Properties

Label 572.2.bg.a.9.6
Level $572$
Weight $2$
Character 572.9
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(9,572)]
 
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, 18, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.bg (of order \(15\), 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 \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 9.6
Character \(\chi\) \(=\) 572.9
Dual form 572.2.bg.a.445.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0694093 - 0.660385i) q^{3} +(-0.596743 - 1.83659i) q^{5} +(-0.373949 + 3.55789i) q^{7} +(2.50315 - 0.532061i) q^{9} +O(q^{10})\) \(q+(-0.0694093 - 0.660385i) q^{3} +(-0.596743 - 1.83659i) q^{5} +(-0.373949 + 3.55789i) q^{7} +(2.50315 - 0.532061i) q^{9} +(0.296716 + 3.30333i) q^{11} +(3.59752 - 0.240552i) q^{13} +(-1.17143 + 0.521556i) q^{15} +(1.31217 - 1.45731i) q^{17} +(0.403370 + 0.179592i) q^{19} +2.37553 q^{21} +(2.75014 - 4.76339i) q^{23} +(1.02814 - 0.746987i) q^{25} +(-1.14069 - 3.51068i) q^{27} +(4.83102 - 2.15091i) q^{29} +(0.523420 - 1.61092i) q^{31} +(2.16087 - 0.425228i) q^{33} +(6.75752 - 1.43635i) q^{35} +(-7.83466 + 3.48821i) q^{37} +(-0.408558 - 2.35905i) q^{39} +(-0.663858 - 6.31619i) q^{41} +(4.33947 + 7.51618i) q^{43} +(-2.47091 - 4.27975i) q^{45} +(1.63874 - 1.19061i) q^{47} +(-5.67170 - 1.20556i) q^{49} +(-1.05346 - 0.765384i) q^{51} +(-2.00019 + 6.15594i) q^{53} +(5.88978 - 2.51618i) q^{55} +(0.0906021 - 0.278845i) q^{57} +(-0.660129 + 6.28071i) q^{59} +(-2.94065 + 3.26592i) q^{61} +(0.956963 + 9.10490i) q^{63} +(-2.58859 - 6.46360i) q^{65} +(-0.387949 + 0.671947i) q^{67} +(-3.33656 - 1.48553i) q^{69} +(-0.187482 + 0.208220i) q^{71} +(11.6845 + 8.48929i) q^{73} +(-0.564662 - 0.627121i) q^{75} +(-11.8638 - 0.179595i) q^{77} +(-0.115224 + 0.354622i) q^{79} +(4.77426 - 2.12564i) q^{81} +(0.852596 + 2.62402i) q^{83} +(-3.45950 - 1.54027i) q^{85} +(-1.75575 - 3.04104i) q^{87} +(3.10372 - 5.37580i) q^{89} +(-0.489431 + 12.8895i) q^{91} +(-1.10016 - 0.233846i) q^{93} +(0.0891276 - 0.847993i) q^{95} +(-4.66133 + 0.990797i) q^{97} +(2.50030 + 8.11085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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
\(3\) −0.0694093 0.660385i −0.0400735 0.381274i −0.996116 0.0880467i \(-0.971938\pi\)
0.956043 0.293227i \(-0.0947291\pi\)
\(4\) 0 0
\(5\) −0.596743 1.83659i −0.266872 0.821346i −0.991256 0.131950i \(-0.957876\pi\)
0.724385 0.689396i \(-0.242124\pi\)
\(6\) 0 0
\(7\) −0.373949 + 3.55789i −0.141339 + 1.34476i 0.662121 + 0.749397i \(0.269657\pi\)
−0.803460 + 0.595358i \(0.797010\pi\)
\(8\) 0 0
\(9\) 2.50315 0.532061i 0.834384 0.177354i
\(10\) 0 0
\(11\) 0.296716 + 3.30333i 0.0894631 + 0.995990i
\(12\) 0 0
\(13\) 3.59752 0.240552i 0.997772 0.0667171i
\(14\) 0 0
\(15\) −1.17143 + 0.521556i −0.302463 + 0.134665i
\(16\) 0 0
\(17\) 1.31217 1.45731i 0.318247 0.353449i −0.562702 0.826659i \(-0.690238\pi\)
0.880949 + 0.473211i \(0.156905\pi\)
\(18\) 0 0
\(19\) 0.403370 + 0.179592i 0.0925393 + 0.0412012i 0.452484 0.891772i \(-0.350538\pi\)
−0.359945 + 0.932974i \(0.617205\pi\)
\(20\) 0 0
\(21\) 2.37553 0.518384
\(22\) 0 0
\(23\) 2.75014 4.76339i 0.573444 0.993235i −0.422764 0.906240i \(-0.638940\pi\)
0.996209 0.0869952i \(-0.0277265\pi\)
\(24\) 0 0
\(25\) 1.02814 0.746987i 0.205628 0.149397i
\(26\) 0 0
\(27\) −1.14069 3.51068i −0.219526 0.675631i
\(28\) 0 0
\(29\) 4.83102 2.15091i 0.897098 0.399414i 0.0942162 0.995552i \(-0.469965\pi\)
0.802882 + 0.596138i \(0.203299\pi\)
\(30\) 0 0
\(31\) 0.523420 1.61092i 0.0940090 0.289330i −0.892985 0.450086i \(-0.851393\pi\)
0.986994 + 0.160756i \(0.0513933\pi\)
\(32\) 0 0
\(33\) 2.16087 0.425228i 0.376160 0.0740227i
\(34\) 0 0
\(35\) 6.75752 1.43635i 1.14223 0.242788i
\(36\) 0 0
\(37\) −7.83466 + 3.48821i −1.28801 + 0.573459i −0.932485 0.361208i \(-0.882364\pi\)
−0.355525 + 0.934667i \(0.615698\pi\)
\(38\) 0 0
\(39\) −0.408558 2.35905i −0.0654217 0.377750i
\(40\) 0 0
\(41\) −0.663858 6.31619i −0.103677 0.986423i −0.915445 0.402443i \(-0.868161\pi\)
0.811768 0.583980i \(-0.198505\pi\)
\(42\) 0 0
\(43\) 4.33947 + 7.51618i 0.661763 + 1.14621i 0.980152 + 0.198247i \(0.0635248\pi\)
−0.318389 + 0.947960i \(0.603142\pi\)
\(44\) 0 0
\(45\) −2.47091 4.27975i −0.368342 0.637987i
\(46\) 0 0
\(47\) 1.63874 1.19061i 0.239035 0.173669i −0.461818 0.886974i \(-0.652803\pi\)
0.700853 + 0.713306i \(0.252803\pi\)
\(48\) 0 0
\(49\) −5.67170 1.20556i −0.810242 0.172222i
\(50\) 0 0
\(51\) −1.05346 0.765384i −0.147514 0.107175i
\(52\) 0 0
\(53\) −2.00019 + 6.15594i −0.274747 + 0.845584i 0.714540 + 0.699595i \(0.246636\pi\)
−0.989286 + 0.145988i \(0.953364\pi\)
\(54\) 0 0
\(55\) 5.88978 2.51618i 0.794177 0.339282i
\(56\) 0 0
\(57\) 0.0906021 0.278845i 0.0120005 0.0369339i
\(58\) 0 0
\(59\) −0.660129 + 6.28071i −0.0859415 + 0.817679i 0.863630 + 0.504127i \(0.168186\pi\)
−0.949571 + 0.313552i \(0.898481\pi\)
\(60\) 0 0
\(61\) −2.94065 + 3.26592i −0.376512 + 0.418159i −0.901383 0.433023i \(-0.857447\pi\)
0.524871 + 0.851182i \(0.324114\pi\)
\(62\) 0 0
\(63\) 0.956963 + 9.10490i 0.120566 + 1.14711i
\(64\) 0 0
\(65\) −2.58859 6.46360i −0.321075 0.801711i
\(66\) 0 0
\(67\) −0.387949 + 0.671947i −0.0473955 + 0.0820914i −0.888750 0.458392i \(-0.848425\pi\)
0.841354 + 0.540484i \(0.181759\pi\)
\(68\) 0 0
\(69\) −3.33656 1.48553i −0.401674 0.178837i
\(70\) 0 0
\(71\) −0.187482 + 0.208220i −0.0222500 + 0.0247112i −0.754167 0.656683i \(-0.771959\pi\)
0.731917 + 0.681394i \(0.238626\pi\)
\(72\) 0 0
\(73\) 11.6845 + 8.48929i 1.36757 + 0.993597i 0.997923 + 0.0644241i \(0.0205210\pi\)
0.369646 + 0.929173i \(0.379479\pi\)
\(74\) 0 0
\(75\) −0.564662 0.627121i −0.0652015 0.0724136i
\(76\) 0 0
\(77\) −11.8638 0.179595i −1.35201 0.0204668i
\(78\) 0 0
\(79\) −0.115224 + 0.354622i −0.0129637 + 0.0398981i −0.957329 0.289000i \(-0.906677\pi\)
0.944365 + 0.328898i \(0.106677\pi\)
\(80\) 0 0
\(81\) 4.77426 2.12564i 0.530473 0.236182i
\(82\) 0 0
\(83\) 0.852596 + 2.62402i 0.0935845 + 0.288024i 0.986882 0.161442i \(-0.0516145\pi\)
−0.893298 + 0.449466i \(0.851614\pi\)
\(84\) 0 0
\(85\) −3.45950 1.54027i −0.375235 0.167065i
\(86\) 0 0
\(87\) −1.75575 3.04104i −0.188236 0.326034i
\(88\) 0 0
\(89\) 3.10372 5.37580i 0.328993 0.569833i −0.653319 0.757083i \(-0.726624\pi\)
0.982312 + 0.187249i \(0.0599573\pi\)
\(90\) 0 0
\(91\) −0.489431 + 12.8895i −0.0513063 + 1.35119i
\(92\) 0 0
\(93\) −1.10016 0.233846i −0.114081 0.0242487i
\(94\) 0 0
\(95\) 0.0891276 0.847993i 0.00914430 0.0870022i
\(96\) 0 0
\(97\) −4.66133 + 0.990797i −0.473286 + 0.100600i −0.438379 0.898790i \(-0.644447\pi\)
−0.0349078 + 0.999391i \(0.511114\pi\)
\(98\) 0 0
\(99\) 2.50030 + 8.11085i 0.251289 + 0.815172i
\(100\) 0 0
\(101\) −5.18901 5.76298i −0.516326 0.573438i 0.427443 0.904042i \(-0.359414\pi\)
−0.943770 + 0.330604i \(0.892748\pi\)
\(102\) 0 0
\(103\) −11.2330 8.16126i −1.10682 0.804153i −0.124662 0.992199i \(-0.539785\pi\)
−0.982160 + 0.188046i \(0.939785\pi\)
\(104\) 0 0
\(105\) −1.41758 4.36287i −0.138342 0.425772i
\(106\) 0 0
\(107\) 0.785366 + 7.47226i 0.0759242 + 0.722370i 0.964579 + 0.263794i \(0.0849738\pi\)
−0.888655 + 0.458577i \(0.848359\pi\)
\(108\) 0 0
\(109\) −1.99560 −0.191144 −0.0955718 0.995423i \(-0.530468\pi\)
−0.0955718 + 0.995423i \(0.530468\pi\)
\(110\) 0 0
\(111\) 2.84736 + 4.93178i 0.270260 + 0.468104i
\(112\) 0 0
\(113\) −6.52571 2.90543i −0.613887 0.273320i 0.0761473 0.997097i \(-0.475738\pi\)
−0.690035 + 0.723776i \(0.742405\pi\)
\(114\) 0 0
\(115\) −10.3895 2.20836i −0.968826 0.205930i
\(116\) 0 0
\(117\) 8.87714 2.51624i 0.820692 0.232626i
\(118\) 0 0
\(119\) 4.69425 + 5.21350i 0.430322 + 0.477920i
\(120\) 0 0
\(121\) −10.8239 + 1.96030i −0.983993 + 0.178209i
\(122\) 0 0
\(123\) −4.12504 + 0.876804i −0.371942 + 0.0790588i
\(124\) 0 0
\(125\) −9.79691 7.11787i −0.876262 0.636642i
\(126\) 0 0
\(127\) −8.06917 1.71516i −0.716023 0.152195i −0.164527 0.986373i \(-0.552610\pi\)
−0.551497 + 0.834177i \(0.685943\pi\)
\(128\) 0 0
\(129\) 4.66238 3.38741i 0.410499 0.298245i
\(130\) 0 0
\(131\) 6.93275 0.605717 0.302859 0.953035i \(-0.402059\pi\)
0.302859 + 0.953035i \(0.402059\pi\)
\(132\) 0 0
\(133\) −0.789807 + 1.36799i −0.0684849 + 0.118619i
\(134\) 0 0
\(135\) −5.76697 + 4.18995i −0.496342 + 0.360614i
\(136\) 0 0
\(137\) 9.45614 10.5021i 0.807892 0.897255i −0.188504 0.982072i \(-0.560364\pi\)
0.996397 + 0.0848171i \(0.0270306\pi\)
\(138\) 0 0
\(139\) 1.55568 14.8013i 0.131951 1.25543i −0.705416 0.708793i \(-0.749240\pi\)
0.837368 0.546640i \(-0.184093\pi\)
\(140\) 0 0
\(141\) −0.900007 0.999559i −0.0757943 0.0841781i
\(142\) 0 0
\(143\) 1.86206 + 11.8124i 0.155713 + 0.987802i
\(144\) 0 0
\(145\) −6.83321 7.58905i −0.567467 0.630236i
\(146\) 0 0
\(147\) −0.402463 + 3.82918i −0.0331946 + 0.315826i
\(148\) 0 0
\(149\) −8.38364 + 9.31097i −0.686814 + 0.762784i −0.981219 0.192896i \(-0.938212\pi\)
0.294405 + 0.955681i \(0.404879\pi\)
\(150\) 0 0
\(151\) −8.42520 + 6.12126i −0.685633 + 0.498141i −0.875222 0.483722i \(-0.839284\pi\)
0.189589 + 0.981864i \(0.439284\pi\)
\(152\) 0 0
\(153\) 2.50917 4.34601i 0.202855 0.351354i
\(154\) 0 0
\(155\) −3.27094 −0.262728
\(156\) 0 0
\(157\) −16.1665 + 11.7457i −1.29023 + 0.937405i −0.999810 0.0194946i \(-0.993794\pi\)
−0.290418 + 0.956900i \(0.593794\pi\)
\(158\) 0 0
\(159\) 4.20412 + 0.893614i 0.333409 + 0.0708682i
\(160\) 0 0
\(161\) 15.9192 + 11.5660i 1.25461 + 0.911526i
\(162\) 0 0
\(163\) −17.9456 + 3.81446i −1.40561 + 0.298771i −0.847411 0.530937i \(-0.821840\pi\)
−0.558197 + 0.829709i \(0.688507\pi\)
\(164\) 0 0
\(165\) −2.07045 3.71488i −0.161185 0.289203i
\(166\) 0 0
\(167\) −14.3987 15.9914i −1.11421 1.23745i −0.968738 0.248087i \(-0.920198\pi\)
−0.145468 0.989363i \(-0.546469\pi\)
\(168\) 0 0
\(169\) 12.8843 1.73078i 0.991098 0.133137i
\(170\) 0 0
\(171\) 1.10525 + 0.234928i 0.0845205 + 0.0179654i
\(172\) 0 0
\(173\) 3.01956 + 1.34439i 0.229573 + 0.102212i 0.518300 0.855199i \(-0.326565\pi\)
−0.288727 + 0.957412i \(0.593232\pi\)
\(174\) 0 0
\(175\) 2.27323 + 3.93734i 0.171840 + 0.297635i
\(176\) 0 0
\(177\) 4.19351 0.315203
\(178\) 0 0
\(179\) 1.89275 + 18.0083i 0.141471 + 1.34600i 0.802952 + 0.596043i \(0.203261\pi\)
−0.661481 + 0.749962i \(0.730072\pi\)
\(180\) 0 0
\(181\) 1.42543 + 4.38703i 0.105952 + 0.326086i 0.989953 0.141399i \(-0.0451602\pi\)
−0.884001 + 0.467485i \(0.845160\pi\)
\(182\) 0 0
\(183\) 2.36088 + 1.71528i 0.174521 + 0.126797i
\(184\) 0 0
\(185\) 11.0817 + 12.3075i 0.814741 + 0.904862i
\(186\) 0 0
\(187\) 5.20330 + 3.90210i 0.380503 + 0.285350i
\(188\) 0 0
\(189\) 12.9172 2.74563i 0.939587 0.199715i
\(190\) 0 0
\(191\) 1.68965 16.0759i 0.122258 1.16321i −0.745598 0.666396i \(-0.767836\pi\)
0.867856 0.496815i \(-0.165497\pi\)
\(192\) 0 0
\(193\) −10.8562 2.30757i −0.781450 0.166102i −0.200121 0.979771i \(-0.564134\pi\)
−0.581328 + 0.813669i \(0.697467\pi\)
\(194\) 0 0
\(195\) −4.08880 + 2.15810i −0.292805 + 0.154545i
\(196\) 0 0
\(197\) 2.00057 3.46508i 0.142534 0.246877i −0.785916 0.618333i \(-0.787808\pi\)
0.928450 + 0.371457i \(0.121142\pi\)
\(198\) 0 0
\(199\) 5.18148 + 8.97458i 0.367305 + 0.636191i 0.989143 0.146955i \(-0.0469472\pi\)
−0.621838 + 0.783146i \(0.713614\pi\)
\(200\) 0 0
\(201\) 0.470671 + 0.209556i 0.0331986 + 0.0147810i
\(202\) 0 0
\(203\) 5.84614 + 17.9926i 0.410319 + 1.26283i
\(204\) 0 0
\(205\) −11.2041 + 4.98837i −0.782526 + 0.348403i
\(206\) 0 0
\(207\) 4.34961 13.3867i 0.302319 0.930442i
\(208\) 0 0
\(209\) −0.473564 + 1.38575i −0.0327571 + 0.0958542i
\(210\) 0 0
\(211\) −16.9078 18.7780i −1.16398 1.29273i −0.948700 0.316177i \(-0.897601\pi\)
−0.215278 0.976553i \(-0.569066\pi\)
\(212\) 0 0
\(213\) 0.150519 + 0.109358i 0.0103134 + 0.00749309i
\(214\) 0 0
\(215\) 11.2146 12.4550i 0.764827 0.849426i
\(216\) 0 0
\(217\) 5.53575 + 2.46467i 0.375791 + 0.167313i
\(218\) 0 0
\(219\) 4.79519 8.30551i 0.324029 0.561235i
\(220\) 0 0
\(221\) 4.36998 5.55833i 0.293957 0.373894i
\(222\) 0 0
\(223\) 1.25376 + 11.9288i 0.0839581 + 0.798808i 0.952776 + 0.303676i \(0.0982139\pi\)
−0.868817 + 0.495133i \(0.835119\pi\)
\(224\) 0 0
\(225\) 2.17615 2.41686i 0.145076 0.161124i
\(226\) 0 0
\(227\) −0.933964 + 8.88607i −0.0619894 + 0.589789i 0.918801 + 0.394722i \(0.129159\pi\)
−0.980790 + 0.195067i \(0.937508\pi\)
\(228\) 0 0
\(229\) 6.36729 19.5965i 0.420763 1.29497i −0.486231 0.873830i \(-0.661629\pi\)
0.906994 0.421144i \(-0.138371\pi\)
\(230\) 0 0
\(231\) 0.704857 + 7.84716i 0.0463762 + 0.516305i
\(232\) 0 0
\(233\) 4.65279 14.3198i 0.304814 0.938122i −0.674932 0.737880i \(-0.735827\pi\)
0.979746 0.200242i \(-0.0641728\pi\)
\(234\) 0 0
\(235\) −3.16457 2.29919i −0.206434 0.149983i
\(236\) 0 0
\(237\) 0.242185 + 0.0514780i 0.0157316 + 0.00334386i
\(238\) 0 0
\(239\) 10.6335 7.72570i 0.687825 0.499734i −0.188119 0.982146i \(-0.560239\pi\)
0.875944 + 0.482412i \(0.160239\pi\)
\(240\) 0 0
\(241\) −12.6539 21.9172i −0.815110 1.41181i −0.909249 0.416253i \(-0.863343\pi\)
0.0941386 0.995559i \(-0.469990\pi\)
\(242\) 0 0
\(243\) −7.27215 12.5957i −0.466508 0.808016i
\(244\) 0 0
\(245\) 1.17044 + 11.1360i 0.0747765 + 0.711451i
\(246\) 0 0
\(247\) 1.49433 + 0.549053i 0.0950820 + 0.0349354i
\(248\) 0 0
\(249\) 1.67369 0.745173i 0.106066 0.0472234i
\(250\) 0 0
\(251\) 10.7226 2.27916i 0.676804 0.143859i 0.143329 0.989675i \(-0.454219\pi\)
0.533475 + 0.845816i \(0.320886\pi\)
\(252\) 0 0
\(253\) 16.5510 + 7.67125i 1.04055 + 0.482287i
\(254\) 0 0
\(255\) −0.777048 + 2.39151i −0.0486606 + 0.149762i
\(256\) 0 0
\(257\) −26.0036 + 11.5775i −1.62206 + 0.722187i −0.998236 0.0593775i \(-0.981088\pi\)
−0.623824 + 0.781565i \(0.714422\pi\)
\(258\) 0 0
\(259\) −9.48091 29.1793i −0.589115 1.81311i
\(260\) 0 0
\(261\) 10.9484 7.95445i 0.677687 0.492368i
\(262\) 0 0
\(263\) −11.6538 + 20.1850i −0.718604 + 1.24466i 0.242949 + 0.970039i \(0.421885\pi\)
−0.961553 + 0.274620i \(0.911448\pi\)
\(264\) 0 0
\(265\) 12.4995 0.767839
\(266\) 0 0
\(267\) −3.76552 1.67652i −0.230446 0.102601i
\(268\) 0 0
\(269\) 19.9710 22.1800i 1.21765 1.35234i 0.300508 0.953779i \(-0.402844\pi\)
0.917143 0.398559i \(-0.130490\pi\)
\(270\) 0 0
\(271\) −9.14427 + 4.07129i −0.555475 + 0.247313i −0.665221 0.746646i \(-0.731663\pi\)
0.109747 + 0.993960i \(0.464996\pi\)
\(272\) 0 0
\(273\) 8.54602 0.571439i 0.517229 0.0345851i
\(274\) 0 0
\(275\) 2.77261 + 3.17464i 0.167195 + 0.191438i
\(276\) 0 0
\(277\) −16.8041 + 3.57183i −1.00966 + 0.214611i −0.682913 0.730500i \(-0.739287\pi\)
−0.326751 + 0.945111i \(0.605954\pi\)
\(278\) 0 0
\(279\) 0.453091 4.31087i 0.0271259 0.258085i
\(280\) 0 0
\(281\) 9.48935 + 29.2052i 0.566087 + 1.74224i 0.664698 + 0.747112i \(0.268560\pi\)
−0.0986108 + 0.995126i \(0.531440\pi\)
\(282\) 0 0
\(283\) −0.986122 9.38232i −0.0586188 0.557721i −0.983935 0.178525i \(-0.942867\pi\)
0.925316 0.379196i \(-0.123799\pi\)
\(284\) 0 0
\(285\) −0.566188 −0.0335381
\(286\) 0 0
\(287\) 22.7205 1.34115
\(288\) 0 0
\(289\) 1.37502 + 13.0824i 0.0808834 + 0.769554i
\(290\) 0 0
\(291\) 0.977847 + 3.00950i 0.0573224 + 0.176420i
\(292\) 0 0
\(293\) 1.41442 13.4573i 0.0826312 0.786183i −0.872223 0.489108i \(-0.837322\pi\)
0.954854 0.297075i \(-0.0960111\pi\)
\(294\) 0 0
\(295\) 11.9290 2.53559i 0.694533 0.147627i
\(296\) 0 0
\(297\) 11.2585 4.80975i 0.653283 0.279090i
\(298\) 0 0
\(299\) 8.74785 17.7979i 0.505901 1.02928i
\(300\) 0 0
\(301\) −28.3645 + 12.6287i −1.63490 + 0.727905i
\(302\) 0 0
\(303\) −3.44562 + 3.82675i −0.197946 + 0.219841i
\(304\) 0 0
\(305\) 7.75296 + 3.45184i 0.443933 + 0.197652i
\(306\) 0 0
\(307\) 33.4366 1.90833 0.954163 0.299287i \(-0.0967490\pi\)
0.954163 + 0.299287i \(0.0967490\pi\)
\(308\) 0 0
\(309\) −4.60990 + 7.98458i −0.262248 + 0.454227i
\(310\) 0 0
\(311\) 0.832146 0.604589i 0.0471867 0.0342831i −0.563942 0.825814i \(-0.690716\pi\)
0.611129 + 0.791531i \(0.290716\pi\)
\(312\) 0 0
\(313\) 5.36875 + 16.5233i 0.303460 + 0.933953i 0.980248 + 0.197775i \(0.0633714\pi\)
−0.676788 + 0.736178i \(0.736629\pi\)
\(314\) 0 0
\(315\) 16.1509 7.19083i 0.909998 0.405157i
\(316\) 0 0
\(317\) −5.26704 + 16.2103i −0.295827 + 0.910460i 0.687116 + 0.726548i \(0.258876\pi\)
−0.982943 + 0.183913i \(0.941124\pi\)
\(318\) 0 0
\(319\) 8.53859 + 15.3202i 0.478070 + 0.857768i
\(320\) 0 0
\(321\) 4.88006 1.03729i 0.272378 0.0578958i
\(322\) 0 0
\(323\) 0.791008 0.352179i 0.0440129 0.0195958i
\(324\) 0 0
\(325\) 3.51906 2.93462i 0.195202 0.162784i
\(326\) 0 0
\(327\) 0.138513 + 1.31786i 0.00765978 + 0.0728780i
\(328\) 0 0
\(329\) 3.62326 + 6.27568i 0.199757 + 0.345989i
\(330\) 0 0
\(331\) 8.81428 + 15.2668i 0.484477 + 0.839138i 0.999841 0.0178331i \(-0.00567676\pi\)
−0.515364 + 0.856971i \(0.672343\pi\)
\(332\) 0 0
\(333\) −17.7554 + 12.9000i −0.972990 + 0.706918i
\(334\) 0 0
\(335\) 1.46559 + 0.311522i 0.0800740 + 0.0170203i
\(336\) 0 0
\(337\) 19.0115 + 13.8127i 1.03562 + 0.752425i 0.969427 0.245382i \(-0.0789133\pi\)
0.0661974 + 0.997807i \(0.478913\pi\)
\(338\) 0 0
\(339\) −1.46576 + 4.51115i −0.0796092 + 0.245012i
\(340\) 0 0
\(341\) 5.47671 + 1.25104i 0.296580 + 0.0677477i
\(342\) 0 0
\(343\) −1.32837 + 4.08829i −0.0717251 + 0.220747i
\(344\) 0 0
\(345\) −0.737238 + 7.01435i −0.0396916 + 0.377640i
\(346\) 0 0
\(347\) 20.2180 22.4544i 1.08536 1.20541i 0.107929 0.994159i \(-0.465578\pi\)
0.977431 0.211256i \(-0.0677553\pi\)
\(348\) 0 0
\(349\) 0.801387 + 7.62469i 0.0428973 + 0.408140i 0.994808 + 0.101766i \(0.0324492\pi\)
−0.951911 + 0.306374i \(0.900884\pi\)
\(350\) 0 0
\(351\) −4.94816 12.3554i −0.264113 0.659480i
\(352\) 0 0
\(353\) 3.13896 5.43683i 0.167070 0.289373i −0.770319 0.637659i \(-0.779903\pi\)
0.937388 + 0.348286i \(0.113236\pi\)
\(354\) 0 0
\(355\) 0.494293 + 0.220073i 0.0262343 + 0.0116803i
\(356\) 0 0
\(357\) 3.11709 3.46188i 0.164974 0.183222i
\(358\) 0 0
\(359\) −1.71570 1.24653i −0.0905510 0.0657892i 0.541589 0.840644i \(-0.317823\pi\)
−0.632140 + 0.774855i \(0.717823\pi\)
\(360\) 0 0
\(361\) −12.5830 13.9749i −0.662265 0.735519i
\(362\) 0 0
\(363\) 2.04583 + 7.01189i 0.107378 + 0.368029i
\(364\) 0 0
\(365\) 8.61867 26.5255i 0.451122 1.38841i
\(366\) 0 0
\(367\) 7.22736 3.21783i 0.377265 0.167969i −0.209339 0.977843i \(-0.567131\pi\)
0.586604 + 0.809874i \(0.300465\pi\)
\(368\) 0 0
\(369\) −5.02234 15.4572i −0.261452 0.804668i
\(370\) 0 0
\(371\) −21.1542 9.41845i −1.09827 0.488981i
\(372\) 0 0
\(373\) 9.00016 + 15.5887i 0.466011 + 0.807154i 0.999247 0.0388124i \(-0.0123575\pi\)
−0.533236 + 0.845967i \(0.679024\pi\)
\(374\) 0 0
\(375\) −4.02054 + 6.96378i −0.207620 + 0.359608i
\(376\) 0 0
\(377\) 16.8623 8.90005i 0.868452 0.458376i
\(378\) 0 0
\(379\) −26.1459 5.55749i −1.34303 0.285469i −0.520337 0.853961i \(-0.674194\pi\)
−0.822689 + 0.568492i \(0.807527\pi\)
\(380\) 0 0
\(381\) −0.572588 + 5.44781i −0.0293346 + 0.279100i
\(382\) 0 0
\(383\) −35.4061 + 7.52580i −1.80917 + 0.384551i −0.983688 0.179881i \(-0.942429\pi\)
−0.825480 + 0.564431i \(0.809095\pi\)
\(384\) 0 0
\(385\) 6.74981 + 21.8961i 0.344002 + 1.11593i
\(386\) 0 0
\(387\) 14.8614 + 16.5053i 0.755448 + 0.839011i
\(388\) 0 0
\(389\) −31.8478 23.1388i −1.61475 1.17318i −0.844810 0.535067i \(-0.820287\pi\)
−0.769939 0.638117i \(-0.779713\pi\)
\(390\) 0 0
\(391\) −3.33308 10.2582i −0.168561 0.518777i
\(392\) 0 0
\(393\) −0.481197 4.57829i −0.0242732 0.230944i
\(394\) 0 0
\(395\) 0.720053 0.0362298
\(396\) 0 0
\(397\) −3.88486 6.72877i −0.194975 0.337707i 0.751917 0.659258i \(-0.229129\pi\)
−0.946892 + 0.321551i \(0.895796\pi\)
\(398\) 0 0
\(399\) 0.958217 + 0.426626i 0.0479709 + 0.0213580i
\(400\) 0 0
\(401\) −23.6483 5.02659i −1.18094 0.251016i −0.424713 0.905328i \(-0.639625\pi\)
−0.756225 + 0.654312i \(0.772958\pi\)
\(402\) 0 0
\(403\) 1.49550 5.92123i 0.0744963 0.294957i
\(404\) 0 0
\(405\) −6.75292 7.49988i −0.335555 0.372672i
\(406\) 0 0
\(407\) −13.8474 24.8454i −0.686389 1.23154i
\(408\) 0 0
\(409\) 28.0518 5.96259i 1.38707 0.294831i 0.546921 0.837184i \(-0.315800\pi\)
0.840150 + 0.542353i \(0.182467\pi\)
\(410\) 0 0
\(411\) −7.59178 5.51575i −0.374475 0.272072i
\(412\) 0 0
\(413\) −22.0992 4.69733i −1.08743 0.231141i
\(414\) 0 0
\(415\) 4.31046 3.13173i 0.211592 0.153731i
\(416\) 0 0
\(417\) −9.88257 −0.483951
\(418\) 0 0
\(419\) 16.9379 29.3373i 0.827469 1.43322i −0.0725480 0.997365i \(-0.523113\pi\)
0.900017 0.435854i \(-0.143554\pi\)
\(420\) 0 0
\(421\) −13.4515 + 9.77312i −0.655588 + 0.476312i −0.865170 0.501479i \(-0.832790\pi\)
0.209582 + 0.977791i \(0.432790\pi\)
\(422\) 0 0
\(423\) 3.46853 3.85220i 0.168646 0.187300i
\(424\) 0 0
\(425\) 0.260500 2.47849i 0.0126361 0.120224i
\(426\) 0 0
\(427\) −10.5201 11.6838i −0.509105 0.565419i
\(428\) 0 0
\(429\) 7.67149 2.04957i 0.370383 0.0989541i
\(430\) 0 0
\(431\) 9.26865 + 10.2939i 0.446455 + 0.495838i 0.923799 0.382878i \(-0.125067\pi\)
−0.477344 + 0.878717i \(0.658400\pi\)
\(432\) 0 0
\(433\) −1.42847 + 13.5910i −0.0686480 + 0.653142i 0.905051 + 0.425303i \(0.139833\pi\)
−0.973699 + 0.227839i \(0.926834\pi\)
\(434\) 0 0
\(435\) −4.53741 + 5.03930i −0.217552 + 0.241616i
\(436\) 0 0
\(437\) 1.96479 1.42750i 0.0939886 0.0682867i
\(438\) 0 0
\(439\) 0.946165 1.63881i 0.0451580 0.0782159i −0.842563 0.538598i \(-0.818954\pi\)
0.887721 + 0.460382i \(0.152288\pi\)
\(440\) 0 0
\(441\) −14.8385 −0.706598
\(442\) 0 0
\(443\) −13.5793 + 9.86595i −0.645173 + 0.468746i −0.861623 0.507548i \(-0.830552\pi\)
0.216451 + 0.976294i \(0.430552\pi\)
\(444\) 0 0
\(445\) −11.7252 2.49228i −0.555829 0.118145i
\(446\) 0 0
\(447\) 6.73073 + 4.89016i 0.318353 + 0.231297i
\(448\) 0 0
\(449\) 7.93559 1.68676i 0.374503 0.0796032i −0.0168147 0.999859i \(-0.505353\pi\)
0.391318 + 0.920255i \(0.372019\pi\)
\(450\) 0 0
\(451\) 20.6675 4.06705i 0.973192 0.191510i
\(452\) 0 0
\(453\) 4.62718 + 5.13900i 0.217404 + 0.241451i
\(454\) 0 0
\(455\) 23.9648 6.79285i 1.12349 0.318454i
\(456\) 0 0
\(457\) 32.6389 + 6.93761i 1.52678 + 0.324527i 0.893382 0.449297i \(-0.148326\pi\)
0.633400 + 0.773825i \(0.281659\pi\)
\(458\) 0 0
\(459\) −6.61292 2.94426i −0.308665 0.137426i
\(460\) 0 0
\(461\) 3.32818 + 5.76458i 0.155009 + 0.268483i 0.933062 0.359715i \(-0.117126\pi\)
−0.778053 + 0.628198i \(0.783793\pi\)
\(462\) 0 0
\(463\) 25.1883 1.17060 0.585299 0.810818i \(-0.300977\pi\)
0.585299 + 0.810818i \(0.300977\pi\)
\(464\) 0 0
\(465\) 0.227034 + 2.16008i 0.0105284 + 0.100171i
\(466\) 0 0
\(467\) 8.72820 + 26.8626i 0.403893 + 1.24305i 0.921816 + 0.387628i \(0.126705\pi\)
−0.517923 + 0.855427i \(0.673295\pi\)
\(468\) 0 0
\(469\) −2.24564 1.63155i −0.103694 0.0753381i
\(470\) 0 0
\(471\) 8.87876 + 9.86087i 0.409112 + 0.454365i
\(472\) 0 0
\(473\) −23.5408 + 16.5648i −1.08241 + 0.761653i
\(474\) 0 0
\(475\) 0.548873 0.116667i 0.0251840 0.00535303i
\(476\) 0 0
\(477\) −1.73143 + 16.4735i −0.0792768 + 0.754269i
\(478\) 0 0
\(479\) −11.2201 2.38491i −0.512660 0.108969i −0.0556845 0.998448i \(-0.517734\pi\)
−0.456976 + 0.889479i \(0.651067\pi\)
\(480\) 0 0
\(481\) −27.3462 + 14.4336i −1.24688 + 0.658114i
\(482\) 0 0
\(483\) 6.53305 11.3156i 0.297264 0.514877i
\(484\) 0 0
\(485\) 4.60130 + 7.96968i 0.208934 + 0.361885i
\(486\) 0 0
\(487\) −35.5853 15.8436i −1.61252 0.717942i −0.615018 0.788513i \(-0.710851\pi\)
−0.997507 + 0.0705709i \(0.977518\pi\)
\(488\) 0 0
\(489\) 3.76460 + 11.5863i 0.170241 + 0.523948i
\(490\) 0 0
\(491\) 14.8484 6.61092i 0.670097 0.298347i −0.0433454 0.999060i \(-0.513802\pi\)
0.713443 + 0.700714i \(0.247135\pi\)
\(492\) 0 0
\(493\) 3.20456 9.86263i 0.144326 0.444191i
\(494\) 0 0
\(495\) 13.4042 9.43210i 0.602476 0.423941i
\(496\) 0 0
\(497\) −0.670715 0.744905i −0.0300857 0.0334135i
\(498\) 0 0
\(499\) −30.7128 22.3142i −1.37489 0.998919i −0.997337 0.0729326i \(-0.976764\pi\)
−0.377557 0.925986i \(-0.623236\pi\)
\(500\) 0 0
\(501\) −9.56107 + 10.6186i −0.427157 + 0.474406i
\(502\) 0 0
\(503\) −22.6076 10.0656i −1.00802 0.448801i −0.164778 0.986331i \(-0.552691\pi\)
−0.843245 + 0.537530i \(0.819358\pi\)
\(504\) 0 0
\(505\) −7.48771 + 12.9691i −0.333199 + 0.577117i
\(506\) 0 0
\(507\) −2.03727 8.38845i −0.0904783 0.372544i
\(508\) 0 0
\(509\) 0.450347 + 4.28477i 0.0199613 + 0.189919i 0.999959 0.00909143i \(-0.00289393\pi\)
−0.979997 + 0.199010i \(0.936227\pi\)
\(510\) 0 0
\(511\) −34.5734 + 38.3976i −1.52944 + 1.69861i
\(512\) 0 0
\(513\) 0.170370 1.62096i 0.00752202 0.0715672i
\(514\) 0 0
\(515\) −8.28564 + 25.5006i −0.365109 + 1.12369i
\(516\) 0 0
\(517\) 4.41922 + 5.06001i 0.194357 + 0.222539i
\(518\) 0 0
\(519\) 0.678233 2.08739i 0.0297711 0.0916261i
\(520\) 0 0
\(521\) 15.7477 + 11.4413i 0.689917 + 0.501254i 0.876633 0.481160i \(-0.159784\pi\)
−0.186716 + 0.982414i \(0.559784\pi\)
\(522\) 0 0
\(523\) −26.6433 5.66321i −1.16503 0.247635i −0.415493 0.909596i \(-0.636391\pi\)
−0.749538 + 0.661961i \(0.769724\pi\)
\(524\) 0 0
\(525\) 2.44238 1.77449i 0.106594 0.0774452i
\(526\) 0 0
\(527\) −1.66079 2.87658i −0.0723453 0.125306i
\(528\) 0 0
\(529\) −3.62657 6.28140i −0.157677 0.273105i
\(530\) 0 0
\(531\) 1.68932 + 16.0728i 0.0733102 + 0.697500i
\(532\) 0 0
\(533\) −3.90761 22.5629i −0.169258 0.977308i
\(534\) 0 0
\(535\) 13.2548 5.90141i 0.573054 0.255140i
\(536\) 0 0
\(537\) 11.7611 2.49989i 0.507527 0.107878i
\(538\) 0 0
\(539\) 2.29946 19.0932i 0.0990450 0.822401i
\(540\) 0 0
\(541\) −6.15806 + 18.9525i −0.264755 + 0.814834i 0.726994 + 0.686644i \(0.240917\pi\)
−0.991750 + 0.128190i \(0.959083\pi\)
\(542\) 0 0
\(543\) 2.79819 1.24584i 0.120082 0.0534640i
\(544\) 0 0
\(545\) 1.19086 + 3.66508i 0.0510108 + 0.156995i
\(546\) 0 0
\(547\) −20.1427 + 14.6345i −0.861238 + 0.625726i −0.928222 0.372028i \(-0.878663\pi\)
0.0669834 + 0.997754i \(0.478663\pi\)
\(548\) 0 0
\(549\) −5.62322 + 9.73971i −0.239993 + 0.415681i
\(550\) 0 0
\(551\) 2.33497 0.0994732
\(552\) 0 0
\(553\) −1.21862 0.542564i −0.0518209 0.0230722i
\(554\) 0 0
\(555\) 7.35849 8.17243i 0.312350 0.346900i
\(556\) 0 0
\(557\) −28.4875 + 12.6834i −1.20705 + 0.537414i −0.908864 0.417093i \(-0.863049\pi\)
−0.298189 + 0.954507i \(0.596382\pi\)
\(558\) 0 0
\(559\) 17.4194 + 25.9957i 0.736760 + 1.09950i
\(560\) 0 0
\(561\) 2.21573 3.70703i 0.0935484 0.156511i
\(562\) 0 0
\(563\) −33.4613 + 7.11243i −1.41023 + 0.299753i −0.849212 0.528052i \(-0.822922\pi\)
−0.561015 + 0.827805i \(0.689589\pi\)
\(564\) 0 0
\(565\) −1.44191 + 13.7188i −0.0606615 + 0.577155i
\(566\) 0 0
\(567\) 5.77745 + 17.7812i 0.242630 + 0.746739i
\(568\) 0 0
\(569\) −1.98993 18.9329i −0.0834223 0.793710i −0.953621 0.301009i \(-0.902676\pi\)
0.870199 0.492701i \(-0.163990\pi\)
\(570\) 0 0
\(571\) −19.7614 −0.826987 −0.413493 0.910507i \(-0.635692\pi\)
−0.413493 + 0.910507i \(0.635692\pi\)
\(572\) 0 0
\(573\) −10.7336 −0.448401
\(574\) 0 0
\(575\) −0.730658 6.95175i −0.0304706 0.289908i
\(576\) 0 0
\(577\) 6.16748 + 18.9815i 0.256755 + 0.790212i 0.993479 + 0.114018i \(0.0363720\pi\)
−0.736723 + 0.676194i \(0.763628\pi\)
\(578\) 0 0
\(579\) −0.770358 + 7.32947i −0.0320150 + 0.304602i
\(580\) 0 0
\(581\) −9.65480 + 2.05219i −0.400548 + 0.0851392i
\(582\) 0 0
\(583\) −20.9286 4.78070i −0.866773 0.197997i
\(584\) 0 0
\(585\) −9.91866 14.8021i −0.410086 0.611991i
\(586\) 0 0
\(587\) −34.8200 + 15.5029i −1.43718 + 0.639872i −0.969737 0.244153i \(-0.921490\pi\)
−0.467440 + 0.884025i \(0.654824\pi\)
\(588\) 0 0
\(589\) 0.500440 0.555795i 0.0206203 0.0229011i
\(590\) 0 0
\(591\) −2.42715 1.08064i −0.0998395 0.0444514i
\(592\) 0 0
\(593\) 25.9203 1.06442 0.532210 0.846613i \(-0.321362\pi\)
0.532210 + 0.846613i \(0.321362\pi\)
\(594\) 0 0
\(595\) 6.77377 11.7325i 0.277698 0.480986i
\(596\) 0 0
\(597\) 5.56704 4.04469i 0.227844 0.165538i
\(598\) 0 0
\(599\) −14.2025 43.7107i −0.580297 1.78597i −0.617389 0.786658i \(-0.711809\pi\)
0.0370921 0.999312i \(-0.488191\pi\)
\(600\) 0 0
\(601\) 25.5941 11.3952i 1.04401 0.464821i 0.188206 0.982130i \(-0.439733\pi\)
0.855799 + 0.517308i \(0.173066\pi\)
\(602\) 0 0
\(603\) −0.613578 + 1.88840i −0.0249868 + 0.0769016i
\(604\) 0 0
\(605\) 10.0593 + 18.7093i 0.408971 + 0.760640i
\(606\) 0 0
\(607\) −11.6983 + 2.48655i −0.474820 + 0.100926i −0.439105 0.898436i \(-0.644704\pi\)
−0.0357152 + 0.999362i \(0.511371\pi\)
\(608\) 0 0
\(609\) 11.4762 5.10956i 0.465041 0.207050i
\(610\) 0 0
\(611\) 5.60899 4.67745i 0.226915 0.189230i
\(612\) 0 0
\(613\) 0.958966 + 9.12395i 0.0387323 + 0.368513i 0.996670 + 0.0815377i \(0.0259831\pi\)
−0.957938 + 0.286975i \(0.907350\pi\)
\(614\) 0 0
\(615\) 4.07191 + 7.05276i 0.164195 + 0.284395i
\(616\) 0 0
\(617\) −4.41413 7.64550i −0.177706 0.307796i 0.763388 0.645940i \(-0.223534\pi\)
−0.941095 + 0.338144i \(0.890201\pi\)
\(618\) 0 0
\(619\) 30.2540 21.9809i 1.21601 0.883485i 0.220250 0.975443i \(-0.429313\pi\)
0.995763 + 0.0919585i \(0.0293127\pi\)
\(620\) 0 0
\(621\) −19.8598 4.22133i −0.796947 0.169396i
\(622\) 0 0
\(623\) 17.9659 + 13.0530i 0.719787 + 0.522956i
\(624\) 0 0
\(625\) −5.26277 + 16.1971i −0.210511 + 0.647886i
\(626\) 0 0
\(627\) 0.947998 + 0.216551i 0.0378594 + 0.00864820i
\(628\) 0 0
\(629\) −5.19697 + 15.9946i −0.207217 + 0.637747i
\(630\) 0 0
\(631\) 2.71983 25.8774i 0.108275 1.03016i −0.796606 0.604499i \(-0.793374\pi\)
0.904881 0.425665i \(-0.139960\pi\)
\(632\) 0 0
\(633\) −11.2271 + 12.4690i −0.446239 + 0.495599i
\(634\) 0 0
\(635\) 1.66519 + 15.8432i 0.0660811 + 0.628719i
\(636\) 0 0
\(637\) −20.6940 2.97267i −0.819927 0.117782i
\(638\) 0 0
\(639\) −0.358511 + 0.620959i −0.0141825 + 0.0245647i
\(640\) 0 0
\(641\) 25.5609 + 11.3805i 1.00960 + 0.449501i 0.843799 0.536659i \(-0.180314\pi\)
0.165796 + 0.986160i \(0.446981\pi\)
\(642\) 0 0
\(643\) −0.967123 + 1.07410i −0.0381396 + 0.0423583i −0.761913 0.647680i \(-0.775740\pi\)
0.723773 + 0.690038i \(0.242406\pi\)
\(644\) 0 0
\(645\) −9.00352 6.54144i −0.354513 0.257569i
\(646\) 0 0
\(647\) −2.33620 2.59461i −0.0918454 0.102005i 0.695470 0.718555i \(-0.255196\pi\)
−0.787315 + 0.616551i \(0.788530\pi\)
\(648\) 0 0
\(649\) −20.9431 0.317038i −0.822089 0.0124448i
\(650\) 0 0
\(651\) 1.24340 3.82680i 0.0487328 0.149984i
\(652\) 0 0
\(653\) 45.6913 20.3431i 1.78804 0.796087i 0.810377 0.585908i \(-0.199262\pi\)
0.977663 0.210178i \(-0.0674045\pi\)
\(654\) 0 0
\(655\) −4.13707 12.7326i −0.161649 0.497504i
\(656\) 0 0
\(657\) 33.7649 + 15.0331i 1.31730 + 0.586498i
\(658\) 0 0
\(659\) 1.21638 + 2.10683i 0.0473833 + 0.0820703i 0.888744 0.458403i \(-0.151578\pi\)
−0.841361 + 0.540474i \(0.818245\pi\)
\(660\) 0 0
\(661\) 1.68250 2.91417i 0.0654416 0.113348i −0.831448 0.555602i \(-0.812488\pi\)
0.896890 + 0.442254i \(0.145821\pi\)
\(662\) 0 0
\(663\) −3.97396 2.50007i −0.154336 0.0970947i
\(664\) 0 0
\(665\) 2.98373 + 0.634212i 0.115704 + 0.0245937i
\(666\) 0 0
\(667\) 3.04039 28.9273i 0.117724 1.12007i
\(668\) 0 0
\(669\) 7.79055 1.65593i 0.301200 0.0640220i
\(670\) 0 0
\(671\) −11.6609 8.74488i −0.450166 0.337592i
\(672\) 0 0
\(673\) 12.2294 + 13.5821i 0.471407 + 0.523550i 0.931216 0.364467i \(-0.118749\pi\)
−0.459809 + 0.888018i \(0.652082\pi\)
\(674\) 0 0
\(675\) −3.79523 2.75739i −0.146078 0.106132i
\(676\) 0 0
\(677\) 3.73109 + 11.4831i 0.143397 + 0.441332i 0.996801 0.0799182i \(-0.0254659\pi\)
−0.853404 + 0.521250i \(0.825466\pi\)
\(678\) 0 0
\(679\) −1.78204 16.9550i −0.0683885 0.650673i
\(680\) 0 0
\(681\) 5.93306 0.227355
\(682\) 0 0
\(683\) 8.91959 + 15.4492i 0.341299 + 0.591147i 0.984674 0.174404i \(-0.0557999\pi\)
−0.643375 + 0.765551i \(0.722467\pi\)
\(684\) 0 0
\(685\) −24.9309 11.0999i −0.952561 0.424107i
\(686\) 0 0
\(687\) −13.3832 2.84469i −0.510601 0.108532i
\(688\) 0 0
\(689\) −5.71488 + 22.6273i −0.217720 + 0.862030i
\(690\) 0 0
\(691\) 5.88483 + 6.53577i 0.223870 + 0.248632i 0.844608 0.535386i \(-0.179834\pi\)
−0.620738 + 0.784018i \(0.713167\pi\)
\(692\) 0 0
\(693\) −29.7925 + 5.86273i −1.13172 + 0.222707i
\(694\) 0 0
\(695\) −28.1123 + 5.97545i −1.06636 + 0.226662i
\(696\) 0 0
\(697\) −10.0757 7.32044i −0.381645 0.277281i
\(698\) 0 0
\(699\) −9.77953 2.07870i −0.369896 0.0786238i
\(700\) 0 0
\(701\) −16.4694 + 11.9657i −0.622039 + 0.451938i −0.853633 0.520875i \(-0.825606\pi\)
0.231594 + 0.972813i \(0.425606\pi\)
\(702\) 0 0
\(703\) −3.78672 −0.142819
\(704\) 0 0
\(705\) −1.29870 + 2.24942i −0.0489120 + 0.0847181i
\(706\) 0 0
\(707\) 22.4445 16.3069i 0.844112 0.613283i
\(708\) 0 0
\(709\) 19.0995 21.2121i 0.717297 0.796639i −0.268732 0.963215i \(-0.586605\pi\)
0.986029 + 0.166576i \(0.0532712\pi\)
\(710\) 0 0
\(711\) −0.0997418 + 0.948980i −0.00374061 + 0.0355895i
\(712\) 0 0
\(713\) −6.23396 6.92352i −0.233464 0.259288i
\(714\) 0 0
\(715\) 20.5833 10.4688i 0.769772 0.391511i
\(716\) 0 0
\(717\) −5.84000 6.48598i −0.218099 0.242223i
\(718\) 0 0
\(719\) 0.414282 3.94163i 0.0154501 0.146998i −0.984077 0.177742i \(-0.943121\pi\)
0.999527 + 0.0307435i \(0.00978751\pi\)
\(720\) 0 0
\(721\) 33.2374 36.9139i 1.23783 1.37475i
\(722\) 0 0
\(723\) −13.5955 + 9.87772i −0.505622 + 0.367356i
\(724\) 0 0
\(725\) 3.36026 5.82015i 0.124797 0.216155i
\(726\) 0 0
\(727\) −1.08990 −0.0404220 −0.0202110 0.999796i \(-0.506434\pi\)
−0.0202110 + 0.999796i \(0.506434\pi\)
\(728\) 0 0
\(729\) 4.87068 3.53876i 0.180396 0.131065i
\(730\) 0 0
\(731\) 16.6475 + 3.53853i 0.615730 + 0.130877i
\(732\) 0 0
\(733\) 10.4754 + 7.61084i 0.386918 + 0.281113i 0.764192 0.644989i \(-0.223138\pi\)
−0.377273 + 0.926102i \(0.623138\pi\)
\(734\) 0 0
\(735\) 7.27279 1.54588i 0.268261 0.0570206i
\(736\) 0 0
\(737\) −2.33477 1.08214i −0.0860024 0.0398613i
\(738\) 0 0
\(739\) −3.13387 3.48051i −0.115281 0.128033i 0.682742 0.730660i \(-0.260787\pi\)
−0.798023 + 0.602627i \(0.794121\pi\)
\(740\) 0 0
\(741\) 0.258866 1.02494i 0.00950968 0.0376522i
\(742\) 0 0
\(743\) 37.2973 + 7.92778i 1.36830 + 0.290842i 0.832745 0.553656i \(-0.186768\pi\)
0.535559 + 0.844498i \(0.320101\pi\)
\(744\) 0 0
\(745\) 22.1033 + 9.84101i 0.809801 + 0.360547i
\(746\) 0 0
\(747\) 3.53032 + 6.11469i 0.129168 + 0.223725i
\(748\) 0 0
\(749\) −26.8791 −0.982142
\(750\) 0 0
\(751\) −0.488493 4.64770i −0.0178253 0.169597i 0.981987 0.188946i \(-0.0605072\pi\)
−0.999813 + 0.0193494i \(0.993841\pi\)
\(752\) 0 0
\(753\) −2.24937 6.92284i −0.0819715 0.252282i
\(754\) 0 0
\(755\) 16.2699 + 11.8208i 0.592122 + 0.430202i
\(756\) 0 0
\(757\) 18.0709 + 20.0698i 0.656798 + 0.729448i 0.975887 0.218277i \(-0.0700435\pi\)
−0.319089 + 0.947725i \(0.603377\pi\)
\(758\) 0 0
\(759\) 3.91718 11.4625i 0.142185 0.416063i
\(760\) 0 0
\(761\) 13.0287 2.76933i 0.472289 0.100388i 0.0343827 0.999409i \(-0.489053\pi\)
0.437906 + 0.899021i \(0.355720\pi\)
\(762\) 0 0
\(763\) 0.746252 7.10011i 0.0270161 0.257041i
\(764\) 0 0
\(765\) −9.47916 2.01486i −0.342720 0.0728473i
\(766\) 0 0
\(767\) −0.863989 + 22.7538i −0.0311968 + 0.821591i
\(768\) 0 0
\(769\) 25.3860 43.9699i 0.915443 1.58559i 0.109192 0.994021i \(-0.465174\pi\)
0.806251 0.591574i \(-0.201493\pi\)
\(770\) 0 0
\(771\) 9.45053 + 16.3688i 0.340353 + 0.589508i
\(772\) 0 0
\(773\) −16.2812 7.24884i −0.585593 0.260723i 0.0924834 0.995714i \(-0.470519\pi\)
−0.678076 + 0.734991i \(0.737186\pi\)
\(774\) 0 0
\(775\) −0.665189 2.04724i −0.0238943 0.0735391i
\(776\) 0 0
\(777\) −18.6115 + 8.28637i −0.667683 + 0.297272i
\(778\) 0 0
\(779\) 0.866555 2.66698i 0.0310476 0.0955545i
\(780\) 0 0
\(781\) −0.743448 0.557533i −0.0266027 0.0199501i
\(782\) 0 0
\(783\) −13.0619 14.5067i −0.466793 0.518426i
\(784\) 0 0
\(785\) 31.2192 + 22.6820i 1.11426 + 0.809557i
\(786\) 0 0
\(787\) −3.49684 + 3.88364i −0.124649 + 0.138437i −0.802239 0.597003i \(-0.796358\pi\)
0.677590 + 0.735440i \(0.263025\pi\)
\(788\) 0 0
\(789\) 14.1387 + 6.29497i 0.503352 + 0.224107i
\(790\) 0 0
\(791\) 12.7775 22.1313i 0.454315 0.786897i
\(792\) 0 0
\(793\) −9.79342 + 12.4566i −0.347775 + 0.442347i
\(794\) 0 0
\(795\) −0.867582 8.25449i −0.0307700 0.292757i
\(796\) 0 0
\(797\) 18.0422 20.0379i 0.639088 0.709779i −0.333386 0.942790i \(-0.608191\pi\)
0.972474 + 0.233011i \(0.0748580\pi\)
\(798\) 0 0
\(799\) 0.415207 3.95043i 0.0146890 0.139756i
\(800\) 0 0
\(801\) 4.90882 15.1078i 0.173445 0.533808i
\(802\) 0 0
\(803\) −24.5759 + 41.1167i −0.867266 + 1.45098i
\(804\) 0 0
\(805\) 11.7422 36.1389i 0.413859 1.27373i
\(806\) 0 0
\(807\) −16.0335 11.6490i −0.564406 0.410065i
\(808\) 0 0
\(809\) −42.1616 8.96172i −1.48232 0.315077i −0.605482 0.795859i \(-0.707019\pi\)
−0.876840 + 0.480782i \(0.840353\pi\)
\(810\) 0 0
\(811\) 28.5848 20.7680i 1.00375 0.729265i 0.0408585 0.999165i \(-0.486991\pi\)
0.962888 + 0.269900i \(0.0869907\pi\)
\(812\) 0 0
\(813\) 3.32332 + 5.75615i 0.116554 + 0.201877i
\(814\) 0 0
\(815\) 17.7145 + 30.6824i 0.620511 + 1.07476i
\(816\) 0 0
\(817\) 0.400566 + 3.81113i 0.0140140 + 0.133335i
\(818\) 0 0
\(819\) 5.63289 + 32.5248i 0.196829 + 1.13651i
\(820\) 0 0
\(821\) −35.7902 + 15.9348i −1.24909 + 0.556129i −0.921384 0.388653i \(-0.872941\pi\)
−0.327701 + 0.944781i \(0.606274\pi\)
\(822\) 0 0
\(823\) 29.8731 6.34972i 1.04131 0.221337i 0.344645 0.938733i \(-0.387999\pi\)
0.696666 + 0.717396i \(0.254666\pi\)
\(824\) 0 0
\(825\) 1.90404 2.05134i 0.0662901 0.0714184i
\(826\) 0 0
\(827\) 3.07140 9.45280i 0.106803 0.328706i −0.883346 0.468721i \(-0.844715\pi\)
0.990149 + 0.140015i \(0.0447150\pi\)
\(828\) 0 0
\(829\) 33.7810 15.0403i 1.17326 0.522371i 0.274835 0.961491i \(-0.411377\pi\)
0.898428 + 0.439121i \(0.144710\pi\)
\(830\) 0 0
\(831\) 3.52515 + 10.8493i 0.122286 + 0.376358i
\(832\) 0 0
\(833\) −9.19907 + 6.68352i −0.318729 + 0.231570i
\(834\) 0 0
\(835\) −20.7772 + 35.9872i −0.719025 + 1.24539i
\(836\) 0 0
\(837\) −6.25250 −0.216118
\(838\) 0 0
\(839\) 34.2678 + 15.2570i 1.18305 + 0.526730i 0.901485 0.432811i \(-0.142478\pi\)
0.281570 + 0.959541i \(0.409145\pi\)
\(840\) 0 0
\(841\) −0.692422 + 0.769013i −0.0238766 + 0.0265177i
\(842\) 0 0
\(843\) 18.6281 8.29374i 0.641584 0.285652i
\(844\) 0 0
\(845\) −10.8673 22.6302i −0.373847 0.778504i
\(846\) 0 0
\(847\) −2.92692 39.2433i −0.100570 1.34842i
\(848\) 0 0
\(849\) −6.12750 + 1.30244i −0.210295 + 0.0446996i
\(850\) 0 0
\(851\) −4.93071 + 46.9126i −0.169023 + 1.60814i
\(852\) 0 0
\(853\) 10.4669 + 32.2137i 0.358379 + 1.10298i 0.954024 + 0.299729i \(0.0968962\pi\)
−0.595646 + 0.803247i \(0.703104\pi\)
\(854\) 0 0
\(855\) −0.228084 2.17008i −0.00780032 0.0742150i
\(856\) 0 0
\(857\) −1.12486 −0.0384244 −0.0192122 0.999815i \(-0.506116\pi\)
−0.0192122 + 0.999815i \(0.506116\pi\)
\(858\) 0 0
\(859\) −15.2919 −0.521752 −0.260876 0.965372i \(-0.584011\pi\)
−0.260876 + 0.965372i \(0.584011\pi\)
\(860\) 0 0
\(861\) −1.57702 15.0043i −0.0537446 0.511346i
\(862\) 0 0
\(863\) −3.68927 11.3544i −0.125584 0.386509i 0.868423 0.495824i \(-0.165134\pi\)
−0.994007 + 0.109316i \(0.965134\pi\)
\(864\) 0 0
\(865\) 0.667195 6.34794i 0.0226853 0.215836i
\(866\) 0 0
\(867\) 8.54399 1.81608i 0.290169 0.0616774i
\(868\) 0 0
\(869\) −1.20562 0.275400i −0.0408979 0.00934230i
\(870\) 0 0
\(871\) −1.23402 + 2.51066i −0.0418130 + 0.0850706i
\(872\) 0 0
\(873\) −11.1409 + 4.96023i −0.377061 + 0.167878i
\(874\) 0 0
\(875\) 28.9881 32.1946i 0.979978 1.08838i
\(876\) 0 0
\(877\) 44.2899 + 19.7192i 1.49557 + 0.665868i 0.981426 0.191839i \(-0.0614450\pi\)
0.514139 + 0.857707i \(0.328112\pi\)
\(878\) 0 0
\(879\) −8.98517 −0.303062
\(880\) 0 0
\(881\) 24.0372 41.6337i 0.809834 1.40267i −0.103144 0.994666i \(-0.532890\pi\)
0.912978 0.408008i \(-0.133776\pi\)
\(882\) 0 0
\(883\) 6.91318 5.02272i 0.232647 0.169028i −0.465354 0.885125i \(-0.654073\pi\)
0.698001 + 0.716097i \(0.254073\pi\)
\(884\) 0 0
\(885\) −2.50245 7.70174i −0.0841188 0.258891i
\(886\) 0 0
\(887\) −26.2424 + 11.6839i −0.881134 + 0.392306i −0.796880 0.604138i \(-0.793517\pi\)
−0.0842543 + 0.996444i \(0.526851\pi\)
\(888\) 0 0
\(889\) 9.11979 28.0678i 0.305868 0.941365i
\(890\) 0 0
\(891\) 8.43827 + 15.1402i 0.282693 + 0.507217i
\(892\) 0 0
\(893\) 0.874842 0.185953i 0.0292755 0.00622269i
\(894\) 0 0
\(895\) 31.9443 14.2225i 1.06778 0.475407i
\(896\) 0 0
\(897\) −12.3607 4.54161i −0.412711 0.151640i
\(898\) 0 0
\(899\) −0.936293 8.90823i −0.0312271 0.297106i
\(900\) 0 0
\(901\) 6.34652 + 10.9925i 0.211433 + 0.366213i
\(902\) 0 0
\(903\) 10.3085 + 17.8549i 0.343047 + 0.594175i
\(904\) 0 0
\(905\) 7.20655 5.23586i 0.239554 0.174046i
\(906\) 0 0
\(907\) 17.5323 + 3.72661i 0.582152 + 0.123740i 0.489569 0.871965i \(-0.337154\pi\)
0.0925830 + 0.995705i \(0.470488\pi\)
\(908\) 0 0
\(909\) −16.0552 11.6648i −0.532516 0.386895i
\(910\) 0 0
\(911\) −2.87260 + 8.84095i −0.0951734 + 0.292914i −0.987299 0.158874i \(-0.949214\pi\)
0.892125 + 0.451788i \(0.149214\pi\)
\(912\) 0 0
\(913\) −8.41501 + 3.59499i −0.278496 + 0.118977i
\(914\) 0 0
\(915\) 1.74142 5.35953i 0.0575695 0.177181i
\(916\) 0 0
\(917\) −2.59250 + 24.6660i −0.0856118 + 0.814542i
\(918\) 0 0
\(919\) 7.64107 8.48627i 0.252056 0.279936i −0.603817 0.797123i \(-0.706354\pi\)
0.855872 + 0.517187i \(0.173021\pi\)
\(920\) 0 0
\(921\) −2.32081 22.0810i −0.0764732 0.727594i
\(922\) 0 0
\(923\) −0.624383 + 0.794175i −0.0205518 + 0.0261406i
\(924\) 0 0
\(925\) −5.44947 + 9.43876i −0.179178 + 0.310345i
\(926\) 0 0
\(927\) −32.4602 14.4522i −1.06613 0.474673i
\(928\) 0 0
\(929\) 24.9927 27.7572i 0.819985 0.910685i −0.177313 0.984155i \(-0.556740\pi\)
0.997297 + 0.0734695i \(0.0234071\pi\)
\(930\) 0 0
\(931\) −2.07128 1.50487i −0.0678835 0.0493203i
\(932\) 0 0
\(933\) −0.457020 0.507573i −0.0149622 0.0166172i
\(934\) 0 0
\(935\) 4.06152 11.8849i 0.132826 0.388677i
\(936\) 0 0
\(937\) −6.17911 + 19.0173i −0.201863 + 0.621269i 0.797965 + 0.602704i \(0.205910\pi\)
−0.999828 + 0.0185655i \(0.994090\pi\)
\(938\) 0 0
\(939\) 10.5391 4.69231i 0.343931 0.153128i
\(940\) 0 0
\(941\) 6.92548 + 21.3144i 0.225764 + 0.694830i 0.998213 + 0.0597536i \(0.0190315\pi\)
−0.772449 + 0.635077i \(0.780968\pi\)
\(942\) 0 0
\(943\) −31.9122 14.2082i −1.03920 0.462683i
\(944\) 0 0
\(945\) −12.7508 22.0851i −0.414784 0.718428i
\(946\) 0 0
\(947\) −12.1433 + 21.0329i −0.394605 + 0.683477i −0.993051 0.117687i \(-0.962452\pi\)
0.598445 + 0.801164i \(0.295785\pi\)
\(948\) 0 0
\(949\) 44.0774 + 27.7297i 1.43081 + 0.900143i
\(950\) 0 0
\(951\) 11.0706 + 2.35313i 0.358989 + 0.0763055i
\(952\) 0 0
\(953\) −1.68601 + 16.0413i −0.0546152 + 0.519628i 0.932677 + 0.360713i \(0.117467\pi\)
−0.987292 + 0.158916i \(0.949200\pi\)
\(954\) 0 0
\(955\) −30.5331 + 6.49000i −0.988027 + 0.210012i
\(956\) 0 0
\(957\) 9.52460 6.70213i 0.307886 0.216649i
\(958\) 0 0
\(959\) 33.8292 + 37.5711i 1.09240 + 1.21323i
\(960\) 0 0
\(961\) 22.7584 + 16.5350i 0.734143 + 0.533386i
\(962\) 0 0
\(963\) 5.94159 + 18.2863i 0.191465 + 0.589269i
\(964\) 0 0
\(965\) 2.24034 + 21.3154i 0.0721192 + 0.686168i
\(966\) 0 0
\(967\) −9.01198 −0.289806 −0.144903 0.989446i \(-0.546287\pi\)
−0.144903 + 0.989446i \(0.546287\pi\)
\(968\) 0 0
\(969\) −0.287477 0.497925i −0.00923510 0.0159957i
\(970\) 0 0
\(971\) 7.37054 + 3.28158i 0.236532 + 0.105311i 0.521580 0.853202i \(-0.325343\pi\)
−0.285048 + 0.958513i \(0.592010\pi\)
\(972\) 0 0
\(973\) 52.0798 + 11.0699i 1.66960 + 0.354885i
\(974\) 0 0
\(975\) −2.18224 2.12025i −0.0698875 0.0679022i
\(976\) 0 0
\(977\) −12.0992 13.4375i −0.387088 0.429905i 0.517834 0.855481i \(-0.326738\pi\)
−0.904923 + 0.425576i \(0.860072\pi\)
\(978\) 0 0
\(979\) 18.6789 + 8.65751i 0.596981 + 0.276695i
\(980\) 0 0
\(981\) −4.99528 + 1.06178i −0.159487 + 0.0339000i
\(982\) 0 0
\(983\) −34.6162 25.1501i −1.10409 0.802165i −0.122364 0.992485i \(-0.539047\pi\)
−0.981722 + 0.190320i \(0.939047\pi\)
\(984\) 0 0
\(985\) −7.55774 1.60645i −0.240810 0.0511857i
\(986\) 0 0
\(987\) 3.89288 2.82834i 0.123912 0.0900271i
\(988\) 0 0
\(989\) 47.7366 1.51794
\(990\) 0 0
\(991\) −24.5823 + 42.5778i −0.780883 + 1.35253i 0.150546 + 0.988603i \(0.451897\pi\)
−0.931428 + 0.363925i \(0.881436\pi\)
\(992\) 0 0
\(993\) 9.47016 6.88048i 0.300526 0.218345i
\(994\) 0 0
\(995\) 13.3906 14.8717i 0.424510 0.471466i
\(996\) 0 0
\(997\) 6.11835 58.2122i 0.193770 1.84360i −0.276424 0.961036i \(-0.589149\pi\)
0.470194 0.882563i \(-0.344184\pi\)
\(998\) 0 0
\(999\) 21.1829 + 23.5260i 0.670199 + 0.744331i
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.bg.a.9.6 112
11.5 even 5 inner 572.2.bg.a.269.9 yes 112
13.3 even 3 inner 572.2.bg.a.185.9 yes 112
143.16 even 15 inner 572.2.bg.a.445.6 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.bg.a.9.6 112 1.1 even 1 trivial
572.2.bg.a.185.9 yes 112 13.3 even 3 inner
572.2.bg.a.269.9 yes 112 11.5 even 5 inner
572.2.bg.a.445.6 yes 112 143.16 even 15 inner