Properties

Label 920.2.bv.a.433.4
Level $920$
Weight $2$
Character 920.433
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 433.4
Character \(\chi\) \(=\) 920.433
Dual form 920.2.bv.a.17.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.47093 - 1.34923i) q^{3} +(-0.998659 - 2.00067i) q^{5} +(0.191158 - 0.255357i) q^{7} +(2.66315 + 4.14394i) q^{9} +(-4.15304 - 1.89663i) q^{11} +(-4.13246 + 3.09352i) q^{13} +(-0.231747 + 6.29094i) q^{15} +(-0.227137 + 3.17579i) q^{17} +(3.00031 - 3.46254i) q^{19} +(-0.816873 + 0.373054i) q^{21} +(-3.40605 - 3.37622i) q^{23} +(-3.00536 + 3.99597i) q^{25} +(-0.386803 - 5.40822i) q^{27} +(5.27704 - 4.57258i) q^{29} +(1.08214 + 0.317745i) q^{31} +(7.70288 + 10.2898i) q^{33} +(-0.701787 - 0.127429i) q^{35} +(4.74880 + 1.03304i) q^{37} +(14.3849 - 2.06824i) q^{39} +(-0.580499 - 0.373064i) q^{41} +(-1.90880 + 3.49571i) q^{43} +(5.63109 - 9.46647i) q^{45} +(-3.43722 + 3.43722i) q^{47} +(1.94346 + 6.61882i) q^{49} +(4.84612 - 7.54070i) q^{51} +(4.05640 + 3.03658i) q^{53} +(0.352940 + 10.2029i) q^{55} +(-12.0853 + 4.50759i) q^{57} +(2.01165 + 0.289231i) q^{59} +(-1.29502 + 4.41043i) q^{61} +(1.56727 + 0.112093i) q^{63} +(10.3160 + 5.17832i) q^{65} +(-0.262976 + 0.705066i) q^{67} +(3.86081 + 12.9379i) q^{69} +(3.29427 + 7.21344i) q^{71} +(7.11789 - 0.509081i) q^{73} +(12.8175 - 5.81885i) q^{75} +(-1.27820 + 0.697952i) q^{77} +(0.450734 - 3.13492i) q^{79} +(-0.202267 + 0.442902i) q^{81} +(-0.313966 + 1.44328i) q^{83} +(6.58055 - 2.71711i) q^{85} +(-19.2087 + 4.17859i) q^{87} +(11.8297 - 3.47350i) q^{89} +1.64661i q^{91} +(-2.24518 - 2.24518i) q^{93} +(-9.92369 - 2.54473i) q^{95} +(3.86140 + 17.7506i) q^{97} +(-3.20064 - 22.2610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.47093 1.34923i −1.42659 0.778978i −0.434051 0.900888i \(-0.642916\pi\)
−0.992541 + 0.121910i \(0.961098\pi\)
\(4\) 0 0
\(5\) −0.998659 2.00067i −0.446614 0.894727i
\(6\) 0 0
\(7\) 0.191158 0.255357i 0.0722509 0.0965159i −0.762960 0.646446i \(-0.776255\pi\)
0.835211 + 0.549930i \(0.185346\pi\)
\(8\) 0 0
\(9\) 2.66315 + 4.14394i 0.887717 + 1.38131i
\(10\) 0 0
\(11\) −4.15304 1.89663i −1.25219 0.571855i −0.324739 0.945804i \(-0.605276\pi\)
−0.927449 + 0.373949i \(0.878004\pi\)
\(12\) 0 0
\(13\) −4.13246 + 3.09352i −1.14614 + 0.857989i −0.991516 0.129984i \(-0.958507\pi\)
−0.154623 + 0.987974i \(0.549416\pi\)
\(14\) 0 0
\(15\) −0.231747 + 6.29094i −0.0598369 + 1.62431i
\(16\) 0 0
\(17\) −0.227137 + 3.17579i −0.0550889 + 0.770243i 0.892560 + 0.450929i \(0.148907\pi\)
−0.947649 + 0.319314i \(0.896547\pi\)
\(18\) 0 0
\(19\) 3.00031 3.46254i 0.688319 0.794362i −0.298806 0.954314i \(-0.596588\pi\)
0.987125 + 0.159952i \(0.0511339\pi\)
\(20\) 0 0
\(21\) −0.816873 + 0.373054i −0.178256 + 0.0814070i
\(22\) 0 0
\(23\) −3.40605 3.37622i −0.710210 0.703990i
\(24\) 0 0
\(25\) −3.00536 + 3.99597i −0.601072 + 0.799195i
\(26\) 0 0
\(27\) −0.386803 5.40822i −0.0744404 1.04081i
\(28\) 0 0
\(29\) 5.27704 4.57258i 0.979921 0.849107i −0.00863436 0.999963i \(-0.502748\pi\)
0.988556 + 0.150856i \(0.0482030\pi\)
\(30\) 0 0
\(31\) 1.08214 + 0.317745i 0.194358 + 0.0570687i 0.377463 0.926025i \(-0.376797\pi\)
−0.183105 + 0.983093i \(0.558615\pi\)
\(32\) 0 0
\(33\) 7.70288 + 10.2898i 1.34090 + 1.79123i
\(34\) 0 0
\(35\) −0.701787 0.127429i −0.118624 0.0215395i
\(36\) 0 0
\(37\) 4.74880 + 1.03304i 0.780698 + 0.169830i 0.585217 0.810877i \(-0.301010\pi\)
0.195481 + 0.980707i \(0.437373\pi\)
\(38\) 0 0
\(39\) 14.3849 2.06824i 2.30343 0.331183i
\(40\) 0 0
\(41\) −0.580499 0.373064i −0.0906587 0.0582628i 0.494526 0.869163i \(-0.335342\pi\)
−0.585185 + 0.810900i \(0.698978\pi\)
\(42\) 0 0
\(43\) −1.90880 + 3.49571i −0.291090 + 0.533091i −0.981771 0.190068i \(-0.939129\pi\)
0.690681 + 0.723160i \(0.257311\pi\)
\(44\) 0 0
\(45\) 5.63109 9.46647i 0.839433 1.41118i
\(46\) 0 0
\(47\) −3.43722 + 3.43722i −0.501370 + 0.501370i −0.911864 0.410493i \(-0.865357\pi\)
0.410493 + 0.911864i \(0.365357\pi\)
\(48\) 0 0
\(49\) 1.94346 + 6.61882i 0.277637 + 0.945546i
\(50\) 0 0
\(51\) 4.84612 7.54070i 0.678592 1.05591i
\(52\) 0 0
\(53\) 4.05640 + 3.03658i 0.557189 + 0.417107i 0.840412 0.541947i \(-0.182313\pi\)
−0.283223 + 0.959054i \(0.591404\pi\)
\(54\) 0 0
\(55\) 0.352940 + 10.2029i 0.0475905 + 1.37576i
\(56\) 0 0
\(57\) −12.0853 + 4.50759i −1.60074 + 0.597045i
\(58\) 0 0
\(59\) 2.01165 + 0.289231i 0.261894 + 0.0376547i 0.272011 0.962294i \(-0.412311\pi\)
−0.0101170 + 0.999949i \(0.503220\pi\)
\(60\) 0 0
\(61\) −1.29502 + 4.41043i −0.165810 + 0.564698i 0.834104 + 0.551607i \(0.185985\pi\)
−0.999914 + 0.0130906i \(0.995833\pi\)
\(62\) 0 0
\(63\) 1.56727 + 0.112093i 0.197457 + 0.0141224i
\(64\) 0 0
\(65\) 10.3160 + 5.17832i 1.27955 + 0.642292i
\(66\) 0 0
\(67\) −0.262976 + 0.705066i −0.0321276 + 0.0861375i −0.952023 0.306026i \(-0.901001\pi\)
0.919896 + 0.392164i \(0.128273\pi\)
\(68\) 0 0
\(69\) 3.86081 + 12.9379i 0.464787 + 1.55754i
\(70\) 0 0
\(71\) 3.29427 + 7.21344i 0.390958 + 0.856078i 0.998108 + 0.0614909i \(0.0195855\pi\)
−0.607150 + 0.794587i \(0.707687\pi\)
\(72\) 0 0
\(73\) 7.11789 0.509081i 0.833086 0.0595835i 0.351722 0.936104i \(-0.385596\pi\)
0.481364 + 0.876521i \(0.340142\pi\)
\(74\) 0 0
\(75\) 12.8175 5.81885i 1.48004 0.671903i
\(76\) 0 0
\(77\) −1.27820 + 0.697952i −0.145665 + 0.0795390i
\(78\) 0 0
\(79\) 0.450734 3.13492i 0.0507115 0.352706i −0.948629 0.316391i \(-0.897529\pi\)
0.999340 0.0363153i \(-0.0115621\pi\)
\(80\) 0 0
\(81\) −0.202267 + 0.442902i −0.0224741 + 0.0492114i
\(82\) 0 0
\(83\) −0.313966 + 1.44328i −0.0344622 + 0.158420i −0.991162 0.132656i \(-0.957650\pi\)
0.956700 + 0.291076i \(0.0940132\pi\)
\(84\) 0 0
\(85\) 6.58055 2.71711i 0.713761 0.294712i
\(86\) 0 0
\(87\) −19.2087 + 4.17859i −2.05938 + 0.447992i
\(88\) 0 0
\(89\) 11.8297 3.47350i 1.25394 0.368191i 0.413706 0.910411i \(-0.364234\pi\)
0.840236 + 0.542220i \(0.182416\pi\)
\(90\) 0 0
\(91\) 1.64661i 0.172611i
\(92\) 0 0
\(93\) −2.24518 2.24518i −0.232814 0.232814i
\(94\) 0 0
\(95\) −9.92369 2.54473i −1.01815 0.261084i
\(96\) 0 0
\(97\) 3.86140 + 17.7506i 0.392066 + 1.80230i 0.573850 + 0.818960i \(0.305449\pi\)
−0.181784 + 0.983338i \(0.558187\pi\)
\(98\) 0 0
\(99\) −3.20064 22.2610i −0.321677 2.23731i
\(100\) 0 0
\(101\) −2.78246 + 1.78818i −0.276865 + 0.177930i −0.671703 0.740820i \(-0.734437\pi\)
0.394838 + 0.918751i \(0.370801\pi\)
\(102\) 0 0
\(103\) 3.88377 + 10.4128i 0.382679 + 1.02600i 0.975371 + 0.220572i \(0.0707925\pi\)
−0.592692 + 0.805429i \(0.701935\pi\)
\(104\) 0 0
\(105\) 1.56213 + 1.26174i 0.152449 + 0.123133i
\(106\) 0 0
\(107\) −9.19283 16.8354i −0.888704 1.62754i −0.773136 0.634241i \(-0.781313\pi\)
−0.115569 0.993299i \(-0.536869\pi\)
\(108\) 0 0
\(109\) −12.4592 14.3786i −1.19337 1.37722i −0.908088 0.418780i \(-0.862458\pi\)
−0.285283 0.958443i \(-0.592088\pi\)
\(110\) 0 0
\(111\) −10.3401 8.95979i −0.981443 0.850425i
\(112\) 0 0
\(113\) −16.3985 6.11631i −1.54264 0.575374i −0.572922 0.819610i \(-0.694190\pi\)
−0.969716 + 0.244236i \(0.921463\pi\)
\(114\) 0 0
\(115\) −3.35322 + 10.1861i −0.312689 + 0.949856i
\(116\) 0 0
\(117\) −23.8248 8.88618i −2.20260 0.821527i
\(118\) 0 0
\(119\) 0.767542 + 0.665079i 0.0703605 + 0.0609677i
\(120\) 0 0
\(121\) 6.44706 + 7.44030i 0.586096 + 0.676391i
\(122\) 0 0
\(123\) 0.931023 + 1.70504i 0.0839476 + 0.153738i
\(124\) 0 0
\(125\) 10.9960 + 2.02212i 0.983508 + 0.180864i
\(126\) 0 0
\(127\) −4.27483 11.4613i −0.379330 1.01702i −0.976615 0.214994i \(-0.931027\pi\)
0.597285 0.802029i \(-0.296246\pi\)
\(128\) 0 0
\(129\) 9.43304 6.06225i 0.830533 0.533751i
\(130\) 0 0
\(131\) 1.56280 + 10.8695i 0.136542 + 0.949673i 0.936762 + 0.349967i \(0.113807\pi\)
−0.800220 + 0.599707i \(0.795284\pi\)
\(132\) 0 0
\(133\) −0.310652 1.42804i −0.0269369 0.123827i
\(134\) 0 0
\(135\) −10.4338 + 6.17483i −0.897996 + 0.531445i
\(136\) 0 0
\(137\) −16.3201 16.3201i −1.39432 1.39432i −0.815354 0.578963i \(-0.803458\pi\)
−0.578963 0.815354i \(-0.696542\pi\)
\(138\) 0 0
\(139\) 13.8056i 1.17098i 0.810681 + 0.585488i \(0.199097\pi\)
−0.810681 + 0.585488i \(0.800903\pi\)
\(140\) 0 0
\(141\) 13.1307 3.85553i 1.10581 0.324694i
\(142\) 0 0
\(143\) 23.0295 5.00977i 1.92583 0.418938i
\(144\) 0 0
\(145\) −14.4182 5.99116i −1.19737 0.497539i
\(146\) 0 0
\(147\) 4.12816 18.9768i 0.340485 1.56518i
\(148\) 0 0
\(149\) −8.02048 + 17.5624i −0.657064 + 1.43877i 0.228170 + 0.973621i \(0.426726\pi\)
−0.885233 + 0.465147i \(0.846001\pi\)
\(150\) 0 0
\(151\) −1.62791 + 11.3223i −0.132477 + 0.921399i 0.809833 + 0.586660i \(0.199557\pi\)
−0.942311 + 0.334740i \(0.891352\pi\)
\(152\) 0 0
\(153\) −13.7652 + 7.51638i −1.11285 + 0.607663i
\(154\) 0 0
\(155\) −0.444986 2.48232i −0.0357421 0.199385i
\(156\) 0 0
\(157\) −3.04579 + 0.217839i −0.243081 + 0.0173855i −0.192348 0.981327i \(-0.561610\pi\)
−0.0507328 + 0.998712i \(0.516156\pi\)
\(158\) 0 0
\(159\) −5.92603 12.9762i −0.469965 1.02908i
\(160\) 0 0
\(161\) −1.51323 + 0.224368i −0.119260 + 0.0176826i
\(162\) 0 0
\(163\) −6.06826 + 16.2696i −0.475302 + 1.27434i 0.449293 + 0.893385i \(0.351676\pi\)
−0.924595 + 0.380951i \(0.875597\pi\)
\(164\) 0 0
\(165\) 12.8940 25.6870i 1.00380 1.99973i
\(166\) 0 0
\(167\) 16.4315 + 1.17521i 1.27151 + 0.0909402i 0.690726 0.723117i \(-0.257291\pi\)
0.580785 + 0.814057i \(0.302746\pi\)
\(168\) 0 0
\(169\) 3.84484 13.0943i 0.295757 1.00726i
\(170\) 0 0
\(171\) 22.3389 + 3.21184i 1.70830 + 0.245616i
\(172\) 0 0
\(173\) −18.2117 + 6.79263i −1.38461 + 0.516434i −0.927783 0.373120i \(-0.878288\pi\)
−0.456830 + 0.889554i \(0.651015\pi\)
\(174\) 0 0
\(175\) 0.445902 + 1.53130i 0.0337070 + 0.115756i
\(176\) 0 0
\(177\) −4.58040 3.42884i −0.344284 0.257728i
\(178\) 0 0
\(179\) −3.70390 + 5.76338i −0.276843 + 0.430775i −0.951634 0.307233i \(-0.900597\pi\)
0.674792 + 0.738008i \(0.264233\pi\)
\(180\) 0 0
\(181\) −3.70057 12.6030i −0.275061 0.936772i −0.974932 0.222503i \(-0.928577\pi\)
0.699871 0.714269i \(-0.253241\pi\)
\(182\) 0 0
\(183\) 9.15058 9.15058i 0.676431 0.676431i
\(184\) 0 0
\(185\) −2.67566 10.5324i −0.196719 0.774360i
\(186\) 0 0
\(187\) 6.96661 12.7584i 0.509449 0.932987i
\(188\) 0 0
\(189\) −1.45497 0.935051i −0.105833 0.0680149i
\(190\) 0 0
\(191\) 7.90289 1.13626i 0.571833 0.0822172i 0.149668 0.988736i \(-0.452179\pi\)
0.422165 + 0.906519i \(0.361270\pi\)
\(192\) 0 0
\(193\) −14.8218 3.22428i −1.06689 0.232089i −0.355352 0.934732i \(-0.615639\pi\)
−0.711542 + 0.702644i \(0.752003\pi\)
\(194\) 0 0
\(195\) −18.5035 26.7140i −1.32506 1.91303i
\(196\) 0 0
\(197\) 11.2972 + 15.0913i 0.804893 + 1.07521i 0.995613 + 0.0935664i \(0.0298267\pi\)
−0.190720 + 0.981644i \(0.561082\pi\)
\(198\) 0 0
\(199\) 8.94437 + 2.62631i 0.634050 + 0.186174i 0.582935 0.812519i \(-0.301904\pi\)
0.0511151 + 0.998693i \(0.483722\pi\)
\(200\) 0 0
\(201\) 1.60109 1.38735i 0.112932 0.0978564i
\(202\) 0 0
\(203\) −0.158893 2.22161i −0.0111521 0.155927i
\(204\) 0 0
\(205\) −0.166658 + 1.53395i −0.0116399 + 0.107136i
\(206\) 0 0
\(207\) 4.92004 23.1058i 0.341966 1.60597i
\(208\) 0 0
\(209\) −19.0276 + 8.68960i −1.31616 + 0.601072i
\(210\) 0 0
\(211\) −15.1346 + 17.4663i −1.04191 + 1.20243i −0.0630253 + 0.998012i \(0.520075\pi\)
−0.978884 + 0.204416i \(0.934471\pi\)
\(212\) 0 0
\(213\) 1.59268 22.2686i 0.109129 1.52582i
\(214\) 0 0
\(215\) 8.90001 + 0.327861i 0.606976 + 0.0223599i
\(216\) 0 0
\(217\) 0.287998 0.215593i 0.0195506 0.0146354i
\(218\) 0 0
\(219\) −18.2747 8.34576i −1.23489 0.563954i
\(220\) 0 0
\(221\) −8.88576 13.8265i −0.597721 0.930072i
\(222\) 0 0
\(223\) −15.0593 + 20.1169i −1.00844 + 1.34712i −0.0715786 + 0.997435i \(0.522804\pi\)
−0.936866 + 0.349689i \(0.886287\pi\)
\(224\) 0 0
\(225\) −24.5628 1.81216i −1.63752 0.120811i
\(226\) 0 0
\(227\) 2.01279 + 1.09907i 0.133594 + 0.0729478i 0.544656 0.838660i \(-0.316660\pi\)
−0.411062 + 0.911607i \(0.634842\pi\)
\(228\) 0 0
\(229\) −19.5250 −1.29025 −0.645125 0.764077i \(-0.723195\pi\)
−0.645125 + 0.764077i \(0.723195\pi\)
\(230\) 0 0
\(231\) 4.10005 0.269763
\(232\) 0 0
\(233\) 7.68616 + 4.19696i 0.503537 + 0.274952i 0.710876 0.703317i \(-0.248299\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(234\) 0 0
\(235\) 10.3094 + 3.44413i 0.672508 + 0.224671i
\(236\) 0 0
\(237\) −5.34346 + 7.13803i −0.347095 + 0.463665i
\(238\) 0 0
\(239\) 5.19130 + 8.07783i 0.335798 + 0.522511i 0.967557 0.252653i \(-0.0813032\pi\)
−0.631759 + 0.775165i \(0.717667\pi\)
\(240\) 0 0
\(241\) 10.0367 + 4.58359i 0.646519 + 0.295255i 0.711558 0.702628i \(-0.247990\pi\)
−0.0650392 + 0.997883i \(0.520717\pi\)
\(242\) 0 0
\(243\) −11.9243 + 8.92643i −0.764945 + 0.572631i
\(244\) 0 0
\(245\) 11.3012 10.4982i 0.722009 0.670704i
\(246\) 0 0
\(247\) −1.68722 + 23.5904i −0.107355 + 1.50102i
\(248\) 0 0
\(249\) 2.72310 3.14262i 0.172569 0.199156i
\(250\) 0 0
\(251\) −16.1155 + 7.35971i −1.01720 + 0.464540i −0.853014 0.521889i \(-0.825228\pi\)
−0.164188 + 0.986429i \(0.552500\pi\)
\(252\) 0 0
\(253\) 7.74201 + 20.4816i 0.486736 + 1.28767i
\(254\) 0 0
\(255\) −19.9261 2.16489i −1.24782 0.135571i
\(256\) 0 0
\(257\) 0.638793 + 8.93150i 0.0398468 + 0.557131i 0.977687 + 0.210065i \(0.0673676\pi\)
−0.937841 + 0.347066i \(0.887178\pi\)
\(258\) 0 0
\(259\) 1.17156 1.01517i 0.0727975 0.0630793i
\(260\) 0 0
\(261\) 33.0021 + 9.69028i 2.04278 + 0.599813i
\(262\) 0 0
\(263\) −13.2070 17.6425i −0.814378 1.08788i −0.994551 0.104247i \(-0.966757\pi\)
0.180173 0.983635i \(-0.442334\pi\)
\(264\) 0 0
\(265\) 2.02424 11.1480i 0.124348 0.684818i
\(266\) 0 0
\(267\) −33.9168 7.37815i −2.07568 0.451536i
\(268\) 0 0
\(269\) 9.10920 1.30971i 0.555398 0.0798541i 0.141100 0.989995i \(-0.454936\pi\)
0.414298 + 0.910141i \(0.364027\pi\)
\(270\) 0 0
\(271\) −14.0938 9.05752i −0.856136 0.550205i 0.0373468 0.999302i \(-0.488109\pi\)
−0.893483 + 0.449097i \(0.851746\pi\)
\(272\) 0 0
\(273\) 2.22165 4.06865i 0.134460 0.246246i
\(274\) 0 0
\(275\) 20.0603 10.8954i 1.20968 0.657016i
\(276\) 0 0
\(277\) 17.1195 17.1195i 1.02861 1.02861i 0.0290345 0.999578i \(-0.490757\pi\)
0.999578 0.0290345i \(-0.00924325\pi\)
\(278\) 0 0
\(279\) 1.56519 + 5.33053i 0.0937052 + 0.319131i
\(280\) 0 0
\(281\) −6.80305 + 10.5858i −0.405836 + 0.631493i −0.982669 0.185369i \(-0.940652\pi\)
0.576833 + 0.816862i \(0.304288\pi\)
\(282\) 0 0
\(283\) 11.5763 + 8.66593i 0.688141 + 0.515136i 0.885174 0.465261i \(-0.154039\pi\)
−0.197032 + 0.980397i \(0.563130\pi\)
\(284\) 0 0
\(285\) 21.0873 + 19.6772i 1.24911 + 1.16558i
\(286\) 0 0
\(287\) −0.206232 + 0.0769204i −0.0121735 + 0.00454047i
\(288\) 0 0
\(289\) 6.79289 + 0.976670i 0.399582 + 0.0574512i
\(290\) 0 0
\(291\) 14.4084 49.0704i 0.844633 2.87656i
\(292\) 0 0
\(293\) 17.8800 + 1.27881i 1.04456 + 0.0747086i 0.583059 0.812430i \(-0.301856\pi\)
0.461504 + 0.887138i \(0.347310\pi\)
\(294\) 0 0
\(295\) −1.43029 4.31348i −0.0832748 0.251141i
\(296\) 0 0
\(297\) −8.65097 + 23.1942i −0.501980 + 1.34586i
\(298\) 0 0
\(299\) 24.5198 + 3.41541i 1.41802 + 0.197518i
\(300\) 0 0
\(301\) 0.527772 + 1.15566i 0.0304203 + 0.0666111i
\(302\) 0 0
\(303\) 9.28792 0.664285i 0.533577 0.0381622i
\(304\) 0 0
\(305\) 10.1171 1.81361i 0.579303 0.103847i
\(306\) 0 0
\(307\) 8.05467 4.39818i 0.459704 0.251018i −0.232670 0.972556i \(-0.574746\pi\)
0.692375 + 0.721538i \(0.256565\pi\)
\(308\) 0 0
\(309\) 4.45272 30.9693i 0.253306 1.76178i
\(310\) 0 0
\(311\) 9.77141 21.3964i 0.554086 1.21328i −0.400761 0.916183i \(-0.631254\pi\)
0.954847 0.297097i \(-0.0960184\pi\)
\(312\) 0 0
\(313\) −2.41447 + 11.0992i −0.136474 + 0.627361i 0.857193 + 0.514996i \(0.172206\pi\)
−0.993667 + 0.112366i \(0.964157\pi\)
\(314\) 0 0
\(315\) −1.34090 3.24753i −0.0755514 0.182978i
\(316\) 0 0
\(317\) 24.3390 5.29462i 1.36701 0.297375i 0.531598 0.846997i \(-0.321592\pi\)
0.835414 + 0.549621i \(0.185228\pi\)
\(318\) 0 0
\(319\) −30.5882 + 8.98151i −1.71261 + 0.502868i
\(320\) 0 0
\(321\) 54.0024i 3.01412i
\(322\) 0 0
\(323\) 10.3148 + 10.3148i 0.573933 + 0.573933i
\(324\) 0 0
\(325\) 0.0579034 25.8104i 0.00321191 1.43170i
\(326\) 0 0
\(327\) 11.3856 + 52.3389i 0.629626 + 2.89435i
\(328\) 0 0
\(329\) 0.220667 + 1.53477i 0.0121658 + 0.0846147i
\(330\) 0 0
\(331\) −28.1933 + 18.1187i −1.54964 + 0.995895i −0.564250 + 0.825604i \(0.690834\pi\)
−0.985394 + 0.170291i \(0.945529\pi\)
\(332\) 0 0
\(333\) 8.36592 + 22.4299i 0.458450 + 1.22915i
\(334\) 0 0
\(335\) 1.67323 0.177992i 0.0914182 0.00972476i
\(336\) 0 0
\(337\) 1.33800 + 2.45036i 0.0728855 + 0.133480i 0.911581 0.411122i \(-0.134863\pi\)
−0.838695 + 0.544601i \(0.816681\pi\)
\(338\) 0 0
\(339\) 32.2671 + 37.2383i 1.75251 + 2.02251i
\(340\) 0 0
\(341\) −3.89152 3.37203i −0.210738 0.182605i
\(342\) 0 0
\(343\) 4.15375 + 1.54927i 0.224282 + 0.0836527i
\(344\) 0 0
\(345\) 22.0289 20.6448i 1.18600 1.11148i
\(346\) 0 0
\(347\) −30.2838 11.2953i −1.62572 0.606361i −0.639058 0.769159i \(-0.720675\pi\)
−0.986659 + 0.162798i \(0.947948\pi\)
\(348\) 0 0
\(349\) −24.6327 21.3444i −1.31856 1.14254i −0.979427 0.201799i \(-0.935321\pi\)
−0.339132 0.940739i \(-0.610133\pi\)
\(350\) 0 0
\(351\) 18.3289 + 21.1527i 0.978324 + 1.12905i
\(352\) 0 0
\(353\) −11.9250 21.8390i −0.634702 1.16237i −0.975032 0.222064i \(-0.928721\pi\)
0.340330 0.940306i \(-0.389461\pi\)
\(354\) 0 0
\(355\) 11.1419 13.7945i 0.591349 0.732137i
\(356\) 0 0
\(357\) −0.999199 2.67896i −0.0528832 0.141785i
\(358\) 0 0
\(359\) −3.41487 + 2.19460i −0.180230 + 0.115827i −0.627645 0.778500i \(-0.715981\pi\)
0.447415 + 0.894326i \(0.352345\pi\)
\(360\) 0 0
\(361\) −0.283360 1.97081i −0.0149137 0.103727i
\(362\) 0 0
\(363\) −5.89155 27.0830i −0.309226 1.42149i
\(364\) 0 0
\(365\) −8.12685 13.7321i −0.425379 0.718773i
\(366\) 0 0
\(367\) 9.76278 + 9.76278i 0.509613 + 0.509613i 0.914408 0.404795i \(-0.132657\pi\)
−0.404795 + 0.914408i \(0.632657\pi\)
\(368\) 0 0
\(369\) 3.39908i 0.176949i
\(370\) 0 0
\(371\) 1.55083 0.455363i 0.0805148 0.0236413i
\(372\) 0 0
\(373\) 8.16402 1.77597i 0.422717 0.0919564i 0.00382530 0.999993i \(-0.498782\pi\)
0.418892 + 0.908036i \(0.362419\pi\)
\(374\) 0 0
\(375\) −24.4419 19.8326i −1.26218 1.02415i
\(376\) 0 0
\(377\) −7.66179 + 35.2207i −0.394602 + 1.81396i
\(378\) 0 0
\(379\) −4.67661 + 10.2403i −0.240221 + 0.526011i −0.990891 0.134666i \(-0.957004\pi\)
0.750670 + 0.660678i \(0.229731\pi\)
\(380\) 0 0
\(381\) −4.90107 + 34.0877i −0.251090 + 1.74637i
\(382\) 0 0
\(383\) 8.16491 4.45838i 0.417207 0.227812i −0.256912 0.966435i \(-0.582705\pi\)
0.674119 + 0.738622i \(0.264523\pi\)
\(384\) 0 0
\(385\) 2.67286 + 1.86025i 0.136222 + 0.0948070i
\(386\) 0 0
\(387\) −19.5695 + 1.39964i −0.994772 + 0.0711475i
\(388\) 0 0
\(389\) −0.628717 1.37670i −0.0318772 0.0698013i 0.893024 0.450010i \(-0.148580\pi\)
−0.924901 + 0.380208i \(0.875852\pi\)
\(390\) 0 0
\(391\) 11.4958 10.0500i 0.581368 0.508252i
\(392\) 0 0
\(393\) 10.8039 28.9664i 0.544985 1.46116i
\(394\) 0 0
\(395\) −6.72207 + 2.22895i −0.338224 + 0.112151i
\(396\) 0 0
\(397\) 10.9626 + 0.784061i 0.550197 + 0.0393509i 0.343671 0.939090i \(-0.388330\pi\)
0.206526 + 0.978441i \(0.433784\pi\)
\(398\) 0 0
\(399\) −1.15916 + 3.94774i −0.0580306 + 0.197634i
\(400\) 0 0
\(401\) −6.84218 0.983757i −0.341682 0.0491265i −0.0306620 0.999530i \(-0.509762\pi\)
−0.311020 + 0.950403i \(0.600671\pi\)
\(402\) 0 0
\(403\) −5.45486 + 2.03456i −0.271726 + 0.101348i
\(404\) 0 0
\(405\) 1.08810 0.0376394i 0.0540680 0.00187032i
\(406\) 0 0
\(407\) −17.7627 13.2970i −0.880462 0.659106i
\(408\) 0 0
\(409\) −6.24459 + 9.71677i −0.308775 + 0.480464i −0.960611 0.277897i \(-0.910363\pi\)
0.651836 + 0.758360i \(0.273999\pi\)
\(410\) 0 0
\(411\) 18.3062 + 62.3452i 0.902979 + 3.07526i
\(412\) 0 0
\(413\) 0.458399 0.458399i 0.0225563 0.0225563i
\(414\) 0 0
\(415\) 3.20106 0.813200i 0.157134 0.0399184i
\(416\) 0 0
\(417\) 18.6269 34.1127i 0.912165 1.67050i
\(418\) 0 0
\(419\) −5.72563 3.67964i −0.279715 0.179762i 0.393260 0.919427i \(-0.371347\pi\)
−0.672975 + 0.739666i \(0.734984\pi\)
\(420\) 0 0
\(421\) 24.1849 3.47726i 1.17870 0.169471i 0.475011 0.879980i \(-0.342444\pi\)
0.703688 + 0.710509i \(0.251535\pi\)
\(422\) 0 0
\(423\) −23.3975 5.08981i −1.13763 0.247475i
\(424\) 0 0
\(425\) −12.0078 10.4520i −0.582462 0.506998i
\(426\) 0 0
\(427\) 0.878681 + 1.17378i 0.0425224 + 0.0568032i
\(428\) 0 0
\(429\) −63.6637 18.6934i −3.07371 0.902524i
\(430\) 0 0
\(431\) 13.4728 11.6743i 0.648962 0.562329i −0.266949 0.963711i \(-0.586015\pi\)
0.915911 + 0.401382i \(0.131470\pi\)
\(432\) 0 0
\(433\) 2.39587 + 33.4986i 0.115138 + 1.60984i 0.646647 + 0.762789i \(0.276171\pi\)
−0.531509 + 0.847053i \(0.678375\pi\)
\(434\) 0 0
\(435\) 27.5429 + 34.2572i 1.32058 + 1.64251i
\(436\) 0 0
\(437\) −21.9095 + 1.66388i −1.04807 + 0.0795944i
\(438\) 0 0
\(439\) −3.19723 + 1.46013i −0.152596 + 0.0696881i −0.490249 0.871582i \(-0.663094\pi\)
0.337653 + 0.941271i \(0.390367\pi\)
\(440\) 0 0
\(441\) −22.2523 + 25.6805i −1.05963 + 1.22288i
\(442\) 0 0
\(443\) −1.85444 + 25.9285i −0.0881072 + 1.23190i 0.740495 + 0.672062i \(0.234591\pi\)
−0.828602 + 0.559838i \(0.810863\pi\)
\(444\) 0 0
\(445\) −18.7631 20.1984i −0.889458 0.957497i
\(446\) 0 0
\(447\) 43.5138 32.5740i 2.05813 1.54070i
\(448\) 0 0
\(449\) −12.6424 5.77358i −0.596631 0.272472i 0.0941247 0.995560i \(-0.469995\pi\)
−0.690756 + 0.723088i \(0.742722\pi\)
\(450\) 0 0
\(451\) 1.70327 + 2.65034i 0.0802039 + 0.124800i
\(452\) 0 0
\(453\) 19.2989 25.7803i 0.906741 1.21126i
\(454\) 0 0
\(455\) 3.29431 1.64440i 0.154440 0.0770905i
\(456\) 0 0
\(457\) 13.5683 + 7.40886i 0.634699 + 0.346572i 0.764173 0.645011i \(-0.223147\pi\)
−0.129474 + 0.991583i \(0.541329\pi\)
\(458\) 0 0
\(459\) 17.2632 0.805779
\(460\) 0 0
\(461\) −19.1442 −0.891635 −0.445818 0.895124i \(-0.647087\pi\)
−0.445818 + 0.895124i \(0.647087\pi\)
\(462\) 0 0
\(463\) −11.9635 6.53256i −0.555991 0.303594i 0.176578 0.984287i \(-0.443497\pi\)
−0.732569 + 0.680693i \(0.761679\pi\)
\(464\) 0 0
\(465\) −2.24970 + 6.73404i −0.104327 + 0.312284i
\(466\) 0 0
\(467\) −10.1700 + 13.5855i −0.470612 + 0.628664i −0.971554 0.236817i \(-0.923896\pi\)
0.500942 + 0.865481i \(0.332987\pi\)
\(468\) 0 0
\(469\) 0.129774 + 0.201932i 0.00599239 + 0.00932434i
\(470\) 0 0
\(471\) 7.81986 + 3.57121i 0.360320 + 0.164553i
\(472\) 0 0
\(473\) 14.5574 10.8975i 0.669350 0.501069i
\(474\) 0 0
\(475\) 4.81922 + 22.3954i 0.221121 + 1.02757i
\(476\) 0 0
\(477\) −1.78062 + 24.8964i −0.0815291 + 1.13993i
\(478\) 0 0
\(479\) −28.5207 + 32.9146i −1.30314 + 1.50391i −0.575925 + 0.817502i \(0.695358\pi\)
−0.727219 + 0.686406i \(0.759187\pi\)
\(480\) 0 0
\(481\) −22.8200 + 10.4215i −1.04050 + 0.475181i
\(482\) 0 0
\(483\) 4.04182 + 1.48730i 0.183909 + 0.0676747i
\(484\) 0 0
\(485\) 31.6568 25.4522i 1.43746 1.15572i
\(486\) 0 0
\(487\) −1.52098 21.2661i −0.0689221 0.963657i −0.907818 0.419365i \(-0.862253\pi\)
0.838896 0.544292i \(-0.183202\pi\)
\(488\) 0 0
\(489\) 36.9457 32.0136i 1.67074 1.44771i
\(490\) 0 0
\(491\) 36.4623 + 10.7063i 1.64552 + 0.483168i 0.967709 0.252069i \(-0.0811112\pi\)
0.677810 + 0.735237i \(0.262929\pi\)
\(492\) 0 0
\(493\) 13.3230 + 17.7974i 0.600036 + 0.801554i
\(494\) 0 0
\(495\) −41.3405 + 28.6346i −1.85812 + 1.28703i
\(496\) 0 0
\(497\) 2.47173 + 0.537692i 0.110872 + 0.0241188i
\(498\) 0 0
\(499\) 23.3456 3.35659i 1.04509 0.150261i 0.401678 0.915781i \(-0.368427\pi\)
0.643413 + 0.765519i \(0.277518\pi\)
\(500\) 0 0
\(501\) −39.0156 25.0738i −1.74309 1.12021i
\(502\) 0 0
\(503\) 19.1159 35.0082i 0.852338 1.56094i 0.0246878 0.999695i \(-0.492141\pi\)
0.827650 0.561245i \(-0.189677\pi\)
\(504\) 0 0
\(505\) 6.35628 + 3.78100i 0.282851 + 0.168252i
\(506\) 0 0
\(507\) −27.1676 + 27.1676i −1.20656 + 1.20656i
\(508\) 0 0
\(509\) 6.39700 + 21.7862i 0.283542 + 0.965655i 0.970930 + 0.239365i \(0.0769391\pi\)
−0.687388 + 0.726291i \(0.741243\pi\)
\(510\) 0 0
\(511\) 1.23064 1.91492i 0.0544404 0.0847110i
\(512\) 0 0
\(513\) −19.8867 14.8870i −0.878020 0.657278i
\(514\) 0 0
\(515\) 16.9540 18.1689i 0.747081 0.800620i
\(516\) 0 0
\(517\) 20.7941 7.75578i 0.914521 0.341099i
\(518\) 0 0
\(519\) 54.1647 + 7.78771i 2.37757 + 0.341843i
\(520\) 0 0
\(521\) 8.50895 28.9788i 0.372784 1.26958i −0.533098 0.846054i \(-0.678972\pi\)
0.905881 0.423531i \(-0.139210\pi\)
\(522\) 0 0
\(523\) −20.4894 1.46543i −0.895938 0.0640787i −0.384229 0.923238i \(-0.625533\pi\)
−0.511709 + 0.859159i \(0.670987\pi\)
\(524\) 0 0
\(525\) 0.964286 4.38536i 0.0420849 0.191393i
\(526\) 0 0
\(527\) −1.25489 + 3.36448i −0.0546637 + 0.146559i
\(528\) 0 0
\(529\) 0.202313 + 22.9991i 0.00879623 + 0.999961i
\(530\) 0 0
\(531\) 4.15876 + 9.10641i 0.180475 + 0.395185i
\(532\) 0 0
\(533\) 3.55297 0.254114i 0.153896 0.0110069i
\(534\) 0 0
\(535\) −24.5016 + 35.2046i −1.05930 + 1.52203i
\(536\) 0 0
\(537\) 16.9282 9.24350i 0.730506 0.398887i
\(538\) 0 0
\(539\) 4.48218 31.1743i 0.193061 1.34277i
\(540\) 0 0
\(541\) 11.2889 24.7192i 0.485346 1.06276i −0.495612 0.868544i \(-0.665056\pi\)
0.980959 0.194217i \(-0.0622164\pi\)
\(542\) 0 0
\(543\) −7.86047 + 36.1340i −0.337325 + 1.55066i
\(544\) 0 0
\(545\) −16.3245 + 39.2860i −0.699263 + 1.68283i
\(546\) 0 0
\(547\) −2.13442 + 0.464314i −0.0912612 + 0.0198527i −0.257964 0.966155i \(-0.583052\pi\)
0.166703 + 0.986007i \(0.446688\pi\)
\(548\) 0 0
\(549\) −21.7254 + 6.37915i −0.927218 + 0.272256i
\(550\) 0 0
\(551\) 31.9911i 1.36287i
\(552\) 0 0
\(553\) −0.714363 0.714363i −0.0303778 0.0303778i
\(554\) 0 0
\(555\) −7.59930 + 29.6350i −0.322572 + 1.25794i
\(556\) 0 0
\(557\) 2.07071 + 9.51889i 0.0877387 + 0.403328i 0.999980 0.00632509i \(-0.00201335\pi\)
−0.912241 + 0.409653i \(0.865650\pi\)
\(558\) 0 0
\(559\) −2.92601 20.3508i −0.123757 0.860749i
\(560\) 0 0
\(561\) −34.4280 + 22.1255i −1.45355 + 0.934141i
\(562\) 0 0
\(563\) 1.50834 + 4.04402i 0.0635690 + 0.170435i 0.964851 0.262798i \(-0.0846454\pi\)
−0.901282 + 0.433233i \(0.857373\pi\)
\(564\) 0 0
\(565\) 4.13975 + 38.9160i 0.174161 + 1.63721i
\(566\) 0 0
\(567\) 0.0744334 + 0.136315i 0.00312591 + 0.00572467i
\(568\) 0 0
\(569\) −11.2072 12.9338i −0.469830 0.542213i 0.470534 0.882382i \(-0.344061\pi\)
−0.940364 + 0.340169i \(0.889516\pi\)
\(570\) 0 0
\(571\) −6.63720 5.75116i −0.277758 0.240679i 0.504830 0.863219i \(-0.331555\pi\)
−0.782588 + 0.622540i \(0.786101\pi\)
\(572\) 0 0
\(573\) −21.0606 7.85518i −0.879818 0.328155i
\(574\) 0 0
\(575\) 23.7277 3.46373i 0.989512 0.144447i
\(576\) 0 0
\(577\) −23.3973 8.72672i −0.974040 0.363298i −0.188476 0.982078i \(-0.560355\pi\)
−0.785565 + 0.618780i \(0.787627\pi\)
\(578\) 0 0
\(579\) 32.2733 + 27.9649i 1.34123 + 1.16218i
\(580\) 0 0
\(581\) 0.308534 + 0.356067i 0.0128001 + 0.0147722i
\(582\) 0 0
\(583\) −11.0871 20.3045i −0.459181 0.840927i
\(584\) 0 0
\(585\) 6.01451 + 56.5398i 0.248669 + 2.33763i
\(586\) 0 0
\(587\) 8.30941 + 22.2784i 0.342966 + 0.919528i 0.987873 + 0.155266i \(0.0496236\pi\)
−0.644906 + 0.764261i \(0.723104\pi\)
\(588\) 0 0
\(589\) 4.34696 2.79362i 0.179113 0.115109i
\(590\) 0 0
\(591\) −7.55297 52.5321i −0.310688 2.16088i
\(592\) 0 0
\(593\) −2.73951 12.5933i −0.112498 0.517146i −0.998563 0.0535849i \(-0.982935\pi\)
0.886065 0.463561i \(-0.153428\pi\)
\(594\) 0 0
\(595\) 0.564091 2.19979i 0.0231255 0.0901825i
\(596\) 0 0
\(597\) −18.5574 18.5574i −0.759505 0.759505i
\(598\) 0 0
\(599\) 12.8581i 0.525368i −0.964882 0.262684i \(-0.915392\pi\)
0.964882 0.262684i \(-0.0846076\pi\)
\(600\) 0 0
\(601\) −16.2507 + 4.77162i −0.662878 + 0.194639i −0.595829 0.803111i \(-0.703176\pi\)
−0.0670488 + 0.997750i \(0.521358\pi\)
\(602\) 0 0
\(603\) −3.62210 + 0.787940i −0.147503 + 0.0320874i
\(604\) 0 0
\(605\) 8.44717 20.3288i 0.343426 0.826481i
\(606\) 0 0
\(607\) −4.94579 + 22.7354i −0.200743 + 0.922802i 0.760979 + 0.648776i \(0.224719\pi\)
−0.961722 + 0.274026i \(0.911645\pi\)
\(608\) 0 0
\(609\) −2.60485 + 5.70384i −0.105554 + 0.231131i
\(610\) 0 0
\(611\) 3.57107 24.8373i 0.144470 1.00481i
\(612\) 0 0
\(613\) 12.5755 6.86674i 0.507919 0.277345i −0.204788 0.978806i \(-0.565651\pi\)
0.712707 + 0.701461i \(0.247469\pi\)
\(614\) 0 0
\(615\) 2.48145 3.56543i 0.100062 0.143772i
\(616\) 0 0
\(617\) 15.1480 1.08341i 0.609835 0.0436163i 0.236993 0.971511i \(-0.423838\pi\)
0.372842 + 0.927895i \(0.378383\pi\)
\(618\) 0 0
\(619\) 18.5706 + 40.6639i 0.746414 + 1.63442i 0.772706 + 0.634764i \(0.218903\pi\)
−0.0262919 + 0.999654i \(0.508370\pi\)
\(620\) 0 0
\(621\) −16.9418 + 19.7266i −0.679853 + 0.791600i
\(622\) 0 0
\(623\) 1.37435 3.68478i 0.0550622 0.147627i
\(624\) 0 0
\(625\) −6.93562 24.0187i −0.277425 0.960747i
\(626\) 0 0
\(627\) 58.7401 + 4.20117i 2.34585 + 0.167779i
\(628\) 0 0
\(629\) −4.35935 + 14.8466i −0.173818 + 0.591971i
\(630\) 0 0
\(631\) 3.03854 + 0.436875i 0.120962 + 0.0173917i 0.202530 0.979276i \(-0.435084\pi\)
−0.0815678 + 0.996668i \(0.525993\pi\)
\(632\) 0 0
\(633\) 60.9626 22.7379i 2.42304 0.903749i
\(634\) 0 0
\(635\) −18.6611 + 19.9984i −0.740544 + 0.793613i
\(636\) 0 0
\(637\) −28.5068 21.3399i −1.12948 0.845518i
\(638\) 0 0
\(639\) −21.1190 + 32.8618i −0.835454 + 1.29999i
\(640\) 0 0
\(641\) 3.40954 + 11.6118i 0.134669 + 0.458639i 0.999021 0.0442482i \(-0.0140893\pi\)
−0.864352 + 0.502887i \(0.832271\pi\)
\(642\) 0 0
\(643\) −7.93740 + 7.93740i −0.313020 + 0.313020i −0.846079 0.533058i \(-0.821043\pi\)
0.533058 + 0.846079i \(0.321043\pi\)
\(644\) 0 0
\(645\) −21.5489 12.8183i −0.848489 0.504719i
\(646\) 0 0
\(647\) 17.5701 32.1772i 0.690750 1.26502i −0.263110 0.964766i \(-0.584748\pi\)
0.953861 0.300249i \(-0.0970699\pi\)
\(648\) 0 0
\(649\) −7.80588 5.01653i −0.306407 0.196916i
\(650\) 0 0
\(651\) −1.00251 + 0.144139i −0.0392914 + 0.00564924i
\(652\) 0 0
\(653\) 9.77101 + 2.12555i 0.382369 + 0.0831794i 0.399642 0.916671i \(-0.369135\pi\)
−0.0172723 + 0.999851i \(0.505498\pi\)
\(654\) 0 0
\(655\) 20.1856 13.9816i 0.788717 0.546306i
\(656\) 0 0
\(657\) 21.0656 + 28.1404i 0.821848 + 1.09786i
\(658\) 0 0
\(659\) 12.0317 + 3.53283i 0.468689 + 0.137619i 0.507545 0.861625i \(-0.330553\pi\)
−0.0388560 + 0.999245i \(0.512371\pi\)
\(660\) 0 0
\(661\) −7.38771 + 6.40149i −0.287349 + 0.248989i −0.786592 0.617473i \(-0.788157\pi\)
0.499244 + 0.866462i \(0.333611\pi\)
\(662\) 0 0
\(663\) 3.30095 + 46.1533i 0.128198 + 1.79244i
\(664\) 0 0
\(665\) −2.54681 + 2.04764i −0.0987610 + 0.0794041i
\(666\) 0 0
\(667\) −33.4119 2.24201i −1.29371 0.0868108i
\(668\) 0 0
\(669\) 64.3527 29.3889i 2.48802 1.13624i
\(670\) 0 0
\(671\) 13.7432 15.8605i 0.530551 0.612288i
\(672\) 0 0
\(673\) 0.342916 4.79459i 0.0132184 0.184818i −0.986553 0.163441i \(-0.947741\pi\)
0.999771 0.0213765i \(-0.00680486\pi\)
\(674\) 0 0
\(675\) 22.7736 + 14.7080i 0.876556 + 0.566111i
\(676\) 0 0
\(677\) 0.905472 0.677828i 0.0348001 0.0260510i −0.581736 0.813378i \(-0.697626\pi\)
0.616536 + 0.787327i \(0.288535\pi\)
\(678\) 0 0
\(679\) 5.27088 + 2.40713i 0.202278 + 0.0923771i
\(680\) 0 0
\(681\) −3.49058 5.43144i −0.133759 0.208133i
\(682\) 0 0
\(683\) −24.2872 + 32.4439i −0.929323 + 1.24143i 0.0408865 + 0.999164i \(0.486982\pi\)
−0.970210 + 0.242267i \(0.922109\pi\)
\(684\) 0 0
\(685\) −16.3529 + 48.9492i −0.624811 + 1.87025i
\(686\) 0 0
\(687\) 48.2450 + 26.3437i 1.84066 + 1.00508i
\(688\) 0 0
\(689\) −26.1567 −0.996489
\(690\) 0 0
\(691\) −30.7526 −1.16988 −0.584942 0.811075i \(-0.698883\pi\)
−0.584942 + 0.811075i \(0.698883\pi\)
\(692\) 0 0
\(693\) −6.29633 3.43805i −0.239178 0.130601i
\(694\) 0 0
\(695\) 27.6204 13.7871i 1.04770 0.522974i
\(696\) 0 0
\(697\) 1.31663 1.75881i 0.0498708 0.0666196i
\(698\) 0 0
\(699\) −13.3293 20.7408i −0.504160 0.784489i
\(700\) 0 0
\(701\) 5.55420 + 2.53652i 0.209779 + 0.0958030i 0.517534 0.855663i \(-0.326850\pi\)
−0.307754 + 0.951466i \(0.599577\pi\)
\(702\) 0 0
\(703\) 17.8248 13.3435i 0.672276 0.503259i
\(704\) 0 0
\(705\) −20.8268 22.4199i −0.784382 0.844383i
\(706\) 0 0
\(707\) −0.0752652 + 1.05235i −0.00283064 + 0.0395775i
\(708\) 0 0
\(709\) 18.5484 21.4060i 0.696600 0.803919i −0.291689 0.956513i \(-0.594217\pi\)
0.988289 + 0.152594i \(0.0487627\pi\)
\(710\) 0 0
\(711\) 14.1913 6.48096i 0.532216 0.243055i
\(712\) 0 0
\(713\) −2.61304 4.73579i −0.0978593 0.177357i
\(714\) 0 0
\(715\) −33.0216 41.0715i −1.23494 1.53599i
\(716\) 0 0
\(717\) −1.92850 26.9640i −0.0720213 1.00699i
\(718\) 0 0
\(719\) −12.3866 + 10.7331i −0.461943 + 0.400275i −0.854500 0.519452i \(-0.826136\pi\)
0.392557 + 0.919728i \(0.371591\pi\)
\(720\) 0 0
\(721\) 3.40139 + 0.998738i 0.126674 + 0.0371950i
\(722\) 0 0
\(723\) −18.6156 24.8675i −0.692321 0.924833i
\(724\) 0 0
\(725\) 2.41251 + 34.8292i 0.0895983 + 1.29352i
\(726\) 0 0
\(727\) 19.7853 + 4.30402i 0.733795 + 0.159627i 0.563910 0.825836i \(-0.309297\pi\)
0.169885 + 0.985464i \(0.445660\pi\)
\(728\) 0 0
\(729\) 42.9538 6.17583i 1.59088 0.228734i
\(730\) 0 0
\(731\) −10.6681 6.85597i −0.394574 0.253577i
\(732\) 0 0
\(733\) −14.9339 + 27.3494i −0.551596 + 1.01017i 0.441982 + 0.897024i \(0.354276\pi\)
−0.993578 + 0.113149i \(0.963906\pi\)
\(734\) 0 0
\(735\) −42.0890 + 10.6923i −1.55248 + 0.394391i
\(736\) 0 0
\(737\) 2.42940 2.42940i 0.0894881 0.0894881i
\(738\) 0 0
\(739\) 8.97815 + 30.5768i 0.330267 + 1.12478i 0.942527 + 0.334129i \(0.108442\pi\)
−0.612261 + 0.790656i \(0.709740\pi\)
\(740\) 0 0
\(741\) 35.9978 56.0137i 1.32241 2.05771i
\(742\) 0 0
\(743\) 20.3742 + 15.2520i 0.747458 + 0.559540i 0.903694 0.428180i \(-0.140845\pi\)
−0.156236 + 0.987720i \(0.549936\pi\)
\(744\) 0 0
\(745\) 43.1463 1.49252i 1.58076 0.0546816i
\(746\) 0 0
\(747\) −6.81700 + 2.54261i −0.249421 + 0.0930292i
\(748\) 0 0
\(749\) −6.05632 0.870768i −0.221293 0.0318172i
\(750\) 0 0
\(751\) 3.53649 12.0442i 0.129048 0.439499i −0.869466 0.493993i \(-0.835537\pi\)
0.998514 + 0.0544949i \(0.0173549\pi\)
\(752\) 0 0
\(753\) 49.7502 + 3.55821i 1.81300 + 0.129668i
\(754\) 0 0
\(755\) 24.2780 8.05026i 0.883567 0.292979i
\(756\) 0 0
\(757\) −4.38153 + 11.7473i −0.159249 + 0.426964i −0.991930 0.126790i \(-0.959533\pi\)
0.832680 + 0.553754i \(0.186805\pi\)
\(758\) 0 0
\(759\) 8.50437 61.0543i 0.308689 2.21613i
\(760\) 0 0
\(761\) 0.945262 + 2.06983i 0.0342657 + 0.0750315i 0.925991 0.377546i \(-0.123232\pi\)
−0.891725 + 0.452577i \(0.850505\pi\)
\(762\) 0 0
\(763\) −6.05335 + 0.432944i −0.219146 + 0.0156736i
\(764\) 0 0
\(765\) 28.7845 + 20.0334i 1.04071 + 0.724308i
\(766\) 0 0
\(767\) −9.20779 + 5.02784i −0.332474 + 0.181545i
\(768\) 0 0
\(769\) −3.79339 + 26.3836i −0.136793 + 0.951417i 0.799617 + 0.600510i \(0.205036\pi\)
−0.936410 + 0.350907i \(0.885873\pi\)
\(770\) 0 0
\(771\) 10.4722 22.9310i 0.377148 0.825839i
\(772\) 0 0
\(773\) 7.89966 36.3141i 0.284131 1.30613i −0.584793 0.811183i \(-0.698824\pi\)
0.868924 0.494946i \(-0.164812\pi\)
\(774\) 0 0
\(775\) −4.52192 + 3.36927i −0.162432 + 0.121028i
\(776\) 0 0
\(777\) −4.26455 + 0.927695i −0.152990 + 0.0332809i
\(778\) 0 0
\(779\) −3.03343 + 0.890695i −0.108684 + 0.0319125i
\(780\) 0 0
\(781\) 36.2057i 1.29554i
\(782\) 0 0
\(783\) −26.7707 26.7707i −0.956706 0.956706i
\(784\) 0 0
\(785\) 3.47753 + 5.87608i 0.124118 + 0.209726i
\(786\) 0 0
\(787\) −7.84305 36.0539i −0.279575 1.28518i −0.875920 0.482456i \(-0.839745\pi\)
0.596346 0.802728i \(-0.296619\pi\)
\(788\) 0 0
\(789\) 8.82980 + 61.4126i 0.314349 + 2.18635i
\(790\) 0 0
\(791\) −4.69654 + 3.01828i −0.166990 + 0.107318i
\(792\) 0 0
\(793\) −8.29215 22.2321i −0.294463 0.789485i
\(794\) 0 0
\(795\) −20.0430 + 24.8148i −0.710852 + 0.880091i
\(796\) 0 0
\(797\) −0.916435 1.67833i −0.0324618 0.0594493i 0.860945 0.508699i \(-0.169873\pi\)
−0.893406 + 0.449249i \(0.851691\pi\)
\(798\) 0 0
\(799\) −10.1352 11.6966i −0.358557 0.413797i
\(800\) 0 0
\(801\) 45.8982 + 39.7710i 1.62173 + 1.40524i
\(802\) 0 0
\(803\) −30.5264 11.3858i −1.07725 0.401795i
\(804\) 0 0
\(805\) 1.96009 + 2.80341i 0.0690841 + 0.0988074i
\(806\) 0 0
\(807\) −24.2753 9.05422i −0.854531 0.318723i
\(808\) 0 0
\(809\) −34.7977 30.1524i −1.22342 1.06010i −0.996274 0.0862421i \(-0.972514\pi\)
−0.227149 0.973860i \(-0.572940\pi\)
\(810\) 0 0
\(811\) 0.598397 + 0.690587i 0.0210126 + 0.0242498i 0.766159 0.642652i \(-0.222166\pi\)
−0.745146 + 0.666901i \(0.767620\pi\)
\(812\) 0 0
\(813\) 22.6041 + 41.3963i 0.792759 + 1.45183i
\(814\) 0 0
\(815\) 38.6103 4.10723i 1.35246 0.143870i
\(816\) 0 0
\(817\) 6.37705 + 17.0975i 0.223105 + 0.598167i
\(818\) 0 0
\(819\) −6.82344 + 4.38516i −0.238430 + 0.153230i
\(820\) 0 0
\(821\) −5.21892 36.2984i −0.182142 1.26682i −0.851687 0.524051i \(-0.824420\pi\)
0.669545 0.742771i \(-0.266489\pi\)
\(822\) 0 0
\(823\) −2.16138 9.93569i −0.0753408 0.346336i 0.924010 0.382369i \(-0.124892\pi\)
−0.999351 + 0.0360326i \(0.988528\pi\)
\(824\) 0 0
\(825\) −64.2679 0.144180i −2.23752 0.00501969i
\(826\) 0 0
\(827\) −7.46991 7.46991i −0.259754 0.259754i 0.565200 0.824954i \(-0.308799\pi\)
−0.824954 + 0.565200i \(0.808799\pi\)
\(828\) 0 0
\(829\) 28.2182i 0.980057i −0.871706 0.490029i \(-0.836986\pi\)
0.871706 0.490029i \(-0.163014\pi\)
\(830\) 0 0
\(831\) −65.3993 + 19.2030i −2.26868 + 0.666144i
\(832\) 0 0
\(833\) −21.4615 + 4.66865i −0.743595 + 0.161759i
\(834\) 0 0
\(835\) −14.0583 34.0477i −0.486508 1.17827i
\(836\) 0 0
\(837\) 1.29986 5.97535i 0.0449297 0.206538i
\(838\) 0 0
\(839\) −4.76827 + 10.4411i −0.164619 + 0.360465i −0.973907 0.226947i \(-0.927126\pi\)
0.809288 + 0.587412i \(0.199853\pi\)
\(840\) 0 0
\(841\) 2.81152 19.5545i 0.0969489 0.674294i
\(842\) 0 0
\(843\) 31.0925 16.9778i 1.07088 0.584746i
\(844\) 0 0
\(845\) −30.0371 + 5.38451i −1.03331 + 0.185233i
\(846\) 0 0
\(847\) 3.13234 0.224029i 0.107628 0.00769774i
\(848\) 0 0
\(849\) −16.9120 37.0320i −0.580417 1.27094i
\(850\) 0 0
\(851\) −12.6869 19.5516i −0.434900 0.670219i
\(852\) 0 0
\(853\) −9.83689 + 26.3737i −0.336809 + 0.903019i 0.652579 + 0.757720i \(0.273687\pi\)
−0.989388 + 0.145298i \(0.953586\pi\)
\(854\) 0 0
\(855\) −15.8831 47.9002i −0.543190 1.63815i
\(856\) 0 0
\(857\) 11.6102 + 0.830376i 0.396596 + 0.0283651i 0.268213 0.963360i \(-0.413567\pi\)
0.128383 + 0.991725i \(0.459021\pi\)
\(858\) 0 0
\(859\) 14.5817 49.6607i 0.497521 1.69440i −0.201661 0.979455i \(-0.564634\pi\)
0.699181 0.714944i \(-0.253548\pi\)
\(860\) 0 0
\(861\) 0.613367 + 0.0881889i 0.0209035 + 0.00300547i
\(862\) 0 0
\(863\) −47.9200 + 17.8732i −1.63122 + 0.608412i −0.987608 0.156943i \(-0.949836\pi\)
−0.643608 + 0.765355i \(0.722563\pi\)
\(864\) 0 0
\(865\) 31.7771 + 29.6522i 1.08045 + 1.00820i
\(866\) 0 0
\(867\) −15.4670 11.5784i −0.525287 0.393225i
\(868\) 0 0
\(869\) −7.81770 + 12.1646i −0.265197 + 0.412655i
\(870\) 0 0
\(871\) −1.09440 3.72718i −0.0370823 0.126291i
\(872\) 0 0
\(873\) −63.2739 + 63.2739i −2.14150 + 2.14150i
\(874\) 0 0
\(875\) 2.61833 2.42135i 0.0885156 0.0818566i
\(876\) 0 0
\(877\) −19.3351 + 35.4096i −0.652900 + 1.19570i 0.316120 + 0.948719i \(0.397620\pi\)
−0.969021 + 0.246979i \(0.920562\pi\)
\(878\) 0 0
\(879\) −42.4549 27.2841i −1.43197 0.920271i
\(880\) 0 0
\(881\) 2.99299 0.430327i 0.100836 0.0144981i −0.0917119 0.995786i \(-0.529234\pi\)
0.192548 + 0.981287i \(0.438325\pi\)
\(882\) 0 0
\(883\) −35.2432 7.66670i −1.18603 0.258005i −0.424070 0.905629i \(-0.639399\pi\)
−0.761960 + 0.647625i \(0.775763\pi\)
\(884\) 0 0
\(885\) −2.28573 + 12.5881i −0.0768339 + 0.423145i
\(886\) 0 0
\(887\) −21.1342 28.2320i −0.709617 0.947938i 0.290342 0.956923i \(-0.406231\pi\)
−0.999960 + 0.00898495i \(0.997140\pi\)
\(888\) 0 0
\(889\) −3.74388 1.09930i −0.125566 0.0368694i
\(890\) 0 0
\(891\) 1.68004 1.45577i 0.0562835 0.0487700i
\(892\) 0 0
\(893\) 1.58880 + 22.2143i 0.0531670 + 0.743372i
\(894\) 0 0
\(895\) 15.2296 + 1.65463i 0.509068 + 0.0553082i
\(896\) 0 0
\(897\) −55.9785 41.5220i −1.86907 1.38638i
\(898\) 0 0
\(899\) 7.16341 3.27142i 0.238913 0.109108i
\(900\) 0 0
\(901\) −10.5649 + 12.1926i −0.351968 + 0.406193i
\(902\) 0 0
\(903\) 0.255163 3.56764i 0.00849128 0.118724i
\(904\) 0 0
\(905\) −21.5188 + 19.9897i −0.715309 + 0.664480i
\(906\) 0 0
\(907\) 27.0094 20.2190i 0.896832 0.671360i −0.0480238 0.998846i \(-0.515292\pi\)
0.944856 + 0.327486i \(0.106201\pi\)
\(908\) 0 0
\(909\) −14.8202 6.76817i −0.491556 0.224486i
\(910\) 0 0
\(911\) −15.9877 24.8773i −0.529695 0.824221i 0.468550 0.883437i \(-0.344776\pi\)
−0.998245 + 0.0592155i \(0.981140\pi\)
\(912\) 0 0
\(913\) 4.04127 5.39851i 0.133747 0.178665i
\(914\) 0 0
\(915\) −27.4456 9.16899i −0.907324 0.303117i
\(916\) 0 0
\(917\) 3.07435 + 1.67872i 0.101524 + 0.0554362i
\(918\) 0 0
\(919\) 50.7741 1.67488 0.837442 0.546526i \(-0.184050\pi\)
0.837442 + 0.546526i \(0.184050\pi\)
\(920\) 0 0
\(921\) −25.8367 −0.851348
\(922\) 0 0
\(923\) −35.9284 19.6184i −1.18260 0.645747i
\(924\) 0 0
\(925\) −18.3998 + 15.8714i −0.604983 + 0.521849i
\(926\) 0 0
\(927\) −32.8069 + 43.8249i −1.07752 + 1.43940i
\(928\) 0 0
\(929\) 15.4337 + 24.0153i 0.506363 + 0.787916i 0.996488 0.0837363i \(-0.0266854\pi\)
−0.490125 + 0.871652i \(0.663049\pi\)
\(930\) 0 0
\(931\) 28.7490 + 13.1292i 0.942209 + 0.430292i
\(932\) 0 0
\(933\) −53.0132 + 39.6852i −1.73557 + 1.29923i
\(934\) 0 0
\(935\) −32.4826 1.19660i −1.06230 0.0391331i
\(936\) 0 0
\(937\) 2.23830 31.2955i 0.0731220 1.02238i −0.819941 0.572448i \(-0.805994\pi\)
0.893063 0.449931i \(-0.148551\pi\)
\(938\) 0 0
\(939\) 20.9413 24.1675i 0.683393 0.788678i
\(940\) 0 0
\(941\) −10.4386 + 4.76713i −0.340287 + 0.155404i −0.578227 0.815876i \(-0.696255\pi\)
0.237940 + 0.971280i \(0.423528\pi\)
\(942\) 0 0
\(943\) 0.717662 + 3.23057i 0.0233703 + 0.105202i
\(944\) 0 0
\(945\) −0.417712 + 3.84471i −0.0135882 + 0.125068i
\(946\) 0 0
\(947\) −0.873303 12.2104i −0.0283785 0.396784i −0.991712 0.128478i \(-0.958991\pi\)
0.963334 0.268306i \(-0.0864637\pi\)
\(948\) 0 0
\(949\) −27.8396 + 24.1231i −0.903710 + 0.783069i
\(950\) 0 0
\(951\) −67.2835 19.7562i −2.18182 0.640640i
\(952\) 0 0
\(953\) 11.8993 + 15.8956i 0.385456 + 0.514909i 0.950741 0.309987i \(-0.100325\pi\)
−0.565285 + 0.824896i \(0.691234\pi\)
\(954\) 0 0
\(955\) −10.1656 14.6763i −0.328950 0.474915i
\(956\) 0 0
\(957\) 87.6995 + 19.0779i 2.83492 + 0.616700i
\(958\) 0 0
\(959\) −7.28715 + 1.04773i −0.235314 + 0.0338331i
\(960\) 0 0
\(961\) −25.0088 16.0722i −0.806735 0.518457i
\(962\) 0 0
\(963\) 45.2831 82.9298i 1.45923 2.67238i
\(964\) 0 0
\(965\) 8.35117 + 32.8734i 0.268834 + 1.05823i
\(966\) 0 0
\(967\) 25.5921 25.5921i 0.822985 0.822985i −0.163550 0.986535i \(-0.552294\pi\)
0.986535 + 0.163550i \(0.0522945\pi\)
\(968\) 0 0
\(969\) −11.5702 39.4044i −0.371687 1.26585i
\(970\) 0 0
\(971\) −13.6108 + 21.1788i −0.436792 + 0.679661i −0.987956 0.154736i \(-0.950547\pi\)
0.551164 + 0.834397i \(0.314184\pi\)
\(972\) 0 0
\(973\) 3.52536 + 2.63905i 0.113018 + 0.0846041i
\(974\) 0 0
\(975\) −34.9672 + 63.6975i −1.11985 + 2.03995i
\(976\) 0 0
\(977\) −44.4716 + 16.5871i −1.42277 + 0.530667i −0.938814 0.344424i \(-0.888074\pi\)
−0.483958 + 0.875091i \(0.660801\pi\)
\(978\) 0 0
\(979\) −55.7170 8.01090i −1.78072 0.256029i
\(980\) 0 0
\(981\) 26.4036 89.9225i 0.843003 2.87101i
\(982\) 0 0
\(983\) −39.3722 2.81596i −1.25578 0.0898150i −0.572458 0.819934i \(-0.694010\pi\)
−0.683320 + 0.730119i \(0.739465\pi\)
\(984\) 0 0
\(985\) 18.9107 37.6730i 0.602544 1.20036i
\(986\) 0 0
\(987\) 1.52551 4.09004i 0.0485574 0.130187i
\(988\) 0 0
\(989\) 18.3038 5.46203i 0.582026 0.173682i
\(990\) 0 0
\(991\) −3.27709 7.17582i −0.104100 0.227947i 0.850413 0.526115i \(-0.176352\pi\)
−0.954514 + 0.298168i \(0.903625\pi\)
\(992\) 0 0
\(993\) 94.1100 6.73088i 2.98649 0.213598i
\(994\) 0 0
\(995\) −3.67801 20.5175i −0.116601 0.650449i
\(996\) 0 0
\(997\) 42.0804 22.9777i 1.33270 0.727710i 0.354438 0.935079i \(-0.384672\pi\)
0.978263 + 0.207370i \(0.0664904\pi\)
\(998\) 0 0
\(999\) 3.75004 26.0821i 0.118646 0.825202i
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.433.4 yes 720
5.2 odd 4 inner 920.2.bv.a.617.4 yes 720
23.17 odd 22 inner 920.2.bv.a.753.4 yes 720
115.17 even 44 inner 920.2.bv.a.17.4 720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bv.a.17.4 720 115.17 even 44 inner
920.2.bv.a.433.4 yes 720 1.1 even 1 trivial
920.2.bv.a.617.4 yes 720 5.2 odd 4 inner
920.2.bv.a.753.4 yes 720 23.17 odd 22 inner