 + 1.86722i) q^{9} +(0.454564 + 0.787328i) q^{11} +5.66349i q^{13} +(-4.78547 + 1.69696i) q^{15} +(3.14931 + 5.45476i) q^{17} +(0.966292 + 0.557889i) q^{19} +(5.71500 - 1.85239i) q^{21} +(-1.14508 + 1.98334i) q^{23} +(-4.66945 - 1.78780i) q^{25} -1.91628 q^{27} +6.21463i q^{29} +(1.41914 + 2.45801i) q^{31} +(1.03218 - 1.78779i) q^{33} +(5.46510 + 2.26553i) q^{35} +(-0.789609 + 1.36764i) q^{37} +(11.1372 - 6.43005i) q^{39} +0.163067i q^{41} -8.29346i q^{43} +(3.66738 + 3.12950i) q^{45} +(8.56191 + 4.94322i) q^{47} +(-6.39073 - 2.85631i) q^{49} +(7.15113 - 12.3861i) q^{51} +(-2.56505 - 4.44280i) q^{53} +(1.91598 - 0.679417i) q^{55} -2.53360i q^{57} +(-9.97768 + 5.76061i) q^{59} +(0.977217 - 1.69259i) q^{61} +(-4.23650 - 3.82006i) q^{63} +(12.4529 + 2.30243i) q^{65} +(6.09472 - 3.51879i) q^{67} +5.20028 q^{69} +0.811490i q^{71} +(-4.54031 - 7.86404i) q^{73} +(1.78579 + 11.2122i) q^{75} +(-2.28813 + 0.741649i) q^{77} +(9.82237 + 5.67095i) q^{79} +(5.40978 + 9.37001i) q^{81} -7.80839 q^{83} +(13.2742 - 4.70713i) q^{85} +(12.2210 - 7.05578i) q^{87} +(12.4104 + 7.16517i) q^{89} +(-14.6545 - 3.12589i) q^{91} +(3.22243 - 5.58142i) q^{93} +(1.61952 - 1.89788i) q^{95} -9.99774 q^{97} -1.96016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(421\) \(801\) \(897\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −1.13535 1.96648i −0.655495 1.13535i −0.981769 0.190075i \(-0.939127\pi\)
0.326275 0.945275i \(-0.394207\pi\)
\(4\) 0 0
\(5\) 0.406539 2.19880i 0.181810 0.983334i
\(6\) 0 0
\(7\) −0.551936 + 2.58754i −0.208612 + 0.977998i
\(8\) 0 0
\(9\) −1.07804 + 1.86722i −0.359347 + 0.622407i
\(10\) 0 0
\(11\) 0.454564 + 0.787328i 0.137056 + 0.237388i 0.926381 0.376587i \(-0.122903\pi\)
−0.789325 + 0.613976i \(0.789569\pi\)
\(12\) 0 0
\(13\) 5.66349i 1.57077i 0.619007 + 0.785385i \(0.287535\pi\)
−0.619007 + 0.785385i \(0.712465\pi\)
\(14\) 0 0
\(15\) −4.78547 + 1.69696i −1.23560 + 0.438153i
\(16\) 0 0
\(17\) 3.14931 + 5.45476i 0.763819 + 1.32297i 0.940869 + 0.338771i \(0.110011\pi\)
−0.177050 + 0.984202i \(0.556655\pi\)
\(18\) 0 0
\(19\) 0.966292 + 0.557889i 0.221683 + 0.127989i 0.606729 0.794909i \(-0.292481\pi\)
−0.385047 + 0.922897i \(0.625815\pi\)
\(20\) 0 0
\(21\) 5.71500 1.85239i 1.24712 0.404225i
\(22\) 0 0
\(23\) −1.14508 + 1.98334i −0.238766 + 0.413555i −0.960360 0.278761i \(-0.910076\pi\)
0.721594 + 0.692316i \(0.243410\pi\)
\(24\) 0 0
\(25\) −4.66945 1.78780i −0.933891 0.357559i
\(26\) 0 0
\(27\) −1.91628 −0.368789
\(28\) 0 0
\(29\) 6.21463i 1.15403i 0.816734 + 0.577014i \(0.195782\pi\)
−0.816734 + 0.577014i \(0.804218\pi\)
\(30\) 0 0
\(31\) 1.41914 + 2.45801i 0.254884 + 0.441472i 0.964864 0.262750i \(-0.0846293\pi\)
−0.709980 + 0.704222i \(0.751296\pi\)
\(32\) 0 0
\(33\) 1.03218 1.78779i 0.179679 0.311214i
\(34\) 0 0
\(35\) 5.46510 + 2.26553i 0.923771 + 0.382945i
\(36\) 0 0
\(37\) −0.789609 + 1.36764i −0.129811 + 0.224839i −0.923603 0.383350i \(-0.874770\pi\)
0.793792 + 0.608189i \(0.208104\pi\)
\(38\) 0 0
\(39\) 11.1372 6.43005i 1.78337 1.02963i
\(40\) 0 0
\(41\) 0.163067i 0.0254668i 0.999919 + 0.0127334i \(0.00405327\pi\)
−0.999919 + 0.0127334i \(0.995947\pi\)
\(42\) 0 0
\(43\) 8.29346i 1.26474i −0.774666 0.632370i \(-0.782082\pi\)
0.774666 0.632370i \(-0.217918\pi\)
\(44\) 0 0
\(45\) 3.66738 + 3.12950i 0.546701 + 0.466518i
\(46\) 0 0
\(47\) 8.56191 + 4.94322i 1.24888 + 0.721043i 0.970887 0.239540i \(-0.0769965\pi\)
0.277996 + 0.960582i \(0.410330\pi\)
\(48\) 0 0
\(49\) −6.39073 2.85631i −0.912962 0.408045i
\(50\) 0 0
\(51\) 7.15113 12.3861i 1.00136 1.73440i
\(52\) 0 0
\(53\) −2.56505 4.44280i −0.352337 0.610266i 0.634321 0.773070i \(-0.281280\pi\)
−0.986659 + 0.162803i \(0.947946\pi\)
\(54\) 0 0
\(55\) 1.91598 0.679417i 0.258350 0.0916125i
\(56\) 0 0
\(57\) 2.53360i 0.335583i
\(58\) 0 0
\(59\) −9.97768 + 5.76061i −1.29898 + 0.749968i −0.980228 0.197869i \(-0.936598\pi\)
−0.318754 + 0.947837i \(0.603264\pi\)
\(60\) 0 0
\(61\) 0.977217 1.69259i 0.125120 0.216714i −0.796660 0.604428i \(-0.793402\pi\)
0.921780 + 0.387714i \(0.126735\pi\)
\(62\) 0 0
\(63\) −4.23650 3.82006i −0.533749 0.481283i
\(64\) 0 0
\(65\) 12.4529 + 2.30243i 1.54459 + 0.285581i
\(66\) 0 0
\(67\) 6.09472 3.51879i 0.744589 0.429889i −0.0791464 0.996863i \(-0.525219\pi\)
0.823735 + 0.566974i \(0.191886\pi\)
\(68\) 0 0
\(69\) 5.20028 0.626040
\(70\) 0 0
\(71\) 0.811490i 0.0963061i 0.998840 + 0.0481531i \(0.0153335\pi\)
−0.998840 + 0.0481531i \(0.984666\pi\)
\(72\) 0 0
\(73\) −4.54031 7.86404i −0.531403 0.920417i −0.999328 0.0366487i \(-0.988332\pi\)
0.467925 0.883768i \(-0.345002\pi\)
\(74\) 0 0
\(75\) 1.78579 + 11.2122i 0.206206 + 1.29467i
\(76\) 0 0
\(77\) −2.28813 + 0.741649i −0.260757 + 0.0845187i
\(78\) 0 0
\(79\) 9.82237 + 5.67095i 1.10510 + 0.638031i 0.937557 0.347833i \(-0.113082\pi\)
0.167546 + 0.985864i \(0.446416\pi\)
\(80\) 0 0
\(81\) 5.40978 + 9.37001i 0.601086 + 1.04111i
\(82\) 0 0
\(83\) −7.80839 −0.857082 −0.428541 0.903522i \(-0.640972\pi\)
−0.428541 + 0.903522i \(0.640972\pi\)
\(84\) 0 0
\(85\) 13.2742 4.70713i 1.43979 0.510560i
\(86\) 0 0
\(87\) 12.2210 7.05578i 1.31023 0.756459i
\(88\) 0 0
\(89\) 12.4104 + 7.16517i 1.31550 + 0.759506i 0.983002 0.183597i \(-0.0587740\pi\)
0.332502 + 0.943103i \(0.392107\pi\)
\(90\) 0 0
\(91\) −14.6545 3.12589i −1.53621 0.327682i
\(92\) 0 0
\(93\) 3.22243 5.58142i 0.334151 0.578766i
\(94\) 0 0
\(95\) 1.61952 1.89788i 0.166159 0.194718i
\(96\) 0 0
\(97\) −9.99774 −1.01512 −0.507558 0.861618i \(-0.669452\pi\)
−0.507558 + 0.861618i \(0.669452\pi\)
\(98\) 0 0
\(99\) −1.96016 −0.197003
\(100\) 0 0
\(101\) 8.69267 + 15.0562i 0.864953 + 1.49814i 0.867093 + 0.498146i \(0.165985\pi\)
−0.00214005 + 0.999998i \(0.500681\pi\)
\(102\) 0 0
\(103\) −1.56602 0.904144i −0.154305 0.0890880i 0.420859 0.907126i \(-0.361729\pi\)
−0.575164 + 0.818038i \(0.695062\pi\)
\(104\) 0 0
\(105\) −1.74967 13.3192i −0.170751 1.29982i
\(106\) 0 0
\(107\) 3.08558 + 1.78146i 0.298294 + 0.172220i 0.641676 0.766976i \(-0.278239\pi\)
−0.343382 + 0.939196i \(0.611573\pi\)
\(108\) 0 0
\(109\) 1.72947 0.998508i 0.165653 0.0956398i −0.414882 0.909875i \(-0.636177\pi\)
0.580534 + 0.814236i \(0.302844\pi\)
\(110\) 0 0
\(111\) 3.58593 0.340361
\(112\) 0 0
\(113\) 13.5251i 1.27234i −0.771551 0.636168i \(-0.780519\pi\)
0.771551 0.636168i \(-0.219481\pi\)
\(114\) 0 0
\(115\) 3.89545 + 3.32411i 0.363253 + 0.309975i
\(116\) 0 0
\(117\) −10.5750 6.10548i −0.977659 0.564452i
\(118\) 0 0
\(119\) −15.8526 + 5.13828i −1.45321 + 0.471025i
\(120\) 0 0
\(121\) 5.08674 8.81050i 0.462431 0.800954i
\(122\) 0 0
\(123\) 0.320669 0.185138i 0.0289137 0.0166933i
\(124\) 0 0
\(125\) −5.82932 + 9.54039i −0.521390 + 0.853318i
\(126\) 0 0
\(127\) −1.34956 −0.119754 −0.0598772 0.998206i \(-0.519071\pi\)
−0.0598772 + 0.998206i \(0.519071\pi\)
\(128\) 0 0
\(129\) −16.3090 + 9.41598i −1.43592 + 0.829031i
\(130\) 0 0
\(131\) 7.08950 + 4.09312i 0.619412 + 0.357618i 0.776640 0.629944i \(-0.216922\pi\)
−0.157228 + 0.987562i \(0.550256\pi\)
\(132\) 0 0
\(133\) −1.97689 + 2.19240i −0.171418 + 0.190105i
\(134\) 0 0
\(135\) −0.779044 + 4.21353i −0.0670494 + 0.362643i
\(136\) 0 0
\(137\) −4.43159 + 2.55858i −0.378616 + 0.218594i −0.677216 0.735784i \(-0.736814\pi\)
0.298600 + 0.954378i \(0.403480\pi\)
\(138\) 0 0
\(139\) 17.9166i 1.51967i 0.650117 + 0.759834i \(0.274720\pi\)
−0.650117 + 0.759834i \(0.725280\pi\)
\(140\) 0 0
\(141\) 22.4491i 1.89056i
\(142\) 0 0
\(143\) −4.45903 + 2.57442i −0.372883 + 0.215284i
\(144\) 0 0
\(145\) 13.6647 + 2.52649i 1.13479 + 0.209813i
\(146\) 0 0
\(147\) 1.63883 + 15.8102i 0.135168 + 1.30400i
\(148\) 0 0
\(149\) −6.16993 3.56221i −0.505460 0.291827i 0.225505 0.974242i \(-0.427597\pi\)
−0.730965 + 0.682414i \(0.760930\pi\)
\(150\) 0 0
\(151\) −2.46560 + 1.42352i −0.200648 + 0.115844i −0.596958 0.802273i \(-0.703624\pi\)
0.396310 + 0.918117i \(0.370291\pi\)
\(152\) 0 0
\(153\) −13.5803 −1.09790
\(154\) 0 0
\(155\) 5.98162 2.12112i 0.480455 0.170372i
\(156\) 0 0
\(157\) −11.4030 + 6.58353i −0.910059 + 0.525423i −0.880450 0.474139i \(-0.842760\pi\)
−0.0296091 + 0.999562i \(0.509426\pi\)
\(158\) 0 0
\(159\) −5.82447 + 10.0883i −0.461911 + 0.800053i
\(160\) 0 0
\(161\) −4.49996 4.05762i −0.354647 0.319785i
\(162\) 0 0
\(163\) 14.9075 + 8.60684i 1.16764 + 0.674139i 0.953124 0.302580i \(-0.0978480\pi\)
0.214520 + 0.976720i \(0.431181\pi\)
\(164\) 0 0
\(165\) −3.51137 2.99636i −0.273360 0.233266i
\(166\) 0 0
\(167\) 0.285811i 0.0221167i 0.999939 + 0.0110584i \(0.00352006\pi\)
−0.999939 + 0.0110584i \(0.996480\pi\)
\(168\) 0 0
\(169\) −19.0752 −1.46732
\(170\) 0 0
\(171\) −2.08341 + 1.20285i −0.159322 + 0.0919846i
\(172\) 0 0
\(173\) 16.6842 + 9.63264i 1.26848 + 0.732356i 0.974700 0.223518i \(-0.0717541\pi\)
0.293778 + 0.955874i \(0.405087\pi\)
\(174\) 0 0
\(175\) 7.20323 11.0956i 0.544513 0.838752i
\(176\) 0 0
\(177\) 22.6563 + 13.0806i 1.70295 + 0.983200i
\(178\) 0 0
\(179\) −0.701703 1.21539i −0.0524478 0.0908422i 0.838610 0.544733i \(-0.183369\pi\)
−0.891057 + 0.453891i \(0.850036\pi\)
\(180\) 0 0
\(181\) −15.3818 −1.14332 −0.571660 0.820491i \(-0.693700\pi\)
−0.571660 + 0.820491i \(0.693700\pi\)
\(182\) 0 0
\(183\) −4.43794 −0.328062
\(184\) 0 0
\(185\) 2.68617 + 2.29219i 0.197491 + 0.168525i
\(186\) 0 0
\(187\) −2.86312 + 4.95908i −0.209372 + 0.362644i
\(188\) 0 0
\(189\) 1.05767 4.95847i 0.0769339 0.360675i
\(190\) 0 0
\(191\) −19.4587 11.2345i −1.40798 0.812898i −0.412787 0.910828i \(-0.635444\pi\)
−0.995193 + 0.0979302i \(0.968778\pi\)
\(192\) 0 0
\(193\) 14.3435 8.28125i 1.03247 0.596097i 0.114779 0.993391i \(-0.463384\pi\)
0.917691 + 0.397294i \(0.130051\pi\)
\(194\) 0 0
\(195\) −9.61071 27.1025i −0.688237 1.94085i
\(196\) 0 0
\(197\) −16.1344 −1.14953 −0.574765 0.818318i \(-0.694907\pi\)
−0.574765 + 0.818318i \(0.694907\pi\)
\(198\) 0 0
\(199\) −10.9134 18.9025i −0.773629 1.33996i −0.935562 0.353163i \(-0.885106\pi\)
0.161933 0.986802i \(-0.448227\pi\)
\(200\) 0 0
\(201\) −13.8393 7.99012i −0.976149 0.563580i
\(202\) 0 0
\(203\) −16.0806 3.43008i −1.12864 0.240744i
\(204\) 0 0
\(205\) 0.358552 + 0.0662930i 0.0250423 + 0.00463011i
\(206\) 0 0
\(207\) −2.46889 4.27624i −0.171600 0.297219i
\(208\) 0 0
\(209\) 1.01439i 0.0701665i
\(210\) 0 0
\(211\) 9.76612 0.672328 0.336164 0.941804i \(-0.390870\pi\)
0.336164 + 0.941804i \(0.390870\pi\)
\(212\) 0 0
\(213\) 1.59578 0.921325i 0.109341 0.0631282i
\(214\) 0 0
\(215\) −18.2357 3.37161i −1.24366 0.229942i
\(216\) 0 0
\(217\) −7.14348 + 2.31540i −0.484931 + 0.157180i
\(218\) 0 0
\(219\) −10.3097 + 17.8569i −0.696664 + 1.20666i
\(220\) 0 0
\(221\) −30.8930 + 17.8361i −2.07809 + 1.19978i
\(222\) 0 0
\(223\) 17.6951i 1.18495i 0.805589 + 0.592474i \(0.201849\pi\)
−0.805589 + 0.592474i \(0.798151\pi\)
\(224\) 0 0
\(225\) 8.37207 6.79159i 0.558138 0.452772i
\(226\) 0 0
\(227\) −8.76537 15.1821i −0.581778 1.00767i −0.995269 0.0971611i \(-0.969024\pi\)
0.413490 0.910509i \(-0.364310\pi\)
\(228\) 0 0
\(229\) 3.45967 5.99232i 0.228621 0.395984i −0.728778 0.684750i \(-0.759912\pi\)
0.957400 + 0.288766i \(0.0932449\pi\)
\(230\) 0 0
\(231\) 4.05627 + 3.65755i 0.266883 + 0.240649i
\(232\) 0 0
\(233\) −3.78953 2.18788i −0.248260 0.143333i 0.370707 0.928750i \(-0.379115\pi\)
−0.618967 + 0.785417i \(0.712449\pi\)
\(234\) 0 0
\(235\) 14.3499 16.8163i 0.936084 1.09698i
\(236\) 0 0
\(237\) 25.7540i 1.67291i
\(238\) 0 0
\(239\) 14.1535i 0.915511i 0.889078 + 0.457756i \(0.151347\pi\)
−0.889078 + 0.457756i \(0.848653\pi\)
\(240\) 0 0
\(241\) 13.4126 7.74379i 0.863984 0.498821i −0.00136057 0.999999i \(-0.500433\pi\)
0.865344 + 0.501178i \(0.167100\pi\)
\(242\) 0 0
\(243\) 9.40956 16.2978i 0.603624 1.04551i
\(244\) 0 0
\(245\) −8.87855 + 12.8907i −0.567229 + 0.823560i
\(246\) 0 0
\(247\) −3.15960 + 5.47259i −0.201041 + 0.348213i
\(248\) 0 0
\(249\) 8.86526 + 15.3551i 0.561813 + 0.973088i
\(250\) 0 0
\(251\) 6.13020i 0.386935i −0.981107 0.193467i \(-0.938027\pi\)
0.981107 0.193467i \(-0.0619734\pi\)
\(252\) 0 0
\(253\) −2.08205 −0.130898
\(254\) 0 0
\(255\) −24.3274 20.7594i −1.52344 1.30000i
\(256\) 0 0
\(257\) 3.21050 5.56075i 0.200266 0.346870i −0.748348 0.663306i \(-0.769153\pi\)
0.948614 + 0.316436i \(0.102486\pi\)
\(258\) 0 0
\(259\) −3.10302 2.79800i −0.192812 0.173859i
\(260\) 0 0
\(261\) −11.6041 6.69962i −0.718275 0.414696i
\(262\) 0 0
\(263\) 3.23009 + 5.59468i 0.199176 + 0.344983i 0.948261 0.317491i \(-0.102840\pi\)
−0.749086 + 0.662473i \(0.769507\pi\)
\(264\) 0 0
\(265\) −10.8116 + 3.83387i −0.664154 + 0.235513i
\(266\) 0 0
\(267\) 32.5399i 1.99141i
\(268\) 0 0
\(269\) −0.755340 1.30829i −0.0460539 0.0797677i 0.842080 0.539353i \(-0.181331\pi\)
−0.888133 + 0.459586i \(0.847998\pi\)
\(270\) 0 0
\(271\) 8.66274 15.0043i 0.526224 0.911447i −0.473309 0.880896i \(-0.656941\pi\)
0.999533 0.0305504i \(-0.00972602\pi\)
\(272\) 0 0
\(273\) 10.4910 + 32.3669i 0.634945 + 1.95893i
\(274\) 0 0
\(275\) −0.714984 4.48906i −0.0431152 0.270701i
\(276\) 0 0
\(277\) 5.77685 + 10.0058i 0.347097 + 0.601190i 0.985733 0.168319i \(-0.0538340\pi\)
−0.638635 + 0.769510i \(0.720501\pi\)
\(278\) 0 0
\(279\) −6.11954 −0.366368
\(280\) 0 0
\(281\) 16.6526 0.993408 0.496704 0.867920i \(-0.334543\pi\)
0.496704 + 0.867920i \(0.334543\pi\)
\(282\) 0 0
\(283\) 11.3769 + 19.7053i 0.676285 + 1.17136i 0.976091 + 0.217360i \(0.0697447\pi\)
−0.299806 + 0.954000i \(0.596922\pi\)
\(284\) 0 0
\(285\) −5.57088 1.03001i −0.329990 0.0610123i
\(286\) 0 0
\(287\) −0.421942 0.0900025i −0.0249065 0.00531268i
\(288\) 0 0
\(289\) −11.3363 + 19.6350i −0.666839 + 1.15500i
\(290\) 0 0
\(291\) 11.3509 + 19.6604i 0.665404 + 1.15251i
\(292\) 0 0
\(293\) 8.66311i 0.506104i −0.967453 0.253052i \(-0.918566\pi\)
0.967453 0.253052i \(-0.0814344\pi\)
\(294\) 0 0
\(295\) 8.61013 + 24.2808i 0.501301 + 1.41368i
\(296\) 0 0
\(297\) −0.871075 1.50875i −0.0505449 0.0875463i
\(298\) 0 0
\(299\) −11.2326 6.48516i −0.649600 0.375047i
\(300\) 0 0
\(301\) 21.4597 + 4.57746i 1.23691 + 0.263840i
\(302\) 0 0
\(303\) 19.7385 34.1880i 1.13395 1.96405i
\(304\) 0 0
\(305\) −3.32439 2.83681i −0.190354 0.162435i
\(306\) 0 0
\(307\) −11.6862 −0.666967 −0.333484 0.942756i \(-0.608224\pi\)
−0.333484 + 0.942756i \(0.608224\pi\)
\(308\) 0 0
\(309\) 4.10608i 0.233587i
\(310\) 0 0
\(311\) 5.66670 + 9.81500i 0.321329 + 0.556558i 0.980762 0.195205i \(-0.0625372\pi\)
−0.659434 + 0.751763i \(0.729204\pi\)
\(312\) 0 0
\(313\) −12.7012 + 21.9992i −0.717916 + 1.24347i 0.243908 + 0.969798i \(0.421570\pi\)
−0.961824 + 0.273668i \(0.911763\pi\)
\(314\) 0 0
\(315\) −10.1219 + 7.76222i −0.570302 + 0.437352i
\(316\) 0 0
\(317\) 11.9131 20.6342i 0.669109 1.15893i −0.309045 0.951048i \(-0.600009\pi\)
0.978154 0.207883i \(-0.0666574\pi\)
\(318\) 0 0
\(319\) −4.89295 + 2.82495i −0.273953 + 0.158167i
\(320\) 0 0
\(321\) 8.09033i 0.451558i
\(322\) 0 0
\(323\) 7.02785i 0.391040i
\(324\) 0 0
\(325\) 10.1252 26.4454i 0.561643 1.46693i
\(326\) 0 0
\(327\) −3.92710 2.26731i −0.217169 0.125383i
\(328\) 0 0
\(329\) −17.5164 + 19.4259i −0.965711 + 1.07099i
\(330\) 0 0
\(331\) 2.35173 4.07331i 0.129263 0.223889i −0.794129 0.607750i \(-0.792072\pi\)
0.923391 + 0.383861i \(0.125406\pi\)
\(332\) 0 0
\(333\) −1.70246 2.94875i −0.0932943 0.161590i
\(334\) 0 0
\(335\) −5.25938 14.8316i −0.287351 0.810337i
\(336\) 0 0
\(337\) 10.0355i 0.546669i −0.961919 0.273335i \(-0.911873\pi\)
0.961919 0.273335i \(-0.0881267\pi\)
\(338\) 0 0
\(339\) −26.5969 + 15.3557i −1.44455 + 0.834009i
\(340\) 0 0
\(341\) −1.29018 + 2.23465i −0.0698670 + 0.121013i
\(342\) 0 0
\(343\) 10.9181 14.9598i 0.589522 0.807752i
\(344\) 0 0
\(345\) 2.11411 11.4344i 0.113820 0.615606i
\(346\) 0 0
\(347\) −6.86288 + 3.96228i −0.368418 + 0.212706i −0.672767 0.739854i \(-0.734894\pi\)
0.304349 + 0.952561i \(0.401561\pi\)
\(348\) 0 0
\(349\) −6.06729 −0.324775 −0.162387 0.986727i \(-0.551919\pi\)
−0.162387 + 0.986727i \(0.551919\pi\)
\(350\) 0 0
\(351\) 10.8529i 0.579283i
\(352\) 0 0
\(353\) 17.3298 + 30.0161i 0.922371 + 1.59759i 0.795735 + 0.605644i \(0.207085\pi\)
0.126636 + 0.991949i \(0.459582\pi\)
\(354\) 0 0
\(355\) 1.78430 + 0.329902i 0.0947010 + 0.0175094i
\(356\) 0 0
\(357\) 28.1026 + 25.3402i 1.48735 + 1.34115i
\(358\) 0 0
\(359\) 4.46664 + 2.57881i 0.235740 + 0.136105i 0.613217 0.789914i \(-0.289875\pi\)
−0.377477 + 0.926019i \(0.623208\pi\)
\(360\) 0 0
\(361\) −8.87752 15.3763i −0.467238 0.809280i
\(362\) 0 0
\(363\) −23.1009 −1.21248
\(364\) 0 0
\(365\) −19.1373 + 6.78619i −1.00169 + 0.355206i
\(366\) 0 0
\(367\) 12.5217 7.22938i 0.653625 0.377371i −0.136218 0.990679i \(-0.543495\pi\)
0.789844 + 0.613308i \(0.210162\pi\)
\(368\) 0 0
\(369\) −0.304482 0.175793i −0.0158507 0.00915141i
\(370\) 0 0
\(371\) 12.9117 4.18504i 0.670341 0.217276i
\(372\) 0 0
\(373\) −3.13591 + 5.43156i −0.162372 + 0.281236i −0.935719 0.352747i \(-0.885248\pi\)
0.773347 + 0.633983i \(0.218581\pi\)
\(374\) 0 0
\(375\) 25.3793 + 0.631584i 1.31058 + 0.0326148i
\(376\) 0 0
\(377\) −35.1965 −1.81271
\(378\) 0 0
\(379\) 24.4959 1.25827 0.629135 0.777296i \(-0.283409\pi\)
0.629135 + 0.777296i \(0.283409\pi\)
\(380\) 0 0
\(381\) 1.53223 + 2.65390i 0.0784984 + 0.135963i
\(382\) 0 0
\(383\) −7.48398 4.32088i −0.382413 0.220786i 0.296454 0.955047i \(-0.404196\pi\)
−0.678868 + 0.734261i \(0.737529\pi\)
\(384\) 0 0
\(385\) 0.700523 + 5.33266i 0.0357019 + 0.271778i
\(386\) 0 0
\(387\) 15.4857 + 8.94069i 0.787184 + 0.454481i
\(388\) 0 0
\(389\) −8.34342 + 4.81708i −0.423028 + 0.244235i −0.696372 0.717681i \(-0.745204\pi\)
0.273344 + 0.961916i \(0.411870\pi\)
\(390\) 0 0
\(391\) −14.4249 −0.729496
\(392\) 0 0
\(393\) 18.5885i 0.937667i
\(394\) 0 0
\(395\) 16.4625 19.2920i 0.828316 0.970685i
\(396\) 0 0
\(397\) 13.5336 + 7.81361i 0.679230 + 0.392154i 0.799565 0.600580i \(-0.205063\pi\)
−0.120335 + 0.992733i \(0.538397\pi\)
\(398\) 0 0
\(399\) 6.55579 + 1.39838i 0.328200 + 0.0700068i
\(400\) 0 0
\(401\) −13.4230 + 23.2493i −0.670311 + 1.16101i 0.307505 + 0.951546i \(0.400506\pi\)
−0.977816 + 0.209466i \(0.932827\pi\)
\(402\) 0 0
\(403\) −13.9209 + 8.03726i −0.693452 + 0.400365i
\(404\) 0 0
\(405\) 22.8021 8.08575i 1.13304 0.401784i
\(406\) 0 0
\(407\) −1.43571 −0.0711656
\(408\) 0 0
\(409\) 9.54259 5.50941i 0.471850 0.272423i −0.245164 0.969482i \(-0.578842\pi\)
0.717014 + 0.697059i \(0.245508\pi\)
\(410\) 0 0
\(411\) 10.0628 + 5.80976i 0.496362 + 0.286574i
\(412\) 0 0
\(413\) −9.39878 28.9971i −0.462484 1.42686i
\(414\) 0 0
\(415\) −3.17441 + 17.1691i −0.155826 + 0.842797i
\(416\) 0 0
\(417\) 35.2327 20.3416i 1.72536 0.996134i
\(418\) 0 0
\(419\) 5.97226i 0.291764i 0.989302 + 0.145882i \(0.0466020\pi\)
−0.989302 + 0.145882i \(0.953398\pi\)
\(420\) 0 0
\(421\) 20.0534i 0.977344i −0.872468 0.488672i \(-0.837482\pi\)
0.872468 0.488672i \(-0.162518\pi\)
\(422\) 0 0
\(423\) −18.4602 + 10.6580i −0.897564 + 0.518209i
\(424\) 0 0
\(425\) −4.95354 31.1010i −0.240282 1.50862i
\(426\) 0 0
\(427\) 3.84028 + 3.46279i 0.185844 + 0.167576i
\(428\) 0 0
\(429\) 10.1251 + 5.84574i 0.488845 + 0.282235i
\(430\) 0 0
\(431\) −21.7452 + 12.5546i −1.04743 + 0.604734i −0.921929 0.387359i \(-0.873387\pi\)
−0.125501 + 0.992093i \(0.540054\pi\)
\(432\) 0 0
\(433\) 15.4250 0.741276 0.370638 0.928777i \(-0.379139\pi\)
0.370638 + 0.928777i \(0.379139\pi\)
\(434\) 0 0
\(435\) −10.5460 29.7399i −0.505640 1.42592i
\(436\) 0 0
\(437\) −2.21297 + 1.27766i −0.105861 + 0.0611186i
\(438\) 0 0
\(439\) 8.54597 14.8021i 0.407877 0.706464i −0.586775 0.809750i \(-0.699603\pi\)
0.994652 + 0.103287i \(0.0329359\pi\)
\(440\) 0 0
\(441\) 12.2228 8.85369i 0.582040 0.421605i
\(442\) 0 0
\(443\) 34.3644 + 19.8403i 1.63270 + 0.942640i 0.983256 + 0.182231i \(0.0583320\pi\)
0.649445 + 0.760409i \(0.275001\pi\)
\(444\) 0 0
\(445\) 20.8001 24.3752i 0.986019 1.15549i
\(446\) 0 0
\(447\) 16.1774i 0.765166i
\(448\) 0 0
\(449\) −7.32288 −0.345588 −0.172794 0.984958i \(-0.555279\pi\)
−0.172794 + 0.984958i \(0.555279\pi\)
\(450\) 0 0
\(451\) −0.128387 + 0.0741244i −0.00604552 + 0.00349038i
\(452\) 0 0
\(453\) 5.59865 + 3.23238i 0.263048 + 0.151871i
\(454\) 0 0
\(455\) −12.8308 + 30.9516i −0.601519 + 1.45103i
\(456\) 0 0
\(457\) −21.0598 12.1589i −0.985137 0.568769i −0.0813202 0.996688i \(-0.525914\pi\)
−0.903817 + 0.427919i \(0.859247\pi\)
\(458\) 0 0
\(459\) −6.03497 10.4529i −0.281688 0.487898i
\(460\) 0 0
\(461\) 16.3772 0.762764 0.381382 0.924417i \(-0.375448\pi\)
0.381382 + 0.924417i \(0.375448\pi\)
\(462\) 0 0
\(463\) −1.64446 −0.0764246 −0.0382123 0.999270i \(-0.512166\pi\)
−0.0382123 + 0.999270i \(0.512166\pi\)
\(464\) 0 0
\(465\) −10.9624 9.35455i −0.508368 0.433807i
\(466\) 0 0
\(467\) 7.96501 13.7958i 0.368577 0.638393i −0.620767 0.783995i \(-0.713179\pi\)
0.989343 + 0.145602i \(0.0465119\pi\)
\(468\) 0 0
\(469\) 5.74112 + 17.7125i 0.265100 + 0.817887i
\(470\) 0 0
\(471\) 25.8928 + 14.9492i 1.19308 + 0.688824i
\(472\) 0 0
\(473\) 6.52967 3.76991i 0.300235 0.173341i
\(474\) 0 0
\(475\) −3.51466 4.33257i −0.161264 0.198792i
\(476\) 0 0
\(477\) 11.0609 0.506445
\(478\) 0 0
\(479\) 13.4844 + 23.3556i 0.616116 + 1.06714i 0.990188 + 0.139745i \(0.0446282\pi\)
−0.374071 + 0.927400i \(0.622038\pi\)
\(480\) 0 0
\(481\) −7.74563 4.47194i −0.353170 0.203903i
\(482\) 0 0
\(483\) −2.87022 + 13.4559i −0.130599 + 0.612266i
\(484\) 0 0
\(485\) −4.06447 + 21.9830i −0.184558 + 0.998198i
\(486\) 0 0
\(487\) −6.04240 10.4658i −0.273808 0.474249i 0.696026 0.718017i \(-0.254950\pi\)
−0.969834 + 0.243768i \(0.921616\pi\)
\(488\) 0 0
\(489\) 39.0871i 1.76758i
\(490\) 0 0
\(491\) −18.7339 −0.845450 −0.422725 0.906258i \(-0.638926\pi\)
−0.422725 + 0.906258i \(0.638926\pi\)
\(492\) 0 0
\(493\) −33.8993 + 19.5718i −1.52675 + 0.881468i
\(494\) 0 0
\(495\) −0.796879 + 4.30999i −0.0358171 + 0.193720i
\(496\) 0 0
\(497\) −2.09976 0.447890i −0.0941872 0.0200906i
\(498\) 0 0
\(499\) −12.4806 + 21.6171i −0.558710 + 0.967714i 0.438895 + 0.898539i \(0.355370\pi\)
−0.997605 + 0.0691754i \(0.977963\pi\)
\(500\) 0 0
\(501\) 0.562043 0.324496i 0.0251102 0.0144974i
\(502\) 0 0
\(503\) 13.3328i 0.594481i −0.954803 0.297241i \(-0.903934\pi\)
0.954803 0.297241i \(-0.0960663\pi\)
\(504\) 0 0
\(505\) 36.6394 12.9926i 1.63043 0.578161i
\(506\) 0 0
\(507\) 21.6570 + 37.5110i 0.961821 + 1.66592i
\(508\) 0 0
\(509\) −3.32935 + 5.76661i −0.147571 + 0.255600i −0.930329 0.366726i \(-0.880479\pi\)
0.782758 + 0.622326i \(0.213812\pi\)
\(510\) 0 0
\(511\) 22.8545 7.40778i 1.01102 0.327701i
\(512\) 0 0
\(513\) −1.85169 1.06907i −0.0817542 0.0472008i
\(514\) 0 0
\(515\) −2.62468 + 3.07580i −0.115657 + 0.135536i
\(516\) 0 0
\(517\) 8.98804i 0.395294i
\(518\) 0 0
\(519\) 43.7457i 1.92022i
\(520\) 0 0
\(521\) 6.14654 3.54871i 0.269285 0.155472i −0.359278 0.933231i \(-0.616977\pi\)
0.628563 + 0.777759i \(0.283644\pi\)
\(522\) 0 0
\(523\) 8.40071 14.5505i 0.367337 0.636247i −0.621811 0.783167i \(-0.713603\pi\)
0.989148 + 0.146920i \(0.0469361\pi\)
\(524\) 0 0
\(525\) −29.9976 1.56759i −1.30920 0.0684155i
\(526\) 0 0
\(527\) −8.93858 + 15.4821i −0.389371 + 0.674410i
\(528\) 0 0
\(529\) 8.87758 + 15.3764i 0.385982 + 0.668540i
\(530\) 0 0
\(531\) 24.8407i 1.07800i
\(532\) 0 0
\(533\) −0.923529 −0.0400025
\(534\) 0 0
\(535\) 5.17148 6.06034i 0.223583 0.262012i
\(536\) 0 0
\(537\) −1.59336 + 2.75978i −0.0687585 + 0.119093i
\(538\) 0 0
\(539\) −0.656142 6.32998i −0.0282621 0.272652i
\(540\) 0 0
\(541\) 14.2808 + 8.24501i 0.613979 + 0.354481i 0.774521 0.632548i \(-0.217991\pi\)
−0.160542 + 0.987029i \(0.551324\pi\)
\(542\) 0 0
\(543\) 17.4637 + 30.2481i 0.749441 + 1.29807i
\(544\) 0 0
\(545\) −1.49243 4.20869i −0.0639285 0.180280i
\(546\) 0 0
\(547\) 4.86184i 0.207877i 0.994584 + 0.103939i \(0.0331446\pi\)
−0.994584 + 0.103939i \(0.966855\pi\)
\(548\) 0 0
\(549\) 2.10696 + 3.64936i 0.0899229 + 0.155751i
\(550\) 0 0
\(551\) −3.46707 + 6.00515i −0.147702 + 0.255828i
\(552\) 0 0
\(553\) −20.0951 + 22.2858i −0.854532 + 0.947688i
\(554\) 0 0
\(555\) 1.45782 7.88475i 0.0618810 0.334689i
\(556\) 0 0
\(557\) 11.4750 + 19.8753i 0.486211 + 0.842142i 0.999874 0.0158495i \(-0.00504525\pi\)
−0.513663 + 0.857992i \(0.671712\pi\)
\(558\) 0 0
\(559\) 46.9699 1.98662
\(560\) 0 0
\(561\) 13.0026 0.548970
\(562\) 0 0
\(563\) 7.57987 + 13.1287i 0.319453 + 0.553309i 0.980374 0.197146i \(-0.0631674\pi\)
−0.660921 + 0.750456i \(0.729834\pi\)
\(564\) 0 0
\(565\) −29.7390 5.49848i −1.25113 0.231323i
\(566\) 0 0
\(567\) −27.2311 + 8.82638i −1.14360 + 0.370673i
\(568\) 0 0
\(569\) 0.815340 1.41221i 0.0341808 0.0592030i −0.848429 0.529309i \(-0.822451\pi\)
0.882610 + 0.470106i \(0.155784\pi\)
\(570\) 0 0
\(571\) −17.5826 30.4540i −0.735811 1.27446i −0.954367 0.298637i \(-0.903468\pi\)
0.218556 0.975824i \(-0.429865\pi\)
\(572\) 0 0
\(573\) 51.0202i 2.13140i
\(574\) 0 0
\(575\) 8.89271 7.21394i 0.370852 0.300842i
\(576\) 0 0
\(577\) 7.78749 + 13.4883i 0.324198 + 0.561527i 0.981350 0.192231i \(-0.0615724\pi\)
−0.657152 + 0.753758i \(0.728239\pi\)
\(578\) 0 0
\(579\) −32.5699 18.8042i −1.35356 0.781477i
\(580\) 0 0
\(581\) 4.30973 20.2045i 0.178798 0.838225i
\(582\) 0 0
\(583\) 2.33196 4.03908i 0.0965801 0.167282i
\(584\) 0 0
\(585\) −17.7239 + 20.7702i −0.732792 + 0.858742i
\(586\) 0 0
\(587\) −17.6761 −0.729572 −0.364786 0.931091i \(-0.618858\pi\)
−0.364786 + 0.931091i \(0.618858\pi\)
\(588\) 0 0
\(589\) 3.16688i 0.130489i
\(590\) 0 0
\(591\) 18.3182 + 31.7281i 0.753511 + 1.30512i
\(592\) 0 0
\(593\) 4.15344 7.19397i 0.170561 0.295421i −0.768055 0.640384i \(-0.778775\pi\)
0.938616 + 0.344963i \(0.112109\pi\)
\(594\) 0 0
\(595\) 4.85335 + 36.9457i 0.198968 + 1.51463i
\(596\) 0 0
\(597\) −24.7810 + 42.9220i −1.01422 + 1.75668i
\(598\) 0 0
\(599\) 1.64713 0.950974i 0.0673001 0.0388557i −0.465972 0.884799i \(-0.654295\pi\)
0.533272 + 0.845944i \(0.320962\pi\)
\(600\) 0 0
\(601\) 3.61199i 0.147336i −0.997283 0.0736680i \(-0.976529\pi\)
0.997283 0.0736680i \(-0.0234705\pi\)
\(602\) 0 0
\(603\) 15.1736i 0.617917i
\(604\) 0 0
\(605\) −17.3046 14.7665i −0.703531 0.600345i
\(606\) 0 0
\(607\) −23.1622 13.3727i −0.940124 0.542781i −0.0501251 0.998743i \(-0.515962\pi\)
−0.889999 + 0.455962i \(0.849295\pi\)
\(608\) 0 0
\(609\) 11.5119 + 35.5166i 0.466487 + 1.43921i
\(610\) 0 0
\(611\) −27.9959 + 48.4903i −1.13259 + 1.96171i
\(612\) 0 0
\(613\) −4.16951 7.22180i −0.168405 0.291686i 0.769454 0.638702i \(-0.220528\pi\)
−0.937859 + 0.347016i \(0.887195\pi\)
\(614\) 0 0
\(615\) −0.276718 0.780352i −0.0111583 0.0314668i
\(616\) 0 0
\(617\) 24.3929i 0.982021i −0.871154 0.491011i \(-0.836628\pi\)
0.871154 0.491011i \(-0.163372\pi\)
\(618\) 0 0
\(619\) 35.5991 20.5532i 1.43085 0.826102i 0.433664 0.901075i \(-0.357220\pi\)
0.997186 + 0.0749730i \(0.0238870\pi\)
\(620\) 0 0
\(621\) 2.19430 3.80064i 0.0880543 0.152515i
\(622\) 0 0
\(623\) −25.3899 + 28.1578i −1.01723 + 1.12812i
\(624\) 0 0
\(625\) 18.6076 + 16.6961i 0.744303 + 0.667842i
\(626\) 0 0
\(627\) 1.99477 1.15168i 0.0796636 0.0459938i
\(628\) 0 0
\(629\) −9.94688 −0.396608
\(630\) 0 0
\(631\) 35.0578i 1.39563i −0.716279 0.697814i \(-0.754156\pi\)
0.716279 0.697814i \(-0.245844\pi\)
\(632\) 0 0
\(633\) −11.0880 19.2049i −0.440707 0.763327i
\(634\) 0 0
\(635\) −0.548650 + 2.96742i −0.0217725 + 0.117759i
\(636\) 0 0
\(637\) 16.1767 36.1939i 0.640945 1.43405i
\(638\) 0 0
\(639\) −1.51523 0.874819i −0.0599416 0.0346073i
\(640\) 0 0
\(641\) −3.51329 6.08519i −0.138766 0.240351i 0.788264 0.615338i \(-0.210980\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(642\) 0 0
\(643\) −4.42331 −0.174438 −0.0872191 0.996189i \(-0.527798\pi\)
−0.0872191 + 0.996189i \(0.527798\pi\)
\(644\) 0 0
\(645\) 14.0736 + 39.6881i 0.554149 + 1.56272i
\(646\) 0 0
\(647\) 0.327418 0.189035i 0.0128721 0.00743172i −0.493550 0.869717i \(-0.664301\pi\)
0.506422 + 0.862286i \(0.330968\pi\)
\(648\) 0 0
\(649\) −9.07099 5.23714i −0.356067 0.205576i
\(650\) 0 0
\(651\) 12.6636 + 11.4188i 0.496324 + 0.447536i
\(652\) 0 0
\(653\) 22.4109 38.8168i 0.877005 1.51902i 0.0223938 0.999749i \(-0.492871\pi\)
0.854611 0.519268i \(-0.173795\pi\)
\(654\) 0 0
\(655\) 11.8821 13.9244i 0.464273 0.544071i
\(656\) 0 0
\(657\) 19.5786 0.763832
\(658\) 0 0
\(659\) 24.4018 0.950557 0.475279 0.879835i \(-0.342347\pi\)
0.475279 + 0.879835i \(0.342347\pi\)
\(660\) 0 0
\(661\) 14.4940 + 25.1043i 0.563751 + 0.976445i 0.997165 + 0.0752499i \(0.0239754\pi\)
−0.433414 + 0.901195i \(0.642691\pi\)
\(662\) 0 0
\(663\) 70.1487 + 40.5004i 2.72435 + 1.57290i
\(664\) 0 0
\(665\) 4.01697 + 5.23809i 0.155771 + 0.203124i
\(666\) 0 0
\(667\) −12.3257 7.11626i −0.477254 0.275543i
\(668\) 0 0
\(669\) 34.7971 20.0901i 1.34533 0.776728i
\(670\) 0 0
\(671\) 1.77683 0.0685938
\(672\) 0 0
\(673\) 1.93910i 0.0747467i −0.999301 0.0373733i \(-0.988101\pi\)
0.999301 0.0373733i \(-0.0118991\pi\)
\(674\) 0 0
\(675\) 8.94800 + 3.42593i 0.344409 + 0.131864i
\(676\) 0 0
\(677\) −36.9976 21.3606i −1.42193 0.820954i −0.425470 0.904972i \(-0.639891\pi\)
−0.996464 + 0.0840182i \(0.973225\pi\)
\(678\) 0 0
\(679\) 5.51811 25.8695i 0.211766 0.992782i
\(680\) 0 0
\(681\) −19.9035 + 34.4739i −0.762705 + 1.32104i
\(682\) 0 0
\(683\) 32.6952 18.8766i 1.25105 0.722293i 0.279730 0.960079i \(-0.409755\pi\)
0.971318 + 0.237786i \(0.0764217\pi\)
\(684\) 0 0
\(685\) 3.82419 + 10.7843i 0.146115 + 0.412048i
\(686\) 0 0
\(687\) −15.7117 −0.599440
\(688\) 0 0
\(689\) 25.1618 14.5272i 0.958588 0.553441i
\(690\) 0 0
\(691\) −17.4603 10.0807i −0.664220 0.383487i 0.129663 0.991558i \(-0.458610\pi\)
−0.793883 + 0.608071i \(0.791944\pi\)
\(692\) 0 0
\(693\) 1.08188 5.07198i 0.0410972 0.192669i
\(694\) 0 0
\(695\) 39.3951 + 7.28380i 1.49434 + 0.276290i
\(696\) 0 0
\(697\) −0.889491 + 0.513548i −0.0336919 + 0.0194520i
\(698\) 0 0
\(699\) 9.93606i 0.375816i
\(700\) 0 0
\(701\) 20.2036i 0.763080i 0.924352 + 0.381540i \(0.124606\pi\)
−0.924352 + 0.381540i \(0.875394\pi\)
\(702\) 0 0
\(703\) −1.52599 + 0.881028i −0.0575536 + 0.0332286i
\(704\) 0 0
\(705\) −49.3612 9.12645i −1.85905 0.343722i
\(706\) 0 0
\(707\) −43.7562 + 14.1826i −1.64562 + 0.533392i
\(708\) 0 0
\(709\) 11.7495 + 6.78358i 0.441262 + 0.254763i 0.704133 0.710068i \(-0.251336\pi\)
−0.262871 + 0.964831i \(0.584669\pi\)
\(710\) 0 0
\(711\) −21.1778 + 12.2270i −0.794231 + 0.458549i
\(712\) 0 0
\(713\) −6.50010 −0.243431
\(714\) 0 0
\(715\) 3.84787 + 10.8511i 0.143902 + 0.405809i
\(716\) 0 0
\(717\) 27.8326 16.0691i 1.03943 0.600113i
\(718\) 0 0
\(719\) −20.1941 + 34.9772i −0.753113 + 1.30443i 0.193194 + 0.981161i \(0.438115\pi\)
−0.946307 + 0.323270i \(0.895218\pi\)
\(720\) 0 0
\(721\) 3.20385 3.55312i 0.119318 0.132325i
\(722\) 0 0
\(723\) −30.4561 17.5838i −1.13267 0.653950i
\(724\) 0 0
\(725\) 11.1105 29.0189i 0.412633 1.07774i
\(726\) 0 0
\(727\) 7.15590i 0.265397i 0.991156 + 0.132699i \(0.0423643\pi\)
−0.991156 + 0.132699i \(0.957636\pi\)
\(728\) 0 0
\(729\) −10.2739 −0.380516
\(730\) 0 0
\(731\) 45.2388 26.1186i 1.67322 0.966033i
\(732\) 0 0
\(733\) 24.8024 + 14.3197i 0.916097 + 0.528909i 0.882388 0.470523i \(-0.155935\pi\)
0.0337089 + 0.999432i \(0.489268\pi\)
\(734\) 0 0
\(735\) 35.4297 + 2.82400i 1.30684 + 0.104165i
\(736\) 0 0
\(737\) 5.54089 + 3.19903i 0.204101 + 0.117838i
\(738\) 0 0
\(739\) 16.4535 + 28.4983i 0.605252 + 1.04833i 0.992012 + 0.126147i \(0.0402610\pi\)
−0.386760 + 0.922181i \(0.626406\pi\)
\(740\) 0 0
\(741\) 14.3490 0.527124
\(742\) 0 0
\(743\) −22.3184 −0.818782 −0.409391 0.912359i \(-0.634259\pi\)
−0.409391 + 0.912359i \(0.634259\pi\)
\(744\) 0 0
\(745\) −10.3409 + 12.1183i −0.378861 + 0.443979i
\(746\) 0 0
\(747\) 8.41776 14.5800i 0.307990 0.533454i
\(748\) 0 0
\(749\) −6.31264 + 7.00081i −0.230659 + 0.255804i
\(750\) 0 0
\(751\) −39.6036 22.8651i −1.44516 0.834361i −0.446968 0.894550i \(-0.647496\pi\)
−0.998187 + 0.0601891i \(0.980830\pi\)
\(752\) 0 0
\(753\) −12.0549 + 6.95993i −0.439307 + 0.253634i
\(754\) 0 0
\(755\) 2.12767 + 6.00009i 0.0774338 + 0.218366i
\(756\) 0 0
\(757\) 28.8916 1.05008 0.525042 0.851076i \(-0.324050\pi\)
0.525042 + 0.851076i \(0.324050\pi\)
\(758\) 0 0
\(759\) 2.36386 + 4.09432i 0.0858027 + 0.148615i
\(760\) 0 0
\(761\) 27.9186 + 16.1188i 1.01205 + 0.584306i 0.911791 0.410655i \(-0.134700\pi\)
0.100258 + 0.994962i \(0.468033\pi\)
\(762\) 0 0
\(763\) 1.62913 + 5.02618i 0.0589783 + 0.181960i
\(764\) 0 0
\(765\) −5.52093 + 29.8604i −0.199610 + 1.07961i
\(766\) 0 0
\(767\) −32.6252 56.5085i −1.17803 2.04040i
\(768\) 0 0
\(769\) 8.89606i 0.320800i −0.987052 0.160400i \(-0.948722\pi\)
0.987052 0.160400i \(-0.0512784\pi\)
\(770\) 0 0
\(771\) −14.5802 −0.525092
\(772\) 0 0
\(773\) 24.6869 14.2530i 0.887925 0.512644i 0.0146619 0.999893i \(-0.495333\pi\)
0.873263 + 0.487249i \(0.161999\pi\)
\(774\) 0 0
\(775\) −2.23216 14.0147i −0.0801815 0.503423i
\(776\) 0 0
\(777\) −1.97920 + 9.27874i −0.0710035 + 0.332873i
\(778\) 0 0
\(779\) −0.0909733 + 0.157570i −0.00325946 + 0.00564554i
\(780\) 0 0
\(781\) −0.638909 + 0.368874i −0.0228620 + 0.0131994i
\(782\) 0 0
\(783\) 11.9090i 0.425593i
\(784\) 0 0
\(785\) 9.84011 + 27.7494i 0.351209 + 0.990419i
\(786\) 0 0
\(787\) −21.7112 37.6050i −0.773922 1.34047i −0.935398 0.353595i \(-0.884959\pi\)
0.161477 0.986877i \(-0.448374\pi\)
\(788\) 0 0
\(789\) 7.33456 12.7038i 0.261117 0.452269i
\(790\) 0 0
\(791\) 34.9968 + 7.46500i 1.24434 + 0.265425i
\(792\) 0 0
\(793\) 9.58597 + 5.53446i 0.340408 + 0.196535i
\(794\) 0 0
\(795\) 19.8142 + 16.9081i 0.702739 + 0.599670i
\(796\) 0 0
\(797\) 11.3329i 0.401432i 0.979649 + 0.200716i \(0.0643268\pi\)
−0.979649 + 0.200716i \(0.935673\pi\)
\(798\) 0 0
\(799\) 62.2708i 2.20298i
\(800\) 0 0
\(801\) −26.7579 + 15.4487i −0.945444 + 0.545853i
\(802\) 0 0
\(803\) 4.12772 7.14942i 0.145664 0.252298i
\(804\) 0 0
\(805\) −10.7513 + 8.24494i −0.378934 + 0.290596i
\(806\) 0 0
\(807\) −1.71515 + 2.97073i −0.0603762 + 0.104575i
\(808\) 0 0
\(809\) −27.3202 47.3199i −0.960526 1.66368i −0.721183 0.692745i \(-0.756401\pi\)
−0.239343 0.970935i \(-0.576932\pi\)
\(810\) 0 0
\(811\) 34.1338i 1.19860i −0.800525 0.599300i \(-0.795446\pi\)
0.800525 0.599300i \(-0.204554\pi\)
\(812\) 0 0
\(813\) −39.3410 −1.37975
\(814\) 0 0
\(815\) 24.9852 29.2796i 0.875193 1.02562i
\(816\) 0 0
\(817\) 4.62683 8.01390i 0.161872 0.280371i
\(818\) 0 0
\(819\) 21.6349 23.9934i 0.755984 0.838398i
\(820\) 0 0
\(821\) −21.4373 12.3768i −0.748168 0.431955i 0.0768637 0.997042i \(-0.475509\pi\)
−0.825032 + 0.565087i \(0.808843\pi\)
\(822\) 0 0
\(823\) −12.2123 21.1523i −0.425694 0.737324i 0.570791 0.821096i \(-0.306637\pi\)
−0.996485 + 0.0837714i \(0.973303\pi\)
\(824\) 0 0
\(825\) −8.01591 + 6.50266i −0.279078 + 0.226394i
\(826\) 0 0
\(827\) 20.7945i 0.723096i 0.932353 + 0.361548i \(0.117752\pi\)
−0.932353 + 0.361548i \(0.882248\pi\)
\(828\) 0 0
\(829\) −21.8195 37.7924i −0.757822 1.31259i −0.943959 0.330062i \(-0.892930\pi\)
0.186137 0.982524i \(-0.440403\pi\)
\(830\) 0 0
\(831\) 13.1175 22.7202i 0.455041 0.788154i
\(832\) 0 0
\(833\) −4.54588 43.8553i −0.157505 1.51950i
\(834\) 0 0
\(835\) 0.628441 + 0.116193i 0.0217481 + 0.00402103i
\(836\) 0 0
\(837\) −2.71947 4.71026i −0.0939986 0.162810i
\(838\) 0 0
\(839\) −25.4129 −0.877351 −0.438675 0.898646i \(-0.644552\pi\)
−0.438675 + 0.898646i \(0.644552\pi\)
\(840\) 0 0
\(841\) −9.62161 −0.331779
\(842\) 0 0
\(843\) −18.9065 32.7470i −0.651174 1.12787i
\(844\) 0 0
\(845\) −7.75479 + 41.9425i −0.266773 + 1.44287i
\(846\) 0 0
\(847\) 19.9900 + 18.0250i 0.686863 + 0.619346i
\(848\) 0 0
\(849\) 25.8335 44.7449i 0.886603 1.53564i
\(850\) 0 0
\(851\) −1.80833 3.13212i −0.0619888 0.107368i
\(852\) 0 0
\(853\) 3.10531i 0.106324i −0.998586 0.0531619i \(-0.983070\pi\)
0.998586 0.0531619i \(-0.0169299\pi\)
\(854\) 0 0
\(855\) 1.79785 + 5.07000i 0.0614853 + 0.173390i
\(856\) 0 0
\(857\) 11.1563 + 19.3233i 0.381093 + 0.660072i 0.991219 0.132233i \(-0.0422146\pi\)
−0.610126 + 0.792304i \(0.708881\pi\)
\(858\) 0 0
\(859\) −18.2253 10.5224i −0.621838 0.359018i 0.155746 0.987797i \(-0.450222\pi\)
−0.777584 + 0.628779i \(0.783555\pi\)
\(860\) 0 0
\(861\) 0.302064 + 0.931928i 0.0102943 + 0.0317600i
\(862\) 0 0
\(863\) 17.4205 30.1732i 0.593001 1.02711i −0.400825 0.916155i \(-0.631277\pi\)
0.993826 0.110953i \(-0.0353902\pi\)
\(864\) 0 0
\(865\) 27.9630 32.7692i 0.950772 1.11419i
\(866\) 0 0
\(867\) 51.4825 1.74844
\(868\) 0 0
\(869\) 10.3112i 0.349785i
\(870\) 0 0
\(871\) 19.9286 + 34.5174i 0.675256 + 1.16958i
\(872\) 0 0
\(873\) 10.7780 18.6680i 0.364779 0.631816i
\(874\) 0 0
\(875\) −21.4687 20.3493i −0.725776 0.687931i
\(876\) 0 0
\(877\) 19.9212 34.5045i 0.672691 1.16513i −0.304448 0.952529i \(-0.598472\pi\)
0.977138 0.212605i \(-0.0681948\pi\)
\(878\) 0 0
\(879\) −17.0359 + 9.83567i −0.574606 + 0.331749i
\(880\) 0 0
\(881\) 32.2170i 1.08542i 0.839921 + 0.542709i \(0.182601\pi\)
−0.839921 + 0.542709i \(0.817399\pi\)
\(882\) 0 0
\(883\) 57.8919i 1.94822i −0.226080 0.974109i \(-0.572591\pi\)
0.226080 0.974109i \(-0.427409\pi\)
\(884\) 0 0
\(885\) 37.9724 44.4989i 1.27643 1.49582i
\(886\) 0 0
\(887\) −7.94580 4.58751i −0.266794 0.154033i 0.360636 0.932707i \(-0.382560\pi\)
−0.627430 + 0.778673i \(0.715893\pi\)
\(888\) 0 0
\(889\) 0.744873 3.49205i 0.0249822 0.117120i
\(890\) 0 0
\(891\) −4.91818 + 8.51854i −0.164765 + 0.285382i
\(892\) 0 0
\(893\) 5.51553 + 9.55319i 0.184570 + 0.319685i
\(894\) 0 0
\(895\) −2.95766 + 1.04880i −0.0988637 + 0.0350577i
\(896\) 0 0
\(897\) 29.4517i 0.983365i
\(898\) 0 0
\(899\) −15.2756 + 8.81940i −0.509471 + 0.294143i
\(900\) 0 0
\(901\) 16.1563 27.9835i 0.538244 0.932266i
\(902\) 0 0
\(903\) −15.3627 47.3971i −0.511240 1.57728i
\(904\) 0 0
\(905\) −6.25330 + 33.8215i −0.207867 + 1.12427i
\(906\) 0 0
\(907\) −9.48163 + 5.47422i −0.314832 + 0.181769i −0.649087 0.760714i \(-0.724849\pi\)
0.334254 + 0.942483i \(0.391516\pi\)
\(908\) 0 0
\(909\) −37.4842 −1.24327
\(910\) 0 0
\(911\) 10.3120i 0.341653i −0.985301 0.170827i \(-0.945356\pi\)
0.985301 0.170827i \(-0.0546438\pi\)
\(912\) 0 0
\(913\) −3.54941 6.14776i −0.117468 0.203461i
\(914\) 0 0
\(915\) −1.80419 + 9.75814i −0.0596448 + 0.322594i
\(916\) 0 0
\(917\) −14.5041 + 16.0852i −0.478967 + 0.531181i
\(918\) 0 0
\(919\) −42.1983 24.3632i −1.39199 0.803669i −0.398459 0.917186i \(-0.630455\pi\)
−0.993536 + 0.113518i \(0.963788\pi\)
\(920\) 0 0
\(921\) 13.2679 + 22.9808i 0.437194 + 0.757242i
\(922\) 0 0
\(923\) −4.59587 −0.151275
\(924\) 0 0
\(925\) 6.13210 4.97448i 0.201622 0.163560i
\(926\) 0 0
\(927\) 3.37647 1.94941i 0.110898 0.0640270i
\(928\) 0 0
\(929\) 30.8399 + 17.8054i 1.01182 + 0.584177i 0.911725 0.410801i \(-0.134751\pi\)
0.100099 + 0.994977i \(0.468084\pi\)
\(930\) 0 0
\(931\) −4.58181 6.32535i −0.150163 0.207305i
\(932\) 0 0
\(933\) 12.8674 22.2869i 0.421259 0.729642i
\(934\) 0 0
\(935\) 9.74005 + 8.31150i 0.318534 + 0.271815i
\(936\) 0 0
\(937\) 1.16006 0.0378974 0.0189487 0.999820i \(-0.493968\pi\)
0.0189487 + 0.999820i \(0.493968\pi\)
\(938\) 0 0
\(939\) 57.6814 1.88236
\(940\) 0 0
\(941\) 4.49867 + 7.79192i 0.146652 + 0.254009i 0.929988 0.367589i \(-0.119817\pi\)
−0.783336 + 0.621599i \(0.786483\pi\)
\(942\) 0 0
\(943\) −0.323417 0.186725i −0.0105319 0.00608060i
\(944\) 0 0
\(945\) −10.4727 4.34141i −0.340677 0.141226i
\(946\) 0 0
\(947\) 19.2076 + 11.0895i 0.624165 + 0.360362i 0.778489 0.627659i \(-0.215987\pi\)
−0.154324 + 0.988020i \(0.549320\pi\)
\(948\) 0 0
\(949\) 44.5380 25.7140i 1.44576 0.834712i
\(950\) 0 0
\(951\) −54.1024 −1.75439
\(952\) 0 0
\(953\) 31.9975i 1.03650i 0.855229 + 0.518250i \(0.173416\pi\)
−0.855229 + 0.518250i \(0.826584\pi\)
\(954\) 0 0
\(955\) −32.6131 + 38.2185i −1.05533 + 1.23672i
\(956\) 0 0
\(957\) 11.1104 + 6.41461i 0.359149 + 0.207355i
\(958\) 0 0
\(959\) −4.17447 12.8791i −0.134801 0.415887i
\(960\) 0 0
\(961\) 11.4721 19.8703i 0.370068 0.640977i
\(962\) 0 0
\(963\) −6.65276 + 3.84097i −0.214382 + 0.123774i
\(964\) 0 0
\(965\) −12.3776 34.9052i −0.398449 1.12364i
\(966\) 0 0
\(967\) 40.0936 1.28932 0.644662 0.764468i \(-0.276998\pi\)
0.644662 + 0.764468i \(0.276998\pi\)
\(968\) 0 0
\(969\) 13.8202 7.97908i 0.443968 0.256325i
\(970\) 0 0
\(971\) 26.9006 + 15.5311i 0.863282 + 0.498416i 0.865110 0.501582i \(-0.167249\pi\)
−0.00182815 + 0.999998i \(0.500582\pi\)
\(972\) 0 0
\(973\) −46.3600 9.88882i −1.48623 0.317021i
\(974\) 0 0
\(975\) −63.5001 + 10.1138i −2.03363 + 0.323902i
\(976\) 0 0
\(977\) −48.2743 + 27.8712i −1.54443 + 0.891678i −0.545881 + 0.837863i \(0.683805\pi\)
−0.998551 + 0.0538151i \(0.982862\pi\)
\(978\) 0 0
\(979\) 13.0281i 0.416380i
\(980\) 0 0
\(981\) 4.30573i 0.137471i
\(982\) 0 0
\(983\) −39.4861 + 22.7973i −1.25941 + 0.727122i −0.972960 0.230973i \(-0.925809\pi\)
−0.286452 + 0.958095i \(0.592476\pi\)
\(984\) 0 0
\(985\) −6.55927 + 35.4764i −0.208996 + 1.13037i
\(986\) 0 0
\(987\) 58.0881 + 12.3905i 1.84896 + 0.394394i
\(988\) 0 0
\(989\) 16.4487 + 9.49669i 0.523040 + 0.301977i
\(990\) 0 0
\(991\) −30.9667 + 17.8786i −0.983689 + 0.567933i −0.903382 0.428837i \(-0.858923\pi\)
−0.0803071 + 0.996770i \(0.525590\pi\)
\(992\) 0 0
\(993\) −10.6801 −0.338924
\(994\) 0 0
\(995\) −45.9996 + 16.3117i −1.45829 + 0.517117i
\(996\) 0 0
\(997\) −9.48099 + 5.47385i −0.300266 + 0.173359i −0.642562 0.766233i \(-0.722129\pi\)
0.342296 + 0.939592i \(0.388795\pi\)
\(998\) 0 0
\(999\) 1.51312 2.62079i 0.0478728 0.0829182i
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 1120.2.bq.b.719.7 80
4.3 odd 2 280.2.ba.b.19.28 yes 80
5.4 even 2 inner 1120.2.bq.b.719.33 80
7.3 odd 6 inner 1120.2.bq.b.1039.34 80
8.3 odd 2 inner 1120.2.bq.b.719.8 80
8.5 even 2 280.2.ba.b.19.15 yes 80
20.19 odd 2 280.2.ba.b.19.13 80
28.3 even 6 280.2.ba.b.59.26 yes 80
35.24 odd 6 inner 1120.2.bq.b.1039.8 80
40.19 odd 2 inner 1120.2.bq.b.719.34 80
40.29 even 2 280.2.ba.b.19.26 yes 80
56.3 even 6 inner 1120.2.bq.b.1039.33 80
56.45 odd 6 280.2.ba.b.59.13 yes 80
140.59 even 6 280.2.ba.b.59.15 yes 80
280.59 even 6 inner 1120.2.bq.b.1039.7 80
280.269 odd 6 280.2.ba.b.59.28 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.ba.b.19.13 80 20.19 odd 2
280.2.ba.b.19.15 yes 80 8.5 even 2
280.2.ba.b.19.26 yes 80 40.29 even 2
280.2.ba.b.19.28 yes 80 4.3 odd 2
280.2.ba.b.59.13 yes 80 56.45 odd 6
280.2.ba.b.59.15 yes 80 140.59 even 6
280.2.ba.b.59.26 yes 80 28.3 even 6
280.2.ba.b.59.28 yes 80 280.269 odd 6
1120.2.bq.b.719.7 80 1.1 even 1 trivial
1120.2.bq.b.719.8 80 8.3 odd 2 inner
1120.2.bq.b.719.33 80 5.4 even 2 inner
1120.2.bq.b.719.34 80 40.19 odd 2 inner
1120.2.bq.b.1039.7 80 280.59 even 6 inner
1120.2.bq.b.1039.8 80 35.24 odd 6 inner
1120.2.bq.b.1039.33 80 56.3 even 6 inner
1120.2.bq.b.1039.34 80 7.3 odd 6 inner