Properties

Label 1323.2.s.b.962.1
Level $1323$
Weight $2$
Character 1323.962
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(656,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.656");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 962.1
Root \(0.827154 - 1.43267i\) of defining polynomial
Character \(\chi\) \(=\) 1323.962
Dual form 1323.2.s.b.656.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.81474 - 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} -2.08983 q^{5} -0.819421i q^{8} +O(q^{10})\) \(q+(-1.81474 - 1.04774i) q^{2} +(1.19552 + 2.07070i) q^{4} -2.08983 q^{5} -0.819421i q^{8} +(3.79250 + 2.18960i) q^{10} +3.22878i q^{11} +(-2.68740 - 1.55157i) q^{13} +(1.53250 - 2.65437i) q^{16} +(-0.816304 + 1.41388i) q^{17} +(-4.79094 + 2.76605i) q^{19} +(-2.49844 - 4.32742i) q^{20} +(3.38292 - 5.85939i) q^{22} +1.16078i q^{23} -0.632608 q^{25} +(3.25129 + 5.63139i) q^{26} +(7.05749 - 4.07464i) q^{29} +(5.16886 - 2.98424i) q^{31} +(-6.98146 + 4.03075i) q^{32} +(2.96276 - 1.71055i) q^{34} +(2.82656 + 4.89575i) q^{37} +11.5924 q^{38} +1.71245i q^{40} +(-1.35369 + 2.34465i) q^{41} +(-0.974903 - 1.68858i) q^{43} +(-6.68583 + 3.86007i) q^{44} +(1.21620 - 2.10652i) q^{46} +(4.06759 - 7.04527i) q^{47} +(1.14802 + 0.662809i) q^{50} -7.41974i q^{52} +(-5.27766 - 3.04706i) q^{53} -6.74759i q^{55} -17.0767 q^{58} +(-1.98103 - 3.43124i) q^{59} +(4.15016 + 2.39609i) q^{61} -12.5068 q^{62} +10.7627 q^{64} +(5.61621 + 3.24252i) q^{65} +(0.336981 + 0.583668i) q^{67} -3.90363 q^{68} -7.01535i q^{71} +(2.96276 + 1.71055i) q^{73} -11.8460i q^{74} +(-11.4553 - 6.61374i) q^{76} +(7.07973 - 12.2625i) q^{79} +(-3.20267 + 5.54718i) q^{80} +(4.91318 - 2.83662i) q^{82} +(1.54535 + 2.67662i) q^{83} +(1.70594 - 2.95477i) q^{85} +4.08578i q^{86} +2.64572 q^{88} +(-2.45766 - 4.25679i) q^{89} +(-2.40363 + 1.38774i) q^{92} +(-14.7632 + 8.52356i) q^{94} +(10.0122 - 5.78057i) q^{95} +(-2.07939 + 1.20054i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{4} + 15 q^{10} - 6 q^{13} - 6 q^{16} - 12 q^{17} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 14 q^{25} + 3 q^{26} + 15 q^{29} + 9 q^{31} - 48 q^{32} - 3 q^{34} + 6 q^{37} + 36 q^{38} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} + 15 q^{47} - 3 q^{50} + 9 q^{53} - 16 q^{58} - 18 q^{59} - 12 q^{61} + 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} - 54 q^{68} - 3 q^{73} - 9 q^{76} + 20 q^{79} - 30 q^{80} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 16 q^{88} + 24 q^{89} - 39 q^{92} + 3 q^{94} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81474 1.04774i −1.28321 0.740865i −0.305780 0.952102i \(-0.598917\pi\)
−0.977435 + 0.211238i \(0.932251\pi\)
\(3\) 0 0
\(4\) 1.19552 + 2.07070i 0.597760 + 1.03535i
\(5\) −2.08983 −0.934601 −0.467300 0.884099i \(-0.654773\pi\)
−0.467300 + 0.884099i \(0.654773\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.819421i 0.289709i
\(9\) 0 0
\(10\) 3.79250 + 2.18960i 1.19929 + 0.692412i
\(11\) 3.22878i 0.973512i 0.873538 + 0.486756i \(0.161820\pi\)
−0.873538 + 0.486756i \(0.838180\pi\)
\(12\) 0 0
\(13\) −2.68740 1.55157i −0.745350 0.430328i 0.0786612 0.996901i \(-0.474935\pi\)
−0.824011 + 0.566573i \(0.808269\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.53250 2.65437i 0.383125 0.663593i
\(17\) −0.816304 + 1.41388i −0.197983 + 0.342916i −0.947874 0.318645i \(-0.896772\pi\)
0.749891 + 0.661561i \(0.230106\pi\)
\(18\) 0 0
\(19\) −4.79094 + 2.76605i −1.09912 + 0.634575i −0.935989 0.352030i \(-0.885491\pi\)
−0.163127 + 0.986605i \(0.552158\pi\)
\(20\) −2.49844 4.32742i −0.558667 0.967640i
\(21\) 0 0
\(22\) 3.38292 5.85939i 0.721241 1.24923i
\(23\) 1.16078i 0.242040i 0.992650 + 0.121020i \(0.0386165\pi\)
−0.992650 + 0.121020i \(0.961384\pi\)
\(24\) 0 0
\(25\) −0.632608 −0.126522
\(26\) 3.25129 + 5.63139i 0.637630 + 1.10441i
\(27\) 0 0
\(28\) 0 0
\(29\) 7.05749 4.07464i 1.31054 0.756643i 0.328357 0.944554i \(-0.393505\pi\)
0.982186 + 0.187911i \(0.0601717\pi\)
\(30\) 0 0
\(31\) 5.16886 2.98424i 0.928355 0.535986i 0.0420638 0.999115i \(-0.486607\pi\)
0.886291 + 0.463129i \(0.153273\pi\)
\(32\) −6.98146 + 4.03075i −1.23416 + 0.712542i
\(33\) 0 0
\(34\) 2.96276 1.71055i 0.508109 0.293357i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.82656 + 4.89575i 0.464684 + 0.804857i 0.999187 0.0403097i \(-0.0128345\pi\)
−0.534503 + 0.845167i \(0.679501\pi\)
\(38\) 11.5924 1.88054
\(39\) 0 0
\(40\) 1.71245i 0.270762i
\(41\) −1.35369 + 2.34465i −0.211410 + 0.366173i −0.952156 0.305612i \(-0.901139\pi\)
0.740746 + 0.671785i \(0.234472\pi\)
\(42\) 0 0
\(43\) −0.974903 1.68858i −0.148671 0.257506i 0.782065 0.623196i \(-0.214166\pi\)
−0.930737 + 0.365690i \(0.880833\pi\)
\(44\) −6.68583 + 3.86007i −1.00793 + 0.581927i
\(45\) 0 0
\(46\) 1.21620 2.10652i 0.179319 0.310589i
\(47\) 4.06759 7.04527i 0.593319 1.02766i −0.400463 0.916313i \(-0.631151\pi\)
0.993782 0.111346i \(-0.0355161\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.14802 + 0.662809i 0.162354 + 0.0937353i
\(51\) 0 0
\(52\) 7.41974i 1.02893i
\(53\) −5.27766 3.04706i −0.724943 0.418546i 0.0916264 0.995793i \(-0.470793\pi\)
−0.816569 + 0.577248i \(0.804127\pi\)
\(54\) 0 0
\(55\) 6.74759i 0.909845i
\(56\) 0 0
\(57\) 0 0
\(58\) −17.0767 −2.24228
\(59\) −1.98103 3.43124i −0.257908 0.446709i 0.707773 0.706439i \(-0.249700\pi\)
−0.965681 + 0.259730i \(0.916366\pi\)
\(60\) 0 0
\(61\) 4.15016 + 2.39609i 0.531373 + 0.306788i 0.741575 0.670869i \(-0.234079\pi\)
−0.210202 + 0.977658i \(0.567412\pi\)
\(62\) −12.5068 −1.58837
\(63\) 0 0
\(64\) 10.7627 1.34534
\(65\) 5.61621 + 3.24252i 0.696605 + 0.402185i
\(66\) 0 0
\(67\) 0.336981 + 0.583668i 0.0411687 + 0.0713063i 0.885876 0.463923i \(-0.153559\pi\)
−0.844707 + 0.535229i \(0.820225\pi\)
\(68\) −3.90363 −0.473385
\(69\) 0 0
\(70\) 0 0
\(71\) 7.01535i 0.832568i −0.909235 0.416284i \(-0.863332\pi\)
0.909235 0.416284i \(-0.136668\pi\)
\(72\) 0 0
\(73\) 2.96276 + 1.71055i 0.346765 + 0.200205i 0.663259 0.748390i \(-0.269173\pi\)
−0.316495 + 0.948594i \(0.602506\pi\)
\(74\) 11.8460i 1.37707i
\(75\) 0 0
\(76\) −11.4553 6.61374i −1.31402 0.758648i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.07973 12.2625i 0.796532 1.37963i −0.125330 0.992115i \(-0.539999\pi\)
0.921862 0.387519i \(-0.126668\pi\)
\(80\) −3.20267 + 5.54718i −0.358069 + 0.620194i
\(81\) 0 0
\(82\) 4.91318 2.83662i 0.542570 0.313253i
\(83\) 1.54535 + 2.67662i 0.169624 + 0.293798i 0.938288 0.345856i \(-0.112411\pi\)
−0.768664 + 0.639653i \(0.779078\pi\)
\(84\) 0 0
\(85\) 1.70594 2.95477i 0.185035 0.320490i
\(86\) 4.08578i 0.440581i
\(87\) 0 0
\(88\) 2.64572 0.282035
\(89\) −2.45766 4.25679i −0.260511 0.451219i 0.705867 0.708345i \(-0.250558\pi\)
−0.966378 + 0.257126i \(0.917224\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.40363 + 1.38774i −0.250596 + 0.144682i
\(93\) 0 0
\(94\) −14.7632 + 8.52356i −1.52271 + 0.879138i
\(95\) 10.0122 5.78057i 1.02723 0.593074i
\(96\) 0 0
\(97\) −2.07939 + 1.20054i −0.211130 + 0.121896i −0.601837 0.798619i \(-0.705564\pi\)
0.390706 + 0.920515i \(0.372231\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.756296 1.30994i −0.0756296 0.130994i
\(101\) −3.52051 −0.350304 −0.175152 0.984541i \(-0.556042\pi\)
−0.175152 + 0.984541i \(0.556042\pi\)
\(102\) 0 0
\(103\) 15.6846i 1.54545i −0.634743 0.772723i \(-0.718894\pi\)
0.634743 0.772723i \(-0.281106\pi\)
\(104\) −1.27139 + 2.20211i −0.124670 + 0.215935i
\(105\) 0 0
\(106\) 6.38506 + 11.0592i 0.620172 + 1.07417i
\(107\) 1.41984 0.819746i 0.137261 0.0792478i −0.429797 0.902926i \(-0.641415\pi\)
0.567058 + 0.823678i \(0.308081\pi\)
\(108\) 0 0
\(109\) 2.90672 5.03459i 0.278414 0.482227i −0.692577 0.721344i \(-0.743525\pi\)
0.970991 + 0.239117i \(0.0768581\pi\)
\(110\) −7.06973 + 12.2451i −0.674072 + 1.16753i
\(111\) 0 0
\(112\) 0 0
\(113\) −13.9931 8.07894i −1.31636 0.760003i −0.333222 0.942848i \(-0.608136\pi\)
−0.983142 + 0.182845i \(0.941469\pi\)
\(114\) 0 0
\(115\) 2.42584i 0.226210i
\(116\) 16.8748 + 9.74265i 1.56678 + 0.904582i
\(117\) 0 0
\(118\) 8.30241i 0.764299i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.575009 0.0522736
\(122\) −5.02097 8.69658i −0.454577 0.787351i
\(123\) 0 0
\(124\) 12.3590 + 7.13545i 1.10987 + 0.640782i
\(125\) 11.7712 1.05285
\(126\) 0 0
\(127\) −9.59240 −0.851188 −0.425594 0.904914i \(-0.639935\pi\)
−0.425594 + 0.904914i \(0.639935\pi\)
\(128\) −5.56860 3.21503i −0.492199 0.284171i
\(129\) 0 0
\(130\) −6.79464 11.7687i −0.595929 1.03218i
\(131\) 2.46122 0.215038 0.107519 0.994203i \(-0.465709\pi\)
0.107519 + 0.994203i \(0.465709\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.41227i 0.122002i
\(135\) 0 0
\(136\) 1.15856 + 0.668896i 0.0993459 + 0.0573574i
\(137\) 17.3864i 1.48542i −0.669611 0.742712i \(-0.733539\pi\)
0.669611 0.742712i \(-0.266461\pi\)
\(138\) 0 0
\(139\) 8.61174 + 4.97199i 0.730438 + 0.421719i 0.818582 0.574389i \(-0.194760\pi\)
−0.0881443 + 0.996108i \(0.528094\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.35026 + 12.7310i −0.616820 + 1.06836i
\(143\) 5.00967 8.67701i 0.418930 0.725608i
\(144\) 0 0
\(145\) −14.7490 + 8.51532i −1.22483 + 0.707159i
\(146\) −3.58442 6.20840i −0.296649 0.513811i
\(147\) 0 0
\(148\) −6.75843 + 11.7060i −0.555540 + 0.962223i
\(149\) 9.25717i 0.758377i −0.925319 0.379189i \(-0.876203\pi\)
0.925319 0.379189i \(-0.123797\pi\)
\(150\) 0 0
\(151\) −11.9698 −0.974087 −0.487044 0.873378i \(-0.661925\pi\)
−0.487044 + 0.873378i \(0.661925\pi\)
\(152\) 2.26656 + 3.92579i 0.183842 + 0.318424i
\(153\) 0 0
\(154\) 0 0
\(155\) −10.8020 + 6.23656i −0.867641 + 0.500933i
\(156\) 0 0
\(157\) −15.4598 + 8.92569i −1.23382 + 0.712348i −0.967825 0.251626i \(-0.919035\pi\)
−0.265998 + 0.963974i \(0.585702\pi\)
\(158\) −25.6957 + 14.8354i −2.04424 + 1.18024i
\(159\) 0 0
\(160\) 14.5901 8.42358i 1.15345 0.665943i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.91768 15.4459i −0.698486 1.20981i −0.968991 0.247095i \(-0.920524\pi\)
0.270505 0.962719i \(-0.412809\pi\)
\(164\) −6.47344 −0.505491
\(165\) 0 0
\(166\) 6.47650i 0.502674i
\(167\) −6.16899 + 10.6850i −0.477371 + 0.826830i −0.999664 0.0259359i \(-0.991743\pi\)
0.522293 + 0.852766i \(0.325077\pi\)
\(168\) 0 0
\(169\) −1.68526 2.91896i −0.129635 0.224535i
\(170\) −6.19166 + 3.57476i −0.474879 + 0.274171i
\(171\) 0 0
\(172\) 2.33103 4.03747i 0.177740 0.307854i
\(173\) 4.53368 7.85256i 0.344689 0.597019i −0.640608 0.767868i \(-0.721318\pi\)
0.985297 + 0.170849i \(0.0546509\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 8.57037 + 4.94810i 0.646016 + 0.372977i
\(177\) 0 0
\(178\) 10.2999i 0.772014i
\(179\) 13.0086 + 7.51051i 0.972307 + 0.561362i 0.899939 0.436016i \(-0.143611\pi\)
0.0723682 + 0.997378i \(0.476944\pi\)
\(180\) 0 0
\(181\) 2.34159i 0.174049i −0.996206 0.0870246i \(-0.972264\pi\)
0.996206 0.0870246i \(-0.0277359\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.951168 0.0701210
\(185\) −5.90704 10.2313i −0.434294 0.752220i
\(186\) 0 0
\(187\) −4.56510 2.63566i −0.333833 0.192739i
\(188\) 19.4516 1.41865
\(189\) 0 0
\(190\) −24.2262 −1.75755
\(191\) −7.82585 4.51825i −0.566258 0.326929i 0.189395 0.981901i \(-0.439347\pi\)
−0.755654 + 0.654972i \(0.772681\pi\)
\(192\) 0 0
\(193\) 2.74134 + 4.74815i 0.197326 + 0.341779i 0.947661 0.319279i \(-0.103441\pi\)
−0.750334 + 0.661058i \(0.770108\pi\)
\(194\) 5.03141 0.361234
\(195\) 0 0
\(196\) 0 0
\(197\) 2.88946i 0.205865i 0.994688 + 0.102933i \(0.0328226\pi\)
−0.994688 + 0.102933i \(0.967177\pi\)
\(198\) 0 0
\(199\) −4.45419 2.57163i −0.315749 0.182298i 0.333747 0.942663i \(-0.391687\pi\)
−0.649496 + 0.760365i \(0.725020\pi\)
\(200\) 0.518372i 0.0366544i
\(201\) 0 0
\(202\) 6.38881 + 3.68858i 0.449515 + 0.259528i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.82897 4.89993i 0.197584 0.342226i
\(206\) −16.4334 + 28.4634i −1.14497 + 1.98314i
\(207\) 0 0
\(208\) −8.23688 + 4.75557i −0.571125 + 0.329739i
\(209\) −8.93095 15.4689i −0.617767 1.07000i
\(210\) 0 0
\(211\) 7.93224 13.7390i 0.546078 0.945835i −0.452460 0.891785i \(-0.649454\pi\)
0.998538 0.0540502i \(-0.0172131\pi\)
\(212\) 14.5713i 1.00076i
\(213\) 0 0
\(214\) −3.43552 −0.234848
\(215\) 2.03738 + 3.52885i 0.138948 + 0.240666i
\(216\) 0 0
\(217\) 0 0
\(218\) −10.5499 + 6.09099i −0.714529 + 0.412534i
\(219\) 0 0
\(220\) 13.9723 8.06689i 0.942010 0.543870i
\(221\) 4.38747 2.53311i 0.295133 0.170395i
\(222\) 0 0
\(223\) −13.5288 + 7.81085i −0.905955 + 0.523053i −0.879127 0.476587i \(-0.841874\pi\)
−0.0268275 + 0.999640i \(0.508540\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 16.9293 + 29.3224i 1.12612 + 1.95049i
\(227\) 2.08089 0.138114 0.0690569 0.997613i \(-0.478001\pi\)
0.0690569 + 0.997613i \(0.478001\pi\)
\(228\) 0 0
\(229\) 6.43437i 0.425195i 0.977140 + 0.212598i \(0.0681923\pi\)
−0.977140 + 0.212598i \(0.931808\pi\)
\(230\) −2.54165 + 4.40226i −0.167591 + 0.290277i
\(231\) 0 0
\(232\) −3.33885 5.78305i −0.219206 0.379676i
\(233\) 13.5222 7.80704i 0.885868 0.511456i 0.0132791 0.999912i \(-0.495773\pi\)
0.872589 + 0.488456i \(0.162440\pi\)
\(234\) 0 0
\(235\) −8.50057 + 14.7234i −0.554516 + 0.960450i
\(236\) 4.73672 8.20424i 0.308334 0.534050i
\(237\) 0 0
\(238\) 0 0
\(239\) 14.8777 + 8.58964i 0.962358 + 0.555618i 0.896898 0.442238i \(-0.145815\pi\)
0.0654600 + 0.997855i \(0.479149\pi\)
\(240\) 0 0
\(241\) 11.2184i 0.722642i −0.932441 0.361321i \(-0.882326\pi\)
0.932441 0.361321i \(-0.117674\pi\)
\(242\) −1.04349 0.602460i −0.0670782 0.0387276i
\(243\) 0 0
\(244\) 11.4583i 0.733544i
\(245\) 0 0
\(246\) 0 0
\(247\) 17.1669 1.09230
\(248\) −2.44535 4.23547i −0.155280 0.268953i
\(249\) 0 0
\(250\) −21.3617 12.3332i −1.35103 0.780018i
\(251\) 11.3837 0.718535 0.359267 0.933235i \(-0.383027\pi\)
0.359267 + 0.933235i \(0.383027\pi\)
\(252\) 0 0
\(253\) −3.74790 −0.235629
\(254\) 17.4077 + 10.0504i 1.09226 + 0.630615i
\(255\) 0 0
\(256\) −4.02567 6.97267i −0.251604 0.435792i
\(257\) 9.38048 0.585138 0.292569 0.956244i \(-0.405490\pi\)
0.292569 + 0.956244i \(0.405490\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.5060i 0.961641i
\(261\) 0 0
\(262\) −4.46647 2.57872i −0.275940 0.159314i
\(263\) 8.80306i 0.542820i −0.962464 0.271410i \(-0.912510\pi\)
0.962464 0.271410i \(-0.0874899\pi\)
\(264\) 0 0
\(265\) 11.0294 + 6.36784i 0.677532 + 0.391173i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.805735 + 1.39557i −0.0492181 + 0.0852482i
\(269\) 8.16473 14.1417i 0.497812 0.862236i −0.502184 0.864761i \(-0.667470\pi\)
0.999997 + 0.00252412i \(0.000803452\pi\)
\(270\) 0 0
\(271\) 12.6186 7.28538i 0.766528 0.442555i −0.0651065 0.997878i \(-0.520739\pi\)
0.831635 + 0.555323i \(0.187405\pi\)
\(272\) 2.50197 + 4.33355i 0.151704 + 0.262760i
\(273\) 0 0
\(274\) −18.2165 + 31.5519i −1.10050 + 1.90612i
\(275\) 2.04255i 0.123170i
\(276\) 0 0
\(277\) 28.7137 1.72524 0.862618 0.505855i \(-0.168823\pi\)
0.862618 + 0.505855i \(0.168823\pi\)
\(278\) −10.4187 18.0457i −0.624873 1.08231i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.76893 2.75334i 0.284490 0.164251i −0.350964 0.936389i \(-0.614146\pi\)
0.635455 + 0.772138i \(0.280813\pi\)
\(282\) 0 0
\(283\) 26.2257 15.1414i 1.55896 0.900065i 0.561601 0.827408i \(-0.310186\pi\)
0.997357 0.0726567i \(-0.0231477\pi\)
\(284\) 14.5267 8.38699i 0.862001 0.497676i
\(285\) 0 0
\(286\) −18.1825 + 10.4977i −1.07515 + 0.620740i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.16730 + 12.4141i 0.421606 + 0.730242i
\(290\) 35.6874 2.09564
\(291\) 0 0
\(292\) 8.17999i 0.478698i
\(293\) −3.54362 + 6.13773i −0.207021 + 0.358570i −0.950775 0.309883i \(-0.899710\pi\)
0.743754 + 0.668453i \(0.233043\pi\)
\(294\) 0 0
\(295\) 4.14001 + 7.17071i 0.241041 + 0.417495i
\(296\) 4.01168 2.31615i 0.233174 0.134623i
\(297\) 0 0
\(298\) −9.69912 + 16.7994i −0.561855 + 0.973161i
\(299\) 1.80103 3.11948i 0.104156 0.180404i
\(300\) 0 0
\(301\) 0 0
\(302\) 21.7220 + 12.5412i 1.24996 + 0.721667i
\(303\) 0 0
\(304\) 16.9559i 0.972487i
\(305\) −8.67313 5.00743i −0.496622 0.286725i
\(306\) 0 0
\(307\) 3.11346i 0.177695i 0.996045 + 0.0888473i \(0.0283183\pi\)
−0.996045 + 0.0888473i \(0.971682\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 26.1372 1.48449
\(311\) 9.72605 + 16.8460i 0.551514 + 0.955249i 0.998166 + 0.0605417i \(0.0192828\pi\)
−0.446652 + 0.894708i \(0.647384\pi\)
\(312\) 0 0
\(313\) 22.1224 + 12.7724i 1.25043 + 0.721937i 0.971195 0.238285i \(-0.0765852\pi\)
0.279237 + 0.960222i \(0.409919\pi\)
\(314\) 37.4073 2.11101
\(315\) 0 0
\(316\) 33.8559 1.90454
\(317\) 14.0534 + 8.11372i 0.789316 + 0.455712i 0.839722 0.543017i \(-0.182718\pi\)
−0.0504056 + 0.998729i \(0.516051\pi\)
\(318\) 0 0
\(319\) 13.1561 + 22.7871i 0.736601 + 1.27583i
\(320\) −22.4922 −1.25735
\(321\) 0 0
\(322\) 0 0
\(323\) 9.03174i 0.502540i
\(324\) 0 0
\(325\) 1.70007 + 0.981535i 0.0943029 + 0.0544458i
\(326\) 37.3736i 2.06993i
\(327\) 0 0
\(328\) 1.92126 + 1.10924i 0.106084 + 0.0612474i
\(329\) 0 0
\(330\) 0 0
\(331\) −11.6558 + 20.1885i −0.640662 + 1.10966i 0.344623 + 0.938741i \(0.388007\pi\)
−0.985285 + 0.170919i \(0.945326\pi\)
\(332\) −3.69499 + 6.39992i −0.202789 + 0.351241i
\(333\) 0 0
\(334\) 22.3902 12.9270i 1.22514 0.707334i
\(335\) −0.704232 1.21977i −0.0384763 0.0666430i
\(336\) 0 0
\(337\) 5.93515 10.2800i 0.323308 0.559986i −0.657860 0.753140i \(-0.728538\pi\)
0.981168 + 0.193154i \(0.0618717\pi\)
\(338\) 7.06286i 0.384169i
\(339\) 0 0
\(340\) 8.15793 0.442426
\(341\) 9.63545 + 16.6891i 0.521789 + 0.903765i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.38366 + 0.798855i −0.0746019 + 0.0430714i
\(345\) 0 0
\(346\) −16.4549 + 9.50024i −0.884621 + 0.510736i
\(347\) −18.7979 + 10.8530i −1.00913 + 0.582619i −0.910936 0.412549i \(-0.864639\pi\)
−0.0981903 + 0.995168i \(0.531305\pi\)
\(348\) 0 0
\(349\) −2.20868 + 1.27518i −0.118228 + 0.0682588i −0.557948 0.829876i \(-0.688411\pi\)
0.439720 + 0.898135i \(0.355078\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −13.0144 22.5416i −0.693669 1.20147i
\(353\) −25.3747 −1.35056 −0.675279 0.737563i \(-0.735977\pi\)
−0.675279 + 0.737563i \(0.735977\pi\)
\(354\) 0 0
\(355\) 14.6609i 0.778119i
\(356\) 5.87636 10.1782i 0.311446 0.539441i
\(357\) 0 0
\(358\) −15.7381 27.2592i −0.831786 1.44070i
\(359\) 9.73735 5.62186i 0.513918 0.296711i −0.220525 0.975381i \(-0.570777\pi\)
0.734443 + 0.678671i \(0.237444\pi\)
\(360\) 0 0
\(361\) 5.80204 10.0494i 0.305371 0.528917i
\(362\) −2.45338 + 4.24938i −0.128947 + 0.223342i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.19166 3.57476i −0.324086 0.187111i
\(366\) 0 0
\(367\) 3.31180i 0.172874i −0.996257 0.0864372i \(-0.972452\pi\)
0.996257 0.0864372i \(-0.0275482\pi\)
\(368\) 3.08114 + 1.77890i 0.160616 + 0.0927315i
\(369\) 0 0
\(370\) 24.7562i 1.28701i
\(371\) 0 0
\(372\) 0 0
\(373\) −6.64541 −0.344087 −0.172043 0.985089i \(-0.555037\pi\)
−0.172043 + 0.985089i \(0.555037\pi\)
\(374\) 5.52298 + 9.56608i 0.285586 + 0.494650i
\(375\) 0 0
\(376\) −5.77304 3.33307i −0.297722 0.171890i
\(377\) −25.2884 −1.30242
\(378\) 0 0
\(379\) −3.84940 −0.197730 −0.0988652 0.995101i \(-0.531521\pi\)
−0.0988652 + 0.995101i \(0.531521\pi\)
\(380\) 23.9397 + 13.8216i 1.22808 + 0.709033i
\(381\) 0 0
\(382\) 9.46792 + 16.3989i 0.484421 + 0.839041i
\(383\) −34.2223 −1.74868 −0.874339 0.485316i \(-0.838705\pi\)
−0.874339 + 0.485316i \(0.838705\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 11.4889i 0.584768i
\(387\) 0 0
\(388\) −4.97191 2.87054i −0.252411 0.145729i
\(389\) 13.4796i 0.683445i 0.939801 + 0.341723i \(0.111010\pi\)
−0.939801 + 0.341723i \(0.888990\pi\)
\(390\) 0 0
\(391\) −1.64121 0.947550i −0.0829993 0.0479197i
\(392\) 0 0
\(393\) 0 0
\(394\) 3.02740 5.24361i 0.152518 0.264169i
\(395\) −14.7954 + 25.6265i −0.744440 + 1.28941i
\(396\) 0 0
\(397\) 25.5501 14.7513i 1.28232 0.740349i 0.305049 0.952337i \(-0.401327\pi\)
0.977272 + 0.211988i \(0.0679938\pi\)
\(398\) 5.38880 + 9.33367i 0.270116 + 0.467855i
\(399\) 0 0
\(400\) −0.969472 + 1.67918i −0.0484736 + 0.0839588i
\(401\) 29.0446i 1.45042i 0.688528 + 0.725209i \(0.258257\pi\)
−0.688528 + 0.725209i \(0.741743\pi\)
\(402\) 0 0
\(403\) −18.5210 −0.922599
\(404\) −4.20884 7.28993i −0.209398 0.362687i
\(405\) 0 0
\(406\) 0 0
\(407\) −15.8073 + 9.12634i −0.783538 + 0.452376i
\(408\) 0 0
\(409\) 26.2193 15.1377i 1.29646 0.748513i 0.316671 0.948536i \(-0.397435\pi\)
0.979791 + 0.200023i \(0.0641017\pi\)
\(410\) −10.2677 + 5.92806i −0.507086 + 0.292766i
\(411\) 0 0
\(412\) 32.4781 18.7512i 1.60008 0.923806i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.22952 5.59369i −0.158531 0.274583i
\(416\) 25.0160 1.22651
\(417\) 0 0
\(418\) 37.4293i 1.83073i
\(419\) 18.2902 31.6795i 0.893534 1.54765i 0.0579246 0.998321i \(-0.481552\pi\)
0.835609 0.549325i \(-0.185115\pi\)
\(420\) 0 0
\(421\) 3.85999 + 6.68570i 0.188124 + 0.325841i 0.944625 0.328152i \(-0.106426\pi\)
−0.756501 + 0.653993i \(0.773093\pi\)
\(422\) −28.7899 + 16.6219i −1.40147 + 0.809140i
\(423\) 0 0
\(424\) −2.49682 + 4.32463i −0.121256 + 0.210022i
\(425\) 0.516400 0.894431i 0.0250491 0.0433863i
\(426\) 0 0
\(427\) 0 0
\(428\) 3.39490 + 1.96005i 0.164099 + 0.0947424i
\(429\) 0 0
\(430\) 8.53859i 0.411767i
\(431\) 20.0311 + 11.5650i 0.964865 + 0.557065i 0.897667 0.440674i \(-0.145261\pi\)
0.0671983 + 0.997740i \(0.478594\pi\)
\(432\) 0 0
\(433\) 34.9265i 1.67846i −0.543776 0.839230i \(-0.683006\pi\)
0.543776 0.839230i \(-0.316994\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 13.9002 0.665699
\(437\) −3.21078 5.56123i −0.153592 0.266030i
\(438\) 0 0
\(439\) −33.6842 19.4476i −1.60766 0.928184i −0.989892 0.141824i \(-0.954703\pi\)
−0.617770 0.786359i \(-0.711964\pi\)
\(440\) −5.52912 −0.263590
\(441\) 0 0
\(442\) −10.6161 −0.504959
\(443\) −32.3277 18.6644i −1.53594 0.886774i −0.999070 0.0431065i \(-0.986275\pi\)
−0.536867 0.843667i \(-0.680392\pi\)
\(444\) 0 0
\(445\) 5.13609 + 8.89596i 0.243474 + 0.421709i
\(446\) 32.7350 1.55005
\(447\) 0 0
\(448\) 0 0
\(449\) 23.9224i 1.12897i 0.825445 + 0.564483i \(0.190924\pi\)
−0.825445 + 0.564483i \(0.809076\pi\)
\(450\) 0 0
\(451\) −7.57036 4.37075i −0.356474 0.205810i
\(452\) 38.6342i 1.81720i
\(453\) 0 0
\(454\) −3.77628 2.18024i −0.177230 0.102324i
\(455\) 0 0
\(456\) 0 0
\(457\) −4.99031 + 8.64348i −0.233437 + 0.404325i −0.958817 0.284024i \(-0.908331\pi\)
0.725380 + 0.688348i \(0.241664\pi\)
\(458\) 6.74155 11.6767i 0.315012 0.545617i
\(459\) 0 0
\(460\) 5.02319 2.90014i 0.234207 0.135220i
\(461\) 16.7279 + 28.9735i 0.779094 + 1.34943i 0.932465 + 0.361261i \(0.117654\pi\)
−0.153371 + 0.988169i \(0.549013\pi\)
\(462\) 0 0
\(463\) 11.5353 19.9798i 0.536092 0.928538i −0.463018 0.886349i \(-0.653233\pi\)
0.999110 0.0421893i \(-0.0134333\pi\)
\(464\) 24.9776i 1.15956i
\(465\) 0 0
\(466\) −32.7190 −1.51568
\(467\) 20.1395 + 34.8827i 0.931946 + 1.61418i 0.779991 + 0.625791i \(0.215224\pi\)
0.151955 + 0.988387i \(0.451443\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 30.8527 17.8128i 1.42313 0.821643i
\(471\) 0 0
\(472\) −2.81163 + 1.62329i −0.129416 + 0.0747182i
\(473\) 5.45205 3.14774i 0.250686 0.144733i
\(474\) 0 0
\(475\) 3.03078 1.74982i 0.139062 0.0802874i
\(476\) 0 0
\(477\) 0 0
\(478\) −17.9994 31.1759i −0.823275 1.42595i
\(479\) −0.155503 −0.00710509 −0.00355255 0.999994i \(-0.501131\pi\)
−0.00355255 + 0.999994i \(0.501131\pi\)
\(480\) 0 0
\(481\) 17.5425i 0.799867i
\(482\) −11.7540 + 20.3585i −0.535380 + 0.927305i
\(483\) 0 0
\(484\) 0.687435 + 1.19067i 0.0312471 + 0.0541215i
\(485\) 4.34558 2.50892i 0.197323 0.113924i
\(486\) 0 0
\(487\) 8.25111 14.2913i 0.373893 0.647602i −0.616267 0.787537i \(-0.711356\pi\)
0.990161 + 0.139935i \(0.0446892\pi\)
\(488\) 1.96341 3.40072i 0.0888793 0.153944i
\(489\) 0 0
\(490\) 0 0
\(491\) −8.10003 4.67655i −0.365549 0.211050i 0.305963 0.952043i \(-0.401022\pi\)
−0.671512 + 0.740993i \(0.734355\pi\)
\(492\) 0 0
\(493\) 13.3046i 0.599209i
\(494\) −31.1534 17.9864i −1.40166 0.809248i
\(495\) 0 0
\(496\) 18.2934i 0.821399i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.99623 0.0893637 0.0446818 0.999001i \(-0.485773\pi\)
0.0446818 + 0.999001i \(0.485773\pi\)
\(500\) 14.0727 + 24.3746i 0.629351 + 1.09007i
\(501\) 0 0
\(502\) −20.6585 11.9272i −0.922035 0.532337i
\(503\) −15.7008 −0.700063 −0.350032 0.936738i \(-0.613829\pi\)
−0.350032 + 0.936738i \(0.613829\pi\)
\(504\) 0 0
\(505\) 7.35727 0.327394
\(506\) 6.80147 + 3.92683i 0.302362 + 0.174569i
\(507\) 0 0
\(508\) −11.4679 19.8630i −0.508807 0.881279i
\(509\) −15.1979 −0.673633 −0.336817 0.941570i \(-0.609350\pi\)
−0.336817 + 0.941570i \(0.609350\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 29.7316i 1.31396i
\(513\) 0 0
\(514\) −17.0231 9.82831i −0.750858 0.433508i
\(515\) 32.7781i 1.44437i
\(516\) 0 0
\(517\) 22.7476 + 13.1333i 1.00044 + 0.577603i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.65699 4.60204i 0.116517 0.201813i
\(521\) 20.6160 35.7080i 0.903204 1.56440i 0.0798940 0.996803i \(-0.474542\pi\)
0.823310 0.567592i \(-0.192125\pi\)
\(522\) 0 0
\(523\) −37.0311 + 21.3799i −1.61926 + 0.934878i −0.632143 + 0.774852i \(0.717824\pi\)
−0.987113 + 0.160026i \(0.948842\pi\)
\(524\) 2.94244 + 5.09645i 0.128541 + 0.222640i
\(525\) 0 0
\(526\) −9.22332 + 15.9753i −0.402156 + 0.696554i
\(527\) 9.74419i 0.424464i
\(528\) 0 0
\(529\) 21.6526 0.941417
\(530\) −13.3437 23.1119i −0.579613 1.00392i
\(531\) 0 0
\(532\) 0 0
\(533\) 7.27579 4.20068i 0.315149 0.181952i
\(534\) 0 0
\(535\) −2.96723 + 1.71313i −0.128284 + 0.0740650i
\(536\) 0.478269 0.276129i 0.0206581 0.0119270i
\(537\) 0 0
\(538\) −29.6337 + 17.1090i −1.27760 + 0.737623i
\(539\) 0 0
\(540\) 0 0
\(541\) 8.04309 + 13.9310i 0.345800 + 0.598942i 0.985499 0.169683i \(-0.0542744\pi\)
−0.639699 + 0.768625i \(0.720941\pi\)
\(542\) −30.5328 −1.31149
\(543\) 0 0
\(544\) 13.1613i 0.564284i
\(545\) −6.07456 + 10.5214i −0.260206 + 0.450689i
\(546\) 0 0
\(547\) −5.94015 10.2886i −0.253982 0.439910i 0.710636 0.703560i \(-0.248407\pi\)
−0.964619 + 0.263649i \(0.915074\pi\)
\(548\) 36.0021 20.7858i 1.53794 0.887927i
\(549\) 0 0
\(550\) −2.14006 + 3.70669i −0.0912525 + 0.158054i
\(551\) −22.5413 + 39.0427i −0.960293 + 1.66328i
\(552\) 0 0
\(553\) 0 0
\(554\) −52.1078 30.0845i −2.21385 1.27817i
\(555\) 0 0
\(556\) 23.7765i 1.00835i
\(557\) 26.4006 + 15.2424i 1.11863 + 0.645841i 0.941051 0.338265i \(-0.109840\pi\)
0.177579 + 0.984107i \(0.443173\pi\)
\(558\) 0 0
\(559\) 6.05052i 0.255910i
\(560\) 0 0
\(561\) 0 0
\(562\) −11.5392 −0.486750
\(563\) −11.2686 19.5177i −0.474914 0.822575i 0.524673 0.851304i \(-0.324187\pi\)
−0.999587 + 0.0287288i \(0.990854\pi\)
\(564\) 0 0
\(565\) 29.2433 + 16.8836i 1.23027 + 0.710300i
\(566\) −63.4572 −2.66730
\(567\) 0 0
\(568\) −5.74852 −0.241202
\(569\) −38.5935 22.2819i −1.61792 0.934108i −0.987457 0.157890i \(-0.949531\pi\)
−0.630465 0.776218i \(-0.717136\pi\)
\(570\) 0 0
\(571\) −17.6415 30.5560i −0.738274 1.27873i −0.953272 0.302113i \(-0.902308\pi\)
0.214998 0.976614i \(-0.431025\pi\)
\(572\) 23.9567 1.00168
\(573\) 0 0
\(574\) 0 0
\(575\) 0.734319i 0.0306232i
\(576\) 0 0
\(577\) −3.25158 1.87730i −0.135365 0.0781531i 0.430788 0.902453i \(-0.358236\pi\)
−0.566153 + 0.824300i \(0.691569\pi\)
\(578\) 30.0379i 1.24941i
\(579\) 0 0
\(580\) −35.2654 20.3605i −1.46432 0.845423i
\(581\) 0 0
\(582\) 0 0
\(583\) 9.83827 17.0404i 0.407460 0.705741i
\(584\) 1.40166 2.42775i 0.0580011 0.100461i
\(585\) 0 0
\(586\) 12.8615 7.42559i 0.531304 0.306748i
\(587\) −15.8021 27.3700i −0.652222 1.12968i −0.982583 0.185826i \(-0.940504\pi\)
0.330361 0.943855i \(-0.392829\pi\)
\(588\) 0 0
\(589\) −16.5091 + 28.5946i −0.680246 + 1.17822i
\(590\) 17.3506i 0.714314i
\(591\) 0 0
\(592\) 17.3269 0.712129
\(593\) −18.5588 32.1448i −0.762120 1.32003i −0.941756 0.336297i \(-0.890825\pi\)
0.179636 0.983733i \(-0.442508\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 19.1689 11.0671i 0.785187 0.453328i
\(597\) 0 0
\(598\) −6.53682 + 3.77403i −0.267310 + 0.154332i
\(599\) 24.5188 14.1559i 1.00181 0.578396i 0.0930277 0.995664i \(-0.470345\pi\)
0.908784 + 0.417267i \(0.137012\pi\)
\(600\) 0 0
\(601\) −20.8341 + 12.0286i −0.849840 + 0.490655i −0.860597 0.509287i \(-0.829909\pi\)
0.0107568 + 0.999942i \(0.496576\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −14.3101 24.7859i −0.582271 1.00852i
\(605\) −1.20167 −0.0488549
\(606\) 0 0
\(607\) 9.52047i 0.386424i 0.981157 + 0.193212i \(0.0618905\pi\)
−0.981157 + 0.193212i \(0.938110\pi\)
\(608\) 22.2985 38.6221i 0.904323 1.56633i
\(609\) 0 0
\(610\) 10.4930 + 18.1744i 0.424848 + 0.735859i
\(611\) −21.8625 + 12.6223i −0.884461 + 0.510644i
\(612\) 0 0
\(613\) 1.23108 2.13230i 0.0497230 0.0861227i −0.840093 0.542443i \(-0.817499\pi\)
0.889816 + 0.456320i \(0.150833\pi\)
\(614\) 3.26210 5.65012i 0.131648 0.228020i
\(615\) 0 0
\(616\) 0 0
\(617\) −18.7738 10.8390i −0.755804 0.436364i 0.0719831 0.997406i \(-0.477067\pi\)
−0.827787 + 0.561042i \(0.810401\pi\)
\(618\) 0 0
\(619\) 24.1063i 0.968915i 0.874815 + 0.484457i \(0.160983\pi\)
−0.874815 + 0.484457i \(0.839017\pi\)
\(620\) −25.8281 14.9119i −1.03728 0.598875i
\(621\) 0 0
\(622\) 40.7615i 1.63439i
\(623\) 0 0
\(624\) 0 0
\(625\) −21.4368 −0.857471
\(626\) −26.7643 46.3571i −1.06972 1.85280i
\(627\) 0 0
\(628\) −36.9649 21.3417i −1.47506 0.851627i
\(629\) −9.22934 −0.367998
\(630\) 0 0
\(631\) 3.37520 0.134365 0.0671824 0.997741i \(-0.478599\pi\)
0.0671824 + 0.997741i \(0.478599\pi\)
\(632\) −10.0481 5.80128i −0.399692 0.230762i
\(633\) 0 0
\(634\) −17.0021 29.4486i −0.675242 1.16955i
\(635\) 20.0465 0.795521
\(636\) 0 0
\(637\) 0 0
\(638\) 55.1368i 2.18289i
\(639\) 0 0
\(640\) 11.6374 + 6.71887i 0.460010 + 0.265587i
\(641\) 35.6978i 1.40998i −0.709218 0.704989i \(-0.750952\pi\)
0.709218 0.704989i \(-0.249048\pi\)
\(642\) 0 0
\(643\) −3.03956 1.75489i −0.119868 0.0692060i 0.438867 0.898552i \(-0.355380\pi\)
−0.558735 + 0.829346i \(0.688713\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −9.46292 + 16.3903i −0.372314 + 0.644866i
\(647\) −7.02996 + 12.1762i −0.276376 + 0.478698i −0.970481 0.241176i \(-0.922467\pi\)
0.694105 + 0.719874i \(0.255800\pi\)
\(648\) 0 0
\(649\) 11.0787 6.39629i 0.434877 0.251076i
\(650\) −2.05679 3.56246i −0.0806739 0.139731i
\(651\) 0 0
\(652\) 21.3225 36.9317i 0.835055 1.44636i
\(653\) 11.8558i 0.463955i 0.972721 + 0.231978i \(0.0745196\pi\)
−0.972721 + 0.231978i \(0.925480\pi\)
\(654\) 0 0
\(655\) −5.14353 −0.200974
\(656\) 4.14905 + 7.18637i 0.161993 + 0.280581i
\(657\) 0 0
\(658\) 0 0
\(659\) −5.03144 + 2.90491i −0.195997 + 0.113159i −0.594787 0.803883i \(-0.702764\pi\)
0.398790 + 0.917042i \(0.369430\pi\)
\(660\) 0 0
\(661\) −8.41592 + 4.85893i −0.327341 + 0.188991i −0.654660 0.755923i \(-0.727188\pi\)
0.327319 + 0.944914i \(0.393855\pi\)
\(662\) 42.3046 24.4246i 1.64422 0.949288i
\(663\) 0 0
\(664\) 2.19328 1.26629i 0.0851158 0.0491416i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.72977 + 8.19220i 0.183137 + 0.317203i
\(668\) −29.5006 −1.14141
\(669\) 0 0
\(670\) 2.95141i 0.114023i
\(671\) −7.73645 + 13.3999i −0.298662 + 0.517298i
\(672\) 0 0
\(673\) 13.4646 + 23.3214i 0.519023 + 0.898975i 0.999756 + 0.0221072i \(0.00703750\pi\)
−0.480732 + 0.876867i \(0.659629\pi\)
\(674\) −21.5415 + 12.4370i −0.829747 + 0.479055i
\(675\) 0 0
\(676\) 4.02953 6.97935i 0.154982 0.268436i
\(677\) 22.7056 39.3273i 0.872648 1.51147i 0.0134007 0.999910i \(-0.495734\pi\)
0.859247 0.511560i \(-0.170932\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.42120 1.39788i −0.0928487 0.0536062i
\(681\) 0 0
\(682\) 40.3818i 1.54630i
\(683\) −37.6543 21.7397i −1.44080 0.831848i −0.442900 0.896571i \(-0.646050\pi\)
−0.997903 + 0.0647226i \(0.979384\pi\)
\(684\) 0 0
\(685\) 36.3347i 1.38828i
\(686\) 0 0
\(687\) 0 0
\(688\) −5.97616 −0.227839
\(689\) 9.45546 + 16.3773i 0.360224 + 0.623927i
\(690\) 0 0
\(691\) 23.6991 + 13.6827i 0.901557 + 0.520514i 0.877705 0.479201i \(-0.159074\pi\)
0.0238522 + 0.999715i \(0.492407\pi\)
\(692\) 21.6804 0.824166
\(693\) 0 0
\(694\) 45.4845 1.72657
\(695\) −17.9971 10.3906i −0.682668 0.394139i
\(696\) 0 0
\(697\) −2.21004 3.82790i −0.0837112 0.144992i
\(698\) 5.34423 0.202282
\(699\) 0 0
\(700\) 0 0
\(701\) 8.26437i 0.312141i 0.987746 + 0.156070i \(0.0498827\pi\)
−0.987746 + 0.156070i \(0.950117\pi\)
\(702\) 0 0
\(703\) −27.0838 15.6368i −1.02148 0.589754i
\(704\) 34.7504i 1.30970i
\(705\) 0 0
\(706\) 46.0484 + 26.5861i 1.73306 + 1.00058i
\(707\) 0 0
\(708\) 0 0
\(709\) −21.4086 + 37.0807i −0.804015 + 1.39260i 0.112938 + 0.993602i \(0.463974\pi\)
−0.916954 + 0.398994i \(0.869360\pi\)
\(710\) 15.3608 26.6057i 0.576481 0.998494i
\(711\) 0 0
\(712\) −3.48810 + 2.01385i −0.130722 + 0.0754724i
\(713\) 3.46405 + 5.99992i 0.129730 + 0.224699i
\(714\) 0 0
\(715\) −10.4694 + 18.1335i −0.391532 + 0.678153i
\(716\) 35.9159i 1.34224i
\(717\) 0 0
\(718\) −23.5610 −0.879289
\(719\) 11.5725 + 20.0442i 0.431583 + 0.747523i 0.997010 0.0772751i \(-0.0246220\pi\)
−0.565427 + 0.824798i \(0.691289\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −21.0584 + 12.1581i −0.783712 + 0.452477i
\(723\) 0 0
\(724\) 4.84874 2.79942i 0.180202 0.104040i
\(725\) −4.46462 + 2.57765i −0.165812 + 0.0957316i
\(726\) 0 0
\(727\) −4.76878 + 2.75326i −0.176864 + 0.102113i −0.585819 0.810442i \(-0.699227\pi\)
0.408954 + 0.912555i \(0.365894\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.49084 + 12.9745i 0.277248 + 0.480208i
\(731\) 3.18327 0.117737
\(732\) 0 0
\(733\) 3.98999i 0.147373i −0.997281 0.0736867i \(-0.976524\pi\)
0.997281 0.0736867i \(-0.0234765\pi\)
\(734\) −3.46991 + 6.01005i −0.128077 + 0.221835i
\(735\) 0 0
\(736\) −4.67882 8.10395i −0.172463 0.298716i
\(737\) −1.88453 + 1.08803i −0.0694176 + 0.0400783i
\(738\) 0 0
\(739\) 0.871657 1.50976i 0.0320644 0.0555372i −0.849548 0.527512i \(-0.823125\pi\)
0.881612 + 0.471974i \(0.156458\pi\)
\(740\) 14.1240 24.4635i 0.519208 0.899295i
\(741\) 0 0
\(742\) 0 0
\(743\) −8.70204 5.02413i −0.319247 0.184317i 0.331810 0.943346i \(-0.392341\pi\)
−0.651057 + 0.759029i \(0.725674\pi\)
\(744\) 0 0
\(745\) 19.3459i 0.708780i
\(746\) 12.0597 + 6.96267i 0.441537 + 0.254921i
\(747\) 0 0
\(748\) 12.6040i 0.460846i
\(749\) 0 0
\(750\) 0 0
\(751\) −23.3450 −0.851872 −0.425936 0.904753i \(-0.640055\pi\)
−0.425936 + 0.904753i \(0.640055\pi\)
\(752\) −12.4672 21.5938i −0.454631 0.787444i
\(753\) 0 0
\(754\) 45.8919 + 26.4957i 1.67128 + 0.964916i
\(755\) 25.0148 0.910383
\(756\) 0 0
\(757\) −14.3334 −0.520957 −0.260479 0.965480i \(-0.583880\pi\)
−0.260479 + 0.965480i \(0.583880\pi\)
\(758\) 6.98566 + 4.03317i 0.253730 + 0.146491i
\(759\) 0 0
\(760\) −4.73672 8.20424i −0.171819 0.297599i
\(761\) 22.6355 0.820537 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.6067i 0.781702i
\(765\) 0 0
\(766\) 62.1046 + 35.8561i 2.24393 + 1.29553i
\(767\) 12.2948i 0.443940i
\(768\) 0 0
\(769\) −42.6873 24.6455i −1.53934 0.888741i −0.998877 0.0473762i \(-0.984914\pi\)
−0.540468 0.841365i \(-0.681753\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.55467 + 11.3530i −0.235908 + 0.408604i
\(773\) −11.0083 + 19.0670i −0.395943 + 0.685793i −0.993221 0.116241i \(-0.962915\pi\)
0.597278 + 0.802034i \(0.296249\pi\)
\(774\) 0 0
\(775\) −3.26986 + 1.88785i −0.117457 + 0.0678137i
\(776\) 0.983745 + 1.70390i 0.0353144 + 0.0611663i
\(777\) 0 0
\(778\) 14.1232 24.4621i 0.506340 0.877007i
\(779\) 14.9774i 0.536622i
\(780\) 0 0
\(781\) 22.6510 0.810516
\(782\) 1.98557 + 3.43911i 0.0710040 + 0.122982i
\(783\) 0 0
\(784\) 0 0
\(785\) 32.3083 18.6532i 1.15313 0.665761i
\(786\) 0 0
\(787\) −9.40107 + 5.42771i −0.335112 + 0.193477i −0.658108 0.752923i \(-0.728643\pi\)
0.322996 + 0.946400i \(0.395310\pi\)
\(788\) −5.98320 + 3.45440i −0.213143 + 0.123058i
\(789\) 0 0
\(790\) 53.6998 31.0036i 1.91055 1.10306i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.43542 12.8785i −0.264039 0.457330i
\(794\) −61.8223 −2.19399
\(795\) 0 0
\(796\) 12.2977i 0.435882i
\(797\) 1.98299 3.43465i 0.0702412 0.121661i −0.828766 0.559596i \(-0.810956\pi\)
0.899007 + 0.437934i \(0.144290\pi\)
\(798\) 0 0
\(799\) 6.64078 + 11.5022i 0.234934 + 0.406917i
\(800\) 4.41653 2.54988i 0.156148 0.0901520i
\(801\) 0 0
\(802\) 30.4312 52.7084i 1.07456 1.86120i
\(803\) −5.52298 + 9.56608i −0.194902 + 0.337580i
\(804\) 0 0
\(805\) 0 0
\(806\) 33.6109 + 19.4053i 1.18389 + 0.683521i
\(807\) 0 0
\(808\) 2.88478i 0.101486i
\(809\) −36.0199 20.7961i −1.26639 0.731152i −0.292088 0.956391i \(-0.594350\pi\)
−0.974303 + 0.225240i \(0.927683\pi\)
\(810\) 0 0
\(811\) 13.3293i 0.468056i −0.972230 0.234028i \(-0.924809\pi\)
0.972230 0.234028i \(-0.0751907\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 38.2482 1.34060
\(815\) 18.6364 + 32.2792i 0.652806 + 1.13069i
\(816\) 0 0
\(817\) 9.34139 + 5.39326i 0.326814 + 0.188686i
\(818\) −63.4417 −2.21819
\(819\) 0 0
\(820\) 13.5284 0.472432
\(821\) 33.4332 + 19.3027i 1.16683 + 0.673668i 0.952931 0.303188i \(-0.0980510\pi\)
0.213897 + 0.976856i \(0.431384\pi\)
\(822\) 0 0
\(823\) 5.34881 + 9.26442i 0.186448 + 0.322937i 0.944063 0.329764i \(-0.106969\pi\)
−0.757616 + 0.652701i \(0.773636\pi\)
\(824\) −12.8523 −0.447729
\(825\) 0 0
\(826\) 0 0
\(827\) 11.7079i 0.407125i −0.979062 0.203562i \(-0.934748\pi\)
0.979062 0.203562i \(-0.0652520\pi\)
\(828\) 0 0
\(829\) 15.0948 + 8.71498i 0.524263 + 0.302684i 0.738677 0.674059i \(-0.235451\pi\)
−0.214414 + 0.976743i \(0.568784\pi\)
\(830\) 13.5348i 0.469799i
\(831\) 0 0
\(832\) −28.9237 16.6991i −1.00275 0.578937i
\(833\) 0 0
\(834\) 0 0
\(835\) 12.8921 22.3298i 0.446151 0.772756i
\(836\) 21.3543 36.9867i 0.738553 1.27921i
\(837\) 0 0
\(838\) −66.3838 + 38.3267i −2.29319 + 1.32397i
\(839\) 0.704502 + 1.22023i 0.0243221 + 0.0421271i 0.877930 0.478789i \(-0.158924\pi\)
−0.853608 + 0.520916i \(0.825591\pi\)
\(840\) 0 0
\(841\) 18.7055 32.3988i 0.645016 1.11720i
\(842\) 16.1771i 0.557498i
\(843\) 0 0
\(844\) 37.9326 1.30570
\(845\) 3.52191 + 6.10012i 0.121157 + 0.209851i
\(846\) 0 0
\(847\) 0 0
\(848\) −16.1761 + 9.33925i −0.555488 + 0.320711i
\(849\) 0 0
\(850\) −1.87426 + 1.08211i −0.0642867 + 0.0371160i
\(851\) −5.68290 + 3.28102i −0.194807 + 0.112472i
\(852\) 0 0
\(853\) 28.0716 16.2071i 0.961153 0.554922i 0.0646255 0.997910i \(-0.479415\pi\)
0.896528 + 0.442987i \(0.146081\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.671716 1.16345i −0.0229588 0.0397658i
\(857\) 44.4539 1.51852 0.759258 0.650789i \(-0.225562\pi\)
0.759258 + 0.650789i \(0.225562\pi\)
\(858\) 0 0
\(859\) 15.6494i 0.533952i 0.963703 + 0.266976i \(0.0860245\pi\)
−0.963703 + 0.266976i \(0.913976\pi\)
\(860\) −4.87147 + 8.43763i −0.166116 + 0.287721i
\(861\) 0 0
\(862\) −24.2342 41.9748i −0.825420 1.42967i
\(863\) 15.6911 9.05927i 0.534132 0.308381i −0.208565 0.978008i \(-0.566879\pi\)
0.742697 + 0.669627i \(0.233546\pi\)
\(864\) 0 0
\(865\) −9.47462 + 16.4105i −0.322147 + 0.557975i
\(866\) −36.5939 + 63.3825i −1.24351 + 2.15383i
\(867\) 0 0
\(868\) 0 0
\(869\) 39.5927 + 22.8589i 1.34309 + 0.775434i
\(870\) 0 0
\(871\) 2.09140i 0.0708643i
\(872\) −4.12545 2.38183i −0.139705 0.0806589i
\(873\) 0 0
\(874\) 13.4562i 0.455164i
\(875\) 0 0
\(876\) 0 0
\(877\) −2.77853 −0.0938243 −0.0469121 0.998899i \(-0.514938\pi\)
−0.0469121 + 0.998899i \(0.514938\pi\)
\(878\) 40.7521 + 70.5847i 1.37532 + 2.38212i
\(879\) 0 0
\(880\) −17.9106 10.3407i −0.603767 0.348585i
\(881\) −1.96106 −0.0660696 −0.0330348 0.999454i \(-0.510517\pi\)
−0.0330348 + 0.999454i \(0.510517\pi\)
\(882\) 0 0
\(883\) −36.9657 −1.24400 −0.621998 0.783019i \(-0.713679\pi\)
−0.621998 + 0.783019i \(0.713679\pi\)
\(884\) 10.4906 + 6.05676i 0.352838 + 0.203711i
\(885\) 0 0
\(886\) 39.1110 + 67.7422i 1.31396 + 2.27584i
\(887\) −22.5168 −0.756040 −0.378020 0.925797i \(-0.623395\pi\)
−0.378020 + 0.925797i \(0.623395\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 21.5251i 0.721525i
\(891\) 0 0
\(892\) −32.3479 18.6761i −1.08309 0.625321i
\(893\) 45.0046i 1.50602i
\(894\) 0 0
\(895\) −27.1857 15.6957i −0.908719 0.524649i
\(896\) 0 0
\(897\) 0 0
\(898\) 25.0644 43.4129i 0.836411 1.44871i
\(899\) 24.3195 42.1225i 0.811099 1.40487i
\(900\) 0 0
\(901\) 8.61635 4.97465i 0.287052 0.165730i
\(902\) 9.15882 + 15.8635i 0.304955 + 0.528198i
\(903\) 0 0
\(904\) −6.62005 + 11.4663i −0.220180 + 0.381362i
\(905\) 4.89353i 0.162666i
\(906\) 0 0
\(907\) −19.1196 −0.634857 −0.317428 0.948282i \(-0.602819\pi\)
−0.317428 + 0.948282i \(0.602819\pi\)
\(908\) 2.48775 + 4.30891i 0.0825589 + 0.142996i
\(909\) 0 0
\(910\) 0 0
\(911\) −4.92610 + 2.84408i −0.163209 + 0.0942287i −0.579380 0.815058i \(-0.696705\pi\)
0.416171 + 0.909286i \(0.363372\pi\)
\(912\) 0 0
\(913\) −8.64222 + 4.98959i −0.286016 + 0.165131i
\(914\) 18.1122 10.4571i 0.599100 0.345890i
\(915\) 0 0
\(916\) −13.3237 + 7.69242i −0.440226 + 0.254165i
\(917\) 0 0
\(918\) 0 0
\(919\) −10.9255 18.9235i −0.360399 0.624230i 0.627627 0.778514i \(-0.284026\pi\)
−0.988027 + 0.154284i \(0.950693\pi\)
\(920\) −1.98778 −0.0655352
\(921\) 0 0
\(922\) 70.1058i 2.30881i
\(923\) −10.8848 + 18.8530i −0.358278 + 0.620555i
\(924\) 0 0
\(925\) −1.78811 3.09709i −0.0587926 0.101832i
\(926\) −41.8672 + 24.1720i −1.37584 + 0.794343i
\(927\) 0 0
\(928\) −32.8477 + 56.8940i −1.07828 + 1.86764i
\(929\) 8.08806 14.0089i 0.265361 0.459618i −0.702297 0.711884i \(-0.747842\pi\)
0.967658 + 0.252266i \(0.0811756\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 32.3321 + 18.6669i 1.05907 + 0.611456i
\(933\) 0 0
\(934\) 84.4040i 2.76178i
\(935\) 9.54029 + 5.50809i 0.312001 + 0.180134i
\(936\) 0 0
\(937\) 14.0440i 0.458799i 0.973332 + 0.229400i \(0.0736762\pi\)
−0.973332 + 0.229400i \(0.926324\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −40.6505 −1.32587
\(941\) 21.5934 + 37.4009i 0.703924 + 1.21923i 0.967078 + 0.254479i \(0.0819040\pi\)
−0.263154 + 0.964754i \(0.584763\pi\)
\(942\) 0 0
\(943\) −2.72163 1.57133i −0.0886284 0.0511696i
\(944\) −12.1437 −0.395244
\(945\) 0 0
\(946\) −13.1921 −0.428911
\(947\) −16.6235 9.59758i −0.540191 0.311879i 0.204965 0.978769i \(-0.434292\pi\)
−0.745156 + 0.666890i \(0.767625\pi\)
\(948\) 0 0
\(949\) −5.30807 9.19386i −0.172307 0.298445i
\(950\) −7.33344 −0.237928
\(951\) 0 0
\(952\) 0 0
\(953\) 5.62718i 0.182282i 0.995838 + 0.0911411i \(0.0290514\pi\)
−0.995838 + 0.0911411i \(0.970949\pi\)
\(954\) 0 0
\(955\) 16.3547 + 9.44239i 0.529225 + 0.305548i
\(956\) 41.0764i 1.32850i
\(957\) 0 0
\(958\) 0.282197 + 0.162926i 0.00911736 + 0.00526391i
\(959\) 0 0
\(960\) 0 0
\(961\) 2.31141 4.00348i 0.0745616 0.129144i
\(962\) −18.3799 + 31.8350i −0.592593 + 1.02640i
\(963\) 0 0
\(964\) 23.2300 13.4119i 0.748189 0.431967i
\(965\) −5.72894 9.92282i −0.184421 0.319427i
\(966\) 0 0
\(967\) −7.62091 + 13.1998i −0.245072 + 0.424477i −0.962152 0.272514i \(-0.912145\pi\)
0.717080 + 0.696991i \(0.245478\pi\)
\(968\) 0.471174i 0.0151441i
\(969\) 0 0
\(970\) −10.5148 −0.337610
\(971\) −20.4479 35.4168i −0.656205 1.13658i −0.981590 0.190998i \(-0.938828\pi\)
0.325386 0.945581i \(-0.394506\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −29.9472 + 17.2900i −0.959571 + 0.554009i
\(975\) 0 0
\(976\) 12.7202 7.34404i 0.407165 0.235077i
\(977\) −8.98296 + 5.18631i −0.287390 + 0.165925i −0.636764 0.771058i \(-0.719728\pi\)
0.349374 + 0.936983i \(0.386394\pi\)
\(978\) 0 0
\(979\) 13.7442 7.93522i 0.439267 0.253611i
\(980\) 0 0
\(981\) 0 0
\(982\) 9.79963 + 16.9735i 0.312719 + 0.541645i
\(983\) 2.11700 0.0675219 0.0337609 0.999430i \(-0.489252\pi\)
0.0337609 + 0.999430i \(0.489252\pi\)
\(984\) 0 0
\(985\) 6.03847i 0.192402i
\(986\) 13.9398 24.1444i 0.443932 0.768914i
\(987\) 0 0
\(988\) 20.5234 + 35.5475i 0.652935 + 1.13092i
\(989\) 1.96007 1.13165i 0.0623267 0.0359843i
\(990\) 0 0
\(991\) −17.0581 + 29.5456i −0.541870 + 0.938546i 0.456927 + 0.889504i \(0.348950\pi\)
−0.998797 + 0.0490418i \(0.984383\pi\)
\(992\) −24.0575 + 41.6688i −0.763825 + 1.32298i
\(993\) 0 0
\(994\) 0 0
\(995\) 9.30850 + 5.37427i 0.295099 + 0.170376i
\(996\) 0 0
\(997\) 45.8235i 1.45125i −0.688093 0.725623i \(-0.741552\pi\)
0.688093 0.725623i \(-0.258448\pi\)
\(998\) −3.62264 2.09153i −0.114673 0.0662064i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1323.2.s.b.962.1 10
3.2 odd 2 441.2.s.b.374.5 10
7.2 even 3 189.2.i.b.152.5 10
7.3 odd 6 1323.2.o.d.881.5 10
7.4 even 3 1323.2.o.c.881.5 10
7.5 odd 6 1323.2.i.b.1097.5 10
7.6 odd 2 189.2.s.b.17.1 10
9.2 odd 6 1323.2.i.b.521.1 10
9.7 even 3 441.2.i.b.227.5 10
21.2 odd 6 63.2.i.b.5.1 10
21.5 even 6 441.2.i.b.68.1 10
21.11 odd 6 441.2.o.d.293.1 10
21.17 even 6 441.2.o.c.293.1 10
21.20 even 2 63.2.s.b.59.5 yes 10
28.23 odd 6 3024.2.ca.b.2609.5 10
28.27 even 2 3024.2.df.b.17.5 10
63.2 odd 6 189.2.s.b.89.1 10
63.11 odd 6 1323.2.o.d.440.5 10
63.13 odd 6 567.2.p.d.80.5 10
63.16 even 3 63.2.s.b.47.5 yes 10
63.20 even 6 189.2.i.b.143.1 10
63.23 odd 6 567.2.p.d.404.5 10
63.25 even 3 441.2.o.c.146.1 10
63.34 odd 6 63.2.i.b.38.5 yes 10
63.38 even 6 1323.2.o.c.440.5 10
63.41 even 6 567.2.p.c.80.1 10
63.47 even 6 inner 1323.2.s.b.656.1 10
63.52 odd 6 441.2.o.d.146.1 10
63.58 even 3 567.2.p.c.404.1 10
63.61 odd 6 441.2.s.b.362.5 10
84.23 even 6 1008.2.ca.b.257.5 10
84.83 odd 2 1008.2.df.b.689.3 10
252.79 odd 6 1008.2.df.b.929.3 10
252.83 odd 6 3024.2.ca.b.2033.5 10
252.191 even 6 3024.2.df.b.1601.5 10
252.223 even 6 1008.2.ca.b.353.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.1 10 21.2 odd 6
63.2.i.b.38.5 yes 10 63.34 odd 6
63.2.s.b.47.5 yes 10 63.16 even 3
63.2.s.b.59.5 yes 10 21.20 even 2
189.2.i.b.143.1 10 63.20 even 6
189.2.i.b.152.5 10 7.2 even 3
189.2.s.b.17.1 10 7.6 odd 2
189.2.s.b.89.1 10 63.2 odd 6
441.2.i.b.68.1 10 21.5 even 6
441.2.i.b.227.5 10 9.7 even 3
441.2.o.c.146.1 10 63.25 even 3
441.2.o.c.293.1 10 21.17 even 6
441.2.o.d.146.1 10 63.52 odd 6
441.2.o.d.293.1 10 21.11 odd 6
441.2.s.b.362.5 10 63.61 odd 6
441.2.s.b.374.5 10 3.2 odd 2
567.2.p.c.80.1 10 63.41 even 6
567.2.p.c.404.1 10 63.58 even 3
567.2.p.d.80.5 10 63.13 odd 6
567.2.p.d.404.5 10 63.23 odd 6
1008.2.ca.b.257.5 10 84.23 even 6
1008.2.ca.b.353.5 10 252.223 even 6
1008.2.df.b.689.3 10 84.83 odd 2
1008.2.df.b.929.3 10 252.79 odd 6
1323.2.i.b.521.1 10 9.2 odd 6
1323.2.i.b.1097.5 10 7.5 odd 6
1323.2.o.c.440.5 10 63.38 even 6
1323.2.o.c.881.5 10 7.4 even 3
1323.2.o.d.440.5 10 63.11 odd 6
1323.2.o.d.881.5 10 7.3 odd 6
1323.2.s.b.656.1 10 63.47 even 6 inner
1323.2.s.b.962.1 10 1.1 even 1 trivial
3024.2.ca.b.2033.5 10 252.83 odd 6
3024.2.ca.b.2609.5 10 28.23 odd 6
3024.2.df.b.17.5 10 28.27 even 2
3024.2.df.b.1601.5 10 252.191 even 6