Properties

Label 1368.2.e.f.379.21
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 379.21
Character \(\chi\) \(=\) 1368.379
Dual form 1368.2.e.f.379.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39298 - 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} +3.10261i q^{5} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +O(q^{10})\) \(q+(1.39298 - 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} +3.10261i q^{5} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +(0.757512 + 4.32187i) q^{10} -2.65647 q^{11} -5.10176 q^{13} +(1.06083 + 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} +3.48821 q^{17} +(1.86464 - 3.93994i) q^{19} +(2.11040 + 5.83533i) q^{20} +(-3.70041 + 0.648586i) q^{22} +5.31965i q^{23} -4.62620 q^{25} +(-7.10664 + 1.24561i) q^{26} +(2.95543 + 8.17189i) q^{28} -7.98077 q^{29} -3.19471 q^{31} +(3.65824 - 4.31478i) q^{32} +(4.85901 - 0.851658i) q^{34} -13.4807 q^{35} +4.57585 q^{37} +(1.63546 - 5.94351i) q^{38} +(4.36445 + 7.61322i) q^{40} +4.51800i q^{41} +6.28467 q^{43} +(-4.99624 + 1.80693i) q^{44} +(1.29881 + 7.41015i) q^{46} +7.68246i q^{47} -11.8786 q^{49} +(-6.44419 + 1.12950i) q^{50} +(-9.59527 + 3.47021i) q^{52} +9.81525 q^{53} -8.24201i q^{55} +(6.11205 + 10.6617i) q^{56} +(-11.1170 + 1.94853i) q^{58} +4.94021i q^{59} -11.9988i q^{61} +(-4.45016 + 0.779998i) q^{62} +(4.04238 - 6.90356i) q^{64} -15.8288i q^{65} +0.406143i q^{67} +(6.56056 - 2.37268i) q^{68} +(-18.7783 + 3.29135i) q^{70} +2.40885 q^{71} +0.373802 q^{73} +(6.37406 - 1.11721i) q^{74} +(0.827031 - 8.67848i) q^{76} -11.5422i q^{77} +17.2835 q^{79} +(7.93838 + 9.53946i) q^{80} +(1.10308 + 6.29348i) q^{82} +12.2894 q^{83} +10.8226i q^{85} +(8.75441 - 1.53442i) q^{86} +(-6.51849 + 3.73687i) q^{88} -1.95322i q^{89} -22.1669i q^{91} +(3.61842 + 10.0051i) q^{92} +(1.87570 + 10.7015i) q^{94} +(12.2241 + 5.78526i) q^{95} -4.87939i q^{97} +(-16.5466 + 2.90019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39298 0.244153i 0.984985 0.172642i
\(3\) 0 0
\(4\) 1.88078 0.680200i 0.940389 0.340100i
\(5\) 3.10261i 1.38753i 0.720201 + 0.693765i \(0.244049\pi\)
−0.720201 + 0.693765i \(0.755951\pi\)
\(6\) 0 0
\(7\) 4.34495i 1.64224i 0.570758 + 0.821118i \(0.306650\pi\)
−0.570758 + 0.821118i \(0.693350\pi\)
\(8\) 2.45381 1.40670i 0.867553 0.497344i
\(9\) 0 0
\(10\) 0.757512 + 4.32187i 0.239546 + 1.36670i
\(11\) −2.65647 −0.800957 −0.400479 0.916306i \(-0.631156\pi\)
−0.400479 + 0.916306i \(0.631156\pi\)
\(12\) 0 0
\(13\) −5.10176 −1.41497 −0.707486 0.706727i \(-0.750171\pi\)
−0.707486 + 0.706727i \(0.750171\pi\)
\(14\) 1.06083 + 6.05242i 0.283520 + 1.61758i
\(15\) 0 0
\(16\) 3.07466 2.55861i 0.768664 0.639653i
\(17\) 3.48821 0.846016 0.423008 0.906126i \(-0.360974\pi\)
0.423008 + 0.906126i \(0.360974\pi\)
\(18\) 0 0
\(19\) 1.86464 3.93994i 0.427778 0.903884i
\(20\) 2.11040 + 5.83533i 0.471899 + 1.30482i
\(21\) 0 0
\(22\) −3.70041 + 0.648586i −0.788930 + 0.138279i
\(23\) 5.31965i 1.10922i 0.832110 + 0.554611i \(0.187133\pi\)
−0.832110 + 0.554611i \(0.812867\pi\)
\(24\) 0 0
\(25\) −4.62620 −0.925240
\(26\) −7.10664 + 1.24561i −1.39373 + 0.244284i
\(27\) 0 0
\(28\) 2.95543 + 8.17189i 0.558525 + 1.54434i
\(29\) −7.98077 −1.48199 −0.740996 0.671510i \(-0.765646\pi\)
−0.740996 + 0.671510i \(0.765646\pi\)
\(30\) 0 0
\(31\) −3.19471 −0.573787 −0.286893 0.957963i \(-0.592623\pi\)
−0.286893 + 0.957963i \(0.592623\pi\)
\(32\) 3.65824 4.31478i 0.646691 0.762752i
\(33\) 0 0
\(34\) 4.85901 0.851658i 0.833313 0.146058i
\(35\) −13.4807 −2.27865
\(36\) 0 0
\(37\) 4.57585 0.752265 0.376132 0.926566i \(-0.377254\pi\)
0.376132 + 0.926566i \(0.377254\pi\)
\(38\) 1.63546 5.94351i 0.265306 0.964164i
\(39\) 0 0
\(40\) 4.36445 + 7.61322i 0.690080 + 1.20376i
\(41\) 4.51800i 0.705593i 0.935700 + 0.352797i \(0.114769\pi\)
−0.935700 + 0.352797i \(0.885231\pi\)
\(42\) 0 0
\(43\) 6.28467 0.958403 0.479202 0.877705i \(-0.340926\pi\)
0.479202 + 0.877705i \(0.340926\pi\)
\(44\) −4.99624 + 1.80693i −0.753211 + 0.272405i
\(45\) 0 0
\(46\) 1.29881 + 7.41015i 0.191499 + 1.09257i
\(47\) 7.68246i 1.12060i 0.828289 + 0.560301i \(0.189315\pi\)
−0.828289 + 0.560301i \(0.810685\pi\)
\(48\) 0 0
\(49\) −11.8786 −1.69694
\(50\) −6.44419 + 1.12950i −0.911347 + 0.159735i
\(51\) 0 0
\(52\) −9.59527 + 3.47021i −1.33062 + 0.481232i
\(53\) 9.81525 1.34823 0.674114 0.738627i \(-0.264526\pi\)
0.674114 + 0.738627i \(0.264526\pi\)
\(54\) 0 0
\(55\) 8.24201i 1.11135i
\(56\) 6.11205 + 10.6617i 0.816757 + 1.42473i
\(57\) 0 0
\(58\) −11.1170 + 1.94853i −1.45974 + 0.255854i
\(59\) 4.94021i 0.643161i 0.946882 + 0.321580i \(0.104214\pi\)
−0.946882 + 0.321580i \(0.895786\pi\)
\(60\) 0 0
\(61\) 11.9988i 1.53629i −0.640274 0.768146i \(-0.721179\pi\)
0.640274 0.768146i \(-0.278821\pi\)
\(62\) −4.45016 + 0.779998i −0.565171 + 0.0990598i
\(63\) 0 0
\(64\) 4.04238 6.90356i 0.505298 0.862945i
\(65\) 15.8288i 1.96332i
\(66\) 0 0
\(67\) 0.406143i 0.0496183i 0.999692 + 0.0248092i \(0.00789781\pi\)
−0.999692 + 0.0248092i \(0.992102\pi\)
\(68\) 6.56056 2.37268i 0.795584 0.287730i
\(69\) 0 0
\(70\) −18.7783 + 3.29135i −2.24444 + 0.393392i
\(71\) 2.40885 0.285878 0.142939 0.989731i \(-0.454345\pi\)
0.142939 + 0.989731i \(0.454345\pi\)
\(72\) 0 0
\(73\) 0.373802 0.0437502 0.0218751 0.999761i \(-0.493036\pi\)
0.0218751 + 0.999761i \(0.493036\pi\)
\(74\) 6.37406 1.11721i 0.740969 0.129873i
\(75\) 0 0
\(76\) 0.827031 8.67848i 0.0948670 0.995490i
\(77\) 11.5422i 1.31536i
\(78\) 0 0
\(79\) 17.2835 1.94455 0.972273 0.233850i \(-0.0751324\pi\)
0.972273 + 0.233850i \(0.0751324\pi\)
\(80\) 7.93838 + 9.53946i 0.887537 + 1.06654i
\(81\) 0 0
\(82\) 1.10308 + 6.29348i 0.121815 + 0.694998i
\(83\) 12.2894 1.34893 0.674467 0.738305i \(-0.264373\pi\)
0.674467 + 0.738305i \(0.264373\pi\)
\(84\) 0 0
\(85\) 10.8226i 1.17387i
\(86\) 8.75441 1.53442i 0.944013 0.165461i
\(87\) 0 0
\(88\) −6.51849 + 3.73687i −0.694873 + 0.398351i
\(89\) 1.95322i 0.207041i −0.994627 0.103521i \(-0.966989\pi\)
0.994627 0.103521i \(-0.0330108\pi\)
\(90\) 0 0
\(91\) 22.1669i 2.32372i
\(92\) 3.61842 + 10.0051i 0.377247 + 1.04310i
\(93\) 0 0
\(94\) 1.87570 + 10.7015i 0.193463 + 1.10378i
\(95\) 12.2241 + 5.78526i 1.25417 + 0.593555i
\(96\) 0 0
\(97\) 4.87939i 0.495427i −0.968833 0.247713i \(-0.920321\pi\)
0.968833 0.247713i \(-0.0796791\pi\)
\(98\) −16.5466 + 2.90019i −1.67146 + 0.292964i
\(99\) 0 0
\(100\) −8.70085 + 3.14674i −0.870085 + 0.314674i
\(101\) 2.87407i 0.285981i −0.989724 0.142990i \(-0.954328\pi\)
0.989724 0.142990i \(-0.0456718\pi\)
\(102\) 0 0
\(103\) −10.6359 −1.04799 −0.523995 0.851721i \(-0.675559\pi\)
−0.523995 + 0.851721i \(0.675559\pi\)
\(104\) −12.5187 + 7.17665i −1.22756 + 0.703728i
\(105\) 0 0
\(106\) 13.6724 2.39642i 1.32798 0.232761i
\(107\) 10.7564i 1.03986i 0.854210 + 0.519928i \(0.174041\pi\)
−0.854210 + 0.519928i \(0.825959\pi\)
\(108\) 0 0
\(109\) 13.0593 1.25085 0.625425 0.780284i \(-0.284926\pi\)
0.625425 + 0.780284i \(0.284926\pi\)
\(110\) −2.01231 11.4809i −0.191866 1.09466i
\(111\) 0 0
\(112\) 11.1170 + 13.3592i 1.05046 + 1.26233i
\(113\) 14.9843i 1.40961i 0.709402 + 0.704804i \(0.248965\pi\)
−0.709402 + 0.704804i \(0.751035\pi\)
\(114\) 0 0
\(115\) −16.5048 −1.53908
\(116\) −15.0101 + 5.42852i −1.39365 + 0.504025i
\(117\) 0 0
\(118\) 1.20617 + 6.88161i 0.111037 + 0.633503i
\(119\) 15.1561i 1.38936i
\(120\) 0 0
\(121\) −3.94315 −0.358468
\(122\) −2.92955 16.7141i −0.265229 1.51322i
\(123\) 0 0
\(124\) −6.00854 + 2.17304i −0.539583 + 0.195145i
\(125\) 1.15976i 0.103732i
\(126\) 0 0
\(127\) 17.4704 1.55025 0.775126 0.631807i \(-0.217686\pi\)
0.775126 + 0.631807i \(0.217686\pi\)
\(128\) 3.94542 10.6035i 0.348730 0.937223i
\(129\) 0 0
\(130\) −3.86464 22.0491i −0.338951 1.93384i
\(131\) 5.78511 0.505447 0.252724 0.967538i \(-0.418674\pi\)
0.252724 + 0.967538i \(0.418674\pi\)
\(132\) 0 0
\(133\) 17.1188 + 8.10177i 1.48439 + 0.702513i
\(134\) 0.0991612 + 0.565749i 0.00856622 + 0.0488733i
\(135\) 0 0
\(136\) 8.55942 4.90688i 0.733964 0.420761i
\(137\) 0.359578 0.0307208 0.0153604 0.999882i \(-0.495110\pi\)
0.0153604 + 0.999882i \(0.495110\pi\)
\(138\) 0 0
\(139\) 2.96772 0.251719 0.125860 0.992048i \(-0.459831\pi\)
0.125860 + 0.992048i \(0.459831\pi\)
\(140\) −25.3542 + 9.16957i −2.14282 + 0.774970i
\(141\) 0 0
\(142\) 3.35548 0.588129i 0.281586 0.0493547i
\(143\) 13.5527 1.13333
\(144\) 0 0
\(145\) 24.7612i 2.05631i
\(146\) 0.520698 0.0912649i 0.0430933 0.00755313i
\(147\) 0 0
\(148\) 8.60616 3.11249i 0.707422 0.255845i
\(149\) 9.69069i 0.793892i −0.917842 0.396946i \(-0.870070\pi\)
0.917842 0.396946i \(-0.129930\pi\)
\(150\) 0 0
\(151\) −9.32599 −0.758938 −0.379469 0.925204i \(-0.623893\pi\)
−0.379469 + 0.925204i \(0.623893\pi\)
\(152\) −0.966841 12.2909i −0.0784211 0.996920i
\(153\) 0 0
\(154\) −2.81808 16.0781i −0.227087 1.29561i
\(155\) 9.91194i 0.796146i
\(156\) 0 0
\(157\) 9.86616i 0.787405i −0.919238 0.393703i \(-0.871194\pi\)
0.919238 0.393703i \(-0.128806\pi\)
\(158\) 24.0755 4.21982i 1.91535 0.335711i
\(159\) 0 0
\(160\) 13.3871 + 11.3501i 1.05834 + 0.897303i
\(161\) −23.1136 −1.82161
\(162\) 0 0
\(163\) −1.52311 −0.119300 −0.0596498 0.998219i \(-0.518998\pi\)
−0.0596498 + 0.998219i \(0.518998\pi\)
\(164\) 3.07314 + 8.49736i 0.239972 + 0.663532i
\(165\) 0 0
\(166\) 17.1188 3.00049i 1.32868 0.232883i
\(167\) 2.40885 0.186403 0.0932013 0.995647i \(-0.470290\pi\)
0.0932013 + 0.995647i \(0.470290\pi\)
\(168\) 0 0
\(169\) 13.0279 1.00215
\(170\) 2.64236 + 15.0756i 0.202660 + 1.15625i
\(171\) 0 0
\(172\) 11.8201 4.27483i 0.901272 0.325953i
\(173\) −14.6330 −1.11252 −0.556261 0.831007i \(-0.687765\pi\)
−0.556261 + 0.831007i \(0.687765\pi\)
\(174\) 0 0
\(175\) 20.1006i 1.51946i
\(176\) −8.16774 + 6.79688i −0.615667 + 0.512334i
\(177\) 0 0
\(178\) −0.476886 2.72080i −0.0357441 0.203933i
\(179\) 4.70734i 0.351843i 0.984404 + 0.175922i \(0.0562906\pi\)
−0.984404 + 0.175922i \(0.943709\pi\)
\(180\) 0 0
\(181\) −18.2196 −1.35425 −0.677124 0.735869i \(-0.736774\pi\)
−0.677124 + 0.735869i \(0.736774\pi\)
\(182\) −5.41211 30.8780i −0.401172 2.28883i
\(183\) 0 0
\(184\) 7.48315 + 13.0534i 0.551665 + 0.962310i
\(185\) 14.1971i 1.04379i
\(186\) 0 0
\(187\) −9.26635 −0.677623
\(188\) 5.22561 + 14.4490i 0.381117 + 1.05380i
\(189\) 0 0
\(190\) 18.4404 + 5.07419i 1.33781 + 0.368120i
\(191\) 9.07076i 0.656337i −0.944619 0.328169i \(-0.893569\pi\)
0.944619 0.328169i \(-0.106431\pi\)
\(192\) 0 0
\(193\) 25.5735i 1.84082i −0.390953 0.920411i \(-0.627855\pi\)
0.390953 0.920411i \(-0.372145\pi\)
\(194\) −1.19132 6.79688i −0.0855316 0.487988i
\(195\) 0 0
\(196\) −22.3410 + 8.07982i −1.59579 + 0.577130i
\(197\) 24.0614i 1.71430i −0.515066 0.857151i \(-0.672233\pi\)
0.515066 0.857151i \(-0.327767\pi\)
\(198\) 0 0
\(199\) 17.3002i 1.22638i 0.789936 + 0.613189i \(0.210114\pi\)
−0.789936 + 0.613189i \(0.789886\pi\)
\(200\) −11.3518 + 6.50768i −0.802695 + 0.460163i
\(201\) 0 0
\(202\) −0.701713 4.00352i −0.0493724 0.281687i
\(203\) 34.6760i 2.43378i
\(204\) 0 0
\(205\) −14.0176 −0.979032
\(206\) −14.8156 + 2.59680i −1.03225 + 0.180927i
\(207\) 0 0
\(208\) −15.6861 + 13.0534i −1.08764 + 0.905091i
\(209\) −4.95337 + 10.4663i −0.342632 + 0.723972i
\(210\) 0 0
\(211\) 20.2880i 1.39668i −0.715765 0.698341i \(-0.753922\pi\)
0.715765 0.698341i \(-0.246078\pi\)
\(212\) 18.4603 6.67633i 1.26786 0.458532i
\(213\) 0 0
\(214\) 2.62620 + 14.9834i 0.179523 + 1.02424i
\(215\) 19.4989i 1.32981i
\(216\) 0 0
\(217\) 13.8809i 0.942294i
\(218\) 18.1913 3.18846i 1.23207 0.215950i
\(219\) 0 0
\(220\) −5.60621 15.5014i −0.377971 1.04510i
\(221\) −17.7960 −1.19709
\(222\) 0 0
\(223\) 1.62662 0.108927 0.0544633 0.998516i \(-0.482655\pi\)
0.0544633 + 0.998516i \(0.482655\pi\)
\(224\) 18.7475 + 15.8949i 1.25262 + 1.06202i
\(225\) 0 0
\(226\) 3.65847 + 20.8729i 0.243358 + 1.38844i
\(227\) 19.8674i 1.31865i 0.751860 + 0.659323i \(0.229157\pi\)
−0.751860 + 0.659323i \(0.770843\pi\)
\(228\) 0 0
\(229\) 10.8226i 0.715176i −0.933880 0.357588i \(-0.883599\pi\)
0.933880 0.357588i \(-0.116401\pi\)
\(230\) −22.9908 + 4.02970i −1.51597 + 0.265710i
\(231\) 0 0
\(232\) −19.5833 + 11.2266i −1.28571 + 0.737060i
\(233\) 23.4732 1.53778 0.768889 0.639382i \(-0.220810\pi\)
0.768889 + 0.639382i \(0.220810\pi\)
\(234\) 0 0
\(235\) −23.8357 −1.55487
\(236\) 3.36033 + 9.29144i 0.218739 + 0.604821i
\(237\) 0 0
\(238\) 3.70041 + 21.1121i 0.239862 + 1.36850i
\(239\) 26.0413i 1.68447i 0.539108 + 0.842237i \(0.318761\pi\)
−0.539108 + 0.842237i \(0.681239\pi\)
\(240\) 0 0
\(241\) 14.6931i 0.946468i 0.880937 + 0.473234i \(0.156914\pi\)
−0.880937 + 0.473234i \(0.843086\pi\)
\(242\) −5.49272 + 0.962731i −0.353085 + 0.0618867i
\(243\) 0 0
\(244\) −8.16160 22.5671i −0.522493 1.44471i
\(245\) 36.8547i 2.35456i
\(246\) 0 0
\(247\) −9.51294 + 20.1006i −0.605294 + 1.27897i
\(248\) −7.83921 + 4.49400i −0.497791 + 0.285369i
\(249\) 0 0
\(250\) 0.283159 + 1.61552i 0.0179086 + 0.102175i
\(251\) −9.63290 −0.608023 −0.304012 0.952668i \(-0.598326\pi\)
−0.304012 + 0.952668i \(0.598326\pi\)
\(252\) 0 0
\(253\) 14.1315i 0.888440i
\(254\) 24.3360 4.26546i 1.52697 0.267639i
\(255\) 0 0
\(256\) 2.90702 15.7337i 0.181689 0.983356i
\(257\) 21.5127i 1.34193i −0.741491 0.670963i \(-0.765881\pi\)
0.741491 0.670963i \(-0.234119\pi\)
\(258\) 0 0
\(259\) 19.8818i 1.23540i
\(260\) −10.7667 29.7704i −0.667724 1.84628i
\(261\) 0 0
\(262\) 8.05853 1.41245i 0.497858 0.0872616i
\(263\) 3.50520i 0.216140i −0.994143 0.108070i \(-0.965533\pi\)
0.994143 0.108070i \(-0.0344670\pi\)
\(264\) 0 0
\(265\) 30.4529i 1.87071i
\(266\) 25.8242 + 7.10598i 1.58339 + 0.435696i
\(267\) 0 0
\(268\) 0.276259 + 0.763866i 0.0168752 + 0.0466605i
\(269\) −3.48912 −0.212736 −0.106368 0.994327i \(-0.533922\pi\)
−0.106368 + 0.994327i \(0.533922\pi\)
\(270\) 0 0
\(271\) 7.14536i 0.434050i −0.976166 0.217025i \(-0.930365\pi\)
0.976166 0.217025i \(-0.0696353\pi\)
\(272\) 10.7251 8.92498i 0.650302 0.541156i
\(273\) 0 0
\(274\) 0.500884 0.0877921i 0.0302595 0.00530371i
\(275\) 12.2894 0.741077
\(276\) 0 0
\(277\) 5.38097i 0.323311i 0.986847 + 0.161656i \(0.0516834\pi\)
−0.986847 + 0.161656i \(0.948317\pi\)
\(278\) 4.13398 0.724579i 0.247939 0.0434574i
\(279\) 0 0
\(280\) −33.0791 + 18.9633i −1.97685 + 1.13327i
\(281\) 22.9687i 1.37020i −0.728450 0.685099i \(-0.759759\pi\)
0.728450 0.685099i \(-0.240241\pi\)
\(282\) 0 0
\(283\) −6.19221 −0.368089 −0.184044 0.982918i \(-0.558919\pi\)
−0.184044 + 0.982918i \(0.558919\pi\)
\(284\) 4.53052 1.63850i 0.268837 0.0972272i
\(285\) 0 0
\(286\) 18.8786 3.30893i 1.11631 0.195661i
\(287\) −19.6305 −1.15875
\(288\) 0 0
\(289\) −4.83237 −0.284257
\(290\) −6.04553 34.4918i −0.355006 2.02543i
\(291\) 0 0
\(292\) 0.703039 0.254260i 0.0411422 0.0148794i
\(293\) −1.32858 −0.0776166 −0.0388083 0.999247i \(-0.512356\pi\)
−0.0388083 + 0.999247i \(0.512356\pi\)
\(294\) 0 0
\(295\) −15.3276 −0.892405
\(296\) 11.2283 6.43685i 0.652630 0.374134i
\(297\) 0 0
\(298\) −2.36601 13.4989i −0.137059 0.781971i
\(299\) 27.1395i 1.56952i
\(300\) 0 0
\(301\) 27.3066i 1.57393i
\(302\) −12.9909 + 2.27697i −0.747543 + 0.131025i
\(303\) 0 0
\(304\) −4.34764 16.8848i −0.249354 0.968412i
\(305\) 37.2277 2.13165
\(306\) 0 0
\(307\) 12.4081i 0.708167i 0.935214 + 0.354084i \(0.115207\pi\)
−0.935214 + 0.354084i \(0.884793\pi\)
\(308\) −7.85104 21.7084i −0.447354 1.23695i
\(309\) 0 0
\(310\) −2.42003 13.8071i −0.137449 0.784192i
\(311\) 2.11690i 0.120038i 0.998197 + 0.0600191i \(0.0191162\pi\)
−0.998197 + 0.0600191i \(0.980884\pi\)
\(312\) 0 0
\(313\) 31.0741 1.75641 0.878207 0.478281i \(-0.158740\pi\)
0.878207 + 0.478281i \(0.158740\pi\)
\(314\) −2.40885 13.7433i −0.135939 0.775582i
\(315\) 0 0
\(316\) 32.5064 11.7562i 1.82863 0.661340i
\(317\) −32.4290 −1.82139 −0.910696 0.413077i \(-0.864454\pi\)
−0.910696 + 0.413077i \(0.864454\pi\)
\(318\) 0 0
\(319\) 21.2007 1.18701
\(320\) 21.4191 + 12.5419i 1.19736 + 0.701116i
\(321\) 0 0
\(322\) −32.1967 + 5.64325i −1.79425 + 0.314486i
\(323\) 6.50427 13.7433i 0.361907 0.764700i
\(324\) 0 0
\(325\) 23.6017 1.30919
\(326\) −2.12167 + 0.371873i −0.117508 + 0.0205961i
\(327\) 0 0
\(328\) 6.35548 + 11.0863i 0.350923 + 0.612140i
\(329\) −33.3799 −1.84029
\(330\) 0 0
\(331\) 22.1669i 1.21840i 0.793016 + 0.609201i \(0.208510\pi\)
−0.793016 + 0.609201i \(0.791490\pi\)
\(332\) 23.1136 8.35923i 1.26852 0.458772i
\(333\) 0 0
\(334\) 3.35548 0.588129i 0.183604 0.0321810i
\(335\) −1.26011 −0.0688469
\(336\) 0 0
\(337\) 9.00147i 0.490341i 0.969480 + 0.245171i \(0.0788440\pi\)
−0.969480 + 0.245171i \(0.921156\pi\)
\(338\) 18.1476 3.18080i 0.987099 0.173013i
\(339\) 0 0
\(340\) 7.36151 + 20.3549i 0.399234 + 1.10390i
\(341\) 8.48666 0.459579
\(342\) 0 0
\(343\) 21.1972i 1.14454i
\(344\) 15.4214 8.84066i 0.831466 0.476656i
\(345\) 0 0
\(346\) −20.3834 + 3.57268i −1.09582 + 0.192068i
\(347\) −9.63290 −0.517121 −0.258561 0.965995i \(-0.583248\pi\)
−0.258561 + 0.965995i \(0.583248\pi\)
\(348\) 0 0
\(349\) 23.0412i 1.23337i 0.787210 + 0.616685i \(0.211525\pi\)
−0.787210 + 0.616685i \(0.788475\pi\)
\(350\) −4.90762 27.9997i −0.262323 1.49665i
\(351\) 0 0
\(352\) −9.71801 + 11.4621i −0.517972 + 0.610932i
\(353\) 23.8328 1.26849 0.634245 0.773132i \(-0.281311\pi\)
0.634245 + 0.773132i \(0.281311\pi\)
\(354\) 0 0
\(355\) 7.47373i 0.396665i
\(356\) −1.32858 3.67358i −0.0704148 0.194699i
\(357\) 0 0
\(358\) 1.14931 + 6.55723i 0.0607430 + 0.346560i
\(359\) 21.8641i 1.15394i −0.816765 0.576971i \(-0.804235\pi\)
0.816765 0.576971i \(-0.195765\pi\)
\(360\) 0 0
\(361\) −12.0462 14.6931i −0.634012 0.773323i
\(362\) −25.3794 + 4.44836i −1.33391 + 0.233801i
\(363\) 0 0
\(364\) −15.0779 41.6910i −0.790297 2.18520i
\(365\) 1.15976i 0.0607047i
\(366\) 0 0
\(367\) 33.0558i 1.72550i −0.505630 0.862751i \(-0.668740\pi\)
0.505630 0.862751i \(-0.331260\pi\)
\(368\) 13.6109 + 16.3561i 0.709517 + 0.852620i
\(369\) 0 0
\(370\) 3.46626 + 19.7762i 0.180202 + 1.02812i
\(371\) 42.6468i 2.21411i
\(372\) 0 0
\(373\) −9.95803 −0.515607 −0.257804 0.966197i \(-0.582999\pi\)
−0.257804 + 0.966197i \(0.582999\pi\)
\(374\) −12.9078 + 2.26241i −0.667448 + 0.116986i
\(375\) 0 0
\(376\) 10.8069 + 18.8513i 0.557325 + 0.972182i
\(377\) 40.7159 2.09698
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 26.9260 + 2.56596i 1.38127 + 0.131631i
\(381\) 0 0
\(382\) −2.21465 12.6354i −0.113312 0.646482i
\(383\) −27.1054 −1.38502 −0.692510 0.721409i \(-0.743495\pi\)
−0.692510 + 0.721409i \(0.743495\pi\)
\(384\) 0 0
\(385\) 35.8111 1.82510
\(386\) −6.24385 35.6233i −0.317804 1.81318i
\(387\) 0 0
\(388\) −3.31896 9.17705i −0.168495 0.465894i
\(389\) 30.0380i 1.52299i −0.648171 0.761495i \(-0.724466\pi\)
0.648171 0.761495i \(-0.275534\pi\)
\(390\) 0 0
\(391\) 18.5561i 0.938420i
\(392\) −29.1478 + 16.7096i −1.47219 + 0.843964i
\(393\) 0 0
\(394\) −5.87465 33.5170i −0.295961 1.68856i
\(395\) 53.6240i 2.69812i
\(396\) 0 0
\(397\) 28.4828i 1.42951i −0.699373 0.714756i \(-0.746538\pi\)
0.699373 0.714756i \(-0.253462\pi\)
\(398\) 4.22389 + 24.0988i 0.211725 + 1.20796i
\(399\) 0 0
\(400\) −14.2240 + 11.8366i −0.711198 + 0.591832i
\(401\) 5.94834i 0.297046i −0.988909 0.148523i \(-0.952548\pi\)
0.988909 0.148523i \(-0.0474519\pi\)
\(402\) 0 0
\(403\) 16.2986 0.811892
\(404\) −1.95494 5.40549i −0.0972621 0.268933i
\(405\) 0 0
\(406\) −8.46626 48.3030i −0.420173 2.39724i
\(407\) −12.1556 −0.602532
\(408\) 0 0
\(409\) 14.9475i 0.739105i 0.929210 + 0.369552i \(0.120489\pi\)
−0.929210 + 0.369552i \(0.879511\pi\)
\(410\) −19.5262 + 3.42244i −0.964331 + 0.169022i
\(411\) 0 0
\(412\) −20.0039 + 7.23457i −0.985519 + 0.356422i
\(413\) −21.4650 −1.05622
\(414\) 0 0
\(415\) 38.1292i 1.87169i
\(416\) −18.6634 + 22.0129i −0.915050 + 1.07927i
\(417\) 0 0
\(418\) −4.34455 + 15.7888i −0.212499 + 0.772254i
\(419\) −7.69558 −0.375954 −0.187977 0.982173i \(-0.560193\pi\)
−0.187977 + 0.982173i \(0.560193\pi\)
\(420\) 0 0
\(421\) 1.48425 0.0723379 0.0361689 0.999346i \(-0.488485\pi\)
0.0361689 + 0.999346i \(0.488485\pi\)
\(422\) −4.95337 28.2607i −0.241126 1.37571i
\(423\) 0 0
\(424\) 24.0848 13.8071i 1.16966 0.670533i
\(425\) −16.1372 −0.782768
\(426\) 0 0
\(427\) 52.1343 2.52296
\(428\) 7.31648 + 20.2303i 0.353655 + 0.977870i
\(429\) 0 0
\(430\) 4.76071 + 27.1615i 0.229582 + 1.30985i
\(431\) 33.1832 1.59838 0.799189 0.601080i \(-0.205263\pi\)
0.799189 + 0.601080i \(0.205263\pi\)
\(432\) 0 0
\(433\) 23.6946i 1.13869i 0.822099 + 0.569345i \(0.192803\pi\)
−0.822099 + 0.569345i \(0.807197\pi\)
\(434\) −3.38905 19.3357i −0.162680 0.928145i
\(435\) 0 0
\(436\) 24.5616 8.88291i 1.17629 0.425414i
\(437\) 20.9591 + 9.91923i 1.00261 + 0.474501i
\(438\) 0 0
\(439\) −18.8516 −0.899737 −0.449869 0.893095i \(-0.648529\pi\)
−0.449869 + 0.893095i \(0.648529\pi\)
\(440\) −11.5940 20.2243i −0.552724 0.964157i
\(441\) 0 0
\(442\) −24.7895 + 4.34495i −1.17911 + 0.206668i
\(443\) −9.63290 −0.457673 −0.228836 0.973465i \(-0.573492\pi\)
−0.228836 + 0.973465i \(0.573492\pi\)
\(444\) 0 0
\(445\) 6.06010 0.287276
\(446\) 2.26585 0.397145i 0.107291 0.0188053i
\(447\) 0 0
\(448\) 29.9956 + 17.5639i 1.41716 + 0.829818i
\(449\) 19.1808i 0.905198i −0.891714 0.452599i \(-0.850497\pi\)
0.891714 0.452599i \(-0.149503\pi\)
\(450\) 0 0
\(451\) 12.0020i 0.565150i
\(452\) 10.1924 + 28.1822i 0.479408 + 1.32558i
\(453\) 0 0
\(454\) 4.85069 + 27.6749i 0.227654 + 1.29885i
\(455\) 68.7752 3.22423
\(456\) 0 0
\(457\) −21.9894 −1.02862 −0.514310 0.857604i \(-0.671952\pi\)
−0.514310 + 0.857604i \(0.671952\pi\)
\(458\) −2.64236 15.0756i −0.123470 0.704437i
\(459\) 0 0
\(460\) −31.0419 + 11.2266i −1.44733 + 0.523441i
\(461\) 13.4851i 0.628064i −0.949412 0.314032i \(-0.898320\pi\)
0.949412 0.314032i \(-0.101680\pi\)
\(462\) 0 0
\(463\) 0.816179i 0.0379310i −0.999820 0.0189655i \(-0.993963\pi\)
0.999820 0.0189655i \(-0.00603727\pi\)
\(464\) −24.5381 + 20.4197i −1.13915 + 0.947960i
\(465\) 0 0
\(466\) 32.6976 5.73105i 1.51469 0.265486i
\(467\) −41.1881 −1.90596 −0.952979 0.303038i \(-0.901999\pi\)
−0.952979 + 0.303038i \(0.901999\pi\)
\(468\) 0 0
\(469\) −1.76467 −0.0814850
\(470\) −33.2026 + 5.81956i −1.53152 + 0.268436i
\(471\) 0 0
\(472\) 6.94940 + 12.1223i 0.319872 + 0.557976i
\(473\) −16.6951 −0.767640
\(474\) 0 0
\(475\) −8.62620 + 18.2269i −0.395797 + 0.836309i
\(476\) 10.3092 + 28.5053i 0.472521 + 1.30654i
\(477\) 0 0
\(478\) 6.35807 + 36.2750i 0.290811 + 1.65918i
\(479\) 29.3354i 1.34037i 0.742195 + 0.670184i \(0.233785\pi\)
−0.742195 + 0.670184i \(0.766215\pi\)
\(480\) 0 0
\(481\) −23.3449 −1.06443
\(482\) 3.58737 + 20.4672i 0.163400 + 0.932257i
\(483\) 0 0
\(484\) −7.41618 + 2.68213i −0.337099 + 0.121915i
\(485\) 15.1388 0.687420
\(486\) 0 0
\(487\) 31.8174 1.44178 0.720891 0.693048i \(-0.243733\pi\)
0.720891 + 0.693048i \(0.243733\pi\)
\(488\) −16.8788 29.4429i −0.764066 1.33282i
\(489\) 0 0
\(490\) −8.99818 51.3378i −0.406496 2.31920i
\(491\) −2.18431 −0.0985767 −0.0492883 0.998785i \(-0.515695\pi\)
−0.0492883 + 0.998785i \(0.515695\pi\)
\(492\) 0 0
\(493\) −27.8386 −1.25379
\(494\) −8.34370 + 30.3223i −0.375401 + 1.36427i
\(495\) 0 0
\(496\) −9.82263 + 8.17402i −0.441049 + 0.367024i
\(497\) 10.4663i 0.469480i
\(498\) 0 0
\(499\) 35.0881 1.57076 0.785379 0.619015i \(-0.212468\pi\)
0.785379 + 0.619015i \(0.212468\pi\)
\(500\) 0.788870 + 2.18126i 0.0352793 + 0.0975487i
\(501\) 0 0
\(502\) −13.4184 + 2.35190i −0.598894 + 0.104971i
\(503\) 11.2681i 0.502418i −0.967933 0.251209i \(-0.919172\pi\)
0.967933 0.251209i \(-0.0808282\pi\)
\(504\) 0 0
\(505\) 8.91713 0.396807
\(506\) −3.45025 19.6849i −0.153382 0.875100i
\(507\) 0 0
\(508\) 32.8580 11.8834i 1.45784 0.527240i
\(509\) 22.7936 1.01031 0.505153 0.863030i \(-0.331436\pi\)
0.505153 + 0.863030i \(0.331436\pi\)
\(510\) 0 0
\(511\) 1.62415i 0.0718482i
\(512\) 0.207989 22.6265i 0.00919190 0.999958i
\(513\) 0 0
\(514\) −5.25240 29.9668i −0.231673 1.32178i
\(515\) 32.9992i 1.45412i
\(516\) 0 0
\(517\) 20.4083i 0.897554i
\(518\) 4.85421 + 27.6950i 0.213282 + 1.21685i
\(519\) 0 0
\(520\) −22.2663 38.8408i −0.976444 1.70328i
\(521\) 41.2795i 1.80849i −0.427019 0.904243i \(-0.640436\pi\)
0.427019 0.904243i \(-0.359564\pi\)
\(522\) 0 0
\(523\) 22.5730i 0.987049i 0.869732 + 0.493525i \(0.164292\pi\)
−0.869732 + 0.493525i \(0.835708\pi\)
\(524\) 10.8805 3.93503i 0.475317 0.171903i
\(525\) 0 0
\(526\) −0.855805 4.88267i −0.0373149 0.212894i
\(527\) −11.1438 −0.485433
\(528\) 0 0
\(529\) −5.29862 −0.230375
\(530\) 7.43517 + 42.4202i 0.322963 + 1.84262i
\(531\) 0 0
\(532\) 37.7076 + 3.59341i 1.63483 + 0.155794i
\(533\) 23.0497i 0.998395i
\(534\) 0 0
\(535\) −33.3728 −1.44283
\(536\) 0.571323 + 0.996599i 0.0246774 + 0.0430465i
\(537\) 0 0
\(538\) −4.86027 + 0.851880i −0.209541 + 0.0367271i
\(539\) 31.5552 1.35918
\(540\) 0 0
\(541\) 13.0159i 0.559596i 0.960059 + 0.279798i \(0.0902675\pi\)
−0.960059 + 0.279798i \(0.909733\pi\)
\(542\) −1.74456 9.95333i −0.0749353 0.427532i
\(543\) 0 0
\(544\) 12.7607 15.0509i 0.547111 0.645300i
\(545\) 40.5178i 1.73559i
\(546\) 0 0
\(547\) 27.1012i 1.15877i −0.815056 0.579383i \(-0.803294\pi\)
0.815056 0.579383i \(-0.196706\pi\)
\(548\) 0.676287 0.244585i 0.0288895 0.0104481i
\(549\) 0 0
\(550\) 17.1188 3.00049i 0.729950 0.127941i
\(551\) −14.8813 + 31.4437i −0.633963 + 1.33955i
\(552\) 0 0
\(553\) 75.0959i 3.19340i
\(554\) 1.31378 + 7.49558i 0.0558172 + 0.318457i
\(555\) 0 0
\(556\) 5.58163 2.01865i 0.236714 0.0856097i
\(557\) 27.1183i 1.14904i 0.818490 + 0.574520i \(0.194811\pi\)
−0.818490 + 0.574520i \(0.805189\pi\)
\(558\) 0 0
\(559\) −32.0629 −1.35611
\(560\) −41.4485 + 34.4918i −1.75152 + 1.45755i
\(561\) 0 0
\(562\) −5.60788 31.9949i −0.236554 1.34962i
\(563\) 4.40370i 0.185594i −0.995685 0.0927969i \(-0.970419\pi\)
0.995685 0.0927969i \(-0.0295807\pi\)
\(564\) 0 0
\(565\) −46.4906 −1.95587
\(566\) −8.62562 + 1.51185i −0.362562 + 0.0635477i
\(567\) 0 0
\(568\) 5.91087 3.38854i 0.248015 0.142180i
\(569\) 17.8135i 0.746781i 0.927674 + 0.373391i \(0.121805\pi\)
−0.927674 + 0.373391i \(0.878195\pi\)
\(570\) 0 0
\(571\) 27.4219 1.14757 0.573786 0.819005i \(-0.305474\pi\)
0.573786 + 0.819005i \(0.305474\pi\)
\(572\) 25.4896 9.21853i 1.06577 0.385446i
\(573\) 0 0
\(574\) −27.3449 + 4.79284i −1.14135 + 0.200049i
\(575\) 24.6097i 1.02630i
\(576\) 0 0
\(577\) −28.3651 −1.18085 −0.590427 0.807091i \(-0.701040\pi\)
−0.590427 + 0.807091i \(0.701040\pi\)
\(578\) −6.73138 + 1.17984i −0.279989 + 0.0490747i
\(579\) 0 0
\(580\) −16.8426 46.5704i −0.699350 1.93373i
\(581\) 53.3967i 2.21527i
\(582\) 0 0
\(583\) −26.0739 −1.07987
\(584\) 0.917239 0.525828i 0.0379556 0.0217589i
\(585\) 0 0
\(586\) −1.85069 + 0.324378i −0.0764512 + 0.0133999i
\(587\) −2.85480 −0.117830 −0.0589150 0.998263i \(-0.518764\pi\)
−0.0589150 + 0.998263i \(0.518764\pi\)
\(588\) 0 0
\(589\) −5.95699 + 12.5870i −0.245453 + 0.518637i
\(590\) −21.3510 + 3.74227i −0.879005 + 0.154067i
\(591\) 0 0
\(592\) 14.0692 11.7078i 0.578239 0.481188i
\(593\) −14.4737 −0.594363 −0.297182 0.954821i \(-0.596047\pi\)
−0.297182 + 0.954821i \(0.596047\pi\)
\(594\) 0 0
\(595\) −47.0235 −1.92778
\(596\) −6.59160 18.2260i −0.270003 0.746568i
\(597\) 0 0
\(598\) −6.62620 37.8048i −0.270965 1.54595i
\(599\) 3.91727 0.160055 0.0800277 0.996793i \(-0.474499\pi\)
0.0800277 + 0.996793i \(0.474499\pi\)
\(600\) 0 0
\(601\) 0.0549752i 0.00224249i −0.999999 0.00112124i \(-0.999643\pi\)
0.999999 0.00112124i \(-0.000356903\pi\)
\(602\) 6.66699 + 38.0375i 0.271726 + 1.55029i
\(603\) 0 0
\(604\) −17.5401 + 6.34354i −0.713698 + 0.258115i
\(605\) 12.2340i 0.497385i
\(606\) 0 0
\(607\) 29.9200 1.21441 0.607207 0.794544i \(-0.292290\pi\)
0.607207 + 0.794544i \(0.292290\pi\)
\(608\) −10.1787 22.4587i −0.412799 0.910822i
\(609\) 0 0
\(610\) 51.8574 9.08926i 2.09964 0.368013i
\(611\) 39.1940i 1.58562i
\(612\) 0 0
\(613\) 31.5719i 1.27518i 0.770377 + 0.637589i \(0.220068\pi\)
−0.770377 + 0.637589i \(0.779932\pi\)
\(614\) 3.02947 + 17.2842i 0.122260 + 0.697534i
\(615\) 0 0
\(616\) −16.2365 28.3225i −0.654187 1.14115i
\(617\) 42.9373 1.72859 0.864295 0.502985i \(-0.167765\pi\)
0.864295 + 0.502985i \(0.167765\pi\)
\(618\) 0 0
\(619\) −27.3169 −1.09796 −0.548980 0.835835i \(-0.684984\pi\)
−0.548980 + 0.835835i \(0.684984\pi\)
\(620\) −6.74210 18.6422i −0.270769 0.748687i
\(621\) 0 0
\(622\) 0.516846 + 2.94879i 0.0207237 + 0.118236i
\(623\) 8.48666 0.340011
\(624\) 0 0
\(625\) −26.7293 −1.06917
\(626\) 43.2856 7.58684i 1.73004 0.303231i
\(627\) 0 0
\(628\) −6.71096 18.5561i −0.267796 0.740467i
\(629\) 15.9615 0.636428
\(630\) 0 0
\(631\) 11.8586i 0.472083i −0.971743 0.236042i \(-0.924150\pi\)
0.971743 0.236042i \(-0.0758502\pi\)
\(632\) 42.4104 24.3127i 1.68700 0.967108i
\(633\) 0 0
\(634\) −45.1729 + 7.91763i −1.79404 + 0.314449i
\(635\) 54.2040i 2.15102i
\(636\) 0 0
\(637\) 60.6017 2.40113
\(638\) 29.5321 5.17622i 1.16919 0.204928i
\(639\) 0 0
\(640\) 32.8985 + 12.2411i 1.30043 + 0.483873i
\(641\) 26.6994i 1.05456i 0.849690 + 0.527282i \(0.176789\pi\)
−0.849690 + 0.527282i \(0.823211\pi\)
\(642\) 0 0
\(643\) 35.7711 1.41068 0.705338 0.708871i \(-0.250795\pi\)
0.705338 + 0.708871i \(0.250795\pi\)
\(644\) −43.4716 + 15.7219i −1.71302 + 0.619528i
\(645\) 0 0
\(646\) 5.70482 20.7322i 0.224453 0.815698i
\(647\) 6.84253i 0.269008i −0.990913 0.134504i \(-0.957056\pi\)
0.990913 0.134504i \(-0.0429440\pi\)
\(648\) 0 0
\(649\) 13.1235i 0.515144i
\(650\) 32.8767 5.76243i 1.28953 0.226021i
\(651\) 0 0
\(652\) −2.86464 + 1.03602i −0.112188 + 0.0405738i
\(653\) 10.1996i 0.399141i 0.979883 + 0.199570i \(0.0639547\pi\)
−0.979883 + 0.199570i \(0.936045\pi\)
\(654\) 0 0
\(655\) 17.9489i 0.701323i
\(656\) 11.5598 + 13.8913i 0.451335 + 0.542364i
\(657\) 0 0
\(658\) −46.4975 + 8.14981i −1.81266 + 0.317713i
\(659\) 14.8086i 0.576862i −0.957501 0.288431i \(-0.906866\pi\)
0.957501 0.288431i \(-0.0931336\pi\)
\(660\) 0 0
\(661\) −8.06062 −0.313522 −0.156761 0.987637i \(-0.550105\pi\)
−0.156761 + 0.987637i \(0.550105\pi\)
\(662\) 5.41211 + 30.8780i 0.210348 + 1.20011i
\(663\) 0 0
\(664\) 30.1558 17.2875i 1.17027 0.670885i
\(665\) −25.1367 + 53.1131i −0.974758 + 2.05964i
\(666\) 0 0
\(667\) 42.4548i 1.64386i
\(668\) 4.53052 1.63850i 0.175291 0.0633955i
\(669\) 0 0
\(670\) −1.75530 + 0.307659i −0.0678131 + 0.0118859i
\(671\) 31.8746i 1.23050i
\(672\) 0 0
\(673\) 11.6927i 0.450719i −0.974276 0.225359i \(-0.927644\pi\)
0.974276 0.225359i \(-0.0723556\pi\)
\(674\) 2.19774 + 12.5388i 0.0846536 + 0.482978i
\(675\) 0 0
\(676\) 24.5026 8.86158i 0.942408 0.340830i
\(677\) 7.98077 0.306726 0.153363 0.988170i \(-0.450990\pi\)
0.153363 + 0.988170i \(0.450990\pi\)
\(678\) 0 0
\(679\) 21.2007 0.813608
\(680\) 15.2241 + 26.5566i 0.583819 + 1.01840i
\(681\) 0 0
\(682\) 11.8217 2.07204i 0.452678 0.0793427i
\(683\) 23.1580i 0.886118i −0.896493 0.443059i \(-0.853893\pi\)
0.896493 0.443059i \(-0.146107\pi\)
\(684\) 0 0
\(685\) 1.11563i 0.0426261i
\(686\) −5.17537 29.5273i −0.197597 1.12736i
\(687\) 0 0
\(688\) 19.3232 16.0800i 0.736690 0.613045i
\(689\) −50.0750 −1.90770
\(690\) 0 0
\(691\) 11.4446 0.435373 0.217687 0.976019i \(-0.430149\pi\)
0.217687 + 0.976019i \(0.430149\pi\)
\(692\) −27.5213 + 9.95333i −1.04620 + 0.378369i
\(693\) 0 0
\(694\) −13.4184 + 2.35190i −0.509356 + 0.0892770i
\(695\) 9.20770i 0.349268i
\(696\) 0 0
\(697\) 15.7598i 0.596943i
\(698\) 5.62559 + 32.0960i 0.212932 + 1.21485i
\(699\) 0 0
\(700\) −13.6724 37.8048i −0.516769 1.42889i
\(701\) 11.4506i 0.432485i 0.976340 + 0.216242i \(0.0693801\pi\)
−0.976340 + 0.216242i \(0.930620\pi\)
\(702\) 0 0
\(703\) 8.53231 18.0286i 0.321802 0.679960i
\(704\) −10.7385 + 18.3391i −0.404722 + 0.691182i
\(705\) 0 0
\(706\) 33.1985 5.81884i 1.24944 0.218995i
\(707\) 12.4877 0.469648
\(708\) 0 0
\(709\) 45.3623i 1.70362i −0.523852 0.851809i \(-0.675506\pi\)
0.523852 0.851809i \(-0.324494\pi\)
\(710\) 1.82473 + 10.4108i 0.0684811 + 0.390708i
\(711\) 0 0
\(712\) −2.74760 4.79284i −0.102971 0.179619i
\(713\) 16.9947i 0.636457i
\(714\) 0 0
\(715\) 42.0487i 1.57253i
\(716\) 3.20194 + 8.85347i 0.119662 + 0.330870i
\(717\) 0 0
\(718\) −5.33818 30.4562i −0.199219 1.13661i
\(719\) 12.4081i 0.462744i −0.972865 0.231372i \(-0.925679\pi\)
0.972865 0.231372i \(-0.0743214\pi\)
\(720\) 0 0
\(721\) 46.2126i 1.72105i
\(722\) −20.3675 17.5261i −0.758000 0.652254i
\(723\) 0 0
\(724\) −34.2669 + 12.3929i −1.27352 + 0.460580i
\(725\) 36.9206 1.37120
\(726\) 0 0
\(727\) 14.0519i 0.521156i 0.965453 + 0.260578i \(0.0839131\pi\)
−0.965453 + 0.260578i \(0.916087\pi\)
\(728\) −31.1822 54.3933i −1.15569 2.01595i
\(729\) 0 0
\(730\) 0.283159 + 1.61552i 0.0104802 + 0.0597932i
\(731\) 21.9223 0.810825
\(732\) 0 0
\(733\) 19.7323i 0.728830i 0.931237 + 0.364415i \(0.118731\pi\)
−0.931237 + 0.364415i \(0.881269\pi\)
\(734\) −8.07068 46.0461i −0.297894 1.69959i
\(735\) 0 0
\(736\) 22.9531 + 19.4605i 0.846062 + 0.717325i
\(737\) 1.07891i 0.0397421i
\(738\) 0 0
\(739\) 31.2297 1.14880 0.574402 0.818574i \(-0.305235\pi\)
0.574402 + 0.818574i \(0.305235\pi\)
\(740\) 9.65685 + 26.7016i 0.354993 + 0.981569i
\(741\) 0 0
\(742\) 10.4123 + 59.4060i 0.382249 + 2.18086i
\(743\) −5.06602 −0.185854 −0.0929271 0.995673i \(-0.529622\pi\)
−0.0929271 + 0.995673i \(0.529622\pi\)
\(744\) 0 0
\(745\) 30.0664 1.10155
\(746\) −13.8713 + 2.43128i −0.507865 + 0.0890156i
\(747\) 0 0
\(748\) −17.4280 + 6.30297i −0.637229 + 0.230459i
\(749\) −46.7359 −1.70769
\(750\) 0 0
\(751\) 4.05958 0.148136 0.0740680 0.997253i \(-0.476402\pi\)
0.0740680 + 0.997253i \(0.476402\pi\)
\(752\) 19.6564 + 23.6209i 0.716796 + 0.861367i
\(753\) 0 0
\(754\) 56.7164 9.94092i 2.06549 0.362027i
\(755\) 28.9349i 1.05305i
\(756\) 0 0
\(757\) 0.219844i 0.00799035i −0.999992 0.00399518i \(-0.998728\pi\)
0.999992 0.00399518i \(-0.00127171\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 38.1338 2.99973i 1.38326 0.108812i
\(761\) −30.9704 −1.12268 −0.561339 0.827586i \(-0.689713\pi\)
−0.561339 + 0.827586i \(0.689713\pi\)
\(762\) 0 0
\(763\) 56.7418i 2.05419i
\(764\) −6.16993 17.0601i −0.223220 0.617213i
\(765\) 0 0
\(766\) −37.7572 + 6.61786i −1.36422 + 0.239113i
\(767\) 25.2037i 0.910054i
\(768\) 0 0
\(769\) 27.5770 0.994453 0.497227 0.867621i \(-0.334352\pi\)
0.497227 + 0.867621i \(0.334352\pi\)
\(770\) 49.8841 8.74339i 1.79770 0.315090i
\(771\) 0 0
\(772\) −17.3951 48.0981i −0.626063 1.73109i
\(773\) −17.9758 −0.646546 −0.323273 0.946306i \(-0.604783\pi\)
−0.323273 + 0.946306i \(0.604783\pi\)
\(774\) 0 0
\(775\) 14.7794 0.530890
\(776\) −6.86384 11.9731i −0.246398 0.429809i
\(777\) 0 0
\(778\) −7.33388 41.8424i −0.262932 1.50012i
\(779\) 17.8006 + 8.42445i 0.637774 + 0.301837i
\(780\) 0 0
\(781\) −6.39905 −0.228976
\(782\) 4.53052 + 25.8482i 0.162011 + 0.924329i
\(783\) 0 0
\(784\) −36.5226 + 30.3927i −1.30438 + 1.08545i
\(785\) 30.6109 1.09255
\(786\) 0 0
\(787\) 26.6951i 0.951577i 0.879560 + 0.475789i \(0.157837\pi\)
−0.879560 + 0.475789i \(0.842163\pi\)
\(788\) −16.3665 45.2541i −0.583034 1.61211i
\(789\) 0 0
\(790\) 13.0925 + 74.6971i 0.465809 + 2.65760i
\(791\) −65.1062 −2.31491
\(792\) 0 0
\(793\) 61.2151i 2.17381i
\(794\) −6.95417 39.6760i −0.246794 1.40805i
\(795\) 0 0
\(796\) 11.7676 + 32.5378i 0.417091 + 1.15327i
\(797\) −5.82023 −0.206163 −0.103082 0.994673i \(-0.532870\pi\)
−0.103082 + 0.994673i \(0.532870\pi\)
\(798\) 0 0
\(799\) 26.7981i 0.948047i
\(800\) −16.9237 + 19.9610i −0.598344 + 0.705728i
\(801\) 0 0
\(802\) −1.45231 8.28591i −0.0512827 0.292586i
\(803\) −0.992995 −0.0350420
\(804\) 0 0
\(805\) 71.7125i 2.52753i
\(806\) 22.7036 3.97936i 0.799701 0.140167i
\(807\) 0 0
\(808\) −4.04296 7.05243i −0.142231 0.248104i
\(809\) −48.0519 −1.68942 −0.844708 0.535228i \(-0.820226\pi\)
−0.844708 + 0.535228i \(0.820226\pi\)
\(810\) 0 0
\(811\) 36.8600i 1.29433i −0.762350 0.647165i \(-0.775954\pi\)
0.762350 0.647165i \(-0.224046\pi\)
\(812\) −23.5866 65.2179i −0.827729 2.28870i
\(813\) 0 0
\(814\) −16.9325 + 2.96783i −0.593484 + 0.104022i
\(815\) 4.72563i 0.165532i
\(816\) 0 0
\(817\) 11.7187 24.7612i 0.409984 0.866285i
\(818\) 3.64947 + 20.8215i 0.127601 + 0.728007i
\(819\) 0 0
\(820\) −26.3640 + 9.53477i −0.920671 + 0.332969i
\(821\) 36.1520i 1.26171i 0.775900 + 0.630856i \(0.217296\pi\)
−0.775900 + 0.630856i \(0.782704\pi\)
\(822\) 0 0
\(823\) 15.3874i 0.536370i 0.963367 + 0.268185i \(0.0864238\pi\)
−0.963367 + 0.268185i \(0.913576\pi\)
\(824\) −26.0986 + 14.9616i −0.909188 + 0.521212i
\(825\) 0 0
\(826\) −29.9002 + 5.24074i −1.04036 + 0.182349i
\(827\) 1.84666i 0.0642147i −0.999484 0.0321073i \(-0.989778\pi\)
0.999484 0.0321073i \(-0.0102218\pi\)
\(828\) 0 0
\(829\) −20.3039 −0.705184 −0.352592 0.935777i \(-0.614700\pi\)
−0.352592 + 0.935777i \(0.614700\pi\)
\(830\) 9.30935 + 53.1131i 0.323132 + 1.84358i
\(831\) 0 0
\(832\) −20.6232 + 35.2203i −0.714982 + 1.22104i
\(833\) −41.4351 −1.43564
\(834\) 0 0
\(835\) 7.47373i 0.258639i
\(836\) −2.19699 + 23.0542i −0.0759844 + 0.797345i
\(837\) 0 0
\(838\) −10.7198 + 1.87890i −0.370309 + 0.0649055i
\(839\) 53.7141 1.85442 0.927208 0.374546i \(-0.122201\pi\)
0.927208 + 0.374546i \(0.122201\pi\)
\(840\) 0 0
\(841\) 34.6926 1.19630
\(842\) 2.06753 0.362384i 0.0712517 0.0124886i
\(843\) 0 0
\(844\) −13.7999 38.1572i −0.475011 1.31342i
\(845\) 40.4205i 1.39051i
\(846\) 0 0
\(847\) 17.1328i 0.588689i
\(848\) 30.1785 25.1134i 1.03633 0.862397i
\(849\) 0 0
\(850\) −22.4787 + 3.93994i −0.771014 + 0.135139i
\(851\) 24.3419i 0.834429i
\(852\) 0 0
\(853\) 39.1842i 1.34164i 0.741620 + 0.670820i \(0.234058\pi\)
−0.741620 + 0.670820i \(0.765942\pi\)
\(854\) 72.6220 12.7288i 2.48507 0.435569i
\(855\) 0 0
\(856\) 15.1310 + 26.3941i 0.517167 + 0.902131i
\(857\) 37.5744i 1.28352i −0.766907 0.641758i \(-0.778205\pi\)
0.766907 0.641758i \(-0.221795\pi\)
\(858\) 0 0
\(859\) −33.0235 −1.12675 −0.563374 0.826202i \(-0.690497\pi\)
−0.563374 + 0.826202i \(0.690497\pi\)
\(860\) 13.2631 + 36.6731i 0.452270 + 1.25054i
\(861\) 0 0
\(862\) 46.2234 8.10177i 1.57438 0.275947i
\(863\) −34.0836 −1.16022 −0.580110 0.814538i \(-0.696990\pi\)
−0.580110 + 0.814538i \(0.696990\pi\)
\(864\) 0 0
\(865\) 45.4004i 1.54366i
\(866\) 5.78511 + 33.0061i 0.196586 + 1.12159i
\(867\) 0 0
\(868\) −9.44176 26.1068i −0.320474 0.886123i
\(869\) −45.9132 −1.55750
\(870\) 0 0
\(871\) 2.07204i 0.0702085i
\(872\) 32.0450 18.3705i 1.08518 0.622103i
\(873\) 0 0
\(874\) 31.6174 + 8.70005i 1.06947 + 0.294284i
\(875\) −5.03911 −0.170353
\(876\) 0 0
\(877\) 20.8395 0.703698 0.351849 0.936057i \(-0.385553\pi\)
0.351849 + 0.936057i \(0.385553\pi\)
\(878\) −26.2599 + 4.60267i −0.886227 + 0.155333i
\(879\) 0 0
\(880\) −21.0881 25.3413i −0.710879 0.854256i
\(881\) −4.20737 −0.141750 −0.0708749 0.997485i \(-0.522579\pi\)
−0.0708749 + 0.997485i \(0.522579\pi\)
\(882\) 0 0
\(883\) 4.68449 0.157646 0.0788228 0.996889i \(-0.474884\pi\)
0.0788228 + 0.996889i \(0.474884\pi\)
\(884\) −33.4704 + 12.1048i −1.12573 + 0.407130i
\(885\) 0 0
\(886\) −13.4184 + 2.35190i −0.450801 + 0.0790137i
\(887\) −42.8186 −1.43771 −0.718854 0.695161i \(-0.755333\pi\)
−0.718854 + 0.695161i \(0.755333\pi\)
\(888\) 0 0
\(889\) 75.9082i 2.54588i
\(890\) 8.44158 1.47959i 0.282963 0.0495960i
\(891\) 0 0
\(892\) 3.05931 1.10643i 0.102433 0.0370459i
\(893\) 30.2684 + 14.3250i 1.01289 + 0.479369i
\(894\) 0 0
\(895\) −14.6051 −0.488193
\(896\) 46.0716 + 17.1427i 1.53914 + 0.572697i
\(897\) 0 0
\(898\) −4.68305 26.7185i −0.156276 0.891606i
\(899\) 25.4962 0.850347
\(900\) 0 0
\(901\) 34.2377 1.14062
\(902\) −2.93031 16.7185i −0.0975688 0.556664i
\(903\) 0 0
\(904\) 21.0785 + 36.7688i 0.701061 + 1.22291i
\(905\) 56.5282i 1.87906i
\(906\) 0 0
\(907\) 56.3357i 1.87060i −0.353861 0.935298i \(-0.615131\pi\)
0.353861 0.935298i \(-0.384869\pi\)
\(908\) 13.5138 + 37.3662i 0.448471 + 1.24004i
\(909\) 0 0
\(910\) 95.8024 16.7917i 3.17582 0.556639i
\(911\) 21.1389 0.700363 0.350182 0.936682i \(-0.386120\pi\)
0.350182 + 0.936682i \(0.386120\pi\)
\(912\) 0 0
\(913\) −32.6464 −1.08044
\(914\) −30.6307 + 5.36877i −1.01317 + 0.177583i
\(915\) 0 0
\(916\) −7.36151 20.3549i −0.243231 0.672544i
\(917\) 25.1360i 0.830064i
\(918\) 0 0
\(919\) 27.6142i 0.910910i −0.890259 0.455455i \(-0.849477\pi\)
0.890259 0.455455i \(-0.150523\pi\)
\(920\) −40.4996 + 23.2173i −1.33523 + 0.765452i
\(921\) 0 0
\(922\) −3.29243 18.7845i −0.108430 0.618633i
\(923\) −12.2894 −0.404510
\(924\) 0 0
\(925\) −21.1688 −0.696025
\(926\) −0.199272 1.13692i −0.00654850 0.0373615i
\(927\) 0 0
\(928\) −29.1955 + 34.4352i −0.958391 + 1.13039i
\(929\) 43.2969 1.42052 0.710262 0.703937i \(-0.248576\pi\)
0.710262 + 0.703937i \(0.248576\pi\)
\(930\) 0 0
\(931\) −22.1493 + 46.8009i −0.725914 + 1.53384i
\(932\) 44.1478 15.9664i 1.44611 0.522998i
\(933\) 0 0
\(934\) −57.3741 + 10.0562i −1.87734 + 0.329049i
\(935\) 28.7499i 0.940222i
\(936\) 0 0
\(937\) 27.8603 0.910155 0.455078 0.890452i \(-0.349611\pi\)
0.455078 + 0.890452i \(0.349611\pi\)
\(938\) −2.45815 + 0.430850i −0.0802615 + 0.0140678i
\(939\) 0 0
\(940\) −44.8297 + 16.2130i −1.46218 + 0.528811i
\(941\) −3.98575 −0.129932 −0.0649658 0.997887i \(-0.520694\pi\)
−0.0649658 + 0.997887i \(0.520694\pi\)
\(942\) 0 0
\(943\) −24.0342 −0.782660
\(944\) 12.6401 + 15.1894i 0.411399 + 0.494374i
\(945\) 0 0
\(946\) −23.2559 + 4.07615i −0.756114 + 0.132527i
\(947\) 9.87990 0.321053 0.160527 0.987031i \(-0.448681\pi\)
0.160527 + 0.987031i \(0.448681\pi\)
\(948\) 0 0
\(949\) −1.90705 −0.0619053
\(950\) −7.56595 + 27.4958i −0.245472 + 0.892083i
\(951\) 0 0
\(952\) 21.3201 + 37.1902i 0.690989 + 1.20534i
\(953\) 52.2372i 1.69213i 0.533082 + 0.846064i \(0.321034\pi\)
−0.533082 + 0.846064i \(0.678966\pi\)
\(954\) 0 0
\(955\) 28.1431 0.910688
\(956\) 17.7133 + 48.9780i 0.572889 + 1.58406i
\(957\) 0 0
\(958\) 7.16232 + 40.8635i 0.231404 + 1.32024i
\(959\) 1.56235i 0.0504509i
\(960\) 0 0
\(961\) −20.7938 −0.670769
\(962\) −32.5189 + 5.69972i −1.04845 + 0.183766i
\(963\) 0 0
\(964\) 9.99427 + 27.6345i 0.321894 + 0.890049i
\(965\) 79.3447 2.55419
\(966\) 0 0
\(967\) 23.4702i 0.754749i −0.926061 0.377375i \(-0.876827\pi\)
0.926061 0.377375i \(-0.123173\pi\)
\(968\) −9.67573 + 5.54683i −0.310990 + 0.178282i
\(969\) 0 0
\(970\) 21.0881 3.69620i 0.677098 0.118678i
\(971\) 23.8446i 0.765211i 0.923912 + 0.382605i \(0.124973\pi\)
−0.923912 + 0.382605i \(0.875027\pi\)
\(972\) 0 0
\(973\) 12.8946i 0.413382i
\(974\) 44.3209 7.76831i 1.42013 0.248913i
\(975\) 0 0
\(976\) −30.7003 36.8923i −0.982694 1.18089i
\(977\) 43.5227i 1.39241i −0.717841 0.696207i \(-0.754869\pi\)
0.717841 0.696207i \(-0.245131\pi\)
\(978\) 0 0
\(979\) 5.18869i 0.165831i
\(980\) −25.0685 69.3155i −0.800785 2.21420i
\(981\) 0 0
\(982\) −3.04270 + 0.533307i −0.0970965 + 0.0170185i
\(983\) −28.1172 −0.896798 −0.448399 0.893834i \(-0.648006\pi\)
−0.448399 + 0.893834i \(0.648006\pi\)
\(984\) 0 0
\(985\) 74.6531 2.37864
\(986\) −38.7786 + 6.79688i −1.23496 + 0.216457i
\(987\) 0 0
\(988\) −4.21931 + 44.2755i −0.134234 + 1.40859i
\(989\) 33.4322i 1.06308i
\(990\) 0 0
\(991\) −37.7810 −1.20015 −0.600076 0.799943i \(-0.704863\pi\)
−0.600076 + 0.799943i \(0.704863\pi\)
\(992\) −11.6870 + 13.7845i −0.371063 + 0.437657i
\(993\) 0 0
\(994\) 2.55539 + 14.5794i 0.0810520 + 0.462430i
\(995\) −53.6758 −1.70164
\(996\) 0 0
\(997\) 46.5992i 1.47581i 0.674904 + 0.737906i \(0.264185\pi\)
−0.674904 + 0.737906i \(0.735815\pi\)
\(998\) 48.8770 8.56686i 1.54717 0.271179i
\(999\) 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.379.21 yes 24
3.2 odd 2 inner 1368.2.e.f.379.3 yes 24
4.3 odd 2 5472.2.e.f.5167.4 24
8.3 odd 2 inner 1368.2.e.f.379.2 yes 24
8.5 even 2 5472.2.e.f.5167.23 24
12.11 even 2 5472.2.e.f.5167.5 24
19.18 odd 2 inner 1368.2.e.f.379.4 yes 24
24.5 odd 2 5472.2.e.f.5167.16 24
24.11 even 2 inner 1368.2.e.f.379.24 yes 24
57.56 even 2 inner 1368.2.e.f.379.22 yes 24
76.75 even 2 5472.2.e.f.5167.24 24
152.37 odd 2 5472.2.e.f.5167.3 24
152.75 even 2 inner 1368.2.e.f.379.23 yes 24
228.227 odd 2 5472.2.e.f.5167.15 24
456.227 odd 2 inner 1368.2.e.f.379.1 24
456.341 even 2 5472.2.e.f.5167.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.e.f.379.1 24 456.227 odd 2 inner
1368.2.e.f.379.2 yes 24 8.3 odd 2 inner
1368.2.e.f.379.3 yes 24 3.2 odd 2 inner
1368.2.e.f.379.4 yes 24 19.18 odd 2 inner
1368.2.e.f.379.21 yes 24 1.1 even 1 trivial
1368.2.e.f.379.22 yes 24 57.56 even 2 inner
1368.2.e.f.379.23 yes 24 152.75 even 2 inner
1368.2.e.f.379.24 yes 24 24.11 even 2 inner
5472.2.e.f.5167.3 24 152.37 odd 2
5472.2.e.f.5167.4 24 4.3 odd 2
5472.2.e.f.5167.5 24 12.11 even 2
5472.2.e.f.5167.6 24 456.341 even 2
5472.2.e.f.5167.15 24 228.227 odd 2
5472.2.e.f.5167.16 24 24.5 odd 2
5472.2.e.f.5167.23 24 8.5 even 2
5472.2.e.f.5167.24 24 76.75 even 2