Properties

Label 756.2.bq.a.25.3
Level $756$
Weight $2$
Character 756.25
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(25,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bq (of order \(9\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.3
Character \(\chi\) \(=\) 756.25
Dual form 756.2.bq.a.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.63641 - 0.567600i) q^{3} +(-2.66918 - 0.971502i) q^{5} +(-0.492567 - 2.59950i) q^{7} +(2.35566 + 1.85765i) q^{9} +O(q^{10})\) \(q+(-1.63641 - 0.567600i) q^{3} +(-2.66918 - 0.971502i) q^{5} +(-0.492567 - 2.59950i) q^{7} +(2.35566 + 1.85765i) q^{9} +(2.08935 - 0.760461i) q^{11} +(-0.722049 - 4.09495i) q^{13} +(3.81644 + 3.10480i) q^{15} +1.23040 q^{17} -7.21574 q^{19} +(-0.669432 + 4.53342i) q^{21} +(0.458850 + 2.60226i) q^{23} +(2.35048 + 1.97229i) q^{25} +(-2.80042 - 4.37694i) q^{27} +(-1.59718 + 9.05809i) q^{29} +(-1.68234 + 1.41165i) q^{31} +(-3.85066 + 0.0585105i) q^{33} +(-1.21067 + 7.41705i) q^{35} +(-2.96015 + 5.12713i) q^{37} +(-1.14272 + 7.11084i) q^{39} +(1.03634 + 5.87737i) q^{41} +(-5.42059 - 4.54841i) q^{43} +(-4.48297 - 7.24693i) q^{45} +(7.60266 + 6.37939i) q^{47} +(-6.51476 + 2.56085i) q^{49} +(-2.01343 - 0.698374i) q^{51} +(0.892450 - 1.54577i) q^{53} -6.31564 q^{55} +(11.8079 + 4.09565i) q^{57} +(-1.19550 - 6.78002i) q^{59} +(10.7272 + 9.00123i) q^{61} +(3.66863 - 7.03855i) q^{63} +(-2.05097 + 11.6316i) q^{65} +(-6.04732 - 2.20104i) q^{67} +(0.726179 - 4.51881i) q^{69} +(-7.09591 - 12.2905i) q^{71} +(0.302622 + 0.524156i) q^{73} +(-2.72688 - 4.56160i) q^{75} +(-3.00596 - 5.05667i) q^{77} +(7.26788 - 2.64529i) q^{79} +(2.09828 + 8.75198i) q^{81} +(0.00883471 - 0.0501041i) q^{83} +(-3.28416 - 1.19534i) q^{85} +(7.75501 - 13.9162i) q^{87} -16.3288 q^{89} +(-10.2891 + 3.89400i) q^{91} +(3.55425 - 1.35514i) q^{93} +(19.2601 + 7.01010i) q^{95} +(-10.8061 - 9.06742i) q^{97} +(6.33447 + 2.08989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.63641 0.567600i −0.944781 0.327704i
\(4\) 0 0
\(5\) −2.66918 0.971502i −1.19369 0.434469i −0.332675 0.943042i \(-0.607951\pi\)
−0.861019 + 0.508573i \(0.830173\pi\)
\(6\) 0 0
\(7\) −0.492567 2.59950i −0.186173 0.982517i
\(8\) 0 0
\(9\) 2.35566 + 1.85765i 0.785220 + 0.619216i
\(10\) 0 0
\(11\) 2.08935 0.760461i 0.629962 0.229288i −0.00725263 0.999974i \(-0.502309\pi\)
0.637215 + 0.770686i \(0.280086\pi\)
\(12\) 0 0
\(13\) −0.722049 4.09495i −0.200260 1.13573i −0.904726 0.425995i \(-0.859924\pi\)
0.704465 0.709739i \(-0.251187\pi\)
\(14\) 0 0
\(15\) 3.81644 + 3.10480i 0.985401 + 0.801656i
\(16\) 0 0
\(17\) 1.23040 0.298416 0.149208 0.988806i \(-0.452328\pi\)
0.149208 + 0.988806i \(0.452328\pi\)
\(18\) 0 0
\(19\) −7.21574 −1.65540 −0.827702 0.561168i \(-0.810352\pi\)
−0.827702 + 0.561168i \(0.810352\pi\)
\(20\) 0 0
\(21\) −0.669432 + 4.53342i −0.146082 + 0.989272i
\(22\) 0 0
\(23\) 0.458850 + 2.60226i 0.0956767 + 0.542610i 0.994538 + 0.104376i \(0.0332846\pi\)
−0.898861 + 0.438234i \(0.855604\pi\)
\(24\) 0 0
\(25\) 2.35048 + 1.97229i 0.470096 + 0.394458i
\(26\) 0 0
\(27\) −2.80042 4.37694i −0.538942 0.842343i
\(28\) 0 0
\(29\) −1.59718 + 9.05809i −0.296590 + 1.68204i 0.364080 + 0.931368i \(0.381383\pi\)
−0.660670 + 0.750677i \(0.729728\pi\)
\(30\) 0 0
\(31\) −1.68234 + 1.41165i −0.302157 + 0.253540i −0.781242 0.624229i \(-0.785413\pi\)
0.479084 + 0.877769i \(0.340969\pi\)
\(32\) 0 0
\(33\) −3.85066 + 0.0585105i −0.670314 + 0.0101854i
\(34\) 0 0
\(35\) −1.21067 + 7.41705i −0.204640 + 1.25371i
\(36\) 0 0
\(37\) −2.96015 + 5.12713i −0.486645 + 0.842895i −0.999882 0.0153525i \(-0.995113\pi\)
0.513237 + 0.858247i \(0.328446\pi\)
\(38\) 0 0
\(39\) −1.14272 + 7.11084i −0.182982 + 1.13865i
\(40\) 0 0
\(41\) 1.03634 + 5.87737i 0.161849 + 0.917891i 0.952254 + 0.305306i \(0.0987589\pi\)
−0.790405 + 0.612584i \(0.790130\pi\)
\(42\) 0 0
\(43\) −5.42059 4.54841i −0.826632 0.693626i 0.127883 0.991789i \(-0.459182\pi\)
−0.954515 + 0.298163i \(0.903626\pi\)
\(44\) 0 0
\(45\) −4.48297 7.24693i −0.668282 1.08031i
\(46\) 0 0
\(47\) 7.60266 + 6.37939i 1.10896 + 0.930529i 0.997995 0.0632947i \(-0.0201608\pi\)
0.110967 + 0.993824i \(0.464605\pi\)
\(48\) 0 0
\(49\) −6.51476 + 2.56085i −0.930679 + 0.365836i
\(50\) 0 0
\(51\) −2.01343 0.698374i −0.281937 0.0977919i
\(52\) 0 0
\(53\) 0.892450 1.54577i 0.122587 0.212328i −0.798200 0.602393i \(-0.794214\pi\)
0.920787 + 0.390065i \(0.127547\pi\)
\(54\) 0 0
\(55\) −6.31564 −0.851600
\(56\) 0 0
\(57\) 11.8079 + 4.09565i 1.56399 + 0.542482i
\(58\) 0 0
\(59\) −1.19550 6.78002i −0.155641 0.882683i −0.958198 0.286107i \(-0.907639\pi\)
0.802557 0.596576i \(-0.203472\pi\)
\(60\) 0 0
\(61\) 10.7272 + 9.00123i 1.37348 + 1.15249i 0.971554 + 0.236819i \(0.0761048\pi\)
0.401930 + 0.915671i \(0.368340\pi\)
\(62\) 0 0
\(63\) 3.66863 7.03855i 0.462204 0.886774i
\(64\) 0 0
\(65\) −2.05097 + 11.6316i −0.254391 + 1.44272i
\(66\) 0 0
\(67\) −6.04732 2.20104i −0.738798 0.268900i −0.0549136 0.998491i \(-0.517488\pi\)
−0.683884 + 0.729591i \(0.739711\pi\)
\(68\) 0 0
\(69\) 0.726179 4.51881i 0.0874217 0.544001i
\(70\) 0 0
\(71\) −7.09591 12.2905i −0.842129 1.45861i −0.888091 0.459668i \(-0.847969\pi\)
0.0459616 0.998943i \(-0.485365\pi\)
\(72\) 0 0
\(73\) 0.302622 + 0.524156i 0.0354192 + 0.0613479i 0.883192 0.469012i \(-0.155390\pi\)
−0.847772 + 0.530360i \(0.822057\pi\)
\(74\) 0 0
\(75\) −2.72688 4.56160i −0.314873 0.526728i
\(76\) 0 0
\(77\) −3.00596 5.05667i −0.342561 0.576261i
\(78\) 0 0
\(79\) 7.26788 2.64529i 0.817700 0.297619i 0.100900 0.994897i \(-0.467828\pi\)
0.716801 + 0.697278i \(0.245606\pi\)
\(80\) 0 0
\(81\) 2.09828 + 8.75198i 0.233142 + 0.972443i
\(82\) 0 0
\(83\) 0.00883471 0.0501041i 0.000969735 0.00549964i −0.984319 0.176397i \(-0.943556\pi\)
0.985289 + 0.170898i \(0.0546668\pi\)
\(84\) 0 0
\(85\) −3.28416 1.19534i −0.356217 0.129652i
\(86\) 0 0
\(87\) 7.75501 13.9162i 0.831425 1.49197i
\(88\) 0 0
\(89\) −16.3288 −1.73085 −0.865427 0.501035i \(-0.832953\pi\)
−0.865427 + 0.501035i \(0.832953\pi\)
\(90\) 0 0
\(91\) −10.2891 + 3.89400i −1.07859 + 0.408202i
\(92\) 0 0
\(93\) 3.55425 1.35514i 0.368558 0.140522i
\(94\) 0 0
\(95\) 19.2601 + 7.01010i 1.97605 + 0.719222i
\(96\) 0 0
\(97\) −10.8061 9.06742i −1.09720 0.920657i −0.0999629 0.994991i \(-0.531872\pi\)
−0.997233 + 0.0743341i \(0.976317\pi\)
\(98\) 0 0
\(99\) 6.33447 + 2.08989i 0.636638 + 0.210042i
\(100\) 0 0
\(101\) −2.55863 + 14.5107i −0.254593 + 1.44387i 0.542521 + 0.840042i \(0.317470\pi\)
−0.797115 + 0.603828i \(0.793641\pi\)
\(102\) 0 0
\(103\) 12.8713 + 4.68477i 1.26825 + 0.461604i 0.886528 0.462675i \(-0.153110\pi\)
0.381718 + 0.924279i \(0.375333\pi\)
\(104\) 0 0
\(105\) 6.19106 11.4501i 0.604185 1.11742i
\(106\) 0 0
\(107\) 0.233044 + 0.403645i 0.0225292 + 0.0390218i 0.877070 0.480362i \(-0.159495\pi\)
−0.854541 + 0.519384i \(0.826161\pi\)
\(108\) 0 0
\(109\) 4.12987 7.15314i 0.395570 0.685147i −0.597604 0.801791i \(-0.703881\pi\)
0.993174 + 0.116645i \(0.0372138\pi\)
\(110\) 0 0
\(111\) 7.75417 6.70989i 0.735993 0.636875i
\(112\) 0 0
\(113\) −1.32727 + 1.11371i −0.124859 + 0.104769i −0.703079 0.711112i \(-0.748192\pi\)
0.578220 + 0.815881i \(0.303747\pi\)
\(114\) 0 0
\(115\) 1.30335 7.39169i 0.121538 0.689278i
\(116\) 0 0
\(117\) 5.90607 10.9876i 0.546016 1.01581i
\(118\) 0 0
\(119\) −0.606054 3.19842i −0.0555569 0.293198i
\(120\) 0 0
\(121\) −4.63941 + 3.89293i −0.421765 + 0.353903i
\(122\) 0 0
\(123\) 1.64012 10.2060i 0.147885 0.920244i
\(124\) 0 0
\(125\) 2.74343 + 4.75175i 0.245380 + 0.425010i
\(126\) 0 0
\(127\) 0.358039 0.620141i 0.0317708 0.0550286i −0.849703 0.527262i \(-0.823219\pi\)
0.881474 + 0.472233i \(0.156552\pi\)
\(128\) 0 0
\(129\) 6.28861 + 10.5198i 0.553682 + 0.926215i
\(130\) 0 0
\(131\) −0.494193 2.80271i −0.0431778 0.244874i 0.955578 0.294738i \(-0.0952323\pi\)
−0.998756 + 0.0498641i \(0.984121\pi\)
\(132\) 0 0
\(133\) 3.55424 + 18.7573i 0.308191 + 1.62646i
\(134\) 0 0
\(135\) 3.22262 + 14.4035i 0.277359 + 1.23965i
\(136\) 0 0
\(137\) 3.92125 + 3.29032i 0.335015 + 0.281111i 0.794740 0.606951i \(-0.207607\pi\)
−0.459725 + 0.888062i \(0.652052\pi\)
\(138\) 0 0
\(139\) −21.0738 7.67023i −1.78746 0.650581i −0.999388 0.0349931i \(-0.988859\pi\)
−0.788068 0.615588i \(-0.788919\pi\)
\(140\) 0 0
\(141\) −8.82011 14.7545i −0.742787 1.24256i
\(142\) 0 0
\(143\) −4.62266 8.00668i −0.386566 0.669552i
\(144\) 0 0
\(145\) 13.0631 22.6260i 1.08483 1.87899i
\(146\) 0 0
\(147\) 12.1143 0.492826i 0.999174 0.0406476i
\(148\) 0 0
\(149\) −10.4632 + 8.77965i −0.857177 + 0.719257i −0.961358 0.275301i \(-0.911222\pi\)
0.104181 + 0.994558i \(0.466778\pi\)
\(150\) 0 0
\(151\) 1.53448 0.558504i 0.124874 0.0454504i −0.278827 0.960341i \(-0.589946\pi\)
0.403701 + 0.914891i \(0.367724\pi\)
\(152\) 0 0
\(153\) 2.89840 + 2.28565i 0.234322 + 0.184784i
\(154\) 0 0
\(155\) 5.86189 2.13355i 0.470838 0.171371i
\(156\) 0 0
\(157\) 1.48942 + 8.44693i 0.118869 + 0.674138i 0.984762 + 0.173909i \(0.0556399\pi\)
−0.865893 + 0.500229i \(0.833249\pi\)
\(158\) 0 0
\(159\) −2.33779 + 2.02295i −0.185399 + 0.160431i
\(160\) 0 0
\(161\) 6.53856 2.47457i 0.515311 0.195023i
\(162\) 0 0
\(163\) −3.28752 5.69416i −0.257499 0.446001i 0.708072 0.706140i \(-0.249565\pi\)
−0.965571 + 0.260139i \(0.916232\pi\)
\(164\) 0 0
\(165\) 10.3350 + 3.58475i 0.804575 + 0.279073i
\(166\) 0 0
\(167\) −8.07957 + 6.77957i −0.625216 + 0.524619i −0.899438 0.437048i \(-0.856024\pi\)
0.274222 + 0.961666i \(0.411580\pi\)
\(168\) 0 0
\(169\) −4.03122 + 1.46725i −0.310094 + 0.112865i
\(170\) 0 0
\(171\) −16.9978 13.4043i −1.29986 1.02505i
\(172\) 0 0
\(173\) 3.01856 17.1191i 0.229497 1.30154i −0.624401 0.781104i \(-0.714657\pi\)
0.853898 0.520440i \(-0.174232\pi\)
\(174\) 0 0
\(175\) 3.96919 7.08155i 0.300042 0.535315i
\(176\) 0 0
\(177\) −1.89201 + 11.7734i −0.142212 + 0.884946i
\(178\) 0 0
\(179\) 0.958408 0.0716348 0.0358174 0.999358i \(-0.488597\pi\)
0.0358174 + 0.999358i \(0.488597\pi\)
\(180\) 0 0
\(181\) 9.98698 17.2980i 0.742326 1.28575i −0.209107 0.977893i \(-0.567056\pi\)
0.951434 0.307854i \(-0.0996108\pi\)
\(182\) 0 0
\(183\) −12.4451 20.8185i −0.919965 1.53895i
\(184\) 0 0
\(185\) 12.8822 10.8094i 0.947117 0.794725i
\(186\) 0 0
\(187\) 2.57073 0.935670i 0.187991 0.0684230i
\(188\) 0 0
\(189\) −9.99845 + 9.43562i −0.727280 + 0.686341i
\(190\) 0 0
\(191\) 0.682129 0.248275i 0.0493571 0.0179645i −0.317224 0.948351i \(-0.602751\pi\)
0.366581 + 0.930386i \(0.380528\pi\)
\(192\) 0 0
\(193\) 2.56936 2.15595i 0.184947 0.155189i −0.545614 0.838037i \(-0.683703\pi\)
0.730560 + 0.682848i \(0.239259\pi\)
\(194\) 0 0
\(195\) 9.95832 17.8699i 0.713130 1.27969i
\(196\) 0 0
\(197\) 8.27513 14.3329i 0.589579 1.02118i −0.404709 0.914446i \(-0.632627\pi\)
0.994288 0.106735i \(-0.0340395\pi\)
\(198\) 0 0
\(199\) −17.2879 −1.22550 −0.612752 0.790275i \(-0.709938\pi\)
−0.612752 + 0.790275i \(0.709938\pi\)
\(200\) 0 0
\(201\) 8.64657 + 7.03426i 0.609882 + 0.496159i
\(202\) 0 0
\(203\) 24.3332 0.309839i 1.70785 0.0217465i
\(204\) 0 0
\(205\) 2.94370 16.6946i 0.205597 1.16600i
\(206\) 0 0
\(207\) −3.75320 + 6.98244i −0.260865 + 0.485313i
\(208\) 0 0
\(209\) −15.0762 + 5.48729i −1.04284 + 0.379563i
\(210\) 0 0
\(211\) 1.49453 1.25406i 0.102887 0.0863328i −0.589893 0.807482i \(-0.700830\pi\)
0.692780 + 0.721149i \(0.256386\pi\)
\(212\) 0 0
\(213\) 4.63573 + 24.1399i 0.317635 + 1.65404i
\(214\) 0 0
\(215\) 10.0497 + 17.4066i 0.685386 + 1.18712i
\(216\) 0 0
\(217\) 4.49825 + 3.67790i 0.305361 + 0.249672i
\(218\) 0 0
\(219\) −0.197702 1.02950i −0.0133595 0.0695673i
\(220\) 0 0
\(221\) −0.888409 5.03842i −0.0597609 0.338921i
\(222\) 0 0
\(223\) 1.43245 0.521370i 0.0959242 0.0349135i −0.293612 0.955925i \(-0.594857\pi\)
0.389536 + 0.921011i \(0.372635\pi\)
\(224\) 0 0
\(225\) 1.87312 + 9.01242i 0.124875 + 0.600828i
\(226\) 0 0
\(227\) −15.3767 + 5.59667i −1.02059 + 0.371464i −0.797490 0.603332i \(-0.793839\pi\)
−0.223099 + 0.974796i \(0.571617\pi\)
\(228\) 0 0
\(229\) −2.65761 + 2.23000i −0.175620 + 0.147362i −0.726360 0.687314i \(-0.758790\pi\)
0.550741 + 0.834676i \(0.314345\pi\)
\(230\) 0 0
\(231\) 2.04881 + 9.98096i 0.134802 + 0.656699i
\(232\) 0 0
\(233\) −7.58173 + 13.1319i −0.496696 + 0.860302i −0.999993 0.00381143i \(-0.998787\pi\)
0.503297 + 0.864113i \(0.332120\pi\)
\(234\) 0 0
\(235\) −14.0953 24.4137i −0.919474 1.59258i
\(236\) 0 0
\(237\) −13.3947 + 0.203531i −0.870078 + 0.0132208i
\(238\) 0 0
\(239\) −1.55011 0.564194i −0.100268 0.0364947i 0.291399 0.956602i \(-0.405879\pi\)
−0.391667 + 0.920107i \(0.628102\pi\)
\(240\) 0 0
\(241\) 11.8645 + 9.95552i 0.764262 + 0.641292i 0.939232 0.343282i \(-0.111539\pi\)
−0.174971 + 0.984574i \(0.555983\pi\)
\(242\) 0 0
\(243\) 1.53398 15.5128i 0.0984046 0.995146i
\(244\) 0 0
\(245\) 19.8769 0.506276i 1.26989 0.0323448i
\(246\) 0 0
\(247\) 5.21012 + 29.5481i 0.331512 + 1.88010i
\(248\) 0 0
\(249\) −0.0428963 + 0.0769762i −0.00271844 + 0.00487817i
\(250\) 0 0
\(251\) −8.29533 + 14.3679i −0.523597 + 0.906896i 0.476026 + 0.879431i \(0.342077\pi\)
−0.999623 + 0.0274648i \(0.991257\pi\)
\(252\) 0 0
\(253\) 2.93762 + 5.08810i 0.184686 + 0.319886i
\(254\) 0 0
\(255\) 4.69575 + 3.82014i 0.294059 + 0.239227i
\(256\) 0 0
\(257\) 15.6725 13.1508i 0.977622 0.820322i −0.00610721 0.999981i \(-0.501944\pi\)
0.983729 + 0.179659i \(0.0574996\pi\)
\(258\) 0 0
\(259\) 14.7860 + 5.16944i 0.918758 + 0.321213i
\(260\) 0 0
\(261\) −20.5892 + 18.3708i −1.27444 + 1.13712i
\(262\) 0 0
\(263\) −2.04301 + 11.5865i −0.125978 + 0.714454i 0.854745 + 0.519048i \(0.173714\pi\)
−0.980722 + 0.195406i \(0.937398\pi\)
\(264\) 0 0
\(265\) −3.88383 + 3.25892i −0.238582 + 0.200194i
\(266\) 0 0
\(267\) 26.7206 + 9.26824i 1.63528 + 0.567207i
\(268\) 0 0
\(269\) −10.3873 + 17.9913i −0.633324 + 1.09695i 0.353544 + 0.935418i \(0.384977\pi\)
−0.986868 + 0.161531i \(0.948357\pi\)
\(270\) 0 0
\(271\) −6.22260 10.7779i −0.377996 0.654709i 0.612774 0.790258i \(-0.290053\pi\)
−0.990771 + 0.135549i \(0.956720\pi\)
\(272\) 0 0
\(273\) 19.0475 0.532063i 1.15280 0.0322019i
\(274\) 0 0
\(275\) 6.41082 + 2.33335i 0.386587 + 0.140706i
\(276\) 0 0
\(277\) 5.21699 29.5870i 0.313458 1.77771i −0.267279 0.963619i \(-0.586124\pi\)
0.580737 0.814091i \(-0.302765\pi\)
\(278\) 0 0
\(279\) −6.58538 + 0.200175i −0.394256 + 0.0119842i
\(280\) 0 0
\(281\) −3.68561 3.09260i −0.219865 0.184489i 0.526202 0.850360i \(-0.323616\pi\)
−0.746067 + 0.665871i \(0.768060\pi\)
\(282\) 0 0
\(283\) −24.9993 9.09902i −1.48606 0.540880i −0.533649 0.845706i \(-0.679179\pi\)
−0.952408 + 0.304826i \(0.901402\pi\)
\(284\) 0 0
\(285\) −27.5385 22.4034i −1.63124 1.32706i
\(286\) 0 0
\(287\) 14.7677 5.58896i 0.871711 0.329906i
\(288\) 0 0
\(289\) −15.4861 −0.910948
\(290\) 0 0
\(291\) 12.5366 + 20.9716i 0.734907 + 1.22937i
\(292\) 0 0
\(293\) 6.39612 + 2.32800i 0.373665 + 0.136003i 0.522025 0.852930i \(-0.325177\pi\)
−0.148359 + 0.988934i \(0.547399\pi\)
\(294\) 0 0
\(295\) −3.39580 + 19.2585i −0.197711 + 1.12127i
\(296\) 0 0
\(297\) −9.17955 7.01535i −0.532652 0.407072i
\(298\) 0 0
\(299\) 10.3248 3.75793i 0.597100 0.217327i
\(300\) 0 0
\(301\) −9.15358 + 16.3312i −0.527603 + 0.941314i
\(302\) 0 0
\(303\) 12.4232 22.2932i 0.713696 1.28071i
\(304\) 0 0
\(305\) −19.8882 34.4474i −1.13880 1.97245i
\(306\) 0 0
\(307\) −4.91071 8.50560i −0.280269 0.485440i 0.691182 0.722681i \(-0.257090\pi\)
−0.971451 + 0.237241i \(0.923757\pi\)
\(308\) 0 0
\(309\) −18.4036 14.9719i −1.04694 0.851723i
\(310\) 0 0
\(311\) −7.04368 2.56369i −0.399410 0.145373i 0.134502 0.990913i \(-0.457057\pi\)
−0.533912 + 0.845540i \(0.679279\pi\)
\(312\) 0 0
\(313\) −1.19311 + 6.76648i −0.0674388 + 0.382464i 0.932343 + 0.361575i \(0.117761\pi\)
−0.999782 + 0.0208892i \(0.993350\pi\)
\(314\) 0 0
\(315\) −16.6302 + 15.2231i −0.937005 + 0.857723i
\(316\) 0 0
\(317\) −15.3240 12.8583i −0.860680 0.722196i 0.101435 0.994842i \(-0.467657\pi\)
−0.962114 + 0.272646i \(0.912101\pi\)
\(318\) 0 0
\(319\) 3.55124 + 20.1401i 0.198831 + 1.12763i
\(320\) 0 0
\(321\) −0.152247 0.792803i −0.00849760 0.0442500i
\(322\) 0 0
\(323\) −8.87824 −0.493998
\(324\) 0 0
\(325\) 6.37925 11.0492i 0.353857 0.612899i
\(326\) 0 0
\(327\) −10.8183 + 9.36135i −0.598252 + 0.517684i
\(328\) 0 0
\(329\) 12.8384 22.9054i 0.707802 1.26281i
\(330\) 0 0
\(331\) 5.16458 + 4.33360i 0.283871 + 0.238196i 0.773593 0.633682i \(-0.218457\pi\)
−0.489722 + 0.871878i \(0.662902\pi\)
\(332\) 0 0
\(333\) −16.4975 + 6.57886i −0.904058 + 0.360519i
\(334\) 0 0
\(335\) 14.0031 + 11.7500i 0.765069 + 0.641969i
\(336\) 0 0
\(337\) 3.41987 + 19.3950i 0.186292 + 1.05652i 0.924284 + 0.381706i \(0.124663\pi\)
−0.737992 + 0.674810i \(0.764226\pi\)
\(338\) 0 0
\(339\) 2.80409 1.06912i 0.152297 0.0580669i
\(340\) 0 0
\(341\) −2.44149 + 4.22879i −0.132214 + 0.229002i
\(342\) 0 0
\(343\) 9.86588 + 15.6737i 0.532707 + 0.846300i
\(344\) 0 0
\(345\) −6.32834 + 11.3560i −0.340706 + 0.611388i
\(346\) 0 0
\(347\) −8.53677 + 7.16320i −0.458278 + 0.384541i −0.842497 0.538701i \(-0.818915\pi\)
0.384219 + 0.923242i \(0.374471\pi\)
\(348\) 0 0
\(349\) −1.18076 + 6.69644i −0.0632048 + 0.358452i 0.936759 + 0.349974i \(0.113810\pi\)
−0.999964 + 0.00847787i \(0.997301\pi\)
\(350\) 0 0
\(351\) −15.9013 + 14.6279i −0.848749 + 0.780782i
\(352\) 0 0
\(353\) −3.49296 2.93094i −0.185911 0.155998i 0.545082 0.838383i \(-0.316499\pi\)
−0.730993 + 0.682385i \(0.760943\pi\)
\(354\) 0 0
\(355\) 7.00004 + 39.6992i 0.371523 + 2.10701i
\(356\) 0 0
\(357\) −0.823669 + 5.57791i −0.0435932 + 0.295214i
\(358\) 0 0
\(359\) −35.3481 −1.86560 −0.932800 0.360395i \(-0.882642\pi\)
−0.932800 + 0.360395i \(0.882642\pi\)
\(360\) 0 0
\(361\) 33.0669 1.74036
\(362\) 0 0
\(363\) 9.80160 3.73709i 0.514450 0.196146i
\(364\) 0 0
\(365\) −0.298533 1.69307i −0.0156259 0.0886191i
\(366\) 0 0
\(367\) 15.4786 5.63376i 0.807978 0.294080i 0.0951897 0.995459i \(-0.469654\pi\)
0.712788 + 0.701379i \(0.247432\pi\)
\(368\) 0 0
\(369\) −8.47682 + 15.7702i −0.441286 + 0.820966i
\(370\) 0 0
\(371\) −4.45781 1.55853i −0.231438 0.0809146i
\(372\) 0 0
\(373\) −25.4152 9.25038i −1.31595 0.478966i −0.413791 0.910372i \(-0.635796\pi\)
−0.902158 + 0.431405i \(0.858018\pi\)
\(374\) 0 0
\(375\) −1.79227 9.33298i −0.0925525 0.481953i
\(376\) 0 0
\(377\) 38.2456 1.96975
\(378\) 0 0
\(379\) 23.3318 1.19848 0.599238 0.800571i \(-0.295470\pi\)
0.599238 + 0.800571i \(0.295470\pi\)
\(380\) 0 0
\(381\) −0.937889 + 0.811581i −0.0480495 + 0.0415786i
\(382\) 0 0
\(383\) 20.8199 + 7.57781i 1.06385 + 0.387208i 0.813872 0.581045i \(-0.197356\pi\)
0.249974 + 0.968253i \(0.419578\pi\)
\(384\) 0 0
\(385\) 3.11087 + 16.4175i 0.158545 + 0.836712i
\(386\) 0 0
\(387\) −4.31972 20.7841i −0.219583 1.05651i
\(388\) 0 0
\(389\) −15.4261 + 5.61463i −0.782133 + 0.284673i −0.702062 0.712116i \(-0.747737\pi\)
−0.0800711 + 0.996789i \(0.525515\pi\)
\(390\) 0 0
\(391\) 0.564568 + 3.20182i 0.0285514 + 0.161923i
\(392\) 0 0
\(393\) −0.782114 + 4.86688i −0.0394524 + 0.245501i
\(394\) 0 0
\(395\) −21.9692 −1.10539
\(396\) 0 0
\(397\) −27.5789 −1.38415 −0.692073 0.721828i \(-0.743302\pi\)
−0.692073 + 0.721828i \(0.743302\pi\)
\(398\) 0 0
\(399\) 4.83045 32.7119i 0.241825 1.63765i
\(400\) 0 0
\(401\) −4.89853 27.7809i −0.244621 1.38731i −0.821371 0.570394i \(-0.806791\pi\)
0.576750 0.816920i \(-0.304321\pi\)
\(402\) 0 0
\(403\) 6.99537 + 5.86981i 0.348464 + 0.292396i
\(404\) 0 0
\(405\) 2.90188 25.3991i 0.144195 1.26209i
\(406\) 0 0
\(407\) −2.28580 + 12.9634i −0.113303 + 0.642573i
\(408\) 0 0
\(409\) −0.978228 + 0.820831i −0.0483703 + 0.0405875i −0.666652 0.745369i \(-0.732273\pi\)
0.618282 + 0.785956i \(0.287829\pi\)
\(410\) 0 0
\(411\) −4.54918 7.61000i −0.224394 0.375374i
\(412\) 0 0
\(413\) −17.0358 + 6.44731i −0.838275 + 0.317251i
\(414\) 0 0
\(415\) −0.0722577 + 0.125154i −0.00354699 + 0.00614357i
\(416\) 0 0
\(417\) 30.1317 + 24.5131i 1.47556 + 1.20041i
\(418\) 0 0
\(419\) −2.98110 16.9067i −0.145636 0.825944i −0.966854 0.255329i \(-0.917816\pi\)
0.821218 0.570615i \(-0.193295\pi\)
\(420\) 0 0
\(421\) 6.61491 + 5.55057i 0.322391 + 0.270518i 0.789591 0.613634i \(-0.210293\pi\)
−0.467200 + 0.884152i \(0.654737\pi\)
\(422\) 0 0
\(423\) 6.05863 + 29.1507i 0.294581 + 1.41736i
\(424\) 0 0
\(425\) 2.89203 + 2.42670i 0.140284 + 0.117712i
\(426\) 0 0
\(427\) 18.1148 32.3191i 0.876635 1.56403i
\(428\) 0 0
\(429\) 3.01997 + 15.7260i 0.145805 + 0.759259i
\(430\) 0 0
\(431\) 11.4964 19.9124i 0.553763 0.959145i −0.444236 0.895910i \(-0.646525\pi\)
0.997999 0.0632353i \(-0.0201419\pi\)
\(432\) 0 0
\(433\) −9.47220 −0.455205 −0.227603 0.973754i \(-0.573089\pi\)
−0.227603 + 0.973754i \(0.573089\pi\)
\(434\) 0 0
\(435\) −34.2191 + 29.6107i −1.64068 + 1.41973i
\(436\) 0 0
\(437\) −3.31094 18.7773i −0.158384 0.898238i
\(438\) 0 0
\(439\) −6.46610 5.42570i −0.308610 0.258955i 0.475307 0.879820i \(-0.342337\pi\)
−0.783917 + 0.620865i \(0.786781\pi\)
\(440\) 0 0
\(441\) −20.1037 6.06963i −0.957320 0.289030i
\(442\) 0 0
\(443\) −6.10216 + 34.6071i −0.289922 + 1.64423i 0.397230 + 0.917719i \(0.369971\pi\)
−0.687153 + 0.726513i \(0.741140\pi\)
\(444\) 0 0
\(445\) 43.5846 + 15.8635i 2.06611 + 0.752002i
\(446\) 0 0
\(447\) 22.1054 8.42819i 1.04555 0.398640i
\(448\) 0 0
\(449\) −19.9052 34.4768i −0.939383 1.62706i −0.766626 0.642094i \(-0.778066\pi\)
−0.172757 0.984964i \(-0.555268\pi\)
\(450\) 0 0
\(451\) 6.63478 + 11.4918i 0.312420 + 0.541126i
\(452\) 0 0
\(453\) −2.82803 + 0.0429718i −0.132873 + 0.00201899i
\(454\) 0 0
\(455\) 31.2466 0.397869i 1.46486 0.0186524i
\(456\) 0 0
\(457\) −2.30969 + 0.840658i −0.108043 + 0.0393243i −0.395476 0.918476i \(-0.629420\pi\)
0.287433 + 0.957801i \(0.407198\pi\)
\(458\) 0 0
\(459\) −3.44564 5.38539i −0.160829 0.251368i
\(460\) 0 0
\(461\) 3.11944 17.6912i 0.145287 0.823962i −0.821850 0.569704i \(-0.807058\pi\)
0.967136 0.254258i \(-0.0818312\pi\)
\(462\) 0 0
\(463\) −18.6713 6.79580i −0.867729 0.315828i −0.130482 0.991451i \(-0.541652\pi\)
−0.737247 + 0.675623i \(0.763875\pi\)
\(464\) 0 0
\(465\) −10.8034 + 0.164158i −0.500998 + 0.00761263i
\(466\) 0 0
\(467\) −14.9033 −0.689644 −0.344822 0.938668i \(-0.612061\pi\)
−0.344822 + 0.938668i \(0.612061\pi\)
\(468\) 0 0
\(469\) −2.74289 + 16.8041i −0.126655 + 0.775943i
\(470\) 0 0
\(471\) 2.35717 14.6680i 0.108613 0.675867i
\(472\) 0 0
\(473\) −14.7844 5.38108i −0.679787 0.247422i
\(474\) 0 0
\(475\) −16.9605 14.2315i −0.778200 0.652987i
\(476\) 0 0
\(477\) 4.97381 1.98345i 0.227735 0.0908159i
\(478\) 0 0
\(479\) −5.38451 + 30.5371i −0.246025 + 1.39527i 0.572077 + 0.820200i \(0.306138\pi\)
−0.818101 + 0.575074i \(0.804973\pi\)
\(480\) 0 0
\(481\) 23.1327 + 8.41961i 1.05476 + 0.383901i
\(482\) 0 0
\(483\) −12.1043 + 0.338116i −0.550766 + 0.0153848i
\(484\) 0 0
\(485\) 20.0345 + 34.7008i 0.909719 + 1.57568i
\(486\) 0 0
\(487\) 6.10330 10.5712i 0.276567 0.479028i −0.693962 0.720011i \(-0.744137\pi\)
0.970529 + 0.240984i \(0.0774700\pi\)
\(488\) 0 0
\(489\) 2.14773 + 11.1840i 0.0971236 + 0.505756i
\(490\) 0 0
\(491\) −8.90208 + 7.46973i −0.401745 + 0.337104i −0.821168 0.570687i \(-0.806677\pi\)
0.419423 + 0.907791i \(0.362233\pi\)
\(492\) 0 0
\(493\) −1.96518 + 11.1451i −0.0885070 + 0.501948i
\(494\) 0 0
\(495\) −14.8775 11.7322i −0.668694 0.527325i
\(496\) 0 0
\(497\) −28.4538 + 24.4997i −1.27633 + 1.09896i
\(498\) 0 0
\(499\) 0.126329 0.106002i 0.00565525 0.00474532i −0.639956 0.768412i \(-0.721047\pi\)
0.645611 + 0.763667i \(0.276603\pi\)
\(500\) 0 0
\(501\) 17.0696 6.50817i 0.762611 0.290764i
\(502\) 0 0
\(503\) −19.1072 33.0947i −0.851949 1.47562i −0.879447 0.475998i \(-0.842087\pi\)
0.0274972 0.999622i \(-0.491246\pi\)
\(504\) 0 0
\(505\) 20.9266 36.2460i 0.931223 1.61293i
\(506\) 0 0
\(507\) 7.42953 0.112891i 0.329957 0.00501367i
\(508\) 0 0
\(509\) −0.133077 0.754719i −0.00589855 0.0334523i 0.981716 0.190349i \(-0.0609621\pi\)
−0.987615 + 0.156897i \(0.949851\pi\)
\(510\) 0 0
\(511\) 1.21348 1.04485i 0.0536812 0.0462213i
\(512\) 0 0
\(513\) 20.2071 + 31.5829i 0.892166 + 1.39442i
\(514\) 0 0
\(515\) −29.8045 25.0090i −1.31334 1.10203i
\(516\) 0 0
\(517\) 20.7359 + 7.54724i 0.911963 + 0.331927i
\(518\) 0 0
\(519\) −14.6564 + 26.3005i −0.643345 + 1.15447i
\(520\) 0 0
\(521\) −0.298486 0.516993i −0.0130769 0.0226499i 0.859413 0.511282i \(-0.170829\pi\)
−0.872490 + 0.488632i \(0.837496\pi\)
\(522\) 0 0
\(523\) −20.9406 + 36.2703i −0.915670 + 1.58599i −0.109754 + 0.993959i \(0.535006\pi\)
−0.805917 + 0.592029i \(0.798327\pi\)
\(524\) 0 0
\(525\) −10.5147 + 9.33540i −0.458899 + 0.407430i
\(526\) 0 0
\(527\) −2.06995 + 1.73689i −0.0901685 + 0.0756603i
\(528\) 0 0
\(529\) 15.0517 5.47837i 0.654421 0.238190i
\(530\) 0 0
\(531\) 9.77870 18.1922i 0.424359 0.789476i
\(532\) 0 0
\(533\) 23.3192 8.48750i 1.01007 0.367634i
\(534\) 0 0
\(535\) −0.229896 1.30380i −0.00993926 0.0563683i
\(536\) 0 0
\(537\) −1.56835 0.543992i −0.0676791 0.0234750i
\(538\) 0 0
\(539\) −11.6642 + 10.3047i −0.502411 + 0.443856i
\(540\) 0 0
\(541\) 4.10808 + 7.11540i 0.176620 + 0.305915i 0.940721 0.339182i \(-0.110150\pi\)
−0.764101 + 0.645097i \(0.776817\pi\)
\(542\) 0 0
\(543\) −26.1611 + 22.6379i −1.12268 + 0.971485i
\(544\) 0 0
\(545\) −17.9727 + 15.0808i −0.769864 + 0.645993i
\(546\) 0 0
\(547\) 7.99139 2.90863i 0.341687 0.124364i −0.165476 0.986214i \(-0.552916\pi\)
0.507164 + 0.861850i \(0.330694\pi\)
\(548\) 0 0
\(549\) 8.54864 + 41.1313i 0.364847 + 1.75544i
\(550\) 0 0
\(551\) 11.5249 65.3608i 0.490976 2.78446i
\(552\) 0 0
\(553\) −10.4563 17.5898i −0.444649 0.747996i
\(554\) 0 0
\(555\) −27.2159 + 10.3767i −1.15525 + 0.440467i
\(556\) 0 0
\(557\) −18.9531 −0.803067 −0.401534 0.915844i \(-0.631523\pi\)
−0.401534 + 0.915844i \(0.631523\pi\)
\(558\) 0 0
\(559\) −14.7116 + 25.4812i −0.622233 + 1.07774i
\(560\) 0 0
\(561\) −4.73785 + 0.0719913i −0.200032 + 0.00303948i
\(562\) 0 0
\(563\) 22.3983 18.7944i 0.943976 0.792090i −0.0342970 0.999412i \(-0.510919\pi\)
0.978273 + 0.207322i \(0.0664748\pi\)
\(564\) 0 0
\(565\) 4.62468 1.68325i 0.194562 0.0708147i
\(566\) 0 0
\(567\) 21.7172 9.76541i 0.912037 0.410109i
\(568\) 0 0
\(569\) 12.0155 4.37329i 0.503717 0.183338i −0.0776483 0.996981i \(-0.524741\pi\)
0.581365 + 0.813643i \(0.302519\pi\)
\(570\) 0 0
\(571\) 34.9888 29.3591i 1.46424 1.22864i 0.542946 0.839767i \(-0.317309\pi\)
0.921291 0.388874i \(-0.127136\pi\)
\(572\) 0 0
\(573\) −1.25716 + 0.0191025i −0.0525187 + 0.000798017i
\(574\) 0 0
\(575\) −4.05390 + 7.02156i −0.169059 + 0.292819i
\(576\) 0 0
\(577\) 6.03738 0.251340 0.125670 0.992072i \(-0.459892\pi\)
0.125670 + 0.992072i \(0.459892\pi\)
\(578\) 0 0
\(579\) −5.42824 + 2.06965i −0.225590 + 0.0860115i
\(580\) 0 0
\(581\) −0.134597 + 0.00171385i −0.00558403 + 7.11026e-5i
\(582\) 0 0
\(583\) 0.689143 3.90832i 0.0285414 0.161866i
\(584\) 0 0
\(585\) −26.4389 + 23.5902i −1.09311 + 0.975334i
\(586\) 0 0
\(587\) 13.7636 5.00954i 0.568084 0.206766i −0.0419789 0.999118i \(-0.513366\pi\)
0.610063 + 0.792353i \(0.291144\pi\)
\(588\) 0 0
\(589\) 12.1393 10.1861i 0.500192 0.419711i
\(590\) 0 0
\(591\) −21.6769 + 18.7576i −0.891667 + 0.771584i
\(592\) 0 0
\(593\) −1.71826 2.97612i −0.0705607 0.122215i 0.828586 0.559861i \(-0.189146\pi\)
−0.899147 + 0.437646i \(0.855812\pi\)
\(594\) 0 0
\(595\) −1.48960 + 9.12593i −0.0610677 + 0.374127i
\(596\) 0 0
\(597\) 28.2900 + 9.81259i 1.15783 + 0.401603i
\(598\) 0 0
\(599\) 3.36954 + 19.1096i 0.137676 + 0.780797i 0.972959 + 0.230978i \(0.0741924\pi\)
−0.835283 + 0.549820i \(0.814696\pi\)
\(600\) 0 0
\(601\) −8.74705 + 3.18367i −0.356800 + 0.129864i −0.514200 0.857670i \(-0.671911\pi\)
0.157400 + 0.987535i \(0.449689\pi\)
\(602\) 0 0
\(603\) −10.1567 16.4187i −0.413612 0.668622i
\(604\) 0 0
\(605\) 16.1654 5.88373i 0.657218 0.239208i
\(606\) 0 0
\(607\) −5.75650 + 4.83028i −0.233649 + 0.196055i −0.752093 0.659057i \(-0.770956\pi\)
0.518444 + 0.855111i \(0.326511\pi\)
\(608\) 0 0
\(609\) −39.9949 13.3045i −1.62067 0.539125i
\(610\) 0 0
\(611\) 20.6338 35.7387i 0.834752 1.44583i
\(612\) 0 0
\(613\) 11.6494 + 20.1773i 0.470514 + 0.814954i 0.999431 0.0337194i \(-0.0107353\pi\)
−0.528918 + 0.848673i \(0.677402\pi\)
\(614\) 0 0
\(615\) −14.2929 + 25.6483i −0.576346 + 1.03424i
\(616\) 0 0
\(617\) −14.6336 5.32620i −0.589128 0.214425i 0.0302181 0.999543i \(-0.490380\pi\)
−0.619346 + 0.785118i \(0.712602\pi\)
\(618\) 0 0
\(619\) 18.7896 + 15.7663i 0.755217 + 0.633703i 0.936877 0.349659i \(-0.113702\pi\)
−0.181660 + 0.983361i \(0.558147\pi\)
\(620\) 0 0
\(621\) 10.1050 9.29580i 0.405499 0.373028i
\(622\) 0 0
\(623\) 8.04305 + 42.4467i 0.322238 + 1.70059i
\(624\) 0 0
\(625\) −5.37042 30.4571i −0.214817 1.21829i
\(626\) 0 0
\(627\) 27.7854 0.422197i 1.10964 0.0168609i
\(628\) 0 0
\(629\) −3.64216 + 6.30841i −0.145223 + 0.251533i
\(630\) 0 0
\(631\) 14.9402 + 25.8773i 0.594762 + 1.03016i 0.993580 + 0.113128i \(0.0360869\pi\)
−0.398819 + 0.917030i \(0.630580\pi\)
\(632\) 0 0
\(633\) −3.15745 + 1.20385i −0.125498 + 0.0478489i
\(634\) 0 0
\(635\) −1.55814 + 1.30743i −0.0618328 + 0.0518839i
\(636\) 0 0
\(637\) 15.1905 + 24.8285i 0.601871 + 0.983741i
\(638\) 0 0
\(639\) 6.11583 42.1339i 0.241938 1.66679i
\(640\) 0 0
\(641\) 1.66603 9.44853i 0.0658043 0.373195i −0.934066 0.357100i \(-0.883766\pi\)
0.999870 0.0160947i \(-0.00512331\pi\)
\(642\) 0 0
\(643\) −25.7814 + 21.6332i −1.01672 + 0.853129i −0.989212 0.146493i \(-0.953202\pi\)
−0.0275077 + 0.999622i \(0.508757\pi\)
\(644\) 0 0
\(645\) −6.56545 34.1886i −0.258515 1.34617i
\(646\) 0 0
\(647\) 6.00802 10.4062i 0.236200 0.409110i −0.723421 0.690407i \(-0.757431\pi\)
0.959621 + 0.281297i \(0.0907647\pi\)
\(648\) 0 0
\(649\) −7.65375 13.2567i −0.300436 0.520370i
\(650\) 0 0
\(651\) −5.27339 8.57175i −0.206680 0.335954i
\(652\) 0 0
\(653\) −9.89469 3.60137i −0.387209 0.140933i 0.141078 0.989999i \(-0.454943\pi\)
−0.528287 + 0.849066i \(0.677165\pi\)
\(654\) 0 0
\(655\) −1.40375 + 7.96104i −0.0548489 + 0.311064i
\(656\) 0 0
\(657\) −0.260824 + 1.79690i −0.0101757 + 0.0701037i
\(658\) 0 0
\(659\) 25.7075 + 21.5712i 1.00142 + 0.840294i 0.987181 0.159604i \(-0.0510218\pi\)
0.0142429 + 0.999899i \(0.495466\pi\)
\(660\) 0 0
\(661\) −27.1449 9.87993i −1.05581 0.384285i −0.244960 0.969533i \(-0.578775\pi\)
−0.810854 + 0.585248i \(0.800997\pi\)
\(662\) 0 0
\(663\) −1.40600 + 8.74917i −0.0546047 + 0.339790i
\(664\) 0 0
\(665\) 8.73584 53.5195i 0.338761 2.07540i
\(666\) 0 0
\(667\) −24.3044 −0.941070
\(668\) 0 0
\(669\) −2.64001 + 0.0401147i −0.102069 + 0.00155092i
\(670\) 0 0
\(671\) 29.2580 + 10.6491i 1.12949 + 0.411102i
\(672\) 0 0
\(673\) 6.77748 38.4370i 0.261253 1.48164i −0.518245 0.855232i \(-0.673415\pi\)
0.779498 0.626405i \(-0.215474\pi\)
\(674\) 0 0
\(675\) 2.05025 15.8112i 0.0789143 0.608572i
\(676\) 0 0
\(677\) 30.9229 11.2550i 1.18846 0.432565i 0.329279 0.944233i \(-0.393194\pi\)
0.859184 + 0.511668i \(0.170972\pi\)
\(678\) 0 0
\(679\) −18.2480 + 32.5568i −0.700293 + 1.24942i
\(680\) 0 0
\(681\) 28.3393 0.430613i 1.08596 0.0165011i
\(682\) 0 0
\(683\) 1.42785 + 2.47311i 0.0546352 + 0.0946309i 0.892049 0.451938i \(-0.149267\pi\)
−0.837414 + 0.546569i \(0.815934\pi\)
\(684\) 0 0
\(685\) −7.26997 12.5920i −0.277771 0.481114i
\(686\) 0 0
\(687\) 5.61467 2.14073i 0.214213 0.0816738i
\(688\) 0 0
\(689\) −6.97424 2.53841i −0.265697 0.0967059i
\(690\) 0 0
\(691\) −2.65879 + 15.0788i −0.101145 + 0.573623i 0.891545 + 0.452932i \(0.149622\pi\)
−0.992690 + 0.120691i \(0.961489\pi\)
\(692\) 0 0
\(693\) 2.31250 17.4958i 0.0878448 0.664612i
\(694\) 0 0
\(695\) 48.7981 + 40.9465i 1.85102 + 1.55319i
\(696\) 0 0
\(697\) 1.27511 + 7.23151i 0.0482982 + 0.273913i
\(698\) 0 0
\(699\) 19.8605 17.1858i 0.751192 0.650028i
\(700\) 0 0
\(701\) 34.7791 1.31359 0.656795 0.754070i \(-0.271912\pi\)
0.656795 + 0.754070i \(0.271912\pi\)
\(702\) 0 0
\(703\) 21.3597 36.9960i 0.805595 1.39533i
\(704\) 0 0
\(705\) 9.20839 + 47.9513i 0.346808 + 1.80595i
\(706\) 0 0
\(707\) 38.9808 0.496351i 1.46603 0.0186672i
\(708\) 0 0
\(709\) −7.34268 6.16124i −0.275760 0.231390i 0.494410 0.869229i \(-0.335384\pi\)
−0.770170 + 0.637839i \(0.779829\pi\)
\(710\) 0 0
\(711\) 22.0347 + 7.26976i 0.826365 + 0.272637i
\(712\) 0 0
\(713\) −4.44543 3.73016i −0.166483 0.139696i
\(714\) 0 0
\(715\) 4.56020 + 25.8622i 0.170542 + 0.967191i
\(716\) 0 0
\(717\) 2.21638 + 1.80309i 0.0827722 + 0.0673378i
\(718\) 0 0
\(719\) 19.2972 33.4238i 0.719665 1.24650i −0.241468 0.970409i \(-0.577629\pi\)
0.961133 0.276087i \(-0.0890378\pi\)
\(720\) 0 0
\(721\) 5.83806 35.7664i 0.217421 1.33201i
\(722\) 0 0
\(723\) −13.7645 23.0256i −0.511906 0.856331i
\(724\) 0 0
\(725\) −21.6193 + 18.1408i −0.802921 + 0.673731i
\(726\) 0 0
\(727\) 8.94631 50.7371i 0.331800 1.88173i −0.124988 0.992158i \(-0.539889\pi\)
0.456789 0.889575i \(-0.349000\pi\)
\(728\) 0 0
\(729\) −11.3153 + 24.5146i −0.419084 + 0.907947i
\(730\) 0 0
\(731\) −6.66949 5.59636i −0.246680 0.206989i
\(732\) 0 0
\(733\) −4.01993 22.7981i −0.148479 0.842068i −0.964507 0.264056i \(-0.914940\pi\)
0.816028 0.578012i \(-0.196172\pi\)
\(734\) 0 0
\(735\) −32.8141 10.4537i −1.21037 0.385589i
\(736\) 0 0
\(737\) −14.3088 −0.527070
\(738\) 0 0
\(739\) −41.9581 −1.54345 −0.771727 0.635954i \(-0.780607\pi\)
−0.771727 + 0.635954i \(0.780607\pi\)
\(740\) 0 0
\(741\) 8.24558 51.3099i 0.302909 1.88492i
\(742\) 0 0
\(743\) −8.66867 49.1625i −0.318023 1.80360i −0.554747 0.832019i \(-0.687185\pi\)
0.236724 0.971577i \(-0.423926\pi\)
\(744\) 0 0
\(745\) 36.4576 13.2695i 1.33570 0.486156i
\(746\) 0 0
\(747\) 0.113887 0.101617i 0.00416692 0.00371796i
\(748\) 0 0
\(749\) 0.934483 0.804620i 0.0341453 0.0294002i
\(750\) 0 0
\(751\) 2.28250 + 0.830761i 0.0832895 + 0.0303149i 0.383329 0.923612i \(-0.374778\pi\)
−0.300039 + 0.953927i \(0.597000\pi\)
\(752\) 0 0
\(753\) 21.7298 18.8034i 0.791877 0.685233i
\(754\) 0 0
\(755\) −4.63838 −0.168808
\(756\) 0 0
\(757\) 40.3823 1.46772 0.733859 0.679301i \(-0.237717\pi\)
0.733859 + 0.679301i \(0.237717\pi\)
\(758\) 0 0
\(759\) −1.91913 9.99360i −0.0696602 0.362745i
\(760\) 0 0
\(761\) −33.0259 12.0204i −1.19719 0.435741i −0.334946 0.942237i \(-0.608718\pi\)
−0.862242 + 0.506497i \(0.830940\pi\)
\(762\) 0 0
\(763\) −20.6288 7.21217i −0.746813 0.261098i
\(764\) 0 0
\(765\) −5.51585 8.91661i −0.199426 0.322381i
\(766\) 0 0
\(767\) −26.9006 + 9.79101i −0.971324 + 0.353533i
\(768\) 0 0
\(769\) −2.14242 12.1503i −0.0772577 0.438150i −0.998760 0.0497781i \(-0.984149\pi\)
0.921503 0.388372i \(-0.126963\pi\)
\(770\) 0 0
\(771\) −33.1109 + 12.6243i −1.19246 + 0.454654i
\(772\) 0 0
\(773\) 41.7847 1.50289 0.751446 0.659795i \(-0.229357\pi\)
0.751446 + 0.659795i \(0.229357\pi\)
\(774\) 0 0
\(775\) −6.73850 −0.242054
\(776\) 0 0
\(777\) −21.2618 16.8518i −0.762762 0.604557i
\(778\) 0 0
\(779\) −7.47795 42.4096i −0.267925 1.51948i
\(780\) 0 0
\(781\) −24.1722 20.2829i −0.864951 0.725780i
\(782\) 0 0
\(783\) 44.1195 18.3757i 1.57670 0.656693i
\(784\) 0 0
\(785\) 4.23068 23.9934i 0.150999 0.856359i
\(786\) 0 0
\(787\) 20.5306 17.2272i 0.731838 0.614085i −0.198794 0.980041i \(-0.563702\pi\)
0.930632 + 0.365956i \(0.119258\pi\)
\(788\) 0 0
\(789\) 9.91970 17.8006i 0.353151 0.633719i
\(790\) 0 0
\(791\) 3.54885 + 2.90164i 0.126182 + 0.103171i
\(792\) 0 0
\(793\) 29.1139 50.4268i 1.03387 1.79071i
\(794\) 0 0
\(795\) 8.20529 3.12846i 0.291012 0.110955i
\(796\) 0 0
\(797\) 7.81502 + 44.3212i 0.276822 + 1.56994i 0.733113 + 0.680107i \(0.238067\pi\)
−0.456291 + 0.889831i \(0.650822\pi\)
\(798\) 0 0
\(799\) 9.35430 + 7.84919i 0.330932 + 0.277685i
\(800\) 0 0
\(801\) −38.4652 30.3332i −1.35910 1.07177i
\(802\) 0 0
\(803\) 1.03088 + 0.865013i 0.0363791 + 0.0305257i
\(804\) 0 0
\(805\) −19.8566 + 0.252839i −0.699855 + 0.00891139i
\(806\) 0 0
\(807\) 27.2097 23.5453i 0.957827 0.828834i
\(808\) 0 0
\(809\) −13.7505 + 23.8166i −0.483443 + 0.837348i −0.999819 0.0190140i \(-0.993947\pi\)
0.516376 + 0.856362i \(0.327281\pi\)
\(810\) 0 0
\(811\) −42.7704 −1.50187 −0.750936 0.660375i \(-0.770397\pi\)
−0.750936 + 0.660375i \(0.770397\pi\)
\(812\) 0 0
\(813\) 4.06521 + 21.1689i 0.142573 + 0.742427i
\(814\) 0 0
\(815\) 3.24311 + 18.3926i 0.113601 + 0.644264i
\(816\) 0 0
\(817\) 39.1135 + 32.8202i 1.36841 + 1.14823i
\(818\) 0 0
\(819\) −31.4714 9.94066i −1.09970 0.347355i
\(820\) 0 0
\(821\) 5.95102 33.7499i 0.207692 1.17788i −0.685455 0.728115i \(-0.740397\pi\)
0.893147 0.449765i \(-0.148492\pi\)
\(822\) 0 0
\(823\) −4.07675 1.48381i −0.142106 0.0517225i 0.269988 0.962864i \(-0.412980\pi\)
−0.412094 + 0.911141i \(0.635203\pi\)
\(824\) 0 0
\(825\) −9.16632 7.45709i −0.319130 0.259623i
\(826\) 0 0
\(827\) 4.64312 + 8.04211i 0.161457 + 0.279652i 0.935391 0.353614i \(-0.115047\pi\)
−0.773934 + 0.633266i \(0.781714\pi\)
\(828\) 0 0
\(829\) −10.0346 17.3804i −0.348515 0.603646i 0.637471 0.770475i \(-0.279981\pi\)
−0.985986 + 0.166828i \(0.946647\pi\)
\(830\) 0 0
\(831\) −25.3307 + 45.4552i −0.878712 + 1.57682i
\(832\) 0 0
\(833\) −8.01575 + 3.15087i −0.277729 + 0.109171i
\(834\) 0 0
\(835\) 28.1522 10.2466i 0.974247 0.354597i
\(836\) 0 0
\(837\) 10.8900 + 3.41029i 0.376413 + 0.117877i
\(838\) 0 0
\(839\) −9.23820 + 52.3924i −0.318938 + 1.80879i 0.230297 + 0.973120i \(0.426030\pi\)
−0.549236 + 0.835668i \(0.685081\pi\)
\(840\) 0 0
\(841\) −52.2468 19.0163i −1.80161 0.655734i
\(842\) 0 0
\(843\) 4.27581 + 7.15271i 0.147267 + 0.246352i
\(844\) 0 0
\(845\) 12.1855 0.419194
\(846\) 0 0
\(847\) 12.4049 + 10.1426i 0.426237 + 0.348504i
\(848\) 0 0
\(849\) 35.7445 + 29.0793i 1.22675 + 0.998000i
\(850\) 0 0
\(851\) −14.7004 5.35051i −0.503923 0.183413i
\(852\) 0 0
\(853\) 28.1219 + 23.5971i 0.962875 + 0.807948i 0.981418 0.191880i \(-0.0614584\pi\)
−0.0185434 + 0.999828i \(0.505903\pi\)
\(854\) 0 0
\(855\) 32.3480 + 52.2919i 1.10628 + 1.78835i
\(856\) 0 0
\(857\) 7.86132 44.5838i 0.268538 1.52295i −0.490231 0.871593i \(-0.663088\pi\)
0.758769 0.651360i \(-0.225801\pi\)
\(858\) 0 0
\(859\) 14.7230 + 5.35872i 0.502341 + 0.182837i 0.580746 0.814084i \(-0.302761\pi\)
−0.0784058 + 0.996922i \(0.524983\pi\)
\(860\) 0 0
\(861\) −27.3383 + 0.763656i −0.931687 + 0.0260253i
\(862\) 0 0
\(863\) 14.2234 + 24.6356i 0.484169 + 0.838606i 0.999835 0.0181843i \(-0.00578855\pi\)
−0.515665 + 0.856790i \(0.672455\pi\)
\(864\) 0 0
\(865\) −24.6884 + 42.7615i −0.839429 + 1.45393i
\(866\) 0 0
\(867\) 25.3416 + 8.78991i 0.860646 + 0.298521i
\(868\) 0 0
\(869\) 13.1735 11.0539i 0.446880 0.374977i
\(870\) 0 0
\(871\) −4.64669 + 26.3527i −0.157447 + 0.892927i
\(872\) 0 0
\(873\) −8.61150 41.4338i −0.291455 1.40232i
\(874\) 0 0
\(875\) 11.0008 9.47208i 0.371896 0.320215i
\(876\) 0 0
\(877\) 21.7836 18.2786i 0.735579 0.617224i −0.196067 0.980590i \(-0.562817\pi\)
0.931646 + 0.363366i \(0.118373\pi\)
\(878\) 0 0
\(879\) −9.14529 7.43999i −0.308463 0.250945i
\(880\) 0 0
\(881\) 23.2485 + 40.2676i 0.783262 + 1.35665i 0.930032 + 0.367478i \(0.119779\pi\)
−0.146771 + 0.989171i \(0.546888\pi\)
\(882\) 0 0
\(883\) −2.72232 + 4.71519i −0.0916132 + 0.158679i −0.908190 0.418558i \(-0.862536\pi\)
0.816577 + 0.577237i \(0.195869\pi\)
\(884\) 0 0
\(885\) 16.4880 29.5873i 0.554239 0.994567i
\(886\) 0 0
\(887\) 0.281794 + 1.59813i 0.00946172 + 0.0536601i 0.989173 0.146754i \(-0.0468825\pi\)
−0.979711 + 0.200414i \(0.935771\pi\)
\(888\) 0 0
\(889\) −1.78841 0.625259i −0.0599814 0.0209705i
\(890\) 0 0
\(891\) 11.0396 + 16.6903i 0.369840 + 0.559145i
\(892\) 0 0
\(893\) −54.8588 46.0320i −1.83578 1.54040i
\(894\) 0 0
\(895\) −2.55816 0.931095i −0.0855099 0.0311231i
\(896\) 0 0
\(897\) −19.0286 + 0.289138i −0.635347 + 0.00965405i
\(898\) 0 0
\(899\) −10.0999 17.4935i −0.336849 0.583439i
\(900\) 0 0
\(901\) 1.09807 1.90191i 0.0365820 0.0633619i
\(902\) 0 0
\(903\) 24.2486 21.5289i 0.806942 0.716438i
\(904\) 0 0
\(905\) −43.4620 + 36.4690i −1.44473 + 1.21227i
\(906\) 0 0
\(907\) 16.6192 6.04889i 0.551831 0.200850i −0.0510286 0.998697i \(-0.516250\pi\)
0.602860 + 0.797847i \(0.294028\pi\)
\(908\) 0 0
\(909\) −32.9831 + 29.4293i −1.09398 + 0.976108i
\(910\) 0 0
\(911\) −37.8940 + 13.7923i −1.25548 + 0.456959i −0.882251 0.470779i \(-0.843973\pi\)
−0.373233 + 0.927738i \(0.621751\pi\)
\(912\) 0 0
\(913\) −0.0196434 0.111403i −0.000650102 0.00368691i
\(914\) 0 0
\(915\) 12.9929 + 67.6586i 0.429533 + 2.23673i
\(916\) 0 0
\(917\) −7.04220 + 2.66517i −0.232554 + 0.0880118i
\(918\) 0 0
\(919\) 8.08348 + 14.0010i 0.266649 + 0.461850i 0.967994 0.250972i \(-0.0807501\pi\)
−0.701345 + 0.712822i \(0.747417\pi\)
\(920\) 0 0
\(921\) 3.20815 + 16.7060i 0.105712 + 0.550480i
\(922\) 0 0
\(923\) −45.2052 + 37.9317i −1.48795 + 1.24854i
\(924\) 0 0
\(925\) −17.0700 + 6.21295i −0.561257 + 0.204281i
\(926\) 0 0
\(927\) 21.6178 + 34.9461i 0.710020 + 1.14778i
\(928\) 0 0
\(929\) 2.31381 13.1223i 0.0759136 0.430528i −0.923036 0.384713i \(-0.874300\pi\)
0.998950 0.0458148i \(-0.0145884\pi\)
\(930\) 0 0
\(931\) 47.0088 18.4784i 1.54065 0.605606i
\(932\) 0 0
\(933\) 10.0712 + 8.19323i 0.329716 + 0.268234i
\(934\) 0 0
\(935\) −7.77075 −0.254131
\(936\) 0 0
\(937\) −14.2562 + 24.6924i −0.465728 + 0.806665i −0.999234 0.0391314i \(-0.987541\pi\)
0.533506 + 0.845796i \(0.320874\pi\)
\(938\) 0 0
\(939\) 5.79307 10.3955i 0.189050 0.339245i
\(940\) 0 0
\(941\) −16.5773 + 13.9100i −0.540406 + 0.453454i −0.871677 0.490082i \(-0.836967\pi\)
0.331271 + 0.943536i \(0.392523\pi\)
\(942\) 0 0
\(943\) −14.8189 + 5.39365i −0.482571 + 0.175642i
\(944\) 0 0
\(945\) 35.8544 15.4719i 1.16634 0.503300i
\(946\) 0 0
\(947\) −0.937338 + 0.341163i −0.0304594 + 0.0110863i −0.357205 0.934026i \(-0.616270\pi\)
0.326746 + 0.945112i \(0.394048\pi\)
\(948\) 0 0
\(949\) 1.92788 1.61769i 0.0625818 0.0525123i
\(950\) 0 0
\(951\) 17.7779 + 29.7394i 0.576487 + 0.964365i
\(952\) 0 0
\(953\) −26.1992 + 45.3784i −0.848677 + 1.46995i 0.0337131 + 0.999432i \(0.489267\pi\)
−0.882390 + 0.470519i \(0.844067\pi\)
\(954\) 0 0
\(955\) −2.06192 −0.0667223
\(956\) 0 0
\(957\) 5.62023 34.9731i 0.181676 1.13052i
\(958\) 0 0
\(959\) 6.62169 11.8140i 0.213826 0.381493i
\(960\) 0 0
\(961\) −4.54558 + 25.7793i −0.146632 + 0.831590i
\(962\) 0 0
\(963\) −0.200856 + 1.38376i −0.00647251 + 0.0445912i
\(964\) 0 0
\(965\) −8.95260 + 3.25848i −0.288194 + 0.104894i
\(966\) 0 0
\(967\) 11.3231 9.50124i 0.364128 0.305539i −0.442306 0.896864i \(-0.645839\pi\)
0.806433 + 0.591325i \(0.201395\pi\)
\(968\) 0 0
\(969\) 14.5284 + 5.03928i 0.466720 + 0.161885i
\(970\) 0 0
\(971\) 24.9123 + 43.1494i 0.799475 + 1.38473i 0.919958 + 0.392016i \(0.128222\pi\)
−0.120483 + 0.992715i \(0.538444\pi\)
\(972\) 0 0
\(973\) −9.55848 + 58.5593i −0.306431 + 1.87733i
\(974\) 0 0
\(975\) −16.7106 + 14.4601i −0.535167 + 0.463094i
\(976\) 0 0
\(977\) 2.65154 + 15.0376i 0.0848301 + 0.481096i 0.997393 + 0.0721594i \(0.0229890\pi\)
−0.912563 + 0.408936i \(0.865900\pi\)
\(978\) 0 0
\(979\) −34.1166 + 12.4174i −1.09037 + 0.396863i
\(980\) 0 0
\(981\) 23.0166 9.17854i 0.734863 0.293048i
\(982\) 0 0
\(983\) −29.5168 + 10.7432i −0.941439 + 0.342656i −0.766734 0.641965i \(-0.778119\pi\)
−0.174705 + 0.984621i \(0.555897\pi\)
\(984\) 0 0
\(985\) −36.0123 + 30.2179i −1.14745 + 0.962823i
\(986\) 0 0
\(987\) −34.0099 + 30.1954i −1.08255 + 0.961132i
\(988\) 0 0
\(989\) 9.34894 16.1928i 0.297279 0.514902i
\(990\) 0 0
\(991\) 24.0599 + 41.6729i 0.764287 + 1.32378i 0.940623 + 0.339453i \(0.110242\pi\)
−0.176336 + 0.984330i \(0.556425\pi\)
\(992\) 0 0
\(993\) −5.99161 10.0229i −0.190138 0.318068i
\(994\) 0 0
\(995\) 46.1444 + 16.7952i 1.46288 + 0.532444i
\(996\) 0 0
\(997\) −16.0592 13.4753i −0.508601 0.426767i 0.352035 0.935987i \(-0.385490\pi\)
−0.860637 + 0.509220i \(0.829934\pi\)
\(998\) 0 0
\(999\) 30.7308 1.40172i 0.972280 0.0443485i
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 756.2.bq.a.25.3 yes 144
7.2 even 3 756.2.bp.a.457.20 yes 144
27.13 even 9 756.2.bp.a.445.20 144
189.121 even 9 inner 756.2.bq.a.121.3 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.445.20 144 27.13 even 9
756.2.bp.a.457.20 yes 144 7.2 even 3
756.2.bq.a.25.3 yes 144 1.1 even 1 trivial
756.2.bq.a.121.3 yes 144 189.121 even 9 inner