Properties

Label 1008.2.q.g.625.1
Level $1008$
Weight $2$
Character 1008.625
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(529,1008)]
 
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, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.q (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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.1
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1008.625
Dual form 1008.2.q.g.529.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71053 + 0.272169i) q^{3} +(1.59097 + 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +(2.85185 - 0.931107i) q^{9} +O(q^{10})\) \(q+(-1.71053 + 0.272169i) q^{3} +(1.59097 + 2.75564i) q^{5} +(2.56238 + 0.658939i) q^{7} +(2.85185 - 0.931107i) q^{9} +(1.59097 - 2.75564i) q^{11} +(2.85185 - 4.93955i) q^{13} +(-3.47141 - 4.28061i) q^{15} +(-0.760877 - 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(-4.56238 - 0.429736i) q^{21} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(-4.62476 + 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +9.42107 q^{31} +(-1.97141 + 5.14663i) q^{33} +(2.26088 + 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-3.53379 + 9.22544i) q^{39} +(-2.80150 + 4.85235i) q^{41} +(-3.41423 - 5.91362i) q^{43} +(7.10301 + 6.37731i) q^{45} +5.82846 q^{47} +(6.13160 + 3.37690i) q^{49} +(1.66019 + 2.04719i) q^{51} +(1.02859 + 1.78157i) q^{53} +10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +1.12476 q^{59} +3.12476 q^{61} +(7.92107 - 0.506659i) q^{63} +18.1488 q^{65} -10.9669 q^{67} +(-2.44282 - 3.01225i) q^{69} -8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(3.17511 - 8.28905i) q^{75} +(5.89248 - 6.01266i) q^{77} +4.13844 q^{79} +(7.26608 - 5.31075i) q^{81} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(7.72545 + 9.52628i) q^{87} +(0.112725 - 0.195246i) q^{89} +(10.5624 - 10.7778i) q^{91} +(-16.1150 + 2.56412i) q^{93} +4.08126 q^{95} +(7.42107 + 12.8537i) q^{97} +(1.97141 - 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} + q^{5} - 2 q^{7} + 8 q^{9} + q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} + 2 q^{25} + 7 q^{27} - 5 q^{29} + 40 q^{31} - 3 q^{33} + 13 q^{35} + 3 q^{37} + 5 q^{39} + 6 q^{43} + 9 q^{45} - 18 q^{47} + 12 q^{49} - 6 q^{51} + 15 q^{53} + 26 q^{55} + 22 q^{57} - 28 q^{59} - 16 q^{61} + 31 q^{63} + 24 q^{65} + 2 q^{67} + 3 q^{69} - 14 q^{71} + 19 q^{73} - 8 q^{75} + 10 q^{77} + 10 q^{79} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 27 q^{87} - 9 q^{89} + 46 q^{91} - 38 q^{93} - 8 q^{95} + 28 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.71053 + 0.272169i −0.987577 + 0.157137i
\(4\) 0 0
\(5\) 1.59097 + 2.75564i 0.711504 + 1.23236i 0.964292 + 0.264840i \(0.0853191\pi\)
−0.252788 + 0.967522i \(0.581348\pi\)
\(6\) 0 0
\(7\) 2.56238 + 0.658939i 0.968489 + 0.249055i
\(8\) 0 0
\(9\) 2.85185 0.931107i 0.950616 0.310369i
\(10\) 0 0
\(11\) 1.59097 2.75564i 0.479696 0.830858i −0.520033 0.854146i \(-0.674080\pi\)
0.999729 + 0.0232884i \(0.00741361\pi\)
\(12\) 0 0
\(13\) 2.85185 4.93955i 0.790960 1.36998i −0.134412 0.990925i \(-0.542915\pi\)
0.925373 0.379058i \(-0.123752\pi\)
\(14\) 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
\(21\) −4.56238 0.429736i −0.995593 0.0937761i
\(22\) 0 0
\(23\) 1.11956 + 1.93914i 0.233445 + 0.404338i 0.958820 0.284016i \(-0.0916669\pi\)
−0.725375 + 0.688354i \(0.758334\pi\)
\(24\) 0 0
\(25\) −2.56238 + 4.43818i −0.512476 + 0.887635i
\(26\) 0 0
\(27\) −4.62476 + 2.36887i −0.890036 + 0.455890i
\(28\) 0 0
\(29\) −3.54063 6.13255i −0.657478 1.13879i −0.981266 0.192656i \(-0.938290\pi\)
0.323788 0.946130i \(-0.395043\pi\)
\(30\) 0 0
\(31\) 9.42107 1.69207 0.846037 0.533125i \(-0.178982\pi\)
0.846037 + 0.533125i \(0.178982\pi\)
\(32\) 0 0
\(33\) −1.97141 + 5.14663i −0.343178 + 0.895914i
\(34\) 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
\(39\) −3.53379 + 9.22544i −0.565860 + 1.47725i
\(40\) 0 0
\(41\) −2.80150 + 4.85235i −0.437522 + 0.757810i −0.997498 0.0706992i \(-0.977477\pi\)
0.559976 + 0.828509i \(0.310810\pi\)
\(42\) 0 0
\(43\) −3.41423 5.91362i −0.520665 0.901819i −0.999711 0.0240288i \(-0.992351\pi\)
0.479046 0.877790i \(-0.340983\pi\)
\(44\) 0 0
\(45\) 7.10301 + 6.37731i 1.05885 + 0.950674i
\(46\) 0 0
\(47\) 5.82846 0.850168 0.425084 0.905154i \(-0.360245\pi\)
0.425084 + 0.905154i \(0.360245\pi\)
\(48\) 0 0
\(49\) 6.13160 + 3.37690i 0.875943 + 0.482415i
\(50\) 0 0
\(51\) 1.66019 + 2.04719i 0.232473 + 0.286663i
\(52\) 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
\(59\) 1.12476 0.146432 0.0732159 0.997316i \(-0.476674\pi\)
0.0732159 + 0.997316i \(0.476674\pi\)
\(60\) 0 0
\(61\) 3.12476 0.400085 0.200042 0.979787i \(-0.435892\pi\)
0.200042 + 0.979787i \(0.435892\pi\)
\(62\) 0 0
\(63\) 7.92107 0.506659i 0.997961 0.0638331i
\(64\) 0 0
\(65\) 18.1488 2.25109
\(66\) 0 0
\(67\) −10.9669 −1.33982 −0.669910 0.742442i \(-0.733667\pi\)
−0.669910 + 0.742442i \(0.733667\pi\)
\(68\) 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
\(75\) 3.17511 8.28905i 0.366630 0.957137i
\(76\) 0 0
\(77\) 5.89248 6.01266i 0.671510 0.685206i
\(78\) 0 0
\(79\) 4.13844 0.465610 0.232805 0.972523i \(-0.425210\pi\)
0.232805 + 0.972523i \(0.425210\pi\)
\(80\) 0 0
\(81\) 7.26608 5.31075i 0.807342 0.590084i
\(82\) 0 0
\(83\) 4.03379 + 6.98673i 0.442766 + 0.766893i 0.997894 0.0648718i \(-0.0206639\pi\)
−0.555127 + 0.831765i \(0.687331\pi\)
\(84\) 0 0
\(85\) 2.42107 4.19341i 0.262602 0.454839i
\(86\) 0 0
\(87\) 7.72545 + 9.52628i 0.828255 + 1.02132i
\(88\) 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
\(93\) −16.1150 + 2.56412i −1.67105 + 0.265887i
\(94\) 0 0
\(95\) 4.08126 0.418728
\(96\) 0 0
\(97\) 7.42107 + 12.8537i 0.753495 + 1.30509i 0.946119 + 0.323819i \(0.104967\pi\)
−0.192624 + 0.981273i \(0.561700\pi\)
\(98\) 0 0
\(99\) 1.97141 9.34004i 0.198134 0.938710i
\(100\) 0 0
\(101\) −9.29467 + 16.0988i −0.924854 + 1.60189i −0.133058 + 0.991108i \(0.542480\pi\)
−0.791796 + 0.610786i \(0.790854\pi\)
\(102\) 0 0
\(103\) −0.141315 0.244765i −0.0139242 0.0241174i 0.858979 0.512010i \(-0.171099\pi\)
−0.872904 + 0.487893i \(0.837766\pi\)
\(104\) 0 0
\(105\) −6.07442 13.2560i −0.592803 1.29365i
\(106\) 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 −0.931677 0.363287i \(-0.881655\pi\)
0.780454 + 0.625213i \(0.214988\pi\)
\(114\) 0 0
\(115\) −3.56238 + 6.17023i −0.332194 + 0.575377i
\(116\) 0 0
\(117\) 3.53379 16.7422i 0.326699 1.54782i
\(118\) 0 0
\(119\) −1.08126 3.87828i −0.0991186 0.355521i
\(120\) 0 0
\(121\) 0.437618 + 0.757977i 0.0397835 + 0.0689070i
\(122\) 0 0
\(123\) 3.47141 9.06259i 0.313007 0.817146i
\(124\) 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
\(129\) 7.44966 + 9.18620i 0.655906 + 0.808800i
\(130\) 0 0
\(131\) 3.18194 + 5.51129i 0.278008 + 0.481523i 0.970890 0.239528i \(-0.0769926\pi\)
−0.692882 + 0.721051i \(0.743659\pi\)
\(132\) 0 0
\(133\) 2.37524 2.42368i 0.205959 0.210160i
\(134\) 0 0
\(135\) −13.8856 8.97539i −1.19509 0.772479i
\(136\) 0 0
\(137\) −1.37072 + 2.37416i −0.117109 + 0.202838i −0.918621 0.395140i \(-0.870696\pi\)
0.801512 + 0.597979i \(0.204029\pi\)
\(138\) 0 0
\(139\) 3.98345 6.89953i 0.337872 0.585211i −0.646161 0.763202i \(-0.723626\pi\)
0.984032 + 0.177991i \(0.0569597\pi\)
\(140\) 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
\(147\) −11.4074 4.10748i −0.940866 0.338779i
\(148\) 0 0
\(149\) 11.6300 + 20.1437i 0.952764 + 1.65024i 0.739404 + 0.673262i \(0.235107\pi\)
0.213360 + 0.976974i \(0.431559\pi\)
\(150\) 0 0
\(151\) −4.06238 + 7.03625i −0.330592 + 0.572602i −0.982628 0.185586i \(-0.940582\pi\)
0.652036 + 0.758188i \(0.273915\pi\)
\(152\) 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
\(157\) −11.2632 −0.898901 −0.449451 0.893305i \(-0.648380\pi\)
−0.449451 + 0.893305i \(0.648380\pi\)
\(158\) 0 0
\(159\) −2.24433 2.76748i −0.177987 0.219476i
\(160\) 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
\(165\) −17.3187 + 2.75564i −1.34826 + 0.214527i
\(166\) 0 0
\(167\) −2.61956 + 4.53721i −0.202708 + 0.351100i −0.949400 0.314070i \(-0.898307\pi\)
0.746692 + 0.665170i \(0.231641\pi\)
\(168\) 0 0
\(169\) −9.76608 16.9153i −0.751237 1.30118i
\(170\) 0 0
\(171\) 0.794668 3.76494i 0.0607698 0.287912i
\(172\) 0 0
\(173\) 2.55159 0.193994 0.0969968 0.995285i \(-0.469076\pi\)
0.0969968 + 0.995285i \(0.469076\pi\)
\(174\) 0 0
\(175\) −9.49028 + 9.68385i −0.717398 + 0.732030i
\(176\) 0 0
\(177\) −1.92395 + 0.306125i −0.144613 + 0.0230098i
\(178\) 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
\(185\) 3.18194 0.233941
\(186\) 0 0
\(187\) −4.84213 −0.354092
\(188\) 0 0
\(189\) −13.4114 + 3.02252i −0.975532 + 0.219856i
\(190\) 0 0
\(191\) −1.98057 −0.143309 −0.0716545 0.997430i \(-0.522828\pi\)
−0.0716545 + 0.997430i \(0.522828\pi\)
\(192\) 0 0
\(193\) −4.54583 −0.327216 −0.163608 0.986525i \(-0.552313\pi\)
−0.163608 + 0.986525i \(0.552313\pi\)
\(194\) 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
\(201\) 18.7592 2.98485i 1.32317 0.210535i
\(202\) 0 0
\(203\) −5.03147 18.0470i −0.353140 1.26665i
\(204\) 0 0
\(205\) −17.8285 −1.24519
\(206\) 0 0
\(207\) 4.99837 + 4.48769i 0.347410 + 0.311916i
\(208\) 0 0
\(209\) −2.04063 3.53447i −0.141153 0.244485i
\(210\) 0 0
\(211\) 8.32846 14.4253i 0.573355 0.993080i −0.422863 0.906193i \(-0.638975\pi\)
0.996218 0.0868863i \(-0.0276917\pi\)
\(212\) 0 0
\(213\) 14.8646 2.36515i 1.01850 0.162058i
\(214\) 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
\(219\) 5.41874 + 6.68187i 0.366165 + 0.451519i
\(220\) 0 0
\(221\) −8.67962 −0.583854
\(222\) 0 0
\(223\) 5.32846 + 9.22916i 0.356820 + 0.618031i 0.987428 0.158071i \(-0.0505276\pi\)
−0.630608 + 0.776102i \(0.717194\pi\)
\(224\) 0 0
\(225\) −3.17511 + 15.0429i −0.211674 + 1.00286i
\(226\) 0 0
\(227\) −7.25404 + 12.5644i −0.481468 + 0.833926i −0.999774 0.0212688i \(-0.993229\pi\)
0.518306 + 0.855195i \(0.326563\pi\)
\(228\) 0 0
\(229\) −5.12476 8.87635i −0.338654 0.586566i 0.645526 0.763738i \(-0.276638\pi\)
−0.984180 + 0.177173i \(0.943305\pi\)
\(230\) 0 0
\(231\) −8.44282 + 11.8886i −0.555497 + 0.782212i
\(232\) 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 −0.595068 0.803676i \(-0.702875\pi\)
0.993537 + 0.113506i \(0.0362081\pi\)
\(240\) 0 0
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 0 0
\(243\) −10.9834 + 11.0618i −0.704589 + 0.709616i
\(244\) 0 0
\(245\) 0.449657 + 22.2691i 0.0287275 + 1.42272i
\(246\) 0 0
\(247\) −3.65787 6.33561i −0.232744 0.403125i
\(248\) 0 0
\(249\) −8.80150 10.8532i −0.557773 0.687791i
\(250\) 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
\(255\) −3.00000 + 7.83191i −0.187867 + 0.490453i
\(256\) 0 0
\(257\) −3.83009 6.63392i −0.238915 0.413813i 0.721488 0.692427i \(-0.243458\pi\)
−0.960403 + 0.278614i \(0.910125\pi\)
\(258\) 0 0
\(259\) 1.85185 1.88962i 0.115068 0.117415i
\(260\) 0 0
\(261\) −15.8074 14.1924i −0.978453 0.878487i
\(262\) 0 0
\(263\) −1.54746 + 2.68029i −0.0954208 + 0.165274i −0.909784 0.415082i \(-0.863753\pi\)
0.814363 + 0.580355i \(0.197086\pi\)
\(264\) 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
\(273\) −15.1339 + 21.3106i −0.915947 + 1.28977i
\(274\) 0 0
\(275\) 8.15335 + 14.1220i 0.491666 + 0.851590i
\(276\) 0 0
\(277\) 7.31875 12.6764i 0.439741 0.761653i −0.557928 0.829889i \(-0.688404\pi\)
0.997669 + 0.0682357i \(0.0217370\pi\)
\(278\) 0 0
\(279\) 26.8675 8.77202i 1.60851 0.525167i
\(280\) 0 0
\(281\) 11.6992 + 20.2636i 0.697915 + 1.20882i 0.969188 + 0.246322i \(0.0792219\pi\)
−0.271273 + 0.962502i \(0.587445\pi\)
\(282\) 0 0
\(283\) 26.1248 1.55296 0.776478 0.630144i \(-0.217004\pi\)
0.776478 + 0.630144i \(0.217004\pi\)
\(284\) 0 0
\(285\) −6.98113 + 1.11079i −0.413526 + 0.0657975i
\(286\) 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
\(291\) −16.1923 19.9668i −0.949212 1.17048i
\(292\) 0 0
\(293\) 12.9315 22.3980i 0.755465 1.30850i −0.189678 0.981846i \(-0.560745\pi\)
0.945143 0.326657i \(-0.105922\pi\)
\(294\) 0 0
\(295\) 1.78947 + 3.09945i 0.104187 + 0.180457i
\(296\) 0 0
\(297\) −0.830095 + 16.5130i −0.0481670 + 0.958182i
\(298\) 0 0
\(299\) 12.7713 0.738582
\(300\) 0 0
\(301\) −4.85185 17.4027i −0.279656 1.00308i
\(302\) 0 0
\(303\) 11.5172 30.0673i 0.661648 1.72732i
\(304\) 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
\(311\) −1.70370 −0.0966078 −0.0483039 0.998833i \(-0.515382\pi\)
−0.0483039 + 0.998833i \(0.515382\pi\)
\(312\) 0 0
\(313\) −2.84213 −0.160647 −0.0803234 0.996769i \(-0.525595\pi\)
−0.0803234 + 0.996769i \(0.525595\pi\)
\(314\) 0 0
\(315\) 13.9984 + 21.0216i 0.788719 + 1.18443i
\(316\) 0 0
\(317\) −24.9201 −1.39965 −0.699827 0.714313i \(-0.746739\pi\)
−0.699827 + 0.714313i \(0.746739\pi\)
\(318\) 0 0
\(319\) −22.5322 −1.26156
\(320\) 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
\(327\) 4.82326 + 5.94758i 0.266727 + 0.328902i
\(328\) 0 0
\(329\) 14.9347 + 3.84060i 0.823379 + 0.211739i
\(330\) 0 0
\(331\) 7.17154 0.394183 0.197092 0.980385i \(-0.436850\pi\)
0.197092 + 0.980385i \(0.436850\pi\)
\(332\) 0 0
\(333\) 0.619562 2.93533i 0.0339518 0.160855i
\(334\) 0 0
\(335\) −17.4480 30.2209i −0.953287 1.65114i
\(336\) 0 0
\(337\) −10.9211 + 18.9158i −0.594908 + 1.03041i 0.398651 + 0.917103i \(0.369478\pi\)
−0.993560 + 0.113309i \(0.963855\pi\)
\(338\) 0 0
\(339\) 1.99192 5.20018i 0.108186 0.282435i
\(340\) 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
\(345\) 4.41423 11.5239i 0.237654 0.620428i
\(346\) 0 0
\(347\) 2.11109 0.113329 0.0566646 0.998393i \(-0.481953\pi\)
0.0566646 + 0.998393i \(0.481953\pi\)
\(348\) 0 0
\(349\) 18.1082 + 31.3643i 0.969310 + 1.67889i 0.697559 + 0.716527i \(0.254269\pi\)
0.271751 + 0.962368i \(0.412397\pi\)
\(350\) 0 0
\(351\) −1.48796 + 29.5999i −0.0794215 + 1.57993i
\(352\) 0 0
\(353\) 5.24433 9.08344i 0.279127 0.483463i −0.692041 0.721858i \(-0.743288\pi\)
0.971168 + 0.238396i \(0.0766215\pi\)
\(354\) 0 0
\(355\) −13.8256 23.9466i −0.733786 1.27095i
\(356\) 0 0
\(357\) 2.90507 + 6.33963i 0.153753 + 0.335529i
\(358\) 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
\(367\) −9.05555 + 15.6847i −0.472696 + 0.818733i −0.999512 0.0312465i \(-0.990052\pi\)
0.526816 + 0.849979i \(0.323386\pi\)
\(368\) 0 0
\(369\) −3.47141 + 16.4467i −0.180714 + 0.856179i
\(370\) 0 0
\(371\) 1.46169 + 5.24284i 0.0758874 + 0.272195i
\(372\) 0 0
\(373\) 5.83530 + 10.1070i 0.302140 + 0.523322i 0.976621 0.214971i \(-0.0689656\pi\)
−0.674480 + 0.738293i \(0.735632\pi\)
\(374\) 0 0
\(375\) 0.679065 0.108048i 0.0350668 0.00557959i
\(376\) 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
\(381\) 34.3908 5.47204i 1.76190 0.280341i
\(382\) 0 0
\(383\) −0.824893 1.42876i −0.0421501 0.0730061i 0.844181 0.536059i \(-0.180087\pi\)
−0.886331 + 0.463053i \(0.846754\pi\)
\(384\) 0 0
\(385\) 25.9435 + 6.67160i 1.32220 + 0.340016i
\(386\) 0 0
\(387\) −15.2431 13.6857i −0.774849 0.695685i
\(388\) 0 0
\(389\) 16.0338 27.7713i 0.812946 1.40806i −0.0978483 0.995201i \(-0.531196\pi\)
0.910794 0.412862i \(-0.135471\pi\)
\(390\) 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
\(399\) −3.40327 + 4.79225i −0.170377 + 0.239913i
\(400\) 0 0
\(401\) −5.30959 9.19647i −0.265148 0.459250i 0.702454 0.711729i \(-0.252087\pi\)
−0.967602 + 0.252479i \(0.918754\pi\)
\(402\) 0 0
\(403\) 26.8675 46.5358i 1.33836 2.31811i
\(404\) 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
\(409\) 5.54583 0.274224 0.137112 0.990556i \(-0.456218\pi\)
0.137112 + 0.990556i \(0.456218\pi\)
\(410\) 0 0
\(411\) 1.69850 4.43415i 0.0837806 0.218721i
\(412\) 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
\(417\) −4.93598 + 12.8861i −0.241716 + 0.631033i
\(418\) 0 0
\(419\) −2.77455 + 4.80566i −0.135546 + 0.234772i −0.925806 0.378000i \(-0.876612\pi\)
0.790260 + 0.612772i \(0.209945\pi\)
\(420\) 0 0
\(421\) −3.42107 5.92546i −0.166733 0.288789i 0.770537 0.637396i \(-0.219988\pi\)
−0.937269 + 0.348606i \(0.886655\pi\)
\(422\) 0 0
\(423\) 16.6219 5.42692i 0.808184 0.263866i
\(424\) 0 0
\(425\) 7.79863 0.378289
\(426\) 0 0
\(427\) 8.00684 + 2.05903i 0.387478 + 0.0996433i
\(428\) 0 0
\(429\) 19.7999 + 24.4153i 0.955947 + 1.17878i
\(430\) 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
\(437\) 2.87197 0.137385
\(438\) 0 0
\(439\) 8.83422 0.421634 0.210817 0.977526i \(-0.432388\pi\)
0.210817 + 0.977526i \(0.432388\pi\)
\(440\) 0 0
\(441\) 20.6307 + 3.92124i 0.982412 + 0.186726i
\(442\) 0 0
\(443\) −17.5185 −0.832328 −0.416164 0.909290i \(-0.636626\pi\)
−0.416164 + 0.909290i \(0.636626\pi\)
\(444\) 0 0
\(445\) 0.717370 0.0340066
\(446\) 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
\(453\) 5.03379 13.1414i 0.236508 0.617437i
\(454\) 0 0
\(455\) 46.5043 + 11.9590i 2.18015 + 0.560645i
\(456\) 0 0
\(457\) −32.1248 −1.50273 −0.751367 0.659885i \(-0.770605\pi\)
−0.751367 + 0.659885i \(0.770605\pi\)
\(458\) 0 0
\(459\) 6.64076 + 4.29245i 0.309964 + 0.200354i
\(460\) 0 0
\(461\) 1.23229 + 2.13438i 0.0573933 + 0.0994081i 0.893295 0.449472i \(-0.148388\pi\)
−0.835901 + 0.548880i \(0.815054\pi\)
\(462\) 0 0
\(463\) −15.1735 + 26.2812i −0.705171 + 1.22139i 0.261459 + 0.965215i \(0.415796\pi\)
−0.966630 + 0.256177i \(0.917537\pi\)
\(464\) 0 0
\(465\) −32.7044 40.3279i −1.51663 1.87016i
\(466\) 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
\(471\) 19.2661 3.06549i 0.887734 0.141250i
\(472\) 0 0
\(473\) −21.7278 −0.999044
\(474\) 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
\(479\) −11.5865 + 20.0683i −0.529399 + 0.916946i 0.470013 + 0.882659i \(0.344249\pi\)
−0.999412 + 0.0342863i \(0.989084\pi\)
\(480\) 0 0
\(481\) −2.85185 4.93955i −0.130033 0.225224i
\(482\) 0 0
\(483\) −4.27455 9.32820i −0.194499 0.424448i
\(484\) 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 −0.564564 0.825389i \(-0.690956\pi\)
0.997090 + 0.0762323i \(0.0242890\pi\)
\(492\) 0 0
\(493\) −5.38796 + 9.33223i −0.242662 + 0.420302i
\(494\) 0 0
\(495\) 28.8743 9.42724i 1.29780 0.423723i
\(496\) 0 0
\(497\) −22.2672 5.72619i −0.998819 0.256855i
\(498\) 0 0
\(499\) 20.5848 + 35.6540i 0.921503 + 1.59609i 0.797090 + 0.603860i \(0.206371\pi\)
0.124413 + 0.992231i \(0.460295\pi\)
\(500\) 0 0
\(501\) 3.24596 8.47402i 0.145019 0.378591i
\(502\) 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
\(507\) 21.3090 + 26.2762i 0.946367 + 1.16697i
\(508\) 0 0
\(509\) −6.38564 11.0603i −0.283039 0.490237i 0.689093 0.724673i \(-0.258009\pi\)
−0.972132 + 0.234436i \(0.924676\pi\)
\(510\) 0 0
\(511\) −3.52915 12.6584i −0.156120 0.559975i
\(512\) 0 0
\(513\) −0.334608 + 6.65634i −0.0147733 + 0.293884i
\(514\) 0 0
\(515\) 0.449657 0.778828i 0.0198142 0.0343193i
\(516\) 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
\(525\) 13.5978 19.1475i 0.593457 0.835665i
\(526\) 0 0
\(527\) −7.16827 12.4158i −0.312255 0.540841i
\(528\) 0 0
\(529\) 8.99316 15.5766i 0.391007 0.677244i
\(530\) 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
\(535\) −36.2028 −1.56518
\(536\) 0 0
\(537\) 7.67799 + 9.46775i 0.331330 + 0.408564i
\(538\) 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
\(543\) 22.1803 3.52918i 0.951848 0.151452i
\(544\) 0 0
\(545\) 7.03379 12.1829i 0.301295 0.521857i
\(546\) 0 0
\(547\) −17.6150 30.5102i −0.753165 1.30452i −0.946281 0.323344i \(-0.895193\pi\)
0.193116 0.981176i \(-0.438141\pi\)
\(548\) 0 0
\(549\) 8.91135 2.90949i 0.380327 0.124174i
\(550\) 0 0
\(551\) −9.08263 −0.386933
\(552\) 0 0
\(553\) 10.6043 + 2.72698i 0.450939 + 0.115963i
\(554\) 0 0
\(555\) −5.44282 + 0.866025i −0.231035 + 0.0367607i
\(556\) 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
\(563\) 1.45993 0.0615286 0.0307643 0.999527i \(-0.490206\pi\)
0.0307643 + 0.999527i \(0.490206\pi\)
\(564\) 0 0
\(565\) −10.2301 −0.430383
\(566\) 0 0
\(567\) 22.1179 8.82028i 0.928866 0.370417i
\(568\) 0 0
\(569\) 19.5653 0.820218 0.410109 0.912036i \(-0.365491\pi\)
0.410109 + 0.912036i \(0.365491\pi\)
\(570\) 0 0
\(571\) 21.9259 0.917569 0.458785 0.888547i \(-0.348285\pi\)
0.458785 + 0.888547i \(0.348285\pi\)
\(572\) 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
\(579\) 7.77579 1.23723i 0.323151 0.0514176i
\(580\) 0 0
\(581\) 5.73229 + 20.5607i 0.237815 + 0.853001i
\(582\) 0 0
\(583\) 6.54583 0.271101
\(584\) 0 0
\(585\) 51.7577 16.8985i 2.13992 0.698668i
\(586\) 0 0
\(587\) 18.0796 + 31.3148i 0.746226 + 1.29250i 0.949620 + 0.313404i \(0.101469\pi\)
−0.203394 + 0.979097i \(0.565197\pi\)
\(588\) 0 0
\(589\) 6.04187 10.4648i 0.248951 0.431196i
\(590\) 0 0
\(591\) 37.3149 5.93730i 1.53493 0.244228i
\(592\) 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
\(597\) 13.4000 + 16.5236i 0.548426 + 0.676265i
\(598\) 0 0
\(599\) 5.45417 0.222851 0.111426 0.993773i \(-0.464458\pi\)
0.111426 + 0.993773i \(0.464458\pi\)
\(600\) 0 0
\(601\) −3.36840 5.83424i −0.137400 0.237984i 0.789112 0.614250i \(-0.210541\pi\)
−0.926512 + 0.376266i \(0.877208\pi\)
\(602\) 0 0
\(603\) −31.2759 + 10.2114i −1.27365 + 0.415839i
\(604\) 0 0
\(605\) −1.39248 + 2.41184i −0.0566122 + 0.0980553i
\(606\) 0 0
\(607\) 3.33530 + 5.77690i 0.135376 + 0.234477i 0.925741 0.378159i \(-0.123443\pi\)
−0.790365 + 0.612636i \(0.790109\pi\)
\(608\) 0 0
\(609\) 13.5183 + 29.5006i 0.547790 + 1.19542i
\(610\) 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 −0.275996 0.961159i \(-0.589008\pi\)
0.970386 0.241560i \(-0.0776589\pi\)
\(618\) 0 0
\(619\) −8.22421 + 14.2447i −0.330559 + 0.572545i −0.982622 0.185620i \(-0.940571\pi\)
0.652063 + 0.758165i \(0.273904\pi\)
\(620\) 0 0
\(621\) −9.77128 6.31595i −0.392108 0.253450i
\(622\) 0 0
\(623\) 0.417500 0.426015i 0.0167268 0.0170679i
\(624\) 0 0
\(625\) 12.1803 + 21.0969i 0.487212 + 0.843877i
\(626\) 0 0
\(627\) 4.45254 + 5.49044i 0.177817 + 0.219267i
\(628\) 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
\(633\) −10.3200 + 26.9417i −0.410183 + 1.07084i
\(634\) 0 0
\(635\) −31.9870 55.4031i −1.26937 2.19861i
\(636\) 0 0
\(637\) 34.1668 20.6569i 1.35374 0.818456i
\(638\) 0 0
\(639\) −24.7826 + 8.09134i −0.980386 + 0.320089i
\(640\) 0 0
\(641\) −13.9497 + 24.1615i −0.550978 + 0.954322i 0.447226 + 0.894421i \(0.352412\pi\)
−0.998204 + 0.0599014i \(0.980921\pi\)
\(642\) 0 0
\(643\) −14.2524 + 24.6859i −0.562060 + 0.973516i 0.435257 + 0.900306i \(0.356658\pi\)
−0.997317 + 0.0732100i \(0.976676\pi\)
\(644\) 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
\(651\) −42.9825 4.04857i −1.68462 0.158676i
\(652\) 0 0
\(653\) −19.0825 33.0519i −0.746756 1.29342i −0.949370 0.314161i \(-0.898277\pi\)
0.202614 0.979259i \(-0.435056\pi\)
\(654\) 0 0
\(655\) −10.1248 + 17.5366i −0.395607 + 0.685212i
\(656\) 0 0
\(657\) −11.0875 9.95475i −0.432566 0.388372i
\(658\) 0 0
\(659\) −4.37072 7.57031i −0.170259 0.294898i 0.768251 0.640148i \(-0.221127\pi\)
−0.938510 + 0.345251i \(0.887794\pi\)
\(660\) 0 0
\(661\) −20.0837 −0.781167 −0.390584 0.920567i \(-0.627727\pi\)
−0.390584 + 0.920567i \(0.627727\pi\)
\(662\) 0 0
\(663\) 14.8468 2.36232i 0.576601 0.0917449i
\(664\) 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
\(669\) −11.6264 14.3366i −0.449503 0.554283i
\(670\) 0 0
\(671\) 4.97141 8.61073i 0.191919 0.332414i
\(672\) 0 0
\(673\) −17.0264 29.4906i −0.656319 1.13678i −0.981561 0.191148i \(-0.938779\pi\)
0.325242 0.945631i \(-0.394554\pi\)
\(674\) 0 0
\(675\) 1.33693 26.5955i 0.0514585 1.02366i
\(676\) 0 0
\(677\) −0.717370 −0.0275708 −0.0137854 0.999905i \(-0.504388\pi\)
−0.0137854 + 0.999905i \(0.504388\pi\)
\(678\) 0 0
\(679\) 10.5458 + 37.8260i 0.404712 + 1.45163i
\(680\) 0 0
\(681\) 8.98865 23.4661i 0.344446 0.899223i
\(682\) 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
\(689\) 11.7335 0.447012
\(690\) 0 0
\(691\) −5.84789 −0.222464 −0.111232 0.993794i \(-0.535480\pi\)
−0.111232 + 0.993794i \(0.535480\pi\)
\(692\) 0 0
\(693\) 11.2060 22.6337i 0.425681 0.859784i
\(694\) 0 0
\(695\) 25.3502 0.961588
\(696\) 0 0
\(697\) 8.52640 0.322960
\(698\) 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
\(705\) −20.2330 24.9494i −0.762018 0.939647i
\(706\) 0 0
\(707\) −34.4246 + 35.1268i −1.29467 + 1.32108i
\(708\) 0 0
\(709\) 43.4854 1.63313 0.816564 0.577255i \(-0.195876\pi\)
0.816564 + 0.577255i \(0.195876\pi\)
\(710\) 0 0
\(711\) 11.8022 3.85333i 0.442617 0.144511i
\(712\) 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
\(717\) −7.63323 + 19.9276i −0.285068 + 0.744210i
\(718\) 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
\(723\) −8.05430 + 21.0268i −0.299543 + 0.781997i
\(724\) 0 0
\(725\) 36.2898 1.34777
\(726\) 0 0
\(727\) −6.07210 10.5172i −0.225202 0.390061i 0.731178 0.682186i \(-0.238971\pi\)
−0.956380 + 0.292126i \(0.905637\pi\)
\(728\) 0 0
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) 0 0
\(731\) −5.19562 + 8.99907i −0.192167 + 0.332843i
\(732\) 0 0
\(733\) 23.0848 + 39.9841i 0.852657 + 1.47685i 0.878801 + 0.477188i \(0.158344\pi\)
−0.0261440 + 0.999658i \(0.508323\pi\)
\(734\) 0 0
\(735\) −6.83009 37.9696i −0.251932 1.40053i
\(736\) 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 −0.419712 0.907657i \(-0.637869\pi\)
0.995910 0.0903470i \(-0.0287976\pi\)
\(744\) 0 0
\(745\) −37.0059 + 64.0961i −1.35579 + 2.34830i
\(746\) 0 0
\(747\) 18.0092 + 16.1692i 0.658921 + 0.591600i
\(748\) 0 0
\(749\) −21.0695 + 21.4992i −0.769863 + 0.785565i
\(750\) 0 0
\(751\) 1.64815 + 2.85468i 0.0601419 + 0.104169i 0.894529 0.447010i \(-0.147511\pi\)
−0.834387 + 0.551179i \(0.814178\pi\)
\(752\) 0 0
\(753\) 8.74269 1.39108i 0.318601 0.0506937i
\(754\) 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
\(759\) −12.1871 + 1.93914i −0.442365 + 0.0703862i
\(760\) 0 0
\(761\) −7.03379 12.1829i −0.254975 0.441629i 0.709914 0.704288i \(-0.248734\pi\)
−0.964889 + 0.262659i \(0.915400\pi\)
\(762\) 0 0
\(763\) −3.14132 11.2673i −0.113723 0.407905i
\(764\) 0 0
\(765\) 3.00000 14.2132i 0.108465 0.513881i
\(766\) 0 0
\(767\) 3.20765 5.55582i 0.115822 0.200609i
\(768\) 0 0
\(769\) 11.3461 19.6520i 0.409151 0.708669i −0.585644 0.810568i \(-0.699158\pi\)
0.994795 + 0.101899i \(0.0324918\pi\)
\(770\) 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
\(777\) −2.65335 + 3.73627i −0.0951885 + 0.134038i
\(778\) 0 0
\(779\) 3.59329 + 6.22377i 0.128743 + 0.222990i
\(780\) 0 0
\(781\) −13.8256 + 23.9466i −0.494718 + 0.856877i
\(782\) 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
\(787\) −0.540073 −0.0192515 −0.00962576 0.999954i \(-0.503064\pi\)
−0.00962576 + 0.999954i \(0.503064\pi\)
\(788\) 0 0
\(789\) 1.91750 5.00589i 0.0682648 0.178215i
\(790\) 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
\(795\) 4.05555 10.5876i 0.143835 0.375502i
\(796\) 0 0
\(797\) −12.5550 + 21.7459i −0.444721 + 0.770279i −0.998033 0.0626954i \(-0.980030\pi\)
0.553312 + 0.832974i \(0.313364\pi\)
\(798\) 0 0
\(799\) −4.43474 7.68119i −0.156890 0.271741i
\(800\) 0 0
\(801\) 0.139680 0.661770i 0.00493536 0.0233825i
\(802\) 0 0
\(803\) −15.8044 −0.557725
\(804\) 0 0
\(805\) −13.1940 + 13.4631i −0.465027 + 0.474511i
\(806\) 0 0
\(807\) 29.3365 + 36.1750i 1.03270 + 1.27342i
\(808\) 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
\(815\) 12.6659 0.443669
\(816\) 0 0
\(817\) −8.75839 −0.306417
\(818\) 0 0
\(819\) 20.0870 40.5714i 0.701897 1.41768i
\(820\) 0 0
\(821\) 8.48727 0.296208 0.148104 0.988972i \(-0.452683\pi\)
0.148104 + 0.988972i \(0.452683\pi\)
\(822\) 0 0
\(823\) −29.0974 −1.01427 −0.507136 0.861866i \(-0.669296\pi\)
−0.507136 + 0.861866i \(0.669296\pi\)
\(824\) 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
\(831\) −9.06883 + 23.6754i −0.314594 + 0.821291i
\(832\) 0 0
\(833\) −0.215047 10.6501i −0.00745093 0.369004i
\(834\) 0 0
\(835\) −16.6706 −0.576910
\(836\) 0 0
\(837\) −43.5702 + 22.3173i −1.50601 + 0.771399i
\(838\) 0 0
\(839\) −21.2947 36.8834i −0.735174 1.27336i −0.954647 0.297740i \(-0.903767\pi\)
0.219474 0.975618i \(-0.429566\pi\)
\(840\) 0 0
\(841\) −10.5721 + 18.3114i −0.364555 + 0.631428i
\(842\) 0 0
\(843\) −25.5270 31.4774i −0.879195 1.08414i
\(844\) 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
\(849\) −44.6873 + 7.11034i −1.53366 + 0.244026i
\(850\) 0 0
\(851\) 2.23912 0.0767562
\(852\) 0 0
\(853\) −10.6969 18.5275i −0.366254 0.634370i 0.622723 0.782442i \(-0.286026\pi\)
−0.988976 + 0.148073i \(0.952693\pi\)
\(854\) 0 0
\(855\) 11.6391 3.80009i 0.398050 0.129960i
\(856\) 0 0
\(857\) 18.4218 31.9074i 0.629275 1.08994i −0.358422 0.933560i \(-0.616685\pi\)
0.987697 0.156377i \(-0.0499815\pi\)
\(858\) 0 0
\(859\) −8.81875 15.2745i −0.300892 0.521160i 0.675446 0.737409i \(-0.263951\pi\)
−0.976338 + 0.216249i \(0.930618\pi\)
\(860\) 0 0
\(861\) 14.8668 20.9344i 0.506658 0.713441i
\(862\) 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
\(871\) −31.2759 + 54.1715i −1.05974 + 1.83553i
\(872\) 0 0
\(873\) 33.1319 + 29.7469i 1.12134 + 1.00678i
\(874\) 0 0
\(875\) −1.01724 0.261592i −0.0343890 0.00884343i
\(876\) 0 0
\(877\) 20.7495 + 35.9392i 0.700662 + 1.21358i 0.968234 + 0.250044i \(0.0804451\pi\)
−0.267573 + 0.963538i \(0.586222\pi\)
\(878\) 0 0
\(879\) −16.0237 + 41.8320i −0.540466 + 1.41096i
\(880\) 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
\(885\) −3.90451 4.81467i −0.131249 0.161843i
\(886\) 0 0
\(887\) −18.5550 32.1382i −0.623016 1.07909i −0.988921 0.148443i \(-0.952574\pi\)
0.365905 0.930652i \(-0.380759\pi\)
\(888\) 0 0
\(889\) −51.5175 13.2482i −1.72784 0.444330i
\(890\) 0 0
\(891\) −3.07442 28.4720i −0.102997 0.953847i
\(892\) 0 0
\(893\) 3.73788 6.47420i 0.125083 0.216651i
\(894\) 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
\(903\) 13.0357 + 28.4474i 0.433802 + 0.946671i
\(904\) 0 0
\(905\) −20.6300 35.7321i −0.685763 1.18778i
\(906\) 0 0
\(907\) −24.0751 + 41.6993i −0.799401 + 1.38460i 0.120606 + 0.992700i \(0.461516\pi\)
−0.920007 + 0.391902i \(0.871817\pi\)
\(908\) 0 0
\(909\) −11.5172 + 54.5658i −0.382003 + 1.80983i
\(910\) 0 0
\(911\) −17.4428 30.2119i −0.577906 1.00096i −0.995719 0.0924301i \(-0.970537\pi\)
0.417813 0.908533i \(-0.362797\pi\)
\(912\) 0 0
\(913\) 25.6706 0.849573
\(914\) 0 0
\(915\) −10.8473 13.3759i −0.358602 0.442193i
\(916\) 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
\(921\) 6.04187 0.961343i 0.199086 0.0316773i
\(922\) 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
\(927\) −0.630912 0.566453i −0.0207219 0.0186048i
\(928\) 0 0
\(929\) −50.8285 −1.66763 −0.833814 0.552046i \(-0.813847\pi\)
−0.833814 + 0.552046i \(0.813847\pi\)
\(930\) 0 0
\(931\) 7.68332 4.64526i 0.251811 0.152242i
\(932\) 0 0
\(933\) 2.91423 0.463693i 0.0954076 0.0151806i
\(934\) 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
\(941\) 1.15787 0.0377454 0.0188727 0.999822i \(-0.493992\pi\)
0.0188727 + 0.999822i \(0.493992\pi\)
\(942\) 0 0
\(943\) −12.5458 −0.408548
\(944\) 0 0
\(945\) −29.6661 32.1482i −0.965038 1.04578i
\(946\) 0 0
\(947\) −9.81479 −0.318938 −0.159469 0.987203i \(-0.550978\pi\)
−0.159469 + 0.987203i \(0.550978\pi\)
\(948\) 0 0
\(949\) −28.3297 −0.919620
\(950\) 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
\(957\) 38.5420 6.13255i 1.24589 0.198237i
\(958\) 0 0
\(959\) −5.07674 + 5.18029i −0.163937 + 0.167280i
\(960\) 0 0
\(961\) 57.7565 1.86311
\(962\) 0 0
\(963\) −7.04910 + 33.3969i −0.227154 + 1.07620i
\(964\) 0 0
\(965\) −7.23229 12.5267i −0.232816 0.403248i
\(966\) 0 0
\(967\) −14.4445 + 25.0185i −0.464502 + 0.804542i −0.999179 0.0405151i \(-0.987100\pi\)
0.534677 + 0.845057i \(0.320433\pi\)
\(968\) 0 0
\(969\) 3.33870 0.531232i 0.107254 0.0170656i
\(970\) 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
\(975\) −31.8892 39.3227i −1.02127 1.25933i
\(976\) 0 0
\(977\) −48.0722 −1.53797 −0.768983 0.639269i \(-0.779237\pi\)
−0.768983 + 0.639269i \(0.779237\pi\)
\(978\) 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
\(983\) 14.7313 25.5154i 0.469857 0.813816i −0.529549 0.848279i \(-0.677639\pi\)
0.999406 + 0.0344634i \(0.0109722\pi\)
\(984\) 0 0
\(985\) −34.7067 60.1138i −1.10585 1.91538i
\(986\) 0 0
\(987\) −26.5917 2.50470i −0.846422 0.0797255i
\(988\) 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
\(997\) −2.77292 + 4.80283i −0.0878191 + 0.152107i −0.906589 0.422015i \(-0.861323\pi\)
0.818770 + 0.574122i \(0.194656\pi\)
\(998\) 0 0
\(999\) −0.260877 + 5.18960i −0.00825377 + 0.164192i
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.q.g.625.1 6
3.2 odd 2 3024.2.q.g.2305.1 6
4.3 odd 2 126.2.e.c.121.3 yes 6
7.4 even 3 1008.2.t.h.193.3 6
9.2 odd 6 3024.2.t.h.289.3 6
9.7 even 3 1008.2.t.h.961.3 6
12.11 even 2 378.2.e.d.37.1 6
21.11 odd 6 3024.2.t.h.1873.3 6
28.3 even 6 882.2.h.p.67.3 6
28.11 odd 6 126.2.h.d.67.1 yes 6
28.19 even 6 882.2.f.o.589.2 6
28.23 odd 6 882.2.f.n.589.2 6
28.27 even 2 882.2.e.o.373.1 6
36.7 odd 6 126.2.h.d.79.1 yes 6
36.11 even 6 378.2.h.c.289.3 6
36.23 even 6 1134.2.g.l.163.1 6
36.31 odd 6 1134.2.g.m.163.3 6
63.11 odd 6 3024.2.q.g.2881.1 6
63.25 even 3 inner 1008.2.q.g.529.1 6
84.11 even 6 378.2.h.c.361.3 6
84.23 even 6 2646.2.f.l.1765.1 6
84.47 odd 6 2646.2.f.m.1765.3 6
84.59 odd 6 2646.2.h.o.361.1 6
84.83 odd 2 2646.2.e.p.1549.3 6
252.11 even 6 378.2.e.d.235.1 6
252.23 even 6 7938.2.a.ca.1.3 3
252.47 odd 6 2646.2.f.m.883.3 6
252.67 odd 6 1134.2.g.m.487.3 6
252.79 odd 6 882.2.f.n.295.2 6
252.83 odd 6 2646.2.h.o.667.1 6
252.95 even 6 1134.2.g.l.487.1 6
252.103 even 6 7938.2.a.bw.1.3 3
252.115 even 6 882.2.e.o.655.1 6
252.131 odd 6 7938.2.a.bz.1.1 3
252.151 odd 6 126.2.e.c.25.3 6
252.187 even 6 882.2.f.o.295.2 6
252.191 even 6 2646.2.f.l.883.1 6
252.223 even 6 882.2.h.p.79.3 6
252.227 odd 6 2646.2.e.p.2125.3 6
252.247 odd 6 7938.2.a.bv.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.3 6 252.151 odd 6
126.2.e.c.121.3 yes 6 4.3 odd 2
126.2.h.d.67.1 yes 6 28.11 odd 6
126.2.h.d.79.1 yes 6 36.7 odd 6
378.2.e.d.37.1 6 12.11 even 2
378.2.e.d.235.1 6 252.11 even 6
378.2.h.c.289.3 6 36.11 even 6
378.2.h.c.361.3 6 84.11 even 6
882.2.e.o.373.1 6 28.27 even 2
882.2.e.o.655.1 6 252.115 even 6
882.2.f.n.295.2 6 252.79 odd 6
882.2.f.n.589.2 6 28.23 odd 6
882.2.f.o.295.2 6 252.187 even 6
882.2.f.o.589.2 6 28.19 even 6
882.2.h.p.67.3 6 28.3 even 6
882.2.h.p.79.3 6 252.223 even 6
1008.2.q.g.529.1 6 63.25 even 3 inner
1008.2.q.g.625.1 6 1.1 even 1 trivial
1008.2.t.h.193.3 6 7.4 even 3
1008.2.t.h.961.3 6 9.7 even 3
1134.2.g.l.163.1 6 36.23 even 6
1134.2.g.l.487.1 6 252.95 even 6
1134.2.g.m.163.3 6 36.31 odd 6
1134.2.g.m.487.3 6 252.67 odd 6
2646.2.e.p.1549.3 6 84.83 odd 2
2646.2.e.p.2125.3 6 252.227 odd 6
2646.2.f.l.883.1 6 252.191 even 6
2646.2.f.l.1765.1 6 84.23 even 6
2646.2.f.m.883.3 6 252.47 odd 6
2646.2.f.m.1765.3 6 84.47 odd 6
2646.2.h.o.361.1 6 84.59 odd 6
2646.2.h.o.667.1 6 252.83 odd 6
3024.2.q.g.2305.1 6 3.2 odd 2
3024.2.q.g.2881.1 6 63.11 odd 6
3024.2.t.h.289.3 6 9.2 odd 6
3024.2.t.h.1873.3 6 21.11 odd 6
7938.2.a.bv.1.1 3 252.247 odd 6
7938.2.a.bw.1.3 3 252.103 even 6
7938.2.a.bz.1.1 3 252.131 odd 6
7938.2.a.ca.1.3 3 252.23 even 6