Properties

Label 260.2.bk.c.33.5
Level $260$
Weight $2$
Character 260.33
Analytic conductor $2.076$
Analytic rank $0$
Dimension $20$
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] = [260,2,Mod(33,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), 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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.5
Root \(-0.402430i\) of defining polynomial
Character \(\chi\) \(=\) 260.33
Dual form 260.2.bk.c.197.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.49316 - 0.668040i) q^{3} +(-0.380790 - 2.20341i) q^{5} +(-0.749297 + 0.432607i) q^{7} +(3.17149 - 1.83106i) q^{9} +O(q^{10})\) \(q+(2.49316 - 0.668040i) q^{3} +(-0.380790 - 2.20341i) q^{5} +(-0.749297 + 0.432607i) q^{7} +(3.17149 - 1.83106i) q^{9} +(0.417628 + 1.55861i) q^{11} +(1.32514 - 3.35321i) q^{13} +(-2.42134 - 5.23906i) q^{15} +(-1.33873 + 4.99621i) q^{17} +(-1.16619 - 0.312480i) q^{19} +(-1.57912 + 1.57912i) q^{21} +(0.704305 + 2.62850i) q^{23} +(-4.71000 + 1.67807i) q^{25} +(1.20845 - 1.20845i) q^{27} +(5.94138 + 3.43026i) q^{29} +(0.191663 + 0.191663i) q^{31} +(2.08243 + 3.60687i) q^{33} +(1.23853 + 1.48627i) q^{35} +(-8.22242 - 4.74722i) q^{37} +(1.06370 - 9.24533i) q^{39} +(0.417297 - 0.111814i) q^{41} +(11.5499 + 3.09480i) q^{43} +(-5.24225 - 6.29083i) q^{45} -1.52128i q^{47} +(-3.12570 + 5.41387i) q^{49} +13.3507i q^{51} +(-4.88398 - 4.88398i) q^{53} +(3.27522 - 1.51371i) q^{55} -3.11625 q^{57} +(-3.05172 + 11.3892i) q^{59} +(-2.94152 - 5.09486i) q^{61} +(-1.58426 + 2.74402i) q^{63} +(-7.89308 - 1.64294i) q^{65} +(6.76168 - 11.7116i) q^{67} +(3.51189 + 6.08277i) q^{69} +(-3.85102 + 14.3722i) q^{71} -10.9921 q^{73} +(-10.6218 + 7.33017i) q^{75} +(-0.987192 - 0.987192i) q^{77} -3.98168i q^{79} +(-3.28761 + 5.69431i) q^{81} -6.25583i q^{83} +(11.5185 + 1.04726i) q^{85} +(17.1044 + 4.58310i) q^{87} +(-9.80805 + 2.62806i) q^{89} +(0.457701 + 3.08581i) q^{91} +(0.605885 + 0.349808i) q^{93} +(-0.244446 + 2.68858i) q^{95} +(-0.728593 - 1.26196i) q^{97} +(4.17841 + 4.17841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



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
\(3\) 2.49316 0.668040i 1.43943 0.385693i 0.547094 0.837071i \(-0.315734\pi\)
0.892333 + 0.451378i \(0.149067\pi\)
\(4\) 0 0
\(5\) −0.380790 2.20341i −0.170295 0.985393i
\(6\) 0 0
\(7\) −0.749297 + 0.432607i −0.283208 + 0.163510i −0.634875 0.772615i \(-0.718948\pi\)
0.351667 + 0.936125i \(0.385615\pi\)
\(8\) 0 0
\(9\) 3.17149 1.83106i 1.05716 0.610354i
\(10\) 0 0
\(11\) 0.417628 + 1.55861i 0.125920 + 0.469938i 0.999871 0.0160756i \(-0.00511723\pi\)
−0.873951 + 0.486014i \(0.838451\pi\)
\(12\) 0 0
\(13\) 1.32514 3.35321i 0.367527 0.930013i
\(14\) 0 0
\(15\) −2.42134 5.23906i −0.625186 1.35272i
\(16\) 0 0
\(17\) −1.33873 + 4.99621i −0.324690 + 1.21176i 0.589933 + 0.807452i \(0.299154\pi\)
−0.914623 + 0.404308i \(0.867513\pi\)
\(18\) 0 0
\(19\) −1.16619 0.312480i −0.267543 0.0716878i 0.122554 0.992462i \(-0.460892\pi\)
−0.390096 + 0.920774i \(0.627558\pi\)
\(20\) 0 0
\(21\) −1.57912 + 1.57912i −0.344592 + 0.344592i
\(22\) 0 0
\(23\) 0.704305 + 2.62850i 0.146858 + 0.548080i 0.999666 + 0.0258557i \(0.00823103\pi\)
−0.852808 + 0.522225i \(0.825102\pi\)
\(24\) 0 0
\(25\) −4.71000 + 1.67807i −0.941999 + 0.335614i
\(26\) 0 0
\(27\) 1.20845 1.20845i 0.232567 0.232567i
\(28\) 0 0
\(29\) 5.94138 + 3.43026i 1.10329 + 0.636983i 0.937082 0.349109i \(-0.113516\pi\)
0.166204 + 0.986091i \(0.446849\pi\)
\(30\) 0 0
\(31\) 0.191663 + 0.191663i 0.0344237 + 0.0344237i 0.724109 0.689685i \(-0.242251\pi\)
−0.689685 + 0.724109i \(0.742251\pi\)
\(32\) 0 0
\(33\) 2.08243 + 3.60687i 0.362504 + 0.627875i
\(34\) 0 0
\(35\) 1.23853 + 1.48627i 0.209351 + 0.251226i
\(36\) 0 0
\(37\) −8.22242 4.74722i −1.35176 0.780438i −0.363262 0.931687i \(-0.618337\pi\)
−0.988496 + 0.151249i \(0.951670\pi\)
\(38\) 0 0
\(39\) 1.06370 9.24533i 0.170328 1.48044i
\(40\) 0 0
\(41\) 0.417297 0.111814i 0.0651709 0.0174625i −0.226086 0.974107i \(-0.572593\pi\)
0.291257 + 0.956645i \(0.405926\pi\)
\(42\) 0 0
\(43\) 11.5499 + 3.09480i 1.76135 + 0.471952i 0.986989 0.160791i \(-0.0514044\pi\)
0.774362 + 0.632743i \(0.218071\pi\)
\(44\) 0 0
\(45\) −5.24225 6.29083i −0.781468 0.937782i
\(46\) 0 0
\(47\) 1.52128i 0.221902i −0.993826 0.110951i \(-0.964610\pi\)
0.993826 0.110951i \(-0.0353897\pi\)
\(48\) 0 0
\(49\) −3.12570 + 5.41387i −0.446529 + 0.773411i
\(50\) 0 0
\(51\) 13.3507i 1.86947i
\(52\) 0 0
\(53\) −4.88398 4.88398i −0.670867 0.670867i 0.287049 0.957916i \(-0.407326\pi\)
−0.957916 + 0.287049i \(0.907326\pi\)
\(54\) 0 0
\(55\) 3.27522 1.51371i 0.441630 0.204108i
\(56\) 0 0
\(57\) −3.11625 −0.412757
\(58\) 0 0
\(59\) −3.05172 + 11.3892i −0.397300 + 1.48274i 0.420528 + 0.907279i \(0.361845\pi\)
−0.817828 + 0.575463i \(0.804822\pi\)
\(60\) 0 0
\(61\) −2.94152 5.09486i −0.376623 0.652330i 0.613946 0.789348i \(-0.289581\pi\)
−0.990569 + 0.137018i \(0.956248\pi\)
\(62\) 0 0
\(63\) −1.58426 + 2.74402i −0.199598 + 0.345714i
\(64\) 0 0
\(65\) −7.89308 1.64294i −0.979016 0.203782i
\(66\) 0 0
\(67\) 6.76168 11.7116i 0.826070 1.43080i −0.0750284 0.997181i \(-0.523905\pi\)
0.901099 0.433614i \(-0.142762\pi\)
\(68\) 0 0
\(69\) 3.51189 + 6.08277i 0.422782 + 0.732279i
\(70\) 0 0
\(71\) −3.85102 + 14.3722i −0.457031 + 1.70566i 0.225015 + 0.974355i \(0.427757\pi\)
−0.682046 + 0.731309i \(0.738910\pi\)
\(72\) 0 0
\(73\) −10.9921 −1.28653 −0.643266 0.765643i \(-0.722421\pi\)
−0.643266 + 0.765643i \(0.722421\pi\)
\(74\) 0 0
\(75\) −10.6218 + 7.33017i −1.22649 + 0.846415i
\(76\) 0 0
\(77\) −0.987192 0.987192i −0.112501 0.112501i
\(78\) 0 0
\(79\) 3.98168i 0.447974i −0.974592 0.223987i \(-0.928093\pi\)
0.974592 0.223987i \(-0.0719074\pi\)
\(80\) 0 0
\(81\) −3.28761 + 5.69431i −0.365290 + 0.632701i
\(82\) 0 0
\(83\) 6.25583i 0.686667i −0.939214 0.343333i \(-0.888444\pi\)
0.939214 0.343333i \(-0.111556\pi\)
\(84\) 0 0
\(85\) 11.5185 + 1.04726i 1.24935 + 0.113591i
\(86\) 0 0
\(87\) 17.1044 + 4.58310i 1.83378 + 0.491360i
\(88\) 0 0
\(89\) −9.80805 + 2.62806i −1.03965 + 0.278574i −0.737969 0.674835i \(-0.764215\pi\)
−0.301683 + 0.953408i \(0.597548\pi\)
\(90\) 0 0
\(91\) 0.457701 + 3.08581i 0.0479801 + 0.323481i
\(92\) 0 0
\(93\) 0.605885 + 0.349808i 0.0628274 + 0.0362734i
\(94\) 0 0
\(95\) −0.244446 + 2.68858i −0.0250796 + 0.275843i
\(96\) 0 0
\(97\) −0.728593 1.26196i −0.0739774 0.128133i 0.826664 0.562696i \(-0.190236\pi\)
−0.900641 + 0.434564i \(0.856903\pi\)
\(98\) 0 0
\(99\) 4.17841 + 4.17841i 0.419946 + 0.419946i
\(100\) 0 0
\(101\) −10.0529 5.80403i −1.00030 0.577523i −0.0919621 0.995763i \(-0.529314\pi\)
−0.908337 + 0.418240i \(0.862647\pi\)
\(102\) 0 0
\(103\) 10.8660 10.8660i 1.07066 1.07066i 0.0733504 0.997306i \(-0.476631\pi\)
0.997306 0.0733504i \(-0.0233691\pi\)
\(104\) 0 0
\(105\) 4.08076 + 2.87813i 0.398241 + 0.280877i
\(106\) 0 0
\(107\) −1.84601 6.88942i −0.178461 0.666025i −0.995936 0.0900615i \(-0.971294\pi\)
0.817475 0.575964i \(-0.195373\pi\)
\(108\) 0 0
\(109\) 4.56805 4.56805i 0.437540 0.437540i −0.453643 0.891183i \(-0.649876\pi\)
0.891183 + 0.453643i \(0.149876\pi\)
\(110\) 0 0
\(111\) −23.6711 6.34266i −2.24677 0.602019i
\(112\) 0 0
\(113\) 2.23652 8.34679i 0.210394 0.785200i −0.777344 0.629076i \(-0.783433\pi\)
0.987737 0.156124i \(-0.0498999\pi\)
\(114\) 0 0
\(115\) 5.52346 2.55278i 0.515065 0.238048i
\(116\) 0 0
\(117\) −1.93727 13.0611i −0.179101 1.20750i
\(118\) 0 0
\(119\) −1.15829 4.32280i −0.106180 0.396270i
\(120\) 0 0
\(121\) 7.27143 4.19816i 0.661039 0.381651i
\(122\) 0 0
\(123\) 0.965692 0.557543i 0.0870735 0.0502719i
\(124\) 0 0
\(125\) 5.49100 + 9.73904i 0.491130 + 0.871086i
\(126\) 0 0
\(127\) −4.54494 + 1.21781i −0.403299 + 0.108064i −0.454766 0.890611i \(-0.650277\pi\)
0.0514670 + 0.998675i \(0.483610\pi\)
\(128\) 0 0
\(129\) 30.8633 2.71736
\(130\) 0 0
\(131\) 15.3255 1.33900 0.669498 0.742814i \(-0.266509\pi\)
0.669498 + 0.742814i \(0.266509\pi\)
\(132\) 0 0
\(133\) 1.00900 0.270362i 0.0874918 0.0234434i
\(134\) 0 0
\(135\) −3.12288 2.20255i −0.268775 0.189565i
\(136\) 0 0
\(137\) 14.6738 8.47191i 1.25367 0.723804i 0.281830 0.959464i \(-0.409059\pi\)
0.971835 + 0.235661i \(0.0757253\pi\)
\(138\) 0 0
\(139\) −2.69425 + 1.55553i −0.228524 + 0.131938i −0.609891 0.792485i \(-0.708787\pi\)
0.381367 + 0.924424i \(0.375453\pi\)
\(140\) 0 0
\(141\) −1.01628 3.79280i −0.0855861 0.319412i
\(142\) 0 0
\(143\) 5.77975 + 0.664975i 0.483327 + 0.0556080i
\(144\) 0 0
\(145\) 5.29583 14.3975i 0.439795 1.19565i
\(146\) 0 0
\(147\) −4.17619 + 15.5857i −0.344446 + 1.28549i
\(148\) 0 0
\(149\) 15.9563 + 4.27549i 1.30719 + 0.350262i 0.844166 0.536082i \(-0.180096\pi\)
0.463029 + 0.886343i \(0.346763\pi\)
\(150\) 0 0
\(151\) 12.3067 12.3067i 1.00151 1.00151i 0.00150662 0.999999i \(-0.499520\pi\)
0.999999 0.00150662i \(-0.000479574\pi\)
\(152\) 0 0
\(153\) 4.90260 + 18.2968i 0.396352 + 1.47920i
\(154\) 0 0
\(155\) 0.349328 0.495295i 0.0280587 0.0397830i
\(156\) 0 0
\(157\) −5.83463 + 5.83463i −0.465654 + 0.465654i −0.900503 0.434849i \(-0.856802\pi\)
0.434849 + 0.900503i \(0.356802\pi\)
\(158\) 0 0
\(159\) −15.4392 8.91385i −1.22441 0.706914i
\(160\) 0 0
\(161\) −1.66484 1.66484i −0.131208 0.131208i
\(162\) 0 0
\(163\) −2.64140 4.57504i −0.206890 0.358344i 0.743843 0.668354i \(-0.233001\pi\)
−0.950733 + 0.310010i \(0.899668\pi\)
\(164\) 0 0
\(165\) 7.15442 5.96189i 0.556971 0.464132i
\(166\) 0 0
\(167\) −6.81358 3.93382i −0.527251 0.304408i 0.212645 0.977129i \(-0.431792\pi\)
−0.739896 + 0.672721i \(0.765125\pi\)
\(168\) 0 0
\(169\) −9.48803 8.88692i −0.729848 0.683609i
\(170\) 0 0
\(171\) −4.27073 + 1.14434i −0.326591 + 0.0875098i
\(172\) 0 0
\(173\) −19.2622 5.16129i −1.46448 0.392406i −0.563444 0.826154i \(-0.690524\pi\)
−0.901034 + 0.433749i \(0.857191\pi\)
\(174\) 0 0
\(175\) 2.80324 3.29495i 0.211905 0.249075i
\(176\) 0 0
\(177\) 30.4337i 2.28753i
\(178\) 0 0
\(179\) −1.53139 + 2.65244i −0.114461 + 0.198253i −0.917564 0.397588i \(-0.869847\pi\)
0.803103 + 0.595840i \(0.203181\pi\)
\(180\) 0 0
\(181\) 23.3657i 1.73676i 0.495901 + 0.868379i \(0.334838\pi\)
−0.495901 + 0.868379i \(0.665162\pi\)
\(182\) 0 0
\(183\) −10.7372 10.7372i −0.793720 0.793720i
\(184\) 0 0
\(185\) −7.32903 + 19.9250i −0.538841 + 1.46492i
\(186\) 0 0
\(187\) −8.34623 −0.610337
\(188\) 0 0
\(189\) −0.382706 + 1.42828i −0.0278377 + 0.103892i
\(190\) 0 0
\(191\) 3.73743 + 6.47341i 0.270431 + 0.468400i 0.968972 0.247170i \(-0.0795006\pi\)
−0.698541 + 0.715570i \(0.746167\pi\)
\(192\) 0 0
\(193\) −1.00100 + 1.73378i −0.0720536 + 0.124800i −0.899801 0.436300i \(-0.856289\pi\)
0.827748 + 0.561101i \(0.189622\pi\)
\(194\) 0 0
\(195\) −20.7763 + 1.17678i −1.48782 + 0.0842707i
\(196\) 0 0
\(197\) 1.59042 2.75469i 0.113313 0.196264i −0.803791 0.594912i \(-0.797187\pi\)
0.917104 + 0.398648i \(0.130520\pi\)
\(198\) 0 0
\(199\) −8.20225 14.2067i −0.581442 1.00709i −0.995309 0.0967496i \(-0.969155\pi\)
0.413867 0.910337i \(-0.364178\pi\)
\(200\) 0 0
\(201\) 9.03414 33.7159i 0.637219 2.37813i
\(202\) 0 0
\(203\) −5.93581 −0.416612
\(204\) 0 0
\(205\) −0.405275 0.876897i −0.0283057 0.0612452i
\(206\) 0 0
\(207\) 7.04664 + 7.04664i 0.489775 + 0.489775i
\(208\) 0 0
\(209\) 1.94813i 0.134755i
\(210\) 0 0
\(211\) 5.66213 9.80710i 0.389797 0.675149i −0.602625 0.798025i \(-0.705878\pi\)
0.992422 + 0.122876i \(0.0392117\pi\)
\(212\) 0 0
\(213\) 38.4048i 2.63145i
\(214\) 0 0
\(215\) 2.42099 26.6277i 0.165110 1.81599i
\(216\) 0 0
\(217\) −0.226527 0.0606978i −0.0153777 0.00412044i
\(218\) 0 0
\(219\) −27.4051 + 7.34318i −1.85187 + 0.496206i
\(220\) 0 0
\(221\) 14.9794 + 11.1097i 1.00762 + 0.747320i
\(222\) 0 0
\(223\) 8.74357 + 5.04810i 0.585513 + 0.338046i 0.763321 0.646019i \(-0.223567\pi\)
−0.177808 + 0.984065i \(0.556901\pi\)
\(224\) 0 0
\(225\) −11.8651 + 13.9463i −0.791004 + 0.929752i
\(226\) 0 0
\(227\) 6.86958 + 11.8985i 0.455950 + 0.789728i 0.998742 0.0501387i \(-0.0159663\pi\)
−0.542792 + 0.839867i \(0.682633\pi\)
\(228\) 0 0
\(229\) −3.36743 3.36743i −0.222526 0.222526i 0.587035 0.809561i \(-0.300295\pi\)
−0.809561 + 0.587035i \(0.800295\pi\)
\(230\) 0 0
\(231\) −3.12071 1.80174i −0.205328 0.118546i
\(232\) 0 0
\(233\) 19.1541 19.1541i 1.25482 1.25482i 0.301293 0.953532i \(-0.402582\pi\)
0.953532 0.301293i \(-0.0974181\pi\)
\(234\) 0 0
\(235\) −3.35201 + 0.579291i −0.218661 + 0.0377888i
\(236\) 0 0
\(237\) −2.65992 9.92697i −0.172781 0.644826i
\(238\) 0 0
\(239\) −18.4667 + 18.4667i −1.19451 + 1.19451i −0.218727 + 0.975786i \(0.570190\pi\)
−0.975786 + 0.218727i \(0.929810\pi\)
\(240\) 0 0
\(241\) 0.850786 + 0.227967i 0.0548040 + 0.0146847i 0.286117 0.958195i \(-0.407635\pi\)
−0.231313 + 0.972879i \(0.574302\pi\)
\(242\) 0 0
\(243\) −5.71949 + 21.3454i −0.366905 + 1.36931i
\(244\) 0 0
\(245\) 13.1192 + 4.82564i 0.838155 + 0.308299i
\(246\) 0 0
\(247\) −2.59317 + 3.49640i −0.165000 + 0.222471i
\(248\) 0 0
\(249\) −4.17915 15.5968i −0.264843 0.988406i
\(250\) 0 0
\(251\) 5.62276 3.24630i 0.354905 0.204905i −0.311938 0.950102i \(-0.600978\pi\)
0.666844 + 0.745198i \(0.267645\pi\)
\(252\) 0 0
\(253\) −3.80266 + 2.19547i −0.239071 + 0.138028i
\(254\) 0 0
\(255\) 29.4170 5.08381i 1.84216 0.318361i
\(256\) 0 0
\(257\) −10.3489 + 2.77298i −0.645547 + 0.172974i −0.566715 0.823914i \(-0.691786\pi\)
−0.0788324 + 0.996888i \(0.525119\pi\)
\(258\) 0 0
\(259\) 8.21472 0.510438
\(260\) 0 0
\(261\) 25.1240 1.55514
\(262\) 0 0
\(263\) −9.80873 + 2.62824i −0.604832 + 0.162064i −0.548223 0.836332i \(-0.684696\pi\)
−0.0566092 + 0.998396i \(0.518029\pi\)
\(264\) 0 0
\(265\) −8.90162 + 12.6212i −0.546822 + 0.775312i
\(266\) 0 0
\(267\) −22.6974 + 13.1043i −1.38906 + 0.801973i
\(268\) 0 0
\(269\) −16.1943 + 9.34977i −0.987383 + 0.570066i −0.904491 0.426493i \(-0.859749\pi\)
−0.0828917 + 0.996559i \(0.526416\pi\)
\(270\) 0 0
\(271\) −4.74484 17.7080i −0.288228 1.07568i −0.946448 0.322856i \(-0.895357\pi\)
0.658220 0.752826i \(-0.271310\pi\)
\(272\) 0 0
\(273\) 3.20257 + 7.38767i 0.193828 + 0.447122i
\(274\) 0 0
\(275\) −4.58248 6.64023i −0.276334 0.400421i
\(276\) 0 0
\(277\) 3.50958 13.0979i 0.210870 0.786979i −0.776709 0.629859i \(-0.783113\pi\)
0.987580 0.157120i \(-0.0502208\pi\)
\(278\) 0 0
\(279\) 0.958804 + 0.256911i 0.0574021 + 0.0153809i
\(280\) 0 0
\(281\) 17.1478 17.1478i 1.02295 1.02295i 0.0232200 0.999730i \(-0.492608\pi\)
0.999730 0.0232200i \(-0.00739181\pi\)
\(282\) 0 0
\(283\) 2.37015 + 8.84554i 0.140891 + 0.525813i 0.999904 + 0.0138586i \(0.00441148\pi\)
−0.859013 + 0.511954i \(0.828922\pi\)
\(284\) 0 0
\(285\) 1.18664 + 6.86636i 0.0702904 + 0.406728i
\(286\) 0 0
\(287\) −0.264308 + 0.264308i −0.0156016 + 0.0156016i
\(288\) 0 0
\(289\) −8.44752 4.87718i −0.496913 0.286893i
\(290\) 0 0
\(291\) −2.65954 2.65954i −0.155905 0.155905i
\(292\) 0 0
\(293\) 9.09083 + 15.7458i 0.531092 + 0.919878i 0.999342 + 0.0362820i \(0.0115515\pi\)
−0.468250 + 0.883596i \(0.655115\pi\)
\(294\) 0 0
\(295\) 26.2570 + 2.38729i 1.52874 + 0.138993i
\(296\) 0 0
\(297\) 2.38819 + 1.37882i 0.138577 + 0.0800073i
\(298\) 0 0
\(299\) 9.74721 + 1.12144i 0.563696 + 0.0648546i
\(300\) 0 0
\(301\) −9.99318 + 2.67766i −0.575997 + 0.154338i
\(302\) 0 0
\(303\) −28.9408 7.75465i −1.66260 0.445493i
\(304\) 0 0
\(305\) −10.1059 + 8.42144i −0.578665 + 0.482210i
\(306\) 0 0
\(307\) 28.0356i 1.60008i 0.599948 + 0.800039i \(0.295188\pi\)
−0.599948 + 0.800039i \(0.704812\pi\)
\(308\) 0 0
\(309\) 19.8317 34.3495i 1.12819 1.95408i
\(310\) 0 0
\(311\) 11.5168i 0.653060i −0.945187 0.326530i \(-0.894121\pi\)
0.945187 0.326530i \(-0.105879\pi\)
\(312\) 0 0
\(313\) −10.3376 10.3376i −0.584316 0.584316i 0.351771 0.936086i \(-0.385580\pi\)
−0.936086 + 0.351771i \(0.885580\pi\)
\(314\) 0 0
\(315\) 6.64946 + 2.44587i 0.374655 + 0.137809i
\(316\) 0 0
\(317\) 2.31106 0.129802 0.0649010 0.997892i \(-0.479327\pi\)
0.0649010 + 0.997892i \(0.479327\pi\)
\(318\) 0 0
\(319\) −2.86514 + 10.6928i −0.160417 + 0.598685i
\(320\) 0 0
\(321\) −9.20481 15.9432i −0.513763 0.889863i
\(322\) 0 0
\(323\) 3.12243 5.40821i 0.173737 0.300921i
\(324\) 0 0
\(325\) −0.614460 + 18.0173i −0.0340841 + 0.999419i
\(326\) 0 0
\(327\) 8.33724 14.4405i 0.461050 0.798563i
\(328\) 0 0
\(329\) 0.658118 + 1.13989i 0.0362832 + 0.0628444i
\(330\) 0 0
\(331\) −9.10127 + 33.9664i −0.500251 + 1.86696i −0.00188163 + 0.999998i \(0.500599\pi\)
−0.498370 + 0.866965i \(0.666068\pi\)
\(332\) 0 0
\(333\) −34.7698 −1.90537
\(334\) 0 0
\(335\) −28.3801 10.4391i −1.55057 0.570347i
\(336\) 0 0
\(337\) −4.04414 4.04414i −0.220298 0.220298i 0.588326 0.808624i \(-0.299787\pi\)
−0.808624 + 0.588326i \(0.799787\pi\)
\(338\) 0 0
\(339\) 22.3040i 1.21139i
\(340\) 0 0
\(341\) −0.218684 + 0.378771i −0.0118424 + 0.0205116i
\(342\) 0 0
\(343\) 11.4653i 0.619068i
\(344\) 0 0
\(345\) 12.0655 10.0544i 0.649585 0.541309i
\(346\) 0 0
\(347\) −0.216132 0.0579124i −0.0116026 0.00310890i 0.253013 0.967463i \(-0.418578\pi\)
−0.264616 + 0.964354i \(0.585245\pi\)
\(348\) 0 0
\(349\) −11.9175 + 3.19329i −0.637930 + 0.170933i −0.563266 0.826276i \(-0.690455\pi\)
−0.0746643 + 0.997209i \(0.523789\pi\)
\(350\) 0 0
\(351\) −2.45083 5.65356i −0.130816 0.301765i
\(352\) 0 0
\(353\) −11.0318 6.36920i −0.587162 0.338998i 0.176812 0.984245i \(-0.443421\pi\)
−0.763975 + 0.645246i \(0.776755\pi\)
\(354\) 0 0
\(355\) 33.1342 + 3.01256i 1.75858 + 0.159890i
\(356\) 0 0
\(357\) −5.77560 10.0036i −0.305677 0.529449i
\(358\) 0 0
\(359\) 18.8285 + 18.8285i 0.993730 + 0.993730i 0.999980 0.00625094i \(-0.00198975\pi\)
−0.00625094 + 0.999980i \(0.501990\pi\)
\(360\) 0 0
\(361\) −15.1921 8.77118i −0.799586 0.461641i
\(362\) 0 0
\(363\) 15.3243 15.3243i 0.804317 0.804317i
\(364\) 0 0
\(365\) 4.18570 + 24.2201i 0.219089 + 1.26774i
\(366\) 0 0
\(367\) 5.35985 + 20.0032i 0.279782 + 1.04416i 0.952569 + 0.304324i \(0.0984305\pi\)
−0.672787 + 0.739837i \(0.734903\pi\)
\(368\) 0 0
\(369\) 1.11872 1.11872i 0.0582380 0.0582380i
\(370\) 0 0
\(371\) 5.77240 + 1.54671i 0.299688 + 0.0803012i
\(372\) 0 0
\(373\) 1.10162 4.11130i 0.0570397 0.212875i −0.931524 0.363680i \(-0.881520\pi\)
0.988563 + 0.150805i \(0.0481867\pi\)
\(374\) 0 0
\(375\) 20.1960 + 20.6128i 1.04292 + 1.06444i
\(376\) 0 0
\(377\) 19.3755 15.3771i 0.997889 0.791962i
\(378\) 0 0
\(379\) 2.81310 + 10.4986i 0.144499 + 0.539278i 0.999777 + 0.0211086i \(0.00671957\pi\)
−0.855278 + 0.518169i \(0.826614\pi\)
\(380\) 0 0
\(381\) −10.5177 + 6.07241i −0.538839 + 0.311099i
\(382\) 0 0
\(383\) −11.6937 + 6.75134i −0.597518 + 0.344977i −0.768065 0.640372i \(-0.778780\pi\)
0.170546 + 0.985350i \(0.445447\pi\)
\(384\) 0 0
\(385\) −1.79927 + 2.55110i −0.0916994 + 0.130016i
\(386\) 0 0
\(387\) 42.2973 11.3335i 2.15009 0.576116i
\(388\) 0 0
\(389\) −7.82344 −0.396664 −0.198332 0.980135i \(-0.563552\pi\)
−0.198332 + 0.980135i \(0.563552\pi\)
\(390\) 0 0
\(391\) −14.0754 −0.711825
\(392\) 0 0
\(393\) 38.2090 10.2381i 1.92739 0.516442i
\(394\) 0 0
\(395\) −8.77327 + 1.51619i −0.441431 + 0.0762877i
\(396\) 0 0
\(397\) 10.4670 6.04313i 0.525324 0.303296i −0.213786 0.976881i \(-0.568579\pi\)
0.739110 + 0.673584i \(0.235246\pi\)
\(398\) 0 0
\(399\) 2.33500 1.34811i 0.116896 0.0674900i
\(400\) 0 0
\(401\) −3.23948 12.0899i −0.161772 0.603740i −0.998430 0.0560149i \(-0.982161\pi\)
0.836658 0.547725i \(-0.184506\pi\)
\(402\) 0 0
\(403\) 0.896666 0.388707i 0.0446661 0.0193629i
\(404\) 0 0
\(405\) 13.7988 + 5.07561i 0.685666 + 0.252209i
\(406\) 0 0
\(407\) 3.96514 14.7981i 0.196545 0.733515i
\(408\) 0 0
\(409\) 12.0227 + 3.22147i 0.594484 + 0.159292i 0.543502 0.839408i \(-0.317098\pi\)
0.0509825 + 0.998700i \(0.483765\pi\)
\(410\) 0 0
\(411\) 30.9245 30.9245i 1.52539 1.52539i
\(412\) 0 0
\(413\) −2.64039 9.85406i −0.129925 0.484887i
\(414\) 0 0
\(415\) −13.7841 + 2.38216i −0.676637 + 0.116936i
\(416\) 0 0
\(417\) −5.67805 + 5.67805i −0.278055 + 0.278055i
\(418\) 0 0
\(419\) −6.12710 3.53748i −0.299328 0.172817i 0.342813 0.939404i \(-0.388620\pi\)
−0.642141 + 0.766586i \(0.721954\pi\)
\(420\) 0 0
\(421\) −12.6378 12.6378i −0.615930 0.615930i 0.328555 0.944485i \(-0.393438\pi\)
−0.944485 + 0.328555i \(0.893438\pi\)
\(422\) 0 0
\(423\) −2.78557 4.82474i −0.135439 0.234587i
\(424\) 0 0
\(425\) −2.07859 25.7786i −0.100826 1.25045i
\(426\) 0 0
\(427\) 4.40815 + 2.54504i 0.213325 + 0.123163i
\(428\) 0 0
\(429\) 14.8541 2.20322i 0.717162 0.106372i
\(430\) 0 0
\(431\) 1.66350 0.445735i 0.0801282 0.0214703i −0.218532 0.975830i \(-0.570127\pi\)
0.298660 + 0.954359i \(0.403460\pi\)
\(432\) 0 0
\(433\) 15.5451 + 4.16531i 0.747052 + 0.200172i 0.612210 0.790695i \(-0.290281\pi\)
0.134842 + 0.990867i \(0.456947\pi\)
\(434\) 0 0
\(435\) 3.58525 39.4330i 0.171900 1.89067i
\(436\) 0 0
\(437\) 3.28541i 0.157163i
\(438\) 0 0
\(439\) −7.54892 + 13.0751i −0.360290 + 0.624041i −0.988008 0.154400i \(-0.950656\pi\)
0.627718 + 0.778441i \(0.283989\pi\)
\(440\) 0 0
\(441\) 22.8934i 1.09016i
\(442\) 0 0
\(443\) −13.3798 13.3798i −0.635694 0.635694i 0.313797 0.949490i \(-0.398399\pi\)
−0.949490 + 0.313797i \(0.898399\pi\)
\(444\) 0 0
\(445\) 9.52550 + 20.6104i 0.451552 + 0.977026i
\(446\) 0 0
\(447\) 42.6379 2.01670
\(448\) 0 0
\(449\) −4.77864 + 17.8341i −0.225518 + 0.841645i 0.756678 + 0.653788i \(0.226821\pi\)
−0.982196 + 0.187858i \(0.939846\pi\)
\(450\) 0 0
\(451\) 0.348550 + 0.603706i 0.0164126 + 0.0284274i
\(452\) 0 0
\(453\) 22.4612 38.9040i 1.05532 1.82787i
\(454\) 0 0
\(455\) 6.62502 2.18355i 0.310585 0.102366i
\(456\) 0 0
\(457\) −7.52390 + 13.0318i −0.351953 + 0.609601i −0.986592 0.163208i \(-0.947816\pi\)
0.634638 + 0.772809i \(0.281149\pi\)
\(458\) 0 0
\(459\) 4.41990 + 7.65549i 0.206303 + 0.357328i
\(460\) 0 0
\(461\) 3.12241 11.6530i 0.145425 0.542734i −0.854311 0.519762i \(-0.826021\pi\)
0.999736 0.0229718i \(-0.00731278\pi\)
\(462\) 0 0
\(463\) −32.5516 −1.51280 −0.756400 0.654109i \(-0.773044\pi\)
−0.756400 + 0.654109i \(0.773044\pi\)
\(464\) 0 0
\(465\) 0.540054 1.46821i 0.0250444 0.0680868i
\(466\) 0 0
\(467\) −19.4091 19.4091i −0.898145 0.898145i 0.0971268 0.995272i \(-0.469035\pi\)
−0.995272 + 0.0971268i \(0.969035\pi\)
\(468\) 0 0
\(469\) 11.7006i 0.540283i
\(470\) 0 0
\(471\) −10.6489 + 18.4444i −0.490675 + 0.849874i
\(472\) 0 0
\(473\) 19.2943i 0.887153i
\(474\) 0 0
\(475\) 6.01712 0.485173i 0.276084 0.0222613i
\(476\) 0 0
\(477\) −24.4324 6.54664i −1.11868 0.299750i
\(478\) 0 0
\(479\) 5.16289 1.38339i 0.235899 0.0632088i −0.138933 0.990302i \(-0.544367\pi\)
0.374831 + 0.927093i \(0.377701\pi\)
\(480\) 0 0
\(481\) −26.8142 + 21.2808i −1.22262 + 0.970321i
\(482\) 0 0
\(483\) −5.26290 3.03853i −0.239470 0.138258i
\(484\) 0 0
\(485\) −2.50317 + 2.08593i −0.113663 + 0.0947171i
\(486\) 0 0
\(487\) 5.93242 + 10.2752i 0.268823 + 0.465616i 0.968558 0.248787i \(-0.0800319\pi\)
−0.699735 + 0.714403i \(0.746699\pi\)
\(488\) 0 0
\(489\) −9.64173 9.64173i −0.436014 0.436014i
\(490\) 0 0
\(491\) 16.9915 + 9.81007i 0.766817 + 0.442722i 0.831738 0.555168i \(-0.187346\pi\)
−0.0649209 + 0.997890i \(0.520680\pi\)
\(492\) 0 0
\(493\) −25.0922 + 25.0922i −1.13010 + 1.13010i
\(494\) 0 0
\(495\) 7.61564 10.7978i 0.342297 0.485326i
\(496\) 0 0
\(497\) −3.33195 12.4350i −0.149459 0.557787i
\(498\) 0 0
\(499\) 25.2879 25.2879i 1.13204 1.13204i 0.142203 0.989837i \(-0.454581\pi\)
0.989837 0.142203i \(-0.0454187\pi\)
\(500\) 0 0
\(501\) −19.6153 5.25591i −0.876347 0.234817i
\(502\) 0 0
\(503\) −3.69726 + 13.7984i −0.164853 + 0.615239i 0.833206 + 0.552962i \(0.186503\pi\)
−0.998059 + 0.0622762i \(0.980164\pi\)
\(504\) 0 0
\(505\) −8.96060 + 24.3607i −0.398741 + 1.08404i
\(506\) 0 0
\(507\) −29.5920 15.8181i −1.31423 0.702508i
\(508\) 0 0
\(509\) 9.01986 + 33.6626i 0.399798 + 1.49207i 0.813451 + 0.581633i \(0.197586\pi\)
−0.413653 + 0.910435i \(0.635747\pi\)
\(510\) 0 0
\(511\) 8.23637 4.75527i 0.364356 0.210361i
\(512\) 0 0
\(513\) −1.78690 + 1.03167i −0.0788938 + 0.0455493i
\(514\) 0 0
\(515\) −28.0798 19.8045i −1.23734 0.872691i
\(516\) 0 0
\(517\) 2.37109 0.635331i 0.104280 0.0279418i
\(518\) 0 0
\(519\) −51.4717 −2.25936
\(520\) 0 0
\(521\) 20.2982 0.889281 0.444641 0.895709i \(-0.353331\pi\)
0.444641 + 0.895709i \(0.353331\pi\)
\(522\) 0 0
\(523\) 18.2457 4.88891i 0.797827 0.213777i 0.163197 0.986593i \(-0.447819\pi\)
0.634630 + 0.772816i \(0.281153\pi\)
\(524\) 0 0
\(525\) 4.78777 10.0875i 0.208955 0.440256i
\(526\) 0 0
\(527\) −1.21417 + 0.701004i −0.0528903 + 0.0305362i
\(528\) 0 0
\(529\) 13.5056 7.79747i 0.587201 0.339020i
\(530\) 0 0
\(531\) 11.1758 + 41.7085i 0.484987 + 1.80999i
\(532\) 0 0
\(533\) 0.178038 1.54745i 0.00771170 0.0670277i
\(534\) 0 0
\(535\) −14.4772 + 6.69094i −0.625906 + 0.289275i
\(536\) 0 0
\(537\) −2.04605 + 7.63598i −0.0882938 + 0.329517i
\(538\) 0 0
\(539\) −9.74349 2.61076i −0.419682 0.112453i
\(540\) 0 0
\(541\) −20.5158 + 20.5158i −0.882042 + 0.882042i −0.993742 0.111700i \(-0.964371\pi\)
0.111700 + 0.993742i \(0.464371\pi\)
\(542\) 0 0
\(543\) 15.6092 + 58.2544i 0.669856 + 2.49993i
\(544\) 0 0
\(545\) −11.8047 8.32580i −0.505660 0.356638i
\(546\) 0 0
\(547\) −28.8176 + 28.8176i −1.23215 + 1.23215i −0.269018 + 0.963135i \(0.586699\pi\)
−0.963135 + 0.269018i \(0.913301\pi\)
\(548\) 0 0
\(549\) −18.6580 10.7722i −0.796304 0.459747i
\(550\) 0 0
\(551\) −5.85689 5.85689i −0.249512 0.249512i
\(552\) 0 0
\(553\) 1.72250 + 2.98347i 0.0732484 + 0.126870i
\(554\) 0 0
\(555\) −4.96172 + 54.5724i −0.210613 + 2.31647i
\(556\) 0 0
\(557\) 6.50881 + 3.75786i 0.275787 + 0.159226i 0.631515 0.775364i \(-0.282434\pi\)
−0.355727 + 0.934590i \(0.615767\pi\)
\(558\) 0 0
\(559\) 25.6828 34.6284i 1.08627 1.46462i
\(560\) 0 0
\(561\) −20.8085 + 5.57562i −0.878535 + 0.235403i
\(562\) 0 0
\(563\) 23.0668 + 6.18074i 0.972151 + 0.260487i 0.709736 0.704468i \(-0.248814\pi\)
0.262415 + 0.964955i \(0.415481\pi\)
\(564\) 0 0
\(565\) −19.2430 1.74957i −0.809560 0.0736051i
\(566\) 0 0
\(567\) 5.68898i 0.238915i
\(568\) 0 0
\(569\) 1.39258 2.41202i 0.0583801 0.101117i −0.835358 0.549706i \(-0.814740\pi\)
0.893738 + 0.448589i \(0.148073\pi\)
\(570\) 0 0
\(571\) 28.8794i 1.20857i 0.796769 + 0.604284i \(0.206541\pi\)
−0.796769 + 0.604284i \(0.793459\pi\)
\(572\) 0 0
\(573\) 13.6425 + 13.6425i 0.569924 + 0.569924i
\(574\) 0 0
\(575\) −7.72809 11.1984i −0.322283 0.467004i
\(576\) 0 0
\(577\) 4.20458 0.175039 0.0875196 0.996163i \(-0.472106\pi\)
0.0875196 + 0.996163i \(0.472106\pi\)
\(578\) 0 0
\(579\) −1.33742 + 4.99131i −0.0555811 + 0.207432i
\(580\) 0 0
\(581\) 2.70632 + 4.68748i 0.112277 + 0.194469i
\(582\) 0 0
\(583\) 5.57253 9.65190i 0.230790 0.399741i
\(584\) 0 0
\(585\) −28.0412 + 9.24214i −1.15936 + 0.382115i
\(586\) 0 0
\(587\) 2.71072 4.69510i 0.111883 0.193787i −0.804646 0.593754i \(-0.797645\pi\)
0.916530 + 0.399967i \(0.130978\pi\)
\(588\) 0 0
\(589\) −0.163625 0.283406i −0.00674204 0.0116776i
\(590\) 0 0
\(591\) 2.12493 7.93036i 0.0874081 0.326211i
\(592\) 0 0
\(593\) −15.8446 −0.650660 −0.325330 0.945601i \(-0.605475\pi\)
−0.325330 + 0.945601i \(0.605475\pi\)
\(594\) 0 0
\(595\) −9.08381 + 4.19826i −0.372400 + 0.172112i
\(596\) 0 0
\(597\) −29.9402 29.9402i −1.22537 1.22537i
\(598\) 0 0
\(599\) 34.8884i 1.42550i 0.701418 + 0.712750i \(0.252550\pi\)
−0.701418 + 0.712750i \(0.747450\pi\)
\(600\) 0 0
\(601\) 11.6867 20.2419i 0.476710 0.825686i −0.522934 0.852373i \(-0.675163\pi\)
0.999644 + 0.0266875i \(0.00849591\pi\)
\(602\) 0 0
\(603\) 49.5242i 2.01678i
\(604\) 0 0
\(605\) −12.0192 14.4233i −0.488648 0.586391i
\(606\) 0 0
\(607\) −31.2836 8.38242i −1.26976 0.340232i −0.439823 0.898085i \(-0.644959\pi\)
−0.829940 + 0.557853i \(0.811625\pi\)
\(608\) 0 0
\(609\) −14.7989 + 3.96536i −0.599683 + 0.160685i
\(610\) 0 0
\(611\) −5.10118 2.01591i −0.206372 0.0815549i
\(612\) 0 0
\(613\) 33.8649 + 19.5519i 1.36779 + 0.789695i 0.990646 0.136458i \(-0.0435720\pi\)
0.377146 + 0.926154i \(0.376905\pi\)
\(614\) 0 0
\(615\) −1.59622 1.91550i −0.0643658 0.0772406i
\(616\) 0 0
\(617\) 7.14533 + 12.3761i 0.287660 + 0.498242i 0.973251 0.229745i \(-0.0737893\pi\)
−0.685591 + 0.727987i \(0.740456\pi\)
\(618\) 0 0
\(619\) −6.85038 6.85038i −0.275340 0.275340i 0.555906 0.831245i \(-0.312372\pi\)
−0.831245 + 0.555906i \(0.812372\pi\)
\(620\) 0 0
\(621\) 4.02754 + 2.32530i 0.161620 + 0.0933111i
\(622\) 0 0
\(623\) 6.21223 6.21223i 0.248888 0.248888i
\(624\) 0 0
\(625\) 19.3681 15.8074i 0.774726 0.632297i
\(626\) 0 0
\(627\) −1.30143 4.85701i −0.0519742 0.193970i
\(628\) 0 0
\(629\) 34.7257 34.7257i 1.38461 1.38461i
\(630\) 0 0
\(631\) 37.2254 + 9.97452i 1.48192 + 0.397080i 0.907000 0.421130i \(-0.138366\pi\)
0.574921 + 0.818209i \(0.305033\pi\)
\(632\) 0 0
\(633\) 7.56506 28.2332i 0.300684 1.12217i
\(634\) 0 0
\(635\) 4.41401 + 9.55063i 0.175165 + 0.379005i
\(636\) 0 0
\(637\) 14.0119 + 17.6553i 0.555171 + 0.699527i
\(638\) 0 0
\(639\) 14.1029 + 52.6327i 0.557902 + 2.08212i
\(640\) 0 0
\(641\) 6.48111 3.74187i 0.255988 0.147795i −0.366515 0.930412i \(-0.619449\pi\)
0.622503 + 0.782617i \(0.286116\pi\)
\(642\) 0 0
\(643\) −20.7800 + 11.9973i −0.819482 + 0.473128i −0.850238 0.526399i \(-0.823542\pi\)
0.0307558 + 0.999527i \(0.490209\pi\)
\(644\) 0 0
\(645\) −11.7525 68.0044i −0.462752 2.67767i
\(646\) 0 0
\(647\) 22.5414 6.03995i 0.886195 0.237455i 0.213117 0.977027i \(-0.431639\pi\)
0.673078 + 0.739572i \(0.264972\pi\)
\(648\) 0 0
\(649\) −19.0257 −0.746825
\(650\) 0 0
\(651\) −0.605318 −0.0237243
\(652\) 0 0
\(653\) 20.3843 5.46196i 0.797700 0.213743i 0.163126 0.986605i \(-0.447842\pi\)
0.634574 + 0.772862i \(0.281176\pi\)
\(654\) 0 0
\(655\) −5.83581 33.7683i −0.228024 1.31944i
\(656\) 0 0
\(657\) −34.8614 + 20.1273i −1.36007 + 0.785239i
\(658\) 0 0
\(659\) 13.0042 7.50797i 0.506571 0.292469i −0.224852 0.974393i \(-0.572190\pi\)
0.731423 + 0.681924i \(0.238856\pi\)
\(660\) 0 0
\(661\) 1.43378 + 5.35096i 0.0557677 + 0.208128i 0.988188 0.153249i \(-0.0489735\pi\)
−0.932420 + 0.361377i \(0.882307\pi\)
\(662\) 0 0
\(663\) 44.7676 + 17.6915i 1.73863 + 0.687080i
\(664\) 0 0
\(665\) −0.979937 2.12030i −0.0380003 0.0822216i
\(666\) 0 0
\(667\) −4.83189 + 18.0329i −0.187092 + 0.698235i
\(668\) 0 0
\(669\) 25.1715 + 6.74467i 0.973185 + 0.260764i
\(670\) 0 0
\(671\) 6.71243 6.71243i 0.259130 0.259130i
\(672\) 0 0
\(673\) 8.14271 + 30.3890i 0.313878 + 1.17141i 0.925029 + 0.379896i \(0.124040\pi\)
−0.611151 + 0.791514i \(0.709293\pi\)
\(674\) 0 0
\(675\) −3.66394 + 7.71969i −0.141025 + 0.297131i
\(676\) 0 0
\(677\) 19.4080 19.4080i 0.745910 0.745910i −0.227798 0.973708i \(-0.573153\pi\)
0.973708 + 0.227798i \(0.0731527\pi\)
\(678\) 0 0
\(679\) 1.09187 + 0.630389i 0.0419019 + 0.0241921i
\(680\) 0 0
\(681\) 25.0756 + 25.0756i 0.960899 + 0.960899i
\(682\) 0 0
\(683\) −12.1706 21.0802i −0.465697 0.806610i 0.533536 0.845777i \(-0.320863\pi\)
−0.999233 + 0.0391672i \(0.987530\pi\)
\(684\) 0 0
\(685\) −24.2547 29.1063i −0.926724 1.11209i
\(686\) 0 0
\(687\) −10.6451 6.14597i −0.406137 0.234483i
\(688\) 0 0
\(689\) −22.8490 + 9.90507i −0.870476 + 0.377353i
\(690\) 0 0
\(691\) −11.5308 + 3.08967i −0.438652 + 0.117537i −0.471385 0.881928i \(-0.656246\pi\)
0.0327325 + 0.999464i \(0.489579\pi\)
\(692\) 0 0
\(693\) −4.93848 1.32326i −0.187597 0.0502666i
\(694\) 0 0
\(695\) 4.45341 + 5.34420i 0.168927 + 0.202717i
\(696\) 0 0
\(697\) 2.23460i 0.0846413i
\(698\) 0 0
\(699\) 34.9585 60.5498i 1.32225 2.29020i
\(700\) 0 0
\(701\) 21.2613i 0.803029i −0.915853 0.401515i \(-0.868484\pi\)
0.915853 0.401515i \(-0.131516\pi\)
\(702\) 0 0
\(703\) 8.10550 + 8.10550i 0.305705 + 0.305705i
\(704\) 0 0
\(705\) −7.97010 + 3.68354i −0.300171 + 0.138730i
\(706\) 0 0
\(707\) 10.0435 0.377723
\(708\) 0 0
\(709\) −5.58329 + 20.8371i −0.209685 + 0.782555i 0.778285 + 0.627911i \(0.216090\pi\)
−0.987970 + 0.154644i \(0.950577\pi\)
\(710\) 0 0
\(711\) −7.29071 12.6279i −0.273423 0.473582i
\(712\) 0 0
\(713\) −0.368797 + 0.638775i −0.0138116 + 0.0239223i
\(714\) 0 0
\(715\) −0.735666 12.9884i −0.0275123 0.485737i
\(716\) 0 0
\(717\) −33.7040 + 58.3770i −1.25870 + 2.18013i
\(718\) 0 0
\(719\) −4.13804 7.16730i −0.154323 0.267295i 0.778489 0.627658i \(-0.215986\pi\)
−0.932812 + 0.360363i \(0.882653\pi\)
\(720\) 0 0
\(721\) −3.44115 + 12.8425i −0.128155 + 0.478282i
\(722\) 0 0
\(723\) 2.27344 0.0845500
\(724\) 0 0
\(725\) −33.7401 6.18644i −1.25308 0.229758i
\(726\) 0 0
\(727\) −2.41639 2.41639i −0.0896190 0.0896190i 0.660876 0.750495i \(-0.270185\pi\)
−0.750495 + 0.660876i \(0.770185\pi\)
\(728\) 0 0
\(729\) 37.3127i 1.38195i
\(730\) 0 0
\(731\) −30.9246 + 53.5629i −1.14379 + 1.98110i
\(732\) 0 0
\(733\) 32.4183i 1.19740i −0.800974 0.598699i \(-0.795685\pi\)
0.800974 0.598699i \(-0.204315\pi\)
\(734\) 0 0
\(735\) 35.9320 + 3.26694i 1.32537 + 0.120503i
\(736\) 0 0
\(737\) 21.0776 + 5.64773i 0.776404 + 0.208037i
\(738\) 0 0
\(739\) 43.7773 11.7301i 1.61038 0.431499i 0.662221 0.749309i \(-0.269614\pi\)
0.948154 + 0.317810i \(0.102947\pi\)
\(740\) 0 0
\(741\) −4.12945 + 10.4494i −0.151699 + 0.383870i
\(742\) 0 0
\(743\) 13.1203 + 7.57500i 0.481336 + 0.277900i 0.720973 0.692963i \(-0.243695\pi\)
−0.239637 + 0.970863i \(0.577028\pi\)
\(744\) 0 0
\(745\) 3.34462 36.7864i 0.122537 1.34775i
\(746\) 0 0
\(747\) −11.4548 19.8403i −0.419110 0.725919i
\(748\) 0 0
\(749\) 4.36362 + 4.36362i 0.159443 + 0.159443i
\(750\) 0 0
\(751\) −5.51200 3.18236i −0.201136 0.116126i 0.396049 0.918229i \(-0.370381\pi\)
−0.597185 + 0.802103i \(0.703714\pi\)
\(752\) 0 0
\(753\) 11.8498 11.8498i 0.431830 0.431830i
\(754\) 0 0
\(755\) −31.8029 22.4304i −1.15743 0.816326i
\(756\) 0 0
\(757\) −7.31666 27.3061i −0.265928 0.992459i −0.961680 0.274176i \(-0.911595\pi\)
0.695751 0.718283i \(-0.255072\pi\)
\(758\) 0 0
\(759\) −8.01399 + 8.01399i −0.290889 + 0.290889i
\(760\) 0 0
\(761\) 31.4842 + 8.43618i 1.14130 + 0.305811i 0.779475 0.626434i \(-0.215486\pi\)
0.361828 + 0.932245i \(0.382153\pi\)
\(762\) 0 0
\(763\) −1.44666 + 5.39900i −0.0523725 + 0.195457i
\(764\) 0 0
\(765\) 38.4483 17.7696i 1.39010 0.642463i
\(766\) 0 0
\(767\) 34.1463 + 25.3252i 1.23295 + 0.914441i
\(768\) 0 0
\(769\) −10.7440 40.0972i −0.387439 1.44594i −0.834286 0.551331i \(-0.814120\pi\)
0.446848 0.894610i \(-0.352547\pi\)
\(770\) 0 0
\(771\) −23.9490 + 13.8270i −0.862503 + 0.497966i
\(772\) 0 0
\(773\) −1.93793 + 1.11886i −0.0697025 + 0.0402427i −0.534446 0.845202i \(-0.679480\pi\)
0.464744 + 0.885445i \(0.346146\pi\)
\(774\) 0 0
\(775\) −1.22436 0.581108i −0.0439802 0.0208740i
\(776\) 0 0
\(777\) 20.4806 5.48776i 0.734738 0.196872i
\(778\) 0 0
\(779\) −0.521588 −0.0186878
\(780\) 0 0
\(781\) −24.0089 −0.859106
\(782\) 0 0
\(783\) 11.3252 3.03457i 0.404729 0.108447i
\(784\) 0 0
\(785\) 15.0778 + 10.6343i 0.538150 + 0.379554i
\(786\) 0 0
\(787\) 37.4425 21.6174i 1.33468 0.770577i 0.348666 0.937247i \(-0.386635\pi\)
0.986013 + 0.166669i \(0.0533013\pi\)
\(788\) 0 0
\(789\) −22.6990 + 13.1053i −0.808105 + 0.466559i
\(790\) 0 0
\(791\) 1.93507 + 7.22176i 0.0688030 + 0.256776i
\(792\) 0 0
\(793\) −20.9820 + 3.11215i −0.745094 + 0.110516i
\(794\) 0 0
\(795\) −13.7617 + 37.4132i −0.488078 + 1.32691i
\(796\) 0 0
\(797\) 5.89049 21.9836i 0.208652 0.778699i −0.779653 0.626211i \(-0.784605\pi\)
0.988305 0.152488i \(-0.0487286\pi\)
\(798\) 0 0
\(799\) 7.60066 + 2.03659i 0.268892 + 0.0720494i
\(800\) 0 0
\(801\) −26.2940 + 26.2940i −0.929053 + 0.929053i
\(802\) 0 0
\(803\) −4.59062 17.1324i −0.161999 0.604590i
\(804\) 0 0
\(805\) −3.03437 + 4.30228i −0.106947 + 0.151635i
\(806\) 0 0
\(807\) −34.1289 + 34.1289i −1.20139 + 1.20139i
\(808\) 0 0
\(809\) 25.3301 + 14.6243i 0.890558 + 0.514164i 0.874125 0.485701i \(-0.161436\pi\)
0.0164333 + 0.999865i \(0.494769\pi\)
\(810\) 0 0
\(811\) −16.1564 16.1564i −0.567327 0.567327i 0.364052 0.931379i \(-0.381393\pi\)
−0.931379 + 0.364052i \(0.881393\pi\)
\(812\) 0 0
\(813\) −23.6593 40.9790i −0.829767 1.43720i
\(814\) 0 0
\(815\) −9.07484 + 7.56220i −0.317878 + 0.264892i
\(816\) 0 0
\(817\) −12.5024 7.21825i −0.437403 0.252535i
\(818\) 0 0
\(819\) 7.10191 + 8.94856i 0.248161 + 0.312688i
\(820\) 0 0
\(821\) 25.6639 6.87663i 0.895677 0.239996i 0.218518 0.975833i \(-0.429878\pi\)
0.677159 + 0.735837i \(0.263211\pi\)
\(822\) 0 0
\(823\) 40.5702 + 10.8708i 1.41419 + 0.378931i 0.883418 0.468585i \(-0.155236\pi\)
0.530770 + 0.847516i \(0.321903\pi\)
\(824\) 0 0
\(825\) −15.8608 13.4939i −0.552202 0.469796i
\(826\) 0 0
\(827\) 48.4948i 1.68633i −0.537655 0.843165i \(-0.680690\pi\)
0.537655 0.843165i \(-0.319310\pi\)
\(828\) 0 0
\(829\) 20.4336 35.3921i 0.709689 1.22922i −0.255284 0.966866i \(-0.582169\pi\)
0.964973 0.262351i \(-0.0844978\pi\)
\(830\) 0 0
\(831\) 34.9998i 1.21413i
\(832\) 0 0
\(833\) −22.8644 22.8644i −0.792205 0.792205i
\(834\) 0 0
\(835\) −6.07327 + 16.5111i −0.210174 + 0.571389i
\(836\) 0 0
\(837\) 0.463232 0.0160116
\(838\) 0 0
\(839\) 7.70239 28.7457i 0.265916 0.992412i −0.695771 0.718263i \(-0.744937\pi\)
0.961687 0.274149i \(-0.0883960\pi\)
\(840\) 0 0
\(841\) 9.03332 + 15.6462i 0.311494 + 0.539523i
\(842\) 0 0
\(843\) 31.2967 54.2075i 1.07792 1.86701i
\(844\) 0 0
\(845\) −15.9685 + 24.2900i −0.549334 + 0.835603i
\(846\) 0 0
\(847\) −3.63231 + 6.29135i −0.124808 + 0.216173i
\(848\) 0 0
\(849\) 11.8183 + 20.4700i 0.405605 + 0.702528i
\(850\) 0 0
\(851\) 6.68697 24.9561i 0.229227 0.855485i
\(852\) 0 0
\(853\) −8.67930 −0.297174 −0.148587 0.988899i \(-0.547472\pi\)
−0.148587 + 0.988899i \(0.547472\pi\)
\(854\) 0 0
\(855\) 4.14770 + 8.97441i 0.141848 + 0.306918i
\(856\) 0 0
\(857\) −2.38807 2.38807i −0.0815751 0.0815751i 0.665142 0.746717i \(-0.268371\pi\)
−0.746717 + 0.665142i \(0.768371\pi\)
\(858\) 0 0
\(859\) 0.237935i 0.00811823i −0.999992 0.00405912i \(-0.998708\pi\)
0.999992 0.00405912i \(-0.00129206\pi\)
\(860\) 0 0
\(861\) −0.482394 + 0.835530i −0.0164399 + 0.0284748i
\(862\) 0 0
\(863\) 48.8736i 1.66368i 0.555017 + 0.831839i \(0.312712\pi\)
−0.555017 + 0.831839i \(0.687288\pi\)
\(864\) 0 0
\(865\) −4.03756 + 44.4078i −0.137281 + 1.50991i
\(866\) 0 0
\(867\) −24.3192 6.51630i −0.825922 0.221305i
\(868\) 0 0
\(869\) 6.20588 1.66286i 0.210520 0.0564087i
\(870\) 0 0
\(871\) −30.3112 38.1927i −1.02706 1.29411i
\(872\) 0 0
\(873\) −4.62145 2.66820i −0.156412 0.0903048i
\(874\) 0 0
\(875\) −8.32757 4.92200i −0.281523 0.166394i
\(876\) 0 0
\(877\) 17.4333 + 30.1953i 0.588680 + 1.01962i 0.994406 + 0.105629i \(0.0336856\pi\)
−0.405725 + 0.913995i \(0.632981\pi\)
\(878\) 0 0
\(879\) 33.1837 + 33.1837i 1.11926 + 1.11926i
\(880\) 0 0
\(881\) −24.6799 14.2489i −0.831486 0.480058i 0.0228755 0.999738i \(-0.492718\pi\)
−0.854361 + 0.519680i \(0.826051\pi\)
\(882\) 0 0
\(883\) −10.7320 + 10.7320i −0.361160 + 0.361160i −0.864240 0.503080i \(-0.832200\pi\)
0.503080 + 0.864240i \(0.332200\pi\)
\(884\) 0 0
\(885\) 67.0577 11.5888i 2.25412 0.389555i
\(886\) 0 0
\(887\) −3.36490 12.5580i −0.112982 0.421655i 0.886146 0.463406i \(-0.153373\pi\)
−0.999128 + 0.0417512i \(0.986706\pi\)
\(888\) 0 0
\(889\) 2.87868 2.87868i 0.0965478 0.0965478i
\(890\) 0 0
\(891\) −10.2482 2.74600i −0.343328 0.0919943i
\(892\) 0 0
\(893\) −0.475371 + 1.77411i −0.0159077 + 0.0593683i
\(894\) 0 0
\(895\) 6.42754 + 2.36424i 0.214849 + 0.0790279i
\(896\) 0 0
\(897\) 25.0505 3.71560i 0.836413 0.124060i
\(898\) 0 0
\(899\) 0.481289 + 1.79620i 0.0160519 + 0.0599065i
\(900\) 0 0
\(901\) 30.9398 17.8631i 1.03075 0.595105i
\(902\) 0 0
\(903\) −23.1258 + 13.3517i −0.769578 + 0.444316i
\(904\) 0 0
\(905\) 51.4841 8.89743i 1.71139 0.295761i
\(906\) 0 0
\(907\) 49.3926 13.2347i 1.64006 0.439451i 0.683251 0.730184i \(-0.260566\pi\)
0.956804 + 0.290732i \(0.0938990\pi\)
\(908\) 0 0
\(909\) −42.5102 −1.40997
\(910\) 0 0
\(911\) −45.3842 −1.50365 −0.751823 0.659365i \(-0.770825\pi\)
−0.751823 + 0.659365i \(0.770825\pi\)
\(912\) 0 0
\(913\) 9.75039 2.61261i 0.322691 0.0864647i
\(914\) 0 0
\(915\) −19.5699 + 27.7472i −0.646960 + 0.917293i
\(916\) 0 0
\(917\) −11.4834 + 6.62993i −0.379214 + 0.218940i
\(918\) 0 0
\(919\) −26.3431 + 15.2092i −0.868977 + 0.501704i −0.867008 0.498294i \(-0.833960\pi\)
−0.00196918 + 0.999998i \(0.500627\pi\)
\(920\) 0 0
\(921\) 18.7289 + 69.8973i 0.617139 + 2.30319i
\(922\) 0 0
\(923\) 43.0898 + 31.9584i 1.41832 + 1.05192i
\(924\) 0 0
\(925\) 46.6938 + 8.56156i 1.53528 + 0.281503i
\(926\) 0 0
\(927\) 14.5651 54.3576i 0.478380 1.78534i
\(928\) 0 0
\(929\) 23.9374 + 6.41401i 0.785361 + 0.210437i 0.629147 0.777286i \(-0.283404\pi\)
0.156214 + 0.987723i \(0.450071\pi\)
\(930\) 0 0
\(931\) 5.33689 5.33689i 0.174910 0.174910i
\(932\) 0 0
\(933\) −7.69371 28.7133i −0.251881 0.940031i
\(934\) 0 0
\(935\) 3.17817 + 18.3901i 0.103937 + 0.601422i
\(936\) 0 0
\(937\) 25.3459 25.3459i 0.828014 0.828014i −0.159228 0.987242i \(-0.550901\pi\)
0.987242 + 0.159228i \(0.0509005\pi\)
\(938\) 0 0
\(939\) −32.6792 18.8674i −1.06645 0.615713i
\(940\) 0 0
\(941\) 27.5969 + 27.5969i 0.899632 + 0.899632i 0.995403 0.0957715i \(-0.0305318\pi\)
−0.0957715 + 0.995403i \(0.530532\pi\)
\(942\) 0 0
\(943\) 0.587809 + 1.01811i 0.0191417 + 0.0331544i
\(944\) 0 0
\(945\) 3.29280 + 0.299382i 0.107115 + 0.00973889i
\(946\) 0 0
\(947\) −45.7982 26.4416i −1.48824 0.859237i −0.488332 0.872658i \(-0.662394\pi\)
−0.999910 + 0.0134210i \(0.995728\pi\)
\(948\) 0 0
\(949\) −14.5661 + 36.8589i −0.472835 + 1.19649i
\(950\) 0 0
\(951\) 5.76184 1.54388i 0.186840 0.0500637i
\(952\) 0 0
\(953\) −45.8852 12.2949i −1.48637 0.398271i −0.577860 0.816136i \(-0.696112\pi\)
−0.908509 + 0.417865i \(0.862779\pi\)
\(954\) 0 0
\(955\) 12.8404 10.7001i 0.415505 0.346247i
\(956\) 0 0
\(957\) 28.5730i 0.923634i
\(958\) 0 0
\(959\) −7.33001 + 12.6960i −0.236699 + 0.409974i
\(960\) 0 0
\(961\) 30.9265i 0.997630i
\(962\) 0 0
\(963\) −18.4696 18.4696i −0.595173 0.595173i
\(964\) 0 0
\(965\) 4.20140 + 1.54540i 0.135248 + 0.0497482i
\(966\) 0 0
\(967\) −39.7754 −1.27909 −0.639546 0.768753i \(-0.720878\pi\)
−0.639546 + 0.768753i \(0.720878\pi\)
\(968\) 0 0
\(969\) 4.17182 15.5694i 0.134018 0.500163i
\(970\) 0 0
\(971\) −0.597739 1.03531i −0.0191824 0.0332248i 0.856275 0.516520i \(-0.172773\pi\)
−0.875457 + 0.483296i \(0.839440\pi\)
\(972\) 0 0
\(973\) 1.34586 2.33111i 0.0431464 0.0747318i
\(974\) 0 0
\(975\) 10.5043 + 45.3304i 0.336407 + 1.45174i
\(976\) 0 0
\(977\) −8.23433 + 14.2623i −0.263439 + 0.456291i −0.967154 0.254193i \(-0.918190\pi\)
0.703714 + 0.710483i \(0.251524\pi\)
\(978\) 0 0
\(979\) −8.19223 14.1894i −0.261825 0.453494i
\(980\) 0 0
\(981\) 6.12315 22.8519i 0.195497 0.729605i
\(982\) 0 0
\(983\) −1.80446 −0.0575534 −0.0287767 0.999586i \(-0.509161\pi\)
−0.0287767 + 0.999586i \(0.509161\pi\)
\(984\) 0 0
\(985\) −6.67533 2.45539i −0.212694 0.0782351i
\(986\) 0 0
\(987\) 2.40229 + 2.40229i 0.0764657 + 0.0764657i
\(988\) 0 0
\(989\) 32.5387i 1.03467i
\(990\) 0 0
\(991\) 0.661562 1.14586i 0.0210152 0.0363994i −0.855327 0.518089i \(-0.826643\pi\)
0.876342 + 0.481690i \(0.159977\pi\)
\(992\) 0 0
\(993\) 90.7637i 2.88030i
\(994\) 0 0
\(995\) −28.1798 + 23.4827i −0.893360 + 0.744451i
\(996\) 0 0
\(997\) 45.5416 + 12.2028i 1.44232 + 0.386467i 0.893344 0.449373i \(-0.148353\pi\)
0.548972 + 0.835841i \(0.315019\pi\)
\(998\) 0 0
\(999\) −15.6732 + 4.19962i −0.495878 + 0.132870i
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 260.2.bk.c.33.5 yes 20
5.2 odd 4 260.2.bf.c.137.1 yes 20
5.3 odd 4 1300.2.bn.d.657.5 20
5.4 even 2 1300.2.bs.d.293.1 20
13.2 odd 12 260.2.bf.c.93.1 20
65.2 even 12 inner 260.2.bk.c.197.5 yes 20
65.28 even 12 1300.2.bs.d.457.1 20
65.54 odd 12 1300.2.bn.d.93.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.bf.c.93.1 20 13.2 odd 12
260.2.bf.c.137.1 yes 20 5.2 odd 4
260.2.bk.c.33.5 yes 20 1.1 even 1 trivial
260.2.bk.c.197.5 yes 20 65.2 even 12 inner
1300.2.bn.d.93.5 20 65.54 odd 12
1300.2.bn.d.657.5 20 5.3 odd 4
1300.2.bs.d.293.1 20 5.4 even 2
1300.2.bs.d.457.1 20 65.28 even 12