Properties

Label 460.2.s.a.29.4
Level $460$
Weight $2$
Character 460.29
Analytic conductor $3.673$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(9,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.s (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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(12\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 29.4
Character \(\chi\) \(=\) 460.29
Dual form 460.2.s.a.349.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.384428 + 1.30924i) q^{3} +(2.22428 - 0.229290i) q^{5} +(-2.93912 - 0.422582i) q^{7} +(0.957431 + 0.615303i) q^{9} +O(q^{10})\) \(q+(-0.384428 + 1.30924i) q^{3} +(2.22428 - 0.229290i) q^{5} +(-2.93912 - 0.422582i) q^{7} +(0.957431 + 0.615303i) q^{9} +(1.86724 + 4.08869i) q^{11} +(0.760621 - 0.109361i) q^{13} +(-0.554880 + 3.00027i) q^{15} +(1.51940 + 1.31657i) q^{17} +(-1.48804 - 1.71729i) q^{19} +(1.68314 - 3.68557i) q^{21} +(2.15316 + 4.28531i) q^{23} +(4.89485 - 1.02001i) q^{25} +(-4.26734 + 3.69767i) q^{27} +(-4.48297 + 5.17363i) q^{29} +(2.59661 - 0.762433i) q^{31} +(-6.07090 + 0.872864i) q^{33} +(-6.63432 - 0.266029i) q^{35} +(2.97221 - 4.62485i) q^{37} +(-0.149224 + 1.03788i) q^{39} +(-2.30458 + 1.48106i) q^{41} +(-2.22810 + 7.58820i) q^{43} +(2.27068 + 1.14908i) q^{45} -11.1516i q^{47} +(1.74340 + 0.511908i) q^{49} +(-2.30781 + 1.48314i) q^{51} +(8.84763 + 1.27210i) q^{53} +(5.09076 + 8.66625i) q^{55} +(2.82039 - 1.28803i) q^{57} +(0.431796 + 3.00321i) q^{59} +(-3.64886 + 1.07140i) q^{61} +(-2.55399 - 2.21304i) q^{63} +(1.66676 - 0.417652i) q^{65} +(-0.444820 - 0.203142i) q^{67} +(-6.43825 + 1.17162i) q^{69} +(5.94113 - 13.0093i) q^{71} +(2.74468 - 2.37828i) q^{73} +(-0.546277 + 6.80067i) q^{75} +(-3.76024 - 12.8062i) q^{77} +(-1.00769 - 7.00860i) q^{79} +(-1.78231 - 3.90271i) q^{81} +(9.53948 - 14.8437i) q^{83} +(3.68146 + 2.58004i) q^{85} +(-5.05015 - 7.85819i) q^{87} +(8.21076 + 2.41090i) q^{89} -2.28177 q^{91} +3.69269i q^{93} +(-3.70358 - 3.47854i) q^{95} +(-9.36679 - 14.5750i) q^{97} +(-0.728029 + 5.06355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{9}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.384428 + 1.30924i −0.221950 + 0.755891i 0.770946 + 0.636901i \(0.219784\pi\)
−0.992895 + 0.118990i \(0.962034\pi\)
\(4\) 0 0
\(5\) 2.22428 0.229290i 0.994729 0.102542i
\(6\) 0 0
\(7\) −2.93912 0.422582i −1.11088 0.159721i −0.437646 0.899147i \(-0.644188\pi\)
−0.673237 + 0.739427i \(0.735097\pi\)
\(8\) 0 0
\(9\) 0.957431 + 0.615303i 0.319144 + 0.205101i
\(10\) 0 0
\(11\) 1.86724 + 4.08869i 0.562994 + 1.23279i 0.950444 + 0.310895i \(0.100629\pi\)
−0.387450 + 0.921891i \(0.626644\pi\)
\(12\) 0 0
\(13\) 0.760621 0.109361i 0.210958 0.0303312i −0.0360254 0.999351i \(-0.511470\pi\)
0.246984 + 0.969020i \(0.420561\pi\)
\(14\) 0 0
\(15\) −0.554880 + 3.00027i −0.143269 + 0.774666i
\(16\) 0 0
\(17\) 1.51940 + 1.31657i 0.368509 + 0.319315i 0.819355 0.573287i \(-0.194332\pi\)
−0.450845 + 0.892602i \(0.648877\pi\)
\(18\) 0 0
\(19\) −1.48804 1.71729i −0.341380 0.393973i 0.558936 0.829211i \(-0.311210\pi\)
−0.900316 + 0.435238i \(0.856664\pi\)
\(20\) 0 0
\(21\) 1.68314 3.68557i 0.367292 0.804257i
\(22\) 0 0
\(23\) 2.15316 + 4.28531i 0.448966 + 0.893549i
\(24\) 0 0
\(25\) 4.89485 1.02001i 0.978970 0.204002i
\(26\) 0 0
\(27\) −4.26734 + 3.69767i −0.821250 + 0.711617i
\(28\) 0 0
\(29\) −4.48297 + 5.17363i −0.832467 + 0.960718i −0.999682 0.0252021i \(-0.991977\pi\)
0.167215 + 0.985920i \(0.446523\pi\)
\(30\) 0 0
\(31\) 2.59661 0.762433i 0.466364 0.136937i −0.0401039 0.999196i \(-0.512769\pi\)
0.506468 + 0.862259i \(0.330951\pi\)
\(32\) 0 0
\(33\) −6.07090 + 0.872864i −1.05681 + 0.151946i
\(34\) 0 0
\(35\) −6.63432 0.266029i −1.12141 0.0449672i
\(36\) 0 0
\(37\) 2.97221 4.62485i 0.488628 0.760320i −0.506143 0.862450i \(-0.668929\pi\)
0.994771 + 0.102129i \(0.0325655\pi\)
\(38\) 0 0
\(39\) −0.149224 + 1.03788i −0.0238950 + 0.166194i
\(40\) 0 0
\(41\) −2.30458 + 1.48106i −0.359915 + 0.231303i −0.708084 0.706129i \(-0.750440\pi\)
0.348169 + 0.937432i \(0.386804\pi\)
\(42\) 0 0
\(43\) −2.22810 + 7.58820i −0.339782 + 1.15719i 0.595521 + 0.803340i \(0.296946\pi\)
−0.935302 + 0.353850i \(0.884872\pi\)
\(44\) 0 0
\(45\) 2.27068 + 1.14908i 0.338493 + 0.171294i
\(46\) 0 0
\(47\) 11.1516i 1.62663i −0.581821 0.813317i \(-0.697660\pi\)
0.581821 0.813317i \(-0.302340\pi\)
\(48\) 0 0
\(49\) 1.74340 + 0.511908i 0.249057 + 0.0731297i
\(50\) 0 0
\(51\) −2.30781 + 1.48314i −0.323158 + 0.207681i
\(52\) 0 0
\(53\) 8.84763 + 1.27210i 1.21532 + 0.174736i 0.719998 0.693976i \(-0.244143\pi\)
0.495318 + 0.868712i \(0.335052\pi\)
\(54\) 0 0
\(55\) 5.09076 + 8.66625i 0.686439 + 1.16856i
\(56\) 0 0
\(57\) 2.82039 1.28803i 0.373570 0.170604i
\(58\) 0 0
\(59\) 0.431796 + 3.00321i 0.0562150 + 0.390984i 0.998432 + 0.0559805i \(0.0178285\pi\)
−0.942217 + 0.335004i \(0.891262\pi\)
\(60\) 0 0
\(61\) −3.64886 + 1.07140i −0.467189 + 0.137179i −0.506850 0.862034i \(-0.669190\pi\)
0.0396612 + 0.999213i \(0.487372\pi\)
\(62\) 0 0
\(63\) −2.55399 2.21304i −0.321772 0.278817i
\(64\) 0 0
\(65\) 1.66676 0.417652i 0.206736 0.0518033i
\(66\) 0 0
\(67\) −0.444820 0.203142i −0.0543434 0.0248178i 0.388058 0.921635i \(-0.373146\pi\)
−0.442401 + 0.896817i \(0.645873\pi\)
\(68\) 0 0
\(69\) −6.43825 + 1.17162i −0.775074 + 0.141046i
\(70\) 0 0
\(71\) 5.94113 13.0093i 0.705083 1.54392i −0.128615 0.991695i \(-0.541053\pi\)
0.833697 0.552221i \(-0.186220\pi\)
\(72\) 0 0
\(73\) 2.74468 2.37828i 0.321240 0.278356i −0.479280 0.877662i \(-0.659102\pi\)
0.800520 + 0.599306i \(0.204557\pi\)
\(74\) 0 0
\(75\) −0.546277 + 6.80067i −0.0630787 + 0.785273i
\(76\) 0 0
\(77\) −3.76024 12.8062i −0.428519 1.45940i
\(78\) 0 0
\(79\) −1.00769 7.00860i −0.113373 0.788530i −0.964597 0.263727i \(-0.915048\pi\)
0.851224 0.524803i \(-0.175861\pi\)
\(80\) 0 0
\(81\) −1.78231 3.90271i −0.198034 0.433635i
\(82\) 0 0
\(83\) 9.53948 14.8437i 1.04709 1.62931i 0.313679 0.949529i \(-0.398439\pi\)
0.733415 0.679781i \(-0.237925\pi\)
\(84\) 0 0
\(85\) 3.68146 + 2.58004i 0.399310 + 0.279844i
\(86\) 0 0
\(87\) −5.05015 7.85819i −0.541433 0.842486i
\(88\) 0 0
\(89\) 8.21076 + 2.41090i 0.870338 + 0.255554i 0.686259 0.727357i \(-0.259252\pi\)
0.184079 + 0.982911i \(0.441070\pi\)
\(90\) 0 0
\(91\) −2.28177 −0.239194
\(92\) 0 0
\(93\) 3.69269i 0.382914i
\(94\) 0 0
\(95\) −3.70358 3.47854i −0.379979 0.356891i
\(96\) 0 0
\(97\) −9.36679 14.5750i −0.951054 1.47987i −0.875783 0.482705i \(-0.839654\pi\)
−0.0752709 0.997163i \(-0.523982\pi\)
\(98\) 0 0
\(99\) −0.728029 + 5.06355i −0.0731697 + 0.508906i
\(100\) 0 0
\(101\) −14.3888 9.24712i −1.43174 0.920123i −0.999834 0.0182031i \(-0.994205\pi\)
−0.431904 0.901919i \(-0.642158\pi\)
\(102\) 0 0
\(103\) −7.12332 + 3.25311i −0.701882 + 0.320539i −0.734194 0.678939i \(-0.762440\pi\)
0.0323129 + 0.999478i \(0.489713\pi\)
\(104\) 0 0
\(105\) 2.89872 8.58367i 0.282886 0.837680i
\(106\) 0 0
\(107\) −1.77110 6.03182i −0.171219 0.583118i −0.999732 0.0231483i \(-0.992631\pi\)
0.828513 0.559970i \(-0.189187\pi\)
\(108\) 0 0
\(109\) 5.77196 6.66120i 0.552854 0.638027i −0.408692 0.912672i \(-0.634015\pi\)
0.961546 + 0.274645i \(0.0885604\pi\)
\(110\) 0 0
\(111\) 4.91244 + 5.66926i 0.466269 + 0.538103i
\(112\) 0 0
\(113\) 1.21327 + 0.554081i 0.114135 + 0.0521235i 0.471664 0.881778i \(-0.343654\pi\)
−0.357529 + 0.933902i \(0.616381\pi\)
\(114\) 0 0
\(115\) 5.77182 + 9.03803i 0.538225 + 0.842801i
\(116\) 0 0
\(117\) 0.795532 + 0.363307i 0.0735469 + 0.0335878i
\(118\) 0 0
\(119\) −3.90935 4.51163i −0.358369 0.413580i
\(120\) 0 0
\(121\) −6.02731 + 6.95589i −0.547937 + 0.632353i
\(122\) 0 0
\(123\) −1.05313 3.58662i −0.0949571 0.323394i
\(124\) 0 0
\(125\) 10.6536 3.39113i 0.952891 0.303312i
\(126\) 0 0
\(127\) −4.89329 + 2.23469i −0.434209 + 0.198297i −0.620514 0.784195i \(-0.713076\pi\)
0.186305 + 0.982492i \(0.440349\pi\)
\(128\) 0 0
\(129\) −9.07825 5.83424i −0.799295 0.513676i
\(130\) 0 0
\(131\) −2.14748 + 14.9361i −0.187626 + 1.30497i 0.650505 + 0.759502i \(0.274557\pi\)
−0.838131 + 0.545469i \(0.816352\pi\)
\(132\) 0 0
\(133\) 3.64783 + 5.67614i 0.316307 + 0.492184i
\(134\) 0 0
\(135\) −8.64392 + 9.20311i −0.743950 + 0.792078i
\(136\) 0 0
\(137\) 7.04424i 0.601830i −0.953651 0.300915i \(-0.902708\pi\)
0.953651 0.300915i \(-0.0972920\pi\)
\(138\) 0 0
\(139\) 10.7928 0.915434 0.457717 0.889098i \(-0.348667\pi\)
0.457717 + 0.889098i \(0.348667\pi\)
\(140\) 0 0
\(141\) 14.6002 + 4.28700i 1.22956 + 0.361031i
\(142\) 0 0
\(143\) 1.86740 + 2.90574i 0.156160 + 0.242990i
\(144\) 0 0
\(145\) −8.78513 + 12.5355i −0.729565 + 1.04102i
\(146\) 0 0
\(147\) −1.34042 + 2.08574i −0.110556 + 0.172029i
\(148\) 0 0
\(149\) −3.27571 7.17280i −0.268356 0.587618i 0.726697 0.686958i \(-0.241054\pi\)
−0.995054 + 0.0993394i \(0.968327\pi\)
\(150\) 0 0
\(151\) 2.66368 + 18.5263i 0.216767 + 1.50765i 0.749862 + 0.661594i \(0.230120\pi\)
−0.533095 + 0.846056i \(0.678971\pi\)
\(152\) 0 0
\(153\) 0.644633 + 2.19542i 0.0521155 + 0.177489i
\(154\) 0 0
\(155\) 5.60077 2.29124i 0.449864 0.184037i
\(156\) 0 0
\(157\) 10.0309 8.69181i 0.800552 0.693682i −0.155191 0.987884i \(-0.549599\pi\)
0.955743 + 0.294202i \(0.0950540\pi\)
\(158\) 0 0
\(159\) −5.06676 + 11.0947i −0.401820 + 0.879864i
\(160\) 0 0
\(161\) −4.51752 13.5049i −0.356030 1.06434i
\(162\) 0 0
\(163\) −2.25982 1.03203i −0.177003 0.0808346i 0.324943 0.945734i \(-0.394655\pi\)
−0.501946 + 0.864899i \(0.667382\pi\)
\(164\) 0 0
\(165\) −13.3033 + 3.33349i −1.03566 + 0.259512i
\(166\) 0 0
\(167\) 0.645927 + 0.559699i 0.0499833 + 0.0433108i 0.679494 0.733681i \(-0.262199\pi\)
−0.629511 + 0.776992i \(0.716745\pi\)
\(168\) 0 0
\(169\) −11.9068 + 3.49616i −0.915910 + 0.268935i
\(170\) 0 0
\(171\) −0.368041 2.55978i −0.0281448 0.195751i
\(172\) 0 0
\(173\) −3.98737 + 1.82097i −0.303154 + 0.138446i −0.561184 0.827691i \(-0.689654\pi\)
0.258030 + 0.966137i \(0.416927\pi\)
\(174\) 0 0
\(175\) −14.8176 + 0.929460i −1.12010 + 0.0702606i
\(176\) 0 0
\(177\) −4.09792 0.589192i −0.308018 0.0442864i
\(178\) 0 0
\(179\) 8.99343 5.77972i 0.672200 0.431997i −0.159518 0.987195i \(-0.550994\pi\)
0.831718 + 0.555198i \(0.187358\pi\)
\(180\) 0 0
\(181\) −2.42900 0.713219i −0.180546 0.0530132i 0.190210 0.981743i \(-0.439083\pi\)
−0.370756 + 0.928730i \(0.620901\pi\)
\(182\) 0 0
\(183\) 5.18912i 0.383591i
\(184\) 0 0
\(185\) 5.55060 10.9685i 0.408088 0.806417i
\(186\) 0 0
\(187\) −2.54595 + 8.67072i −0.186178 + 0.634066i
\(188\) 0 0
\(189\) 14.1048 9.06460i 1.02597 0.659352i
\(190\) 0 0
\(191\) 0.661370 4.59993i 0.0478551 0.332839i −0.951803 0.306709i \(-0.900772\pi\)
0.999659 0.0261307i \(-0.00831859\pi\)
\(192\) 0 0
\(193\) −12.5217 + 19.4842i −0.901335 + 1.40250i 0.0140393 + 0.999901i \(0.495531\pi\)
−0.915374 + 0.402603i \(0.868105\pi\)
\(194\) 0 0
\(195\) −0.0939417 + 2.34275i −0.00672731 + 0.167768i
\(196\) 0 0
\(197\) 16.0266 2.30427i 1.14185 0.164173i 0.454667 0.890661i \(-0.349758\pi\)
0.687178 + 0.726489i \(0.258849\pi\)
\(198\) 0 0
\(199\) 14.7459 4.32977i 1.04531 0.306929i 0.286386 0.958114i \(-0.407546\pi\)
0.758919 + 0.651185i \(0.225728\pi\)
\(200\) 0 0
\(201\) 0.436964 0.504283i 0.0308211 0.0355694i
\(202\) 0 0
\(203\) 15.3623 13.3115i 1.07822 0.934283i
\(204\) 0 0
\(205\) −4.78644 + 3.82272i −0.334300 + 0.266990i
\(206\) 0 0
\(207\) −0.575260 + 5.42774i −0.0399833 + 0.377254i
\(208\) 0 0
\(209\) 4.24293 9.29073i 0.293490 0.642653i
\(210\) 0 0
\(211\) −4.14260 4.78081i −0.285188 0.329125i 0.595021 0.803710i \(-0.297144\pi\)
−0.880210 + 0.474585i \(0.842598\pi\)
\(212\) 0 0
\(213\) 14.7483 + 12.7795i 1.01054 + 0.875638i
\(214\) 0 0
\(215\) −3.21601 + 17.3892i −0.219330 + 1.18593i
\(216\) 0 0
\(217\) −7.95393 + 1.14360i −0.539948 + 0.0776328i
\(218\) 0 0
\(219\) 2.05861 + 4.50772i 0.139108 + 0.304604i
\(220\) 0 0
\(221\) 1.29967 + 0.835247i 0.0874253 + 0.0561848i
\(222\) 0 0
\(223\) −11.2931 1.62371i −0.756244 0.108731i −0.246600 0.969117i \(-0.579314\pi\)
−0.509643 + 0.860386i \(0.670223\pi\)
\(224\) 0 0
\(225\) 5.31410 + 2.03523i 0.354273 + 0.135682i
\(226\) 0 0
\(227\) 0.608044 2.07081i 0.0403573 0.137444i −0.936850 0.349731i \(-0.886273\pi\)
0.977207 + 0.212287i \(0.0680911\pi\)
\(228\) 0 0
\(229\) 17.7382 1.17218 0.586088 0.810248i \(-0.300667\pi\)
0.586088 + 0.810248i \(0.300667\pi\)
\(230\) 0 0
\(231\) 18.2120 1.19826
\(232\) 0 0
\(233\) −2.98201 + 10.1558i −0.195358 + 0.665329i 0.802299 + 0.596922i \(0.203610\pi\)
−0.997658 + 0.0684068i \(0.978208\pi\)
\(234\) 0 0
\(235\) −2.55696 24.8044i −0.166798 1.61806i
\(236\) 0 0
\(237\) 9.56334 + 1.37500i 0.621206 + 0.0893159i
\(238\) 0 0
\(239\) −14.8499 9.54344i −0.960559 0.617314i −0.0364064 0.999337i \(-0.511591\pi\)
−0.924153 + 0.382023i \(0.875227\pi\)
\(240\) 0 0
\(241\) 8.68519 + 19.0179i 0.559462 + 1.22505i 0.952221 + 0.305410i \(0.0987934\pi\)
−0.392759 + 0.919641i \(0.628479\pi\)
\(242\) 0 0
\(243\) −10.9723 + 1.57758i −0.703874 + 0.101202i
\(244\) 0 0
\(245\) 3.99518 + 0.738883i 0.255243 + 0.0472055i
\(246\) 0 0
\(247\) −1.31964 1.14347i −0.0839666 0.0727575i
\(248\) 0 0
\(249\) 15.7668 + 18.1958i 0.999179 + 1.15311i
\(250\) 0 0
\(251\) −0.704529 + 1.54270i −0.0444695 + 0.0973746i −0.930563 0.366132i \(-0.880682\pi\)
0.886093 + 0.463507i \(0.153409\pi\)
\(252\) 0 0
\(253\) −13.5008 + 16.8053i −0.848789 + 1.05654i
\(254\) 0 0
\(255\) −4.79315 + 3.82808i −0.300159 + 0.239723i
\(256\) 0 0
\(257\) −15.1648 + 13.1404i −0.945957 + 0.819677i −0.983738 0.179609i \(-0.942517\pi\)
0.0377807 + 0.999286i \(0.487971\pi\)
\(258\) 0 0
\(259\) −10.6901 + 12.3370i −0.664248 + 0.766583i
\(260\) 0 0
\(261\) −7.47548 + 2.19500i −0.462721 + 0.135867i
\(262\) 0 0
\(263\) 13.1464 1.89017i 0.810644 0.116553i 0.275486 0.961305i \(-0.411161\pi\)
0.535158 + 0.844752i \(0.320252\pi\)
\(264\) 0 0
\(265\) 19.9713 + 0.800828i 1.22683 + 0.0491945i
\(266\) 0 0
\(267\) −6.31289 + 9.82305i −0.386343 + 0.601161i
\(268\) 0 0
\(269\) −1.13242 + 7.87617i −0.0690450 + 0.480219i 0.925735 + 0.378173i \(0.123448\pi\)
−0.994780 + 0.102045i \(0.967461\pi\)
\(270\) 0 0
\(271\) 8.24766 5.30045i 0.501009 0.321979i −0.265610 0.964080i \(-0.585573\pi\)
0.766620 + 0.642101i \(0.221937\pi\)
\(272\) 0 0
\(273\) 0.877176 2.98739i 0.0530891 0.180805i
\(274\) 0 0
\(275\) 13.3104 + 18.1089i 0.802646 + 1.09201i
\(276\) 0 0
\(277\) 26.6094i 1.59881i 0.600795 + 0.799403i \(0.294851\pi\)
−0.600795 + 0.799403i \(0.705149\pi\)
\(278\) 0 0
\(279\) 2.95520 + 0.867724i 0.176923 + 0.0519493i
\(280\) 0 0
\(281\) −26.3968 + 16.9642i −1.57470 + 1.01200i −0.596937 + 0.802288i \(0.703616\pi\)
−0.977764 + 0.209710i \(0.932748\pi\)
\(282\) 0 0
\(283\) 12.2705 + 1.76424i 0.729407 + 0.104873i 0.497006 0.867747i \(-0.334433\pi\)
0.232401 + 0.972620i \(0.425342\pi\)
\(284\) 0 0
\(285\) 5.97801 3.51163i 0.354107 0.208011i
\(286\) 0 0
\(287\) 7.39931 3.37915i 0.436767 0.199465i
\(288\) 0 0
\(289\) −1.84412 12.8262i −0.108478 0.754480i
\(290\) 0 0
\(291\) 22.6831 6.66035i 1.32971 0.390437i
\(292\) 0 0
\(293\) −14.2814 12.3749i −0.834326 0.722947i 0.128895 0.991658i \(-0.458857\pi\)
−0.963221 + 0.268711i \(0.913402\pi\)
\(294\) 0 0
\(295\) 1.64904 + 6.58097i 0.0960109 + 0.383159i
\(296\) 0 0
\(297\) −23.0868 10.5434i −1.33963 0.611789i
\(298\) 0 0
\(299\) 2.10639 + 3.02402i 0.121815 + 0.174884i
\(300\) 0 0
\(301\) 9.75528 21.3611i 0.562285 1.23123i
\(302\) 0 0
\(303\) 17.6382 15.2836i 1.01329 0.878018i
\(304\) 0 0
\(305\) −7.87044 + 3.21975i −0.450660 + 0.184362i
\(306\) 0 0
\(307\) 3.11586 + 10.6116i 0.177832 + 0.605639i 0.999370 + 0.0354857i \(0.0112978\pi\)
−0.821539 + 0.570153i \(0.806884\pi\)
\(308\) 0 0
\(309\) −1.52071 10.5767i −0.0865099 0.601690i
\(310\) 0 0
\(311\) −10.8139 23.6790i −0.613197 1.34272i −0.920365 0.391060i \(-0.872109\pi\)
0.307168 0.951655i \(-0.400619\pi\)
\(312\) 0 0
\(313\) −14.9750 + 23.3016i −0.846438 + 1.31708i 0.100259 + 0.994961i \(0.468033\pi\)
−0.946698 + 0.322123i \(0.895604\pi\)
\(314\) 0 0
\(315\) −6.18821 4.33682i −0.348666 0.244352i
\(316\) 0 0
\(317\) 11.0151 + 17.1398i 0.618668 + 0.962666i 0.999280 + 0.0379311i \(0.0120767\pi\)
−0.380613 + 0.924735i \(0.624287\pi\)
\(318\) 0 0
\(319\) −29.5241 8.66907i −1.65303 0.485375i
\(320\) 0 0
\(321\) 8.57797 0.478776
\(322\) 0 0
\(323\) 4.56836i 0.254191i
\(324\) 0 0
\(325\) 3.61158 1.31115i 0.200334 0.0727293i
\(326\) 0 0
\(327\) 6.50222 + 10.1176i 0.359573 + 0.559507i
\(328\) 0 0
\(329\) −4.71248 + 32.7760i −0.259807 + 1.80700i
\(330\) 0 0
\(331\) −29.4189 18.9064i −1.61701 1.03919i −0.957884 0.287155i \(-0.907290\pi\)
−0.659125 0.752034i \(-0.729073\pi\)
\(332\) 0 0
\(333\) 5.69137 2.59916i 0.311885 0.142433i
\(334\) 0 0
\(335\) −1.03598 0.349853i −0.0566018 0.0191145i
\(336\) 0 0
\(337\) −9.63752 32.8224i −0.524989 1.78795i −0.610972 0.791652i \(-0.709221\pi\)
0.0859829 0.996297i \(-0.472597\pi\)
\(338\) 0 0
\(339\) −1.19184 + 1.37546i −0.0647319 + 0.0747046i
\(340\) 0 0
\(341\) 7.96584 + 9.19307i 0.431374 + 0.497833i
\(342\) 0 0
\(343\) 13.9993 + 6.39328i 0.755893 + 0.345205i
\(344\) 0 0
\(345\) −14.0518 + 4.08224i −0.756525 + 0.219780i
\(346\) 0 0
\(347\) 6.81652 + 3.11300i 0.365930 + 0.167115i 0.589890 0.807484i \(-0.299171\pi\)
−0.223960 + 0.974598i \(0.571898\pi\)
\(348\) 0 0
\(349\) −1.39403 1.60879i −0.0746205 0.0861166i 0.717212 0.696855i \(-0.245418\pi\)
−0.791832 + 0.610739i \(0.790873\pi\)
\(350\) 0 0
\(351\) −2.84145 + 3.27920i −0.151665 + 0.175031i
\(352\) 0 0
\(353\) −9.80538 33.3940i −0.521887 1.77739i −0.622678 0.782478i \(-0.713956\pi\)
0.100791 0.994908i \(-0.467863\pi\)
\(354\) 0 0
\(355\) 10.2319 30.2985i 0.543050 1.60808i
\(356\) 0 0
\(357\) 7.40968 3.38389i 0.392162 0.179094i
\(358\) 0 0
\(359\) −16.0116 10.2900i −0.845058 0.543086i 0.0449720 0.998988i \(-0.485680\pi\)
−0.890030 + 0.455903i \(0.849316\pi\)
\(360\) 0 0
\(361\) 1.96916 13.6958i 0.103640 0.720832i
\(362\) 0 0
\(363\) −6.78987 10.5652i −0.356376 0.554532i
\(364\) 0 0
\(365\) 5.55962 5.91928i 0.291004 0.309829i
\(366\) 0 0
\(367\) 3.47090i 0.181180i −0.995888 0.0905898i \(-0.971125\pi\)
0.995888 0.0905898i \(-0.0288752\pi\)
\(368\) 0 0
\(369\) −3.11778 −0.162305
\(370\) 0 0
\(371\) −25.4667 7.47769i −1.32216 0.388223i
\(372\) 0 0
\(373\) 13.2286 + 20.5841i 0.684951 + 1.06581i 0.993415 + 0.114569i \(0.0365488\pi\)
−0.308464 + 0.951236i \(0.599815\pi\)
\(374\) 0 0
\(375\) 0.344251 + 15.2519i 0.0177771 + 0.787602i
\(376\) 0 0
\(377\) −2.84405 + 4.42543i −0.146476 + 0.227921i
\(378\) 0 0
\(379\) 14.3045 + 31.3226i 0.734775 + 1.60893i 0.791962 + 0.610570i \(0.209059\pi\)
−0.0571873 + 0.998363i \(0.518213\pi\)
\(380\) 0 0
\(381\) −1.04463 7.26558i −0.0535182 0.372227i
\(382\) 0 0
\(383\) −4.06059 13.8291i −0.207487 0.706634i −0.995816 0.0913809i \(-0.970872\pi\)
0.788330 0.615253i \(-0.210946\pi\)
\(384\) 0 0
\(385\) −11.3002 27.6224i −0.575910 1.40777i
\(386\) 0 0
\(387\) −6.80229 + 5.89422i −0.345780 + 0.299620i
\(388\) 0 0
\(389\) −0.422071 + 0.924206i −0.0213998 + 0.0468591i −0.920030 0.391848i \(-0.871836\pi\)
0.898630 + 0.438707i \(0.144563\pi\)
\(390\) 0 0
\(391\) −2.37039 + 9.34590i −0.119876 + 0.472643i
\(392\) 0 0
\(393\) −18.7294 8.55342i −0.944772 0.431463i
\(394\) 0 0
\(395\) −3.84838 15.3581i −0.193633 0.772747i
\(396\) 0 0
\(397\) 19.8315 + 17.1841i 0.995316 + 0.862446i 0.990496 0.137542i \(-0.0439203\pi\)
0.00482001 + 0.999988i \(0.498466\pi\)
\(398\) 0 0
\(399\) −8.83377 + 2.59383i −0.442242 + 0.129854i
\(400\) 0 0
\(401\) 3.58050 + 24.9030i 0.178802 + 1.24359i 0.859540 + 0.511068i \(0.170750\pi\)
−0.680739 + 0.732526i \(0.738341\pi\)
\(402\) 0 0
\(403\) 1.89165 0.863889i 0.0942300 0.0430334i
\(404\) 0 0
\(405\) −4.85921 8.27206i −0.241456 0.411042i
\(406\) 0 0
\(407\) 24.4594 + 3.51673i 1.21241 + 0.174318i
\(408\) 0 0
\(409\) −11.6057 + 7.45853i −0.573865 + 0.368801i −0.795154 0.606408i \(-0.792610\pi\)
0.221289 + 0.975208i \(0.428974\pi\)
\(410\) 0 0
\(411\) 9.22261 + 2.70800i 0.454918 + 0.133576i
\(412\) 0 0
\(413\) 9.00925i 0.443316i
\(414\) 0 0
\(415\) 17.8150 35.2039i 0.874502 1.72809i
\(416\) 0 0
\(417\) −4.14906 + 14.1304i −0.203180 + 0.691969i
\(418\) 0 0
\(419\) 7.47509 4.80395i 0.365182 0.234688i −0.345162 0.938543i \(-0.612176\pi\)
0.710344 + 0.703855i \(0.248539\pi\)
\(420\) 0 0
\(421\) −2.27023 + 15.7898i −0.110644 + 0.769548i 0.856651 + 0.515896i \(0.172541\pi\)
−0.967296 + 0.253652i \(0.918368\pi\)
\(422\) 0 0
\(423\) 6.86164 10.6769i 0.333624 0.519129i
\(424\) 0 0
\(425\) 8.78017 + 4.89461i 0.425901 + 0.237423i
\(426\) 0 0
\(427\) 11.1772 1.60704i 0.540903 0.0777701i
\(428\) 0 0
\(429\) −4.52220 + 1.32784i −0.218334 + 0.0641086i
\(430\) 0 0
\(431\) 4.19893 4.84583i 0.202255 0.233415i −0.645556 0.763713i \(-0.723374\pi\)
0.847812 + 0.530298i \(0.177920\pi\)
\(432\) 0 0
\(433\) 12.8935 11.1723i 0.619622 0.536905i −0.287496 0.957782i \(-0.592823\pi\)
0.907118 + 0.420877i \(0.138277\pi\)
\(434\) 0 0
\(435\) −13.0348 16.3209i −0.624969 0.782525i
\(436\) 0 0
\(437\) 4.15512 10.0743i 0.198767 0.481920i
\(438\) 0 0
\(439\) 7.82363 17.1314i 0.373402 0.817635i −0.625887 0.779914i \(-0.715263\pi\)
0.999288 0.0377214i \(-0.0120099\pi\)
\(440\) 0 0
\(441\) 1.35420 + 1.56284i 0.0644859 + 0.0744207i
\(442\) 0 0
\(443\) −5.41830 4.69499i −0.257431 0.223065i 0.516577 0.856241i \(-0.327206\pi\)
−0.774009 + 0.633175i \(0.781751\pi\)
\(444\) 0 0
\(445\) 18.8158 + 3.47986i 0.891956 + 0.164961i
\(446\) 0 0
\(447\) 10.6502 1.53127i 0.503737 0.0724265i
\(448\) 0 0
\(449\) −8.72624 19.1078i −0.411817 0.901753i −0.995934 0.0900838i \(-0.971287\pi\)
0.584117 0.811669i \(-0.301441\pi\)
\(450\) 0 0
\(451\) −10.3588 6.65721i −0.487778 0.313476i
\(452\) 0 0
\(453\) −25.2794 3.63463i −1.18773 0.170770i
\(454\) 0 0
\(455\) −5.07530 + 0.523187i −0.237934 + 0.0245274i
\(456\) 0 0
\(457\) 0.482996 1.64493i 0.0225936 0.0769468i −0.947425 0.319979i \(-0.896324\pi\)
0.970018 + 0.243033i \(0.0781422\pi\)
\(458\) 0 0
\(459\) −11.3520 −0.529868
\(460\) 0 0
\(461\) 37.0638 1.72624 0.863118 0.505003i \(-0.168509\pi\)
0.863118 + 0.505003i \(0.168509\pi\)
\(462\) 0 0
\(463\) 9.60593 32.7148i 0.446425 1.52038i −0.362222 0.932092i \(-0.617982\pi\)
0.808648 0.588293i \(-0.200200\pi\)
\(464\) 0 0
\(465\) 0.846697 + 8.21358i 0.0392646 + 0.380895i
\(466\) 0 0
\(467\) 20.4241 + 2.93654i 0.945113 + 0.135887i 0.597605 0.801790i \(-0.296119\pi\)
0.347508 + 0.937677i \(0.387028\pi\)
\(468\) 0 0
\(469\) 1.22153 + 0.785032i 0.0564052 + 0.0362494i
\(470\) 0 0
\(471\) 7.52353 + 16.4742i 0.346666 + 0.759093i
\(472\) 0 0
\(473\) −35.1862 + 5.05901i −1.61786 + 0.232613i
\(474\) 0 0
\(475\) −9.03539 6.88806i −0.414572 0.316046i
\(476\) 0 0
\(477\) 7.68827 + 6.66192i 0.352022 + 0.305028i
\(478\) 0 0
\(479\) 7.60220 + 8.77341i 0.347353 + 0.400867i 0.902363 0.430977i \(-0.141831\pi\)
−0.555010 + 0.831844i \(0.687285\pi\)
\(480\) 0 0
\(481\) 1.75495 3.84280i 0.0800187 0.175217i
\(482\) 0 0
\(483\) 19.4179 0.722847i 0.883544 0.0328907i
\(484\) 0 0
\(485\) −24.1763 30.2712i −1.09779 1.37455i
\(486\) 0 0
\(487\) −25.9777 + 22.5098i −1.17716 + 1.02002i −0.177809 + 0.984065i \(0.556901\pi\)
−0.999354 + 0.0359517i \(0.988554\pi\)
\(488\) 0 0
\(489\) 2.21991 2.56192i 0.100388 0.115854i
\(490\) 0 0
\(491\) −6.11033 + 1.79415i −0.275755 + 0.0809690i −0.416686 0.909050i \(-0.636809\pi\)
0.140931 + 0.990019i \(0.454990\pi\)
\(492\) 0 0
\(493\) −13.6229 + 1.95867i −0.613544 + 0.0882143i
\(494\) 0 0
\(495\) −0.458319 + 11.4297i −0.0205999 + 0.513727i
\(496\) 0 0
\(497\) −22.9592 + 35.7252i −1.02986 + 1.60249i
\(498\) 0 0
\(499\) −0.250900 + 1.74505i −0.0112318 + 0.0781192i −0.994666 0.103144i \(-0.967110\pi\)
0.983435 + 0.181264i \(0.0580187\pi\)
\(500\) 0 0
\(501\) −0.981093 + 0.630511i −0.0438320 + 0.0281691i
\(502\) 0 0
\(503\) 6.97593 23.7578i 0.311041 1.05931i −0.644537 0.764573i \(-0.722950\pi\)
0.955579 0.294736i \(-0.0952318\pi\)
\(504\) 0 0
\(505\) −34.1250 17.2690i −1.51854 0.768459i
\(506\) 0 0
\(507\) 16.9329i 0.752018i
\(508\) 0 0
\(509\) −19.7685 5.80454i −0.876221 0.257282i −0.187462 0.982272i \(-0.560026\pi\)
−0.688759 + 0.724990i \(0.741844\pi\)
\(510\) 0 0
\(511\) −9.07195 + 5.83019i −0.401320 + 0.257912i
\(512\) 0 0
\(513\) 12.6999 + 1.82598i 0.560716 + 0.0806188i
\(514\) 0 0
\(515\) −15.0984 + 8.86914i −0.665313 + 0.390821i
\(516\) 0 0
\(517\) 45.5956 20.8228i 2.00529 0.915785i
\(518\) 0 0
\(519\) −0.851235 5.92047i −0.0373651 0.259880i
\(520\) 0 0
\(521\) 35.2335 10.3455i 1.54361 0.453244i 0.604425 0.796662i \(-0.293403\pi\)
0.939183 + 0.343418i \(0.111585\pi\)
\(522\) 0 0
\(523\) −5.10044 4.41955i −0.223026 0.193254i 0.536179 0.844104i \(-0.319867\pi\)
−0.759206 + 0.650850i \(0.774412\pi\)
\(524\) 0 0
\(525\) 4.47941 19.7571i 0.195498 0.862272i
\(526\) 0 0
\(527\) 4.94909 + 2.26017i 0.215586 + 0.0984547i
\(528\) 0 0
\(529\) −13.7278 + 18.4540i −0.596859 + 0.802346i
\(530\) 0 0
\(531\) −1.43447 + 3.14105i −0.0622506 + 0.136310i
\(532\) 0 0
\(533\) −1.59094 + 1.37856i −0.0689113 + 0.0597120i
\(534\) 0 0
\(535\) −5.32246 13.0104i −0.230110 0.562487i
\(536\) 0 0
\(537\) 4.10973 + 13.9965i 0.177348 + 0.603992i
\(538\) 0 0
\(539\) 1.16231 + 8.08407i 0.0500644 + 0.348206i
\(540\) 0 0
\(541\) −7.51911 16.4646i −0.323272 0.707866i 0.676315 0.736613i \(-0.263576\pi\)
−0.999587 + 0.0287461i \(0.990849\pi\)
\(542\) 0 0
\(543\) 1.86755 2.90597i 0.0801444 0.124707i
\(544\) 0 0
\(545\) 11.3111 16.1398i 0.484515 0.691354i
\(546\) 0 0
\(547\) −8.67579 13.4998i −0.370950 0.577209i 0.604724 0.796435i \(-0.293283\pi\)
−0.975674 + 0.219226i \(0.929647\pi\)
\(548\) 0 0
\(549\) −4.15277 1.21936i −0.177236 0.0520412i
\(550\) 0 0
\(551\) 15.5555 0.662685
\(552\) 0 0
\(553\) 21.0250i 0.894072i
\(554\) 0 0
\(555\) 12.2266 + 11.4837i 0.518989 + 0.487454i
\(556\) 0 0
\(557\) 2.10838 + 3.28070i 0.0893349 + 0.139008i 0.883045 0.469289i \(-0.155490\pi\)
−0.793710 + 0.608296i \(0.791853\pi\)
\(558\) 0 0
\(559\) −0.864885 + 6.01541i −0.0365807 + 0.254425i
\(560\) 0 0
\(561\) −10.3733 6.66654i −0.437962 0.281461i
\(562\) 0 0
\(563\) 12.4992 5.70822i 0.526781 0.240573i −0.134229 0.990950i \(-0.542856\pi\)
0.661009 + 0.750378i \(0.270128\pi\)
\(564\) 0 0
\(565\) 2.82569 + 0.954241i 0.118878 + 0.0401452i
\(566\) 0 0
\(567\) 3.58920 + 12.2237i 0.150732 + 0.513347i
\(568\) 0 0
\(569\) 13.6883 15.7972i 0.573844 0.662251i −0.392426 0.919784i \(-0.628364\pi\)
0.966270 + 0.257532i \(0.0829094\pi\)
\(570\) 0 0
\(571\) 1.00515 + 1.16000i 0.0420641 + 0.0485445i 0.776392 0.630251i \(-0.217048\pi\)
−0.734328 + 0.678795i \(0.762502\pi\)
\(572\) 0 0
\(573\) 5.76817 + 2.63424i 0.240969 + 0.110047i
\(574\) 0 0
\(575\) 14.9105 + 18.7797i 0.621810 + 0.783168i
\(576\) 0 0
\(577\) 6.92070 + 3.16058i 0.288113 + 0.131577i 0.554229 0.832364i \(-0.313013\pi\)
−0.266116 + 0.963941i \(0.585741\pi\)
\(578\) 0 0
\(579\) −20.6959 23.8843i −0.860090 0.992597i
\(580\) 0 0
\(581\) −34.3104 + 39.5963i −1.42343 + 1.64273i
\(582\) 0 0
\(583\) 11.3195 + 38.5505i 0.468804 + 1.59660i
\(584\) 0 0
\(585\) 1.85279 + 0.625690i 0.0766034 + 0.0258691i
\(586\) 0 0
\(587\) −14.1186 + 6.44776i −0.582738 + 0.266127i −0.684896 0.728641i \(-0.740152\pi\)
0.102158 + 0.994768i \(0.467425\pi\)
\(588\) 0 0
\(589\) −5.17317 3.32460i −0.213157 0.136988i
\(590\) 0 0
\(591\) −3.14421 + 21.8685i −0.129336 + 0.899549i
\(592\) 0 0
\(593\) 5.62163 + 8.74742i 0.230853 + 0.359214i 0.937283 0.348569i \(-0.113332\pi\)
−0.706431 + 0.707782i \(0.749696\pi\)
\(594\) 0 0
\(595\) −9.72996 9.13875i −0.398890 0.374652i
\(596\) 0 0
\(597\) 20.9704i 0.858260i
\(598\) 0 0
\(599\) 30.5817 1.24954 0.624768 0.780811i \(-0.285194\pi\)
0.624768 + 0.780811i \(0.285194\pi\)
\(600\) 0 0
\(601\) −25.0967 7.36907i −1.02372 0.300591i −0.273564 0.961854i \(-0.588202\pi\)
−0.750154 + 0.661263i \(0.770021\pi\)
\(602\) 0 0
\(603\) −0.300890 0.468194i −0.0122532 0.0190663i
\(604\) 0 0
\(605\) −11.8115 + 16.8539i −0.480206 + 0.685207i
\(606\) 0 0
\(607\) −2.12169 + 3.30142i −0.0861168 + 0.134000i −0.881640 0.471923i \(-0.843560\pi\)
0.795523 + 0.605924i \(0.207196\pi\)
\(608\) 0 0
\(609\) 11.5223 + 25.2302i 0.466906 + 1.02238i
\(610\) 0 0
\(611\) −1.21955 8.48217i −0.0493378 0.343152i
\(612\) 0 0
\(613\) 6.76231 + 23.0303i 0.273127 + 0.930185i 0.975799 + 0.218671i \(0.0701721\pi\)
−0.702672 + 0.711514i \(0.748010\pi\)
\(614\) 0 0
\(615\) −3.16482 7.73617i −0.127618 0.311953i
\(616\) 0 0
\(617\) −22.9557 + 19.8912i −0.924162 + 0.800791i −0.980276 0.197633i \(-0.936674\pi\)
0.0561140 + 0.998424i \(0.482129\pi\)
\(618\) 0 0
\(619\) 12.2299 26.7797i 0.491560 1.07637i −0.487561 0.873089i \(-0.662113\pi\)
0.979121 0.203278i \(-0.0651594\pi\)
\(620\) 0 0
\(621\) −25.0339 10.3252i −1.00458 0.414335i
\(622\) 0 0
\(623\) −23.1136 10.5556i −0.926027 0.422902i
\(624\) 0 0
\(625\) 22.9192 9.98561i 0.916766 0.399424i
\(626\) 0 0
\(627\) 10.5327 + 9.12664i 0.420636 + 0.364483i
\(628\) 0 0
\(629\) 10.6049 3.11389i 0.422846 0.124159i
\(630\) 0 0
\(631\) 2.95097 + 20.5244i 0.117476 + 0.817065i 0.960319 + 0.278905i \(0.0899713\pi\)
−0.842843 + 0.538160i \(0.819120\pi\)
\(632\) 0 0
\(633\) 7.85177 3.58578i 0.312080 0.142522i
\(634\) 0 0
\(635\) −10.3717 + 6.09256i −0.411587 + 0.241776i
\(636\) 0 0
\(637\) 1.38205 + 0.198709i 0.0547587 + 0.00787312i
\(638\) 0 0
\(639\) 13.6929 8.79987i 0.541681 0.348118i
\(640\) 0 0
\(641\) 24.7620 + 7.27079i 0.978042 + 0.287179i 0.731416 0.681932i \(-0.238860\pi\)
0.246626 + 0.969111i \(0.420678\pi\)
\(642\) 0 0
\(643\) 7.91582i 0.312169i −0.987744 0.156085i \(-0.950113\pi\)
0.987744 0.156085i \(-0.0498873\pi\)
\(644\) 0 0
\(645\) −21.5303 10.8954i −0.847755 0.429007i
\(646\) 0 0
\(647\) −13.4139 + 45.6835i −0.527354 + 1.79600i 0.0742885 + 0.997237i \(0.476331\pi\)
−0.601642 + 0.798766i \(0.705487\pi\)
\(648\) 0 0
\(649\) −11.4729 + 7.37319i −0.450351 + 0.289423i
\(650\) 0 0
\(651\) 1.56046 10.8533i 0.0611593 0.425373i
\(652\) 0 0
\(653\) −6.14094 + 9.55549i −0.240314 + 0.373935i −0.940371 0.340152i \(-0.889522\pi\)
0.700057 + 0.714087i \(0.253158\pi\)
\(654\) 0 0
\(655\) −1.35191 + 33.7144i −0.0528236 + 1.31733i
\(656\) 0 0
\(657\) 4.09120 0.588226i 0.159613 0.0229489i
\(658\) 0 0
\(659\) 19.5907 5.75235i 0.763145 0.224080i 0.123076 0.992397i \(-0.460724\pi\)
0.640069 + 0.768318i \(0.278906\pi\)
\(660\) 0 0
\(661\) 17.7466 20.4807i 0.690264 0.796607i −0.297139 0.954834i \(-0.596033\pi\)
0.987403 + 0.158228i \(0.0505780\pi\)
\(662\) 0 0
\(663\) −1.59317 + 1.38049i −0.0618736 + 0.0536138i
\(664\) 0 0
\(665\) 9.41529 + 11.7889i 0.365109 + 0.457155i
\(666\) 0 0
\(667\) −31.8232 8.07126i −1.23220 0.312520i
\(668\) 0 0
\(669\) 6.46722 14.1612i 0.250037 0.547505i
\(670\) 0 0
\(671\) −11.1939 12.9185i −0.432137 0.498713i
\(672\) 0 0
\(673\) −17.7307 15.3638i −0.683469 0.592229i 0.242353 0.970188i \(-0.422081\pi\)
−0.925822 + 0.377959i \(0.876626\pi\)
\(674\) 0 0
\(675\) −17.1163 + 22.4523i −0.658808 + 0.864189i
\(676\) 0 0
\(677\) −49.4021 + 7.10295i −1.89868 + 0.272989i −0.989623 0.143688i \(-0.954104\pi\)
−0.909055 + 0.416676i \(0.863195\pi\)
\(678\) 0 0
\(679\) 21.3710 + 46.7959i 0.820143 + 1.79586i
\(680\) 0 0
\(681\) 2.47744 + 1.59215i 0.0949356 + 0.0610114i
\(682\) 0 0
\(683\) 8.55182 + 1.22957i 0.327226 + 0.0470480i 0.303970 0.952681i \(-0.401688\pi\)
0.0232560 + 0.999730i \(0.492597\pi\)
\(684\) 0 0
\(685\) −1.61517 15.6684i −0.0617126 0.598657i
\(686\) 0 0
\(687\) −6.81908 + 23.2236i −0.260164 + 0.886037i
\(688\) 0 0
\(689\) 6.86881 0.261681
\(690\) 0 0
\(691\) 29.4428 1.12006 0.560028 0.828474i \(-0.310790\pi\)
0.560028 + 0.828474i \(0.310790\pi\)
\(692\) 0 0
\(693\) 4.27953 14.5747i 0.162566 0.553649i
\(694\) 0 0
\(695\) 24.0062 2.47468i 0.910609 0.0938701i
\(696\) 0 0
\(697\) −5.45151 0.783809i −0.206491 0.0296889i
\(698\) 0 0
\(699\) −12.1500 7.80835i −0.459557 0.295339i
\(700\) 0 0
\(701\) −14.4236 31.5833i −0.544772 1.19288i −0.959181 0.282793i \(-0.908739\pi\)
0.414410 0.910091i \(-0.363988\pi\)
\(702\) 0 0
\(703\) −12.3650 + 1.77781i −0.466354 + 0.0670516i
\(704\) 0 0
\(705\) 33.4579 + 6.18782i 1.26010 + 0.233047i
\(706\) 0 0
\(707\) 38.3827 + 33.2588i 1.44353 + 1.25083i
\(708\) 0 0
\(709\) 25.7118 + 29.6729i 0.965625 + 1.11439i 0.993391 + 0.114776i \(0.0366152\pi\)
−0.0277662 + 0.999614i \(0.508839\pi\)
\(710\) 0 0
\(711\) 3.34763 7.33028i 0.125546 0.274907i
\(712\) 0 0
\(713\) 8.85818 + 9.48562i 0.331742 + 0.355239i
\(714\) 0 0
\(715\) 4.81989 + 6.03500i 0.180254 + 0.225696i
\(716\) 0 0
\(717\) 18.2034 15.7733i 0.679818 0.589066i
\(718\) 0 0
\(719\) −1.41153 + 1.62899i −0.0526412 + 0.0607512i −0.781459 0.623956i \(-0.785524\pi\)
0.728818 + 0.684707i \(0.240070\pi\)
\(720\) 0 0
\(721\) 22.3110 6.55110i 0.830905 0.243976i
\(722\) 0 0
\(723\) −28.2379 + 4.05999i −1.05018 + 0.150993i
\(724\) 0 0
\(725\) −16.6663 + 29.8968i −0.618972 + 1.11034i
\(726\) 0 0
\(727\) 5.33368 8.29937i 0.197815 0.307807i −0.728148 0.685420i \(-0.759619\pi\)
0.925963 + 0.377613i \(0.123255\pi\)
\(728\) 0 0
\(729\) 3.98441 27.7122i 0.147571 1.02638i
\(730\) 0 0
\(731\) −13.3758 + 8.59609i −0.494721 + 0.317938i
\(732\) 0 0
\(733\) −9.46870 + 32.2474i −0.349735 + 1.19109i 0.577433 + 0.816438i \(0.304055\pi\)
−0.927167 + 0.374648i \(0.877764\pi\)
\(734\) 0 0
\(735\) −2.50324 + 4.94662i −0.0923334 + 0.182459i
\(736\) 0 0
\(737\) 2.19805i 0.0809660i
\(738\) 0 0
\(739\) 30.4774 + 8.94898i 1.12113 + 0.329193i 0.789216 0.614116i \(-0.210487\pi\)
0.331914 + 0.943310i \(0.392306\pi\)
\(740\) 0 0
\(741\) 2.00439 1.28814i 0.0736331 0.0473211i
\(742\) 0 0
\(743\) 21.6490 + 3.11265i 0.794224 + 0.114192i 0.527471 0.849573i \(-0.323140\pi\)
0.266753 + 0.963765i \(0.414049\pi\)
\(744\) 0 0
\(745\) −8.93074 15.2032i −0.327197 0.557003i
\(746\) 0 0
\(747\) 18.2668 8.34216i 0.668346 0.305224i
\(748\) 0 0
\(749\) 2.65654 + 18.4767i 0.0970680 + 0.675123i
\(750\) 0 0
\(751\) −35.1249 + 10.3136i −1.28173 + 0.376349i −0.850538 0.525913i \(-0.823724\pi\)
−0.431188 + 0.902262i \(0.641906\pi\)
\(752\) 0 0
\(753\) −1.74893 1.51546i −0.0637346 0.0552263i
\(754\) 0 0
\(755\) 10.1727 + 40.5970i 0.370222 + 1.47747i
\(756\) 0 0
\(757\) 46.0786 + 21.0434i 1.67475 + 0.764834i 0.999632 + 0.0271282i \(0.00863625\pi\)
0.675122 + 0.737706i \(0.264091\pi\)
\(758\) 0 0
\(759\) −16.8121 24.1363i −0.610242 0.876092i
\(760\) 0 0
\(761\) −3.24573 + 7.10716i −0.117658 + 0.257634i −0.959293 0.282411i \(-0.908866\pi\)
0.841636 + 0.540046i \(0.181593\pi\)
\(762\) 0 0
\(763\) −19.7794 + 17.1389i −0.716062 + 0.620471i
\(764\) 0 0
\(765\) 1.93723 + 4.73542i 0.0700408 + 0.171209i
\(766\) 0 0
\(767\) 0.656866 + 2.23708i 0.0237180 + 0.0807763i
\(768\) 0 0
\(769\) −3.93750 27.3859i −0.141990 0.987562i −0.928857 0.370439i \(-0.879207\pi\)
0.786867 0.617123i \(-0.211702\pi\)
\(770\) 0 0
\(771\) −11.3742 24.9060i −0.409632 0.896968i
\(772\) 0 0
\(773\) 4.66212 7.25440i 0.167685 0.260923i −0.747234 0.664561i \(-0.768618\pi\)
0.914918 + 0.403639i \(0.132255\pi\)
\(774\) 0 0
\(775\) 11.9323 6.38056i 0.428622 0.229197i
\(776\) 0 0
\(777\) −12.0425 18.7386i −0.432024 0.672242i
\(778\) 0 0
\(779\) 5.97273 + 1.75375i 0.213995 + 0.0628346i
\(780\) 0 0
\(781\) 64.2844 2.30028
\(782\) 0 0
\(783\) 38.6542i 1.38139i
\(784\) 0 0
\(785\) 20.3186 21.6330i 0.725201 0.772115i
\(786\) 0 0
\(787\) 2.90386 + 4.51849i 0.103511 + 0.161067i 0.889146 0.457624i \(-0.151300\pi\)
−0.785634 + 0.618691i \(0.787663\pi\)
\(788\) 0 0
\(789\) −2.57917 + 17.9385i −0.0918208 + 0.638628i
\(790\) 0 0
\(791\) −3.33179 2.14121i −0.118465 0.0761328i
\(792\) 0 0
\(793\) −2.65823 + 1.21397i −0.0943966 + 0.0431095i
\(794\) 0 0
\(795\) −8.72601 + 25.8394i −0.309480 + 0.916429i
\(796\) 0 0
\(797\) −6.17074 21.0156i −0.218579 0.744411i −0.993648 0.112534i \(-0.964103\pi\)
0.775069 0.631877i \(-0.217715\pi\)
\(798\) 0 0
\(799\) 14.6819 16.9438i 0.519409 0.599429i
\(800\) 0 0
\(801\) 6.37780 + 7.36037i 0.225348 + 0.260066i
\(802\) 0 0
\(803\) 14.8490 + 6.78131i 0.524010 + 0.239307i
\(804\) 0 0
\(805\) −13.1448 29.0029i −0.463292 1.02222i
\(806\) 0 0
\(807\) −9.87648 4.51044i −0.347668 0.158775i
\(808\) 0 0
\(809\) 7.28937 + 8.41238i 0.256281 + 0.295764i 0.869280 0.494320i \(-0.164583\pi\)
−0.613000 + 0.790083i \(0.710037\pi\)
\(810\) 0 0
\(811\) −28.5626 + 32.9630i −1.00297 + 1.15749i −0.0154666 + 0.999880i \(0.504923\pi\)
−0.987502 + 0.157607i \(0.949622\pi\)
\(812\) 0 0
\(813\) 3.76894 + 12.8358i 0.132182 + 0.450172i
\(814\) 0 0
\(815\) −5.26311 1.77736i −0.184359 0.0622583i
\(816\) 0 0
\(817\) 16.3466 7.46526i 0.571896 0.261176i
\(818\) 0 0
\(819\) −2.18464 1.40398i −0.0763373 0.0490590i
\(820\) 0 0
\(821\) −3.17825 + 22.1052i −0.110922 + 0.771477i 0.856105 + 0.516802i \(0.172878\pi\)
−0.967027 + 0.254675i \(0.918032\pi\)
\(822\) 0 0
\(823\) 2.04845 + 3.18744i 0.0714043 + 0.111107i 0.875119 0.483907i \(-0.160783\pi\)
−0.803715 + 0.595014i \(0.797146\pi\)
\(824\) 0 0
\(825\) −28.8258 + 10.4649i −1.00359 + 0.364342i
\(826\) 0 0
\(827\) 43.9455i 1.52813i −0.645137 0.764067i \(-0.723200\pi\)
0.645137 0.764067i \(-0.276800\pi\)
\(828\) 0 0
\(829\) −42.0680 −1.46108 −0.730540 0.682870i \(-0.760732\pi\)
−0.730540 + 0.682870i \(0.760732\pi\)
\(830\) 0 0
\(831\) −34.8382 10.2294i −1.20852 0.354855i
\(832\) 0 0
\(833\) 1.97496 + 3.07310i 0.0684284 + 0.106477i
\(834\) 0 0
\(835\) 1.56506 + 1.09682i 0.0541610 + 0.0379571i
\(836\) 0 0
\(837\) −8.26138 + 12.8550i −0.285555 + 0.444332i
\(838\) 0 0
\(839\) −9.35515 20.4849i −0.322976 0.707218i 0.676600 0.736351i \(-0.263453\pi\)
−0.999576 + 0.0291326i \(0.990725\pi\)
\(840\) 0 0
\(841\) −2.54224 17.6816i −0.0876633 0.609712i
\(842\) 0 0
\(843\) −12.0626 41.0813i −0.415457 1.41492i
\(844\) 0 0
\(845\) −25.6825 + 10.5066i −0.883504 + 0.361437i
\(846\) 0 0
\(847\) 20.6544 17.8972i 0.709694 0.614954i
\(848\) 0 0
\(849\) −7.02695 + 15.3869i −0.241164 + 0.528076i
\(850\) 0 0
\(851\) 26.2186 + 2.77878i 0.898761 + 0.0952553i
\(852\) 0 0
\(853\) −10.7291 4.89983i −0.367359 0.167767i 0.223178 0.974778i \(-0.428357\pi\)
−0.590537 + 0.807011i \(0.701084\pi\)
\(854\) 0 0
\(855\) −1.40556 5.60929i −0.0480691 0.191834i
\(856\) 0 0
\(857\) 20.0481 + 17.3718i 0.684829 + 0.593408i 0.926203 0.377024i \(-0.123053\pi\)
−0.241374 + 0.970432i \(0.577598\pi\)
\(858\) 0 0
\(859\) 11.5010 3.37700i 0.392409 0.115222i −0.0795746 0.996829i \(-0.525356\pi\)
0.471984 + 0.881607i \(0.343538\pi\)
\(860\) 0 0
\(861\) 1.57962 + 10.9865i 0.0538334 + 0.374420i
\(862\) 0 0
\(863\) −35.1099 + 16.0341i −1.19515 + 0.545808i −0.910775 0.412904i \(-0.864515\pi\)
−0.284379 + 0.958712i \(0.591787\pi\)
\(864\) 0 0
\(865\) −8.45151 + 4.96462i −0.287360 + 0.168802i
\(866\) 0 0
\(867\) 17.5015 + 2.51633i 0.594382 + 0.0854592i
\(868\) 0 0
\(869\) 26.7744 17.2069i 0.908259 0.583703i
\(870\) 0 0
\(871\) −0.360555 0.105868i −0.0122169 0.00358722i
\(872\) 0 0
\(873\) 19.7180i 0.667353i
\(874\) 0 0
\(875\) −32.7454 + 5.46491i −1.10700 + 0.184748i
\(876\) 0 0
\(877\) 13.2409 45.0944i 0.447114 1.52273i −0.360352 0.932816i \(-0.617343\pi\)
0.807466 0.589914i \(-0.200838\pi\)
\(878\) 0 0
\(879\) 21.6919 13.9405i 0.731648 0.470202i
\(880\) 0 0
\(881\) 0.665893 4.63139i 0.0224345 0.156036i −0.975525 0.219890i \(-0.929430\pi\)
0.997959 + 0.0638543i \(0.0203393\pi\)
\(882\) 0 0
\(883\) −14.9841 + 23.3158i −0.504257 + 0.784639i −0.996301 0.0859315i \(-0.972613\pi\)
0.492044 + 0.870570i \(0.336250\pi\)
\(884\) 0 0
\(885\) −9.25002 0.370916i −0.310936 0.0124682i
\(886\) 0 0
\(887\) −18.3071 + 2.63216i −0.614692 + 0.0883794i −0.442627 0.896706i \(-0.645953\pi\)
−0.172066 + 0.985085i \(0.555044\pi\)
\(888\) 0 0
\(889\) 15.3263 4.50021i 0.514028 0.150932i
\(890\) 0 0
\(891\) 12.6290 14.5746i 0.423086 0.488268i
\(892\) 0 0
\(893\) −19.1506 + 16.5941i −0.640850 + 0.555300i
\(894\) 0 0
\(895\) 18.6787 14.9178i 0.624359 0.498648i
\(896\) 0 0
\(897\) −4.76893 + 1.59525i −0.159230 + 0.0532638i
\(898\) 0 0
\(899\) −7.69598 + 16.8518i −0.256675 + 0.562040i
\(900\) 0 0
\(901\) 11.7683 + 13.5814i 0.392059 + 0.452461i
\(902\) 0 0
\(903\) 24.2166 + 20.9838i 0.805879 + 0.698298i
\(904\) 0 0
\(905\) −5.56632 1.02945i −0.185031 0.0342202i
\(906\) 0 0
\(907\) −45.7196 + 6.57349i −1.51809 + 0.218269i −0.850388 0.526156i \(-0.823633\pi\)
−0.667706 + 0.744425i \(0.732724\pi\)
\(908\) 0 0
\(909\) −8.08649 17.7069i −0.268212 0.587302i
\(910\) 0 0
\(911\) −5.37851 3.45656i −0.178198 0.114521i 0.448501 0.893782i \(-0.351958\pi\)
−0.626699 + 0.779261i \(0.715594\pi\)
\(912\) 0 0
\(913\) 78.5038 + 11.2871i 2.59810 + 0.373550i
\(914\) 0 0
\(915\) −1.18981 11.5421i −0.0393341 0.381569i
\(916\) 0 0
\(917\) 12.6234 42.9914i 0.416862 1.41970i
\(918\) 0 0
\(919\) −52.7571 −1.74030 −0.870148 0.492791i \(-0.835977\pi\)
−0.870148 + 0.492791i \(0.835977\pi\)
\(920\) 0 0
\(921\) −15.0910 −0.497267
\(922\) 0 0
\(923\) 3.09625 10.5448i 0.101914 0.347088i
\(924\) 0 0
\(925\) 9.83113 25.6696i 0.323245 0.844012i
\(926\) 0 0
\(927\) −8.82173 1.26837i −0.289744 0.0416589i
\(928\) 0 0
\(929\) −2.30375 1.48053i −0.0755835 0.0485745i 0.502303 0.864692i \(-0.332486\pi\)
−0.577887 + 0.816117i \(0.696122\pi\)
\(930\) 0 0
\(931\) −1.71515 3.75566i −0.0562119 0.123087i
\(932\) 0 0
\(933\) 35.1587 5.05507i 1.15105 0.165495i
\(934\) 0 0
\(935\) −3.67480 + 19.8699i −0.120179 + 0.649814i
\(936\) 0 0
\(937\) −7.48390 6.48484i −0.244488 0.211850i 0.523993 0.851723i \(-0.324442\pi\)
−0.768481 + 0.639872i \(0.778987\pi\)
\(938\) 0 0
\(939\) −24.7506 28.5637i −0.807706 0.932142i
\(940\) 0 0
\(941\) −18.1808 + 39.8104i −0.592677 + 1.29778i 0.341134 + 0.940015i \(0.389189\pi\)
−0.933811 + 0.357767i \(0.883538\pi\)
\(942\) 0 0
\(943\) −11.3090 6.68687i −0.368270 0.217754i
\(944\) 0 0
\(945\) 29.2946 23.3963i 0.952953 0.761082i
\(946\) 0 0
\(947\) −40.5533 + 35.1397i −1.31781 + 1.14189i −0.338175 + 0.941083i \(0.609810\pi\)
−0.979632 + 0.200803i \(0.935645\pi\)
\(948\) 0 0
\(949\) 1.82757 2.10913i 0.0593254 0.0684652i
\(950\) 0 0
\(951\) −26.6746 + 7.83237i −0.864984 + 0.253982i
\(952\) 0 0
\(953\) 23.4287 3.36853i 0.758929 0.109117i 0.248023 0.968754i \(-0.420219\pi\)
0.510906 + 0.859637i \(0.329310\pi\)
\(954\) 0 0
\(955\) 0.416355 10.3832i 0.0134729 0.335992i
\(956\) 0 0
\(957\) 22.6998 35.3216i 0.733781 1.14179i
\(958\) 0 0
\(959\) −2.97677 + 20.7039i −0.0961248 + 0.668562i
\(960\) 0 0
\(961\) −19.9178 + 12.8004i −0.642510 + 0.412916i
\(962\) 0 0
\(963\) 2.01569 6.86481i 0.0649547 0.221215i
\(964\) 0 0
\(965\) −23.3843 + 46.2095i −0.752769 + 1.48754i
\(966\) 0 0
\(967\) 16.2612i 0.522924i 0.965214 + 0.261462i \(0.0842046\pi\)
−0.965214 + 0.261462i \(0.915795\pi\)
\(968\) 0 0
\(969\) 5.98110 + 1.75621i 0.192140 + 0.0564175i
\(970\) 0 0
\(971\) 31.6393 20.3333i 1.01535 0.652527i 0.0765793 0.997063i \(-0.475600\pi\)
0.938773 + 0.344536i \(0.111964\pi\)
\(972\) 0 0
\(973\) −31.7214 4.56084i −1.01694 0.146214i
\(974\) 0 0
\(975\) 0.328216 + 5.23247i 0.0105113 + 0.167573i
\(976\) 0 0
\(977\) −25.6816 + 11.7284i −0.821627 + 0.375225i −0.781450 0.623968i \(-0.785520\pi\)
−0.0401773 + 0.999193i \(0.512792\pi\)
\(978\) 0 0
\(979\) 5.47406 + 38.0729i 0.174952 + 1.21682i
\(980\) 0 0
\(981\) 9.62491 2.82613i 0.307300 0.0902313i
\(982\) 0 0
\(983\) −4.31306 3.73729i −0.137565 0.119201i 0.583360 0.812213i \(-0.301738\pi\)
−0.720925 + 0.693013i \(0.756283\pi\)
\(984\) 0 0
\(985\) 35.1192 8.80008i 1.11899 0.280394i
\(986\) 0 0
\(987\) −41.1001 18.7698i −1.30823 0.597449i
\(988\) 0 0
\(989\) −37.3152 + 6.79056i −1.18656 + 0.215927i
\(990\) 0 0
\(991\) −11.6269 + 25.4594i −0.369342 + 0.808745i 0.630138 + 0.776483i \(0.282998\pi\)
−0.999479 + 0.0322621i \(0.989729\pi\)
\(992\) 0 0
\(993\) 36.0625 31.2483i 1.14441 0.991635i
\(994\) 0 0
\(995\) 31.8061 13.0117i 1.00832 0.412499i
\(996\) 0 0
\(997\) −11.6252 39.5918i −0.368174 1.25389i −0.910427 0.413670i \(-0.864247\pi\)
0.542253 0.840216i \(-0.317572\pi\)
\(998\) 0 0
\(999\) 4.41774 + 30.7260i 0.139771 + 0.972129i
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 460.2.s.a.29.4 120
5.4 even 2 inner 460.2.s.a.29.9 yes 120
23.4 even 11 inner 460.2.s.a.349.9 yes 120
115.4 even 22 inner 460.2.s.a.349.4 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.s.a.29.4 120 1.1 even 1 trivial
460.2.s.a.29.9 yes 120 5.4 even 2 inner
460.2.s.a.349.4 yes 120 115.4 even 22 inner
460.2.s.a.349.9 yes 120 23.4 even 11 inner