Properties

Label 504.2.c.d.253.1
Level $504$
Weight $2$
Character 504.253
Analytic conductor $4.024$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(253,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.253");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.c (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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.1
Root \(-0.780776 - 1.17915i\) of defining polynomial
Character \(\chi\) \(=\) 504.253
Dual form 504.2.c.d.253.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} -1.00000 q^{7} +(2.78078 - 0.516994i) q^{8} +O(q^{10})\) \(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} -1.00000 q^{7} +(2.78078 - 0.516994i) q^{8} +(-2.00000 + 1.32431i) q^{10} -1.32431i q^{11} -1.69614i q^{13} +(0.780776 + 1.17915i) q^{14} +(-2.78078 - 2.87529i) q^{16} -2.00000 q^{17} -3.02045i q^{19} +(3.12311 + 1.32431i) q^{20} +(-1.56155 + 1.03399i) q^{22} -5.12311 q^{23} +2.12311 q^{25} +(-2.00000 + 1.32431i) q^{26} +(0.780776 - 1.84130i) q^{28} -6.04090i q^{29} -10.2462 q^{31} +(-1.21922 + 5.52390i) q^{32} +(1.56155 + 2.35829i) q^{34} +1.69614i q^{35} -6.04090i q^{37} +(-3.56155 + 2.35829i) q^{38} +(-0.876894 - 4.71659i) q^{40} -4.24621 q^{41} +1.32431i q^{43} +(2.43845 + 1.03399i) q^{44} +(4.00000 + 6.04090i) q^{46} +1.00000 q^{49} +(-1.65767 - 2.50345i) q^{50} +(3.12311 + 1.32431i) q^{52} -2.64861i q^{53} -2.24621 q^{55} +(-2.78078 + 0.516994i) q^{56} +(-7.12311 + 4.71659i) q^{58} -0.371834i q^{59} -1.69614i q^{61} +(8.00000 + 12.0818i) q^{62} +(7.46543 - 2.87529i) q^{64} -2.87689 q^{65} +11.5012i q^{67} +(1.56155 - 3.68260i) q^{68} +(2.00000 - 1.32431i) q^{70} +8.00000 q^{71} -6.00000 q^{73} +(-7.12311 + 4.71659i) q^{74} +(5.56155 + 2.35829i) q^{76} +1.32431i q^{77} +(-4.87689 + 4.71659i) q^{80} +(3.31534 + 5.00691i) q^{82} -5.66906i q^{83} +3.39228i q^{85} +(1.56155 - 1.03399i) q^{86} +(-0.684658 - 3.68260i) q^{88} +16.2462 q^{89} +1.69614i q^{91} +(4.00000 - 9.43318i) q^{92} -5.12311 q^{95} +12.2462 q^{97} +(-0.780776 - 1.17915i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{4} - 4 q^{7} + 7 q^{8} - 8 q^{10} - q^{14} - 7 q^{16} - 8 q^{17} - 4 q^{20} + 2 q^{22} - 4 q^{23} - 8 q^{25} - 8 q^{26} - q^{28} - 8 q^{31} - 9 q^{32} - 2 q^{34} - 6 q^{38} - 20 q^{40} + 16 q^{41} + 18 q^{44} + 16 q^{46} + 4 q^{49} - 19 q^{50} - 4 q^{52} + 24 q^{55} - 7 q^{56} - 12 q^{58} + 32 q^{62} + q^{64} - 28 q^{65} - 2 q^{68} + 8 q^{70} + 32 q^{71} - 24 q^{73} - 12 q^{74} + 14 q^{76} - 36 q^{80} + 38 q^{82} - 2 q^{86} + 22 q^{88} + 32 q^{89} + 16 q^{92} - 4 q^{95} + 16 q^{97} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 1.17915i −0.552092 0.833783i
\(3\) 0 0
\(4\) −0.780776 + 1.84130i −0.390388 + 0.920650i
\(5\) 1.69614i 0.758537i −0.925287 0.379269i \(-0.876176\pi\)
0.925287 0.379269i \(-0.123824\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.78078 0.516994i 0.983153 0.182785i
\(9\) 0 0
\(10\) −2.00000 + 1.32431i −0.632456 + 0.418783i
\(11\) 1.32431i 0.399294i −0.979868 0.199647i \(-0.936021\pi\)
0.979868 0.199647i \(-0.0639795\pi\)
\(12\) 0 0
\(13\) 1.69614i 0.470425i −0.971944 0.235212i \(-0.924421\pi\)
0.971944 0.235212i \(-0.0755786\pi\)
\(14\) 0.780776 + 1.17915i 0.208671 + 0.315140i
\(15\) 0 0
\(16\) −2.78078 2.87529i −0.695194 0.718822i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 3.02045i 0.692938i −0.938061 0.346469i \(-0.887381\pi\)
0.938061 0.346469i \(-0.112619\pi\)
\(20\) 3.12311 + 1.32431i 0.698348 + 0.296124i
\(21\) 0 0
\(22\) −1.56155 + 1.03399i −0.332924 + 0.220447i
\(23\) −5.12311 −1.06824 −0.534121 0.845408i \(-0.679357\pi\)
−0.534121 + 0.845408i \(0.679357\pi\)
\(24\) 0 0
\(25\) 2.12311 0.424621
\(26\) −2.00000 + 1.32431i −0.392232 + 0.259718i
\(27\) 0 0
\(28\) 0.780776 1.84130i 0.147553 0.347973i
\(29\) 6.04090i 1.12177i −0.827895 0.560883i \(-0.810462\pi\)
0.827895 0.560883i \(-0.189538\pi\)
\(30\) 0 0
\(31\) −10.2462 −1.84027 −0.920137 0.391597i \(-0.871923\pi\)
−0.920137 + 0.391597i \(0.871923\pi\)
\(32\) −1.21922 + 5.52390i −0.215530 + 0.976497i
\(33\) 0 0
\(34\) 1.56155 + 2.35829i 0.267804 + 0.404444i
\(35\) 1.69614i 0.286700i
\(36\) 0 0
\(37\) 6.04090i 0.993117i −0.868003 0.496559i \(-0.834597\pi\)
0.868003 0.496559i \(-0.165403\pi\)
\(38\) −3.56155 + 2.35829i −0.577760 + 0.382566i
\(39\) 0 0
\(40\) −0.876894 4.71659i −0.138649 0.745758i
\(41\) −4.24621 −0.663147 −0.331573 0.943429i \(-0.607579\pi\)
−0.331573 + 0.943429i \(0.607579\pi\)
\(42\) 0 0
\(43\) 1.32431i 0.201955i 0.994889 + 0.100977i \(0.0321970\pi\)
−0.994889 + 0.100977i \(0.967803\pi\)
\(44\) 2.43845 + 1.03399i 0.367610 + 0.155879i
\(45\) 0 0
\(46\) 4.00000 + 6.04090i 0.589768 + 0.890681i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.65767 2.50345i −0.234430 0.354042i
\(51\) 0 0
\(52\) 3.12311 + 1.32431i 0.433097 + 0.183648i
\(53\) 2.64861i 0.363815i −0.983316 0.181908i \(-0.941773\pi\)
0.983316 0.181908i \(-0.0582272\pi\)
\(54\) 0 0
\(55\) −2.24621 −0.302879
\(56\) −2.78078 + 0.516994i −0.371597 + 0.0690862i
\(57\) 0 0
\(58\) −7.12311 + 4.71659i −0.935310 + 0.619318i
\(59\) 0.371834i 0.0484087i −0.999707 0.0242043i \(-0.992295\pi\)
0.999707 0.0242043i \(-0.00770523\pi\)
\(60\) 0 0
\(61\) 1.69614i 0.217169i −0.994087 0.108584i \(-0.965368\pi\)
0.994087 0.108584i \(-0.0346317\pi\)
\(62\) 8.00000 + 12.0818i 1.01600 + 1.53439i
\(63\) 0 0
\(64\) 7.46543 2.87529i 0.933179 0.359411i
\(65\) −2.87689 −0.356835
\(66\) 0 0
\(67\) 11.5012i 1.40509i 0.711640 + 0.702545i \(0.247953\pi\)
−0.711640 + 0.702545i \(0.752047\pi\)
\(68\) 1.56155 3.68260i 0.189366 0.446581i
\(69\) 0 0
\(70\) 2.00000 1.32431i 0.239046 0.158285i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −7.12311 + 4.71659i −0.828044 + 0.548292i
\(75\) 0 0
\(76\) 5.56155 + 2.35829i 0.637954 + 0.270515i
\(77\) 1.32431i 0.150919i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −4.87689 + 4.71659i −0.545253 + 0.527331i
\(81\) 0 0
\(82\) 3.31534 + 5.00691i 0.366118 + 0.552921i
\(83\) 5.66906i 0.622260i −0.950367 0.311130i \(-0.899292\pi\)
0.950367 0.311130i \(-0.100708\pi\)
\(84\) 0 0
\(85\) 3.39228i 0.367945i
\(86\) 1.56155 1.03399i 0.168387 0.111498i
\(87\) 0 0
\(88\) −0.684658 3.68260i −0.0729848 0.392567i
\(89\) 16.2462 1.72209 0.861047 0.508525i \(-0.169809\pi\)
0.861047 + 0.508525i \(0.169809\pi\)
\(90\) 0 0
\(91\) 1.69614i 0.177804i
\(92\) 4.00000 9.43318i 0.417029 0.983477i
\(93\) 0 0
\(94\) 0 0
\(95\) −5.12311 −0.525620
\(96\) 0 0
\(97\) 12.2462 1.24341 0.621707 0.783250i \(-0.286439\pi\)
0.621707 + 0.783250i \(0.286439\pi\)
\(98\) −0.780776 1.17915i −0.0788703 0.119112i
\(99\) 0 0
\(100\) −1.65767 + 3.90928i −0.165767 + 0.390928i
\(101\) 10.3857i 1.03341i −0.856163 0.516705i \(-0.827158\pi\)
0.856163 0.516705i \(-0.172842\pi\)
\(102\) 0 0
\(103\) 2.24621 0.221326 0.110663 0.993858i \(-0.464703\pi\)
0.110663 + 0.993858i \(0.464703\pi\)
\(104\) −0.876894 4.71659i −0.0859866 0.462500i
\(105\) 0 0
\(106\) −3.12311 + 2.06798i −0.303343 + 0.200860i
\(107\) 14.1498i 1.36791i 0.729524 + 0.683955i \(0.239741\pi\)
−0.729524 + 0.683955i \(0.760259\pi\)
\(108\) 0 0
\(109\) 18.1227i 1.73584i −0.496705 0.867919i \(-0.665457\pi\)
0.496705 0.867919i \(-0.334543\pi\)
\(110\) 1.75379 + 2.64861i 0.167217 + 0.252535i
\(111\) 0 0
\(112\) 2.78078 + 2.87529i 0.262759 + 0.271689i
\(113\) −4.87689 −0.458780 −0.229390 0.973335i \(-0.573673\pi\)
−0.229390 + 0.973335i \(0.573673\pi\)
\(114\) 0 0
\(115\) 8.68951i 0.810301i
\(116\) 11.1231 + 4.71659i 1.03275 + 0.437924i
\(117\) 0 0
\(118\) −0.438447 + 0.290319i −0.0403623 + 0.0267261i
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) 9.24621 0.840565
\(122\) −2.00000 + 1.32431i −0.181071 + 0.119897i
\(123\) 0 0
\(124\) 8.00000 18.8664i 0.718421 1.69425i
\(125\) 12.0818i 1.08063i
\(126\) 0 0
\(127\) 13.1231 1.16449 0.582244 0.813014i \(-0.302175\pi\)
0.582244 + 0.813014i \(0.302175\pi\)
\(128\) −9.21922 6.55789i −0.814872 0.579641i
\(129\) 0 0
\(130\) 2.24621 + 3.39228i 0.197006 + 0.297523i
\(131\) 12.4536i 1.08808i −0.839060 0.544039i \(-0.816894\pi\)
0.839060 0.544039i \(-0.183106\pi\)
\(132\) 0 0
\(133\) 3.02045i 0.261906i
\(134\) 13.5616 8.97983i 1.17154 0.775739i
\(135\) 0 0
\(136\) −5.56155 + 1.03399i −0.476899 + 0.0886637i
\(137\) 16.2462 1.38801 0.694004 0.719971i \(-0.255845\pi\)
0.694004 + 0.719971i \(0.255845\pi\)
\(138\) 0 0
\(139\) 8.31768i 0.705496i −0.935718 0.352748i \(-0.885247\pi\)
0.935718 0.352748i \(-0.114753\pi\)
\(140\) −3.12311 1.32431i −0.263951 0.111924i
\(141\) 0 0
\(142\) −6.24621 9.43318i −0.524170 0.791615i
\(143\) −2.24621 −0.187838
\(144\) 0 0
\(145\) −10.2462 −0.850902
\(146\) 4.68466 + 7.07488i 0.387705 + 0.585522i
\(147\) 0 0
\(148\) 11.1231 + 4.71659i 0.914314 + 0.387701i
\(149\) 14.7304i 1.20676i 0.797453 + 0.603381i \(0.206180\pi\)
−0.797453 + 0.603381i \(0.793820\pi\)
\(150\) 0 0
\(151\) 10.8769 0.885149 0.442575 0.896732i \(-0.354065\pi\)
0.442575 + 0.896732i \(0.354065\pi\)
\(152\) −1.56155 8.39919i −0.126659 0.681264i
\(153\) 0 0
\(154\) 1.56155 1.03399i 0.125834 0.0833211i
\(155\) 17.3790i 1.39592i
\(156\) 0 0
\(157\) 8.48071i 0.676834i −0.940996 0.338417i \(-0.890109\pi\)
0.940996 0.338417i \(-0.109891\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 9.36932 + 2.06798i 0.740710 + 0.163488i
\(161\) 5.12311 0.403757
\(162\) 0 0
\(163\) 13.4061i 1.05005i 0.851088 + 0.525023i \(0.175943\pi\)
−0.851088 + 0.525023i \(0.824057\pi\)
\(164\) 3.31534 7.81855i 0.258885 0.610526i
\(165\) 0 0
\(166\) −6.68466 + 4.42627i −0.518830 + 0.343545i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 10.1231 0.778700
\(170\) 4.00000 2.64861i 0.306786 0.203139i
\(171\) 0 0
\(172\) −2.43845 1.03399i −0.185930 0.0788408i
\(173\) 19.0752i 1.45026i 0.688613 + 0.725129i \(0.258220\pi\)
−0.688613 + 0.725129i \(0.741780\pi\)
\(174\) 0 0
\(175\) −2.12311 −0.160492
\(176\) −3.80776 + 3.68260i −0.287021 + 0.277587i
\(177\) 0 0
\(178\) −12.6847 19.1567i −0.950755 1.43585i
\(179\) 4.71659i 0.352534i −0.984342 0.176267i \(-0.943598\pi\)
0.984342 0.176267i \(-0.0564023\pi\)
\(180\) 0 0
\(181\) 6.99337i 0.519813i −0.965634 0.259906i \(-0.916308\pi\)
0.965634 0.259906i \(-0.0836917\pi\)
\(182\) 2.00000 1.32431i 0.148250 0.0981642i
\(183\) 0 0
\(184\) −14.2462 + 2.64861i −1.05024 + 0.195258i
\(185\) −10.2462 −0.753316
\(186\) 0 0
\(187\) 2.64861i 0.193686i
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 + 6.04090i 0.290191 + 0.438253i
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −11.1231 −0.800659 −0.400329 0.916371i \(-0.631104\pi\)
−0.400329 + 0.916371i \(0.631104\pi\)
\(194\) −9.56155 14.4401i −0.686479 1.03674i
\(195\) 0 0
\(196\) −0.780776 + 1.84130i −0.0557697 + 0.131521i
\(197\) 21.5150i 1.53288i 0.642317 + 0.766439i \(0.277973\pi\)
−0.642317 + 0.766439i \(0.722027\pi\)
\(198\) 0 0
\(199\) −18.2462 −1.29344 −0.646720 0.762728i \(-0.723860\pi\)
−0.646720 + 0.762728i \(0.723860\pi\)
\(200\) 5.90388 1.09763i 0.417468 0.0776143i
\(201\) 0 0
\(202\) −12.2462 + 8.10887i −0.861640 + 0.570538i
\(203\) 6.04090i 0.423988i
\(204\) 0 0
\(205\) 7.20217i 0.503022i
\(206\) −1.75379 2.64861i −0.122192 0.184538i
\(207\) 0 0
\(208\) −4.87689 + 4.71659i −0.338152 + 0.327037i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 4.71659i 0.324703i 0.986733 + 0.162352i \(0.0519079\pi\)
−0.986733 + 0.162352i \(0.948092\pi\)
\(212\) 4.87689 + 2.06798i 0.334946 + 0.142029i
\(213\) 0 0
\(214\) 16.6847 11.0478i 1.14054 0.755212i
\(215\) 2.24621 0.153190
\(216\) 0 0
\(217\) 10.2462 0.695558
\(218\) −21.3693 + 14.1498i −1.44731 + 0.958343i
\(219\) 0 0
\(220\) 1.75379 4.13595i 0.118240 0.278846i
\(221\) 3.39228i 0.228190i
\(222\) 0 0
\(223\) −5.75379 −0.385302 −0.192651 0.981267i \(-0.561709\pi\)
−0.192651 + 0.981267i \(0.561709\pi\)
\(224\) 1.21922 5.52390i 0.0814628 0.369081i
\(225\) 0 0
\(226\) 3.80776 + 5.75058i 0.253289 + 0.382523i
\(227\) 9.80501i 0.650782i 0.945580 + 0.325391i \(0.105496\pi\)
−0.945580 + 0.325391i \(0.894504\pi\)
\(228\) 0 0
\(229\) 25.8597i 1.70886i 0.519568 + 0.854429i \(0.326093\pi\)
−0.519568 + 0.854429i \(0.673907\pi\)
\(230\) 10.2462 6.78456i 0.675615 0.447361i
\(231\) 0 0
\(232\) −3.12311 16.7984i −0.205042 1.10287i
\(233\) 16.2462 1.06432 0.532162 0.846642i \(-0.321380\pi\)
0.532162 + 0.846642i \(0.321380\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.684658 + 0.290319i 0.0445675 + 0.0188982i
\(237\) 0 0
\(238\) −1.56155 2.35829i −0.101220 0.152866i
\(239\) 17.6155 1.13945 0.569727 0.821834i \(-0.307049\pi\)
0.569727 + 0.821834i \(0.307049\pi\)
\(240\) 0 0
\(241\) −3.75379 −0.241803 −0.120901 0.992665i \(-0.538578\pi\)
−0.120901 + 0.992665i \(0.538578\pi\)
\(242\) −7.21922 10.9026i −0.464069 0.700849i
\(243\) 0 0
\(244\) 3.12311 + 1.32431i 0.199936 + 0.0847801i
\(245\) 1.69614i 0.108362i
\(246\) 0 0
\(247\) −5.12311 −0.325975
\(248\) −28.4924 + 5.29723i −1.80927 + 0.336374i
\(249\) 0 0
\(250\) −14.2462 + 9.43318i −0.901010 + 0.596607i
\(251\) 10.9663i 0.692186i −0.938200 0.346093i \(-0.887508\pi\)
0.938200 0.346093i \(-0.112492\pi\)
\(252\) 0 0
\(253\) 6.78456i 0.426542i
\(254\) −10.2462 15.4741i −0.642904 0.970930i
\(255\) 0 0
\(256\) −0.534565 + 15.9911i −0.0334103 + 0.999442i
\(257\) −22.4924 −1.40304 −0.701519 0.712650i \(-0.747495\pi\)
−0.701519 + 0.712650i \(0.747495\pi\)
\(258\) 0 0
\(259\) 6.04090i 0.375363i
\(260\) 2.24621 5.29723i 0.139304 0.328520i
\(261\) 0 0
\(262\) −14.6847 + 9.72350i −0.907221 + 0.600720i
\(263\) −12.4924 −0.770316 −0.385158 0.922851i \(-0.625853\pi\)
−0.385158 + 0.922851i \(0.625853\pi\)
\(264\) 0 0
\(265\) −4.49242 −0.275967
\(266\) 3.56155 2.35829i 0.218373 0.144596i
\(267\) 0 0
\(268\) −21.1771 8.97983i −1.29360 0.548530i
\(269\) 11.8730i 0.723909i −0.932196 0.361954i \(-0.882110\pi\)
0.932196 0.361954i \(-0.117890\pi\)
\(270\) 0 0
\(271\) 10.2462 0.622413 0.311207 0.950342i \(-0.399267\pi\)
0.311207 + 0.950342i \(0.399267\pi\)
\(272\) 5.56155 + 5.75058i 0.337219 + 0.348680i
\(273\) 0 0
\(274\) −12.6847 19.1567i −0.766308 1.15730i
\(275\) 2.81164i 0.169548i
\(276\) 0 0
\(277\) 2.64861i 0.159140i 0.996829 + 0.0795699i \(0.0253547\pi\)
−0.996829 + 0.0795699i \(0.974645\pi\)
\(278\) −9.80776 + 6.49424i −0.588231 + 0.389499i
\(279\) 0 0
\(280\) 0.876894 + 4.71659i 0.0524045 + 0.281870i
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 21.8868i 1.30104i −0.759491 0.650518i \(-0.774552\pi\)
0.759491 0.650518i \(-0.225448\pi\)
\(284\) −6.24621 + 14.7304i −0.370644 + 0.874089i
\(285\) 0 0
\(286\) 1.75379 + 2.64861i 0.103704 + 0.156616i
\(287\) 4.24621 0.250646
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 8.00000 + 12.0818i 0.469776 + 0.709467i
\(291\) 0 0
\(292\) 4.68466 11.0478i 0.274149 0.646524i
\(293\) 10.3857i 0.606736i −0.952873 0.303368i \(-0.901889\pi\)
0.952873 0.303368i \(-0.0981112\pi\)
\(294\) 0 0
\(295\) −0.630683 −0.0367198
\(296\) −3.12311 16.7984i −0.181527 0.976386i
\(297\) 0 0
\(298\) 17.3693 11.5012i 1.00618 0.666244i
\(299\) 8.68951i 0.502527i
\(300\) 0 0
\(301\) 1.32431i 0.0763318i
\(302\) −8.49242 12.8255i −0.488684 0.738022i
\(303\) 0 0
\(304\) −8.68466 + 8.39919i −0.498099 + 0.481727i
\(305\) −2.87689 −0.164730
\(306\) 0 0
\(307\) 25.2791i 1.44275i −0.692543 0.721377i \(-0.743510\pi\)
0.692543 0.721377i \(-0.256490\pi\)
\(308\) −2.43845 1.03399i −0.138943 0.0589169i
\(309\) 0 0
\(310\) 20.4924 13.5691i 1.16389 0.770675i
\(311\) 12.4924 0.708380 0.354190 0.935173i \(-0.384757\pi\)
0.354190 + 0.935173i \(0.384757\pi\)
\(312\) 0 0
\(313\) −20.7386 −1.17222 −0.586108 0.810233i \(-0.699341\pi\)
−0.586108 + 0.810233i \(0.699341\pi\)
\(314\) −10.0000 + 6.62153i −0.564333 + 0.373675i
\(315\) 0 0
\(316\) 0 0
\(317\) 4.13595i 0.232298i −0.993232 0.116149i \(-0.962945\pi\)
0.993232 0.116149i \(-0.0370550\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) −4.87689 12.6624i −0.272627 0.707851i
\(321\) 0 0
\(322\) −4.00000 6.04090i −0.222911 0.336646i
\(323\) 6.04090i 0.336124i
\(324\) 0 0
\(325\) 3.60109i 0.199752i
\(326\) 15.8078 10.4672i 0.875511 0.579723i
\(327\) 0 0
\(328\) −11.8078 + 2.19526i −0.651975 + 0.121213i
\(329\) 0 0
\(330\) 0 0
\(331\) 14.8934i 0.818617i 0.912396 + 0.409309i \(0.134230\pi\)
−0.912396 + 0.409309i \(0.865770\pi\)
\(332\) 10.4384 + 4.42627i 0.572884 + 0.242923i
\(333\) 0 0
\(334\) 6.24621 + 9.43318i 0.341777 + 0.516161i
\(335\) 19.5076 1.06581
\(336\) 0 0
\(337\) −0.876894 −0.0477675 −0.0238837 0.999715i \(-0.507603\pi\)
−0.0238837 + 0.999715i \(0.507603\pi\)
\(338\) −7.90388 11.9366i −0.429915 0.649267i
\(339\) 0 0
\(340\) −6.24621 2.64861i −0.338748 0.143641i
\(341\) 13.5691i 0.734809i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0.684658 + 3.68260i 0.0369143 + 0.198553i
\(345\) 0 0
\(346\) 22.4924 14.8934i 1.20920 0.800676i
\(347\) 8.10887i 0.435307i −0.976026 0.217654i \(-0.930160\pi\)
0.976026 0.217654i \(-0.0698403\pi\)
\(348\) 0 0
\(349\) 27.3471i 1.46385i 0.681383 + 0.731927i \(0.261379\pi\)
−0.681383 + 0.731927i \(0.738621\pi\)
\(350\) 1.65767 + 2.50345i 0.0886062 + 0.133815i
\(351\) 0 0
\(352\) 7.31534 + 1.61463i 0.389909 + 0.0860599i
\(353\) −7.75379 −0.412693 −0.206346 0.978479i \(-0.566157\pi\)
−0.206346 + 0.978479i \(0.566157\pi\)
\(354\) 0 0
\(355\) 13.5691i 0.720175i
\(356\) −12.6847 + 29.9142i −0.672286 + 1.58545i
\(357\) 0 0
\(358\) −5.56155 + 3.68260i −0.293937 + 0.194632i
\(359\) 31.3693 1.65561 0.827805 0.561017i \(-0.189590\pi\)
0.827805 + 0.561017i \(0.189590\pi\)
\(360\) 0 0
\(361\) 9.87689 0.519837
\(362\) −8.24621 + 5.46026i −0.433411 + 0.286985i
\(363\) 0 0
\(364\) −3.12311 1.32431i −0.163695 0.0694125i
\(365\) 10.1768i 0.532680i
\(366\) 0 0
\(367\) 10.2462 0.534848 0.267424 0.963579i \(-0.413828\pi\)
0.267424 + 0.963579i \(0.413828\pi\)
\(368\) 14.2462 + 14.7304i 0.742635 + 0.767875i
\(369\) 0 0
\(370\) 8.00000 + 12.0818i 0.415900 + 0.628102i
\(371\) 2.64861i 0.137509i
\(372\) 0 0
\(373\) 14.7304i 0.762711i −0.924428 0.381356i \(-0.875457\pi\)
0.924428 0.381356i \(-0.124543\pi\)
\(374\) 3.12311 2.06798i 0.161492 0.106932i
\(375\) 0 0
\(376\) 0 0
\(377\) −10.2462 −0.527707
\(378\) 0 0
\(379\) 36.4084i 1.87017i −0.354418 0.935087i \(-0.615321\pi\)
0.354418 0.935087i \(-0.384679\pi\)
\(380\) 4.00000 9.43318i 0.205196 0.483912i
\(381\) 0 0
\(382\) 12.4924 + 18.8664i 0.639168 + 0.965287i
\(383\) 4.49242 0.229552 0.114776 0.993391i \(-0.463385\pi\)
0.114776 + 0.993391i \(0.463385\pi\)
\(384\) 0 0
\(385\) 2.24621 0.114478
\(386\) 8.68466 + 13.1158i 0.442037 + 0.667576i
\(387\) 0 0
\(388\) −9.56155 + 22.5490i −0.485414 + 1.14475i
\(389\) 24.9073i 1.26285i −0.775438 0.631424i \(-0.782471\pi\)
0.775438 0.631424i \(-0.217529\pi\)
\(390\) 0 0
\(391\) 10.2462 0.518173
\(392\) 2.78078 0.516994i 0.140450 0.0261121i
\(393\) 0 0
\(394\) 25.3693 16.7984i 1.27809 0.846290i
\(395\) 0 0
\(396\) 0 0
\(397\) 20.5625i 1.03200i 0.856588 + 0.516001i \(0.172580\pi\)
−0.856588 + 0.516001i \(0.827420\pi\)
\(398\) 14.2462 + 21.5150i 0.714098 + 1.07845i
\(399\) 0 0
\(400\) −5.90388 6.10454i −0.295194 0.305227i
\(401\) 0.876894 0.0437900 0.0218950 0.999760i \(-0.493030\pi\)
0.0218950 + 0.999760i \(0.493030\pi\)
\(402\) 0 0
\(403\) 17.3790i 0.865711i
\(404\) 19.1231 + 8.10887i 0.951410 + 0.403431i
\(405\) 0 0
\(406\) 7.12311 4.71659i 0.353514 0.234080i
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 8.49242 5.62329i 0.419411 0.277714i
\(411\) 0 0
\(412\) −1.75379 + 4.13595i −0.0864030 + 0.203764i
\(413\) 0.371834i 0.0182968i
\(414\) 0 0
\(415\) −9.61553 −0.472008
\(416\) 9.36932 + 2.06798i 0.459369 + 0.101391i
\(417\) 0 0
\(418\) 3.12311 + 4.71659i 0.152756 + 0.230696i
\(419\) 27.9277i 1.36436i −0.731185 0.682179i \(-0.761033\pi\)
0.731185 0.682179i \(-0.238967\pi\)
\(420\) 0 0
\(421\) 26.8122i 1.30675i 0.757036 + 0.653373i \(0.226647\pi\)
−0.757036 + 0.653373i \(0.773353\pi\)
\(422\) 5.56155 3.68260i 0.270732 0.179266i
\(423\) 0 0
\(424\) −1.36932 7.36520i −0.0664999 0.357686i
\(425\) −4.24621 −0.205971
\(426\) 0 0
\(427\) 1.69614i 0.0820820i
\(428\) −26.0540 11.0478i −1.25937 0.534016i
\(429\) 0 0
\(430\) −1.75379 2.64861i −0.0845752 0.127727i
\(431\) −17.6155 −0.848510 −0.424255 0.905543i \(-0.639464\pi\)
−0.424255 + 0.905543i \(0.639464\pi\)
\(432\) 0 0
\(433\) −18.4924 −0.888689 −0.444345 0.895856i \(-0.646563\pi\)
−0.444345 + 0.895856i \(0.646563\pi\)
\(434\) −8.00000 12.0818i −0.384012 0.579945i
\(435\) 0 0
\(436\) 33.3693 + 14.1498i 1.59810 + 0.677651i
\(437\) 15.4741i 0.740225i
\(438\) 0 0
\(439\) 22.7386 1.08526 0.542628 0.839973i \(-0.317429\pi\)
0.542628 + 0.839973i \(0.317429\pi\)
\(440\) −6.24621 + 1.16128i −0.297776 + 0.0553617i
\(441\) 0 0
\(442\) 4.00000 2.64861i 0.190261 0.125982i
\(443\) 7.36520i 0.349931i 0.984575 + 0.174966i \(0.0559814\pi\)
−0.984575 + 0.174966i \(0.944019\pi\)
\(444\) 0 0
\(445\) 27.5559i 1.30627i
\(446\) 4.49242 + 6.78456i 0.212722 + 0.321258i
\(447\) 0 0
\(448\) −7.46543 + 2.87529i −0.352709 + 0.135845i
\(449\) −16.7386 −0.789945 −0.394972 0.918693i \(-0.629246\pi\)
−0.394972 + 0.918693i \(0.629246\pi\)
\(450\) 0 0
\(451\) 5.62329i 0.264790i
\(452\) 3.80776 8.97983i 0.179102 0.422376i
\(453\) 0 0
\(454\) 11.5616 7.65552i 0.542611 0.359291i
\(455\) 2.87689 0.134871
\(456\) 0 0
\(457\) 17.3693 0.812502 0.406251 0.913761i \(-0.366836\pi\)
0.406251 + 0.913761i \(0.366836\pi\)
\(458\) 30.4924 20.1907i 1.42482 0.943448i
\(459\) 0 0
\(460\) −16.0000 6.78456i −0.746004 0.316332i
\(461\) 24.3724i 1.13514i −0.823327 0.567568i \(-0.807885\pi\)
0.823327 0.567568i \(-0.192115\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) −17.3693 + 16.7984i −0.806350 + 0.779845i
\(465\) 0 0
\(466\) −12.6847 19.1567i −0.587605 0.887416i
\(467\) 3.02045i 0.139770i 0.997555 + 0.0698848i \(0.0222632\pi\)
−0.997555 + 0.0698848i \(0.977737\pi\)
\(468\) 0 0
\(469\) 11.5012i 0.531074i
\(470\) 0 0
\(471\) 0 0
\(472\) −0.192236 1.03399i −0.00884838 0.0475931i
\(473\) 1.75379 0.0806393
\(474\) 0 0
\(475\) 6.41273i 0.294236i
\(476\) −1.56155 + 3.68260i −0.0715737 + 0.168792i
\(477\) 0 0
\(478\) −13.7538 20.7713i −0.629084 0.950057i
\(479\) −10.2462 −0.468161 −0.234081 0.972217i \(-0.575208\pi\)
−0.234081 + 0.972217i \(0.575208\pi\)
\(480\) 0 0
\(481\) −10.2462 −0.467187
\(482\) 2.93087 + 4.42627i 0.133497 + 0.201611i
\(483\) 0 0
\(484\) −7.21922 + 17.0251i −0.328147 + 0.773866i
\(485\) 20.7713i 0.943176i
\(486\) 0 0
\(487\) 0.630683 0.0285790 0.0142895 0.999898i \(-0.495451\pi\)
0.0142895 + 0.999898i \(0.495451\pi\)
\(488\) −0.876894 4.71659i −0.0396951 0.213510i
\(489\) 0 0
\(490\) −2.00000 + 1.32431i −0.0903508 + 0.0598261i
\(491\) 34.1774i 1.54240i −0.636590 0.771202i \(-0.719656\pi\)
0.636590 0.771202i \(-0.280344\pi\)
\(492\) 0 0
\(493\) 12.0818i 0.544137i
\(494\) 4.00000 + 6.04090i 0.179969 + 0.271793i
\(495\) 0 0
\(496\) 28.4924 + 29.4608i 1.27935 + 1.32283i
\(497\) −8.00000 −0.358849
\(498\) 0 0
\(499\) 8.85254i 0.396294i −0.980172 0.198147i \(-0.936508\pi\)
0.980172 0.198147i \(-0.0634924\pi\)
\(500\) 22.2462 + 9.43318i 0.994881 + 0.421865i
\(501\) 0 0
\(502\) −12.9309 + 8.56222i −0.577133 + 0.382151i
\(503\) −13.7538 −0.613251 −0.306626 0.951830i \(-0.599200\pi\)
−0.306626 + 0.951830i \(0.599200\pi\)
\(504\) 0 0
\(505\) −17.6155 −0.783881
\(506\) 8.00000 5.29723i 0.355643 0.235490i
\(507\) 0 0
\(508\) −10.2462 + 24.1636i −0.454602 + 1.07209i
\(509\) 30.7393i 1.36250i 0.732052 + 0.681249i \(0.238563\pi\)
−0.732052 + 0.681249i \(0.761437\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) 19.2732 11.8551i 0.851763 0.523927i
\(513\) 0 0
\(514\) 17.5616 + 26.5219i 0.774607 + 1.16983i
\(515\) 3.80989i 0.167884i
\(516\) 0 0
\(517\) 0 0
\(518\) 7.12311 4.71659i 0.312971 0.207235i
\(519\) 0 0
\(520\) −8.00000 + 1.48734i −0.350823 + 0.0652240i
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 41.1708i 1.80027i −0.435609 0.900136i \(-0.643467\pi\)
0.435609 0.900136i \(-0.356533\pi\)
\(524\) 22.9309 + 9.72350i 1.00174 + 0.424773i
\(525\) 0 0
\(526\) 9.75379 + 14.7304i 0.425285 + 0.642276i
\(527\) 20.4924 0.892664
\(528\) 0 0
\(529\) 3.24621 0.141140
\(530\) 3.50758 + 5.29723i 0.152359 + 0.230097i
\(531\) 0 0
\(532\) −5.56155 2.35829i −0.241124 0.102245i
\(533\) 7.20217i 0.311961i
\(534\) 0 0
\(535\) 24.0000 1.03761
\(536\) 5.94602 + 31.9821i 0.256829 + 1.38142i
\(537\) 0 0
\(538\) −14.0000 + 9.27015i −0.603583 + 0.399664i
\(539\) 1.32431i 0.0570419i
\(540\) 0 0
\(541\) 13.2431i 0.569364i −0.958622 0.284682i \(-0.908112\pi\)
0.958622 0.284682i \(-0.0918880\pi\)
\(542\) −8.00000 12.0818i −0.343629 0.518957i
\(543\) 0 0
\(544\) 2.43845 11.0478i 0.104548 0.473671i
\(545\) −30.7386 −1.31670
\(546\) 0 0
\(547\) 9.59621i 0.410304i 0.978730 + 0.205152i \(0.0657689\pi\)
−0.978730 + 0.205152i \(0.934231\pi\)
\(548\) −12.6847 + 29.9142i −0.541862 + 1.27787i
\(549\) 0 0
\(550\) −3.31534 + 2.19526i −0.141367 + 0.0936064i
\(551\) −18.2462 −0.777315
\(552\) 0 0
\(553\) 0 0
\(554\) 3.12311 2.06798i 0.132688 0.0878598i
\(555\) 0 0
\(556\) 15.3153 + 6.49424i 0.649515 + 0.275417i
\(557\) 2.64861i 0.112225i 0.998424 + 0.0561127i \(0.0178706\pi\)
−0.998424 + 0.0561127i \(0.982129\pi\)
\(558\) 0 0
\(559\) 2.24621 0.0950046
\(560\) 4.87689 4.71659i 0.206086 0.199312i
\(561\) 0 0
\(562\) −4.68466 7.07488i −0.197610 0.298436i
\(563\) 29.8326i 1.25730i −0.777690 0.628648i \(-0.783609\pi\)
0.777690 0.628648i \(-0.216391\pi\)
\(564\) 0 0
\(565\) 8.27190i 0.348001i
\(566\) −25.8078 + 17.0887i −1.08478 + 0.718292i
\(567\) 0 0
\(568\) 22.2462 4.13595i 0.933430 0.173541i
\(569\) 13.3693 0.560471 0.280235 0.959931i \(-0.409587\pi\)
0.280235 + 0.959931i \(0.409587\pi\)
\(570\) 0 0
\(571\) 9.27015i 0.387944i −0.981007 0.193972i \(-0.937863\pi\)
0.981007 0.193972i \(-0.0621370\pi\)
\(572\) 1.75379 4.13595i 0.0733296 0.172933i
\(573\) 0 0
\(574\) −3.31534 5.00691i −0.138380 0.208984i
\(575\) −10.8769 −0.453598
\(576\) 0 0
\(577\) 7.75379 0.322794 0.161397 0.986890i \(-0.448400\pi\)
0.161397 + 0.986890i \(0.448400\pi\)
\(578\) 10.1501 + 15.3289i 0.422188 + 0.637599i
\(579\) 0 0
\(580\) 8.00000 18.8664i 0.332182 0.783383i
\(581\) 5.66906i 0.235192i
\(582\) 0 0
\(583\) −3.50758 −0.145269
\(584\) −16.6847 + 3.10196i −0.690416 + 0.128360i
\(585\) 0 0
\(586\) −12.2462 + 8.10887i −0.505886 + 0.334974i
\(587\) 21.8868i 0.903365i 0.892179 + 0.451683i \(0.149176\pi\)
−0.892179 + 0.451683i \(0.850824\pi\)
\(588\) 0 0
\(589\) 30.9481i 1.27520i
\(590\) 0.492423 + 0.743668i 0.0202727 + 0.0306163i
\(591\) 0 0
\(592\) −17.3693 + 16.7984i −0.713875 + 0.690409i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 3.39228i 0.139070i
\(596\) −27.1231 11.5012i −1.11101 0.471106i
\(597\) 0 0
\(598\) 10.2462 6.78456i 0.418999 0.277441i
\(599\) 12.4924 0.510427 0.255213 0.966885i \(-0.417854\pi\)
0.255213 + 0.966885i \(0.417854\pi\)
\(600\) 0 0
\(601\) −16.2462 −0.662697 −0.331348 0.943508i \(-0.607504\pi\)
−0.331348 + 0.943508i \(0.607504\pi\)
\(602\) −1.56155 + 1.03399i −0.0636441 + 0.0421422i
\(603\) 0 0
\(604\) −8.49242 + 20.0276i −0.345552 + 0.814913i
\(605\) 15.6829i 0.637600i
\(606\) 0 0
\(607\) 40.9848 1.66352 0.831762 0.555133i \(-0.187333\pi\)
0.831762 + 0.555133i \(0.187333\pi\)
\(608\) 16.6847 + 3.68260i 0.676652 + 0.149349i
\(609\) 0 0
\(610\) 2.24621 + 3.39228i 0.0909464 + 0.137349i
\(611\) 0 0
\(612\) 0 0
\(613\) 2.23100i 0.0901094i −0.998985 0.0450547i \(-0.985654\pi\)
0.998985 0.0450547i \(-0.0143462\pi\)
\(614\) −29.8078 + 19.7373i −1.20294 + 0.796533i
\(615\) 0 0
\(616\) 0.684658 + 3.68260i 0.0275857 + 0.148376i
\(617\) 29.3693 1.18236 0.591182 0.806538i \(-0.298661\pi\)
0.591182 + 0.806538i \(0.298661\pi\)
\(618\) 0 0
\(619\) 19.6558i 0.790033i 0.918674 + 0.395017i \(0.129261\pi\)
−0.918674 + 0.395017i \(0.870739\pi\)
\(620\) −32.0000 13.5691i −1.28515 0.544949i
\(621\) 0 0
\(622\) −9.75379 14.7304i −0.391091 0.590635i
\(623\) −16.2462 −0.650891
\(624\) 0 0
\(625\) −9.87689 −0.395076
\(626\) 16.1922 + 24.4539i 0.647172 + 0.977375i
\(627\) 0 0
\(628\) 15.6155 + 6.62153i 0.623127 + 0.264228i
\(629\) 12.0818i 0.481733i
\(630\) 0 0
\(631\) −3.50758 −0.139634 −0.0698172 0.997560i \(-0.522242\pi\)
−0.0698172 + 0.997560i \(0.522242\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −4.87689 + 3.22925i −0.193686 + 0.128250i
\(635\) 22.2586i 0.883307i
\(636\) 0 0
\(637\) 1.69614i 0.0672036i
\(638\) 6.24621 + 9.43318i 0.247290 + 0.373463i
\(639\) 0 0
\(640\) −11.1231 + 15.6371i −0.439679 + 0.618111i
\(641\) 5.36932 0.212075 0.106038 0.994362i \(-0.466184\pi\)
0.106038 + 0.994362i \(0.466184\pi\)
\(642\) 0 0
\(643\) 5.66906i 0.223566i 0.993733 + 0.111783i \(0.0356562\pi\)
−0.993733 + 0.111783i \(0.964344\pi\)
\(644\) −4.00000 + 9.43318i −0.157622 + 0.371719i
\(645\) 0 0
\(646\) 7.12311 4.71659i 0.280255 0.185572i
\(647\) −43.2311 −1.69959 −0.849794 0.527115i \(-0.823274\pi\)
−0.849794 + 0.527115i \(0.823274\pi\)
\(648\) 0 0
\(649\) −0.492423 −0.0193293
\(650\) −4.24621 + 2.81164i −0.166550 + 0.110282i
\(651\) 0 0
\(652\) −24.6847 10.4672i −0.966726 0.409926i
\(653\) 31.6918i 1.24020i 0.784524 + 0.620098i \(0.212907\pi\)
−0.784524 + 0.620098i \(0.787093\pi\)
\(654\) 0 0
\(655\) −21.1231 −0.825348
\(656\) 11.8078 + 12.2091i 0.461016 + 0.476685i
\(657\) 0 0
\(658\) 0 0
\(659\) 6.62153i 0.257938i −0.991649 0.128969i \(-0.958833\pi\)
0.991649 0.128969i \(-0.0411668\pi\)
\(660\) 0 0
\(661\) 44.7261i 1.73964i −0.493367 0.869821i \(-0.664234\pi\)
0.493367 0.869821i \(-0.335766\pi\)
\(662\) 17.5616 11.6284i 0.682549 0.451952i
\(663\) 0 0
\(664\) −2.93087 15.7644i −0.113740 0.611777i
\(665\) 5.12311 0.198666
\(666\) 0 0
\(667\) 30.9481i 1.19832i
\(668\) 6.24621 14.7304i 0.241673 0.569936i
\(669\) 0 0
\(670\) −15.2311 23.0023i −0.588427 0.888657i
\(671\) −2.24621 −0.0867140
\(672\) 0 0
\(673\) −38.9848 −1.50276 −0.751378 0.659872i \(-0.770610\pi\)
−0.751378 + 0.659872i \(0.770610\pi\)
\(674\) 0.684658 + 1.03399i 0.0263721 + 0.0398277i
\(675\) 0 0
\(676\) −7.90388 + 18.6397i −0.303995 + 0.716911i
\(677\) 17.1702i 0.659905i −0.943998 0.329952i \(-0.892967\pi\)
0.943998 0.329952i \(-0.107033\pi\)
\(678\) 0 0
\(679\) −12.2462 −0.469966
\(680\) 1.75379 + 9.43318i 0.0672547 + 0.361746i
\(681\) 0 0
\(682\) 16.0000 10.5945i 0.612672 0.405683i
\(683\) 0.580639i 0.0222175i 0.999938 + 0.0111088i \(0.00353610\pi\)
−0.999938 + 0.0111088i \(0.996464\pi\)
\(684\) 0 0
\(685\) 27.5559i 1.05286i
\(686\) 0.780776 + 1.17915i 0.0298102 + 0.0450201i
\(687\) 0 0
\(688\) 3.80776 3.68260i 0.145170 0.140398i
\(689\) −4.49242 −0.171148
\(690\) 0 0
\(691\) 38.8482i 1.47786i −0.673785 0.738928i \(-0.735332\pi\)
0.673785 0.738928i \(-0.264668\pi\)
\(692\) −35.1231 14.8934i −1.33518 0.566163i
\(693\) 0 0
\(694\) −9.56155 + 6.33122i −0.362952 + 0.240330i
\(695\) −14.1080 −0.535145
\(696\) 0 0
\(697\) 8.49242 0.321673
\(698\) 32.2462 21.3519i 1.22054 0.808183i
\(699\) 0 0
\(700\) 1.65767 3.90928i 0.0626541 0.147757i
\(701\) 2.23100i 0.0842639i −0.999112 0.0421319i \(-0.986585\pi\)
0.999112 0.0421319i \(-0.0134150\pi\)
\(702\) 0 0
\(703\) −18.2462 −0.688169
\(704\) −3.80776 9.88653i −0.143511 0.372612i
\(705\) 0 0
\(706\) 6.05398 + 9.14286i 0.227844 + 0.344096i
\(707\) 10.3857i 0.390593i
\(708\) 0 0
\(709\) 28.7171i 1.07849i 0.842147 + 0.539247i \(0.181291\pi\)
−0.842147 + 0.539247i \(0.818709\pi\)
\(710\) −16.0000 + 10.5945i −0.600469 + 0.397603i
\(711\) 0 0
\(712\) 45.1771 8.39919i 1.69308 0.314773i
\(713\) 52.4924 1.96586
\(714\) 0 0
\(715\) 3.80989i 0.142482i
\(716\) 8.68466 + 3.68260i 0.324561 + 0.137625i
\(717\) 0 0
\(718\) −24.4924 36.9890i −0.914049 1.38042i
\(719\) 52.4924 1.95764 0.978819 0.204730i \(-0.0656316\pi\)
0.978819 + 0.204730i \(0.0656316\pi\)
\(720\) 0 0
\(721\) −2.24621 −0.0836533
\(722\) −7.71165 11.6463i −0.286998 0.433431i
\(723\) 0 0
\(724\) 12.8769 + 5.46026i 0.478566 + 0.202929i
\(725\) 12.8255i 0.476326i
\(726\) 0 0
\(727\) −16.9848 −0.629933 −0.314967 0.949103i \(-0.601993\pi\)
−0.314967 + 0.949103i \(0.601993\pi\)
\(728\) 0.876894 + 4.71659i 0.0324999 + 0.174808i
\(729\) 0 0
\(730\) 12.0000 7.94584i 0.444140 0.294089i
\(731\) 2.64861i 0.0979625i
\(732\) 0 0
\(733\) 29.2520i 1.08045i 0.841521 + 0.540224i \(0.181660\pi\)
−0.841521 + 0.540224i \(0.818340\pi\)
\(734\) −8.00000 12.0818i −0.295285 0.445947i
\(735\) 0 0
\(736\) 6.24621 28.2995i 0.230238 1.04313i
\(737\) 15.2311 0.561043
\(738\) 0 0
\(739\) 21.3519i 0.785444i −0.919657 0.392722i \(-0.871533\pi\)
0.919657 0.392722i \(-0.128467\pi\)
\(740\) 8.00000 18.8664i 0.294086 0.693541i
\(741\) 0 0
\(742\) 3.12311 2.06798i 0.114653 0.0759178i
\(743\) −0.630683 −0.0231375 −0.0115688 0.999933i \(-0.503683\pi\)
−0.0115688 + 0.999933i \(0.503683\pi\)
\(744\) 0 0
\(745\) 24.9848 0.915374
\(746\) −17.3693 + 11.5012i −0.635936 + 0.421087i
\(747\) 0 0
\(748\) −4.87689 2.06798i −0.178317 0.0756127i
\(749\) 14.1498i 0.517021i
\(750\) 0 0
\(751\) 8.63068 0.314938 0.157469 0.987524i \(-0.449667\pi\)
0.157469 + 0.987524i \(0.449667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 8.00000 + 12.0818i 0.291343 + 0.439993i
\(755\) 18.4487i 0.671419i
\(756\) 0 0
\(757\) 26.3946i 0.959328i −0.877452 0.479664i \(-0.840759\pi\)
0.877452 0.479664i \(-0.159241\pi\)
\(758\) −42.9309 + 28.4268i −1.55932 + 1.03251i
\(759\) 0 0
\(760\) −14.2462 + 2.64861i −0.516764 + 0.0960753i
\(761\) −8.73863 −0.316775 −0.158388 0.987377i \(-0.550630\pi\)
−0.158388 + 0.987377i \(0.550630\pi\)
\(762\) 0 0
\(763\) 18.1227i 0.656085i
\(764\) 12.4924 29.4608i 0.451960 1.06585i
\(765\) 0 0
\(766\) −3.50758 5.29723i −0.126734 0.191397i
\(767\) −0.630683 −0.0227726
\(768\) 0 0
\(769\) −40.2462 −1.45132 −0.725658 0.688056i \(-0.758464\pi\)
−0.725658 + 0.688056i \(0.758464\pi\)
\(770\) −1.75379 2.64861i −0.0632022 0.0954494i
\(771\) 0 0
\(772\) 8.68466 20.4810i 0.312568 0.737127i
\(773\) 1.69614i 0.0610060i −0.999535 0.0305030i \(-0.990289\pi\)
0.999535 0.0305030i \(-0.00971091\pi\)
\(774\) 0 0
\(775\) −21.7538 −0.781419
\(776\) 34.0540 6.33122i 1.22247 0.227277i
\(777\) 0 0
\(778\) −29.3693 + 19.4470i −1.05294 + 0.697209i
\(779\) 12.8255i 0.459520i
\(780\) 0 0
\(781\) 10.5945i 0.379099i
\(782\) −8.00000 12.0818i −0.286079 0.432044i
\(783\) 0 0
\(784\) −2.78078 2.87529i −0.0993134 0.102689i
\(785\) −14.3845 −0.513404
\(786\) 0 0
\(787\) 10.5487i 0.376020i 0.982167 + 0.188010i \(0.0602037\pi\)
−0.982167 + 0.188010i \(0.939796\pi\)
\(788\) −39.6155 16.7984i −1.41124 0.598418i
\(789\) 0 0
\(790\) 0 0
\(791\) 4.87689 0.173402
\(792\) 0 0
\(793\) −2.87689 −0.102162
\(794\) 24.2462 16.0547i 0.860466 0.569760i
\(795\) 0 0
\(796\) 14.2462 33.5968i 0.504944 1.19081i
\(797\) 25.8597i 0.915998i 0.888953 + 0.457999i \(0.151434\pi\)
−0.888953 + 0.457999i \(0.848566\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.58854 + 11.7278i −0.0915187 + 0.414641i
\(801\) 0 0
\(802\) −0.684658 1.03399i −0.0241761 0.0365114i
\(803\) 7.94584i 0.280403i
\(804\) 0 0
\(805\) 8.68951i 0.306265i
\(806\) 20.4924 13.5691i 0.721815 0.477952i
\(807\) 0 0
\(808\) −5.36932 28.8802i −0.188892 1.01600i
\(809\) −37.8617 −1.33115 −0.665574 0.746332i \(-0.731813\pi\)
−0.665574 + 0.746332i \(0.731813\pi\)
\(810\) 0 0
\(811\) 15.8459i 0.556425i 0.960520 + 0.278213i \(0.0897420\pi\)
−0.960520 + 0.278213i \(0.910258\pi\)
\(812\) −11.1231 4.71659i −0.390344 0.165520i
\(813\) 0 0
\(814\) 6.24621 + 9.43318i 0.218930 + 0.330633i
\(815\) 22.7386 0.796500
\(816\) 0 0
\(817\) 4.00000 0.139942
\(818\) −20.3002 30.6578i −0.709779 1.07193i
\(819\) 0 0
\(820\) −13.2614 5.62329i −0.463107 0.196374i
\(821\) 33.5968i 1.17254i −0.810118 0.586268i \(-0.800597\pi\)
0.810118 0.586268i \(-0.199403\pi\)
\(822\) 0 0
\(823\) −32.9848 −1.14978 −0.574890 0.818231i \(-0.694955\pi\)
−0.574890 + 0.818231i \(0.694955\pi\)
\(824\) 6.24621 1.16128i 0.217597 0.0404550i
\(825\) 0 0
\(826\) 0.438447 0.290319i 0.0152555 0.0101015i
\(827\) 6.20393i 0.215732i −0.994165 0.107866i \(-0.965598\pi\)
0.994165 0.107866i \(-0.0344017\pi\)
\(828\) 0 0
\(829\) 46.6310i 1.61956i 0.586732 + 0.809781i \(0.300414\pi\)
−0.586732 + 0.809781i \(0.699586\pi\)
\(830\) 7.50758 + 11.3381i 0.260592 + 0.393552i
\(831\) 0 0
\(832\) −4.87689 12.6624i −0.169076 0.438991i
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) 13.5691i 0.469579i
\(836\) 3.12311 7.36520i 0.108015 0.254731i
\(837\) 0 0
\(838\) −32.9309 + 21.8053i −1.13758 + 0.753251i
\(839\) 6.73863 0.232643 0.116322 0.993212i \(-0.462890\pi\)
0.116322 + 0.993212i \(0.462890\pi\)
\(840\) 0 0
\(841\) −7.49242 −0.258359
\(842\) 31.6155 20.9343i 1.08954 0.721445i
\(843\) 0 0
\(844\) −8.68466 3.68260i −0.298938 0.126760i
\(845\) 17.1702i 0.590673i
\(846\) 0 0
\(847\) −9.24621 −0.317704
\(848\) −7.61553 + 7.36520i −0.261518 + 0.252922i
\(849\) 0 0
\(850\) 3.31534 + 5.00691i 0.113715 + 0.171736i
\(851\) 30.9481i 1.06089i
\(852\) 0 0
\(853\) 25.4421i 0.871121i −0.900159 0.435561i \(-0.856550\pi\)
0.900159 0.435561i \(-0.143450\pi\)
\(854\) 2.00000 1.32431i 0.0684386 0.0453168i
\(855\) 0 0
\(856\) 7.31534 + 39.3473i 0.250033 + 1.34486i
\(857\) 46.9848 1.60497 0.802486 0.596671i \(-0.203510\pi\)
0.802486 + 0.596671i \(0.203510\pi\)
\(858\) 0 0
\(859\) 28.3453i 0.967129i 0.875309 + 0.483565i \(0.160658\pi\)
−0.875309 + 0.483565i \(0.839342\pi\)
\(860\) −1.75379 + 4.13595i −0.0598037 + 0.141035i
\(861\) 0 0
\(862\) 13.7538 + 20.7713i 0.468456 + 0.707473i
\(863\) −36.4924 −1.24222 −0.621108 0.783725i \(-0.713317\pi\)
−0.621108 + 0.783725i \(0.713317\pi\)
\(864\) 0 0
\(865\) 32.3542 1.10007
\(866\) 14.4384 + 21.8053i 0.490638 + 0.740974i
\(867\) 0 0
\(868\) −8.00000 + 18.8664i −0.271538 + 0.640366i
\(869\) 0 0
\(870\) 0 0
\(871\) 19.5076 0.660989
\(872\) −9.36932 50.3951i −0.317285 1.70659i
\(873\) 0 0
\(874\) 18.2462 12.0818i 0.617187 0.408673i
\(875\) 12.0818i 0.408439i
\(876\) 0 0
\(877\) 35.5017i 1.19881i −0.800447 0.599404i \(-0.795404\pi\)
0.800447 0.599404i \(-0.204596\pi\)
\(878\) −17.7538 26.8122i −0.599161 0.904868i
\(879\) 0 0
\(880\) 6.24621 + 6.45850i 0.210560 + 0.217716i
\(881\) −44.2462 −1.49069 −0.745346 0.666677i \(-0.767716\pi\)
−0.745346 + 0.666677i \(0.767716\pi\)
\(882\) 0 0
\(883\) 4.71659i 0.158726i 0.996846 + 0.0793629i \(0.0252886\pi\)
−0.996846 + 0.0793629i \(0.974711\pi\)
\(884\) −6.24621 2.64861i −0.210083 0.0890825i
\(885\) 0 0
\(886\) 8.68466 5.75058i 0.291767 0.193194i
\(887\) 28.4924 0.956682 0.478341 0.878174i \(-0.341238\pi\)
0.478341 + 0.878174i \(0.341238\pi\)
\(888\) 0 0
\(889\) −13.1231 −0.440135
\(890\) −32.4924 + 21.5150i −1.08915 + 0.721183i
\(891\) 0 0
\(892\) 4.49242 10.5945i 0.150417 0.354729i
\(893\) 0 0
\(894\) 0 0
\(895\) −8.00000 −0.267411
\(896\) 9.21922 + 6.55789i 0.307993 + 0.219084i
\(897\) 0 0
\(898\) 13.0691 + 19.7373i 0.436123 + 0.658643i
\(899\) 61.8963i 2.06436i
\(900\) 0 0
\(901\) 5.29723i 0.176476i
\(902\) 6.63068 4.39053i 0.220778 0.146189i
\(903\) 0 0
\(904\) −13.5616 + 2.52132i −0.451051 + 0.0838580i
\(905\) −11.8617 −0.394298
\(906\) 0 0
\(907\) 51.5564i 1.71190i 0.517056 + 0.855951i \(0.327028\pi\)
−0.517056 + 0.855951i \(0.672972\pi\)
\(908\) −18.0540 7.65552i −0.599142 0.254057i
\(909\) 0 0
\(910\) −2.24621 3.39228i −0.0744612 0.112453i
\(911\) −11.8617 −0.392997 −0.196498 0.980504i \(-0.562957\pi\)
−0.196498 + 0.980504i \(0.562957\pi\)
\(912\) 0 0
\(913\) −7.50758 −0.248465
\(914\) −13.5616 20.4810i −0.448576 0.677451i
\(915\) 0 0
\(916\) −47.6155 20.1907i −1.57326 0.667118i
\(917\) 12.4536i 0.411255i
\(918\) 0 0
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 4.49242 + 24.1636i 0.148111 + 0.796650i
\(921\) 0 0
\(922\) −28.7386 + 19.0294i −0.946456 + 0.626699i
\(923\) 13.5691i 0.446633i
\(924\) 0 0
\(925\) 12.8255i 0.421699i
\(926\) 0 0
\(927\) 0 0
\(928\) 33.3693 + 7.36520i 1.09540 + 0.241775i
\(929\) 2.49242 0.0817737 0.0408869 0.999164i \(-0.486982\pi\)
0.0408869 + 0.999164i \(0.486982\pi\)
\(930\) 0 0
\(931\) 3.02045i 0.0989912i
\(932\) −12.6847 + 29.9142i −0.415500 + 0.979871i
\(933\) 0 0
\(934\) 3.56155 2.35829i 0.116538 0.0771658i
\(935\) 4.49242 0.146918
\(936\) 0 0
\(937\) 34.9848 1.14291 0.571453 0.820635i \(-0.306380\pi\)
0.571453 + 0.820635i \(0.306380\pi\)
\(938\) −13.5616 + 8.97983i −0.442800 + 0.293202i
\(939\) 0 0
\(940\) 0 0
\(941\) 30.7393i 1.00207i 0.865426 + 0.501037i \(0.167048\pi\)
−0.865426 + 0.501037i \(0.832952\pi\)
\(942\) 0 0
\(943\) 21.7538 0.708401
\(944\) −1.06913 + 1.03399i −0.0347972 + 0.0336534i
\(945\) 0 0
\(946\) −1.36932 2.06798i −0.0445203 0.0672357i
\(947\) 41.7056i 1.35525i 0.735407 + 0.677625i \(0.236991\pi\)
−0.735407 + 0.677625i \(0.763009\pi\)
\(948\) 0 0
\(949\) 10.1768i 0.330354i
\(950\) −7.56155 + 5.00691i −0.245329 + 0.162446i
\(951\) 0 0
\(952\) 5.56155 1.03399i 0.180251 0.0335117i
\(953\) 17.5076 0.567126 0.283563 0.958954i \(-0.408483\pi\)
0.283563 + 0.958954i \(0.408483\pi\)
\(954\) 0 0
\(955\) 27.1383i 0.878173i
\(956\) −13.7538 + 32.4355i −0.444829 + 1.04904i
\(957\) 0 0
\(958\) 8.00000 + 12.0818i 0.258468 + 0.390345i
\(959\) −16.2462 −0.524618
\(960\) 0 0
\(961\) 73.9848 2.38661
\(962\) 8.00000 + 12.0818i 0.257930 + 0.389533i
\(963\) 0 0
\(964\) 2.93087 6.91185i 0.0943970 0.222616i
\(965\) 18.8664i 0.607329i
\(966\) 0 0
\(967\) −10.8769 −0.349777 −0.174889 0.984588i \(-0.555957\pi\)
−0.174889 + 0.984588i \(0.555957\pi\)
\(968\) 25.7116 4.78023i 0.826404 0.153643i
\(969\) 0 0
\(970\) −24.4924 + 16.2177i −0.786404 + 0.520720i
\(971\) 10.9663i 0.351925i −0.984397 0.175962i \(-0.943696\pi\)
0.984397 0.175962i \(-0.0563037\pi\)
\(972\) 0 0
\(973\) 8.31768i 0.266652i
\(974\) −0.492423 0.743668i −0.0157782 0.0238287i
\(975\) 0 0
\(976\) −4.87689 + 4.71659i −0.156106 + 0.150974i
\(977\) −23.7538 −0.759951 −0.379976 0.924997i \(-0.624068\pi\)
−0.379976 + 0.924997i \(0.624068\pi\)
\(978\) 0 0
\(979\) 21.5150i 0.687621i
\(980\) 3.12311 + 1.32431i 0.0997639 + 0.0423034i
\(981\) 0 0
\(982\) −40.3002 + 26.6849i −1.28603 + 0.851550i
\(983\) 34.2462 1.09228 0.546142 0.837692i \(-0.316096\pi\)
0.546142 + 0.837692i \(0.316096\pi\)
\(984\) 0 0
\(985\) 36.4924 1.16275
\(986\) 14.2462 9.43318i 0.453692 0.300414i
\(987\) 0 0
\(988\) 4.00000 9.43318i 0.127257 0.300109i
\(989\) 6.78456i 0.215737i
\(990\) 0 0
\(991\) −36.4924 −1.15922 −0.579610 0.814894i \(-0.696795\pi\)
−0.579610 + 0.814894i \(0.696795\pi\)
\(992\) 12.4924 56.5991i 0.396635 1.79702i
\(993\) 0 0
\(994\) 6.24621 + 9.43318i 0.198118 + 0.299202i
\(995\) 30.9481i 0.981122i
\(996\) 0 0
\(997\) 33.0619i 1.04708i −0.852001 0.523540i \(-0.824611\pi\)
0.852001 0.523540i \(-0.175389\pi\)
\(998\) −10.4384 + 6.91185i −0.330423 + 0.218791i
\(999\) 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 504.2.c.d.253.1 4
3.2 odd 2 56.2.b.b.29.4 yes 4
4.3 odd 2 2016.2.c.c.1009.2 4
8.3 odd 2 2016.2.c.c.1009.3 4
8.5 even 2 inner 504.2.c.d.253.2 4
12.11 even 2 224.2.b.b.113.4 4
21.2 odd 6 392.2.p.f.165.3 8
21.5 even 6 392.2.p.e.165.3 8
21.11 odd 6 392.2.p.f.373.1 8
21.17 even 6 392.2.p.e.373.1 8
21.20 even 2 392.2.b.c.197.4 4
24.5 odd 2 56.2.b.b.29.3 4
24.11 even 2 224.2.b.b.113.1 4
48.5 odd 4 1792.2.a.x.1.1 4
48.11 even 4 1792.2.a.v.1.4 4
48.29 odd 4 1792.2.a.x.1.4 4
48.35 even 4 1792.2.a.v.1.1 4
84.11 even 6 1568.2.t.d.177.4 8
84.23 even 6 1568.2.t.d.753.1 8
84.47 odd 6 1568.2.t.e.753.4 8
84.59 odd 6 1568.2.t.e.177.1 8
84.83 odd 2 1568.2.b.d.785.1 4
168.5 even 6 392.2.p.e.165.1 8
168.11 even 6 1568.2.t.d.177.1 8
168.53 odd 6 392.2.p.f.373.3 8
168.59 odd 6 1568.2.t.e.177.4 8
168.83 odd 2 1568.2.b.d.785.4 4
168.101 even 6 392.2.p.e.373.3 8
168.107 even 6 1568.2.t.d.753.4 8
168.125 even 2 392.2.b.c.197.3 4
168.131 odd 6 1568.2.t.e.753.1 8
168.149 odd 6 392.2.p.f.165.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.b.b.29.3 4 24.5 odd 2
56.2.b.b.29.4 yes 4 3.2 odd 2
224.2.b.b.113.1 4 24.11 even 2
224.2.b.b.113.4 4 12.11 even 2
392.2.b.c.197.3 4 168.125 even 2
392.2.b.c.197.4 4 21.20 even 2
392.2.p.e.165.1 8 168.5 even 6
392.2.p.e.165.3 8 21.5 even 6
392.2.p.e.373.1 8 21.17 even 6
392.2.p.e.373.3 8 168.101 even 6
392.2.p.f.165.1 8 168.149 odd 6
392.2.p.f.165.3 8 21.2 odd 6
392.2.p.f.373.1 8 21.11 odd 6
392.2.p.f.373.3 8 168.53 odd 6
504.2.c.d.253.1 4 1.1 even 1 trivial
504.2.c.d.253.2 4 8.5 even 2 inner
1568.2.b.d.785.1 4 84.83 odd 2
1568.2.b.d.785.4 4 168.83 odd 2
1568.2.t.d.177.1 8 168.11 even 6
1568.2.t.d.177.4 8 84.11 even 6
1568.2.t.d.753.1 8 84.23 even 6
1568.2.t.d.753.4 8 168.107 even 6
1568.2.t.e.177.1 8 84.59 odd 6
1568.2.t.e.177.4 8 168.59 odd 6
1568.2.t.e.753.1 8 168.131 odd 6
1568.2.t.e.753.4 8 84.47 odd 6
1792.2.a.v.1.1 4 48.35 even 4
1792.2.a.v.1.4 4 48.11 even 4
1792.2.a.x.1.1 4 48.5 odd 4
1792.2.a.x.1.4 4 48.29 odd 4
2016.2.c.c.1009.2 4 4.3 odd 2
2016.2.c.c.1009.3 4 8.3 odd 2