Properties

Label 528.2.y.f.289.1
Level $528$
Weight $2$
Character 528.289
Analytic conductor $4.216$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [528,2,Mod(49,528)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(528, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("528.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.y (of order \(5\), degree \(4\), 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: \(4.21610122672\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 289.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 528.289
Dual form 528.2.y.f.433.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{3} +(0.309017 + 0.224514i) q^{5} +(-0.927051 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{3} +(0.309017 + 0.224514i) q^{5} +(-0.927051 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-2.80902 + 1.76336i) q^{11} +(-5.04508 + 3.66547i) q^{13} +(0.118034 - 0.363271i) q^{15} +(0.500000 + 0.363271i) q^{17} +(0.263932 + 0.812299i) q^{19} +3.00000 q^{21} +5.47214 q^{23} +(-1.50000 - 4.61653i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(-3.11803 + 2.26538i) q^{31} +(2.54508 + 2.12663i) q^{33} +(-0.927051 + 0.673542i) q^{35} +(-1.30902 + 4.02874i) q^{37} +(5.04508 + 3.66547i) q^{39} +(1.83688 + 5.65334i) q^{41} -1.76393 q^{43} -0.381966 q^{45} +(0.190983 + 0.587785i) q^{47} +(-1.61803 - 1.17557i) q^{49} +(0.190983 - 0.587785i) q^{51} +(5.97214 - 4.33901i) q^{53} +(-1.26393 - 0.0857567i) q^{55} +(0.690983 - 0.502029i) q^{57} +(1.64590 - 5.06555i) q^{59} +(-0.927051 - 0.673542i) q^{61} +(-0.927051 - 2.85317i) q^{63} -2.38197 q^{65} -10.5623 q^{67} +(-1.69098 - 5.20431i) q^{69} +(11.7812 + 8.55951i) q^{71} +(0.381966 - 1.17557i) q^{73} +(-3.92705 + 2.85317i) q^{75} +(-2.42705 - 9.64932i) q^{77} +(0.427051 - 0.310271i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-10.2812 - 7.46969i) q^{83} +(0.0729490 + 0.224514i) q^{85} +4.47214 q^{87} +9.47214 q^{89} +(-5.78115 - 17.7926i) q^{91} +(3.11803 + 2.26538i) q^{93} +(-0.100813 + 0.310271i) q^{95} +(-12.1631 + 8.83702i) q^{97} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} - q^{5} + 3 q^{7} - q^{9} - 9 q^{11} - 9 q^{13} - 4 q^{15} + 2 q^{17} + 10 q^{19} + 12 q^{21} + 4 q^{23} - 6 q^{25} + q^{27} - 10 q^{29} - 8 q^{31} - q^{33} + 3 q^{35} - 3 q^{37} + 9 q^{39} + 23 q^{41} - 16 q^{43} - 6 q^{45} + 3 q^{47} - 2 q^{49} + 3 q^{51} + 6 q^{53} - 14 q^{55} + 5 q^{57} + 20 q^{59} + 3 q^{61} + 3 q^{63} - 14 q^{65} - 2 q^{67} - 9 q^{69} + 27 q^{71} + 6 q^{73} - 9 q^{75} - 3 q^{77} - 5 q^{79} - q^{81} - 21 q^{83} + 7 q^{85} + 20 q^{89} - 3 q^{91} + 8 q^{93} - 25 q^{95} - 33 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/528\mathbb{Z}\right)^\times\).

\(n\) \(133\) \(145\) \(353\) \(463\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

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
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0 0
\(5\) 0.309017 + 0.224514i 0.138197 + 0.100406i 0.654736 0.755858i \(-0.272780\pi\)
−0.516539 + 0.856264i \(0.672780\pi\)
\(6\) 0 0
\(7\) −0.927051 + 2.85317i −0.350392 + 1.07840i 0.608241 + 0.793752i \(0.291875\pi\)
−0.958633 + 0.284644i \(0.908125\pi\)
\(8\) 0 0
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) −2.80902 + 1.76336i −0.846950 + 0.531672i
\(12\) 0 0
\(13\) −5.04508 + 3.66547i −1.39925 + 1.01662i −0.404478 + 0.914548i \(0.632547\pi\)
−0.994777 + 0.102070i \(0.967453\pi\)
\(14\) 0 0
\(15\) 0.118034 0.363271i 0.0304762 0.0937962i
\(16\) 0 0
\(17\) 0.500000 + 0.363271i 0.121268 + 0.0881062i 0.646766 0.762688i \(-0.276121\pi\)
−0.525498 + 0.850795i \(0.676121\pi\)
\(18\) 0 0
\(19\) 0.263932 + 0.812299i 0.0605502 + 0.186354i 0.976756 0.214353i \(-0.0687644\pi\)
−0.916206 + 0.400707i \(0.868764\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) 5.47214 1.14102 0.570510 0.821291i \(-0.306746\pi\)
0.570510 + 0.821291i \(0.306746\pi\)
\(24\) 0 0
\(25\) −1.50000 4.61653i −0.300000 0.923305i
\(26\) 0 0
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 0 0
\(29\) −1.38197 + 4.25325i −0.256625 + 0.789809i 0.736881 + 0.676023i \(0.236298\pi\)
−0.993505 + 0.113787i \(0.963702\pi\)
\(30\) 0 0
\(31\) −3.11803 + 2.26538i −0.560015 + 0.406875i −0.831465 0.555578i \(-0.812497\pi\)
0.271449 + 0.962453i \(0.412497\pi\)
\(32\) 0 0
\(33\) 2.54508 + 2.12663i 0.443042 + 0.370198i
\(34\) 0 0
\(35\) −0.927051 + 0.673542i −0.156700 + 0.113849i
\(36\) 0 0
\(37\) −1.30902 + 4.02874i −0.215201 + 0.662321i 0.783938 + 0.620839i \(0.213208\pi\)
−0.999139 + 0.0414819i \(0.986792\pi\)
\(38\) 0 0
\(39\) 5.04508 + 3.66547i 0.807860 + 0.586945i
\(40\) 0 0
\(41\) 1.83688 + 5.65334i 0.286873 + 0.882903i 0.985831 + 0.167741i \(0.0536472\pi\)
−0.698958 + 0.715162i \(0.746353\pi\)
\(42\) 0 0
\(43\) −1.76393 −0.268997 −0.134499 0.990914i \(-0.542942\pi\)
−0.134499 + 0.990914i \(0.542942\pi\)
\(44\) 0 0
\(45\) −0.381966 −0.0569401
\(46\) 0 0
\(47\) 0.190983 + 0.587785i 0.0278577 + 0.0857373i 0.964019 0.265834i \(-0.0856474\pi\)
−0.936161 + 0.351572i \(0.885647\pi\)
\(48\) 0 0
\(49\) −1.61803 1.17557i −0.231148 0.167939i
\(50\) 0 0
\(51\) 0.190983 0.587785i 0.0267430 0.0823064i
\(52\) 0 0
\(53\) 5.97214 4.33901i 0.820336 0.596009i −0.0964728 0.995336i \(-0.530756\pi\)
0.916809 + 0.399327i \(0.130756\pi\)
\(54\) 0 0
\(55\) −1.26393 0.0857567i −0.170429 0.0115634i
\(56\) 0 0
\(57\) 0.690983 0.502029i 0.0915229 0.0664953i
\(58\) 0 0
\(59\) 1.64590 5.06555i 0.214278 0.659479i −0.784926 0.619589i \(-0.787299\pi\)
0.999204 0.0398899i \(-0.0127007\pi\)
\(60\) 0 0
\(61\) −0.927051 0.673542i −0.118697 0.0862382i 0.526853 0.849956i \(-0.323372\pi\)
−0.645550 + 0.763718i \(0.723372\pi\)
\(62\) 0 0
\(63\) −0.927051 2.85317i −0.116797 0.359466i
\(64\) 0 0
\(65\) −2.38197 −0.295447
\(66\) 0 0
\(67\) −10.5623 −1.29039 −0.645196 0.764017i \(-0.723224\pi\)
−0.645196 + 0.764017i \(0.723224\pi\)
\(68\) 0 0
\(69\) −1.69098 5.20431i −0.203570 0.626525i
\(70\) 0 0
\(71\) 11.7812 + 8.55951i 1.39817 + 1.01583i 0.994913 + 0.100738i \(0.0321204\pi\)
0.403253 + 0.915089i \(0.367880\pi\)
\(72\) 0 0
\(73\) 0.381966 1.17557i 0.0447057 0.137590i −0.926212 0.377003i \(-0.876955\pi\)
0.970918 + 0.239412i \(0.0769548\pi\)
\(74\) 0 0
\(75\) −3.92705 + 2.85317i −0.453457 + 0.329456i
\(76\) 0 0
\(77\) −2.42705 9.64932i −0.276588 1.09964i
\(78\) 0 0
\(79\) 0.427051 0.310271i 0.0480470 0.0349082i −0.563503 0.826114i \(-0.690547\pi\)
0.611550 + 0.791206i \(0.290547\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −10.2812 7.46969i −1.12850 0.819906i −0.143027 0.989719i \(-0.545684\pi\)
−0.985476 + 0.169813i \(0.945684\pi\)
\(84\) 0 0
\(85\) 0.0729490 + 0.224514i 0.00791243 + 0.0243520i
\(86\) 0 0
\(87\) 4.47214 0.479463
\(88\) 0 0
\(89\) 9.47214 1.00404 0.502022 0.864855i \(-0.332590\pi\)
0.502022 + 0.864855i \(0.332590\pi\)
\(90\) 0 0
\(91\) −5.78115 17.7926i −0.606029 1.86517i
\(92\) 0 0
\(93\) 3.11803 + 2.26538i 0.323325 + 0.234909i
\(94\) 0 0
\(95\) −0.100813 + 0.310271i −0.0103432 + 0.0318331i
\(96\) 0 0
\(97\) −12.1631 + 8.83702i −1.23498 + 0.897264i −0.997253 0.0740689i \(-0.976402\pi\)
−0.237724 + 0.971333i \(0.576402\pi\)
\(98\) 0 0
\(99\) 1.23607 3.07768i 0.124230 0.309319i
\(100\) 0 0
\(101\) 2.42705 1.76336i 0.241501 0.175460i −0.460451 0.887685i \(-0.652312\pi\)
0.701952 + 0.712225i \(0.252312\pi\)
\(102\) 0 0
\(103\) 1.85410 5.70634i 0.182690 0.562262i −0.817211 0.576339i \(-0.804481\pi\)
0.999901 + 0.0140765i \(0.00448085\pi\)
\(104\) 0 0
\(105\) 0.927051 + 0.673542i 0.0904709 + 0.0657310i
\(106\) 0 0
\(107\) −0.0729490 0.224514i −0.00705225 0.0217046i 0.947468 0.319849i \(-0.103632\pi\)
−0.954521 + 0.298145i \(0.903632\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 4.23607 0.402070
\(112\) 0 0
\(113\) −3.92705 12.0862i −0.369426 1.13698i −0.947163 0.320753i \(-0.896064\pi\)
0.577737 0.816223i \(-0.303936\pi\)
\(114\) 0 0
\(115\) 1.69098 + 1.22857i 0.157685 + 0.114565i
\(116\) 0 0
\(117\) 1.92705 5.93085i 0.178156 0.548308i
\(118\) 0 0
\(119\) −1.50000 + 1.08981i −0.137505 + 0.0999031i
\(120\) 0 0
\(121\) 4.78115 9.90659i 0.434650 0.900599i
\(122\) 0 0
\(123\) 4.80902 3.49396i 0.433614 0.315039i
\(124\) 0 0
\(125\) 1.16312 3.57971i 0.104033 0.320179i
\(126\) 0 0
\(127\) 7.85410 + 5.70634i 0.696939 + 0.506356i 0.878934 0.476944i \(-0.158255\pi\)
−0.181995 + 0.983299i \(0.558255\pi\)
\(128\) 0 0
\(129\) 0.545085 + 1.67760i 0.0479921 + 0.147704i
\(130\) 0 0
\(131\) 13.8541 1.21044 0.605219 0.796059i \(-0.293085\pi\)
0.605219 + 0.796059i \(0.293085\pi\)
\(132\) 0 0
\(133\) −2.56231 −0.222180
\(134\) 0 0
\(135\) 0.118034 + 0.363271i 0.0101587 + 0.0312654i
\(136\) 0 0
\(137\) 1.19098 + 0.865300i 0.101753 + 0.0739276i 0.637498 0.770452i \(-0.279969\pi\)
−0.535746 + 0.844379i \(0.679969\pi\)
\(138\) 0 0
\(139\) −1.80902 + 5.56758i −0.153439 + 0.472236i −0.997999 0.0632239i \(-0.979862\pi\)
0.844561 + 0.535460i \(0.179862\pi\)
\(140\) 0 0
\(141\) 0.500000 0.363271i 0.0421076 0.0305930i
\(142\) 0 0
\(143\) 7.70820 19.1926i 0.644592 1.60497i
\(144\) 0 0
\(145\) −1.38197 + 1.00406i −0.114766 + 0.0833824i
\(146\) 0 0
\(147\) −0.618034 + 1.90211i −0.0509746 + 0.156884i
\(148\) 0 0
\(149\) −12.1353 8.81678i −0.994159 0.722299i −0.0333309 0.999444i \(-0.510612\pi\)
−0.960828 + 0.277146i \(0.910612\pi\)
\(150\) 0 0
\(151\) −0.618034 1.90211i −0.0502949 0.154792i 0.922755 0.385388i \(-0.125932\pi\)
−0.973050 + 0.230596i \(0.925932\pi\)
\(152\) 0 0
\(153\) −0.618034 −0.0499651
\(154\) 0 0
\(155\) −1.47214 −0.118245
\(156\) 0 0
\(157\) 3.00000 + 9.23305i 0.239426 + 0.736878i 0.996503 + 0.0835524i \(0.0266266\pi\)
−0.757077 + 0.653325i \(0.773373\pi\)
\(158\) 0 0
\(159\) −5.97214 4.33901i −0.473621 0.344106i
\(160\) 0 0
\(161\) −5.07295 + 15.6129i −0.399804 + 1.23047i
\(162\) 0 0
\(163\) −12.3541 + 8.97578i −0.967648 + 0.703037i −0.954914 0.296882i \(-0.904053\pi\)
−0.0127336 + 0.999919i \(0.504053\pi\)
\(164\) 0 0
\(165\) 0.309017 + 1.22857i 0.0240569 + 0.0956441i
\(166\) 0 0
\(167\) −15.3992 + 11.1882i −1.19162 + 0.865766i −0.993435 0.114398i \(-0.963506\pi\)
−0.198190 + 0.980164i \(0.563506\pi\)
\(168\) 0 0
\(169\) 8.00000 24.6215i 0.615385 1.89396i
\(170\) 0 0
\(171\) −0.690983 0.502029i −0.0528408 0.0383911i
\(172\) 0 0
\(173\) 5.44427 + 16.7557i 0.413920 + 1.27392i 0.913213 + 0.407482i \(0.133593\pi\)
−0.499293 + 0.866433i \(0.666407\pi\)
\(174\) 0 0
\(175\) 14.5623 1.10081
\(176\) 0 0
\(177\) −5.32624 −0.400345
\(178\) 0 0
\(179\) −0.690983 2.12663i −0.0516465 0.158952i 0.921907 0.387412i \(-0.126631\pi\)
−0.973553 + 0.228460i \(0.926631\pi\)
\(180\) 0 0
\(181\) 6.89919 + 5.01255i 0.512813 + 0.372580i 0.813889 0.581020i \(-0.197346\pi\)
−0.301077 + 0.953600i \(0.597346\pi\)
\(182\) 0 0
\(183\) −0.354102 + 1.08981i −0.0261760 + 0.0805614i
\(184\) 0 0
\(185\) −1.30902 + 0.951057i −0.0962408 + 0.0699231i
\(186\) 0 0
\(187\) −2.04508 0.138757i −0.149551 0.0101469i
\(188\) 0 0
\(189\) −2.42705 + 1.76336i −0.176542 + 0.128265i
\(190\) 0 0
\(191\) −0.454915 + 1.40008i −0.0329165 + 0.101307i −0.966165 0.257925i \(-0.916961\pi\)
0.933248 + 0.359232i \(0.116961\pi\)
\(192\) 0 0
\(193\) −1.26393 0.918300i −0.0909798 0.0661007i 0.541365 0.840787i \(-0.317908\pi\)
−0.632345 + 0.774687i \(0.717908\pi\)
\(194\) 0 0
\(195\) 0.736068 + 2.26538i 0.0527109 + 0.162228i
\(196\) 0 0
\(197\) 26.6180 1.89646 0.948228 0.317590i \(-0.102873\pi\)
0.948228 + 0.317590i \(0.102873\pi\)
\(198\) 0 0
\(199\) 3.29180 0.233349 0.116675 0.993170i \(-0.462777\pi\)
0.116675 + 0.993170i \(0.462777\pi\)
\(200\) 0 0
\(201\) 3.26393 + 10.0453i 0.230220 + 0.708544i
\(202\) 0 0
\(203\) −10.8541 7.88597i −0.761809 0.553486i
\(204\) 0 0
\(205\) −0.701626 + 2.15938i −0.0490037 + 0.150818i
\(206\) 0 0
\(207\) −4.42705 + 3.21644i −0.307701 + 0.223558i
\(208\) 0 0
\(209\) −2.17376 1.81636i −0.150362 0.125640i
\(210\) 0 0
\(211\) 9.11803 6.62464i 0.627711 0.456059i −0.227895 0.973686i \(-0.573184\pi\)
0.855607 + 0.517627i \(0.173184\pi\)
\(212\) 0 0
\(213\) 4.50000 13.8496i 0.308335 0.948957i
\(214\) 0 0
\(215\) −0.545085 0.396027i −0.0371745 0.0270088i
\(216\) 0 0
\(217\) −3.57295 10.9964i −0.242548 0.746485i
\(218\) 0 0
\(219\) −1.23607 −0.0835257
\(220\) 0 0
\(221\) −3.85410 −0.259255
\(222\) 0 0
\(223\) 3.92705 + 12.0862i 0.262975 + 0.809353i 0.992153 + 0.125029i \(0.0399025\pi\)
−0.729178 + 0.684324i \(0.760097\pi\)
\(224\) 0 0
\(225\) 3.92705 + 2.85317i 0.261803 + 0.190211i
\(226\) 0 0
\(227\) −3.36475 + 10.3556i −0.223326 + 0.687327i 0.775131 + 0.631800i \(0.217684\pi\)
−0.998457 + 0.0555264i \(0.982316\pi\)
\(228\) 0 0
\(229\) −8.09017 + 5.87785i −0.534613 + 0.388419i −0.822081 0.569371i \(-0.807187\pi\)
0.287467 + 0.957790i \(0.407187\pi\)
\(230\) 0 0
\(231\) −8.42705 + 5.29007i −0.554459 + 0.348061i
\(232\) 0 0
\(233\) −7.01722 + 5.09831i −0.459713 + 0.334001i −0.793419 0.608676i \(-0.791701\pi\)
0.333705 + 0.942677i \(0.391701\pi\)
\(234\) 0 0
\(235\) −0.0729490 + 0.224514i −0.00475867 + 0.0146457i
\(236\) 0 0
\(237\) −0.427051 0.310271i −0.0277399 0.0201542i
\(238\) 0 0
\(239\) 5.42705 + 16.7027i 0.351047 + 1.08041i 0.958266 + 0.285877i \(0.0922848\pi\)
−0.607220 + 0.794534i \(0.707715\pi\)
\(240\) 0 0
\(241\) 17.1246 1.10309 0.551547 0.834144i \(-0.314038\pi\)
0.551547 + 0.834144i \(0.314038\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −0.236068 0.726543i −0.0150818 0.0464171i
\(246\) 0 0
\(247\) −4.30902 3.13068i −0.274176 0.199201i
\(248\) 0 0
\(249\) −3.92705 + 12.0862i −0.248867 + 0.765933i
\(250\) 0 0
\(251\) 13.5902 9.87384i 0.857804 0.623231i −0.0694827 0.997583i \(-0.522135\pi\)
0.927287 + 0.374352i \(0.122135\pi\)
\(252\) 0 0
\(253\) −15.3713 + 9.64932i −0.966387 + 0.606648i
\(254\) 0 0
\(255\) 0.190983 0.138757i 0.0119598 0.00868932i
\(256\) 0 0
\(257\) −8.44427 + 25.9888i −0.526739 + 1.62114i 0.234112 + 0.972210i \(0.424782\pi\)
−0.760851 + 0.648927i \(0.775218\pi\)
\(258\) 0 0
\(259\) −10.2812 7.46969i −0.638840 0.464144i
\(260\) 0 0
\(261\) −1.38197 4.25325i −0.0855415 0.263270i
\(262\) 0 0
\(263\) 0.673762 0.0415459 0.0207730 0.999784i \(-0.493387\pi\)
0.0207730 + 0.999784i \(0.493387\pi\)
\(264\) 0 0
\(265\) 2.81966 0.173210
\(266\) 0 0
\(267\) −2.92705 9.00854i −0.179133 0.551313i
\(268\) 0 0
\(269\) −19.7984 14.3844i −1.20713 0.877030i −0.212161 0.977235i \(-0.568050\pi\)
−0.994967 + 0.100205i \(0.968050\pi\)
\(270\) 0 0
\(271\) −1.93769 + 5.96361i −0.117707 + 0.362263i −0.992502 0.122229i \(-0.960996\pi\)
0.874795 + 0.484493i \(0.160996\pi\)
\(272\) 0 0
\(273\) −15.1353 + 10.9964i −0.916027 + 0.665533i
\(274\) 0 0
\(275\) 12.3541 + 10.3229i 0.744980 + 0.622492i
\(276\) 0 0
\(277\) −8.44427 + 6.13512i −0.507367 + 0.368624i −0.811824 0.583902i \(-0.801525\pi\)
0.304457 + 0.952526i \(0.401525\pi\)
\(278\) 0 0
\(279\) 1.19098 3.66547i 0.0713023 0.219446i
\(280\) 0 0
\(281\) 4.23607 + 3.07768i 0.252703 + 0.183599i 0.706924 0.707290i \(-0.250082\pi\)
−0.454221 + 0.890889i \(0.650082\pi\)
\(282\) 0 0
\(283\) 6.85410 + 21.0948i 0.407434 + 1.25395i 0.918846 + 0.394617i \(0.129123\pi\)
−0.511412 + 0.859336i \(0.670877\pi\)
\(284\) 0 0
\(285\) 0.326238 0.0193247
\(286\) 0 0
\(287\) −17.8328 −1.05264
\(288\) 0 0
\(289\) −5.13525 15.8047i −0.302074 0.929688i
\(290\) 0 0
\(291\) 12.1631 + 8.83702i 0.713015 + 0.518035i
\(292\) 0 0
\(293\) 5.54508 17.0660i 0.323947 0.997007i −0.647966 0.761669i \(-0.724380\pi\)
0.971914 0.235338i \(-0.0756198\pi\)
\(294\) 0 0
\(295\) 1.64590 1.19581i 0.0958279 0.0696230i
\(296\) 0 0
\(297\) −3.30902 0.224514i −0.192009 0.0130276i
\(298\) 0 0
\(299\) −27.6074 + 20.0579i −1.59658 + 1.15998i
\(300\) 0 0
\(301\) 1.63525 5.03280i 0.0942545 0.290086i
\(302\) 0 0
\(303\) −2.42705 1.76336i −0.139430 0.101302i
\(304\) 0 0
\(305\) −0.135255 0.416272i −0.00774467 0.0238357i
\(306\) 0 0
\(307\) 19.5623 1.11648 0.558240 0.829680i \(-0.311477\pi\)
0.558240 + 0.829680i \(0.311477\pi\)
\(308\) 0 0
\(309\) −6.00000 −0.341328
\(310\) 0 0
\(311\) −3.54508 10.9106i −0.201023 0.618686i −0.999853 0.0171293i \(-0.994547\pi\)
0.798830 0.601557i \(-0.205453\pi\)
\(312\) 0 0
\(313\) 22.5172 + 16.3597i 1.27275 + 0.924706i 0.999308 0.0371831i \(-0.0118385\pi\)
0.273440 + 0.961889i \(0.411838\pi\)
\(314\) 0 0
\(315\) 0.354102 1.08981i 0.0199514 0.0614041i
\(316\) 0 0
\(317\) −20.5172 + 14.9066i −1.15236 + 0.837240i −0.988793 0.149292i \(-0.952301\pi\)
−0.163569 + 0.986532i \(0.552301\pi\)
\(318\) 0 0
\(319\) −3.61803 14.3844i −0.202571 0.805370i
\(320\) 0 0
\(321\) −0.190983 + 0.138757i −0.0106596 + 0.00774468i
\(322\) 0 0
\(323\) −0.163119 + 0.502029i −0.00907618 + 0.0279336i
\(324\) 0 0
\(325\) 24.4894 + 17.7926i 1.35843 + 0.986954i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.85410 −0.102220
\(330\) 0 0
\(331\) 22.5967 1.24203 0.621015 0.783799i \(-0.286721\pi\)
0.621015 + 0.783799i \(0.286721\pi\)
\(332\) 0 0
\(333\) −1.30902 4.02874i −0.0717337 0.220774i
\(334\) 0 0
\(335\) −3.26393 2.37139i −0.178328 0.129563i
\(336\) 0 0
\(337\) −4.23607 + 13.0373i −0.230753 + 0.710186i 0.766903 + 0.641763i \(0.221797\pi\)
−0.997656 + 0.0684228i \(0.978203\pi\)
\(338\) 0 0
\(339\) −10.2812 + 7.46969i −0.558396 + 0.405698i
\(340\) 0 0
\(341\) 4.76393 11.8617i 0.257981 0.642347i
\(342\) 0 0
\(343\) −12.1353 + 8.81678i −0.655242 + 0.476061i
\(344\) 0 0
\(345\) 0.645898 1.98787i 0.0347740 0.107023i
\(346\) 0 0
\(347\) −2.47214 1.79611i −0.132711 0.0964203i 0.519449 0.854501i \(-0.326137\pi\)
−0.652160 + 0.758081i \(0.726137\pi\)
\(348\) 0 0
\(349\) 9.30902 + 28.6502i 0.498300 + 1.53361i 0.811750 + 0.584006i \(0.198515\pi\)
−0.313449 + 0.949605i \(0.601485\pi\)
\(350\) 0 0
\(351\) −6.23607 −0.332857
\(352\) 0 0
\(353\) −1.52786 −0.0813200 −0.0406600 0.999173i \(-0.512946\pi\)
−0.0406600 + 0.999173i \(0.512946\pi\)
\(354\) 0 0
\(355\) 1.71885 + 5.29007i 0.0912269 + 0.280768i
\(356\) 0 0
\(357\) 1.50000 + 1.08981i 0.0793884 + 0.0576791i
\(358\) 0 0
\(359\) 5.32624 16.3925i 0.281108 0.865162i −0.706430 0.707783i \(-0.749696\pi\)
0.987538 0.157379i \(-0.0503044\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) 0 0
\(363\) −10.8992 1.48584i −0.572059 0.0779864i
\(364\) 0 0
\(365\) 0.381966 0.277515i 0.0199930 0.0145258i
\(366\) 0 0
\(367\) 4.50000 13.8496i 0.234898 0.722942i −0.762237 0.647298i \(-0.775899\pi\)
0.997135 0.0756437i \(-0.0241012\pi\)
\(368\) 0 0
\(369\) −4.80902 3.49396i −0.250347 0.181888i
\(370\) 0 0
\(371\) 6.84346 + 21.0620i 0.355295 + 1.09348i
\(372\) 0 0
\(373\) 22.4164 1.16068 0.580339 0.814375i \(-0.302920\pi\)
0.580339 + 0.814375i \(0.302920\pi\)
\(374\) 0 0
\(375\) −3.76393 −0.194369
\(376\) 0 0
\(377\) −8.61803 26.5236i −0.443851 1.36603i
\(378\) 0 0
\(379\) 22.9894 + 16.7027i 1.18088 + 0.857962i 0.992271 0.124089i \(-0.0396009\pi\)
0.188613 + 0.982052i \(0.439601\pi\)
\(380\) 0 0
\(381\) 3.00000 9.23305i 0.153695 0.473024i
\(382\) 0 0
\(383\) −7.19098 + 5.22455i −0.367442 + 0.266962i −0.756149 0.654399i \(-0.772922\pi\)
0.388707 + 0.921361i \(0.372922\pi\)
\(384\) 0 0
\(385\) 1.41641 3.52671i 0.0721868 0.179738i
\(386\) 0 0
\(387\) 1.42705 1.03681i 0.0725411 0.0527042i
\(388\) 0 0
\(389\) −2.86475 + 8.81678i −0.145248 + 0.447028i −0.997043 0.0768476i \(-0.975515\pi\)
0.851795 + 0.523876i \(0.175515\pi\)
\(390\) 0 0
\(391\) 2.73607 + 1.98787i 0.138369 + 0.100531i
\(392\) 0 0
\(393\) −4.28115 13.1760i −0.215956 0.664643i
\(394\) 0 0
\(395\) 0.201626 0.0101449
\(396\) 0 0
\(397\) −25.2918 −1.26936 −0.634679 0.772776i \(-0.718868\pi\)
−0.634679 + 0.772776i \(0.718868\pi\)
\(398\) 0 0
\(399\) 0.791796 + 2.43690i 0.0396394 + 0.121997i
\(400\) 0 0
\(401\) 12.0623 + 8.76378i 0.602363 + 0.437642i 0.846717 0.532044i \(-0.178576\pi\)
−0.244354 + 0.969686i \(0.578576\pi\)
\(402\) 0 0
\(403\) 7.42705 22.8581i 0.369968 1.13864i
\(404\) 0 0
\(405\) 0.309017 0.224514i 0.0153552 0.0111562i
\(406\) 0 0
\(407\) −3.42705 13.6251i −0.169873 0.675369i
\(408\) 0 0
\(409\) 23.4164 17.0130i 1.15787 0.841240i 0.168360 0.985726i \(-0.446153\pi\)
0.989507 + 0.144486i \(0.0461529\pi\)
\(410\) 0 0
\(411\) 0.454915 1.40008i 0.0224393 0.0690611i
\(412\) 0 0
\(413\) 12.9271 + 9.39205i 0.636099 + 0.462153i
\(414\) 0 0
\(415\) −1.50000 4.61653i −0.0736321 0.226616i
\(416\) 0 0
\(417\) 5.85410 0.286677
\(418\) 0 0
\(419\) 21.5066 1.05067 0.525333 0.850897i \(-0.323941\pi\)
0.525333 + 0.850897i \(0.323941\pi\)
\(420\) 0 0
\(421\) −1.15248 3.54696i −0.0561682 0.172868i 0.919037 0.394172i \(-0.128969\pi\)
−0.975205 + 0.221304i \(0.928969\pi\)
\(422\) 0 0
\(423\) −0.500000 0.363271i −0.0243108 0.0176629i
\(424\) 0 0
\(425\) 0.927051 2.85317i 0.0449686 0.138399i
\(426\) 0 0
\(427\) 2.78115 2.02063i 0.134589 0.0977849i
\(428\) 0 0
\(429\) −20.6353 1.40008i −0.996279 0.0675967i
\(430\) 0 0
\(431\) −1.20820 + 0.877812i −0.0581971 + 0.0422827i −0.616503 0.787352i \(-0.711451\pi\)
0.558306 + 0.829635i \(0.311451\pi\)
\(432\) 0 0
\(433\) −1.85410 + 5.70634i −0.0891025 + 0.274229i −0.985672 0.168674i \(-0.946051\pi\)
0.896569 + 0.442903i \(0.146051\pi\)
\(434\) 0 0
\(435\) 1.38197 + 1.00406i 0.0662602 + 0.0481409i
\(436\) 0 0
\(437\) 1.44427 + 4.44501i 0.0690889 + 0.212634i
\(438\) 0 0
\(439\) −16.7082 −0.797439 −0.398720 0.917073i \(-0.630545\pi\)
−0.398720 + 0.917073i \(0.630545\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 0.270510 + 0.832544i 0.0128523 + 0.0395553i 0.957277 0.289172i \(-0.0933801\pi\)
−0.944425 + 0.328728i \(0.893380\pi\)
\(444\) 0 0
\(445\) 2.92705 + 2.12663i 0.138756 + 0.100812i
\(446\) 0 0
\(447\) −4.63525 + 14.2658i −0.219240 + 0.674751i
\(448\) 0 0
\(449\) 12.5623 9.12705i 0.592852 0.430732i −0.250483 0.968121i \(-0.580589\pi\)
0.843334 + 0.537389i \(0.180589\pi\)
\(450\) 0 0
\(451\) −15.1287 12.6412i −0.712382 0.595253i
\(452\) 0 0
\(453\) −1.61803 + 1.17557i −0.0760219 + 0.0552331i
\(454\) 0 0
\(455\) 2.20820 6.79615i 0.103522 0.318609i
\(456\) 0 0
\(457\) −26.5344 19.2784i −1.24123 0.901806i −0.243549 0.969889i \(-0.578312\pi\)
−0.997680 + 0.0680830i \(0.978312\pi\)
\(458\) 0 0
\(459\) 0.190983 + 0.587785i 0.00891432 + 0.0274355i
\(460\) 0 0
\(461\) −9.90983 −0.461547 −0.230773 0.973008i \(-0.574126\pi\)
−0.230773 + 0.973008i \(0.574126\pi\)
\(462\) 0 0
\(463\) −8.79837 −0.408895 −0.204448 0.978878i \(-0.565540\pi\)
−0.204448 + 0.978878i \(0.565540\pi\)
\(464\) 0 0
\(465\) 0.454915 + 1.40008i 0.0210962 + 0.0649274i
\(466\) 0 0
\(467\) −11.5172 8.36775i −0.532953 0.387213i 0.288508 0.957478i \(-0.406841\pi\)
−0.821461 + 0.570264i \(0.806841\pi\)
\(468\) 0 0
\(469\) 9.79180 30.1360i 0.452143 1.39155i
\(470\) 0 0
\(471\) 7.85410 5.70634i 0.361898 0.262934i
\(472\) 0 0
\(473\) 4.95492 3.11044i 0.227827 0.143018i
\(474\) 0 0
\(475\) 3.35410 2.43690i 0.153897 0.111813i
\(476\) 0 0
\(477\) −2.28115 + 7.02067i −0.104447 + 0.321454i
\(478\) 0 0
\(479\) −13.6803 9.93935i −0.625071 0.454140i 0.229618 0.973281i \(-0.426252\pi\)
−0.854689 + 0.519140i \(0.826252\pi\)
\(480\) 0 0
\(481\) −8.16312 25.1235i −0.372206 1.14553i
\(482\) 0 0
\(483\) 16.4164 0.746972
\(484\) 0 0
\(485\) −5.74265 −0.260760
\(486\) 0 0
\(487\) −12.1074 37.2627i −0.548638 1.68853i −0.712179 0.701998i \(-0.752291\pi\)
0.163540 0.986537i \(-0.447709\pi\)
\(488\) 0 0
\(489\) 12.3541 + 8.97578i 0.558672 + 0.405899i
\(490\) 0 0
\(491\) 8.10081 24.9317i 0.365585 1.12515i −0.584030 0.811732i \(-0.698525\pi\)
0.949614 0.313421i \(-0.101475\pi\)
\(492\) 0 0
\(493\) −2.23607 + 1.62460i −0.100707 + 0.0731682i
\(494\) 0 0
\(495\) 1.07295 0.673542i 0.0482255 0.0302735i
\(496\) 0 0
\(497\) −35.3435 + 25.6785i −1.58537 + 1.15184i
\(498\) 0 0
\(499\) −0.791796 + 2.43690i −0.0354457 + 0.109091i −0.967214 0.253963i \(-0.918266\pi\)
0.931768 + 0.363054i \(0.118266\pi\)
\(500\) 0 0
\(501\) 15.3992 + 11.1882i 0.687985 + 0.499850i
\(502\) 0 0
\(503\) 9.29180 + 28.5972i 0.414301 + 1.27509i 0.912875 + 0.408239i \(0.133857\pi\)
−0.498574 + 0.866847i \(0.666143\pi\)
\(504\) 0 0
\(505\) 1.14590 0.0509918
\(506\) 0 0
\(507\) −25.8885 −1.14975
\(508\) 0 0
\(509\) 6.60739 + 20.3355i 0.292867 + 0.901353i 0.983929 + 0.178558i \(0.0571432\pi\)
−0.691062 + 0.722796i \(0.742857\pi\)
\(510\) 0 0
\(511\) 3.00000 + 2.17963i 0.132712 + 0.0964210i
\(512\) 0 0
\(513\) −0.263932 + 0.812299i −0.0116529 + 0.0358639i
\(514\) 0 0
\(515\) 1.85410 1.34708i 0.0817015 0.0593596i
\(516\) 0 0
\(517\) −1.57295 1.31433i −0.0691782 0.0578041i
\(518\) 0 0
\(519\) 14.2533 10.3556i 0.625650 0.454561i
\(520\) 0 0
\(521\) 12.0000 36.9322i 0.525730 1.61803i −0.237139 0.971476i \(-0.576210\pi\)
0.762869 0.646553i \(-0.223790\pi\)
\(522\) 0 0
\(523\) 28.2984 + 20.5600i 1.23740 + 0.899025i 0.997422 0.0717533i \(-0.0228594\pi\)
0.239979 + 0.970778i \(0.422859\pi\)
\(524\) 0 0
\(525\) −4.50000 13.8496i −0.196396 0.604445i
\(526\) 0 0
\(527\) −2.38197 −0.103760
\(528\) 0 0
\(529\) 6.94427 0.301925
\(530\) 0 0
\(531\) 1.64590 + 5.06555i 0.0714259 + 0.219826i
\(532\) 0 0
\(533\) −29.9894 21.7885i −1.29898 0.943767i
\(534\) 0 0
\(535\) 0.0278640 0.0857567i 0.00120467 0.00370759i
\(536\) 0 0
\(537\) −1.80902 + 1.31433i −0.0780648 + 0.0567174i
\(538\) 0 0
\(539\) 6.61803 + 0.449028i 0.285059 + 0.0193410i
\(540\) 0 0
\(541\) 0.454915 0.330515i 0.0195583 0.0142100i −0.577963 0.816063i \(-0.696152\pi\)
0.597521 + 0.801853i \(0.296152\pi\)
\(542\) 0 0
\(543\) 2.63525 8.11048i 0.113090 0.348054i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.98936 18.4333i −0.256086 0.788153i −0.993614 0.112836i \(-0.964007\pi\)
0.737527 0.675317i \(-0.235993\pi\)
\(548\) 0 0
\(549\) 1.14590 0.0489057
\(550\) 0 0
\(551\) −3.81966 −0.162723
\(552\) 0 0
\(553\) 0.489357 + 1.50609i 0.0208096 + 0.0640453i
\(554\) 0 0
\(555\) 1.30902 + 0.951057i 0.0555647 + 0.0403701i
\(556\) 0 0
\(557\) 8.06231 24.8132i 0.341611 1.05137i −0.621762 0.783206i \(-0.713583\pi\)
0.963373 0.268164i \(-0.0864170\pi\)
\(558\) 0 0
\(559\) 8.89919 6.46564i 0.376396 0.273467i
\(560\) 0 0
\(561\) 0.500000 + 1.98787i 0.0211100 + 0.0839279i
\(562\) 0 0
\(563\) 21.7533 15.8047i 0.916792 0.666088i −0.0259316 0.999664i \(-0.508255\pi\)
0.942723 + 0.333575i \(0.108255\pi\)
\(564\) 0 0
\(565\) 1.50000 4.61653i 0.0631055 0.194219i
\(566\) 0 0
\(567\) 2.42705 + 1.76336i 0.101927 + 0.0740540i
\(568\) 0 0
\(569\) 10.5279 + 32.4014i 0.441351 + 1.35834i 0.886436 + 0.462851i \(0.153173\pi\)
−0.445085 + 0.895488i \(0.646827\pi\)
\(570\) 0 0
\(571\) 25.6869 1.07496 0.537482 0.843275i \(-0.319376\pi\)
0.537482 + 0.843275i \(0.319376\pi\)
\(572\) 0 0
\(573\) 1.47214 0.0614994
\(574\) 0 0
\(575\) −8.20820 25.2623i −0.342306 1.05351i
\(576\) 0 0
\(577\) −12.3262 8.95554i −0.513148 0.372824i 0.300868 0.953666i \(-0.402723\pi\)
−0.814016 + 0.580842i \(0.802723\pi\)
\(578\) 0 0
\(579\) −0.482779 + 1.48584i −0.0200636 + 0.0617495i
\(580\) 0 0
\(581\) 30.8435 22.4091i 1.27960 0.929685i
\(582\) 0 0
\(583\) −9.12461 + 22.7194i −0.377903 + 0.940940i
\(584\) 0 0
\(585\) 1.92705 1.40008i 0.0796738 0.0578864i
\(586\) 0 0
\(587\) −7.51064 + 23.1154i −0.309997 + 0.954074i 0.667767 + 0.744370i \(0.267250\pi\)
−0.977765 + 0.209704i \(0.932750\pi\)
\(588\) 0 0
\(589\) −2.66312 1.93487i −0.109732 0.0797249i
\(590\) 0 0
\(591\) −8.22542 25.3153i −0.338349 1.04133i
\(592\) 0 0
\(593\) −29.2148 −1.19971 −0.599854 0.800110i \(-0.704775\pi\)
−0.599854 + 0.800110i \(0.704775\pi\)
\(594\) 0 0
\(595\) −0.708204 −0.0290335
\(596\) 0 0
\(597\) −1.01722 3.13068i −0.0416321 0.128130i
\(598\) 0 0
\(599\) −17.5623 12.7598i −0.717576 0.521350i 0.168033 0.985781i \(-0.446259\pi\)
−0.885609 + 0.464432i \(0.846259\pi\)
\(600\) 0 0
\(601\) −6.12868 + 18.8621i −0.249994 + 0.769402i 0.744781 + 0.667309i \(0.232554\pi\)
−0.994775 + 0.102093i \(0.967446\pi\)
\(602\) 0 0
\(603\) 8.54508 6.20837i 0.347983 0.252824i
\(604\) 0 0
\(605\) 3.70163 1.98787i 0.150493 0.0808184i
\(606\) 0 0
\(607\) −1.88197 + 1.36733i −0.0763866 + 0.0554981i −0.625323 0.780366i \(-0.715033\pi\)
0.548937 + 0.835864i \(0.315033\pi\)
\(608\) 0 0
\(609\) −4.14590 + 12.7598i −0.168000 + 0.517052i
\(610\) 0 0
\(611\) −3.11803 2.26538i −0.126142 0.0916476i
\(612\) 0 0
\(613\) 1.03444 + 3.18368i 0.0417807 + 0.128588i 0.969771 0.244016i \(-0.0784650\pi\)
−0.927990 + 0.372604i \(0.878465\pi\)
\(614\) 0 0
\(615\) 2.27051 0.0915558
\(616\) 0 0
\(617\) 46.4164 1.86865 0.934327 0.356417i \(-0.116002\pi\)
0.934327 + 0.356417i \(0.116002\pi\)
\(618\) 0 0
\(619\) 9.63525 + 29.6543i 0.387274 + 1.19191i 0.934817 + 0.355129i \(0.115563\pi\)
−0.547544 + 0.836777i \(0.684437\pi\)
\(620\) 0 0
\(621\) 4.42705 + 3.21644i 0.177651 + 0.129071i
\(622\) 0 0
\(623\) −8.78115 + 27.0256i −0.351809 + 1.08276i
\(624\) 0 0
\(625\) −18.4721 + 13.4208i −0.738885 + 0.536832i
\(626\) 0 0
\(627\) −1.05573 + 2.62866i −0.0421617 + 0.104978i
\(628\) 0 0
\(629\) −2.11803 + 1.53884i −0.0844515 + 0.0613576i
\(630\) 0 0
\(631\) −3.93363 + 12.1065i −0.156595 + 0.481951i −0.998319 0.0579577i \(-0.981541\pi\)
0.841724 + 0.539908i \(0.181541\pi\)
\(632\) 0 0
\(633\) −9.11803 6.62464i −0.362409 0.263306i
\(634\) 0 0
\(635\) 1.14590 + 3.52671i 0.0454736 + 0.139953i
\(636\) 0 0
\(637\) 12.4721 0.494164
\(638\) 0 0
\(639\) −14.5623 −0.576076
\(640\) 0 0
\(641\) −2.08359 6.41264i −0.0822969 0.253284i 0.901439 0.432907i \(-0.142512\pi\)
−0.983736 + 0.179623i \(0.942512\pi\)
\(642\) 0 0
\(643\) −14.9164 10.8374i −0.588246 0.427386i 0.253442 0.967351i \(-0.418437\pi\)
−0.841687 + 0.539965i \(0.818437\pi\)
\(644\) 0 0
\(645\) −0.208204 + 0.640786i −0.00819802 + 0.0252309i
\(646\) 0 0
\(647\) 2.59017 1.88187i 0.101830 0.0739839i −0.535705 0.844405i \(-0.679954\pi\)
0.637535 + 0.770421i \(0.279954\pi\)
\(648\) 0 0
\(649\) 4.30902 + 17.1315i 0.169144 + 0.672471i
\(650\) 0 0
\(651\) −9.35410 + 6.79615i −0.366616 + 0.266362i
\(652\) 0 0
\(653\) 6.78773 20.8905i 0.265624 0.817508i −0.725924 0.687774i \(-0.758588\pi\)
0.991549 0.129734i \(-0.0414122\pi\)
\(654\) 0 0
\(655\) 4.28115 + 3.11044i 0.167278 + 0.121535i
\(656\) 0 0
\(657\) 0.381966 + 1.17557i 0.0149019 + 0.0458634i
\(658\) 0 0
\(659\) −20.6525 −0.804506 −0.402253 0.915528i \(-0.631773\pi\)
−0.402253 + 0.915528i \(0.631773\pi\)
\(660\) 0 0
\(661\) −21.0902 −0.820313 −0.410156 0.912015i \(-0.634526\pi\)
−0.410156 + 0.912015i \(0.634526\pi\)
\(662\) 0 0
\(663\) 1.19098 + 3.66547i 0.0462539 + 0.142355i
\(664\) 0 0
\(665\) −0.791796 0.575274i −0.0307045 0.0223082i
\(666\) 0 0
\(667\) −7.56231 + 23.2744i −0.292814 + 0.901188i
\(668\) 0 0
\(669\) 10.2812 7.46969i 0.397492 0.288795i
\(670\) 0 0
\(671\) 3.79180 + 0.257270i 0.146381 + 0.00993180i
\(672\) 0 0
\(673\) 11.6631 8.47375i 0.449580 0.326639i −0.339850 0.940480i \(-0.610376\pi\)
0.789430 + 0.613841i \(0.210376\pi\)
\(674\) 0 0
\(675\) 1.50000 4.61653i 0.0577350 0.177690i
\(676\) 0 0
\(677\) −18.1803 13.2088i −0.698727 0.507655i 0.180790 0.983522i \(-0.442134\pi\)
−0.879517 + 0.475867i \(0.842134\pi\)
\(678\) 0 0
\(679\) −13.9377 42.8958i −0.534880 1.64619i
\(680\) 0 0
\(681\) 10.8885 0.417250
\(682\) 0 0
\(683\) 38.8885 1.48803 0.744014 0.668164i \(-0.232919\pi\)
0.744014 + 0.668164i \(0.232919\pi\)
\(684\) 0 0
\(685\) 0.173762 + 0.534785i 0.00663911 + 0.0204331i
\(686\) 0 0
\(687\) 8.09017 + 5.87785i 0.308659 + 0.224254i
\(688\) 0 0
\(689\) −14.2254 + 43.7814i −0.541946 + 1.66794i
\(690\) 0 0
\(691\) −32.1246 + 23.3399i −1.22208 + 0.887892i −0.996271 0.0862806i \(-0.972502\pi\)
−0.225807 + 0.974172i \(0.572502\pi\)
\(692\) 0 0
\(693\) 7.63525 + 6.37988i 0.290039 + 0.242352i
\(694\) 0 0
\(695\) −1.80902 + 1.31433i −0.0686199 + 0.0498553i
\(696\) 0 0
\(697\) −1.13525 + 3.49396i −0.0430008 + 0.132343i
\(698\) 0 0
\(699\) 7.01722 + 5.09831i 0.265416 + 0.192836i
\(700\) 0 0
\(701\) 15.3541 + 47.2551i 0.579916 + 1.78480i 0.618792 + 0.785555i \(0.287623\pi\)
−0.0388752 + 0.999244i \(0.512377\pi\)
\(702\) 0 0
\(703\) −3.61803 −0.136457
\(704\) 0 0
\(705\) 0.236068 0.00889083
\(706\) 0 0
\(707\) 2.78115 + 8.55951i 0.104596 + 0.321913i
\(708\) 0 0
\(709\) −5.06231 3.67798i −0.190119 0.138129i 0.488654 0.872478i \(-0.337488\pi\)
−0.678773 + 0.734348i \(0.737488\pi\)
\(710\) 0 0
\(711\) −0.163119 + 0.502029i −0.00611744 + 0.0188275i
\(712\) 0 0
\(713\) −17.0623 + 12.3965i −0.638988 + 0.464252i
\(714\) 0 0
\(715\) 6.69098 4.20025i 0.250229 0.157081i
\(716\) 0 0
\(717\) 14.2082 10.3229i 0.530615 0.385514i
\(718\) 0 0
\(719\) 8.78115 27.0256i 0.327482 1.00789i −0.642826 0.766012i \(-0.722238\pi\)
0.970308 0.241873i \(-0.0777618\pi\)
\(720\) 0 0
\(721\) 14.5623 + 10.5801i 0.542329 + 0.394025i
\(722\) 0 0
\(723\) −5.29180 16.2865i −0.196804 0.605700i
\(724\) 0 0
\(725\) 21.7082 0.806222
\(726\) 0 0
\(727\) −32.1459 −1.19223 −0.596113 0.802901i \(-0.703289\pi\)
−0.596113 + 0.802901i \(0.703289\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −0.881966 0.640786i −0.0326207 0.0237003i
\(732\) 0 0
\(733\) −7.50658 + 23.1029i −0.277262 + 0.853324i 0.711350 + 0.702838i \(0.248084\pi\)
−0.988612 + 0.150486i \(0.951916\pi\)
\(734\) 0 0
\(735\) −0.618034 + 0.449028i −0.0227965 + 0.0165626i
\(736\) 0 0
\(737\) 29.6697 18.6251i 1.09290 0.686064i
\(738\) 0 0
\(739\) −20.2254 + 14.6946i −0.744004 + 0.540551i −0.893963 0.448142i \(-0.852086\pi\)
0.149958 + 0.988692i \(0.452086\pi\)
\(740\) 0 0
\(741\) −1.64590 + 5.06555i −0.0604636 + 0.186088i
\(742\) 0 0
\(743\) 10.3713 + 7.53521i 0.380487 + 0.276440i 0.761546 0.648111i \(-0.224441\pi\)
−0.381059 + 0.924551i \(0.624441\pi\)
\(744\) 0 0
\(745\) −1.77051 5.44907i −0.0648665 0.199638i
\(746\) 0 0
\(747\) 12.7082 0.464969
\(748\) 0 0
\(749\) 0.708204 0.0258772
\(750\) 0 0
\(751\) 16.3541 + 50.3328i 0.596770 + 1.83667i 0.545713 + 0.837972i \(0.316259\pi\)
0.0510571 + 0.998696i \(0.483741\pi\)
\(752\) 0 0
\(753\) −13.5902 9.87384i −0.495253 0.359823i
\(754\) 0 0
\(755\) 0.236068 0.726543i 0.00859139 0.0264416i
\(756\) 0 0
\(757\) 12.8992 9.37181i 0.468829 0.340624i −0.328156 0.944624i \(-0.606427\pi\)
0.796985 + 0.603999i \(0.206427\pi\)
\(758\) 0 0
\(759\) 13.9271 + 11.6372i 0.505520 + 0.422403i
\(760\) 0 0
\(761\) −3.95492 + 2.87341i −0.143366 + 0.104161i −0.657156 0.753754i \(-0.728241\pi\)
0.513791 + 0.857916i \(0.328241\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.190983 0.138757i −0.00690501 0.00501678i
\(766\) 0 0
\(767\) 10.2639 + 31.5891i 0.370609 + 1.14062i
\(768\) 0 0
\(769\) −47.6869 −1.71963 −0.859817 0.510602i \(-0.829423\pi\)
−0.859817 + 0.510602i \(0.829423\pi\)
\(770\) 0 0
\(771\) 27.3262 0.984130
\(772\) 0 0
\(773\) 15.2188 + 46.8388i 0.547384 + 1.68467i 0.715253 + 0.698865i \(0.246311\pi\)
−0.167870 + 0.985809i \(0.553689\pi\)
\(774\) 0 0
\(775\) 15.1353 + 10.9964i 0.543674 + 0.395003i
\(776\) 0 0
\(777\) −3.92705 + 12.0862i −0.140882 + 0.433591i
\(778\) 0 0
\(779\) −4.10739 + 2.98419i −0.147163 + 0.106920i
\(780\) 0 0
\(781\) −48.1869 3.26944i −1.72426 0.116990i
\(782\) 0 0
\(783\) −3.61803 + 2.62866i −0.129298 + 0.0939405i
\(784\) 0 0
\(785\) −1.14590 + 3.52671i −0.0408989 + 0.125874i
\(786\) 0 0
\(787\) −19.1803 13.9353i −0.683705 0.496741i 0.190880 0.981613i \(-0.438866\pi\)
−0.874585 + 0.484873i \(0.838866\pi\)
\(788\) 0 0
\(789\) −0.208204 0.640786i −0.00741226 0.0228126i
\(790\) 0 0
\(791\) 38.1246 1.35556
\(792\) 0 0
\(793\) 7.14590 0.253758
\(794\) 0 0
\(795\) −0.871323 2.68166i −0.0309026 0.0951085i
\(796\) 0 0
\(797\) −12.3262 8.95554i −0.436618 0.317221i 0.347672 0.937616i \(-0.386972\pi\)
−0.784290 + 0.620395i \(0.786972\pi\)
\(798\) 0 0
\(799\) −0.118034 + 0.363271i −0.00417574 + 0.0128516i
\(800\) 0 0
\(801\) −7.66312 + 5.56758i −0.270763 + 0.196721i
\(802\) 0 0
\(803\) 1.00000 + 3.97574i 0.0352892 + 0.140301i
\(804\) 0 0
\(805\) −5.07295 + 3.68571i −0.178798 + 0.129904i
\(806\) 0 0
\(807\) −7.56231 + 23.2744i −0.266206 + 0.819297i
\(808\) 0 0
\(809\) −20.4894 14.8864i −0.720367 0.523378i 0.166134 0.986103i \(-0.446872\pi\)
−0.886502 + 0.462726i \(0.846872\pi\)
\(810\) 0 0
\(811\) −14.1353 43.5038i −0.496356 1.52763i −0.814833 0.579696i \(-0.803171\pi\)
0.318477 0.947931i \(-0.396829\pi\)
\(812\) 0 0
\(813\) 6.27051 0.219916
\(814\) 0 0
\(815\) −5.83282 −0.204315
\(816\) 0 0
\(817\) −0.465558 1.43284i −0.0162878 0.0501287i
\(818\) 0 0
\(819\) 15.1353 + 10.9964i 0.528869 + 0.384246i
\(820\) 0 0
\(821\) 4.19756 12.9188i 0.146496 0.450868i −0.850704 0.525644i \(-0.823824\pi\)
0.997200 + 0.0747763i \(0.0238243\pi\)
\(822\) 0 0
\(823\) −21.4615 + 15.5927i −0.748101 + 0.543527i −0.895238 0.445589i \(-0.852994\pi\)
0.147137 + 0.989116i \(0.452994\pi\)
\(824\) 0 0
\(825\) 6.00000 14.9394i 0.208893 0.520123i
\(826\) 0 0
\(827\) 10.4164 7.56796i 0.362214 0.263164i −0.391761 0.920067i \(-0.628134\pi\)
0.753975 + 0.656903i \(0.228134\pi\)
\(828\) 0 0
\(829\) −13.1910 + 40.5977i −0.458142 + 1.41002i 0.409265 + 0.912416i \(0.365785\pi\)
−0.867407 + 0.497600i \(0.834215\pi\)
\(830\) 0 0
\(831\) 8.44427 + 6.13512i 0.292929 + 0.212825i
\(832\) 0 0
\(833\) −0.381966 1.17557i −0.0132343 0.0407311i
\(834\) 0 0
\(835\) −7.27051 −0.251606
\(836\) 0 0
\(837\) −3.85410 −0.133217
\(838\) 0 0
\(839\) 7.19756 + 22.1518i 0.248487 + 0.764766i 0.995043 + 0.0994428i \(0.0317060\pi\)
−0.746556 + 0.665323i \(0.768294\pi\)
\(840\) 0 0
\(841\) 7.28115 + 5.29007i 0.251074 + 0.182416i
\(842\) 0 0
\(843\) 1.61803 4.97980i 0.0557281 0.171513i
\(844\) 0 0
\(845\) 8.00000 5.81234i 0.275208 0.199951i
\(846\) 0 0
\(847\) 23.8328 + 22.8254i 0.818905 + 0.784289i
\(848\) 0 0
\(849\) 17.9443 13.0373i 0.615846 0.447438i
\(850\) 0 0
\(851\) −7.16312 + 22.0458i −0.245549 + 0.755721i
\(852\) 0 0
\(853\) −6.42705 4.66953i −0.220058 0.159882i 0.472295 0.881441i \(-0.343426\pi\)
−0.692353 + 0.721559i \(0.743426\pi\)
\(854\) 0 0
\(855\) −0.100813 0.310271i −0.00344773 0.0106110i
\(856\) 0 0
\(857\) −41.7214 −1.42517 −0.712587 0.701584i \(-0.752477\pi\)
−0.712587 + 0.701584i \(0.752477\pi\)
\(858\) 0 0
\(859\) −42.8885 −1.46334 −0.731669 0.681660i \(-0.761258\pi\)
−0.731669 + 0.681660i \(0.761258\pi\)
\(860\) 0 0
\(861\) 5.51064 + 16.9600i 0.187802 + 0.577996i
\(862\) 0 0
\(863\) −19.3262 14.0413i −0.657873 0.477973i 0.208071 0.978114i \(-0.433281\pi\)
−0.865944 + 0.500141i \(0.833281\pi\)
\(864\) 0 0
\(865\) −2.07953 + 6.40013i −0.0707060 + 0.217611i
\(866\) 0 0
\(867\) −13.4443 + 9.76784i −0.456591 + 0.331733i
\(868\) 0 0
\(869\) −0.652476 + 1.62460i −0.0221337 + 0.0551107i
\(870\) 0 0
\(871\) 53.2877 38.7158i 1.80559 1.31183i
\(872\) 0 0
\(873\) 4.64590 14.2986i 0.157240 0.483934i
\(874\) 0 0
\(875\) 9.13525 + 6.63715i 0.308828 + 0.224377i
\(876\) 0 0
\(877\) −6.30902 19.4172i −0.213040 0.655671i −0.999287 0.0377579i \(-0.987978\pi\)
0.786247 0.617913i \(-0.212022\pi\)
\(878\) 0 0
\(879\) −17.9443 −0.605245
\(880\) 0 0
\(881\) 25.0902 0.845309 0.422655 0.906291i \(-0.361098\pi\)
0.422655 + 0.906291i \(0.361098\pi\)
\(882\) 0 0
\(883\) −11.5623 35.5851i −0.389103 1.19753i −0.933460 0.358681i \(-0.883226\pi\)
0.544358 0.838853i \(-0.316774\pi\)
\(884\) 0 0
\(885\) −1.64590 1.19581i −0.0553263 0.0401969i
\(886\) 0 0
\(887\) −0.927051 + 2.85317i −0.0311273 + 0.0958001i −0.965413 0.260725i \(-0.916038\pi\)
0.934286 + 0.356525i \(0.116038\pi\)
\(888\) 0 0
\(889\) −23.5623 + 17.1190i −0.790254 + 0.574153i
\(890\) 0 0
\(891\) 0.809017 + 3.21644i 0.0271031 + 0.107755i
\(892\) 0 0
\(893\) −0.427051 + 0.310271i −0.0142907 + 0.0103828i
\(894\) 0 0
\(895\) 0.263932 0.812299i 0.00882227 0.0271522i
\(896\) 0 0
\(897\) 27.6074 + 20.0579i 0.921784 + 0.669715i
\(898\) 0 0
\(899\) −5.32624 16.3925i −0.177640 0.546720i
\(900\) 0 0
\(901\) 4.56231 0.151992
\(902\) 0 0
\(903\) −5.29180 −0.176100
\(904\) 0 0
\(905\) 1.00658 + 3.09793i 0.0334598 + 0.102979i
\(906\) 0 0
\(907\) 3.21885 + 2.33863i 0.106880 + 0.0776529i 0.639942 0.768424i \(-0.278959\pi\)
−0.533061 + 0.846077i \(0.678959\pi\)
\(908\) 0 0
\(909\) −0.927051 + 2.85317i −0.0307483 + 0.0946337i
\(910\) 0 0
\(911\) 29.0795 21.1275i 0.963448 0.699986i 0.00949880 0.999955i \(-0.496976\pi\)
0.953949 + 0.299969i \(0.0969764\pi\)
\(912\) 0 0
\(913\) 42.0517 + 2.85317i 1.39171 + 0.0944261i
\(914\) 0 0
\(915\) −0.354102 + 0.257270i −0.0117062 + 0.00850509i
\(916\) 0 0
\(917\) −12.8435 + 39.5281i −0.424128 + 1.30533i
\(918\) 0 0
\(919\) −37.9894 27.6009i −1.25315 0.910469i −0.254753 0.967006i \(-0.581994\pi\)
−0.998400 + 0.0565371i \(0.981994\pi\)
\(920\) 0 0
\(921\) −6.04508 18.6049i −0.199192 0.613051i
\(922\) 0 0
\(923\) −90.8115 −2.98910
\(924\) 0 0
\(925\) 20.5623 0.676084
\(926\) 0 0
\(927\) 1.85410 + 5.70634i 0.0608967 + 0.187421i
\(928\) 0 0
\(929\) −2.33688 1.69784i −0.0766706 0.0557044i 0.548790 0.835960i \(-0.315089\pi\)
−0.625460 + 0.780256i \(0.715089\pi\)
\(930\) 0 0
\(931\) 0.527864 1.62460i 0.0173000 0.0532441i
\(932\) 0 0
\(933\) −9.28115 + 6.74315i −0.303851 + 0.220761i
\(934\) 0 0
\(935\) −0.600813 0.502029i −0.0196487 0.0164181i
\(936\) 0 0
\(937\) −26.3713 + 19.1599i −0.861514 + 0.625926i −0.928296 0.371841i \(-0.878727\pi\)
0.0667827 + 0.997768i \(0.478727\pi\)
\(938\) 0 0
\(939\) 8.60081 26.4706i 0.280677 0.863835i
\(940\) 0 0
\(941\) −27.2082 19.7679i −0.886962 0.644416i 0.0481221 0.998841i \(-0.484676\pi\)
−0.935084 + 0.354426i \(0.884676\pi\)
\(942\) 0 0
\(943\) 10.0517 + 30.9358i 0.327327 + 1.00741i
\(944\) 0 0
\(945\) −1.14590 −0.0372761
\(946\) 0 0
\(947\) −2.67376 −0.0868856 −0.0434428 0.999056i \(-0.513833\pi\)
−0.0434428 + 0.999056i \(0.513833\pi\)
\(948\) 0 0
\(949\) 2.38197 + 7.33094i 0.0773219 + 0.237972i
\(950\) 0 0
\(951\) 20.5172 + 14.9066i 0.665316 + 0.483381i
\(952\) 0 0
\(953\) 18.5967 57.2349i 0.602408 1.85402i 0.0886937 0.996059i \(-0.471731\pi\)
0.513714 0.857961i \(-0.328269\pi\)
\(954\) 0 0
\(955\) −0.454915 + 0.330515i −0.0147207 + 0.0106952i
\(956\) 0 0
\(957\) −12.5623 + 7.88597i −0.406082 + 0.254917i
\(958\) 0 0
\(959\) −3.57295 + 2.59590i −0.115377 + 0.0838260i
\(960\) 0 0
\(961\) −4.98936 + 15.3557i −0.160947 + 0.495344i
\(962\) 0 0
\(963\) 0.190983 + 0.138757i 0.00615434 + 0.00447139i
\(964\) 0 0
\(965\) −0.184405 0.567541i −0.00593621 0.0182698i
\(966\) 0 0
\(967\) −25.6869 −0.826036 −0.413018 0.910723i \(-0.635525\pi\)
−0.413018 + 0.910723i \(0.635525\pi\)
\(968\) 0 0
\(969\) 0.527864 0.0169574
\(970\) 0 0
\(971\) 10.4377 + 32.1239i 0.334962 + 1.03091i 0.966741 + 0.255757i \(0.0823248\pi\)
−0.631779 + 0.775148i \(0.717675\pi\)
\(972\) 0 0
\(973\) −14.2082 10.3229i −0.455494 0.330936i
\(974\) 0 0
\(975\) 9.35410 28.7890i 0.299571 0.921985i
\(976\) 0 0
\(977\) 39.9336 29.0135i 1.27759 0.928223i 0.278113 0.960548i \(-0.410291\pi\)
0.999477 + 0.0323250i \(0.0102912\pi\)
\(978\) 0 0
\(979\) −26.6074 + 16.7027i −0.850376 + 0.533822i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −10.9098 + 33.5770i −0.347970 + 1.07094i 0.612005 + 0.790854i \(0.290363\pi\)
−0.959975 + 0.280086i \(0.909637\pi\)
\(984\) 0 0
\(985\) 8.22542 + 5.97612i 0.262084 + 0.190415i
\(986\) 0 0
\(987\) 0.572949 + 1.76336i 0.0182372 + 0.0561282i
\(988\) 0 0
\(989\) −9.65248 −0.306931
\(990\) 0 0
\(991\) 12.2705 0.389786 0.194893 0.980825i \(-0.437564\pi\)
0.194893 + 0.980825i \(0.437564\pi\)
\(992\) 0 0
\(993\) −6.98278 21.4908i −0.221592 0.681989i
\(994\) 0 0
\(995\) 1.01722 + 0.739054i 0.0322481 + 0.0234296i
\(996\) 0 0
\(997\) 10.5000 32.3157i 0.332538 1.02345i −0.635384 0.772197i \(-0.719158\pi\)
0.967922 0.251251i \(-0.0808420\pi\)
\(998\) 0 0
\(999\) −3.42705 + 2.48990i −0.108427 + 0.0787769i
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 528.2.y.f.289.1 4
4.3 odd 2 33.2.e.a.25.1 yes 4
11.2 odd 10 5808.2.a.bm.1.2 2
11.4 even 5 inner 528.2.y.f.433.1 4
11.9 even 5 5808.2.a.bl.1.2 2
12.11 even 2 99.2.f.b.91.1 4
20.3 even 4 825.2.bx.b.124.2 8
20.7 even 4 825.2.bx.b.124.1 8
20.19 odd 2 825.2.n.f.751.1 4
36.7 odd 6 891.2.n.d.190.1 8
36.11 even 6 891.2.n.a.190.1 8
36.23 even 6 891.2.n.a.784.1 8
36.31 odd 6 891.2.n.d.784.1 8
44.3 odd 10 363.2.e.h.148.1 4
44.7 even 10 363.2.e.j.202.1 4
44.15 odd 10 33.2.e.a.4.1 4
44.19 even 10 363.2.e.c.148.1 4
44.27 odd 10 363.2.e.h.130.1 4
44.31 odd 10 363.2.a.h.1.2 2
44.35 even 10 363.2.a.e.1.1 2
44.39 even 10 363.2.e.c.130.1 4
44.43 even 2 363.2.e.j.124.1 4
132.35 odd 10 1089.2.a.s.1.2 2
132.59 even 10 99.2.f.b.37.1 4
132.119 even 10 1089.2.a.m.1.1 2
220.59 odd 10 825.2.n.f.301.1 4
220.79 even 10 9075.2.a.bv.1.2 2
220.103 even 20 825.2.bx.b.499.1 8
220.119 odd 10 9075.2.a.x.1.1 2
220.147 even 20 825.2.bx.b.499.2 8
396.59 even 30 891.2.n.a.136.1 8
396.103 odd 30 891.2.n.d.136.1 8
396.191 even 30 891.2.n.a.433.1 8
396.367 odd 30 891.2.n.d.433.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.4.1 4 44.15 odd 10
33.2.e.a.25.1 yes 4 4.3 odd 2
99.2.f.b.37.1 4 132.59 even 10
99.2.f.b.91.1 4 12.11 even 2
363.2.a.e.1.1 2 44.35 even 10
363.2.a.h.1.2 2 44.31 odd 10
363.2.e.c.130.1 4 44.39 even 10
363.2.e.c.148.1 4 44.19 even 10
363.2.e.h.130.1 4 44.27 odd 10
363.2.e.h.148.1 4 44.3 odd 10
363.2.e.j.124.1 4 44.43 even 2
363.2.e.j.202.1 4 44.7 even 10
528.2.y.f.289.1 4 1.1 even 1 trivial
528.2.y.f.433.1 4 11.4 even 5 inner
825.2.n.f.301.1 4 220.59 odd 10
825.2.n.f.751.1 4 20.19 odd 2
825.2.bx.b.124.1 8 20.7 even 4
825.2.bx.b.124.2 8 20.3 even 4
825.2.bx.b.499.1 8 220.103 even 20
825.2.bx.b.499.2 8 220.147 even 20
891.2.n.a.136.1 8 396.59 even 30
891.2.n.a.190.1 8 36.11 even 6
891.2.n.a.433.1 8 396.191 even 30
891.2.n.a.784.1 8 36.23 even 6
891.2.n.d.136.1 8 396.103 odd 30
891.2.n.d.190.1 8 36.7 odd 6
891.2.n.d.433.1 8 396.367 odd 30
891.2.n.d.784.1 8 36.31 odd 6
1089.2.a.m.1.1 2 132.119 even 10
1089.2.a.s.1.2 2 132.35 odd 10
5808.2.a.bl.1.2 2 11.9 even 5
5808.2.a.bm.1.2 2 11.2 odd 10
9075.2.a.x.1.1 2 220.119 odd 10
9075.2.a.bv.1.2 2 220.79 even 10