Properties

Label 1368.2.e.f.379.7
Level $1368$
Weight $2$
Character 1368.379
Analytic conductor $10.924$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,2,Mod(379,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1368.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.e (of order \(2\), degree \(1\), 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: \(10.9235349965\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.7
Character \(\chi\) \(=\) 1368.379
Dual form 1368.2.e.f.379.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26128 + 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(-0.458259 + 2.79106i) q^{8} +O(q^{10})\) \(q+(-1.26128 + 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(-0.458259 + 2.79106i) q^{8} +(-1.25652 - 2.47760i) q^{10} +3.11106 q^{11} -0.401637 q^{13} +(0.803023 + 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} +4.88644 q^{17} +(-2.50466 - 3.56744i) q^{19} +(3.16965 + 2.32120i) q^{20} +(-3.92392 + 1.99003i) q^{22} -3.34225i q^{23} +1.14134 q^{25} +(0.506577 - 0.256912i) q^{26} +(-2.02568 - 1.48344i) q^{28} -3.79561 q^{29} +2.06495 q^{31} +(3.96211 + 4.03753i) q^{32} +(-6.16318 + 3.12567i) q^{34} +2.46601 q^{35} +1.55353 q^{37} +(5.44105 + 2.89741i) q^{38} +(-5.48261 - 0.900181i) q^{40} +2.92028i q^{41} +2.08998 q^{43} +(3.67623 - 5.01997i) q^{44} +(2.13791 + 4.21552i) q^{46} -4.59290i q^{47} +5.42401 q^{49} +(-1.43955 + 0.730070i) q^{50} +(-0.474600 + 0.648077i) q^{52} -1.83304 q^{53} +6.11121i q^{55} +(3.50385 + 0.575292i) q^{56} +(4.78734 - 2.42791i) q^{58} +7.40388i q^{59} +1.71150i q^{61} +(-2.60448 + 1.32087i) q^{62} +(-7.58000 - 2.55806i) q^{64} -0.788954i q^{65} -10.2314i q^{67} +(5.77413 - 7.88471i) q^{68} +(-3.11034 + 1.57742i) q^{70} +8.84074 q^{71} +6.14134 q^{73} +(-1.95944 + 0.993733i) q^{74} +(-8.71606 - 0.174021i) q^{76} -3.90558i q^{77} -1.51739 q^{79} +(7.49093 - 2.37164i) q^{80} +(-1.86799 - 3.68330i) q^{82} +3.55077 q^{83} +9.59867i q^{85} +(-2.63606 + 1.33688i) q^{86} +(-1.42567 + 8.68315i) q^{88} +5.11730i q^{89} +0.504209i q^{91} +(-5.39302 - 3.94942i) q^{92} +(2.93790 + 5.79294i) q^{94} +(7.00770 - 4.92003i) q^{95} -9.40618i q^{97} +(-6.84120 + 3.46953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).

\(n\) \(343\) \(685\) \(1009\) \(1217\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26128 + 0.639662i −0.891861 + 0.452310i
\(3\) 0 0
\(4\) 1.18166 1.61359i 0.590832 0.806795i
\(5\) 1.96435i 0.878483i 0.898369 + 0.439242i \(0.144753\pi\)
−0.898369 + 0.439242i \(0.855247\pi\)
\(6\) 0 0
\(7\) 1.25539i 0.474491i −0.971450 0.237245i \(-0.923755\pi\)
0.971450 0.237245i \(-0.0762446\pi\)
\(8\) −0.458259 + 2.79106i −0.162019 + 0.986788i
\(9\) 0 0
\(10\) −1.25652 2.47760i −0.397346 0.783485i
\(11\) 3.11106 0.938020 0.469010 0.883193i \(-0.344611\pi\)
0.469010 + 0.883193i \(0.344611\pi\)
\(12\) 0 0
\(13\) −0.401637 −0.111394 −0.0556970 0.998448i \(-0.517738\pi\)
−0.0556970 + 0.998448i \(0.517738\pi\)
\(14\) 0.803023 + 1.58339i 0.214617 + 0.423180i
\(15\) 0 0
\(16\) −1.20734 3.81344i −0.301835 0.953360i
\(17\) 4.88644 1.18514 0.592568 0.805520i \(-0.298114\pi\)
0.592568 + 0.805520i \(0.298114\pi\)
\(18\) 0 0
\(19\) −2.50466 3.56744i −0.574609 0.818428i
\(20\) 3.16965 + 2.32120i 0.708755 + 0.519036i
\(21\) 0 0
\(22\) −3.92392 + 1.99003i −0.836583 + 0.424275i
\(23\) 3.34225i 0.696907i −0.937326 0.348454i \(-0.886707\pi\)
0.937326 0.348454i \(-0.113293\pi\)
\(24\) 0 0
\(25\) 1.14134 0.228267
\(26\) 0.506577 0.256912i 0.0993479 0.0503846i
\(27\) 0 0
\(28\) −2.02568 1.48344i −0.382817 0.280344i
\(29\) −3.79561 −0.704827 −0.352414 0.935844i \(-0.614639\pi\)
−0.352414 + 0.935844i \(0.614639\pi\)
\(30\) 0 0
\(31\) 2.06495 0.370876 0.185438 0.982656i \(-0.440630\pi\)
0.185438 + 0.982656i \(0.440630\pi\)
\(32\) 3.96211 + 4.03753i 0.700409 + 0.713742i
\(33\) 0 0
\(34\) −6.16318 + 3.12567i −1.05698 + 0.536049i
\(35\) 2.46601 0.416832
\(36\) 0 0
\(37\) 1.55353 0.255398 0.127699 0.991813i \(-0.459241\pi\)
0.127699 + 0.991813i \(0.459241\pi\)
\(38\) 5.44105 + 2.89741i 0.882654 + 0.470022i
\(39\) 0 0
\(40\) −5.48261 0.900181i −0.866876 0.142331i
\(41\) 2.92028i 0.456071i 0.973653 + 0.228035i \(0.0732302\pi\)
−0.973653 + 0.228035i \(0.926770\pi\)
\(42\) 0 0
\(43\) 2.08998 0.318720 0.159360 0.987221i \(-0.449057\pi\)
0.159360 + 0.987221i \(0.449057\pi\)
\(44\) 3.67623 5.01997i 0.554212 0.756789i
\(45\) 0 0
\(46\) 2.13791 + 4.21552i 0.315218 + 0.621545i
\(47\) 4.59290i 0.669943i −0.942228 0.334971i \(-0.891273\pi\)
0.942228 0.334971i \(-0.108727\pi\)
\(48\) 0 0
\(49\) 5.42401 0.774858
\(50\) −1.43955 + 0.730070i −0.203583 + 0.103247i
\(51\) 0 0
\(52\) −0.474600 + 0.648077i −0.0658151 + 0.0898720i
\(53\) −1.83304 −0.251787 −0.125894 0.992044i \(-0.540180\pi\)
−0.125894 + 0.992044i \(0.540180\pi\)
\(54\) 0 0
\(55\) 6.11121i 0.824035i
\(56\) 3.50385 + 0.575292i 0.468222 + 0.0768766i
\(57\) 0 0
\(58\) 4.78734 2.42791i 0.628608 0.318800i
\(59\) 7.40388i 0.963903i 0.876198 + 0.481952i \(0.160072\pi\)
−0.876198 + 0.481952i \(0.839928\pi\)
\(60\) 0 0
\(61\) 1.71150i 0.219135i 0.993979 + 0.109568i \(0.0349466\pi\)
−0.993979 + 0.109568i \(0.965053\pi\)
\(62\) −2.60448 + 1.32087i −0.330770 + 0.167751i
\(63\) 0 0
\(64\) −7.58000 2.55806i −0.947500 0.319757i
\(65\) 0.788954i 0.0978577i
\(66\) 0 0
\(67\) 10.2314i 1.24996i −0.780639 0.624982i \(-0.785106\pi\)
0.780639 0.624982i \(-0.214894\pi\)
\(68\) 5.77413 7.88471i 0.700217 0.956162i
\(69\) 0 0
\(70\) −3.11034 + 1.57742i −0.371757 + 0.188537i
\(71\) 8.84074 1.04920 0.524601 0.851348i \(-0.324214\pi\)
0.524601 + 0.851348i \(0.324214\pi\)
\(72\) 0 0
\(73\) 6.14134 0.718789 0.359395 0.933186i \(-0.382983\pi\)
0.359395 + 0.933186i \(0.382983\pi\)
\(74\) −1.95944 + 0.993733i −0.227780 + 0.115519i
\(75\) 0 0
\(76\) −8.71606 0.174021i −0.999801 0.0199616i
\(77\) 3.90558i 0.445082i
\(78\) 0 0
\(79\) −1.51739 −0.170719 −0.0853597 0.996350i \(-0.527204\pi\)
−0.0853597 + 0.996350i \(0.527204\pi\)
\(80\) 7.49093 2.37164i 0.837511 0.265157i
\(81\) 0 0
\(82\) −1.86799 3.68330i −0.206285 0.406752i
\(83\) 3.55077 0.389747 0.194874 0.980828i \(-0.437570\pi\)
0.194874 + 0.980828i \(0.437570\pi\)
\(84\) 0 0
\(85\) 9.59867i 1.04112i
\(86\) −2.63606 + 1.33688i −0.284254 + 0.144160i
\(87\) 0 0
\(88\) −1.42567 + 8.68315i −0.151977 + 0.925626i
\(89\) 5.11730i 0.542433i 0.962518 + 0.271216i \(0.0874259\pi\)
−0.962518 + 0.271216i \(0.912574\pi\)
\(90\) 0 0
\(91\) 0.504209i 0.0528554i
\(92\) −5.39302 3.94942i −0.562261 0.411755i
\(93\) 0 0
\(94\) 2.93790 + 5.79294i 0.303022 + 0.597496i
\(95\) 7.00770 4.92003i 0.718975 0.504785i
\(96\) 0 0
\(97\) 9.40618i 0.955053i −0.878617 0.477526i \(-0.841533\pi\)
0.878617 0.477526i \(-0.158467\pi\)
\(98\) −6.84120 + 3.46953i −0.691066 + 0.350476i
\(99\) 0 0
\(100\) 1.34868 1.84165i 0.134868 0.184165i
\(101\) 13.2549i 1.31892i 0.751742 + 0.659458i \(0.229214\pi\)
−0.751742 + 0.659458i \(0.770786\pi\)
\(102\) 0 0
\(103\) 8.49863 0.837395 0.418697 0.908126i \(-0.362487\pi\)
0.418697 + 0.908126i \(0.362487\pi\)
\(104\) 0.184054 1.12099i 0.0180480 0.109922i
\(105\) 0 0
\(106\) 2.31198 1.17252i 0.224559 0.113886i
\(107\) 4.91093i 0.474757i 0.971417 + 0.237379i \(0.0762882\pi\)
−0.971417 + 0.237379i \(0.923712\pi\)
\(108\) 0 0
\(109\) 16.1902 1.55074 0.775372 0.631505i \(-0.217562\pi\)
0.775372 + 0.631505i \(0.217562\pi\)
\(110\) −3.90911 7.70795i −0.372719 0.734924i
\(111\) 0 0
\(112\) −4.78734 + 1.51568i −0.452361 + 0.143218i
\(113\) 8.17825i 0.769345i −0.923053 0.384673i \(-0.874314\pi\)
0.923053 0.384673i \(-0.125686\pi\)
\(114\) 0 0
\(115\) 6.56534 0.612222
\(116\) −4.48514 + 6.12456i −0.416435 + 0.568651i
\(117\) 0 0
\(118\) −4.73599 9.33838i −0.435983 0.859668i
\(119\) 6.13437i 0.562337i
\(120\) 0 0
\(121\) −1.32131 −0.120119
\(122\) −1.09478 2.15869i −0.0991170 0.195438i
\(123\) 0 0
\(124\) 2.44008 3.33198i 0.219125 0.299221i
\(125\) 12.0637i 1.07901i
\(126\) 0 0
\(127\) 14.7826 1.31175 0.655873 0.754871i \(-0.272300\pi\)
0.655873 + 0.754871i \(0.272300\pi\)
\(128\) 11.1968 1.62221i 0.989667 0.143384i
\(129\) 0 0
\(130\) 0.504664 + 0.995094i 0.0442620 + 0.0872755i
\(131\) 15.7897 1.37955 0.689775 0.724024i \(-0.257710\pi\)
0.689775 + 0.724024i \(0.257710\pi\)
\(132\) 0 0
\(133\) −4.47852 + 3.14432i −0.388337 + 0.272647i
\(134\) 6.54464 + 12.9047i 0.565371 + 1.11479i
\(135\) 0 0
\(136\) −2.23926 + 13.6383i −0.192015 + 1.16948i
\(137\) −14.0143 −1.19732 −0.598660 0.801003i \(-0.704300\pi\)
−0.598660 + 0.801003i \(0.704300\pi\)
\(138\) 0 0
\(139\) −4.37266 −0.370884 −0.185442 0.982655i \(-0.559372\pi\)
−0.185442 + 0.982655i \(0.559372\pi\)
\(140\) 2.91400 3.97913i 0.246278 0.336298i
\(141\) 0 0
\(142\) −11.1507 + 5.65509i −0.935743 + 0.474564i
\(143\) −1.24952 −0.104490
\(144\) 0 0
\(145\) 7.45590i 0.619179i
\(146\) −7.74596 + 3.92838i −0.641060 + 0.325115i
\(147\) 0 0
\(148\) 1.83575 2.50676i 0.150898 0.206054i
\(149\) 6.84807i 0.561016i 0.959852 + 0.280508i \(0.0905029\pi\)
−0.959852 + 0.280508i \(0.909497\pi\)
\(150\) 0 0
\(151\) 17.3060 1.40834 0.704171 0.710031i \(-0.251319\pi\)
0.704171 + 0.710031i \(0.251319\pi\)
\(152\) 11.1047 5.35585i 0.900712 0.434416i
\(153\) 0 0
\(154\) 2.49825 + 4.92604i 0.201315 + 0.396951i
\(155\) 4.05628i 0.325808i
\(156\) 0 0
\(157\) 13.8209i 1.10303i 0.834164 + 0.551516i \(0.185950\pi\)
−0.834164 + 0.551516i \(0.814050\pi\)
\(158\) 1.91385 0.970615i 0.152258 0.0772180i
\(159\) 0 0
\(160\) −7.93112 + 7.78296i −0.627010 + 0.615297i
\(161\) −4.19581 −0.330676
\(162\) 0 0
\(163\) 1.27334 0.0997360 0.0498680 0.998756i \(-0.484120\pi\)
0.0498680 + 0.998756i \(0.484120\pi\)
\(164\) 4.71213 + 3.45079i 0.367956 + 0.269461i
\(165\) 0 0
\(166\) −4.47852 + 2.27129i −0.347600 + 0.176286i
\(167\) 8.84074 0.684117 0.342058 0.939679i \(-0.388876\pi\)
0.342058 + 0.939679i \(0.388876\pi\)
\(168\) 0 0
\(169\) −12.8387 −0.987591
\(170\) −6.13991 12.1066i −0.470910 0.928537i
\(171\) 0 0
\(172\) 2.46966 3.37238i 0.188310 0.257141i
\(173\) −15.8484 −1.20493 −0.602467 0.798144i \(-0.705816\pi\)
−0.602467 + 0.798144i \(0.705816\pi\)
\(174\) 0 0
\(175\) 1.43282i 0.108311i
\(176\) −3.75611 11.8638i −0.283127 0.894271i
\(177\) 0 0
\(178\) −3.27334 6.45436i −0.245347 0.483774i
\(179\) 11.5916i 0.866393i 0.901299 + 0.433197i \(0.142614\pi\)
−0.901299 + 0.433197i \(0.857386\pi\)
\(180\) 0 0
\(181\) 25.3101 1.88128 0.940641 0.339402i \(-0.110225\pi\)
0.940641 + 0.339402i \(0.110225\pi\)
\(182\) −0.322523 0.635949i −0.0239070 0.0471397i
\(183\) 0 0
\(184\) 9.32841 + 1.53162i 0.687700 + 0.112912i
\(185\) 3.05167i 0.224363i
\(186\) 0 0
\(187\) 15.2020 1.11168
\(188\) −7.41105 5.42726i −0.540506 0.395824i
\(189\) 0 0
\(190\) −5.69153 + 10.6881i −0.412907 + 0.775397i
\(191\) 22.6901i 1.64180i −0.571073 0.820899i \(-0.693473\pi\)
0.571073 0.820899i \(-0.306527\pi\)
\(192\) 0 0
\(193\) 13.0069i 0.936257i 0.883660 + 0.468129i \(0.155072\pi\)
−0.883660 + 0.468129i \(0.844928\pi\)
\(194\) 6.01678 + 11.8638i 0.431980 + 0.851774i
\(195\) 0 0
\(196\) 6.40936 8.75212i 0.457811 0.625151i
\(197\) 5.77092i 0.411161i 0.978640 + 0.205580i \(0.0659082\pi\)
−0.978640 + 0.205580i \(0.934092\pi\)
\(198\) 0 0
\(199\) 20.4527i 1.44986i 0.688825 + 0.724928i \(0.258127\pi\)
−0.688825 + 0.724928i \(0.741873\pi\)
\(200\) −0.523028 + 3.18553i −0.0369837 + 0.225251i
\(201\) 0 0
\(202\) −8.47869 16.7182i −0.596558 1.17629i
\(203\) 4.76495i 0.334434i
\(204\) 0 0
\(205\) −5.73644 −0.400651
\(206\) −10.7192 + 5.43625i −0.746840 + 0.378762i
\(207\) 0 0
\(208\) 0.484912 + 1.53162i 0.0336226 + 0.106199i
\(209\) −7.79216 11.0985i −0.538995 0.767702i
\(210\) 0 0
\(211\) 12.1817i 0.838621i 0.907843 + 0.419311i \(0.137728\pi\)
−0.907843 + 0.419311i \(0.862272\pi\)
\(212\) −2.16603 + 2.95777i −0.148764 + 0.203140i
\(213\) 0 0
\(214\) −3.14134 6.19407i −0.214737 0.423418i
\(215\) 4.10546i 0.279990i
\(216\) 0 0
\(217\) 2.59231i 0.175977i
\(218\) −20.4205 + 10.3563i −1.38305 + 0.701416i
\(219\) 0 0
\(220\) 9.86097 + 7.22139i 0.664827 + 0.486866i
\(221\) −1.96257 −0.132017
\(222\) 0 0
\(223\) −21.9834 −1.47212 −0.736060 0.676916i \(-0.763316\pi\)
−0.736060 + 0.676916i \(0.763316\pi\)
\(224\) 5.06866 4.97397i 0.338664 0.332338i
\(225\) 0 0
\(226\) 5.23132 + 10.3151i 0.347982 + 0.686149i
\(227\) 20.9715i 1.39193i −0.718077 0.695964i \(-0.754977\pi\)
0.718077 0.695964i \(-0.245023\pi\)
\(228\) 0 0
\(229\) 9.59867i 0.634298i −0.948376 0.317149i \(-0.897274\pi\)
0.948376 0.317149i \(-0.102726\pi\)
\(230\) −8.28075 + 4.19960i −0.546016 + 0.276914i
\(231\) 0 0
\(232\) 1.73937 10.5938i 0.114196 0.695515i
\(233\) −9.81847 −0.643229 −0.321615 0.946871i \(-0.604226\pi\)
−0.321615 + 0.946871i \(0.604226\pi\)
\(234\) 0 0
\(235\) 9.02205 0.588533
\(236\) 11.9468 + 8.74890i 0.777672 + 0.569505i
\(237\) 0 0
\(238\) 3.92392 + 7.73717i 0.254350 + 0.501526i
\(239\) 5.71955i 0.369967i 0.982742 + 0.184983i \(0.0592232\pi\)
−0.982742 + 0.184983i \(0.940777\pi\)
\(240\) 0 0
\(241\) 17.8705i 1.15114i −0.817752 0.575570i \(-0.804780\pi\)
0.817752 0.575570i \(-0.195220\pi\)
\(242\) 1.66654 0.845189i 0.107129 0.0543308i
\(243\) 0 0
\(244\) 2.76166 + 2.02242i 0.176797 + 0.129472i
\(245\) 10.6546i 0.680700i
\(246\) 0 0
\(247\) 1.00597 + 1.43282i 0.0640080 + 0.0911679i
\(248\) −0.946282 + 5.76339i −0.0600890 + 0.365976i
\(249\) 0 0
\(250\) −7.71671 15.2158i −0.488048 0.962329i
\(251\) −6.66183 −0.420491 −0.210245 0.977649i \(-0.567426\pi\)
−0.210245 + 0.977649i \(0.567426\pi\)
\(252\) 0 0
\(253\) 10.3979i 0.653713i
\(254\) −18.6451 + 9.45590i −1.16990 + 0.593316i
\(255\) 0 0
\(256\) −13.0847 + 9.20824i −0.817791 + 0.575515i
\(257\) 9.82186i 0.612671i −0.951924 0.306335i \(-0.900897\pi\)
0.951924 0.306335i \(-0.0991029\pi\)
\(258\) 0 0
\(259\) 1.95028i 0.121184i
\(260\) −1.27305 0.932279i −0.0789511 0.0578175i
\(261\) 0 0
\(262\) −19.9152 + 10.1001i −1.23037 + 0.623983i
\(263\) 7.49394i 0.462096i −0.972942 0.231048i \(-0.925784\pi\)
0.972942 0.231048i \(-0.0742155\pi\)
\(264\) 0 0
\(265\) 3.60072i 0.221191i
\(266\) 3.63737 6.83061i 0.223021 0.418812i
\(267\) 0 0
\(268\) −16.5093 12.0901i −1.00846 0.738519i
\(269\) −25.9387 −1.58151 −0.790755 0.612133i \(-0.790312\pi\)
−0.790755 + 0.612133i \(0.790312\pi\)
\(270\) 0 0
\(271\) 20.2753i 1.23164i 0.787888 + 0.615818i \(0.211175\pi\)
−0.787888 + 0.615818i \(0.788825\pi\)
\(272\) −5.89960 18.6342i −0.357716 1.12986i
\(273\) 0 0
\(274\) 17.6760 8.96441i 1.06784 0.541560i
\(275\) 3.55077 0.214119
\(276\) 0 0
\(277\) 3.31004i 0.198881i −0.995044 0.0994405i \(-0.968295\pi\)
0.995044 0.0994405i \(-0.0317053\pi\)
\(278\) 5.51515 2.79702i 0.330777 0.167754i
\(279\) 0 0
\(280\) −1.13007 + 6.88278i −0.0675348 + 0.411325i
\(281\) 31.9439i 1.90562i −0.303574 0.952808i \(-0.598180\pi\)
0.303574 0.952808i \(-0.401820\pi\)
\(282\) 0 0
\(283\) −13.1834 −0.783669 −0.391835 0.920036i \(-0.628159\pi\)
−0.391835 + 0.920036i \(0.628159\pi\)
\(284\) 10.4468 14.2653i 0.619903 0.846491i
\(285\) 0 0
\(286\) 1.57599 0.799268i 0.0931903 0.0472617i
\(287\) 3.66607 0.216402
\(288\) 0 0
\(289\) 6.87732 0.404548
\(290\) 4.76926 + 9.40400i 0.280061 + 0.552222i
\(291\) 0 0
\(292\) 7.25700 9.90959i 0.424684 0.579915i
\(293\) 8.25722 0.482392 0.241196 0.970476i \(-0.422460\pi\)
0.241196 + 0.970476i \(0.422460\pi\)
\(294\) 0 0
\(295\) −14.5438 −0.846773
\(296\) −0.711919 + 4.33598i −0.0413794 + 0.252024i
\(297\) 0 0
\(298\) −4.38045 8.63735i −0.253753 0.500348i
\(299\) 1.34237i 0.0776313i
\(300\) 0 0
\(301\) 2.62374i 0.151230i
\(302\) −21.8277 + 11.0700i −1.25604 + 0.637006i
\(303\) 0 0
\(304\) −10.5803 + 13.8585i −0.606819 + 0.794840i
\(305\) −3.36199 −0.192507
\(306\) 0 0
\(307\) 19.3166i 1.10245i −0.834355 0.551227i \(-0.814160\pi\)
0.834355 0.551227i \(-0.185840\pi\)
\(308\) −6.30200 4.61508i −0.359090 0.262969i
\(309\) 0 0
\(310\) −2.59465 5.11611i −0.147366 0.290576i
\(311\) 19.7891i 1.12213i −0.827770 0.561067i \(-0.810391\pi\)
0.827770 0.561067i \(-0.189609\pi\)
\(312\) 0 0
\(313\) −0.385375 −0.0217827 −0.0108913 0.999941i \(-0.503467\pi\)
−0.0108913 + 0.999941i \(0.503467\pi\)
\(314\) −8.84074 17.4321i −0.498912 0.983751i
\(315\) 0 0
\(316\) −1.79304 + 2.44844i −0.100866 + 0.137735i
\(317\) −17.8110 −1.00037 −0.500183 0.865920i \(-0.666734\pi\)
−0.500183 + 0.865920i \(0.666734\pi\)
\(318\) 0 0
\(319\) −11.8084 −0.661142
\(320\) 5.02491 14.8898i 0.280901 0.832363i
\(321\) 0 0
\(322\) 5.29210 2.68390i 0.294917 0.149568i
\(323\) −12.2389 17.4321i −0.680991 0.969949i
\(324\) 0 0
\(325\) −0.458402 −0.0254276
\(326\) −1.60605 + 0.814510i −0.0889506 + 0.0451115i
\(327\) 0 0
\(328\) −8.15066 1.33825i −0.450045 0.0738922i
\(329\) −5.76585 −0.317882
\(330\) 0 0
\(331\) 0.504209i 0.0277138i −0.999904 0.0138569i \(-0.995589\pi\)
0.999904 0.0138569i \(-0.00441093\pi\)
\(332\) 4.19581 5.72948i 0.230275 0.314446i
\(333\) 0 0
\(334\) −11.1507 + 5.65509i −0.610137 + 0.309433i
\(335\) 20.0980 1.09807
\(336\) 0 0
\(337\) 6.81387i 0.371175i −0.982628 0.185588i \(-0.940581\pi\)
0.982628 0.185588i \(-0.0594189\pi\)
\(338\) 16.1932 8.21243i 0.880794 0.446697i
\(339\) 0 0
\(340\) 15.4883 + 11.3424i 0.839972 + 0.615129i
\(341\) 6.42418 0.347889
\(342\) 0 0
\(343\) 15.5969i 0.842154i
\(344\) −0.957755 + 5.83327i −0.0516387 + 0.314509i
\(345\) 0 0
\(346\) 19.9894 10.1377i 1.07463 0.545004i
\(347\) −6.66183 −0.357626 −0.178813 0.983883i \(-0.557226\pi\)
−0.178813 + 0.983883i \(0.557226\pi\)
\(348\) 0 0
\(349\) 26.8426i 1.43685i −0.695603 0.718426i \(-0.744863\pi\)
0.695603 0.718426i \(-0.255137\pi\)
\(350\) 0.916519 + 1.80719i 0.0489900 + 0.0965981i
\(351\) 0 0
\(352\) 12.3264 + 12.5610i 0.656997 + 0.669504i
\(353\) −23.8328 −1.26849 −0.634245 0.773132i \(-0.718689\pi\)
−0.634245 + 0.773132i \(0.718689\pi\)
\(354\) 0 0
\(355\) 17.3663i 0.921707i
\(356\) 8.25722 + 6.04693i 0.437632 + 0.320487i
\(357\) 0 0
\(358\) −7.41468 14.6202i −0.391878 0.772702i
\(359\) 17.8064i 0.939785i −0.882724 0.469893i \(-0.844293\pi\)
0.882724 0.469893i \(-0.155707\pi\)
\(360\) 0 0
\(361\) −6.45331 + 17.8705i −0.339648 + 0.940553i
\(362\) −31.9231 + 16.1899i −1.67784 + 0.850922i
\(363\) 0 0
\(364\) 0.813586 + 0.595805i 0.0426435 + 0.0312287i
\(365\) 12.0637i 0.631444i
\(366\) 0 0
\(367\) 23.1409i 1.20795i −0.797004 0.603974i \(-0.793583\pi\)
0.797004 0.603974i \(-0.206417\pi\)
\(368\) −12.7455 + 4.03523i −0.664404 + 0.210351i
\(369\) 0 0
\(370\) −1.95204 3.84902i −0.101482 0.200101i
\(371\) 2.30117i 0.119471i
\(372\) 0 0
\(373\) −26.4052 −1.36721 −0.683605 0.729852i \(-0.739589\pi\)
−0.683605 + 0.729852i \(0.739589\pi\)
\(374\) −19.1740 + 9.72416i −0.991465 + 0.502824i
\(375\) 0 0
\(376\) 12.8190 + 2.10474i 0.661091 + 0.108544i
\(377\) 1.52446 0.0785135
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.341839 17.1214i 0.0175359 0.878308i
\(381\) 0 0
\(382\) 14.5140 + 28.6186i 0.742601 + 1.46426i
\(383\) 2.49903 0.127695 0.0638473 0.997960i \(-0.479663\pi\)
0.0638473 + 0.997960i \(0.479663\pi\)
\(384\) 0 0
\(385\) 7.67192 0.390997
\(386\) −8.32003 16.4054i −0.423478 0.835011i
\(387\) 0 0
\(388\) −15.1777 11.1149i −0.770531 0.564276i
\(389\) 17.0615i 0.865053i 0.901621 + 0.432526i \(0.142378\pi\)
−0.901621 + 0.432526i \(0.857622\pi\)
\(390\) 0 0
\(391\) 16.3317i 0.825930i
\(392\) −2.48560 + 15.1387i −0.125542 + 0.764621i
\(393\) 0 0
\(394\) −3.69144 7.27876i −0.185972 0.366698i
\(395\) 2.98068i 0.149974i
\(396\) 0 0
\(397\) 13.9339i 0.699323i 0.936876 + 0.349662i \(0.113703\pi\)
−0.936876 + 0.349662i \(0.886297\pi\)
\(398\) −13.0828 25.7967i −0.655784 1.29307i
\(399\) 0 0
\(400\) −1.37798 4.35242i −0.0688990 0.217621i
\(401\) 14.0188i 0.700066i 0.936737 + 0.350033i \(0.113830\pi\)
−0.936737 + 0.350033i \(0.886170\pi\)
\(402\) 0 0
\(403\) −0.829359 −0.0413133
\(404\) 21.3880 + 15.6629i 1.06409 + 0.779258i
\(405\) 0 0
\(406\) −3.04796 6.00995i −0.151268 0.298269i
\(407\) 4.83312 0.239569
\(408\) 0 0
\(409\) 34.7326i 1.71742i 0.512465 + 0.858708i \(0.328732\pi\)
−0.512465 + 0.858708i \(0.671268\pi\)
\(410\) 7.23527 3.66939i 0.357325 0.181218i
\(411\) 0 0
\(412\) 10.0425 13.7133i 0.494760 0.675606i
\(413\) 9.29472 0.457363
\(414\) 0 0
\(415\) 6.97494i 0.342386i
\(416\) −1.59133 1.62162i −0.0780213 0.0795065i
\(417\) 0 0
\(418\) 16.9274 + 9.01403i 0.827947 + 0.440890i
\(419\) 18.2557 0.891848 0.445924 0.895071i \(-0.352875\pi\)
0.445924 + 0.895071i \(0.352875\pi\)
\(420\) 0 0
\(421\) −11.6057 −0.565626 −0.282813 0.959175i \(-0.591268\pi\)
−0.282813 + 0.959175i \(0.591268\pi\)
\(422\) −7.79216 15.3645i −0.379316 0.747934i
\(423\) 0 0
\(424\) 0.840006 5.11611i 0.0407943 0.248460i
\(425\) 5.57707 0.270528
\(426\) 0 0
\(427\) 2.14859 0.103978
\(428\) 7.92422 + 5.80307i 0.383032 + 0.280502i
\(429\) 0 0
\(430\) −2.62611 5.17814i −0.126642 0.249712i
\(431\) −4.91559 −0.236776 −0.118388 0.992967i \(-0.537773\pi\)
−0.118388 + 0.992967i \(0.537773\pi\)
\(432\) 0 0
\(433\) 24.6844i 1.18626i −0.805108 0.593128i \(-0.797893\pi\)
0.805108 0.593128i \(-0.202107\pi\)
\(434\) 1.65820 + 3.26963i 0.0795962 + 0.156947i
\(435\) 0 0
\(436\) 19.1314 26.1244i 0.916229 1.25113i
\(437\) −11.9233 + 8.37122i −0.570368 + 0.400450i
\(438\) 0 0
\(439\) −18.4011 −0.878237 −0.439119 0.898429i \(-0.644709\pi\)
−0.439119 + 0.898429i \(0.644709\pi\)
\(440\) −17.0567 2.80052i −0.813147 0.133509i
\(441\) 0 0
\(442\) 2.47536 1.25539i 0.117741 0.0597126i
\(443\) −6.66183 −0.316513 −0.158256 0.987398i \(-0.550587\pi\)
−0.158256 + 0.987398i \(0.550587\pi\)
\(444\) 0 0
\(445\) −10.0522 −0.476518
\(446\) 27.7273 14.0620i 1.31293 0.665854i
\(447\) 0 0
\(448\) −3.21134 + 9.51581i −0.151722 + 0.449580i
\(449\) 2.40339i 0.113423i 0.998391 + 0.0567115i \(0.0180615\pi\)
−0.998391 + 0.0567115i \(0.981938\pi\)
\(450\) 0 0
\(451\) 9.08516i 0.427804i
\(452\) −13.1963 9.66395i −0.620704 0.454554i
\(453\) 0 0
\(454\) 13.4147 + 26.4510i 0.629582 + 1.24141i
\(455\) −0.990441 −0.0464326
\(456\) 0 0
\(457\) −13.7746 −0.644349 −0.322175 0.946680i \(-0.604414\pi\)
−0.322175 + 0.946680i \(0.604414\pi\)
\(458\) 6.13991 + 12.1066i 0.286899 + 0.565706i
\(459\) 0 0
\(460\) 7.75803 10.5938i 0.361720 0.493937i
\(461\) 6.19380i 0.288474i 0.989543 + 0.144237i \(0.0460727\pi\)
−0.989543 + 0.144237i \(0.953927\pi\)
\(462\) 0 0
\(463\) 32.6751i 1.51854i −0.650774 0.759271i \(-0.725556\pi\)
0.650774 0.759271i \(-0.274444\pi\)
\(464\) 4.58259 + 14.4743i 0.212742 + 0.671954i
\(465\) 0 0
\(466\) 12.3839 6.28051i 0.573671 0.290939i
\(467\) −23.5362 −1.08913 −0.544564 0.838720i \(-0.683305\pi\)
−0.544564 + 0.838720i \(0.683305\pi\)
\(468\) 0 0
\(469\) −12.8444 −0.593097
\(470\) −11.3793 + 5.77106i −0.524890 + 0.266199i
\(471\) 0 0
\(472\) −20.6647 3.39290i −0.951168 0.156171i
\(473\) 6.50207 0.298965
\(474\) 0 0
\(475\) −2.85866 4.07165i −0.131164 0.186820i
\(476\) −9.89835 7.24876i −0.453690 0.332246i
\(477\) 0 0
\(478\) −3.65858 7.21397i −0.167340 0.329959i
\(479\) 1.31334i 0.0600081i 0.999550 + 0.0300041i \(0.00955202\pi\)
−0.999550 + 0.0300041i \(0.990448\pi\)
\(480\) 0 0
\(481\) −0.623954 −0.0284498
\(482\) 11.4311 + 22.5397i 0.520672 + 1.02666i
\(483\) 0 0
\(484\) −1.56134 + 2.13204i −0.0709700 + 0.0969111i
\(485\) 18.4770 0.838998
\(486\) 0 0
\(487\) 26.4413 1.19817 0.599086 0.800685i \(-0.295531\pi\)
0.599086 + 0.800685i \(0.295531\pi\)
\(488\) −4.77690 0.784312i −0.216240 0.0355041i
\(489\) 0 0
\(490\) −6.81537 13.4385i −0.307887 0.607090i
\(491\) 25.1228 1.13378 0.566889 0.823794i \(-0.308147\pi\)
0.566889 + 0.823794i \(0.308147\pi\)
\(492\) 0 0
\(493\) −18.5470 −0.835317
\(494\) −2.18532 1.16371i −0.0983224 0.0523577i
\(495\) 0 0
\(496\) −2.49310 7.87456i −0.111943 0.353578i
\(497\) 11.0985i 0.497837i
\(498\) 0 0
\(499\) −9.30472 −0.416536 −0.208268 0.978072i \(-0.566783\pi\)
−0.208268 + 0.978072i \(0.566783\pi\)
\(500\) 19.4659 + 14.2553i 0.870541 + 0.637515i
\(501\) 0 0
\(502\) 8.40244 4.26132i 0.375019 0.190192i
\(503\) 0.887197i 0.0395582i 0.999804 + 0.0197791i \(0.00629629\pi\)
−0.999804 + 0.0197791i \(0.993704\pi\)
\(504\) 0 0
\(505\) −26.0373 −1.15865
\(506\) 6.65117 + 13.1147i 0.295681 + 0.583021i
\(507\) 0 0
\(508\) 17.4681 23.8531i 0.775022 1.05831i
\(509\) −17.5519 −0.777976 −0.388988 0.921243i \(-0.627175\pi\)
−0.388988 + 0.921243i \(0.627175\pi\)
\(510\) 0 0
\(511\) 7.70974i 0.341059i
\(512\) 10.6133 19.9839i 0.469045 0.883174i
\(513\) 0 0
\(514\) 6.28267 + 12.3881i 0.277117 + 0.546417i
\(515\) 16.6943i 0.735637i
\(516\) 0 0
\(517\) 14.2888i 0.628420i
\(518\) 1.24752 + 2.45985i 0.0548128 + 0.108079i
\(519\) 0 0
\(520\) 2.20202 + 0.361546i 0.0965648 + 0.0158548i
\(521\) 18.4878i 0.809967i 0.914324 + 0.404983i \(0.132723\pi\)
−0.914324 + 0.404983i \(0.867277\pi\)
\(522\) 0 0
\(523\) 10.7356i 0.469436i −0.972064 0.234718i \(-0.924583\pi\)
0.972064 0.234718i \(-0.0754166\pi\)
\(524\) 18.6581 25.4780i 0.815082 1.11301i
\(525\) 0 0
\(526\) 4.79359 + 9.45198i 0.209011 + 0.412126i
\(527\) 10.0903 0.439538
\(528\) 0 0
\(529\) 11.8294 0.514320
\(530\) 2.30325 + 4.54153i 0.100047 + 0.197271i
\(531\) 0 0
\(532\) −0.218464 + 10.9420i −0.00947161 + 0.474396i
\(533\) 1.17289i 0.0508036i
\(534\) 0 0
\(535\) −9.64677 −0.417066
\(536\) 28.5564 + 4.68864i 1.23345 + 0.202518i
\(537\) 0 0
\(538\) 32.7160 16.5920i 1.41049 0.715332i
\(539\) 16.8744 0.726833
\(540\) 0 0
\(541\) 37.9269i 1.63060i 0.579036 + 0.815302i \(0.303429\pi\)
−0.579036 + 0.815302i \(0.696571\pi\)
\(542\) −12.9693 25.5729i −0.557081 1.09845i
\(543\) 0 0
\(544\) 19.3606 + 19.7292i 0.830080 + 0.845882i
\(545\) 31.8033i 1.36230i
\(546\) 0 0
\(547\) 37.1871i 1.59000i 0.606607 + 0.795002i \(0.292530\pi\)
−0.606607 + 0.795002i \(0.707470\pi\)
\(548\) −16.5602 + 22.6133i −0.707416 + 0.965992i
\(549\) 0 0
\(550\) −4.47852 + 2.27129i −0.190965 + 0.0968482i
\(551\) 9.50673 + 13.5406i 0.405000 + 0.576850i
\(552\) 0 0
\(553\) 1.90490i 0.0810048i
\(554\) 2.11731 + 4.17489i 0.0899558 + 0.177374i
\(555\) 0 0
\(556\) −5.16701 + 7.05567i −0.219130 + 0.299227i
\(557\) 6.61994i 0.280496i 0.990116 + 0.140248i \(0.0447900\pi\)
−0.990116 + 0.140248i \(0.955210\pi\)
\(558\) 0 0
\(559\) −0.839414 −0.0355035
\(560\) −2.97732 9.40400i −0.125815 0.397391i
\(561\) 0 0
\(562\) 20.4333 + 40.2903i 0.861928 + 1.69954i
\(563\) 37.4740i 1.57934i 0.613532 + 0.789670i \(0.289748\pi\)
−0.613532 + 0.789670i \(0.710252\pi\)
\(564\) 0 0
\(565\) 16.0649 0.675857
\(566\) 16.6279 8.43290i 0.698924 0.354461i
\(567\) 0 0
\(568\) −4.05135 + 24.6750i −0.169991 + 1.03534i
\(569\) 23.1924i 0.972276i −0.873882 0.486138i \(-0.838405\pi\)
0.873882 0.486138i \(-0.161595\pi\)
\(570\) 0 0
\(571\) −30.6027 −1.28068 −0.640341 0.768091i \(-0.721207\pi\)
−0.640341 + 0.768091i \(0.721207\pi\)
\(572\) −1.47651 + 2.01621i −0.0617359 + 0.0843018i
\(573\) 0 0
\(574\) −4.62395 + 2.34505i −0.193000 + 0.0978805i
\(575\) 3.81463i 0.159081i
\(576\) 0 0
\(577\) 32.2814 1.34389 0.671945 0.740601i \(-0.265459\pi\)
0.671945 + 0.740601i \(0.265459\pi\)
\(578\) −8.67424 + 4.39916i −0.360801 + 0.182981i
\(579\) 0 0
\(580\) −12.0308 8.81037i −0.499550 0.365831i
\(581\) 4.45758i 0.184931i
\(582\) 0 0
\(583\) −5.70269 −0.236181
\(584\) −2.81432 + 17.1408i −0.116458 + 0.709292i
\(585\) 0 0
\(586\) −10.4147 + 5.28183i −0.430226 + 0.218190i
\(587\) −9.97823 −0.411845 −0.205923 0.978568i \(-0.566020\pi\)
−0.205923 + 0.978568i \(0.566020\pi\)
\(588\) 0 0
\(589\) −5.17200 7.36659i −0.213109 0.303535i
\(590\) 18.3438 9.30312i 0.755204 0.383004i
\(591\) 0 0
\(592\) −1.87564 5.92429i −0.0770882 0.243487i
\(593\) 21.5721 0.885859 0.442930 0.896556i \(-0.353939\pi\)
0.442930 + 0.896556i \(0.353939\pi\)
\(594\) 0 0
\(595\) 12.0500 0.494003
\(596\) 11.0500 + 8.09212i 0.452624 + 0.331466i
\(597\) 0 0
\(598\) −0.858664 1.69311i −0.0351134 0.0692363i
\(599\) −36.6125 −1.49595 −0.747973 0.663730i \(-0.768973\pi\)
−0.747973 + 0.663730i \(0.768973\pi\)
\(600\) 0 0
\(601\) 46.0890i 1.88001i 0.341159 + 0.940005i \(0.389180\pi\)
−0.341159 + 0.940005i \(0.610820\pi\)
\(602\) 1.67830 + 3.30927i 0.0684026 + 0.134876i
\(603\) 0 0
\(604\) 20.4499 27.9248i 0.832093 1.13624i
\(605\) 2.59550i 0.105522i
\(606\) 0 0
\(607\) 0.600582 0.0243769 0.0121884 0.999926i \(-0.496120\pi\)
0.0121884 + 0.999926i \(0.496120\pi\)
\(608\) 4.47992 24.2473i 0.181685 0.983357i
\(609\) 0 0
\(610\) 4.24041 2.15054i 0.171689 0.0870726i
\(611\) 1.84468i 0.0746276i
\(612\) 0 0
\(613\) 21.5952i 0.872220i 0.899893 + 0.436110i \(0.143644\pi\)
−0.899893 + 0.436110i \(0.856356\pi\)
\(614\) 12.3561 + 24.3636i 0.498651 + 0.983236i
\(615\) 0 0
\(616\) 10.9007 + 1.78977i 0.439201 + 0.0721118i
\(617\) 16.5945 0.668068 0.334034 0.942561i \(-0.391590\pi\)
0.334034 + 0.942561i \(0.391590\pi\)
\(618\) 0 0
\(619\) −30.4626 −1.22440 −0.612198 0.790704i \(-0.709715\pi\)
−0.612198 + 0.790704i \(0.709715\pi\)
\(620\) 6.54517 + 4.79316i 0.262860 + 0.192498i
\(621\) 0 0
\(622\) 12.6583 + 24.9596i 0.507552 + 1.00079i
\(623\) 6.42418 0.257379
\(624\) 0 0
\(625\) −17.9907 −0.719627
\(626\) 0.486067 0.246510i 0.0194271 0.00985252i
\(627\) 0 0
\(628\) 22.3013 + 16.3317i 0.889920 + 0.651706i
\(629\) 7.59122 0.302682
\(630\) 0 0
\(631\) 7.54402i 0.300323i −0.988661 0.150161i \(-0.952021\pi\)
0.988661 0.150161i \(-0.0479793\pi\)
\(632\) 0.695357 4.23511i 0.0276598 0.168464i
\(633\) 0 0
\(634\) 22.4647 11.3930i 0.892188 0.452475i
\(635\) 29.0382i 1.15235i
\(636\) 0 0
\(637\) −2.17848 −0.0863145
\(638\) 14.8937 7.55337i 0.589647 0.299041i
\(639\) 0 0
\(640\) 3.18658 + 21.9944i 0.125961 + 0.869406i
\(641\) 46.0941i 1.82061i 0.413939 + 0.910305i \(0.364153\pi\)
−0.413939 + 0.910305i \(0.635847\pi\)
\(642\) 0 0
\(643\) −11.7674 −0.464059 −0.232030 0.972709i \(-0.574537\pi\)
−0.232030 + 0.972709i \(0.574537\pi\)
\(644\) −4.95804 + 6.77032i −0.195374 + 0.266788i
\(645\) 0 0
\(646\) 26.5874 + 14.1580i 1.04607 + 0.557041i
\(647\) 22.2904i 0.876324i 0.898896 + 0.438162i \(0.144370\pi\)
−0.898896 + 0.438162i \(0.855630\pi\)
\(648\) 0 0
\(649\) 23.0339i 0.904161i
\(650\) 0.578175 0.293223i 0.0226779 0.0115011i
\(651\) 0 0
\(652\) 1.50466 2.05465i 0.0589272 0.0804664i
\(653\) 33.8039i 1.32285i −0.750011 0.661425i \(-0.769952\pi\)
0.750011 0.661425i \(-0.230048\pi\)
\(654\) 0 0
\(655\) 31.0164i 1.21191i
\(656\) 11.1363 3.52577i 0.434800 0.137658i
\(657\) 0 0
\(658\) 7.27237 3.68820i 0.283506 0.143781i
\(659\) 16.2065i 0.631317i −0.948873 0.315659i \(-0.897775\pi\)
0.948873 0.315659i \(-0.102225\pi\)
\(660\) 0 0
\(661\) −0.564440 −0.0219542 −0.0109771 0.999940i \(-0.503494\pi\)
−0.0109771 + 0.999940i \(0.503494\pi\)
\(662\) 0.322523 + 0.635949i 0.0125352 + 0.0247169i
\(663\) 0 0
\(664\) −1.62717 + 9.91039i −0.0631465 + 0.384598i
\(665\) −6.17654 8.79736i −0.239516 0.341147i
\(666\) 0 0
\(667\) 12.6859i 0.491200i
\(668\) 10.4468 14.2653i 0.404198 0.551942i
\(669\) 0 0
\(670\) −25.3493 + 12.8560i −0.979329 + 0.496669i
\(671\) 5.32459i 0.205553i
\(672\) 0 0
\(673\) 15.5992i 0.601305i 0.953734 + 0.300653i \(0.0972045\pi\)
−0.953734 + 0.300653i \(0.902796\pi\)
\(674\) 4.35858 + 8.59421i 0.167886 + 0.331037i
\(675\) 0 0
\(676\) −15.1710 + 20.7164i −0.583501 + 0.796783i
\(677\) 3.79561 0.145877 0.0729386 0.997336i \(-0.476762\pi\)
0.0729386 + 0.997336i \(0.476762\pi\)
\(678\) 0 0
\(679\) −11.8084 −0.453164
\(680\) −26.7904 4.39868i −1.02737 0.168682i
\(681\) 0 0
\(682\) −8.10270 + 4.10931i −0.310269 + 0.157353i
\(683\) 40.6152i 1.55410i −0.629440 0.777049i \(-0.716716\pi\)
0.629440 0.777049i \(-0.283284\pi\)
\(684\) 0 0
\(685\) 27.5289i 1.05183i
\(686\) 9.97676 + 19.6721i 0.380914 + 0.751085i
\(687\) 0 0
\(688\) −2.52332 7.97003i −0.0962007 0.303855i
\(689\) 0.736215 0.0280476
\(690\) 0 0
\(691\) 6.90069 0.262514 0.131257 0.991348i \(-0.458099\pi\)
0.131257 + 0.991348i \(0.458099\pi\)
\(692\) −18.7275 + 25.5729i −0.711914 + 0.972135i
\(693\) 0 0
\(694\) 8.40244 4.26132i 0.318952 0.161757i
\(695\) 8.58942i 0.325815i
\(696\) 0 0
\(697\) 14.2698i 0.540506i
\(698\) 17.1702 + 33.8561i 0.649902 + 1.28147i
\(699\) 0 0
\(700\) −2.31198 1.69311i −0.0873845 0.0639935i
\(701\) 42.5932i 1.60872i −0.594139 0.804362i \(-0.702507\pi\)
0.594139 0.804362i \(-0.297493\pi\)
\(702\) 0 0
\(703\) −3.89107 5.54212i −0.146754 0.209025i
\(704\) −23.5818 7.95826i −0.888773 0.299938i
\(705\) 0 0
\(706\) 30.0598 15.2449i 1.13132 0.573750i
\(707\) 16.6401 0.625814
\(708\) 0 0
\(709\) 34.2854i 1.28761i −0.765188 0.643807i \(-0.777354\pi\)
0.765188 0.643807i \(-0.222646\pi\)
\(710\) −11.1086 21.9038i −0.416897 0.822035i
\(711\) 0 0
\(712\) −14.2827 2.34505i −0.535266 0.0878845i
\(713\) 6.90158i 0.258466i
\(714\) 0 0
\(715\) 2.45448i 0.0917925i
\(716\) 18.7040 + 13.6973i 0.699001 + 0.511893i
\(717\) 0 0
\(718\) 11.3901 + 22.4589i 0.425074 + 0.838158i
\(719\) 7.09419i 0.264568i 0.991212 + 0.132284i \(0.0422312\pi\)
−0.991212 + 0.132284i \(0.957769\pi\)
\(720\) 0 0
\(721\) 10.6691i 0.397336i
\(722\) −3.29164 26.6677i −0.122502 0.992468i
\(723\) 0 0
\(724\) 29.9080 40.8401i 1.11152 1.51781i
\(725\) −4.33207 −0.160889
\(726\) 0 0
\(727\) 35.8722i 1.33043i 0.746653 + 0.665213i \(0.231659\pi\)
−0.746653 + 0.665213i \(0.768341\pi\)
\(728\) −1.40728 0.231058i −0.0521571 0.00856359i
\(729\) 0 0
\(730\) −7.71671 15.2158i −0.285608 0.563160i
\(731\) 10.2126 0.377726
\(732\) 0 0
\(733\) 27.6419i 1.02098i −0.859885 0.510488i \(-0.829465\pi\)
0.859885 0.510488i \(-0.170535\pi\)
\(734\) 14.8024 + 29.1872i 0.546366 + 1.07732i
\(735\) 0 0
\(736\) 13.4945 13.2424i 0.497412 0.488120i
\(737\) 31.8305i 1.17249i
\(738\) 0 0
\(739\) −33.7860 −1.24284 −0.621419 0.783478i \(-0.713444\pi\)
−0.621419 + 0.783478i \(0.713444\pi\)
\(740\) 4.92414 + 3.60605i 0.181015 + 0.132561i
\(741\) 0 0
\(742\) −1.47197 2.90242i −0.0540377 0.106551i
\(743\) 7.67370 0.281521 0.140760 0.990044i \(-0.455045\pi\)
0.140760 + 0.990044i \(0.455045\pi\)
\(744\) 0 0
\(745\) −13.4520 −0.492843
\(746\) 33.3044 16.8904i 1.21936 0.618402i
\(747\) 0 0
\(748\) 17.9637 24.5298i 0.656817 0.896899i
\(749\) 6.16511 0.225268
\(750\) 0 0
\(751\) −20.6688 −0.754214 −0.377107 0.926170i \(-0.623081\pi\)
−0.377107 + 0.926170i \(0.623081\pi\)
\(752\) −17.5147 + 5.54519i −0.638697 + 0.202212i
\(753\) 0 0
\(754\) −1.92277 + 0.975138i −0.0700232 + 0.0355124i
\(755\) 33.9950i 1.23720i
\(756\) 0 0
\(757\) 34.7298i 1.26228i 0.775671 + 0.631138i \(0.217412\pi\)
−0.775671 + 0.631138i \(0.782588\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 10.5207 + 21.8135i 0.381628 + 0.791260i
\(761\) 41.1634 1.49217 0.746087 0.665849i \(-0.231930\pi\)
0.746087 + 0.665849i \(0.231930\pi\)
\(762\) 0 0
\(763\) 20.3250i 0.735814i
\(764\) −36.6125 26.8121i −1.32459 0.970027i
\(765\) 0 0
\(766\) −3.15198 + 1.59854i −0.113886 + 0.0577575i
\(767\) 2.97367i 0.107373i
\(768\) 0 0
\(769\) 31.2466 1.12678 0.563390 0.826191i \(-0.309497\pi\)
0.563390 + 0.826191i \(0.309497\pi\)
\(770\) −9.67645 + 4.90744i −0.348715 + 0.176852i
\(771\) 0 0
\(772\) 20.9878 + 15.3698i 0.755367 + 0.553171i
\(773\) 35.2334 1.26726 0.633629 0.773637i \(-0.281565\pi\)
0.633629 + 0.773637i \(0.281565\pi\)
\(774\) 0 0
\(775\) 2.35680 0.0846588
\(776\) 26.2532 + 4.31047i 0.942434 + 0.154737i
\(777\) 0 0
\(778\) −10.9136 21.5194i −0.391272 0.771507i
\(779\) 10.4179 7.31432i 0.373261 0.262063i
\(780\) 0 0
\(781\) 27.5041 0.984173
\(782\) 10.4468 + 20.5989i 0.373576 + 0.736615i
\(783\) 0 0
\(784\) −6.54862 20.6841i −0.233879 0.738719i
\(785\) −27.1492 −0.968995
\(786\) 0 0
\(787\) 26.9557i 0.960866i −0.877032 0.480433i \(-0.840480\pi\)
0.877032 0.480433i \(-0.159520\pi\)
\(788\) 9.31189 + 6.81929i 0.331722 + 0.242927i
\(789\) 0 0
\(790\) 1.90663 + 3.75947i 0.0678347 + 0.133756i
\(791\) −10.2669 −0.365047
\(792\) 0 0
\(793\) 0.687402i 0.0244104i
\(794\) −8.91300 17.5746i −0.316311 0.623699i
\(795\) 0 0
\(796\) 33.0023 + 24.1683i 1.16974 + 0.856621i
\(797\) 30.4003 1.07683 0.538417 0.842679i \(-0.319023\pi\)
0.538417 + 0.842679i \(0.319023\pi\)
\(798\) 0 0
\(799\) 22.4429i 0.793974i
\(800\) 4.52210 + 4.60818i 0.159880 + 0.162924i
\(801\) 0 0
\(802\) −8.96731 17.6817i −0.316647 0.624362i
\(803\) 19.1061 0.674238
\(804\) 0 0
\(805\) 8.24204i 0.290494i
\(806\) 1.04606 0.530510i 0.0368457 0.0186864i
\(807\) 0 0
\(808\) −36.9953 6.07420i −1.30149 0.213690i
\(809\) 2.71694 0.0955225 0.0477612 0.998859i \(-0.484791\pi\)
0.0477612 + 0.998859i \(0.484791\pi\)
\(810\) 0 0
\(811\) 18.3747i 0.645223i 0.946531 + 0.322612i \(0.104561\pi\)
−0.946531 + 0.322612i \(0.895439\pi\)
\(812\) 7.68868 + 5.63058i 0.269820 + 0.197594i
\(813\) 0 0
\(814\) −6.09592 + 3.09156i −0.213662 + 0.108359i
\(815\) 2.50129i 0.0876164i
\(816\) 0 0
\(817\) −5.23471 7.45590i −0.183139 0.260849i
\(818\) −22.2171 43.8076i −0.776804 1.53170i
\(819\) 0 0
\(820\) −6.77855 + 9.25627i −0.236717 + 0.323243i
\(821\) 7.72021i 0.269437i 0.990884 + 0.134719i \(0.0430130\pi\)
−0.990884 + 0.134719i \(0.956987\pi\)
\(822\) 0 0
\(823\) 26.3865i 0.919776i −0.887977 0.459888i \(-0.847890\pi\)
0.887977 0.459888i \(-0.152110\pi\)
\(824\) −3.89458 + 23.7202i −0.135674 + 0.826331i
\(825\) 0 0
\(826\) −11.7233 + 5.94549i −0.407905 + 0.206870i
\(827\) 45.4697i 1.58114i −0.612373 0.790569i \(-0.709785\pi\)
0.612373 0.790569i \(-0.290215\pi\)
\(828\) 0 0
\(829\) −16.8307 −0.584555 −0.292277 0.956334i \(-0.594413\pi\)
−0.292277 + 0.956334i \(0.594413\pi\)
\(830\) −4.46161 8.79736i −0.154865 0.305361i
\(831\) 0 0
\(832\) 3.04440 + 1.02741i 0.105546 + 0.0356190i
\(833\) 26.5041 0.918313
\(834\) 0 0
\(835\) 17.3663i 0.600985i
\(836\) −27.1162 0.541391i −0.937833 0.0187244i
\(837\) 0 0
\(838\) −23.0256 + 11.6775i −0.795405 + 0.403391i
\(839\) 45.7123 1.57816 0.789082 0.614288i \(-0.210557\pi\)
0.789082 + 0.614288i \(0.210557\pi\)
\(840\) 0 0
\(841\) −14.5933 −0.503218
\(842\) 14.6380 7.42372i 0.504460 0.255838i
\(843\) 0 0
\(844\) 19.6562 + 14.3947i 0.676595 + 0.495484i
\(845\) 25.2197i 0.867582i
\(846\) 0 0
\(847\) 1.65875i 0.0569952i
\(848\) 2.21310 + 6.99018i 0.0759981 + 0.240044i
\(849\) 0 0
\(850\) −7.03426 + 3.56744i −0.241273 + 0.122362i
\(851\) 5.19228i 0.177989i
\(852\) 0 0
\(853\) 36.7727i 1.25907i −0.776970 0.629537i \(-0.783244\pi\)
0.776970 0.629537i \(-0.216756\pi\)
\(854\) −2.70998 + 1.37437i −0.0927337 + 0.0470301i
\(855\) 0 0
\(856\) −13.7067 2.25048i −0.468485 0.0769198i
\(857\) 6.42314i 0.219410i −0.993964 0.109705i \(-0.965009\pi\)
0.993964 0.109705i \(-0.0349907\pi\)
\(858\) 0 0
\(859\) 26.0500 0.888816 0.444408 0.895825i \(-0.353414\pi\)
0.444408 + 0.895825i \(0.353414\pi\)
\(860\) 6.62452 + 4.85127i 0.225894 + 0.165427i
\(861\) 0 0
\(862\) 6.19995 3.14432i 0.211171 0.107096i
\(863\) −49.3784 −1.68086 −0.840430 0.541921i \(-0.817697\pi\)
−0.840430 + 0.541921i \(0.817697\pi\)
\(864\) 0 0
\(865\) 31.1319i 1.05851i
\(866\) 15.7897 + 31.1340i 0.536555 + 1.05797i
\(867\) 0 0
\(868\) −4.18292 3.06324i −0.141977 0.103973i
\(869\) −4.72068 −0.160138
\(870\) 0 0
\(871\) 4.10931i 0.139239i
\(872\) −7.41933 + 45.1879i −0.251250 + 1.53025i
\(873\) 0 0
\(874\) 9.68388 18.1853i 0.327562 0.615128i
\(875\) 15.1446 0.511982
\(876\) 0 0
\(877\) −7.69536 −0.259854 −0.129927 0.991524i \(-0.541474\pi\)
−0.129927 + 0.991524i \(0.541474\pi\)
\(878\) 23.2090 11.7705i 0.783266 0.397235i
\(879\) 0 0
\(880\) 23.3047 7.37830i 0.785602 0.248722i
\(881\) 23.1421 0.779678 0.389839 0.920883i \(-0.372531\pi\)
0.389839 + 0.920883i \(0.372531\pi\)
\(882\) 0 0
\(883\) 38.5899 1.29865 0.649327 0.760509i \(-0.275050\pi\)
0.649327 + 0.760509i \(0.275050\pi\)
\(884\) −2.31910 + 3.16679i −0.0779999 + 0.106511i
\(885\) 0 0
\(886\) 8.40244 4.26132i 0.282285 0.143162i
\(887\) −30.4474 −1.02232 −0.511161 0.859485i \(-0.670785\pi\)
−0.511161 + 0.859485i \(0.670785\pi\)
\(888\) 0 0
\(889\) 18.5579i 0.622412i
\(890\) 12.6786 6.42999i 0.424988 0.215534i
\(891\) 0 0
\(892\) −25.9771 + 35.4723i −0.869776 + 1.18770i
\(893\) −16.3849 + 11.5037i −0.548300 + 0.384955i
\(894\) 0 0
\(895\) −22.7698 −0.761112
\(896\) −2.03650 14.0563i −0.0680346 0.469588i
\(897\) 0 0
\(898\) −1.53736 3.03135i −0.0513023 0.101158i
\(899\) −7.83775 −0.261403
\(900\) 0 0
\(901\) −8.95703 −0.298402
\(902\) −5.81144 11.4590i −0.193500 0.381541i
\(903\) 0 0
\(904\) 22.8260 + 3.74776i 0.759180 + 0.124649i
\(905\) 49.7178i 1.65268i
\(906\) 0 0
\(907\) 10.0936i 0.335152i 0.985859 + 0.167576i \(0.0535939\pi\)
−0.985859 + 0.167576i \(0.946406\pi\)
\(908\) −33.8394 24.7813i −1.12300 0.822395i
\(909\) 0 0
\(910\) 1.24923 0.633548i 0.0414114 0.0210019i
\(911\) −49.1193 −1.62739 −0.813697 0.581289i \(-0.802549\pi\)
−0.813697 + 0.581289i \(0.802549\pi\)
\(912\) 0 0
\(913\) 11.0466 0.365591
\(914\) 17.3737 8.81111i 0.574670 0.291445i
\(915\) 0 0
\(916\) −15.4883 11.3424i −0.511748 0.374764i
\(917\) 19.8221i 0.654584i
\(918\) 0 0
\(919\) 10.2322i 0.337530i −0.985656 0.168765i \(-0.946022\pi\)
0.985656 0.168765i \(-0.0539779\pi\)
\(920\) −3.00863 + 18.3242i −0.0991916 + 0.604133i
\(921\) 0 0
\(922\) −3.96194 7.81212i −0.130479 0.257279i
\(923\) −3.55077 −0.116875
\(924\) 0 0
\(925\) 1.77310 0.0582991
\(926\) 20.9011 + 41.2126i 0.686851 + 1.35433i
\(927\) 0 0
\(928\) −15.0386 15.3249i −0.493667 0.503065i
\(929\) 2.58019 0.0846532 0.0423266 0.999104i \(-0.486523\pi\)
0.0423266 + 0.999104i \(0.486523\pi\)
\(930\) 0 0
\(931\) −13.5853 19.3498i −0.445241 0.634166i
\(932\) −11.6021 + 15.8430i −0.380041 + 0.518954i
\(933\) 0 0
\(934\) 29.6858 15.0552i 0.971350 0.492623i
\(935\) 29.8621i 0.976594i
\(936\) 0 0
\(937\) −9.71601 −0.317408 −0.158704 0.987326i \(-0.550732\pi\)
−0.158704 + 0.987326i \(0.550732\pi\)
\(938\) 16.2003 8.21605i 0.528960 0.268263i
\(939\) 0 0
\(940\) 10.6610 14.5579i 0.347724 0.474826i
\(941\) 24.7717 0.807533 0.403766 0.914862i \(-0.367701\pi\)
0.403766 + 0.914862i \(0.367701\pi\)
\(942\) 0 0
\(943\) 9.76031 0.317839
\(944\) 28.2343 8.93900i 0.918947 0.290940i
\(945\) 0 0
\(946\) −8.20094 + 4.15913i −0.266636 + 0.135225i
\(947\) −43.3785 −1.40961 −0.704806 0.709400i \(-0.748966\pi\)
−0.704806 + 0.709400i \(0.748966\pi\)
\(948\) 0 0
\(949\) −2.46659 −0.0800688
\(950\) 6.21006 + 3.30692i 0.201481 + 0.107291i
\(951\) 0 0
\(952\) 17.1214 + 2.81113i 0.554907 + 0.0911093i
\(953\) 1.09947i 0.0356154i 0.999841 + 0.0178077i \(0.00566867\pi\)
−0.999841 + 0.0178077i \(0.994331\pi\)
\(954\) 0 0
\(955\) 44.5713 1.44229
\(956\) 9.22900 + 6.75859i 0.298487 + 0.218588i
\(957\) 0 0
\(958\) −0.840095 1.65649i −0.0271422 0.0535189i
\(959\) 17.5933i 0.568118i
\(960\) 0 0
\(961\) −26.7360 −0.862451
\(962\) 0.786981 0.399120i 0.0253733 0.0128681i
\(963\) 0 0
\(964\) −28.8356 21.1169i −0.928734 0.680130i
\(965\) −25.5501 −0.822486
\(966\) 0 0
\(967\) 18.4508i 0.593339i −0.954980 0.296669i \(-0.904124\pi\)
0.954980 0.296669i \(-0.0958760\pi\)
\(968\) 0.605501 3.68784i 0.0194615 0.118532i
\(969\) 0 0
\(970\) −23.3047 + 11.8190i −0.748269 + 0.379487i
\(971\) 22.0471i 0.707525i 0.935335 + 0.353763i \(0.115098\pi\)
−0.935335 + 0.353763i \(0.884902\pi\)
\(972\) 0 0
\(973\) 5.48937i 0.175981i
\(974\) −33.3500 + 16.9135i −1.06860 + 0.541944i
\(975\) 0 0
\(976\) 6.52671 2.06636i 0.208915 0.0661427i
\(977\) 7.59567i 0.243007i 0.992591 + 0.121503i \(0.0387716\pi\)
−0.992591 + 0.121503i \(0.961228\pi\)
\(978\) 0 0
\(979\) 15.9202i 0.508813i
\(980\) 17.1922 + 12.5902i 0.549185 + 0.402179i
\(981\) 0 0
\(982\) −31.6870 + 16.0701i −1.01117 + 0.512819i
\(983\) −2.75811 −0.0879699 −0.0439850 0.999032i \(-0.514005\pi\)
−0.0439850 + 0.999032i \(0.514005\pi\)
\(984\) 0 0
\(985\) −11.3361 −0.361198
\(986\) 23.3930 11.8638i 0.744986 0.377822i
\(987\) 0 0
\(988\) 3.50069 + 0.0698934i 0.111372 + 0.00222360i
\(989\) 6.98525i 0.222118i
\(990\) 0 0
\(991\) 51.8481 1.64701 0.823504 0.567310i \(-0.192016\pi\)
0.823504 + 0.567310i \(0.192016\pi\)
\(992\) 8.18156 + 8.33730i 0.259765 + 0.264710i
\(993\) 0 0
\(994\) 7.09931 + 13.9984i 0.225177 + 0.444002i
\(995\) −40.1763 −1.27367
\(996\) 0 0
\(997\) 39.1940i 1.24129i 0.784094 + 0.620643i \(0.213128\pi\)
−0.784094 + 0.620643i \(0.786872\pi\)
\(998\) 11.7359 5.95188i 0.371493 0.188403i
\(999\) 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 1368.2.e.f.379.7 yes 24
3.2 odd 2 inner 1368.2.e.f.379.17 yes 24
4.3 odd 2 5472.2.e.f.5167.12 24
8.3 odd 2 inner 1368.2.e.f.379.20 yes 24
8.5 even 2 5472.2.e.f.5167.17 24
12.11 even 2 5472.2.e.f.5167.9 24
19.18 odd 2 inner 1368.2.e.f.379.18 yes 24
24.5 odd 2 5472.2.e.f.5167.20 24
24.11 even 2 inner 1368.2.e.f.379.6 yes 24
57.56 even 2 inner 1368.2.e.f.379.8 yes 24
76.75 even 2 5472.2.e.f.5167.18 24
152.37 odd 2 5472.2.e.f.5167.11 24
152.75 even 2 inner 1368.2.e.f.379.5 24
228.227 odd 2 5472.2.e.f.5167.19 24
456.227 odd 2 inner 1368.2.e.f.379.19 yes 24
456.341 even 2 5472.2.e.f.5167.10 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.e.f.379.5 24 152.75 even 2 inner
1368.2.e.f.379.6 yes 24 24.11 even 2 inner
1368.2.e.f.379.7 yes 24 1.1 even 1 trivial
1368.2.e.f.379.8 yes 24 57.56 even 2 inner
1368.2.e.f.379.17 yes 24 3.2 odd 2 inner
1368.2.e.f.379.18 yes 24 19.18 odd 2 inner
1368.2.e.f.379.19 yes 24 456.227 odd 2 inner
1368.2.e.f.379.20 yes 24 8.3 odd 2 inner
5472.2.e.f.5167.9 24 12.11 even 2
5472.2.e.f.5167.10 24 456.341 even 2
5472.2.e.f.5167.11 24 152.37 odd 2
5472.2.e.f.5167.12 24 4.3 odd 2
5472.2.e.f.5167.17 24 8.5 even 2
5472.2.e.f.5167.18 24 76.75 even 2
5472.2.e.f.5167.19 24 228.227 odd 2
5472.2.e.f.5167.20 24 24.5 odd 2