Properties

Label 1008.2.t.h.961.3
Level $1008$
Weight $2$
Character 1008.961
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
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] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.3
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1008.961
Dual form 1008.2.t.h.193.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09097 - 1.34528i) q^{3} -3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})\) \(q+(1.09097 - 1.34528i) q^{3} -3.18194 q^{5} +(-0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} -3.18194 q^{11} +(2.85185 + 4.93955i) q^{13} +(-3.47141 + 4.28061i) q^{15} +(-0.760877 - 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(-4.20370 - 1.82454i) q^{21} -2.23912 q^{23} +5.12476 q^{25} +(-4.62476 - 2.36887i) q^{27} +(-3.54063 + 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-3.47141 + 4.28061i) q^{33} +(2.26088 + 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(9.75636 + 1.55237i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(-3.41423 + 5.91362i) q^{43} +(1.97141 + 9.34004i) q^{45} +(-2.91423 - 5.04759i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(-2.60301 - 0.414174i) q^{51} +(1.02859 + 1.78157i) q^{53} +10.1248 q^{55} +(-0.794668 - 2.07459i) q^{57} +(-0.562382 + 0.974074i) q^{59} +(-1.56238 - 2.70612i) q^{61} +(-7.04063 + 3.66464i) q^{63} +(-9.07442 - 15.7174i) q^{65} +(5.48345 - 9.49761i) q^{67} +(-2.44282 + 3.01225i) q^{69} -8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(5.59097 - 6.89425i) q^{75} +(2.26088 + 8.10936i) q^{77} +(-2.06922 - 3.58399i) q^{79} +(-8.23229 + 3.63723i) q^{81} +(4.03379 - 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(4.38727 + 11.4536i) q^{87} +(0.112725 - 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} +(5.83693 + 15.2381i) q^{93} +(-2.04063 + 3.53447i) q^{95} +(7.42107 - 12.8537i) q^{97} +(1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9} - 2 q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} - 4 q^{25} + 7 q^{27} - 5 q^{29} - 20 q^{31} - 12 q^{33} + 13 q^{35} + 3 q^{37} - q^{39} + 6 q^{43} + 3 q^{45} + 9 q^{47} - 12 q^{49} + 18 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} + 14 q^{59} + 8 q^{61} - 26 q^{63} - 12 q^{65} - q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} + 25 q^{75} + 13 q^{77} - 5 q^{79} - 40 q^{81} - 2 q^{83} - 2 q^{85} + 36 q^{87} - 9 q^{89} + 46 q^{91} + 37 q^{93} + 4 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.09097 1.34528i 0.629873 0.776698i
\(4\) 0 0
\(5\) −3.18194 −1.42301 −0.711504 0.702682i \(-0.751986\pi\)
−0.711504 + 0.702682i \(0.751986\pi\)
\(6\) 0 0
\(7\) −0.710533 2.54856i −0.268556 0.963264i
\(8\) 0 0
\(9\) −0.619562 2.93533i −0.206521 0.978442i
\(10\) 0 0
\(11\) −3.18194 −0.959392 −0.479696 0.877435i \(-0.659253\pi\)
−0.479696 + 0.877435i \(0.659253\pi\)
\(12\) 0 0
\(13\) 2.85185 + 4.93955i 0.790960 + 1.36998i 0.925373 + 0.379058i \(0.123752\pi\)
−0.134412 + 0.990925i \(0.542915\pi\)
\(14\) 0 0
\(15\) −3.47141 + 4.28061i −0.896314 + 1.10525i
\(16\) 0 0
\(17\) −0.760877 1.31788i −0.184540 0.319632i 0.758882 0.651229i \(-0.225746\pi\)
−0.943421 + 0.331596i \(0.892413\pi\)
\(18\) 0 0
\(19\) 0.641315 1.11079i 0.147128 0.254833i −0.783037 0.621975i \(-0.786330\pi\)
0.930165 + 0.367142i \(0.119664\pi\)
\(20\) 0 0
\(21\) −4.20370 1.82454i −0.917322 0.398147i
\(22\) 0 0
\(23\) −2.23912 −0.466889 −0.233445 0.972370i \(-0.575000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(24\) 0 0
\(25\) 5.12476 1.02495
\(26\) 0 0
\(27\) −4.62476 2.36887i −0.890036 0.455890i
\(28\) 0 0
\(29\) −3.54063 + 6.13255i −0.657478 + 1.13879i 0.323788 + 0.946130i \(0.395043\pi\)
−0.981266 + 0.192656i \(0.938290\pi\)
\(30\) 0 0
\(31\) −4.71053 + 8.15888i −0.846037 + 1.46538i 0.0386810 + 0.999252i \(0.487684\pi\)
−0.884718 + 0.466127i \(0.845649\pi\)
\(32\) 0 0
\(33\) −3.47141 + 4.28061i −0.604295 + 0.745158i
\(34\) 0 0
\(35\) 2.26088 + 8.10936i 0.382158 + 1.37073i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 9.75636 + 1.55237i 1.56227 + 0.248578i
\(40\) 0 0
\(41\) −2.80150 4.85235i −0.437522 0.757810i 0.559976 0.828509i \(-0.310810\pi\)
−0.997498 + 0.0706992i \(0.977477\pi\)
\(42\) 0 0
\(43\) −3.41423 + 5.91362i −0.520665 + 0.901819i 0.479046 + 0.877790i \(0.340983\pi\)
−0.999711 + 0.0240288i \(0.992351\pi\)
\(44\) 0 0
\(45\) 1.97141 + 9.34004i 0.293880 + 1.39233i
\(46\) 0 0
\(47\) −2.91423 5.04759i −0.425084 0.736267i 0.571344 0.820711i \(-0.306422\pi\)
−0.996428 + 0.0844432i \(0.973089\pi\)
\(48\) 0 0
\(49\) −5.99028 + 3.62167i −0.855755 + 0.517381i
\(50\) 0 0
\(51\) −2.60301 0.414174i −0.364494 0.0579959i
\(52\) 0 0
\(53\) 1.02859 + 1.78157i 0.141288 + 0.244717i 0.927982 0.372626i \(-0.121542\pi\)
−0.786694 + 0.617343i \(0.788209\pi\)
\(54\) 0 0
\(55\) 10.1248 1.36522
\(56\) 0 0
\(57\) −0.794668 2.07459i −0.105256 0.274786i
\(58\) 0 0
\(59\) −0.562382 + 0.974074i −0.0732159 + 0.126814i −0.900309 0.435251i \(-0.856660\pi\)
0.827093 + 0.562065i \(0.189993\pi\)
\(60\) 0 0
\(61\) −1.56238 2.70612i −0.200042 0.346484i 0.748499 0.663135i \(-0.230775\pi\)
−0.948542 + 0.316652i \(0.897441\pi\)
\(62\) 0 0
\(63\) −7.04063 + 3.66464i −0.887036 + 0.461701i
\(64\) 0 0
\(65\) −9.07442 15.7174i −1.12554 1.94950i
\(66\) 0 0
\(67\) 5.48345 9.49761i 0.669910 1.16032i −0.308019 0.951380i \(-0.599666\pi\)
0.977929 0.208938i \(-0.0670006\pi\)
\(68\) 0 0
\(69\) −2.44282 + 3.01225i −0.294081 + 0.362632i
\(70\) 0 0
\(71\) −8.69002 −1.03132 −0.515658 0.856794i \(-0.672452\pi\)
−0.515658 + 0.856794i \(0.672452\pi\)
\(72\) 0 0
\(73\) −2.48345 4.30146i −0.290666 0.503448i 0.683302 0.730136i \(-0.260543\pi\)
−0.973967 + 0.226689i \(0.927210\pi\)
\(74\) 0 0
\(75\) 5.59097 6.89425i 0.645590 0.796079i
\(76\) 0 0
\(77\) 2.26088 + 8.10936i 0.257651 + 0.924148i
\(78\) 0 0
\(79\) −2.06922 3.58399i −0.232805 0.403231i 0.725827 0.687877i \(-0.241457\pi\)
−0.958633 + 0.284646i \(0.908124\pi\)
\(80\) 0 0
\(81\) −8.23229 + 3.63723i −0.914699 + 0.404137i
\(82\) 0 0
\(83\) 4.03379 6.98673i 0.442766 0.766893i −0.555127 0.831765i \(-0.687331\pi\)
0.997894 + 0.0648718i \(0.0206639\pi\)
\(84\) 0 0
\(85\) 2.42107 + 4.19341i 0.262602 + 0.454839i
\(86\) 0 0
\(87\) 4.38727 + 11.4536i 0.470365 + 1.22795i
\(88\) 0 0
\(89\) 0.112725 0.195246i 0.0119488 0.0206960i −0.859989 0.510312i \(-0.829530\pi\)
0.871938 + 0.489616i \(0.162863\pi\)
\(90\) 0 0
\(91\) 10.5624 10.7778i 1.10724 1.12982i
\(92\) 0 0
\(93\) 5.83693 + 15.2381i 0.605262 + 1.58012i
\(94\) 0 0
\(95\) −2.04063 + 3.53447i −0.209364 + 0.362629i
\(96\) 0 0
\(97\) 7.42107 12.8537i 0.753495 1.30509i −0.192624 0.981273i \(-0.561700\pi\)
0.946119 0.323819i \(-0.104967\pi\)
\(98\) 0 0
\(99\) 1.97141 + 9.34004i 0.198134 + 0.938710i
\(100\) 0 0
\(101\) 18.5893 1.84971 0.924854 0.380322i \(-0.124187\pi\)
0.924854 + 0.380322i \(0.124187\pi\)
\(102\) 0 0
\(103\) 0.282630 0.0278484 0.0139242 0.999903i \(-0.495568\pi\)
0.0139242 + 0.999903i \(0.495568\pi\)
\(104\) 0 0
\(105\) 13.3759 + 5.80557i 1.30536 + 0.566566i
\(106\) 0 0
\(107\) −5.68878 + 9.85326i −0.549955 + 0.952550i 0.448322 + 0.893872i \(0.352022\pi\)
−0.998277 + 0.0586780i \(0.981311\pi\)
\(108\) 0 0
\(109\) −2.21053 3.82876i −0.211731 0.366728i 0.740526 0.672028i \(-0.234577\pi\)
−0.952256 + 0.305300i \(0.901243\pi\)
\(110\) 0 0
\(111\) −0.619562 1.61745i −0.0588062 0.153522i
\(112\) 0 0
\(113\) −1.60752 2.78431i −0.151223 0.261926i 0.780454 0.625213i \(-0.214988\pi\)
−0.931677 + 0.363287i \(0.881655\pi\)
\(114\) 0 0
\(115\) 7.12476 0.664388
\(116\) 0 0
\(117\) 12.7323 11.4315i 1.17710 1.05684i
\(118\) 0 0
\(119\) −2.81806 + 2.87553i −0.258331 + 0.263600i
\(120\) 0 0
\(121\) −0.875237 −0.0795670
\(122\) 0 0
\(123\) −9.58414 1.52496i −0.864172 0.137501i
\(124\) 0 0
\(125\) −0.396990 −0.0355079
\(126\) 0 0
\(127\) −20.1053 −1.78406 −0.892030 0.451976i \(-0.850719\pi\)
−0.892030 + 0.451976i \(0.850719\pi\)
\(128\) 0 0
\(129\) 4.23065 + 11.0447i 0.372488 + 0.972431i
\(130\) 0 0
\(131\) −6.36389 −0.556015 −0.278008 0.960579i \(-0.589674\pi\)
−0.278008 + 0.960579i \(0.589674\pi\)
\(132\) 0 0
\(133\) −3.28659 0.845174i −0.284983 0.0732859i
\(134\) 0 0
\(135\) 14.7157 + 7.53762i 1.26653 + 0.648735i
\(136\) 0 0
\(137\) 2.74145 0.234218 0.117109 0.993119i \(-0.462637\pi\)
0.117109 + 0.993119i \(0.462637\pi\)
\(138\) 0 0
\(139\) 3.98345 + 6.89953i 0.337872 + 0.585211i 0.984032 0.177991i \(-0.0569597\pi\)
−0.646161 + 0.763202i \(0.723626\pi\)
\(140\) 0 0
\(141\) −9.96978 1.58632i −0.839607 0.133593i
\(142\) 0 0
\(143\) −9.07442 15.7174i −0.758841 1.31435i
\(144\) 0 0
\(145\) 11.2661 19.5134i 0.935597 1.62050i
\(146\) 0 0
\(147\) −1.66307 + 12.0098i −0.137168 + 0.990548i
\(148\) 0 0
\(149\) −23.2599 −1.90553 −0.952764 0.303712i \(-0.901774\pi\)
−0.952764 + 0.303712i \(0.901774\pi\)
\(150\) 0 0
\(151\) 8.12476 0.661184 0.330592 0.943774i \(-0.392752\pi\)
0.330592 + 0.943774i \(0.392752\pi\)
\(152\) 0 0
\(153\) −3.39699 + 3.04993i −0.274630 + 0.246572i
\(154\) 0 0
\(155\) 14.9887 25.9611i 1.20392 2.08525i
\(156\) 0 0
\(157\) 5.63160 9.75422i 0.449451 0.778471i −0.548900 0.835888i \(-0.684953\pi\)
0.998350 + 0.0574170i \(0.0182864\pi\)
\(158\) 0 0
\(159\) 3.51887 + 0.559900i 0.279065 + 0.0444030i
\(160\) 0 0
\(161\) 1.59097 + 5.70653i 0.125386 + 0.449738i
\(162\) 0 0
\(163\) 1.99028 3.44727i 0.155891 0.270011i −0.777492 0.628893i \(-0.783508\pi\)
0.933383 + 0.358881i \(0.116842\pi\)
\(164\) 0 0
\(165\) 11.0458 13.6207i 0.859917 1.06037i
\(166\) 0 0
\(167\) −2.61956 4.53721i −0.202708 0.351100i 0.746692 0.665170i \(-0.231641\pi\)
−0.949400 + 0.314070i \(0.898307\pi\)
\(168\) 0 0
\(169\) −9.76608 + 16.9153i −0.751237 + 1.30118i
\(170\) 0 0
\(171\) −3.65787 1.19427i −0.279724 0.0913278i
\(172\) 0 0
\(173\) −1.27579 2.20974i −0.0969968 0.168003i 0.813443 0.581644i \(-0.197590\pi\)
−0.910440 + 0.413641i \(0.864257\pi\)
\(174\) 0 0
\(175\) −3.64132 13.0608i −0.275258 0.987300i
\(176\) 0 0
\(177\) 0.696860 + 1.81925i 0.0523792 + 0.136743i
\(178\) 0 0
\(179\) −3.51887 6.09487i −0.263013 0.455552i 0.704028 0.710172i \(-0.251383\pi\)
−0.967041 + 0.254620i \(0.918050\pi\)
\(180\) 0 0
\(181\) −12.9669 −0.963822 −0.481911 0.876220i \(-0.660057\pi\)
−0.481911 + 0.876220i \(0.660057\pi\)
\(182\) 0 0
\(183\) −5.34501 0.850463i −0.395115 0.0628680i
\(184\) 0 0
\(185\) −1.59097 + 2.75564i −0.116971 + 0.202599i
\(186\) 0 0
\(187\) 2.42107 + 4.19341i 0.177046 + 0.306653i
\(188\) 0 0
\(189\) −2.75116 + 13.4696i −0.200118 + 0.979772i
\(190\) 0 0
\(191\) 0.990285 + 1.71522i 0.0716545 + 0.124109i 0.899627 0.436660i \(-0.143839\pi\)
−0.827972 + 0.560769i \(0.810505\pi\)
\(192\) 0 0
\(193\) 2.27292 3.93680i 0.163608 0.283377i −0.772552 0.634951i \(-0.781020\pi\)
0.936160 + 0.351574i \(0.114353\pi\)
\(194\) 0 0
\(195\) −31.0442 4.93955i −2.22312 0.353728i
\(196\) 0 0
\(197\) −21.8148 −1.55424 −0.777120 0.629353i \(-0.783320\pi\)
−0.777120 + 0.629353i \(0.783320\pi\)
\(198\) 0 0
\(199\) −6.14132 10.6371i −0.435346 0.754042i 0.561978 0.827152i \(-0.310041\pi\)
−0.997324 + 0.0731106i \(0.976707\pi\)
\(200\) 0 0
\(201\) −6.79467 17.7384i −0.479259 1.25117i
\(202\) 0 0
\(203\) 18.1449 + 4.66611i 1.27352 + 0.327497i
\(204\) 0 0
\(205\) 8.91423 + 15.4399i 0.622597 + 1.07837i
\(206\) 0 0
\(207\) 1.38727 + 6.57256i 0.0964223 + 0.456824i
\(208\) 0 0
\(209\) −2.04063 + 3.53447i −0.141153 + 0.244485i
\(210\) 0 0
\(211\) 8.32846 + 14.4253i 0.573355 + 0.993080i 0.996218 + 0.0868863i \(0.0276917\pi\)
−0.422863 + 0.906193i \(0.638975\pi\)
\(212\) 0 0
\(213\) −9.48057 + 11.6905i −0.649598 + 0.801021i
\(214\) 0 0
\(215\) 10.8639 18.8168i 0.740911 1.28330i
\(216\) 0 0
\(217\) 24.1404 + 6.20790i 1.63876 + 0.421420i
\(218\) 0 0
\(219\) −8.49604 1.35183i −0.574109 0.0913485i
\(220\) 0 0
\(221\) 4.33981 7.51677i 0.291927 0.505633i
\(222\) 0 0
\(223\) 5.32846 9.22916i 0.356820 0.618031i −0.630608 0.776102i \(-0.717194\pi\)
0.987428 + 0.158071i \(0.0505276\pi\)
\(224\) 0 0
\(225\) −3.17511 15.0429i −0.211674 1.00286i
\(226\) 0 0
\(227\) 14.5081 0.962935 0.481468 0.876464i \(-0.340104\pi\)
0.481468 + 0.876464i \(0.340104\pi\)
\(228\) 0 0
\(229\) 10.2495 0.677308 0.338654 0.940911i \(-0.390028\pi\)
0.338654 + 0.940911i \(0.390028\pi\)
\(230\) 0 0
\(231\) 13.3759 + 5.80557i 0.880071 + 0.381979i
\(232\) 0 0
\(233\) 0.540628 0.936396i 0.0354177 0.0613453i −0.847773 0.530359i \(-0.822057\pi\)
0.883191 + 0.469014i \(0.155390\pi\)
\(234\) 0 0
\(235\) 9.27292 + 16.0612i 0.604898 + 1.04771i
\(236\) 0 0
\(237\) −7.07893 1.12635i −0.459826 0.0731645i
\(238\) 0 0
\(239\) 6.16019 + 10.6698i 0.398470 + 0.690170i 0.993537 0.113506i \(-0.0362081\pi\)
−0.595068 + 0.803676i \(0.702875\pi\)
\(240\) 0 0
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 0 0
\(243\) −4.08809 + 15.0429i −0.262251 + 0.965000i
\(244\) 0 0
\(245\) 19.0607 11.5239i 1.21775 0.736238i
\(246\) 0 0
\(247\) 7.31573 0.465489
\(248\) 0 0
\(249\) −4.99837 13.0489i −0.316759 0.826941i
\(250\) 0 0
\(251\) −5.11109 −0.322609 −0.161305 0.986905i \(-0.551570\pi\)
−0.161305 + 0.986905i \(0.551570\pi\)
\(252\) 0 0
\(253\) 7.12476 0.447930
\(254\) 0 0
\(255\) 8.28263 + 1.31788i 0.518678 + 0.0825287i
\(256\) 0 0
\(257\) 7.66019 0.477830 0.238915 0.971041i \(-0.423208\pi\)
0.238915 + 0.971041i \(0.423208\pi\)
\(258\) 0 0
\(259\) −2.56238 0.658939i −0.159219 0.0409445i
\(260\) 0 0
\(261\) 20.1947 + 6.59341i 1.25002 + 0.408122i
\(262\) 0 0
\(263\) 3.09493 0.190842 0.0954208 0.995437i \(-0.469580\pi\)
0.0954208 + 0.995437i \(0.469580\pi\)
\(264\) 0 0
\(265\) −3.27292 5.66886i −0.201054 0.348235i
\(266\) 0 0
\(267\) −0.139680 0.364654i −0.00854830 0.0223165i
\(268\) 0 0
\(269\) −13.4451 23.2877i −0.819765 1.41987i −0.905855 0.423587i \(-0.860771\pi\)
0.0860906 0.996287i \(-0.472563\pi\)
\(270\) 0 0
\(271\) 11.1082 19.2400i 0.674776 1.16875i −0.301759 0.953384i \(-0.597574\pi\)
0.976534 0.215362i \(-0.0690930\pi\)
\(272\) 0 0
\(273\) −2.97592 25.9677i −0.180111 1.57163i
\(274\) 0 0
\(275\) −16.3067 −0.983331
\(276\) 0 0
\(277\) −14.6375 −0.879482 −0.439741 0.898125i \(-0.644930\pi\)
−0.439741 + 0.898125i \(0.644930\pi\)
\(278\) 0 0
\(279\) 26.8675 + 8.77202i 1.60851 + 0.525167i
\(280\) 0 0
\(281\) 11.6992 20.2636i 0.697915 1.20882i −0.271273 0.962502i \(-0.587445\pi\)
0.969188 0.246322i \(-0.0792219\pi\)
\(282\) 0 0
\(283\) −13.0624 + 22.6247i −0.776478 + 1.34490i 0.157482 + 0.987522i \(0.449662\pi\)
−0.933960 + 0.357377i \(0.883671\pi\)
\(284\) 0 0
\(285\) 2.52859 + 6.60123i 0.149781 + 0.391023i
\(286\) 0 0
\(287\) −10.3759 + 10.5876i −0.612471 + 0.624963i
\(288\) 0 0
\(289\) 7.34213 12.7169i 0.431890 0.748056i
\(290\) 0 0
\(291\) −9.19562 24.0064i −0.539057 1.40728i
\(292\) 0 0
\(293\) 12.9315 + 22.3980i 0.755465 + 1.30850i 0.945143 + 0.326657i \(0.105922\pi\)
−0.189678 + 0.981846i \(0.560745\pi\)
\(294\) 0 0
\(295\) 1.78947 3.09945i 0.104187 0.180457i
\(296\) 0 0
\(297\) 14.7157 + 7.53762i 0.853894 + 0.437377i
\(298\) 0 0
\(299\) −6.38564 11.0603i −0.369291 0.639631i
\(300\) 0 0
\(301\) 17.4971 + 4.49954i 1.00852 + 0.259349i
\(302\) 0 0
\(303\) 20.2804 25.0079i 1.16508 1.43667i
\(304\) 0 0
\(305\) 4.97141 + 8.61073i 0.284662 + 0.493049i
\(306\) 0 0
\(307\) −3.53216 −0.201591 −0.100795 0.994907i \(-0.532139\pi\)
−0.100795 + 0.994907i \(0.532139\pi\)
\(308\) 0 0
\(309\) 0.308342 0.380217i 0.0175409 0.0216298i
\(310\) 0 0
\(311\) 0.851848 1.47544i 0.0483039 0.0836648i −0.840863 0.541249i \(-0.817952\pi\)
0.889166 + 0.457584i \(0.151285\pi\)
\(312\) 0 0
\(313\) 1.42107 + 2.46136i 0.0803234 + 0.139124i 0.903389 0.428822i \(-0.141071\pi\)
−0.823065 + 0.567947i \(0.807738\pi\)
\(314\) 0 0
\(315\) 22.4029 11.6607i 1.26226 0.657004i
\(316\) 0 0
\(317\) 12.4601 + 21.5815i 0.699827 + 1.21214i 0.968526 + 0.248911i \(0.0800728\pi\)
−0.268700 + 0.963224i \(0.586594\pi\)
\(318\) 0 0
\(319\) 11.2661 19.5134i 0.630779 1.09254i
\(320\) 0 0
\(321\) 7.04910 + 18.4026i 0.393442 + 1.02713i
\(322\) 0 0
\(323\) −1.95185 −0.108604
\(324\) 0 0
\(325\) 14.6150 + 25.3140i 0.810697 + 1.40417i
\(326\) 0 0
\(327\) −7.56238 1.20328i −0.418201 0.0665413i
\(328\) 0 0
\(329\) −10.7934 + 11.0136i −0.595061 + 0.607198i
\(330\) 0 0
\(331\) −3.58577 6.21074i −0.197092 0.341373i 0.750492 0.660879i \(-0.229816\pi\)
−0.947584 + 0.319506i \(0.896483\pi\)
\(332\) 0 0
\(333\) −2.85185 0.931107i −0.156280 0.0510244i
\(334\) 0 0
\(335\) −17.4480 + 30.2209i −0.953287 + 1.65114i
\(336\) 0 0
\(337\) −10.9211 18.9158i −0.594908 1.03041i −0.993560 0.113309i \(-0.963855\pi\)
0.398651 0.917103i \(-0.369478\pi\)
\(338\) 0 0
\(339\) −5.49944 0.875035i −0.298689 0.0475254i
\(340\) 0 0
\(341\) 14.9887 25.9611i 0.811681 1.40587i
\(342\) 0 0
\(343\) 13.4863 + 12.6933i 0.728193 + 0.685372i
\(344\) 0 0
\(345\) 7.77292 9.58481i 0.418480 0.516029i
\(346\) 0 0
\(347\) −1.05555 + 1.82826i −0.0566646 + 0.0981460i −0.892966 0.450124i \(-0.851380\pi\)
0.836302 + 0.548270i \(0.184713\pi\)
\(348\) 0 0
\(349\) 18.1082 31.3643i 0.969310 1.67889i 0.271751 0.962368i \(-0.412397\pi\)
0.697559 0.716527i \(-0.254269\pi\)
\(350\) 0 0
\(351\) −1.48796 29.5999i −0.0794215 1.57993i
\(352\) 0 0
\(353\) −10.4887 −0.558255 −0.279127 0.960254i \(-0.590045\pi\)
−0.279127 + 0.960254i \(0.590045\pi\)
\(354\) 0 0
\(355\) 27.6512 1.46757
\(356\) 0 0
\(357\) 0.793980 + 6.92820i 0.0420219 + 0.366679i
\(358\) 0 0
\(359\) −16.2209 + 28.0955i −0.856108 + 1.48282i 0.0195047 + 0.999810i \(0.493791\pi\)
−0.875613 + 0.483013i \(0.839542\pi\)
\(360\) 0 0
\(361\) 8.67743 + 15.0297i 0.456707 + 0.791039i
\(362\) 0 0
\(363\) −0.954858 + 1.17744i −0.0501171 + 0.0617995i
\(364\) 0 0
\(365\) 7.90219 + 13.6870i 0.413620 + 0.716410i
\(366\) 0 0
\(367\) 18.1111 0.945391 0.472696 0.881226i \(-0.343281\pi\)
0.472696 + 0.881226i \(0.343281\pi\)
\(368\) 0 0
\(369\) −12.5075 + 11.2297i −0.651116 + 0.584593i
\(370\) 0 0
\(371\) 3.80959 3.88728i 0.197784 0.201818i
\(372\) 0 0
\(373\) −11.6706 −0.604280 −0.302140 0.953263i \(-0.597701\pi\)
−0.302140 + 0.953263i \(0.597701\pi\)
\(374\) 0 0
\(375\) −0.433105 + 0.534063i −0.0223654 + 0.0275789i
\(376\) 0 0
\(377\) −40.3893 −2.08016
\(378\) 0 0
\(379\) −14.2690 −0.732947 −0.366474 0.930428i \(-0.619435\pi\)
−0.366474 + 0.930428i \(0.619435\pi\)
\(380\) 0 0
\(381\) −21.9343 + 27.0473i −1.12373 + 1.38568i
\(382\) 0 0
\(383\) 1.64979 0.0843001 0.0421501 0.999111i \(-0.486579\pi\)
0.0421501 + 0.999111i \(0.486579\pi\)
\(384\) 0 0
\(385\) −7.19398 25.8035i −0.366639 1.31507i
\(386\) 0 0
\(387\) 19.4737 + 6.35803i 0.989905 + 0.323197i
\(388\) 0 0
\(389\) −32.0676 −1.62589 −0.812946 0.582340i \(-0.802137\pi\)
−0.812946 + 0.582340i \(0.802137\pi\)
\(390\) 0 0
\(391\) 1.70370 + 2.95089i 0.0861596 + 0.149233i
\(392\) 0 0
\(393\) −6.94282 + 8.56122i −0.350219 + 0.431856i
\(394\) 0 0
\(395\) 6.58414 + 11.4041i 0.331284 + 0.573800i
\(396\) 0 0
\(397\) −18.9669 + 32.8516i −0.951921 + 1.64878i −0.210660 + 0.977559i \(0.567561\pi\)
−0.741261 + 0.671217i \(0.765772\pi\)
\(398\) 0 0
\(399\) −4.72257 + 3.49932i −0.236424 + 0.175185i
\(400\) 0 0
\(401\) 10.6192 0.530296 0.265148 0.964208i \(-0.414579\pi\)
0.265148 + 0.964208i \(0.414579\pi\)
\(402\) 0 0
\(403\) −53.7349 −2.67673
\(404\) 0 0
\(405\) 26.1947 11.5735i 1.30162 0.575090i
\(406\) 0 0
\(407\) −1.59097 + 2.75564i −0.0788615 + 0.136592i
\(408\) 0 0
\(409\) −2.77292 + 4.80283i −0.137112 + 0.237485i −0.926402 0.376535i \(-0.877115\pi\)
0.789290 + 0.614020i \(0.210449\pi\)
\(410\) 0 0
\(411\) 2.99084 3.68802i 0.147527 0.181916i
\(412\) 0 0
\(413\) 2.88207 + 0.741150i 0.141818 + 0.0364696i
\(414\) 0 0
\(415\) −12.8353 + 22.2314i −0.630060 + 1.09130i
\(416\) 0 0
\(417\) 13.6276 + 2.16834i 0.667349 + 0.106184i
\(418\) 0 0
\(419\) −2.77455 4.80566i −0.135546 0.234772i 0.790260 0.612772i \(-0.209945\pi\)
−0.925806 + 0.378000i \(0.876612\pi\)
\(420\) 0 0
\(421\) −3.42107 + 5.92546i −0.166733 + 0.288789i −0.937269 0.348606i \(-0.886655\pi\)
0.770537 + 0.637396i \(0.219988\pi\)
\(422\) 0 0
\(423\) −13.0108 + 11.6815i −0.632606 + 0.567975i
\(424\) 0 0
\(425\) −3.89931 6.75381i −0.189144 0.327608i
\(426\) 0 0
\(427\) −5.78659 + 5.90461i −0.280033 + 0.285744i
\(428\) 0 0
\(429\) −31.0442 4.93955i −1.49883 0.238484i
\(430\) 0 0
\(431\) −16.5539 28.6722i −0.797374 1.38109i −0.921321 0.388803i \(-0.872889\pi\)
0.123947 0.992289i \(-0.460445\pi\)
\(432\) 0 0
\(433\) −12.1111 −0.582022 −0.291011 0.956720i \(-0.593992\pi\)
−0.291011 + 0.956720i \(0.593992\pi\)
\(434\) 0 0
\(435\) −13.9601 36.4446i −0.669334 1.74739i
\(436\) 0 0
\(437\) −1.43598 + 2.48720i −0.0686924 + 0.118979i
\(438\) 0 0
\(439\) −4.41711 7.65066i −0.210817 0.365146i 0.741153 0.671336i \(-0.234279\pi\)
−0.951970 + 0.306190i \(0.900946\pi\)
\(440\) 0 0
\(441\) 14.3421 + 15.3396i 0.682959 + 0.730457i
\(442\) 0 0
\(443\) 8.75924 + 15.1715i 0.416164 + 0.720817i 0.995550 0.0942360i \(-0.0300408\pi\)
−0.579386 + 0.815053i \(0.696708\pi\)
\(444\) 0 0
\(445\) −0.358685 + 0.621261i −0.0170033 + 0.0294506i
\(446\) 0 0
\(447\) −25.3759 + 31.2911i −1.20024 + 1.48002i
\(448\) 0 0
\(449\) 31.2301 1.47384 0.736920 0.675980i \(-0.236280\pi\)
0.736920 + 0.675980i \(0.236280\pi\)
\(450\) 0 0
\(451\) 8.91423 + 15.4399i 0.419755 + 0.727036i
\(452\) 0 0
\(453\) 8.86389 10.9301i 0.416462 0.513540i
\(454\) 0 0
\(455\) −33.6089 + 34.2944i −1.57561 + 1.60775i
\(456\) 0 0
\(457\) 16.0624 + 27.8209i 0.751367 + 1.30140i 0.947161 + 0.320760i \(0.103938\pi\)
−0.195794 + 0.980645i \(0.562728\pi\)
\(458\) 0 0
\(459\) 0.396990 + 7.89729i 0.0185299 + 0.368614i
\(460\) 0 0
\(461\) 1.23229 2.13438i 0.0573933 0.0994081i −0.835901 0.548880i \(-0.815054\pi\)
0.893295 + 0.449472i \(0.148388\pi\)
\(462\) 0 0
\(463\) −15.1735 26.2812i −0.705171 1.22139i −0.966630 0.256177i \(-0.917537\pi\)
0.261459 0.965215i \(-0.415796\pi\)
\(464\) 0 0
\(465\) −18.5728 48.4868i −0.861292 2.24852i
\(466\) 0 0
\(467\) 7.98181 13.8249i 0.369354 0.639740i −0.620110 0.784515i \(-0.712912\pi\)
0.989465 + 0.144774i \(0.0462456\pi\)
\(468\) 0 0
\(469\) −28.1014 7.22651i −1.29760 0.333689i
\(470\) 0 0
\(471\) −6.97825 18.2177i −0.321541 0.839425i
\(472\) 0 0
\(473\) 10.8639 18.8168i 0.499522 0.865198i
\(474\) 0 0
\(475\) 3.28659 5.69254i 0.150799 0.261192i
\(476\) 0 0
\(477\) 4.59222 4.12304i 0.210263 0.188781i
\(478\) 0 0
\(479\) 23.1729 1.05880 0.529399 0.848373i \(-0.322418\pi\)
0.529399 + 0.848373i \(0.322418\pi\)
\(480\) 0 0
\(481\) 5.70370 0.260066
\(482\) 0 0
\(483\) 9.41260 + 4.08536i 0.428288 + 0.185890i
\(484\) 0 0
\(485\) −23.6134 + 40.8996i −1.07223 + 1.85716i
\(486\) 0 0
\(487\) −1.70658 2.95588i −0.0773323 0.133943i 0.824766 0.565474i \(-0.191307\pi\)
−0.902098 + 0.431531i \(0.857974\pi\)
\(488\) 0 0
\(489\) −2.46621 6.43837i −0.111526 0.291153i
\(490\) 0 0
\(491\) 9.58414 + 16.6002i 0.432526 + 0.749157i 0.997090 0.0762323i \(-0.0242890\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(492\) 0 0
\(493\) 10.7759 0.485323
\(494\) 0 0
\(495\) −6.27292 29.7195i −0.281947 1.33579i
\(496\) 0 0
\(497\) 6.17455 + 22.1470i 0.276966 + 0.993430i
\(498\) 0 0
\(499\) −41.1696 −1.84301 −0.921503 0.388371i \(-0.873038\pi\)
−0.921503 + 0.388371i \(0.873038\pi\)
\(500\) 0 0
\(501\) −8.96169 1.42593i −0.400379 0.0637056i
\(502\) 0 0
\(503\) 26.4542 1.17953 0.589767 0.807574i \(-0.299220\pi\)
0.589767 + 0.807574i \(0.299220\pi\)
\(504\) 0 0
\(505\) −59.1502 −2.63215
\(506\) 0 0
\(507\) 12.1014 + 31.5923i 0.537441 + 1.40306i
\(508\) 0 0
\(509\) 12.7713 0.566077 0.283039 0.959109i \(-0.408658\pi\)
0.283039 + 0.959109i \(0.408658\pi\)
\(510\) 0 0
\(511\) −9.19794 + 9.38554i −0.406893 + 0.415192i
\(512\) 0 0
\(513\) −5.59725 + 3.61795i −0.247125 + 0.159736i
\(514\) 0 0
\(515\) −0.899313 −0.0396285
\(516\) 0 0
\(517\) 9.27292 + 16.0612i 0.407822 + 0.706369i
\(518\) 0 0
\(519\) −4.36458 0.694462i −0.191584 0.0304835i
\(520\) 0 0
\(521\) −3.40615 5.89962i −0.149226 0.258467i 0.781716 0.623635i \(-0.214345\pi\)
−0.930942 + 0.365168i \(0.881012\pi\)
\(522\) 0 0
\(523\) −14.7535 + 25.5538i −0.645125 + 1.11739i 0.339148 + 0.940733i \(0.389861\pi\)
−0.984273 + 0.176656i \(0.943472\pi\)
\(524\) 0 0
\(525\) −21.5430 9.35032i −0.940211 0.408081i
\(526\) 0 0
\(527\) 14.3365 0.624510
\(528\) 0 0
\(529\) −17.9863 −0.782014
\(530\) 0 0
\(531\) 3.20765 + 1.04728i 0.139200 + 0.0454479i
\(532\) 0 0
\(533\) 15.9789 27.6763i 0.692125 1.19879i
\(534\) 0 0
\(535\) 18.1014 31.3525i 0.782591 1.35549i
\(536\) 0 0
\(537\) −12.0383 1.91546i −0.519491 0.0826580i
\(538\) 0 0
\(539\) 19.0607 11.5239i 0.821004 0.496371i
\(540\) 0 0
\(541\) 14.7008 25.4626i 0.632038 1.09472i −0.355097 0.934829i \(-0.615552\pi\)
0.987135 0.159892i \(-0.0511145\pi\)
\(542\) 0 0
\(543\) −14.1465 + 17.4441i −0.607085 + 0.748599i
\(544\) 0 0
\(545\) 7.03379 + 12.1829i 0.301295 + 0.521857i
\(546\) 0 0
\(547\) −17.6150 + 30.5102i −0.753165 + 1.30452i 0.193116 + 0.981176i \(0.438141\pi\)
−0.946281 + 0.323344i \(0.895193\pi\)
\(548\) 0 0
\(549\) −6.97537 + 6.26271i −0.297701 + 0.267286i
\(550\) 0 0
\(551\) 4.54132 + 7.86579i 0.193467 + 0.335094i
\(552\) 0 0
\(553\) −7.66376 + 7.82007i −0.325896 + 0.332543i
\(554\) 0 0
\(555\) 1.97141 + 5.14663i 0.0836817 + 0.218462i
\(556\) 0 0
\(557\) −3.36909 5.83543i −0.142753 0.247255i 0.785779 0.618507i \(-0.212262\pi\)
−0.928532 + 0.371252i \(0.878929\pi\)
\(558\) 0 0
\(559\) −38.9475 −1.64730
\(560\) 0 0
\(561\) 8.28263 + 1.31788i 0.349693 + 0.0556408i
\(562\) 0 0
\(563\) −0.729964 + 1.26433i −0.0307643 + 0.0532853i −0.880998 0.473121i \(-0.843127\pi\)
0.850233 + 0.526406i \(0.176461\pi\)
\(564\) 0 0
\(565\) 5.11505 + 8.85952i 0.215192 + 0.372723i
\(566\) 0 0
\(567\) 15.1190 + 18.3961i 0.634939 + 0.772563i
\(568\) 0 0
\(569\) −9.78263 16.9440i −0.410109 0.710330i 0.584792 0.811183i \(-0.301176\pi\)
−0.994901 + 0.100853i \(0.967843\pi\)
\(570\) 0 0
\(571\) −10.9629 + 18.9884i −0.458785 + 0.794638i −0.998897 0.0469545i \(-0.985048\pi\)
0.540112 + 0.841593i \(0.318382\pi\)
\(572\) 0 0
\(573\) 3.38783 + 0.539049i 0.141529 + 0.0225191i
\(574\) 0 0
\(575\) −11.4750 −0.478540
\(576\) 0 0
\(577\) 12.3655 + 21.4177i 0.514783 + 0.891631i 0.999853 + 0.0171554i \(0.00546099\pi\)
−0.485069 + 0.874476i \(0.661206\pi\)
\(578\) 0 0
\(579\) −2.81642 7.35265i −0.117046 0.305566i
\(580\) 0 0
\(581\) −20.6722 5.31604i −0.857629 0.220547i
\(582\) 0 0
\(583\) −3.27292 5.66886i −0.135550 0.234780i
\(584\) 0 0
\(585\) −40.5134 + 36.3743i −1.67502 + 1.50389i
\(586\) 0 0
\(587\) 18.0796 31.3148i 0.746226 1.29250i −0.203394 0.979097i \(-0.565197\pi\)
0.949620 0.313404i \(-0.101469\pi\)
\(588\) 0 0
\(589\) 6.04187 + 10.4648i 0.248951 + 0.431196i
\(590\) 0 0
\(591\) −23.7993 + 29.3470i −0.978973 + 1.20717i
\(592\) 0 0
\(593\) −7.55391 + 13.0838i −0.310202 + 0.537285i −0.978406 0.206693i \(-0.933730\pi\)
0.668204 + 0.743978i \(0.267063\pi\)
\(594\) 0 0
\(595\) 8.96690 9.14978i 0.367607 0.375105i
\(596\) 0 0
\(597\) −21.0098 3.34295i −0.859876 0.136818i
\(598\) 0 0
\(599\) −2.72708 + 4.72345i −0.111426 + 0.192995i −0.916345 0.400389i \(-0.868875\pi\)
0.804920 + 0.593384i \(0.202208\pi\)
\(600\) 0 0
\(601\) −3.36840 + 5.83424i −0.137400 + 0.237984i −0.926512 0.376266i \(-0.877208\pi\)
0.789112 + 0.614250i \(0.210541\pi\)
\(602\) 0 0
\(603\) −31.2759 10.2114i −1.27365 0.415839i
\(604\) 0 0
\(605\) 2.78495 0.113224
\(606\) 0 0
\(607\) −6.67059 −0.270751 −0.135376 0.990794i \(-0.543224\pi\)
−0.135376 + 0.990794i \(0.543224\pi\)
\(608\) 0 0
\(609\) 26.0728 19.3194i 1.05652 0.782860i
\(610\) 0 0
\(611\) 16.6219 28.7899i 0.672449 1.16472i
\(612\) 0 0
\(613\) 0.654988 + 1.13447i 0.0264547 + 0.0458209i 0.878950 0.476915i \(-0.158245\pi\)
−0.852495 + 0.522735i \(0.824912\pi\)
\(614\) 0 0
\(615\) 30.4962 + 4.85235i 1.22972 + 0.195666i
\(616\) 0 0
\(617\) 17.2483 + 29.8749i 0.694390 + 1.20272i 0.970386 + 0.241560i \(0.0776589\pi\)
−0.275996 + 0.961159i \(0.589008\pi\)
\(618\) 0 0
\(619\) 16.4484 0.661118 0.330559 0.943785i \(-0.392763\pi\)
0.330559 + 0.943785i \(0.392763\pi\)
\(620\) 0 0
\(621\) 10.3554 + 5.30420i 0.415549 + 0.212850i
\(622\) 0 0
\(623\) −0.577690 0.148558i −0.0231446 0.00595184i
\(624\) 0 0
\(625\) −24.3606 −0.974425
\(626\) 0 0
\(627\) 2.52859 + 6.60123i 0.100982 + 0.263628i
\(628\) 0 0
\(629\) −1.52175 −0.0606763
\(630\) 0 0
\(631\) 30.0118 1.19475 0.597375 0.801962i \(-0.296210\pi\)
0.597375 + 0.801962i \(0.296210\pi\)
\(632\) 0 0
\(633\) 28.4922 + 4.53349i 1.13246 + 0.180190i
\(634\) 0 0
\(635\) 63.9740 2.53873
\(636\) 0 0
\(637\) −34.9728 19.2608i −1.38567 0.763142i
\(638\) 0 0
\(639\) 5.38401 + 25.5081i 0.212988 + 1.00908i
\(640\) 0 0
\(641\) 27.8993 1.10196 0.550978 0.834520i \(-0.314255\pi\)
0.550978 + 0.834520i \(0.314255\pi\)
\(642\) 0 0
\(643\) −14.2524 24.6859i −0.562060 0.973516i −0.997317 0.0732100i \(-0.976676\pi\)
0.435257 0.900306i \(-0.356658\pi\)
\(644\) 0 0
\(645\) −13.4617 35.1436i −0.530054 1.38378i
\(646\) 0 0
\(647\) −8.35705 14.4748i −0.328550 0.569065i 0.653675 0.756776i \(-0.273226\pi\)
−0.982224 + 0.187711i \(0.939893\pi\)
\(648\) 0 0
\(649\) 1.78947 3.09945i 0.0702427 0.121664i
\(650\) 0 0
\(651\) 34.6878 25.7029i 1.35952 1.00738i
\(652\) 0 0
\(653\) 38.1650 1.49351 0.746756 0.665098i \(-0.231610\pi\)
0.746756 + 0.665098i \(0.231610\pi\)
\(654\) 0 0
\(655\) 20.2495 0.791214
\(656\) 0 0
\(657\) −11.0875 + 9.95475i −0.432566 + 0.388372i
\(658\) 0 0
\(659\) −4.37072 + 7.57031i −0.170259 + 0.294898i −0.938510 0.345251i \(-0.887794\pi\)
0.768251 + 0.640148i \(0.221127\pi\)
\(660\) 0 0
\(661\) 10.0419 17.3930i 0.390584 0.676511i −0.601943 0.798539i \(-0.705607\pi\)
0.992527 + 0.122028i \(0.0389399\pi\)
\(662\) 0 0
\(663\) −5.37756 14.0388i −0.208847 0.545224i
\(664\) 0 0
\(665\) 10.4577 + 2.68930i 0.405534 + 0.104286i
\(666\) 0 0
\(667\) 7.92790 13.7315i 0.306970 0.531687i
\(668\) 0 0
\(669\) −6.60262 17.2370i −0.255272 0.666422i
\(670\) 0 0
\(671\) 4.97141 + 8.61073i 0.191919 + 0.332414i
\(672\) 0 0
\(673\) −17.0264 + 29.4906i −0.656319 + 1.13678i 0.325242 + 0.945631i \(0.394554\pi\)
−0.981561 + 0.191148i \(0.938779\pi\)
\(674\) 0 0
\(675\) −23.7008 12.1399i −0.912245 0.467266i
\(676\) 0 0
\(677\) 0.358685 + 0.621261i 0.0137854 + 0.0238770i 0.872836 0.488014i \(-0.162279\pi\)
−0.859050 + 0.511891i \(0.828945\pi\)
\(678\) 0 0
\(679\) −38.0312 9.78005i −1.45950 0.375324i
\(680\) 0 0
\(681\) 15.8279 19.5174i 0.606527 0.747910i
\(682\) 0 0
\(683\) 10.5270 + 18.2332i 0.402803 + 0.697675i 0.994063 0.108806i \(-0.0347027\pi\)
−0.591260 + 0.806481i \(0.701369\pi\)
\(684\) 0 0
\(685\) −8.72313 −0.333294
\(686\) 0 0
\(687\) 11.1819 13.7885i 0.426618 0.526064i
\(688\) 0 0
\(689\) −5.86677 + 10.1615i −0.223506 + 0.387124i
\(690\) 0 0
\(691\) 2.92395 + 5.06442i 0.111232 + 0.192660i 0.916267 0.400567i \(-0.131187\pi\)
−0.805035 + 0.593227i \(0.797854\pi\)
\(692\) 0 0
\(693\) 22.4029 11.6607i 0.851015 0.442952i
\(694\) 0 0
\(695\) −12.6751 21.9539i −0.480794 0.832760i
\(696\) 0 0
\(697\) −4.26320 + 7.38408i −0.161480 + 0.279692i
\(698\) 0 0
\(699\) −0.669905 1.74888i −0.0253381 0.0661486i
\(700\) 0 0
\(701\) 10.2711 0.387935 0.193967 0.981008i \(-0.437864\pi\)
0.193967 + 0.981008i \(0.437864\pi\)
\(702\) 0 0
\(703\) −0.641315 1.11079i −0.0241877 0.0418942i
\(704\) 0 0
\(705\) 31.7233 + 5.04759i 1.19477 + 0.190103i
\(706\) 0 0
\(707\) −13.2083 47.3760i −0.496751 1.78176i
\(708\) 0 0
\(709\) −21.7427 37.6594i −0.816564 1.41433i −0.908200 0.418538i \(-0.862543\pi\)
0.0916356 0.995793i \(-0.470790\pi\)
\(710\) 0 0
\(711\) −9.23818 + 8.29434i −0.346459 + 0.311062i
\(712\) 0 0
\(713\) 10.5475 18.2687i 0.395006 0.684170i
\(714\) 0 0
\(715\) 28.8743 + 50.0117i 1.07984 + 1.87033i
\(716\) 0 0
\(717\) 21.0744 + 3.35322i 0.787039 + 0.125228i
\(718\) 0 0
\(719\) −25.4412 + 44.0654i −0.948796 + 1.64336i −0.200830 + 0.979626i \(0.564364\pi\)
−0.747966 + 0.663737i \(0.768969\pi\)
\(720\) 0 0
\(721\) −0.200818 0.720299i −0.00747886 0.0268253i
\(722\) 0 0
\(723\) −14.1826 + 17.4887i −0.527458 + 0.650410i
\(724\) 0 0
\(725\) −18.1449 + 31.4279i −0.673884 + 1.16720i
\(726\) 0 0
\(727\) −6.07210 + 10.5172i −0.225202 + 0.390061i −0.956380 0.292126i \(-0.905637\pi\)
0.731178 + 0.682186i \(0.238971\pi\)
\(728\) 0 0
\(729\) 15.7769 + 21.9110i 0.584329 + 0.811517i
\(730\) 0 0
\(731\) 10.3912 0.384334
\(732\) 0 0
\(733\) −46.1696 −1.70531 −0.852657 0.522470i \(-0.825011\pi\)
−0.852657 + 0.522470i \(0.825011\pi\)
\(734\) 0 0
\(735\) 5.29179 38.2144i 0.195191 1.40956i
\(736\) 0 0
\(737\) −17.4480 + 30.2209i −0.642706 + 1.11320i
\(738\) 0 0
\(739\) 2.49604 + 4.32327i 0.0918184 + 0.159034i 0.908276 0.418371i \(-0.137399\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(740\) 0 0
\(741\) 7.98126 9.84172i 0.293199 0.361545i
\(742\) 0 0
\(743\) 15.7060 + 27.2036i 0.576198 + 0.998004i 0.995910 + 0.0903470i \(0.0287976\pi\)
−0.419712 + 0.907657i \(0.637869\pi\)
\(744\) 0 0
\(745\) 74.0118 2.71158
\(746\) 0 0
\(747\) −23.0075 7.51179i −0.841801 0.274842i
\(748\) 0 0
\(749\) 29.1537 + 7.49711i 1.06525 + 0.273939i
\(750\) 0 0
\(751\) −3.29630 −0.120284 −0.0601419 0.998190i \(-0.519155\pi\)
−0.0601419 + 0.998190i \(0.519155\pi\)
\(752\) 0 0
\(753\) −5.57605 + 6.87585i −0.203203 + 0.250570i
\(754\) 0 0
\(755\) −25.8525 −0.940870
\(756\) 0 0
\(757\) −10.1384 −0.368488 −0.184244 0.982881i \(-0.558984\pi\)
−0.184244 + 0.982881i \(0.558984\pi\)
\(758\) 0 0
\(759\) 7.77292 9.58481i 0.282139 0.347907i
\(760\) 0 0
\(761\) 14.0676 0.509950 0.254975 0.966948i \(-0.417933\pi\)
0.254975 + 0.966948i \(0.417933\pi\)
\(762\) 0 0
\(763\) −8.18715 + 8.35413i −0.296395 + 0.302440i
\(764\) 0 0
\(765\) 10.8090 9.70470i 0.390801 0.350874i
\(766\) 0 0
\(767\) −6.41531 −0.231643
\(768\) 0 0
\(769\) 11.3461 + 19.6520i 0.409151 + 0.708669i 0.994795 0.101899i \(-0.0324918\pi\)
−0.585644 + 0.810568i \(0.699158\pi\)
\(770\) 0 0
\(771\) 8.35705 10.3051i 0.300972 0.371129i
\(772\) 0 0
\(773\) 0.327772 + 0.567717i 0.0117891 + 0.0204194i 0.871860 0.489756i \(-0.162914\pi\)
−0.860071 + 0.510175i \(0.829581\pi\)
\(774\) 0 0
\(775\) −24.1404 + 41.8123i −0.867148 + 1.50194i
\(776\) 0 0
\(777\) −3.68194 + 2.72824i −0.132089 + 0.0978751i
\(778\) 0 0
\(779\) −7.18659 −0.257486
\(780\) 0 0
\(781\) 27.6512 0.989436
\(782\) 0 0
\(783\) 30.9018 19.9743i 1.10434 0.713823i
\(784\) 0 0
\(785\) −17.9194 + 31.0374i −0.639572 + 1.10777i
\(786\) 0 0
\(787\) 0.270036 0.467717i 0.00962576 0.0166723i −0.861172 0.508313i \(-0.830269\pi\)
0.870798 + 0.491641i \(0.163603\pi\)
\(788\) 0 0
\(789\) 3.37648 4.16355i 0.120206 0.148226i
\(790\) 0 0
\(791\) −5.95378 + 6.07521i −0.211692 + 0.216010i
\(792\) 0 0
\(793\) 8.91135 15.4349i 0.316451 0.548110i
\(794\) 0 0
\(795\) −11.1969 1.78157i −0.397112 0.0631858i
\(796\) 0 0
\(797\) −12.5550 21.7459i −0.444721 0.770279i 0.553312 0.832974i \(-0.313364\pi\)
−0.998033 + 0.0626954i \(0.980030\pi\)
\(798\) 0 0
\(799\) −4.43474 + 7.68119i −0.156890 + 0.271741i
\(800\) 0 0
\(801\) −0.642950 0.209918i −0.0227175 0.00741710i
\(802\) 0 0
\(803\) 7.90219 + 13.6870i 0.278862 + 0.483004i
\(804\) 0 0
\(805\) −5.06238 18.1579i −0.178426 0.639981i
\(806\) 0 0
\(807\) −45.9967 7.31869i −1.61916 0.257630i
\(808\) 0 0
\(809\) −14.5865 25.2645i −0.512833 0.888252i −0.999889 0.0148817i \(-0.995263\pi\)
0.487057 0.873370i \(-0.338071\pi\)
\(810\) 0 0
\(811\) 15.4290 0.541785 0.270892 0.962610i \(-0.412681\pi\)
0.270892 + 0.962610i \(0.412681\pi\)
\(812\) 0 0
\(813\) −13.7644 35.9339i −0.482740 1.26026i
\(814\) 0 0
\(815\) −6.33297 + 10.9690i −0.221834 + 0.384228i
\(816\) 0 0
\(817\) 4.37919 + 7.58499i 0.153209 + 0.265365i
\(818\) 0 0
\(819\) −38.1804 24.3265i −1.33413 0.850038i
\(820\) 0 0
\(821\) −4.24364 7.35019i −0.148104 0.256524i 0.782423 0.622748i \(-0.213984\pi\)
−0.930527 + 0.366224i \(0.880650\pi\)
\(822\) 0 0
\(823\) 14.5487 25.1991i 0.507136 0.878385i −0.492830 0.870126i \(-0.664037\pi\)
0.999966 0.00825976i \(-0.00262919\pi\)
\(824\) 0 0
\(825\) −17.7902 + 21.9371i −0.619374 + 0.763752i
\(826\) 0 0
\(827\) 25.9396 0.902007 0.451003 0.892522i \(-0.351066\pi\)
0.451003 + 0.892522i \(0.351066\pi\)
\(828\) 0 0
\(829\) 3.10821 + 5.38358i 0.107953 + 0.186979i 0.914941 0.403588i \(-0.132237\pi\)
−0.806988 + 0.590568i \(0.798904\pi\)
\(830\) 0 0
\(831\) −15.9691 + 19.6915i −0.553961 + 0.683092i
\(832\) 0 0
\(833\) 9.33078 + 5.13882i 0.323292 + 0.178049i
\(834\) 0 0
\(835\) 8.33530 + 14.4372i 0.288455 + 0.499618i
\(836\) 0 0
\(837\) 41.1125 26.5742i 1.42105 0.918540i
\(838\) 0 0
\(839\) −21.2947 + 36.8834i −0.735174 + 1.27336i 0.219474 + 0.975618i \(0.429566\pi\)
−0.954647 + 0.297740i \(0.903767\pi\)
\(840\) 0 0
\(841\) −10.5721 18.3114i −0.364555 0.631428i
\(842\) 0 0
\(843\) −14.4967 37.8457i −0.499294 1.30347i
\(844\) 0 0
\(845\) 31.0751 53.8237i 1.06902 1.85159i
\(846\) 0 0
\(847\) 0.621885 + 2.23059i 0.0213682 + 0.0766440i
\(848\) 0 0
\(849\) 16.1859 + 42.2555i 0.555499 + 1.45020i
\(850\) 0 0
\(851\) −1.11956 + 1.93914i −0.0383781 + 0.0664728i
\(852\) 0 0
\(853\) −10.6969 + 18.5275i −0.366254 + 0.634370i −0.988976 0.148073i \(-0.952693\pi\)
0.622723 + 0.782442i \(0.286026\pi\)
\(854\) 0 0
\(855\) 11.6391 + 3.80009i 0.398050 + 0.129960i
\(856\) 0 0
\(857\) −36.8435 −1.25855 −0.629275 0.777183i \(-0.716648\pi\)
−0.629275 + 0.777183i \(0.716648\pi\)
\(858\) 0 0
\(859\) 17.6375 0.601783 0.300892 0.953658i \(-0.402716\pi\)
0.300892 + 0.953658i \(0.402716\pi\)
\(860\) 0 0
\(861\) 2.92339 + 25.5093i 0.0996289 + 0.869353i
\(862\) 0 0
\(863\) 0.380438 0.658939i 0.0129503 0.0224305i −0.859478 0.511173i \(-0.829211\pi\)
0.872428 + 0.488743i \(0.162544\pi\)
\(864\) 0 0
\(865\) 4.05950 + 7.03127i 0.138027 + 0.239070i
\(866\) 0 0
\(867\) −9.09781 23.7511i −0.308978 0.806628i
\(868\) 0 0
\(869\) 6.58414 + 11.4041i 0.223351 + 0.386856i
\(870\) 0 0
\(871\) 62.5519 2.11949
\(872\) 0 0
\(873\) −42.3275 13.8196i −1.43257 0.467723i
\(874\) 0 0
\(875\) 0.282075 + 1.01175i 0.00953586 + 0.0342035i
\(876\) 0 0
\(877\) −41.4991 −1.40132 −0.700662 0.713494i \(-0.747112\pi\)
−0.700662 + 0.713494i \(0.747112\pi\)
\(878\) 0 0
\(879\) 44.2394 + 7.03908i 1.49216 + 0.237422i
\(880\) 0 0
\(881\) 8.35486 0.281482 0.140741 0.990046i \(-0.455051\pi\)
0.140741 + 0.990046i \(0.455051\pi\)
\(882\) 0 0
\(883\) −35.6181 −1.19864 −0.599322 0.800508i \(-0.704563\pi\)
−0.599322 + 0.800508i \(0.704563\pi\)
\(884\) 0 0
\(885\) −2.21737 5.78874i −0.0745361 0.194587i
\(886\) 0 0
\(887\) 37.1100 1.24603 0.623016 0.782209i \(-0.285907\pi\)
0.623016 + 0.782209i \(0.285907\pi\)
\(888\) 0 0
\(889\) 14.2855 + 51.2396i 0.479121 + 1.71852i
\(890\) 0 0
\(891\) 26.1947 11.5735i 0.877554 0.387726i
\(892\) 0 0
\(893\) −7.47576 −0.250167
\(894\) 0 0
\(895\) 11.1969 + 19.3935i 0.374270 + 0.648254i
\(896\) 0 0
\(897\) −21.8457 3.47594i −0.729407 0.116058i
\(898\) 0 0
\(899\) −33.3565 57.7751i −1.11250 1.92691i
\(900\) 0 0
\(901\) 1.56526 2.71111i 0.0521464 0.0903202i
\(902\) 0 0
\(903\) 25.1420 18.6297i 0.836673 0.619957i
\(904\) 0 0
\(905\) 41.2599 1.37153
\(906\) 0 0
\(907\) 48.1502 1.59880 0.799401 0.600798i \(-0.205150\pi\)
0.799401 + 0.600798i \(0.205150\pi\)
\(908\) 0 0
\(909\) −11.5172 54.5658i −0.382003 1.80983i
\(910\) 0 0
\(911\) −17.4428 + 30.2119i −0.577906 + 1.00096i 0.417813 + 0.908533i \(0.362797\pi\)
−0.995719 + 0.0924301i \(0.970537\pi\)
\(912\) 0 0
\(913\) −12.8353 + 22.2314i −0.424786 + 0.735751i
\(914\) 0 0
\(915\) 17.0075 + 2.70612i 0.562251 + 0.0894617i
\(916\) 0 0
\(917\) 4.52175 + 16.2187i 0.149321 + 0.535590i
\(918\) 0 0
\(919\) 25.8675 44.8037i 0.853289 1.47794i −0.0249351 0.999689i \(-0.507938\pi\)
0.878224 0.478250i \(-0.158729\pi\)
\(920\) 0 0
\(921\) −3.85348 + 4.75174i −0.126977 + 0.156575i
\(922\) 0 0
\(923\) −24.7826 42.9248i −0.815730 1.41289i
\(924\) 0 0
\(925\) 2.56238 4.43818i 0.0842506 0.145926i
\(926\) 0 0
\(927\) −0.175107 0.829612i −0.00575126 0.0272480i
\(928\) 0 0
\(929\) 25.4142 + 44.0187i 0.833814 + 1.44421i 0.894993 + 0.446081i \(0.147181\pi\)
−0.0611787 + 0.998127i \(0.519486\pi\)
\(930\) 0 0
\(931\) 0.181255 + 8.97658i 0.00594039 + 0.294196i
\(932\) 0 0
\(933\) −1.05555 2.75564i −0.0345570 0.0902157i
\(934\) 0 0
\(935\) −7.70370 13.3432i −0.251938 0.436369i
\(936\) 0 0
\(937\) 2.54583 0.0831686 0.0415843 0.999135i \(-0.486759\pi\)
0.0415843 + 0.999135i \(0.486759\pi\)
\(938\) 0 0
\(939\) 4.86156 + 0.773540i 0.158651 + 0.0252435i
\(940\) 0 0
\(941\) −0.578933 + 1.00274i −0.0188727 + 0.0326885i −0.875308 0.483567i \(-0.839341\pi\)
0.856435 + 0.516255i \(0.172674\pi\)
\(942\) 0 0
\(943\) 6.27292 + 10.8650i 0.204274 + 0.353813i
\(944\) 0 0
\(945\) 8.75404 42.8596i 0.284769 1.39422i
\(946\) 0 0
\(947\) 4.90739 + 8.49985i 0.159469 + 0.276208i 0.934677 0.355497i \(-0.115689\pi\)
−0.775208 + 0.631706i \(0.782355\pi\)
\(948\) 0 0
\(949\) 14.1648 24.5342i 0.459810 0.796414i
\(950\) 0 0
\(951\) 42.6267 + 6.78248i 1.38227 + 0.219937i
\(952\) 0 0
\(953\) 6.53791 0.211784 0.105892 0.994378i \(-0.466230\pi\)
0.105892 + 0.994378i \(0.466230\pi\)
\(954\) 0 0
\(955\) −3.15103 5.45774i −0.101965 0.176608i
\(956\) 0 0
\(957\) −13.9601 36.4446i −0.451265 1.17809i
\(958\) 0 0
\(959\) −1.94789 6.98673i −0.0629006 0.225613i
\(960\) 0 0
\(961\) −28.8782 50.0186i −0.931556 1.61350i
\(962\) 0 0
\(963\) 32.4471 + 10.5937i 1.04559 + 0.341378i
\(964\) 0 0
\(965\) −7.23229 + 12.5267i −0.232816 + 0.403248i
\(966\) 0 0
\(967\) −14.4445 25.0185i −0.464502 0.804542i 0.534677 0.845057i \(-0.320433\pi\)
−0.999179 + 0.0405151i \(0.987100\pi\)
\(968\) 0 0
\(969\) −2.12941 + 2.62578i −0.0684065 + 0.0843523i
\(970\) 0 0
\(971\) −2.66827 + 4.62158i −0.0856289 + 0.148314i −0.905659 0.424007i \(-0.860623\pi\)
0.820030 + 0.572320i \(0.193957\pi\)
\(972\) 0 0
\(973\) 14.7535 15.0544i 0.472975 0.482622i
\(974\) 0 0
\(975\) 49.9991 + 7.95552i 1.60125 + 0.254780i
\(976\) 0 0
\(977\) 24.0361 41.6318i 0.768983 1.33192i −0.169131 0.985594i \(-0.554096\pi\)
0.938115 0.346325i \(-0.112571\pi\)
\(978\) 0 0
\(979\) −0.358685 + 0.621261i −0.0114636 + 0.0198556i
\(980\) 0 0
\(981\) −9.86909 + 8.86079i −0.315096 + 0.282903i
\(982\) 0 0
\(983\) −29.4627 −0.939714 −0.469857 0.882743i \(-0.655694\pi\)
−0.469857 + 0.882743i \(0.655694\pi\)
\(984\) 0 0
\(985\) 69.4134 2.21170
\(986\) 0 0
\(987\) 3.04102 + 26.5357i 0.0967967 + 0.844640i
\(988\) 0 0
\(989\) 7.64488 13.2413i 0.243093 0.421050i
\(990\) 0 0
\(991\) −15.4142 26.6982i −0.489649 0.848097i 0.510280 0.860008i \(-0.329542\pi\)
−0.999929 + 0.0119112i \(0.996208\pi\)
\(992\) 0 0
\(993\) −12.2672 1.95187i −0.389286 0.0619407i
\(994\) 0 0
\(995\) 19.5413 + 33.8466i 0.619501 + 1.07301i
\(996\) 0 0
\(997\) 5.54583 0.175638 0.0878191 0.996136i \(-0.472010\pi\)
0.0878191 + 0.996136i \(0.472010\pi\)
\(998\) 0 0
\(999\) −4.36389 + 2.82073i −0.138067 + 0.0892438i
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 1008.2.t.h.961.3 6
3.2 odd 2 3024.2.t.h.289.3 6
4.3 odd 2 126.2.h.d.79.1 yes 6
7.4 even 3 1008.2.q.g.529.1 6
9.4 even 3 1008.2.q.g.625.1 6
9.5 odd 6 3024.2.q.g.2305.1 6
12.11 even 2 378.2.h.c.289.3 6
21.11 odd 6 3024.2.q.g.2881.1 6
28.3 even 6 882.2.e.o.655.1 6
28.11 odd 6 126.2.e.c.25.3 6
28.19 even 6 882.2.f.o.295.2 6
28.23 odd 6 882.2.f.n.295.2 6
28.27 even 2 882.2.h.p.79.3 6
36.7 odd 6 1134.2.g.m.163.3 6
36.11 even 6 1134.2.g.l.163.1 6
36.23 even 6 378.2.e.d.37.1 6
36.31 odd 6 126.2.e.c.121.3 yes 6
63.4 even 3 inner 1008.2.t.h.193.3 6
63.32 odd 6 3024.2.t.h.1873.3 6
84.11 even 6 378.2.e.d.235.1 6
84.23 even 6 2646.2.f.l.883.1 6
84.47 odd 6 2646.2.f.m.883.3 6
84.59 odd 6 2646.2.e.p.2125.3 6
84.83 odd 2 2646.2.h.o.667.1 6
252.11 even 6 1134.2.g.l.487.1 6
252.23 even 6 2646.2.f.l.1765.1 6
252.31 even 6 882.2.h.p.67.3 6
252.47 odd 6 7938.2.a.bz.1.1 3
252.59 odd 6 2646.2.h.o.361.1 6
252.67 odd 6 126.2.h.d.67.1 yes 6
252.79 odd 6 7938.2.a.bv.1.1 3
252.95 even 6 378.2.h.c.361.3 6
252.103 even 6 882.2.f.o.589.2 6
252.131 odd 6 2646.2.f.m.1765.3 6
252.139 even 6 882.2.e.o.373.1 6
252.151 odd 6 1134.2.g.m.487.3 6
252.167 odd 6 2646.2.e.p.1549.3 6
252.187 even 6 7938.2.a.bw.1.3 3
252.191 even 6 7938.2.a.ca.1.3 3
252.247 odd 6 882.2.f.n.589.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.3 6 28.11 odd 6
126.2.e.c.121.3 yes 6 36.31 odd 6
126.2.h.d.67.1 yes 6 252.67 odd 6
126.2.h.d.79.1 yes 6 4.3 odd 2
378.2.e.d.37.1 6 36.23 even 6
378.2.e.d.235.1 6 84.11 even 6
378.2.h.c.289.3 6 12.11 even 2
378.2.h.c.361.3 6 252.95 even 6
882.2.e.o.373.1 6 252.139 even 6
882.2.e.o.655.1 6 28.3 even 6
882.2.f.n.295.2 6 28.23 odd 6
882.2.f.n.589.2 6 252.247 odd 6
882.2.f.o.295.2 6 28.19 even 6
882.2.f.o.589.2 6 252.103 even 6
882.2.h.p.67.3 6 252.31 even 6
882.2.h.p.79.3 6 28.27 even 2
1008.2.q.g.529.1 6 7.4 even 3
1008.2.q.g.625.1 6 9.4 even 3
1008.2.t.h.193.3 6 63.4 even 3 inner
1008.2.t.h.961.3 6 1.1 even 1 trivial
1134.2.g.l.163.1 6 36.11 even 6
1134.2.g.l.487.1 6 252.11 even 6
1134.2.g.m.163.3 6 36.7 odd 6
1134.2.g.m.487.3 6 252.151 odd 6
2646.2.e.p.1549.3 6 252.167 odd 6
2646.2.e.p.2125.3 6 84.59 odd 6
2646.2.f.l.883.1 6 84.23 even 6
2646.2.f.l.1765.1 6 252.23 even 6
2646.2.f.m.883.3 6 84.47 odd 6
2646.2.f.m.1765.3 6 252.131 odd 6
2646.2.h.o.361.1 6 252.59 odd 6
2646.2.h.o.667.1 6 84.83 odd 2
3024.2.q.g.2305.1 6 9.5 odd 6
3024.2.q.g.2881.1 6 21.11 odd 6
3024.2.t.h.289.3 6 3.2 odd 2
3024.2.t.h.1873.3 6 63.32 odd 6
7938.2.a.bv.1.1 3 252.79 odd 6
7938.2.a.bw.1.3 3 252.187 even 6
7938.2.a.bz.1.1 3 252.47 odd 6
7938.2.a.ca.1.3 3 252.191 even 6