Properties

Label 252.2.bm.a.185.1
Level $252$
Weight $2$
Character 252.185
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
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] = [252,2,Mod(173,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.173");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 185.1
Root \(1.68042 + 0.419752i\) of defining polynomial
Character \(\chi\) \(=\) 252.185
Dual form 252.2.bm.a.173.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.60579 - 0.649187i) q^{3} -2.96988 q^{5} +(2.38485 + 1.14563i) q^{7} +(2.15711 + 2.08491i) q^{9} +O(q^{10})\) \(q+(-1.60579 - 0.649187i) q^{3} -2.96988 q^{5} +(2.38485 + 1.14563i) q^{7} +(2.15711 + 2.08491i) q^{9} +4.72811i q^{11} +(3.54045 + 2.04408i) q^{13} +(4.76900 + 1.92801i) q^{15} +(0.835278 - 1.44674i) q^{17} +(-4.25377 + 2.45592i) q^{19} +(-3.08584 - 3.38786i) q^{21} +4.91090i q^{23} +3.82018 q^{25} +(-2.11037 - 4.74830i) q^{27} +(0.238557 - 0.137731i) q^{29} +(-1.38847 + 0.801636i) q^{31} +(3.06943 - 7.59235i) q^{33} +(-7.08273 - 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(-4.35823 - 5.58078i) q^{39} +(3.55632 - 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +(-6.40637 - 6.19194i) q^{45} +(-5.49885 + 9.52430i) q^{47} +(4.37505 + 5.46433i) q^{49} +(-2.28049 + 1.78091i) q^{51} +(-0.707381 - 0.408407i) q^{53} -14.0419i q^{55} +(8.42500 - 1.18219i) q^{57} +(1.37428 + 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(2.75585 + 7.44347i) q^{63} +(-10.5147 - 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} +(3.18809 - 7.88587i) q^{69} -10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(-6.13440 - 2.48001i) q^{75} +(-5.41668 + 11.2759i) q^{77} +(6.15163 - 10.6549i) q^{79} +(0.306275 + 8.99479i) q^{81} +(4.03981 + 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(-0.472485 + 0.0662987i) q^{87} +(-4.60872 - 7.98254i) q^{89} +(6.10169 + 8.93089i) q^{91} +(2.75001 - 0.385879i) q^{93} +(12.6332 - 7.29377i) q^{95} +(-7.00772 + 4.04591i) q^{97} +(-9.85770 + 10.1991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.60579 0.649187i −0.927102 0.374808i
\(4\) 0 0
\(5\) −2.96988 −1.32817 −0.664085 0.747657i \(-0.731179\pi\)
−0.664085 + 0.747657i \(0.731179\pi\)
\(6\) 0 0
\(7\) 2.38485 + 1.14563i 0.901390 + 0.433009i
\(8\) 0 0
\(9\) 2.15711 + 2.08491i 0.719038 + 0.694971i
\(10\) 0 0
\(11\) 4.72811i 1.42558i 0.701378 + 0.712790i \(0.252569\pi\)
−0.701378 + 0.712790i \(0.747431\pi\)
\(12\) 0 0
\(13\) 3.54045 + 2.04408i 0.981945 + 0.566926i 0.902857 0.429942i \(-0.141466\pi\)
0.0790880 + 0.996868i \(0.474799\pi\)
\(14\) 0 0
\(15\) 4.76900 + 1.92801i 1.23135 + 0.497809i
\(16\) 0 0
\(17\) 0.835278 1.44674i 0.202585 0.350887i −0.746776 0.665076i \(-0.768399\pi\)
0.949360 + 0.314189i \(0.101733\pi\)
\(18\) 0 0
\(19\) −4.25377 + 2.45592i −0.975882 + 0.563426i −0.901024 0.433768i \(-0.857184\pi\)
−0.0748577 + 0.997194i \(0.523850\pi\)
\(20\) 0 0
\(21\) −3.08584 3.38786i −0.673385 0.739292i
\(22\) 0 0
\(23\) 4.91090i 1.02399i 0.858987 + 0.511997i \(0.171094\pi\)
−0.858987 + 0.511997i \(0.828906\pi\)
\(24\) 0 0
\(25\) 3.82018 0.764036
\(26\) 0 0
\(27\) −2.11037 4.74830i −0.406141 0.913811i
\(28\) 0 0
\(29\) 0.238557 0.137731i 0.0442989 0.0255760i −0.477687 0.878530i \(-0.658525\pi\)
0.521986 + 0.852954i \(0.325191\pi\)
\(30\) 0 0
\(31\) −1.38847 + 0.801636i −0.249377 + 0.143978i −0.619479 0.785013i \(-0.712656\pi\)
0.370102 + 0.928991i \(0.379323\pi\)
\(32\) 0 0
\(33\) 3.06943 7.59235i 0.534319 1.32166i
\(34\) 0 0
\(35\) −7.08273 3.40239i −1.19720 0.575109i
\(36\) 0 0
\(37\) −1.69681 2.93896i −0.278954 0.483162i 0.692171 0.721733i \(-0.256654\pi\)
−0.971125 + 0.238571i \(0.923321\pi\)
\(38\) 0 0
\(39\) −4.35823 5.58078i −0.697875 0.893639i
\(40\) 0 0
\(41\) 3.55632 6.15972i 0.555404 0.961987i −0.442468 0.896784i \(-0.645897\pi\)
0.997872 0.0652031i \(-0.0207695\pi\)
\(42\) 0 0
\(43\) 5.22930 + 9.05742i 0.797461 + 1.38124i 0.921265 + 0.388936i \(0.127157\pi\)
−0.123804 + 0.992307i \(0.539509\pi\)
\(44\) 0 0
\(45\) −6.40637 6.19194i −0.955005 0.923040i
\(46\) 0 0
\(47\) −5.49885 + 9.52430i −0.802090 + 1.38926i 0.116148 + 0.993232i \(0.462945\pi\)
−0.918238 + 0.396029i \(0.870388\pi\)
\(48\) 0 0
\(49\) 4.37505 + 5.46433i 0.625007 + 0.780619i
\(50\) 0 0
\(51\) −2.28049 + 1.78091i −0.319332 + 0.249378i
\(52\) 0 0
\(53\) −0.707381 0.408407i −0.0971663 0.0560990i 0.450629 0.892711i \(-0.351200\pi\)
−0.547796 + 0.836612i \(0.684533\pi\)
\(54\) 0 0
\(55\) 14.0419i 1.89341i
\(56\) 0 0
\(57\) 8.42500 1.18219i 1.11592 0.156585i
\(58\) 0 0
\(59\) 1.37428 + 2.38032i 0.178916 + 0.309891i 0.941509 0.336986i \(-0.109408\pi\)
−0.762594 + 0.646878i \(0.776074\pi\)
\(60\) 0 0
\(61\) −6.23807 3.60155i −0.798703 0.461131i 0.0443147 0.999018i \(-0.485890\pi\)
−0.843017 + 0.537886i \(0.819223\pi\)
\(62\) 0 0
\(63\) 2.75585 + 7.44347i 0.347205 + 0.937789i
\(64\) 0 0
\(65\) −10.5147 6.07067i −1.30419 0.752974i
\(66\) 0 0
\(67\) −5.80513 10.0548i −0.709210 1.22839i −0.965151 0.261695i \(-0.915719\pi\)
0.255941 0.966692i \(-0.417615\pi\)
\(68\) 0 0
\(69\) 3.18809 7.88587i 0.383801 0.949347i
\(70\) 0 0
\(71\) 10.4406i 1.23907i −0.784968 0.619537i \(-0.787320\pi\)
0.784968 0.619537i \(-0.212680\pi\)
\(72\) 0 0
\(73\) 13.6493 + 7.88042i 1.59753 + 0.922334i 0.991962 + 0.126539i \(0.0403870\pi\)
0.605567 + 0.795794i \(0.292946\pi\)
\(74\) 0 0
\(75\) −6.13440 2.48001i −0.708340 0.286367i
\(76\) 0 0
\(77\) −5.41668 + 11.2759i −0.617288 + 1.28500i
\(78\) 0 0
\(79\) 6.15163 10.6549i 0.692112 1.19877i −0.279032 0.960282i \(-0.590014\pi\)
0.971145 0.238492i \(-0.0766530\pi\)
\(80\) 0 0
\(81\) 0.306275 + 8.99479i 0.0340305 + 0.999421i
\(82\) 0 0
\(83\) 4.03981 + 6.99715i 0.443426 + 0.768037i 0.997941 0.0641368i \(-0.0204294\pi\)
−0.554515 + 0.832174i \(0.687096\pi\)
\(84\) 0 0
\(85\) −2.48067 + 4.29665i −0.269067 + 0.466037i
\(86\) 0 0
\(87\) −0.472485 + 0.0662987i −0.0506557 + 0.00710797i
\(88\) 0 0
\(89\) −4.60872 7.98254i −0.488523 0.846147i 0.511390 0.859349i \(-0.329131\pi\)
−0.999913 + 0.0132019i \(0.995798\pi\)
\(90\) 0 0
\(91\) 6.10169 + 8.93089i 0.639631 + 0.936212i
\(92\) 0 0
\(93\) 2.75001 0.385879i 0.285163 0.0400138i
\(94\) 0 0
\(95\) 12.6332 7.29377i 1.29614 0.748325i
\(96\) 0 0
\(97\) −7.00772 + 4.04591i −0.711527 + 0.410800i −0.811626 0.584177i \(-0.801417\pi\)
0.100099 + 0.994977i \(0.468084\pi\)
\(98\) 0 0
\(99\) −9.85770 + 10.1991i −0.990736 + 1.02505i
\(100\) 0 0
\(101\) −7.30730 −0.727103 −0.363552 0.931574i \(-0.618436\pi\)
−0.363552 + 0.931574i \(0.618436\pi\)
\(102\) 0 0
\(103\) 7.02530i 0.692224i 0.938193 + 0.346112i \(0.112498\pi\)
−0.938193 + 0.346112i \(0.887502\pi\)
\(104\) 0 0
\(105\) 9.16457 + 10.0615i 0.894371 + 0.981905i
\(106\) 0 0
\(107\) 12.2618 7.07938i 1.18540 0.684389i 0.228140 0.973628i \(-0.426735\pi\)
0.957257 + 0.289239i \(0.0934022\pi\)
\(108\) 0 0
\(109\) −2.82203 + 4.88789i −0.270301 + 0.468175i −0.968939 0.247300i \(-0.920457\pi\)
0.698638 + 0.715476i \(0.253790\pi\)
\(110\) 0 0
\(111\) 0.816783 + 5.82089i 0.0775256 + 0.552495i
\(112\) 0 0
\(113\) 11.6411 + 6.72099i 1.09510 + 0.632258i 0.934930 0.354831i \(-0.115462\pi\)
0.160172 + 0.987089i \(0.448795\pi\)
\(114\) 0 0
\(115\) 14.5848i 1.36004i
\(116\) 0 0
\(117\) 3.37542 + 11.7908i 0.312058 + 1.09006i
\(118\) 0 0
\(119\) 3.64945 2.49335i 0.334545 0.228565i
\(120\) 0 0
\(121\) −11.3550 −1.03228
\(122\) 0 0
\(123\) −9.70951 + 7.58250i −0.875477 + 0.683691i
\(124\) 0 0
\(125\) 3.50392 0.313400
\(126\) 0 0
\(127\) −12.7730 −1.13342 −0.566712 0.823916i \(-0.691785\pi\)
−0.566712 + 0.823916i \(0.691785\pi\)
\(128\) 0 0
\(129\) −2.51720 17.9391i −0.221627 1.57945i
\(130\) 0 0
\(131\) 13.4178 1.17232 0.586159 0.810196i \(-0.300639\pi\)
0.586159 + 0.810196i \(0.300639\pi\)
\(132\) 0 0
\(133\) −12.9582 + 0.983737i −1.12362 + 0.0853008i
\(134\) 0 0
\(135\) 6.26754 + 14.1019i 0.539424 + 1.21370i
\(136\) 0 0
\(137\) 9.00030i 0.768948i 0.923136 + 0.384474i \(0.125617\pi\)
−0.923136 + 0.384474i \(0.874383\pi\)
\(138\) 0 0
\(139\) −1.54902 0.894326i −0.131386 0.0758557i 0.432866 0.901458i \(-0.357502\pi\)
−0.564252 + 0.825602i \(0.690836\pi\)
\(140\) 0 0
\(141\) 15.0130 11.7242i 1.26433 0.987357i
\(142\) 0 0
\(143\) −9.66464 + 16.7397i −0.808198 + 1.39984i
\(144\) 0 0
\(145\) −0.708485 + 0.409044i −0.0588365 + 0.0339693i
\(146\) 0 0
\(147\) −3.47803 11.6148i −0.286863 0.957972i
\(148\) 0 0
\(149\) 12.9072i 1.05740i −0.848810 0.528698i \(-0.822680\pi\)
0.848810 0.528698i \(-0.177320\pi\)
\(150\) 0 0
\(151\) −12.9673 −1.05526 −0.527631 0.849473i \(-0.676920\pi\)
−0.527631 + 0.849473i \(0.676920\pi\)
\(152\) 0 0
\(153\) 4.81812 1.37931i 0.389522 0.111510i
\(154\) 0 0
\(155\) 4.12360 2.38076i 0.331216 0.191227i
\(156\) 0 0
\(157\) 14.8720 8.58638i 1.18692 0.685268i 0.229314 0.973353i \(-0.426352\pi\)
0.957605 + 0.288085i \(0.0930185\pi\)
\(158\) 0 0
\(159\) 0.870773 + 1.11504i 0.0690568 + 0.0884282i
\(160\) 0 0
\(161\) −5.62609 + 11.7118i −0.443398 + 0.923017i
\(162\) 0 0
\(163\) 2.53107 + 4.38394i 0.198249 + 0.343377i 0.947961 0.318387i \(-0.103141\pi\)
−0.749712 + 0.661764i \(0.769808\pi\)
\(164\) 0 0
\(165\) −9.11583 + 22.5484i −0.709666 + 1.75539i
\(166\) 0 0
\(167\) 5.79673 10.0402i 0.448564 0.776936i −0.549729 0.835343i \(-0.685269\pi\)
0.998293 + 0.0584072i \(0.0186022\pi\)
\(168\) 0 0
\(169\) 1.85653 + 3.21561i 0.142810 + 0.247354i
\(170\) 0 0
\(171\) −14.2962 3.57105i −1.09326 0.273085i
\(172\) 0 0
\(173\) 3.13346 5.42730i 0.238232 0.412630i −0.721975 0.691919i \(-0.756765\pi\)
0.960207 + 0.279289i \(0.0900987\pi\)
\(174\) 0 0
\(175\) 9.11057 + 4.37653i 0.688694 + 0.330834i
\(176\) 0 0
\(177\) −0.661528 4.71446i −0.0497235 0.354360i
\(178\) 0 0
\(179\) 12.7668 + 7.37089i 0.954233 + 0.550927i 0.894393 0.447281i \(-0.147608\pi\)
0.0598395 + 0.998208i \(0.480941\pi\)
\(180\) 0 0
\(181\) 0.0833642i 0.00619641i 0.999995 + 0.00309821i \(0.000986191\pi\)
−0.999995 + 0.00309821i \(0.999014\pi\)
\(182\) 0 0
\(183\) 7.67894 + 9.83300i 0.567643 + 0.726876i
\(184\) 0 0
\(185\) 5.03932 + 8.72835i 0.370498 + 0.641721i
\(186\) 0 0
\(187\) 6.84036 + 3.94929i 0.500217 + 0.288800i
\(188\) 0 0
\(189\) 0.406887 13.7417i 0.0295967 0.999562i
\(190\) 0 0
\(191\) 13.3672 + 7.71754i 0.967214 + 0.558421i 0.898386 0.439207i \(-0.144741\pi\)
0.0688282 + 0.997629i \(0.478074\pi\)
\(192\) 0 0
\(193\) −10.7779 18.6678i −0.775808 1.34374i −0.934339 0.356385i \(-0.884009\pi\)
0.158532 0.987354i \(-0.449324\pi\)
\(194\) 0 0
\(195\) 12.9434 + 16.5742i 0.926896 + 1.18691i
\(196\) 0 0
\(197\) 9.88306i 0.704139i −0.935974 0.352069i \(-0.885478\pi\)
0.935974 0.352069i \(-0.114522\pi\)
\(198\) 0 0
\(199\) −9.14623 5.28058i −0.648359 0.374330i 0.139468 0.990227i \(-0.455461\pi\)
−0.787827 + 0.615896i \(0.788794\pi\)
\(200\) 0 0
\(201\) 2.79438 + 19.9145i 0.197100 + 1.40466i
\(202\) 0 0
\(203\) 0.726712 0.0551692i 0.0510052 0.00387212i
\(204\) 0 0
\(205\) −10.5618 + 18.2936i −0.737670 + 1.27768i
\(206\) 0 0
\(207\) −10.2388 + 10.5934i −0.711646 + 0.736290i
\(208\) 0 0
\(209\) −11.6118 20.1123i −0.803208 1.39120i
\(210\) 0 0
\(211\) 6.08453 10.5387i 0.418876 0.725514i −0.576951 0.816779i \(-0.695758\pi\)
0.995827 + 0.0912645i \(0.0290909\pi\)
\(212\) 0 0
\(213\) −6.77791 + 16.7654i −0.464415 + 1.14875i
\(214\) 0 0
\(215\) −15.5304 26.8994i −1.05916 1.83453i
\(216\) 0 0
\(217\) −4.22969 + 0.321102i −0.287130 + 0.0217978i
\(218\) 0 0
\(219\) −16.8020 21.5152i −1.13537 1.45386i
\(220\) 0 0
\(221\) 5.91452 3.41475i 0.397854 0.229701i
\(222\) 0 0
\(223\) −0.714485 + 0.412508i −0.0478455 + 0.0276236i −0.523732 0.851883i \(-0.675461\pi\)
0.475886 + 0.879507i \(0.342127\pi\)
\(224\) 0 0
\(225\) 8.24056 + 7.96475i 0.549371 + 0.530983i
\(226\) 0 0
\(227\) 0.333557 0.0221390 0.0110695 0.999939i \(-0.496476\pi\)
0.0110695 + 0.999939i \(0.496476\pi\)
\(228\) 0 0
\(229\) 14.4214i 0.952996i −0.879176 0.476498i \(-0.841906\pi\)
0.879176 0.476498i \(-0.158094\pi\)
\(230\) 0 0
\(231\) 16.0182 14.5902i 1.05392 0.959964i
\(232\) 0 0
\(233\) 12.7953 7.38739i 0.838250 0.483964i −0.0184192 0.999830i \(-0.505863\pi\)
0.856669 + 0.515867i \(0.172530\pi\)
\(234\) 0 0
\(235\) 16.3309 28.2860i 1.06531 1.84518i
\(236\) 0 0
\(237\) −16.7953 + 13.1160i −1.09097 + 0.851976i
\(238\) 0 0
\(239\) −22.5339 13.0100i −1.45760 0.841545i −0.458707 0.888588i \(-0.651687\pi\)
−0.998893 + 0.0470423i \(0.985020\pi\)
\(240\) 0 0
\(241\) 1.92021i 0.123692i 0.998086 + 0.0618458i \(0.0196987\pi\)
−0.998086 + 0.0618458i \(0.980301\pi\)
\(242\) 0 0
\(243\) 5.34748 14.6426i 0.343041 0.939320i
\(244\) 0 0
\(245\) −12.9934 16.2284i −0.830116 1.03680i
\(246\) 0 0
\(247\) −20.0804 −1.27768
\(248\) 0 0
\(249\) −1.94462 13.8585i −0.123235 0.878249i
\(250\) 0 0
\(251\) −9.97663 −0.629719 −0.314860 0.949138i \(-0.601957\pi\)
−0.314860 + 0.949138i \(0.601957\pi\)
\(252\) 0 0
\(253\) −23.2193 −1.45978
\(254\) 0 0
\(255\) 6.77277 5.28909i 0.424127 0.331216i
\(256\) 0 0
\(257\) 15.0073 0.936129 0.468064 0.883694i \(-0.344952\pi\)
0.468064 + 0.883694i \(0.344952\pi\)
\(258\) 0 0
\(259\) −0.679670 8.95291i −0.0422327 0.556306i
\(260\) 0 0
\(261\) 0.801751 + 0.200269i 0.0496271 + 0.0123964i
\(262\) 0 0
\(263\) 7.05534i 0.435051i −0.976055 0.217525i \(-0.930202\pi\)
0.976055 0.217525i \(-0.0697985\pi\)
\(264\) 0 0
\(265\) 2.10084 + 1.21292i 0.129053 + 0.0745090i
\(266\) 0 0
\(267\) 2.21847 + 15.8102i 0.135768 + 0.967568i
\(268\) 0 0
\(269\) −14.8898 + 25.7898i −0.907844 + 1.57243i −0.0907911 + 0.995870i \(0.528940\pi\)
−0.817053 + 0.576562i \(0.804394\pi\)
\(270\) 0 0
\(271\) −2.41462 + 1.39408i −0.146677 + 0.0846843i −0.571543 0.820572i \(-0.693655\pi\)
0.424865 + 0.905257i \(0.360321\pi\)
\(272\) 0 0
\(273\) −4.00021 18.3023i −0.242104 1.10770i
\(274\) 0 0
\(275\) 18.0622i 1.08919i
\(276\) 0 0
\(277\) 13.5815 0.816032 0.408016 0.912975i \(-0.366221\pi\)
0.408016 + 0.912975i \(0.366221\pi\)
\(278\) 0 0
\(279\) −4.66644 1.16563i −0.279372 0.0697844i
\(280\) 0 0
\(281\) −3.95777 + 2.28502i −0.236101 + 0.136313i −0.613383 0.789785i \(-0.710192\pi\)
0.377283 + 0.926098i \(0.376859\pi\)
\(282\) 0 0
\(283\) 17.6685 10.2009i 1.05029 0.606383i 0.127556 0.991831i \(-0.459287\pi\)
0.922729 + 0.385449i \(0.125953\pi\)
\(284\) 0 0
\(285\) −25.0212 + 3.51096i −1.48213 + 0.207971i
\(286\) 0 0
\(287\) 15.5381 10.6158i 0.917184 0.626631i
\(288\) 0 0
\(289\) 7.10462 + 12.3056i 0.417919 + 0.723857i
\(290\) 0 0
\(291\) 13.8795 1.94756i 0.813629 0.114168i
\(292\) 0 0
\(293\) −6.41037 + 11.1031i −0.374498 + 0.648649i −0.990252 0.139289i \(-0.955518\pi\)
0.615754 + 0.787939i \(0.288852\pi\)
\(294\) 0 0
\(295\) −4.08144 7.06926i −0.237631 0.411589i
\(296\) 0 0
\(297\) 22.4505 9.97806i 1.30271 0.578986i
\(298\) 0 0
\(299\) −10.0383 + 17.3868i −0.580529 + 1.00551i
\(300\) 0 0
\(301\) 2.09464 + 27.5915i 0.120733 + 1.59035i
\(302\) 0 0
\(303\) 11.7340 + 4.74380i 0.674099 + 0.272524i
\(304\) 0 0
\(305\) 18.5263 + 10.6962i 1.06081 + 0.612461i
\(306\) 0 0
\(307\) 1.93411i 0.110386i 0.998476 + 0.0551928i \(0.0175773\pi\)
−0.998476 + 0.0551928i \(0.982423\pi\)
\(308\) 0 0
\(309\) 4.56073 11.2812i 0.259451 0.641762i
\(310\) 0 0
\(311\) 1.04458 + 1.80926i 0.0592326 + 0.102594i 0.894121 0.447825i \(-0.147801\pi\)
−0.834889 + 0.550419i \(0.814468\pi\)
\(312\) 0 0
\(313\) 19.4066 + 11.2044i 1.09692 + 0.633309i 0.935411 0.353562i \(-0.115030\pi\)
0.161512 + 0.986871i \(0.448363\pi\)
\(314\) 0 0
\(315\) −8.18455 22.1062i −0.461147 1.24554i
\(316\) 0 0
\(317\) −3.01788 1.74237i −0.169501 0.0978614i 0.412850 0.910799i \(-0.364534\pi\)
−0.582350 + 0.812938i \(0.697867\pi\)
\(318\) 0 0
\(319\) 0.651207 + 1.12792i 0.0364606 + 0.0631516i
\(320\) 0 0
\(321\) −24.2858 + 3.40776i −1.35550 + 0.190203i
\(322\) 0 0
\(323\) 8.20549i 0.456565i
\(324\) 0 0
\(325\) 13.5252 + 7.80876i 0.750241 + 0.433152i
\(326\) 0 0
\(327\) 7.70473 6.01690i 0.426073 0.332735i
\(328\) 0 0
\(329\) −24.0253 + 16.4144i −1.32456 + 0.904954i
\(330\) 0 0
\(331\) 2.28857 3.96392i 0.125791 0.217877i −0.796251 0.604967i \(-0.793186\pi\)
0.922042 + 0.387090i \(0.126520\pi\)
\(332\) 0 0
\(333\) 2.46727 9.87737i 0.135205 0.541276i
\(334\) 0 0
\(335\) 17.2405 + 29.8615i 0.941951 + 1.63151i
\(336\) 0 0
\(337\) −14.7062 + 25.4720i −0.801100 + 1.38755i 0.117793 + 0.993038i \(0.462418\pi\)
−0.918893 + 0.394508i \(0.870915\pi\)
\(338\) 0 0
\(339\) −14.3300 18.3497i −0.778297 0.996621i
\(340\) 0 0
\(341\) −3.79023 6.56486i −0.205252 0.355507i
\(342\) 0 0
\(343\) 4.17373 + 18.0438i 0.225360 + 0.974276i
\(344\) 0 0
\(345\) −9.46825 + 23.4201i −0.509753 + 1.26089i
\(346\) 0 0
\(347\) 17.0245 9.82911i 0.913924 0.527654i 0.0322323 0.999480i \(-0.489738\pi\)
0.881692 + 0.471826i \(0.156405\pi\)
\(348\) 0 0
\(349\) 8.47286 4.89181i 0.453542 0.261852i −0.255783 0.966734i \(-0.582333\pi\)
0.709325 + 0.704882i \(0.249000\pi\)
\(350\) 0 0
\(351\) 2.23424 21.1249i 0.119255 1.12756i
\(352\) 0 0
\(353\) 25.0645 1.33405 0.667023 0.745037i \(-0.267568\pi\)
0.667023 + 0.745037i \(0.267568\pi\)
\(354\) 0 0
\(355\) 31.0074i 1.64570i
\(356\) 0 0
\(357\) −7.47890 + 1.63461i −0.395825 + 0.0865130i
\(358\) 0 0
\(359\) 8.09861 4.67574i 0.427428 0.246776i −0.270822 0.962629i \(-0.587296\pi\)
0.698251 + 0.715853i \(0.253962\pi\)
\(360\) 0 0
\(361\) 2.56305 4.43933i 0.134897 0.233649i
\(362\) 0 0
\(363\) 18.2338 + 7.37154i 0.957026 + 0.386906i
\(364\) 0 0
\(365\) −40.5367 23.4039i −2.12179 1.22502i
\(366\) 0 0
\(367\) 21.8850i 1.14239i 0.820815 + 0.571194i \(0.193520\pi\)
−0.820815 + 0.571194i \(0.806480\pi\)
\(368\) 0 0
\(369\) 20.5139 5.87261i 1.06791 0.305716i
\(370\) 0 0
\(371\) −1.21912 1.78439i −0.0632934 0.0926409i
\(372\) 0 0
\(373\) 4.61644 0.239030 0.119515 0.992832i \(-0.461866\pi\)
0.119515 + 0.992832i \(0.461866\pi\)
\(374\) 0 0
\(375\) −5.62655 2.27470i −0.290554 0.117465i
\(376\) 0 0
\(377\) 1.12613 0.0579988
\(378\) 0 0
\(379\) −6.22396 −0.319703 −0.159852 0.987141i \(-0.551102\pi\)
−0.159852 + 0.987141i \(0.551102\pi\)
\(380\) 0 0
\(381\) 20.5108 + 8.29209i 1.05080 + 0.424817i
\(382\) 0 0
\(383\) −21.9977 −1.12403 −0.562015 0.827127i \(-0.689974\pi\)
−0.562015 + 0.827127i \(0.689974\pi\)
\(384\) 0 0
\(385\) 16.0869 33.4879i 0.819864 1.70670i
\(386\) 0 0
\(387\) −7.60373 + 30.4405i −0.386519 + 1.54738i
\(388\) 0 0
\(389\) 9.82776i 0.498287i 0.968467 + 0.249144i \(0.0801491\pi\)
−0.968467 + 0.249144i \(0.919851\pi\)
\(390\) 0 0
\(391\) 7.10481 + 4.10197i 0.359306 + 0.207445i
\(392\) 0 0
\(393\) −21.5462 8.71066i −1.08686 0.439395i
\(394\) 0 0
\(395\) −18.2696 + 31.6439i −0.919243 + 1.59218i
\(396\) 0 0
\(397\) 4.55324 2.62881i 0.228520 0.131936i −0.381369 0.924423i \(-0.624547\pi\)
0.609889 + 0.792487i \(0.291214\pi\)
\(398\) 0 0
\(399\) 21.4468 + 6.83262i 1.07368 + 0.342059i
\(400\) 0 0
\(401\) 17.0719i 0.852529i 0.904598 + 0.426265i \(0.140171\pi\)
−0.904598 + 0.426265i \(0.859829\pi\)
\(402\) 0 0
\(403\) −6.55444 −0.326500
\(404\) 0 0
\(405\) −0.909599 26.7134i −0.0451983 1.32740i
\(406\) 0 0
\(407\) 13.8957 8.02270i 0.688786 0.397671i
\(408\) 0 0
\(409\) 16.9484 9.78516i 0.838044 0.483845i −0.0185546 0.999828i \(-0.505906\pi\)
0.856599 + 0.515983i \(0.172573\pi\)
\(410\) 0 0
\(411\) 5.84288 14.4526i 0.288208 0.712893i
\(412\) 0 0
\(413\) 0.550478 + 7.25114i 0.0270873 + 0.356805i
\(414\) 0 0
\(415\) −11.9977 20.7807i −0.588946 1.02008i
\(416\) 0 0
\(417\) 1.90681 + 2.44170i 0.0933769 + 0.119571i
\(418\) 0 0
\(419\) −10.3073 + 17.8529i −0.503547 + 0.872169i 0.496445 + 0.868068i \(0.334639\pi\)
−0.999992 + 0.00410056i \(0.998695\pi\)
\(420\) 0 0
\(421\) 0.704748 + 1.22066i 0.0343473 + 0.0594913i 0.882688 0.469959i \(-0.155731\pi\)
−0.848341 + 0.529451i \(0.822398\pi\)
\(422\) 0 0
\(423\) −31.7190 + 9.08035i −1.54223 + 0.441502i
\(424\) 0 0
\(425\) 3.19091 5.52682i 0.154782 0.268090i
\(426\) 0 0
\(427\) −10.7508 15.7357i −0.520268 0.761504i
\(428\) 0 0
\(429\) 26.3865 20.6062i 1.27395 0.994876i
\(430\) 0 0
\(431\) −11.6666 6.73569i −0.561959 0.324447i 0.191973 0.981400i \(-0.438512\pi\)
−0.753931 + 0.656953i \(0.771845\pi\)
\(432\) 0 0
\(433\) 12.9356i 0.621646i 0.950468 + 0.310823i \(0.100605\pi\)
−0.950468 + 0.310823i \(0.899395\pi\)
\(434\) 0 0
\(435\) 1.40322 0.196899i 0.0672794 0.00944059i
\(436\) 0 0
\(437\) −12.0608 20.8899i −0.576944 0.999297i
\(438\) 0 0
\(439\) 8.75023 + 5.05195i 0.417626 + 0.241116i 0.694061 0.719916i \(-0.255820\pi\)
−0.276435 + 0.961033i \(0.589153\pi\)
\(440\) 0 0
\(441\) −1.95519 + 20.9088i −0.0931041 + 0.995656i
\(442\) 0 0
\(443\) −25.1220 14.5042i −1.19358 0.689115i −0.234466 0.972124i \(-0.575334\pi\)
−0.959117 + 0.283009i \(0.908667\pi\)
\(444\) 0 0
\(445\) 13.6873 + 23.7072i 0.648842 + 1.12383i
\(446\) 0 0
\(447\) −8.37916 + 20.7262i −0.396321 + 0.980314i
\(448\) 0 0
\(449\) 7.94881i 0.375127i −0.982252 0.187564i \(-0.939941\pi\)
0.982252 0.187564i \(-0.0600591\pi\)
\(450\) 0 0
\(451\) 29.1239 + 16.8147i 1.37139 + 0.791772i
\(452\) 0 0
\(453\) 20.8227 + 8.41819i 0.978337 + 0.395521i
\(454\) 0 0
\(455\) −18.1213 26.5237i −0.849539 1.24345i
\(456\) 0 0
\(457\) 6.98084 12.0912i 0.326550 0.565601i −0.655275 0.755391i \(-0.727447\pi\)
0.981825 + 0.189789i \(0.0607805\pi\)
\(458\) 0 0
\(459\) −8.63231 0.912985i −0.402922 0.0426145i
\(460\) 0 0
\(461\) 16.4030 + 28.4108i 0.763964 + 1.32322i 0.940793 + 0.338983i \(0.110083\pi\)
−0.176829 + 0.984242i \(0.556584\pi\)
\(462\) 0 0
\(463\) −13.8812 + 24.0429i −0.645112 + 1.11737i 0.339163 + 0.940727i \(0.389856\pi\)
−0.984276 + 0.176640i \(0.943477\pi\)
\(464\) 0 0
\(465\) −8.16719 + 1.14601i −0.378744 + 0.0531451i
\(466\) 0 0
\(467\) 11.4311 + 19.7992i 0.528966 + 0.916196i 0.999429 + 0.0337767i \(0.0107535\pi\)
−0.470463 + 0.882420i \(0.655913\pi\)
\(468\) 0 0
\(469\) −2.32529 30.6297i −0.107372 1.41435i
\(470\) 0 0
\(471\) −29.4555 + 4.13318i −1.35724 + 0.190447i
\(472\) 0 0
\(473\) −42.8245 + 24.7247i −1.96907 + 1.13684i
\(474\) 0 0
\(475\) −16.2502 + 9.38204i −0.745609 + 0.430478i
\(476\) 0 0
\(477\) −0.674409 2.35581i −0.0308791 0.107865i
\(478\) 0 0
\(479\) 2.42425 0.110767 0.0553834 0.998465i \(-0.482362\pi\)
0.0553834 + 0.998465i \(0.482362\pi\)
\(480\) 0 0
\(481\) 13.8737i 0.632584i
\(482\) 0 0
\(483\) 16.6374 15.1543i 0.757030 0.689542i
\(484\) 0 0
\(485\) 20.8121 12.0159i 0.945028 0.545612i
\(486\) 0 0
\(487\) 5.19651 9.00061i 0.235476 0.407857i −0.723935 0.689868i \(-0.757668\pi\)
0.959411 + 0.282012i \(0.0910017\pi\)
\(488\) 0 0
\(489\) −1.21837 8.68282i −0.0550964 0.392651i
\(490\) 0 0
\(491\) −2.93014 1.69172i −0.132235 0.0763462i 0.432423 0.901671i \(-0.357659\pi\)
−0.564658 + 0.825325i \(0.690992\pi\)
\(492\) 0 0
\(493\) 0.460174i 0.0207252i
\(494\) 0 0
\(495\) 29.2762 30.2900i 1.31587 1.36143i
\(496\) 0 0
\(497\) 11.9611 24.8993i 0.536530 1.11689i
\(498\) 0 0
\(499\) 39.5603 1.77096 0.885481 0.464676i \(-0.153829\pi\)
0.885481 + 0.464676i \(0.153829\pi\)
\(500\) 0 0
\(501\) −15.8263 + 12.3593i −0.707067 + 0.552174i
\(502\) 0 0
\(503\) −14.5476 −0.648645 −0.324323 0.945947i \(-0.605136\pi\)
−0.324323 + 0.945947i \(0.605136\pi\)
\(504\) 0 0
\(505\) 21.7018 0.965717
\(506\) 0 0
\(507\) −0.893668 6.36882i −0.0396892 0.282849i
\(508\) 0 0
\(509\) 20.3916 0.903841 0.451921 0.892058i \(-0.350739\pi\)
0.451921 + 0.892058i \(0.350739\pi\)
\(510\) 0 0
\(511\) 23.5235 + 34.4307i 1.04062 + 1.52313i
\(512\) 0 0
\(513\) 20.6385 + 15.0153i 0.911210 + 0.662941i
\(514\) 0 0
\(515\) 20.8643i 0.919391i
\(516\) 0 0
\(517\) −45.0319 25.9992i −1.98050 1.14344i
\(518\) 0 0
\(519\) −8.55500 + 6.68091i −0.375523 + 0.293259i
\(520\) 0 0
\(521\) 7.75122 13.4255i 0.339587 0.588182i −0.644768 0.764379i \(-0.723046\pi\)
0.984355 + 0.176196i \(0.0563793\pi\)
\(522\) 0 0
\(523\) 9.35989 5.40394i 0.409280 0.236298i −0.281201 0.959649i \(-0.590733\pi\)
0.690480 + 0.723351i \(0.257399\pi\)
\(524\) 0 0
\(525\) −11.7885 12.9422i −0.514491 0.564846i
\(526\) 0 0
\(527\) 2.67836i 0.116671i
\(528\) 0 0
\(529\) −1.11695 −0.0485631
\(530\) 0 0
\(531\) −1.99829 + 7.99987i −0.0867183 + 0.347165i
\(532\) 0 0
\(533\) 25.1819 14.5388i 1.09075 0.629745i
\(534\) 0 0
\(535\) −36.4162 + 21.0249i −1.57441 + 0.908986i
\(536\) 0 0
\(537\) −15.7156 20.1241i −0.678180 0.868419i
\(538\) 0 0
\(539\) −25.8360 + 20.6857i −1.11283 + 0.890997i
\(540\) 0 0
\(541\) −8.79357 15.2309i −0.378065 0.654828i 0.612716 0.790303i \(-0.290077\pi\)
−0.990781 + 0.135476i \(0.956744\pi\)
\(542\) 0 0
\(543\) 0.0541189 0.133865i 0.00232247 0.00574471i
\(544\) 0 0
\(545\) 8.38108 14.5165i 0.359006 0.621817i
\(546\) 0 0
\(547\) −5.72451 9.91513i −0.244762 0.423940i 0.717303 0.696762i \(-0.245377\pi\)
−0.962065 + 0.272821i \(0.912043\pi\)
\(548\) 0 0
\(549\) −5.94730 20.7748i −0.253824 0.886646i
\(550\) 0 0
\(551\) −0.676511 + 1.17175i −0.0288203 + 0.0499183i
\(552\) 0 0
\(553\) 26.8774 18.3629i 1.14294 0.780871i
\(554\) 0 0
\(555\) −2.42575 17.2873i −0.102967 0.733807i
\(556\) 0 0
\(557\) 32.9159 + 19.0040i 1.39469 + 0.805226i 0.993830 0.110912i \(-0.0353771\pi\)
0.400863 + 0.916138i \(0.368710\pi\)
\(558\) 0 0
\(559\) 42.7565i 1.80841i
\(560\) 0 0
\(561\) −8.42035 10.7824i −0.355508 0.455233i
\(562\) 0 0
\(563\) −8.88438 15.3882i −0.374432 0.648535i 0.615810 0.787895i \(-0.288829\pi\)
−0.990242 + 0.139360i \(0.955496\pi\)
\(564\) 0 0
\(565\) −34.5727 19.9605i −1.45448 0.839746i
\(566\) 0 0
\(567\) −9.57431 + 21.8021i −0.402083 + 0.915603i
\(568\) 0 0
\(569\) −33.7404 19.4801i −1.41447 0.816646i −0.418667 0.908140i \(-0.637503\pi\)
−0.995806 + 0.0914936i \(0.970836\pi\)
\(570\) 0 0
\(571\) −8.45245 14.6401i −0.353724 0.612668i 0.633175 0.774009i \(-0.281752\pi\)
−0.986899 + 0.161341i \(0.948418\pi\)
\(572\) 0 0
\(573\) −16.4547 21.0705i −0.687406 0.880233i
\(574\) 0 0
\(575\) 18.7605i 0.782368i
\(576\) 0 0
\(577\) −40.9329 23.6326i −1.70406 0.983840i −0.941555 0.336858i \(-0.890636\pi\)
−0.762506 0.646982i \(-0.776031\pi\)
\(578\) 0 0
\(579\) 5.18808 + 36.9734i 0.215609 + 1.53656i
\(580\) 0 0
\(581\) 1.61818 + 21.3153i 0.0671333 + 0.884308i
\(582\) 0 0
\(583\) 1.93099 3.34458i 0.0799736 0.138518i
\(584\) 0 0
\(585\) −10.0246 35.0174i −0.414466 1.44779i
\(586\) 0 0
\(587\) −11.6343 20.1513i −0.480200 0.831731i 0.519542 0.854445i \(-0.326103\pi\)
−0.999742 + 0.0227138i \(0.992769\pi\)
\(588\) 0 0
\(589\) 3.93750 6.81995i 0.162242 0.281011i
\(590\) 0 0
\(591\) −6.41595 + 15.8701i −0.263917 + 0.652809i
\(592\) 0 0
\(593\) 18.5962 + 32.2095i 0.763654 + 1.32269i 0.940955 + 0.338530i \(0.109930\pi\)
−0.177302 + 0.984157i \(0.556737\pi\)
\(594\) 0 0
\(595\) −10.8384 + 7.40494i −0.444332 + 0.303573i
\(596\) 0 0
\(597\) 11.2588 + 14.4171i 0.460793 + 0.590053i
\(598\) 0 0
\(599\) 27.9591 16.1422i 1.14238 0.659552i 0.195359 0.980732i \(-0.437413\pi\)
0.947018 + 0.321180i \(0.104079\pi\)
\(600\) 0 0
\(601\) 14.7559 8.51933i 0.601906 0.347511i −0.167885 0.985807i \(-0.553694\pi\)
0.769791 + 0.638296i \(0.220360\pi\)
\(602\) 0 0
\(603\) 8.44102 33.7925i 0.343745 1.37614i
\(604\) 0 0
\(605\) 33.7231 1.37104
\(606\) 0 0
\(607\) 9.75021i 0.395749i −0.980227 0.197874i \(-0.936596\pi\)
0.980227 0.197874i \(-0.0634038\pi\)
\(608\) 0 0
\(609\) −1.20276 0.383182i −0.0487383 0.0155273i
\(610\) 0 0
\(611\) −38.9369 + 22.4802i −1.57522 + 0.909452i
\(612\) 0 0
\(613\) −6.86332 + 11.8876i −0.277207 + 0.480136i −0.970690 0.240337i \(-0.922742\pi\)
0.693483 + 0.720473i \(0.256075\pi\)
\(614\) 0 0
\(615\) 28.8361 22.5191i 1.16278 0.908058i
\(616\) 0 0
\(617\) −2.84301 1.64141i −0.114455 0.0660807i 0.441680 0.897173i \(-0.354383\pi\)
−0.556135 + 0.831092i \(0.687716\pi\)
\(618\) 0 0
\(619\) 17.3098i 0.695740i −0.937543 0.347870i \(-0.886905\pi\)
0.937543 0.347870i \(-0.113095\pi\)
\(620\) 0 0
\(621\) 23.3184 10.3638i 0.935736 0.415886i
\(622\) 0 0
\(623\) −1.84606 24.3171i −0.0739608 0.974243i
\(624\) 0 0
\(625\) −29.5071 −1.18028
\(626\) 0 0
\(627\) 5.58952 + 39.8344i 0.223224 + 1.59083i
\(628\) 0 0
\(629\) −5.66923 −0.226047
\(630\) 0 0
\(631\) −6.27821 −0.249932 −0.124966 0.992161i \(-0.539882\pi\)
−0.124966 + 0.992161i \(0.539882\pi\)
\(632\) 0 0
\(633\) −16.6120 + 12.9729i −0.660270 + 0.515628i
\(634\) 0 0
\(635\) 37.9344 1.50538
\(636\) 0 0
\(637\) 4.32011 + 28.2892i 0.171169 + 1.12086i
\(638\) 0 0
\(639\) 21.7678 22.5216i 0.861120 0.890941i
\(640\) 0 0
\(641\) 20.7601i 0.819976i 0.912091 + 0.409988i \(0.134467\pi\)
−0.912091 + 0.409988i \(0.865533\pi\)
\(642\) 0 0
\(643\) 17.2553 + 9.96236i 0.680483 + 0.392877i 0.800037 0.599950i \(-0.204813\pi\)
−0.119554 + 0.992828i \(0.538146\pi\)
\(644\) 0 0
\(645\) 7.47577 + 53.2769i 0.294358 + 2.09778i
\(646\) 0 0
\(647\) 14.7670 25.5772i 0.580551 1.00554i −0.414863 0.909884i \(-0.636170\pi\)
0.995414 0.0956605i \(-0.0304963\pi\)
\(648\) 0 0
\(649\) −11.2544 + 6.49774i −0.441775 + 0.255059i
\(650\) 0 0
\(651\) 7.00044 + 2.23024i 0.274369 + 0.0874099i
\(652\) 0 0
\(653\) 15.9250i 0.623193i 0.950215 + 0.311596i \(0.100864\pi\)
−0.950215 + 0.311596i \(0.899136\pi\)
\(654\) 0 0
\(655\) −39.8493 −1.55704
\(656\) 0 0
\(657\) 13.0131 + 45.4565i 0.507688 + 1.77343i
\(658\) 0 0
\(659\) 2.80283 1.61822i 0.109183 0.0630368i −0.444414 0.895821i \(-0.646588\pi\)
0.553597 + 0.832785i \(0.313255\pi\)
\(660\) 0 0
\(661\) 7.71194 4.45249i 0.299960 0.173182i −0.342465 0.939531i \(-0.611262\pi\)
0.642425 + 0.766349i \(0.277928\pi\)
\(662\) 0 0
\(663\) −11.7143 + 1.64374i −0.454945 + 0.0638375i
\(664\) 0 0
\(665\) 38.4843 2.92158i 1.49236 0.113294i
\(666\) 0 0
\(667\) 0.676383 + 1.17153i 0.0261896 + 0.0453618i
\(668\) 0 0
\(669\) 1.41511 0.198567i 0.0547112 0.00767703i
\(670\) 0 0
\(671\) 17.0285 29.4943i 0.657379 1.13861i
\(672\) 0 0
\(673\) −13.2311 22.9169i −0.510021 0.883382i −0.999933 0.0116101i \(-0.996304\pi\)
0.489912 0.871772i \(-0.337029\pi\)
\(674\) 0 0
\(675\) −8.06199 18.1394i −0.310306 0.698184i
\(676\) 0 0
\(677\) 4.46424 7.73229i 0.171575 0.297176i −0.767396 0.641174i \(-0.778448\pi\)
0.938971 + 0.343997i \(0.111781\pi\)
\(678\) 0 0
\(679\) −21.3475 + 1.62062i −0.819243 + 0.0621938i
\(680\) 0 0
\(681\) −0.535622 0.216541i −0.0205251 0.00829786i
\(682\) 0 0
\(683\) −32.7902 18.9314i −1.25468 0.724390i −0.282645 0.959225i \(-0.591212\pi\)
−0.972035 + 0.234834i \(0.924545\pi\)
\(684\) 0 0
\(685\) 26.7298i 1.02129i
\(686\) 0 0
\(687\) −9.36221 + 23.1578i −0.357191 + 0.883525i
\(688\) 0 0
\(689\) −1.66963 2.89189i −0.0636080 0.110172i
\(690\) 0 0
\(691\) −4.94211 2.85333i −0.188007 0.108546i 0.403042 0.915181i \(-0.367953\pi\)
−0.591049 + 0.806636i \(0.701286\pi\)
\(692\) 0 0
\(693\) −35.1936 + 13.0300i −1.33689 + 0.494968i
\(694\) 0 0
\(695\) 4.60039 + 2.65604i 0.174503 + 0.100749i
\(696\) 0 0
\(697\) −5.94103 10.2902i −0.225032 0.389768i
\(698\) 0 0
\(699\) −25.3424 + 3.55602i −0.958537 + 0.134501i
\(700\) 0 0
\(701\) 8.19949i 0.309690i 0.987939 + 0.154845i \(0.0494879\pi\)
−0.987939 + 0.154845i \(0.950512\pi\)
\(702\) 0 0
\(703\) 14.4357 + 8.33444i 0.544452 + 0.314339i
\(704\) 0 0
\(705\) −44.5869 + 34.8195i −1.67924 + 1.31138i
\(706\) 0 0
\(707\) −17.4268 8.37148i −0.655403 0.314842i
\(708\) 0 0
\(709\) −10.0757 + 17.4517i −0.378402 + 0.655412i −0.990830 0.135115i \(-0.956860\pi\)
0.612428 + 0.790527i \(0.290193\pi\)
\(710\) 0 0
\(711\) 35.4844 10.1583i 1.33077 0.380965i
\(712\) 0 0
\(713\) −3.93676 6.81866i −0.147433 0.255361i
\(714\) 0 0
\(715\) 28.7028 49.7147i 1.07342 1.85923i
\(716\) 0 0
\(717\) 27.7388 + 35.5200i 1.03593 + 1.32652i
\(718\) 0 0
\(719\) −25.5996 44.3397i −0.954702 1.65359i −0.735048 0.678015i \(-0.762841\pi\)
−0.219654 0.975578i \(-0.570493\pi\)
\(720\) 0 0
\(721\) −8.04842 + 16.7543i −0.299739 + 0.623963i
\(722\) 0 0
\(723\) 1.24657 3.08345i 0.0463606 0.114675i
\(724\) 0 0
\(725\) 0.911330 0.526157i 0.0338460 0.0195410i
\(726\) 0 0
\(727\) −13.7848 + 7.95865i −0.511249 + 0.295170i −0.733347 0.679854i \(-0.762043\pi\)
0.222098 + 0.975024i \(0.428710\pi\)
\(728\) 0 0
\(729\) −18.0927 + 20.0413i −0.670099 + 0.742271i
\(730\) 0 0
\(731\) 17.4717 0.646213
\(732\) 0 0
\(733\) 4.24025i 0.156617i −0.996929 0.0783086i \(-0.975048\pi\)
0.996929 0.0783086i \(-0.0249519\pi\)
\(734\) 0 0
\(735\) 10.3293 + 34.4945i 0.381003 + 1.27235i
\(736\) 0 0
\(737\) 47.5401 27.4473i 1.75116 1.01103i
\(738\) 0 0
\(739\) −14.1835 + 24.5665i −0.521747 + 0.903693i 0.477933 + 0.878397i \(0.341386\pi\)
−0.999680 + 0.0252966i \(0.991947\pi\)
\(740\) 0 0
\(741\) 32.2448 + 13.0359i 1.18454 + 0.478886i
\(742\) 0 0
\(743\) 21.8850 + 12.6353i 0.802884 + 0.463545i 0.844479 0.535589i \(-0.179910\pi\)
−0.0415945 + 0.999135i \(0.513244\pi\)
\(744\) 0 0
\(745\) 38.3327i 1.40440i
\(746\) 0 0
\(747\) −5.87413 + 23.5163i −0.214923 + 0.860416i
\(748\) 0 0
\(749\) 37.3531 2.83570i 1.36485 0.103614i
\(750\) 0 0
\(751\) 47.5460 1.73498 0.867490 0.497455i \(-0.165732\pi\)
0.867490 + 0.497455i \(0.165732\pi\)
\(752\) 0 0
\(753\) 16.0204 + 6.47670i 0.583814 + 0.236024i
\(754\) 0 0
\(755\) 38.5113 1.40157
\(756\) 0 0
\(757\) 37.3922 1.35904 0.679521 0.733656i \(-0.262188\pi\)
0.679521 + 0.733656i \(0.262188\pi\)
\(758\) 0 0
\(759\) 37.2853 + 15.0737i 1.35337 + 0.547139i
\(760\) 0 0
\(761\) −8.24283 −0.298802 −0.149401 0.988777i \(-0.547735\pi\)
−0.149401 + 0.988777i \(0.547735\pi\)
\(762\) 0 0
\(763\) −12.3299 + 8.42390i −0.446371 + 0.304966i
\(764\) 0 0
\(765\) −14.3092 + 4.09638i −0.517352 + 0.148105i
\(766\) 0 0
\(767\) 11.2365i 0.405728i
\(768\) 0 0
\(769\) 20.2182 + 11.6730i 0.729086 + 0.420938i 0.818088 0.575094i \(-0.195034\pi\)
−0.0890020 + 0.996031i \(0.528368\pi\)
\(770\) 0 0
\(771\) −24.0985 9.74253i −0.867887 0.350869i
\(772\) 0 0
\(773\) −17.2201 + 29.8261i −0.619364 + 1.07277i 0.370238 + 0.928937i \(0.379276\pi\)
−0.989602 + 0.143833i \(0.954057\pi\)
\(774\) 0 0
\(775\) −5.30422 + 3.06240i −0.190533 + 0.110004i
\(776\) 0 0
\(777\) −4.72070 + 14.8177i −0.169354 + 0.531582i
\(778\) 0 0
\(779\) 34.9361i 1.25171i
\(780\) 0 0
\(781\) 49.3644 1.76640
\(782\) 0 0
\(783\) −1.15743 0.842076i −0.0413632 0.0300933i
\(784\) 0 0
\(785\) −44.1682 + 25.5005i −1.57643 + 0.910152i
\(786\) 0 0
\(787\) −7.19975 + 4.15678i −0.256643 + 0.148173i −0.622802 0.782379i \(-0.714006\pi\)
0.366159 + 0.930552i \(0.380673\pi\)
\(788\) 0 0
\(789\) −4.58023 + 11.3294i −0.163061 + 0.403337i
\(790\) 0 0
\(791\) 20.0625 + 29.3650i 0.713341 + 1.04410i
\(792\) 0 0
\(793\) −14.7237 25.5022i −0.522854 0.905610i
\(794\) 0 0
\(795\) −2.58609 3.31153i −0.0917191 0.117448i
\(796\) 0 0
\(797\) 0.426036 0.737916i 0.0150910 0.0261383i −0.858381 0.513012i \(-0.828530\pi\)
0.873472 + 0.486874i \(0.161863\pi\)
\(798\) 0 0
\(799\) 9.18614 + 15.9109i 0.324982 + 0.562886i
\(800\) 0 0
\(801\) 6.70136 26.8280i 0.236781 0.947921i
\(802\) 0 0
\(803\) −37.2595 + 64.5354i −1.31486 + 2.27740i
\(804\) 0 0
\(805\) 16.7088 34.7826i 0.588908 1.22592i
\(806\) 0 0
\(807\) 40.6522 31.7467i 1.43102 1.11754i
\(808\) 0 0
\(809\) −31.5580 18.2200i −1.10952 0.640581i −0.170814 0.985303i \(-0.554640\pi\)
−0.938705 + 0.344722i \(0.887973\pi\)
\(810\) 0 0
\(811\) 1.08986i 0.0382702i −0.999817 0.0191351i \(-0.993909\pi\)
0.999817 0.0191351i \(-0.00609126\pi\)
\(812\) 0 0
\(813\) 4.78238 0.671060i 0.167725 0.0235351i
\(814\) 0 0
\(815\) −7.51697 13.0198i −0.263308 0.456063i
\(816\) 0 0
\(817\) −44.4885 25.6855i −1.55646 0.898620i
\(818\) 0 0
\(819\) −5.45810 + 31.9864i −0.190721 + 1.11770i
\(820\) 0 0
\(821\) −20.9748 12.1098i −0.732025 0.422635i 0.0871374 0.996196i \(-0.472228\pi\)
−0.819163 + 0.573561i \(0.805561\pi\)
\(822\) 0 0
\(823\) −2.85592 4.94660i −0.0995512 0.172428i 0.811948 0.583730i \(-0.198407\pi\)
−0.911499 + 0.411302i \(0.865074\pi\)
\(824\) 0 0
\(825\) 11.7258 29.0041i 0.408239 1.00979i
\(826\) 0 0
\(827\) 36.4579i 1.26777i 0.773429 + 0.633883i \(0.218540\pi\)
−0.773429 + 0.633883i \(0.781460\pi\)
\(828\) 0 0
\(829\) −0.498269 0.287676i −0.0173056 0.00999140i 0.491322 0.870978i \(-0.336514\pi\)
−0.508628 + 0.860986i \(0.669847\pi\)
\(830\) 0 0
\(831\) −21.8090 8.81692i −0.756545 0.305856i
\(832\) 0 0
\(833\) 11.5599 1.76534i 0.400526 0.0611653i
\(834\) 0 0
\(835\) −17.2156 + 29.8183i −0.595770 + 1.03190i
\(836\) 0 0
\(837\) 6.73660 + 4.90114i 0.232851 + 0.169408i
\(838\) 0 0
\(839\) −23.9341 41.4550i −0.826295 1.43119i −0.900925 0.433974i \(-0.857111\pi\)
0.0746300 0.997211i \(-0.476222\pi\)
\(840\) 0 0
\(841\) −14.4621 + 25.0490i −0.498692 + 0.863759i
\(842\) 0 0
\(843\) 7.83874 1.09993i 0.269981 0.0378835i
\(844\) 0 0
\(845\) −5.51368 9.54997i −0.189676 0.328529i
\(846\) 0 0
\(847\) −27.0801 13.0087i −0.930483 0.446985i
\(848\) 0 0
\(849\) −34.9943 + 4.91036i −1.20100 + 0.168523i
\(850\) 0 0
\(851\) 14.4329 8.33286i 0.494755 0.285647i
\(852\) 0 0
\(853\) 40.5393 23.4054i 1.38804 0.801385i 0.394945 0.918705i \(-0.370764\pi\)
0.993094 + 0.117320i \(0.0374303\pi\)
\(854\) 0 0
\(855\) 42.4581 + 10.6056i 1.45204 + 0.362704i
\(856\) 0 0
\(857\) 9.56441 0.326714 0.163357 0.986567i \(-0.447768\pi\)
0.163357 + 0.986567i \(0.447768\pi\)
\(858\) 0 0
\(859\) 5.40759i 0.184505i 0.995736 + 0.0922523i \(0.0294066\pi\)
−0.995736 + 0.0922523i \(0.970593\pi\)
\(860\) 0 0
\(861\) −31.8425 + 6.95961i −1.08519 + 0.237183i
\(862\) 0 0
\(863\) 35.5402 20.5191i 1.20980 0.698480i 0.247086 0.968994i \(-0.420527\pi\)
0.962716 + 0.270514i \(0.0871936\pi\)
\(864\) 0 0
\(865\) −9.30598 + 16.1184i −0.316413 + 0.548043i
\(866\) 0 0
\(867\) −3.41991 24.3724i −0.116146 0.827729i
\(868\) 0 0
\(869\) 50.3777 + 29.0856i 1.70895 + 0.986661i
\(870\) 0 0
\(871\) 47.4646i 1.60828i
\(872\) 0 0
\(873\) −23.5518 5.88301i −0.797109 0.199110i
\(874\) 0 0
\(875\) 8.35633 + 4.01421i 0.282496 + 0.135705i
\(876\) 0 0
\(877\) −14.6502 −0.494701 −0.247351 0.968926i \(-0.579560\pi\)
−0.247351 + 0.968926i \(0.579560\pi\)
\(878\) 0 0
\(879\) 17.5017 13.6677i 0.590317 0.460999i
\(880\) 0 0
\(881\) −44.8295 −1.51034 −0.755172 0.655527i \(-0.772447\pi\)
−0.755172 + 0.655527i \(0.772447\pi\)
\(882\) 0 0
\(883\) 33.8527 1.13923 0.569617 0.821910i \(-0.307091\pi\)
0.569617 + 0.821910i \(0.307091\pi\)
\(884\) 0 0
\(885\) 1.96466 + 14.0014i 0.0660413 + 0.470651i
\(886\) 0 0
\(887\) −26.6844 −0.895973 −0.447987 0.894040i \(-0.647859\pi\)
−0.447987 + 0.894040i \(0.647859\pi\)
\(888\) 0 0
\(889\) −30.4618 14.6332i −1.02166 0.490783i
\(890\) 0 0
\(891\) −42.5284 + 1.44810i −1.42475 + 0.0485132i
\(892\) 0 0
\(893\) 54.0189i 1.80767i
\(894\) 0 0
\(895\) −37.9157 21.8907i −1.26738 0.731724i
\(896\) 0 0
\(897\) 27.4066 21.4028i 0.915081 0.714619i
\(898\) 0 0
\(899\) −0.220820 + 0.382472i −0.00736476 + 0.0127561i
\(900\) 0 0
\(901\) −1.18172 + 0.682266i −0.0393688 + 0.0227296i
\(902\) 0 0
\(903\) 14.5485 45.6659i 0.484143 1.51967i
\(904\) 0 0
\(905\) 0.247582i 0.00822989i
\(906\) 0 0
\(907\) −15.9442 −0.529419 −0.264710 0.964328i \(-0.585276\pi\)
−0.264710 + 0.964328i \(0.585276\pi\)
\(908\) 0 0
\(909\) −15.7627 15.2351i −0.522815 0.505316i
\(910\) 0 0
\(911\) 40.9207 23.6256i 1.35576 0.782750i 0.366713 0.930334i \(-0.380483\pi\)
0.989050 + 0.147584i \(0.0471496\pi\)
\(912\) 0 0
\(913\) −33.0833 + 19.1007i −1.09490 + 0.632140i
\(914\) 0 0
\(915\) −22.8055 29.2028i −0.753927 0.965415i
\(916\) 0 0
\(917\) 31.9995 + 15.3719i 1.05672 + 0.507624i
\(918\) 0 0
\(919\) 14.8163 + 25.6625i 0.488743 + 0.846528i 0.999916 0.0129500i \(-0.00412223\pi\)
−0.511173 + 0.859478i \(0.670789\pi\)
\(920\) 0 0
\(921\) 1.25560 3.10578i 0.0413734 0.102339i
\(922\) 0 0
\(923\) 21.3415 36.9645i 0.702463 1.21670i
\(924\) 0 0
\(925\) −6.48212 11.2274i −0.213131 0.369153i
\(926\) 0 0
\(927\) −14.6471 + 15.1544i −0.481075 + 0.497735i
\(928\) 0 0
\(929\) 16.6186 28.7842i 0.545238 0.944380i −0.453354 0.891331i \(-0.649773\pi\)
0.998592 0.0530496i \(-0.0168941\pi\)
\(930\) 0 0
\(931\) −32.0304 12.4993i −1.04975 0.409647i
\(932\) 0 0
\(933\) −0.502822 3.58342i −0.0164617 0.117316i
\(934\) 0 0
\(935\) −20.3151 11.7289i −0.664373 0.383576i
\(936\) 0 0
\(937\) 23.8190i 0.778134i −0.921209 0.389067i \(-0.872797\pi\)
0.921209 0.389067i \(-0.127203\pi\)
\(938\) 0 0
\(939\) −23.8891 30.5903i −0.779591 0.998278i
\(940\) 0 0
\(941\) −27.1201 46.9734i −0.884091 1.53129i −0.846752 0.531988i \(-0.821445\pi\)
−0.0373389 0.999303i \(-0.511888\pi\)
\(942\) 0 0
\(943\) 30.2498 + 17.4647i 0.985069 + 0.568730i
\(944\) 0 0
\(945\) −1.20841 + 40.8112i −0.0393095 + 1.32759i
\(946\) 0 0
\(947\) 18.2427 + 10.5324i 0.592807 + 0.342257i 0.766207 0.642594i \(-0.222142\pi\)
−0.173399 + 0.984852i \(0.555475\pi\)
\(948\) 0 0
\(949\) 32.2164 + 55.8005i 1.04579 + 1.81136i
\(950\) 0 0
\(951\) 3.71495 + 4.75705i 0.120465 + 0.154258i
\(952\) 0 0
\(953\) 4.50028i 0.145778i 0.997340 + 0.0728892i \(0.0232219\pi\)
−0.997340 + 0.0728892i \(0.976778\pi\)
\(954\) 0 0
\(955\) −39.6989 22.9201i −1.28462 0.741679i
\(956\) 0 0
\(957\) −0.313468 2.23396i −0.0101330 0.0722137i
\(958\) 0 0
\(959\) −10.3110 + 21.4644i −0.332961 + 0.693122i
\(960\) 0 0
\(961\) −14.2148 + 24.6207i −0.458541 + 0.794216i
\(962\) 0 0
\(963\) 41.2101 + 10.2939i 1.32798 + 0.331715i
\(964\) 0 0
\(965\) 32.0090 + 55.4411i 1.03040 + 1.78471i
\(966\) 0 0
\(967\) −10.8811 + 18.8466i −0.349912 + 0.606065i −0.986233 0.165359i \(-0.947122\pi\)
0.636322 + 0.771424i \(0.280455\pi\)
\(968\) 0 0
\(969\) 5.32689 13.1763i 0.171124 0.423283i
\(970\) 0 0
\(971\) −23.5222 40.7416i −0.754862 1.30746i −0.945443 0.325788i \(-0.894371\pi\)
0.190581 0.981671i \(-0.438963\pi\)
\(972\) 0 0
\(973\) −2.66961 3.90744i −0.0855838 0.125267i
\(974\) 0 0
\(975\) −16.6492 21.3196i −0.533202 0.682773i
\(976\) 0 0
\(977\) −21.7766 + 12.5727i −0.696695 + 0.402237i −0.806115 0.591758i \(-0.798434\pi\)
0.109420 + 0.993996i \(0.465101\pi\)
\(978\) 0 0
\(979\) 37.7423 21.7905i 1.20625 0.696429i
\(980\) 0 0
\(981\) −16.2783 + 4.66006i −0.519725 + 0.148784i
\(982\) 0 0
\(983\) −36.2142 −1.15505 −0.577527 0.816372i \(-0.695982\pi\)
−0.577527 + 0.816372i \(0.695982\pi\)
\(984\) 0 0
\(985\) 29.3515i 0.935216i
\(986\) 0 0
\(987\) 49.2356 10.7611i 1.56719 0.342530i
\(988\) 0 0
\(989\) −44.4801 + 25.6806i −1.41438 + 0.816595i
\(990\) 0 0
\(991\) −9.32769 + 16.1560i −0.296304 + 0.513213i −0.975287 0.220940i \(-0.929087\pi\)
0.678984 + 0.734153i \(0.262421\pi\)
\(992\) 0 0
\(993\) −6.24829 + 4.87951i −0.198284 + 0.154847i
\(994\) 0 0
\(995\) 27.1632 + 15.6827i 0.861131 + 0.497174i
\(996\) 0 0
\(997\) 17.4836i 0.553712i −0.960911 0.276856i \(-0.910708\pi\)
0.960911 0.276856i \(-0.0892925\pi\)
\(998\) 0 0
\(999\) −10.3742 + 14.2592i −0.328224 + 0.451143i
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 252.2.bm.a.185.1 yes 16
3.2 odd 2 756.2.bm.a.17.7 16
4.3 odd 2 1008.2.df.d.689.8 16
7.2 even 3 1764.2.w.b.509.6 16
7.3 odd 6 1764.2.x.a.293.4 16
7.4 even 3 1764.2.x.b.293.5 16
7.5 odd 6 252.2.w.a.5.3 16
7.6 odd 2 1764.2.bm.a.1697.8 16
9.2 odd 6 252.2.w.a.101.3 yes 16
9.4 even 3 2268.2.t.a.1781.7 16
9.5 odd 6 2268.2.t.b.1781.2 16
9.7 even 3 756.2.w.a.521.7 16
12.11 even 2 3024.2.df.d.17.7 16
21.2 odd 6 5292.2.w.b.1097.2 16
21.5 even 6 756.2.w.a.341.7 16
21.11 odd 6 5292.2.x.b.881.2 16
21.17 even 6 5292.2.x.a.881.7 16
21.20 even 2 5292.2.bm.a.2285.2 16
28.19 even 6 1008.2.ca.d.257.6 16
36.7 odd 6 3024.2.ca.d.2033.7 16
36.11 even 6 1008.2.ca.d.353.6 16
63.2 odd 6 1764.2.bm.a.1685.8 16
63.5 even 6 2268.2.t.a.2105.7 16
63.11 odd 6 1764.2.x.a.1469.4 16
63.16 even 3 5292.2.bm.a.4625.2 16
63.20 even 6 1764.2.w.b.1109.6 16
63.25 even 3 5292.2.x.a.4409.7 16
63.34 odd 6 5292.2.w.b.521.2 16
63.38 even 6 1764.2.x.b.1469.5 16
63.40 odd 6 2268.2.t.b.2105.2 16
63.47 even 6 inner 252.2.bm.a.173.1 yes 16
63.52 odd 6 5292.2.x.b.4409.2 16
63.61 odd 6 756.2.bm.a.89.7 16
84.47 odd 6 3024.2.ca.d.2609.7 16
252.47 odd 6 1008.2.df.d.929.8 16
252.187 even 6 3024.2.df.d.1601.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.w.a.5.3 16 7.5 odd 6
252.2.w.a.101.3 yes 16 9.2 odd 6
252.2.bm.a.173.1 yes 16 63.47 even 6 inner
252.2.bm.a.185.1 yes 16 1.1 even 1 trivial
756.2.w.a.341.7 16 21.5 even 6
756.2.w.a.521.7 16 9.7 even 3
756.2.bm.a.17.7 16 3.2 odd 2
756.2.bm.a.89.7 16 63.61 odd 6
1008.2.ca.d.257.6 16 28.19 even 6
1008.2.ca.d.353.6 16 36.11 even 6
1008.2.df.d.689.8 16 4.3 odd 2
1008.2.df.d.929.8 16 252.47 odd 6
1764.2.w.b.509.6 16 7.2 even 3
1764.2.w.b.1109.6 16 63.20 even 6
1764.2.x.a.293.4 16 7.3 odd 6
1764.2.x.a.1469.4 16 63.11 odd 6
1764.2.x.b.293.5 16 7.4 even 3
1764.2.x.b.1469.5 16 63.38 even 6
1764.2.bm.a.1685.8 16 63.2 odd 6
1764.2.bm.a.1697.8 16 7.6 odd 2
2268.2.t.a.1781.7 16 9.4 even 3
2268.2.t.a.2105.7 16 63.5 even 6
2268.2.t.b.1781.2 16 9.5 odd 6
2268.2.t.b.2105.2 16 63.40 odd 6
3024.2.ca.d.2033.7 16 36.7 odd 6
3024.2.ca.d.2609.7 16 84.47 odd 6
3024.2.df.d.17.7 16 12.11 even 2
3024.2.df.d.1601.7 16 252.187 even 6
5292.2.w.b.521.2 16 63.34 odd 6
5292.2.w.b.1097.2 16 21.2 odd 6
5292.2.x.a.881.7 16 21.17 even 6
5292.2.x.a.4409.7 16 63.25 even 3
5292.2.x.b.881.2 16 21.11 odd 6
5292.2.x.b.4409.2 16 63.52 odd 6
5292.2.bm.a.2285.2 16 21.20 even 2
5292.2.bm.a.4625.2 16 63.16 even 3