Properties

Label 1323.2.o.e.881.11
Level $1323$
Weight $2$
Character 1323.881
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(440,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.440");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.11
Character \(\chi\) \(=\) 1323.881
Dual form 1323.2.o.e.440.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.105953 + 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} +(-0.264715 + 0.458500i) q^{5} -0.487547i q^{8} +O(q^{10})\) \(q+(-0.105953 + 0.0611722i) q^{2} +(-0.992516 + 1.71909i) q^{4} +(-0.264715 + 0.458500i) q^{5} -0.487547i q^{8} -0.0647728i q^{10} +(3.64120 - 2.10225i) q^{11} +(1.74714 + 1.00871i) q^{13} +(-1.95521 - 3.38652i) q^{16} +4.38762 q^{17} +5.24685i q^{19} +(-0.525467 - 0.910136i) q^{20} +(-0.257198 + 0.445480i) q^{22} +(-5.43444 - 3.13757i) q^{23} +(2.35985 + 4.08738i) q^{25} -0.246821 q^{26} +(7.27689 - 4.20131i) q^{29} +(-1.03204 - 0.595849i) q^{31} +(1.25878 + 0.726755i) q^{32} +(-0.464883 + 0.268400i) q^{34} -3.23252 q^{37} +(-0.320962 - 0.555922i) q^{38} +(0.223540 + 0.129061i) q^{40} +(-0.0994958 + 0.172332i) q^{41} +(3.96309 + 6.86427i) q^{43} +8.34605i q^{44} +0.767730 q^{46} +(4.98595 + 8.63591i) q^{47} +(-0.500069 - 0.288715i) q^{50} +(-3.46814 + 2.00233i) q^{52} -4.21753i q^{53} +2.22598i q^{55} +(-0.514008 + 0.890287i) q^{58} +(-6.71960 + 11.6387i) q^{59} +(-11.3564 + 6.55662i) q^{61} +0.145798 q^{62} +7.64300 q^{64} +(-0.924990 + 0.534043i) q^{65} +(3.29001 - 5.69847i) q^{67} +(-4.35478 + 7.54270i) q^{68} +8.50587i q^{71} +5.61202i q^{73} +(0.342497 - 0.197741i) q^{74} +(-9.01980 - 5.20758i) q^{76} +(-0.286342 - 0.495959i) q^{79} +2.07029 q^{80} -0.0243455i q^{82} +(5.42692 + 9.39971i) q^{83} +(-1.16147 + 2.01172i) q^{85} +(-0.839806 - 0.484862i) q^{86} +(-1.02494 - 1.77525i) q^{88} +12.8738 q^{89} +(10.7875 - 6.22819i) q^{92} +(-1.05656 - 0.610003i) q^{94} +(-2.40568 - 1.38892i) q^{95} +(-0.493773 + 0.285080i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.105953 + 0.0611722i −0.0749204 + 0.0432553i −0.536992 0.843587i \(-0.680440\pi\)
0.462072 + 0.886842i \(0.347106\pi\)
\(3\) 0 0
\(4\) −0.992516 + 1.71909i −0.496258 + 0.859544i
\(5\) −0.264715 + 0.458500i −0.118384 + 0.205047i −0.919127 0.393960i \(-0.871105\pi\)
0.800743 + 0.599008i \(0.204438\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.487547i 0.172374i
\(9\) 0 0
\(10\) 0.0647728i 0.0204830i
\(11\) 3.64120 2.10225i 1.09786 0.633851i 0.162204 0.986757i \(-0.448140\pi\)
0.935659 + 0.352906i \(0.114807\pi\)
\(12\) 0 0
\(13\) 1.74714 + 1.00871i 0.484570 + 0.279767i 0.722319 0.691560i \(-0.243076\pi\)
−0.237749 + 0.971327i \(0.576410\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.95521 3.38652i −0.488802 0.846630i
\(17\) 4.38762 1.06415 0.532077 0.846696i \(-0.321412\pi\)
0.532077 + 0.846696i \(0.321412\pi\)
\(18\) 0 0
\(19\) 5.24685i 1.20371i 0.798605 + 0.601855i \(0.205572\pi\)
−0.798605 + 0.601855i \(0.794428\pi\)
\(20\) −0.525467 0.910136i −0.117498 0.203513i
\(21\) 0 0
\(22\) −0.257198 + 0.445480i −0.0548348 + 0.0949767i
\(23\) −5.43444 3.13757i −1.13316 0.654230i −0.188431 0.982086i \(-0.560340\pi\)
−0.944727 + 0.327857i \(0.893674\pi\)
\(24\) 0 0
\(25\) 2.35985 + 4.08738i 0.471970 + 0.817477i
\(26\) −0.246821 −0.0484056
\(27\) 0 0
\(28\) 0 0
\(29\) 7.27689 4.20131i 1.35128 0.780164i 0.362855 0.931846i \(-0.381802\pi\)
0.988429 + 0.151681i \(0.0484687\pi\)
\(30\) 0 0
\(31\) −1.03204 0.595849i −0.185360 0.107018i 0.404449 0.914561i \(-0.367463\pi\)
−0.589809 + 0.807543i \(0.700797\pi\)
\(32\) 1.25878 + 0.726755i 0.222522 + 0.128473i
\(33\) 0 0
\(34\) −0.464883 + 0.268400i −0.0797268 + 0.0460303i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.23252 −0.531424 −0.265712 0.964053i \(-0.585607\pi\)
−0.265712 + 0.964053i \(0.585607\pi\)
\(38\) −0.320962 0.555922i −0.0520668 0.0901824i
\(39\) 0 0
\(40\) 0.223540 + 0.129061i 0.0353448 + 0.0204063i
\(41\) −0.0994958 + 0.172332i −0.0155386 + 0.0269137i −0.873690 0.486483i \(-0.838280\pi\)
0.858152 + 0.513396i \(0.171613\pi\)
\(42\) 0 0
\(43\) 3.96309 + 6.86427i 0.604366 + 1.04679i 0.992151 + 0.125042i \(0.0399067\pi\)
−0.387786 + 0.921750i \(0.626760\pi\)
\(44\) 8.34605i 1.25821i
\(45\) 0 0
\(46\) 0.767730 0.113196
\(47\) 4.98595 + 8.63591i 0.727275 + 1.25968i 0.958031 + 0.286665i \(0.0925468\pi\)
−0.230756 + 0.973012i \(0.574120\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.500069 0.288715i −0.0707204 0.0408304i
\(51\) 0 0
\(52\) −3.46814 + 2.00233i −0.480944 + 0.277673i
\(53\) 4.21753i 0.579323i −0.957129 0.289661i \(-0.906457\pi\)
0.957129 0.289661i \(-0.0935427\pi\)
\(54\) 0 0
\(55\) 2.22598i 0.300152i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.514008 + 0.890287i −0.0674925 + 0.116900i
\(59\) −6.71960 + 11.6387i −0.874817 + 1.51523i −0.0178590 + 0.999841i \(0.505685\pi\)
−0.856958 + 0.515387i \(0.827648\pi\)
\(60\) 0 0
\(61\) −11.3564 + 6.55662i −1.45404 + 0.839489i −0.998707 0.0508335i \(-0.983812\pi\)
−0.455330 + 0.890323i \(0.650479\pi\)
\(62\) 0.145798 0.0185163
\(63\) 0 0
\(64\) 7.64300 0.955375
\(65\) −0.924990 + 0.534043i −0.114731 + 0.0662399i
\(66\) 0 0
\(67\) 3.29001 5.69847i 0.401939 0.696179i −0.592021 0.805923i \(-0.701670\pi\)
0.993960 + 0.109744i \(0.0350030\pi\)
\(68\) −4.35478 + 7.54270i −0.528095 + 0.914687i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.50587i 1.00946i 0.863277 + 0.504730i \(0.168408\pi\)
−0.863277 + 0.504730i \(0.831592\pi\)
\(72\) 0 0
\(73\) 5.61202i 0.656837i 0.944532 + 0.328419i \(0.106516\pi\)
−0.944532 + 0.328419i \(0.893484\pi\)
\(74\) 0.342497 0.197741i 0.0398145 0.0229869i
\(75\) 0 0
\(76\) −9.01980 5.20758i −1.03464 0.597351i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.286342 0.495959i −0.0322160 0.0557997i 0.849468 0.527640i \(-0.176923\pi\)
−0.881684 + 0.471841i \(0.843590\pi\)
\(80\) 2.07029 0.231465
\(81\) 0 0
\(82\) 0.0243455i 0.00268851i
\(83\) 5.42692 + 9.39971i 0.595682 + 1.03175i 0.993450 + 0.114266i \(0.0364516\pi\)
−0.397768 + 0.917486i \(0.630215\pi\)
\(84\) 0 0
\(85\) −1.16147 + 2.01172i −0.125979 + 0.218202i
\(86\) −0.839806 0.484862i −0.0905586 0.0522840i
\(87\) 0 0
\(88\) −1.02494 1.77525i −0.109259 0.189243i
\(89\) 12.8738 1.36461 0.682307 0.731065i \(-0.260977\pi\)
0.682307 + 0.731065i \(0.260977\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.7875 6.22819i 1.12468 0.649333i
\(93\) 0 0
\(94\) −1.05656 0.610003i −0.108975 0.0629170i
\(95\) −2.40568 1.38892i −0.246817 0.142500i
\(96\) 0 0
\(97\) −0.493773 + 0.285080i −0.0501351 + 0.0289455i −0.524858 0.851190i \(-0.675882\pi\)
0.474723 + 0.880135i \(0.342548\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −9.36876 −0.936876
\(101\) −5.81552 10.0728i −0.578666 1.00228i −0.995633 0.0933576i \(-0.970240\pi\)
0.416966 0.908922i \(-0.363093\pi\)
\(102\) 0 0
\(103\) −5.54001 3.19853i −0.545874 0.315160i 0.201582 0.979472i \(-0.435392\pi\)
−0.747456 + 0.664311i \(0.768725\pi\)
\(104\) 0.491795 0.851814i 0.0482245 0.0835272i
\(105\) 0 0
\(106\) 0.257996 + 0.446862i 0.0250588 + 0.0434031i
\(107\) 0.253263i 0.0244839i 0.999925 + 0.0122419i \(0.00389683\pi\)
−0.999925 + 0.0122419i \(0.996103\pi\)
\(108\) 0 0
\(109\) 11.9720 1.14671 0.573357 0.819306i \(-0.305641\pi\)
0.573357 + 0.819306i \(0.305641\pi\)
\(110\) −0.136168 0.235851i −0.0129831 0.0224875i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.28636 2.47473i −0.403227 0.232803i 0.284648 0.958632i \(-0.408123\pi\)
−0.687875 + 0.725829i \(0.741456\pi\)
\(114\) 0 0
\(115\) 2.87715 1.66113i 0.268296 0.154901i
\(116\) 16.6795i 1.54865i
\(117\) 0 0
\(118\) 1.64421i 0.151362i
\(119\) 0 0
\(120\) 0 0
\(121\) 3.33888 5.78311i 0.303535 0.525737i
\(122\) 0.802166 1.38939i 0.0726247 0.125790i
\(123\) 0 0
\(124\) 2.04863 1.18278i 0.183973 0.106217i
\(125\) −5.14590 −0.460263
\(126\) 0 0
\(127\) −3.68446 −0.326943 −0.163472 0.986548i \(-0.552269\pi\)
−0.163472 + 0.986548i \(0.552269\pi\)
\(128\) −3.32736 + 1.92105i −0.294100 + 0.169798i
\(129\) 0 0
\(130\) 0.0653372 0.113167i 0.00573045 0.00992543i
\(131\) −2.72837 + 4.72567i −0.238379 + 0.412884i −0.960249 0.279144i \(-0.909949\pi\)
0.721871 + 0.692028i \(0.243283\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.805030i 0.0695440i
\(135\) 0 0
\(136\) 2.13917i 0.183432i
\(137\) 1.39996 0.808270i 0.119607 0.0690551i −0.439003 0.898486i \(-0.644668\pi\)
0.558610 + 0.829431i \(0.311335\pi\)
\(138\) 0 0
\(139\) 9.79085 + 5.65275i 0.830449 + 0.479460i 0.854006 0.520262i \(-0.174166\pi\)
−0.0235572 + 0.999722i \(0.507499\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.520323 0.901226i −0.0436645 0.0756292i
\(143\) 8.48226 0.709322
\(144\) 0 0
\(145\) 4.44860i 0.369436i
\(146\) −0.343300 0.594613i −0.0284117 0.0492105i
\(147\) 0 0
\(148\) 3.20833 5.55699i 0.263723 0.456782i
\(149\) −4.61426 2.66404i −0.378015 0.218247i 0.298939 0.954272i \(-0.403367\pi\)
−0.676954 + 0.736025i \(0.736700\pi\)
\(150\) 0 0
\(151\) 1.32132 + 2.28859i 0.107527 + 0.186243i 0.914768 0.403980i \(-0.132373\pi\)
−0.807241 + 0.590222i \(0.799040\pi\)
\(152\) 2.55808 0.207488
\(153\) 0 0
\(154\) 0 0
\(155\) 0.546393 0.315460i 0.0438873 0.0253384i
\(156\) 0 0
\(157\) 11.3181 + 6.53448i 0.903279 + 0.521508i 0.878263 0.478179i \(-0.158703\pi\)
0.0250163 + 0.999687i \(0.492036\pi\)
\(158\) 0.0606778 + 0.0350324i 0.00482727 + 0.00278703i
\(159\) 0 0
\(160\) −0.666434 + 0.384766i −0.0526862 + 0.0304184i
\(161\) 0 0
\(162\) 0 0
\(163\) 17.0269 1.33365 0.666825 0.745214i \(-0.267653\pi\)
0.666825 + 0.745214i \(0.267653\pi\)
\(164\) −0.197502 0.342084i −0.0154223 0.0267123i
\(165\) 0 0
\(166\) −1.15000 0.663954i −0.0892575 0.0515328i
\(167\) 10.6605 18.4645i 0.824932 1.42882i −0.0770396 0.997028i \(-0.524547\pi\)
0.901971 0.431796i \(-0.142120\pi\)
\(168\) 0 0
\(169\) −4.46499 7.73360i −0.343461 0.594892i
\(170\) 0.284198i 0.0217970i
\(171\) 0 0
\(172\) −15.7337 −1.19968
\(173\) −10.2433 17.7418i −0.778781 1.34889i −0.932645 0.360796i \(-0.882505\pi\)
0.153864 0.988092i \(-0.450828\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −14.2386 8.22066i −1.07327 0.619655i
\(177\) 0 0
\(178\) −1.36402 + 0.787516i −0.102237 + 0.0590268i
\(179\) 14.4071i 1.07684i −0.842676 0.538420i \(-0.819021\pi\)
0.842676 0.538420i \(-0.180979\pi\)
\(180\) 0 0
\(181\) 6.97309i 0.518306i 0.965836 + 0.259153i \(0.0834434\pi\)
−0.965836 + 0.259153i \(0.916557\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.52971 + 2.64954i −0.112772 + 0.195327i
\(185\) 0.855697 1.48211i 0.0629121 0.108967i
\(186\) 0 0
\(187\) 15.9762 9.22386i 1.16829 0.674515i
\(188\) −19.7945 −1.44366
\(189\) 0 0
\(190\) 0.339853 0.0246555
\(191\) 9.38310 5.41734i 0.678937 0.391985i −0.120517 0.992711i \(-0.538455\pi\)
0.799455 + 0.600727i \(0.205122\pi\)
\(192\) 0 0
\(193\) −5.26223 + 9.11444i −0.378783 + 0.656072i −0.990886 0.134707i \(-0.956991\pi\)
0.612102 + 0.790779i \(0.290324\pi\)
\(194\) 0.0348780 0.0604104i 0.00250409 0.00433722i
\(195\) 0 0
\(196\) 0 0
\(197\) 15.5156i 1.10544i 0.833366 + 0.552721i \(0.186410\pi\)
−0.833366 + 0.552721i \(0.813590\pi\)
\(198\) 0 0
\(199\) 12.5479i 0.889495i −0.895656 0.444748i \(-0.853293\pi\)
0.895656 0.444748i \(-0.146707\pi\)
\(200\) 1.99279 1.15054i 0.140912 0.0813553i
\(201\) 0 0
\(202\) 1.23235 + 0.711497i 0.0867078 + 0.0500608i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0526760 0.0912375i −0.00367905 0.00637231i
\(206\) 0.782644 0.0545294
\(207\) 0 0
\(208\) 7.88898i 0.547002i
\(209\) 11.0302 + 19.1048i 0.762973 + 1.32151i
\(210\) 0 0
\(211\) −1.19765 + 2.07438i −0.0824494 + 0.142807i −0.904302 0.426894i \(-0.859608\pi\)
0.821852 + 0.569701i \(0.192941\pi\)
\(212\) 7.25031 + 4.18597i 0.497953 + 0.287493i
\(213\) 0 0
\(214\) −0.0154927 0.0268341i −0.00105906 0.00183434i
\(215\) −4.19636 −0.286189
\(216\) 0 0
\(217\) 0 0
\(218\) −1.26848 + 0.732357i −0.0859123 + 0.0496015i
\(219\) 0 0
\(220\) −3.82666 2.20932i −0.257993 0.148953i
\(221\) 7.66580 + 4.42585i 0.515657 + 0.297715i
\(222\) 0 0
\(223\) 2.42193 1.39830i 0.162184 0.0936370i −0.416711 0.909039i \(-0.636817\pi\)
0.578895 + 0.815402i \(0.303484\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.605540 0.0402799
\(227\) −1.42300 2.46471i −0.0944480 0.163589i 0.814930 0.579559i \(-0.196775\pi\)
−0.909378 + 0.415970i \(0.863442\pi\)
\(228\) 0 0
\(229\) 20.5460 + 11.8623i 1.35772 + 0.783880i 0.989316 0.145786i \(-0.0465711\pi\)
0.368404 + 0.929666i \(0.379904\pi\)
\(230\) −0.203229 + 0.352004i −0.0134006 + 0.0232104i
\(231\) 0 0
\(232\) −2.04834 3.54782i −0.134480 0.232926i
\(233\) 18.7298i 1.22703i −0.789684 0.613514i \(-0.789755\pi\)
0.789684 0.613514i \(-0.210245\pi\)
\(234\) 0 0
\(235\) −5.27942 −0.344391
\(236\) −13.3386 23.1032i −0.868270 1.50389i
\(237\) 0 0
\(238\) 0 0
\(239\) −11.1421 6.43288i −0.720721 0.416109i 0.0942969 0.995544i \(-0.469940\pi\)
−0.815018 + 0.579436i \(0.803273\pi\)
\(240\) 0 0
\(241\) −3.64082 + 2.10203i −0.234526 + 0.135403i −0.612658 0.790348i \(-0.709900\pi\)
0.378132 + 0.925752i \(0.376566\pi\)
\(242\) 0.816987i 0.0525179i
\(243\) 0 0
\(244\) 26.0302i 1.66641i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.29257 + 9.16700i −0.336758 + 0.583282i
\(248\) −0.290504 + 0.503168i −0.0184470 + 0.0319512i
\(249\) 0 0
\(250\) 0.545226 0.314786i 0.0344831 0.0199088i
\(251\) −7.50592 −0.473770 −0.236885 0.971538i \(-0.576126\pi\)
−0.236885 + 0.971538i \(0.576126\pi\)
\(252\) 0 0
\(253\) −26.3838 −1.65874
\(254\) 0.390381 0.225387i 0.0244947 0.0141420i
\(255\) 0 0
\(256\) −7.40797 + 12.8310i −0.462998 + 0.801936i
\(257\) 2.51960 4.36408i 0.157169 0.272224i −0.776678 0.629898i \(-0.783097\pi\)
0.933847 + 0.357674i \(0.116430\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.12018i 0.131488i
\(261\) 0 0
\(262\) 0.667601i 0.0412445i
\(263\) −12.2494 + 7.07220i −0.755331 + 0.436091i −0.827617 0.561293i \(-0.810304\pi\)
0.0722856 + 0.997384i \(0.476971\pi\)
\(264\) 0 0
\(265\) 1.93374 + 1.11644i 0.118789 + 0.0685826i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.53078 + 11.3116i 0.398931 + 0.690969i
\(269\) 15.7771 0.961948 0.480974 0.876735i \(-0.340283\pi\)
0.480974 + 0.876735i \(0.340283\pi\)
\(270\) 0 0
\(271\) 16.8078i 1.02100i −0.859877 0.510501i \(-0.829460\pi\)
0.859877 0.510501i \(-0.170540\pi\)
\(272\) −8.57871 14.8588i −0.520160 0.900944i
\(273\) 0 0
\(274\) −0.0988873 + 0.171278i −0.00597400 + 0.0103473i
\(275\) 17.1854 + 9.92198i 1.03632 + 0.598318i
\(276\) 0 0
\(277\) −8.91066 15.4337i −0.535390 0.927322i −0.999144 0.0413586i \(-0.986831\pi\)
0.463755 0.885964i \(-0.346502\pi\)
\(278\) −1.38317 −0.0829568
\(279\) 0 0
\(280\) 0 0
\(281\) −7.59774 + 4.38656i −0.453243 + 0.261680i −0.709199 0.705008i \(-0.750943\pi\)
0.255956 + 0.966688i \(0.417610\pi\)
\(282\) 0 0
\(283\) −18.7047 10.7991i −1.11188 0.641942i −0.172562 0.984999i \(-0.555204\pi\)
−0.939315 + 0.343056i \(0.888538\pi\)
\(284\) −14.6223 8.44221i −0.867676 0.500953i
\(285\) 0 0
\(286\) −0.898724 + 0.518879i −0.0531427 + 0.0306819i
\(287\) 0 0
\(288\) 0 0
\(289\) 2.25120 0.132424
\(290\) −0.272131 0.471344i −0.0159801 0.0276783i
\(291\) 0 0
\(292\) −9.64756 5.57002i −0.564581 0.325961i
\(293\) 9.79756 16.9699i 0.572379 0.991390i −0.423942 0.905690i \(-0.639354\pi\)
0.996321 0.0857006i \(-0.0273128\pi\)
\(294\) 0 0
\(295\) −3.55755 6.16186i −0.207129 0.358758i
\(296\) 1.57601i 0.0916035i
\(297\) 0 0
\(298\) 0.651862 0.0377613
\(299\) −6.32983 10.9636i −0.366063 0.634040i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.279996 0.161656i −0.0161120 0.00930224i
\(303\) 0 0
\(304\) 17.7686 10.2587i 1.01910 0.588376i
\(305\) 6.94254i 0.397529i
\(306\) 0 0
\(307\) 27.7677i 1.58478i 0.610012 + 0.792392i \(0.291165\pi\)
−0.610012 + 0.792392i \(0.708835\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.0385948 + 0.0668482i −0.00219204 + 0.00379672i
\(311\) −10.0080 + 17.3344i −0.567501 + 0.982941i 0.429311 + 0.903157i \(0.358756\pi\)
−0.996812 + 0.0797841i \(0.974577\pi\)
\(312\) 0 0
\(313\) 15.9654 9.21765i 0.902420 0.521012i 0.0244352 0.999701i \(-0.492221\pi\)
0.877984 + 0.478689i \(0.158888\pi\)
\(314\) −1.59891 −0.0902320
\(315\) 0 0
\(316\) 1.13680 0.0639498
\(317\) 12.5992 7.27416i 0.707642 0.408558i −0.102545 0.994728i \(-0.532699\pi\)
0.810187 + 0.586171i \(0.199365\pi\)
\(318\) 0 0
\(319\) 17.6644 30.5956i 0.989016 1.71303i
\(320\) −2.02322 + 3.50431i −0.113101 + 0.195897i
\(321\) 0 0
\(322\) 0 0
\(323\) 23.0212i 1.28093i
\(324\) 0 0
\(325\) 9.52166i 0.528167i
\(326\) −1.80406 + 1.04157i −0.0999176 + 0.0576874i
\(327\) 0 0
\(328\) 0.0840197 + 0.0485088i 0.00463921 + 0.00267845i
\(329\) 0 0
\(330\) 0 0
\(331\) 14.8446 + 25.7115i 0.815930 + 1.41323i 0.908658 + 0.417541i \(0.137108\pi\)
−0.0927274 + 0.995692i \(0.529559\pi\)
\(332\) −21.5452 −1.18245
\(333\) 0 0
\(334\) 2.60850i 0.142731i
\(335\) 1.74183 + 3.01694i 0.0951664 + 0.164833i
\(336\) 0 0
\(337\) −4.60606 + 7.97793i −0.250908 + 0.434586i −0.963776 0.266713i \(-0.914063\pi\)
0.712868 + 0.701298i \(0.247396\pi\)
\(338\) 0.946163 + 0.546267i 0.0514645 + 0.0297130i
\(339\) 0 0
\(340\) −2.30555 3.99333i −0.125036 0.216569i
\(341\) −5.01049 −0.271333
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34665 1.93219i 0.180439 0.104177i
\(345\) 0 0
\(346\) 2.17062 + 1.25321i 0.116693 + 0.0673728i
\(347\) −15.7313 9.08247i −0.844501 0.487573i 0.0142910 0.999898i \(-0.495451\pi\)
−0.858791 + 0.512325i \(0.828784\pi\)
\(348\) 0 0
\(349\) 5.70494 3.29375i 0.305378 0.176310i −0.339478 0.940614i \(-0.610250\pi\)
0.644856 + 0.764304i \(0.276917\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.11128 0.325732
\(353\) −10.4692 18.1332i −0.557221 0.965135i −0.997727 0.0673857i \(-0.978534\pi\)
0.440506 0.897750i \(-0.354799\pi\)
\(354\) 0 0
\(355\) −3.89994 2.25163i −0.206987 0.119504i
\(356\) −12.7774 + 22.1311i −0.677201 + 1.17295i
\(357\) 0 0
\(358\) 0.881317 + 1.52649i 0.0465791 + 0.0806773i
\(359\) 14.2265i 0.750845i 0.926854 + 0.375422i \(0.122502\pi\)
−0.926854 + 0.375422i \(0.877498\pi\)
\(360\) 0 0
\(361\) −8.52944 −0.448918
\(362\) −0.426560 0.738823i −0.0224195 0.0388317i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.57311 1.48559i −0.134683 0.0777591i
\(366\) 0 0
\(367\) −10.7237 + 6.19136i −0.559775 + 0.323186i −0.753055 0.657957i \(-0.771421\pi\)
0.193280 + 0.981144i \(0.438087\pi\)
\(368\) 24.5384i 1.27915i
\(369\) 0 0
\(370\) 0.209380i 0.0108851i
\(371\) 0 0
\(372\) 0 0
\(373\) 10.6559 18.4565i 0.551740 0.955642i −0.446409 0.894829i \(-0.647297\pi\)
0.998149 0.0608130i \(-0.0193693\pi\)
\(374\) −1.12849 + 1.95460i −0.0583527 + 0.101070i
\(375\) 0 0
\(376\) 4.21041 2.43088i 0.217135 0.125363i
\(377\) 16.9517 0.873057
\(378\) 0 0
\(379\) 10.6001 0.544489 0.272244 0.962228i \(-0.412234\pi\)
0.272244 + 0.962228i \(0.412234\pi\)
\(380\) 4.77535 2.75705i 0.244970 0.141434i
\(381\) 0 0
\(382\) −0.662781 + 1.14797i −0.0339108 + 0.0587353i
\(383\) 6.32174 10.9496i 0.323026 0.559497i −0.658085 0.752944i \(-0.728633\pi\)
0.981111 + 0.193446i \(0.0619666\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.28761i 0.0655375i
\(387\) 0 0
\(388\) 1.13179i 0.0574578i
\(389\) −11.4538 + 6.61286i −0.580732 + 0.335286i −0.761424 0.648254i \(-0.775499\pi\)
0.180692 + 0.983540i \(0.442166\pi\)
\(390\) 0 0
\(391\) −23.8442 13.7665i −1.20586 0.696201i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.949125 1.64393i −0.0478162 0.0828201i
\(395\) 0.303196 0.0152554
\(396\) 0 0
\(397\) 24.7882i 1.24409i −0.782983 0.622043i \(-0.786303\pi\)
0.782983 0.622043i \(-0.213697\pi\)
\(398\) 0.767582 + 1.32949i 0.0384754 + 0.0666413i
\(399\) 0 0
\(400\) 9.22800 15.9834i 0.461400 0.799168i
\(401\) −3.19615 1.84530i −0.159608 0.0921499i 0.418068 0.908416i \(-0.362707\pi\)
−0.577677 + 0.816266i \(0.696041\pi\)
\(402\) 0 0
\(403\) −1.20208 2.08207i −0.0598800 0.103715i
\(404\) 23.0880 1.14867
\(405\) 0 0
\(406\) 0 0
\(407\) −11.7703 + 6.79556i −0.583430 + 0.336843i
\(408\) 0 0
\(409\) 16.0535 + 9.26852i 0.793797 + 0.458299i 0.841297 0.540573i \(-0.181792\pi\)
−0.0475008 + 0.998871i \(0.515126\pi\)
\(410\) 0.0111624 + 0.00644462i 0.000551272 + 0.000318277i
\(411\) 0 0
\(412\) 10.9971 6.34918i 0.541788 0.312802i
\(413\) 0 0
\(414\) 0 0
\(415\) −5.74635 −0.282077
\(416\) 1.46618 + 2.53949i 0.0718852 + 0.124509i
\(417\) 0 0
\(418\) −2.33737 1.34948i −0.114324 0.0660053i
\(419\) 1.46994 2.54600i 0.0718111 0.124380i −0.827884 0.560899i \(-0.810455\pi\)
0.899695 + 0.436519i \(0.143789\pi\)
\(420\) 0 0
\(421\) −14.1081 24.4359i −0.687585 1.19093i −0.972617 0.232415i \(-0.925337\pi\)
0.285031 0.958518i \(-0.407996\pi\)
\(422\) 0.293051i 0.0142655i
\(423\) 0 0
\(424\) −2.05624 −0.0998600
\(425\) 10.3541 + 17.9339i 0.502249 + 0.869921i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.435382 0.251368i −0.0210450 0.0121503i
\(429\) 0 0
\(430\) 0.444618 0.256700i 0.0214414 0.0123792i
\(431\) 6.76465i 0.325842i 0.986639 + 0.162921i \(0.0520915\pi\)
−0.986639 + 0.162921i \(0.947908\pi\)
\(432\) 0 0
\(433\) 28.3475i 1.36229i −0.732146 0.681147i \(-0.761481\pi\)
0.732146 0.681147i \(-0.238519\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.8824 + 20.5810i −0.569066 + 0.985651i
\(437\) 16.4624 28.5137i 0.787503 1.36399i
\(438\) 0 0
\(439\) −22.8208 + 13.1756i −1.08918 + 0.628837i −0.933358 0.358948i \(-0.883136\pi\)
−0.155821 + 0.987785i \(0.549802\pi\)
\(440\) 1.08527 0.0517382
\(441\) 0 0
\(442\) −1.08296 −0.0515110
\(443\) 4.75958 2.74795i 0.226135 0.130559i −0.382653 0.923892i \(-0.624989\pi\)
0.608788 + 0.793333i \(0.291656\pi\)
\(444\) 0 0
\(445\) −3.40787 + 5.90261i −0.161549 + 0.279810i
\(446\) −0.171074 + 0.296309i −0.00810060 + 0.0140306i
\(447\) 0 0
\(448\) 0 0
\(449\) 7.38342i 0.348445i −0.984706 0.174223i \(-0.944259\pi\)
0.984706 0.174223i \(-0.0557412\pi\)
\(450\) 0 0
\(451\) 0.836659i 0.0393967i
\(452\) 8.50857 4.91242i 0.400209 0.231061i
\(453\) 0 0
\(454\) 0.301544 + 0.174097i 0.0141522 + 0.00817076i
\(455\) 0 0
\(456\) 0 0
\(457\) −20.7109 35.8724i −0.968817 1.67804i −0.698991 0.715130i \(-0.746367\pi\)
−0.269826 0.962909i \(-0.586966\pi\)
\(458\) −2.90256 −0.135628
\(459\) 0 0
\(460\) 6.59477i 0.307483i
\(461\) 5.44638 + 9.43341i 0.253663 + 0.439357i 0.964532 0.263968i \(-0.0850312\pi\)
−0.710868 + 0.703325i \(0.751698\pi\)
\(462\) 0 0
\(463\) −2.87980 + 4.98796i −0.133836 + 0.231810i −0.925152 0.379597i \(-0.876063\pi\)
0.791316 + 0.611407i \(0.209396\pi\)
\(464\) −28.4557 16.4289i −1.32102 0.762692i
\(465\) 0 0
\(466\) 1.14574 + 1.98448i 0.0530755 + 0.0919294i
\(467\) −23.8882 −1.10541 −0.552707 0.833376i \(-0.686405\pi\)
−0.552707 + 0.833376i \(0.686405\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.559372 0.322954i 0.0258019 0.0148967i
\(471\) 0 0
\(472\) 5.67440 + 3.27612i 0.261185 + 0.150795i
\(473\) 28.8608 + 16.6628i 1.32702 + 0.766156i
\(474\) 0 0
\(475\) −21.4459 + 12.3818i −0.984005 + 0.568116i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.57406 0.0719956
\(479\) 0.947645 + 1.64137i 0.0432990 + 0.0749961i 0.886863 0.462033i \(-0.152880\pi\)
−0.843564 + 0.537029i \(0.819547\pi\)
\(480\) 0 0
\(481\) −5.64768 3.26069i −0.257512 0.148675i
\(482\) 0.257171 0.445434i 0.0117138 0.0202890i
\(483\) 0 0
\(484\) 6.62778 + 11.4797i 0.301263 + 0.521803i
\(485\) 0.301860i 0.0137067i
\(486\) 0 0
\(487\) 28.2248 1.27899 0.639494 0.768796i \(-0.279144\pi\)
0.639494 + 0.768796i \(0.279144\pi\)
\(488\) 3.19666 + 5.53677i 0.144706 + 0.250638i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.30250 + 1.32935i 0.103910 + 0.0599927i 0.551055 0.834469i \(-0.314226\pi\)
−0.447144 + 0.894462i \(0.647559\pi\)
\(492\) 0 0
\(493\) 31.9282 18.4338i 1.43797 0.830215i
\(494\) 1.29503i 0.0582663i
\(495\) 0 0
\(496\) 4.66003i 0.209242i
\(497\) 0 0
\(498\) 0 0
\(499\) 6.27844 10.8746i 0.281062 0.486813i −0.690585 0.723251i \(-0.742647\pi\)
0.971646 + 0.236438i \(0.0759801\pi\)
\(500\) 5.10739 8.84625i 0.228409 0.395617i
\(501\) 0 0
\(502\) 0.795278 0.459154i 0.0354950 0.0204930i
\(503\) 18.1502 0.809278 0.404639 0.914476i \(-0.367397\pi\)
0.404639 + 0.914476i \(0.367397\pi\)
\(504\) 0 0
\(505\) 6.15782 0.274020
\(506\) 2.79546 1.61396i 0.124273 0.0717491i
\(507\) 0 0
\(508\) 3.65689 6.33391i 0.162248 0.281022i
\(509\) 9.33827 16.1744i 0.413912 0.716916i −0.581402 0.813617i \(-0.697496\pi\)
0.995314 + 0.0967005i \(0.0308289\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 9.49685i 0.419705i
\(513\) 0 0
\(514\) 0.616519i 0.0271935i
\(515\) 2.93305 1.69340i 0.129245 0.0746199i
\(516\) 0 0
\(517\) 36.3096 + 20.9634i 1.59690 + 0.921968i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.260371 + 0.450975i 0.0114180 + 0.0197766i
\(521\) 18.0665 0.791508 0.395754 0.918357i \(-0.370483\pi\)
0.395754 + 0.918357i \(0.370483\pi\)
\(522\) 0 0
\(523\) 21.1338i 0.924116i 0.886850 + 0.462058i \(0.152889\pi\)
−0.886850 + 0.462058i \(0.847111\pi\)
\(524\) −5.41590 9.38061i −0.236595 0.409794i
\(525\) 0 0
\(526\) 0.865245 1.49865i 0.0377265 0.0653442i
\(527\) −4.52820 2.61436i −0.197252 0.113883i
\(528\) 0 0
\(529\) 8.18875 + 14.1833i 0.356033 + 0.616666i
\(530\) −0.273181 −0.0118662
\(531\) 0 0
\(532\) 0 0
\(533\) −0.347667 + 0.200725i −0.0150591 + 0.00869439i
\(534\) 0 0
\(535\) −0.116121 0.0670425i −0.00502035 0.00289850i
\(536\) −2.77827 1.60403i −0.120003 0.0692837i
\(537\) 0 0
\(538\) −1.67164 + 0.965122i −0.0720695 + 0.0416093i
\(539\) 0 0
\(540\) 0 0
\(541\) 17.7732 0.764131 0.382065 0.924135i \(-0.375213\pi\)
0.382065 + 0.924135i \(0.375213\pi\)
\(542\) 1.02817 + 1.78084i 0.0441637 + 0.0764938i
\(543\) 0 0
\(544\) 5.52304 + 3.18873i 0.236798 + 0.136715i
\(545\) −3.16918 + 5.48918i −0.135753 + 0.235131i
\(546\) 0 0
\(547\) 14.1560 + 24.5190i 0.605268 + 1.04835i 0.992009 + 0.126166i \(0.0402673\pi\)
−0.386741 + 0.922188i \(0.626399\pi\)
\(548\) 3.20888i 0.137077i
\(549\) 0 0
\(550\) −2.42780 −0.103522
\(551\) 22.0437 + 38.1808i 0.939092 + 1.62655i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.88823 + 1.09017i 0.0802232 + 0.0463169i
\(555\) 0 0
\(556\) −19.4352 + 11.2209i −0.824234 + 0.475872i
\(557\) 11.7214i 0.496651i −0.968677 0.248326i \(-0.920120\pi\)
0.968677 0.248326i \(-0.0798803\pi\)
\(558\) 0 0
\(559\) 15.9905i 0.676326i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.536671 0.929541i 0.0226381 0.0392103i
\(563\) −18.3014 + 31.6990i −0.771314 + 1.33595i 0.165529 + 0.986205i \(0.447067\pi\)
−0.936843 + 0.349750i \(0.886267\pi\)
\(564\) 0 0
\(565\) 2.26933 1.31020i 0.0954713 0.0551204i
\(566\) 2.64243 0.111070
\(567\) 0 0
\(568\) 4.14701 0.174005
\(569\) −32.6468 + 18.8486i −1.36862 + 0.790176i −0.990752 0.135682i \(-0.956677\pi\)
−0.377872 + 0.925858i \(0.623344\pi\)
\(570\) 0 0
\(571\) −14.1123 + 24.4432i −0.590581 + 1.02292i 0.403574 + 0.914947i \(0.367768\pi\)
−0.994154 + 0.107968i \(0.965565\pi\)
\(572\) −8.41878 + 14.5817i −0.352007 + 0.609694i
\(573\) 0 0
\(574\) 0 0
\(575\) 29.6168i 1.23511i
\(576\) 0 0
\(577\) 9.38512i 0.390708i 0.980733 + 0.195354i \(0.0625855\pi\)
−0.980733 + 0.195354i \(0.937414\pi\)
\(578\) −0.238523 + 0.137711i −0.00992123 + 0.00572802i
\(579\) 0 0
\(580\) −7.64754 4.41531i −0.317547 0.183336i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.86629 15.3569i −0.367204 0.636017i
\(584\) 2.73612 0.113222
\(585\) 0 0
\(586\) 2.39735i 0.0990338i
\(587\) −23.1819 40.1523i −0.956821 1.65726i −0.730146 0.683291i \(-0.760548\pi\)
−0.226675 0.973971i \(-0.572785\pi\)
\(588\) 0 0
\(589\) 3.12633 5.41496i 0.128818 0.223120i
\(590\) 0.753870 + 0.435247i 0.0310363 + 0.0179188i
\(591\) 0 0
\(592\) 6.32025 + 10.9470i 0.259761 + 0.449919i
\(593\) −18.1416 −0.744986 −0.372493 0.928035i \(-0.621497\pi\)
−0.372493 + 0.928035i \(0.621497\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.15945 5.28821i 0.375186 0.216613i
\(597\) 0 0
\(598\) 1.34133 + 0.774419i 0.0548512 + 0.0316684i
\(599\) −6.02771 3.48010i −0.246286 0.142193i 0.371777 0.928322i \(-0.378749\pi\)
−0.618062 + 0.786129i \(0.712082\pi\)
\(600\) 0 0
\(601\) −2.08865 + 1.20588i −0.0851976 + 0.0491889i −0.541994 0.840383i \(-0.682330\pi\)
0.456796 + 0.889572i \(0.348997\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.24571 −0.213445
\(605\) 1.76770 + 3.06175i 0.0718673 + 0.124478i
\(606\) 0 0
\(607\) 11.0306 + 6.36850i 0.447717 + 0.258489i 0.706865 0.707348i \(-0.250109\pi\)
−0.259149 + 0.965837i \(0.583442\pi\)
\(608\) −3.81318 + 6.60462i −0.154645 + 0.267853i
\(609\) 0 0
\(610\) 0.424690 + 0.735585i 0.0171952 + 0.0297830i
\(611\) 20.1176i 0.813870i
\(612\) 0 0
\(613\) −10.3352 −0.417436 −0.208718 0.977976i \(-0.566929\pi\)
−0.208718 + 0.977976i \(0.566929\pi\)
\(614\) −1.69861 2.94208i −0.0685503 0.118733i
\(615\) 0 0
\(616\) 0 0
\(617\) 41.3741 + 23.8873i 1.66566 + 0.961668i 0.969937 + 0.243355i \(0.0782481\pi\)
0.695721 + 0.718313i \(0.255085\pi\)
\(618\) 0 0
\(619\) −35.2626 + 20.3588i −1.41732 + 0.818291i −0.996063 0.0886491i \(-0.971745\pi\)
−0.421259 + 0.906940i \(0.638412\pi\)
\(620\) 1.25240i 0.0502975i
\(621\) 0 0
\(622\) 2.44884i 0.0981897i
\(623\) 0 0
\(624\) 0 0
\(625\) −10.4371 + 18.0775i −0.417483 + 0.723101i
\(626\) −1.12773 + 1.95328i −0.0450731 + 0.0780689i
\(627\) 0 0
\(628\) −22.4667 + 12.9711i −0.896519 + 0.517605i
\(629\) −14.1831 −0.565517
\(630\) 0 0
\(631\) 11.4782 0.456942 0.228471 0.973551i \(-0.426627\pi\)
0.228471 + 0.973551i \(0.426627\pi\)
\(632\) −0.241803 + 0.139605i −0.00961841 + 0.00555319i
\(633\) 0 0
\(634\) −0.889953 + 1.54144i −0.0353446 + 0.0612186i
\(635\) 0.975332 1.68932i 0.0387049 0.0670388i
\(636\) 0 0
\(637\) 0 0
\(638\) 4.32228i 0.171121i
\(639\) 0 0
\(640\) 2.03412i 0.0804057i
\(641\) 30.5823 17.6567i 1.20793 0.697398i 0.245622 0.969366i \(-0.421008\pi\)
0.962306 + 0.271968i \(0.0876744\pi\)
\(642\) 0 0
\(643\) −6.09416 3.51846i −0.240330 0.138755i 0.374998 0.927025i \(-0.377643\pi\)
−0.615328 + 0.788271i \(0.710977\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.40826 2.43917i −0.0554071 0.0959680i
\(647\) −14.9942 −0.589482 −0.294741 0.955577i \(-0.595233\pi\)
−0.294741 + 0.955577i \(0.595233\pi\)
\(648\) 0 0
\(649\) 56.5050i 2.21801i
\(650\) −0.582461 1.00885i −0.0228460 0.0395704i
\(651\) 0 0
\(652\) −16.8995 + 29.2708i −0.661835 + 1.14633i
\(653\) −4.15597 2.39945i −0.162636 0.0938977i 0.416473 0.909148i \(-0.363266\pi\)
−0.579109 + 0.815250i \(0.696599\pi\)
\(654\) 0 0
\(655\) −1.44448 2.50191i −0.0564405 0.0977577i
\(656\) 0.778140 0.0303812
\(657\) 0 0
\(658\) 0 0
\(659\) 13.4562 7.76893i 0.524179 0.302635i −0.214464 0.976732i \(-0.568800\pi\)
0.738643 + 0.674097i \(0.235467\pi\)
\(660\) 0 0
\(661\) −18.2131 10.5154i −0.708409 0.409000i 0.102062 0.994778i \(-0.467456\pi\)
−0.810472 + 0.585778i \(0.800789\pi\)
\(662\) −3.14566 1.81615i −0.122260 0.0705866i
\(663\) 0 0
\(664\) 4.58280 2.64588i 0.177847 0.102680i
\(665\) 0 0
\(666\) 0 0
\(667\) −52.7277 −2.04163
\(668\) 21.1614 + 36.6526i 0.818758 + 1.41813i
\(669\) 0 0
\(670\) −0.369106 0.213103i −0.0142598 0.00823290i
\(671\) −27.5673 + 47.7479i −1.06422 + 1.84329i
\(672\) 0 0
\(673\) 10.7194 + 18.5665i 0.413201 + 0.715686i 0.995238 0.0974770i \(-0.0310772\pi\)
−0.582036 + 0.813163i \(0.697744\pi\)
\(674\) 1.12705i 0.0434124i
\(675\) 0 0
\(676\) 17.7263 0.681781
\(677\) 9.03150 + 15.6430i 0.347109 + 0.601210i 0.985735 0.168308i \(-0.0538302\pi\)
−0.638626 + 0.769517i \(0.720497\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.980808 + 0.566270i 0.0376123 + 0.0217155i
\(681\) 0 0
\(682\) 0.530878 0.306503i 0.0203284 0.0117366i
\(683\) 45.5647i 1.74349i −0.489963 0.871743i \(-0.662990\pi\)
0.489963 0.871743i \(-0.337010\pi\)
\(684\) 0 0
\(685\) 0.855844i 0.0327001i
\(686\) 0 0
\(687\) 0 0
\(688\) 15.4973 26.8422i 0.590830 1.02335i
\(689\) 4.25428 7.36863i 0.162075 0.280723i
\(690\) 0 0
\(691\) −3.33627 + 1.92620i −0.126918 + 0.0732760i −0.562115 0.827059i \(-0.690012\pi\)
0.435197 + 0.900335i \(0.356679\pi\)
\(692\) 40.6664 1.54590
\(693\) 0 0
\(694\) 2.22238 0.0843604
\(695\) −5.18357 + 2.99273i −0.196624 + 0.113521i
\(696\) 0 0
\(697\) −0.436550 + 0.756126i −0.0165355 + 0.0286403i
\(698\) −0.402972 + 0.697967i −0.0152527 + 0.0264185i
\(699\) 0 0
\(700\) 0 0
\(701\) 46.5216i 1.75710i −0.477653 0.878549i \(-0.658512\pi\)
0.477653 0.878549i \(-0.341488\pi\)
\(702\) 0 0
\(703\) 16.9606i 0.639680i
\(704\) 27.8297 16.0675i 1.04887 0.605566i
\(705\) 0 0
\(706\) 2.21850 + 1.28085i 0.0834944 + 0.0482055i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.6187 + 25.3203i 0.549017 + 0.950925i 0.998342 + 0.0575566i \(0.0183310\pi\)
−0.449326 + 0.893368i \(0.648336\pi\)
\(710\) 0.550949 0.0206767
\(711\) 0 0
\(712\) 6.27655i 0.235224i
\(713\) 3.73904 + 6.47621i 0.140028 + 0.242536i
\(714\) 0 0
\(715\) −2.24538 + 3.88911i −0.0839724 + 0.145445i
\(716\) 24.7672 + 14.2993i 0.925592 + 0.534391i
\(717\) 0 0
\(718\) −0.870265 1.50734i −0.0324780 0.0562536i
\(719\) 3.37122 0.125725 0.0628627 0.998022i \(-0.479977\pi\)
0.0628627 + 0.998022i \(0.479977\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.903723 0.521765i 0.0336331 0.0194181i
\(723\) 0 0
\(724\) −11.9874 6.92091i −0.445507 0.257214i
\(725\) 34.3448 + 19.8290i 1.27553 + 0.736429i
\(726\) 0 0
\(727\) 4.34397 2.50799i 0.161109 0.0930164i −0.417278 0.908779i \(-0.637016\pi\)
0.578387 + 0.815763i \(0.303682\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.363506 0.0134540
\(731\) 17.3885 + 30.1178i 0.643138 + 1.11395i
\(732\) 0 0
\(733\) −19.6875 11.3666i −0.727175 0.419835i 0.0902126 0.995923i \(-0.471245\pi\)
−0.817388 + 0.576088i \(0.804579\pi\)
\(734\) 0.757478 1.31199i 0.0279590 0.0484265i
\(735\) 0 0
\(736\) −4.56050 7.89901i −0.168102 0.291162i
\(737\) 27.6657i 1.01908i
\(738\) 0 0
\(739\) −2.39022 −0.0879256 −0.0439628 0.999033i \(-0.513998\pi\)
−0.0439628 + 0.999033i \(0.513998\pi\)
\(740\) 1.69859 + 2.94204i 0.0624413 + 0.108151i
\(741\) 0 0
\(742\) 0 0
\(743\) 36.1039 + 20.8446i 1.32453 + 0.764715i 0.984447 0.175682i \(-0.0562131\pi\)
0.340078 + 0.940397i \(0.389546\pi\)
\(744\) 0 0
\(745\) 2.44292 1.41042i 0.0895018 0.0516739i
\(746\) 2.60737i 0.0954627i
\(747\) 0 0
\(748\) 36.6193i 1.33893i
\(749\) 0 0
\(750\) 0 0
\(751\) −13.2710 + 22.9861i −0.484267 + 0.838775i −0.999837 0.0180728i \(-0.994247\pi\)
0.515570 + 0.856848i \(0.327580\pi\)
\(752\) 19.4971 33.7700i 0.710987 1.23147i
\(753\) 0 0
\(754\) −1.79609 + 1.03697i −0.0654097 + 0.0377643i
\(755\) −1.39909 −0.0509180
\(756\) 0 0
\(757\) 20.3580 0.739923 0.369961 0.929047i \(-0.379371\pi\)
0.369961 + 0.929047i \(0.379371\pi\)
\(758\) −1.12311 + 0.648430i −0.0407933 + 0.0235520i
\(759\) 0 0
\(760\) −0.677163 + 1.17288i −0.0245633 + 0.0425448i
\(761\) −12.9578 + 22.4436i −0.469720 + 0.813578i −0.999401 0.0346186i \(-0.988978\pi\)
0.529681 + 0.848197i \(0.322312\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.5072i 0.778102i
\(765\) 0 0
\(766\) 1.54686i 0.0558903i
\(767\) −23.4802 + 13.5563i −0.847821 + 0.489489i
\(768\) 0 0
\(769\) −18.8269 10.8697i −0.678914 0.391971i 0.120532 0.992709i \(-0.461540\pi\)
−0.799446 + 0.600738i \(0.794873\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10.4457 18.0925i −0.375948 0.651162i
\(773\) −20.3213 −0.730905 −0.365453 0.930830i \(-0.619086\pi\)
−0.365453 + 0.930830i \(0.619086\pi\)
\(774\) 0 0
\(775\) 5.62446i 0.202037i
\(776\) 0.138990 + 0.240738i 0.00498945 + 0.00864197i
\(777\) 0 0
\(778\) 0.809047 1.40131i 0.0290058 0.0502394i
\(779\) −0.904199 0.522039i −0.0323963 0.0187040i
\(780\) 0 0
\(781\) 17.8814 + 30.9715i 0.639848 + 1.10825i
\(782\) 3.36851 0.120458
\(783\) 0 0
\(784\) 0 0
\(785\) −5.99211 + 3.45955i −0.213868 + 0.123477i
\(786\) 0 0
\(787\) −16.4065 9.47232i −0.584830 0.337652i 0.178221 0.983991i \(-0.442966\pi\)
−0.763051 + 0.646339i \(0.776299\pi\)
\(788\) −26.6727 15.3995i −0.950176 0.548584i
\(789\) 0 0
\(790\) −0.0321246 + 0.0185472i −0.00114294 + 0.000659879i
\(791\) 0 0
\(792\) 0 0
\(793\) −26.4550 −0.939445
\(794\) 1.51635 + 2.62640i 0.0538133 + 0.0932074i
\(795\) 0 0
\(796\) 21.5709 + 12.4540i 0.764560 + 0.441419i
\(797\) 11.4342 19.8047i 0.405022 0.701518i −0.589302 0.807913i \(-0.700597\pi\)
0.994324 + 0.106394i \(0.0339306\pi\)
\(798\) 0 0
\(799\) 21.8764 + 37.8911i 0.773932 + 1.34049i
\(800\) 6.86014i 0.242543i
\(801\) 0 0
\(802\) 0.451525 0.0159439
\(803\) 11.7978 + 20.4345i 0.416337 + 0.721117i
\(804\) 0 0
\(805\) 0 0
\(806\) 0.254729 + 0.147068i 0.00897246 + 0.00518025i
\(807\) 0 0
\(808\) −4.91095 + 2.83534i −0.172767 + 0.0997469i
\(809\) 11.9814i 0.421245i 0.977568 + 0.210622i \(0.0675490\pi\)
−0.977568 + 0.210622i \(0.932451\pi\)
\(810\) 0 0
\(811\) 36.9371i 1.29704i −0.761199 0.648519i \(-0.775389\pi\)
0.761199 0.648519i \(-0.224611\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0.831399 1.44003i 0.0291405 0.0504729i
\(815\) −4.50728 + 7.80683i −0.157883 + 0.273461i
\(816\) 0 0
\(817\) −36.0158 + 20.7937i −1.26003 + 0.727481i
\(818\) −2.26790 −0.0792954
\(819\) 0 0
\(820\) 0.209127 0.00730304
\(821\) −32.6907 + 18.8740i −1.14091 + 0.658707i −0.946657 0.322244i \(-0.895563\pi\)
−0.194257 + 0.980951i \(0.562229\pi\)
\(822\) 0 0
\(823\) 10.5082 18.2008i 0.366293 0.634438i −0.622690 0.782469i \(-0.713960\pi\)
0.988983 + 0.148031i \(0.0472934\pi\)
\(824\) −1.55943 + 2.70101i −0.0543253 + 0.0940943i
\(825\) 0 0
\(826\) 0 0
\(827\) 23.9104i 0.831447i −0.909491 0.415724i \(-0.863528\pi\)
0.909491 0.415724i \(-0.136472\pi\)
\(828\) 0 0
\(829\) 25.0859i 0.871270i 0.900123 + 0.435635i \(0.143476\pi\)
−0.900123 + 0.435635i \(0.856524\pi\)
\(830\) 0.608845 0.351517i 0.0211333 0.0122013i
\(831\) 0 0
\(832\) 13.3534 + 7.70960i 0.462946 + 0.267282i
\(833\) 0 0
\(834\) 0 0
\(835\) 5.64397 + 9.77564i 0.195318 + 0.338300i
\(836\) −43.7905 −1.51453
\(837\) 0 0
\(838\) 0.359677i 0.0124248i
\(839\) 3.72840 + 6.45777i 0.128719 + 0.222947i 0.923180 0.384367i \(-0.125580\pi\)
−0.794462 + 0.607314i \(0.792247\pi\)
\(840\) 0 0
\(841\) 20.8021 36.0303i 0.717313 1.24242i
\(842\) 2.98960 + 1.72604i 0.103028 + 0.0594834i
\(843\) 0 0
\(844\) −2.37737 4.11772i −0.0818323 0.141738i
\(845\) 4.72780 0.162641
\(846\) 0 0
\(847\) 0 0
\(848\) −14.2828 + 8.24615i −0.490472 + 0.283174i
\(849\) 0 0
\(850\) −2.19411 1.26677i −0.0752574 0.0434499i
\(851\) 17.5670 + 10.1423i 0.602187 + 0.347673i
\(852\) 0 0
\(853\) 2.19184 1.26546i 0.0750472 0.0433285i −0.462007 0.886876i \(-0.652870\pi\)
0.537054 + 0.843548i \(0.319537\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.123478 0.00422038
\(857\) 9.52098 + 16.4908i 0.325231 + 0.563316i 0.981559 0.191159i \(-0.0612247\pi\)
−0.656328 + 0.754475i \(0.727891\pi\)
\(858\) 0 0
\(859\) −8.88415 5.12927i −0.303123 0.175008i 0.340722 0.940164i \(-0.389329\pi\)
−0.643845 + 0.765156i \(0.722662\pi\)
\(860\) 4.16495 7.21390i 0.142024 0.245992i
\(861\) 0 0
\(862\) −0.413809 0.716738i −0.0140944 0.0244122i
\(863\) 4.40932i 0.150095i 0.997180 + 0.0750475i \(0.0239108\pi\)
−0.997180 + 0.0750475i \(0.976089\pi\)
\(864\) 0 0
\(865\) 10.8462 0.368781
\(866\) 1.73408 + 3.00352i 0.0589265 + 0.102064i
\(867\) 0 0
\(868\) 0 0
\(869\) −2.08526 1.20392i −0.0707375 0.0408403i
\(870\) 0 0
\(871\) 11.4962 6.63736i 0.389535 0.224898i
\(872\) 5.83693i 0.197663i
\(873\) 0 0
\(874\) 4.02816i 0.136255i
\(875\) 0 0
\(876\) 0 0
\(877\) 25.0586 43.4028i 0.846170 1.46561i −0.0384307 0.999261i \(-0.512236\pi\)
0.884601 0.466349i \(-0.154431\pi\)
\(878\) 1.61196 2.79200i 0.0544011 0.0942255i
\(879\) 0 0
\(880\) 7.53833 4.35226i 0.254117 0.146715i
\(881\) −42.5809 −1.43459 −0.717294 0.696771i \(-0.754619\pi\)
−0.717294 + 0.696771i \(0.754619\pi\)
\(882\) 0 0
\(883\) −15.6590 −0.526967 −0.263483 0.964664i \(-0.584871\pi\)
−0.263483 + 0.964664i \(0.584871\pi\)
\(884\) −15.2169 + 8.78546i −0.511798 + 0.295487i
\(885\) 0 0
\(886\) −0.336196 + 0.582309i −0.0112947 + 0.0195630i
\(887\) 12.3919 21.4634i 0.416080 0.720671i −0.579461 0.815000i \(-0.696737\pi\)
0.995541 + 0.0943286i \(0.0300704\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0.833869i 0.0279513i
\(891\) 0 0
\(892\) 5.55134i 0.185873i
\(893\) −45.3113 + 26.1605i −1.51629 + 0.875428i
\(894\) 0 0
\(895\) 6.60567 + 3.81379i 0.220803 + 0.127481i
\(896\) 0 0
\(897\) 0 0
\(898\) 0.451660 + 0.782299i 0.0150721 + 0.0261056i
\(899\) −10.0134 −0.333965
\(900\) 0 0
\(901\) 18.5049i 0.616488i
\(902\) −0.0511803 0.0886468i −0.00170412 0.00295162i
\(903\) 0 0
\(904\) −1.20655 + 2.08980i −0.0401292 + 0.0695058i
\(905\) −3.19716 1.84588i −0.106277 0.0613592i
\(906\) 0 0
\(907\) −22.0517 38.1946i −0.732213 1.26823i −0.955935 0.293577i \(-0.905154\pi\)
0.223722 0.974653i \(-0.428179\pi\)
\(908\) 5.64941 0.187482
\(909\) 0 0
\(910\) 0 0
\(911\) −22.3259 + 12.8899i −0.739691 + 0.427061i −0.821957 0.569549i \(-0.807118\pi\)
0.0822657 + 0.996610i \(0.473784\pi\)
\(912\) 0 0
\(913\) 39.5210 + 22.8175i 1.30795 + 0.755148i
\(914\) 4.38879 + 2.53387i 0.145168 + 0.0838129i
\(915\) 0 0
\(916\) −40.7845 + 23.5470i −1.34756 + 0.778013i
\(917\) 0 0
\(918\) 0 0
\(919\) 52.7102 1.73875 0.869375 0.494154i \(-0.164522\pi\)
0.869375 + 0.494154i \(0.164522\pi\)
\(920\) −0.809876 1.40275i −0.0267008 0.0462472i
\(921\) 0 0
\(922\) −1.15412 0.666334i −0.0380091 0.0219446i
\(923\) −8.57999 + 14.8610i −0.282414 + 0.489155i
\(924\) 0 0
\(925\) −7.62828 13.2126i −0.250816 0.434426i
\(926\) 0.704655i 0.0231564i
\(927\) 0 0
\(928\) 12.2133 0.400922
\(929\) 1.69009 + 2.92732i 0.0554500 + 0.0960422i 0.892418 0.451210i \(-0.149007\pi\)
−0.836968 + 0.547252i \(0.815674\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 32.1981 + 18.5896i 1.05468 + 0.608922i
\(933\) 0 0
\(934\) 2.53103 1.46129i 0.0828180 0.0478150i
\(935\) 9.76677i 0.319407i
\(936\) 0 0
\(937\) 8.26186i 0.269903i 0.990852 + 0.134952i \(0.0430879\pi\)
−0.990852 + 0.134952i \(0.956912\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 5.23990 9.07578i 0.170907 0.296019i
\(941\) 26.1882 45.3592i 0.853710 1.47867i −0.0241274 0.999709i \(-0.507681\pi\)
0.877837 0.478960i \(-0.158986\pi\)
\(942\) 0 0
\(943\) 1.08141 0.624351i 0.0352155 0.0203317i
\(944\) 52.5528 1.71045
\(945\) 0 0
\(946\) −4.07720 −0.132561
\(947\) 6.53348 3.77211i 0.212310 0.122577i −0.390075 0.920783i \(-0.627551\pi\)
0.602384 + 0.798206i \(0.294217\pi\)
\(948\) 0 0
\(949\) −5.66092 + 9.80500i −0.183761 + 0.318284i
\(950\) 1.51484 2.62379i 0.0491480 0.0851269i
\(951\) 0 0
\(952\) 0 0
\(953\) 45.2795i 1.46675i −0.679825 0.733374i \(-0.737944\pi\)
0.679825 0.733374i \(-0.262056\pi\)
\(954\) 0 0
\(955\) 5.73620i 0.185619i
\(956\) 22.1174 12.7695i 0.715327 0.412994i
\(957\) 0 0
\(958\) −0.200812 0.115939i −0.00648795 0.00374582i
\(959\) 0 0
\(960\) 0 0
\(961\) −14.7899 25.6169i −0.477094 0.826352i
\(962\) 0.797855 0.0257239
\(963\) 0 0
\(964\) 8.34518i 0.268780i
\(965\) −2.78598 4.82546i −0.0896838 0.155337i
\(966\) 0 0
\(967\) −6.82403 + 11.8196i −0.219446 + 0.380092i −0.954639 0.297766i \(-0.903758\pi\)
0.735193 + 0.677858i \(0.237092\pi\)
\(968\) −2.81954 1.62786i −0.0906233 0.0523214i
\(969\) 0 0
\(970\) 0.0184654 + 0.0319831i 0.000592889 + 0.00102691i
\(971\) −3.47104 −0.111391 −0.0556955 0.998448i \(-0.517738\pi\)
−0.0556955 + 0.998448i \(0.517738\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2.99051 + 1.72657i −0.0958222 + 0.0553230i
\(975\) 0 0
\(976\) 44.4082 + 25.6391i 1.42147 + 0.820688i
\(977\) 2.21904 + 1.28116i 0.0709932 + 0.0409880i 0.535076 0.844804i \(-0.320283\pi\)
−0.464083 + 0.885792i \(0.653616\pi\)
\(978\) 0 0
\(979\) 46.8759 27.0638i 1.49816 0.864963i
\(980\) 0 0
\(981\) 0 0
\(982\) −0.325277 −0.0103800
\(983\) −19.5749 33.9047i −0.624343 1.08139i −0.988668 0.150122i \(-0.952033\pi\)
0.364325 0.931272i \(-0.381300\pi\)
\(984\) 0 0
\(985\) −7.11390 4.10721i −0.226668 0.130867i
\(986\) −2.25527 + 3.90624i −0.0718224 + 0.124400i
\(987\) 0 0
\(988\) −10.5059 18.1968i −0.334238 0.578917i
\(989\) 49.7380i 1.58158i
\(990\) 0 0
\(991\) −16.2067 −0.514821 −0.257411 0.966302i \(-0.582869\pi\)
−0.257411 + 0.966302i \(0.582869\pi\)
\(992\) −0.866073 1.50008i −0.0274978 0.0476277i
\(993\) 0 0
\(994\) 0 0
\(995\) 5.75320 + 3.32161i 0.182389 + 0.105302i
\(996\) 0 0
\(997\) 21.5007 12.4134i 0.680933 0.393137i −0.119273 0.992861i \(-0.538057\pi\)
0.800207 + 0.599725i \(0.204723\pi\)
\(998\) 1.53626i 0.0486296i
\(999\) 0 0
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 1323.2.o.e.881.11 48
3.2 odd 2 441.2.o.e.293.13 yes 48
7.2 even 3 1323.2.s.d.962.13 48
7.3 odd 6 1323.2.i.d.1097.11 48
7.4 even 3 1323.2.i.d.1097.12 48
7.5 odd 6 1323.2.s.d.962.14 48
7.6 odd 2 inner 1323.2.o.e.881.12 48
9.2 odd 6 inner 1323.2.o.e.440.12 48
9.7 even 3 441.2.o.e.146.14 yes 48
21.2 odd 6 441.2.s.d.374.12 48
21.5 even 6 441.2.s.d.374.11 48
21.11 odd 6 441.2.i.d.68.13 48
21.17 even 6 441.2.i.d.68.14 48
21.20 even 2 441.2.o.e.293.14 yes 48
63.2 odd 6 1323.2.i.d.521.11 48
63.11 odd 6 1323.2.s.d.656.14 48
63.16 even 3 441.2.i.d.227.12 48
63.20 even 6 inner 1323.2.o.e.440.11 48
63.25 even 3 441.2.s.d.362.11 48
63.34 odd 6 441.2.o.e.146.13 48
63.38 even 6 1323.2.s.d.656.13 48
63.47 even 6 1323.2.i.d.521.12 48
63.52 odd 6 441.2.s.d.362.12 48
63.61 odd 6 441.2.i.d.227.11 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.13 48 21.11 odd 6
441.2.i.d.68.14 48 21.17 even 6
441.2.i.d.227.11 48 63.61 odd 6
441.2.i.d.227.12 48 63.16 even 3
441.2.o.e.146.13 48 63.34 odd 6
441.2.o.e.146.14 yes 48 9.7 even 3
441.2.o.e.293.13 yes 48 3.2 odd 2
441.2.o.e.293.14 yes 48 21.20 even 2
441.2.s.d.362.11 48 63.25 even 3
441.2.s.d.362.12 48 63.52 odd 6
441.2.s.d.374.11 48 21.5 even 6
441.2.s.d.374.12 48 21.2 odd 6
1323.2.i.d.521.11 48 63.2 odd 6
1323.2.i.d.521.12 48 63.47 even 6
1323.2.i.d.1097.11 48 7.3 odd 6
1323.2.i.d.1097.12 48 7.4 even 3
1323.2.o.e.440.11 48 63.20 even 6 inner
1323.2.o.e.440.12 48 9.2 odd 6 inner
1323.2.o.e.881.11 48 1.1 even 1 trivial
1323.2.o.e.881.12 48 7.6 odd 2 inner
1323.2.s.d.656.13 48 63.38 even 6
1323.2.s.d.656.14 48 63.11 odd 6
1323.2.s.d.962.13 48 7.2 even 3
1323.2.s.d.962.14 48 7.5 odd 6