Properties

Label 931.2.f.c.324.1
Level $931$
Weight $2$
Character 931.324
Analytic conductor $7.434$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(324,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.324");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.f (of order \(3\), 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: \(7.43407242818\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 324.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 931.324
Dual form 931.2.f.c.704.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-2.00000 + 3.46410i) q^{12} -4.00000 q^{13} -6.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} -6.00000 q^{20} +(-2.00000 - 3.46410i) q^{25} +4.00000 q^{27} +6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(3.00000 - 5.19615i) q^{33} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-4.00000 - 6.92820i) q^{39} -6.00000 q^{41} -1.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{47} -8.00000 q^{48} +(-3.00000 + 5.19615i) q^{51} +(-4.00000 - 6.92820i) q^{52} +(-6.00000 - 10.3923i) q^{53} +9.00000 q^{55} -2.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-6.00000 - 10.3923i) q^{60} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{71} +(3.50000 + 6.06218i) q^{73} +(4.00000 - 6.92820i) q^{75} -2.00000 q^{76} +(-4.00000 + 6.92820i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(5.50000 + 9.52628i) q^{81} +12.0000 q^{83} -9.00000 q^{85} +(6.00000 + 10.3923i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{95} +8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{4} - 3 q^{5} - q^{9} - 3 q^{11} - 4 q^{12} - 8 q^{13} - 12 q^{15} - 4 q^{16} + 3 q^{17} - q^{19} - 12 q^{20} - 4 q^{25} + 8 q^{27} + 12 q^{29} + 4 q^{31} + 6 q^{33} - 4 q^{36} - 2 q^{37} - 8 q^{39} - 12 q^{41} - 2 q^{43} + 6 q^{44} - 3 q^{45} + 3 q^{47} - 16 q^{48} - 6 q^{51} - 8 q^{52} - 12 q^{53} + 18 q^{55} - 4 q^{57} + 6 q^{59} - 12 q^{60} + q^{61} - 16 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} + 12 q^{71} + 7 q^{73} + 8 q^{75} - 4 q^{76} - 8 q^{79} - 12 q^{80} + 11 q^{81} + 24 q^{83} - 18 q^{85} + 12 q^{87} - 12 q^{89} - 8 q^{93} - 3 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).

\(n\) \(248\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −2.00000 + 3.46410i −0.577350 + 1.00000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −6.00000 −1.54919
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) −6.00000 −1.34164
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 0 0
\(39\) −4.00000 6.92820i −0.640513 1.10940i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) 0 0
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) −8.00000 −1.15470
\(49\) 0 0
\(50\) 0 0
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −4.00000 6.92820i −0.554700 0.960769i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) −6.00000 10.3923i −0.774597 1.34164i
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 4.00000 6.92820i 0.461880 0.800000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −6.00000 10.3923i −0.670820 1.16190i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −9.00000 −0.976187
\(86\) 0 0
\(87\) 6.00000 + 10.3923i 0.643268 + 1.11417i
\(88\) 0 0
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) 0 0
\(95\) −1.50000 2.59808i −0.153897 0.266557i
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 4.00000 6.92820i 0.400000 0.692820i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) 4.00000 + 6.92820i 0.384900 + 0.666667i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.00000 + 10.3923i 0.557086 + 0.964901i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −6.00000 10.3923i −0.541002 0.937043i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) 0 0
\(131\) 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i \(-0.605885\pi\)
0.981824 0.189794i \(-0.0607819\pi\)
\(132\) 12.0000 1.04447
\(133\) 0 0
\(134\) 0 0
\(135\) −6.00000 + 10.3923i −0.516398 + 0.894427i
\(136\) 0 0
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 0 0
\(139\) −13.0000 −1.10265 −0.551323 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) −2.00000 3.46410i −0.166667 0.288675i
\(145\) −9.00000 + 15.5885i −0.747409 + 1.29455i
\(146\) 0 0
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i \(0.496324\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 0 0
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) −12.0000 −0.963863
\(156\) 8.00000 13.8564i 0.640513 1.10940i
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) 12.0000 20.7846i 0.951662 1.64833i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) −6.00000 10.3923i −0.468521 0.811503i
\(165\) 9.00000 + 15.5885i 0.700649 + 1.21356i
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 12.0000 0.904534
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0 0
\(179\) 9.00000 + 15.5885i 0.672692 + 1.16514i 0.977138 + 0.212607i \(0.0681952\pi\)
−0.304446 + 0.952529i \(0.598471\pi\)
\(180\) 3.00000 5.19615i 0.223607 0.387298i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) 4.50000 7.79423i 0.329073 0.569970i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) −8.00000 13.8564i −0.577350 1.00000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) 0 0
\(195\) 24.0000 1.71868
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −5.50000 9.52628i −0.389885 0.675300i 0.602549 0.798082i \(-0.294152\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) −12.0000 −0.840168
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) 0 0
\(207\) 0 0
\(208\) 8.00000 13.8564i 0.554700 0.960769i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 12.0000 20.7846i 0.824163 1.42749i
\(213\) 6.00000 + 10.3923i 0.411113 + 0.712069i
\(214\) 0 0
\(215\) 1.50000 2.59808i 0.102299 0.177187i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 9.00000 + 15.5885i 0.606780 + 1.05097i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 0 0
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) −2.00000 3.46410i −0.132453 0.229416i
\(229\) −2.50000 + 4.33013i −0.165205 + 0.286143i −0.936728 0.350058i \(-0.886162\pi\)
0.771523 + 0.636201i \(0.219495\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) 0 0
\(235\) 4.50000 + 7.79423i 0.293548 + 0.508439i
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 12.0000 20.7846i 0.774597 1.34164i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 0 0
\(247\) 2.00000 3.46410i 0.127257 0.220416i
\(248\) 0 0
\(249\) 12.0000 + 20.7846i 0.760469 + 1.31717i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −9.00000 15.5885i −0.563602 0.976187i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 24.0000 1.48842
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) 0 0
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) 0 0
\(267\) −24.0000 −1.46878
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) −12.0000 −0.727607
\(273\) 0 0
\(274\) 0 0
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0 0
\(277\) 9.50000 + 16.4545i 0.570800 + 0.988654i 0.996484 + 0.0837823i \(0.0267000\pi\)
−0.425684 + 0.904872i \(0.639967\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 3.00000 5.19615i 0.177705 0.307794i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) −18.0000 −1.04800
\(296\) 0 0
\(297\) −6.00000 10.3923i −0.348155 0.603023i
\(298\) 0 0
\(299\) 0 0
\(300\) 16.0000 0.923760
\(301\) 0 0
\(302\) 0 0
\(303\) 6.00000 10.3923i 0.344691 0.597022i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −28.0000 −1.59286
\(310\) 0 0
\(311\) 1.50000 + 2.59808i 0.0850572 + 0.147323i 0.905416 0.424526i \(-0.139559\pi\)
−0.820358 + 0.571850i \(0.806226\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 12.0000 20.7846i 0.670820 1.16190i
\(321\) 36.0000 2.00932
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) −11.0000 + 19.0526i −0.611111 + 1.05848i
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 0 0
\(327\) −16.0000 + 27.7128i −0.884802 + 1.53252i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 12.0000 + 20.7846i 0.658586 + 1.14070i
\(333\) −1.00000 1.73205i −0.0547997 0.0949158i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 32.0000 1.74315 0.871576 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 0 0
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) −9.00000 15.5885i −0.488094 0.845403i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.5000 18.1865i −0.563670 0.976304i −0.997172 0.0751519i \(-0.976056\pi\)
0.433503 0.901152i \(-0.357278\pi\)
\(348\) −12.0000 + 20.7846i −0.643268 + 1.11417i
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) −24.0000 −1.27200
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) 0 0
\(363\) 4.00000 0.209946
\(364\) 0 0
\(365\) −21.0000 −1.09919
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 0 0
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) −16.0000 −0.829561
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 0 0
\(375\) −3.00000 5.19615i −0.154919 0.268328i
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −34.0000 −1.74646 −0.873231 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) 3.00000 5.19615i 0.153897 0.266557i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 0 0
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.500000 0.866025i 0.0254164 0.0440225i
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 30.0000 1.51330
\(394\) 0 0
\(395\) −12.0000 20.7846i −0.603786 1.04579i
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 3.50000 6.06218i 0.175660 0.304252i −0.764730 0.644351i \(-0.777127\pi\)
0.940389 + 0.340099i \(0.110461\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 16.0000 0.800000
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) 6.00000 10.3923i 0.298511 0.517036i
\(405\) −33.0000 −1.63978
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 0 0
\(411\) −3.00000 + 5.19615i −0.147979 + 0.256307i
\(412\) −28.0000 −1.37946
\(413\) 0 0
\(414\) 0 0
\(415\) −18.0000 + 31.1769i −0.883585 + 1.53041i
\(416\) 0 0
\(417\) −13.0000 22.5167i −0.636613 1.10265i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) 0 0
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) 36.0000 1.74013
\(429\) −12.0000 + 20.7846i −0.579365 + 1.00349i
\(430\) 0 0
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) −8.00000 + 13.8564i −0.384900 + 0.666667i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −36.0000 −1.72607
\(436\) −16.0000 + 27.7128i −0.766261 + 1.32720i
\(437\) 0 0
\(438\) 0 0
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.50000 2.59808i 0.0712672 0.123438i −0.828190 0.560448i \(-0.810629\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(444\) −4.00000 6.92820i −0.189832 0.328798i
\(445\) −18.0000 31.1769i −0.853282 1.47793i
\(446\) 0 0
\(447\) −42.0000 −1.98653
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) −10.0000 + 17.3205i −0.469841 + 0.813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.5000 32.0429i 0.865393 1.49891i −0.00126243 0.999999i \(-0.500402\pi\)
0.866656 0.498906i \(-0.166265\pi\)
\(458\) 0 0
\(459\) 6.00000 + 10.3923i 0.280056 + 0.485071i
\(460\) 0 0
\(461\) 9.00000 0.419172 0.209586 0.977790i \(-0.432788\pi\)
0.209586 + 0.977790i \(0.432788\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) −12.0000 + 20.7846i −0.557086 + 0.964901i
\(465\) −12.0000 20.7846i −0.556487 0.963863i
\(466\) 0 0
\(467\) 13.5000 23.3827i 0.624705 1.08202i −0.363892 0.931441i \(-0.618552\pi\)
0.988598 0.150581i \(-0.0481143\pi\)
\(468\) 8.00000 0.369800
\(469\) 0 0
\(470\) 0 0
\(471\) 14.0000 24.2487i 0.645086 1.11732i
\(472\) 0 0
\(473\) 1.50000 + 2.59808i 0.0689701 + 0.119460i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) 6.00000 + 10.3923i 0.274147 + 0.474837i 0.969920 0.243426i \(-0.0782712\pi\)
−0.695773 + 0.718262i \(0.744938\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 0 0
\(483\) 0 0
\(484\) 4.00000 0.181818
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 0 0
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) 0 0
\(489\) −40.0000 −1.80886
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 12.0000 20.7846i 0.541002 0.937043i
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) −4.50000 + 7.79423i −0.202260 + 0.350325i
\(496\) −16.0000 −0.718421
\(497\) 0 0
\(498\) 0 0
\(499\) −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i \(-0.869032\pi\)
0.804627 + 0.593780i \(0.202365\pi\)
\(500\) −3.00000 5.19615i −0.134164 0.232379i
\(501\) −18.0000 31.1769i −0.804181 1.39288i
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 3.00000 + 5.19615i 0.133235 + 0.230769i
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.00000 + 3.46410i −0.0883022 + 0.152944i
\(514\) 0 0
\(515\) −21.0000 36.3731i −0.925371 1.60279i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) 36.0000 1.58022
\(520\) 0 0
\(521\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 0 0
\(523\) −19.0000 + 32.9090i −0.830812 + 1.43901i 0.0665832 + 0.997781i \(0.478790\pi\)
−0.897395 + 0.441228i \(0.854543\pi\)
\(524\) 30.0000 1.31056
\(525\) 0 0
\(526\) 0 0
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 12.0000 + 20.7846i 0.522233 + 0.904534i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) 27.0000 + 46.7654i 1.16731 + 2.02184i
\(536\) 0 0
\(537\) −18.0000 + 31.1769i −0.776757 + 1.34538i
\(538\) 0 0
\(539\) 0 0
\(540\) −24.0000 −1.03280
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 2.00000 + 3.46410i 0.0858282 + 0.148659i
\(544\) 0 0
\(545\) −48.0000 −2.05609
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) 0.500000 + 0.866025i 0.0213395 + 0.0369611i
\(550\) 0 0
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.00000 10.3923i 0.254686 0.441129i
\(556\) −13.0000 22.5167i −0.551323 0.954919i
\(557\) −10.5000 18.1865i −0.444899 0.770588i 0.553146 0.833084i \(-0.313427\pi\)
−0.998045 + 0.0624962i \(0.980094\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) −3.00000 5.19615i −0.126435 0.218992i 0.795858 0.605483i \(-0.207020\pi\)
−0.922293 + 0.386492i \(0.873687\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.0000 20.7846i 0.503066 0.871336i −0.496928 0.867792i \(-0.665539\pi\)
0.999994 0.00354413i \(-0.00112814\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) −12.0000 + 20.7846i −0.501745 + 0.869048i
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −5.50000 9.52628i −0.228968 0.396584i 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 0 0
\(579\) −4.00000 + 6.92820i −0.166234 + 0.287926i
\(580\) −36.0000 −1.49482
\(581\) 0 0
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) 45.0000 1.85735 0.928674 0.370896i \(-0.120949\pi\)
0.928674 + 0.370896i \(0.120949\pi\)
\(588\) 0 0
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 18.0000 + 31.1769i 0.740421 + 1.28245i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 21.0000 36.3731i 0.862367 1.49366i −0.00727173 0.999974i \(-0.502315\pi\)
0.869638 0.493689i \(-0.164352\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −42.0000 −1.72039
\(597\) 11.0000 19.0526i 0.450200 0.779769i
\(598\) 0 0
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −10.0000 + 17.3205i −0.406894 + 0.704761i
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) −14.5000 25.1147i −0.585649 1.01437i −0.994794 0.101905i \(-0.967506\pi\)
0.409145 0.912470i \(-0.365827\pi\)
\(614\) 0 0
\(615\) 36.0000 1.45166
\(616\) 0 0
\(617\) 9.00000 0.362326 0.181163 0.983453i \(-0.442014\pi\)
0.181163 + 0.983453i \(0.442014\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) −12.0000 20.7846i −0.481932 0.834730i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 32.0000 1.28103
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) 3.00000 + 5.19615i 0.119808 + 0.207514i
\(628\) 14.0000 24.2487i 0.558661 0.967629i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 11.0000 0.437903 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(632\) 0 0
\(633\) 14.0000 + 24.2487i 0.556450 + 0.963800i
\(634\) 0 0
\(635\) −3.00000 + 5.19615i −0.119051 + 0.206203i
\(636\) 48.0000 1.90332
\(637\) 0 0
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0 0
\(643\) −13.0000 −0.512670 −0.256335 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −13.5000 23.3827i −0.530740 0.919268i −0.999357 0.0358667i \(-0.988581\pi\)
0.468617 0.883402i \(-0.344753\pi\)
\(648\) 0 0
\(649\) 9.00000 15.5885i 0.353281 0.611900i
\(650\) 0 0
\(651\) 0 0
\(652\) −40.0000 −1.56652
\(653\) 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) 0 0
\(655\) 22.5000 + 38.9711i 0.879148 + 1.52273i
\(656\) 12.0000 20.7846i 0.468521 0.811503i
\(657\) −7.00000 −0.273096
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) −18.0000 + 31.1769i −0.700649 + 1.21356i
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 0 0
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −18.0000 31.1769i −0.696441 1.20627i
\(669\) −10.0000 17.3205i −0.386622 0.669650i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 0 0
\(675\) −8.00000 13.8564i −0.307920 0.533333i
\(676\) 3.00000 + 5.19615i 0.115385 + 0.199852i
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 20.7846i 0.459841 0.796468i
\(682\) 0 0
\(683\) −18.0000 31.1769i −0.688751 1.19295i −0.972242 0.233977i \(-0.924826\pi\)
0.283491 0.958975i \(-0.408507\pi\)
\(684\) 1.00000 1.73205i 0.0382360 0.0662266i
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 24.0000 + 41.5692i 0.914327 + 1.58366i
\(690\) 0 0
\(691\) −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) 36.0000 1.36851
\(693\) 0 0
\(694\) 0 0
\(695\) 19.5000 33.7750i 0.739677 1.28116i
\(696\) 0 0
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 0 0
\(699\) 42.0000 1.58859
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −1.00000 1.73205i −0.0377157 0.0653255i
\(704\) 12.0000 + 20.7846i 0.452267 + 0.783349i
\(705\) −9.00000 + 15.5885i −0.338960 + 0.587095i
\(706\) 0 0
\(707\) 0 0
\(708\) −24.0000 −0.901975
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) −18.0000 + 31.1769i −0.672692 + 1.16514i
\(717\) 15.0000 + 25.9808i 0.560185 + 0.970269i
\(718\) 0 0
\(719\) −7.50000 + 12.9904i −0.279703 + 0.484459i −0.971311 0.237814i \(-0.923569\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(720\) 12.0000 0.447214
\(721\) 0 0
\(722\) 0 0
\(723\) −10.0000 + 17.3205i −0.371904 + 0.644157i
\(724\) 2.00000 + 3.46410i 0.0743294 + 0.128742i
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) −5.50000 9.52628i −0.202321 0.350430i 0.746955 0.664875i \(-0.231515\pi\)
−0.949276 + 0.314445i \(0.898182\pi\)
\(740\) 6.00000 10.3923i 0.220564 0.382029i
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) −31.5000 54.5596i −1.15407 1.99891i
\(746\) 0 0
\(747\) −6.00000 + 10.3923i −0.219529 + 0.380235i
\(748\) 18.0000 0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 6.00000 + 10.3923i 0.218797 + 0.378968i
\(753\) 21.0000 + 36.3731i 0.765283 + 1.32551i
\(754\) 0 0
\(755\) −30.0000 −1.09181
\(756\) 0 0
\(757\) −25.0000 −0.908640 −0.454320 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16.5000 + 28.5788i −0.598125 + 1.03598i 0.394973 + 0.918693i \(0.370754\pi\)
−0.993098 + 0.117289i \(0.962579\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 4.50000 7.79423i 0.162698 0.281801i
\(766\) 0 0
\(767\) −12.0000 20.7846i −0.433295 0.750489i
\(768\) 16.0000 27.7128i 0.577350 1.00000i
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.00000 + 6.92820i −0.143963 + 0.249351i
\(773\) 3.00000 + 5.19615i 0.107903 + 0.186893i 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) 0 0
\(775\) 8.00000 13.8564i 0.287368 0.497737i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 24.0000 + 41.5692i 0.859338 + 1.48842i
\(781\) −9.00000 15.5885i −0.322045 0.557799i
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) 0 0
\(785\) 42.0000 1.49904
\(786\) 0 0
\(787\) 2.00000 + 3.46410i 0.0712923 + 0.123482i 0.899468 0.436987i \(-0.143954\pi\)
−0.828176 + 0.560469i \(0.810621\pi\)
\(788\) 18.0000 + 31.1769i 0.641223 + 1.11063i
\(789\) 9.00000 15.5885i 0.320408 0.554964i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 + 3.46410i −0.0710221 + 0.123014i
\(794\) 0 0
\(795\) 36.0000 + 62.3538i 1.27679 + 2.21146i
\(796\) 11.0000 19.0526i 0.389885 0.675300i
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0 0
\(801\) −6.00000 10.3923i −0.212000 0.367194i
\(802\) 0 0
\(803\) 10.5000 18.1865i 0.370537 0.641789i
\(804\) −16.0000 −0.564276
\(805\) 0 0
\(806\) 0 0
\(807\) 24.0000 41.5692i 0.844840 1.46331i
\(808\) 0 0
\(809\) 4.50000 + 7.79423i 0.158212 + 0.274030i 0.934224 0.356687i \(-0.116094\pi\)
−0.776012 + 0.630718i \(0.782761\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) 32.0000 1.12229
\(814\) 0 0
\(815\) −30.0000 51.9615i −1.05085 1.82013i
\(816\) −12.0000 20.7846i −0.420084 0.727607i
\(817\) 0.500000 0.866025i 0.0174928 0.0302984i
\(818\) 0 0
\(819\) 0 0
\(820\) 36.0000 1.25717
\(821\) −16.5000 + 28.5788i −0.575854 + 0.997408i 0.420094 + 0.907480i \(0.361997\pi\)
−0.995948 + 0.0899279i \(0.971336\pi\)
\(822\) 0 0
\(823\) 24.5000 + 42.4352i 0.854016 + 1.47920i 0.877555 + 0.479477i \(0.159174\pi\)
−0.0235383 + 0.999723i \(0.507493\pi\)
\(824\) 0 0
\(825\) −24.0000 −0.835573
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 8.00000 + 13.8564i 0.277851 + 0.481253i 0.970851 0.239686i \(-0.0770444\pi\)
−0.692999 + 0.720938i \(0.743711\pi\)
\(830\) 0 0
\(831\) −19.0000 + 32.9090i −0.659103 + 1.14160i
\(832\) 32.0000 1.10940
\(833\) 0 0
\(834\) 0 0
\(835\) 27.0000 46.7654i 0.934374 1.61838i
\(836\) 3.00000 + 5.19615i 0.103757 + 0.179713i
\(837\) 8.00000 + 13.8564i 0.276520 + 0.478947i
\(838\) 0 0
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 6.00000 + 10.3923i 0.206651 + 0.357930i
\(844\) 14.0000 + 24.2487i 0.481900 + 0.834675i
\(845\) −4.50000 + 7.79423i −0.154805 + 0.268130i
\(846\) 0 0
\(847\) 0 0
\(848\) 48.0000 1.64833
\(849\) −13.0000 + 22.5167i −0.446159 + 0.772770i
\(850\) 0 0
\(851\) 0 0
\(852\) −12.0000 + 20.7846i −0.411113 + 0.712069i
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 3.00000 0.102598
\(856\) 0 0
\(857\) −9.00000 15.5885i −0.307434 0.532492i 0.670366 0.742030i \(-0.266137\pi\)
−0.977800 + 0.209539i \(0.932804\pi\)
\(858\) 0 0
\(859\) 24.5000 42.4352i 0.835929 1.44787i −0.0573424 0.998355i \(-0.518263\pi\)
0.893272 0.449517i \(-0.148404\pi\)
\(860\) 6.00000 0.204598
\(861\) 0 0
\(862\) 0 0
\(863\) −9.00000 + 15.5885i −0.306364 + 0.530637i −0.977564 0.210639i \(-0.932446\pi\)
0.671200 + 0.741276i \(0.265779\pi\)
\(864\) 0 0
\(865\) 27.0000 + 46.7654i 0.918028 + 1.59007i
\(866\) 0 0
\(867\) 16.0000 0.543388
\(868\) 0 0
\(869\) 24.0000 0.814144
\(870\) 0 0
\(871\) −8.00000 13.8564i −0.271070 0.469506i
\(872\) 0 0
\(873\) −4.00000 + 6.92820i −0.135379 + 0.234484i
\(874\) 0 0
\(875\) 0 0
\(876\) −28.0000 −0.946032
\(877\) 11.0000 19.0526i 0.371444 0.643359i −0.618344 0.785907i \(-0.712196\pi\)
0.989788 + 0.142548i \(0.0455296\pi\)
\(878\) 0 0
\(879\) −12.0000 20.7846i −0.404750 0.701047i
\(880\) −18.0000 + 31.1769i −0.606780 + 1.05097i
\(881\) −27.0000 −0.909653 −0.454827 0.890580i \(-0.650299\pi\)
−0.454827 + 0.890580i \(0.650299\pi\)
\(882\) 0 0
\(883\) 47.0000 1.58168 0.790838 0.612026i \(-0.209645\pi\)
0.790838 + 0.612026i \(0.209645\pi\)
\(884\) 12.0000 20.7846i 0.403604 0.699062i
\(885\) −18.0000 31.1769i −0.605063 1.04800i
\(886\) 0 0
\(887\) −9.00000 + 15.5885i −0.302190 + 0.523409i −0.976632 0.214919i \(-0.931051\pi\)
0.674441 + 0.738328i \(0.264385\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 16.5000 28.5788i 0.552771 0.957427i
\(892\) −10.0000 17.3205i −0.334825 0.579934i
\(893\) 1.50000 + 2.59808i 0.0501956 + 0.0869413i
\(894\) 0 0
\(895\) −54.0000 −1.80502
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 12.0000 + 20.7846i 0.400222 + 0.693206i
\(900\) 4.00000 + 6.92820i 0.133333 + 0.230940i
\(901\) 18.0000 31.1769i 0.599667 1.03865i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.00000 + 5.19615i −0.0997234 + 0.172726i
\(906\) 0 0
\(907\) −4.00000 6.92820i −0.132818 0.230047i 0.791944 0.610594i \(-0.209069\pi\)
−0.924762 + 0.380547i \(0.875736\pi\)
\(908\) 12.0000 20.7846i 0.398234 0.689761i
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 4.00000 6.92820i 0.132453 0.229416i
\(913\) −18.0000 31.1769i −0.595713 1.03181i
\(914\) 0 0
\(915\) −3.00000 + 5.19615i −0.0991769 + 0.171780i
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 0 0
\(919\) −10.0000 + 17.3205i −0.329870 + 0.571351i −0.982486 0.186338i \(-0.940338\pi\)
0.652616 + 0.757689i \(0.273671\pi\)
\(920\) 0 0
\(921\) 20.0000 + 34.6410i 0.659022 + 1.14146i
\(922\) 0 0
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 0 0
\(927\) −7.00000 12.1244i −0.229910 0.398216i
\(928\) 0 0
\(929\) 9.00000 15.5885i 0.295280 0.511441i −0.679770 0.733426i \(-0.737920\pi\)
0.975050 + 0.221985i \(0.0712536\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 42.0000 1.37576
\(933\) −3.00000 + 5.19615i −0.0982156 + 0.170114i
\(934\) 0 0
\(935\) 13.5000 + 23.3827i 0.441497 + 0.764696i
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 0 0
\(939\) 20.0000 0.652675
\(940\) −9.00000 + 15.5885i −0.293548 + 0.508439i
\(941\) 9.00000 + 15.5885i 0.293392 + 0.508169i 0.974609 0.223912i \(-0.0718827\pi\)
−0.681218 + 0.732081i \(0.738549\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −24.0000 −0.781133
\(945\) 0 0
\(946\) 0 0
\(947\) 18.0000 31.1769i 0.584921 1.01311i −0.409964 0.912102i \(-0.634459\pi\)
0.994885 0.101012i \(-0.0322080\pi\)
\(948\) −16.0000 27.7128i −0.519656 0.900070i
\(949\) −14.0000 24.2487i −0.454459 0.787146i
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −48.0000 −1.55487 −0.777436 0.628962i \(-0.783480\pi\)
−0.777436 + 0.628962i \(0.783480\pi\)
\(954\) 0 0
\(955\) −4.50000 7.79423i −0.145617 0.252215i
\(956\) 15.0000 + 25.9808i 0.485135 + 0.840278i
\(957\) 18.0000 31.1769i 0.581857 1.00781i
\(958\) 0 0
\(959\) 0 0
\(960\) 48.0000 1.54919
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) 0 0
\(963\) 9.00000 + 15.5885i 0.290021 + 0.502331i
\(964\) −10.0000 + 17.3205i −0.322078 + 0.557856i
\(965\) −12.0000 −0.386294
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) −3.00000 5.19615i −0.0963739 0.166924i
\(970\) 0 0
\(971\) −30.0000 + 51.9615i −0.962746 + 1.66752i −0.247193 + 0.968966i \(0.579508\pi\)
−0.715553 + 0.698558i \(0.753825\pi\)
\(972\) −20.0000 −0.641500
\(973\) 0 0
\(974\) 0 0
\(975\) −16.0000 + 27.7128i −0.512410 + 0.887520i
\(976\) 2.00000 + 3.46410i 0.0640184 + 0.110883i
\(977\) −12.0000 20.7846i −0.383914 0.664959i 0.607704 0.794164i \(-0.292091\pi\)
−0.991618 + 0.129205i \(0.958757\pi\)
\(978\) 0 0
\(979\) 36.0000 1.15056
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) 18.0000 + 31.1769i 0.574111 + 0.994389i 0.996138 + 0.0878058i \(0.0279855\pi\)
−0.422027 + 0.906583i \(0.638681\pi\)
\(984\) 0 0
\(985\) −27.0000 + 46.7654i −0.860292 + 1.49007i
\(986\) 0 0
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) 0 0
\(990\) 0 0
\(991\) 17.0000 + 29.4449i 0.540023 + 0.935347i 0.998902 + 0.0468483i \(0.0149177\pi\)
−0.458879 + 0.888499i \(0.651749\pi\)
\(992\) 0 0
\(993\) 56.0000 1.77711
\(994\) 0 0
\(995\) 33.0000 1.04617
\(996\) −24.0000 + 41.5692i −0.760469 + 1.31717i
\(997\) −8.50000 14.7224i −0.269198 0.466264i 0.699457 0.714675i \(-0.253425\pi\)
−0.968655 + 0.248410i \(0.920092\pi\)
\(998\) 0 0
\(999\) −4.00000 + 6.92820i −0.126554 + 0.219199i
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 931.2.f.c.324.1 2
7.2 even 3 19.2.a.a.1.1 1
7.3 odd 6 931.2.f.b.704.1 2
7.4 even 3 inner 931.2.f.c.704.1 2
7.5 odd 6 931.2.a.a.1.1 1
7.6 odd 2 931.2.f.b.324.1 2
21.2 odd 6 171.2.a.b.1.1 1
21.5 even 6 8379.2.a.j.1.1 1
28.23 odd 6 304.2.a.f.1.1 1
35.2 odd 12 475.2.b.a.324.2 2
35.9 even 6 475.2.a.b.1.1 1
35.23 odd 12 475.2.b.a.324.1 2
56.37 even 6 1216.2.a.o.1.1 1
56.51 odd 6 1216.2.a.b.1.1 1
77.65 odd 6 2299.2.a.b.1.1 1
84.23 even 6 2736.2.a.c.1.1 1
91.51 even 6 3211.2.a.a.1.1 1
105.44 odd 6 4275.2.a.i.1.1 1
119.16 even 6 5491.2.a.b.1.1 1
133.2 odd 18 361.2.e.e.99.1 6
133.9 even 9 361.2.e.d.62.1 6
133.16 even 9 361.2.e.d.28.1 6
133.23 even 9 361.2.e.d.54.1 6
133.30 even 3 361.2.c.c.292.1 2
133.37 odd 6 361.2.a.b.1.1 1
133.44 even 9 361.2.e.d.245.1 6
133.51 odd 18 361.2.e.e.245.1 6
133.65 odd 6 361.2.c.a.292.1 2
133.72 odd 18 361.2.e.e.54.1 6
133.79 odd 18 361.2.e.e.28.1 6
133.86 odd 18 361.2.e.e.62.1 6
133.93 even 9 361.2.e.d.99.1 6
133.100 even 9 361.2.e.d.234.1 6
133.107 odd 6 361.2.c.a.68.1 2
133.121 even 3 361.2.c.c.68.1 2
133.128 odd 18 361.2.e.e.234.1 6
140.79 odd 6 7600.2.a.c.1.1 1
399.170 even 6 3249.2.a.d.1.1 1
532.303 even 6 5776.2.a.c.1.1 1
665.569 odd 6 9025.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.a.a.1.1 1 7.2 even 3
171.2.a.b.1.1 1 21.2 odd 6
304.2.a.f.1.1 1 28.23 odd 6
361.2.a.b.1.1 1 133.37 odd 6
361.2.c.a.68.1 2 133.107 odd 6
361.2.c.a.292.1 2 133.65 odd 6
361.2.c.c.68.1 2 133.121 even 3
361.2.c.c.292.1 2 133.30 even 3
361.2.e.d.28.1 6 133.16 even 9
361.2.e.d.54.1 6 133.23 even 9
361.2.e.d.62.1 6 133.9 even 9
361.2.e.d.99.1 6 133.93 even 9
361.2.e.d.234.1 6 133.100 even 9
361.2.e.d.245.1 6 133.44 even 9
361.2.e.e.28.1 6 133.79 odd 18
361.2.e.e.54.1 6 133.72 odd 18
361.2.e.e.62.1 6 133.86 odd 18
361.2.e.e.99.1 6 133.2 odd 18
361.2.e.e.234.1 6 133.128 odd 18
361.2.e.e.245.1 6 133.51 odd 18
475.2.a.b.1.1 1 35.9 even 6
475.2.b.a.324.1 2 35.23 odd 12
475.2.b.a.324.2 2 35.2 odd 12
931.2.a.a.1.1 1 7.5 odd 6
931.2.f.b.324.1 2 7.6 odd 2
931.2.f.b.704.1 2 7.3 odd 6
931.2.f.c.324.1 2 1.1 even 1 trivial
931.2.f.c.704.1 2 7.4 even 3 inner
1216.2.a.b.1.1 1 56.51 odd 6
1216.2.a.o.1.1 1 56.37 even 6
2299.2.a.b.1.1 1 77.65 odd 6
2736.2.a.c.1.1 1 84.23 even 6
3211.2.a.a.1.1 1 91.51 even 6
3249.2.a.d.1.1 1 399.170 even 6
4275.2.a.i.1.1 1 105.44 odd 6
5491.2.a.b.1.1 1 119.16 even 6
5776.2.a.c.1.1 1 532.303 even 6
7600.2.a.c.1.1 1 140.79 odd 6
8379.2.a.j.1.1 1 21.5 even 6
9025.2.a.d.1.1 1 665.569 odd 6