Properties

Label 576.2.bb.e.337.11
Level $576$
Weight $2$
Character 576.337
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,2,Mod(49,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), 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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 337.11
Character \(\chi\) \(=\) 576.337
Dual form 576.2.bb.e.241.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.215523 + 1.71859i) q^{3} +(-0.733432 - 2.73721i) q^{5} +(-1.14487 + 0.660988i) q^{7} +(-2.90710 - 0.740791i) q^{9} +O(q^{10})\) \(q+(-0.215523 + 1.71859i) q^{3} +(-0.733432 - 2.73721i) q^{5} +(-1.14487 + 0.660988i) q^{7} +(-2.90710 - 0.740791i) q^{9} +(-1.28367 - 0.343957i) q^{11} +(3.36696 - 0.902174i) q^{13} +(4.86220 - 0.670538i) q^{15} -7.60772 q^{17} +(-4.32297 - 4.32297i) q^{19} +(-0.889223 - 2.11001i) q^{21} +(-3.46087 - 1.99814i) q^{23} +(-2.62424 + 1.51511i) q^{25} +(1.89966 - 4.83645i) q^{27} +(0.950303 - 3.54658i) q^{29} +(-0.569129 + 0.985760i) q^{31} +(0.867781 - 2.13197i) q^{33} +(2.64894 + 2.64894i) q^{35} +(2.26014 - 2.26014i) q^{37} +(0.824810 + 5.98086i) q^{39} +(1.42311 + 0.821634i) q^{41} +(6.17424 + 1.65438i) q^{43} +(0.104463 + 8.50065i) q^{45} +(-4.58731 - 7.94546i) q^{47} +(-2.62619 + 4.54869i) q^{49} +(1.63964 - 13.0746i) q^{51} +(7.72215 - 7.72215i) q^{53} +3.76593i q^{55} +(8.36111 - 6.49771i) q^{57} +(-1.28879 - 4.80982i) q^{59} +(-2.66068 + 9.92979i) q^{61} +(3.81789 - 1.07345i) q^{63} +(-4.93887 - 8.55438i) q^{65} +(-13.9276 + 3.73189i) q^{67} +(4.17987 - 5.51718i) q^{69} +7.87498i q^{71} -0.577222i q^{73} +(-2.03826 - 4.83654i) q^{75} +(1.69698 - 0.454704i) q^{77} +(-0.716890 - 1.24169i) q^{79} +(7.90246 + 4.30711i) q^{81} +(0.885341 - 3.30414i) q^{83} +(5.57975 + 20.8239i) q^{85} +(5.89030 + 2.39755i) q^{87} +16.2114i q^{89} +(-3.25839 + 3.25839i) q^{91} +(-1.57146 - 1.19055i) q^{93} +(-8.66225 + 15.0035i) q^{95} +(-0.648931 - 1.12398i) q^{97} +(3.47695 + 1.95085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.215523 + 1.71859i −0.124432 + 0.992228i
\(4\) 0 0
\(5\) −0.733432 2.73721i −0.328001 1.22412i −0.911261 0.411830i \(-0.864890\pi\)
0.583260 0.812286i \(-0.301777\pi\)
\(6\) 0 0
\(7\) −1.14487 + 0.660988i −0.432718 + 0.249830i −0.700504 0.713648i \(-0.747041\pi\)
0.267786 + 0.963479i \(0.413708\pi\)
\(8\) 0 0
\(9\) −2.90710 0.740791i −0.969033 0.246930i
\(10\) 0 0
\(11\) −1.28367 0.343957i −0.387040 0.103707i 0.0600515 0.998195i \(-0.480874\pi\)
−0.447092 + 0.894488i \(0.647540\pi\)
\(12\) 0 0
\(13\) 3.36696 0.902174i 0.933827 0.250218i 0.240341 0.970689i \(-0.422741\pi\)
0.693486 + 0.720470i \(0.256074\pi\)
\(14\) 0 0
\(15\) 4.86220 0.670538i 1.25542 0.173132i
\(16\) 0 0
\(17\) −7.60772 −1.84514 −0.922572 0.385825i \(-0.873917\pi\)
−0.922572 + 0.385825i \(0.873917\pi\)
\(18\) 0 0
\(19\) −4.32297 4.32297i −0.991757 0.991757i 0.00820954 0.999966i \(-0.497387\pi\)
−0.999966 + 0.00820954i \(0.997387\pi\)
\(20\) 0 0
\(21\) −0.889223 2.11001i −0.194044 0.460442i
\(22\) 0 0
\(23\) −3.46087 1.99814i −0.721642 0.416640i 0.0937148 0.995599i \(-0.470126\pi\)
−0.815357 + 0.578959i \(0.803459\pi\)
\(24\) 0 0
\(25\) −2.62424 + 1.51511i −0.524849 + 0.303021i
\(26\) 0 0
\(27\) 1.89966 4.83645i 0.365590 0.930776i
\(28\) 0 0
\(29\) 0.950303 3.54658i 0.176467 0.658583i −0.819830 0.572606i \(-0.805932\pi\)
0.996297 0.0859765i \(-0.0274010\pi\)
\(30\) 0 0
\(31\) −0.569129 + 0.985760i −0.102219 + 0.177048i −0.912598 0.408857i \(-0.865927\pi\)
0.810380 + 0.585905i \(0.199261\pi\)
\(32\) 0 0
\(33\) 0.867781 2.13197i 0.151061 0.371128i
\(34\) 0 0
\(35\) 2.64894 + 2.64894i 0.447753 + 0.447753i
\(36\) 0 0
\(37\) 2.26014 2.26014i 0.371565 0.371565i −0.496482 0.868047i \(-0.665375\pi\)
0.868047 + 0.496482i \(0.165375\pi\)
\(38\) 0 0
\(39\) 0.824810 + 5.98086i 0.132075 + 0.957704i
\(40\) 0 0
\(41\) 1.42311 + 0.821634i 0.222253 + 0.128318i 0.606993 0.794707i \(-0.292376\pi\)
−0.384740 + 0.923025i \(0.625709\pi\)
\(42\) 0 0
\(43\) 6.17424 + 1.65438i 0.941563 + 0.252291i 0.696778 0.717287i \(-0.254616\pi\)
0.244784 + 0.969578i \(0.421283\pi\)
\(44\) 0 0
\(45\) 0.104463 + 8.50065i 0.0155724 + 1.26720i
\(46\) 0 0
\(47\) −4.58731 7.94546i −0.669129 1.15896i −0.978148 0.207909i \(-0.933334\pi\)
0.309020 0.951056i \(-0.399999\pi\)
\(48\) 0 0
\(49\) −2.62619 + 4.54869i −0.375170 + 0.649813i
\(50\) 0 0
\(51\) 1.63964 13.0746i 0.229595 1.83080i
\(52\) 0 0
\(53\) 7.72215 7.72215i 1.06072 1.06072i 0.0626852 0.998033i \(-0.480034\pi\)
0.998033 0.0626852i \(-0.0199664\pi\)
\(54\) 0 0
\(55\) 3.76593i 0.507798i
\(56\) 0 0
\(57\) 8.36111 6.49771i 1.10746 0.860642i
\(58\) 0 0
\(59\) −1.28879 4.80982i −0.167786 0.626185i −0.997668 0.0682473i \(-0.978259\pi\)
0.829883 0.557938i \(-0.188407\pi\)
\(60\) 0 0
\(61\) −2.66068 + 9.92979i −0.340665 + 1.27138i 0.556931 + 0.830559i \(0.311979\pi\)
−0.897596 + 0.440820i \(0.854688\pi\)
\(62\) 0 0
\(63\) 3.81789 1.07345i 0.481009 0.135242i
\(64\) 0 0
\(65\) −4.93887 8.55438i −0.612592 1.06104i
\(66\) 0 0
\(67\) −13.9276 + 3.73189i −1.70153 + 0.455923i −0.973324 0.229436i \(-0.926312\pi\)
−0.728205 + 0.685359i \(0.759645\pi\)
\(68\) 0 0
\(69\) 4.17987 5.51718i 0.503198 0.664190i
\(70\) 0 0
\(71\) 7.87498i 0.934588i 0.884102 + 0.467294i \(0.154771\pi\)
−0.884102 + 0.467294i \(0.845229\pi\)
\(72\) 0 0
\(73\) 0.577222i 0.0675588i −0.999429 0.0337794i \(-0.989246\pi\)
0.999429 0.0337794i \(-0.0107544\pi\)
\(74\) 0 0
\(75\) −2.03826 4.83654i −0.235358 0.558475i
\(76\) 0 0
\(77\) 1.69698 0.454704i 0.193389 0.0518183i
\(78\) 0 0
\(79\) −0.716890 1.24169i −0.0806564 0.139701i 0.822876 0.568221i \(-0.192368\pi\)
−0.903532 + 0.428521i \(0.859035\pi\)
\(80\) 0 0
\(81\) 7.90246 + 4.30711i 0.878051 + 0.478567i
\(82\) 0 0
\(83\) 0.885341 3.30414i 0.0971788 0.362676i −0.900162 0.435555i \(-0.856552\pi\)
0.997341 + 0.0728790i \(0.0232187\pi\)
\(84\) 0 0
\(85\) 5.57975 + 20.8239i 0.605208 + 2.25867i
\(86\) 0 0
\(87\) 5.89030 + 2.39755i 0.631506 + 0.257044i
\(88\) 0 0
\(89\) 16.2114i 1.71841i 0.511635 + 0.859203i \(0.329040\pi\)
−0.511635 + 0.859203i \(0.670960\pi\)
\(90\) 0 0
\(91\) −3.25839 + 3.25839i −0.341572 + 0.341572i
\(92\) 0 0
\(93\) −1.57146 1.19055i −0.162952 0.123455i
\(94\) 0 0
\(95\) −8.66225 + 15.0035i −0.888728 + 1.53932i
\(96\) 0 0
\(97\) −0.648931 1.12398i −0.0658889 0.114123i 0.831199 0.555975i \(-0.187655\pi\)
−0.897088 + 0.441852i \(0.854322\pi\)
\(98\) 0 0
\(99\) 3.47695 + 1.95085i 0.349446 + 0.196068i
\(100\) 0 0
\(101\) −9.73900 2.60956i −0.969067 0.259661i −0.260633 0.965438i \(-0.583931\pi\)
−0.708434 + 0.705777i \(0.750598\pi\)
\(102\) 0 0
\(103\) 8.04850 + 4.64680i 0.793042 + 0.457863i 0.841033 0.540985i \(-0.181948\pi\)
−0.0479901 + 0.998848i \(0.515282\pi\)
\(104\) 0 0
\(105\) −5.12335 + 3.98154i −0.499988 + 0.388558i
\(106\) 0 0
\(107\) −1.89502 + 1.89502i −0.183199 + 0.183199i −0.792748 0.609549i \(-0.791350\pi\)
0.609549 + 0.792748i \(0.291350\pi\)
\(108\) 0 0
\(109\) −8.63272 8.63272i −0.826864 0.826864i 0.160217 0.987082i \(-0.448780\pi\)
−0.987082 + 0.160217i \(0.948780\pi\)
\(110\) 0 0
\(111\) 3.39715 + 4.37137i 0.322443 + 0.414912i
\(112\) 0 0
\(113\) −1.70180 + 2.94761i −0.160092 + 0.277288i −0.934902 0.354907i \(-0.884512\pi\)
0.774809 + 0.632195i \(0.217846\pi\)
\(114\) 0 0
\(115\) −2.93099 + 10.9386i −0.273317 + 1.02003i
\(116\) 0 0
\(117\) −10.4564 + 0.128497i −0.966695 + 0.0118796i
\(118\) 0 0
\(119\) 8.70982 5.02862i 0.798428 0.460972i
\(120\) 0 0
\(121\) −7.99679 4.61695i −0.726981 0.419722i
\(122\) 0 0
\(123\) −1.71877 + 2.26866i −0.154976 + 0.204559i
\(124\) 0 0
\(125\) −3.94700 3.94700i −0.353031 0.353031i
\(126\) 0 0
\(127\) 5.24504 0.465422 0.232711 0.972546i \(-0.425240\pi\)
0.232711 + 0.972546i \(0.425240\pi\)
\(128\) 0 0
\(129\) −4.17390 + 10.2544i −0.367491 + 0.902852i
\(130\) 0 0
\(131\) 6.27080 1.68026i 0.547883 0.146805i 0.0257490 0.999668i \(-0.491803\pi\)
0.522134 + 0.852864i \(0.325136\pi\)
\(132\) 0 0
\(133\) 7.80665 + 2.09178i 0.676922 + 0.181381i
\(134\) 0 0
\(135\) −14.6316 1.65256i −1.25929 0.142229i
\(136\) 0 0
\(137\) 6.16622 3.56007i 0.526816 0.304157i −0.212903 0.977073i \(-0.568292\pi\)
0.739719 + 0.672916i \(0.234958\pi\)
\(138\) 0 0
\(139\) 1.09091 + 4.07133i 0.0925298 + 0.345326i 0.996633 0.0819876i \(-0.0261268\pi\)
−0.904104 + 0.427313i \(0.859460\pi\)
\(140\) 0 0
\(141\) 14.6437 6.17128i 1.23322 0.519716i
\(142\) 0 0
\(143\) −4.63236 −0.387378
\(144\) 0 0
\(145\) −10.4047 −0.864063
\(146\) 0 0
\(147\) −7.25133 5.49369i −0.598080 0.453112i
\(148\) 0 0
\(149\) 2.25338 + 8.40971i 0.184604 + 0.688950i 0.994715 + 0.102674i \(0.0327399\pi\)
−0.810111 + 0.586276i \(0.800593\pi\)
\(150\) 0 0
\(151\) 17.8103 10.2828i 1.44938 0.836803i 0.450940 0.892554i \(-0.351089\pi\)
0.998445 + 0.0557515i \(0.0177554\pi\)
\(152\) 0 0
\(153\) 22.1164 + 5.63573i 1.78801 + 0.455622i
\(154\) 0 0
\(155\) 3.11564 + 0.834834i 0.250255 + 0.0670555i
\(156\) 0 0
\(157\) 8.90879 2.38710i 0.710999 0.190512i 0.114847 0.993383i \(-0.463362\pi\)
0.596152 + 0.802872i \(0.296696\pi\)
\(158\) 0 0
\(159\) 11.6069 + 14.9355i 0.920487 + 1.18446i
\(160\) 0 0
\(161\) 5.28298 0.416357
\(162\) 0 0
\(163\) 10.4053 + 10.4053i 0.815004 + 0.815004i 0.985379 0.170375i \(-0.0544981\pi\)
−0.170375 + 0.985379i \(0.554498\pi\)
\(164\) 0 0
\(165\) −6.47209 0.811644i −0.503851 0.0631864i
\(166\) 0 0
\(167\) −5.95392 3.43750i −0.460728 0.266001i 0.251622 0.967826i \(-0.419036\pi\)
−0.712350 + 0.701824i \(0.752369\pi\)
\(168\) 0 0
\(169\) −0.735830 + 0.424832i −0.0566023 + 0.0326794i
\(170\) 0 0
\(171\) 9.36488 + 15.7697i 0.716150 + 1.20594i
\(172\) 0 0
\(173\) 0.823927 3.07494i 0.0626420 0.233783i −0.927506 0.373808i \(-0.878052\pi\)
0.990148 + 0.140025i \(0.0447184\pi\)
\(174\) 0 0
\(175\) 2.00294 3.46919i 0.151408 0.262246i
\(176\) 0 0
\(177\) 8.54387 1.17827i 0.642197 0.0885642i
\(178\) 0 0
\(179\) 3.73648 + 3.73648i 0.279278 + 0.279278i 0.832821 0.553543i \(-0.186725\pi\)
−0.553543 + 0.832821i \(0.686725\pi\)
\(180\) 0 0
\(181\) 0.169132 0.169132i 0.0125715 0.0125715i −0.700793 0.713365i \(-0.747170\pi\)
0.713365 + 0.700793i \(0.247170\pi\)
\(182\) 0 0
\(183\) −16.4918 6.71271i −1.21911 0.496218i
\(184\) 0 0
\(185\) −7.84414 4.52882i −0.576713 0.332965i
\(186\) 0 0
\(187\) 9.76578 + 2.61673i 0.714145 + 0.191354i
\(188\) 0 0
\(189\) 1.02198 + 6.79274i 0.0743383 + 0.494099i
\(190\) 0 0
\(191\) −11.0451 19.1306i −0.799194 1.38424i −0.920142 0.391586i \(-0.871927\pi\)
0.120947 0.992659i \(-0.461407\pi\)
\(192\) 0 0
\(193\) 7.90683 13.6950i 0.569146 0.985790i −0.427505 0.904013i \(-0.640607\pi\)
0.996651 0.0817767i \(-0.0260594\pi\)
\(194\) 0 0
\(195\) 15.7659 6.64423i 1.12902 0.475803i
\(196\) 0 0
\(197\) 1.19611 1.19611i 0.0852196 0.0852196i −0.663212 0.748432i \(-0.730807\pi\)
0.748432 + 0.663212i \(0.230807\pi\)
\(198\) 0 0
\(199\) 6.39170i 0.453095i 0.974000 + 0.226548i \(0.0727439\pi\)
−0.974000 + 0.226548i \(0.927256\pi\)
\(200\) 0 0
\(201\) −3.41187 24.7402i −0.240655 1.74504i
\(202\) 0 0
\(203\) 1.25628 + 4.68849i 0.0881734 + 0.329068i
\(204\) 0 0
\(205\) 1.20523 4.49796i 0.0841766 0.314151i
\(206\) 0 0
\(207\) 8.58090 + 8.37256i 0.596414 + 0.581933i
\(208\) 0 0
\(209\) 4.06233 + 7.03617i 0.280997 + 0.486702i
\(210\) 0 0
\(211\) 2.01376 0.539586i 0.138633 0.0371466i −0.188835 0.982009i \(-0.560471\pi\)
0.327468 + 0.944862i \(0.393805\pi\)
\(212\) 0 0
\(213\) −13.5339 1.69724i −0.927324 0.116293i
\(214\) 0 0
\(215\) 18.1135i 1.23533i
\(216\) 0 0
\(217\) 1.50475i 0.102149i
\(218\) 0 0
\(219\) 0.992008 + 0.124405i 0.0670337 + 0.00840649i
\(220\) 0 0
\(221\) −25.6149 + 6.86349i −1.72304 + 0.461688i
\(222\) 0 0
\(223\) −13.6496 23.6417i −0.914042 1.58317i −0.808297 0.588775i \(-0.799611\pi\)
−0.105745 0.994393i \(-0.533723\pi\)
\(224\) 0 0
\(225\) 8.75131 2.46055i 0.583421 0.164037i
\(226\) 0 0
\(227\) 0.752368 2.80787i 0.0499364 0.186365i −0.936452 0.350794i \(-0.885912\pi\)
0.986389 + 0.164429i \(0.0525782\pi\)
\(228\) 0 0
\(229\) 1.73787 + 6.48583i 0.114842 + 0.428596i 0.999275 0.0380710i \(-0.0121213\pi\)
−0.884433 + 0.466667i \(0.845455\pi\)
\(230\) 0 0
\(231\) 0.415712 + 3.01441i 0.0273518 + 0.198333i
\(232\) 0 0
\(233\) 11.8159i 0.774086i 0.922062 + 0.387043i \(0.126503\pi\)
−0.922062 + 0.387043i \(0.873497\pi\)
\(234\) 0 0
\(235\) −18.3839 + 18.3839i −1.19923 + 1.19923i
\(236\) 0 0
\(237\) 2.28846 0.964426i 0.148651 0.0626462i
\(238\) 0 0
\(239\) 1.75364 3.03739i 0.113433 0.196472i −0.803719 0.595009i \(-0.797148\pi\)
0.917152 + 0.398537i \(0.130482\pi\)
\(240\) 0 0
\(241\) −4.35635 7.54543i −0.280617 0.486044i 0.690920 0.722932i \(-0.257206\pi\)
−0.971537 + 0.236888i \(0.923873\pi\)
\(242\) 0 0
\(243\) −9.10531 + 12.6528i −0.584106 + 0.811678i
\(244\) 0 0
\(245\) 14.3768 + 3.85226i 0.918502 + 0.246112i
\(246\) 0 0
\(247\) −18.4553 10.6552i −1.17428 0.677973i
\(248\) 0 0
\(249\) 5.48765 + 2.23366i 0.347766 + 0.141552i
\(250\) 0 0
\(251\) 9.70213 9.70213i 0.612393 0.612393i −0.331176 0.943569i \(-0.607445\pi\)
0.943569 + 0.331176i \(0.107445\pi\)
\(252\) 0 0
\(253\) 3.75533 + 3.75533i 0.236096 + 0.236096i
\(254\) 0 0
\(255\) −36.9903 + 5.10127i −2.31642 + 0.319454i
\(256\) 0 0
\(257\) −9.26857 + 16.0536i −0.578158 + 1.00140i 0.417533 + 0.908662i \(0.362895\pi\)
−0.995691 + 0.0927366i \(0.970439\pi\)
\(258\) 0 0
\(259\) −1.09363 + 4.08149i −0.0679550 + 0.253611i
\(260\) 0 0
\(261\) −5.38990 + 9.60628i −0.333626 + 0.594614i
\(262\) 0 0
\(263\) 3.42692 1.97853i 0.211313 0.122002i −0.390608 0.920557i \(-0.627735\pi\)
0.601922 + 0.798555i \(0.294402\pi\)
\(264\) 0 0
\(265\) −26.8008 15.4734i −1.64636 0.950525i
\(266\) 0 0
\(267\) −27.8608 3.49393i −1.70505 0.213825i
\(268\) 0 0
\(269\) 17.6742 + 17.6742i 1.07762 + 1.07762i 0.996723 + 0.0808951i \(0.0257779\pi\)
0.0808951 + 0.996723i \(0.474222\pi\)
\(270\) 0 0
\(271\) 26.9563 1.63748 0.818738 0.574167i \(-0.194674\pi\)
0.818738 + 0.574167i \(0.194674\pi\)
\(272\) 0 0
\(273\) −4.89758 6.30209i −0.296415 0.381420i
\(274\) 0 0
\(275\) 3.88979 1.04226i 0.234563 0.0628509i
\(276\) 0 0
\(277\) −9.24514 2.47723i −0.555487 0.148842i −0.0298548 0.999554i \(-0.509504\pi\)
−0.525632 + 0.850712i \(0.676171\pi\)
\(278\) 0 0
\(279\) 2.38476 2.44410i 0.142772 0.146324i
\(280\) 0 0
\(281\) −8.51476 + 4.91600i −0.507948 + 0.293264i −0.731990 0.681316i \(-0.761408\pi\)
0.224042 + 0.974580i \(0.428075\pi\)
\(282\) 0 0
\(283\) −8.06496 30.0988i −0.479412 1.78919i −0.604003 0.796982i \(-0.706428\pi\)
0.124591 0.992208i \(-0.460238\pi\)
\(284\) 0 0
\(285\) −23.9179 18.1204i −1.41677 1.07336i
\(286\) 0 0
\(287\) −2.17236 −0.128231
\(288\) 0 0
\(289\) 40.8774 2.40456
\(290\) 0 0
\(291\) 2.07152 0.873002i 0.121435 0.0511763i
\(292\) 0 0
\(293\) −8.20472 30.6204i −0.479325 1.78886i −0.604360 0.796711i \(-0.706571\pi\)
0.125035 0.992152i \(-0.460096\pi\)
\(294\) 0 0
\(295\) −12.2202 + 7.05535i −0.711489 + 0.410778i
\(296\) 0 0
\(297\) −4.10207 + 5.55499i −0.238026 + 0.322333i
\(298\) 0 0
\(299\) −13.4553 3.60533i −0.778139 0.208502i
\(300\) 0 0
\(301\) −8.16220 + 2.18706i −0.470462 + 0.126060i
\(302\) 0 0
\(303\) 6.58374 16.1749i 0.378226 0.929225i
\(304\) 0 0
\(305\) 29.1313 1.66805
\(306\) 0 0
\(307\) −17.2513 17.2513i −0.984581 0.984581i 0.0153018 0.999883i \(-0.495129\pi\)
−0.999883 + 0.0153018i \(0.995129\pi\)
\(308\) 0 0
\(309\) −9.72059 + 12.8306i −0.552985 + 0.729906i
\(310\) 0 0
\(311\) −8.53625 4.92841i −0.484046 0.279464i 0.238055 0.971252i \(-0.423490\pi\)
−0.722101 + 0.691787i \(0.756824\pi\)
\(312\) 0 0
\(313\) 8.45774 4.88308i 0.478060 0.276008i −0.241548 0.970389i \(-0.577655\pi\)
0.719608 + 0.694381i \(0.244322\pi\)
\(314\) 0 0
\(315\) −5.73843 9.66305i −0.323324 0.544451i
\(316\) 0 0
\(317\) 3.43237 12.8098i 0.192781 0.719469i −0.800049 0.599935i \(-0.795193\pi\)
0.992830 0.119534i \(-0.0381401\pi\)
\(318\) 0 0
\(319\) −2.43974 + 4.22576i −0.136599 + 0.236597i
\(320\) 0 0
\(321\) −2.84834 3.66519i −0.158979 0.204571i
\(322\) 0 0
\(323\) 32.8879 + 32.8879i 1.82993 + 1.82993i
\(324\) 0 0
\(325\) −7.46883 + 7.46883i −0.414296 + 0.414296i
\(326\) 0 0
\(327\) 16.6966 12.9756i 0.923327 0.717550i
\(328\) 0 0
\(329\) 10.5037 + 6.06432i 0.579089 + 0.334337i
\(330\) 0 0
\(331\) 1.02314 + 0.274151i 0.0562371 + 0.0150687i 0.286828 0.957982i \(-0.407399\pi\)
−0.230591 + 0.973051i \(0.574066\pi\)
\(332\) 0 0
\(333\) −8.24476 + 4.89617i −0.451810 + 0.268308i
\(334\) 0 0
\(335\) 20.4299 + 35.3857i 1.11621 + 1.93332i
\(336\) 0 0
\(337\) −2.50387 + 4.33683i −0.136395 + 0.236242i −0.926129 0.377206i \(-0.876885\pi\)
0.789735 + 0.613448i \(0.210218\pi\)
\(338\) 0 0
\(339\) −4.69895 3.55998i −0.255212 0.193351i
\(340\) 0 0
\(341\) 1.06963 1.06963i 0.0579238 0.0579238i
\(342\) 0 0
\(343\) 16.1974i 0.874575i
\(344\) 0 0
\(345\) −18.1673 7.39470i −0.978094 0.398117i
\(346\) 0 0
\(347\) 1.57745 + 5.88711i 0.0846817 + 0.316036i 0.995254 0.0973140i \(-0.0310251\pi\)
−0.910572 + 0.413350i \(0.864358\pi\)
\(348\) 0 0
\(349\) 1.45289 5.42227i 0.0777715 0.290247i −0.916076 0.401005i \(-0.868661\pi\)
0.993847 + 0.110758i \(0.0353277\pi\)
\(350\) 0 0
\(351\) 2.03276 17.9980i 0.108501 0.960661i
\(352\) 0 0
\(353\) −5.06146 8.76671i −0.269395 0.466605i 0.699311 0.714817i \(-0.253490\pi\)
−0.968706 + 0.248212i \(0.920157\pi\)
\(354\) 0 0
\(355\) 21.5554 5.77576i 1.14404 0.306546i
\(356\) 0 0
\(357\) 6.76496 + 16.0524i 0.358040 + 0.849582i
\(358\) 0 0
\(359\) 5.28081i 0.278710i −0.990242 0.139355i \(-0.955497\pi\)
0.990242 0.139355i \(-0.0445030\pi\)
\(360\) 0 0
\(361\) 18.3761i 0.967163i
\(362\) 0 0
\(363\) 9.65813 12.7481i 0.506920 0.669104i
\(364\) 0 0
\(365\) −1.57998 + 0.423353i −0.0826997 + 0.0221593i
\(366\) 0 0
\(367\) −5.01941 8.69388i −0.262011 0.453817i 0.704765 0.709441i \(-0.251052\pi\)
−0.966776 + 0.255624i \(0.917719\pi\)
\(368\) 0 0
\(369\) −3.52847 3.44280i −0.183685 0.179225i
\(370\) 0 0
\(371\) −3.73657 + 13.9451i −0.193993 + 0.723992i
\(372\) 0 0
\(373\) −6.74869 25.1865i −0.349434 1.30411i −0.887346 0.461105i \(-0.847453\pi\)
0.537912 0.843001i \(-0.319213\pi\)
\(374\) 0 0
\(375\) 7.63395 5.93261i 0.394215 0.306359i
\(376\) 0 0
\(377\) 12.7985i 0.659157i
\(378\) 0 0
\(379\) 11.3259 11.3259i 0.581771 0.581771i −0.353619 0.935390i \(-0.615049\pi\)
0.935390 + 0.353619i \(0.115049\pi\)
\(380\) 0 0
\(381\) −1.13043 + 9.01407i −0.0579135 + 0.461805i
\(382\) 0 0
\(383\) −2.50076 + 4.33145i −0.127783 + 0.221327i −0.922817 0.385238i \(-0.874119\pi\)
0.795034 + 0.606564i \(0.207453\pi\)
\(384\) 0 0
\(385\) −2.48924 4.31148i −0.126863 0.219733i
\(386\) 0 0
\(387\) −16.7236 9.38328i −0.850107 0.476979i
\(388\) 0 0
\(389\) 12.9035 + 3.45749i 0.654235 + 0.175302i 0.570643 0.821198i \(-0.306694\pi\)
0.0835921 + 0.996500i \(0.473361\pi\)
\(390\) 0 0
\(391\) 26.3294 + 15.2013i 1.33153 + 0.768761i
\(392\) 0 0
\(393\) 1.53617 + 11.1391i 0.0774895 + 0.561892i
\(394\) 0 0
\(395\) −2.87297 + 2.87297i −0.144555 + 0.144555i
\(396\) 0 0
\(397\) −18.7165 18.7165i −0.939356 0.939356i 0.0589078 0.998263i \(-0.481238\pi\)
−0.998263 + 0.0589078i \(0.981238\pi\)
\(398\) 0 0
\(399\) −5.27743 + 12.9656i −0.264202 + 0.649092i
\(400\) 0 0
\(401\) 6.66124 11.5376i 0.332647 0.576161i −0.650383 0.759606i \(-0.725392\pi\)
0.983030 + 0.183445i \(0.0587250\pi\)
\(402\) 0 0
\(403\) −1.02691 + 3.83247i −0.0511538 + 0.190909i
\(404\) 0 0
\(405\) 5.99352 24.7896i 0.297820 1.23181i
\(406\) 0 0
\(407\) −3.67866 + 2.12388i −0.182345 + 0.105277i
\(408\) 0 0
\(409\) 10.6037 + 6.12206i 0.524320 + 0.302717i 0.738701 0.674034i \(-0.235440\pi\)
−0.214380 + 0.976750i \(0.568773\pi\)
\(410\) 0 0
\(411\) 4.78934 + 11.3645i 0.236241 + 0.560568i
\(412\) 0 0
\(413\) 4.65472 + 4.65472i 0.229044 + 0.229044i
\(414\) 0 0
\(415\) −9.69344 −0.475832
\(416\) 0 0
\(417\) −7.23206 + 0.997361i −0.354156 + 0.0488410i
\(418\) 0 0
\(419\) −32.0424 + 8.58573i −1.56537 + 0.419440i −0.934360 0.356332i \(-0.884027\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(420\) 0 0
\(421\) −24.7035 6.61930i −1.20398 0.322605i −0.399581 0.916698i \(-0.630844\pi\)
−0.804396 + 0.594093i \(0.797511\pi\)
\(422\) 0 0
\(423\) 7.44985 + 26.4965i 0.362224 + 1.28830i
\(424\) 0 0
\(425\) 19.9645 11.5265i 0.968421 0.559118i
\(426\) 0 0
\(427\) −3.51736 13.1269i −0.170217 0.635258i
\(428\) 0 0
\(429\) 0.998381 7.96113i 0.0482023 0.384367i
\(430\) 0 0
\(431\) 10.3041 0.496332 0.248166 0.968717i \(-0.420172\pi\)
0.248166 + 0.968717i \(0.420172\pi\)
\(432\) 0 0
\(433\) −11.7692 −0.565591 −0.282795 0.959180i \(-0.591262\pi\)
−0.282795 + 0.959180i \(0.591262\pi\)
\(434\) 0 0
\(435\) 2.24245 17.8814i 0.107517 0.857347i
\(436\) 0 0
\(437\) 6.32337 + 23.5991i 0.302488 + 1.12890i
\(438\) 0 0
\(439\) −23.9893 + 13.8502i −1.14494 + 0.661034i −0.947650 0.319310i \(-0.896549\pi\)
−0.197294 + 0.980344i \(0.563215\pi\)
\(440\) 0 0
\(441\) 11.0042 11.2780i 0.524011 0.537050i
\(442\) 0 0
\(443\) 24.2836 + 6.50677i 1.15375 + 0.309146i 0.784466 0.620172i \(-0.212937\pi\)
0.369282 + 0.929317i \(0.379604\pi\)
\(444\) 0 0
\(445\) 44.3739 11.8900i 2.10353 0.563638i
\(446\) 0 0
\(447\) −14.9385 + 2.06014i −0.706567 + 0.0974413i
\(448\) 0 0
\(449\) −20.0988 −0.948522 −0.474261 0.880384i \(-0.657285\pi\)
−0.474261 + 0.880384i \(0.657285\pi\)
\(450\) 0 0
\(451\) −1.54419 1.54419i −0.0727133 0.0727133i
\(452\) 0 0
\(453\) 13.8334 + 32.8248i 0.649949 + 1.54225i
\(454\) 0 0
\(455\) 11.3087 + 6.52907i 0.530159 + 0.306088i
\(456\) 0 0
\(457\) 20.8270 12.0245i 0.974244 0.562480i 0.0737167 0.997279i \(-0.476514\pi\)
0.900527 + 0.434799i \(0.143181\pi\)
\(458\) 0 0
\(459\) −14.4521 + 36.7944i −0.674566 + 1.71742i
\(460\) 0 0
\(461\) 1.04759 3.90967i 0.0487913 0.182092i −0.937230 0.348713i \(-0.886619\pi\)
0.986021 + 0.166621i \(0.0532856\pi\)
\(462\) 0 0
\(463\) −5.16489 + 8.94585i −0.240033 + 0.415749i −0.960723 0.277508i \(-0.910492\pi\)
0.720691 + 0.693257i \(0.243825\pi\)
\(464\) 0 0
\(465\) −2.10623 + 5.17459i −0.0976741 + 0.239966i
\(466\) 0 0
\(467\) −11.8966 11.8966i −0.550509 0.550509i 0.376079 0.926588i \(-0.377272\pi\)
−0.926588 + 0.376079i \(0.877272\pi\)
\(468\) 0 0
\(469\) 13.4785 13.4785i 0.622380 0.622380i
\(470\) 0 0
\(471\) 2.18240 + 15.8250i 0.100560 + 0.729179i
\(472\) 0 0
\(473\) −7.35663 4.24735i −0.338258 0.195293i
\(474\) 0 0
\(475\) 17.8943 + 4.79476i 0.821046 + 0.219999i
\(476\) 0 0
\(477\) −28.1695 + 16.7286i −1.28980 + 0.765948i
\(478\) 0 0
\(479\) 7.47878 + 12.9536i 0.341714 + 0.591866i 0.984751 0.173969i \(-0.0556593\pi\)
−0.643037 + 0.765835i \(0.722326\pi\)
\(480\) 0 0
\(481\) 5.57077 9.64886i 0.254005 0.439950i
\(482\) 0 0
\(483\) −1.13860 + 9.07927i −0.0518082 + 0.413121i
\(484\) 0 0
\(485\) −2.60062 + 2.60062i −0.118088 + 0.118088i
\(486\) 0 0
\(487\) 27.0362i 1.22513i −0.790420 0.612565i \(-0.790138\pi\)
0.790420 0.612565i \(-0.209862\pi\)
\(488\) 0 0
\(489\) −20.1250 + 15.6398i −0.910082 + 0.707257i
\(490\) 0 0
\(491\) 1.45189 + 5.41853i 0.0655229 + 0.244535i 0.990918 0.134470i \(-0.0429331\pi\)
−0.925395 + 0.379005i \(0.876266\pi\)
\(492\) 0 0
\(493\) −7.22964 + 26.9814i −0.325607 + 1.21518i
\(494\) 0 0
\(495\) 2.78977 10.9479i 0.125391 0.492073i
\(496\) 0 0
\(497\) −5.20527 9.01579i −0.233488 0.404413i
\(498\) 0 0
\(499\) 21.2035 5.68146i 0.949198 0.254337i 0.249176 0.968458i \(-0.419840\pi\)
0.700022 + 0.714121i \(0.253174\pi\)
\(500\) 0 0
\(501\) 7.19085 9.49148i 0.321264 0.424048i
\(502\) 0 0
\(503\) 23.1955i 1.03423i 0.855915 + 0.517117i \(0.172995\pi\)
−0.855915 + 0.517117i \(0.827005\pi\)
\(504\) 0 0
\(505\) 28.5716i 1.27142i
\(506\) 0 0
\(507\) −0.571523 1.35615i −0.0253822 0.0602288i
\(508\) 0 0
\(509\) 12.5788 3.37049i 0.557547 0.149394i 0.0309681 0.999520i \(-0.490141\pi\)
0.526579 + 0.850126i \(0.323474\pi\)
\(510\) 0 0
\(511\) 0.381537 + 0.660842i 0.0168782 + 0.0292339i
\(512\) 0 0
\(513\) −29.1200 + 12.6957i −1.28568 + 0.560527i
\(514\) 0 0
\(515\) 6.81623 25.4385i 0.300359 1.12095i
\(516\) 0 0
\(517\) 3.15568 + 11.7772i 0.138787 + 0.517959i
\(518\) 0 0
\(519\) 5.10698 + 2.07871i 0.224171 + 0.0912453i
\(520\) 0 0
\(521\) 21.4547i 0.939949i −0.882680 0.469974i \(-0.844263\pi\)
0.882680 0.469974i \(-0.155737\pi\)
\(522\) 0 0
\(523\) −2.07495 + 2.07495i −0.0907314 + 0.0907314i −0.751016 0.660284i \(-0.770436\pi\)
0.660284 + 0.751016i \(0.270436\pi\)
\(524\) 0 0
\(525\) 5.53043 + 4.18992i 0.241368 + 0.182863i
\(526\) 0 0
\(527\) 4.32977 7.49939i 0.188608 0.326678i
\(528\) 0 0
\(529\) −3.51490 6.08799i −0.152822 0.264695i
\(530\) 0 0
\(531\) 0.183562 + 14.9374i 0.00796593 + 0.648226i
\(532\) 0 0
\(533\) 5.53282 + 1.48251i 0.239653 + 0.0642148i
\(534\) 0 0
\(535\) 6.57693 + 3.79719i 0.284346 + 0.164167i
\(536\) 0 0
\(537\) −7.22677 + 5.61618i −0.311858 + 0.242356i
\(538\) 0 0
\(539\) 4.93571 4.93571i 0.212596 0.212596i
\(540\) 0 0
\(541\) 22.7947 + 22.7947i 0.980022 + 0.980022i 0.999804 0.0197819i \(-0.00629719\pi\)
−0.0197819 + 0.999804i \(0.506297\pi\)
\(542\) 0 0
\(543\) 0.254217 + 0.327121i 0.0109095 + 0.0140381i
\(544\) 0 0
\(545\) −17.2980 + 29.9610i −0.740965 + 1.28339i
\(546\) 0 0
\(547\) 3.58528 13.3804i 0.153295 0.572106i −0.845950 0.533262i \(-0.820966\pi\)
0.999245 0.0388438i \(-0.0123675\pi\)
\(548\) 0 0
\(549\) 15.0908 26.8959i 0.644058 1.14789i
\(550\) 0 0
\(551\) −19.4399 + 11.2236i −0.828166 + 0.478142i
\(552\) 0 0
\(553\) 1.64148 + 0.947711i 0.0698030 + 0.0403008i
\(554\) 0 0
\(555\) 9.47377 12.5048i 0.402139 0.530799i
\(556\) 0 0
\(557\) −8.62660 8.62660i −0.365521 0.365521i 0.500320 0.865841i \(-0.333216\pi\)
−0.865841 + 0.500320i \(0.833216\pi\)
\(558\) 0 0
\(559\) 22.2810 0.942384
\(560\) 0 0
\(561\) −6.60184 + 16.2194i −0.278730 + 0.684784i
\(562\) 0 0
\(563\) −20.3923 + 5.46409i −0.859432 + 0.230284i −0.661513 0.749934i \(-0.730085\pi\)
−0.197920 + 0.980218i \(0.563418\pi\)
\(564\) 0 0
\(565\) 9.31636 + 2.49631i 0.391942 + 0.105021i
\(566\) 0 0
\(567\) −11.8942 + 0.292376i −0.499509 + 0.0122786i
\(568\) 0 0
\(569\) −21.4776 + 12.4001i −0.900389 + 0.519840i −0.877326 0.479894i \(-0.840675\pi\)
−0.0230625 + 0.999734i \(0.507342\pi\)
\(570\) 0 0
\(571\) 4.74438 + 17.7063i 0.198546 + 0.740985i 0.991320 + 0.131469i \(0.0419694\pi\)
−0.792774 + 0.609516i \(0.791364\pi\)
\(572\) 0 0
\(573\) 35.2582 14.8589i 1.47293 0.620738i
\(574\) 0 0
\(575\) 12.1096 0.505004
\(576\) 0 0
\(577\) −23.4462 −0.976078 −0.488039 0.872822i \(-0.662288\pi\)
−0.488039 + 0.872822i \(0.662288\pi\)
\(578\) 0 0
\(579\) 21.8320 + 16.5402i 0.907308 + 0.687387i
\(580\) 0 0
\(581\) 1.17040 + 4.36800i 0.0485564 + 0.181215i
\(582\) 0 0
\(583\) −12.5688 + 7.25657i −0.520545 + 0.300537i
\(584\) 0 0
\(585\) 8.02079 + 28.5271i 0.331619 + 1.17945i
\(586\) 0 0
\(587\) 16.1657 + 4.33159i 0.667230 + 0.178784i 0.576507 0.817092i \(-0.304415\pi\)
0.0907235 + 0.995876i \(0.471082\pi\)
\(588\) 0 0
\(589\) 6.72173 1.80108i 0.276964 0.0742123i
\(590\) 0 0
\(591\) 1.79784 + 2.31342i 0.0739532 + 0.0951613i
\(592\) 0 0
\(593\) 6.18675 0.254059 0.127030 0.991899i \(-0.459456\pi\)
0.127030 + 0.991899i \(0.459456\pi\)
\(594\) 0 0
\(595\) −20.1524 20.1524i −0.826168 0.826168i
\(596\) 0 0
\(597\) −10.9847 1.37756i −0.449574 0.0563797i
\(598\) 0 0
\(599\) 7.98730 + 4.61147i 0.326352 + 0.188420i 0.654220 0.756304i \(-0.272997\pi\)
−0.327868 + 0.944723i \(0.606330\pi\)
\(600\) 0 0
\(601\) 15.0097 8.66586i 0.612259 0.353488i −0.161590 0.986858i \(-0.551662\pi\)
0.773849 + 0.633370i \(0.218329\pi\)
\(602\) 0 0
\(603\) 43.2535 0.531535i 1.76142 0.0216458i
\(604\) 0 0
\(605\) −6.77243 + 25.2751i −0.275339 + 1.02758i
\(606\) 0 0
\(607\) −11.8418 + 20.5106i −0.480643 + 0.832498i −0.999753 0.0222090i \(-0.992930\pi\)
0.519110 + 0.854707i \(0.326263\pi\)
\(608\) 0 0
\(609\) −8.32835 + 1.14855i −0.337482 + 0.0465415i
\(610\) 0 0
\(611\) −22.6135 22.6135i −0.914844 0.914844i
\(612\) 0 0
\(613\) 15.4110 15.4110i 0.622445 0.622445i −0.323711 0.946156i \(-0.604930\pi\)
0.946156 + 0.323711i \(0.104930\pi\)
\(614\) 0 0
\(615\) 7.47040 + 3.04070i 0.301236 + 0.122613i
\(616\) 0 0
\(617\) 11.9979 + 6.92700i 0.483018 + 0.278870i 0.721673 0.692234i \(-0.243373\pi\)
−0.238655 + 0.971104i \(0.576707\pi\)
\(618\) 0 0
\(619\) −38.6333 10.3518i −1.55280 0.416072i −0.622427 0.782678i \(-0.713853\pi\)
−0.930376 + 0.366606i \(0.880520\pi\)
\(620\) 0 0
\(621\) −16.2384 + 12.9426i −0.651624 + 0.519367i
\(622\) 0 0
\(623\) −10.7156 18.5599i −0.429310 0.743586i
\(624\) 0 0
\(625\) −15.4844 + 26.8198i −0.619377 + 1.07279i
\(626\) 0 0
\(627\) −12.9678 + 5.46503i −0.517884 + 0.218252i
\(628\) 0 0
\(629\) −17.1945 + 17.1945i −0.685591 + 0.685591i
\(630\) 0 0
\(631\) 16.7956i 0.668624i 0.942462 + 0.334312i \(0.108504\pi\)
−0.942462 + 0.334312i \(0.891496\pi\)
\(632\) 0 0
\(633\) 0.493315 + 3.57712i 0.0196075 + 0.142178i
\(634\) 0 0
\(635\) −3.84688 14.3567i −0.152659 0.569730i
\(636\) 0 0
\(637\) −4.73856 + 17.6845i −0.187749 + 0.700687i
\(638\) 0 0
\(639\) 5.83371 22.8933i 0.230778 0.905647i
\(640\) 0 0
\(641\) 20.0246 + 34.6837i 0.790925 + 1.36992i 0.925395 + 0.379005i \(0.123734\pi\)
−0.134470 + 0.990918i \(0.542933\pi\)
\(642\) 0 0
\(643\) −1.07859 + 0.289008i −0.0425356 + 0.0113974i −0.280024 0.959993i \(-0.590342\pi\)
0.237489 + 0.971390i \(0.423676\pi\)
\(644\) 0 0
\(645\) 31.1297 + 3.90388i 1.22573 + 0.153715i
\(646\) 0 0
\(647\) 31.9272i 1.25519i 0.778541 + 0.627594i \(0.215960\pi\)
−0.778541 + 0.627594i \(0.784040\pi\)
\(648\) 0 0
\(649\) 6.61750i 0.259759i
\(650\) 0 0
\(651\) 2.58605 + 0.324308i 0.101355 + 0.0127106i
\(652\) 0 0
\(653\) 12.5651 3.36682i 0.491712 0.131754i −0.00443888 0.999990i \(-0.501413\pi\)
0.496151 + 0.868236i \(0.334746\pi\)
\(654\) 0 0
\(655\) −9.19841 15.9321i −0.359412 0.622519i
\(656\) 0 0
\(657\) −0.427601 + 1.67804i −0.0166823 + 0.0654667i
\(658\) 0 0
\(659\) 4.15007 15.4883i 0.161664 0.603337i −0.836779 0.547541i \(-0.815564\pi\)
0.998442 0.0557954i \(-0.0177695\pi\)
\(660\) 0 0
\(661\) −5.89283 21.9923i −0.229204 0.855403i −0.980676 0.195637i \(-0.937322\pi\)
0.751472 0.659765i \(-0.229344\pi\)
\(662\) 0 0
\(663\) −6.27493 45.5007i −0.243698 1.76710i
\(664\) 0 0
\(665\) 22.9026i 0.888124i
\(666\) 0 0
\(667\) −10.3754 + 10.3754i −0.401738 + 0.401738i
\(668\) 0 0
\(669\) 43.5722 18.3627i 1.68460 0.709941i
\(670\) 0 0
\(671\) 6.83085 11.8314i 0.263702 0.456745i
\(672\) 0 0
\(673\) 16.3212 + 28.2692i 0.629136 + 1.08970i 0.987725 + 0.156201i \(0.0499246\pi\)
−0.358589 + 0.933496i \(0.616742\pi\)
\(674\) 0 0
\(675\) 2.34257 + 15.5702i 0.0901656 + 0.599298i
\(676\) 0 0
\(677\) −14.3681 3.84993i −0.552212 0.147965i −0.0280861 0.999606i \(-0.508941\pi\)
−0.524126 + 0.851641i \(0.675608\pi\)
\(678\) 0 0
\(679\) 1.48588 + 0.857871i 0.0570227 + 0.0329221i
\(680\) 0 0
\(681\) 4.66343 + 1.89817i 0.178703 + 0.0727381i
\(682\) 0 0
\(683\) −21.4912 + 21.4912i −0.822338 + 0.822338i −0.986443 0.164105i \(-0.947526\pi\)
0.164105 + 0.986443i \(0.447526\pi\)
\(684\) 0 0
\(685\) −14.2671 14.2671i −0.545120 0.545120i
\(686\) 0 0
\(687\) −11.5210 + 1.58885i −0.439555 + 0.0606183i
\(688\) 0 0
\(689\) 19.0334 32.9669i 0.725116 1.25594i
\(690\) 0 0
\(691\) −2.36807 + 8.83775i −0.0900855 + 0.336204i −0.996229 0.0867676i \(-0.972346\pi\)
0.906143 + 0.422971i \(0.139013\pi\)
\(692\) 0 0
\(693\) −5.27012 + 0.0647636i −0.200195 + 0.00246017i
\(694\) 0 0
\(695\) 10.3440 5.97209i 0.392369 0.226534i
\(696\) 0 0
\(697\) −10.8266 6.25077i −0.410088 0.236765i
\(698\) 0 0
\(699\) −20.3067 2.54660i −0.768070 0.0963212i
\(700\) 0 0
\(701\) −4.05144 4.05144i −0.153021 0.153021i 0.626445 0.779466i \(-0.284509\pi\)
−0.779466 + 0.626445i \(0.784509\pi\)
\(702\) 0 0
\(703\) −19.5411 −0.737005
\(704\) 0 0
\(705\) −27.6322 35.5565i −1.04069 1.33913i
\(706\) 0 0
\(707\) 12.8747 3.44978i 0.484204 0.129742i
\(708\) 0 0
\(709\) 3.76098 + 1.00775i 0.141247 + 0.0378469i 0.328750 0.944417i \(-0.393373\pi\)
−0.187503 + 0.982264i \(0.560039\pi\)
\(710\) 0 0
\(711\) 1.16424 + 4.14078i 0.0436623 + 0.155291i
\(712\) 0 0
\(713\) 3.93936 2.27439i 0.147530 0.0851767i
\(714\) 0 0
\(715\) 3.39752 + 12.6797i 0.127060 + 0.474195i
\(716\) 0 0
\(717\) 4.84208 + 3.66841i 0.180831 + 0.136999i
\(718\) 0 0
\(719\) 37.0063 1.38010 0.690050 0.723761i \(-0.257588\pi\)
0.690050 + 0.723761i \(0.257588\pi\)
\(720\) 0 0
\(721\) −12.2859 −0.457552
\(722\) 0 0
\(723\) 13.9064 5.86057i 0.517184 0.217957i
\(724\) 0 0
\(725\) 2.87962 + 10.7469i 0.106946 + 0.399129i
\(726\) 0 0
\(727\) 28.4066 16.4006i 1.05354 0.608264i 0.129905 0.991526i \(-0.458533\pi\)
0.923640 + 0.383262i \(0.125199\pi\)
\(728\) 0 0
\(729\) −19.7826 18.3753i −0.732688 0.680565i
\(730\) 0 0
\(731\) −46.9719 12.5861i −1.73732 0.465513i
\(732\) 0 0
\(733\) −40.9566 + 10.9743i −1.51277 + 0.405345i −0.917353 0.398075i \(-0.869678\pi\)
−0.595413 + 0.803419i \(0.703012\pi\)
\(734\) 0 0
\(735\) −9.71899 + 23.8776i −0.358490 + 0.880740i
\(736\) 0 0
\(737\) 19.1620 0.705842
\(738\) 0 0
\(739\) 15.3761 + 15.3761i 0.565620 + 0.565620i 0.930898 0.365278i \(-0.119026\pi\)
−0.365278 + 0.930898i \(0.619026\pi\)
\(740\) 0 0
\(741\) 22.2894 29.4207i 0.818823 1.08080i
\(742\) 0 0
\(743\) 40.4824 + 23.3725i 1.48516 + 0.857456i 0.999857 0.0168926i \(-0.00537734\pi\)
0.485299 + 0.874348i \(0.338711\pi\)
\(744\) 0 0
\(745\) 21.3664 12.3359i 0.782805 0.451952i
\(746\) 0 0
\(747\) −5.02145 + 8.94961i −0.183725 + 0.327449i
\(748\) 0 0
\(749\) 0.916958 3.42213i 0.0335049 0.125042i
\(750\) 0 0
\(751\) −25.7074 + 44.5265i −0.938077 + 1.62480i −0.169023 + 0.985612i \(0.554061\pi\)
−0.769054 + 0.639184i \(0.779272\pi\)
\(752\) 0 0
\(753\) 14.5829 + 18.7650i 0.531432 + 0.683835i
\(754\) 0 0
\(755\) −41.2088 41.2088i −1.49974 1.49974i
\(756\) 0 0
\(757\) 25.4143 25.4143i 0.923698 0.923698i −0.0735910 0.997289i \(-0.523446\pi\)
0.997289 + 0.0735910i \(0.0234459\pi\)
\(758\) 0 0
\(759\) −7.26324 + 5.64452i −0.263639 + 0.204883i
\(760\) 0 0
\(761\) −20.2336 11.6819i −0.733467 0.423467i 0.0862220 0.996276i \(-0.472521\pi\)
−0.819689 + 0.572808i \(0.805854\pi\)
\(762\) 0 0
\(763\) 15.5894 + 4.17717i 0.564375 + 0.151224i
\(764\) 0 0
\(765\) −0.794725 64.6706i −0.0287334 2.33817i
\(766\) 0 0
\(767\) −8.67859 15.0318i −0.313366 0.542765i
\(768\) 0 0
\(769\) −12.7645 + 22.1087i −0.460299 + 0.797261i −0.998976 0.0452513i \(-0.985591\pi\)
0.538677 + 0.842513i \(0.318924\pi\)
\(770\) 0 0
\(771\) −25.5920 19.3888i −0.921674 0.698270i
\(772\) 0 0
\(773\) −19.2256 + 19.2256i −0.691496 + 0.691496i −0.962561 0.271065i \(-0.912624\pi\)
0.271065 + 0.962561i \(0.412624\pi\)
\(774\) 0 0
\(775\) 3.44916i 0.123898i
\(776\) 0 0
\(777\) −6.77870 2.75916i −0.243185 0.0989843i
\(778\) 0 0
\(779\) −2.60017 9.70397i −0.0931608 0.347681i
\(780\) 0 0
\(781\) 2.70866 10.1088i 0.0969234 0.361723i
\(782\) 0 0
\(783\) −15.3476 11.3334i −0.548479 0.405022i
\(784\) 0 0
\(785\) −13.0680 22.6344i −0.466416 0.807857i
\(786\) 0 0
\(787\) 19.2671 5.16260i 0.686797 0.184027i 0.101488 0.994837i \(-0.467640\pi\)
0.585309 + 0.810810i \(0.300973\pi\)
\(788\) 0 0
\(789\) 2.66171 + 6.31589i 0.0947593 + 0.224852i
\(790\) 0 0
\(791\) 4.49949i 0.159983i
\(792\) 0 0
\(793\) 35.8336i 1.27249i
\(794\) 0 0
\(795\) 32.3687 42.7246i 1.14800 1.51529i
\(796\) 0 0
\(797\) 11.2772 3.02171i 0.399458 0.107035i −0.0534965 0.998568i \(-0.517037\pi\)
0.452955 + 0.891534i \(0.350370\pi\)
\(798\) 0 0
\(799\) 34.8990 + 60.4469i 1.23464 + 2.13846i
\(800\) 0 0
\(801\) 12.0093 47.1282i 0.424326 1.66519i
\(802\) 0 0
\(803\) −0.198540 + 0.740961i −0.00700632 + 0.0261479i
\(804\) 0 0
\(805\) −3.87471 14.4606i −0.136565 0.509669i
\(806\) 0 0
\(807\) −34.1840 + 26.5656i −1.20333 + 0.935152i
\(808\) 0 0
\(809\) 13.1110i 0.460958i 0.973077 + 0.230479i \(0.0740292\pi\)
−0.973077 + 0.230479i \(0.925971\pi\)
\(810\) 0 0
\(811\) 34.1945 34.1945i 1.20073 1.20073i 0.226789 0.973944i \(-0.427177\pi\)
0.973944 0.226789i \(-0.0728227\pi\)
\(812\) 0 0
\(813\) −5.80969 + 46.3267i −0.203755 + 1.62475i
\(814\) 0 0
\(815\) 20.8498 36.1129i 0.730337 1.26498i
\(816\) 0 0
\(817\) −19.5392 33.8429i −0.683590 1.18401i
\(818\) 0 0
\(819\) 11.8862 7.05868i 0.415339 0.246650i
\(820\) 0 0
\(821\) −23.8714 6.39631i −0.833116 0.223233i −0.183044 0.983105i \(-0.558595\pi\)
−0.650073 + 0.759872i \(0.725262\pi\)
\(822\) 0 0
\(823\) −16.2152 9.36184i −0.565226 0.326333i 0.190014 0.981781i \(-0.439147\pi\)
−0.755240 + 0.655448i \(0.772480\pi\)
\(824\) 0 0
\(825\) 0.952888 + 6.90958i 0.0331753 + 0.240561i
\(826\) 0 0
\(827\) 24.1212 24.1212i 0.838775 0.838775i −0.149923 0.988698i \(-0.547902\pi\)
0.988698 + 0.149923i \(0.0479025\pi\)
\(828\) 0 0
\(829\) −20.8683 20.8683i −0.724787 0.724787i 0.244789 0.969576i \(-0.421281\pi\)
−0.969576 + 0.244789i \(0.921281\pi\)
\(830\) 0 0
\(831\) 6.24988 15.3547i 0.216806 0.532649i
\(832\) 0 0
\(833\) 19.9793 34.6052i 0.692242 1.19900i
\(834\) 0 0
\(835\) −5.04234 + 18.8183i −0.174497 + 0.651233i
\(836\) 0 0
\(837\) 3.68643 + 4.62517i 0.127422 + 0.159869i
\(838\) 0 0
\(839\) −5.01977 + 2.89816i −0.173302 + 0.100056i −0.584142 0.811652i \(-0.698569\pi\)
0.410840 + 0.911707i \(0.365235\pi\)
\(840\) 0 0
\(841\) 13.4396 + 7.75936i 0.463435 + 0.267564i
\(842\) 0 0
\(843\) −6.61346 15.6929i −0.227780 0.540492i
\(844\) 0 0
\(845\) 1.70253 + 1.70253i 0.0585689 + 0.0585689i
\(846\) 0 0
\(847\) 12.2070 0.419437
\(848\) 0 0
\(849\) 53.4657 7.37337i 1.83494 0.253053i
\(850\) 0 0
\(851\) −12.3381 + 3.30600i −0.422946 + 0.113328i
\(852\) 0 0
\(853\) 1.72171 + 0.461332i 0.0589504 + 0.0157957i 0.288174 0.957578i \(-0.406952\pi\)
−0.229223 + 0.973374i \(0.573619\pi\)
\(854\) 0 0
\(855\) 36.2964 37.1996i 1.24131 1.27220i
\(856\) 0 0
\(857\) −12.6918 + 7.32760i −0.433543 + 0.250306i −0.700855 0.713304i \(-0.747198\pi\)
0.267312 + 0.963610i \(0.413865\pi\)
\(858\) 0 0
\(859\) −13.7688 51.3859i −0.469786 1.75327i −0.640513 0.767947i \(-0.721278\pi\)
0.170727 0.985318i \(-0.445388\pi\)
\(860\) 0 0
\(861\) 0.468194 3.73340i 0.0159560 0.127234i
\(862\) 0 0
\(863\) −23.9467 −0.815157 −0.407578 0.913170i \(-0.633627\pi\)
−0.407578 + 0.913170i \(0.633627\pi\)
\(864\) 0 0
\(865\) −9.02103 −0.306724
\(866\) 0 0
\(867\) −8.81003 + 70.2515i −0.299204 + 2.38587i
\(868\) 0 0
\(869\) 0.493159 + 1.84049i 0.0167293 + 0.0624345i
\(870\) 0 0
\(871\) −43.5269 + 25.1303i −1.47485 + 0.851507i
\(872\) 0 0
\(873\) 1.05387 + 3.74825i 0.0356681 + 0.126859i
\(874\) 0 0
\(875\) 7.12771 + 1.90986i 0.240961 + 0.0645652i
\(876\) 0 0
\(877\) −39.7266 + 10.6447i −1.34147 + 0.359446i −0.856980 0.515349i \(-0.827662\pi\)
−0.484492 + 0.874796i \(0.660996\pi\)
\(878\) 0 0
\(879\) 54.3922 7.50114i 1.83460 0.253007i
\(880\) 0 0
\(881\) −41.2335 −1.38919 −0.694597 0.719399i \(-0.744417\pi\)
−0.694597 + 0.719399i \(0.744417\pi\)
\(882\) 0 0
\(883\) 11.9719 + 11.9719i 0.402885 + 0.402885i 0.879248 0.476364i \(-0.158045\pi\)
−0.476364 + 0.879248i \(0.658045\pi\)
\(884\) 0 0
\(885\) −9.49151 22.5221i −0.319054 0.757074i
\(886\) 0 0
\(887\) −26.7452 15.4413i −0.898016 0.518470i −0.0214599 0.999770i \(-0.506831\pi\)
−0.876556 + 0.481300i \(0.840165\pi\)
\(888\) 0 0
\(889\) −6.00486 + 3.46691i −0.201397 + 0.116276i
\(890\) 0 0
\(891\) −8.66266 8.24700i −0.290210 0.276285i
\(892\) 0 0
\(893\) −14.5172 + 54.1788i −0.485798 + 1.81302i
\(894\) 0 0
\(895\) 7.48706 12.9680i 0.250265 0.433471i
\(896\) 0 0
\(897\) 9.09601 22.3471i 0.303707 0.746147i
\(898\) 0 0
\(899\) 2.95523 + 2.95523i 0.0985624 + 0.0985624i
\(900\) 0 0
\(901\) −58.7480 + 58.7480i −1.95718 + 1.95718i
\(902\) 0 0
\(903\) −1.99951 14.4988i −0.0665395 0.482491i
\(904\) 0 0
\(905\) −0.586997 0.338903i −0.0195125 0.0112655i
\(906\) 0 0
\(907\) 26.7351 + 7.16365i 0.887725 + 0.237865i 0.673737 0.738971i \(-0.264688\pi\)
0.213988 + 0.976836i \(0.431355\pi\)
\(908\) 0 0
\(909\) 26.3791 + 14.8008i 0.874940 + 0.490912i
\(910\) 0 0
\(911\) 4.83009 + 8.36596i 0.160028 + 0.277177i 0.934878 0.354968i \(-0.115508\pi\)
−0.774850 + 0.632145i \(0.782175\pi\)
\(912\) 0 0
\(913\) −2.27297 + 3.93689i −0.0752242 + 0.130292i
\(914\) 0 0
\(915\) −6.27846 + 50.0647i −0.207560 + 1.65509i
\(916\) 0 0
\(917\) −6.06859 + 6.06859i −0.200403 + 0.200403i
\(918\) 0 0
\(919\) 12.5574i 0.414229i 0.978317 + 0.207115i \(0.0664073\pi\)
−0.978317 + 0.207115i \(0.933593\pi\)
\(920\) 0 0
\(921\) 33.3659 25.9298i 1.09944 0.854415i
\(922\) 0 0
\(923\) 7.10460 + 26.5147i 0.233851 + 0.872743i
\(924\) 0 0
\(925\) −2.50681 + 9.35553i −0.0824233 + 0.307608i
\(926\) 0 0
\(927\) −19.9555 19.4710i −0.655424 0.639511i
\(928\) 0 0
\(929\) 4.50031 + 7.79477i 0.147650 + 0.255738i 0.930359 0.366651i \(-0.119496\pi\)
−0.782708 + 0.622389i \(0.786162\pi\)
\(930\) 0 0
\(931\) 31.0168 8.31092i 1.01653 0.272379i
\(932\) 0 0
\(933\) 10.3097 13.6081i 0.337523 0.445510i
\(934\) 0 0
\(935\) 28.6501i 0.936960i
\(936\) 0 0
\(937\) 59.2265i 1.93485i −0.253166 0.967423i \(-0.581472\pi\)
0.253166 0.967423i \(-0.418528\pi\)
\(938\) 0 0
\(939\) 6.56917 + 15.5878i 0.214377 + 0.508689i
\(940\) 0 0
\(941\) 11.0262 2.95446i 0.359443 0.0963126i −0.0745778 0.997215i \(-0.523761\pi\)
0.434021 + 0.900903i \(0.357094\pi\)
\(942\) 0 0
\(943\) −3.28347 5.68714i −0.106925 0.185199i
\(944\) 0 0
\(945\) 17.8436 7.77939i 0.580452 0.253064i
\(946\) 0 0
\(947\) 2.22949 8.32058i 0.0724488 0.270382i −0.920194 0.391463i \(-0.871969\pi\)
0.992643 + 0.121080i \(0.0386359\pi\)
\(948\) 0 0
\(949\) −0.520755 1.94348i −0.0169044 0.0630882i
\(950\) 0 0
\(951\) 21.2750 + 8.65964i 0.689889 + 0.280808i
\(952\) 0 0
\(953\) 43.5260i 1.40995i −0.709234 0.704973i \(-0.750959\pi\)
0.709234 0.704973i \(-0.249041\pi\)
\(954\) 0 0
\(955\) −44.2637 + 44.2637i −1.43234 + 1.43234i
\(956\) 0 0
\(957\) −6.73653 5.10367i −0.217761 0.164978i
\(958\) 0 0
\(959\) −4.70633 + 8.15160i −0.151975 + 0.263229i
\(960\) 0 0
\(961\) 14.8522 + 25.7247i 0.479103 + 0.829830i
\(962\) 0 0
\(963\) 6.91283 4.10520i 0.222763 0.132288i
\(964\) 0 0
\(965\) −43.2852 11.5982i −1.39340 0.373361i
\(966\) 0 0
\(967\) −26.2267 15.1420i −0.843393 0.486933i 0.0150229 0.999887i \(-0.495218\pi\)
−0.858416 + 0.512954i \(0.828551\pi\)
\(968\) 0 0
\(969\) −63.6090 + 49.4328i −2.04341 + 1.58801i
\(970\) 0 0
\(971\) −9.06755 + 9.06755i −0.290992 + 0.290992i −0.837472 0.546480i \(-0.815967\pi\)
0.546480 + 0.837472i \(0.315967\pi\)
\(972\) 0 0
\(973\) −3.94005 3.94005i −0.126312 0.126312i
\(974\) 0 0
\(975\) −11.2261 14.4456i −0.359524 0.462628i
\(976\) 0 0
\(977\) 10.4475 18.0956i 0.334246 0.578931i −0.649094 0.760708i \(-0.724852\pi\)
0.983340 + 0.181778i \(0.0581851\pi\)
\(978\) 0 0
\(979\) 5.57603 20.8100i 0.178211 0.665092i
\(980\) 0 0
\(981\) 18.7011 + 31.4912i 0.597081 + 1.00544i
\(982\) 0 0
\(983\) −1.14158 + 0.659092i −0.0364108 + 0.0210218i −0.518095 0.855323i \(-0.673359\pi\)
0.481684 + 0.876345i \(0.340025\pi\)
\(984\) 0 0
\(985\) −4.15128 2.39674i −0.132271 0.0763665i
\(986\) 0 0
\(987\) −12.6859 + 16.7446i −0.403796 + 0.532986i
\(988\) 0 0
\(989\) −18.0626 18.0626i −0.574357 0.574357i
\(990\) 0 0
\(991\) −2.51185 −0.0797914 −0.0398957 0.999204i \(-0.512703\pi\)
−0.0398957 + 0.999204i \(0.512703\pi\)
\(992\) 0 0
\(993\) −0.691664 + 1.69928i −0.0219493 + 0.0539250i
\(994\) 0 0
\(995\) 17.4954 4.68788i 0.554641 0.148616i
\(996\) 0 0
\(997\) −44.4227 11.9030i −1.40688 0.376973i −0.526071 0.850441i \(-0.676335\pi\)
−0.880811 + 0.473468i \(0.843002\pi\)
\(998\) 0 0
\(999\) −6.63757 15.2246i −0.210003 0.481685i
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 576.2.bb.e.337.11 72
3.2 odd 2 1728.2.bc.e.145.14 72
4.3 odd 2 144.2.x.e.13.7 72
9.2 odd 6 1728.2.bc.e.721.5 72
9.7 even 3 inner 576.2.bb.e.529.18 72
12.11 even 2 432.2.y.e.253.12 72
16.5 even 4 inner 576.2.bb.e.49.18 72
16.11 odd 4 144.2.x.e.85.17 yes 72
36.7 odd 6 144.2.x.e.61.17 yes 72
36.11 even 6 432.2.y.e.397.2 72
48.5 odd 4 1728.2.bc.e.1009.5 72
48.11 even 4 432.2.y.e.37.2 72
144.11 even 12 432.2.y.e.181.12 72
144.43 odd 12 144.2.x.e.133.7 yes 72
144.101 odd 12 1728.2.bc.e.1585.14 72
144.133 even 12 inner 576.2.bb.e.241.11 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.7 72 4.3 odd 2
144.2.x.e.61.17 yes 72 36.7 odd 6
144.2.x.e.85.17 yes 72 16.11 odd 4
144.2.x.e.133.7 yes 72 144.43 odd 12
432.2.y.e.37.2 72 48.11 even 4
432.2.y.e.181.12 72 144.11 even 12
432.2.y.e.253.12 72 12.11 even 2
432.2.y.e.397.2 72 36.11 even 6
576.2.bb.e.49.18 72 16.5 even 4 inner
576.2.bb.e.241.11 72 144.133 even 12 inner
576.2.bb.e.337.11 72 1.1 even 1 trivial
576.2.bb.e.529.18 72 9.7 even 3 inner
1728.2.bc.e.145.14 72 3.2 odd 2
1728.2.bc.e.721.5 72 9.2 odd 6
1728.2.bc.e.1009.5 72 48.5 odd 4
1728.2.bc.e.1585.14 72 144.101 odd 12