Properties

Label 675.3.j.a.476.1
Level $675$
Weight $3$
Character 675.476
Analytic conductor $18.392$
Analytic rank $0$
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] = [675,3,Mod(251,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.251");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 675.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.3924178443\)
Analytic rank: \(0\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 9)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 476.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 675.476
Dual form 675.3.j.a.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} -8.66025i q^{8} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} -8.66025i q^{8} +(1.50000 - 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} +15.5885i q^{17} +11.0000 q^{19} +(-1.50000 + 2.59808i) q^{22} +(-24.0000 - 13.8564i) q^{23} -6.92820i q^{26} -2.00000 q^{28} +(-39.0000 + 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(13.5000 + 7.79423i) q^{32} +(-13.5000 - 23.3827i) q^{34} +34.0000 q^{37} +(-16.5000 + 9.52628i) q^{38} +(10.5000 + 6.06218i) q^{41} +(-30.5000 - 52.8275i) q^{43} +1.73205i q^{44} +48.0000 q^{46} +(-42.0000 + 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +(-2.00000 - 3.46410i) q^{52} +(15.0000 - 8.66025i) q^{56} +(39.0000 - 67.5500i) q^{58} +(-43.5000 - 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} -55.4256i q^{62} -71.0000 q^{64} +(-15.5000 + 26.8468i) q^{67} +(-13.5000 - 7.79423i) q^{68} +31.1769i q^{71} -65.0000 q^{73} +(-51.0000 + 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(3.00000 + 1.73205i) q^{77} +(-19.0000 - 32.9090i) q^{79} -21.0000 q^{82} +(-42.0000 + 24.2487i) q^{83} +(91.5000 + 52.8275i) q^{86} +(-7.50000 - 12.9904i) q^{88} -124.708i q^{89} -8.00000 q^{91} +(24.0000 - 13.8564i) q^{92} +(42.0000 - 72.7461i) q^{94} +(-57.5000 - 99.5929i) q^{97} +77.9423i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - q^{4} + 2 q^{7} + 3 q^{11} - 4 q^{13} - 6 q^{14} + 11 q^{16} + 22 q^{19} - 3 q^{22} - 48 q^{23} - 4 q^{28} - 78 q^{29} - 32 q^{31} + 27 q^{32} - 27 q^{34} + 68 q^{37} - 33 q^{38} + 21 q^{41} - 61 q^{43} + 96 q^{46} - 84 q^{47} + 45 q^{49} - 4 q^{52} + 30 q^{56} + 78 q^{58} - 87 q^{59} - 56 q^{61} - 142 q^{64} - 31 q^{67} - 27 q^{68} - 130 q^{73} - 102 q^{74} - 11 q^{76} + 6 q^{77} - 38 q^{79} - 42 q^{82} - 84 q^{83} + 183 q^{86} - 15 q^{88} - 16 q^{91} + 48 q^{92} + 84 q^{94} - 115 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 0.866025i −0.750000 + 0.433013i −0.825694 0.564118i \(-0.809216\pi\)
0.0756939 + 0.997131i \(0.475883\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.142857 + 0.247436i 0.928571 0.371154i \(-0.121038\pi\)
−0.785714 + 0.618590i \(0.787704\pi\)
\(8\) 8.66025i 1.08253i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 0.866025i 0.136364 0.0787296i −0.430266 0.902702i \(-0.641580\pi\)
0.566630 + 0.823972i \(0.308247\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.46410i −0.153846 + 0.266469i −0.932638 0.360813i \(-0.882499\pi\)
0.778792 + 0.627282i \(0.215833\pi\)
\(14\) −3.00000 1.73205i −0.214286 0.123718i
\(15\) 0 0
\(16\) 5.50000 + 9.52628i 0.343750 + 0.595392i
\(17\) 15.5885i 0.916968i 0.888703 + 0.458484i \(0.151607\pi\)
−0.888703 + 0.458484i \(0.848393\pi\)
\(18\) 0 0
\(19\) 11.0000 0.578947 0.289474 0.957186i \(-0.406520\pi\)
0.289474 + 0.957186i \(0.406520\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.50000 + 2.59808i −0.0681818 + 0.118094i
\(23\) −24.0000 13.8564i −1.04348 0.602452i −0.122662 0.992449i \(-0.539143\pi\)
−0.920817 + 0.389996i \(0.872476\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 6.92820i 0.266469i
\(27\) 0 0
\(28\) −2.00000 −0.0714286
\(29\) −39.0000 + 22.5167i −1.34483 + 0.776437i −0.987511 0.157547i \(-0.949641\pi\)
−0.357316 + 0.933984i \(0.616308\pi\)
\(30\) 0 0
\(31\) −16.0000 + 27.7128i −0.516129 + 0.893962i 0.483696 + 0.875236i \(0.339294\pi\)
−0.999825 + 0.0187254i \(0.994039\pi\)
\(32\) 13.5000 + 7.79423i 0.421875 + 0.243570i
\(33\) 0 0
\(34\) −13.5000 23.3827i −0.397059 0.687726i
\(35\) 0 0
\(36\) 0 0
\(37\) 34.0000 0.918919 0.459459 0.888199i \(-0.348043\pi\)
0.459459 + 0.888199i \(0.348043\pi\)
\(38\) −16.5000 + 9.52628i −0.434211 + 0.250692i
\(39\) 0 0
\(40\) 0 0
\(41\) 10.5000 + 6.06218i 0.256098 + 0.147858i 0.622553 0.782578i \(-0.286095\pi\)
−0.366456 + 0.930436i \(0.619429\pi\)
\(42\) 0 0
\(43\) −30.5000 52.8275i −0.709302 1.22855i −0.965116 0.261822i \(-0.915677\pi\)
0.255814 0.966726i \(-0.417657\pi\)
\(44\) 1.73205i 0.0393648i
\(45\) 0 0
\(46\) 48.0000 1.04348
\(47\) −42.0000 + 24.2487i −0.893617 + 0.515930i −0.875124 0.483899i \(-0.839220\pi\)
−0.0184931 + 0.999829i \(0.505887\pi\)
\(48\) 0 0
\(49\) 22.5000 38.9711i 0.459184 0.795329i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.00000 3.46410i −0.0384615 0.0666173i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 15.0000 8.66025i 0.267857 0.154647i
\(57\) 0 0
\(58\) 39.0000 67.5500i 0.672414 1.16465i
\(59\) −43.5000 25.1147i −0.737288 0.425674i 0.0837943 0.996483i \(-0.473296\pi\)
−0.821082 + 0.570810i \(0.806629\pi\)
\(60\) 0 0
\(61\) −28.0000 48.4974i −0.459016 0.795040i 0.539893 0.841734i \(-0.318465\pi\)
−0.998909 + 0.0466940i \(0.985131\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 0 0
\(64\) −71.0000 −1.10938
\(65\) 0 0
\(66\) 0 0
\(67\) −15.5000 + 26.8468i −0.231343 + 0.400698i −0.958204 0.286087i \(-0.907645\pi\)
0.726860 + 0.686785i \(0.240979\pi\)
\(68\) −13.5000 7.79423i −0.198529 0.114621i
\(69\) 0 0
\(70\) 0 0
\(71\) 31.1769i 0.439111i 0.975600 + 0.219556i \(0.0704608\pi\)
−0.975600 + 0.219556i \(0.929539\pi\)
\(72\) 0 0
\(73\) −65.0000 −0.890411 −0.445205 0.895428i \(-0.646869\pi\)
−0.445205 + 0.895428i \(0.646869\pi\)
\(74\) −51.0000 + 29.4449i −0.689189 + 0.397904i
\(75\) 0 0
\(76\) −5.50000 + 9.52628i −0.0723684 + 0.125346i
\(77\) 3.00000 + 1.73205i 0.0389610 + 0.0224942i
\(78\) 0 0
\(79\) −19.0000 32.9090i −0.240506 0.416569i 0.720352 0.693608i \(-0.243980\pi\)
−0.960859 + 0.277039i \(0.910647\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −21.0000 −0.256098
\(83\) −42.0000 + 24.2487i −0.506024 + 0.292153i −0.731198 0.682165i \(-0.761038\pi\)
0.225174 + 0.974319i \(0.427705\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 91.5000 + 52.8275i 1.06395 + 0.614274i
\(87\) 0 0
\(88\) −7.50000 12.9904i −0.0852273 0.147618i
\(89\) 124.708i 1.40121i −0.713549 0.700605i \(-0.752914\pi\)
0.713549 0.700605i \(-0.247086\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.0879121
\(92\) 24.0000 13.8564i 0.260870 0.150613i
\(93\) 0 0
\(94\) 42.0000 72.7461i 0.446809 0.773895i
\(95\) 0 0
\(96\) 0 0
\(97\) −57.5000 99.5929i −0.592784 1.02673i −0.993856 0.110685i \(-0.964696\pi\)
0.401072 0.916047i \(-0.368638\pi\)
\(98\) 77.9423i 0.795329i
\(99\) 0 0
\(100\) 0 0
\(101\) −39.0000 + 22.5167i −0.386139 + 0.222937i −0.680486 0.732761i \(-0.738231\pi\)
0.294347 + 0.955699i \(0.404898\pi\)
\(102\) 0 0
\(103\) −20.0000 + 34.6410i −0.194175 + 0.336321i −0.946630 0.322323i \(-0.895536\pi\)
0.752455 + 0.658644i \(0.228870\pi\)
\(104\) 30.0000 + 17.3205i 0.288462 + 0.166543i
\(105\) 0 0
\(106\) 0 0
\(107\) 140.296i 1.31118i −0.755118 0.655589i \(-0.772420\pi\)
0.755118 0.655589i \(-0.227580\pi\)
\(108\) 0 0
\(109\) −52.0000 −0.477064 −0.238532 0.971135i \(-0.576666\pi\)
−0.238532 + 0.971135i \(0.576666\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −11.0000 + 19.0526i −0.0982143 + 0.170112i
\(113\) −78.0000 45.0333i −0.690265 0.398525i 0.113446 0.993544i \(-0.463811\pi\)
−0.803711 + 0.595019i \(0.797144\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 45.0333i 0.388218i
\(117\) 0 0
\(118\) 87.0000 0.737288
\(119\) −27.0000 + 15.5885i −0.226891 + 0.130995i
\(120\) 0 0
\(121\) −59.0000 + 102.191i −0.487603 + 0.844554i
\(122\) 84.0000 + 48.4974i 0.688525 + 0.397520i
\(123\) 0 0
\(124\) −16.0000 27.7128i −0.129032 0.223490i
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000 0.125984 0.0629921 0.998014i \(-0.479936\pi\)
0.0629921 + 0.998014i \(0.479936\pi\)
\(128\) 52.5000 30.3109i 0.410156 0.236804i
\(129\) 0 0
\(130\) 0 0
\(131\) −138.000 79.6743i −1.05344 0.608201i −0.129826 0.991537i \(-0.541442\pi\)
−0.923609 + 0.383336i \(0.874775\pi\)
\(132\) 0 0
\(133\) 11.0000 + 19.0526i 0.0827068 + 0.143252i
\(134\) 53.6936i 0.400698i
\(135\) 0 0
\(136\) 135.000 0.992647
\(137\) −163.500 + 94.3968i −1.19343 + 0.689028i −0.959083 0.283125i \(-0.908629\pi\)
−0.234348 + 0.972153i \(0.575295\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.0179856 + 0.0311520i −0.874878 0.484343i \(-0.839059\pi\)
0.856893 + 0.515495i \(0.172392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −27.0000 46.7654i −0.190141 0.329334i
\(143\) 6.92820i 0.0484490i
\(144\) 0 0
\(145\) 0 0
\(146\) 97.5000 56.2917i 0.667808 0.385559i
\(147\) 0 0
\(148\) −17.0000 + 29.4449i −0.114865 + 0.198952i
\(149\) 132.000 + 76.2102i 0.885906 + 0.511478i 0.872601 0.488433i \(-0.162431\pi\)
0.0133049 + 0.999911i \(0.495765\pi\)
\(150\) 0 0
\(151\) −10.0000 17.3205i −0.0662252 0.114705i 0.831012 0.556255i \(-0.187762\pi\)
−0.897237 + 0.441550i \(0.854429\pi\)
\(152\) 95.2628i 0.626729i
\(153\) 0 0
\(154\) −6.00000 −0.0389610
\(155\) 0 0
\(156\) 0 0
\(157\) −20.0000 + 34.6410i −0.127389 + 0.220643i −0.922664 0.385605i \(-0.873993\pi\)
0.795276 + 0.606248i \(0.207326\pi\)
\(158\) 57.0000 + 32.9090i 0.360759 + 0.208285i
\(159\) 0 0
\(160\) 0 0
\(161\) 55.4256i 0.344259i
\(162\) 0 0
\(163\) 106.000 0.650307 0.325153 0.945661i \(-0.394584\pi\)
0.325153 + 0.945661i \(0.394584\pi\)
\(164\) −10.5000 + 6.06218i −0.0640244 + 0.0369645i
\(165\) 0 0
\(166\) 42.0000 72.7461i 0.253012 0.438230i
\(167\) 165.000 + 95.2628i 0.988024 + 0.570436i 0.904683 0.426085i \(-0.140108\pi\)
0.0833409 + 0.996521i \(0.473441\pi\)
\(168\) 0 0
\(169\) 76.5000 + 132.502i 0.452663 + 0.784035i
\(170\) 0 0
\(171\) 0 0
\(172\) 61.0000 0.354651
\(173\) 201.000 116.047i 1.16185 0.670794i 0.210103 0.977679i \(-0.432620\pi\)
0.951747 + 0.306885i \(0.0992867\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 16.5000 + 9.52628i 0.0937500 + 0.0541266i
\(177\) 0 0
\(178\) 108.000 + 187.061i 0.606742 + 1.05091i
\(179\) 62.3538i 0.348345i −0.984715 0.174173i \(-0.944275\pi\)
0.984715 0.174173i \(-0.0557251\pi\)
\(180\) 0 0
\(181\) −232.000 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(182\) 12.0000 6.92820i 0.0659341 0.0380671i
\(183\) 0 0
\(184\) −120.000 + 207.846i −0.652174 + 1.12960i
\(185\) 0 0
\(186\) 0 0
\(187\) 13.5000 + 23.3827i 0.0721925 + 0.125041i
\(188\) 48.4974i 0.257965i
\(189\) 0 0
\(190\) 0 0
\(191\) −201.000 + 116.047i −1.05236 + 0.607578i −0.923308 0.384060i \(-0.874525\pi\)
−0.129048 + 0.991638i \(0.541192\pi\)
\(192\) 0 0
\(193\) −132.500 + 229.497i −0.686528 + 1.18910i 0.286425 + 0.958103i \(0.407533\pi\)
−0.972954 + 0.231000i \(0.925800\pi\)
\(194\) 172.500 + 99.5929i 0.889175 + 0.513366i
\(195\) 0 0
\(196\) 22.5000 + 38.9711i 0.114796 + 0.198832i
\(197\) 124.708i 0.633034i 0.948587 + 0.316517i \(0.102513\pi\)
−0.948587 + 0.316517i \(0.897487\pi\)
\(198\) 0 0
\(199\) 290.000 1.45729 0.728643 0.684893i \(-0.240151\pi\)
0.728643 + 0.684893i \(0.240151\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 39.0000 67.5500i 0.193069 0.334406i
\(203\) −78.0000 45.0333i −0.384236 0.221839i
\(204\) 0 0
\(205\) 0 0
\(206\) 69.2820i 0.336321i
\(207\) 0 0
\(208\) −44.0000 −0.211538
\(209\) 16.5000 9.52628i 0.0789474 0.0455803i
\(210\) 0 0
\(211\) 47.0000 81.4064i 0.222749 0.385812i −0.732893 0.680344i \(-0.761830\pi\)
0.955642 + 0.294532i \(0.0951637\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 121.500 + 210.444i 0.567757 + 0.983384i
\(215\) 0 0
\(216\) 0 0
\(217\) −64.0000 −0.294931
\(218\) 78.0000 45.0333i 0.357798 0.206575i
\(219\) 0 0
\(220\) 0 0
\(221\) −54.0000 31.1769i −0.244344 0.141072i
\(222\) 0 0
\(223\) −26.0000 45.0333i −0.116592 0.201943i 0.801823 0.597562i \(-0.203864\pi\)
−0.918415 + 0.395618i \(0.870530\pi\)
\(224\) 31.1769i 0.139183i
\(225\) 0 0
\(226\) 156.000 0.690265
\(227\) −163.500 + 94.3968i −0.720264 + 0.415845i −0.814850 0.579672i \(-0.803181\pi\)
0.0945856 + 0.995517i \(0.469847\pi\)
\(228\) 0 0
\(229\) −133.000 + 230.363i −0.580786 + 1.00595i 0.414600 + 0.910004i \(0.363921\pi\)
−0.995386 + 0.0959473i \(0.969412\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 195.000 + 337.750i 0.840517 + 1.45582i
\(233\) 202.650i 0.869742i 0.900493 + 0.434871i \(0.143206\pi\)
−0.900493 + 0.434871i \(0.856794\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 43.5000 25.1147i 0.184322 0.106418i
\(237\) 0 0
\(238\) 27.0000 46.7654i 0.113445 0.196493i
\(239\) 348.000 + 200.918i 1.45607 + 0.840661i 0.998815 0.0486764i \(-0.0155003\pi\)
0.457252 + 0.889337i \(0.348834\pi\)
\(240\) 0 0
\(241\) −59.5000 103.057i −0.246888 0.427623i 0.715773 0.698333i \(-0.246075\pi\)
−0.962661 + 0.270711i \(0.912741\pi\)
\(242\) 204.382i 0.844554i
\(243\) 0 0
\(244\) 56.0000 0.229508
\(245\) 0 0
\(246\) 0 0
\(247\) −22.0000 + 38.1051i −0.0890688 + 0.154272i
\(248\) 240.000 + 138.564i 0.967742 + 0.558726i
\(249\) 0 0
\(250\) 0 0
\(251\) 389.711i 1.55264i 0.630342 + 0.776318i \(0.282915\pi\)
−0.630342 + 0.776318i \(0.717085\pi\)
\(252\) 0 0
\(253\) −48.0000 −0.189723
\(254\) −24.0000 + 13.8564i −0.0944882 + 0.0545528i
\(255\) 0 0
\(256\) 89.5000 155.019i 0.349609 0.605541i
\(257\) 151.500 + 87.4686i 0.589494 + 0.340345i 0.764897 0.644152i \(-0.222790\pi\)
−0.175403 + 0.984497i \(0.556123\pi\)
\(258\) 0 0
\(259\) 34.0000 + 58.8897i 0.131274 + 0.227373i
\(260\) 0 0
\(261\) 0 0
\(262\) 276.000 1.05344
\(263\) 39.0000 22.5167i 0.148289 0.0856147i −0.424020 0.905653i \(-0.639381\pi\)
0.572309 + 0.820038i \(0.306048\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −33.0000 19.0526i −0.124060 0.0716262i
\(267\) 0 0
\(268\) −15.5000 26.8468i −0.0578358 0.100175i
\(269\) 187.061i 0.695396i 0.937607 + 0.347698i \(0.113037\pi\)
−0.937607 + 0.347698i \(0.886963\pi\)
\(270\) 0 0
\(271\) −268.000 −0.988930 −0.494465 0.869198i \(-0.664636\pi\)
−0.494465 + 0.869198i \(0.664636\pi\)
\(272\) −148.500 + 85.7365i −0.545956 + 0.315208i
\(273\) 0 0
\(274\) 163.500 283.190i 0.596715 1.03354i
\(275\) 0 0
\(276\) 0 0
\(277\) 28.0000 + 48.4974i 0.101083 + 0.175081i 0.912131 0.409899i \(-0.134436\pi\)
−0.811048 + 0.584979i \(0.801103\pi\)
\(278\) 8.66025i 0.0311520i
\(279\) 0 0
\(280\) 0 0
\(281\) 42.0000 24.2487i 0.149466 0.0862943i −0.423402 0.905942i \(-0.639164\pi\)
0.572868 + 0.819648i \(0.305831\pi\)
\(282\) 0 0
\(283\) 187.000 323.894i 0.660777 1.14450i −0.319634 0.947541i \(-0.603560\pi\)
0.980412 0.196959i \(-0.0631066\pi\)
\(284\) −27.0000 15.5885i −0.0950704 0.0548889i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.0209790 0.0363367i
\(287\) 24.2487i 0.0844903i
\(288\) 0 0
\(289\) 46.0000 0.159170
\(290\) 0 0
\(291\) 0 0
\(292\) 32.5000 56.2917i 0.111301 0.192780i
\(293\) 219.000 + 126.440i 0.747440 + 0.431535i 0.824768 0.565471i \(-0.191306\pi\)
−0.0773280 + 0.997006i \(0.524639\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 294.449i 0.994759i
\(297\) 0 0
\(298\) −264.000 −0.885906
\(299\) 96.0000 55.4256i 0.321070 0.185370i
\(300\) 0 0
\(301\) 61.0000 105.655i 0.202658 0.351014i
\(302\) 30.0000 + 17.3205i 0.0993377 + 0.0573527i
\(303\) 0 0
\(304\) 60.5000 + 104.789i 0.199013 + 0.344701i
\(305\) 0 0
\(306\) 0 0
\(307\) −533.000 −1.73616 −0.868078 0.496428i \(-0.834645\pi\)
−0.868078 + 0.496428i \(0.834645\pi\)
\(308\) −3.00000 + 1.73205i −0.00974026 + 0.00562354i
\(309\) 0 0
\(310\) 0 0
\(311\) 213.000 + 122.976i 0.684887 + 0.395420i 0.801694 0.597735i \(-0.203932\pi\)
−0.116806 + 0.993155i \(0.537266\pi\)
\(312\) 0 0
\(313\) 77.5000 + 134.234i 0.247604 + 0.428862i 0.962860 0.269999i \(-0.0870235\pi\)
−0.715257 + 0.698862i \(0.753690\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) −42.0000 + 24.2487i −0.132492 + 0.0764944i −0.564781 0.825241i \(-0.691039\pi\)
0.432289 + 0.901735i \(0.357706\pi\)
\(318\) 0 0
\(319\) −39.0000 + 67.5500i −0.122257 + 0.211755i
\(320\) 0 0
\(321\) 0 0
\(322\) 48.0000 + 83.1384i 0.149068 + 0.258194i
\(323\) 171.473i 0.530876i
\(324\) 0 0
\(325\) 0 0
\(326\) −159.000 + 91.7987i −0.487730 + 0.281591i
\(327\) 0 0
\(328\) 52.5000 90.9327i 0.160061 0.277234i
\(329\) −84.0000 48.4974i −0.255319 0.147409i
\(330\) 0 0
\(331\) −1.00000 1.73205i −0.00302115 0.00523278i 0.864511 0.502614i \(-0.167628\pi\)
−0.867532 + 0.497381i \(0.834295\pi\)
\(332\) 48.4974i 0.146077i
\(333\) 0 0
\(334\) −330.000 −0.988024
\(335\) 0 0
\(336\) 0 0
\(337\) 38.5000 66.6840i 0.114243 0.197875i −0.803234 0.595664i \(-0.796889\pi\)
0.917477 + 0.397789i \(0.130222\pi\)
\(338\) −229.500 132.502i −0.678994 0.392017i
\(339\) 0 0
\(340\) 0 0
\(341\) 55.4256i 0.162538i
\(342\) 0 0
\(343\) 188.000 0.548105
\(344\) −457.500 + 264.138i −1.32994 + 0.767842i
\(345\) 0 0
\(346\) −201.000 + 348.142i −0.580925 + 1.00619i
\(347\) 97.5000 + 56.2917i 0.280980 + 0.162224i 0.633867 0.773442i \(-0.281467\pi\)
−0.352887 + 0.935666i \(0.614800\pi\)
\(348\) 0 0
\(349\) −208.000 360.267i −0.595989 1.03228i −0.993407 0.114645i \(-0.963427\pi\)
0.397418 0.917638i \(-0.369906\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 27.0000 0.0767045
\(353\) −1.50000 + 0.866025i −0.00424929 + 0.00245333i −0.502123 0.864796i \(-0.667448\pi\)
0.497874 + 0.867249i \(0.334114\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 108.000 + 62.3538i 0.303371 + 0.175151i
\(357\) 0 0
\(358\) 54.0000 + 93.5307i 0.150838 + 0.261259i
\(359\) 592.361i 1.65003i −0.565110 0.825016i \(-0.691166\pi\)
0.565110 0.825016i \(-0.308834\pi\)
\(360\) 0 0
\(361\) −240.000 −0.664820
\(362\) 348.000 200.918i 0.961326 0.555022i
\(363\) 0 0
\(364\) 4.00000 6.92820i 0.0109890 0.0190335i
\(365\) 0 0
\(366\) 0 0
\(367\) −179.000 310.037i −0.487738 0.844788i 0.512162 0.858889i \(-0.328845\pi\)
−0.999901 + 0.0141011i \(0.995511\pi\)
\(368\) 304.841i 0.828372i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −290.000 + 502.295i −0.777480 + 1.34663i 0.155910 + 0.987771i \(0.450169\pi\)
−0.933390 + 0.358863i \(0.883164\pi\)
\(374\) −40.5000 23.3827i −0.108289 0.0625206i
\(375\) 0 0
\(376\) 210.000 + 363.731i 0.558511 + 0.967369i
\(377\) 180.133i 0.477807i
\(378\) 0 0
\(379\) 83.0000 0.218997 0.109499 0.993987i \(-0.465075\pi\)
0.109499 + 0.993987i \(0.465075\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 201.000 348.142i 0.526178 0.911367i
\(383\) −483.000 278.860i −1.26110 0.728094i −0.287810 0.957688i \(-0.592927\pi\)
−0.973287 + 0.229593i \(0.926260\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 458.993i 1.18910i
\(387\) 0 0
\(388\) 115.000 0.296392
\(389\) 447.000 258.076i 1.14910 0.663433i 0.200432 0.979708i \(-0.435765\pi\)
0.948668 + 0.316274i \(0.102432\pi\)
\(390\) 0 0
\(391\) 216.000 374.123i 0.552430 0.956836i
\(392\) −337.500 194.856i −0.860969 0.497081i
\(393\) 0 0
\(394\) −108.000 187.061i −0.274112 0.474775i
\(395\) 0 0
\(396\) 0 0
\(397\) −362.000 −0.911839 −0.455919 0.890021i \(-0.650689\pi\)
−0.455919 + 0.890021i \(0.650689\pi\)
\(398\) −435.000 + 251.147i −1.09296 + 0.631024i
\(399\) 0 0
\(400\) 0 0
\(401\) −340.500 196.588i −0.849127 0.490244i 0.0112291 0.999937i \(-0.496426\pi\)
−0.860356 + 0.509693i \(0.829759\pi\)
\(402\) 0 0
\(403\) −64.0000 110.851i −0.158809 0.275065i
\(404\) 45.0333i 0.111469i
\(405\) 0 0
\(406\) 156.000 0.384236
\(407\) 51.0000 29.4449i 0.125307 0.0723461i
\(408\) 0 0
\(409\) −110.500 + 191.392i −0.270171 + 0.467950i −0.968905 0.247431i \(-0.920414\pi\)
0.698734 + 0.715381i \(0.253747\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −20.0000 34.6410i −0.0485437 0.0840801i
\(413\) 100.459i 0.243242i
\(414\) 0 0
\(415\) 0 0
\(416\) −54.0000 + 31.1769i −0.129808 + 0.0749445i
\(417\) 0 0
\(418\) −16.5000 + 28.5788i −0.0394737 + 0.0683704i
\(419\) −678.000 391.443i −1.61814 0.934233i −0.987401 0.158236i \(-0.949419\pi\)
−0.630737 0.775997i \(-0.717247\pi\)
\(420\) 0 0
\(421\) 341.000 + 590.629i 0.809976 + 1.40292i 0.912880 + 0.408229i \(0.133853\pi\)
−0.102903 + 0.994691i \(0.532813\pi\)
\(422\) 162.813i 0.385812i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 56.0000 96.9948i 0.131148 0.227154i
\(428\) 121.500 + 70.1481i 0.283879 + 0.163897i
\(429\) 0 0
\(430\) 0 0
\(431\) 280.592i 0.651026i 0.945538 + 0.325513i \(0.105537\pi\)
−0.945538 + 0.325513i \(0.894463\pi\)
\(432\) 0 0
\(433\) 295.000 0.681293 0.340647 0.940191i \(-0.389354\pi\)
0.340647 + 0.940191i \(0.389354\pi\)
\(434\) 96.0000 55.4256i 0.221198 0.127709i
\(435\) 0 0
\(436\) 26.0000 45.0333i 0.0596330 0.103287i
\(437\) −264.000 152.420i −0.604119 0.348788i
\(438\) 0 0
\(439\) −406.000 703.213i −0.924829 1.60185i −0.791836 0.610734i \(-0.790874\pi\)
−0.132993 0.991117i \(-0.542459\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 108.000 0.244344
\(443\) 79.5000 45.8993i 0.179458 0.103610i −0.407580 0.913170i \(-0.633627\pi\)
0.587038 + 0.809559i \(0.300294\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 78.0000 + 45.0333i 0.174888 + 0.100972i
\(447\) 0 0
\(448\) −71.0000 122.976i −0.158482 0.274499i
\(449\) 639.127i 1.42344i 0.702461 + 0.711722i \(0.252085\pi\)
−0.702461 + 0.711722i \(0.747915\pi\)
\(450\) 0 0
\(451\) 21.0000 0.0465632
\(452\) 78.0000 45.0333i 0.172566 0.0996312i
\(453\) 0 0
\(454\) 163.500 283.190i 0.360132 0.623767i
\(455\) 0 0
\(456\) 0 0
\(457\) 32.5000 + 56.2917i 0.0711160 + 0.123176i 0.899391 0.437146i \(-0.144011\pi\)
−0.828275 + 0.560322i \(0.810677\pi\)
\(458\) 460.726i 1.00595i
\(459\) 0 0
\(460\) 0 0
\(461\) 690.000 398.372i 1.49675 0.864147i 0.496753 0.867892i \(-0.334525\pi\)
0.999993 + 0.00374501i \(0.00119208\pi\)
\(462\) 0 0
\(463\) 367.000 635.663i 0.792657 1.37292i −0.131660 0.991295i \(-0.542031\pi\)
0.924317 0.381627i \(-0.124636\pi\)
\(464\) −429.000 247.683i −0.924569 0.533800i
\(465\) 0 0
\(466\) −175.500 303.975i −0.376609 0.652307i
\(467\) 202.650i 0.433940i −0.976178 0.216970i \(-0.930383\pi\)
0.976178 0.216970i \(-0.0696174\pi\)
\(468\) 0 0
\(469\) −62.0000 −0.132196
\(470\) 0 0
\(471\) 0 0
\(472\) −217.500 + 376.721i −0.460805 + 0.798138i
\(473\) −91.5000 52.8275i −0.193446 0.111686i
\(474\) 0 0
\(475\) 0 0
\(476\) 31.1769i 0.0654977i
\(477\) 0 0
\(478\) −696.000 −1.45607
\(479\) −525.000 + 303.109i −1.09603 + 0.632795i −0.935176 0.354183i \(-0.884759\pi\)
−0.160857 + 0.986978i \(0.551426\pi\)
\(480\) 0 0
\(481\) −68.0000 + 117.779i −0.141372 + 0.244864i
\(482\) 178.500 + 103.057i 0.370332 + 0.213811i
\(483\) 0 0
\(484\) −59.0000 102.191i −0.121901 0.211138i
\(485\) 0 0
\(486\) 0 0
\(487\) 106.000 0.217659 0.108830 0.994060i \(-0.465290\pi\)
0.108830 + 0.994060i \(0.465290\pi\)
\(488\) −420.000 + 242.487i −0.860656 + 0.496900i
\(489\) 0 0
\(490\) 0 0
\(491\) 199.500 + 115.181i 0.406314 + 0.234585i 0.689205 0.724567i \(-0.257960\pi\)
−0.282891 + 0.959152i \(0.591293\pi\)
\(492\) 0 0
\(493\) −351.000 607.950i −0.711968 1.23316i
\(494\) 76.2102i 0.154272i
\(495\) 0 0
\(496\) −352.000 −0.709677
\(497\) −54.0000 + 31.1769i −0.108652 + 0.0627302i
\(498\) 0 0
\(499\) 393.500 681.562i 0.788577 1.36586i −0.138261 0.990396i \(-0.544151\pi\)
0.926839 0.375460i \(-0.122515\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −337.500 584.567i −0.672311 1.16448i
\(503\) 623.538i 1.23964i 0.784745 + 0.619819i \(0.212794\pi\)
−0.784745 + 0.619819i \(0.787206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 72.0000 41.5692i 0.142292 0.0821526i
\(507\) 0 0
\(508\) −8.00000 + 13.8564i −0.0157480 + 0.0272764i
\(509\) 186.000 + 107.387i 0.365422 + 0.210977i 0.671457 0.741044i \(-0.265669\pi\)
−0.306034 + 0.952020i \(0.599002\pi\)
\(510\) 0 0
\(511\) −65.0000 112.583i −0.127202 0.220320i
\(512\) 552.524i 1.07915i
\(513\) 0 0
\(514\) −303.000 −0.589494
\(515\) 0 0
\(516\) 0 0
\(517\) −42.0000 + 72.7461i −0.0812379 + 0.140708i
\(518\) −102.000 58.8897i −0.196911 0.113687i
\(519\) 0 0
\(520\) 0 0
\(521\) 202.650i 0.388963i 0.980906 + 0.194482i \(0.0623025\pi\)
−0.980906 + 0.194482i \(0.937698\pi\)
\(522\) 0 0
\(523\) 250.000 0.478011 0.239006 0.971018i \(-0.423179\pi\)
0.239006 + 0.971018i \(0.423179\pi\)
\(524\) 138.000 79.6743i 0.263359 0.152050i
\(525\) 0 0
\(526\) −39.0000 + 67.5500i −0.0741445 + 0.128422i
\(527\) −432.000 249.415i −0.819734 0.473274i
\(528\) 0 0
\(529\) 119.500 + 206.980i 0.225898 + 0.391267i
\(530\) 0 0
\(531\) 0 0
\(532\) −22.0000 −0.0413534
\(533\) −42.0000 + 24.2487i −0.0787992 + 0.0454948i
\(534\) 0 0
\(535\) 0 0
\(536\) 232.500 + 134.234i 0.433769 + 0.250436i
\(537\) 0 0
\(538\) −162.000 280.592i −0.301115 0.521547i
\(539\) 77.9423i 0.144605i
\(540\) 0 0
\(541\) 650.000 1.20148 0.600739 0.799445i \(-0.294873\pi\)
0.600739 + 0.799445i \(0.294873\pi\)
\(542\) 402.000 232.095i 0.741697 0.428219i
\(543\) 0 0
\(544\) −121.500 + 210.444i −0.223346 + 0.386846i
\(545\) 0 0
\(546\) 0 0
\(547\) 311.500 + 539.534i 0.569470 + 0.986351i 0.996618 + 0.0821692i \(0.0261848\pi\)
−0.427149 + 0.904181i \(0.640482\pi\)
\(548\) 188.794i 0.344514i
\(549\) 0 0
\(550\) 0 0
\(551\) −429.000 + 247.683i −0.778584 + 0.449516i
\(552\) 0 0
\(553\) 38.0000 65.8179i 0.0687161 0.119020i
\(554\) −84.0000 48.4974i −0.151625 0.0875405i
\(555\) 0 0
\(556\) −2.50000 4.33013i −0.00449640 0.00778800i
\(557\) 530.008i 0.951540i 0.879570 + 0.475770i \(0.157830\pi\)
−0.879570 + 0.475770i \(0.842170\pi\)
\(558\) 0 0
\(559\) 244.000 0.436494
\(560\) 0 0
\(561\) 0 0
\(562\) −42.0000 + 72.7461i −0.0747331 + 0.129442i
\(563\) 97.5000 + 56.2917i 0.173179 + 0.0999852i 0.584084 0.811693i \(-0.301454\pi\)
−0.410905 + 0.911678i \(0.634787\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 647.787i 1.14450i
\(567\) 0 0
\(568\) 270.000 0.475352
\(569\) −565.500 + 326.492i −0.993849 + 0.573799i −0.906423 0.422372i \(-0.861198\pi\)
−0.0874263 + 0.996171i \(0.527864\pi\)
\(570\) 0 0
\(571\) −272.500 + 471.984i −0.477233 + 0.826592i −0.999660 0.0260926i \(-0.991694\pi\)
0.522427 + 0.852684i \(0.325027\pi\)
\(572\) −6.00000 3.46410i −0.0104895 0.00605612i
\(573\) 0 0
\(574\) −21.0000 36.3731i −0.0365854 0.0633677i
\(575\) 0 0
\(576\) 0 0
\(577\) 871.000 1.50953 0.754766 0.655994i \(-0.227750\pi\)
0.754766 + 0.655994i \(0.227750\pi\)
\(578\) −69.0000 + 39.8372i −0.119377 + 0.0689224i
\(579\) 0 0
\(580\) 0 0
\(581\) −84.0000 48.4974i −0.144578 0.0834723i
\(582\) 0 0
\(583\) 0 0
\(584\) 562.917i 0.963898i
\(585\) 0 0
\(586\) −438.000 −0.747440
\(587\) −1.50000 + 0.866025i −0.00255537 + 0.00147534i −0.501277 0.865287i \(-0.667136\pi\)
0.498722 + 0.866762i \(0.333803\pi\)
\(588\) 0 0
\(589\) −176.000 + 304.841i −0.298812 + 0.517557i
\(590\) 0 0
\(591\) 0 0
\(592\) 187.000 + 323.894i 0.315878 + 0.547117i
\(593\) 187.061i 0.315449i 0.987483 + 0.157725i \(0.0504159\pi\)
−0.987483 + 0.157725i \(0.949584\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −132.000 + 76.2102i −0.221477 + 0.127870i
\(597\) 0 0
\(598\) −96.0000 + 166.277i −0.160535 + 0.278055i
\(599\) −489.000 282.324i −0.816361 0.471326i 0.0327992 0.999462i \(-0.489558\pi\)
−0.849160 + 0.528136i \(0.822891\pi\)
\(600\) 0 0
\(601\) −230.500 399.238i −0.383527 0.664289i 0.608036 0.793909i \(-0.291958\pi\)
−0.991564 + 0.129620i \(0.958624\pi\)
\(602\) 211.310i 0.351014i
\(603\) 0 0
\(604\) 20.0000 0.0331126
\(605\) 0 0
\(606\) 0 0
\(607\) −56.0000 + 96.9948i −0.0922570 + 0.159794i −0.908461 0.417971i \(-0.862741\pi\)
0.816204 + 0.577765i \(0.196075\pi\)
\(608\) 148.500 + 85.7365i 0.244243 + 0.141014i
\(609\) 0 0
\(610\) 0 0
\(611\) 193.990i 0.317495i
\(612\) 0 0
\(613\) −902.000 −1.47145 −0.735726 0.677279i \(-0.763159\pi\)
−0.735726 + 0.677279i \(0.763159\pi\)
\(614\) 799.500 461.592i 1.30212 0.751778i
\(615\) 0 0
\(616\) 15.0000 25.9808i 0.0243506 0.0421766i
\(617\) −307.500 177.535i −0.498379 0.287739i 0.229665 0.973270i \(-0.426237\pi\)
−0.728044 + 0.685530i \(0.759570\pi\)
\(618\) 0 0
\(619\) 399.500 + 691.954i 0.645396 + 1.11786i 0.984210 + 0.177005i \(0.0566409\pi\)
−0.338814 + 0.940853i \(0.610026\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −426.000 −0.684887
\(623\) 216.000 124.708i 0.346709 0.200173i
\(624\) 0 0
\(625\) 0 0
\(626\) −232.500 134.234i −0.371406 0.214431i
\(627\) 0 0
\(628\) −20.0000 34.6410i −0.0318471 0.0551609i
\(629\) 530.008i 0.842619i
\(630\) 0 0
\(631\) 830.000 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(632\) −285.000 + 164.545i −0.450949 + 0.260356i
\(633\) 0 0
\(634\) 42.0000 72.7461i 0.0662461 0.114742i
\(635\) 0 0
\(636\) 0 0
\(637\) 90.0000 + 155.885i 0.141287 + 0.244717i
\(638\) 135.100i 0.211755i
\(639\) 0 0
\(640\) 0 0
\(641\) 325.500 187.928i 0.507800 0.293179i −0.224129 0.974560i \(-0.571954\pi\)
0.731929 + 0.681381i \(0.238620\pi\)
\(642\) 0 0
\(643\) −6.50000 + 11.2583i −0.0101089 + 0.0175091i −0.871036 0.491220i \(-0.836551\pi\)
0.860927 + 0.508729i \(0.169884\pi\)
\(644\) 48.0000 + 27.7128i 0.0745342 + 0.0430323i
\(645\) 0 0
\(646\) −148.500 257.210i −0.229876 0.398157i
\(647\) 467.654i 0.722803i 0.932410 + 0.361402i \(0.117702\pi\)
−0.932410 + 0.361402i \(0.882298\pi\)
\(648\) 0 0
\(649\) −87.0000 −0.134052
\(650\) 0 0
\(651\) 0 0
\(652\) −53.0000 + 91.7987i −0.0812883 + 0.140796i
\(653\) 327.000 + 188.794i 0.500766 + 0.289117i 0.729030 0.684482i \(-0.239972\pi\)
−0.228264 + 0.973599i \(0.573305\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 133.368i 0.203305i
\(657\) 0 0
\(658\) 168.000 0.255319
\(659\) 852.000 491.902i 1.29287 0.746438i 0.313706 0.949520i \(-0.398429\pi\)
0.979162 + 0.203082i \(0.0650959\pi\)
\(660\) 0 0
\(661\) 191.000 330.822i 0.288956 0.500487i −0.684605 0.728915i \(-0.740025\pi\)
0.973561 + 0.228428i \(0.0733585\pi\)
\(662\) 3.00000 + 1.73205i 0.00453172 + 0.00261639i
\(663\) 0 0
\(664\) 210.000 + 363.731i 0.316265 + 0.547787i
\(665\) 0 0
\(666\) 0 0
\(667\) 1248.00 1.87106
\(668\) −165.000 + 95.2628i −0.247006 + 0.142609i
\(669\) 0 0
\(670\) 0 0
\(671\) −84.0000 48.4974i −0.125186 0.0722763i
\(672\) 0 0
\(673\) 289.000 + 500.563i 0.429421 + 0.743778i 0.996822 0.0796633i \(-0.0253845\pi\)
−0.567401 + 0.823441i \(0.692051\pi\)
\(674\) 133.368i 0.197875i
\(675\) 0 0
\(676\) −153.000 −0.226331
\(677\) 606.000 349.874i 0.895126 0.516801i 0.0195100 0.999810i \(-0.493789\pi\)
0.875616 + 0.483009i \(0.160456\pi\)
\(678\) 0 0
\(679\) 115.000 199.186i 0.169367 0.293352i
\(680\) 0 0
\(681\) 0 0
\(682\) −48.0000 83.1384i −0.0703812 0.121904i
\(683\) 1044.43i 1.52918i −0.644520 0.764588i \(-0.722943\pi\)
0.644520 0.764588i \(-0.277057\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −282.000 + 162.813i −0.411079 + 0.237336i
\(687\) 0 0
\(688\) 335.500 581.103i 0.487645 0.844627i
\(689\) 0 0
\(690\) 0 0
\(691\) −91.0000 157.617i −0.131693 0.228099i 0.792636 0.609695i \(-0.208708\pi\)
−0.924329 + 0.381596i \(0.875375\pi\)
\(692\) 232.095i 0.335397i
\(693\) 0 0
\(694\) −195.000 −0.280980
\(695\) 0 0
\(696\) 0 0
\(697\) −94.5000 + 163.679i −0.135581 + 0.234833i
\(698\) 624.000 + 360.267i 0.893983 + 0.516141i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 374.000 0.532006
\(704\) −106.500 + 61.4878i −0.151278 + 0.0873406i
\(705\) 0 0
\(706\) 1.50000 2.59808i 0.00212465 0.00367999i
\(707\) −78.0000 45.0333i −0.110325 0.0636964i
\(708\) 0 0
\(709\) 350.000 + 606.218i 0.493653 + 0.855032i 0.999973 0.00731341i \(-0.00232795\pi\)
−0.506320 + 0.862346i \(0.668995\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1080.00 −1.51685
\(713\) 768.000 443.405i 1.07714 0.621886i
\(714\) 0 0
\(715\) 0 0
\(716\) 54.0000 + 31.1769i 0.0754190 + 0.0435432i
\(717\) 0 0
\(718\) 513.000 + 888.542i 0.714485 + 1.23752i
\(719\) 592.361i 0.823868i 0.911214 + 0.411934i \(0.135147\pi\)
−0.911214 + 0.411934i \(0.864853\pi\)
\(720\) 0 0
\(721\) −80.0000 −0.110957
\(722\) 360.000 207.846i 0.498615 0.287875i
\(723\) 0 0
\(724\) 116.000 200.918i 0.160221 0.277511i
\(725\) 0 0
\(726\) 0 0
\(727\) −332.000 575.041i −0.456671 0.790978i 0.542111 0.840307i \(-0.317625\pi\)
−0.998783 + 0.0493289i \(0.984292\pi\)
\(728\) 69.2820i 0.0951676i
\(729\) 0 0
\(730\) 0 0
\(731\) 823.500 475.448i 1.12654 0.650408i
\(732\) 0 0
\(733\) −335.000 + 580.237i −0.457026 + 0.791592i −0.998802 0.0489306i \(-0.984419\pi\)
0.541776 + 0.840523i \(0.317752\pi\)
\(734\) 537.000 + 310.037i 0.731608 + 0.422394i
\(735\) 0 0
\(736\) −216.000 374.123i −0.293478 0.508319i
\(737\) 53.6936i 0.0728542i
\(738\) 0 0
\(739\) 317.000 0.428958 0.214479 0.976729i \(-0.431195\pi\)
0.214479 + 0.976729i \(0.431195\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −537.000 310.037i −0.722746 0.417277i 0.0930168 0.995665i \(-0.470349\pi\)
−0.815762 + 0.578387i \(0.803682\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1004.59i 1.34663i
\(747\) 0 0
\(748\) −27.0000 −0.0360963
\(749\) 243.000 140.296i 0.324433 0.187311i
\(750\) 0 0
\(751\) −655.000 + 1134.49i −0.872170 + 1.51064i −0.0124237 + 0.999923i \(0.503955\pi\)
−0.859747 + 0.510721i \(0.829379\pi\)
\(752\) −462.000 266.736i −0.614362 0.354702i
\(753\) 0 0
\(754\) 156.000 + 270.200i 0.206897 + 0.358355i
\(755\) 0 0
\(756\) 0 0
\(757\) −218.000 −0.287979 −0.143989 0.989579i \(-0.545993\pi\)
−0.143989 + 0.989579i \(0.545993\pi\)
\(758\) −124.500 + 71.8801i −0.164248 + 0.0948286i
\(759\) 0 0
\(760\) 0 0
\(761\) −570.000 329.090i −0.749014 0.432444i 0.0763232 0.997083i \(-0.475682\pi\)
−0.825338 + 0.564639i \(0.809015\pi\)
\(762\) 0 0
\(763\) −52.0000 90.0666i −0.0681520 0.118043i
\(764\) 232.095i 0.303789i
\(765\) 0 0
\(766\) 966.000 1.26110
\(767\) 174.000 100.459i 0.226858 0.130976i
\(768\) 0 0
\(769\) −511.000 + 885.078i −0.664499 + 1.15095i 0.314921 + 0.949118i \(0.398022\pi\)
−0.979421 + 0.201829i \(0.935312\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −132.500 229.497i −0.171632 0.297276i
\(773\) 1184.72i 1.53263i 0.642465 + 0.766315i \(0.277912\pi\)
−0.642465 + 0.766315i \(0.722088\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −862.500 + 497.965i −1.11147 + 0.641707i
\(777\) 0 0
\(778\) −447.000 + 774.227i −0.574550 + 0.995150i
\(779\) 115.500 + 66.6840i 0.148267 + 0.0856020i
\(780\) 0 0
\(781\) 27.0000 + 46.7654i 0.0345711 + 0.0598788i
\(782\) 748.246i 0.956836i
\(783\) 0 0
\(784\) 495.000 0.631378
\(785\) 0 0
\(786\) 0 0
\(787\) −65.0000 + 112.583i −0.0825921 + 0.143054i −0.904363 0.426765i \(-0.859653\pi\)
0.821771 + 0.569819i \(0.192987\pi\)
\(788\) −108.000 62.3538i −0.137056 0.0791292i
\(789\) 0 0
\(790\) 0 0
\(791\) 180.133i 0.227729i
\(792\) 0 0
\(793\) 224.000 0.282472
\(794\) 543.000 313.501i 0.683879 0.394838i
\(795\) 0 0
\(796\) −145.000 + 251.147i −0.182161 + 0.315512i
\(797\) 273.000 + 157.617i 0.342535 + 0.197762i 0.661392 0.750040i \(-0.269966\pi\)
−0.318858 + 0.947803i \(0.603299\pi\)
\(798\) 0 0
\(799\) −378.000 654.715i −0.473091 0.819418i
\(800\) 0 0
\(801\) 0 0
\(802\) 681.000 0.849127
\(803\) −97.5000 + 56.2917i −0.121420 + 0.0701017i
\(804\) 0 0
\(805\) 0 0
\(806\) 192.000 + 110.851i 0.238213 + 0.137533i
\(807\) 0 0
\(808\) 195.000 + 337.750i 0.241337 + 0.418007i
\(809\) 140.296i 0.173419i 0.996234 + 0.0867096i \(0.0276352\pi\)
−0.996234 + 0.0867096i \(0.972365\pi\)
\(810\) 0 0
\(811\) 299.000 0.368681 0.184340 0.982862i \(-0.440985\pi\)
0.184340 + 0.982862i \(0.440985\pi\)
\(812\) 78.0000 45.0333i 0.0960591 0.0554598i
\(813\) 0 0
\(814\) −51.0000 + 88.3346i −0.0626536 + 0.108519i
\(815\) 0 0
\(816\) 0 0
\(817\) −335.500 581.103i −0.410649 0.711264i
\(818\) 382.783i 0.467950i
\(819\) 0 0
\(820\) 0 0
\(821\) −525.000 + 303.109i −0.639464 + 0.369195i −0.784408 0.620245i \(-0.787033\pi\)
0.144944 + 0.989440i \(0.453700\pi\)
\(822\) 0 0
\(823\) −407.000 + 704.945i −0.494532 + 0.856555i −0.999980 0.00630221i \(-0.997994\pi\)
0.505448 + 0.862857i \(0.331327\pi\)
\(824\) 300.000 + 173.205i 0.364078 + 0.210200i
\(825\) 0 0
\(826\) 87.0000 + 150.688i 0.105327 + 0.182432i
\(827\) 1434.14i 1.73415i −0.498182 0.867073i \(-0.665999\pi\)
0.498182 0.867073i \(-0.334001\pi\)
\(828\) 0 0
\(829\) −718.000 −0.866104 −0.433052 0.901369i \(-0.642563\pi\)
−0.433052 + 0.901369i \(0.642563\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 142.000 245.951i 0.170673 0.295614i
\(833\) 607.500 + 350.740i 0.729292 + 0.421057i
\(834\) 0 0
\(835\) 0 0
\(836\) 19.0526i 0.0227901i
\(837\) 0 0
\(838\) 1356.00 1.61814
\(839\) 690.000 398.372i 0.822408 0.474817i −0.0288384 0.999584i \(-0.509181\pi\)
0.851246 + 0.524767i \(0.175847\pi\)
\(840\) 0 0
\(841\) 593.500 1027.97i 0.705707 1.22232i
\(842\) −1023.00 590.629i −1.21496 0.701460i
\(843\) 0 0
\(844\) 47.0000 + 81.4064i 0.0556872 + 0.0964531i
\(845\) 0 0
\(846\) 0 0
\(847\) −236.000 −0.278630
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −816.000 471.118i −0.958872 0.553605i
\(852\) 0 0
\(853\) 712.000 + 1233.22i 0.834701 + 1.44574i 0.894274 + 0.447521i \(0.147693\pi\)
−0.0595725 + 0.998224i \(0.518974\pi\)
\(854\) 193.990i 0.227154i
\(855\) 0 0
\(856\) −1215.00 −1.41939
\(857\) 606.000 349.874i 0.707118 0.408255i −0.102875 0.994694i \(-0.532804\pi\)
0.809993 + 0.586440i \(0.199471\pi\)
\(858\) 0 0
\(859\) −155.500 + 269.334i −0.181024 + 0.313544i −0.942230 0.334968i \(-0.891275\pi\)
0.761205 + 0.648511i \(0.224608\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −243.000 420.888i −0.281903 0.488270i
\(863\) 1028.84i 1.19216i −0.802923 0.596082i \(-0.796723\pi\)
0.802923 0.596082i \(-0.203277\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −442.500 + 255.477i −0.510970 + 0.295009i
\(867\) 0 0
\(868\) 32.0000 55.4256i 0.0368664 0.0638544i
\(869\) −57.0000 32.9090i −0.0655926 0.0378699i
\(870\) 0 0
\(871\) −62.0000 107.387i −0.0711825 0.123292i
\(872\) 450.333i 0.516437i
\(873\) 0 0
\(874\) 528.000 0.604119
\(875\) 0 0
\(876\) 0 0
\(877\) 52.0000 90.0666i 0.0592930 0.102699i −0.834855 0.550470i \(-0.814449\pi\)
0.894148 + 0.447771i \(0.147782\pi\)
\(878\) 1218.00 + 703.213i 1.38724 + 0.800926i
\(879\) 0 0
\(880\) 0 0
\(881\) 62.3538i 0.0707762i −0.999374 0.0353881i \(-0.988733\pi\)
0.999374 0.0353881i \(-0.0112667\pi\)
\(882\) 0 0
\(883\) −119.000 −0.134768 −0.0673839 0.997727i \(-0.521465\pi\)
−0.0673839 + 0.997727i \(0.521465\pi\)
\(884\) 54.0000 31.1769i 0.0610860 0.0352680i
\(885\) 0 0
\(886\) −79.5000 + 137.698i −0.0897291 + 0.155415i
\(887\) 1029.00 + 594.093i 1.16009 + 0.669778i 0.951326 0.308188i \(-0.0997224\pi\)
0.208765 + 0.977966i \(0.433056\pi\)
\(888\) 0 0
\(889\) 16.0000 + 27.7128i 0.0179978 + 0.0311730i
\(890\) 0 0
\(891\) 0 0
\(892\) 52.0000 0.0582960
\(893\) −462.000 + 266.736i −0.517357 + 0.298696i
\(894\) 0 0
\(895\) 0 0
\(896\) 105.000 + 60.6218i 0.117188 + 0.0676582i
\(897\) 0 0
\(898\) −553.500 958.690i −0.616370 1.06758i
\(899\) 1441.07i 1.60297i
\(900\) 0 0
\(901\) 0 0
\(902\) −31.5000 + 18.1865i −0.0349224 + 0.0201625i
\(903\) 0 0
\(904\) −390.000 + 675.500i −0.431416 + 0.747234i
\(905\) 0 0
\(906\) 0 0
\(907\) 347.500 + 601.888i 0.383131 + 0.663603i 0.991508 0.130046i \(-0.0415124\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(908\) 188.794i 0.207922i
\(909\) 0 0
\(910\) 0 0
\(911\) 1500.00 866.025i 1.64654 0.950632i 0.668110 0.744062i \(-0.267103\pi\)
0.978432 0.206569i \(-0.0662299\pi\)
\(912\) 0 0
\(913\) −42.0000 + 72.7461i −0.0460022 + 0.0796781i
\(914\) −97.5000 56.2917i −0.106674 0.0615882i
\(915\) 0 0
\(916\) −133.000 230.363i −0.145197 0.251488i
\(917\) 318.697i 0.347543i
\(918\) 0 0
\(919\) 56.0000 0.0609358 0.0304679 0.999536i \(-0.490300\pi\)
0.0304679 + 0.999536i \(0.490300\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −690.000 + 1195.12i −0.748373 + 1.29622i
\(923\) −108.000 62.3538i −0.117010 0.0675556i
\(924\) 0 0
\(925\) 0 0
\(926\) 1271.33i 1.37292i
\(927\) 0 0
\(928\) −702.000 −0.756466
\(929\) 690.000 398.372i 0.742734 0.428818i −0.0803285 0.996768i \(-0.525597\pi\)
0.823063 + 0.567951i \(0.192264\pi\)
\(930\) 0 0
\(931\) 247.500 428.683i 0.265843 0.460454i
\(932\) −175.500 101.325i −0.188305 0.108718i
\(933\) 0 0
\(934\) 175.500 + 303.975i 0.187901 + 0.325455i
\(935\) 0 0
\(936\) 0 0
\(937\) −470.000 −0.501601 −0.250800 0.968039i \(-0.580694\pi\)
−0.250800 + 0.968039i \(0.580694\pi\)
\(938\) 93.0000 53.6936i 0.0991471 0.0572426i
\(939\) 0 0
\(940\) 0 0
\(941\) 348.000 + 200.918i 0.369819 + 0.213515i 0.673380 0.739297i \(-0.264842\pi\)
−0.303560 + 0.952812i \(0.598175\pi\)
\(942\) 0 0
\(943\) −168.000 290.985i −0.178155 0.308573i
\(944\) 552.524i 0.585301i
\(945\) 0 0
\(946\) 183.000 0.193446
\(947\) −1.50000 + 0.866025i −0.00158395 + 0.000914494i −0.500792 0.865568i \(-0.666958\pi\)
0.499208 + 0.866482i \(0.333624\pi\)
\(948\) 0 0
\(949\) 130.000 225.167i 0.136986 0.237267i
\(950\) 0 0
\(951\) 0 0
\(952\) 135.000 + 233.827i 0.141807 + 0.245616i
\(953\) 826.188i 0.866934i 0.901169 + 0.433467i \(0.142710\pi\)
−0.901169 + 0.433467i \(0.857290\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −348.000 + 200.918i −0.364017 + 0.210165i
\(957\) 0 0
\(958\) 525.000 909.327i 0.548017 0.949193i
\(959\) −327.000 188.794i −0.340980 0.196865i
\(960\) 0 0
\(961\) −31.5000 54.5596i −0.0327784 0.0567738i
\(962\) 235.559i 0.244864i
\(963\) 0 0
\(964\) 119.000 0.123444
\(965\) 0 0
\(966\) 0 0
\(967\) 601.000 1040.96i 0.621510 1.07649i −0.367695 0.929946i \(-0.619853\pi\)
0.989205 0.146540i \(-0.0468137\pi\)
\(968\) 885.000 + 510.955i 0.914256 + 0.527846i
\(969\) 0 0
\(970\) 0 0
\(971\) 187.061i 0.192648i 0.995350 + 0.0963241i \(0.0307085\pi\)
−0.995350 + 0.0963241i \(0.969291\pi\)
\(972\) 0 0
\(973\) −10.0000 −0.0102775
\(974\) −159.000 + 91.7987i −0.163244 + 0.0942492i
\(975\) 0 0
\(976\) 308.000 533.472i 0.315574 0.546590i
\(977\) −361.500 208.712i −0.370010 0.213626i 0.303453 0.952847i \(-0.401861\pi\)
−0.673463 + 0.739221i \(0.735194\pi\)
\(978\) 0 0
\(979\) −108.000 187.061i −0.110317 0.191074i
\(980\) 0 0
\(981\) 0 0
\(982\) −399.000 −0.406314
\(983\) 1011.00 583.701i 1.02848 0.593796i 0.111934 0.993716i \(-0.464295\pi\)
0.916550 + 0.399920i \(0.130962\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 1053.00 + 607.950i 1.06795 + 0.616582i
\(987\) 0 0
\(988\) −22.0000 38.1051i −0.0222672 0.0385679i
\(989\) 1690.48i 1.70928i
\(990\) 0 0
\(991\) −1420.00 −1.43290 −0.716448 0.697640i \(-0.754233\pi\)
−0.716448 + 0.697640i \(0.754233\pi\)
\(992\) −432.000 + 249.415i −0.435484 + 0.251427i
\(993\) 0 0
\(994\) 54.0000 93.5307i 0.0543260 0.0940953i
\(995\) 0 0
\(996\) 0 0
\(997\) 262.000 + 453.797i 0.262788 + 0.455163i 0.966982 0.254845i \(-0.0820246\pi\)
−0.704193 + 0.710008i \(0.748691\pi\)
\(998\) 1363.12i 1.36586i
\(999\) 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 675.3.j.a.476.1 2
3.2 odd 2 225.3.j.a.176.1 2
5.2 odd 4 675.3.i.a.449.1 4
5.3 odd 4 675.3.i.a.449.2 4
5.4 even 2 27.3.d.a.17.1 2
9.2 odd 6 inner 675.3.j.a.251.1 2
9.7 even 3 225.3.j.a.101.1 2
15.2 even 4 225.3.i.a.149.2 4
15.8 even 4 225.3.i.a.149.1 4
15.14 odd 2 9.3.d.a.5.1 yes 2
20.19 odd 2 432.3.q.a.17.1 2
40.19 odd 2 1728.3.q.b.449.1 2
40.29 even 2 1728.3.q.a.449.1 2
45.2 even 12 675.3.i.a.224.2 4
45.4 even 6 81.3.b.a.80.2 2
45.7 odd 12 225.3.i.a.74.1 4
45.14 odd 6 81.3.b.a.80.1 2
45.29 odd 6 27.3.d.a.8.1 2
45.34 even 6 9.3.d.a.2.1 2
45.38 even 12 675.3.i.a.224.1 4
45.43 odd 12 225.3.i.a.74.2 4
60.59 even 2 144.3.q.a.113.1 2
105.44 odd 6 441.3.n.b.410.1 2
105.59 even 6 441.3.j.b.275.1 2
105.74 odd 6 441.3.j.a.275.1 2
105.89 even 6 441.3.n.a.410.1 2
105.104 even 2 441.3.r.a.50.1 2
120.29 odd 2 576.3.q.b.257.1 2
120.59 even 2 576.3.q.a.257.1 2
180.59 even 6 1296.3.e.a.161.1 2
180.79 odd 6 144.3.q.a.65.1 2
180.119 even 6 432.3.q.a.305.1 2
180.139 odd 6 1296.3.e.a.161.2 2
315.34 odd 6 441.3.r.a.344.1 2
315.79 even 6 441.3.j.a.263.1 2
315.124 odd 6 441.3.j.b.263.1 2
315.214 even 6 441.3.n.b.128.1 2
315.304 odd 6 441.3.n.a.128.1 2
360.29 odd 6 1728.3.q.a.1601.1 2
360.259 odd 6 576.3.q.a.65.1 2
360.299 even 6 1728.3.q.b.1601.1 2
360.349 even 6 576.3.q.b.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.3.d.a.2.1 2 45.34 even 6
9.3.d.a.5.1 yes 2 15.14 odd 2
27.3.d.a.8.1 2 45.29 odd 6
27.3.d.a.17.1 2 5.4 even 2
81.3.b.a.80.1 2 45.14 odd 6
81.3.b.a.80.2 2 45.4 even 6
144.3.q.a.65.1 2 180.79 odd 6
144.3.q.a.113.1 2 60.59 even 2
225.3.i.a.74.1 4 45.7 odd 12
225.3.i.a.74.2 4 45.43 odd 12
225.3.i.a.149.1 4 15.8 even 4
225.3.i.a.149.2 4 15.2 even 4
225.3.j.a.101.1 2 9.7 even 3
225.3.j.a.176.1 2 3.2 odd 2
432.3.q.a.17.1 2 20.19 odd 2
432.3.q.a.305.1 2 180.119 even 6
441.3.j.a.263.1 2 315.79 even 6
441.3.j.a.275.1 2 105.74 odd 6
441.3.j.b.263.1 2 315.124 odd 6
441.3.j.b.275.1 2 105.59 even 6
441.3.n.a.128.1 2 315.304 odd 6
441.3.n.a.410.1 2 105.89 even 6
441.3.n.b.128.1 2 315.214 even 6
441.3.n.b.410.1 2 105.44 odd 6
441.3.r.a.50.1 2 105.104 even 2
441.3.r.a.344.1 2 315.34 odd 6
576.3.q.a.65.1 2 360.259 odd 6
576.3.q.a.257.1 2 120.59 even 2
576.3.q.b.65.1 2 360.349 even 6
576.3.q.b.257.1 2 120.29 odd 2
675.3.i.a.224.1 4 45.38 even 12
675.3.i.a.224.2 4 45.2 even 12
675.3.i.a.449.1 4 5.2 odd 4
675.3.i.a.449.2 4 5.3 odd 4
675.3.j.a.251.1 2 9.2 odd 6 inner
675.3.j.a.476.1 2 1.1 even 1 trivial
1296.3.e.a.161.1 2 180.59 even 6
1296.3.e.a.161.2 2 180.139 odd 6
1728.3.q.a.449.1 2 40.29 even 2
1728.3.q.a.1601.1 2 360.29 odd 6
1728.3.q.b.449.1 2 40.19 odd 2
1728.3.q.b.1601.1 2 360.299 even 6