Properties

Label 920.2.bv.a.17.2
Level $920$
Weight $2$
Character 920.17
Analytic conductor $7.346$
Analytic rank $0$
Dimension $720$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(17,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bv (of order \(44\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(720\)
Relative dimension: \(36\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 920.17
Dual form 920.2.bv.a.433.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.83699 + 1.54911i) q^{3} +(0.823524 - 2.07890i) q^{5} +(-2.50378 - 3.34466i) q^{7} +(4.02684 - 6.26588i) q^{9} +(-2.09151 + 0.955162i) q^{11} +(-3.94512 - 2.95328i) q^{13} +(0.884116 + 7.17354i) q^{15} +(0.306224 + 4.28157i) q^{17} +(3.62640 + 4.18509i) q^{19} +(12.2844 + 5.61012i) q^{21} +(3.71368 - 3.03456i) q^{23} +(-3.64362 - 3.42404i) q^{25} +(-1.02575 + 14.3418i) q^{27} +(4.00107 + 3.46695i) q^{29} +(-7.20387 + 2.11525i) q^{31} +(4.45395 - 5.94977i) q^{33} +(-9.01512 + 2.45069i) q^{35} +(-5.96155 + 1.29686i) q^{37} +(15.7673 + 2.26699i) q^{39} +(2.67857 - 1.72141i) q^{41} +(-0.506766 - 0.928072i) q^{43} +(-9.70992 - 13.5315i) q^{45} +(1.89883 + 1.89883i) q^{47} +(-2.94569 + 10.0321i) q^{49} +(-7.50139 - 11.6724i) q^{51} +(-3.73011 + 2.79232i) q^{53} +(0.263270 + 5.13463i) q^{55} +(-16.7712 - 6.25535i) q^{57} +(-8.23557 + 1.18410i) q^{59} +(3.86637 + 13.1677i) q^{61} +(-31.0395 + 2.21999i) q^{63} +(-9.38847 + 5.76940i) q^{65} +(0.861972 + 2.31104i) q^{67} +(-5.83481 + 14.3619i) q^{69} +(0.667794 - 1.46227i) q^{71} +(7.05309 + 0.504447i) q^{73} +(15.6411 + 4.06960i) q^{75} +(8.43137 + 4.60388i) q^{77} +(-1.31624 - 9.15465i) q^{79} +(-10.0247 - 21.9511i) q^{81} +(0.975600 + 4.48476i) q^{83} +(9.15312 + 2.88937i) q^{85} +(-16.7217 - 3.63758i) q^{87} +(-5.18455 - 1.52232i) q^{89} +20.5895i q^{91} +(17.1606 - 17.1606i) q^{93} +(11.6868 - 4.09239i) q^{95} +(-2.50196 + 11.5013i) q^{97} +(-2.43725 + 16.9514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −2.83699 + 1.54911i −1.63794 + 0.894381i −0.646631 + 0.762803i \(0.723823\pi\)
−0.991306 + 0.131579i \(0.957995\pi\)
\(4\) 0 0
\(5\) 0.823524 2.07890i 0.368291 0.929710i
\(6\) 0 0
\(7\) −2.50378 3.34466i −0.946339 1.26416i −0.964434 0.264325i \(-0.914851\pi\)
0.0180943 0.999836i \(-0.494240\pi\)
\(8\) 0 0
\(9\) 4.02684 6.26588i 1.34228 2.08863i
\(10\) 0 0
\(11\) −2.09151 + 0.955162i −0.630615 + 0.287992i −0.704967 0.709240i \(-0.749038\pi\)
0.0743525 + 0.997232i \(0.476311\pi\)
\(12\) 0 0
\(13\) −3.94512 2.95328i −1.09418 0.819093i −0.109591 0.993977i \(-0.534954\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(14\) 0 0
\(15\) 0.884116 + 7.17354i 0.228278 + 1.85220i
\(16\) 0 0
\(17\) 0.306224 + 4.28157i 0.0742702 + 1.03843i 0.888795 + 0.458305i \(0.151543\pi\)
−0.814525 + 0.580128i \(0.803002\pi\)
\(18\) 0 0
\(19\) 3.62640 + 4.18509i 0.831953 + 0.960125i 0.999669 0.0257099i \(-0.00818461\pi\)
−0.167716 + 0.985835i \(0.553639\pi\)
\(20\) 0 0
\(21\) 12.2844 + 5.61012i 2.68069 + 1.22423i
\(22\) 0 0
\(23\) 3.71368 3.03456i 0.774357 0.632749i
\(24\) 0 0
\(25\) −3.64362 3.42404i −0.728723 0.684809i
\(26\) 0 0
\(27\) −1.02575 + 14.3418i −0.197406 + 2.76009i
\(28\) 0 0
\(29\) 4.00107 + 3.46695i 0.742980 + 0.643796i 0.941774 0.336246i \(-0.109157\pi\)
−0.198795 + 0.980041i \(0.563703\pi\)
\(30\) 0 0
\(31\) −7.20387 + 2.11525i −1.29385 + 0.379910i −0.854990 0.518644i \(-0.826437\pi\)
−0.438864 + 0.898554i \(0.644619\pi\)
\(32\) 0 0
\(33\) 4.45395 5.94977i 0.775332 1.03572i
\(34\) 0 0
\(35\) −9.01512 + 2.45069i −1.52383 + 0.414242i
\(36\) 0 0
\(37\) −5.96155 + 1.29686i −0.980073 + 0.213202i −0.673939 0.738787i \(-0.735399\pi\)
−0.306133 + 0.951989i \(0.599035\pi\)
\(38\) 0 0
\(39\) 15.7673 + 2.26699i 2.52478 + 0.363009i
\(40\) 0 0
\(41\) 2.67857 1.72141i 0.418322 0.268839i −0.314503 0.949256i \(-0.601838\pi\)
0.732825 + 0.680417i \(0.238201\pi\)
\(42\) 0 0
\(43\) −0.506766 0.928072i −0.0772811 0.141530i 0.836181 0.548454i \(-0.184783\pi\)
−0.913462 + 0.406924i \(0.866601\pi\)
\(44\) 0 0
\(45\) −9.70992 13.5315i −1.44747 2.01715i
\(46\) 0 0
\(47\) 1.89883 + 1.89883i 0.276973 + 0.276973i 0.831899 0.554926i \(-0.187254\pi\)
−0.554926 + 0.831899i \(0.687254\pi\)
\(48\) 0 0
\(49\) −2.94569 + 10.0321i −0.420813 + 1.43316i
\(50\) 0 0
\(51\) −7.50139 11.6724i −1.05041 1.63446i
\(52\) 0 0
\(53\) −3.73011 + 2.79232i −0.512369 + 0.383555i −0.823948 0.566665i \(-0.808233\pi\)
0.311579 + 0.950220i \(0.399142\pi\)
\(54\) 0 0
\(55\) 0.263270 + 5.13463i 0.0354993 + 0.692354i
\(56\) 0 0
\(57\) −16.7712 6.25535i −2.22141 0.828542i
\(58\) 0 0
\(59\) −8.23557 + 1.18410i −1.07218 + 0.154156i −0.655725 0.755000i \(-0.727637\pi\)
−0.416455 + 0.909156i \(0.636728\pi\)
\(60\) 0 0
\(61\) 3.86637 + 13.1677i 0.495038 + 1.68595i 0.705802 + 0.708409i \(0.250587\pi\)
−0.210764 + 0.977537i \(0.567595\pi\)
\(62\) 0 0
\(63\) −31.0395 + 2.21999i −3.91061 + 0.279693i
\(64\) 0 0
\(65\) −9.38847 + 5.76940i −1.16450 + 0.715606i
\(66\) 0 0
\(67\) 0.861972 + 2.31104i 0.105307 + 0.282338i 0.978907 0.204306i \(-0.0654937\pi\)
−0.873601 + 0.486644i \(0.838221\pi\)
\(68\) 0 0
\(69\) −5.83481 + 14.3619i −0.702429 + 1.72897i
\(70\) 0 0
\(71\) 0.667794 1.46227i 0.0792526 0.173539i −0.865858 0.500290i \(-0.833227\pi\)
0.945110 + 0.326751i \(0.105954\pi\)
\(72\) 0 0
\(73\) 7.05309 + 0.504447i 0.825502 + 0.0590410i 0.477696 0.878525i \(-0.341472\pi\)
0.347806 + 0.937566i \(0.386927\pi\)
\(74\) 0 0
\(75\) 15.6411 + 4.06960i 1.80608 + 0.469917i
\(76\) 0 0
\(77\) 8.43137 + 4.60388i 0.960844 + 0.524660i
\(78\) 0 0
\(79\) −1.31624 9.15465i −0.148089 1.02998i −0.919344 0.393454i \(-0.871280\pi\)
0.771256 0.636525i \(-0.219629\pi\)
\(80\) 0 0
\(81\) −10.0247 21.9511i −1.11386 2.43902i
\(82\) 0 0
\(83\) 0.975600 + 4.48476i 0.107086 + 0.492266i 0.999183 + 0.0404218i \(0.0128702\pi\)
−0.892097 + 0.451844i \(0.850766\pi\)
\(84\) 0 0
\(85\) 9.15312 + 2.88937i 0.992795 + 0.313396i
\(86\) 0 0
\(87\) −16.7217 3.63758i −1.79275 0.389989i
\(88\) 0 0
\(89\) −5.18455 1.52232i −0.549561 0.161366i −0.00484811 0.999988i \(-0.501543\pi\)
−0.544713 + 0.838623i \(0.683361\pi\)
\(90\) 0 0
\(91\) 20.5895i 2.15836i
\(92\) 0 0
\(93\) 17.1606 17.1606i 1.77947 1.77947i
\(94\) 0 0
\(95\) 11.6868 4.09239i 1.19904 0.419870i
\(96\) 0 0
\(97\) −2.50196 + 11.5013i −0.254036 + 1.16778i 0.656491 + 0.754334i \(0.272040\pi\)
−0.910527 + 0.413450i \(0.864324\pi\)
\(98\) 0 0
\(99\) −2.43725 + 16.9514i −0.244953 + 1.70368i
\(100\) 0 0
\(101\) 5.13105 + 3.29752i 0.510558 + 0.328116i 0.770427 0.637528i \(-0.220043\pi\)
−0.259869 + 0.965644i \(0.583679\pi\)
\(102\) 0 0
\(103\) 5.40218 14.4838i 0.532293 1.42713i −0.341058 0.940042i \(-0.610785\pi\)
0.873351 0.487091i \(-0.161942\pi\)
\(104\) 0 0
\(105\) 21.7794 20.9180i 2.12545 2.04139i
\(106\) 0 0
\(107\) −2.73025 + 5.00008i −0.263943 + 0.483376i −0.975718 0.219032i \(-0.929710\pi\)
0.711774 + 0.702408i \(0.247892\pi\)
\(108\) 0 0
\(109\) 8.99848 10.3848i 0.861898 0.994683i −0.138093 0.990419i \(-0.544097\pi\)
0.999991 0.00426394i \(-0.00135726\pi\)
\(110\) 0 0
\(111\) 14.9039 12.9143i 1.41461 1.22577i
\(112\) 0 0
\(113\) −14.2265 + 5.30620i −1.33831 + 0.499165i −0.913766 0.406240i \(-0.866840\pi\)
−0.424548 + 0.905406i \(0.639567\pi\)
\(114\) 0 0
\(115\) −3.25022 10.2194i −0.303085 0.952964i
\(116\) 0 0
\(117\) −34.3913 + 12.8273i −3.17948 + 1.18588i
\(118\) 0 0
\(119\) 13.5537 11.7443i 1.24246 1.07660i
\(120\) 0 0
\(121\) −3.74138 + 4.31778i −0.340125 + 0.392526i
\(122\) 0 0
\(123\) −4.93241 + 9.03303i −0.444740 + 0.814481i
\(124\) 0 0
\(125\) −10.1188 + 4.75491i −0.905056 + 0.425292i
\(126\) 0 0
\(127\) −5.29327 + 14.1918i −0.469702 + 1.25932i 0.458982 + 0.888446i \(0.348214\pi\)
−0.928684 + 0.370873i \(0.879059\pi\)
\(128\) 0 0
\(129\) 2.87538 + 1.84789i 0.253163 + 0.162698i
\(130\) 0 0
\(131\) −0.00349255 + 0.0242912i −0.000305145 + 0.00212233i −0.989973 0.141254i \(-0.954887\pi\)
0.989668 + 0.143376i \(0.0457958\pi\)
\(132\) 0 0
\(133\) 4.91798 22.6076i 0.426443 1.96033i
\(134\) 0 0
\(135\) 28.9705 + 13.9433i 2.49338 + 1.20005i
\(136\) 0 0
\(137\) 0.503236 0.503236i 0.0429944 0.0429944i −0.685283 0.728277i \(-0.740321\pi\)
0.728277 + 0.685283i \(0.240321\pi\)
\(138\) 0 0
\(139\) 6.91548i 0.586564i 0.956026 + 0.293282i \(0.0947474\pi\)
−0.956026 + 0.293282i \(0.905253\pi\)
\(140\) 0 0
\(141\) −8.32847 2.44546i −0.701384 0.205945i
\(142\) 0 0
\(143\) 11.0721 + 2.40860i 0.925899 + 0.201417i
\(144\) 0 0
\(145\) 10.5024 5.46269i 0.872176 0.453652i
\(146\) 0 0
\(147\) −7.18398 33.0242i −0.592524 2.72379i
\(148\) 0 0
\(149\) −3.47939 7.61881i −0.285043 0.624157i 0.711901 0.702280i \(-0.247835\pi\)
−0.996944 + 0.0781229i \(0.975107\pi\)
\(150\) 0 0
\(151\) −0.590028 4.10373i −0.0480158 0.333957i −0.999643 0.0267033i \(-0.991499\pi\)
0.951628 0.307254i \(-0.0994100\pi\)
\(152\) 0 0
\(153\) 28.0609 + 15.3224i 2.26859 + 1.23874i
\(154\) 0 0
\(155\) −1.53519 + 16.7181i −0.123309 + 1.34283i
\(156\) 0 0
\(157\) 7.23164 + 0.517217i 0.577148 + 0.0412784i 0.356862 0.934157i \(-0.383847\pi\)
0.220286 + 0.975435i \(0.429301\pi\)
\(158\) 0 0
\(159\) 6.25665 13.7002i 0.496185 1.08649i
\(160\) 0 0
\(161\) −19.4478 4.82314i −1.53270 0.380116i
\(162\) 0 0
\(163\) 4.49192 + 12.0433i 0.351834 + 0.943304i 0.985497 + 0.169694i \(0.0542781\pi\)
−0.633663 + 0.773610i \(0.718449\pi\)
\(164\) 0 0
\(165\) −8.70103 14.1591i −0.677374 1.10228i
\(166\) 0 0
\(167\) 15.7539 1.12674i 1.21907 0.0871900i 0.553068 0.833136i \(-0.313457\pi\)
0.666007 + 0.745946i \(0.268002\pi\)
\(168\) 0 0
\(169\) 3.17960 + 10.8287i 0.244585 + 0.832979i
\(170\) 0 0
\(171\) 40.8262 5.86992i 3.12206 0.448884i
\(172\) 0 0
\(173\) −4.21759 1.57308i −0.320657 0.119599i 0.183981 0.982930i \(-0.441101\pi\)
−0.504639 + 0.863331i \(0.668374\pi\)
\(174\) 0 0
\(175\) −2.32944 + 20.7597i −0.176089 + 1.56928i
\(176\) 0 0
\(177\) 21.5299 16.1171i 1.61829 1.21144i
\(178\) 0 0
\(179\) −5.09858 7.93355i −0.381086 0.592981i 0.596731 0.802441i \(-0.296466\pi\)
−0.977817 + 0.209460i \(0.932829\pi\)
\(180\) 0 0
\(181\) −5.76781 + 19.6434i −0.428718 + 1.46008i 0.408272 + 0.912861i \(0.366132\pi\)
−0.836990 + 0.547219i \(0.815687\pi\)
\(182\) 0 0
\(183\) −31.3671 31.3671i −2.31872 2.31872i
\(184\) 0 0
\(185\) −2.21345 + 13.4614i −0.162736 + 0.989704i
\(186\) 0 0
\(187\) −4.73006 8.66246i −0.345896 0.633462i
\(188\) 0 0
\(189\) 50.5368 32.4780i 3.67601 2.36243i
\(190\) 0 0
\(191\) 4.56066 + 0.655723i 0.329997 + 0.0474465i 0.305322 0.952249i \(-0.401236\pi\)
0.0246751 + 0.999696i \(0.492145\pi\)
\(192\) 0 0
\(193\) 2.83082 0.615808i 0.203767 0.0443268i −0.109523 0.993984i \(-0.534932\pi\)
0.313290 + 0.949657i \(0.398569\pi\)
\(194\) 0 0
\(195\) 17.6975 30.9115i 1.26735 2.21362i
\(196\) 0 0
\(197\) −8.75134 + 11.6904i −0.623507 + 0.832908i −0.995444 0.0953500i \(-0.969603\pi\)
0.371937 + 0.928258i \(0.378694\pi\)
\(198\) 0 0
\(199\) −2.62762 + 0.771540i −0.186267 + 0.0546930i −0.373536 0.927616i \(-0.621855\pi\)
0.187269 + 0.982309i \(0.440037\pi\)
\(200\) 0 0
\(201\) −6.02546 5.22109i −0.425003 0.368267i
\(202\) 0 0
\(203\) 1.57795 22.0627i 0.110751 1.54850i
\(204\) 0 0
\(205\) −1.37277 6.98608i −0.0958782 0.487929i
\(206\) 0 0
\(207\) −4.05978 35.4892i −0.282174 2.46667i
\(208\) 0 0
\(209\) −11.5821 5.28937i −0.801151 0.365873i
\(210\) 0 0
\(211\) 7.34378 + 8.47517i 0.505567 + 0.583455i 0.949958 0.312378i \(-0.101125\pi\)
−0.444391 + 0.895833i \(0.646580\pi\)
\(212\) 0 0
\(213\) 0.370690 + 5.18292i 0.0253992 + 0.355128i
\(214\) 0 0
\(215\) −2.34670 + 0.289223i −0.160044 + 0.0197249i
\(216\) 0 0
\(217\) 25.1117 + 18.7984i 1.70469 + 1.27612i
\(218\) 0 0
\(219\) −20.7910 + 9.49493i −1.40492 + 0.641608i
\(220\) 0 0
\(221\) 11.4366 17.7957i 0.769309 1.19707i
\(222\) 0 0
\(223\) 8.65924 + 11.5674i 0.579866 + 0.774610i 0.990548 0.137169i \(-0.0438003\pi\)
−0.410682 + 0.911779i \(0.634709\pi\)
\(224\) 0 0
\(225\) −36.1269 + 9.04240i −2.40846 + 0.602826i
\(226\) 0 0
\(227\) −4.92676 + 2.69021i −0.327000 + 0.178556i −0.634360 0.773038i \(-0.718736\pi\)
0.307360 + 0.951593i \(0.400555\pi\)
\(228\) 0 0
\(229\) 19.0327 1.25771 0.628857 0.777521i \(-0.283523\pi\)
0.628857 + 0.777521i \(0.283523\pi\)
\(230\) 0 0
\(231\) −31.0516 −2.04305
\(232\) 0 0
\(233\) −12.6842 + 6.92611i −0.830971 + 0.453744i −0.837633 0.546234i \(-0.816061\pi\)
0.00666235 + 0.999978i \(0.497879\pi\)
\(234\) 0 0
\(235\) 5.51121 2.38374i 0.359511 0.155498i
\(236\) 0 0
\(237\) 17.9158 + 23.9327i 1.16375 + 1.55459i
\(238\) 0 0
\(239\) 6.95690 10.8251i 0.450004 0.700221i −0.539936 0.841706i \(-0.681552\pi\)
0.989940 + 0.141486i \(0.0451879\pi\)
\(240\) 0 0
\(241\) −2.91855 + 1.33286i −0.188000 + 0.0858568i −0.507191 0.861834i \(-0.669316\pi\)
0.319191 + 0.947690i \(0.396589\pi\)
\(242\) 0 0
\(243\) 27.9132 + 20.8956i 1.79063 + 1.34045i
\(244\) 0 0
\(245\) 18.4299 + 14.3855i 1.17744 + 0.919054i
\(246\) 0 0
\(247\) −1.94685 27.2205i −0.123875 1.73200i
\(248\) 0 0
\(249\) −9.71517 11.2119i −0.615674 0.710526i
\(250\) 0 0
\(251\) 2.58110 + 1.17875i 0.162918 + 0.0744021i 0.495205 0.868776i \(-0.335093\pi\)
−0.332287 + 0.943178i \(0.607820\pi\)
\(252\) 0 0
\(253\) −4.86872 + 9.89398i −0.306094 + 0.622029i
\(254\) 0 0
\(255\) −30.4433 + 5.98211i −1.90643 + 0.374614i
\(256\) 0 0
\(257\) 0.747940 10.4576i 0.0466552 0.652325i −0.919290 0.393580i \(-0.871236\pi\)
0.965946 0.258745i \(-0.0833090\pi\)
\(258\) 0 0
\(259\) 19.2639 + 16.6923i 1.19700 + 1.03721i
\(260\) 0 0
\(261\) 37.8351 11.1094i 2.34194 0.687654i
\(262\) 0 0
\(263\) −4.20686 + 5.61971i −0.259406 + 0.346526i −0.911270 0.411810i \(-0.864897\pi\)
0.651864 + 0.758336i \(0.273987\pi\)
\(264\) 0 0
\(265\) 2.73311 + 10.0540i 0.167894 + 0.617615i
\(266\) 0 0
\(267\) 17.0668 3.71265i 1.04447 0.227210i
\(268\) 0 0
\(269\) −28.2928 4.06789i −1.72504 0.248024i −0.792703 0.609608i \(-0.791327\pi\)
−0.932339 + 0.361584i \(0.882236\pi\)
\(270\) 0 0
\(271\) −17.5599 + 11.2851i −1.06669 + 0.685518i −0.951445 0.307819i \(-0.900401\pi\)
−0.115242 + 0.993337i \(0.536764\pi\)
\(272\) 0 0
\(273\) −31.8954 58.4121i −1.93040 3.53526i
\(274\) 0 0
\(275\) 10.8912 + 3.68119i 0.656763 + 0.221984i
\(276\) 0 0
\(277\) 3.14698 + 3.14698i 0.189084 + 0.189084i 0.795300 0.606216i \(-0.207313\pi\)
−0.606216 + 0.795300i \(0.707313\pi\)
\(278\) 0 0
\(279\) −15.7549 + 53.6564i −0.943223 + 3.21232i
\(280\) 0 0
\(281\) −11.4871 17.8743i −0.685265 1.06629i −0.993372 0.114941i \(-0.963332\pi\)
0.308108 0.951351i \(-0.400304\pi\)
\(282\) 0 0
\(283\) −8.07081 + 6.04173i −0.479760 + 0.359144i −0.811621 0.584185i \(-0.801414\pi\)
0.331861 + 0.943328i \(0.392324\pi\)
\(284\) 0 0
\(285\) −26.8158 + 29.7142i −1.58843 + 1.76012i
\(286\) 0 0
\(287\) −12.4641 4.64885i −0.735730 0.274413i
\(288\) 0 0
\(289\) −1.41110 + 0.202885i −0.0830058 + 0.0119344i
\(290\) 0 0
\(291\) −10.7188 36.5050i −0.628349 2.13996i
\(292\) 0 0
\(293\) 7.30962 0.522794i 0.427033 0.0305420i 0.143831 0.989602i \(-0.454058\pi\)
0.283202 + 0.959060i \(0.408603\pi\)
\(294\) 0 0
\(295\) −4.32058 + 18.0960i −0.251554 + 1.05359i
\(296\) 0 0
\(297\) −11.5534 30.9759i −0.670397 1.79740i
\(298\) 0 0
\(299\) −23.6129 + 1.00415i −1.36557 + 0.0580715i
\(300\) 0 0
\(301\) −1.83525 + 4.01865i −0.105782 + 0.231631i
\(302\) 0 0
\(303\) −19.6650 1.40647i −1.12972 0.0807994i
\(304\) 0 0
\(305\) 30.5582 + 2.80610i 1.74976 + 0.160677i
\(306\) 0 0
\(307\) −21.5092 11.7449i −1.22759 0.670317i −0.271236 0.962513i \(-0.587432\pi\)
−0.956358 + 0.292196i \(0.905614\pi\)
\(308\) 0 0
\(309\) 7.11114 + 49.4590i 0.404538 + 2.81363i
\(310\) 0 0
\(311\) −3.86753 8.46870i −0.219307 0.480216i 0.767717 0.640790i \(-0.221393\pi\)
−0.987024 + 0.160574i \(0.948666\pi\)
\(312\) 0 0
\(313\) −2.87631 13.2222i −0.162579 0.747363i −0.984162 0.177274i \(-0.943272\pi\)
0.821583 0.570089i \(-0.193091\pi\)
\(314\) 0 0
\(315\) −20.9467 + 66.3562i −1.18021 + 3.73875i
\(316\) 0 0
\(317\) −13.2133 2.87438i −0.742133 0.161441i −0.174424 0.984671i \(-0.555806\pi\)
−0.567709 + 0.823230i \(0.692170\pi\)
\(318\) 0 0
\(319\) −11.6798 3.42949i −0.653942 0.192015i
\(320\) 0 0
\(321\) 18.4147i 1.02781i
\(322\) 0 0
\(323\) −16.8083 + 16.8083i −0.935237 + 0.935237i
\(324\) 0 0
\(325\) 4.26235 + 24.2689i 0.236432 + 1.34620i
\(326\) 0 0
\(327\) −9.44136 + 43.4012i −0.522108 + 2.40009i
\(328\) 0 0
\(329\) 1.59669 11.1052i 0.0880281 0.612249i
\(330\) 0 0
\(331\) −23.5800 15.1540i −1.29608 0.832938i −0.303297 0.952896i \(-0.598087\pi\)
−0.992779 + 0.119959i \(0.961724\pi\)
\(332\) 0 0
\(333\) −15.8802 + 42.5766i −0.870232 + 2.33318i
\(334\) 0 0
\(335\) 5.51426 + 0.111245i 0.301276 + 0.00607796i
\(336\) 0 0
\(337\) −9.41546 + 17.2431i −0.512893 + 0.939293i 0.485007 + 0.874511i \(0.338817\pi\)
−0.997899 + 0.0647826i \(0.979365\pi\)
\(338\) 0 0
\(339\) 32.1405 37.0921i 1.74563 2.01456i
\(340\) 0 0
\(341\) 13.0466 11.3049i 0.706512 0.612196i
\(342\) 0 0
\(343\) 13.5273 5.04543i 0.730407 0.272428i
\(344\) 0 0
\(345\) 25.0519 + 23.9574i 1.34875 + 1.28982i
\(346\) 0 0
\(347\) 19.5750 7.30108i 1.05084 0.391943i 0.236075 0.971735i \(-0.424139\pi\)
0.814764 + 0.579792i \(0.196866\pi\)
\(348\) 0 0
\(349\) −12.6493 + 10.9607i −0.677100 + 0.586711i −0.924029 0.382323i \(-0.875124\pi\)
0.246928 + 0.969034i \(0.420579\pi\)
\(350\) 0 0
\(351\) 46.4022 53.5510i 2.47677 2.85834i
\(352\) 0 0
\(353\) 6.47038 11.8496i 0.344383 0.630691i −0.646880 0.762592i \(-0.723926\pi\)
0.991263 + 0.131901i \(0.0421082\pi\)
\(354\) 0 0
\(355\) −2.48995 2.59249i −0.132153 0.137595i
\(356\) 0 0
\(357\) −20.2583 + 54.3147i −1.07218 + 2.87464i
\(358\) 0 0
\(359\) −19.7419 12.6873i −1.04194 0.669611i −0.0964707 0.995336i \(-0.530755\pi\)
−0.945465 + 0.325725i \(0.894392\pi\)
\(360\) 0 0
\(361\) −1.66021 + 11.5470i −0.0873795 + 0.607738i
\(362\) 0 0
\(363\) 3.92552 18.0453i 0.206036 0.947134i
\(364\) 0 0
\(365\) 6.85708 14.2472i 0.358916 0.745733i
\(366\) 0 0
\(367\) −6.54247 + 6.54247i −0.341514 + 0.341514i −0.856936 0.515422i \(-0.827635\pi\)
0.515422 + 0.856936i \(0.327635\pi\)
\(368\) 0 0
\(369\) 23.7154i 1.23458i
\(370\) 0 0
\(371\) 18.6787 + 5.48457i 0.969751 + 0.284745i
\(372\) 0 0
\(373\) 5.26408 + 1.14513i 0.272564 + 0.0592926i 0.346770 0.937950i \(-0.387279\pi\)
−0.0742059 + 0.997243i \(0.523642\pi\)
\(374\) 0 0
\(375\) 21.3411 29.1649i 1.10205 1.50607i
\(376\) 0 0
\(377\) −5.54584 25.4938i −0.285625 1.31300i
\(378\) 0 0
\(379\) −12.7747 27.9727i −0.656193 1.43686i −0.886027 0.463633i \(-0.846546\pi\)
0.229834 0.973230i \(-0.426182\pi\)
\(380\) 0 0
\(381\) −6.96776 48.4619i −0.356969 2.48278i
\(382\) 0 0
\(383\) 1.26972 + 0.693322i 0.0648799 + 0.0354271i 0.511361 0.859366i \(-0.329141\pi\)
−0.446482 + 0.894793i \(0.647323\pi\)
\(384\) 0 0
\(385\) 16.5144 13.7365i 0.841653 0.700079i
\(386\) 0 0
\(387\) −7.85586 0.561862i −0.399336 0.0285610i
\(388\) 0 0
\(389\) 14.7804 32.3645i 0.749394 1.64094i −0.0180581 0.999837i \(-0.505748\pi\)
0.767452 0.641107i \(-0.221524\pi\)
\(390\) 0 0
\(391\) 14.1299 + 14.9711i 0.714579 + 0.757123i
\(392\) 0 0
\(393\) −0.0277215 0.0743242i −0.00139836 0.00374916i
\(394\) 0 0
\(395\) −20.1155 4.80275i −1.01212 0.241653i
\(396\) 0 0
\(397\) −11.1662 + 0.798620i −0.560414 + 0.0400816i −0.348673 0.937244i \(-0.613368\pi\)
−0.211741 + 0.977326i \(0.567913\pi\)
\(398\) 0 0
\(399\) 21.0695 + 71.7561i 1.05479 + 3.59230i
\(400\) 0 0
\(401\) 2.59697 0.373389i 0.129687 0.0186461i −0.0771658 0.997018i \(-0.524587\pi\)
0.206852 + 0.978372i \(0.433678\pi\)
\(402\) 0 0
\(403\) 34.6671 + 12.9302i 1.72689 + 0.644097i
\(404\) 0 0
\(405\) −53.8897 + 2.76311i −2.67780 + 0.137300i
\(406\) 0 0
\(407\) 11.2299 8.40663i 0.556648 0.416701i
\(408\) 0 0
\(409\) 20.8619 + 32.4618i 1.03156 + 1.60513i 0.767957 + 0.640502i \(0.221274\pi\)
0.263600 + 0.964632i \(0.415090\pi\)
\(410\) 0 0
\(411\) −0.648106 + 2.20725i −0.0319687 + 0.108875i
\(412\) 0 0
\(413\) 24.5804 + 24.5804i 1.20952 + 1.20952i
\(414\) 0 0
\(415\) 10.1268 + 1.66514i 0.497104 + 0.0817385i
\(416\) 0 0
\(417\) −10.7129 19.6192i −0.524612 0.960755i
\(418\) 0 0
\(419\) 2.57092 1.65223i 0.125598 0.0807167i −0.476334 0.879265i \(-0.658035\pi\)
0.601931 + 0.798548i \(0.294398\pi\)
\(420\) 0 0
\(421\) −3.89707 0.560315i −0.189932 0.0273081i 0.0466924 0.998909i \(-0.485132\pi\)
−0.236624 + 0.971601i \(0.576041\pi\)
\(422\) 0 0
\(423\) 19.5441 4.25157i 0.950268 0.206718i
\(424\) 0 0
\(425\) 13.5445 16.6489i 0.657005 0.807591i
\(426\) 0 0
\(427\) 34.3608 45.9006i 1.66283 2.22129i
\(428\) 0 0
\(429\) −35.1427 + 10.3188i −1.69671 + 0.498198i
\(430\) 0 0
\(431\) 1.14882 + 0.995462i 0.0553369 + 0.0479497i 0.682090 0.731268i \(-0.261071\pi\)
−0.626753 + 0.779218i \(0.715617\pi\)
\(432\) 0 0
\(433\) −1.13985 + 15.9372i −0.0547777 + 0.765893i 0.893623 + 0.448818i \(0.148155\pi\)
−0.948401 + 0.317074i \(0.897300\pi\)
\(434\) 0 0
\(435\) −21.3329 + 31.7670i −1.02283 + 1.52311i
\(436\) 0 0
\(437\) 26.1672 + 4.53758i 1.25175 + 0.217062i
\(438\) 0 0
\(439\) −13.7224 6.26682i −0.654935 0.299099i 0.0600948 0.998193i \(-0.480860\pi\)
−0.715030 + 0.699094i \(0.753587\pi\)
\(440\) 0 0
\(441\) 50.9982 + 58.8550i 2.42848 + 2.80262i
\(442\) 0 0
\(443\) 0.705750 + 9.86767i 0.0335312 + 0.468827i 0.986281 + 0.165073i \(0.0527858\pi\)
−0.952750 + 0.303755i \(0.901760\pi\)
\(444\) 0 0
\(445\) −7.43435 + 9.52447i −0.352422 + 0.451503i
\(446\) 0 0
\(447\) 21.6734 + 16.2245i 1.02512 + 0.767393i
\(448\) 0 0
\(449\) −18.7693 + 8.57166i −0.885779 + 0.404522i −0.805740 0.592270i \(-0.798232\pi\)
−0.0800395 + 0.996792i \(0.525505\pi\)
\(450\) 0 0
\(451\) −3.95803 + 6.15881i −0.186376 + 0.290007i
\(452\) 0 0
\(453\) 8.03105 + 10.7282i 0.377332 + 0.504056i
\(454\) 0 0
\(455\) 42.8033 + 16.9559i 2.00665 + 0.794906i
\(456\) 0 0
\(457\) −8.71660 + 4.75963i −0.407745 + 0.222646i −0.670013 0.742349i \(-0.733712\pi\)
0.262268 + 0.964995i \(0.415530\pi\)
\(458\) 0 0
\(459\) −61.7197 −2.88083
\(460\) 0 0
\(461\) −14.3758 −0.669549 −0.334775 0.942298i \(-0.608660\pi\)
−0.334775 + 0.942298i \(0.608660\pi\)
\(462\) 0 0
\(463\) 32.8411 17.9326i 1.52626 0.833399i 0.526398 0.850238i \(-0.323542\pi\)
0.999858 + 0.0168394i \(0.00536041\pi\)
\(464\) 0 0
\(465\) −21.5429 49.8072i −0.999027 2.30975i
\(466\) 0 0
\(467\) 17.3214 + 23.1387i 0.801538 + 1.07073i 0.995959 + 0.0898110i \(0.0286263\pi\)
−0.194421 + 0.980918i \(0.562283\pi\)
\(468\) 0 0
\(469\) 5.57143 8.66932i 0.257265 0.400312i
\(470\) 0 0
\(471\) −21.3173 + 9.73530i −0.982250 + 0.448579i
\(472\) 0 0
\(473\) 1.94637 + 1.45703i 0.0894940 + 0.0669944i
\(474\) 0 0
\(475\) 1.11672 27.6658i 0.0512385 1.26939i
\(476\) 0 0
\(477\) 2.47583 + 34.6166i 0.113360 + 1.58499i
\(478\) 0 0
\(479\) −22.9239 26.4556i −1.04742 1.20879i −0.977434 0.211241i \(-0.932250\pi\)
−0.0699870 0.997548i \(-0.522296\pi\)
\(480\) 0 0
\(481\) 27.3490 + 12.4899i 1.24701 + 0.569490i
\(482\) 0 0
\(483\) 62.6448 16.4437i 2.85044 0.748213i
\(484\) 0 0
\(485\) 21.8497 + 14.6730i 0.992142 + 0.666264i
\(486\) 0 0
\(487\) −2.42589 + 33.9184i −0.109928 + 1.53699i 0.580903 + 0.813973i \(0.302700\pi\)
−0.690830 + 0.723017i \(0.742755\pi\)
\(488\) 0 0
\(489\) −31.4000 27.2082i −1.41996 1.23040i
\(490\) 0 0
\(491\) 0.209759 0.0615907i 0.00946627 0.00277955i −0.276996 0.960871i \(-0.589339\pi\)
0.286462 + 0.958092i \(0.407521\pi\)
\(492\) 0 0
\(493\) −13.6187 + 18.1925i −0.613357 + 0.819350i
\(494\) 0 0
\(495\) 33.2332 + 19.0267i 1.49372 + 0.855187i
\(496\) 0 0
\(497\) −6.56278 + 1.42765i −0.294381 + 0.0640387i
\(498\) 0 0
\(499\) −34.2383 4.92272i −1.53271 0.220371i −0.676287 0.736638i \(-0.736412\pi\)
−0.856428 + 0.516267i \(0.827321\pi\)
\(500\) 0 0
\(501\) −42.9483 + 27.6012i −1.91879 + 1.23313i
\(502\) 0 0
\(503\) −3.00930 5.51113i −0.134178 0.245729i 0.801948 0.597394i \(-0.203797\pi\)
−0.936126 + 0.351665i \(0.885616\pi\)
\(504\) 0 0
\(505\) 11.0807 7.95132i 0.493087 0.353829i
\(506\) 0 0
\(507\) −25.7954 25.7954i −1.14562 1.14562i
\(508\) 0 0
\(509\) −11.0233 + 37.5420i −0.488600 + 1.66402i 0.233597 + 0.972333i \(0.424950\pi\)
−0.722198 + 0.691687i \(0.756868\pi\)
\(510\) 0 0
\(511\) −15.9722 24.8532i −0.706567 1.09944i
\(512\) 0 0
\(513\) −63.7417 + 47.7164i −2.81426 + 2.10673i
\(514\) 0 0
\(515\) −25.6615 23.1584i −1.13078 1.02048i
\(516\) 0 0
\(517\) −5.78512 2.15774i −0.254429 0.0948972i
\(518\) 0 0
\(519\) 14.4021 2.07072i 0.632184 0.0908943i
\(520\) 0 0
\(521\) 5.72139 + 19.4853i 0.250659 + 0.853666i 0.984655 + 0.174512i \(0.0558348\pi\)
−0.733996 + 0.679154i \(0.762347\pi\)
\(522\) 0 0
\(523\) −4.38571 + 0.313672i −0.191774 + 0.0137159i −0.166896 0.985975i \(-0.553374\pi\)
−0.0248781 + 0.999690i \(0.507920\pi\)
\(524\) 0 0
\(525\) −25.5505 62.5036i −1.11512 2.72788i
\(526\) 0 0
\(527\) −11.2626 30.1961i −0.490606 1.31536i
\(528\) 0 0
\(529\) 4.58291 22.5388i 0.199257 0.979947i
\(530\) 0 0
\(531\) −25.7439 + 56.3713i −1.11719 + 2.44631i
\(532\) 0 0
\(533\) −15.6511 1.11939i −0.677924 0.0484861i
\(534\) 0 0
\(535\) 8.14622 + 9.79360i 0.352192 + 0.423414i
\(536\) 0 0
\(537\) 26.7546 + 14.6091i 1.15455 + 0.630430i
\(538\) 0 0
\(539\) −3.42133 23.7959i −0.147367 1.02496i
\(540\) 0 0
\(541\) −10.5234 23.0431i −0.452437 0.990699i −0.989147 0.146932i \(-0.953060\pi\)
0.536710 0.843767i \(-0.319667\pi\)
\(542\) 0 0
\(543\) −14.0666 64.6630i −0.603655 2.77496i
\(544\) 0 0
\(545\) −14.1784 27.2590i −0.607338 1.16765i
\(546\) 0 0
\(547\) −18.8955 4.11046i −0.807912 0.175751i −0.210405 0.977614i \(-0.567478\pi\)
−0.597507 + 0.801864i \(0.703842\pi\)
\(548\) 0 0
\(549\) 98.0763 + 28.7978i 4.18579 + 1.22906i
\(550\) 0 0
\(551\) 29.3174i 1.24896i
\(552\) 0 0
\(553\) −27.3236 + 27.3236i −1.16192 + 1.16192i
\(554\) 0 0
\(555\) −14.5737 41.6188i −0.618621 1.76662i
\(556\) 0 0
\(557\) 2.03844 9.37056i 0.0863715 0.397043i −0.913582 0.406654i \(-0.866695\pi\)
0.999954 + 0.00961040i \(0.00305913\pi\)
\(558\) 0 0
\(559\) −0.741606 + 5.15798i −0.0313666 + 0.218159i
\(560\) 0 0
\(561\) 26.8383 + 17.2479i 1.13311 + 0.728207i
\(562\) 0 0
\(563\) 7.68958 20.6166i 0.324077 0.868884i −0.668103 0.744069i \(-0.732893\pi\)
0.992180 0.124815i \(-0.0398339\pi\)
\(564\) 0 0
\(565\) −0.684811 + 33.9451i −0.0288102 + 1.42808i
\(566\) 0 0
\(567\) −48.3193 + 88.4901i −2.02922 + 3.71624i
\(568\) 0 0
\(569\) 25.7436 29.7097i 1.07923 1.24549i 0.111428 0.993773i \(-0.464458\pi\)
0.967799 0.251722i \(-0.0809970\pi\)
\(570\) 0 0
\(571\) 14.2793 12.3731i 0.597570 0.517798i −0.302725 0.953078i \(-0.597896\pi\)
0.900295 + 0.435280i \(0.143351\pi\)
\(572\) 0 0
\(573\) −13.9543 + 5.20469i −0.582950 + 0.217429i
\(574\) 0 0
\(575\) −23.9217 1.65905i −0.997604 0.0691872i
\(576\) 0 0
\(577\) 2.07540 0.774082i 0.0863998 0.0322255i −0.305893 0.952066i \(-0.598955\pi\)
0.392292 + 0.919841i \(0.371682\pi\)
\(578\) 0 0
\(579\) −7.07706 + 6.13231i −0.294113 + 0.254850i
\(580\) 0 0
\(581\) 12.5573 14.4919i 0.520964 0.601225i
\(582\) 0 0
\(583\) 5.13444 9.40303i 0.212647 0.389434i
\(584\) 0 0
\(585\) −1.65547 + 82.0595i −0.0684454 + 3.39274i
\(586\) 0 0
\(587\) −0.0480875 + 0.128928i −0.00198478 + 0.00532141i −0.937938 0.346802i \(-0.887268\pi\)
0.935954 + 0.352123i \(0.114540\pi\)
\(588\) 0 0
\(589\) −34.9766 22.4781i −1.44119 0.926195i
\(590\) 0 0
\(591\) 6.71767 46.7224i 0.276328 1.92190i
\(592\) 0 0
\(593\) 8.32032 38.2479i 0.341675 1.57065i −0.410607 0.911812i \(-0.634683\pi\)
0.752282 0.658841i \(-0.228953\pi\)
\(594\) 0 0
\(595\) −13.2534 37.8484i −0.543338 1.55163i
\(596\) 0 0
\(597\) 6.25934 6.25934i 0.256178 0.256178i
\(598\) 0 0
\(599\) 39.1031i 1.59771i 0.601524 + 0.798855i \(0.294561\pi\)
−0.601524 + 0.798855i \(0.705439\pi\)
\(600\) 0 0
\(601\) −25.6764 7.53926i −1.04736 0.307533i −0.287610 0.957748i \(-0.592861\pi\)
−0.759751 + 0.650215i \(0.774679\pi\)
\(602\) 0 0
\(603\) 17.9517 + 3.90515i 0.731049 + 0.159030i
\(604\) 0 0
\(605\) 5.89510 + 11.3337i 0.239670 + 0.460782i
\(606\) 0 0
\(607\) 8.30081 + 38.1582i 0.336919 + 1.54879i 0.764384 + 0.644761i \(0.223043\pi\)
−0.427464 + 0.904032i \(0.640593\pi\)
\(608\) 0 0
\(609\) 29.7009 + 65.0360i 1.20354 + 2.63539i
\(610\) 0 0
\(611\) −1.88334 13.0989i −0.0761917 0.529925i
\(612\) 0 0
\(613\) −18.8292 10.2815i −0.760503 0.415266i 0.0516836 0.998664i \(-0.483541\pi\)
−0.812187 + 0.583397i \(0.801723\pi\)
\(614\) 0 0
\(615\) 14.7168 + 17.6929i 0.593437 + 0.713446i
\(616\) 0 0
\(617\) −4.53845 0.324597i −0.182711 0.0130678i −0.0203163 0.999794i \(-0.506467\pi\)
−0.162395 + 0.986726i \(0.551922\pi\)
\(618\) 0 0
\(619\) −10.0698 + 22.0498i −0.404740 + 0.886256i 0.592028 + 0.805917i \(0.298328\pi\)
−0.996768 + 0.0803389i \(0.974400\pi\)
\(620\) 0 0
\(621\) 39.7119 + 56.3738i 1.59358 + 2.26220i
\(622\) 0 0
\(623\) 7.88932 + 21.1521i 0.316079 + 0.847441i
\(624\) 0 0
\(625\) 1.55186 + 24.9518i 0.0620745 + 0.998072i
\(626\) 0 0
\(627\) 41.0521 2.93611i 1.63946 0.117257i
\(628\) 0 0
\(629\) −7.37815 25.1277i −0.294186 1.00191i
\(630\) 0 0
\(631\) 22.1266 3.18133i 0.880847 0.126647i 0.312973 0.949762i \(-0.398675\pi\)
0.567874 + 0.823115i \(0.307766\pi\)
\(632\) 0 0
\(633\) −33.9632 12.6676i −1.34992 0.503493i
\(634\) 0 0
\(635\) 25.1441 + 22.6914i 0.997815 + 0.900482i
\(636\) 0 0
\(637\) 41.2488 30.8784i 1.63434 1.22345i
\(638\) 0 0
\(639\) −6.47328 10.0726i −0.256079 0.398467i
\(640\) 0 0
\(641\) −8.14988 + 27.7559i −0.321901 + 1.09629i 0.626553 + 0.779379i \(0.284465\pi\)
−0.948454 + 0.316915i \(0.897353\pi\)
\(642\) 0 0
\(643\) 18.1303 + 18.1303i 0.714991 + 0.714991i 0.967575 0.252584i \(-0.0812804\pi\)
−0.252584 + 0.967575i \(0.581280\pi\)
\(644\) 0 0
\(645\) 6.20952 4.45583i 0.244500 0.175448i
\(646\) 0 0
\(647\) −5.40002 9.88940i −0.212297 0.388792i 0.749732 0.661742i \(-0.230183\pi\)
−0.962028 + 0.272950i \(0.912001\pi\)
\(648\) 0 0
\(649\) 16.0938 10.3429i 0.631737 0.405993i
\(650\) 0 0
\(651\) −100.362 14.4299i −3.93351 0.565554i
\(652\) 0 0
\(653\) −36.1320 + 7.86005i −1.41396 + 0.307587i −0.853714 0.520742i \(-0.825655\pi\)
−0.560242 + 0.828329i \(0.689292\pi\)
\(654\) 0 0
\(655\) 0.0476227 + 0.0272650i 0.00186077 + 0.00106533i
\(656\) 0 0
\(657\) 31.5624 42.1625i 1.23137 1.64492i
\(658\) 0 0
\(659\) −34.0520 + 9.99856i −1.32648 + 0.389489i −0.866826 0.498611i \(-0.833844\pi\)
−0.459651 + 0.888100i \(0.652025\pi\)
\(660\) 0 0
\(661\) 2.19716 + 1.90385i 0.0854598 + 0.0740513i 0.696543 0.717515i \(-0.254721\pi\)
−0.611083 + 0.791566i \(0.709266\pi\)
\(662\) 0 0
\(663\) −4.87796 + 68.2028i −0.189444 + 2.64878i
\(664\) 0 0
\(665\) −42.9488 28.8419i −1.66548 1.11844i
\(666\) 0 0
\(667\) 25.3794 + 0.733665i 0.982693 + 0.0284076i
\(668\) 0 0
\(669\) −42.4854 19.4024i −1.64258 0.750141i
\(670\) 0 0
\(671\) −20.6638 23.8473i −0.797718 0.920615i
\(672\) 0 0
\(673\) −1.23239 17.2311i −0.0475052 0.664210i −0.964293 0.264836i \(-0.914682\pi\)
0.916788 0.399374i \(-0.130772\pi\)
\(674\) 0 0
\(675\) 52.8445 48.7440i 2.03399 1.87616i
\(676\) 0 0
\(677\) −29.9572 22.4257i −1.15135 0.861890i −0.159238 0.987240i \(-0.550904\pi\)
−0.992113 + 0.125350i \(0.959994\pi\)
\(678\) 0 0
\(679\) 44.7324 20.4286i 1.71667 0.783978i
\(680\) 0 0
\(681\) 9.80972 15.2642i 0.375909 0.584926i
\(682\) 0 0
\(683\) −18.8420 25.1699i −0.720968 0.963100i −0.999996 0.00281712i \(-0.999103\pi\)
0.279028 0.960283i \(-0.409988\pi\)
\(684\) 0 0
\(685\) −0.631748 1.46060i −0.0241379 0.0558068i
\(686\) 0 0
\(687\) −53.9955 + 29.4838i −2.06006 + 1.12488i
\(688\) 0 0
\(689\) 22.9623 0.874792
\(690\) 0 0
\(691\) 28.8391 1.09709 0.548546 0.836120i \(-0.315182\pi\)
0.548546 + 0.836120i \(0.315182\pi\)
\(692\) 0 0
\(693\) 62.7991 34.2909i 2.38554 1.30260i
\(694\) 0 0
\(695\) 14.3766 + 5.69507i 0.545334 + 0.216026i
\(696\) 0 0
\(697\) 8.19058 + 10.9413i 0.310240 + 0.414432i
\(698\) 0 0
\(699\) 25.2557 39.2986i 0.955257 1.48641i
\(700\) 0 0
\(701\) 8.28667 3.78439i 0.312983 0.142935i −0.252730 0.967537i \(-0.581328\pi\)
0.565713 + 0.824602i \(0.308601\pi\)
\(702\) 0 0
\(703\) −27.0464 20.2467i −1.02008 0.763619i
\(704\) 0 0
\(705\) −11.9426 + 15.3001i −0.449783 + 0.576236i
\(706\) 0 0
\(707\) −1.81792 25.4179i −0.0683699 0.955937i
\(708\) 0 0
\(709\) 14.7992 + 17.0792i 0.555795 + 0.641422i 0.962223 0.272261i \(-0.0877714\pi\)
−0.406428 + 0.913683i \(0.633226\pi\)
\(710\) 0 0
\(711\) −62.6623 28.6169i −2.35002 1.07322i
\(712\) 0 0
\(713\) −20.3341 + 29.7159i −0.761517 + 1.11287i
\(714\) 0 0
\(715\) 14.1254 21.0343i 0.528260 0.786637i
\(716\) 0 0
\(717\) −2.96727 + 41.4879i −0.110815 + 1.54939i
\(718\) 0 0
\(719\) 31.2180 + 27.0506i 1.16424 + 1.00882i 0.999748 + 0.0224362i \(0.00714225\pi\)
0.164487 + 0.986379i \(0.447403\pi\)
\(720\) 0 0
\(721\) −61.9693 + 18.1958i −2.30786 + 0.677648i
\(722\) 0 0
\(723\) 6.21514 8.30246i 0.231144 0.308772i
\(724\) 0 0
\(725\) −2.70738 26.3320i −0.100550 0.977948i
\(726\) 0 0
\(727\) 8.78260 1.91054i 0.325728 0.0708579i −0.0467277 0.998908i \(-0.514879\pi\)
0.372456 + 0.928050i \(0.378516\pi\)
\(728\) 0 0
\(729\) −39.9004 5.73681i −1.47779 0.212474i
\(730\) 0 0
\(731\) 3.81842 2.45395i 0.141229 0.0907627i
\(732\) 0 0
\(733\) −13.5982 24.9032i −0.502260 0.919820i −0.998661 0.0517271i \(-0.983527\pi\)
0.496401 0.868093i \(-0.334654\pi\)
\(734\) 0 0
\(735\) −74.5701 12.2615i −2.75056 0.452272i
\(736\) 0 0
\(737\) −4.01024 4.01024i −0.147719 0.147719i
\(738\) 0 0
\(739\) −14.1334 + 48.1338i −0.519904 + 1.77063i 0.109972 + 0.993935i \(0.464924\pi\)
−0.629876 + 0.776696i \(0.716894\pi\)
\(740\) 0 0
\(741\) 47.6908 + 74.2084i 1.75197 + 2.72611i
\(742\) 0 0
\(743\) 11.1238 8.32714i 0.408091 0.305493i −0.375439 0.926847i \(-0.622508\pi\)
0.783530 + 0.621354i \(0.213417\pi\)
\(744\) 0 0
\(745\) −18.7041 + 0.959021i −0.685264 + 0.0351358i
\(746\) 0 0
\(747\) 32.0296 + 11.9464i 1.17190 + 0.437096i
\(748\) 0 0
\(749\) 23.5595 3.38735i 0.860845 0.123771i
\(750\) 0 0
\(751\) 6.66147 + 22.6869i 0.243080 + 0.827856i 0.987156 + 0.159760i \(0.0510721\pi\)
−0.744076 + 0.668096i \(0.767110\pi\)
\(752\) 0 0
\(753\) −9.14859 + 0.654320i −0.333393 + 0.0238447i
\(754\) 0 0
\(755\) −9.01714 2.15292i −0.328167 0.0783527i
\(756\) 0 0
\(757\) 1.42978 + 3.83338i 0.0519661 + 0.139327i 0.960339 0.278834i \(-0.0899478\pi\)
−0.908373 + 0.418160i \(0.862675\pi\)
\(758\) 0 0
\(759\) −1.51439 35.6113i −0.0549689 1.29261i
\(760\) 0 0
\(761\) −15.7521 + 34.4922i −0.571012 + 1.25034i 0.375244 + 0.926926i \(0.377559\pi\)
−0.946257 + 0.323417i \(0.895168\pi\)
\(762\) 0 0
\(763\) −57.2638 4.09559i −2.07309 0.148270i
\(764\) 0 0
\(765\) 54.9626 45.7173i 1.98718 1.65291i
\(766\) 0 0
\(767\) 35.9873 + 19.6506i 1.29943 + 0.709541i
\(768\) 0 0
\(769\) −0.722968 5.02835i −0.0260709 0.181327i 0.972625 0.232380i \(-0.0746513\pi\)
−0.998696 + 0.0510530i \(0.983742\pi\)
\(770\) 0 0
\(771\) 14.0781 + 30.8267i 0.507009 + 1.11020i
\(772\) 0 0
\(773\) −2.32974 10.7096i −0.0837950 0.385199i 0.916080 0.400995i \(-0.131336\pi\)
−0.999875 + 0.0157957i \(0.994972\pi\)
\(774\) 0 0
\(775\) 33.4908 + 16.9592i 1.20303 + 0.609193i
\(776\) 0 0
\(777\) −80.5099 17.5138i −2.88828 0.628306i
\(778\) 0 0
\(779\) 16.9178 + 4.96752i 0.606144 + 0.177980i
\(780\) 0 0
\(781\) 3.69620i 0.132260i
\(782\) 0 0
\(783\) −53.8265 + 53.8265i −1.92360 + 1.92360i
\(784\) 0 0
\(785\) 7.03067 14.6079i 0.250936 0.521378i
\(786\) 0 0
\(787\) 5.38497 24.7543i 0.191953 0.882396i −0.775895 0.630862i \(-0.782701\pi\)
0.967848 0.251534i \(-0.0809350\pi\)
\(788\) 0 0
\(789\) 3.22925 22.4600i 0.114964 0.799596i
\(790\) 0 0
\(791\) 53.3673 + 34.2971i 1.89752 + 1.21946i
\(792\) 0 0
\(793\) 23.6345 63.3665i 0.839286 2.25021i
\(794\) 0 0
\(795\) −23.3287 24.2893i −0.827383 0.861454i
\(796\) 0 0
\(797\) 9.97904 18.2752i 0.353476 0.647342i −0.639079 0.769141i \(-0.720684\pi\)
0.992555 + 0.121799i \(0.0388662\pi\)
\(798\) 0 0
\(799\) −7.54851 + 8.71145i −0.267047 + 0.308189i
\(800\) 0 0
\(801\) −30.4160 + 26.3556i −1.07470 + 0.931230i
\(802\) 0 0
\(803\) −15.2334 + 5.68178i −0.537577 + 0.200506i
\(804\) 0 0
\(805\) −26.0425 + 36.4580i −0.917879 + 1.28497i
\(806\) 0 0
\(807\) 86.5680 32.2882i 3.04734 1.13660i
\(808\) 0 0
\(809\) 4.58736 3.97497i 0.161283 0.139753i −0.570480 0.821311i \(-0.693243\pi\)
0.731764 + 0.681559i \(0.238698\pi\)
\(810\) 0 0
\(811\) −33.2168 + 38.3343i −1.16640 + 1.34610i −0.239453 + 0.970908i \(0.576968\pi\)
−0.926948 + 0.375190i \(0.877577\pi\)
\(812\) 0 0
\(813\) 32.3354 59.2179i 1.13405 2.07686i
\(814\) 0 0
\(815\) 28.7360 + 0.579721i 1.00658 + 0.0203067i
\(816\) 0 0
\(817\) 2.04633 5.48642i 0.0715920 0.191946i
\(818\) 0 0
\(819\) 129.011 + 82.9104i 4.50801 + 2.89712i
\(820\) 0 0
\(821\) 1.76169 12.2528i 0.0614835 0.427627i −0.935711 0.352768i \(-0.885240\pi\)
0.997194 0.0748585i \(-0.0238505\pi\)
\(822\) 0 0
\(823\) −2.93089 + 13.4731i −0.102164 + 0.469642i 0.897430 + 0.441157i \(0.145432\pi\)
−0.999594 + 0.0284846i \(0.990932\pi\)
\(824\) 0 0
\(825\) −36.6007 + 6.42819i −1.27427 + 0.223801i
\(826\) 0 0
\(827\) 7.11232 7.11232i 0.247320 0.247320i −0.572550 0.819870i \(-0.694046\pi\)
0.819870 + 0.572550i \(0.194046\pi\)
\(828\) 0 0
\(829\) 42.7316i 1.48413i −0.670329 0.742064i \(-0.733847\pi\)
0.670329 0.742064i \(-0.266153\pi\)
\(830\) 0 0
\(831\) −13.8030 4.05292i −0.478820 0.140594i
\(832\) 0 0
\(833\) −43.8552 9.54012i −1.51949 0.330545i
\(834\) 0 0
\(835\) 10.6314 33.6787i 0.367913 1.16550i
\(836\) 0 0
\(837\) −22.9472 105.487i −0.793171 3.64615i
\(838\) 0 0
\(839\) 14.6209 + 32.0152i 0.504769 + 1.10529i 0.974890 + 0.222687i \(0.0714828\pi\)
−0.470121 + 0.882602i \(0.655790\pi\)
\(840\) 0 0
\(841\) −0.138294 0.961854i −0.00476875 0.0331674i
\(842\) 0 0
\(843\) 60.2782 + 32.9144i 2.07609 + 1.13363i
\(844\) 0 0
\(845\) 25.1303 + 2.30766i 0.864508 + 0.0793860i
\(846\) 0 0
\(847\) 23.8091 + 1.70286i 0.818090 + 0.0585109i
\(848\) 0 0
\(849\) 13.5375 29.6429i 0.464605 1.01734i
\(850\) 0 0
\(851\) −18.2039 + 22.9068i −0.624023 + 0.785234i
\(852\) 0 0
\(853\) 17.0537 + 45.7228i 0.583909 + 1.56552i 0.806893 + 0.590698i \(0.201147\pi\)
−0.222985 + 0.974822i \(0.571580\pi\)
\(854\) 0 0
\(855\) 21.4184 89.7074i 0.732495 3.06793i
\(856\) 0 0
\(857\) −25.6752 + 1.83633i −0.877049 + 0.0627278i −0.502600 0.864519i \(-0.667623\pi\)
−0.374450 + 0.927247i \(0.622168\pi\)
\(858\) 0 0
\(859\) −13.3715 45.5390i −0.456228 1.55377i −0.791209 0.611546i \(-0.790548\pi\)
0.334980 0.942225i \(-0.391270\pi\)
\(860\) 0 0
\(861\) 42.5620 6.11950i 1.45051 0.208552i
\(862\) 0 0
\(863\) −0.0886542 0.0330663i −0.00301782 0.00112559i 0.347955 0.937511i \(-0.386876\pi\)
−0.350973 + 0.936386i \(0.614149\pi\)
\(864\) 0 0
\(865\) −6.74356 + 7.47246i −0.229288 + 0.254071i
\(866\) 0 0
\(867\) 3.68898 2.76154i 0.125284 0.0937867i
\(868\) 0 0
\(869\) 11.4971 + 17.8898i 0.390013 + 0.606871i
\(870\) 0 0
\(871\) 3.42456 11.6630i 0.116037 0.395185i
\(872\) 0 0
\(873\) 61.9910 + 61.9910i 2.09808 + 2.09808i
\(874\) 0 0
\(875\) 41.2389 + 21.9388i 1.39413 + 0.741666i
\(876\) 0 0
\(877\) −13.2605 24.2848i −0.447776 0.820041i 0.552130 0.833758i \(-0.313815\pi\)
−0.999906 + 0.0137174i \(0.995633\pi\)
\(878\) 0 0
\(879\) −19.9275 + 12.8066i −0.672136 + 0.431956i
\(880\) 0 0
\(881\) 17.6335 + 2.53531i 0.594088 + 0.0854169i 0.432799 0.901490i \(-0.357526\pi\)
0.161288 + 0.986907i \(0.448435\pi\)
\(882\) 0 0
\(883\) 22.3469 4.86128i 0.752034 0.163595i 0.179820 0.983699i \(-0.442448\pi\)
0.572214 + 0.820104i \(0.306085\pi\)
\(884\) 0 0
\(885\) −15.7754 58.0313i −0.530283 1.95070i
\(886\) 0 0
\(887\) −30.0775 + 40.1788i −1.00990 + 1.34907i −0.0738299 + 0.997271i \(0.523522\pi\)
−0.936074 + 0.351803i \(0.885569\pi\)
\(888\) 0 0
\(889\) 60.7199 17.8290i 2.03648 0.597964i
\(890\) 0 0
\(891\) 41.9338 + 36.3358i 1.40483 + 1.21730i
\(892\) 0 0
\(893\) −1.06086 + 14.8327i −0.0355002 + 0.496357i
\(894\) 0 0
\(895\) −20.6918 + 4.06595i −0.691651 + 0.135910i
\(896\) 0 0
\(897\) 65.4339 39.4278i 2.18477 1.31645i
\(898\) 0 0
\(899\) −36.1566 16.5122i −1.20589 0.550712i
\(900\) 0 0
\(901\) −13.0978 15.1156i −0.436350 0.503575i
\(902\) 0 0
\(903\) −1.01874 14.2439i −0.0339016 0.474006i
\(904\) 0 0
\(905\) 36.0866 + 28.1675i 1.19956 + 0.936318i
\(906\) 0 0
\(907\) −12.4912 9.35076i −0.414762 0.310487i 0.371439 0.928457i \(-0.378864\pi\)
−0.786202 + 0.617970i \(0.787955\pi\)
\(908\) 0 0
\(909\) 41.3238 18.8719i 1.37062 0.625943i
\(910\) 0 0
\(911\) −11.0404 + 17.1791i −0.365783 + 0.569170i −0.974547 0.224181i \(-0.928029\pi\)
0.608764 + 0.793351i \(0.291666\pi\)
\(912\) 0 0
\(913\) −6.32415 8.44807i −0.209299 0.279590i
\(914\) 0 0
\(915\) −91.0404 + 39.3773i −3.00970 + 1.30177i
\(916\) 0 0
\(917\) 0.0899903 0.0491384i 0.00297174 0.00162269i
\(918\) 0 0
\(919\) 22.4132 0.739343 0.369671 0.929163i \(-0.379470\pi\)
0.369671 + 0.929163i \(0.379470\pi\)
\(920\) 0 0
\(921\) 79.2155 2.61024
\(922\) 0 0
\(923\) −6.95301 + 3.79663i −0.228861 + 0.124968i
\(924\) 0 0
\(925\) 26.1621 + 15.6874i 0.860204 + 0.515797i
\(926\) 0 0
\(927\) −69.0002 92.1734i −2.26626 3.02737i
\(928\) 0 0
\(929\) −11.0398 + 17.1783i −0.362204 + 0.563600i −0.973753 0.227606i \(-0.926910\pi\)
0.611549 + 0.791206i \(0.290547\pi\)
\(930\) 0 0
\(931\) −52.6675 + 24.0525i −1.72611 + 0.788287i
\(932\) 0 0
\(933\) 24.0911 + 18.0344i 0.788708 + 0.590419i
\(934\) 0 0
\(935\) −21.9037 + 2.69956i −0.716327 + 0.0882849i
\(936\) 0 0
\(937\) 1.15364 + 16.1300i 0.0376879 + 0.526946i 0.980869 + 0.194667i \(0.0623627\pi\)
−0.943181 + 0.332278i \(0.892183\pi\)
\(938\) 0 0
\(939\) 28.6428 + 33.0555i 0.934721 + 1.07873i
\(940\) 0 0
\(941\) −51.1471 23.3581i −1.66735 0.761452i −0.999858 0.0168314i \(-0.994642\pi\)
−0.667488 0.744620i \(-0.732631\pi\)
\(942\) 0 0
\(943\) 4.72363 14.5210i 0.153823 0.472870i
\(944\) 0 0
\(945\) −25.9002 131.807i −0.842532 4.28769i
\(946\) 0 0
\(947\) −0.961725 + 13.4467i −0.0312519 + 0.436958i 0.957605 + 0.288086i \(0.0930189\pi\)
−0.988856 + 0.148872i \(0.952436\pi\)
\(948\) 0 0
\(949\) −26.3355 22.8199i −0.854888 0.740764i
\(950\) 0 0
\(951\) 41.9387 12.3143i 1.35996 0.399319i
\(952\) 0 0
\(953\) 30.8133 41.1618i 0.998142 1.33336i 0.0558973 0.998437i \(-0.482198\pi\)
0.942245 0.334925i \(-0.108711\pi\)
\(954\) 0 0
\(955\) 5.11899 8.94112i 0.165647 0.289328i
\(956\) 0 0
\(957\) 38.4481 8.36387i 1.24285 0.270365i
\(958\) 0 0
\(959\) −2.94314 0.423160i −0.0950391 0.0136646i
\(960\) 0 0
\(961\) 21.3427 13.7161i 0.688473 0.442455i
\(962\) 0 0
\(963\) 20.3356 + 37.2419i 0.655307 + 1.20011i
\(964\) 0 0
\(965\) 1.05105 6.39212i 0.0338345 0.205770i
\(966\) 0 0
\(967\) −28.5701 28.5701i −0.918753 0.918753i 0.0781856 0.996939i \(-0.475087\pi\)
−0.996939 + 0.0781856i \(0.975087\pi\)
\(968\) 0 0
\(969\) 21.6470 73.7228i 0.695401 2.36832i
\(970\) 0 0
\(971\) 15.9668 + 24.8448i 0.512399 + 0.797308i 0.996998 0.0774281i \(-0.0246708\pi\)
−0.484599 + 0.874736i \(0.661034\pi\)
\(972\) 0 0
\(973\) 23.1299 17.3148i 0.741511 0.555088i
\(974\) 0 0
\(975\) −49.6875 62.2478i −1.59127 1.99352i
\(976\) 0 0
\(977\) 56.3025 + 20.9997i 1.80128 + 0.671841i 0.996984 + 0.0776081i \(0.0247283\pi\)
0.804293 + 0.594233i \(0.202544\pi\)
\(978\) 0 0
\(979\) 12.2976 1.76813i 0.393033 0.0565097i
\(980\) 0 0
\(981\) −28.8345 98.2013i −0.920615 3.13533i
\(982\) 0 0
\(983\) −8.62160 + 0.616629i −0.274986 + 0.0196674i −0.208151 0.978097i \(-0.566745\pi\)
−0.0668350 + 0.997764i \(0.521290\pi\)
\(984\) 0 0
\(985\) 17.0962 + 27.8205i 0.544731 + 0.886434i
\(986\) 0 0
\(987\) 12.6734 + 33.9788i 0.403400 + 1.08156i
\(988\) 0 0
\(989\) −4.69826 1.90876i −0.149396 0.0606950i
\(990\) 0 0
\(991\) −18.4846 + 40.4757i −0.587184 + 1.28575i 0.349945 + 0.936770i \(0.386200\pi\)
−0.937129 + 0.348983i \(0.886527\pi\)
\(992\) 0 0
\(993\) 90.3716 + 6.46350i 2.86785 + 0.205113i
\(994\) 0 0
\(995\) −0.559961 + 6.09794i −0.0177520 + 0.193318i
\(996\) 0 0
\(997\) 40.7718 + 22.2631i 1.29126 + 0.705080i 0.970275 0.242006i \(-0.0778053\pi\)
0.320982 + 0.947085i \(0.395987\pi\)
\(998\) 0 0
\(999\) −12.4843 86.8299i −0.394984 2.74718i
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 920.2.bv.a.17.2 720
5.3 odd 4 inner 920.2.bv.a.753.2 yes 720
23.19 odd 22 inner 920.2.bv.a.617.2 yes 720
115.88 even 44 inner 920.2.bv.a.433.2 yes 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.17.2 720 1.1 even 1 trivial
920.2.bv.a.433.2 yes 720 115.88 even 44 inner
920.2.bv.a.617.2 yes 720 23.19 odd 22 inner
920.2.bv.a.753.2 yes 720 5.3 odd 4 inner