Properties

Label 1323.2.h.f.226.4
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not 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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.f.802.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 - 1.15593i) q^{5} -1.12285 q^{8} +O(q^{10})\) \(q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 - 1.15593i) q^{5} -1.12285 q^{8} +(-1.22880 - 2.12835i) q^{10} +(0.756508 - 1.31031i) q^{11} +(2.58800 - 4.48254i) q^{13} -4.84777 q^{16} +(0.774463 + 1.34141i) q^{17} +(1.25211 - 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(4.76513 - 8.25344i) q^{26} +(0.0309713 + 0.0536439i) q^{29} +3.84777 q^{31} -6.68021 q^{32} +(1.42597 + 2.46986i) q^{34} +(-0.281608 + 0.487760i) q^{37} +(2.30543 - 3.99313i) q^{38} +(0.749363 + 1.29794i) q^{40} +(4.51188 - 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(1.05167 - 1.82155i) q^{44} +(-6.77649 - 11.7372i) q^{46} -9.51851 q^{47} +(2.96296 - 5.13199i) q^{50} +(3.59775 - 6.23148i) q^{52} +(-0.755374 - 1.30835i) q^{53} -2.01950 q^{55} +(0.0570257 + 0.0987714i) q^{58} -8.44331 q^{59} -3.23917 q^{61} +7.08467 q^{62} -2.60434 q^{64} -6.90868 q^{65} +6.93339 q^{67} +(1.07663 + 1.86478i) q^{68} +12.3304 q^{71} +(1.37936 + 2.38912i) q^{73} +(-0.518508 + 0.898083i) q^{74} +(1.74064 - 3.01488i) q^{76} -5.91938 q^{79} +(3.23529 + 5.60368i) q^{80} +(8.30746 - 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(0.703287 - 1.21813i) q^{89} +(-5.11636 - 8.86180i) q^{92} -17.5259 q^{94} -3.34251 q^{95} +(6.09713 + 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84124 1.30195 0.650977 0.759098i \(-0.274359\pi\)
0.650977 + 0.759098i \(0.274359\pi\)
\(3\) 0 0
\(4\) 1.39017 0.695084
\(5\) −0.667377 1.15593i −0.298460 0.516948i 0.677324 0.735685i \(-0.263140\pi\)
−0.975784 + 0.218737i \(0.929806\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.12285 −0.396987
\(9\) 0 0
\(10\) −1.22880 2.12835i −0.388581 0.673042i
\(11\) 0.756508 1.31031i 0.228096 0.395073i −0.729148 0.684356i \(-0.760083\pi\)
0.957244 + 0.289283i \(0.0934167\pi\)
\(12\) 0 0
\(13\) 2.58800 4.48254i 0.717781 1.24323i −0.244096 0.969751i \(-0.578491\pi\)
0.961877 0.273482i \(-0.0881755\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.84777 −1.21194
\(17\) 0.774463 + 1.34141i 0.187835 + 0.325340i 0.944528 0.328430i \(-0.106520\pi\)
−0.756693 + 0.653770i \(0.773186\pi\)
\(18\) 0 0
\(19\) 1.25211 2.16872i 0.287254 0.497538i −0.685900 0.727696i \(-0.740591\pi\)
0.973153 + 0.230158i \(0.0739244\pi\)
\(20\) −0.927765 1.60694i −0.207455 0.359322i
\(21\) 0 0
\(22\) 1.39291 2.41260i 0.296970 0.514367i
\(23\) −3.68039 6.37463i −0.767415 1.32920i −0.938960 0.344025i \(-0.888209\pi\)
0.171545 0.985176i \(-0.445124\pi\)
\(24\) 0 0
\(25\) 1.60922 2.78725i 0.321843 0.557449i
\(26\) 4.76513 8.25344i 0.934518 1.61863i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.0309713 + 0.0536439i 0.00575123 + 0.00996143i 0.868887 0.495011i \(-0.164836\pi\)
−0.863135 + 0.504972i \(0.831503\pi\)
\(30\) 0 0
\(31\) 3.84777 0.691080 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(32\) −6.68021 −1.18091
\(33\) 0 0
\(34\) 1.42597 + 2.46986i 0.244552 + 0.423577i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.281608 + 0.487760i −0.0462961 + 0.0801872i −0.888245 0.459370i \(-0.848075\pi\)
0.841949 + 0.539557i \(0.181408\pi\)
\(38\) 2.30543 3.99313i 0.373991 0.647771i
\(39\) 0 0
\(40\) 0.749363 + 1.29794i 0.118485 + 0.205222i
\(41\) 4.51188 7.81481i 0.704638 1.22047i −0.262185 0.965018i \(-0.584443\pi\)
0.966822 0.255450i \(-0.0822237\pi\)
\(42\) 0 0
\(43\) 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i \(0.116959\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(44\) 1.05167 1.82155i 0.158546 0.274609i
\(45\) 0 0
\(46\) −6.77649 11.7372i −0.999139 1.73056i
\(47\) −9.51851 −1.38842 −0.694209 0.719774i \(-0.744245\pi\)
−0.694209 + 0.719774i \(0.744245\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.96296 5.13199i 0.419025 0.725773i
\(51\) 0 0
\(52\) 3.59775 6.23148i 0.498918 0.864151i
\(53\) −0.755374 1.30835i −0.103759 0.179715i 0.809472 0.587159i \(-0.199754\pi\)
−0.913230 + 0.407444i \(0.866420\pi\)
\(54\) 0 0
\(55\) −2.01950 −0.272310
\(56\) 0 0
\(57\) 0 0
\(58\) 0.0570257 + 0.0987714i 0.00748784 + 0.0129693i
\(59\) −8.44331 −1.09923 −0.549613 0.835419i \(-0.685225\pi\)
−0.549613 + 0.835419i \(0.685225\pi\)
\(60\) 0 0
\(61\) −3.23917 −0.414733 −0.207367 0.978263i \(-0.566489\pi\)
−0.207367 + 0.978263i \(0.566489\pi\)
\(62\) 7.08467 0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) −6.90868 −0.856916
\(66\) 0 0
\(67\) 6.93339 0.847049 0.423524 0.905885i \(-0.360793\pi\)
0.423524 + 0.905885i \(0.360793\pi\)
\(68\) 1.07663 + 1.86478i 0.130561 + 0.226138i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3304 1.46335 0.731673 0.681656i \(-0.238740\pi\)
0.731673 + 0.681656i \(0.238740\pi\)
\(72\) 0 0
\(73\) 1.37936 + 2.38912i 0.161442 + 0.279625i 0.935386 0.353629i \(-0.115052\pi\)
−0.773944 + 0.633254i \(0.781719\pi\)
\(74\) −0.518508 + 0.898083i −0.0602754 + 0.104400i
\(75\) 0 0
\(76\) 1.74064 3.01488i 0.199665 0.345830i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.91938 −0.665982 −0.332991 0.942930i \(-0.608058\pi\)
−0.332991 + 0.942930i \(0.608058\pi\)
\(80\) 3.23529 + 5.60368i 0.361716 + 0.626511i
\(81\) 0 0
\(82\) 8.30746 14.3889i 0.917406 1.58899i
\(83\) 2.80111 + 4.85167i 0.307462 + 0.532540i 0.977806 0.209510i \(-0.0671870\pi\)
−0.670344 + 0.742050i \(0.733854\pi\)
\(84\) 0 0
\(85\) 1.03372 1.79045i 0.112122 0.194202i
\(86\) 9.39010 + 16.2641i 1.01256 + 1.75381i
\(87\) 0 0
\(88\) −0.849444 + 1.47128i −0.0905511 + 0.156839i
\(89\) 0.703287 1.21813i 0.0745483 0.129121i −0.826341 0.563169i \(-0.809582\pi\)
0.900890 + 0.434048i \(0.142915\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.11636 8.86180i −0.533418 0.923906i
\(93\) 0 0
\(94\) −17.5259 −1.80765
\(95\) −3.34251 −0.342935
\(96\) 0 0
\(97\) 6.09713 + 10.5605i 0.619070 + 1.07226i 0.989656 + 0.143462i \(0.0458236\pi\)
−0.370586 + 0.928798i \(0.620843\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.23708 3.87474i 0.223708 0.387474i
\(101\) −0.559336 + 0.968798i −0.0556560 + 0.0963990i −0.892511 0.451025i \(-0.851058\pi\)
0.836855 + 0.547425i \(0.184392\pi\)
\(102\) 0 0
\(103\) 0.965224 + 1.67182i 0.0951063 + 0.164729i 0.909653 0.415369i \(-0.136348\pi\)
−0.814547 + 0.580098i \(0.803014\pi\)
\(104\) −2.90593 + 5.03322i −0.284950 + 0.493548i
\(105\) 0 0
\(106\) −1.39082 2.40898i −0.135089 0.233981i
\(107\) −2.88969 + 5.00509i −0.279357 + 0.483860i −0.971225 0.238163i \(-0.923455\pi\)
0.691868 + 0.722024i \(0.256788\pi\)
\(108\) 0 0
\(109\) −4.12106 7.13788i −0.394726 0.683685i 0.598340 0.801242i \(-0.295827\pi\)
−0.993066 + 0.117557i \(0.962494\pi\)
\(110\) −3.71839 −0.354535
\(111\) 0 0
\(112\) 0 0
\(113\) −7.25105 + 12.5592i −0.682121 + 1.18147i 0.292211 + 0.956354i \(0.405609\pi\)
−0.974332 + 0.225115i \(0.927724\pi\)
\(114\) 0 0
\(115\) −4.91242 + 8.50856i −0.458085 + 0.793427i
\(116\) 0.0430553 + 0.0745740i 0.00399759 + 0.00692403i
\(117\) 0 0
\(118\) −15.5462 −1.43114
\(119\) 0 0
\(120\) 0 0
\(121\) 4.35539 + 7.54376i 0.395945 + 0.685796i
\(122\) −5.96409 −0.539963
\(123\) 0 0
\(124\) 5.34904 0.480358
\(125\) −10.9696 −0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) 8.56521 0.757065
\(129\) 0 0
\(130\) −12.7205 −1.11566
\(131\) 1.00673 + 1.74371i 0.0879585 + 0.152349i 0.906648 0.421888i \(-0.138632\pi\)
−0.818690 + 0.574236i \(0.805299\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.7660 1.10282
\(135\) 0 0
\(136\) −0.869605 1.50620i −0.0745680 0.129156i
\(137\) 1.10870 1.92032i 0.0947225 0.164064i −0.814770 0.579784i \(-0.803137\pi\)
0.909493 + 0.415720i \(0.136470\pi\)
\(138\) 0 0
\(139\) −0.377669 + 0.654143i −0.0320335 + 0.0554836i −0.881598 0.472002i \(-0.843532\pi\)
0.849564 + 0.527485i \(0.176865\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 22.7032 1.90521
\(143\) −3.91568 6.78216i −0.327446 0.567153i
\(144\) 0 0
\(145\) 0.0413391 0.0716014i 0.00343303 0.00594618i
\(146\) 2.53973 + 4.39894i 0.210189 + 0.364059i
\(147\) 0 0
\(148\) −0.391482 + 0.678068i −0.0321797 + 0.0557368i
\(149\) 3.29249 + 5.70277i 0.269732 + 0.467189i 0.968792 0.247873i \(-0.0797317\pi\)
−0.699061 + 0.715062i \(0.746398\pi\)
\(150\) 0 0
\(151\) −6.33356 + 10.9700i −0.515417 + 0.892729i 0.484422 + 0.874834i \(0.339030\pi\)
−0.999840 + 0.0178950i \(0.994304\pi\)
\(152\) −1.40593 + 2.43514i −0.114036 + 0.197516i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.56791 4.44775i −0.206260 0.357252i
\(156\) 0 0
\(157\) 17.3074 1.38128 0.690642 0.723197i \(-0.257328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(158\) −10.8990 −0.867078
\(159\) 0 0
\(160\) 4.45822 + 7.72186i 0.352453 + 0.610467i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.10963 10.5822i 0.478543 0.828861i −0.521154 0.853463i \(-0.674498\pi\)
0.999697 + 0.0246014i \(0.00783167\pi\)
\(164\) 6.27227 10.8639i 0.489782 0.848327i
\(165\) 0 0
\(166\) 5.15752 + 8.93309i 0.400301 + 0.693342i
\(167\) 1.76248 3.05270i 0.136385 0.236225i −0.789741 0.613440i \(-0.789785\pi\)
0.926126 + 0.377215i \(0.123118\pi\)
\(168\) 0 0
\(169\) −6.89546 11.9433i −0.530420 0.918714i
\(170\) 1.90332 3.29665i 0.145978 0.252842i
\(171\) 0 0
\(172\) 7.08968 + 12.2797i 0.540583 + 0.936318i
\(173\) 10.1409 0.770999 0.385500 0.922708i \(-0.374029\pi\)
0.385500 + 0.922708i \(0.374029\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.66738 + 6.35208i −0.276439 + 0.478806i
\(177\) 0 0
\(178\) 1.29492 2.24287i 0.0970584 0.168110i
\(179\) −0.850579 1.47325i −0.0635752 0.110116i 0.832486 0.554046i \(-0.186917\pi\)
−0.896061 + 0.443931i \(0.853584\pi\)
\(180\) 0 0
\(181\) 16.9941 1.26316 0.631581 0.775310i \(-0.282406\pi\)
0.631581 + 0.775310i \(0.282406\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.13252 + 7.15774i 0.304654 + 0.527676i
\(185\) 0.751755 0.0552701
\(186\) 0 0
\(187\) 2.34355 0.171377
\(188\) −13.2323 −0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) −22.6939 −1.64208 −0.821038 0.570873i \(-0.806605\pi\)
−0.821038 + 0.570873i \(0.806605\pi\)
\(192\) 0 0
\(193\) 6.18698 0.445348 0.222674 0.974893i \(-0.428521\pi\)
0.222674 + 0.974893i \(0.428521\pi\)
\(194\) 11.2263 + 19.4445i 0.806001 + 1.39603i
\(195\) 0 0
\(196\) 0 0
\(197\) −9.77010 −0.696091 −0.348045 0.937478i \(-0.613154\pi\)
−0.348045 + 0.937478i \(0.613154\pi\)
\(198\) 0 0
\(199\) 4.33973 + 7.51664i 0.307636 + 0.532840i 0.977845 0.209332i \(-0.0671289\pi\)
−0.670209 + 0.742172i \(0.733796\pi\)
\(200\) −1.80691 + 3.12965i −0.127768 + 0.221300i
\(201\) 0 0
\(202\) −1.02987 + 1.78379i −0.0724615 + 0.125507i
\(203\) 0 0
\(204\) 0 0
\(205\) −12.0445 −0.841224
\(206\) 1.77721 + 3.07822i 0.123824 + 0.214470i
\(207\) 0 0
\(208\) −12.5460 + 21.7303i −0.869909 + 1.50673i
\(209\) −1.89446 3.28130i −0.131043 0.226973i
\(210\) 0 0
\(211\) −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(212\) −1.05010 1.81882i −0.0721209 0.124917i
\(213\) 0 0
\(214\) −5.32062 + 9.21558i −0.363710 + 0.629964i
\(215\) 6.80708 11.7902i 0.464239 0.804086i
\(216\) 0 0
\(217\) 0 0
\(218\) −7.58786 13.1426i −0.513915 0.890126i
\(219\) 0 0
\(220\) −2.80745 −0.189278
\(221\) 8.01723 0.539298
\(222\) 0 0
\(223\) −5.86133 10.1521i −0.392503 0.679836i 0.600276 0.799793i \(-0.295058\pi\)
−0.992779 + 0.119957i \(0.961724\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −13.3509 + 23.1245i −0.888091 + 1.53822i
\(227\) −5.59154 + 9.68482i −0.371123 + 0.642804i −0.989739 0.142890i \(-0.954361\pi\)
0.618615 + 0.785694i \(0.287694\pi\)
\(228\) 0 0
\(229\) −4.82824 8.36275i −0.319059 0.552626i 0.661233 0.750181i \(-0.270033\pi\)
−0.980292 + 0.197554i \(0.936700\pi\)
\(230\) −9.04494 + 15.6663i −0.596406 + 1.03301i
\(231\) 0 0
\(232\) −0.0347761 0.0602340i −0.00228317 0.00395456i
\(233\) 9.64492 16.7055i 0.631860 1.09441i −0.355311 0.934748i \(-0.615625\pi\)
0.987171 0.159666i \(-0.0510416\pi\)
\(234\) 0 0
\(235\) 6.35243 + 11.0027i 0.414387 + 0.717739i
\(236\) −11.7376 −0.764054
\(237\) 0 0
\(238\) 0 0
\(239\) 0.194641 0.337128i 0.0125903 0.0218070i −0.859662 0.510864i \(-0.829326\pi\)
0.872252 + 0.489057i \(0.162659\pi\)
\(240\) 0 0
\(241\) 5.31807 9.21117i 0.342567 0.593344i −0.642342 0.766419i \(-0.722037\pi\)
0.984909 + 0.173075i \(0.0553703\pi\)
\(242\) 8.01932 + 13.8899i 0.515502 + 0.892875i
\(243\) 0 0
\(244\) −4.50299 −0.288274
\(245\) 0 0
\(246\) 0 0
\(247\) −6.48091 11.2253i −0.412370 0.714247i
\(248\) −4.32046 −0.274350
\(249\) 0 0
\(250\) −20.1976 −1.27741
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) 15.6506 0.982007
\(255\) 0 0
\(256\) 20.9793 1.31121
\(257\) 2.34787 + 4.06663i 0.146456 + 0.253669i 0.929915 0.367774i \(-0.119880\pi\)
−0.783459 + 0.621443i \(0.786547\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −9.60421 −0.595628
\(261\) 0 0
\(262\) 1.85363 + 3.21059i 0.114518 + 0.198351i
\(263\) 9.77491 16.9306i 0.602747 1.04399i −0.389656 0.920960i \(-0.627406\pi\)
0.992403 0.123028i \(-0.0392605\pi\)
\(264\) 0 0
\(265\) −1.00824 + 1.74632i −0.0619355 + 0.107276i
\(266\) 0 0
\(267\) 0 0
\(268\) 9.63858 0.588770
\(269\) 7.88365 + 13.6549i 0.480675 + 0.832553i 0.999754 0.0221730i \(-0.00705846\pi\)
−0.519079 + 0.854726i \(0.673725\pi\)
\(270\) 0 0
\(271\) −7.39882 + 12.8151i −0.449446 + 0.778464i −0.998350 0.0574218i \(-0.981712\pi\)
0.548904 + 0.835886i \(0.315045\pi\)
\(272\) −3.75442 6.50285i −0.227645 0.394293i
\(273\) 0 0
\(274\) 2.04138 3.53578i 0.123324 0.213604i
\(275\) −2.43477 4.21715i −0.146822 0.254304i
\(276\) 0 0
\(277\) 3.72561 6.45295i 0.223850 0.387720i −0.732124 0.681172i \(-0.761471\pi\)
0.955974 + 0.293452i \(0.0948040\pi\)
\(278\) −0.695380 + 1.20443i −0.0417061 + 0.0722371i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9938 + 22.5060i 0.775146 + 1.34259i 0.934712 + 0.355406i \(0.115657\pi\)
−0.159566 + 0.987187i \(0.551009\pi\)
\(282\) 0 0
\(283\) −18.7554 −1.11489 −0.557445 0.830214i \(-0.688218\pi\)
−0.557445 + 0.830214i \(0.688218\pi\)
\(284\) 17.1413 1.01715
\(285\) 0 0
\(286\) −7.20971 12.4876i −0.426319 0.738406i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.30041 12.6447i 0.429436 0.743805i
\(290\) 0.0761152 0.131835i 0.00446964 0.00774165i
\(291\) 0 0
\(292\) 1.91754 + 3.32127i 0.112215 + 0.194363i
\(293\) −1.23089 + 2.13196i −0.0719093 + 0.124551i −0.899738 0.436430i \(-0.856243\pi\)
0.827829 + 0.560981i \(0.189576\pi\)
\(294\) 0 0
\(295\) 5.63487 + 9.75988i 0.328075 + 0.568242i
\(296\) 0.316203 0.547680i 0.0183790 0.0318333i
\(297\) 0 0
\(298\) 6.06227 + 10.5002i 0.351178 + 0.608258i
\(299\) −38.0994 −2.20334
\(300\) 0 0
\(301\) 0 0
\(302\) −11.6616 + 20.1985i −0.671050 + 1.16229i
\(303\) 0 0
\(304\) −6.06994 + 10.5134i −0.348135 + 0.602987i
\(305\) 2.16175 + 3.74425i 0.123781 + 0.214395i
\(306\) 0 0
\(307\) 4.66277 0.266118 0.133059 0.991108i \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.72814 8.18938i −0.268541 0.465126i
\(311\) 27.4821 1.55837 0.779183 0.626797i \(-0.215634\pi\)
0.779183 + 0.626797i \(0.215634\pi\)
\(312\) 0 0
\(313\) −5.49332 −0.310501 −0.155250 0.987875i \(-0.549618\pi\)
−0.155250 + 0.987875i \(0.549618\pi\)
\(314\) 31.8671 1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) −9.87758 −0.554780 −0.277390 0.960757i \(-0.589469\pi\)
−0.277390 + 0.960757i \(0.589469\pi\)
\(318\) 0 0
\(319\) 0.0937203 0.00524733
\(320\) 1.73808 + 3.01044i 0.0971614 + 0.168288i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.87885 0.215825
\(324\) 0 0
\(325\) −8.32930 14.4268i −0.462026 0.800253i
\(326\) 11.2493 19.4844i 0.623041 1.07914i
\(327\) 0 0
\(328\) −5.06616 + 8.77485i −0.279732 + 0.484510i
\(329\) 0 0
\(330\) 0 0
\(331\) −20.6942 −1.13746 −0.568729 0.822525i \(-0.692565\pi\)
−0.568729 + 0.822525i \(0.692565\pi\)
\(332\) 3.89401 + 6.74463i 0.213712 + 0.370160i
\(333\) 0 0
\(334\) 3.24514 5.62076i 0.177566 0.307554i
\(335\) −4.62718 8.01452i −0.252810 0.437880i
\(336\) 0 0
\(337\) 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i \(-0.820347\pi\)
0.885698 + 0.464261i \(0.153680\pi\)
\(338\) −12.6962 21.9905i −0.690582 1.19612i
\(339\) 0 0
\(340\) 1.43704 2.48903i 0.0779344 0.134986i
\(341\) 2.91087 5.04177i 0.157632 0.273027i
\(342\) 0 0
\(343\) 0 0
\(344\) −5.72639 9.91840i −0.308746 0.534764i
\(345\) 0 0
\(346\) 18.6719 1.00381
\(347\) 29.5388 1.58572 0.792862 0.609401i \(-0.208590\pi\)
0.792862 + 0.609401i \(0.208590\pi\)
\(348\) 0 0
\(349\) −18.0006 31.1780i −0.963551 1.66892i −0.713458 0.700698i \(-0.752872\pi\)
−0.250094 0.968222i \(-0.580461\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.05363 + 8.75315i −0.269360 + 0.466545i
\(353\) 14.7465 25.5417i 0.784877 1.35945i −0.144196 0.989549i \(-0.546060\pi\)
0.929073 0.369897i \(-0.120607\pi\)
\(354\) 0 0
\(355\) −8.22900 14.2530i −0.436750 0.756473i
\(356\) 0.977687 1.69340i 0.0518173 0.0897502i
\(357\) 0 0
\(358\) −1.56612 2.71260i −0.0827720 0.143365i
\(359\) −2.70535 + 4.68580i −0.142783 + 0.247307i −0.928544 0.371224i \(-0.878938\pi\)
0.785761 + 0.618531i \(0.212272\pi\)
\(360\) 0 0
\(361\) 6.36444 + 11.0235i 0.334971 + 0.580186i
\(362\) 31.2902 1.64458
\(363\) 0 0
\(364\) 0 0
\(365\) 1.84110 3.18888i 0.0963676 0.166914i
\(366\) 0 0
\(367\) −11.5422 + 19.9916i −0.602496 + 1.04355i 0.389946 + 0.920838i \(0.372494\pi\)
−0.992442 + 0.122715i \(0.960840\pi\)
\(368\) 17.8417 + 30.9027i 0.930063 + 1.61092i
\(369\) 0 0
\(370\) 1.38416 0.0719591
\(371\) 0 0
\(372\) 0 0
\(373\) −10.7515 18.6222i −0.556692 0.964219i −0.997770 0.0667498i \(-0.978737\pi\)
0.441078 0.897469i \(-0.354596\pi\)
\(374\) 4.31504 0.223125
\(375\) 0 0
\(376\) 10.6878 0.551184
\(377\) 0.320615 0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) −4.64665 −0.238368
\(381\) 0 0
\(382\) −41.7850 −2.13791
\(383\) 17.4604 + 30.2424i 0.892187 + 1.54531i 0.837248 + 0.546823i \(0.184163\pi\)
0.0549390 + 0.998490i \(0.482504\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 11.3917 0.579823
\(387\) 0 0
\(388\) 8.47603 + 14.6809i 0.430305 + 0.745311i
\(389\) −14.4411 + 25.0127i −0.732192 + 1.26819i 0.223752 + 0.974646i \(0.428169\pi\)
−0.955944 + 0.293548i \(0.905164\pi\)
\(390\) 0 0
\(391\) 5.70066 9.87383i 0.288295 0.499341i
\(392\) 0 0
\(393\) 0 0
\(394\) −17.9891 −0.906278
\(395\) 3.95046 + 6.84239i 0.198769 + 0.344278i
\(396\) 0 0
\(397\) −5.59226 + 9.68607i −0.280667 + 0.486130i −0.971549 0.236838i \(-0.923889\pi\)
0.690882 + 0.722968i \(0.257222\pi\)
\(398\) 7.99049 + 13.8399i 0.400527 + 0.693734i
\(399\) 0 0
\(400\) −7.80111 + 13.5119i −0.390056 + 0.675596i
\(401\) −0.541061 0.937146i −0.0270193 0.0467988i 0.852200 0.523217i \(-0.175268\pi\)
−0.879219 + 0.476418i \(0.841935\pi\)
\(402\) 0 0
\(403\) 9.95802 17.2478i 0.496044 0.859174i
\(404\) −0.777570 + 1.34679i −0.0386856 + 0.0670054i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.426078 + 0.737988i 0.0211199 + 0.0365807i
\(408\) 0 0
\(409\) 21.7349 1.07472 0.537360 0.843353i \(-0.319422\pi\)
0.537360 + 0.843353i \(0.319422\pi\)
\(410\) −22.1768 −1.09524
\(411\) 0 0
\(412\) 1.34182 + 2.32410i 0.0661069 + 0.114500i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.73879 6.47578i 0.183530 0.317884i
\(416\) −17.2884 + 29.9443i −0.847632 + 1.46814i
\(417\) 0 0
\(418\) −3.48816 6.04167i −0.170611 0.295508i
\(419\) 12.5906 21.8075i 0.615090 1.06537i −0.375279 0.926912i \(-0.622453\pi\)
0.990369 0.138455i \(-0.0442135\pi\)
\(420\) 0 0
\(421\) −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i \(-0.909527\pi\)
0.237090 0.971488i \(-0.423806\pi\)
\(422\) −5.23316 + 9.06411i −0.254746 + 0.441234i
\(423\) 0 0
\(424\) 0.848171 + 1.46907i 0.0411908 + 0.0713446i
\(425\) 4.98512 0.241814
\(426\) 0 0
\(427\) 0 0
\(428\) −4.01715 + 6.95791i −0.194176 + 0.336323i
\(429\) 0 0
\(430\) 12.5335 21.7086i 0.604418 1.04688i
\(431\) −2.44517 4.23516i −0.117780 0.204000i 0.801108 0.598520i \(-0.204244\pi\)
−0.918887 + 0.394520i \(0.870911\pi\)
\(432\) 0 0
\(433\) −9.71430 −0.466839 −0.233420 0.972376i \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.72896 9.92285i −0.274367 0.475218i
\(437\) −18.4330 −0.881771
\(438\) 0 0
\(439\) 14.8235 0.707488 0.353744 0.935342i \(-0.384908\pi\)
0.353744 + 0.935342i \(0.384908\pi\)
\(440\) 2.26760 0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) 21.9020 1.04059 0.520297 0.853986i \(-0.325821\pi\)
0.520297 + 0.853986i \(0.325821\pi\)
\(444\) 0 0
\(445\) −1.87743 −0.0889987
\(446\) −10.7921 18.6925i −0.511021 0.885115i
\(447\) 0 0
\(448\) 0 0
\(449\) −21.4952 −1.01442 −0.507212 0.861822i \(-0.669324\pi\)
−0.507212 + 0.861822i \(0.669324\pi\)
\(450\) 0 0
\(451\) −6.82655 11.8239i −0.321450 0.556767i
\(452\) −10.0802 + 17.4594i −0.474131 + 0.821220i
\(453\) 0 0
\(454\) −10.2954 + 17.8321i −0.483185 + 0.836902i
\(455\) 0 0
\(456\) 0 0
\(457\) 40.6255 1.90038 0.950190 0.311670i \(-0.100888\pi\)
0.950190 + 0.311670i \(0.100888\pi\)
\(458\) −8.88995 15.3978i −0.415400 0.719494i
\(459\) 0 0
\(460\) −6.82908 + 11.8283i −0.318408 + 0.551498i
\(461\) 1.41541 + 2.45155i 0.0659220 + 0.114180i 0.897103 0.441822i \(-0.145668\pi\)
−0.831181 + 0.556003i \(0.812334\pi\)
\(462\) 0 0
\(463\) −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i \(0.390850\pi\)
−0.983719 + 0.179711i \(0.942484\pi\)
\(464\) −0.150142 0.260053i −0.00697016 0.0120727i
\(465\) 0 0
\(466\) 17.7586 30.7588i 0.822653 1.42488i
\(467\) −13.3219 + 23.0742i −0.616464 + 1.06775i 0.373661 + 0.927565i \(0.378102\pi\)
−0.990126 + 0.140182i \(0.955231\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 11.6964 + 20.2587i 0.539513 + 0.934463i
\(471\) 0 0
\(472\) 9.48056 0.436378
\(473\) 15.4324 0.709582
\(474\) 0 0
\(475\) −4.02983 6.97987i −0.184901 0.320258i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.358381 0.620734i 0.0163920 0.0283917i
\(479\) 15.7895 27.3483i 0.721443 1.24958i −0.238979 0.971025i \(-0.576813\pi\)
0.960422 0.278551i \(-0.0898540\pi\)
\(480\) 0 0
\(481\) 1.45760 + 2.52464i 0.0664609 + 0.115114i
\(482\) 9.79185 16.9600i 0.446007 0.772506i
\(483\) 0 0
\(484\) 6.05472 + 10.4871i 0.275215 + 0.476686i
\(485\) 8.13817 14.0957i 0.369535 0.640054i
\(486\) 0 0
\(487\) −0.153087 0.265154i −0.00693703 0.0120153i 0.862536 0.505996i \(-0.168875\pi\)
−0.869473 + 0.493980i \(0.835541\pi\)
\(488\) 3.63710 0.164644
\(489\) 0 0
\(490\) 0 0
\(491\) 9.06981 15.7094i 0.409315 0.708954i −0.585498 0.810674i \(-0.699101\pi\)
0.994813 + 0.101720i \(0.0324345\pi\)
\(492\) 0 0
\(493\) −0.0479723 + 0.0830905i −0.00216057 + 0.00374221i
\(494\) −11.9329 20.6684i −0.536887 0.929916i
\(495\) 0 0
\(496\) −18.6531 −0.837549
\(497\) 0 0
\(498\) 0 0
\(499\) 10.6546 + 18.4543i 0.476964 + 0.826126i 0.999652 0.0263983i \(-0.00840381\pi\)
−0.522687 + 0.852524i \(0.675070\pi\)
\(500\) −15.2496 −0.681981
\(501\) 0 0
\(502\) −6.01401 −0.268418
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) −20.5059 −0.911597
\(507\) 0 0
\(508\) 11.8165 0.524271
\(509\) −18.3868 31.8468i −0.814979 1.41159i −0.909343 0.416048i \(-0.863415\pi\)
0.0943635 0.995538i \(-0.469918\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 21.4975 0.950065
\(513\) 0 0
\(514\) 4.32299 + 7.48764i 0.190679 + 0.330265i
\(515\) 1.28834 2.23146i 0.0567709 0.0983300i
\(516\) 0 0
\(517\) −7.20083 + 12.4722i −0.316692 + 0.548527i
\(518\) 0 0
\(519\) 0 0
\(520\) 7.75740 0.340184
\(521\) −9.57535 16.5850i −0.419504 0.726602i 0.576386 0.817178i \(-0.304463\pi\)
−0.995890 + 0.0905758i \(0.971129\pi\)
\(522\) 0 0
\(523\) 20.9715 36.3236i 0.917018 1.58832i 0.113097 0.993584i \(-0.463923\pi\)
0.803920 0.594737i \(-0.202744\pi\)
\(524\) 1.39952 + 2.42405i 0.0611385 + 0.105895i
\(525\) 0 0
\(526\) 17.9980 31.1734i 0.784749 1.35922i
\(527\) 2.97996 + 5.16144i 0.129809 + 0.224836i
\(528\) 0 0
\(529\) −15.5906 + 27.0037i −0.677851 + 1.17407i
\(530\) −1.85641 + 3.21539i −0.0806372 + 0.139668i
\(531\) 0 0
\(532\) 0 0
\(533\) −23.3535 40.4494i −1.01155 1.75206i
\(534\) 0 0
\(535\) 7.71405 0.333507
\(536\) −7.78515 −0.336267
\(537\) 0 0
\(538\) 14.5157 + 25.1419i 0.625816 + 1.08395i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.44272 + 2.49886i −0.0620273 + 0.107434i −0.895371 0.445320i \(-0.853090\pi\)
0.833344 + 0.552754i \(0.186423\pi\)
\(542\) −13.6230 + 23.5957i −0.585158 + 1.01352i
\(543\) 0 0
\(544\) −5.17358 8.96090i −0.221815 0.384196i
\(545\) −5.50059 + 9.52731i −0.235620 + 0.408105i
\(546\) 0 0
\(547\) 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i \(-0.147773\pi\)
−0.834840 + 0.550492i \(0.814440\pi\)
\(548\) 1.54128 2.66957i 0.0658401 0.114038i
\(549\) 0 0
\(550\) −4.48300 7.76478i −0.191156 0.331091i
\(551\) 0.155118 0.00660825
\(552\) 0 0
\(553\) 0 0
\(554\) 6.85975 11.8814i 0.291443 0.504794i
\(555\) 0 0
\(556\) −0.525024 + 0.909368i −0.0222660 + 0.0385658i
\(557\) −15.5344 26.9064i −0.658214 1.14006i −0.981078 0.193614i \(-0.937979\pi\)
0.322864 0.946445i \(-0.395354\pi\)
\(558\) 0 0
\(559\) 52.7939 2.23294
\(560\) 0 0
\(561\) 0 0
\(562\) 23.9248 + 41.4389i 1.00920 + 1.74799i
\(563\) 0.288041 0.0121395 0.00606973 0.999982i \(-0.498068\pi\)
0.00606973 + 0.999982i \(0.498068\pi\)
\(564\) 0 0
\(565\) 19.3567 0.814344
\(566\) −34.5331 −1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) 16.0801 0.674112 0.337056 0.941485i \(-0.390569\pi\)
0.337056 + 0.941485i \(0.390569\pi\)
\(570\) 0 0
\(571\) −15.2858 −0.639690 −0.319845 0.947470i \(-0.603631\pi\)
−0.319845 + 0.947470i \(0.603631\pi\)
\(572\) −5.44345 9.42834i −0.227602 0.394218i
\(573\) 0 0
\(574\) 0 0
\(575\) −23.6902 −0.987950
\(576\) 0 0
\(577\) −12.0812 20.9253i −0.502949 0.871133i −0.999994 0.00340833i \(-0.998915\pi\)
0.497045 0.867725i \(-0.334418\pi\)
\(578\) 13.4418 23.2819i 0.559106 0.968400i
\(579\) 0 0
\(580\) 0.0574683 0.0995380i 0.00238624 0.00413309i
\(581\) 0 0
\(582\) 0 0
\(583\) −2.28579 −0.0946676
\(584\) −1.54881 2.68262i −0.0640902 0.111007i
\(585\) 0 0
\(586\) −2.26636 + 3.92546i −0.0936226 + 0.162159i
\(587\) 18.0145 + 31.2020i 0.743537 + 1.28784i 0.950875 + 0.309574i \(0.100186\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(588\) 0 0
\(589\) 4.81783 8.34472i 0.198515 0.343838i
\(590\) 10.3752 + 17.9703i 0.427138 + 0.739825i
\(591\) 0 0
\(592\) 1.36517 2.36455i 0.0561082 0.0971823i
\(593\) 12.4668 21.5932i 0.511951 0.886726i −0.487953 0.872870i \(-0.662256\pi\)
0.999904 0.0138558i \(-0.00441057\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.57712 + 7.92780i 0.187486 + 0.324735i
\(597\) 0 0
\(598\) −70.1501 −2.86865
\(599\) −39.5283 −1.61508 −0.807542 0.589810i \(-0.799203\pi\)
−0.807542 + 0.589810i \(0.799203\pi\)
\(600\) 0 0
\(601\) −1.86447 3.22936i −0.0760534 0.131728i 0.825490 0.564416i \(-0.190899\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.80470 + 15.2502i −0.358258 + 0.620521i
\(605\) 5.81337 10.0691i 0.236347 0.409365i
\(606\) 0 0
\(607\) 11.8264 + 20.4839i 0.480018 + 0.831415i 0.999737 0.0229218i \(-0.00729686\pi\)
−0.519719 + 0.854337i \(0.673964\pi\)
\(608\) −8.36436 + 14.4875i −0.339219 + 0.587545i
\(609\) 0 0
\(610\) 3.98029 + 6.89407i 0.161157 + 0.279133i
\(611\) −24.6339 + 42.6671i −0.996580 + 1.72613i
\(612\) 0 0
\(613\) 1.89952 + 3.29006i 0.0767208 + 0.132884i 0.901833 0.432084i \(-0.142222\pi\)
−0.825113 + 0.564968i \(0.808888\pi\)
\(614\) 8.58528 0.346474
\(615\) 0 0
\(616\) 0 0
\(617\) 17.5615 30.4174i 0.706999 1.22456i −0.258966 0.965886i \(-0.583382\pi\)
0.965965 0.258672i \(-0.0832849\pi\)
\(618\) 0 0
\(619\) −10.5816 + 18.3279i −0.425311 + 0.736660i −0.996449 0.0841934i \(-0.973169\pi\)
0.571138 + 0.820854i \(0.306502\pi\)
\(620\) −3.56983 6.18312i −0.143368 0.248320i
\(621\) 0 0
\(622\) 50.6011 2.02892
\(623\) 0 0
\(624\) 0 0
\(625\) −0.725240 1.25615i −0.0290096 0.0502461i
\(626\) −10.1145 −0.404257
\(627\) 0 0
\(628\) 24.0602 0.960107
\(629\) −0.872381 −0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) 6.64657 0.264386
\(633\) 0 0
\(634\) −18.1870 −0.722298
\(635\) −5.67273 9.82546i −0.225115 0.389911i
\(636\) 0 0
\(637\) 0 0
\(638\) 0.172562 0.00683178
\(639\) 0 0
\(640\) −5.71622 9.90078i −0.225953 0.391363i
\(641\) −4.93735 + 8.55174i −0.195013 + 0.337773i −0.946905 0.321514i \(-0.895808\pi\)
0.751891 + 0.659287i \(0.229142\pi\)
\(642\) 0 0
\(643\) −21.9748 + 38.0615i −0.866602 + 1.50100i −0.00115462 + 0.999999i \(0.500368\pi\)
−0.865448 + 0.501000i \(0.832966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 7.14190 0.280994
\(647\) 22.1936 + 38.4404i 0.872521 + 1.51125i 0.859381 + 0.511336i \(0.170849\pi\)
0.0131398 + 0.999914i \(0.495817\pi\)
\(648\) 0 0
\(649\) −6.38743 + 11.0634i −0.250729 + 0.434275i
\(650\) −15.3362 26.5631i −0.601537 1.04189i
\(651\) 0 0
\(652\) 8.49341 14.7110i 0.332628 0.576128i
\(653\) 20.9956 + 36.3655i 0.821622 + 1.42309i 0.904474 + 0.426529i \(0.140264\pi\)
−0.0828523 + 0.996562i \(0.526403\pi\)
\(654\) 0 0
\(655\) 1.34374 2.32742i 0.0525042 0.0909399i
\(656\) −21.8726 + 37.8844i −0.853980 + 1.47914i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.6365 + 34.0114i 0.764928 + 1.32489i 0.940284 + 0.340390i \(0.110559\pi\)
−0.175356 + 0.984505i \(0.556108\pi\)
\(660\) 0 0
\(661\) 0.186739 0.00726330 0.00363165 0.999993i \(-0.498844\pi\)
0.00363165 + 0.999993i \(0.498844\pi\)
\(662\) −38.1030 −1.48092
\(663\) 0 0
\(664\) −3.14522 5.44769i −0.122058 0.211411i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.227973 0.394862i 0.00882717 0.0152891i
\(668\) 2.45014 4.24376i 0.0947987 0.164196i
\(669\) 0 0
\(670\) −8.51976 14.7567i −0.329147 0.570099i
\(671\) −2.45046 + 4.24432i −0.0945989 + 0.163850i
\(672\) 0 0
\(673\) −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(674\) 1.37862 2.38785i 0.0531026 0.0919764i
\(675\) 0 0
\(676\) −9.58584 16.6032i −0.368686 0.638583i
\(677\) 28.3901 1.09112 0.545560 0.838072i \(-0.316317\pi\)
0.545560 + 0.838072i \(0.316317\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.16071 + 2.01041i −0.0445111 + 0.0770956i
\(681\) 0 0
\(682\) 5.35961 9.28312i 0.205230 0.355469i
\(683\) −5.92034 10.2543i −0.226536 0.392371i 0.730243 0.683187i \(-0.239407\pi\)
−0.956779 + 0.290816i \(0.906073\pi\)
\(684\) 0 0
\(685\) −2.95968 −0.113083
\(686\) 0 0
\(687\) 0 0
\(688\) −24.7230 42.8216i −0.942557 1.63256i
\(689\) −7.81962 −0.297904
\(690\) 0 0
\(691\) −11.9083 −0.453014 −0.226507 0.974010i \(-0.572731\pi\)
−0.226507 + 0.974010i \(0.572731\pi\)
\(692\) 14.0976 0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) 1.00819 0.0382429
\(696\) 0 0
\(697\) 13.9771 0.529422
\(698\) −33.1435 57.4062i −1.25450 2.17286i
\(699\) 0 0
\(700\) 0 0
\(701\) 31.3902 1.18559 0.592795 0.805353i \(-0.298024\pi\)
0.592795 + 0.805353i \(0.298024\pi\)
\(702\) 0 0
\(703\) 0.705208 + 1.22146i 0.0265974 + 0.0460681i
\(704\) −1.97020 + 3.41249i −0.0742549 + 0.128613i
\(705\) 0 0
\(706\) 27.1518 47.0284i 1.02187 1.76994i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.625218 0.0234806 0.0117403 0.999931i \(-0.496263\pi\)
0.0117403 + 0.999931i \(0.496263\pi\)
\(710\) −15.1516 26.2433i −0.568628 0.984893i
\(711\) 0 0
\(712\) −0.789685 + 1.36777i −0.0295947 + 0.0512595i
\(713\) −14.1613 24.5281i −0.530345 0.918584i
\(714\) 0 0
\(715\) −5.22647 + 9.05251i −0.195459 + 0.338545i
\(716\) −1.18245 2.04806i −0.0441901 0.0765395i
\(717\) 0 0
\(718\) −4.98119 + 8.62768i −0.185897 + 0.321982i
\(719\) 12.1969 21.1257i 0.454869 0.787857i −0.543811 0.839208i \(-0.683019\pi\)
0.998681 + 0.0513506i \(0.0163526\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11.7185 + 20.2970i 0.436116 + 0.755376i
\(723\) 0 0
\(724\) 23.6246 0.878003
\(725\) 0.199358 0.00740399
\(726\) 0 0
\(727\) 18.9253 + 32.7796i 0.701900 + 1.21573i 0.967799 + 0.251726i \(0.0809980\pi\)
−0.265899 + 0.964001i \(0.585669\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.38991 5.87150i 0.125466 0.217314i
\(731\) −7.89934 + 13.6821i −0.292168 + 0.506049i
\(732\) 0 0
\(733\) 1.20077 + 2.07980i 0.0443516 + 0.0768193i 0.887349 0.461098i \(-0.152544\pi\)
−0.842997 + 0.537918i \(0.819211\pi\)
\(734\) −21.2519 + 36.8093i −0.784421 + 1.35866i
\(735\) 0 0
\(736\) 24.5858 + 42.5839i 0.906245 + 1.56966i
\(737\) 5.24517 9.08490i 0.193208 0.334646i
\(738\) 0 0
\(739\) −15.1940 26.3167i −0.558920 0.968077i −0.997587 0.0694277i \(-0.977883\pi\)
0.438667 0.898650i \(-0.355451\pi\)
\(740\) 1.04507 0.0384174
\(741\) 0 0
\(742\) 0 0
\(743\) 2.54785 4.41300i 0.0934715 0.161897i −0.815498 0.578760i \(-0.803537\pi\)
0.908970 + 0.416862i \(0.136870\pi\)
\(744\) 0 0
\(745\) 4.39467 7.61179i 0.161008 0.278874i
\(746\) −19.7961 34.2879i −0.724787 1.25537i
\(747\) 0 0
\(748\) 3.25793 0.119122
\(749\) 0 0
\(750\) 0 0
\(751\) 0.487506 + 0.844384i 0.0177893 + 0.0308120i 0.874783 0.484515i \(-0.161004\pi\)
−0.856994 + 0.515327i \(0.827671\pi\)
\(752\) 46.1435 1.68268
\(753\) 0 0
\(754\) 0.590329 0.0214985
\(755\) 16.9075 0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) 10.5350 0.382648
\(759\) 0 0
\(760\) 3.75314 0.136141
\(761\) 27.0875 + 46.9169i 0.981920 + 1.70073i 0.654897 + 0.755718i \(0.272712\pi\)
0.327023 + 0.945016i \(0.393955\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −31.5484 −1.14138
\(765\) 0 0
\(766\) 32.1489 + 55.6835i 1.16159 + 2.01193i
\(767\) −21.8513 + 37.8475i −0.789004 + 1.36659i
\(768\) 0 0
\(769\) 10.4326 18.0698i 0.376208 0.651612i −0.614299 0.789074i \(-0.710561\pi\)
0.990507 + 0.137462i \(0.0438943\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.60094 0.309554
\(773\) −27.4972 47.6266i −0.989007 1.71301i −0.622561 0.782572i \(-0.713908\pi\)
−0.366447 0.930439i \(-0.619426\pi\)
\(774\) 0 0
\(775\) 6.19189 10.7247i 0.222419 0.385242i
\(776\) −6.84616 11.8579i −0.245763 0.425674i
\(777\) 0 0
\(778\) −26.5895 + 46.0544i −0.953281 + 1.65113i
\(779\) −11.2987 19.5700i −0.404819 0.701168i
\(780\) 0 0
\(781\) 9.32802 16.1566i 0.333783 0.578129i
\(782\) 10.4963 18.1801i 0.375346 0.650119i
\(783\) 0 0
\(784\) 0 0
\(785\) −11.5506 20.0062i −0.412258 0.714051i
\(786\) 0 0
\(787\) −9.18949 −0.327570 −0.163785 0.986496i \(-0.552370\pi\)
−0.163785 + 0.986496i \(0.552370\pi\)
\(788\) −13.5821 −0.483841
\(789\) 0 0
\(790\) 7.27374 + 12.5985i 0.258788 + 0.448234i
\(791\) 0 0
\(792\) 0 0
\(793\) −8.38296 + 14.5197i −0.297688 + 0.515610i
\(794\) −10.2967 + 17.8344i −0.365416 + 0.632919i
\(795\) 0 0
\(796\) 6.03296 + 10.4494i 0.213832 + 0.370369i
\(797\) 3.53774 6.12754i 0.125313 0.217049i −0.796542 0.604583i \(-0.793340\pi\)
0.921855 + 0.387534i \(0.126673\pi\)
\(798\) 0 0
\(799\) −7.37174 12.7682i −0.260793 0.451707i
\(800\) −10.7499 + 18.6194i −0.380067 + 0.658295i
\(801\) 0 0
\(802\) −0.996224 1.72551i −0.0351779 0.0609299i
\(803\) 4.17398 0.147297
\(804\) 0 0
\(805\) 0 0
\(806\) 18.3351 31.7573i 0.645827 1.11860i
\(807\) 0 0
\(808\) 0.628050 1.08781i 0.0220947 0.0382692i
\(809\) 2.97060 + 5.14522i 0.104441 + 0.180896i 0.913510 0.406817i \(-0.133361\pi\)
−0.809069 + 0.587714i \(0.800028\pi\)
\(810\) 0 0
\(811\) −44.4139 −1.55958 −0.779791 0.626039i \(-0.784675\pi\)
−0.779791 + 0.626039i \(0.784675\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0.784512 + 1.35881i 0.0274971 + 0.0476264i
\(815\) −16.3097 −0.571304
\(816\) 0 0
\(817\) 25.5424 0.893616
\(818\) 40.0191 1.39924
\(819\) 0 0
\(820\) −16.7439 −0.584721
\(821\) −6.35522 −0.221799 −0.110899 0.993832i \(-0.535373\pi\)
−0.110899 + 0.993832i \(0.535373\pi\)
\(822\) 0 0
\(823\) −9.46433 −0.329906 −0.164953 0.986301i \(-0.552747\pi\)
−0.164953 + 0.986301i \(0.552747\pi\)
\(824\) −1.08380 1.87720i −0.0377560 0.0653953i
\(825\) 0 0
\(826\) 0 0
\(827\) 4.86261 0.169090 0.0845448 0.996420i \(-0.473056\pi\)
0.0845448 + 0.996420i \(0.473056\pi\)
\(828\) 0 0
\(829\) −20.3926 35.3211i −0.708266 1.22675i −0.965500 0.260403i \(-0.916145\pi\)
0.257234 0.966349i \(-0.417189\pi\)
\(830\) 6.88402 11.9235i 0.238948 0.413870i
\(831\) 0 0
\(832\) −6.74003 + 11.6741i −0.233668 + 0.404725i
\(833\) 0 0
\(834\) 0 0
\(835\) −4.70494 −0.162821
\(836\) −2.63362 4.56156i −0.0910856 0.157765i
\(837\) 0 0
\(838\) 23.1823 40.1529i 0.800818 1.38706i
\(839\) 9.60171 + 16.6307i 0.331488 + 0.574154i 0.982804 0.184653i \(-0.0591161\pi\)
−0.651316 + 0.758807i \(0.725783\pi\)
\(840\) 0 0
\(841\) 14.4981 25.1114i 0.499934 0.865911i
\(842\) −27.3063 47.2959i −0.941036 1.62992i
\(843\) 0 0
\(844\) −3.95113 + 6.84355i −0.136003 + 0.235565i
\(845\) −9.20374 + 15.9413i −0.316618 + 0.548399i
\(846\) 0 0
\(847\) 0 0
\(848\) 3.66188 + 6.34256i 0.125749 + 0.217804i
\(849\) 0 0
\(850\) 9.17880 0.314830
\(851\) 4.14571 0.142113
\(852\) 0 0
\(853\) 6.95055 + 12.0387i 0.237982 + 0.412198i 0.960135 0.279536i \(-0.0901806\pi\)
−0.722153 + 0.691734i \(0.756847\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 3.24469 5.61996i 0.110901 0.192086i
\(857\) −28.4919 + 49.3494i −0.973265 + 1.68574i −0.287718 + 0.957715i \(0.592897\pi\)
−0.685547 + 0.728029i \(0.740437\pi\)
\(858\) 0 0
\(859\) −10.0501 17.4073i −0.342905 0.593929i 0.642066 0.766650i \(-0.278078\pi\)
−0.984971 + 0.172721i \(0.944744\pi\)
\(860\) 9.46298 16.3904i 0.322685 0.558907i
\(861\) 0 0
\(862\) −4.50214 7.79794i −0.153344 0.265599i
\(863\) 3.08893 5.35018i 0.105148 0.182122i −0.808650 0.588289i \(-0.799802\pi\)
0.913799 + 0.406167i \(0.133135\pi\)
\(864\) 0 0
\(865\) −6.76781 11.7222i −0.230112 0.398566i
\(866\) −17.8864 −0.607803
\(867\) 0 0
\(868\) 0 0
\(869\) −4.47806 + 7.75623i −0.151908 + 0.263112i
\(870\) 0 0
\(871\) 17.9436 31.0792i 0.607996 1.05308i
\(872\) 4.62732 + 8.01476i 0.156701 + 0.271414i
\(873\) 0 0
\(874\) −33.9396 −1.14802
\(875\) 0 0
\(876\) 0 0
\(877\) 18.6287 + 32.2658i 0.629046 + 1.08954i 0.987743 + 0.156086i \(0.0498877\pi\)
−0.358697 + 0.933454i \(0.616779\pi\)
\(878\) 27.2937 0.921117
\(879\) 0 0
\(880\) 9.79009 0.330024
\(881\) −11.7848 −0.397041 −0.198520 0.980097i \(-0.563614\pi\)
−0.198520 + 0.980097i \(0.563614\pi\)
\(882\) 0 0
\(883\) −29.2308 −0.983693 −0.491847 0.870682i \(-0.663678\pi\)
−0.491847 + 0.870682i \(0.663678\pi\)
\(884\) 11.1453 0.374857
\(885\) 0 0
\(886\) 40.3268 1.35480
\(887\) −14.2581 24.6957i −0.478739 0.829201i 0.520964 0.853579i \(-0.325573\pi\)
−0.999703 + 0.0243782i \(0.992239\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −3.45680 −0.115872
\(891\) 0 0
\(892\) −8.14822 14.1131i −0.272823 0.472543i
\(893\) −11.9182 + 20.6430i −0.398828 + 0.690790i
\(894\) 0 0
\(895\) −1.13531 + 1.96642i −0.0379493 + 0.0657301i
\(896\) 0 0
\(897\) 0 0
\(898\) −39.5779 −1.32073
\(899\) 0.119171 + 0.206410i 0.00397456 + 0.00688414i
\(900\) 0 0
\(901\) 1.17002 2.02653i 0.0389790 0.0675135i
\(902\) −12.5693 21.7707i −0.418513 0.724885i
\(903\) 0 0
\(904\) 8.14183 14.1021i 0.270793 0.469028i
\(905\) −11.3415 19.6440i −0.377003 0.652989i
\(906\) 0 0
\(907\) 3.94577 6.83428i 0.131017 0.226929i −0.793052 0.609154i \(-0.791509\pi\)
0.924069 + 0.382226i \(0.124842\pi\)
\(908\) −7.77317 + 13.4635i −0.257962 + 0.446803i
\(909\) 0 0
\(910\) 0 0
\(911\) 14.2206 + 24.6308i 0.471150 + 0.816055i 0.999455 0.0329991i \(-0.0105058\pi\)
−0.528306 + 0.849054i \(0.677173\pi\)
\(912\) 0 0
\(913\) 8.47625 0.280523
\(914\) 74.8013 2.47421
\(915\) 0 0
\(916\) −6.71206 11.6256i −0.221773 0.384121i
\(917\) 0 0
\(918\) 0 0
\(919\) 3.99271 6.91558i 0.131707 0.228124i −0.792627 0.609706i \(-0.791287\pi\)
0.924335 + 0.381582i \(0.124621\pi\)
\(920\) 5.51590 9.55382i 0.181854 0.314980i
\(921\) 0 0
\(922\) 2.60610 + 4.51390i 0.0858274 + 0.148657i
\(923\) 31.9110 55.2714i 1.05036 1.81928i
\(924\) 0 0
\(925\) 0.906337 + 1.56982i 0.0298002 + 0.0516154i
\(926\) −25.6529 + 44.4322i −0.843008 + 1.46013i
\(927\) 0 0
\(928\) −0.206895 0.358353i −0.00679167 0.0117635i
\(929\) 18.8006 0.616829 0.308414 0.951252i \(-0.400202\pi\)
0.308414 + 0.951252i \(0.400202\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 13.4081 23.2234i 0.439196 0.760709i
\(933\) 0 0
\(934\) −24.5288 + 42.4852i −0.802608 + 1.39016i
\(935\) −1.56403 2.70898i −0.0511493 0.0885932i
\(936\) 0 0
\(937\) −48.5788 −1.58700 −0.793500 0.608570i \(-0.791744\pi\)
−0.793500 + 0.608570i \(0.791744\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 8.83094 + 15.2956i 0.288034 + 0.498889i
\(941\) 20.4851 0.667795 0.333898 0.942609i \(-0.391636\pi\)
0.333898 + 0.942609i \(0.391636\pi\)
\(942\) 0 0
\(943\) −66.4220 −2.16300
\(944\) 40.9312 1.33220
\(945\) 0 0
\(946\) 28.4148 0.923843
\(947\) 14.8505 0.482576 0.241288 0.970454i \(-0.422430\pi\)
0.241288 + 0.970454i \(0.422430\pi\)
\(948\) 0 0
\(949\) 14.2791 0.463519
\(950\) −7.41989 12.8516i −0.240733 0.416962i
\(951\) 0 0
\(952\) 0 0
\(953\) −46.4678 −1.50524 −0.752620 0.658456i \(-0.771210\pi\)
−0.752620 + 0.658456i \(0.771210\pi\)
\(954\) 0 0
\(955\) 15.1454 + 26.2326i 0.490094 + 0.848868i
\(956\) 0.270584 0.468665i 0.00875130 0.0151577i
\(957\) 0 0
\(958\) 29.0724 50.3548i 0.939285 1.62689i
\(959\) 0 0
\(960\) 0 0
\(961\) −16.1947 −0.522409
\(962\) 2.68380 + 4.64847i 0.0865291 + 0.149873i
\(963\) 0 0
\(964\) 7.39301 12.8051i 0.238113 0.412423i
\(965\) −4.12905 7.15172i −0.132919 0.230222i
\(966\) 0 0
\(967\) 0.863670 1.49592i 0.0277738 0.0481056i −0.851804 0.523860i \(-0.824492\pi\)
0.879578 + 0.475754i \(0.157825\pi\)
\(968\) −4.89045 8.47050i −0.157185 0.272252i
\(969\) 0 0
\(970\) 14.9843 25.9536i 0.481118 0.833320i
\(971\) −3.78085 + 6.54863i −0.121333 + 0.210156i −0.920294 0.391228i \(-0.872050\pi\)
0.798960 + 0.601384i \(0.205384\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.281870 0.488213i −0.00903169 0.0156434i
\(975\) 0 0
\(976\) 15.7027 0.502633
\(977\) 56.6202 1.81144 0.905721 0.423875i \(-0.139330\pi\)
0.905721 + 0.423875i \(0.139330\pi\)
\(978\) 0 0
\(979\) −1.06408 1.84305i −0.0340083 0.0589041i
\(980\) 0 0
\(981\) 0 0
\(982\) 16.6997 28.9247i 0.532909 0.923025i
\(983\) −16.1486 + 27.9702i −0.515061 + 0.892112i 0.484786 + 0.874633i \(0.338897\pi\)
−0.999847 + 0.0174790i \(0.994436\pi\)
\(984\) 0 0
\(985\) 6.52033 + 11.2936i 0.207755 + 0.359842i
\(986\) −0.0883286 + 0.152990i −0.00281296 + 0.00487218i
\(987\) 0 0
\(988\) −9.00955 15.6050i −0.286632 0.496461i
\(989\) 37.5391 65.0197i 1.19367 2.06750i
\(990\) 0 0
\(991\) −7.15502 12.3929i −0.227287 0.393672i 0.729716 0.683750i \(-0.239652\pi\)
−0.957003 + 0.290078i \(0.906319\pi\)
\(992\) −25.7039 −0.816100
\(993\) 0 0
\(994\) 0 0
\(995\) 5.79247 10.0329i 0.183634 0.318063i
\(996\) 0 0
\(997\) 28.1262 48.7160i 0.890765 1.54285i 0.0518058 0.998657i \(-0.483502\pi\)
0.838960 0.544194i \(-0.183164\pi\)
\(998\) 19.6176 + 33.9787i 0.620985 + 1.07558i
\(999\) 0 0
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 1323.2.h.f.226.4 10
3.2 odd 2 441.2.h.f.373.2 10
7.2 even 3 1323.2.f.f.442.2 10
7.3 odd 6 189.2.g.b.172.2 10
7.4 even 3 1323.2.g.f.361.2 10
7.5 odd 6 1323.2.f.e.442.2 10
7.6 odd 2 189.2.h.b.37.4 10
9.2 odd 6 441.2.g.f.79.4 10
9.7 even 3 1323.2.g.f.667.2 10
21.2 odd 6 441.2.f.f.148.4 10
21.5 even 6 441.2.f.e.148.4 10
21.11 odd 6 441.2.g.f.67.4 10
21.17 even 6 63.2.g.b.4.4 10
21.20 even 2 63.2.h.b.58.2 yes 10
28.3 even 6 3024.2.t.i.1873.2 10
28.27 even 2 3024.2.q.i.2305.4 10
63.2 odd 6 441.2.f.f.295.4 10
63.5 even 6 3969.2.a.z.1.2 5
63.11 odd 6 441.2.h.f.214.2 10
63.13 odd 6 567.2.e.e.163.2 10
63.16 even 3 1323.2.f.f.883.2 10
63.20 even 6 63.2.g.b.16.4 yes 10
63.23 odd 6 3969.2.a.ba.1.2 5
63.25 even 3 inner 1323.2.h.f.802.4 10
63.31 odd 6 567.2.e.e.487.2 10
63.34 odd 6 189.2.g.b.100.2 10
63.38 even 6 63.2.h.b.25.2 yes 10
63.40 odd 6 3969.2.a.bc.1.4 5
63.41 even 6 567.2.e.f.163.4 10
63.47 even 6 441.2.f.e.295.4 10
63.52 odd 6 189.2.h.b.46.4 10
63.58 even 3 3969.2.a.bb.1.4 5
63.59 even 6 567.2.e.f.487.4 10
63.61 odd 6 1323.2.f.e.883.2 10
84.59 odd 6 1008.2.t.i.193.5 10
84.83 odd 2 1008.2.q.i.625.2 10
252.83 odd 6 1008.2.t.i.961.5 10
252.115 even 6 3024.2.q.i.2881.4 10
252.223 even 6 3024.2.t.i.289.2 10
252.227 odd 6 1008.2.q.i.529.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 21.17 even 6
63.2.g.b.16.4 yes 10 63.20 even 6
63.2.h.b.25.2 yes 10 63.38 even 6
63.2.h.b.58.2 yes 10 21.20 even 2
189.2.g.b.100.2 10 63.34 odd 6
189.2.g.b.172.2 10 7.3 odd 6
189.2.h.b.37.4 10 7.6 odd 2
189.2.h.b.46.4 10 63.52 odd 6
441.2.f.e.148.4 10 21.5 even 6
441.2.f.e.295.4 10 63.47 even 6
441.2.f.f.148.4 10 21.2 odd 6
441.2.f.f.295.4 10 63.2 odd 6
441.2.g.f.67.4 10 21.11 odd 6
441.2.g.f.79.4 10 9.2 odd 6
441.2.h.f.214.2 10 63.11 odd 6
441.2.h.f.373.2 10 3.2 odd 2
567.2.e.e.163.2 10 63.13 odd 6
567.2.e.e.487.2 10 63.31 odd 6
567.2.e.f.163.4 10 63.41 even 6
567.2.e.f.487.4 10 63.59 even 6
1008.2.q.i.529.2 10 252.227 odd 6
1008.2.q.i.625.2 10 84.83 odd 2
1008.2.t.i.193.5 10 84.59 odd 6
1008.2.t.i.961.5 10 252.83 odd 6
1323.2.f.e.442.2 10 7.5 odd 6
1323.2.f.e.883.2 10 63.61 odd 6
1323.2.f.f.442.2 10 7.2 even 3
1323.2.f.f.883.2 10 63.16 even 3
1323.2.g.f.361.2 10 7.4 even 3
1323.2.g.f.667.2 10 9.7 even 3
1323.2.h.f.226.4 10 1.1 even 1 trivial
1323.2.h.f.802.4 10 63.25 even 3 inner
3024.2.q.i.2305.4 10 28.27 even 2
3024.2.q.i.2881.4 10 252.115 even 6
3024.2.t.i.289.2 10 252.223 even 6
3024.2.t.i.1873.2 10 28.3 even 6
3969.2.a.z.1.2 5 63.5 even 6
3969.2.a.ba.1.2 5 63.23 odd 6
3969.2.a.bb.1.4 5 63.58 even 3
3969.2.a.bc.1.4 5 63.40 odd 6