Properties

Label 572.2.bq.a.69.1
Level $572$
Weight $2$
Character 572.69
Analytic conductor $4.567$
Analytic rank $0$
Dimension $112$
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] = [572,2,Mod(49,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 12, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.bq (of order \(30\), degree \(8\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 69.1
Character \(\chi\) \(=\) 572.69
Dual form 572.2.bq.a.257.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.10684 - 0.660380i) q^{3} +(-2.01179 + 2.76900i) q^{5} +(0.661166 + 3.11054i) q^{7} +(6.47574 + 2.88318i) q^{9} +O(q^{10})\) \(q+(-3.10684 - 0.660380i) q^{3} +(-2.01179 + 2.76900i) q^{5} +(0.661166 + 3.11054i) q^{7} +(6.47574 + 2.88318i) q^{9} +(-3.30826 + 0.235419i) q^{11} +(0.433383 - 3.57941i) q^{13} +(8.07892 - 7.27429i) q^{15} +(-0.309162 + 2.94148i) q^{17} +(-0.741453 - 0.667607i) q^{19} -10.1006i q^{21} +(-1.96787 + 3.40845i) q^{23} +(-2.07495 - 6.38603i) q^{25} +(-10.5062 - 7.63319i) q^{27} +(3.46531 + 3.84862i) q^{29} +(-6.17751 - 8.50261i) q^{31} +(10.4337 + 1.45330i) q^{33} +(-9.94322 - 4.42701i) q^{35} +(-3.63815 + 3.27581i) q^{37} +(-3.71022 + 10.8345i) q^{39} +(1.61184 - 7.58310i) q^{41} +(-6.09933 - 10.5643i) q^{43} +(-21.0114 + 12.1309i) q^{45} +(1.71766 - 0.558101i) q^{47} +(-2.84352 + 1.26602i) q^{49} +(2.90301 - 8.93455i) q^{51} +(4.20338 - 3.05394i) q^{53} +(6.00366 - 9.63418i) q^{55} +(1.86270 + 2.56379i) q^{57} +(0.00952379 + 0.0448059i) q^{59} +(0.0329676 - 0.313666i) q^{61} +(-4.68673 + 22.0493i) q^{63} +(9.03950 + 8.40108i) q^{65} +(9.11480 + 5.26243i) q^{67} +(8.36474 - 9.28998i) q^{69} +(9.47438 + 0.995797i) q^{71} +(-5.16414 - 1.67793i) q^{73} +(2.22933 + 21.2106i) q^{75} +(-2.91959 - 10.1348i) q^{77} +(6.87387 - 4.99416i) q^{79} +(13.3707 + 14.8497i) q^{81} +(-5.56693 + 7.66223i) q^{83} +(-7.52298 - 6.77372i) q^{85} +(-8.22463 - 14.2455i) q^{87} +(-2.00972 - 1.16031i) q^{89} +(11.4204 - 1.01853i) q^{91} +(13.5776 + 30.4958i) q^{93} +(3.34025 - 0.709993i) q^{95} +(-6.07024 + 13.6340i) q^{97} +(-22.1022 - 8.01381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) −3.10684 0.660380i −1.79374 0.381271i −0.813890 0.581019i \(-0.802654\pi\)
−0.979847 + 0.199749i \(0.935987\pi\)
\(4\) 0 0
\(5\) −2.01179 + 2.76900i −0.899702 + 1.23833i 0.0708611 + 0.997486i \(0.477425\pi\)
−0.970563 + 0.240847i \(0.922575\pi\)
\(6\) 0 0
\(7\) 0.661166 + 3.11054i 0.249897 + 1.17567i 0.906754 + 0.421660i \(0.138552\pi\)
−0.656857 + 0.754015i \(0.728114\pi\)
\(8\) 0 0
\(9\) 6.47574 + 2.88318i 2.15858 + 0.961062i
\(10\) 0 0
\(11\) −3.30826 + 0.235419i −0.997478 + 0.0709815i
\(12\) 0 0
\(13\) 0.433383 3.57941i 0.120199 0.992750i
\(14\) 0 0
\(15\) 8.07892 7.27429i 2.08597 1.87821i
\(16\) 0 0
\(17\) −0.309162 + 2.94148i −0.0749828 + 0.713413i 0.890859 + 0.454280i \(0.150104\pi\)
−0.965842 + 0.259133i \(0.916563\pi\)
\(18\) 0 0
\(19\) −0.741453 0.667607i −0.170101 0.153160i 0.579684 0.814842i \(-0.303176\pi\)
−0.749785 + 0.661682i \(0.769843\pi\)
\(20\) 0 0
\(21\) 10.1006i 2.20413i
\(22\) 0 0
\(23\) −1.96787 + 3.40845i −0.410329 + 0.710711i −0.994926 0.100613i \(-0.967920\pi\)
0.584596 + 0.811324i \(0.301253\pi\)
\(24\) 0 0
\(25\) −2.07495 6.38603i −0.414989 1.27721i
\(26\) 0 0
\(27\) −10.5062 7.63319i −2.02192 1.46901i
\(28\) 0 0
\(29\) 3.46531 + 3.84862i 0.643492 + 0.714671i 0.973341 0.229363i \(-0.0736643\pi\)
−0.329849 + 0.944034i \(0.606998\pi\)
\(30\) 0 0
\(31\) −6.17751 8.50261i −1.10951 1.52711i −0.822131 0.569299i \(-0.807215\pi\)
−0.287383 0.957816i \(-0.592785\pi\)
\(32\) 0 0
\(33\) 10.4337 + 1.45330i 1.81628 + 0.252987i
\(34\) 0 0
\(35\) −9.94322 4.42701i −1.68071 0.748301i
\(36\) 0 0
\(37\) −3.63815 + 3.27581i −0.598109 + 0.538540i −0.911614 0.411047i \(-0.865163\pi\)
0.313505 + 0.949586i \(0.398497\pi\)
\(38\) 0 0
\(39\) −3.71022 + 10.8345i −0.594111 + 1.73490i
\(40\) 0 0
\(41\) 1.61184 7.58310i 0.251727 1.18428i −0.652688 0.757627i \(-0.726359\pi\)
0.904415 0.426655i \(-0.140308\pi\)
\(42\) 0 0
\(43\) −6.09933 10.5643i −0.930139 1.61105i −0.783081 0.621920i \(-0.786353\pi\)
−0.147058 0.989128i \(-0.546980\pi\)
\(44\) 0 0
\(45\) −21.0114 + 12.1309i −3.13219 + 1.80837i
\(46\) 0 0
\(47\) 1.71766 0.558101i 0.250546 0.0814074i −0.181051 0.983474i \(-0.557950\pi\)
0.431598 + 0.902066i \(0.357950\pi\)
\(48\) 0 0
\(49\) −2.84352 + 1.26602i −0.406217 + 0.180860i
\(50\) 0 0
\(51\) 2.90301 8.93455i 0.406503 1.25109i
\(52\) 0 0
\(53\) 4.20338 3.05394i 0.577379 0.419490i −0.260399 0.965501i \(-0.583854\pi\)
0.837778 + 0.546011i \(0.183854\pi\)
\(54\) 0 0
\(55\) 6.00366 9.63418i 0.809534 1.29907i
\(56\) 0 0
\(57\) 1.86270 + 2.56379i 0.246721 + 0.339583i
\(58\) 0 0
\(59\) 0.00952379 + 0.0448059i 0.00123989 + 0.00583323i 0.978763 0.204994i \(-0.0657175\pi\)
−0.977523 + 0.210827i \(0.932384\pi\)
\(60\) 0 0
\(61\) 0.0329676 0.313666i 0.00422107 0.0401608i −0.992209 0.124588i \(-0.960239\pi\)
0.996430 + 0.0844267i \(0.0269059\pi\)
\(62\) 0 0
\(63\) −4.68673 + 22.0493i −0.590473 + 2.77795i
\(64\) 0 0
\(65\) 9.03950 + 8.40108i 1.12121 + 1.04203i
\(66\) 0 0
\(67\) 9.11480 + 5.26243i 1.11355 + 0.642909i 0.939747 0.341872i \(-0.111061\pi\)
0.173804 + 0.984780i \(0.444394\pi\)
\(68\) 0 0
\(69\) 8.36474 9.28998i 1.00700 1.11838i
\(70\) 0 0
\(71\) 9.47438 + 0.995797i 1.12440 + 0.118179i 0.648425 0.761279i \(-0.275428\pi\)
0.475977 + 0.879458i \(0.342095\pi\)
\(72\) 0 0
\(73\) −5.16414 1.67793i −0.604417 0.196387i −0.00920753 0.999958i \(-0.502931\pi\)
−0.595209 + 0.803571i \(0.702931\pi\)
\(74\) 0 0
\(75\) 2.22933 + 21.2106i 0.257421 + 2.44919i
\(76\) 0 0
\(77\) −2.91959 10.1348i −0.332718 1.15497i
\(78\) 0 0
\(79\) 6.87387 4.99416i 0.773370 0.561887i −0.129612 0.991565i \(-0.541373\pi\)
0.902982 + 0.429678i \(0.141373\pi\)
\(80\) 0 0
\(81\) 13.3707 + 14.8497i 1.48563 + 1.64996i
\(82\) 0 0
\(83\) −5.56693 + 7.66223i −0.611050 + 0.841039i −0.996663 0.0816219i \(-0.973990\pi\)
0.385613 + 0.922661i \(0.373990\pi\)
\(84\) 0 0
\(85\) −7.52298 6.77372i −0.815981 0.734713i
\(86\) 0 0
\(87\) −8.22463 14.2455i −0.881773 1.52728i
\(88\) 0 0
\(89\) −2.00972 1.16031i −0.213030 0.122993i 0.389689 0.920947i \(-0.372583\pi\)
−0.602719 + 0.797954i \(0.705916\pi\)
\(90\) 0 0
\(91\) 11.4204 1.01853i 1.19719 0.106771i
\(92\) 0 0
\(93\) 13.5776 + 30.4958i 1.40793 + 3.16227i
\(94\) 0 0
\(95\) 3.34025 0.709993i 0.342703 0.0728437i
\(96\) 0 0
\(97\) −6.07024 + 13.6340i −0.616340 + 1.38432i 0.288050 + 0.957615i \(0.406993\pi\)
−0.904390 + 0.426707i \(0.859674\pi\)
\(98\) 0 0
\(99\) −22.1022 8.01381i −2.22135 0.805418i
\(100\) 0 0
\(101\) −1.40878 13.4036i −0.140179 1.33371i −0.807908 0.589308i \(-0.799400\pi\)
0.667730 0.744404i \(-0.267266\pi\)
\(102\) 0 0
\(103\) 2.05022 6.30993i 0.202014 0.621736i −0.797808 0.602911i \(-0.794007\pi\)
0.999823 0.0188252i \(-0.00599260\pi\)
\(104\) 0 0
\(105\) 27.9685 + 20.3203i 2.72945 + 1.98306i
\(106\) 0 0
\(107\) −8.92647 1.89738i −0.862954 0.183427i −0.244887 0.969552i \(-0.578751\pi\)
−0.618067 + 0.786125i \(0.712084\pi\)
\(108\) 0 0
\(109\) 5.65846i 0.541982i −0.962582 0.270991i \(-0.912649\pi\)
0.962582 0.270991i \(-0.0873514\pi\)
\(110\) 0 0
\(111\) 13.4665 7.77486i 1.27818 0.737957i
\(112\) 0 0
\(113\) −6.49755 + 7.21626i −0.611238 + 0.678849i −0.966721 0.255834i \(-0.917650\pi\)
0.355482 + 0.934683i \(0.384317\pi\)
\(114\) 0 0
\(115\) −5.47904 12.3061i −0.510923 1.14755i
\(116\) 0 0
\(117\) 13.1266 21.9298i 1.21355 2.02741i
\(118\) 0 0
\(119\) −9.35400 + 0.983145i −0.857480 + 0.0901248i
\(120\) 0 0
\(121\) 10.8892 1.55765i 0.989923 0.141605i
\(122\) 0 0
\(123\) −10.0155 + 22.4951i −0.903064 + 2.02831i
\(124\) 0 0
\(125\) 5.58150 + 1.81354i 0.499225 + 0.162208i
\(126\) 0 0
\(127\) −0.319970 + 0.142460i −0.0283927 + 0.0126413i −0.420884 0.907115i \(-0.638280\pi\)
0.392491 + 0.919756i \(0.371613\pi\)
\(128\) 0 0
\(129\) 11.9732 + 36.8496i 1.05418 + 3.24443i
\(130\) 0 0
\(131\) −18.1415 −1.58503 −0.792517 0.609850i \(-0.791230\pi\)
−0.792517 + 0.609850i \(0.791230\pi\)
\(132\) 0 0
\(133\) 1.58640 2.74772i 0.137558 0.238258i
\(134\) 0 0
\(135\) 42.2726 13.7352i 3.63824 1.18214i
\(136\) 0 0
\(137\) −4.71920 0.496008i −0.403189 0.0423768i −0.0992358 0.995064i \(-0.531640\pi\)
−0.303953 + 0.952687i \(0.598306\pi\)
\(138\) 0 0
\(139\) 12.0462 2.56050i 1.02174 0.217178i 0.333571 0.942725i \(-0.391746\pi\)
0.688173 + 0.725546i \(0.258413\pi\)
\(140\) 0 0
\(141\) −5.70506 + 0.599626i −0.480452 + 0.0504976i
\(142\) 0 0
\(143\) −0.591082 + 11.9436i −0.0494288 + 0.998778i
\(144\) 0 0
\(145\) −17.6283 + 1.85281i −1.46395 + 0.153868i
\(146\) 0 0
\(147\) 9.67043 2.05551i 0.797603 0.169536i
\(148\) 0 0
\(149\) 0.516540 + 0.0542906i 0.0423166 + 0.00444766i 0.125663 0.992073i \(-0.459894\pi\)
−0.0833465 + 0.996521i \(0.526561\pi\)
\(150\) 0 0
\(151\) −4.68099 + 1.52095i −0.380934 + 0.123773i −0.493223 0.869903i \(-0.664181\pi\)
0.112290 + 0.993675i \(0.464181\pi\)
\(152\) 0 0
\(153\) −10.4829 + 18.1569i −0.847490 + 1.46790i
\(154\) 0 0
\(155\) 35.9716 2.88931
\(156\) 0 0
\(157\) 2.37306 + 7.30353i 0.189391 + 0.582885i 0.999996 0.00270769i \(-0.000861887\pi\)
−0.810606 + 0.585593i \(0.800862\pi\)
\(158\) 0 0
\(159\) −15.0760 + 6.71227i −1.19561 + 0.532318i
\(160\) 0 0
\(161\) −11.9032 3.86759i −0.938106 0.304809i
\(162\) 0 0
\(163\) −5.63123 + 12.6480i −0.441072 + 0.990664i 0.547065 + 0.837090i \(0.315745\pi\)
−0.988137 + 0.153574i \(0.950922\pi\)
\(164\) 0 0
\(165\) −25.0147 + 25.9672i −1.94739 + 2.02154i
\(166\) 0 0
\(167\) −13.3617 + 1.40437i −1.03396 + 0.108673i −0.606275 0.795255i \(-0.707337\pi\)
−0.427683 + 0.903929i \(0.640670\pi\)
\(168\) 0 0
\(169\) −12.6244 3.10251i −0.971104 0.238655i
\(170\) 0 0
\(171\) −2.87662 6.46100i −0.219981 0.494085i
\(172\) 0 0
\(173\) 4.47536 4.97039i 0.340255 0.377892i −0.548596 0.836088i \(-0.684837\pi\)
0.888851 + 0.458196i \(0.151504\pi\)
\(174\) 0 0
\(175\) 18.4921 10.6764i 1.39787 0.807063i
\(176\) 0 0
\(177\) 0.145494i 0.0109360i
\(178\) 0 0
\(179\) 7.14507 + 1.51873i 0.534047 + 0.113515i 0.467038 0.884237i \(-0.345321\pi\)
0.0670091 + 0.997752i \(0.478654\pi\)
\(180\) 0 0
\(181\) −20.4451 14.8543i −1.51967 1.10411i −0.961649 0.274284i \(-0.911559\pi\)
−0.558025 0.829824i \(-0.688441\pi\)
\(182\) 0 0
\(183\) −0.309564 + 0.952740i −0.0228836 + 0.0704286i
\(184\) 0 0
\(185\) −1.75149 16.6643i −0.128772 1.22518i
\(186\) 0 0
\(187\) 0.330307 9.80396i 0.0241545 0.716936i
\(188\) 0 0
\(189\) 16.7970 37.7268i 1.22180 2.74422i
\(190\) 0 0
\(191\) −9.45899 + 2.01057i −0.684428 + 0.145480i −0.536986 0.843591i \(-0.680437\pi\)
−0.147442 + 0.989071i \(0.547104\pi\)
\(192\) 0 0
\(193\) −5.22572 11.7372i −0.376156 0.844860i −0.998089 0.0617897i \(-0.980319\pi\)
0.621933 0.783070i \(-0.286347\pi\)
\(194\) 0 0
\(195\) −22.5364 32.0703i −1.61387 2.29660i
\(196\) 0 0
\(197\) 7.29189 + 4.20998i 0.519526 + 0.299948i 0.736741 0.676175i \(-0.236364\pi\)
−0.217215 + 0.976124i \(0.569697\pi\)
\(198\) 0 0
\(199\) −8.58861 14.8759i −0.608830 1.05452i −0.991434 0.130612i \(-0.958306\pi\)
0.382603 0.923913i \(-0.375028\pi\)
\(200\) 0 0
\(201\) −24.8431 22.3688i −1.75229 1.57777i
\(202\) 0 0
\(203\) −9.68015 + 13.3236i −0.679413 + 0.935132i
\(204\) 0 0
\(205\) 17.7549 + 19.7188i 1.24006 + 1.37722i
\(206\) 0 0
\(207\) −22.5706 + 16.3985i −1.56877 + 1.13978i
\(208\) 0 0
\(209\) 2.61009 + 2.03407i 0.180543 + 0.140699i
\(210\) 0 0
\(211\) 1.59641 + 15.1889i 0.109902 + 1.04564i 0.900960 + 0.433903i \(0.142864\pi\)
−0.791058 + 0.611741i \(0.790469\pi\)
\(212\) 0 0
\(213\) −28.7778 9.35048i −1.97182 0.640684i
\(214\) 0 0
\(215\) 41.5233 + 4.36427i 2.83186 + 0.297641i
\(216\) 0 0
\(217\) 22.3634 24.8371i 1.51813 1.68605i
\(218\) 0 0
\(219\) 14.9361 + 8.62336i 1.00929 + 0.582713i
\(220\) 0 0
\(221\) 10.3948 + 2.38140i 0.699228 + 0.160191i
\(222\) 0 0
\(223\) −3.20344 + 15.0710i −0.214518 + 1.00923i 0.730677 + 0.682724i \(0.239205\pi\)
−0.945195 + 0.326506i \(0.894129\pi\)
\(224\) 0 0
\(225\) 4.97529 47.3367i 0.331686 3.15578i
\(226\) 0 0
\(227\) 4.32595 + 20.3520i 0.287124 + 1.35081i 0.851093 + 0.525015i \(0.175940\pi\)
−0.563969 + 0.825796i \(0.690726\pi\)
\(228\) 0 0
\(229\) 4.44106 + 6.11260i 0.293474 + 0.403932i 0.930139 0.367209i \(-0.119687\pi\)
−0.636665 + 0.771141i \(0.719687\pi\)
\(230\) 0 0
\(231\) 2.37787 + 33.4154i 0.156452 + 2.19857i
\(232\) 0 0
\(233\) 0.735142 0.534112i 0.0481608 0.0349909i −0.563444 0.826154i \(-0.690524\pi\)
0.611605 + 0.791163i \(0.290524\pi\)
\(234\) 0 0
\(235\) −1.91020 + 5.87898i −0.124607 + 0.383502i
\(236\) 0 0
\(237\) −24.6541 + 10.9767i −1.60145 + 0.713013i
\(238\) 0 0
\(239\) −1.63807 + 0.532240i −0.105958 + 0.0344277i −0.361516 0.932366i \(-0.617741\pi\)
0.255558 + 0.966794i \(0.417741\pi\)
\(240\) 0 0
\(241\) −8.01202 + 4.62574i −0.516100 + 0.297970i −0.735337 0.677701i \(-0.762976\pi\)
0.219238 + 0.975671i \(0.429643\pi\)
\(242\) 0 0
\(243\) −12.2547 21.2258i −0.786142 1.36164i
\(244\) 0 0
\(245\) 2.21498 10.4207i 0.141510 0.665752i
\(246\) 0 0
\(247\) −2.71097 + 2.36464i −0.172495 + 0.150458i
\(248\) 0 0
\(249\) 22.3556 20.1291i 1.41673 1.27563i
\(250\) 0 0
\(251\) 3.29219 + 1.46578i 0.207801 + 0.0925189i 0.507998 0.861358i \(-0.330386\pi\)
−0.300197 + 0.953877i \(0.597052\pi\)
\(252\) 0 0
\(253\) 5.70781 11.7393i 0.358847 0.738044i
\(254\) 0 0
\(255\) 18.8995 + 26.0129i 1.18353 + 1.62899i
\(256\) 0 0
\(257\) −6.35242 7.05508i −0.396253 0.440084i 0.511694 0.859167i \(-0.329018\pi\)
−0.907948 + 0.419084i \(0.862351\pi\)
\(258\) 0 0
\(259\) −12.5950 9.15078i −0.782613 0.568602i
\(260\) 0 0
\(261\) 11.3442 + 34.9138i 0.702187 + 2.16111i
\(262\) 0 0
\(263\) −6.06920 + 10.5122i −0.374243 + 0.648208i −0.990213 0.139561i \(-0.955431\pi\)
0.615970 + 0.787769i \(0.288764\pi\)
\(264\) 0 0
\(265\) 17.7830i 1.09240i
\(266\) 0 0
\(267\) 5.47765 + 4.93209i 0.335227 + 0.301839i
\(268\) 0 0
\(269\) 1.20455 11.4606i 0.0734429 0.698763i −0.894410 0.447247i \(-0.852404\pi\)
0.967853 0.251515i \(-0.0809289\pi\)
\(270\) 0 0
\(271\) 10.0706 9.06764i 0.611747 0.550820i −0.303950 0.952688i \(-0.598306\pi\)
0.915698 + 0.401868i \(0.131639\pi\)
\(272\) 0 0
\(273\) −36.1542 4.37743i −2.18815 0.264934i
\(274\) 0 0
\(275\) 8.36785 + 20.6382i 0.504600 + 1.24453i
\(276\) 0 0
\(277\) −8.25556 3.67561i −0.496029 0.220846i 0.143446 0.989658i \(-0.454182\pi\)
−0.639475 + 0.768812i \(0.720848\pi\)
\(278\) 0 0
\(279\) −15.4893 72.8716i −0.927323 4.36271i
\(280\) 0 0
\(281\) −11.2849 + 15.5324i −0.673203 + 0.926585i −0.999828 0.0185693i \(-0.994089\pi\)
0.326624 + 0.945154i \(0.394089\pi\)
\(282\) 0 0
\(283\) 11.5445 + 2.45385i 0.686247 + 0.145866i 0.537824 0.843057i \(-0.319247\pi\)
0.148424 + 0.988924i \(0.452580\pi\)
\(284\) 0 0
\(285\) −10.8465 −0.642492
\(286\) 0 0
\(287\) 24.6533 1.45524
\(288\) 0 0
\(289\) 8.07179 + 1.71571i 0.474811 + 0.100924i
\(290\) 0 0
\(291\) 27.8629 38.3500i 1.63335 2.24812i
\(292\) 0 0
\(293\) −1.42719 6.71438i −0.0833771 0.392258i 0.916594 0.399818i \(-0.130927\pi\)
−0.999971 + 0.00756016i \(0.997594\pi\)
\(294\) 0 0
\(295\) −0.143227 0.0637689i −0.00833902 0.00371277i
\(296\) 0 0
\(297\) 36.5542 + 22.7792i 2.12109 + 1.32178i
\(298\) 0 0
\(299\) 11.3474 + 8.52098i 0.656237 + 0.492781i
\(300\) 0 0
\(301\) 28.8282 25.9570i 1.66163 1.49614i
\(302\) 0 0
\(303\) −4.47464 + 42.5733i −0.257061 + 2.44577i
\(304\) 0 0
\(305\) 0.802217 + 0.722319i 0.0459348 + 0.0413599i
\(306\) 0 0
\(307\) 15.4574i 0.882201i −0.897458 0.441101i \(-0.854588\pi\)
0.897458 0.441101i \(-0.145412\pi\)
\(308\) 0 0
\(309\) −10.5367 + 18.2501i −0.599410 + 1.03821i
\(310\) 0 0
\(311\) −9.69076 29.8251i −0.549513 1.69123i −0.710011 0.704190i \(-0.751310\pi\)
0.160498 0.987036i \(-0.448690\pi\)
\(312\) 0 0
\(313\) −5.16610 3.75339i −0.292005 0.212154i 0.432132 0.901811i \(-0.357762\pi\)
−0.724137 + 0.689656i \(0.757762\pi\)
\(314\) 0 0
\(315\) −51.6258 57.3363i −2.90879 3.23053i
\(316\) 0 0
\(317\) −9.39386 12.9295i −0.527612 0.726196i 0.459152 0.888358i \(-0.348153\pi\)
−0.986764 + 0.162162i \(0.948153\pi\)
\(318\) 0 0
\(319\) −12.3702 11.9164i −0.692598 0.667192i
\(320\) 0 0
\(321\) 26.4801 + 11.7897i 1.47798 + 0.658038i
\(322\) 0 0
\(323\) 2.19298 1.97457i 0.122021 0.109868i
\(324\) 0 0
\(325\) −23.7575 + 4.65949i −1.31783 + 0.258462i
\(326\) 0 0
\(327\) −3.73673 + 17.5799i −0.206642 + 0.972173i
\(328\) 0 0
\(329\) 2.87166 + 4.97385i 0.158320 + 0.274217i
\(330\) 0 0
\(331\) −15.3314 + 8.85157i −0.842688 + 0.486526i −0.858177 0.513354i \(-0.828403\pi\)
0.0154887 + 0.999880i \(0.495070\pi\)
\(332\) 0 0
\(333\) −33.0045 + 10.7238i −1.80864 + 0.587661i
\(334\) 0 0
\(335\) −32.9088 + 14.6519i −1.79800 + 0.800521i
\(336\) 0 0
\(337\) 1.00551 3.09464i 0.0547735 0.168576i −0.919927 0.392089i \(-0.871753\pi\)
0.974701 + 0.223513i \(0.0717526\pi\)
\(338\) 0 0
\(339\) 24.9524 18.1289i 1.35523 0.984629i
\(340\) 0 0
\(341\) 22.4385 + 26.6745i 1.21511 + 1.44451i
\(342\) 0 0
\(343\) 7.26620 + 10.0011i 0.392338 + 0.540007i
\(344\) 0 0
\(345\) 8.89581 + 41.8515i 0.478934 + 2.25321i
\(346\) 0 0
\(347\) 1.33528 12.7043i 0.0716816 0.682005i −0.898392 0.439194i \(-0.855264\pi\)
0.970074 0.242811i \(-0.0780694\pi\)
\(348\) 0 0
\(349\) −6.38264 + 30.0279i −0.341655 + 1.60736i 0.386732 + 0.922192i \(0.373604\pi\)
−0.728386 + 0.685167i \(0.759729\pi\)
\(350\) 0 0
\(351\) −31.8755 + 34.2979i −1.70139 + 1.83068i
\(352\) 0 0
\(353\) −28.1740 16.2662i −1.49955 0.865765i −0.499549 0.866286i \(-0.666501\pi\)
−1.00000 0.000520868i \(0.999834\pi\)
\(354\) 0 0
\(355\) −21.8179 + 24.2312i −1.15797 + 1.28606i
\(356\) 0 0
\(357\) 29.7107 + 3.12272i 1.57246 + 0.165272i
\(358\) 0 0
\(359\) 25.9657 + 8.43677i 1.37042 + 0.445276i 0.899508 0.436905i \(-0.143925\pi\)
0.470911 + 0.882181i \(0.343925\pi\)
\(360\) 0 0
\(361\) −1.88199 17.9059i −0.0990520 0.942417i
\(362\) 0 0
\(363\) −34.8595 2.35159i −1.82965 0.123427i
\(364\) 0 0
\(365\) 15.0354 10.9238i 0.786988 0.571780i
\(366\) 0 0
\(367\) −3.18688 3.53939i −0.166354 0.184755i 0.654204 0.756318i \(-0.273004\pi\)
−0.820558 + 0.571563i \(0.806337\pi\)
\(368\) 0 0
\(369\) 32.3013 44.4590i 1.68154 2.31444i
\(370\) 0 0
\(371\) 12.2785 + 11.0556i 0.637470 + 0.573980i
\(372\) 0 0
\(373\) −11.9515 20.7007i −0.618827 1.07184i −0.989700 0.143156i \(-0.954275\pi\)
0.370874 0.928683i \(-0.379058\pi\)
\(374\) 0 0
\(375\) −16.1432 9.32030i −0.833633 0.481298i
\(376\) 0 0
\(377\) 15.2776 10.7358i 0.786836 0.552924i
\(378\) 0 0
\(379\) −0.692054 1.55438i −0.0355484 0.0798431i 0.894899 0.446270i \(-0.147248\pi\)
−0.930447 + 0.366427i \(0.880581\pi\)
\(380\) 0 0
\(381\) 1.08817 0.231299i 0.0557489 0.0118498i
\(382\) 0 0
\(383\) −2.74506 + 6.16551i −0.140266 + 0.315043i −0.969995 0.243123i \(-0.921828\pi\)
0.829729 + 0.558166i \(0.188495\pi\)
\(384\) 0 0
\(385\) 33.9369 + 12.3049i 1.72959 + 0.627114i
\(386\) 0 0
\(387\) −9.03870 85.9975i −0.459463 4.37150i
\(388\) 0 0
\(389\) 4.12434 12.6934i 0.209112 0.643582i −0.790407 0.612582i \(-0.790131\pi\)
0.999519 0.0309999i \(-0.00986914\pi\)
\(390\) 0 0
\(391\) −9.41750 6.84221i −0.476263 0.346026i
\(392\) 0 0
\(393\) 56.3629 + 11.9803i 2.84313 + 0.604327i
\(394\) 0 0
\(395\) 29.0809i 1.46322i
\(396\) 0 0
\(397\) −5.06854 + 2.92632i −0.254383 + 0.146868i −0.621769 0.783200i \(-0.713586\pi\)
0.367387 + 0.930068i \(0.380253\pi\)
\(398\) 0 0
\(399\) −6.74323 + 7.48912i −0.337584 + 0.374925i
\(400\) 0 0
\(401\) 6.39645 + 14.3667i 0.319424 + 0.717437i 0.999882 0.0153495i \(-0.00488608\pi\)
−0.680459 + 0.732786i \(0.738219\pi\)
\(402\) 0 0
\(403\) −33.1116 + 18.4270i −1.64941 + 0.917912i
\(404\) 0 0
\(405\) −68.0179 + 7.14897i −3.37983 + 0.355235i
\(406\) 0 0
\(407\) 11.2648 11.6937i 0.558374 0.579636i
\(408\) 0 0
\(409\) 4.35322 9.77748i 0.215253 0.483465i −0.773356 0.633971i \(-0.781424\pi\)
0.988609 + 0.150506i \(0.0480903\pi\)
\(410\) 0 0
\(411\) 14.3343 + 4.65749i 0.707057 + 0.229737i
\(412\) 0 0
\(413\) −0.133074 + 0.0592483i −0.00654814 + 0.00291542i
\(414\) 0 0
\(415\) −10.0172 30.8297i −0.491723 1.51337i
\(416\) 0 0
\(417\) −39.1165 −1.91554
\(418\) 0 0
\(419\) −9.77579 + 16.9322i −0.477579 + 0.827191i −0.999670 0.0256991i \(-0.991819\pi\)
0.522091 + 0.852890i \(0.325152\pi\)
\(420\) 0 0
\(421\) −14.2412 + 4.62726i −0.694076 + 0.225519i −0.634747 0.772720i \(-0.718896\pi\)
−0.0593282 + 0.998239i \(0.518896\pi\)
\(422\) 0 0
\(423\) 12.7322 + 1.33821i 0.619062 + 0.0650660i
\(424\) 0 0
\(425\) 19.4259 4.12909i 0.942292 0.200290i
\(426\) 0 0
\(427\) 0.997469 0.104838i 0.0482709 0.00507348i
\(428\) 0 0
\(429\) 9.72374 36.7167i 0.469467 1.77270i
\(430\) 0 0
\(431\) −32.6359 + 3.43017i −1.57202 + 0.165226i −0.850050 0.526702i \(-0.823429\pi\)
−0.721967 + 0.691927i \(0.756762\pi\)
\(432\) 0 0
\(433\) −6.60293 + 1.40350i −0.317317 + 0.0674477i −0.363817 0.931471i \(-0.618527\pi\)
0.0465001 + 0.998918i \(0.485193\pi\)
\(434\) 0 0
\(435\) 55.9920 + 5.88499i 2.68461 + 0.282164i
\(436\) 0 0
\(437\) 3.73459 1.21344i 0.178650 0.0580468i
\(438\) 0 0
\(439\) 14.2267 24.6413i 0.679002 1.17607i −0.296280 0.955101i \(-0.595746\pi\)
0.975282 0.220965i \(-0.0709206\pi\)
\(440\) 0 0
\(441\) −22.0641 −1.05067
\(442\) 0 0
\(443\) −0.0925713 0.284905i −0.00439820 0.0135363i 0.948833 0.315777i \(-0.102265\pi\)
−0.953232 + 0.302241i \(0.902265\pi\)
\(444\) 0 0
\(445\) 7.25606 3.23060i 0.343970 0.153145i
\(446\) 0 0
\(447\) −1.56896 0.509785i −0.0742091 0.0241120i
\(448\) 0 0
\(449\) 5.54292 12.4496i 0.261587 0.587533i −0.734231 0.678900i \(-0.762457\pi\)
0.995817 + 0.0913668i \(0.0291236\pi\)
\(450\) 0 0
\(451\) −3.54717 + 25.4663i −0.167030 + 1.19916i
\(452\) 0 0
\(453\) 15.5475 1.63411i 0.730486 0.0767771i
\(454\) 0 0
\(455\) −20.1553 + 33.6723i −0.944895 + 1.57858i
\(456\) 0 0
\(457\) −8.54490 19.1922i −0.399714 0.897771i −0.995512 0.0946372i \(-0.969831\pi\)
0.595798 0.803134i \(-0.296836\pi\)
\(458\) 0 0
\(459\) 25.7010 28.5438i 1.19962 1.33231i
\(460\) 0 0
\(461\) −30.4824 + 17.5990i −1.41971 + 0.819669i −0.996273 0.0862581i \(-0.972509\pi\)
−0.423435 + 0.905927i \(0.639176\pi\)
\(462\) 0 0
\(463\) 20.5976i 0.957253i −0.878018 0.478627i \(-0.841135\pi\)
0.878018 0.478627i \(-0.158865\pi\)
\(464\) 0 0
\(465\) −111.758 23.7549i −5.18266 1.10161i
\(466\) 0 0
\(467\) −10.9634 7.96537i −0.507325 0.368593i 0.304483 0.952518i \(-0.401516\pi\)
−0.811808 + 0.583925i \(0.801516\pi\)
\(468\) 0 0
\(469\) −10.3426 + 31.8313i −0.477578 + 1.46983i
\(470\) 0 0
\(471\) −2.54962 24.2580i −0.117480 1.11775i
\(472\) 0 0
\(473\) 22.6652 + 33.5137i 1.04215 + 1.54096i
\(474\) 0 0
\(475\) −2.72488 + 6.12019i −0.125026 + 0.280814i
\(476\) 0 0
\(477\) 36.0251 7.65737i 1.64947 0.350607i
\(478\) 0 0
\(479\) 6.95351 + 15.6179i 0.317714 + 0.713598i 0.999845 0.0176328i \(-0.00561300\pi\)
−0.682130 + 0.731231i \(0.738946\pi\)
\(480\) 0 0
\(481\) 10.1487 + 14.4421i 0.462743 + 0.658504i
\(482\) 0 0
\(483\) 34.4274 + 19.8767i 1.56650 + 0.904419i
\(484\) 0 0
\(485\) −25.5404 44.2373i −1.15973 2.00871i
\(486\) 0 0
\(487\) 22.0544 + 19.8579i 0.999380 + 0.899846i 0.994973 0.100144i \(-0.0319305\pi\)
0.00440721 + 0.999990i \(0.498597\pi\)
\(488\) 0 0
\(489\) 25.8478 35.5765i 1.16888 1.60882i
\(490\) 0 0
\(491\) −17.9463 19.9314i −0.809905 0.899491i 0.186650 0.982427i \(-0.440237\pi\)
−0.996555 + 0.0829355i \(0.973570\pi\)
\(492\) 0 0
\(493\) −12.3920 + 9.00330i −0.558106 + 0.405488i
\(494\) 0 0
\(495\) 66.6553 45.0787i 2.99593 2.02614i
\(496\) 0 0
\(497\) 3.16667 + 30.1288i 0.142045 + 1.35146i
\(498\) 0 0
\(499\) 12.1355 + 3.94308i 0.543262 + 0.176516i 0.567776 0.823183i \(-0.307804\pi\)
−0.0245143 + 0.999699i \(0.507804\pi\)
\(500\) 0 0
\(501\) 42.4401 + 4.46063i 1.89608 + 0.199286i
\(502\) 0 0
\(503\) −18.3027 + 20.3273i −0.816079 + 0.906348i −0.997020 0.0771464i \(-0.975419\pi\)
0.180941 + 0.983494i \(0.442086\pi\)
\(504\) 0 0
\(505\) 39.9488 + 23.0645i 1.77770 + 1.02636i
\(506\) 0 0
\(507\) 37.1731 + 17.9759i 1.65091 + 0.798338i
\(508\) 0 0
\(509\) −3.56415 + 16.7680i −0.157978 + 0.743229i 0.825818 + 0.563937i \(0.190714\pi\)
−0.983796 + 0.179292i \(0.942619\pi\)
\(510\) 0 0
\(511\) 1.80492 17.1727i 0.0798450 0.759674i
\(512\) 0 0
\(513\) 2.69387 + 12.6737i 0.118937 + 0.559556i
\(514\) 0 0
\(515\) 13.3476 + 18.3713i 0.588164 + 0.809538i
\(516\) 0 0
\(517\) −5.55107 + 2.25071i −0.244136 + 0.0989862i
\(518\) 0 0
\(519\) −17.1866 + 12.4868i −0.754408 + 0.548109i
\(520\) 0 0
\(521\) 0.741495 2.28209i 0.0324855 0.0999801i −0.933499 0.358580i \(-0.883261\pi\)
0.965985 + 0.258600i \(0.0832611\pi\)
\(522\) 0 0
\(523\) 5.51711 2.45638i 0.241246 0.107410i −0.282552 0.959252i \(-0.591181\pi\)
0.523799 + 0.851842i \(0.324514\pi\)
\(524\) 0 0
\(525\) −64.5027 + 20.9582i −2.81513 + 0.914690i
\(526\) 0 0
\(527\) 26.9201 15.5423i 1.17266 0.677035i
\(528\) 0 0
\(529\) 3.75497 + 6.50380i 0.163260 + 0.282774i
\(530\) 0 0
\(531\) −0.0675102 + 0.317610i −0.00292969 + 0.0137831i
\(532\) 0 0
\(533\) −26.4445 9.05582i −1.14544 0.392251i
\(534\) 0 0
\(535\) 23.2121 20.9002i 1.00354 0.903596i
\(536\) 0 0
\(537\) −21.1957 9.43692i −0.914661 0.407233i
\(538\) 0 0
\(539\) 9.10906 4.85773i 0.392355 0.209237i
\(540\) 0 0
\(541\) 14.8889 + 20.4928i 0.640124 + 0.881055i 0.998622 0.0524754i \(-0.0167111\pi\)
−0.358498 + 0.933530i \(0.616711\pi\)
\(542\) 0 0
\(543\) 53.7104 + 59.6514i 2.30493 + 2.55989i
\(544\) 0 0
\(545\) 15.6683 + 11.3837i 0.671155 + 0.487622i
\(546\) 0 0
\(547\) 6.80255 + 20.9361i 0.290856 + 0.895162i 0.984582 + 0.174923i \(0.0559678\pi\)
−0.693726 + 0.720239i \(0.744032\pi\)
\(548\) 0 0
\(549\) 1.11785 1.93617i 0.0477086 0.0826336i
\(550\) 0 0
\(551\) 5.16704i 0.220123i
\(552\) 0 0
\(553\) 20.0793 + 18.0795i 0.853859 + 0.768818i
\(554\) 0 0
\(555\) −5.56317 + 52.9300i −0.236143 + 2.24675i
\(556\) 0 0
\(557\) −6.24470 + 5.62275i −0.264596 + 0.238244i −0.790740 0.612152i \(-0.790304\pi\)
0.526144 + 0.850396i \(0.323637\pi\)
\(558\) 0 0
\(559\) −40.4575 + 17.2536i −1.71117 + 0.729749i
\(560\) 0 0
\(561\) −7.50055 + 30.2412i −0.316673 + 1.27679i
\(562\) 0 0
\(563\) 30.7267 + 13.6804i 1.29498 + 0.576560i 0.934419 0.356177i \(-0.115920\pi\)
0.360557 + 0.932737i \(0.382587\pi\)
\(564\) 0 0
\(565\) −6.91008 32.5093i −0.290709 1.36768i
\(566\) 0 0
\(567\) −37.3503 + 51.4083i −1.56857 + 2.15895i
\(568\) 0 0
\(569\) −34.0409 7.23561i −1.42707 0.303332i −0.571320 0.820727i \(-0.693569\pi\)
−0.855747 + 0.517395i \(0.826902\pi\)
\(570\) 0 0
\(571\) 39.1759 1.63946 0.819731 0.572748i \(-0.194123\pi\)
0.819731 + 0.572748i \(0.194123\pi\)
\(572\) 0 0
\(573\) 30.7153 1.28315
\(574\) 0 0
\(575\) 25.8497 + 5.49452i 1.07801 + 0.229137i
\(576\) 0 0
\(577\) 1.64454 2.26351i 0.0684630 0.0942313i −0.773412 0.633903i \(-0.781452\pi\)
0.841875 + 0.539672i \(0.181452\pi\)
\(578\) 0 0
\(579\) 8.48452 + 39.9165i 0.352605 + 1.65887i
\(580\) 0 0
\(581\) −27.5144 12.2502i −1.14149 0.508223i
\(582\) 0 0
\(583\) −13.1869 + 11.0928i −0.546147 + 0.459415i
\(584\) 0 0
\(585\) 34.3156 + 80.4657i 1.41878 + 3.32685i
\(586\) 0 0
\(587\) −4.85272 + 4.36940i −0.200293 + 0.180345i −0.763173 0.646194i \(-0.776360\pi\)
0.562880 + 0.826538i \(0.309693\pi\)
\(588\) 0 0
\(589\) −1.09607 + 10.4284i −0.0451629 + 0.429696i
\(590\) 0 0
\(591\) −19.8746 17.8952i −0.817531 0.736109i
\(592\) 0 0
\(593\) 3.61782i 0.148566i −0.997237 0.0742831i \(-0.976333\pi\)
0.997237 0.0742831i \(-0.0236669\pi\)
\(594\) 0 0
\(595\) 16.0960 27.8791i 0.659872 1.14293i
\(596\) 0 0
\(597\) 16.8597 + 51.8889i 0.690022 + 2.12367i
\(598\) 0 0
\(599\) −34.4119 25.0017i −1.40603 1.02154i −0.993884 0.110425i \(-0.964779\pi\)
−0.412148 0.911117i \(-0.635221\pi\)
\(600\) 0 0
\(601\) 14.7791 + 16.4138i 0.602852 + 0.669535i 0.964898 0.262625i \(-0.0845884\pi\)
−0.362046 + 0.932160i \(0.617922\pi\)
\(602\) 0 0
\(603\) 43.8525 + 60.3578i 1.78581 + 2.45796i
\(604\) 0 0
\(605\) −17.5936 + 33.2857i −0.715282 + 1.35326i
\(606\) 0 0
\(607\) 42.1458 + 18.7645i 1.71064 + 0.761628i 0.998205 + 0.0598949i \(0.0190766\pi\)
0.712440 + 0.701733i \(0.247590\pi\)
\(608\) 0 0
\(609\) 38.8733 35.0017i 1.57523 1.41834i
\(610\) 0 0
\(611\) −1.25327 6.39008i −0.0507018 0.258515i
\(612\) 0 0
\(613\) 4.44060 20.8914i 0.179354 0.843795i −0.792805 0.609475i \(-0.791380\pi\)
0.972160 0.234320i \(-0.0752863\pi\)
\(614\) 0 0
\(615\) −42.1398 72.9883i −1.69924 2.94317i
\(616\) 0 0
\(617\) −5.99996 + 3.46408i −0.241549 + 0.139458i −0.615889 0.787833i \(-0.711203\pi\)
0.374339 + 0.927292i \(0.377870\pi\)
\(618\) 0 0
\(619\) −0.0599154 + 0.0194677i −0.00240820 + 0.000782473i −0.310221 0.950665i \(-0.600403\pi\)
0.307813 + 0.951447i \(0.400403\pi\)
\(620\) 0 0
\(621\) 46.6922 20.7887i 1.87369 0.834222i
\(622\) 0 0
\(623\) 2.28045 7.01849i 0.0913641 0.281190i
\(624\) 0 0
\(625\) 10.9109 7.92722i 0.436435 0.317089i
\(626\) 0 0
\(627\) −6.76587 8.04317i −0.270203 0.321213i
\(628\) 0 0
\(629\) −8.51094 11.7143i −0.339353 0.467080i
\(630\) 0 0
\(631\) −4.90232 23.0636i −0.195158 0.918148i −0.961306 0.275483i \(-0.911162\pi\)
0.766148 0.642665i \(-0.222171\pi\)
\(632\) 0 0
\(633\) 5.07061 48.2436i 0.201539 1.91751i
\(634\) 0 0
\(635\) 0.249243 1.17260i 0.00989091 0.0465331i
\(636\) 0 0
\(637\) 3.29926 + 10.7268i 0.130721 + 0.425011i
\(638\) 0 0
\(639\) 58.4825 + 33.7649i 2.31353 + 1.33572i
\(640\) 0 0
\(641\) −24.8416 + 27.5894i −0.981185 + 1.08972i 0.0147720 + 0.999891i \(0.495298\pi\)
−0.995957 + 0.0898260i \(0.971369\pi\)
\(642\) 0 0
\(643\) −33.3906 3.50949i −1.31680 0.138401i −0.580056 0.814576i \(-0.696969\pi\)
−0.736741 + 0.676175i \(0.763636\pi\)
\(644\) 0 0
\(645\) −126.124 40.9802i −4.96613 1.61359i
\(646\) 0 0
\(647\) −2.85489 27.1624i −0.112237 1.06787i −0.895160 0.445746i \(-0.852938\pi\)
0.782922 0.622119i \(-0.213728\pi\)
\(648\) 0 0
\(649\) −0.0420553 0.145987i −0.00165082 0.00573051i
\(650\) 0 0
\(651\) −85.8814 + 62.3965i −3.36596 + 2.44551i
\(652\) 0 0
\(653\) −22.7820 25.3020i −0.891530 0.990144i 0.108462 0.994101i \(-0.465407\pi\)
−0.999992 + 0.00395612i \(0.998741\pi\)
\(654\) 0 0
\(655\) 36.4970 50.2339i 1.42606 1.96280i
\(656\) 0 0
\(657\) −28.6038 25.7550i −1.11594 1.00480i
\(658\) 0 0
\(659\) 24.6267 + 42.6547i 0.959320 + 1.66159i 0.724158 + 0.689634i \(0.242229\pi\)
0.235161 + 0.971956i \(0.424438\pi\)
\(660\) 0 0
\(661\) 12.6537 + 7.30560i 0.492171 + 0.284155i 0.725475 0.688249i \(-0.241620\pi\)
−0.233304 + 0.972404i \(0.574954\pi\)
\(662\) 0 0
\(663\) −30.7223 14.2632i −1.19316 0.553935i
\(664\) 0 0
\(665\) 4.41693 + 9.92058i 0.171281 + 0.384704i
\(666\) 0 0
\(667\) −19.9371 + 4.23777i −0.771968 + 0.164087i
\(668\) 0 0
\(669\) 19.9052 44.7078i 0.769579 1.72850i
\(670\) 0 0
\(671\) −0.0352225 + 1.04545i −0.00135975 + 0.0403591i
\(672\) 0 0
\(673\) −3.91442 37.2433i −0.150890 1.43562i −0.763792 0.645463i \(-0.776665\pi\)
0.612902 0.790159i \(-0.290002\pi\)
\(674\) 0 0
\(675\) −26.9460 + 82.9312i −1.03715 + 3.19203i
\(676\) 0 0
\(677\) 14.1743 + 10.2982i 0.544762 + 0.395792i 0.825850 0.563889i \(-0.190696\pi\)
−0.281089 + 0.959682i \(0.590696\pi\)
\(678\) 0 0
\(679\) −46.4226 9.86742i −1.78153 0.378677i
\(680\) 0 0
\(681\) 66.0873i 2.53247i
\(682\) 0 0
\(683\) 13.9971 8.08121i 0.535583 0.309219i −0.207704 0.978192i \(-0.566599\pi\)
0.743287 + 0.668973i \(0.233266\pi\)
\(684\) 0 0
\(685\) 10.8675 12.0696i 0.415226 0.461155i
\(686\) 0 0
\(687\) −9.76105 21.9237i −0.372407 0.836440i
\(688\) 0 0
\(689\) −9.10962 16.3692i −0.347049 0.623615i
\(690\) 0 0
\(691\) 11.5131 1.21007i 0.437978 0.0460333i 0.117026 0.993129i \(-0.462664\pi\)
0.320952 + 0.947096i \(0.395997\pi\)
\(692\) 0 0
\(693\) 10.3141 74.0482i 0.391800 2.81286i
\(694\) 0 0
\(695\) −17.1444 + 38.5071i −0.650326 + 1.46066i
\(696\) 0 0
\(697\) 21.8072 + 7.08559i 0.826007 + 0.268386i
\(698\) 0 0
\(699\) −2.63669 + 1.17393i −0.0997288 + 0.0444021i
\(700\) 0 0
\(701\) 1.76226 + 5.42369i 0.0665598 + 0.204850i 0.978805 0.204795i \(-0.0656527\pi\)
−0.912245 + 0.409645i \(0.865653\pi\)
\(702\) 0 0
\(703\) 4.88447 0.184221
\(704\) 0 0
\(705\) 9.81704 17.0036i 0.369731 0.640393i
\(706\) 0 0
\(707\) 40.7612 13.2441i 1.53298 0.498096i
\(708\) 0 0
\(709\) −40.6633 4.27388i −1.52714 0.160509i −0.696598 0.717462i \(-0.745304\pi\)
−0.830544 + 0.556953i \(0.811970\pi\)
\(710\) 0 0
\(711\) 58.9125 12.5222i 2.20939 0.469620i
\(712\) 0 0
\(713\) 41.1373 4.32370i 1.54060 0.161924i
\(714\) 0 0
\(715\) −31.8828 25.6649i −1.19235 0.959812i
\(716\) 0 0
\(717\) 5.44069 0.571840i 0.203186 0.0213558i
\(718\) 0 0
\(719\) 12.2387 2.60141i 0.456425 0.0970162i 0.0260388 0.999661i \(-0.491711\pi\)
0.430386 + 0.902645i \(0.358377\pi\)
\(720\) 0 0
\(721\) 20.9829 + 2.20539i 0.781442 + 0.0821329i
\(722\) 0 0
\(723\) 27.9468 9.08048i 1.03935 0.337707i
\(724\) 0 0
\(725\) 17.3871 30.1153i 0.645739 1.11845i
\(726\) 0 0
\(727\) −40.5143 −1.50259 −0.751295 0.659966i \(-0.770571\pi\)
−0.751295 + 0.659966i \(0.770571\pi\)
\(728\) 0 0
\(729\) 5.53192 + 17.0255i 0.204886 + 0.630574i
\(730\) 0 0
\(731\) 32.9605 14.6750i 1.21909 0.542773i
\(732\) 0 0
\(733\) 7.51325 + 2.44120i 0.277508 + 0.0901679i 0.444465 0.895796i \(-0.353394\pi\)
−0.166956 + 0.985964i \(0.553394\pi\)
\(734\) 0 0
\(735\) −13.7632 + 30.9127i −0.507663 + 1.14023i
\(736\) 0 0
\(737\) −31.3930 15.2637i −1.15638 0.562245i
\(738\) 0 0
\(739\) 31.7455 3.33659i 1.16778 0.122739i 0.499273 0.866445i \(-0.333601\pi\)
0.668506 + 0.743706i \(0.266934\pi\)
\(740\) 0 0
\(741\) 9.98413 5.55628i 0.366776 0.204115i
\(742\) 0 0
\(743\) −11.6547 26.1770i −0.427571 0.960339i −0.990961 0.134149i \(-0.957170\pi\)
0.563391 0.826191i \(-0.309497\pi\)
\(744\) 0 0
\(745\) −1.18950 + 1.32108i −0.0435800 + 0.0484005i
\(746\) 0 0
\(747\) −58.1416 + 33.5681i −2.12729 + 1.22819i
\(748\) 0 0
\(749\) 29.0206i 1.06039i
\(750\) 0 0
\(751\) 7.89098 + 1.67728i 0.287946 + 0.0612048i 0.349620 0.936892i \(-0.386311\pi\)
−0.0616743 + 0.998096i \(0.519644\pi\)
\(752\) 0 0
\(753\) −9.26034 6.72803i −0.337466 0.245183i
\(754\) 0 0
\(755\) 5.20569 16.0215i 0.189455 0.583081i
\(756\) 0 0
\(757\) 4.72565 + 44.9615i 0.171757 + 1.63416i 0.652851 + 0.757486i \(0.273573\pi\)
−0.481094 + 0.876669i \(0.659761\pi\)
\(758\) 0 0
\(759\) −25.4857 + 32.7029i −0.925072 + 1.18704i
\(760\) 0 0
\(761\) −10.5802 + 23.7634i −0.383531 + 0.861424i 0.613873 + 0.789405i \(0.289611\pi\)
−0.997403 + 0.0720189i \(0.977056\pi\)
\(762\) 0 0
\(763\) 17.6009 3.74118i 0.637195 0.135440i
\(764\) 0 0
\(765\) −29.1870 65.5550i −1.05526 2.37015i
\(766\) 0 0
\(767\) 0.164506 0.0146714i 0.00593998 0.000529755i
\(768\) 0 0
\(769\) −8.07767 4.66365i −0.291288 0.168175i 0.347234 0.937778i \(-0.387121\pi\)
−0.638523 + 0.769603i \(0.720454\pi\)
\(770\) 0 0
\(771\) 15.0769 + 26.1140i 0.542983 + 0.940474i
\(772\) 0 0
\(773\) 0.243136 + 0.218921i 0.00874499 + 0.00787402i 0.673492 0.739195i \(-0.264794\pi\)
−0.664747 + 0.747069i \(0.731460\pi\)
\(774\) 0 0
\(775\) −41.4799 + 57.0922i −1.49000 + 2.05081i
\(776\) 0 0
\(777\) 33.0876 + 36.7475i 1.18701 + 1.31831i
\(778\) 0 0
\(779\) −6.25764 + 4.54644i −0.224203 + 0.162893i
\(780\) 0 0
\(781\) −31.5781 1.06391i −1.12995 0.0380696i
\(782\) 0 0
\(783\) −7.02997 66.8857i −0.251231 2.39030i
\(784\) 0 0
\(785\) −24.9976 8.12220i −0.892201 0.289894i
\(786\) 0 0
\(787\) 2.57031 + 0.270151i 0.0916217 + 0.00962983i 0.150228 0.988651i \(-0.451999\pi\)
−0.0586066 + 0.998281i \(0.518666\pi\)
\(788\) 0 0
\(789\) 25.7981 28.6517i 0.918437 1.02003i
\(790\) 0 0
\(791\) −26.7425 15.4398i −0.950852 0.548975i
\(792\) 0 0
\(793\) −1.10845 0.253942i −0.0393623 0.00901776i
\(794\) 0 0
\(795\) 11.7436 55.2492i 0.416501 1.95949i
\(796\) 0 0
\(797\) −3.32268 + 31.6132i −0.117695 + 1.11980i 0.763094 + 0.646288i \(0.223680\pi\)
−0.880789 + 0.473509i \(0.842987\pi\)
\(798\) 0 0
\(799\) 1.11061 + 5.22500i 0.0392905 + 0.184847i
\(800\) 0 0
\(801\) −9.66904 13.3083i −0.341639 0.470225i
\(802\) 0 0
\(803\) 17.4793 + 4.33529i 0.616832 + 0.152989i
\(804\) 0 0
\(805\) 34.6562 25.1792i 1.22147 0.887450i
\(806\) 0 0
\(807\) −11.3107 + 34.8107i −0.398155 + 1.22539i
\(808\) 0 0
\(809\) −50.5313 + 22.4980i −1.77658 + 0.790987i −0.793320 + 0.608805i \(0.791649\pi\)
−0.983265 + 0.182181i \(0.941684\pi\)
\(810\) 0 0
\(811\) −43.5801 + 14.1600i −1.53030 + 0.497226i −0.948682 0.316233i \(-0.897582\pi\)
−0.581622 + 0.813459i \(0.697582\pi\)
\(812\) 0 0
\(813\) −37.2760 + 21.5213i −1.30733 + 0.754785i
\(814\) 0 0
\(815\) −23.6933 41.0380i −0.829939 1.43750i
\(816\) 0 0
\(817\) −2.53047 + 11.9049i −0.0885299 + 0.416501i
\(818\) 0 0
\(819\) 76.8925 + 26.3315i 2.68684 + 0.920099i
\(820\) 0 0
\(821\) 1.65808 1.49294i 0.0578675 0.0521041i −0.639690 0.768633i \(-0.720937\pi\)
0.697557 + 0.716529i \(0.254270\pi\)
\(822\) 0 0
\(823\) −8.40961 3.74420i −0.293140 0.130515i 0.254897 0.966968i \(-0.417958\pi\)
−0.548038 + 0.836454i \(0.684625\pi\)
\(824\) 0 0
\(825\) −12.3686 69.6455i −0.430619 2.42474i
\(826\) 0 0
\(827\) −24.2642 33.3968i −0.843748 1.16132i −0.985206 0.171376i \(-0.945179\pi\)
0.141457 0.989944i \(-0.454821\pi\)
\(828\) 0 0
\(829\) −5.99277 6.65565i −0.208138 0.231160i 0.630033 0.776568i \(-0.283041\pi\)
−0.838171 + 0.545408i \(0.816375\pi\)
\(830\) 0 0
\(831\) 23.2214 + 16.8714i 0.805543 + 0.585261i
\(832\) 0 0
\(833\) −2.84485 8.75556i −0.0985683 0.303362i
\(834\) 0 0
\(835\) 22.9923 39.8238i 0.795680 1.37816i
\(836\) 0 0
\(837\) 136.484i 4.71758i
\(838\) 0 0
\(839\) −37.8876 34.1141i −1.30802 1.17775i −0.971757 0.235983i \(-0.924169\pi\)
−0.336267 0.941767i \(-0.609164\pi\)
\(840\) 0 0
\(841\) 0.227845 2.16780i 0.00785671 0.0747516i
\(842\) 0 0
\(843\) 45.3178 40.8044i 1.56083 1.40538i
\(844\) 0 0
\(845\) 33.9885 28.7152i 1.16924 0.987833i
\(846\) 0 0
\(847\) 12.0447 + 32.8413i 0.413861 + 1.12844i
\(848\) 0 0
\(849\) −34.2464 15.2475i −1.17533 0.523292i
\(850\) 0 0
\(851\) −4.00602 18.8468i −0.137325 0.646061i
\(852\) 0 0
\(853\) −11.0716 + 15.2388i −0.379086 + 0.521767i −0.955342 0.295502i \(-0.904513\pi\)
0.576256 + 0.817269i \(0.304513\pi\)
\(854\) 0 0
\(855\) 23.6777 + 5.03284i 0.809759 + 0.172120i
\(856\) 0 0
\(857\) 32.7622 1.11914 0.559568 0.828784i \(-0.310967\pi\)
0.559568 + 0.828784i \(0.310967\pi\)
\(858\) 0 0
\(859\) −7.93483 −0.270733 −0.135366 0.990796i \(-0.543221\pi\)
−0.135366 + 0.990796i \(0.543221\pi\)
\(860\) 0 0
\(861\) −76.5938 16.2805i −2.61031 0.554839i
\(862\) 0 0
\(863\) −5.60377 + 7.71292i −0.190754 + 0.262551i −0.893672 0.448720i \(-0.851880\pi\)
0.702918 + 0.711271i \(0.251880\pi\)
\(864\) 0 0
\(865\) 4.75950 + 22.3917i 0.161828 + 0.761340i
\(866\) 0 0
\(867\) −23.9448 10.6609i −0.813207 0.362063i
\(868\) 0 0
\(869\) −21.5648 + 18.1402i −0.731536 + 0.615364i
\(870\) 0 0
\(871\) 22.7866 30.3450i 0.772095 1.02820i
\(872\) 0 0
\(873\) −78.6186 + 70.7885i −2.66084 + 2.39583i
\(874\) 0 0
\(875\) −1.95079 + 18.5606i −0.0659488 + 0.627461i
\(876\) 0 0
\(877\) 2.42540 + 2.18384i 0.0819000 + 0.0737431i 0.709064 0.705144i \(-0.249118\pi\)
−0.627164 + 0.778887i \(0.715784\pi\)
\(878\) 0 0
\(879\) 21.8030i 0.735397i
\(880\) 0 0
\(881\) 7.27662 12.6035i 0.245155 0.424622i −0.717020 0.697053i \(-0.754494\pi\)
0.962175 + 0.272431i \(0.0878276\pi\)
\(882\) 0 0
\(883\) −0.888577 2.73476i −0.0299030 0.0920319i 0.934991 0.354671i \(-0.115407\pi\)
−0.964894 + 0.262639i \(0.915407\pi\)
\(884\) 0 0
\(885\) 0.402873 + 0.292705i 0.0135424 + 0.00983916i
\(886\) 0 0
\(887\) 7.21445 + 8.01245i 0.242237 + 0.269032i 0.851988 0.523562i \(-0.175397\pi\)
−0.609750 + 0.792593i \(0.708730\pi\)
\(888\) 0 0
\(889\) −0.654681 0.901091i −0.0219573 0.0302216i
\(890\) 0 0
\(891\) −47.7297 45.9789i −1.59900 1.54035i
\(892\) 0 0
\(893\) −1.64616 0.732916i −0.0550865 0.0245261i
\(894\) 0 0
\(895\) −18.5798 + 16.7293i −0.621053 + 0.559199i
\(896\) 0 0
\(897\) −29.6275 33.9670i −0.989234 1.13412i
\(898\) 0 0
\(899\) 11.3163 53.2391i 0.377420 1.77562i
\(900\) 0 0
\(901\) 7.68356 + 13.3083i 0.255977 + 0.443364i
\(902\) 0 0
\(903\) −106.706 + 61.6068i −3.55096 + 2.05015i
\(904\) 0 0
\(905\) 82.2628 26.7288i 2.73451 0.888495i
\(906\) 0 0
\(907\) −15.2358 + 6.78339i −0.505895 + 0.225239i −0.643782 0.765209i \(-0.722636\pi\)
0.137887 + 0.990448i \(0.455969\pi\)
\(908\) 0 0
\(909\) 29.5223 90.8602i 0.979192 3.01364i
\(910\) 0 0
\(911\) 10.8814 7.90578i 0.360516 0.261930i −0.392751 0.919645i \(-0.628477\pi\)
0.753267 + 0.657715i \(0.228477\pi\)
\(912\) 0 0
\(913\) 16.6130 26.6592i 0.549811 0.882291i
\(914\) 0 0
\(915\) −2.01536 2.77390i −0.0666256 0.0917023i
\(916\) 0 0
\(917\) −11.9946 56.4300i −0.396096 1.86348i
\(918\) 0 0
\(919\) −5.42734 + 51.6377i −0.179031 + 1.70337i 0.424008 + 0.905659i \(0.360623\pi\)
−0.603039 + 0.797712i \(0.706044\pi\)
\(920\) 0 0
\(921\) −10.2078 + 48.0238i −0.336357 + 1.58244i
\(922\) 0 0
\(923\) 7.67040 33.4811i 0.252474 1.10204i
\(924\) 0 0
\(925\) 28.4684 + 16.4362i 0.936034 + 0.540420i
\(926\) 0 0
\(927\) 31.4694 34.9503i 1.03359 1.14792i
\(928\) 0 0
\(929\) −2.26200 0.237745i −0.0742137 0.00780017i 0.0673488 0.997729i \(-0.478546\pi\)
−0.141563 + 0.989929i \(0.545213\pi\)
\(930\) 0 0
\(931\) 2.95354 + 0.959663i 0.0967983 + 0.0314517i
\(932\) 0 0
\(933\) 10.4118 + 99.0615i 0.340867 + 3.24313i
\(934\) 0 0
\(935\) 26.4826 + 20.6382i 0.866074 + 0.674940i
\(936\) 0 0
\(937\) −5.38019 + 3.90894i −0.175763 + 0.127699i −0.672189 0.740380i \(-0.734646\pi\)
0.496425 + 0.868079i \(0.334646\pi\)
\(938\) 0 0
\(939\) 13.5716 + 15.0728i 0.442893 + 0.491882i
\(940\) 0 0
\(941\) 25.3574 34.9014i 0.826626 1.13775i −0.161915 0.986805i \(-0.551767\pi\)
0.988542 0.150949i \(-0.0482328\pi\)
\(942\) 0 0
\(943\) 22.6748 + 20.4164i 0.738392 + 0.664851i
\(944\) 0 0
\(945\) 70.6731 + 122.409i 2.29900 + 3.98198i
\(946\) 0 0
\(947\) −17.9419 10.3588i −0.583033 0.336614i 0.179305 0.983794i \(-0.442615\pi\)
−0.762338 + 0.647179i \(0.775949\pi\)
\(948\) 0 0
\(949\) −8.24406 + 17.7574i −0.267613 + 0.576429i
\(950\) 0 0
\(951\) 20.6469 + 46.3736i 0.669520 + 1.50377i
\(952\) 0 0
\(953\) −52.3457 + 11.1264i −1.69564 + 0.360420i −0.951511 0.307614i \(-0.900469\pi\)
−0.744131 + 0.668034i \(0.767136\pi\)
\(954\) 0 0
\(955\) 13.4623 30.2368i 0.435629 0.978439i
\(956\) 0 0
\(957\) 30.5629 + 45.1915i 0.987957 + 1.46083i
\(958\) 0 0
\(959\) −1.57732 15.0072i −0.0509344 0.484609i
\(960\) 0 0
\(961\) −24.5533 + 75.5672i −0.792041 + 2.43765i
\(962\) 0 0
\(963\) −52.3350 38.0236i −1.68647 1.22529i
\(964\) 0 0
\(965\) 43.0133 + 9.14276i 1.38465 + 0.294316i
\(966\) 0 0
\(967\) 32.1331i 1.03333i −0.856187 0.516666i \(-0.827173\pi\)
0.856187 0.516666i \(-0.172827\pi\)
\(968\) 0 0
\(969\) −8.11722 + 4.68648i −0.260763 + 0.150551i
\(970\) 0 0
\(971\) 5.31076 5.89819i 0.170430 0.189282i −0.651879 0.758323i \(-0.726019\pi\)
0.822309 + 0.569041i \(0.192686\pi\)
\(972\) 0 0
\(973\) 15.9291 + 35.7773i 0.510662 + 1.14697i
\(974\) 0 0
\(975\) 76.8877 + 1.21265i 2.46238 + 0.0388360i
\(976\) 0 0
\(977\) 19.3212 2.03074i 0.618140 0.0649691i 0.209717 0.977762i \(-0.432746\pi\)
0.408423 + 0.912793i \(0.366079\pi\)
\(978\) 0 0
\(979\) 6.92184 + 3.36549i 0.221223 + 0.107562i
\(980\) 0 0
\(981\) 16.3144 36.6427i 0.520878 1.16991i
\(982\) 0 0
\(983\) 22.2939 + 7.24372i 0.711064 + 0.231039i 0.642145 0.766584i \(-0.278045\pi\)
0.0689193 + 0.997622i \(0.478045\pi\)
\(984\) 0 0
\(985\) −26.3272 + 11.7216i −0.838855 + 0.373482i
\(986\) 0 0
\(987\) −5.63715 17.3494i −0.179433 0.552237i
\(988\) 0 0
\(989\) 48.0108 1.52665
\(990\) 0 0
\(991\) 8.08444 14.0027i 0.256811 0.444809i −0.708575 0.705635i \(-0.750662\pi\)
0.965386 + 0.260826i \(0.0839950\pi\)
\(992\) 0 0
\(993\) 53.4776 17.3759i 1.69706 0.551408i
\(994\) 0 0
\(995\) 58.4699 + 6.14543i 1.85362 + 0.194823i
\(996\) 0 0
\(997\) −52.4448 + 11.1475i −1.66094 + 0.353044i −0.940322 0.340286i \(-0.889476\pi\)
−0.720620 + 0.693330i \(0.756143\pi\)
\(998\) 0 0
\(999\) 63.2280 6.64553i 2.00045 0.210255i
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 572.2.bq.a.69.1 112
11.4 even 5 inner 572.2.bq.a.433.14 yes 112
13.10 even 6 inner 572.2.bq.a.465.14 yes 112
143.114 even 30 inner 572.2.bq.a.257.1 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.bq.a.69.1 112 1.1 even 1 trivial
572.2.bq.a.257.1 yes 112 143.114 even 30 inner
572.2.bq.a.433.14 yes 112 11.4 even 5 inner
572.2.bq.a.465.14 yes 112 13.10 even 6 inner