Properties

Label 256.2.i.a.17.1
Level $256$
Weight $2$
Character 256.17
Analytic conductor $2.044$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [256,2,Mod(17,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.i (of order \(16\), degree \(8\), 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: \(2.04417029174\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 17.1
Character \(\chi\) \(=\) 256.17
Dual form 256.2.i.a.241.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40926 - 2.10911i) q^{3} +(-0.573974 - 2.88556i) q^{5} +(0.410118 + 0.990113i) q^{7} +(-1.31428 + 3.17295i) q^{9} +O(q^{10})\) \(q+(-1.40926 - 2.10911i) q^{3} +(-0.573974 - 2.88556i) q^{5} +(0.410118 + 0.990113i) q^{7} +(-1.31428 + 3.17295i) q^{9} +(-2.05695 - 1.37441i) q^{11} +(-0.809767 + 4.07097i) q^{13} +(-5.27710 + 5.27710i) q^{15} +(-5.42249 - 5.42249i) q^{17} +(-0.276199 - 0.0549395i) q^{19} +(1.51030 - 2.26032i) q^{21} +(4.16092 + 1.72351i) q^{23} +(-3.37763 + 1.39906i) q^{25} +(1.08068 - 0.214961i) q^{27} +(3.60695 - 2.41009i) q^{29} -7.05396i q^{31} +6.27526i q^{33} +(2.62164 - 1.75172i) q^{35} +(-1.14453 + 0.227662i) q^{37} +(9.72732 - 4.02919i) q^{39} +(-1.94047 - 0.803770i) q^{41} +(2.38520 - 3.56971i) q^{43} +(9.91012 + 1.97125i) q^{45} +(2.48019 + 2.48019i) q^{47} +(4.13762 - 4.13762i) q^{49} +(-3.79492 + 19.0784i) q^{51} +(4.01758 + 2.68446i) q^{53} +(-2.78532 + 6.72435i) q^{55} +(0.273364 + 0.659960i) q^{57} +(-2.94015 - 14.7811i) q^{59} +(-1.39259 - 2.08416i) q^{61} -3.68059 q^{63} +12.2118 q^{65} +(0.964506 + 1.44349i) q^{67} +(-2.22876 - 11.2047i) q^{69} +(-0.416406 - 1.00529i) q^{71} +(-0.857131 + 2.06930i) q^{73} +(7.71074 + 5.15215i) q^{75} +(0.517230 - 2.60029i) q^{77} +(2.08005 - 2.08005i) q^{79} +(5.30908 + 5.30908i) q^{81} +(-0.161971 - 0.0322180i) q^{83} +(-12.5346 + 18.7593i) q^{85} +(-10.1663 - 4.21102i) q^{87} +(6.46642 - 2.67848i) q^{89} +(-4.36283 + 0.867820i) q^{91} +(-14.8776 + 9.94089i) q^{93} +0.828524i q^{95} -4.46680i q^{97} +(7.06436 - 4.72026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{7}{16}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.40926 2.10911i −0.813639 1.21770i −0.973075 0.230488i \(-0.925968\pi\)
0.159436 0.987208i \(-0.449032\pi\)
\(4\) 0 0
\(5\) −0.573974 2.88556i −0.256689 1.29046i −0.867003 0.498303i \(-0.833957\pi\)
0.610314 0.792160i \(-0.291043\pi\)
\(6\) 0 0
\(7\) 0.410118 + 0.990113i 0.155010 + 0.374228i 0.982238 0.187639i \(-0.0600835\pi\)
−0.827228 + 0.561866i \(0.810083\pi\)
\(8\) 0 0
\(9\) −1.31428 + 3.17295i −0.438093 + 1.05765i
\(10\) 0 0
\(11\) −2.05695 1.37441i −0.620195 0.414401i 0.205389 0.978680i \(-0.434154\pi\)
−0.825584 + 0.564279i \(0.809154\pi\)
\(12\) 0 0
\(13\) −0.809767 + 4.07097i −0.224589 + 1.12909i 0.689723 + 0.724074i \(0.257732\pi\)
−0.914312 + 0.405011i \(0.867268\pi\)
\(14\) 0 0
\(15\) −5.27710 + 5.27710i −1.36254 + 1.36254i
\(16\) 0 0
\(17\) −5.42249 5.42249i −1.31515 1.31515i −0.917567 0.397581i \(-0.869850\pi\)
−0.397581 0.917567i \(-0.630150\pi\)
\(18\) 0 0
\(19\) −0.276199 0.0549395i −0.0633645 0.0126040i 0.163306 0.986575i \(-0.447784\pi\)
−0.226671 + 0.973971i \(0.572784\pi\)
\(20\) 0 0
\(21\) 1.51030 2.26032i 0.329573 0.493241i
\(22\) 0 0
\(23\) 4.16092 + 1.72351i 0.867613 + 0.359377i 0.771680 0.636011i \(-0.219417\pi\)
0.0959326 + 0.995388i \(0.469417\pi\)
\(24\) 0 0
\(25\) −3.37763 + 1.39906i −0.675526 + 0.279812i
\(26\) 0 0
\(27\) 1.08068 0.214961i 0.207977 0.0413692i
\(28\) 0 0
\(29\) 3.60695 2.41009i 0.669795 0.447542i −0.173615 0.984814i \(-0.555545\pi\)
0.843410 + 0.537271i \(0.180545\pi\)
\(30\) 0 0
\(31\) 7.05396i 1.26693i −0.773772 0.633464i \(-0.781632\pi\)
0.773772 0.633464i \(-0.218368\pi\)
\(32\) 0 0
\(33\) 6.27526i 1.09238i
\(34\) 0 0
\(35\) 2.62164 1.75172i 0.443137 0.296095i
\(36\) 0 0
\(37\) −1.14453 + 0.227662i −0.188160 + 0.0374273i −0.288271 0.957549i \(-0.593080\pi\)
0.100111 + 0.994976i \(0.468080\pi\)
\(38\) 0 0
\(39\) 9.72732 4.02919i 1.55762 0.645186i
\(40\) 0 0
\(41\) −1.94047 0.803770i −0.303051 0.125528i 0.225976 0.974133i \(-0.427443\pi\)
−0.529027 + 0.848605i \(0.677443\pi\)
\(42\) 0 0
\(43\) 2.38520 3.56971i 0.363740 0.544375i −0.603786 0.797146i \(-0.706342\pi\)
0.967526 + 0.252771i \(0.0813419\pi\)
\(44\) 0 0
\(45\) 9.91012 + 1.97125i 1.47731 + 0.293856i
\(46\) 0 0
\(47\) 2.48019 + 2.48019i 0.361772 + 0.361772i 0.864465 0.502693i \(-0.167657\pi\)
−0.502693 + 0.864465i \(0.667657\pi\)
\(48\) 0 0
\(49\) 4.13762 4.13762i 0.591089 0.591089i
\(50\) 0 0
\(51\) −3.79492 + 19.0784i −0.531396 + 2.67151i
\(52\) 0 0
\(53\) 4.01758 + 2.68446i 0.551856 + 0.368739i 0.800014 0.599981i \(-0.204825\pi\)
−0.248158 + 0.968720i \(0.579825\pi\)
\(54\) 0 0
\(55\) −2.78532 + 6.72435i −0.375572 + 0.906711i
\(56\) 0 0
\(57\) 0.273364 + 0.659960i 0.0362080 + 0.0874138i
\(58\) 0 0
\(59\) −2.94015 14.7811i −0.382774 1.92434i −0.381577 0.924337i \(-0.624619\pi\)
−0.00119757 0.999999i \(-0.500381\pi\)
\(60\) 0 0
\(61\) −1.39259 2.08416i −0.178303 0.266849i 0.731543 0.681795i \(-0.238801\pi\)
−0.909846 + 0.414946i \(0.863801\pi\)
\(62\) 0 0
\(63\) −3.68059 −0.463711
\(64\) 0 0
\(65\) 12.2118 1.51469
\(66\) 0 0
\(67\) 0.964506 + 1.44349i 0.117833 + 0.176350i 0.885698 0.464263i \(-0.153681\pi\)
−0.767864 + 0.640612i \(0.778681\pi\)
\(68\) 0 0
\(69\) −2.22876 11.2047i −0.268311 1.34889i
\(70\) 0 0
\(71\) −0.416406 1.00529i −0.0494183 0.119306i 0.897243 0.441538i \(-0.145567\pi\)
−0.946661 + 0.322232i \(0.895567\pi\)
\(72\) 0 0
\(73\) −0.857131 + 2.06930i −0.100320 + 0.242193i −0.966069 0.258285i \(-0.916842\pi\)
0.865749 + 0.500478i \(0.166842\pi\)
\(74\) 0 0
\(75\) 7.71074 + 5.15215i 0.890360 + 0.594919i
\(76\) 0 0
\(77\) 0.517230 2.60029i 0.0589438 0.296331i
\(78\) 0 0
\(79\) 2.08005 2.08005i 0.234024 0.234024i −0.580346 0.814370i \(-0.697083\pi\)
0.814370 + 0.580346i \(0.197083\pi\)
\(80\) 0 0
\(81\) 5.30908 + 5.30908i 0.589898 + 0.589898i
\(82\) 0 0
\(83\) −0.161971 0.0322180i −0.0177786 0.00353639i 0.186193 0.982513i \(-0.440385\pi\)
−0.203972 + 0.978977i \(0.565385\pi\)
\(84\) 0 0
\(85\) −12.5346 + 18.7593i −1.35957 + 2.03473i
\(86\) 0 0
\(87\) −10.1663 4.21102i −1.08994 0.451469i
\(88\) 0 0
\(89\) 6.46642 2.67848i 0.685439 0.283918i −0.0126595 0.999920i \(-0.504030\pi\)
0.698098 + 0.716002i \(0.254030\pi\)
\(90\) 0 0
\(91\) −4.36283 + 0.867820i −0.457348 + 0.0909722i
\(92\) 0 0
\(93\) −14.8776 + 9.94089i −1.54274 + 1.03082i
\(94\) 0 0
\(95\) 0.828524i 0.0850048i
\(96\) 0 0
\(97\) 4.46680i 0.453535i −0.973949 0.226768i \(-0.927184\pi\)
0.973949 0.226768i \(-0.0728158\pi\)
\(98\) 0 0
\(99\) 7.06436 4.72026i 0.709995 0.474404i
\(100\) 0 0
\(101\) −3.46425 + 0.689083i −0.344706 + 0.0685663i −0.364407 0.931240i \(-0.618728\pi\)
0.0197014 + 0.999806i \(0.493728\pi\)
\(102\) 0 0
\(103\) −7.09157 + 2.93742i −0.698753 + 0.289433i −0.703642 0.710555i \(-0.748444\pi\)
0.00488851 + 0.999988i \(0.498444\pi\)
\(104\) 0 0
\(105\) −7.38915 3.06069i −0.721108 0.298693i
\(106\) 0 0
\(107\) −3.38729 + 5.06944i −0.327462 + 0.490081i −0.958273 0.285855i \(-0.907722\pi\)
0.630811 + 0.775936i \(0.282722\pi\)
\(108\) 0 0
\(109\) 8.05344 + 1.60193i 0.771380 + 0.153437i 0.565062 0.825048i \(-0.308852\pi\)
0.206317 + 0.978485i \(0.433852\pi\)
\(110\) 0 0
\(111\) 2.09311 + 2.09311i 0.198669 + 0.198669i
\(112\) 0 0
\(113\) 7.45755 7.45755i 0.701548 0.701548i −0.263195 0.964743i \(-0.584776\pi\)
0.964743 + 0.263195i \(0.0847763\pi\)
\(114\) 0 0
\(115\) 2.58504 12.9959i 0.241056 1.21187i
\(116\) 0 0
\(117\) −11.8528 7.91975i −1.09579 0.732182i
\(118\) 0 0
\(119\) 3.14502 7.59275i 0.288303 0.696026i
\(120\) 0 0
\(121\) −1.86747 4.50846i −0.169770 0.409860i
\(122\) 0 0
\(123\) 1.03940 + 5.22540i 0.0937193 + 0.471159i
\(124\) 0 0
\(125\) −2.19696 3.28798i −0.196502 0.294086i
\(126\) 0 0
\(127\) −4.81751 −0.427485 −0.213742 0.976890i \(-0.568565\pi\)
−0.213742 + 0.976890i \(0.568565\pi\)
\(128\) 0 0
\(129\) −10.8903 −0.958837
\(130\) 0 0
\(131\) 8.35213 + 12.4998i 0.729729 + 1.09212i 0.991891 + 0.127093i \(0.0405646\pi\)
−0.262162 + 0.965024i \(0.584435\pi\)
\(132\) 0 0
\(133\) −0.0588781 0.296000i −0.00510538 0.0256665i
\(134\) 0 0
\(135\) −1.24057 2.99499i −0.106771 0.257768i
\(136\) 0 0
\(137\) −4.31867 + 10.4262i −0.368969 + 0.890770i 0.624951 + 0.780664i \(0.285119\pi\)
−0.993920 + 0.110106i \(0.964881\pi\)
\(138\) 0 0
\(139\) 12.9155 + 8.62988i 1.09548 + 0.731977i 0.965724 0.259569i \(-0.0835806\pi\)
0.129756 + 0.991546i \(0.458581\pi\)
\(140\) 0 0
\(141\) 1.73575 8.72622i 0.146177 0.734881i
\(142\) 0 0
\(143\) 7.26086 7.26086i 0.607183 0.607183i
\(144\) 0 0
\(145\) −9.02476 9.02476i −0.749466 0.749466i
\(146\) 0 0
\(147\) −14.5577 2.89571i −1.20070 0.238834i
\(148\) 0 0
\(149\) 5.78374 8.65598i 0.473822 0.709125i −0.515171 0.857088i \(-0.672271\pi\)
0.988993 + 0.147962i \(0.0472715\pi\)
\(150\) 0 0
\(151\) −11.0167 4.56328i −0.896529 0.371354i −0.113644 0.993522i \(-0.536252\pi\)
−0.782884 + 0.622167i \(0.786252\pi\)
\(152\) 0 0
\(153\) 24.3320 10.0786i 1.96713 0.814810i
\(154\) 0 0
\(155\) −20.3546 + 4.04879i −1.63492 + 0.325207i
\(156\) 0 0
\(157\) −13.3867 + 8.94474i −1.06838 + 0.713868i −0.959932 0.280234i \(-0.909588\pi\)
−0.108447 + 0.994102i \(0.534588\pi\)
\(158\) 0 0
\(159\) 12.2566i 0.972014i
\(160\) 0 0
\(161\) 4.82663i 0.380392i
\(162\) 0 0
\(163\) −8.74199 + 5.84121i −0.684725 + 0.457519i −0.848651 0.528954i \(-0.822584\pi\)
0.163925 + 0.986473i \(0.447584\pi\)
\(164\) 0 0
\(165\) 18.1077 3.60184i 1.40968 0.280403i
\(166\) 0 0
\(167\) 20.9509 8.67814i 1.62123 0.671534i 0.627019 0.779004i \(-0.284275\pi\)
0.994208 + 0.107469i \(0.0342747\pi\)
\(168\) 0 0
\(169\) −3.90667 1.61820i −0.300513 0.124477i
\(170\) 0 0
\(171\) 0.537324 0.804162i 0.0410902 0.0614958i
\(172\) 0 0
\(173\) −14.8807 2.95995i −1.13136 0.225041i −0.406307 0.913737i \(-0.633184\pi\)
−0.725051 + 0.688695i \(0.758184\pi\)
\(174\) 0 0
\(175\) −2.77045 2.77045i −0.209427 0.209427i
\(176\) 0 0
\(177\) −27.0316 + 27.0316i −2.03182 + 2.03182i
\(178\) 0 0
\(179\) 0.211084 1.06119i 0.0157771 0.0793170i −0.972095 0.234589i \(-0.924625\pi\)
0.987872 + 0.155272i \(0.0496255\pi\)
\(180\) 0 0
\(181\) 17.9001 + 11.9605i 1.33050 + 0.889014i 0.998526 0.0542727i \(-0.0172840\pi\)
0.331978 + 0.943287i \(0.392284\pi\)
\(182\) 0 0
\(183\) −2.43320 + 5.87427i −0.179867 + 0.434238i
\(184\) 0 0
\(185\) 1.31386 + 3.17195i 0.0965972 + 0.233206i
\(186\) 0 0
\(187\) 3.70108 + 18.6066i 0.270650 + 1.36065i
\(188\) 0 0
\(189\) 0.656042 + 0.981836i 0.0477200 + 0.0714181i
\(190\) 0 0
\(191\) −14.6066 −1.05690 −0.528449 0.848965i \(-0.677226\pi\)
−0.528449 + 0.848965i \(0.677226\pi\)
\(192\) 0 0
\(193\) 1.30887 0.0942148 0.0471074 0.998890i \(-0.485000\pi\)
0.0471074 + 0.998890i \(0.485000\pi\)
\(194\) 0 0
\(195\) −17.2097 25.7561i −1.23241 1.84444i
\(196\) 0 0
\(197\) 3.40826 + 17.1345i 0.242828 + 1.22078i 0.889114 + 0.457685i \(0.151321\pi\)
−0.646286 + 0.763095i \(0.723679\pi\)
\(198\) 0 0
\(199\) 8.67533 + 20.9441i 0.614978 + 1.48469i 0.857470 + 0.514534i \(0.172035\pi\)
−0.242492 + 0.970153i \(0.577965\pi\)
\(200\) 0 0
\(201\) 1.68523 4.06850i 0.118867 0.286970i
\(202\) 0 0
\(203\) 3.86554 + 2.58287i 0.271308 + 0.181282i
\(204\) 0 0
\(205\) −1.20555 + 6.06070i −0.0841992 + 0.423298i
\(206\) 0 0
\(207\) −10.9372 + 10.9372i −0.760191 + 0.760191i
\(208\) 0 0
\(209\) 0.492620 + 0.492620i 0.0340752 + 0.0340752i
\(210\) 0 0
\(211\) 15.8195 + 3.14670i 1.08906 + 0.216628i 0.706790 0.707423i \(-0.250142\pi\)
0.382270 + 0.924051i \(0.375142\pi\)
\(212\) 0 0
\(213\) −1.53345 + 2.29497i −0.105070 + 0.157249i
\(214\) 0 0
\(215\) −11.6697 4.83373i −0.795864 0.329658i
\(216\) 0 0
\(217\) 6.98422 2.89296i 0.474120 0.196387i
\(218\) 0 0
\(219\) 5.57230 1.10840i 0.376541 0.0748987i
\(220\) 0 0
\(221\) 26.4658 17.6839i 1.78028 1.18955i
\(222\) 0 0
\(223\) 19.3726i 1.29728i 0.761094 + 0.648642i \(0.224663\pi\)
−0.761094 + 0.648642i \(0.775337\pi\)
\(224\) 0 0
\(225\) 12.5558i 0.837054i
\(226\) 0 0
\(227\) 14.4527 9.65698i 0.959259 0.640956i 0.0258099 0.999667i \(-0.491784\pi\)
0.933449 + 0.358711i \(0.116784\pi\)
\(228\) 0 0
\(229\) 16.1567 3.21376i 1.06766 0.212371i 0.370171 0.928964i \(-0.379299\pi\)
0.697492 + 0.716592i \(0.254299\pi\)
\(230\) 0 0
\(231\) −6.21322 + 2.57360i −0.408800 + 0.169330i
\(232\) 0 0
\(233\) 20.5399 + 8.50789i 1.34561 + 0.557370i 0.935067 0.354471i \(-0.115339\pi\)
0.410544 + 0.911841i \(0.365339\pi\)
\(234\) 0 0
\(235\) 5.73317 8.58029i 0.373991 0.559717i
\(236\) 0 0
\(237\) −7.31840 1.45572i −0.475381 0.0945592i
\(238\) 0 0
\(239\) 14.4521 + 14.4521i 0.934827 + 0.934827i 0.998002 0.0631755i \(-0.0201228\pi\)
−0.0631755 + 0.998002i \(0.520123\pi\)
\(240\) 0 0
\(241\) 11.6252 11.6252i 0.748843 0.748843i −0.225419 0.974262i \(-0.572375\pi\)
0.974262 + 0.225419i \(0.0723750\pi\)
\(242\) 0 0
\(243\) 4.36043 21.9214i 0.279722 1.40626i
\(244\) 0 0
\(245\) −14.3143 9.56448i −0.914504 0.611052i
\(246\) 0 0
\(247\) 0.447314 1.07991i 0.0284619 0.0687132i
\(248\) 0 0
\(249\) 0.160308 + 0.387019i 0.0101591 + 0.0245263i
\(250\) 0 0
\(251\) −2.33693 11.7485i −0.147506 0.741561i −0.981751 0.190169i \(-0.939097\pi\)
0.834246 0.551393i \(-0.185903\pi\)
\(252\) 0 0
\(253\) −6.19002 9.26401i −0.389163 0.582424i
\(254\) 0 0
\(255\) 57.2300 3.58388
\(256\) 0 0
\(257\) −16.2355 −1.01274 −0.506372 0.862315i \(-0.669014\pi\)
−0.506372 + 0.862315i \(0.669014\pi\)
\(258\) 0 0
\(259\) −0.694804 1.03985i −0.0431730 0.0646130i
\(260\) 0 0
\(261\) 2.90655 + 14.6122i 0.179911 + 0.904474i
\(262\) 0 0
\(263\) −2.60171 6.28109i −0.160429 0.387309i 0.823141 0.567837i \(-0.192219\pi\)
−0.983570 + 0.180528i \(0.942219\pi\)
\(264\) 0 0
\(265\) 5.44019 13.1338i 0.334188 0.806801i
\(266\) 0 0
\(267\) −14.7621 9.86372i −0.903426 0.603650i
\(268\) 0 0
\(269\) 1.90308 9.56742i 0.116033 0.583336i −0.878397 0.477932i \(-0.841387\pi\)
0.994430 0.105404i \(-0.0336135\pi\)
\(270\) 0 0
\(271\) 8.70763 8.70763i 0.528951 0.528951i −0.391309 0.920259i \(-0.627978\pi\)
0.920259 + 0.391309i \(0.127978\pi\)
\(272\) 0 0
\(273\) 7.97870 + 7.97870i 0.482893 + 0.482893i
\(274\) 0 0
\(275\) 8.87051 + 1.76445i 0.534912 + 0.106401i
\(276\) 0 0
\(277\) 11.7635 17.6053i 0.706799 1.05780i −0.288167 0.957580i \(-0.593046\pi\)
0.994965 0.100219i \(-0.0319543\pi\)
\(278\) 0 0
\(279\) 22.3819 + 9.27088i 1.33997 + 0.555033i
\(280\) 0 0
\(281\) −28.4417 + 11.7810i −1.69669 + 0.702793i −0.999895 0.0144755i \(-0.995392\pi\)
−0.696797 + 0.717268i \(0.745392\pi\)
\(282\) 0 0
\(283\) 17.7997 3.54057i 1.05808 0.210465i 0.364765 0.931100i \(-0.381149\pi\)
0.693315 + 0.720635i \(0.256149\pi\)
\(284\) 0 0
\(285\) 1.74745 1.16761i 0.103510 0.0691632i
\(286\) 0 0
\(287\) 2.25093i 0.132868i
\(288\) 0 0
\(289\) 41.8069i 2.45923i
\(290\) 0 0
\(291\) −9.42099 + 6.29490i −0.552268 + 0.369014i
\(292\) 0 0
\(293\) −24.5419 + 4.88168i −1.43375 + 0.285191i −0.850017 0.526755i \(-0.823409\pi\)
−0.583734 + 0.811945i \(0.698409\pi\)
\(294\) 0 0
\(295\) −40.9642 + 16.9679i −2.38503 + 0.987912i
\(296\) 0 0
\(297\) −2.51836 1.04314i −0.146130 0.0605289i
\(298\) 0 0
\(299\) −10.3857 + 15.5434i −0.600623 + 0.898896i
\(300\) 0 0
\(301\) 4.51263 + 0.897618i 0.260104 + 0.0517378i
\(302\) 0 0
\(303\) 6.33540 + 6.33540i 0.363959 + 0.363959i
\(304\) 0 0
\(305\) −5.21467 + 5.21467i −0.298591 + 0.298591i
\(306\) 0 0
\(307\) −1.19463 + 6.00584i −0.0681814 + 0.342771i −0.999786 0.0207031i \(-0.993410\pi\)
0.931604 + 0.363474i \(0.118410\pi\)
\(308\) 0 0
\(309\) 16.1893 + 10.8173i 0.920974 + 0.615375i
\(310\) 0 0
\(311\) −2.62567 + 6.33892i −0.148888 + 0.359447i −0.980674 0.195649i \(-0.937319\pi\)
0.831786 + 0.555096i \(0.187319\pi\)
\(312\) 0 0
\(313\) −8.01019 19.3383i −0.452763 1.09307i −0.971267 0.237991i \(-0.923511\pi\)
0.518504 0.855075i \(-0.326489\pi\)
\(314\) 0 0
\(315\) 2.11257 + 10.6206i 0.119030 + 0.598402i
\(316\) 0 0
\(317\) 3.17251 + 4.74799i 0.178186 + 0.266674i 0.909802 0.415043i \(-0.136234\pi\)
−0.731616 + 0.681717i \(0.761234\pi\)
\(318\) 0 0
\(319\) −10.7318 −0.600865
\(320\) 0 0
\(321\) 15.4656 0.863206
\(322\) 0 0
\(323\) 1.19978 + 1.79560i 0.0667575 + 0.0999097i
\(324\) 0 0
\(325\) −2.96044 14.8831i −0.164216 0.825568i
\(326\) 0 0
\(327\) −7.97077 19.2432i −0.440785 1.06415i
\(328\) 0 0
\(329\) −1.43849 + 3.47283i −0.0793068 + 0.191463i
\(330\) 0 0
\(331\) −24.6126 16.4456i −1.35283 0.903934i −0.353331 0.935498i \(-0.614951\pi\)
−0.999502 + 0.0315644i \(0.989951\pi\)
\(332\) 0 0
\(333\) 0.781876 3.93076i 0.0428466 0.215404i
\(334\) 0 0
\(335\) 3.61167 3.61167i 0.197326 0.197326i
\(336\) 0 0
\(337\) −0.159510 0.159510i −0.00868905 0.00868905i 0.702749 0.711438i \(-0.251956\pi\)
−0.711438 + 0.702749i \(0.751956\pi\)
\(338\) 0 0
\(339\) −26.2385 5.21916i −1.42508 0.283466i
\(340\) 0 0
\(341\) −9.69506 + 14.5097i −0.525017 + 0.785743i
\(342\) 0 0
\(343\) 12.7244 + 5.27063i 0.687054 + 0.284587i
\(344\) 0 0
\(345\) −31.0527 + 12.8625i −1.67182 + 0.692492i
\(346\) 0 0
\(347\) 6.01352 1.19616i 0.322823 0.0642135i −0.0310188 0.999519i \(-0.509875\pi\)
0.353842 + 0.935305i \(0.384875\pi\)
\(348\) 0 0
\(349\) 7.16948 4.79049i 0.383773 0.256429i −0.348686 0.937239i \(-0.613372\pi\)
0.732460 + 0.680810i \(0.238372\pi\)
\(350\) 0 0
\(351\) 4.57349i 0.244115i
\(352\) 0 0
\(353\) 13.1535i 0.700090i −0.936733 0.350045i \(-0.886166\pi\)
0.936733 0.350045i \(-0.113834\pi\)
\(354\) 0 0
\(355\) −2.66183 + 1.77858i −0.141275 + 0.0943971i
\(356\) 0 0
\(357\) −20.4461 + 4.06699i −1.08212 + 0.215248i
\(358\) 0 0
\(359\) −1.21194 + 0.502003i −0.0639638 + 0.0264947i −0.414436 0.910078i \(-0.636021\pi\)
0.350472 + 0.936573i \(0.386021\pi\)
\(360\) 0 0
\(361\) −17.4804 7.24064i −0.920023 0.381086i
\(362\) 0 0
\(363\) −6.87710 + 10.2923i −0.360954 + 0.540206i
\(364\) 0 0
\(365\) 6.46306 + 1.28558i 0.338292 + 0.0672904i
\(366\) 0 0
\(367\) −26.7959 26.7959i −1.39874 1.39874i −0.803699 0.595036i \(-0.797138\pi\)
−0.595036 0.803699i \(-0.702862\pi\)
\(368\) 0 0
\(369\) 5.10065 5.10065i 0.265529 0.265529i
\(370\) 0 0
\(371\) −1.01024 + 5.07880i −0.0524488 + 0.263678i
\(372\) 0 0
\(373\) 13.9514 + 9.32200i 0.722374 + 0.482675i 0.861601 0.507586i \(-0.169462\pi\)
−0.139227 + 0.990260i \(0.544462\pi\)
\(374\) 0 0
\(375\) −3.83862 + 9.26725i −0.198226 + 0.478559i
\(376\) 0 0
\(377\) 6.89062 + 16.6354i 0.354885 + 0.856768i
\(378\) 0 0
\(379\) −1.32647 6.66861i −0.0681362 0.342544i 0.931647 0.363365i \(-0.118372\pi\)
−0.999783 + 0.0208208i \(0.993372\pi\)
\(380\) 0 0
\(381\) 6.78914 + 10.1607i 0.347818 + 0.520547i
\(382\) 0 0
\(383\) −3.93993 −0.201321 −0.100661 0.994921i \(-0.532096\pi\)
−0.100661 + 0.994921i \(0.532096\pi\)
\(384\) 0 0
\(385\) −7.80018 −0.397534
\(386\) 0 0
\(387\) 8.19169 + 12.2597i 0.416407 + 0.623197i
\(388\) 0 0
\(389\) −2.75314 13.8410i −0.139590 0.701765i −0.985667 0.168704i \(-0.946042\pi\)
0.846077 0.533061i \(-0.178958\pi\)
\(390\) 0 0
\(391\) −13.2169 31.9083i −0.668405 1.61367i
\(392\) 0 0
\(393\) 14.5932 35.2312i 0.736131 1.77718i
\(394\) 0 0
\(395\) −7.19601 4.80822i −0.362071 0.241928i
\(396\) 0 0
\(397\) −4.41193 + 22.1803i −0.221428 + 1.11320i 0.696837 + 0.717230i \(0.254590\pi\)
−0.918265 + 0.395966i \(0.870410\pi\)
\(398\) 0 0
\(399\) −0.541323 + 0.541323i −0.0271000 + 0.0271000i
\(400\) 0 0
\(401\) −9.96558 9.96558i −0.497657 0.497657i 0.413051 0.910708i \(-0.364463\pi\)
−0.910708 + 0.413051i \(0.864463\pi\)
\(402\) 0 0
\(403\) 28.7165 + 5.71207i 1.43047 + 0.284538i
\(404\) 0 0
\(405\) 12.2724 18.3670i 0.609821 0.912662i
\(406\) 0 0
\(407\) 2.66715 + 1.10477i 0.132206 + 0.0547614i
\(408\) 0 0
\(409\) −3.17482 + 1.31505i −0.156985 + 0.0650252i −0.459792 0.888027i \(-0.652076\pi\)
0.302807 + 0.953052i \(0.402076\pi\)
\(410\) 0 0
\(411\) 28.0762 5.58470i 1.38490 0.275473i
\(412\) 0 0
\(413\) 13.4292 8.97308i 0.660806 0.441536i
\(414\) 0 0
\(415\) 0.485870i 0.0238504i
\(416\) 0 0
\(417\) 39.4021i 1.92953i
\(418\) 0 0
\(419\) −13.9731 + 9.33655i −0.682632 + 0.456120i −0.847919 0.530125i \(-0.822145\pi\)
0.165287 + 0.986246i \(0.447145\pi\)
\(420\) 0 0
\(421\) −6.70608 + 1.33392i −0.326834 + 0.0650114i −0.355780 0.934570i \(-0.615785\pi\)
0.0289461 + 0.999581i \(0.490785\pi\)
\(422\) 0 0
\(423\) −11.1292 + 4.60985i −0.541119 + 0.224139i
\(424\) 0 0
\(425\) 25.9016 + 10.7288i 1.25641 + 0.520422i
\(426\) 0 0
\(427\) 1.49243 2.23358i 0.0722236 0.108090i
\(428\) 0 0
\(429\) −25.5464 5.08150i −1.23339 0.245337i
\(430\) 0 0
\(431\) −14.3623 14.3623i −0.691807 0.691807i 0.270823 0.962629i \(-0.412704\pi\)
−0.962629 + 0.270823i \(0.912704\pi\)
\(432\) 0 0
\(433\) 3.93497 3.93497i 0.189103 0.189103i −0.606205 0.795308i \(-0.707309\pi\)
0.795308 + 0.606205i \(0.207309\pi\)
\(434\) 0 0
\(435\) −6.31597 + 31.7525i −0.302827 + 1.52242i
\(436\) 0 0
\(437\) −1.05456 0.704631i −0.0504462 0.0337071i
\(438\) 0 0
\(439\) 13.4061 32.3651i 0.639837 1.54470i −0.187060 0.982348i \(-0.559896\pi\)
0.826897 0.562354i \(-0.190104\pi\)
\(440\) 0 0
\(441\) 7.69048 + 18.5665i 0.366214 + 0.884118i
\(442\) 0 0
\(443\) 0.856937 + 4.30811i 0.0407143 + 0.204685i 0.995788 0.0916829i \(-0.0292246\pi\)
−0.955074 + 0.296368i \(0.904225\pi\)
\(444\) 0 0
\(445\) −11.4405 17.1219i −0.542330 0.811655i
\(446\) 0 0
\(447\) −26.4072 −1.24902
\(448\) 0 0
\(449\) −16.4316 −0.775457 −0.387728 0.921774i \(-0.626740\pi\)
−0.387728 + 0.921774i \(0.626740\pi\)
\(450\) 0 0
\(451\) 2.88675 + 4.32033i 0.135932 + 0.203436i
\(452\) 0 0
\(453\) 5.90101 + 29.6664i 0.277254 + 1.39385i
\(454\) 0 0
\(455\) 5.00830 + 12.0911i 0.234793 + 0.566839i
\(456\) 0 0
\(457\) 7.34119 17.7232i 0.343406 0.829057i −0.653960 0.756529i \(-0.726894\pi\)
0.997366 0.0725274i \(-0.0231065\pi\)
\(458\) 0 0
\(459\) −7.02561 4.69436i −0.327927 0.219114i
\(460\) 0 0
\(461\) −2.05091 + 10.3106i −0.0955204 + 0.480214i 0.903181 + 0.429261i \(0.141226\pi\)
−0.998701 + 0.0509529i \(0.983774\pi\)
\(462\) 0 0
\(463\) 6.34023 6.34023i 0.294656 0.294656i −0.544261 0.838916i \(-0.683190\pi\)
0.838916 + 0.544261i \(0.183190\pi\)
\(464\) 0 0
\(465\) 37.2244 + 37.2244i 1.72624 + 1.72624i
\(466\) 0 0
\(467\) −27.9193 5.55349i −1.29195 0.256985i −0.499176 0.866501i \(-0.666364\pi\)
−0.792774 + 0.609516i \(0.791364\pi\)
\(468\) 0 0
\(469\) −1.03365 + 1.54697i −0.0477296 + 0.0714324i
\(470\) 0 0
\(471\) 37.7309 + 15.6287i 1.73855 + 0.720130i
\(472\) 0 0
\(473\) −9.81251 + 4.06447i −0.451180 + 0.186885i
\(474\) 0 0
\(475\) 1.00976 0.200854i 0.0463311 0.00921582i
\(476\) 0 0
\(477\) −13.7979 + 9.21945i −0.631762 + 0.422130i
\(478\) 0 0
\(479\) 37.5371i 1.71512i 0.514388 + 0.857558i \(0.328019\pi\)
−0.514388 + 0.857558i \(0.671981\pi\)
\(480\) 0 0
\(481\) 4.84371i 0.220854i
\(482\) 0 0
\(483\) 10.1799 6.80199i 0.463202 0.309501i
\(484\) 0 0
\(485\) −12.8892 + 2.56383i −0.585270 + 0.116417i
\(486\) 0 0
\(487\) 26.4650 10.9621i 1.19924 0.496742i 0.308488 0.951228i \(-0.400177\pi\)
0.890754 + 0.454486i \(0.150177\pi\)
\(488\) 0 0
\(489\) 24.6395 + 10.2060i 1.11424 + 0.461533i
\(490\) 0 0
\(491\) 12.5638 18.8031i 0.566998 0.848572i −0.431570 0.902080i \(-0.642040\pi\)
0.998567 + 0.0535074i \(0.0170401\pi\)
\(492\) 0 0
\(493\) −32.6274 6.48999i −1.46946 0.292294i
\(494\) 0 0
\(495\) −17.6754 17.6754i −0.794448 0.794448i
\(496\) 0 0
\(497\) 0.824578 0.824578i 0.0369874 0.0369874i
\(498\) 0 0
\(499\) 6.92341 34.8064i 0.309935 1.55815i −0.440839 0.897586i \(-0.645319\pi\)
0.750773 0.660560i \(-0.229681\pi\)
\(500\) 0 0
\(501\) −47.8285 31.9580i −2.13682 1.42778i
\(502\) 0 0
\(503\) 8.55008 20.6417i 0.381229 0.920369i −0.610499 0.792017i \(-0.709031\pi\)
0.991729 0.128352i \(-0.0409688\pi\)
\(504\) 0 0
\(505\) 3.97678 + 9.60080i 0.176965 + 0.427230i
\(506\) 0 0
\(507\) 2.09257 + 10.5201i 0.0929345 + 0.467213i
\(508\) 0 0
\(509\) 22.4174 + 33.5500i 0.993634 + 1.48708i 0.868961 + 0.494880i \(0.164788\pi\)
0.124673 + 0.992198i \(0.460212\pi\)
\(510\) 0 0
\(511\) −2.40036 −0.106186
\(512\) 0 0
\(513\) −0.310293 −0.0136998
\(514\) 0 0
\(515\) 12.5465 + 18.7772i 0.552865 + 0.827421i
\(516\) 0 0
\(517\) −1.69283 8.51043i −0.0744506 0.374288i
\(518\) 0 0
\(519\) 14.7279 + 35.5564i 0.646485 + 1.56075i
\(520\) 0 0
\(521\) −6.91799 + 16.7015i −0.303082 + 0.731706i 0.696813 + 0.717253i \(0.254601\pi\)
−0.999896 + 0.0144530i \(0.995399\pi\)
\(522\) 0 0
\(523\) 21.0603 + 14.0720i 0.920902 + 0.615327i 0.923054 0.384671i \(-0.125685\pi\)
−0.00215221 + 0.999998i \(0.500685\pi\)
\(524\) 0 0
\(525\) −1.93890 + 9.74750i −0.0846205 + 0.425416i
\(526\) 0 0
\(527\) −38.2501 + 38.2501i −1.66620 + 1.66620i
\(528\) 0 0
\(529\) −1.92066 1.92066i −0.0835068 0.0835068i
\(530\) 0 0
\(531\) 50.7639 + 10.0976i 2.20297 + 0.438198i
\(532\) 0 0
\(533\) 4.84346 7.24875i 0.209794 0.313978i
\(534\) 0 0
\(535\) 16.5724 + 6.86451i 0.716487 + 0.296779i
\(536\) 0 0
\(537\) −2.53564 + 1.05030i −0.109421 + 0.0453236i
\(538\) 0 0
\(539\) −14.1977 + 2.82410i −0.611538 + 0.121643i
\(540\) 0 0
\(541\) −4.10594 + 2.74350i −0.176528 + 0.117952i −0.640695 0.767795i \(-0.721354\pi\)
0.464167 + 0.885748i \(0.346354\pi\)
\(542\) 0 0
\(543\) 54.6088i 2.34349i
\(544\) 0 0
\(545\) 24.1582i 1.03482i
\(546\) 0 0
\(547\) −29.7650 + 19.8884i −1.27266 + 0.850364i −0.993931 0.110005i \(-0.964913\pi\)
−0.278729 + 0.960370i \(0.589913\pi\)
\(548\) 0 0
\(549\) 8.44320 1.67946i 0.360347 0.0716775i
\(550\) 0 0
\(551\) −1.12865 + 0.467501i −0.0480820 + 0.0199162i
\(552\) 0 0
\(553\) 2.91255 + 1.20642i 0.123854 + 0.0513021i
\(554\) 0 0
\(555\) 4.83841 7.24120i 0.205379 0.307372i
\(556\) 0 0
\(557\) 22.0208 + 4.38021i 0.933052 + 0.185596i 0.638132 0.769927i \(-0.279707\pi\)
0.294919 + 0.955522i \(0.404707\pi\)
\(558\) 0 0
\(559\) 12.6007 + 12.6007i 0.532954 + 0.532954i
\(560\) 0 0
\(561\) 34.0276 34.0276i 1.43664 1.43664i
\(562\) 0 0
\(563\) 3.20606 16.1180i 0.135119 0.679291i −0.852538 0.522665i \(-0.824938\pi\)
0.987658 0.156627i \(-0.0500620\pi\)
\(564\) 0 0
\(565\) −25.7997 17.2388i −1.08540 0.725242i
\(566\) 0 0
\(567\) −3.07924 + 7.43394i −0.129316 + 0.312196i
\(568\) 0 0
\(569\) −0.0562600 0.135824i −0.00235854 0.00569402i 0.922696 0.385529i \(-0.125981\pi\)
−0.925054 + 0.379835i \(0.875981\pi\)
\(570\) 0 0
\(571\) 2.84345 + 14.2950i 0.118995 + 0.598227i 0.993559 + 0.113317i \(0.0361477\pi\)
−0.874564 + 0.484910i \(0.838852\pi\)
\(572\) 0 0
\(573\) 20.5846 + 30.8070i 0.859933 + 1.28698i
\(574\) 0 0
\(575\) −16.4653 −0.686652
\(576\) 0 0
\(577\) 33.7673 1.40575 0.702876 0.711313i \(-0.251899\pi\)
0.702876 + 0.711313i \(0.251899\pi\)
\(578\) 0 0
\(579\) −1.84455 2.76056i −0.0766568 0.114725i
\(580\) 0 0
\(581\) −0.0345278 0.173583i −0.00143245 0.00720143i
\(582\) 0 0
\(583\) −4.57442 11.0436i −0.189453 0.457380i
\(584\) 0 0
\(585\) −16.0498 + 38.7476i −0.663577 + 1.60202i
\(586\) 0 0
\(587\) 3.34109 + 2.23245i 0.137902 + 0.0921429i 0.622607 0.782534i \(-0.286073\pi\)
−0.484706 + 0.874677i \(0.661073\pi\)
\(588\) 0 0
\(589\) −0.387541 + 1.94830i −0.0159683 + 0.0802783i
\(590\) 0 0
\(591\) 31.3354 31.3354i 1.28897 1.28897i
\(592\) 0 0
\(593\) 0.0990454 + 0.0990454i 0.00406731 + 0.00406731i 0.709138 0.705070i \(-0.249085\pi\)
−0.705070 + 0.709138i \(0.749085\pi\)
\(594\) 0 0
\(595\) −23.7145 4.71711i −0.972200 0.193383i
\(596\) 0 0
\(597\) 31.9476 47.8130i 1.30753 1.95686i
\(598\) 0 0
\(599\) −20.6548 8.55549i −0.843931 0.349568i −0.0815289 0.996671i \(-0.525980\pi\)
−0.762402 + 0.647103i \(0.775980\pi\)
\(600\) 0 0
\(601\) 35.0312 14.5104i 1.42895 0.591892i 0.471861 0.881673i \(-0.343582\pi\)
0.957093 + 0.289781i \(0.0935824\pi\)
\(602\) 0 0
\(603\) −5.84774 + 1.16319i −0.238139 + 0.0473687i
\(604\) 0 0
\(605\) −11.9376 + 7.97643i −0.485331 + 0.324288i
\(606\) 0 0
\(607\) 40.7010i 1.65200i 0.563668 + 0.826001i \(0.309390\pi\)
−0.563668 + 0.826001i \(0.690610\pi\)
\(608\) 0 0
\(609\) 11.7928i 0.477868i
\(610\) 0 0
\(611\) −12.1051 + 8.08840i −0.489722 + 0.327222i
\(612\) 0 0
\(613\) 34.3868 6.83995i 1.38887 0.276263i 0.556666 0.830736i \(-0.312080\pi\)
0.832202 + 0.554473i \(0.187080\pi\)
\(614\) 0 0
\(615\) 14.4816 5.99849i 0.583956 0.241882i
\(616\) 0 0
\(617\) −22.8284 9.45584i −0.919038 0.380678i −0.127528 0.991835i \(-0.540704\pi\)
−0.791509 + 0.611157i \(0.790704\pi\)
\(618\) 0 0
\(619\) 2.49212 3.72973i 0.100167 0.149910i −0.778001 0.628263i \(-0.783766\pi\)
0.878168 + 0.478353i \(0.158766\pi\)
\(620\) 0 0
\(621\) 4.86712 + 0.968130i 0.195311 + 0.0388497i
\(622\) 0 0
\(623\) 5.30399 + 5.30399i 0.212500 + 0.212500i
\(624\) 0 0
\(625\) −21.1523 + 21.1523i −0.846092 + 0.846092i
\(626\) 0 0
\(627\) 0.344759 1.73322i 0.0137684 0.0692182i
\(628\) 0 0
\(629\) 7.44071 + 4.97172i 0.296681 + 0.198236i
\(630\) 0 0
\(631\) −4.15628 + 10.0341i −0.165459 + 0.399453i −0.984762 0.173908i \(-0.944361\pi\)
0.819303 + 0.573361i \(0.194361\pi\)
\(632\) 0 0
\(633\) −15.6571 37.7997i −0.622315 1.50240i
\(634\) 0 0
\(635\) 2.76512 + 13.9012i 0.109731 + 0.551653i
\(636\) 0 0
\(637\) 13.4936 + 20.1947i 0.534637 + 0.800141i
\(638\) 0 0
\(639\) 3.73702 0.147834
\(640\) 0 0
\(641\) 13.5366 0.534665 0.267332 0.963604i \(-0.413858\pi\)
0.267332 + 0.963604i \(0.413858\pi\)
\(642\) 0 0
\(643\) 6.82731 + 10.2178i 0.269243 + 0.402950i 0.941312 0.337538i \(-0.109594\pi\)
−0.672069 + 0.740488i \(0.734594\pi\)
\(644\) 0 0
\(645\) 6.25075 + 31.4246i 0.246123 + 1.23734i
\(646\) 0 0
\(647\) 8.80323 + 21.2529i 0.346091 + 0.835537i 0.997074 + 0.0764449i \(0.0243569\pi\)
−0.650983 + 0.759092i \(0.725643\pi\)
\(648\) 0 0
\(649\) −14.2676 + 34.4450i −0.560053 + 1.35209i
\(650\) 0 0
\(651\) −15.9442 10.6536i −0.624902 0.417546i
\(652\) 0 0
\(653\) 3.10918 15.6309i 0.121672 0.611685i −0.871044 0.491205i \(-0.836557\pi\)
0.992716 0.120480i \(-0.0384434\pi\)
\(654\) 0 0
\(655\) 31.2752 31.2752i 1.22202 1.22202i
\(656\) 0 0
\(657\) −5.43927 5.43927i −0.212206 0.212206i
\(658\) 0 0
\(659\) 44.4902 + 8.84966i 1.73309 + 0.344734i 0.957924 0.287021i \(-0.0926648\pi\)
0.775169 + 0.631754i \(0.217665\pi\)
\(660\) 0 0
\(661\) −26.4902 + 39.6454i −1.03035 + 1.54203i −0.203919 + 0.978988i \(0.565368\pi\)
−0.826430 + 0.563039i \(0.809632\pi\)
\(662\) 0 0
\(663\) −74.5946 30.8981i −2.89701 1.19998i
\(664\) 0 0
\(665\) −0.820333 + 0.339793i −0.0318111 + 0.0131766i
\(666\) 0 0
\(667\) 19.1621 3.81157i 0.741959 0.147585i
\(668\) 0 0
\(669\) 40.8589 27.3011i 1.57970 1.05552i
\(670\) 0 0
\(671\) 6.20102i 0.239388i
\(672\) 0 0
\(673\) 13.0714i 0.503866i 0.967745 + 0.251933i \(0.0810662\pi\)
−0.967745 + 0.251933i \(0.918934\pi\)
\(674\) 0 0
\(675\) −3.34939 + 2.23799i −0.128918 + 0.0861404i
\(676\) 0 0
\(677\) −9.06468 + 1.80308i −0.348384 + 0.0692979i −0.366181 0.930544i \(-0.619335\pi\)
0.0177968 + 0.999842i \(0.494335\pi\)
\(678\) 0 0
\(679\) 4.42264 1.83192i 0.169725 0.0703025i
\(680\) 0 0
\(681\) −40.7353 16.8731i −1.56098 0.646579i
\(682\) 0 0
\(683\) 2.05308 3.07264i 0.0785587 0.117571i −0.790110 0.612966i \(-0.789976\pi\)
0.868668 + 0.495394i \(0.164976\pi\)
\(684\) 0 0
\(685\) 32.5643 + 6.47743i 1.24422 + 0.247490i
\(686\) 0 0
\(687\) −29.5472 29.5472i −1.12730 1.12730i
\(688\) 0 0
\(689\) −14.1817 + 14.1817i −0.540278 + 0.540278i
\(690\) 0 0
\(691\) 3.79296 19.0685i 0.144291 0.725400i −0.839111 0.543960i \(-0.816924\pi\)
0.983402 0.181440i \(-0.0580758\pi\)
\(692\) 0 0
\(693\) 7.57081 + 5.05866i 0.287591 + 0.192162i
\(694\) 0 0
\(695\) 17.4889 42.2219i 0.663391 1.60157i
\(696\) 0 0
\(697\) 6.16377 + 14.8806i 0.233469 + 0.563645i
\(698\) 0 0
\(699\) −11.0020 55.3107i −0.416133 2.09204i
\(700\) 0 0
\(701\) −4.33534 6.48830i −0.163744 0.245060i 0.740520 0.672034i \(-0.234579\pi\)
−0.904264 + 0.426975i \(0.859579\pi\)
\(702\) 0 0
\(703\) 0.328626 0.0123944
\(704\) 0 0
\(705\) −26.1763 −0.985858
\(706\) 0 0
\(707\) −2.10302 3.14740i −0.0790923 0.118370i
\(708\) 0 0
\(709\) −2.46179 12.3763i −0.0924546 0.464801i −0.999081 0.0428660i \(-0.986351\pi\)
0.906626 0.421935i \(-0.138649\pi\)
\(710\) 0 0
\(711\) 3.86613 + 9.33367i 0.144991 + 0.350040i
\(712\) 0 0
\(713\) 12.1576 29.3510i 0.455305 1.09920i
\(714\) 0 0
\(715\) −25.1192 16.7841i −0.939405 0.627690i
\(716\) 0 0
\(717\) 10.1143 50.8478i 0.377724 1.89895i
\(718\) 0 0
\(719\) −26.2578 + 26.2578i −0.979252 + 0.979252i −0.999789 0.0205367i \(-0.993463\pi\)
0.0205367 + 0.999789i \(0.493463\pi\)
\(720\) 0 0
\(721\) −5.81676 5.81676i −0.216628 0.216628i
\(722\) 0 0
\(723\) −40.9017 8.13586i −1.52115 0.302576i
\(724\) 0 0
\(725\) −8.81109 + 13.1867i −0.327236 + 0.489743i
\(726\) 0 0
\(727\) 30.7700 + 12.7453i 1.14120 + 0.472698i 0.871572 0.490267i \(-0.163101\pi\)
0.269623 + 0.962966i \(0.413101\pi\)
\(728\) 0 0
\(729\) −31.5697 + 13.0766i −1.16925 + 0.484319i
\(730\) 0 0
\(731\) −32.2905 + 6.42297i −1.19431 + 0.237562i
\(732\) 0 0
\(733\) −0.875789 + 0.585183i −0.0323480 + 0.0216142i −0.571639 0.820505i \(-0.693692\pi\)
0.539291 + 0.842119i \(0.318692\pi\)
\(734\) 0 0
\(735\) 43.6692i 1.61076i
\(736\) 0 0
\(737\) 4.29481i 0.158202i
\(738\) 0 0
\(739\) −18.8272 + 12.5799i −0.692571 + 0.462761i −0.851381 0.524548i \(-0.824234\pi\)
0.158810 + 0.987309i \(0.449234\pi\)
\(740\) 0 0
\(741\) −2.90804 + 0.578445i −0.106829 + 0.0212497i
\(742\) 0 0
\(743\) −14.5583 + 6.03025i −0.534093 + 0.221228i −0.633395 0.773829i \(-0.718339\pi\)
0.0993020 + 0.995057i \(0.468339\pi\)
\(744\) 0 0
\(745\) −28.2971 11.7210i −1.03672 0.429425i
\(746\) 0 0
\(747\) 0.315101 0.471583i 0.0115290 0.0172543i
\(748\) 0 0
\(749\) −6.40851 1.27473i −0.234162 0.0465777i
\(750\) 0 0
\(751\) 18.4512 + 18.4512i 0.673295 + 0.673295i 0.958474 0.285179i \(-0.0920531\pi\)
−0.285179 + 0.958474i \(0.592053\pi\)
\(752\) 0 0
\(753\) −21.4856 + 21.4856i −0.782980 + 0.782980i
\(754\) 0 0
\(755\) −6.84431 + 34.4087i −0.249090 + 1.25226i
\(756\) 0 0
\(757\) −6.59159 4.40436i −0.239575 0.160079i 0.429987 0.902835i \(-0.358518\pi\)
−0.669562 + 0.742756i \(0.733518\pi\)
\(758\) 0 0
\(759\) −10.8155 + 26.1109i −0.392577 + 0.947765i
\(760\) 0 0
\(761\) 2.59638 + 6.26821i 0.0941186 + 0.227222i 0.963927 0.266168i \(-0.0857575\pi\)
−0.869808 + 0.493390i \(0.835758\pi\)
\(762\) 0 0
\(763\) 1.71677 + 8.63080i 0.0621513 + 0.312456i
\(764\) 0 0
\(765\) −43.0485 64.4266i −1.55642 2.32935i
\(766\) 0 0
\(767\) 62.5543 2.25871
\(768\) 0 0
\(769\) −10.0168 −0.361215 −0.180607 0.983555i \(-0.557806\pi\)
−0.180607 + 0.983555i \(0.557806\pi\)
\(770\) 0 0
\(771\) 22.8801 + 34.2425i 0.824007 + 1.23321i
\(772\) 0 0
\(773\) 1.04420 + 5.24953i 0.0375571 + 0.188812i 0.995010 0.0997782i \(-0.0318133\pi\)
−0.957453 + 0.288591i \(0.906813\pi\)
\(774\) 0 0
\(775\) 9.86891 + 23.8257i 0.354502 + 0.855843i
\(776\) 0 0
\(777\) −1.21399 + 2.93084i −0.0435518 + 0.105143i
\(778\) 0 0
\(779\) 0.491799 + 0.328609i 0.0176205 + 0.0117737i
\(780\) 0 0
\(781\) −0.525160 + 2.64016i −0.0187917 + 0.0944722i
\(782\) 0 0
\(783\) 3.37989 3.37989i 0.120787 0.120787i
\(784\) 0 0
\(785\) 33.4942 + 33.4942i 1.19546 + 1.19546i
\(786\) 0 0
\(787\) −37.8335 7.52555i −1.34862 0.268257i −0.532641 0.846341i \(-0.678801\pi\)
−0.815977 + 0.578084i \(0.803801\pi\)
\(788\) 0 0
\(789\) −9.58103 + 14.3390i −0.341094 + 0.510483i
\(790\) 0 0
\(791\) 10.4423 + 4.32534i 0.371285 + 0.153791i
\(792\) 0 0
\(793\) 9.61224 3.98152i 0.341341 0.141388i
\(794\) 0 0
\(795\) −35.3673 + 7.03499i −1.25435 + 0.249505i
\(796\) 0 0
\(797\) −38.4226 + 25.6731i −1.36100 + 0.909389i −0.999734 0.0230746i \(-0.992654\pi\)
−0.361263 + 0.932464i \(0.617654\pi\)
\(798\) 0 0
\(799\) 26.8976i 0.951568i
\(800\) 0 0
\(801\) 24.0379i 0.849338i
\(802\) 0 0
\(803\) 4.60715 3.07840i 0.162583 0.108634i
\(804\) 0 0
\(805\) 13.9275 2.77036i 0.490881 0.0976424i
\(806\) 0 0
\(807\) −22.8607 + 9.46921i −0.804735 + 0.333332i
\(808\) 0 0
\(809\) 33.9191 + 14.0497i 1.19253 + 0.493963i 0.888578 0.458725i \(-0.151694\pi\)
0.303953 + 0.952687i \(0.401694\pi\)
\(810\) 0 0
\(811\) 18.2057 27.2468i 0.639289 0.956763i −0.360424 0.932789i \(-0.617368\pi\)
0.999713 0.0239744i \(-0.00763201\pi\)
\(812\) 0 0
\(813\) −30.6367 6.09402i −1.07448 0.213727i
\(814\) 0 0
\(815\) 21.8729 + 21.8729i 0.766173 + 0.766173i
\(816\) 0 0
\(817\) −0.854909 + 0.854909i −0.0299095 + 0.0299095i
\(818\) 0 0
\(819\) 2.98042 14.9836i 0.104144 0.523569i
\(820\) 0 0
\(821\) −15.3771 10.2747i −0.536666 0.358588i 0.257511 0.966275i \(-0.417098\pi\)
−0.794177 + 0.607687i \(0.792098\pi\)
\(822\) 0 0
\(823\) −15.9945 + 38.6142i −0.557534 + 1.34601i 0.354178 + 0.935178i \(0.384761\pi\)
−0.911712 + 0.410829i \(0.865239\pi\)
\(824\) 0 0
\(825\) −8.77946 21.1955i −0.305662 0.737932i
\(826\) 0 0
\(827\) −6.85463 34.4606i −0.238359 1.19831i −0.895680 0.444700i \(-0.853310\pi\)
0.657321 0.753611i \(-0.271690\pi\)
\(828\) 0 0
\(829\) −7.70913 11.5375i −0.267749 0.400715i 0.673094 0.739557i \(-0.264965\pi\)
−0.940843 + 0.338842i \(0.889965\pi\)
\(830\) 0 0
\(831\) −53.7094 −1.86316
\(832\) 0 0
\(833\) −44.8724 −1.55474
\(834\) 0 0
\(835\) −37.0666 55.4740i −1.28274 1.91976i
\(836\) 0 0
\(837\) −1.51632 7.62308i −0.0524118 0.263492i
\(838\) 0 0
\(839\) −14.7929 35.7132i −0.510708 1.23296i −0.943473 0.331451i \(-0.892462\pi\)
0.432765 0.901507i \(-0.357538\pi\)
\(840\) 0 0
\(841\) −3.89623 + 9.40634i −0.134353 + 0.324357i
\(842\) 0 0
\(843\) 64.9293 + 43.3844i 2.23628 + 1.49424i
\(844\) 0 0
\(845\) −2.42708 + 12.2018i −0.0834941 + 0.419753i
\(846\) 0 0
\(847\) 3.69801 3.69801i 0.127065 0.127065i
\(848\) 0 0
\(849\) −32.5519 32.5519i −1.11718 1.11718i
\(850\) 0 0
\(851\) −5.15469 1.02533i −0.176700 0.0351479i
\(852\) 0 0
\(853\) 7.85966 11.7628i 0.269110 0.402751i −0.672161 0.740405i \(-0.734634\pi\)
0.941270 + 0.337654i \(0.109634\pi\)
\(854\) 0 0
\(855\) −2.62887 1.08891i −0.0899054 0.0372400i
\(856\) 0 0
\(857\) 10.8078 4.47675i 0.369189 0.152923i −0.190373 0.981712i \(-0.560970\pi\)
0.559561 + 0.828789i \(0.310970\pi\)
\(858\) 0 0
\(859\) 17.8324 3.54708i 0.608433 0.121025i 0.118748 0.992924i \(-0.462112\pi\)
0.489685 + 0.871900i \(0.337112\pi\)
\(860\) 0 0
\(861\) −4.74746 + 3.17215i −0.161793 + 0.108107i
\(862\) 0 0
\(863\) 51.3481i 1.74791i −0.486006 0.873955i \(-0.661547\pi\)
0.486006 0.873955i \(-0.338453\pi\)
\(864\) 0 0
\(865\) 44.6381i 1.51774i
\(866\) 0 0
\(867\) 88.1754 58.9169i 2.99459 2.00092i
\(868\) 0 0
\(869\) −7.13742 + 1.41972i −0.242120 + 0.0481607i
\(870\) 0 0
\(871\) −6.65742 + 2.75759i −0.225578 + 0.0934375i
\(872\) 0 0
\(873\) 14.1730 + 5.87063i 0.479682 + 0.198691i
\(874\) 0 0
\(875\) 2.35446 3.52369i 0.0795952 0.119123i
\(876\) 0 0
\(877\) 48.5667 + 9.66052i 1.63998 + 0.326213i 0.927026 0.374997i \(-0.122356\pi\)
0.712956 + 0.701209i \(0.247356\pi\)
\(878\) 0 0
\(879\) 44.8820 + 44.8820i 1.51383 + 1.51383i
\(880\) 0 0
\(881\) 16.3418 16.3418i 0.550568 0.550568i −0.376037 0.926605i \(-0.622713\pi\)
0.926605 + 0.376037i \(0.122713\pi\)
\(882\) 0 0
\(883\) −0.654361 + 3.28970i −0.0220210 + 0.110707i −0.990233 0.139426i \(-0.955474\pi\)
0.968212 + 0.250133i \(0.0804743\pi\)
\(884\) 0 0
\(885\) 93.5167 + 62.4859i 3.14353 + 2.10044i
\(886\) 0 0
\(887\) −16.8387 + 40.6522i −0.565389 + 1.36497i 0.340016 + 0.940420i \(0.389567\pi\)
−0.905405 + 0.424549i \(0.860433\pi\)
\(888\) 0 0
\(889\) −1.97575 4.76988i −0.0662644 0.159977i
\(890\) 0 0
\(891\) −3.62367 18.2174i −0.121397 0.610306i
\(892\) 0 0
\(893\) −0.548765 0.821285i −0.0183637 0.0274833i
\(894\) 0 0
\(895\) −3.18328 −0.106405
\(896\) 0 0
\(897\) 47.4190 1.58327
\(898\) 0 0
\(899\) −17.0007 25.4433i −0.567004 0.848582i
\(900\) 0 0
\(901\) −7.22882 36.3417i −0.240827 1.21072i
\(902\) 0 0
\(903\) −4.46631 10.7826i −0.148629 0.358823i
\(904\) 0 0
\(905\) 24.2385 58.5169i 0.805714 1.94517i
\(906\) 0 0
\(907\) −20.7405 13.8584i −0.688677 0.460159i 0.161351 0.986897i \(-0.448415\pi\)
−0.850028 + 0.526738i \(0.823415\pi\)
\(908\) 0 0
\(909\) 2.36657 11.8976i 0.0784942 0.394617i
\(910\) 0 0
\(911\) −6.62665 + 6.62665i −0.219551 + 0.219551i −0.808309 0.588758i \(-0.799617\pi\)
0.588758 + 0.808309i \(0.299617\pi\)
\(912\) 0 0
\(913\) 0.288886 + 0.288886i 0.00956073 + 0.00956073i
\(914\) 0 0
\(915\) 18.3472 + 3.64948i 0.606538 + 0.120648i
\(916\) 0 0
\(917\) −8.95090 + 13.3960i −0.295585 + 0.442374i
\(918\) 0 0
\(919\) 15.1621 + 6.28033i 0.500150 + 0.207169i 0.618473 0.785806i \(-0.287752\pi\)
−0.118323 + 0.992975i \(0.537752\pi\)
\(920\) 0 0
\(921\) 14.3505 5.94419i 0.472866 0.195868i
\(922\) 0 0
\(923\) 4.42971 0.881125i 0.145806 0.0290026i
\(924\) 0 0
\(925\) 3.54729 2.37022i 0.116634 0.0779325i
\(926\) 0 0
\(927\) 26.3618i 0.865836i
\(928\) 0 0
\(929\) 34.4393i 1.12992i −0.825119 0.564959i \(-0.808892\pi\)
0.825119 0.564959i \(-0.191108\pi\)
\(930\) 0 0
\(931\) −1.37013 + 0.915489i −0.0449041 + 0.0300039i
\(932\) 0 0
\(933\) 17.0698 3.39539i 0.558839 0.111160i
\(934\) 0 0
\(935\) 51.5661 21.3594i 1.68639 0.698526i
\(936\) 0 0
\(937\) 5.30997 + 2.19946i 0.173469 + 0.0718533i 0.467728 0.883872i \(-0.345073\pi\)
−0.294259 + 0.955726i \(0.595073\pi\)
\(938\) 0 0
\(939\) −29.4982 + 44.1472i −0.962638 + 1.44069i
\(940\) 0 0
\(941\) 0.669760 + 0.133223i 0.0218335 + 0.00434296i 0.205995 0.978553i \(-0.433957\pi\)
−0.184161 + 0.982896i \(0.558957\pi\)
\(942\) 0 0
\(943\) −6.68886 6.68886i −0.217819 0.217819i
\(944\) 0 0
\(945\) 2.45660 2.45660i 0.0799132 0.0799132i
\(946\) 0 0
\(947\) −6.91180 + 34.7479i −0.224603 + 1.12916i 0.689690 + 0.724104i \(0.257747\pi\)
−0.914294 + 0.405052i \(0.867253\pi\)
\(948\) 0 0
\(949\) −7.72998 5.16500i −0.250926 0.167663i
\(950\) 0 0
\(951\) 5.54315 13.3824i 0.179749 0.433952i
\(952\) 0 0
\(953\) 6.17778 + 14.9145i 0.200118 + 0.483127i 0.991799 0.127807i \(-0.0407939\pi\)
−0.791681 + 0.610934i \(0.790794\pi\)
\(954\) 0 0
\(955\) 8.38382 + 42.1483i 0.271294 + 1.36389i
\(956\) 0 0
\(957\) 15.1239 + 22.6346i 0.488888 + 0.731672i
\(958\) 0 0
\(959\) −12.0943 −0.390545
\(960\) 0 0
\(961\) −18.7584 −0.605109
\(962\) 0 0
\(963\) −11.6332 17.4104i −0.374876 0.561042i
\(964\) 0 0
\(965\) −0.751259 3.77684i −0.0241839 0.121581i
\(966\) 0 0
\(967\) −17.5127 42.2794i −0.563171 1.35962i −0.907217 0.420662i \(-0.861798\pi\)
0.344046 0.938953i \(-0.388202\pi\)
\(968\) 0 0
\(969\) 2.09631 5.06094i 0.0673432 0.162581i
\(970\) 0 0
\(971\) 22.7030 + 15.1696i 0.728573 + 0.486817i 0.863697 0.504012i \(-0.168143\pi\)
−0.135124 + 0.990829i \(0.543143\pi\)
\(972\) 0 0
\(973\) −3.24766 + 16.3271i −0.104115 + 0.523423i
\(974\) 0 0
\(975\) −27.2182 + 27.2182i −0.871680 + 0.871680i
\(976\) 0 0
\(977\) −22.0950 22.0950i −0.706883 0.706883i 0.258996 0.965878i \(-0.416608\pi\)
−0.965878 + 0.258996i \(0.916608\pi\)
\(978\) 0 0
\(979\) −16.9825 3.37802i −0.542762 0.107962i
\(980\) 0 0
\(981\) −15.6673 + 23.4478i −0.500219 + 0.748631i
\(982\) 0 0
\(983\) −28.4453 11.7824i −0.907263 0.375801i −0.120255 0.992743i \(-0.538371\pi\)
−0.787008 + 0.616942i \(0.788371\pi\)
\(984\) 0 0
\(985\) 47.4863 19.6695i 1.51304 0.626722i
\(986\) 0 0
\(987\) 9.35181 1.86019i 0.297672 0.0592105i
\(988\) 0 0
\(989\) 16.0771 10.7424i 0.511221 0.341587i
\(990\) 0 0
\(991\) 40.2872i 1.27976i 0.768473 + 0.639882i \(0.221017\pi\)
−0.768473 + 0.639882i \(0.778983\pi\)
\(992\) 0 0
\(993\) 75.0871i 2.38282i
\(994\) 0 0
\(995\) 55.4561 37.0546i 1.75808 1.17471i
\(996\) 0 0
\(997\) −14.0382 + 2.79238i −0.444595 + 0.0884355i −0.412311 0.911043i \(-0.635278\pi\)
−0.0322844 + 0.999479i \(0.510278\pi\)
\(998\) 0 0
\(999\) −1.18793 + 0.492059i −0.0375846 + 0.0155680i
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 256.2.i.a.17.1 56
4.3 odd 2 64.2.i.a.45.5 yes 56
8.3 odd 2 512.2.i.b.289.1 56
8.5 even 2 512.2.i.a.289.7 56
12.11 even 2 576.2.bd.a.109.3 56
64.5 even 16 512.2.i.a.225.7 56
64.27 odd 16 64.2.i.a.37.5 56
64.37 even 16 inner 256.2.i.a.241.1 56
64.59 odd 16 512.2.i.b.225.1 56
192.155 even 16 576.2.bd.a.37.3 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.2.i.a.37.5 56 64.27 odd 16
64.2.i.a.45.5 yes 56 4.3 odd 2
256.2.i.a.17.1 56 1.1 even 1 trivial
256.2.i.a.241.1 56 64.37 even 16 inner
512.2.i.a.225.7 56 64.5 even 16
512.2.i.a.289.7 56 8.5 even 2
512.2.i.b.225.1 56 64.59 odd 16
512.2.i.b.289.1 56 8.3 odd 2
576.2.bd.a.37.3 56 192.155 even 16
576.2.bd.a.109.3 56 12.11 even 2