Properties

Label 1350.2.j.a.199.1
Level $1350$
Weight $2$
Character 1350.199
Analytic conductor $10.780$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(199,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.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: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1350.199
Dual form 1350.2.j.a.1099.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{11} +(1.73205 + 1.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000i q^{17} +1.00000 q^{19} +(2.59808 + 1.50000i) q^{22} +(5.19615 + 3.00000i) q^{23} -2.00000 q^{26} -2.00000i q^{28} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.50000 - 2.59808i) q^{34} -4.00000i q^{37} +(-0.866025 + 0.500000i) q^{38} +(4.50000 - 7.79423i) q^{41} +(0.866025 - 0.500000i) q^{43} -3.00000 q^{44} -6.00000 q^{46} +(5.19615 - 3.00000i) q^{47} +(-1.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{52} +12.0000i q^{53} +(1.00000 + 1.73205i) q^{56} +(5.19615 + 3.00000i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.00000i q^{62} -1.00000 q^{64} +(-4.33013 - 2.50000i) q^{67} +(2.59808 + 1.50000i) q^{68} +12.0000 q^{71} -11.0000i q^{73} +(2.00000 + 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{76} +(-5.19615 - 3.00000i) q^{77} +(-2.00000 - 3.46410i) q^{79} +9.00000i q^{82} +(10.3923 - 6.00000i) q^{83} +(-0.500000 + 0.866025i) q^{86} +(2.59808 - 1.50000i) q^{88} +6.00000 q^{89} +4.00000 q^{91} +(5.19615 - 3.00000i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(4.33013 - 2.50000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 6 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{19} - 8 q^{26} - 12 q^{29} + 8 q^{31} - 6 q^{34} + 18 q^{41} - 12 q^{44} - 24 q^{46} - 6 q^{49} + 4 q^{56} - 6 q^{59} - 16 q^{61} - 4 q^{64} + 48 q^{71} + 8 q^{74} + 2 q^{76} - 8 q^{79} - 2 q^{86} + 24 q^{89} + 16 q^{91} - 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 1.73205 + 1.00000i 0.480384 + 0.277350i 0.720577 0.693375i \(-0.243877\pi\)
−0.240192 + 0.970725i \(0.577210\pi\)
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000i 0.727607i 0.931476 + 0.363803i \(0.118522\pi\)
−0.931476 + 0.363803i \(0.881478\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.59808 + 1.50000i 0.553912 + 0.319801i
\(23\) 5.19615 + 3.00000i 1.08347 + 0.625543i 0.931831 0.362892i \(-0.118211\pi\)
0.151642 + 0.988436i \(0.451544\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) −0.866025 + 0.500000i −0.140488 + 0.0811107i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 0.866025 0.500000i 0.132068 0.0762493i −0.432511 0.901629i \(-0.642372\pi\)
0.564578 + 0.825380i \(0.309039\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 0 0
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.73205 1.00000i 0.240192 0.138675i
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 0 0
\(58\) 5.19615 + 3.00000i 0.682288 + 0.393919i
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.33013 2.50000i −0.529009 0.305424i 0.211604 0.977356i \(-0.432131\pi\)
−0.740613 + 0.671932i \(0.765465\pi\)
\(68\) 2.59808 + 1.50000i 0.315063 + 0.181902i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 11.0000i 1.28745i −0.765256 0.643726i \(-0.777388\pi\)
0.765256 0.643726i \(-0.222612\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 0 0
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) −5.19615 3.00000i −0.592157 0.341882i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 9.00000i 0.993884i
\(83\) 10.3923 6.00000i 1.14070 0.658586i 0.194099 0.980982i \(-0.437822\pi\)
0.946605 + 0.322396i \(0.104488\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) 2.59808 1.50000i 0.276956 0.159901i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 5.19615 3.00000i 0.541736 0.312772i
\(93\) 0 0
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.33013 2.50000i 0.439658 0.253837i −0.263795 0.964579i \(-0.584974\pi\)
0.703452 + 0.710742i \(0.251641\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 12.1244 + 7.00000i 1.19465 + 0.689730i 0.959357 0.282194i \(-0.0910623\pi\)
0.235291 + 0.971925i \(0.424396\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) 3.00000i 0.290021i −0.989430 0.145010i \(-0.953678\pi\)
0.989430 0.145010i \(-0.0463216\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.73205 1.00000i −0.163663 0.0944911i
\(113\) −5.19615 3.00000i −0.488813 0.282216i 0.235269 0.971930i \(-0.424403\pi\)
−0.724082 + 0.689714i \(0.757736\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 3.00000i 0.276172i
\(119\) 3.00000 + 5.19615i 0.275010 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 6.92820 + 4.00000i 0.627250 + 0.362143i
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) 1.73205 1.00000i 0.150188 0.0867110i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 2.59808 1.50000i 0.221969 0.128154i −0.384893 0.922961i \(-0.625762\pi\)
0.606861 + 0.794808i \(0.292428\pi\)
\(138\) 0 0
\(139\) −9.50000 + 16.4545i −0.805779 + 1.39565i 0.109984 + 0.993933i \(0.464920\pi\)
−0.915764 + 0.401718i \(0.868413\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.3923 + 6.00000i −0.872103 + 0.503509i
\(143\) 6.00000i 0.501745i
\(144\) 0 0
\(145\) 0 0
\(146\) 5.50000 + 9.52628i 0.455183 + 0.788400i
\(147\) 0 0
\(148\) −3.46410 2.00000i −0.284747 0.164399i
\(149\) 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
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 0 0
\(157\) 3.46410 + 2.00000i 0.276465 + 0.159617i 0.631822 0.775113i \(-0.282307\pi\)
−0.355357 + 0.934731i \(0.615641\pi\)
\(158\) 3.46410 + 2.00000i 0.275589 + 0.159111i
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −10.3923 6.00000i −0.804181 0.464294i 0.0407502 0.999169i \(-0.487025\pi\)
−0.844931 + 0.534875i \(0.820359\pi\)
\(168\) 0 0
\(169\) −4.50000 7.79423i −0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.00000i 0.0762493i
\(173\) −5.19615 + 3.00000i −0.395056 + 0.228086i −0.684349 0.729155i \(-0.739913\pi\)
0.289292 + 0.957241i \(0.406580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 0 0
\(178\) −5.19615 + 3.00000i −0.389468 + 0.224860i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −3.46410 + 2.00000i −0.256776 + 0.148250i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) 7.79423 4.50000i 0.569970 0.329073i
\(188\) 6.00000i 0.437595i
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 0 0
\(193\) 4.33013 + 2.50000i 0.311689 + 0.179954i 0.647682 0.761911i \(-0.275738\pi\)
−0.335993 + 0.941865i \(0.609072\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.3923 6.00000i −0.729397 0.421117i
\(204\) 0 0
\(205\) 0 0
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) −1.50000 2.59808i −0.103757 0.179713i
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 10.3923 + 6.00000i 0.713746 + 0.412082i
\(213\) 0 0
\(214\) 1.50000 + 2.59808i 0.102538 + 0.177601i
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) −13.8564 + 8.00000i −0.938474 + 0.541828i
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −22.5167 + 13.0000i −1.50783 + 0.870544i −0.507869 + 0.861435i \(0.669566\pi\)
−0.999959 + 0.00910984i \(0.997100\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) −18.1865 + 10.5000i −1.20708 + 0.696909i −0.962121 0.272623i \(-0.912109\pi\)
−0.244962 + 0.969533i \(0.578775\pi\)
\(228\) 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
\(231\) 0 0
\(232\) 5.19615 3.00000i 0.341144 0.196960i
\(233\) 3.00000i 0.196537i 0.995160 + 0.0982683i \(0.0313303\pi\)
−0.995160 + 0.0982683i \(0.968670\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 0 0
\(238\) −5.19615 3.00000i −0.336817 0.194461i
\(239\) −3.00000 + 5.19615i −0.194054 + 0.336111i −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) 1.73205 + 1.00000i 0.110208 + 0.0636285i
\(248\) 3.46410 + 2.00000i 0.219971 + 0.127000i
\(249\) 0 0
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 18.0000i 1.13165i
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −18.1865 10.5000i −1.13444 0.654972i −0.189396 0.981901i \(-0.560653\pi\)
−0.945049 + 0.326929i \(0.893986\pi\)
\(258\) 0 0
\(259\) −4.00000 6.92820i −0.248548 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 15.5885 9.00000i 0.961225 0.554964i 0.0646755 0.997906i \(-0.479399\pi\)
0.896550 + 0.442943i \(0.146065\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 + 1.73205i −0.0613139 + 0.106199i
\(267\) 0 0
\(268\) −4.33013 + 2.50000i −0.264505 + 0.152712i
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 2.59808 1.50000i 0.157532 0.0909509i
\(273\) 0 0
\(274\) −1.50000 + 2.59808i −0.0906183 + 0.156956i
\(275\) 0 0
\(276\) 0 0
\(277\) −8.66025 + 5.00000i −0.520344 + 0.300421i −0.737075 0.675810i \(-0.763794\pi\)
0.216731 + 0.976231i \(0.430460\pi\)
\(278\) 19.0000i 1.13954i
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 + 5.19615i 0.178965 + 0.309976i 0.941526 0.336939i \(-0.109392\pi\)
−0.762561 + 0.646916i \(0.776058\pi\)
\(282\) 0 0
\(283\) −3.46410 2.00000i −0.205919 0.118888i 0.393494 0.919327i \(-0.371266\pi\)
−0.599414 + 0.800439i \(0.704600\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) 3.00000 + 5.19615i 0.177394 + 0.307255i
\(287\) 18.0000i 1.06251i
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) −9.52628 5.50000i −0.557483 0.321863i
\(293\) −25.9808 15.0000i −1.51781 0.876309i −0.999781 0.0209480i \(-0.993332\pi\)
−0.518032 0.855361i \(-0.673335\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) 6.00000i 0.347571i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 0 0
\(301\) 1.00000 1.73205i 0.0576390 0.0998337i
\(302\) −8.66025 5.00000i −0.498342 0.287718i
\(303\) 0 0
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.00000i 0.399511i −0.979846 0.199756i \(-0.935985\pi\)
0.979846 0.199756i \(-0.0640148\pi\)
\(308\) −5.19615 + 3.00000i −0.296078 + 0.170941i
\(309\) 0 0
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 0 0
\(313\) −25.1147 + 14.5000i −1.41957 + 0.819588i −0.996261 0.0863973i \(-0.972465\pi\)
−0.423308 + 0.905986i \(0.639131\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) 0 0
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) −10.3923 + 6.00000i −0.579141 + 0.334367i
\(323\) 3.00000i 0.166924i
\(324\) 0 0
\(325\) 0 0
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) 0 0
\(328\) 7.79423 + 4.50000i 0.430364 + 0.248471i
\(329\) 6.00000 10.3923i 0.330791 0.572946i
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 0.866025 + 0.500000i 0.0471754 + 0.0272367i 0.523402 0.852086i \(-0.324663\pi\)
−0.476227 + 0.879322i \(0.657996\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 28.5788 + 16.5000i 1.53419 + 0.885766i 0.999162 + 0.0409337i \(0.0130332\pi\)
0.535031 + 0.844833i \(0.320300\pi\)
\(348\) 0 0
\(349\) −8.00000 13.8564i −0.428230 0.741716i 0.568486 0.822693i \(-0.307529\pi\)
−0.996716 + 0.0809766i \(0.974196\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.00000i 0.159901i
\(353\) −18.1865 + 10.5000i −0.967972 + 0.558859i −0.898617 0.438733i \(-0.855427\pi\)
−0.0693543 + 0.997592i \(0.522094\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) −10.3923 + 6.00000i −0.549250 + 0.317110i
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −12.1244 + 7.00000i −0.637242 + 0.367912i
\(363\) 0 0
\(364\) 2.00000 3.46410i 0.104828 0.181568i
\(365\) 0 0
\(366\) 0 0
\(367\) −24.2487 + 14.0000i −1.26577 + 0.730794i −0.974185 0.225750i \(-0.927517\pi\)
−0.291587 + 0.956544i \(0.594183\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 0 0
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) −29.4449 17.0000i −1.52460 0.880227i −0.999575 0.0291379i \(-0.990724\pi\)
−0.525022 0.851089i \(-0.675943\pi\)
\(374\) −4.50000 + 7.79423i −0.232689 + 0.403030i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 15.5885 + 9.00000i 0.797575 + 0.460480i
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) 5.00000i 0.253837i
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) −2.59808 1.50000i −0.131223 0.0757614i
\(393\) 0 0
\(394\) −6.00000 10.3923i −0.302276 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000i 1.00377i 0.864934 + 0.501886i \(0.167360\pi\)
−0.864934 + 0.501886i \(0.832640\pi\)
\(398\) −8.66025 + 5.00000i −0.434099 + 0.250627i
\(399\) 0 0
\(400\) 0 0
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) 6.92820 4.00000i 0.345118 0.199254i
\(404\) 0 0
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) −10.3923 + 6.00000i −0.515127 + 0.297409i
\(408\) 0 0
\(409\) 8.50000 14.7224i 0.420298 0.727977i −0.575670 0.817682i \(-0.695259\pi\)
0.995968 + 0.0897044i \(0.0285922\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 12.1244 7.00000i 0.597324 0.344865i
\(413\) 6.00000i 0.295241i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 2.59808 + 1.50000i 0.127076 + 0.0733674i
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 20.0000i 0.973585i
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) 0 0
\(427\) −13.8564 8.00000i −0.670559 0.387147i
\(428\) −2.59808 1.50000i −0.125583 0.0725052i
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) 7.00000i 0.336399i 0.985753 + 0.168199i \(0.0537952\pi\)
−0.985753 + 0.168199i \(0.946205\pi\)
\(434\) 4.00000 + 6.92820i 0.192006 + 0.332564i
\(435\) 0 0
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) 5.19615 + 3.00000i 0.248566 + 0.143509i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000i 0.285391i
\(443\) 2.59808 1.50000i 0.123438 0.0712672i −0.437009 0.899457i \(-0.643962\pi\)
0.560448 + 0.828190i \(0.310629\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −1.73205 + 1.00000i −0.0818317 + 0.0472456i
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −27.0000 −1.27138
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 0 0
\(454\) 10.5000 18.1865i 0.492789 0.853536i
\(455\) 0 0
\(456\) 0 0
\(457\) 14.7224 8.50000i 0.688686 0.397613i −0.114433 0.993431i \(-0.536505\pi\)
0.803120 + 0.595818i \(0.203172\pi\)
\(458\) 14.0000i 0.654177i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) 17.3205 + 10.0000i 0.804952 + 0.464739i 0.845200 0.534450i \(-0.179481\pi\)
−0.0402476 + 0.999190i \(0.512815\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) −1.50000 2.59808i −0.0694862 0.120354i
\(467\) 15.0000i 0.694117i 0.937843 + 0.347059i \(0.112820\pi\)
−0.937843 + 0.347059i \(0.887180\pi\)
\(468\) 0 0
\(469\) −10.0000 −0.461757
\(470\) 0 0
\(471\) 0 0
\(472\) −2.59808 1.50000i −0.119586 0.0690431i
\(473\) −2.59808 1.50000i −0.119460 0.0689701i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 6.00000i 0.274434i
\(479\) 21.0000 + 36.3731i 0.959514 + 1.66193i 0.723681 + 0.690134i \(0.242449\pi\)
0.235833 + 0.971794i \(0.424218\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) −6.06218 3.50000i −0.276125 0.159421i
\(483\) 0 0
\(484\) −1.00000 1.73205i −0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) 26.0000i 1.17817i 0.808070 + 0.589086i \(0.200512\pi\)
−0.808070 + 0.589086i \(0.799488\pi\)
\(488\) 6.92820 4.00000i 0.313625 0.181071i
\(489\) 0 0
\(490\) 0 0
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 0 0
\(493\) 15.5885 9.00000i 0.702069 0.405340i
\(494\) −2.00000 −0.0899843
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 20.7846 12.0000i 0.932317 0.538274i
\(498\) 0 0
\(499\) −6.50000 + 11.2583i −0.290980 + 0.503992i −0.974042 0.226369i \(-0.927315\pi\)
0.683062 + 0.730361i \(0.260648\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.1865 10.5000i 0.811705 0.468638i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 9.00000 + 15.5885i 0.400099 + 0.692991i
\(507\) 0 0
\(508\) 1.73205 + 1.00000i 0.0768473 + 0.0443678i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) −11.0000 19.0526i −0.486611 0.842836i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 21.0000 0.926270
\(515\) 0 0
\(516\) 0 0
\(517\) −15.5885 9.00000i −0.685580 0.395820i
\(518\) 6.92820 + 4.00000i 0.304408 + 0.175750i
\(519\) 0 0
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 0 0
\(523\) 20.0000i 0.874539i −0.899331 0.437269i \(-0.855946\pi\)
0.899331 0.437269i \(-0.144054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −9.00000 + 15.5885i −0.392419 + 0.679689i
\(527\) 10.3923 + 6.00000i 0.452696 + 0.261364i
\(528\) 0 0
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000i 0.0867110i
\(533\) 15.5885 9.00000i 0.675211 0.389833i
\(534\) 0 0
\(535\) 0 0
\(536\) 2.50000 4.33013i 0.107984 0.187033i
\(537\) 0 0
\(538\) 20.7846 12.0000i 0.896088 0.517357i
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −17.3205 + 10.0000i −0.743980 + 0.429537i
\(543\) 0 0
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.866025 + 0.500000i −0.0370286 + 0.0213785i −0.518400 0.855138i \(-0.673472\pi\)
0.481371 + 0.876517i \(0.340139\pi\)
\(548\) 3.00000i 0.128154i
\(549\) 0 0
\(550\) 0 0
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) −6.92820 4.00000i −0.294617 0.170097i
\(554\) 5.00000 8.66025i 0.212430 0.367939i
\(555\) 0 0
\(556\) 9.50000 + 16.4545i 0.402890 + 0.697826i
\(557\) 30.0000i 1.27114i 0.772043 + 0.635570i \(0.219235\pi\)
−0.772043 + 0.635570i \(0.780765\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) −5.19615 3.00000i −0.219186 0.126547i
\(563\) 33.7750 + 19.5000i 1.42345 + 0.821827i 0.996592 0.0824933i \(-0.0262883\pi\)
0.426855 + 0.904320i \(0.359622\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) −22.5000 38.9711i −0.943249 1.63376i −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) 0 0
\(571\) 18.5000 32.0429i 0.774201 1.34096i −0.161042 0.986948i \(-0.551485\pi\)
0.935243 0.354008i \(-0.115181\pi\)
\(572\) −5.19615 3.00000i −0.217262 0.125436i
\(573\) 0 0
\(574\) 9.00000 + 15.5885i 0.375653 + 0.650650i
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000i 0.457936i 0.973434 + 0.228968i \(0.0735351\pi\)
−0.973434 + 0.228968i \(0.926465\pi\)
\(578\) −6.92820 + 4.00000i −0.288175 + 0.166378i
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 20.7846i 0.497844 0.862291i
\(582\) 0 0
\(583\) 31.1769 18.0000i 1.29122 0.745484i
\(584\) 11.0000 0.455183
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 7.79423 4.50000i 0.321702 0.185735i −0.330449 0.943824i \(-0.607200\pi\)
0.652151 + 0.758089i \(0.273867\pi\)
\(588\) 0 0
\(589\) 2.00000 3.46410i 0.0824086 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) −3.46410 + 2.00000i −0.142374 + 0.0821995i
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) −10.3923 6.00000i −0.424973 0.245358i
\(599\) −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 0 0
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) 2.00000i 0.0815139i
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) 24.2487 + 14.0000i 0.984225 + 0.568242i 0.903543 0.428497i \(-0.140957\pi\)
0.0806818 + 0.996740i \(0.474290\pi\)
\(608\) 0.866025 + 0.500000i 0.0351220 + 0.0202777i
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) 16.0000i 0.646234i 0.946359 + 0.323117i \(0.104731\pi\)
−0.946359 + 0.323117i \(0.895269\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) 23.3827 + 13.5000i 0.941351 + 0.543490i 0.890384 0.455211i \(-0.150436\pi\)
0.0509678 + 0.998700i \(0.483769\pi\)
\(618\) 0 0
\(619\) 17.5000 + 30.3109i 0.703384 + 1.21830i 0.967271 + 0.253744i \(0.0816620\pi\)
−0.263887 + 0.964554i \(0.585005\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.0000i 0.721734i
\(623\) 10.3923 6.00000i 0.416359 0.240385i
\(624\) 0 0
\(625\) 0 0
\(626\) 14.5000 25.1147i 0.579537 1.00379i
\(627\) 0 0
\(628\) 3.46410 2.00000i 0.138233 0.0798087i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 3.46410 2.00000i 0.137795 0.0795557i
\(633\) 0 0
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) −5.19615 + 3.00000i −0.205879 + 0.118864i
\(638\) 18.0000i 0.712627i
\(639\) 0 0
\(640\) 0 0
\(641\) −1.50000 2.59808i −0.0592464 0.102618i 0.834881 0.550431i \(-0.185536\pi\)
−0.894127 + 0.447813i \(0.852203\pi\)
\(642\) 0 0
\(643\) 19.9186 + 11.5000i 0.785512 + 0.453516i 0.838380 0.545086i \(-0.183503\pi\)
−0.0528680 + 0.998602i \(0.516836\pi\)
\(644\) 6.00000 10.3923i 0.236433 0.409514i
\(645\) 0 0
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) 18.0000i 0.707653i −0.935311 0.353827i \(-0.884880\pi\)
0.935311 0.353827i \(-0.115120\pi\)
\(648\) 0 0
\(649\) 9.00000 0.353281
\(650\) 0 0
\(651\) 0 0
\(652\) 3.46410 + 2.00000i 0.135665 + 0.0783260i
\(653\) 5.19615 + 3.00000i 0.203341 + 0.117399i 0.598213 0.801337i \(-0.295878\pi\)
−0.394872 + 0.918736i \(0.629211\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −9.00000 −0.351391
\(657\) 0 0
\(658\) 12.0000i 0.467809i
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) −3.46410 2.00000i −0.134636 0.0777322i
\(663\) 0 0
\(664\) 6.00000 + 10.3923i 0.232845 + 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 36.0000i 1.39393i
\(668\) −10.3923 + 6.00000i −0.402090 + 0.232147i
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 + 20.7846i −0.463255 + 0.802381i
\(672\) 0 0
\(673\) 19.0526 11.0000i 0.734422 0.424019i −0.0856156 0.996328i \(-0.527286\pi\)
0.820038 + 0.572309i \(0.193952\pi\)
\(674\) −1.00000 −0.0385186
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −31.1769 + 18.0000i −1.19823 + 0.691796i −0.960159 0.279453i \(-0.909847\pi\)
−0.238067 + 0.971249i \(0.576514\pi\)
\(678\) 0 0
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 0 0
\(681\) 0 0
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) 9.00000i 0.344375i −0.985064 0.172188i \(-0.944916\pi\)
0.985064 0.172188i \(-0.0550836\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 0 0
\(688\) −0.866025 0.500000i −0.0330169 0.0190623i
\(689\) −12.0000 + 20.7846i −0.457164 + 0.791831i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 0 0
\(694\) −33.0000 −1.25266
\(695\) 0 0
\(696\) 0 0
\(697\) 23.3827 + 13.5000i 0.885682 + 0.511349i
\(698\) 13.8564 + 8.00000i 0.524473 + 0.302804i
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 4.00000i 0.150863i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 10.5000 18.1865i 0.395173 0.684459i
\(707\) 0 0
\(708\) 0 0
\(709\) −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i \(-0.190598\pi\)
−0.901135 + 0.433539i \(0.857265\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000i 0.224860i
\(713\) 20.7846 12.0000i 0.778390 0.449404i
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 15.5885 9.00000i 0.581756 0.335877i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) 15.5885 9.00000i 0.580142 0.334945i
\(723\) 0 0
\(724\) 7.00000 12.1244i 0.260153 0.450598i
\(725\) 0 0
\(726\) 0 0
\(727\) 22.5167 13.0000i 0.835097 0.482143i −0.0204978 0.999790i \(-0.506525\pi\)
0.855595 + 0.517647i \(0.173192\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) 12.1244 + 7.00000i 0.447823 + 0.258551i 0.706910 0.707303i \(-0.250088\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(734\) 14.0000 24.2487i 0.516749 0.895036i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 15.0000i 0.552532i
\(738\) 0 0
\(739\) −47.0000 −1.72892 −0.864461 0.502699i \(-0.832340\pi\)
−0.864461 + 0.502699i \(0.832340\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −20.7846 12.0000i −0.763027 0.440534i
\(743\) −5.19615 3.00000i −0.190628 0.110059i 0.401648 0.915794i \(-0.368437\pi\)
−0.592277 + 0.805735i \(0.701771\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 34.0000 1.24483
\(747\) 0 0
\(748\) 9.00000i 0.329073i
\(749\) −3.00000 5.19615i −0.109618 0.189863i
\(750\) 0 0
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) −5.19615 3.00000i −0.189484 0.109399i
\(753\) 0 0
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 19.9186 11.5000i 0.723476 0.417699i
\(759\) 0 0
\(760\) 0 0
\(761\) 21.0000 36.3731i 0.761249 1.31852i −0.180957 0.983491i \(-0.557920\pi\)
0.942207 0.335032i \(-0.108747\pi\)
\(762\) 0 0
\(763\) 27.7128 16.0000i 1.00327 0.579239i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 0 0
\(767\) −5.19615 + 3.00000i −0.187622 + 0.108324i
\(768\) 0 0
\(769\) 1.00000 1.73205i 0.0360609 0.0624593i −0.847432 0.530904i \(-0.821852\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.33013 2.50000i 0.155845 0.0899770i
\(773\) 18.0000i 0.647415i 0.946157 + 0.323708i \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 2.50000 + 4.33013i 0.0897448 + 0.155443i
\(777\) 0 0
\(778\) 15.5885 + 9.00000i 0.558873 + 0.322666i
\(779\) 4.50000 7.79423i 0.161229 0.279257i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 18.0000i 0.643679i
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 0 0
\(786\) 0 0
\(787\) 3.46410 + 2.00000i 0.123482 + 0.0712923i 0.560469 0.828176i \(-0.310621\pi\)
−0.436987 + 0.899468i \(0.643954\pi\)
\(788\) 10.3923 + 6.00000i 0.370211 + 0.213741i
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 16.0000i 0.568177i
\(794\) −10.0000 17.3205i −0.354887 0.614682i
\(795\) 0 0
\(796\) 5.00000 8.66025i 0.177220 0.306955i
\(797\) −10.3923 6.00000i −0.368114 0.212531i 0.304520 0.952506i \(-0.401504\pi\)
−0.672634 + 0.739975i \(0.734837\pi\)
\(798\) 0 0
\(799\) 9.00000 + 15.5885i 0.318397 + 0.551480i
\(800\) 0 0
\(801\) 0 0
\(802\) 27.0000i 0.953403i
\(803\) −28.5788 + 16.5000i −1.00853 + 0.582272i
\(804\) 0 0
\(805\) 0 0
\(806\) −4.00000 + 6.92820i −0.140894 + 0.244036i
\(807\) 0 0
\(808\) 0 0
\(809\) 33.0000 1.16022 0.580109 0.814539i \(-0.303010\pi\)
0.580109 + 0.814539i \(0.303010\pi\)
\(810\) 0 0
\(811\) −7.00000 −0.245803 −0.122902 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(812\) −10.3923 + 6.00000i −0.364698 + 0.210559i
\(813\) 0 0
\(814\) 6.00000 10.3923i 0.210300 0.364250i
\(815\) 0 0
\(816\) 0 0
\(817\) 0.866025 0.500000i 0.0302984 0.0174928i
\(818\) 17.0000i 0.594391i
\(819\) 0 0
\(820\) 0 0
\(821\) −9.00000 15.5885i −0.314102 0.544041i 0.665144 0.746715i \(-0.268370\pi\)
−0.979246 + 0.202674i \(0.935037\pi\)
\(822\) 0 0
\(823\) −13.8564 8.00000i −0.483004 0.278862i 0.238664 0.971102i \(-0.423291\pi\)
−0.721668 + 0.692240i \(0.756624\pi\)
\(824\) −7.00000 + 12.1244i −0.243857 + 0.422372i
\(825\) 0 0
\(826\) −3.00000 5.19615i −0.104383 0.180797i
\(827\) 12.0000i 0.417281i 0.977992 + 0.208640i \(0.0669038\pi\)
−0.977992 + 0.208640i \(0.933096\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.73205 1.00000i −0.0600481 0.0346688i
\(833\) −7.79423 4.50000i −0.270054 0.155916i
\(834\) 0 0
\(835\) 0 0
\(836\) −3.00000 −0.103757
\(837\) 0 0
\(838\) 12.0000i 0.414533i
\(839\) −6.00000 10.3923i −0.207143 0.358782i 0.743670 0.668546i \(-0.233083\pi\)
−0.950813 + 0.309764i \(0.899750\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 17.3205 + 10.0000i 0.596904 + 0.344623i
\(843\) 0 0
\(844\) 10.0000 + 17.3205i 0.344214 + 0.596196i
\(845\) 0 0
\(846\) 0 0
\(847\) 4.00000i 0.137442i
\(848\) 10.3923 6.00000i 0.356873 0.206041i
\(849\) 0 0
\(850\) 0 0
\(851\) 12.0000 20.7846i 0.411355 0.712487i
\(852\) 0 0
\(853\) −22.5167 + 13.0000i −0.770956 + 0.445112i −0.833215 0.552948i \(-0.813503\pi\)
0.0622597 + 0.998060i \(0.480169\pi\)
\(854\) 16.0000 0.547509
\(855\) 0 0
\(856\) 3.00000 0.102538
\(857\) 36.3731 21.0000i 1.24248 0.717346i 0.272882 0.962048i \(-0.412023\pi\)
0.969599 + 0.244701i \(0.0786899\pi\)
\(858\) 0 0
\(859\) 17.5000 30.3109i 0.597092 1.03419i −0.396156 0.918183i \(-0.629656\pi\)
0.993248 0.116011i \(-0.0370107\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −25.9808 + 15.0000i −0.884908 + 0.510902i
\(863\) 24.0000i 0.816970i 0.912765 + 0.408485i \(0.133943\pi\)
−0.912765 + 0.408485i \(0.866057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −3.50000 6.06218i −0.118935 0.206001i
\(867\) 0 0
\(868\) −6.92820 4.00000i −0.235159 0.135769i
\(869\) −6.00000 + 10.3923i −0.203536 + 0.352535i
\(870\) 0 0
\(871\) −5.00000 8.66025i −0.169419 0.293442i
\(872\) 16.0000i 0.541828i
\(873\) 0 0
\(874\) −6.00000 −0.202953
\(875\) 0 0
\(876\) 0 0
\(877\) −6.92820 4.00000i −0.233949 0.135070i 0.378444 0.925624i \(-0.376459\pi\)
−0.612392 + 0.790554i \(0.709793\pi\)
\(878\) −6.92820 4.00000i −0.233816 0.134993i
\(879\) 0 0
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) 0 0
\(883\) 19.0000i 0.639401i 0.947519 + 0.319700i \(0.103582\pi\)
−0.947519 + 0.319700i \(0.896418\pi\)
\(884\) 3.00000 + 5.19615i 0.100901 + 0.174766i
\(885\) 0 0
\(886\) −1.50000 + 2.59808i −0.0503935 + 0.0872841i
\(887\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) 2.00000 + 3.46410i 0.0670778 + 0.116182i
\(890\) 0 0
\(891\) 0 0
\(892\) 26.0000i 0.870544i
\(893\) 5.19615 3.00000i 0.173883 0.100391i
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.73205i 0.0334077 0.0578638i
\(897\) 0 0
\(898\) −7.79423 + 4.50000i −0.260097 + 0.150167i
\(899\) −24.0000 −0.800445
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) 23.3827 13.5000i 0.778558 0.449501i
\(903\) 0 0
\(904\) 3.00000 5.19615i 0.0997785 0.172821i
\(905\) 0 0
\(906\) 0 0
\(907\) −26.8468 + 15.5000i −0.891433 + 0.514669i −0.874411 0.485186i \(-0.838752\pi\)
−0.0170220 + 0.999855i \(0.505419\pi\)
\(908\) 21.0000i 0.696909i
\(909\) 0 0
\(910\) 0 0
\(911\) 24.0000 + 41.5692i 0.795155 + 1.37725i 0.922740 + 0.385422i \(0.125944\pi\)
−0.127585 + 0.991828i \(0.540723\pi\)
\(912\) 0 0
\(913\) −31.1769 18.0000i −1.03181 0.595713i
\(914\) −8.50000 + 14.7224i −0.281155 + 0.486975i
\(915\) 0 0
\(916\) −7.00000 12.1244i −0.231287 0.400600i
\(917\) 0 0
\(918\) 0 0
\(919\) −38.0000 −1.25350 −0.626752 0.779219i \(-0.715616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 25.9808 + 15.0000i 0.855631 + 0.493999i
\(923\) 20.7846 + 12.0000i 0.684134 + 0.394985i
\(924\) 0 0
\(925\) 0 0
\(926\) −20.0000 −0.657241
\(927\) 0 0
\(928\) 6.00000i 0.196960i
\(929\) 3.00000 + 5.19615i 0.0984268 + 0.170480i 0.911034 0.412332i \(-0.135286\pi\)
−0.812607 + 0.582812i \(0.801952\pi\)
\(930\) 0 0
\(931\) −1.50000 + 2.59808i −0.0491605 + 0.0851485i
\(932\) 2.59808 + 1.50000i 0.0851028 + 0.0491341i
\(933\) 0 0
\(934\) −7.50000 12.9904i −0.245407 0.425058i
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0000i 0.457360i 0.973502 + 0.228680i \(0.0734410\pi\)
−0.973502 + 0.228680i \(0.926559\pi\)
\(938\) 8.66025 5.00000i 0.282767 0.163256i
\(939\) 0 0
\(940\) 0 0
\(941\) −30.0000 + 51.9615i −0.977972 + 1.69390i −0.308215 + 0.951317i \(0.599732\pi\)
−0.669757 + 0.742581i \(0.733602\pi\)
\(942\) 0 0
\(943\) 46.7654 27.0000i 1.52289 0.879241i
\(944\) 3.00000 0.0976417
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) −2.59808 + 1.50000i −0.0844261 + 0.0487435i −0.541619 0.840624i \(-0.682188\pi\)
0.457193 + 0.889368i \(0.348855\pi\)
\(948\) 0 0
\(949\) 11.0000 19.0526i 0.357075 0.618472i
\(950\) 0 0
\(951\) 0 0
\(952\) −5.19615 + 3.00000i −0.168408 + 0.0972306i
\(953\) 9.00000i 0.291539i 0.989319 + 0.145769i \(0.0465657\pi\)
−0.989319 + 0.145769i \(0.953434\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 3.00000 + 5.19615i 0.0970269 + 0.168056i
\(957\) 0 0
\(958\) −36.3731 21.0000i −1.17516 0.678479i
\(959\) 3.00000 5.19615i 0.0968751 0.167793i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 8.00000i 0.257930i
\(963\) 0 0
\(964\) 7.00000 0.225455
\(965\) 0 0
\(966\) 0 0
\(967\) 19.0526 + 11.0000i 0.612689 + 0.353736i 0.774017 0.633165i \(-0.218244\pi\)
−0.161328 + 0.986901i \(0.551578\pi\)
\(968\) 1.73205 + 1.00000i 0.0556702 + 0.0321412i
\(969\) 0 0
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 0 0
\(973\) 38.0000i 1.21822i
\(974\) −13.0000 22.5167i −0.416547 0.721480i
\(975\) 0 0
\(976\) −4.00000 + 6.92820i −0.128037 + 0.221766i
\(977\) −44.1673 25.5000i −1.41304 0.815817i −0.417364 0.908740i \(-0.637046\pi\)
−0.995673 + 0.0929223i \(0.970379\pi\)
\(978\) 0 0
\(979\) −9.00000 15.5885i −0.287641 0.498209i
\(980\) 0 0
\(981\) 0 0
\(982\) 15.0000i 0.478669i
\(983\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −9.00000 + 15.5885i −0.286618 + 0.496438i
\(987\) 0 0
\(988\) 1.73205 1.00000i 0.0551039 0.0318142i
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 3.46410 2.00000i 0.109985 0.0635001i
\(993\) 0 0
\(994\) −12.0000 + 20.7846i −0.380617 + 0.659248i
\(995\) 0 0
\(996\) 0 0
\(997\) −24.2487 + 14.0000i −0.767964 + 0.443384i −0.832148 0.554554i \(-0.812889\pi\)
0.0641836 + 0.997938i \(0.479556\pi\)
\(998\) 13.0000i 0.411508i
\(999\) 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 1350.2.j.a.199.1 4
3.2 odd 2 450.2.j.e.49.2 4
5.2 odd 4 1350.2.e.c.901.1 2
5.3 odd 4 54.2.c.a.37.1 2
5.4 even 2 inner 1350.2.j.a.199.2 4
9.2 odd 6 450.2.j.e.349.1 4
9.4 even 3 4050.2.c.r.649.1 2
9.5 odd 6 4050.2.c.c.649.2 2
9.7 even 3 inner 1350.2.j.a.1099.2 4
15.2 even 4 450.2.e.i.301.1 2
15.8 even 4 18.2.c.a.13.1 yes 2
15.14 odd 2 450.2.j.e.49.1 4
20.3 even 4 432.2.i.b.145.1 2
35.3 even 12 2646.2.e.c.1549.1 2
35.13 even 4 2646.2.f.g.1765.1 2
35.18 odd 12 2646.2.e.b.1549.1 2
35.23 odd 12 2646.2.h.h.361.1 2
35.33 even 12 2646.2.h.i.361.1 2
40.3 even 4 1728.2.i.f.577.1 2
40.13 odd 4 1728.2.i.e.577.1 2
45.2 even 12 450.2.e.i.151.1 2
45.4 even 6 4050.2.c.r.649.2 2
45.7 odd 12 1350.2.e.c.451.1 2
45.13 odd 12 162.2.a.b.1.1 1
45.14 odd 6 4050.2.c.c.649.1 2
45.22 odd 12 4050.2.a.v.1.1 1
45.23 even 12 162.2.a.c.1.1 1
45.29 odd 6 450.2.j.e.349.2 4
45.32 even 12 4050.2.a.c.1.1 1
45.34 even 6 inner 1350.2.j.a.1099.1 4
45.38 even 12 18.2.c.a.7.1 2
45.43 odd 12 54.2.c.a.19.1 2
60.23 odd 4 144.2.i.c.49.1 2
105.23 even 12 882.2.h.c.67.1 2
105.38 odd 12 882.2.e.g.373.1 2
105.53 even 12 882.2.e.i.373.1 2
105.68 odd 12 882.2.h.b.67.1 2
105.83 odd 4 882.2.f.d.589.1 2
120.53 even 4 576.2.i.g.193.1 2
120.83 odd 4 576.2.i.a.193.1 2
180.23 odd 12 1296.2.a.g.1.1 1
180.43 even 12 432.2.i.b.289.1 2
180.83 odd 12 144.2.i.c.97.1 2
180.103 even 12 1296.2.a.f.1.1 1
315.13 even 12 7938.2.a.i.1.1 1
315.38 odd 12 882.2.h.b.79.1 2
315.83 odd 12 882.2.f.d.295.1 2
315.88 odd 12 2646.2.h.h.667.1 2
315.128 even 12 882.2.e.i.655.1 2
315.173 odd 12 882.2.e.g.655.1 2
315.178 even 12 2646.2.h.i.667.1 2
315.223 even 12 2646.2.f.g.883.1 2
315.263 even 12 882.2.h.c.79.1 2
315.268 odd 12 2646.2.e.b.2125.1 2
315.293 odd 12 7938.2.a.x.1.1 1
315.313 even 12 2646.2.e.c.2125.1 2
360.13 odd 12 5184.2.a.q.1.1 1
360.43 even 12 1728.2.i.f.1153.1 2
360.83 odd 12 576.2.i.a.385.1 2
360.133 odd 12 1728.2.i.e.1153.1 2
360.173 even 12 576.2.i.g.385.1 2
360.203 odd 12 5184.2.a.o.1.1 1
360.283 even 12 5184.2.a.p.1.1 1
360.293 even 12 5184.2.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.2.c.a.7.1 2 45.38 even 12
18.2.c.a.13.1 yes 2 15.8 even 4
54.2.c.a.19.1 2 45.43 odd 12
54.2.c.a.37.1 2 5.3 odd 4
144.2.i.c.49.1 2 60.23 odd 4
144.2.i.c.97.1 2 180.83 odd 12
162.2.a.b.1.1 1 45.13 odd 12
162.2.a.c.1.1 1 45.23 even 12
432.2.i.b.145.1 2 20.3 even 4
432.2.i.b.289.1 2 180.43 even 12
450.2.e.i.151.1 2 45.2 even 12
450.2.e.i.301.1 2 15.2 even 4
450.2.j.e.49.1 4 15.14 odd 2
450.2.j.e.49.2 4 3.2 odd 2
450.2.j.e.349.1 4 9.2 odd 6
450.2.j.e.349.2 4 45.29 odd 6
576.2.i.a.193.1 2 120.83 odd 4
576.2.i.a.385.1 2 360.83 odd 12
576.2.i.g.193.1 2 120.53 even 4
576.2.i.g.385.1 2 360.173 even 12
882.2.e.g.373.1 2 105.38 odd 12
882.2.e.g.655.1 2 315.173 odd 12
882.2.e.i.373.1 2 105.53 even 12
882.2.e.i.655.1 2 315.128 even 12
882.2.f.d.295.1 2 315.83 odd 12
882.2.f.d.589.1 2 105.83 odd 4
882.2.h.b.67.1 2 105.68 odd 12
882.2.h.b.79.1 2 315.38 odd 12
882.2.h.c.67.1 2 105.23 even 12
882.2.h.c.79.1 2 315.263 even 12
1296.2.a.f.1.1 1 180.103 even 12
1296.2.a.g.1.1 1 180.23 odd 12
1350.2.e.c.451.1 2 45.7 odd 12
1350.2.e.c.901.1 2 5.2 odd 4
1350.2.j.a.199.1 4 1.1 even 1 trivial
1350.2.j.a.199.2 4 5.4 even 2 inner
1350.2.j.a.1099.1 4 45.34 even 6 inner
1350.2.j.a.1099.2 4 9.7 even 3 inner
1728.2.i.e.577.1 2 40.13 odd 4
1728.2.i.e.1153.1 2 360.133 odd 12
1728.2.i.f.577.1 2 40.3 even 4
1728.2.i.f.1153.1 2 360.43 even 12
2646.2.e.b.1549.1 2 35.18 odd 12
2646.2.e.b.2125.1 2 315.268 odd 12
2646.2.e.c.1549.1 2 35.3 even 12
2646.2.e.c.2125.1 2 315.313 even 12
2646.2.f.g.883.1 2 315.223 even 12
2646.2.f.g.1765.1 2 35.13 even 4
2646.2.h.h.361.1 2 35.23 odd 12
2646.2.h.h.667.1 2 315.88 odd 12
2646.2.h.i.361.1 2 35.33 even 12
2646.2.h.i.667.1 2 315.178 even 12
4050.2.a.c.1.1 1 45.32 even 12
4050.2.a.v.1.1 1 45.22 odd 12
4050.2.c.c.649.1 2 45.14 odd 6
4050.2.c.c.649.2 2 9.5 odd 6
4050.2.c.r.649.1 2 9.4 even 3
4050.2.c.r.649.2 2 45.4 even 6
5184.2.a.o.1.1 1 360.203 odd 12
5184.2.a.p.1.1 1 360.283 even 12
5184.2.a.q.1.1 1 360.13 odd 12
5184.2.a.r.1.1 1 360.293 even 12
7938.2.a.i.1.1 1 315.13 even 12
7938.2.a.x.1.1 1 315.293 odd 12