Properties

Label 252.2.i.a.25.1
Level $252$
Weight $2$
Character 252.25
Analytic conductor $2.012$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(25,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.25
Dual form 252.2.i.a.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(-1.50000 - 2.59808i) q^{13} -3.46410i q^{15} +(-3.50000 + 6.06218i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(4.50000 - 0.866025i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} -3.00000 q^{31} +(6.00000 + 3.46410i) q^{33} +(4.00000 - 3.46410i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(4.50000 + 2.59808i) q^{39} +(4.50000 + 7.79423i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(3.00000 + 5.19615i) q^{45} +3.00000 q^{47} +(5.50000 + 4.33013i) q^{49} -12.1244i q^{51} +(-1.50000 + 2.59808i) q^{53} +8.00000 q^{55} +(7.50000 + 4.33013i) q^{57} -7.00000 q^{59} +3.00000 q^{61} +(-6.00000 + 5.19615i) q^{63} +6.00000 q^{65} +13.0000 q^{67} -6.92820i q^{69} -8.00000 q^{71} +(-3.50000 + 6.06218i) q^{73} +(-1.50000 - 0.866025i) q^{75} +(2.00000 + 10.3923i) q^{77} -9.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(-0.500000 + 0.866025i) q^{83} +(-7.00000 - 12.1244i) q^{85} +1.73205i q^{87} +(-7.50000 - 12.9904i) q^{89} +(1.50000 + 7.79423i) q^{91} +(4.50000 - 2.59808i) q^{93} +10.0000 q^{95} +(8.50000 - 14.7224i) q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - 2 q^{5} - 5 q^{7} + 3 q^{9} - 4 q^{11} - 3 q^{13} - 7 q^{17} - 5 q^{19} + 9 q^{21} - 4 q^{23} + q^{25} + q^{29} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 11 q^{37} + 9 q^{39} + 9 q^{41} - 5 q^{43} + 6 q^{45} + 6 q^{47} + 11 q^{49} - 3 q^{53} + 16 q^{55} + 15 q^{57} - 14 q^{59} + 6 q^{61} - 12 q^{63} + 12 q^{65} + 26 q^{67} - 16 q^{71} - 7 q^{73} - 3 q^{75} + 4 q^{77} - 18 q^{79} - 9 q^{81} - q^{83} - 14 q^{85} - 15 q^{89} + 3 q^{91} + 9 q^{93} + 20 q^{95} + 17 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 0 0
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i \(0.489386\pi\)
−0.882213 + 0.470850i \(0.843947\pi\)
\(18\) 0 0
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 0 0
\(21\) 4.50000 0.866025i 0.981981 0.188982i
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0 0
\(33\) 6.00000 + 3.46410i 1.04447 + 0.603023i
\(34\) 0 0
\(35\) 4.00000 3.46410i 0.676123 0.585540i
\(36\) 0 0
\(37\) −5.50000 9.52628i −0.904194 1.56611i −0.821995 0.569495i \(-0.807139\pi\)
−0.0821995 0.996616i \(-0.526194\pi\)
\(38\) 0 0
\(39\) 4.50000 + 2.59808i 0.720577 + 0.416025i
\(40\) 0 0
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i \(-0.957838\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 3.00000 + 5.19615i 0.447214 + 0.774597i
\(46\) 0 0
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 12.1244i 1.69775i
\(52\) 0 0
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) 7.50000 + 4.33013i 0.993399 + 0.573539i
\(58\) 0 0
\(59\) −7.00000 −0.911322 −0.455661 0.890153i \(-0.650597\pi\)
−0.455661 + 0.890153i \(0.650597\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 0 0
\(63\) −6.00000 + 5.19615i −0.755929 + 0.654654i
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 13.0000 1.58820 0.794101 0.607785i \(-0.207942\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −3.50000 + 6.06218i −0.409644 + 0.709524i −0.994850 0.101361i \(-0.967680\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) −1.50000 0.866025i −0.173205 0.100000i
\(76\) 0 0
\(77\) 2.00000 + 10.3923i 0.227921 + 1.18431i
\(78\) 0 0
\(79\) −9.00000 −1.01258 −0.506290 0.862364i \(-0.668983\pi\)
−0.506290 + 0.862364i \(0.668983\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −0.500000 + 0.866025i −0.0548821 + 0.0950586i −0.892161 0.451717i \(-0.850812\pi\)
0.837279 + 0.546776i \(0.184145\pi\)
\(84\) 0 0
\(85\) −7.00000 12.1244i −0.759257 1.31507i
\(86\) 0 0
\(87\) 1.73205i 0.185695i
\(88\) 0 0
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 0 0
\(91\) 1.50000 + 7.79423i 0.157243 + 0.817057i
\(92\) 0 0
\(93\) 4.50000 2.59808i 0.466628 0.269408i
\(94\) 0 0
\(95\) 10.0000 1.02598
\(96\) 0 0
\(97\) 8.50000 14.7224i 0.863044 1.49484i −0.00593185 0.999982i \(-0.501888\pi\)
0.868976 0.494854i \(-0.164778\pi\)
\(98\) 0 0
\(99\) −12.0000 −1.20605
\(100\) 0 0
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 0 0
\(105\) −3.00000 + 8.66025i −0.292770 + 0.845154i
\(106\) 0 0
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 0 0
\(111\) 16.5000 + 9.52628i 1.56611 + 0.904194i
\(112\) 0 0
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) 0 0
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) 0 0
\(117\) −9.00000 −0.832050
\(118\) 0 0
\(119\) 14.0000 12.1244i 1.28338 1.11144i
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) −13.5000 7.79423i −1.21725 0.702782i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 8.66025i 0.762493i
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) 2.50000 + 12.9904i 0.216777 + 1.12641i
\(134\) 0 0
\(135\) −9.00000 5.19615i −0.774597 0.447214i
\(136\) 0 0
\(137\) −7.00000 12.1244i −0.598050 1.03585i −0.993109 0.117198i \(-0.962609\pi\)
0.395058 0.918656i \(-0.370724\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) −4.50000 + 2.59808i −0.378968 + 0.218797i
\(142\) 0 0
\(143\) −6.00000 + 10.3923i −0.501745 + 0.869048i
\(144\) 0 0
\(145\) 1.00000 + 1.73205i 0.0830455 + 0.143839i
\(146\) 0 0
\(147\) −12.0000 1.73205i −0.989743 0.142857i
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 10.5000 + 18.1865i 0.848875 + 1.47029i
\(154\) 0 0
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 0 0
\(159\) 5.19615i 0.412082i
\(160\) 0 0
\(161\) 8.00000 6.92820i 0.630488 0.546019i
\(162\) 0 0
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) 0 0
\(165\) −12.0000 + 6.92820i −0.934199 + 0.539360i
\(166\) 0 0
\(167\) −11.5000 19.9186i −0.889897 1.54135i −0.839996 0.542592i \(-0.817443\pi\)
−0.0499004 0.998754i \(-0.515890\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 0 0
\(171\) −15.0000 −1.14708
\(172\) 0 0
\(173\) −1.00000 −0.0760286 −0.0380143 0.999277i \(-0.512103\pi\)
−0.0380143 + 0.999277i \(0.512103\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 0 0
\(177\) 10.5000 6.06218i 0.789228 0.455661i
\(178\) 0 0
\(179\) 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i \(-0.546095\pi\)
0.929114 0.369792i \(-0.120571\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) −4.50000 + 2.59808i −0.332650 + 0.192055i
\(184\) 0 0
\(185\) 22.0000 1.61747
\(186\) 0 0
\(187\) 28.0000 2.04756
\(188\) 0 0
\(189\) 4.50000 12.9904i 0.327327 0.944911i
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) −1.00000 −0.0719816 −0.0359908 0.999352i \(-0.511459\pi\)
−0.0359908 + 0.999352i \(0.511459\pi\)
\(194\) 0 0
\(195\) −9.00000 + 5.19615i −0.644503 + 0.372104i
\(196\) 0 0
\(197\) −26.0000 −1.85242 −0.926212 0.377004i \(-0.876954\pi\)
−0.926212 + 0.377004i \(0.876954\pi\)
\(198\) 0 0
\(199\) 6.50000 11.2583i 0.460773 0.798082i −0.538227 0.842800i \(-0.680906\pi\)
0.999000 + 0.0447181i \(0.0142390\pi\)
\(200\) 0 0
\(201\) −19.5000 + 11.2583i −1.37542 + 0.794101i
\(202\) 0 0
\(203\) −2.00000 + 1.73205i −0.140372 + 0.121566i
\(204\) 0 0
\(205\) −18.0000 −1.25717
\(206\) 0 0
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) 0 0
\(209\) −10.0000 + 17.3205i −0.691714 + 1.19808i
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) 12.0000 6.92820i 0.822226 0.474713i
\(214\) 0 0
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 0 0
\(217\) 7.50000 + 2.59808i 0.509133 + 0.176369i
\(218\) 0 0
\(219\) 12.1244i 0.819288i
\(220\) 0 0
\(221\) 21.0000 1.41261
\(222\) 0 0
\(223\) 3.50000 6.06218i 0.234377 0.405953i −0.724714 0.689050i \(-0.758028\pi\)
0.959092 + 0.283096i \(0.0913615\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 0 0
\(231\) −12.0000 13.8564i −0.789542 0.911685i
\(232\) 0 0
\(233\) 14.5000 + 25.1147i 0.949927 + 1.64532i 0.745573 + 0.666424i \(0.232176\pi\)
0.204354 + 0.978897i \(0.434491\pi\)
\(234\) 0 0
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 0 0
\(237\) 13.5000 7.79423i 0.876919 0.506290i
\(238\) 0 0
\(239\) 10.5000 + 18.1865i 0.679189 + 1.17639i 0.975226 + 0.221213i \(0.0710015\pi\)
−0.296037 + 0.955176i \(0.595665\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 0 0
\(245\) −13.0000 + 5.19615i −0.830540 + 0.331970i
\(246\) 0 0
\(247\) −7.50000 + 12.9904i −0.477214 + 0.826558i
\(248\) 0 0
\(249\) 1.73205i 0.109764i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 21.0000 + 12.1244i 1.31507 + 0.759257i
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 5.50000 + 28.5788i 0.341753 + 1.77580i
\(260\) 0 0
\(261\) −1.50000 2.59808i −0.0928477 0.160817i
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −3.00000 5.19615i −0.184289 0.319197i
\(266\) 0 0
\(267\) 22.5000 + 12.9904i 1.37698 + 0.794998i
\(268\) 0 0
\(269\) 0.500000 0.866025i 0.0304855 0.0528025i −0.850380 0.526169i \(-0.823628\pi\)
0.880866 + 0.473366i \(0.156961\pi\)
\(270\) 0 0
\(271\) 1.50000 + 2.59808i 0.0911185 + 0.157822i 0.907982 0.419009i \(-0.137622\pi\)
−0.816864 + 0.576831i \(0.804289\pi\)
\(272\) 0 0
\(273\) −9.00000 10.3923i −0.544705 0.628971i
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 0 0
\(279\) −4.50000 + 7.79423i −0.269408 + 0.466628i
\(280\) 0 0
\(281\) 8.50000 14.7224i 0.507067 0.878267i −0.492899 0.870087i \(-0.664063\pi\)
0.999967 0.00818015i \(-0.00260385\pi\)
\(282\) 0 0
\(283\) 1.00000 0.0594438 0.0297219 0.999558i \(-0.490538\pi\)
0.0297219 + 0.999558i \(0.490538\pi\)
\(284\) 0 0
\(285\) −15.0000 + 8.66025i −0.888523 + 0.512989i
\(286\) 0 0
\(287\) −4.50000 23.3827i −0.265627 1.38024i
\(288\) 0 0
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) 29.4449i 1.72609i
\(292\) 0 0
\(293\) −13.5000 23.3827i −0.788678 1.36603i −0.926777 0.375613i \(-0.877432\pi\)
0.138098 0.990419i \(-0.455901\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) 0 0
\(297\) 18.0000 10.3923i 1.04447 0.603023i
\(298\) 0 0
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 10.0000 8.66025i 0.576390 0.499169i
\(302\) 0 0
\(303\) 3.00000 + 1.73205i 0.172345 + 0.0995037i
\(304\) 0 0
\(305\) −3.00000 + 5.19615i −0.171780 + 0.297531i
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 13.8564i 0.788263i
\(310\) 0 0
\(311\) −31.0000 −1.75785 −0.878924 0.476961i \(-0.841738\pi\)
−0.878924 + 0.476961i \(0.841738\pi\)
\(312\) 0 0
\(313\) −17.0000 −0.960897 −0.480448 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 0 0
\(315\) −3.00000 15.5885i −0.169031 0.878310i
\(316\) 0 0
\(317\) −9.00000 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) 0 0
\(319\) −4.00000 −0.223957
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 0 0
\(323\) 35.0000 1.94745
\(324\) 0 0
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) 0 0
\(327\) 12.1244i 0.670478i
\(328\) 0 0
\(329\) −7.50000 2.59808i −0.413488 0.143237i
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) 0 0
\(333\) −33.0000 −1.80839
\(334\) 0 0
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 0 0
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) 0 0
\(339\) −1.50000 0.866025i −0.0814688 0.0470360i
\(340\) 0 0
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 12.0000 + 6.92820i 0.646058 + 0.373002i
\(346\) 0 0
\(347\) −15.0000 −0.805242 −0.402621 0.915367i \(-0.631901\pi\)
−0.402621 + 0.915367i \(0.631901\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 13.5000 7.79423i 0.720577 0.416025i
\(352\) 0 0
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) 0 0
\(357\) −10.5000 + 30.3109i −0.555719 + 1.60422i
\(358\) 0 0
\(359\) 15.5000 + 26.8468i 0.818059 + 1.41692i 0.907111 + 0.420892i \(0.138283\pi\)
−0.0890519 + 0.996027i \(0.528384\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) 8.66025i 0.454545i
\(364\) 0 0
\(365\) −7.00000 12.1244i −0.366397 0.634618i
\(366\) 0 0
\(367\) −16.0000 27.7128i −0.835193 1.44660i −0.893873 0.448320i \(-0.852022\pi\)
0.0586798 0.998277i \(-0.481311\pi\)
\(368\) 0 0
\(369\) 27.0000 1.40556
\(370\) 0 0
\(371\) 6.00000 5.19615i 0.311504 0.269771i
\(372\) 0 0
\(373\) −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) 0 0
\(375\) 18.0000 10.3923i 0.929516 0.536656i
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.00000 + 13.8564i −0.408781 + 0.708029i −0.994753 0.102302i \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) 0 0
\(385\) −20.0000 6.92820i −1.01929 0.353094i
\(386\) 0 0
\(387\) 7.50000 + 12.9904i 0.381246 + 0.660338i
\(388\) 0 0
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) −14.0000 24.2487i −0.708010 1.22631i
\(392\) 0 0
\(393\) 6.92820i 0.349482i
\(394\) 0 0
\(395\) 9.00000 15.5885i 0.452839 0.784340i
\(396\) 0 0
\(397\) 10.5000 + 18.1865i 0.526980 + 0.912756i 0.999506 + 0.0314391i \(0.0100090\pi\)
−0.472526 + 0.881317i \(0.656658\pi\)
\(398\) 0 0
\(399\) −15.0000 17.3205i −0.750939 0.867110i
\(400\) 0 0
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) 4.50000 + 7.79423i 0.224161 + 0.388258i
\(404\) 0 0
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) −22.0000 + 38.1051i −1.09050 + 1.88880i
\(408\) 0 0
\(409\) 23.0000 1.13728 0.568638 0.822588i \(-0.307470\pi\)
0.568638 + 0.822588i \(0.307470\pi\)
\(410\) 0 0
\(411\) 21.0000 + 12.1244i 1.03585 + 0.598050i
\(412\) 0 0
\(413\) 17.5000 + 6.06218i 0.861119 + 0.298300i
\(414\) 0 0
\(415\) −1.00000 1.73205i −0.0490881 0.0850230i
\(416\) 0 0
\(417\) −7.50000 4.33013i −0.367277 0.212047i
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) 0 0
\(421\) 4.50000 7.79423i 0.219317 0.379867i −0.735283 0.677761i \(-0.762951\pi\)
0.954599 + 0.297893i \(0.0962839\pi\)
\(422\) 0 0
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 0 0
\(425\) −7.00000 −0.339550
\(426\) 0 0
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) 0 0
\(429\) 20.7846i 1.00349i
\(430\) 0 0
\(431\) −19.5000 + 33.7750i −0.939282 + 1.62688i −0.172468 + 0.985015i \(0.555174\pi\)
−0.766814 + 0.641869i \(0.778159\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −3.00000 1.73205i −0.143839 0.0830455i
\(436\) 0 0
\(437\) 20.0000 0.956730
\(438\) 0 0
\(439\) −21.0000 −1.00228 −0.501138 0.865368i \(-0.667085\pi\)
−0.501138 + 0.865368i \(0.667085\pi\)
\(440\) 0 0
\(441\) 19.5000 7.79423i 0.928571 0.371154i
\(442\) 0 0
\(443\) −29.0000 −1.37783 −0.688916 0.724841i \(-0.741913\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(444\) 0 0
\(445\) 30.0000 1.42214
\(446\) 0 0
\(447\) 10.3923i 0.491539i
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) 0 0
\(453\) −12.0000 6.92820i −0.563809 0.325515i
\(454\) 0 0
\(455\) −15.0000 5.19615i −0.703211 0.243599i
\(456\) 0 0
\(457\) 31.0000 1.45012 0.725059 0.688686i \(-0.241812\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 0 0
\(459\) −31.5000 18.1865i −1.47029 0.848875i
\(460\) 0 0
\(461\) −11.5000 + 19.9186i −0.535608 + 0.927701i 0.463525 + 0.886084i \(0.346584\pi\)
−0.999134 + 0.0416172i \(0.986749\pi\)
\(462\) 0 0
\(463\) 2.50000 + 4.33013i 0.116185 + 0.201238i 0.918253 0.395995i \(-0.129600\pi\)
−0.802068 + 0.597233i \(0.796267\pi\)
\(464\) 0 0
\(465\) 10.3923i 0.481932i
\(466\) 0 0
\(467\) −8.50000 14.7224i −0.393333 0.681273i 0.599554 0.800334i \(-0.295345\pi\)
−0.992887 + 0.119062i \(0.962011\pi\)
\(468\) 0 0
\(469\) −32.5000 11.2583i −1.50071 0.519861i
\(470\) 0 0
\(471\) 19.5000 11.2583i 0.898513 0.518756i
\(472\) 0 0
\(473\) 20.0000 0.919601
\(474\) 0 0
\(475\) 2.50000 4.33013i 0.114708 0.198680i
\(476\) 0 0
\(477\) 4.50000 + 7.79423i 0.206041 + 0.356873i
\(478\) 0 0
\(479\) 4.00000 + 6.92820i 0.182765 + 0.316558i 0.942821 0.333300i \(-0.108162\pi\)
−0.760056 + 0.649857i \(0.774829\pi\)
\(480\) 0 0
\(481\) −16.5000 + 28.5788i −0.752335 + 1.30308i
\(482\) 0 0
\(483\) −6.00000 + 17.3205i −0.273009 + 0.788110i
\(484\) 0 0
\(485\) 17.0000 + 29.4449i 0.771930 + 1.33702i
\(486\) 0 0
\(487\) 0.500000 0.866025i 0.0226572 0.0392434i −0.854475 0.519493i \(-0.826121\pi\)
0.877132 + 0.480250i \(0.159454\pi\)
\(488\) 0 0
\(489\) −28.5000 16.4545i −1.28881 0.744097i
\(490\) 0 0
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 3.50000 + 6.06218i 0.157632 + 0.273027i
\(494\) 0 0
\(495\) 12.0000 20.7846i 0.539360 0.934199i
\(496\) 0 0
\(497\) 20.0000 + 6.92820i 0.897123 + 0.310772i
\(498\) 0 0
\(499\) −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 0 0
\(501\) 34.5000 + 19.9186i 1.54135 + 0.889897i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 6.92820i 0.307692i
\(508\) 0 0
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) 14.0000 12.1244i 0.619324 0.536350i
\(512\) 0 0
\(513\) 22.5000 12.9904i 0.993399 0.573539i
\(514\) 0 0
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) −6.00000 10.3923i −0.263880 0.457053i
\(518\) 0 0
\(519\) 1.50000 0.866025i 0.0658427 0.0380143i
\(520\) 0 0
\(521\) −1.50000 + 2.59808i −0.0657162 + 0.113824i −0.897011 0.442007i \(-0.854267\pi\)
0.831295 + 0.555831i \(0.187600\pi\)
\(522\) 0 0
\(523\) −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) 0 0
\(525\) 3.00000 + 3.46410i 0.130931 + 0.151186i
\(526\) 0 0
\(527\) 10.5000 18.1865i 0.457387 0.792218i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −10.5000 + 18.1865i −0.455661 + 0.789228i
\(532\) 0 0
\(533\) 13.5000 23.3827i 0.584750 1.01282i
\(534\) 0 0
\(535\) −6.00000 −0.259403
\(536\) 0 0
\(537\) 36.3731i 1.56961i
\(538\) 0 0
\(539\) 4.00000 27.7128i 0.172292 1.19368i
\(540\) 0 0
\(541\) 16.5000 + 28.5788i 0.709390 + 1.22870i 0.965084 + 0.261942i \(0.0843630\pi\)
−0.255693 + 0.966758i \(0.582304\pi\)
\(542\) 0 0
\(543\) 9.00000 5.19615i 0.386227 0.222988i
\(544\) 0 0
\(545\) −7.00000 12.1244i −0.299847 0.519350i
\(546\) 0 0
\(547\) −16.5000 + 28.5788i −0.705489 + 1.22194i 0.261026 + 0.965332i \(0.415939\pi\)
−0.966515 + 0.256611i \(0.917394\pi\)
\(548\) 0 0
\(549\) 4.50000 7.79423i 0.192055 0.332650i
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) 22.5000 + 7.79423i 0.956797 + 0.331444i
\(554\) 0 0
\(555\) −33.0000 + 19.0526i −1.40077 + 0.808736i
\(556\) 0 0
\(557\) −5.50000 + 9.52628i −0.233042 + 0.403641i −0.958702 0.284413i \(-0.908201\pi\)
0.725660 + 0.688054i \(0.241535\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0 0
\(561\) −42.0000 + 24.2487i −1.77324 + 1.02378i
\(562\) 0 0
\(563\) 13.0000 0.547885 0.273942 0.961746i \(-0.411672\pi\)
0.273942 + 0.961746i \(0.411672\pi\)
\(564\) 0 0
\(565\) −2.00000 −0.0841406
\(566\) 0 0
\(567\) 4.50000 + 23.3827i 0.188982 + 0.981981i
\(568\) 0 0
\(569\) 27.0000 1.13190 0.565949 0.824440i \(-0.308510\pi\)
0.565949 + 0.824440i \(0.308510\pi\)
\(570\) 0 0
\(571\) −3.00000 −0.125546 −0.0627730 0.998028i \(-0.519994\pi\)
−0.0627730 + 0.998028i \(0.519994\pi\)
\(572\) 0 0
\(573\) −22.5000 + 12.9904i −0.939951 + 0.542681i
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i \(-0.879879\pi\)
0.783930 + 0.620850i \(0.213212\pi\)
\(578\) 0 0
\(579\) 1.50000 0.866025i 0.0623379 0.0359908i
\(580\) 0 0
\(581\) 2.00000 1.73205i 0.0829740 0.0718576i
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) 0 0
\(585\) 9.00000 15.5885i 0.372104 0.644503i
\(586\) 0 0
\(587\) −18.5000 + 32.0429i −0.763577 + 1.32255i 0.177419 + 0.984135i \(0.443225\pi\)
−0.940996 + 0.338418i \(0.890108\pi\)
\(588\) 0 0
\(589\) 7.50000 + 12.9904i 0.309032 + 0.535259i
\(590\) 0 0
\(591\) 39.0000 22.5167i 1.60425 0.926212i
\(592\) 0 0
\(593\) −13.5000 23.3827i −0.554379 0.960212i −0.997952 0.0639736i \(-0.979623\pi\)
0.443573 0.896238i \(-0.353711\pi\)
\(594\) 0 0
\(595\) 7.00000 + 36.3731i 0.286972 + 1.49115i
\(596\) 0 0
\(597\) 22.5167i 0.921546i
\(598\) 0 0
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) 0 0
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) 24.0000 41.5692i 0.974130 1.68724i 0.291353 0.956616i \(-0.405895\pi\)
0.682777 0.730627i \(-0.260772\pi\)
\(608\) 0 0
\(609\) 1.50000 4.33013i 0.0607831 0.175466i
\(610\) 0 0
\(611\) −4.50000 7.79423i −0.182051 0.315321i
\(612\) 0 0
\(613\) 4.50000 7.79423i 0.181753 0.314806i −0.760724 0.649075i \(-0.775156\pi\)
0.942478 + 0.334269i \(0.108489\pi\)
\(614\) 0 0
\(615\) 27.0000 15.5885i 1.08875 0.628587i
\(616\) 0 0
\(617\) −21.5000 37.2391i −0.865557 1.49919i −0.866493 0.499190i \(-0.833631\pi\)
0.000935233 1.00000i \(-0.499702\pi\)
\(618\) 0 0
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) 0 0
\(621\) −18.0000 10.3923i −0.722315 0.417029i
\(622\) 0 0
\(623\) 7.50000 + 38.9711i 0.300481 + 1.56135i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 34.6410i 1.38343i
\(628\) 0 0
\(629\) 77.0000 3.07019
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −19.5000 11.2583i −0.775055 0.447478i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 20.7846i 0.118864 0.823516i
\(638\) 0 0
\(639\) −12.0000 + 20.7846i −0.474713 + 0.822226i
\(640\) 0 0
\(641\) 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 0 0
\(643\) 6.50000 + 11.2583i 0.256335 + 0.443985i 0.965257 0.261301i \(-0.0841516\pi\)
−0.708922 + 0.705287i \(0.750818\pi\)
\(644\) 0 0
\(645\) 15.0000 + 8.66025i 0.590624 + 0.340997i
\(646\) 0 0
\(647\) −1.50000 + 2.59808i −0.0589711 + 0.102141i −0.894004 0.448059i \(-0.852115\pi\)
0.835033 + 0.550200i \(0.185449\pi\)
\(648\) 0 0
\(649\) 14.0000 + 24.2487i 0.549548 + 0.951845i
\(650\) 0 0
\(651\) −13.5000 + 2.59808i −0.529107 + 0.101827i
\(652\) 0 0
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) 4.00000 + 6.92820i 0.156293 + 0.270707i
\(656\) 0 0
\(657\) 10.5000 + 18.1865i 0.409644 + 0.709524i
\(658\) 0 0
\(659\) −12.5000 + 21.6506i −0.486931 + 0.843389i −0.999887 0.0150258i \(-0.995217\pi\)
0.512956 + 0.858415i \(0.328550\pi\)
\(660\) 0 0
\(661\) −17.0000 −0.661223 −0.330612 0.943767i \(-0.607255\pi\)
−0.330612 + 0.943767i \(0.607255\pi\)
\(662\) 0 0
\(663\) −31.5000 + 18.1865i −1.22336 + 0.706306i
\(664\) 0 0
\(665\) −25.0000 8.66025i −0.969458 0.335830i
\(666\) 0 0
\(667\) 2.00000 + 3.46410i 0.0774403 + 0.134131i
\(668\) 0 0
\(669\) 12.1244i 0.468755i
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) 12.5000 21.6506i 0.481840 0.834571i −0.517943 0.855415i \(-0.673302\pi\)
0.999783 + 0.0208444i \(0.00663546\pi\)
\(674\) 0 0
\(675\) −4.50000 + 2.59808i −0.173205 + 0.100000i
\(676\) 0 0
\(677\) 27.0000 1.03769 0.518847 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(678\) 0 0
\(679\) −34.0000 + 29.4449i −1.30480 + 1.12999i
\(680\) 0 0
\(681\) −18.0000 10.3923i −0.689761 0.398234i
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) 24.2487i 0.925146i
\(688\) 0 0
\(689\) 9.00000 0.342873
\(690\) 0 0
\(691\) 11.0000 0.418460 0.209230 0.977866i \(-0.432904\pi\)
0.209230 + 0.977866i \(0.432904\pi\)
\(692\) 0 0
\(693\) 30.0000 + 10.3923i 1.13961 + 0.394771i
\(694\) 0 0
\(695\) −10.0000 −0.379322
\(696\) 0 0
\(697\) −63.0000 −2.38630
\(698\) 0 0
\(699\) −43.5000 25.1147i −1.64532 0.949927i
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) −27.5000 + 47.6314i −1.03718 + 1.79645i
\(704\) 0 0
\(705\) 10.3923i 0.391397i
\(706\) 0 0
\(707\) 1.00000 + 5.19615i 0.0376089 + 0.195421i
\(708\) 0 0
\(709\) −25.0000 −0.938895 −0.469447 0.882960i \(-0.655547\pi\)
−0.469447 + 0.882960i \(0.655547\pi\)
\(710\) 0 0
\(711\) −13.5000 + 23.3827i −0.506290 + 0.876919i
\(712\) 0 0
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) −12.0000 20.7846i −0.448775 0.777300i
\(716\) 0 0
\(717\) −31.5000 18.1865i −1.17639 0.679189i
\(718\) 0 0
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 0 0
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) 0 0
\(723\) −15.0000 8.66025i −0.557856 0.322078i
\(724\) 0 0
\(725\) 1.00000 0.0371391
\(726\) 0 0
\(727\) 23.5000 40.7032i 0.871567 1.50960i 0.0111912 0.999937i \(-0.496438\pi\)
0.860376 0.509661i \(-0.170229\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −17.5000 30.3109i −0.647261 1.12109i
\(732\) 0 0
\(733\) −15.0000 + 25.9808i −0.554038 + 0.959621i 0.443940 + 0.896056i \(0.353580\pi\)
−0.997978 + 0.0635649i \(0.979753\pi\)
\(734\) 0 0
\(735\) 15.0000 19.0526i 0.553283 0.702764i
\(736\) 0 0
\(737\) −26.0000 45.0333i −0.957722 1.65882i
\(738\) 0 0
\(739\) 10.5000 18.1865i 0.386249 0.669002i −0.605693 0.795699i \(-0.707104\pi\)
0.991942 + 0.126696i \(0.0404373\pi\)
\(740\) 0 0
\(741\) 25.9808i 0.954427i
\(742\) 0 0
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) 0 0
\(747\) 1.50000 + 2.59808i 0.0548821 + 0.0950586i
\(748\) 0 0
\(749\) −1.50000 7.79423i −0.0548088 0.284795i
\(750\) 0 0
\(751\) 12.0000 20.7846i 0.437886 0.758441i −0.559640 0.828736i \(-0.689061\pi\)
0.997526 + 0.0702946i \(0.0223939\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) −24.0000 + 13.8564i −0.871145 + 0.502956i
\(760\) 0 0
\(761\) 1.00000 1.73205i 0.0362500 0.0627868i −0.847331 0.531065i \(-0.821792\pi\)
0.883581 + 0.468278i \(0.155125\pi\)
\(762\) 0 0
\(763\) 14.0000 12.1244i 0.506834 0.438931i
\(764\) 0 0
\(765\) −42.0000 −1.51851
\(766\) 0 0
\(767\) 10.5000 + 18.1865i 0.379133 + 0.656678i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 31.1769i 1.12281i
\(772\) 0 0
\(773\) −11.5000 + 19.9186i −0.413626 + 0.716422i −0.995283 0.0970125i \(-0.969071\pi\)
0.581657 + 0.813434i \(0.302405\pi\)
\(774\) 0 0
\(775\) −1.50000 2.59808i −0.0538816 0.0933257i
\(776\) 0 0
\(777\) −33.0000 38.1051i −1.18387 1.36701i
\(778\) 0 0
\(779\) 22.5000 38.9711i 0.806146 1.39629i
\(780\) 0 0
\(781\) 16.0000 + 27.7128i 0.572525 + 0.991642i
\(782\) 0 0
\(783\) 4.50000 + 2.59808i 0.160817 + 0.0928477i
\(784\) 0 0
\(785\) 13.0000 22.5167i 0.463990 0.803654i
\(786\) 0 0
\(787\) 21.0000 0.748569 0.374285 0.927314i \(-0.377888\pi\)
0.374285 + 0.927314i \(0.377888\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.500000 2.59808i −0.0177780 0.0923770i
\(792\) 0 0
\(793\) −4.50000 7.79423i −0.159800 0.276781i
\(794\) 0 0
\(795\) 9.00000 + 5.19615i 0.319197 + 0.184289i
\(796\) 0 0
\(797\) −7.50000 12.9904i −0.265664 0.460143i 0.702074 0.712104i \(-0.252258\pi\)
−0.967737 + 0.251961i \(0.918924\pi\)
\(798\) 0 0
\(799\) −10.5000 + 18.1865i −0.371463 + 0.643393i
\(800\) 0 0
\(801\) −45.0000 −1.59000
\(802\) 0 0
\(803\) 28.0000 0.988099
\(804\) 0 0
\(805\) 4.00000 + 20.7846i 0.140981 + 0.732561i
\(806\) 0 0
\(807\) 1.73205i 0.0609711i
\(808\) 0 0
\(809\) 0.500000 0.866025i 0.0175791 0.0304478i −0.857102 0.515147i \(-0.827737\pi\)
0.874681 + 0.484699i \(0.161071\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) −4.50000 2.59808i −0.157822 0.0911185i
\(814\) 0 0
\(815\) −38.0000 −1.33108
\(816\) 0 0
\(817\) 25.0000 0.874639
\(818\) 0 0
\(819\) 22.5000 + 7.79423i 0.786214 + 0.272352i
\(820\) 0 0
\(821\) −53.0000 −1.84971 −0.924856 0.380317i \(-0.875815\pi\)
−0.924856 + 0.380317i \(0.875815\pi\)
\(822\) 0 0
\(823\) −23.0000 −0.801730 −0.400865 0.916137i \(-0.631290\pi\)
−0.400865 + 0.916137i \(0.631290\pi\)
\(824\) 0 0
\(825\) 6.92820i 0.241209i
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) −9.50000 + 16.4545i −0.329949 + 0.571488i −0.982501 0.186256i \(-0.940365\pi\)
0.652553 + 0.757743i \(0.273698\pi\)
\(830\) 0 0
\(831\) 3.00000 + 1.73205i 0.104069 + 0.0600842i
\(832\) 0 0
\(833\) −45.5000 + 18.1865i −1.57648 + 0.630126i
\(834\) 0 0
\(835\) 46.0000 1.59190
\(836\) 0 0
\(837\) 15.5885i 0.538816i
\(838\) 0 0
\(839\) 11.5000 19.9186i 0.397024 0.687666i −0.596333 0.802737i \(-0.703376\pi\)
0.993357 + 0.115071i \(0.0367096\pi\)
\(840\) 0 0
\(841\) 14.0000 + 24.2487i 0.482759 + 0.836162i
\(842\) 0 0
\(843\) 29.4449i 1.01413i
\(844\) 0 0
\(845\) 4.00000 + 6.92820i 0.137604 + 0.238337i
\(846\) 0 0
\(847\) 10.0000 8.66025i 0.343604 0.297570i
\(848\) 0 0
\(849\) −1.50000 + 0.866025i −0.0514799 + 0.0297219i
\(850\) 0 0
\(851\) 44.0000 1.50830
\(852\) 0 0
\(853\) −17.5000 + 30.3109i −0.599189 + 1.03783i 0.393753 + 0.919216i \(0.371177\pi\)
−0.992941 + 0.118609i \(0.962157\pi\)
\(854\) 0 0
\(855\) 15.0000 25.9808i 0.512989 0.888523i
\(856\) 0 0
\(857\) 9.00000 + 15.5885i 0.307434 + 0.532492i 0.977800 0.209539i \(-0.0671963\pi\)
−0.670366 + 0.742030i \(0.733863\pi\)
\(858\) 0 0
\(859\) −22.0000 + 38.1051i −0.750630 + 1.30013i 0.196887 + 0.980426i \(0.436917\pi\)
−0.947518 + 0.319704i \(0.896417\pi\)
\(860\) 0 0
\(861\) 27.0000 + 31.1769i 0.920158 + 1.06251i
\(862\) 0 0
\(863\) −20.5000 35.5070i −0.697828 1.20867i −0.969218 0.246204i \(-0.920817\pi\)
0.271390 0.962470i \(-0.412517\pi\)
\(864\) 0 0
\(865\) 1.00000 1.73205i 0.0340010 0.0588915i
\(866\) 0 0
\(867\) 48.0000 + 27.7128i 1.63017 + 0.941176i
\(868\) 0 0
\(869\) 18.0000 + 31.1769i 0.610608 + 1.05760i
\(870\) 0 0
\(871\) −19.5000 33.7750i −0.660732 1.14442i
\(872\) 0 0
\(873\) −25.5000 44.1673i −0.863044 1.49484i
\(874\) 0 0
\(875\) 30.0000 + 10.3923i 1.01419 + 0.351324i
\(876\) 0 0
\(877\) 19.0000 32.9090i 0.641584 1.11126i −0.343495 0.939155i \(-0.611611\pi\)
0.985079 0.172102i \(-0.0550559\pi\)
\(878\) 0 0
\(879\) 40.5000 + 23.3827i 1.36603 + 0.788678i
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) −28.0000 −0.942275 −0.471138 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) 0 0
\(885\) 24.2487i 0.815112i
\(886\) 0 0
\(887\) −6.00000 + 10.3923i −0.201460 + 0.348939i −0.948999 0.315279i \(-0.897902\pi\)
0.747539 + 0.664218i \(0.231235\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −18.0000 + 31.1769i −0.603023 + 1.04447i
\(892\) 0 0
\(893\) −7.50000 12.9904i −0.250978 0.434707i
\(894\) 0 0
\(895\) 21.0000 + 36.3731i 0.701953 + 1.21582i
\(896\) 0 0
\(897\) −18.0000 + 10.3923i −0.601003 + 0.346989i
\(898\) 0 0
\(899\) −1.50000 + 2.59808i −0.0500278 + 0.0866507i
\(900\) 0 0
\(901\) −10.5000 18.1865i −0.349806 0.605881i
\(902\) 0 0
\(903\) −7.50000 + 21.6506i −0.249584 + 0.720488i
\(904\) 0 0
\(905\) 6.00000 10.3923i 0.199447 0.345452i
\(906\) 0 0
\(907\) −18.0000 31.1769i −0.597680 1.03521i −0.993163 0.116739i \(-0.962756\pi\)
0.395482 0.918474i \(-0.370577\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 19.5000 33.7750i 0.646064 1.11902i −0.337991 0.941149i \(-0.609747\pi\)
0.984055 0.177866i \(-0.0569194\pi\)
\(912\) 0 0
\(913\) 4.00000 0.132381
\(914\) 0 0
\(915\) 10.3923i 0.343559i
\(916\) 0 0
\(917\) −8.00000 + 6.92820i −0.264183 + 0.228789i
\(918\) 0 0
\(919\) 17.5000 + 30.3109i 0.577272 + 0.999864i 0.995791 + 0.0916559i \(0.0292160\pi\)
−0.418519 + 0.908208i \(0.637451\pi\)
\(920\) 0 0
\(921\) 12.0000 6.92820i 0.395413 0.228292i
\(922\) 0 0
\(923\) 12.0000 + 20.7846i 0.394985 + 0.684134i
\(924\) 0 0
\(925\) 5.50000 9.52628i 0.180839 0.313222i
\(926\) 0 0
\(927\) 12.0000 + 20.7846i 0.394132 + 0.682656i
\(928\) 0 0
\(929\) 3.00000 0.0984268 0.0492134 0.998788i \(-0.484329\pi\)
0.0492134 + 0.998788i \(0.484329\pi\)
\(930\) 0 0
\(931\) 5.00000 34.6410i 0.163868 1.13531i
\(932\) 0 0
\(933\) 46.5000 26.8468i 1.52234 0.878924i
\(934\) 0 0
\(935\) −28.0000 + 48.4974i −0.915698 + 1.58604i
\(936\) 0 0
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 0 0
\(939\) 25.5000 14.7224i 0.832161 0.480448i
\(940\) 0 0
\(941\) 59.0000 1.92335 0.961673 0.274201i \(-0.0884132\pi\)
0.961673 + 0.274201i \(0.0884132\pi\)
\(942\) 0 0
\(943\) −36.0000 −1.17232
\(944\) 0 0
\(945\) 18.0000 + 20.7846i 0.585540 + 0.676123i
\(946\) 0 0
\(947\) −25.0000 −0.812391 −0.406195 0.913786i \(-0.633145\pi\)
−0.406195 + 0.913786i \(0.633145\pi\)
\(948\) 0 0
\(949\) 21.0000 0.681689
\(950\) 0 0
\(951\) 13.5000 7.79423i 0.437767 0.252745i
\(952\) 0 0
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 0 0
\(955\) −15.0000 + 25.9808i −0.485389 + 0.840718i
\(956\) 0 0
\(957\) 6.00000 3.46410i 0.193952 0.111979i
\(958\) 0 0
\(959\) 7.00000 + 36.3731i 0.226042 + 1.17455i
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) 9.00000 0.290021
\(964\) 0 0
\(965\) 1.00000 1.73205i 0.0321911 0.0557567i
\(966\) 0 0
\(967\) −23.5000 40.7032i −0.755709 1.30893i −0.945021 0.327009i \(-0.893959\pi\)
0.189312 0.981917i \(-0.439374\pi\)
\(968\) 0 0
\(969\) −52.5000 + 30.3109i −1.68654 + 0.973726i
\(970\) 0 0
\(971\) 7.50000 + 12.9904i 0.240686 + 0.416881i 0.960910 0.276861i \(-0.0892941\pi\)
−0.720224 + 0.693742i \(0.755961\pi\)
\(972\) 0 0
\(973\) −2.50000 12.9904i −0.0801463 0.416452i
\(974\) 0 0
\(975\) 5.19615i 0.166410i
\(976\) 0 0
\(977\) 3.00000 0.0959785 0.0479893 0.998848i \(-0.484719\pi\)
0.0479893 + 0.998848i \(0.484719\pi\)
\(978\) 0 0
\(979\) −30.0000 + 51.9615i −0.958804 + 1.66070i
\(980\) 0 0
\(981\) 10.5000 + 18.1865i 0.335239 + 0.580651i
\(982\) 0 0
\(983\) 18.0000 + 31.1769i 0.574111 + 0.994389i 0.996138 + 0.0878058i \(0.0279855\pi\)
−0.422027 + 0.906583i \(0.638681\pi\)
\(984\) 0 0
\(985\) 26.0000 45.0333i 0.828429 1.43488i
\(986\) 0 0
\(987\) 13.5000 2.59808i 0.429710 0.0826977i
\(988\) 0 0
\(989\) −10.0000 17.3205i −0.317982 0.550760i
\(990\) 0 0
\(991\) 18.5000 32.0429i 0.587672 1.01788i −0.406865 0.913488i \(-0.633378\pi\)
0.994537 0.104389i \(-0.0332887\pi\)
\(992\) 0 0
\(993\) 37.5000 21.6506i 1.19003 0.687062i
\(994\) 0 0
\(995\) 13.0000 + 22.5167i 0.412128 + 0.713826i
\(996\) 0 0
\(997\) 11.0000 + 19.0526i 0.348373 + 0.603401i 0.985961 0.166978i \(-0.0534008\pi\)
−0.637587 + 0.770378i \(0.720067\pi\)
\(998\) 0 0
\(999\) 49.5000 28.5788i 1.56611 0.904194i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 252.2.i.a.25.1 2
3.2 odd 2 756.2.i.a.613.1 2
4.3 odd 2 1008.2.q.f.529.1 2
7.2 even 3 252.2.l.a.205.1 yes 2
7.3 odd 6 1764.2.j.a.1177.1 2
7.4 even 3 1764.2.j.c.1177.1 2
7.5 odd 6 1764.2.l.b.961.1 2
7.6 odd 2 1764.2.i.b.1537.1 2
9.2 odd 6 2268.2.k.b.1621.1 2
9.4 even 3 252.2.l.a.193.1 yes 2
9.5 odd 6 756.2.l.a.361.1 2
9.7 even 3 2268.2.k.a.1621.1 2
12.11 even 2 3024.2.q.e.2881.1 2
21.2 odd 6 756.2.l.a.289.1 2
21.5 even 6 5292.2.l.b.3313.1 2
21.11 odd 6 5292.2.j.c.3529.1 2
21.17 even 6 5292.2.j.b.3529.1 2
21.20 even 2 5292.2.i.b.2125.1 2
28.23 odd 6 1008.2.t.b.961.1 2
36.23 even 6 3024.2.t.b.1873.1 2
36.31 odd 6 1008.2.t.b.193.1 2
63.2 odd 6 2268.2.k.b.1297.1 2
63.4 even 3 1764.2.j.c.589.1 2
63.5 even 6 5292.2.i.b.1549.1 2
63.13 odd 6 1764.2.l.b.949.1 2
63.16 even 3 2268.2.k.a.1297.1 2
63.23 odd 6 756.2.i.a.37.1 2
63.31 odd 6 1764.2.j.a.589.1 2
63.32 odd 6 5292.2.j.c.1765.1 2
63.40 odd 6 1764.2.i.b.373.1 2
63.41 even 6 5292.2.l.b.361.1 2
63.58 even 3 inner 252.2.i.a.121.1 yes 2
63.59 even 6 5292.2.j.b.1765.1 2
84.23 even 6 3024.2.t.b.289.1 2
252.23 even 6 3024.2.q.e.2305.1 2
252.247 odd 6 1008.2.q.f.625.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.i.a.25.1 2 1.1 even 1 trivial
252.2.i.a.121.1 yes 2 63.58 even 3 inner
252.2.l.a.193.1 yes 2 9.4 even 3
252.2.l.a.205.1 yes 2 7.2 even 3
756.2.i.a.37.1 2 63.23 odd 6
756.2.i.a.613.1 2 3.2 odd 2
756.2.l.a.289.1 2 21.2 odd 6
756.2.l.a.361.1 2 9.5 odd 6
1008.2.q.f.529.1 2 4.3 odd 2
1008.2.q.f.625.1 2 252.247 odd 6
1008.2.t.b.193.1 2 36.31 odd 6
1008.2.t.b.961.1 2 28.23 odd 6
1764.2.i.b.373.1 2 63.40 odd 6
1764.2.i.b.1537.1 2 7.6 odd 2
1764.2.j.a.589.1 2 63.31 odd 6
1764.2.j.a.1177.1 2 7.3 odd 6
1764.2.j.c.589.1 2 63.4 even 3
1764.2.j.c.1177.1 2 7.4 even 3
1764.2.l.b.949.1 2 63.13 odd 6
1764.2.l.b.961.1 2 7.5 odd 6
2268.2.k.a.1297.1 2 63.16 even 3
2268.2.k.a.1621.1 2 9.7 even 3
2268.2.k.b.1297.1 2 63.2 odd 6
2268.2.k.b.1621.1 2 9.2 odd 6
3024.2.q.e.2305.1 2 252.23 even 6
3024.2.q.e.2881.1 2 12.11 even 2
3024.2.t.b.289.1 2 84.23 even 6
3024.2.t.b.1873.1 2 36.23 even 6
5292.2.i.b.1549.1 2 63.5 even 6
5292.2.i.b.2125.1 2 21.20 even 2
5292.2.j.b.1765.1 2 63.59 even 6
5292.2.j.b.3529.1 2 21.17 even 6
5292.2.j.c.1765.1 2 63.32 odd 6
5292.2.j.c.3529.1 2 21.11 odd 6
5292.2.l.b.361.1 2 63.41 even 6
5292.2.l.b.3313.1 2 21.5 even 6