Properties

Label 552.2.u.a.17.14
Level $552$
Weight $2$
Character 552.17
Analytic conductor $4.408$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(17,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.u (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(24\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 17.14
Character \(\chi\) \(=\) 552.17
Dual form 552.2.u.a.65.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.239483 - 1.71541i) q^{3} +(-1.91532 + 1.23090i) q^{5} +(-2.52083 - 0.362441i) q^{7} +(-2.88530 - 0.821626i) q^{9} +O(q^{10})\) \(q+(0.239483 - 1.71541i) q^{3} +(-1.91532 + 1.23090i) q^{5} +(-2.52083 - 0.362441i) q^{7} +(-2.88530 - 0.821626i) q^{9} +(2.59948 + 5.69206i) q^{11} +(-0.468610 - 3.25925i) q^{13} +(1.65282 + 3.58036i) q^{15} +(-0.929854 + 1.07311i) q^{17} +(-4.59593 + 3.98240i) q^{19} +(-1.22543 + 4.23748i) q^{21} +(-0.945993 + 4.70161i) q^{23} +(0.0762668 - 0.167001i) q^{25} +(-2.10041 + 4.75271i) q^{27} +(-2.85836 - 2.47678i) q^{29} +(-0.0411754 + 0.0120902i) q^{31} +(10.3868 - 3.09603i) q^{33} +(5.27434 - 2.40871i) q^{35} +(-0.178889 + 0.278357i) q^{37} +(-5.70320 + 0.0233237i) q^{39} +(3.34196 + 5.20018i) q^{41} +(1.46419 - 4.98657i) q^{43} +(6.53762 - 1.97784i) q^{45} -0.768936i q^{47} +(-0.493210 - 0.144820i) q^{49} +(1.61814 + 1.85208i) q^{51} +(0.207558 - 1.44359i) q^{53} +(-11.9852 - 7.70244i) q^{55} +(5.73081 + 8.83764i) q^{57} +(-10.4315 + 1.49982i) q^{59} +(-1.49411 - 5.08846i) q^{61} +(6.97556 + 3.11693i) q^{63} +(4.90937 + 5.66572i) q^{65} +(13.0939 + 5.97976i) q^{67} +(7.83865 + 2.74873i) q^{69} +(-10.3469 - 4.72526i) q^{71} +(-4.90704 - 5.66303i) q^{73} +(-0.268211 - 0.170823i) q^{75} +(-4.48981 - 15.2909i) q^{77} +(-11.8371 + 1.70191i) q^{79} +(7.64986 + 4.74127i) q^{81} +(12.7060 + 8.16565i) q^{83} +(0.460078 - 3.19991i) q^{85} +(-4.93324 + 4.31012i) q^{87} +(-9.78309 - 2.87258i) q^{89} +8.38588i q^{91} +(0.0108789 + 0.0735284i) q^{93} +(3.90075 - 13.2847i) q^{95} +(-6.97379 - 10.8514i) q^{97} +(-2.82351 - 18.5591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{7}{22}\right)\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.239483 1.71541i 0.138266 0.990395i
\(4\) 0 0
\(5\) −1.91532 + 1.23090i −0.856559 + 0.550477i −0.893614 0.448836i \(-0.851839\pi\)
0.0370550 + 0.999313i \(0.488202\pi\)
\(6\) 0 0
\(7\) −2.52083 0.362441i −0.952786 0.136990i −0.351645 0.936133i \(-0.614378\pi\)
−0.601140 + 0.799143i \(0.705287\pi\)
\(8\) 0 0
\(9\) −2.88530 0.821626i −0.961765 0.273875i
\(10\) 0 0
\(11\) 2.59948 + 5.69206i 0.783772 + 1.71622i 0.693675 + 0.720289i \(0.255991\pi\)
0.0900976 + 0.995933i \(0.471282\pi\)
\(12\) 0 0
\(13\) −0.468610 3.25925i −0.129969 0.903955i −0.945588 0.325366i \(-0.894513\pi\)
0.815619 0.578589i \(-0.196396\pi\)
\(14\) 0 0
\(15\) 1.65282 + 3.58036i 0.426757 + 0.924444i
\(16\) 0 0
\(17\) −0.929854 + 1.07311i −0.225523 + 0.260267i −0.857223 0.514946i \(-0.827812\pi\)
0.631700 + 0.775213i \(0.282357\pi\)
\(18\) 0 0
\(19\) −4.59593 + 3.98240i −1.05438 + 0.913624i −0.996407 0.0846941i \(-0.973009\pi\)
−0.0579714 + 0.998318i \(0.518463\pi\)
\(20\) 0 0
\(21\) −1.22543 + 4.23748i −0.267412 + 0.924693i
\(22\) 0 0
\(23\) −0.945993 + 4.70161i −0.197253 + 0.980353i
\(24\) 0 0
\(25\) 0.0762668 0.167001i 0.0152534 0.0334002i
\(26\) 0 0
\(27\) −2.10041 + 4.75271i −0.404224 + 0.914660i
\(28\) 0 0
\(29\) −2.85836 2.47678i −0.530784 0.459927i 0.347763 0.937582i \(-0.386941\pi\)
−0.878547 + 0.477655i \(0.841487\pi\)
\(30\) 0 0
\(31\) −0.0411754 + 0.0120902i −0.00739533 + 0.00217146i −0.285428 0.958400i \(-0.592136\pi\)
0.278033 + 0.960572i \(0.410318\pi\)
\(32\) 0 0
\(33\) 10.3868 3.09603i 1.80811 0.538949i
\(34\) 0 0
\(35\) 5.27434 2.40871i 0.891527 0.407147i
\(36\) 0 0
\(37\) −0.178889 + 0.278357i −0.0294092 + 0.0457616i −0.855647 0.517560i \(-0.826840\pi\)
0.826238 + 0.563322i \(0.190477\pi\)
\(38\) 0 0
\(39\) −5.70320 + 0.0233237i −0.913243 + 0.00373478i
\(40\) 0 0
\(41\) 3.34196 + 5.20018i 0.521926 + 0.812132i 0.997725 0.0674219i \(-0.0214773\pi\)
−0.475799 + 0.879554i \(0.657841\pi\)
\(42\) 0 0
\(43\) 1.46419 4.98657i 0.223287 0.760445i −0.769298 0.638890i \(-0.779394\pi\)
0.992585 0.121555i \(-0.0387880\pi\)
\(44\) 0 0
\(45\) 6.53762 1.97784i 0.974571 0.294839i
\(46\) 0 0
\(47\) 0.768936i 0.112161i −0.998426 0.0560804i \(-0.982140\pi\)
0.998426 0.0560804i \(-0.0178603\pi\)
\(48\) 0 0
\(49\) −0.493210 0.144820i −0.0704586 0.0206885i
\(50\) 0 0
\(51\) 1.61814 + 1.85208i 0.226585 + 0.259343i
\(52\) 0 0
\(53\) 0.207558 1.44359i 0.0285102 0.198293i −0.970588 0.240746i \(-0.922608\pi\)
0.999098 + 0.0424526i \(0.0135172\pi\)
\(54\) 0 0
\(55\) −11.9852 7.70244i −1.61609 1.03860i
\(56\) 0 0
\(57\) 5.73081 + 8.83764i 0.759065 + 1.17057i
\(58\) 0 0
\(59\) −10.4315 + 1.49982i −1.35806 + 0.195260i −0.782578 0.622553i \(-0.786096\pi\)
−0.575484 + 0.817813i \(0.695186\pi\)
\(60\) 0 0
\(61\) −1.49411 5.08846i −0.191301 0.651510i −0.998153 0.0607567i \(-0.980649\pi\)
0.806852 0.590754i \(-0.201170\pi\)
\(62\) 0 0
\(63\) 6.97556 + 3.11693i 0.878838 + 0.392697i
\(64\) 0 0
\(65\) 4.90937 + 5.66572i 0.608932 + 0.702746i
\(66\) 0 0
\(67\) 13.0939 + 5.97976i 1.59967 + 0.730544i 0.997688 0.0679663i \(-0.0216510\pi\)
0.601981 + 0.798510i \(0.294378\pi\)
\(68\) 0 0
\(69\) 7.83865 + 2.74873i 0.943663 + 0.330908i
\(70\) 0 0
\(71\) −10.3469 4.72526i −1.22795 0.560785i −0.307462 0.951561i \(-0.599480\pi\)
−0.920486 + 0.390776i \(0.872207\pi\)
\(72\) 0 0
\(73\) −4.90704 5.66303i −0.574326 0.662808i 0.392049 0.919944i \(-0.371766\pi\)
−0.966375 + 0.257137i \(0.917221\pi\)
\(74\) 0 0
\(75\) −0.268211 0.170823i −0.0309704 0.0197250i
\(76\) 0 0
\(77\) −4.48981 15.2909i −0.511662 1.74256i
\(78\) 0 0
\(79\) −11.8371 + 1.70191i −1.33177 + 0.191480i −0.771184 0.636613i \(-0.780335\pi\)
−0.560591 + 0.828093i \(0.689426\pi\)
\(80\) 0 0
\(81\) 7.64986 + 4.74127i 0.849985 + 0.526808i
\(82\) 0 0
\(83\) 12.7060 + 8.16565i 1.39466 + 0.896296i 0.999749 0.0224213i \(-0.00713752\pi\)
0.394915 + 0.918717i \(0.370774\pi\)
\(84\) 0 0
\(85\) 0.460078 3.19991i 0.0499025 0.347079i
\(86\) 0 0
\(87\) −4.93324 + 4.31012i −0.528899 + 0.462094i
\(88\) 0 0
\(89\) −9.78309 2.87258i −1.03701 0.304492i −0.281449 0.959576i \(-0.590815\pi\)
−0.755556 + 0.655084i \(0.772633\pi\)
\(90\) 0 0
\(91\) 8.38588i 0.879080i
\(92\) 0 0
\(93\) 0.0108789 + 0.0735284i 0.00112809 + 0.00762454i
\(94\) 0 0
\(95\) 3.90075 13.2847i 0.400208 1.36298i
\(96\) 0 0
\(97\) −6.97379 10.8514i −0.708081 1.10180i −0.989823 0.142306i \(-0.954548\pi\)
0.281741 0.959490i \(-0.409088\pi\)
\(98\) 0 0
\(99\) −2.82351 18.5591i −0.283774 1.86526i
\(100\) 0 0
\(101\) 8.75508 13.6232i 0.871163 1.35556i −0.0627397 0.998030i \(-0.519984\pi\)
0.933903 0.357527i \(-0.116380\pi\)
\(102\) 0 0
\(103\) −11.3103 + 5.16522i −1.11443 + 0.508945i −0.885566 0.464513i \(-0.846229\pi\)
−0.228867 + 0.973458i \(0.573502\pi\)
\(104\) 0 0
\(105\) −2.86882 9.62454i −0.279969 0.939258i
\(106\) 0 0
\(107\) −1.84236 + 0.540966i −0.178108 + 0.0522972i −0.369570 0.929203i \(-0.620495\pi\)
0.191463 + 0.981500i \(0.438677\pi\)
\(108\) 0 0
\(109\) 5.62744 + 4.87621i 0.539011 + 0.467056i 0.881312 0.472534i \(-0.156661\pi\)
−0.342301 + 0.939590i \(0.611206\pi\)
\(110\) 0 0
\(111\) 0.434657 + 0.373531i 0.0412558 + 0.0354540i
\(112\) 0 0
\(113\) −2.19144 + 4.79859i −0.206154 + 0.451414i −0.984262 0.176717i \(-0.943452\pi\)
0.778108 + 0.628130i \(0.216180\pi\)
\(114\) 0 0
\(115\) −3.97534 10.1695i −0.370703 0.948313i
\(116\) 0 0
\(117\) −1.32581 + 9.78894i −0.122571 + 0.904987i
\(118\) 0 0
\(119\) 2.73295 2.36811i 0.250529 0.217085i
\(120\) 0 0
\(121\) −18.4388 + 21.2795i −1.67626 + 1.93450i
\(122\) 0 0
\(123\) 9.72081 4.48748i 0.876496 0.404623i
\(124\) 0 0
\(125\) −1.56059 10.8541i −0.139583 0.970824i
\(126\) 0 0
\(127\) −0.0542436 0.118777i −0.00481334 0.0105397i 0.907210 0.420678i \(-0.138208\pi\)
−0.912023 + 0.410138i \(0.865480\pi\)
\(128\) 0 0
\(129\) −8.20339 3.70589i −0.722268 0.326286i
\(130\) 0 0
\(131\) −7.94331 1.14207i −0.694010 0.0997836i −0.213722 0.976895i \(-0.568559\pi\)
−0.480288 + 0.877111i \(0.659468\pi\)
\(132\) 0 0
\(133\) 13.0290 8.37320i 1.12975 0.726049i
\(134\) 0 0
\(135\) −1.82717 11.6884i −0.157258 1.00598i
\(136\) 0 0
\(137\) 6.51094 0.556267 0.278134 0.960542i \(-0.410284\pi\)
0.278134 + 0.960542i \(0.410284\pi\)
\(138\) 0 0
\(139\) 20.3981 1.73014 0.865071 0.501649i \(-0.167273\pi\)
0.865071 + 0.501649i \(0.167273\pi\)
\(140\) 0 0
\(141\) −1.31904 0.184147i −0.111084 0.0155080i
\(142\) 0 0
\(143\) 17.3337 11.1397i 1.44952 0.931550i
\(144\) 0 0
\(145\) 8.52337 + 1.22548i 0.707827 + 0.101770i
\(146\) 0 0
\(147\) −0.366541 + 0.811378i −0.0302318 + 0.0669213i
\(148\) 0 0
\(149\) 4.75960 + 10.4221i 0.389922 + 0.853810i 0.998194 + 0.0600808i \(0.0191358\pi\)
−0.608272 + 0.793729i \(0.708137\pi\)
\(150\) 0 0
\(151\) 2.30470 + 16.0296i 0.187554 + 1.30447i 0.838315 + 0.545186i \(0.183541\pi\)
−0.650761 + 0.759283i \(0.725550\pi\)
\(152\) 0 0
\(153\) 3.56460 2.33224i 0.288181 0.188551i
\(154\) 0 0
\(155\) 0.0639824 0.0738397i 0.00513919 0.00593095i
\(156\) 0 0
\(157\) 3.80247 3.29486i 0.303471 0.262959i −0.489791 0.871840i \(-0.662927\pi\)
0.793261 + 0.608881i \(0.208381\pi\)
\(158\) 0 0
\(159\) −2.42666 0.701764i −0.192446 0.0556535i
\(160\) 0 0
\(161\) 4.08875 11.5091i 0.322238 0.907044i
\(162\) 0 0
\(163\) 8.16824 17.8859i 0.639786 1.40094i −0.260431 0.965493i \(-0.583865\pi\)
0.900216 0.435443i \(-0.143408\pi\)
\(164\) 0 0
\(165\) −16.0831 + 18.7150i −1.25207 + 1.45696i
\(166\) 0 0
\(167\) 15.0267 + 13.0207i 1.16280 + 1.00757i 0.999781 + 0.0209502i \(0.00666914\pi\)
0.163021 + 0.986623i \(0.447876\pi\)
\(168\) 0 0
\(169\) 2.07026 0.607884i 0.159251 0.0467603i
\(170\) 0 0
\(171\) 16.5327 7.71425i 1.26428 0.589924i
\(172\) 0 0
\(173\) −14.6245 + 6.67879i −1.11188 + 0.507779i −0.884741 0.466083i \(-0.845665\pi\)
−0.227140 + 0.973862i \(0.572937\pi\)
\(174\) 0 0
\(175\) −0.252784 + 0.393340i −0.0191087 + 0.0297337i
\(176\) 0 0
\(177\) 0.0746491 + 18.2535i 0.00561097 + 1.37202i
\(178\) 0 0
\(179\) 1.94528 + 3.02692i 0.145397 + 0.226243i 0.906312 0.422609i \(-0.138886\pi\)
−0.760915 + 0.648852i \(0.775249\pi\)
\(180\) 0 0
\(181\) 3.03959 10.3519i 0.225931 0.769450i −0.766019 0.642818i \(-0.777765\pi\)
0.991950 0.126632i \(-0.0404167\pi\)
\(182\) 0 0
\(183\) −9.08663 + 1.34441i −0.671703 + 0.0993818i
\(184\) 0 0
\(185\) 0.753339i 0.0553866i
\(186\) 0 0
\(187\) −8.52534 2.50327i −0.623435 0.183057i
\(188\) 0 0
\(189\) 7.01736 11.2195i 0.510438 0.816100i
\(190\) 0 0
\(191\) −3.07920 + 21.4163i −0.222803 + 1.54963i 0.504560 + 0.863377i \(0.331655\pi\)
−0.727363 + 0.686253i \(0.759254\pi\)
\(192\) 0 0
\(193\) 5.91478 + 3.80120i 0.425755 + 0.273616i 0.735923 0.677066i \(-0.236749\pi\)
−0.310167 + 0.950682i \(0.600385\pi\)
\(194\) 0 0
\(195\) 10.8948 7.06476i 0.780190 0.505918i
\(196\) 0 0
\(197\) 1.14464 0.164574i 0.0815521 0.0117254i −0.101418 0.994844i \(-0.532338\pi\)
0.182970 + 0.983118i \(0.441429\pi\)
\(198\) 0 0
\(199\) −7.73961 26.3587i −0.548647 1.86852i −0.492924 0.870072i \(-0.664072\pi\)
−0.0557222 0.998446i \(-0.517746\pi\)
\(200\) 0 0
\(201\) 13.3935 21.0293i 0.944707 1.48329i
\(202\) 0 0
\(203\) 6.30776 + 7.27954i 0.442718 + 0.510924i
\(204\) 0 0
\(205\) −12.8019 5.84641i −0.894120 0.408331i
\(206\) 0 0
\(207\) 6.59243 12.7883i 0.458206 0.888846i
\(208\) 0 0
\(209\) −34.6151 15.8082i −2.39437 1.09347i
\(210\) 0 0
\(211\) 9.60591 + 11.0858i 0.661298 + 0.763179i 0.982989 0.183666i \(-0.0587965\pi\)
−0.321690 + 0.946845i \(0.604251\pi\)
\(212\) 0 0
\(213\) −10.5837 + 16.6176i −0.725182 + 1.13862i
\(214\) 0 0
\(215\) 3.33359 + 11.3532i 0.227349 + 0.774280i
\(216\) 0 0
\(217\) 0.108178 0.0155537i 0.00734363 0.00105585i
\(218\) 0 0
\(219\) −10.8896 + 7.06141i −0.735851 + 0.477166i
\(220\) 0 0
\(221\) 3.93328 + 2.52776i 0.264581 + 0.170036i
\(222\) 0 0
\(223\) −1.15800 + 8.05407i −0.0775455 + 0.539341i 0.913606 + 0.406602i \(0.133286\pi\)
−0.991151 + 0.132739i \(0.957623\pi\)
\(224\) 0 0
\(225\) −0.357265 + 0.419185i −0.0238177 + 0.0279456i
\(226\) 0 0
\(227\) −10.9368 3.21133i −0.725899 0.213143i −0.102151 0.994769i \(-0.532573\pi\)
−0.623748 + 0.781626i \(0.714391\pi\)
\(228\) 0 0
\(229\) 26.7486i 1.76760i 0.467869 + 0.883798i \(0.345022\pi\)
−0.467869 + 0.883798i \(0.654978\pi\)
\(230\) 0 0
\(231\) −27.3055 + 4.03998i −1.79657 + 0.265811i
\(232\) 0 0
\(233\) −1.28660 + 4.38174i −0.0842877 + 0.287057i −0.990841 0.135034i \(-0.956886\pi\)
0.906553 + 0.422091i \(0.138704\pi\)
\(234\) 0 0
\(235\) 0.946486 + 1.47276i 0.0617420 + 0.0960724i
\(236\) 0 0
\(237\) 0.0847078 + 20.7131i 0.00550236 + 1.34546i
\(238\) 0 0
\(239\) 0.615846 0.958275i 0.0398358 0.0619857i −0.820765 0.571267i \(-0.806452\pi\)
0.860600 + 0.509281i \(0.170089\pi\)
\(240\) 0 0
\(241\) −5.51291 + 2.51766i −0.355118 + 0.162177i −0.584983 0.811046i \(-0.698899\pi\)
0.229865 + 0.973222i \(0.426171\pi\)
\(242\) 0 0
\(243\) 9.96526 11.9872i 0.639272 0.768981i
\(244\) 0 0
\(245\) 1.12292 0.329718i 0.0717405 0.0210649i
\(246\) 0 0
\(247\) 15.1333 + 13.1131i 0.962911 + 0.834367i
\(248\) 0 0
\(249\) 17.0503 19.8405i 1.08052 1.25734i
\(250\) 0 0
\(251\) −4.87201 + 10.6682i −0.307518 + 0.673372i −0.998788 0.0492258i \(-0.984325\pi\)
0.691269 + 0.722597i \(0.257052\pi\)
\(252\) 0 0
\(253\) −29.2209 + 6.83707i −1.83710 + 0.429843i
\(254\) 0 0
\(255\) −5.37900 1.55555i −0.336846 0.0974124i
\(256\) 0 0
\(257\) −2.49167 + 2.15904i −0.155426 + 0.134677i −0.729102 0.684405i \(-0.760062\pi\)
0.573676 + 0.819082i \(0.305517\pi\)
\(258\) 0 0
\(259\) 0.551838 0.636855i 0.0342895 0.0395722i
\(260\) 0 0
\(261\) 6.21222 + 9.49475i 0.384527 + 0.587710i
\(262\) 0 0
\(263\) 2.42892 + 16.8935i 0.149774 + 1.04170i 0.916589 + 0.399830i \(0.130931\pi\)
−0.766816 + 0.641867i \(0.778160\pi\)
\(264\) 0 0
\(265\) 1.37939 + 3.02043i 0.0847350 + 0.185544i
\(266\) 0 0
\(267\) −7.27054 + 16.0941i −0.444950 + 0.984945i
\(268\) 0 0
\(269\) 8.11972 + 1.16744i 0.495068 + 0.0711801i 0.385327 0.922780i \(-0.374089\pi\)
0.109741 + 0.993960i \(0.464998\pi\)
\(270\) 0 0
\(271\) −2.31556 + 1.48812i −0.140660 + 0.0903970i −0.609078 0.793110i \(-0.708461\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(272\) 0 0
\(273\) 14.3853 + 2.00828i 0.870636 + 0.121547i
\(274\) 0 0
\(275\) 1.14883 0.0692773
\(276\) 0 0
\(277\) 1.00330 0.0602826 0.0301413 0.999546i \(-0.490404\pi\)
0.0301413 + 0.999546i \(0.490404\pi\)
\(278\) 0 0
\(279\) 0.128737 0.00105298i 0.00770728 6.30401e-5i
\(280\) 0 0
\(281\) −5.41371 + 3.47918i −0.322955 + 0.207550i −0.692065 0.721835i \(-0.743299\pi\)
0.369110 + 0.929386i \(0.379662\pi\)
\(282\) 0 0
\(283\) −19.6434 2.82430i −1.16768 0.167887i −0.468919 0.883241i \(-0.655356\pi\)
−0.698762 + 0.715354i \(0.746265\pi\)
\(284\) 0 0
\(285\) −21.8547 9.87287i −1.29456 0.584818i
\(286\) 0 0
\(287\) −6.53975 14.3201i −0.386029 0.845287i
\(288\) 0 0
\(289\) 2.13242 + 14.8313i 0.125436 + 0.872429i
\(290\) 0 0
\(291\) −20.2848 + 9.36421i −1.18912 + 0.548940i
\(292\) 0 0
\(293\) −5.08863 + 5.87260i −0.297281 + 0.343081i −0.884665 0.466228i \(-0.845613\pi\)
0.587383 + 0.809309i \(0.300158\pi\)
\(294\) 0 0
\(295\) 18.1335 15.7128i 1.05577 0.914834i
\(296\) 0 0
\(297\) −32.5127 + 0.398908i −1.88658 + 0.0231470i
\(298\) 0 0
\(299\) 15.7670 + 0.880011i 0.911831 + 0.0508924i
\(300\) 0 0
\(301\) −5.49832 + 12.0396i −0.316918 + 0.693953i
\(302\) 0 0
\(303\) −21.2727 18.2811i −1.22208 1.05022i
\(304\) 0 0
\(305\) 9.12510 + 7.90695i 0.522502 + 0.452751i
\(306\) 0 0
\(307\) 25.0001 7.34069i 1.42683 0.418955i 0.525021 0.851089i \(-0.324057\pi\)
0.901810 + 0.432134i \(0.142239\pi\)
\(308\) 0 0
\(309\) 6.15188 + 20.6388i 0.349968 + 1.17410i
\(310\) 0 0
\(311\) 7.97874 3.64377i 0.452433 0.206619i −0.176148 0.984364i \(-0.556364\pi\)
0.628580 + 0.777745i \(0.283636\pi\)
\(312\) 0 0
\(313\) 2.78300 4.33044i 0.157305 0.244771i −0.753651 0.657274i \(-0.771709\pi\)
0.910956 + 0.412504i \(0.135346\pi\)
\(314\) 0 0
\(315\) −17.1971 + 2.61631i −0.968947 + 0.147412i
\(316\) 0 0
\(317\) −10.0747 15.6765i −0.565849 0.880479i 0.433941 0.900941i \(-0.357123\pi\)
−0.999791 + 0.0204623i \(0.993486\pi\)
\(318\) 0 0
\(319\) 6.66776 22.7083i 0.373323 1.27142i
\(320\) 0 0
\(321\) 0.486766 + 3.28997i 0.0271687 + 0.183628i
\(322\) 0 0
\(323\) 8.63498i 0.480463i
\(324\) 0 0
\(325\) −0.580038 0.170315i −0.0321747 0.00944736i
\(326\) 0 0
\(327\) 9.71240 8.48563i 0.537097 0.469256i
\(328\) 0 0
\(329\) −0.278694 + 1.93836i −0.0153649 + 0.106865i
\(330\) 0 0
\(331\) −16.5314 10.6241i −0.908650 0.583954i 0.000693682 1.00000i \(-0.499779\pi\)
−0.909344 + 0.416046i \(0.863416\pi\)
\(332\) 0 0
\(333\) 0.744854 0.656162i 0.0408177 0.0359575i
\(334\) 0 0
\(335\) −32.4395 + 4.66409i −1.77236 + 0.254827i
\(336\) 0 0
\(337\) 0.751251 + 2.55853i 0.0409233 + 0.139372i 0.977421 0.211303i \(-0.0677706\pi\)
−0.936497 + 0.350674i \(0.885952\pi\)
\(338\) 0 0
\(339\) 7.70676 + 4.90842i 0.418574 + 0.266589i
\(340\) 0 0
\(341\) −0.175853 0.202945i −0.00952296 0.0109901i
\(342\) 0 0
\(343\) 17.4071 + 7.94955i 0.939894 + 0.429235i
\(344\) 0 0
\(345\) −18.3970 + 4.38393i −0.990460 + 0.236023i
\(346\) 0 0
\(347\) 0.343760 + 0.156990i 0.0184540 + 0.00842766i 0.424621 0.905371i \(-0.360407\pi\)
−0.406167 + 0.913799i \(0.633135\pi\)
\(348\) 0 0
\(349\) 12.7674 + 14.7344i 0.683423 + 0.788712i 0.986413 0.164282i \(-0.0525306\pi\)
−0.302991 + 0.952993i \(0.597985\pi\)
\(350\) 0 0
\(351\) 16.4746 + 4.61860i 0.879348 + 0.246523i
\(352\) 0 0
\(353\) 7.53147 + 25.6498i 0.400860 + 1.36520i 0.874731 + 0.484608i \(0.161038\pi\)
−0.473872 + 0.880594i \(0.657144\pi\)
\(354\) 0 0
\(355\) 25.6339 3.68561i 1.36051 0.195612i
\(356\) 0 0
\(357\) −3.40780 5.25526i −0.180360 0.278138i
\(358\) 0 0
\(359\) −5.42548 3.48675i −0.286346 0.184023i 0.389580 0.920992i \(-0.372620\pi\)
−0.675927 + 0.736969i \(0.736256\pi\)
\(360\) 0 0
\(361\) 2.55911 17.7990i 0.134690 0.936790i
\(362\) 0 0
\(363\) 32.0874 + 36.7263i 1.68415 + 1.92763i
\(364\) 0 0
\(365\) 16.3692 + 4.80644i 0.856805 + 0.251581i
\(366\) 0 0
\(367\) 22.4448i 1.17161i 0.810452 + 0.585805i \(0.199222\pi\)
−0.810452 + 0.585805i \(0.800778\pi\)
\(368\) 0 0
\(369\) −5.36992 17.7499i −0.279547 0.924023i
\(370\) 0 0
\(371\) −1.04644 + 3.56383i −0.0543283 + 0.185025i
\(372\) 0 0
\(373\) 11.0998 + 17.2717i 0.574728 + 0.894294i 0.999942 0.0107993i \(-0.00343758\pi\)
−0.425214 + 0.905093i \(0.639801\pi\)
\(374\) 0 0
\(375\) −18.9931 + 0.0776738i −0.980799 + 0.00401106i
\(376\) 0 0
\(377\) −6.73301 + 10.4768i −0.346768 + 0.539581i
\(378\) 0 0
\(379\) 30.4955 13.9268i 1.56645 0.715374i 0.571968 0.820276i \(-0.306180\pi\)
0.994483 + 0.104902i \(0.0334529\pi\)
\(380\) 0 0
\(381\) −0.216742 + 0.0646051i −0.0111040 + 0.00330982i
\(382\) 0 0
\(383\) 8.95839 2.63042i 0.457753 0.134408i −0.0447235 0.998999i \(-0.514241\pi\)
0.502476 + 0.864591i \(0.332422\pi\)
\(384\) 0 0
\(385\) 27.4211 + 23.7605i 1.39751 + 1.21095i
\(386\) 0 0
\(387\) −8.32172 + 13.1847i −0.423017 + 0.670217i
\(388\) 0 0
\(389\) 4.30198 9.42003i 0.218119 0.477614i −0.768666 0.639651i \(-0.779079\pi\)
0.986785 + 0.162036i \(0.0518062\pi\)
\(390\) 0 0
\(391\) −4.16570 5.38696i −0.210669 0.272430i
\(392\) 0 0
\(393\) −3.86142 + 13.3526i −0.194783 + 0.673547i
\(394\) 0 0
\(395\) 20.5769 17.8300i 1.03534 0.897125i
\(396\) 0 0
\(397\) −1.29062 + 1.48946i −0.0647745 + 0.0747537i −0.787212 0.616682i \(-0.788476\pi\)
0.722438 + 0.691436i \(0.243022\pi\)
\(398\) 0 0
\(399\) −11.2433 24.3553i −0.562869 1.21929i
\(400\) 0 0
\(401\) −1.38491 9.63226i −0.0691591 0.481012i −0.994738 0.102456i \(-0.967330\pi\)
0.925578 0.378556i \(-0.123579\pi\)
\(402\) 0 0
\(403\) 0.0587003 + 0.128536i 0.00292407 + 0.00640282i
\(404\) 0 0
\(405\) −20.4880 + 0.335178i −1.01806 + 0.0166551i
\(406\) 0 0
\(407\) −2.04944 0.294666i −0.101587 0.0146060i
\(408\) 0 0
\(409\) 4.07947 2.62172i 0.201717 0.129635i −0.435883 0.900003i \(-0.643564\pi\)
0.637600 + 0.770368i \(0.279927\pi\)
\(410\) 0 0
\(411\) 1.55926 11.1690i 0.0769127 0.550925i
\(412\) 0 0
\(413\) 26.8396 1.32069
\(414\) 0 0
\(415\) −34.3872 −1.68800
\(416\) 0 0
\(417\) 4.88500 34.9912i 0.239219 1.71352i
\(418\) 0 0
\(419\) −8.61706 + 5.53785i −0.420971 + 0.270541i −0.733930 0.679225i \(-0.762316\pi\)
0.312959 + 0.949767i \(0.398680\pi\)
\(420\) 0 0
\(421\) 12.2035 + 1.75460i 0.594763 + 0.0855141i 0.433122 0.901335i \(-0.357412\pi\)
0.161642 + 0.986850i \(0.448321\pi\)
\(422\) 0 0
\(423\) −0.631778 + 2.21861i −0.0307181 + 0.107872i
\(424\) 0 0
\(425\) 0.108293 + 0.237129i 0.00525300 + 0.0115025i
\(426\) 0 0
\(427\) 1.92213 + 13.3687i 0.0930183 + 0.646956i
\(428\) 0 0
\(429\) −14.9581 32.4023i −0.722184 1.56440i
\(430\) 0 0
\(431\) −17.6821 + 20.4062i −0.851717 + 0.982934i −0.999982 0.00601369i \(-0.998086\pi\)
0.148265 + 0.988948i \(0.452631\pi\)
\(432\) 0 0
\(433\) 15.7264 13.6270i 0.755764 0.654873i −0.189240 0.981931i \(-0.560603\pi\)
0.945004 + 0.327057i \(0.106057\pi\)
\(434\) 0 0
\(435\) 4.14340 14.3276i 0.198661 0.686957i
\(436\) 0 0
\(437\) −14.3759 25.3756i −0.687694 1.21388i
\(438\) 0 0
\(439\) −14.7120 + 32.2149i −0.702168 + 1.53753i 0.135156 + 0.990824i \(0.456847\pi\)
−0.837323 + 0.546708i \(0.815881\pi\)
\(440\) 0 0
\(441\) 1.30407 + 0.823081i 0.0620985 + 0.0391944i
\(442\) 0 0
\(443\) −19.0113 16.4734i −0.903254 0.782674i 0.0734428 0.997299i \(-0.476601\pi\)
−0.976696 + 0.214626i \(0.931147\pi\)
\(444\) 0 0
\(445\) 22.2737 6.54014i 1.05587 0.310032i
\(446\) 0 0
\(447\) 19.0180 5.66878i 0.899522 0.268124i
\(448\) 0 0
\(449\) −32.7813 + 14.9707i −1.54704 + 0.706511i −0.992108 0.125383i \(-0.959984\pi\)
−0.554935 + 0.831894i \(0.687257\pi\)
\(450\) 0 0
\(451\) −20.9124 + 32.5404i −0.984728 + 1.53227i
\(452\) 0 0
\(453\) 28.0493 0.114710i 1.31787 0.00538954i
\(454\) 0 0
\(455\) −10.3222 16.0617i −0.483913 0.752983i
\(456\) 0 0
\(457\) 10.7501 36.6114i 0.502867 1.71261i −0.181429 0.983404i \(-0.558072\pi\)
0.684296 0.729204i \(-0.260110\pi\)
\(458\) 0 0
\(459\) −3.14710 6.67330i −0.146894 0.311483i
\(460\) 0 0
\(461\) 6.90750i 0.321714i 0.986978 + 0.160857i \(0.0514258\pi\)
−0.986978 + 0.160857i \(0.948574\pi\)
\(462\) 0 0
\(463\) 2.65762 + 0.780348i 0.123510 + 0.0362658i 0.342903 0.939371i \(-0.388590\pi\)
−0.219393 + 0.975636i \(0.570408\pi\)
\(464\) 0 0
\(465\) −0.111343 0.127440i −0.00516341 0.00590988i
\(466\) 0 0
\(467\) −0.234889 + 1.63369i −0.0108694 + 0.0755982i −0.994534 0.104412i \(-0.966704\pi\)
0.983665 + 0.180010i \(0.0576130\pi\)
\(468\) 0 0
\(469\) −30.8401 19.8197i −1.42406 0.915191i
\(470\) 0 0
\(471\) −4.74143 7.31189i −0.218473 0.336914i
\(472\) 0 0
\(473\) 32.1900 4.62822i 1.48010 0.212806i
\(474\) 0 0
\(475\) 0.314547 + 1.07125i 0.0144324 + 0.0491523i
\(476\) 0 0
\(477\) −1.78496 + 3.99466i −0.0817277 + 0.182903i
\(478\) 0 0
\(479\) −13.7520 15.8707i −0.628346 0.725150i 0.348923 0.937151i \(-0.386547\pi\)
−0.977269 + 0.212001i \(0.932002\pi\)
\(480\) 0 0
\(481\) 0.991066 + 0.452604i 0.0451887 + 0.0206370i
\(482\) 0 0
\(483\) −18.7637 9.77013i −0.853778 0.444556i
\(484\) 0 0
\(485\) 26.7142 + 12.1999i 1.21303 + 0.553971i
\(486\) 0 0
\(487\) −10.9286 12.6122i −0.495221 0.571515i 0.452032 0.892001i \(-0.350699\pi\)
−0.947253 + 0.320486i \(0.896154\pi\)
\(488\) 0 0
\(489\) −28.7257 18.2953i −1.29902 0.827342i
\(490\) 0 0
\(491\) 2.10764 + 7.17797i 0.0951165 + 0.323937i 0.993282 0.115721i \(-0.0369178\pi\)
−0.898165 + 0.439658i \(0.855100\pi\)
\(492\) 0 0
\(493\) 5.31572 0.764285i 0.239408 0.0344216i
\(494\) 0 0
\(495\) 28.2524 + 32.0712i 1.26985 + 1.44149i
\(496\) 0 0
\(497\) 24.3701 + 15.6617i 1.09315 + 0.702524i
\(498\) 0 0
\(499\) −2.90071 + 20.1749i −0.129853 + 0.903151i 0.815883 + 0.578217i \(0.196251\pi\)
−0.945737 + 0.324934i \(0.894658\pi\)
\(500\) 0 0
\(501\) 25.9346 22.6588i 1.15867 1.01232i
\(502\) 0 0
\(503\) 2.18885 + 0.642704i 0.0975960 + 0.0286568i 0.330166 0.943923i \(-0.392895\pi\)
−0.232570 + 0.972580i \(0.574713\pi\)
\(504\) 0 0
\(505\) 36.8695i 1.64067i
\(506\) 0 0
\(507\) −0.546980 3.69694i −0.0242922 0.164187i
\(508\) 0 0
\(509\) 0.540888 1.84210i 0.0239744 0.0816494i −0.946637 0.322302i \(-0.895543\pi\)
0.970611 + 0.240653i \(0.0773615\pi\)
\(510\) 0 0
\(511\) 10.3173 + 16.0541i 0.456412 + 0.710191i
\(512\) 0 0
\(513\) −9.27385 30.2078i −0.409450 1.33371i
\(514\) 0 0
\(515\) 15.3049 23.8149i 0.674416 1.04941i
\(516\) 0 0
\(517\) 4.37683 1.99883i 0.192493 0.0879085i
\(518\) 0 0
\(519\) 7.95457 + 26.6865i 0.349167 + 1.17141i
\(520\) 0 0
\(521\) 9.06499 2.66172i 0.397144 0.116612i −0.0770610 0.997026i \(-0.524554\pi\)
0.474205 + 0.880414i \(0.342735\pi\)
\(522\) 0 0
\(523\) −14.6443 12.6894i −0.640352 0.554868i 0.273013 0.962010i \(-0.411980\pi\)
−0.913365 + 0.407142i \(0.866525\pi\)
\(524\) 0 0
\(525\) 0.614203 + 0.527828i 0.0268060 + 0.0230363i
\(526\) 0 0
\(527\) 0.0253131 0.0554279i 0.00110265 0.00241448i
\(528\) 0 0
\(529\) −21.2102 8.89537i −0.922182 0.386755i
\(530\) 0 0
\(531\) 31.3302 + 4.24335i 1.35961 + 0.184146i
\(532\) 0 0
\(533\) 15.3826 13.3291i 0.666297 0.577349i
\(534\) 0 0
\(535\) 2.86284 3.30390i 0.123771 0.142840i
\(536\) 0 0
\(537\) 5.65829 2.61207i 0.244173 0.112719i
\(538\) 0 0
\(539\) −0.457767 3.18384i −0.0197174 0.137138i
\(540\) 0 0
\(541\) −15.5895 34.1362i −0.670243 1.46763i −0.872660 0.488329i \(-0.837607\pi\)
0.202416 0.979300i \(-0.435121\pi\)
\(542\) 0 0
\(543\) −17.0299 7.69326i −0.730821 0.330150i
\(544\) 0 0
\(545\) −16.7805 2.41267i −0.718799 0.103348i
\(546\) 0 0
\(547\) 17.9217 11.5176i 0.766275 0.492455i −0.0981780 0.995169i \(-0.531301\pi\)
0.864453 + 0.502714i \(0.167665\pi\)
\(548\) 0 0
\(549\) 0.130127 + 15.9093i 0.00555368 + 0.678993i
\(550\) 0 0
\(551\) 23.0003 0.979847
\(552\) 0 0
\(553\) 30.4561 1.29513
\(554\) 0 0
\(555\) −1.29229 0.180412i −0.0548546 0.00765807i
\(556\) 0 0
\(557\) −37.3757 + 24.0199i −1.58366 + 1.01776i −0.609248 + 0.792979i \(0.708529\pi\)
−0.974410 + 0.224776i \(0.927835\pi\)
\(558\) 0 0
\(559\) −16.9386 2.43541i −0.716428 0.103007i
\(560\) 0 0
\(561\) −6.33582 + 14.0250i −0.267498 + 0.592136i
\(562\) 0 0
\(563\) −0.130393 0.285522i −0.00549543 0.0120333i 0.906864 0.421423i \(-0.138469\pi\)
−0.912360 + 0.409389i \(0.865742\pi\)
\(564\) 0 0
\(565\) −1.70928 11.8883i −0.0719100 0.500145i
\(566\) 0 0
\(567\) −17.5656 14.7246i −0.737686 0.618374i
\(568\) 0 0
\(569\) 12.0499 13.9064i 0.505160 0.582986i −0.444693 0.895683i \(-0.646687\pi\)
0.949853 + 0.312698i \(0.101233\pi\)
\(570\) 0 0
\(571\) −23.9236 + 20.7299i −1.00117 + 0.867519i −0.991192 0.132431i \(-0.957722\pi\)
−0.00997806 + 0.999950i \(0.503176\pi\)
\(572\) 0 0
\(573\) 36.0004 + 10.4110i 1.50394 + 0.434924i
\(574\) 0 0
\(575\) 0.713025 + 0.516558i 0.0297352 + 0.0215420i
\(576\) 0 0
\(577\) 10.1638 22.2557i 0.423125 0.926516i −0.571267 0.820764i \(-0.693548\pi\)
0.994393 0.105751i \(-0.0337248\pi\)
\(578\) 0 0
\(579\) 7.93713 9.23598i 0.329856 0.383834i
\(580\) 0 0
\(581\) −29.0701 25.1894i −1.20603 1.04503i
\(582\) 0 0
\(583\) 8.75657 2.57116i 0.362660 0.106487i
\(584\) 0 0
\(585\) −9.50988 20.3809i −0.393185 0.842648i
\(586\) 0 0
\(587\) 30.4536 13.9077i 1.25695 0.574032i 0.328158 0.944623i \(-0.393572\pi\)
0.928796 + 0.370591i \(0.120845\pi\)
\(588\) 0 0
\(589\) 0.141091 0.219543i 0.00581357 0.00904609i
\(590\) 0 0
\(591\) −0.00819120 2.00294i −0.000336941 0.0823900i
\(592\) 0 0
\(593\) −4.02638 6.26518i −0.165344 0.257280i 0.748688 0.662923i \(-0.230684\pi\)
−0.914032 + 0.405643i \(0.867048\pi\)
\(594\) 0 0
\(595\) −2.31956 + 7.89970i −0.0950927 + 0.323856i
\(596\) 0 0
\(597\) −47.0696 + 6.96418i −1.92643 + 0.285025i
\(598\) 0 0
\(599\) 36.6759i 1.49854i −0.662267 0.749268i \(-0.730405\pi\)
0.662267 0.749268i \(-0.269595\pi\)
\(600\) 0 0
\(601\) −35.4412 10.4065i −1.44568 0.424489i −0.537566 0.843222i \(-0.680656\pi\)
−0.908109 + 0.418733i \(0.862474\pi\)
\(602\) 0 0
\(603\) −32.8665 28.0116i −1.33843 1.14072i
\(604\) 0 0
\(605\) 9.12326 63.4536i 0.370913 2.57976i
\(606\) 0 0
\(607\) −25.5752 16.4362i −1.03806 0.667124i −0.0935575 0.995614i \(-0.529824\pi\)
−0.944507 + 0.328490i \(0.893460\pi\)
\(608\) 0 0
\(609\) 13.9980 9.07710i 0.567229 0.367823i
\(610\) 0 0
\(611\) −2.50616 + 0.360331i −0.101388 + 0.0145774i
\(612\) 0 0
\(613\) 5.81744 + 19.8124i 0.234964 + 0.800214i 0.989572 + 0.144038i \(0.0460088\pi\)
−0.754608 + 0.656176i \(0.772173\pi\)
\(614\) 0 0
\(615\) −13.0949 + 20.5604i −0.528035 + 0.829074i
\(616\) 0 0
\(617\) 8.50846 + 9.81929i 0.342538 + 0.395310i 0.900714 0.434413i \(-0.143044\pi\)
−0.558176 + 0.829723i \(0.688499\pi\)
\(618\) 0 0
\(619\) −4.03421 1.84236i −0.162149 0.0740509i 0.332687 0.943037i \(-0.392045\pi\)
−0.494836 + 0.868986i \(0.664772\pi\)
\(620\) 0 0
\(621\) −20.3584 14.3713i −0.816955 0.576702i
\(622\) 0 0
\(623\) 23.6204 + 10.7871i 0.946332 + 0.432175i
\(624\) 0 0
\(625\) 16.9506 + 19.5620i 0.678023 + 0.782481i
\(626\) 0 0
\(627\) −35.4073 + 55.5934i −1.41403 + 2.22019i
\(628\) 0 0
\(629\) −0.132367 0.450799i −0.00527780 0.0179745i
\(630\) 0 0
\(631\) 19.6316 2.82260i 0.781523 0.112366i 0.260006 0.965607i \(-0.416276\pi\)
0.521517 + 0.853241i \(0.325366\pi\)
\(632\) 0 0
\(633\) 21.3172 13.8233i 0.847284 0.549425i
\(634\) 0 0
\(635\) 0.250097 + 0.160727i 0.00992479 + 0.00637828i
\(636\) 0 0
\(637\) −0.240881 + 1.67536i −0.00954403 + 0.0663802i
\(638\) 0 0
\(639\) 25.9714 + 22.1350i 1.02741 + 0.875648i
\(640\) 0 0
\(641\) 21.8930 + 6.42836i 0.864721 + 0.253905i 0.683868 0.729605i \(-0.260296\pi\)
0.180852 + 0.983510i \(0.442114\pi\)
\(642\) 0 0
\(643\) 24.9469i 0.983811i 0.870649 + 0.491905i \(0.163699\pi\)
−0.870649 + 0.491905i \(0.836301\pi\)
\(644\) 0 0
\(645\) 20.2737 2.99960i 0.798278 0.118109i
\(646\) 0 0
\(647\) 8.62999 29.3911i 0.339280 1.15548i −0.596416 0.802675i \(-0.703409\pi\)
0.935696 0.352806i \(-0.114773\pi\)
\(648\) 0 0
\(649\) −35.6534 55.4778i −1.39952 2.17770i
\(650\) 0 0
\(651\) −0.000774140 0.189296i −3.03410e−5 0.00741909i
\(652\) 0 0
\(653\) −21.7560 + 33.8530i −0.851377 + 1.32477i 0.0929193 + 0.995674i \(0.470380\pi\)
−0.944297 + 0.329095i \(0.893256\pi\)
\(654\) 0 0
\(655\) 16.6198 7.59000i 0.649389 0.296566i
\(656\) 0 0
\(657\) 9.50538 + 20.3713i 0.370840 + 0.794759i
\(658\) 0 0
\(659\) −30.8064 + 9.04556i −1.20005 + 0.352365i −0.819870 0.572550i \(-0.805954\pi\)
−0.380175 + 0.924915i \(0.624136\pi\)
\(660\) 0 0
\(661\) 33.7711 + 29.2628i 1.31354 + 1.13819i 0.980766 + 0.195186i \(0.0625311\pi\)
0.332777 + 0.943006i \(0.392014\pi\)
\(662\) 0 0
\(663\) 5.27812 6.14184i 0.204985 0.238529i
\(664\) 0 0
\(665\) −14.6481 + 32.0748i −0.568028 + 1.24381i
\(666\) 0 0
\(667\) 14.3488 11.0959i 0.555589 0.429633i
\(668\) 0 0
\(669\) 13.5388 + 3.91527i 0.523439 + 0.151373i
\(670\) 0 0
\(671\) 25.0799 21.7319i 0.968200 0.838950i
\(672\) 0 0
\(673\) −11.7156 + 13.5206i −0.451605 + 0.521180i −0.935204 0.354110i \(-0.884784\pi\)
0.483599 + 0.875290i \(0.339329\pi\)
\(674\) 0 0
\(675\) 0.633517 + 0.713245i 0.0243841 + 0.0274528i
\(676\) 0 0
\(677\) −2.29431 15.9573i −0.0881775 0.613288i −0.985214 0.171331i \(-0.945193\pi\)
0.897036 0.441957i \(-0.145716\pi\)
\(678\) 0 0
\(679\) 13.6468 + 29.8823i 0.523715 + 1.14678i
\(680\) 0 0
\(681\) −8.12793 + 17.9920i −0.311463 + 0.689457i
\(682\) 0 0
\(683\) 2.16970 + 0.311955i 0.0830211 + 0.0119366i 0.183700 0.982982i \(-0.441192\pi\)
−0.100679 + 0.994919i \(0.532102\pi\)
\(684\) 0 0
\(685\) −12.4706 + 8.01435i −0.476476 + 0.306212i
\(686\) 0 0
\(687\) 45.8849 + 6.40584i 1.75062 + 0.244398i
\(688\) 0 0
\(689\) −4.80230 −0.182953
\(690\) 0 0
\(691\) 24.4526 0.930220 0.465110 0.885253i \(-0.346015\pi\)
0.465110 + 0.885253i \(0.346015\pi\)
\(692\) 0 0
\(693\) 0.391034 + 47.8077i 0.0148541 + 1.81607i
\(694\) 0 0
\(695\) −39.0689 + 25.1081i −1.48197 + 0.952404i
\(696\) 0 0
\(697\) −8.68790 1.24913i −0.329078 0.0473142i
\(698\) 0 0
\(699\) 7.20839 + 3.25640i 0.272646 + 0.123168i
\(700\) 0 0
\(701\) 15.3838 + 33.6859i 0.581040 + 1.27230i 0.940707 + 0.339219i \(0.110163\pi\)
−0.359668 + 0.933080i \(0.617110\pi\)
\(702\) 0 0
\(703\) −0.286366 1.99172i −0.0108005 0.0751190i
\(704\) 0 0
\(705\) 2.75306 1.27091i 0.103686 0.0478654i
\(706\) 0 0
\(707\) −27.0077 + 31.1686i −1.01573 + 1.17221i
\(708\) 0 0
\(709\) 2.15993 1.87159i 0.0811179 0.0702890i −0.613358 0.789805i \(-0.710182\pi\)
0.694476 + 0.719516i \(0.255636\pi\)
\(710\) 0 0
\(711\) 35.5518 + 4.81512i 1.33330 + 0.180581i
\(712\) 0 0
\(713\) −0.0178917 0.205028i −0.000670049 0.00767836i
\(714\) 0 0
\(715\) −19.4878 + 42.6723i −0.728803 + 1.59586i
\(716\) 0 0
\(717\) −1.49635 1.28592i −0.0558824 0.0480237i
\(718\) 0 0
\(719\) −36.3569 31.5034i −1.35588 1.17488i −0.967350 0.253445i \(-0.918436\pi\)
−0.388533 0.921435i \(-0.627018\pi\)
\(720\) 0 0
\(721\) 30.3834 8.92137i 1.13154 0.332249i
\(722\) 0 0
\(723\) 2.99858 + 10.0599i 0.111519 + 0.374130i
\(724\) 0 0
\(725\) −0.631623 + 0.288453i −0.0234579 + 0.0107129i
\(726\) 0 0
\(727\) 3.85075 5.99189i 0.142816 0.222227i −0.762475 0.647018i \(-0.776016\pi\)
0.905292 + 0.424791i \(0.139652\pi\)
\(728\) 0 0
\(729\) −18.1766 19.9653i −0.673206 0.739455i
\(730\) 0 0
\(731\) 3.98965 + 6.20802i 0.147563 + 0.229612i
\(732\) 0 0
\(733\) 6.76835 23.0509i 0.249995 0.851404i −0.734889 0.678188i \(-0.762766\pi\)
0.984884 0.173217i \(-0.0554161\pi\)
\(734\) 0 0
\(735\) −0.296683 2.00523i −0.0109433 0.0739640i
\(736\) 0 0
\(737\) 90.0753i 3.31797i
\(738\) 0 0
\(739\) −31.5653 9.26842i −1.16115 0.340944i −0.356270 0.934383i \(-0.615952\pi\)
−0.804879 + 0.593439i \(0.797770\pi\)
\(740\) 0 0
\(741\) 26.1186 22.8196i 0.959491 0.838298i
\(742\) 0 0
\(743\) −7.08960 + 49.3093i −0.260092 + 1.80898i 0.272002 + 0.962297i \(0.412314\pi\)
−0.532095 + 0.846685i \(0.678595\pi\)
\(744\) 0 0
\(745\) −21.9448 14.1030i −0.803994 0.516695i
\(746\) 0 0
\(747\) −29.9514 33.9999i −1.09587 1.24399i
\(748\) 0 0
\(749\) 4.84035 0.695938i 0.176863 0.0254290i
\(750\) 0 0
\(751\) −2.90745 9.90188i −0.106095 0.361325i 0.889284 0.457356i \(-0.151203\pi\)
−0.995378 + 0.0960310i \(0.969385\pi\)
\(752\) 0 0
\(753\) 17.1336 + 10.9124i 0.624385 + 0.397669i
\(754\) 0 0
\(755\) −24.1451 27.8650i −0.878731 1.01411i
\(756\) 0 0
\(757\) 1.02326 + 0.467305i 0.0371909 + 0.0169845i 0.433924 0.900950i \(-0.357129\pi\)
−0.396733 + 0.917934i \(0.629856\pi\)
\(758\) 0 0
\(759\) 4.73049 + 51.7634i 0.171706 + 1.87889i
\(760\) 0 0
\(761\) −5.29130 2.41646i −0.191809 0.0875964i 0.317195 0.948360i \(-0.397259\pi\)
−0.509004 + 0.860764i \(0.669986\pi\)
\(762\) 0 0
\(763\) −12.4185 14.3317i −0.449580 0.518843i
\(764\) 0 0
\(765\) −3.95659 + 8.85468i −0.143051 + 0.320142i
\(766\) 0 0
\(767\) 9.77659 + 33.2960i 0.353012 + 1.20225i
\(768\) 0 0
\(769\) 1.20710 0.173555i 0.0435291 0.00625854i −0.120516 0.992711i \(-0.538455\pi\)
0.164045 + 0.986453i \(0.447546\pi\)
\(770\) 0 0
\(771\) 3.10694 + 4.79130i 0.111894 + 0.172554i
\(772\) 0 0
\(773\) −5.09238 3.27268i −0.183160 0.117710i 0.445848 0.895109i \(-0.352902\pi\)
−0.629008 + 0.777399i \(0.716539\pi\)
\(774\) 0 0
\(775\) −0.00112124 + 0.00779842i −4.02763e−5 + 0.000280128i
\(776\) 0 0
\(777\) −0.960314 1.09915i −0.0344511 0.0394317i
\(778\) 0 0
\(779\) −36.0686 10.5907i −1.29229 0.379451i
\(780\) 0 0
\(781\) 71.1782i 2.54696i
\(782\) 0 0
\(783\) 17.7752 8.38270i 0.635232 0.299573i
\(784\) 0 0
\(785\) −3.22731 + 10.9912i −0.115188 + 0.392293i
\(786\) 0 0
\(787\) −12.9360 20.1288i −0.461118 0.717513i 0.530362 0.847771i \(-0.322056\pi\)
−0.991480 + 0.130258i \(0.958420\pi\)
\(788\) 0 0
\(789\) 29.5610 0.120892i 1.05240 0.00430388i
\(790\) 0 0
\(791\) 7.26347 11.3022i 0.258259 0.401860i
\(792\) 0 0
\(793\) −15.8844 + 7.25418i −0.564073 + 0.257603i
\(794\) 0 0
\(795\) 5.51164 1.64288i 0.195478 0.0582668i
\(796\) 0 0
\(797\) 47.2314 13.8684i 1.67302 0.491243i 0.698514 0.715597i \(-0.253845\pi\)
0.974508 + 0.224353i \(0.0720269\pi\)
\(798\) 0 0
\(799\) 0.825152 + 0.714998i 0.0291918 + 0.0252948i
\(800\) 0 0
\(801\) 25.8669 + 16.3263i 0.913963 + 0.576861i
\(802\) 0 0
\(803\) 19.4786 42.6521i 0.687384 1.50516i
\(804\) 0 0
\(805\) 6.33533 + 27.0765i 0.223291 + 0.954322i
\(806\) 0 0
\(807\) 3.94718 13.6491i 0.138947 0.480472i
\(808\) 0 0
\(809\) 16.4449 14.2496i 0.578173 0.500990i −0.315971 0.948769i \(-0.602330\pi\)
0.894144 + 0.447779i \(0.147785\pi\)
\(810\) 0 0
\(811\) −18.1693 + 20.9684i −0.638009 + 0.736301i −0.979021 0.203757i \(-0.934685\pi\)
0.341013 + 0.940059i \(0.389230\pi\)
\(812\) 0 0
\(813\) 1.99821 + 4.32853i 0.0700802 + 0.151808i
\(814\) 0 0
\(815\) 6.37106 + 44.3117i 0.223169 + 1.55217i
\(816\) 0 0
\(817\) 13.1292 + 28.7489i 0.459332 + 1.00580i
\(818\) 0 0
\(819\) 6.89006 24.1958i 0.240758 0.845468i
\(820\) 0 0
\(821\) 34.8734 + 5.01404i 1.21709 + 0.174991i 0.720786 0.693158i \(-0.243781\pi\)
0.496304 + 0.868149i \(0.334690\pi\)
\(822\) 0 0
\(823\) −7.36286 + 4.73182i −0.256653 + 0.164941i −0.662640 0.748938i \(-0.730564\pi\)
0.405987 + 0.913879i \(0.366928\pi\)
\(824\) 0 0
\(825\) 0.275127 1.97073i 0.00957868 0.0686119i
\(826\) 0 0
\(827\) −45.3316 −1.57633 −0.788167 0.615462i \(-0.788969\pi\)
−0.788167 + 0.615462i \(0.788969\pi\)
\(828\) 0 0
\(829\) −48.9886 −1.70144 −0.850722 0.525615i \(-0.823835\pi\)
−0.850722 + 0.525615i \(0.823835\pi\)
\(830\) 0 0
\(831\) 0.240274 1.72108i 0.00833502 0.0597036i
\(832\) 0 0
\(833\) 0.614021 0.394607i 0.0212746 0.0136723i
\(834\) 0 0
\(835\) −44.8083 6.44245i −1.55065 0.222950i
\(836\) 0 0
\(837\) 0.0290240 0.221089i 0.00100322 0.00764197i
\(838\) 0 0
\(839\) −4.90117 10.7321i −0.169207 0.370512i 0.805964 0.591964i \(-0.201647\pi\)
−0.975171 + 0.221453i \(0.928920\pi\)
\(840\) 0 0
\(841\) −2.09136 14.5458i −0.0721160 0.501578i
\(842\) 0 0
\(843\) 4.67174 + 10.1200i 0.160903 + 0.348550i
\(844\) 0 0
\(845\) −3.21698 + 3.71259i −0.110667 + 0.127717i
\(846\) 0 0
\(847\) 54.1938 46.9592i 1.86212 1.61354i
\(848\) 0 0
\(849\) −9.54912 + 33.0203i −0.327725 + 1.13325i
\(850\) 0 0
\(851\) −1.13950 1.10439i −0.0390615 0.0378580i
\(852\) 0 0
\(853\) −16.6935 + 36.5538i −0.571576 + 1.25158i 0.374378 + 0.927276i \(0.377856\pi\)
−0.945954 + 0.324301i \(0.894871\pi\)
\(854\) 0 0
\(855\) −22.1699 + 35.1254i −0.758194 + 1.20126i
\(856\) 0 0
\(857\) −2.31111 2.00259i −0.0789459 0.0684070i 0.614494 0.788922i \(-0.289360\pi\)
−0.693440 + 0.720515i \(0.743906\pi\)
\(858\) 0 0
\(859\) 4.34693 1.27637i 0.148315 0.0435493i −0.206732 0.978398i \(-0.566283\pi\)
0.355048 + 0.934848i \(0.384465\pi\)
\(860\) 0 0
\(861\) −26.1310 + 7.78897i −0.890542 + 0.265448i
\(862\) 0 0
\(863\) 14.5987 6.66701i 0.496946 0.226948i −0.151143 0.988512i \(-0.548295\pi\)
0.648090 + 0.761564i \(0.275568\pi\)
\(864\) 0 0
\(865\) 19.7897 30.7934i 0.672871 1.04701i
\(866\) 0 0
\(867\) 25.9525 0.106135i 0.881393 0.00360453i
\(868\) 0 0
\(869\) −40.4576 62.9532i −1.37243 2.13554i
\(870\) 0 0
\(871\) 13.3537 45.4784i 0.452471 1.54098i
\(872\) 0 0
\(873\) 11.2056 + 37.0394i 0.379253 + 1.25360i
\(874\) 0 0
\(875\) 27.9271i 0.944109i
\(876\) 0 0
\(877\) −4.85540 1.42567i −0.163955 0.0481416i 0.198725 0.980055i \(-0.436320\pi\)
−0.362680 + 0.931914i \(0.618138\pi\)
\(878\) 0 0
\(879\) 8.85529 + 10.1355i 0.298682 + 0.341862i
\(880\) 0 0
\(881\) −6.85750 + 47.6950i −0.231035 + 1.60688i 0.462607 + 0.886564i \(0.346914\pi\)
−0.693642 + 0.720320i \(0.743995\pi\)
\(882\) 0 0
\(883\) −37.0636 23.8193i −1.24729 0.801583i −0.260796 0.965394i \(-0.583985\pi\)
−0.986492 + 0.163811i \(0.947621\pi\)
\(884\) 0 0
\(885\) −22.6113 34.8695i −0.760069 1.17212i
\(886\) 0 0
\(887\) −1.54899 + 0.222712i −0.0520101 + 0.00747792i −0.168271 0.985741i \(-0.553818\pi\)
0.116261 + 0.993219i \(0.462909\pi\)
\(888\) 0 0
\(889\) 0.0936894 + 0.319077i 0.00314224 + 0.0107015i
\(890\) 0 0
\(891\) −7.10196 + 55.8683i −0.237925 + 1.87166i
\(892\) 0 0
\(893\) 3.06221 + 3.53397i 0.102473 + 0.118260i
\(894\) 0 0
\(895\) −7.45170 3.40308i −0.249083 0.113752i
\(896\) 0 0
\(897\) 5.28552 26.8363i 0.176479 0.896036i
\(898\) 0 0
\(899\) 0.147639 + 0.0674245i 0.00492404 + 0.00224873i
\(900\) 0 0
\(901\) 1.35614 + 1.56506i 0.0451794 + 0.0521399i
\(902\) 0 0
\(903\) 19.3362 + 12.3152i 0.643469 + 0.409824i
\(904\) 0 0
\(905\) 6.92039 + 23.5687i 0.230041 + 0.783449i
\(906\) 0 0
\(907\) −15.3564 + 2.20791i −0.509900 + 0.0733125i −0.392463 0.919768i \(-0.628377\pi\)
−0.117437 + 0.993080i \(0.537468\pi\)
\(908\) 0 0
\(909\) −36.4542 + 32.1135i −1.20911 + 1.06514i
\(910\) 0 0
\(911\) 9.24946 + 5.94427i 0.306448 + 0.196942i 0.684822 0.728711i \(-0.259880\pi\)
−0.378373 + 0.925653i \(0.623516\pi\)
\(912\) 0 0
\(913\) −13.4504 + 93.5497i −0.445144 + 3.09604i
\(914\) 0 0
\(915\) 15.7490 13.7598i 0.520646 0.454884i
\(916\) 0 0
\(917\) 19.6098 + 5.75796i 0.647573 + 0.190145i
\(918\) 0 0
\(919\) 31.9646i 1.05441i 0.849737 + 0.527207i \(0.176761\pi\)
−0.849737 + 0.527207i \(0.823239\pi\)
\(920\) 0 0
\(921\) −6.60522 44.6435i −0.217650 1.47105i
\(922\) 0 0
\(923\) −10.5522 + 35.9374i −0.347329 + 1.18289i
\(924\) 0 0
\(925\) 0.0328426 + 0.0511041i 0.00107986 + 0.00168029i
\(926\) 0 0
\(927\) 36.8773 5.61039i 1.21121 0.184269i
\(928\) 0 0
\(929\) 3.12129 4.85682i 0.102406 0.159347i −0.786269 0.617884i \(-0.787990\pi\)
0.888675 + 0.458537i \(0.151626\pi\)
\(930\) 0 0
\(931\) 2.84349 1.29858i 0.0931915 0.0425591i
\(932\) 0 0
\(933\) −4.33980 14.5595i −0.142079 0.476655i
\(934\) 0 0
\(935\) 19.4101 5.69931i 0.634777 0.186387i
\(936\) 0 0
\(937\) −8.35212 7.23716i −0.272852 0.236428i 0.507677 0.861548i \(-0.330505\pi\)
−0.780529 + 0.625120i \(0.785050\pi\)
\(938\) 0 0
\(939\) −6.76201 5.81107i −0.220670 0.189637i
\(940\) 0 0
\(941\) 22.0278 48.2342i 0.718086 1.57239i −0.0984812 0.995139i \(-0.531398\pi\)
0.816567 0.577250i \(-0.195874\pi\)
\(942\) 0 0
\(943\) −27.6107 + 10.7932i −0.899127 + 0.351476i
\(944\) 0 0
\(945\) 0.369634 + 30.1267i 0.0120242 + 0.980023i
\(946\) 0 0
\(947\) −18.7174 + 16.2187i −0.608234 + 0.527038i −0.903617 0.428341i \(-0.859098\pi\)
0.295383 + 0.955379i \(0.404553\pi\)
\(948\) 0 0
\(949\) −16.1578 + 18.6471i −0.524503 + 0.605309i
\(950\) 0 0
\(951\) −29.3044 + 13.5280i −0.950260 + 0.438674i
\(952\) 0 0
\(953\) 4.27703 + 29.7474i 0.138546 + 0.963612i 0.933917 + 0.357489i \(0.116367\pi\)
−0.795371 + 0.606123i \(0.792724\pi\)
\(954\) 0 0
\(955\) −20.4638 44.8094i −0.662191 1.45000i
\(956\) 0 0
\(957\) −37.3573 16.8762i −1.20759 0.545531i
\(958\) 0 0
\(959\) −16.4130 2.35983i −0.530004 0.0762030i
\(960\) 0 0
\(961\) −26.0773 + 16.7589i −0.841204 + 0.540609i
\(962\) 0 0
\(963\) 5.76023 0.0471146i 0.185621 0.00151825i
\(964\) 0 0
\(965\) −16.0076 −0.515304
\(966\) 0 0
\(967\) 6.84894 0.220247 0.110124 0.993918i \(-0.464875\pi\)
0.110124 + 0.993918i \(0.464875\pi\)
\(968\) 0 0
\(969\) −14.8126 2.06793i −0.475848 0.0664316i
\(970\) 0 0
\(971\) 34.5183 22.1835i 1.10774 0.711904i 0.146944 0.989145i \(-0.453056\pi\)
0.960800 + 0.277241i \(0.0894200\pi\)
\(972\) 0 0
\(973\) −51.4202 7.39311i −1.64846 0.237012i
\(974\) 0 0
\(975\) −0.431070 + 0.954219i −0.0138053 + 0.0305595i
\(976\) 0 0
\(977\) 3.66882 + 8.03360i 0.117376 + 0.257017i 0.959197 0.282740i \(-0.0912433\pi\)
−0.841821 + 0.539757i \(0.818516\pi\)
\(978\) 0 0
\(979\) −9.08006 63.1532i −0.290200 2.01838i
\(980\) 0 0
\(981\) −12.2304 18.6930i −0.390487 0.596820i
\(982\) 0 0
\(983\) 17.6918 20.4174i 0.564281 0.651215i −0.399869 0.916572i \(-0.630944\pi\)
0.964150 + 0.265357i \(0.0854898\pi\)
\(984\) 0 0
\(985\) −1.98978 + 1.72415i −0.0633996 + 0.0549361i
\(986\) 0 0
\(987\) 3.25835 + 0.942281i 0.103714 + 0.0299931i
\(988\) 0 0
\(989\) 22.0598 + 11.6013i 0.701460 + 0.368900i
\(990\) 0 0
\(991\) 8.07185 17.6749i 0.256411 0.561461i −0.737023 0.675867i \(-0.763769\pi\)
0.993434 + 0.114406i \(0.0364965\pi\)
\(992\) 0 0
\(993\) −22.1838 + 25.8140i −0.703980 + 0.819182i
\(994\) 0 0
\(995\) 47.2689 + 40.9587i 1.49852 + 1.29848i
\(996\) 0 0
\(997\) −17.6534 + 5.18350i −0.559088 + 0.164163i −0.549054 0.835787i \(-0.685012\pi\)
−0.0100336 + 0.999950i \(0.503194\pi\)
\(998\) 0 0
\(999\) −0.947210 1.43487i −0.0299684 0.0453974i
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 552.2.u.a.17.14 yes 240
3.2 odd 2 inner 552.2.u.a.17.10 240
23.19 odd 22 inner 552.2.u.a.65.10 yes 240
69.65 even 22 inner 552.2.u.a.65.14 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.u.a.17.10 240 3.2 odd 2 inner
552.2.u.a.17.14 yes 240 1.1 even 1 trivial
552.2.u.a.65.10 yes 240 23.19 odd 22 inner
552.2.u.a.65.14 yes 240 69.65 even 22 inner