Properties

Label 864.2.bh.b.47.1
Level $864$
Weight $2$
Character 864.47
Analytic conductor $6.899$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(47,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bh (of order \(18\), degree \(6\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 47.1
Character \(\chi\) \(=\) 864.47
Dual form 864.2.bh.b.239.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71829 - 0.217923i) q^{3} +(-0.693543 - 3.93328i) q^{5} +(2.05979 - 2.45476i) q^{7} +(2.90502 + 0.748909i) q^{9} +O(q^{10})\) \(q+(-1.71829 - 0.217923i) q^{3} +(-0.693543 - 3.93328i) q^{5} +(2.05979 - 2.45476i) q^{7} +(2.90502 + 0.748909i) q^{9} +(4.77912 + 0.842688i) q^{11} +(0.246151 - 0.676295i) q^{13} +(0.334553 + 6.90964i) q^{15} +(0.707869 - 0.408688i) q^{17} +(0.653550 - 1.13198i) q^{19} +(-4.07426 + 3.76911i) q^{21} +(2.96174 - 2.48519i) q^{23} +(-10.2912 + 3.74569i) q^{25} +(-4.82845 - 1.91991i) q^{27} +(5.23351 - 1.90484i) q^{29} +(-0.511632 - 0.609740i) q^{31} +(-8.02826 - 2.48946i) q^{33} +(-11.0838 - 6.39925i) q^{35} +(-2.71792 + 1.56919i) q^{37} +(-0.570338 + 1.10843i) q^{39} +(3.40768 - 9.36253i) q^{41} +(-2.01090 + 11.4044i) q^{43} +(0.930912 - 11.9456i) q^{45} +(-3.89967 - 3.27222i) q^{47} +(-0.567588 - 3.21895i) q^{49} +(-1.30538 + 0.547982i) q^{51} -0.181698 q^{53} -19.3820i q^{55} +(-1.36967 + 1.80265i) q^{57} +(-0.908057 + 0.160115i) q^{59} +(-0.975724 + 1.16282i) q^{61} +(7.82213 - 5.58854i) q^{63} +(-2.83077 - 0.499141i) q^{65} +(-5.95586 - 2.16776i) q^{67} +(-5.63069 + 3.62484i) q^{69} +(4.91251 + 8.50871i) q^{71} +(-0.606035 + 1.04968i) q^{73} +(18.4995 - 4.19348i) q^{75} +(11.9126 - 9.99585i) q^{77} +(-0.336165 - 0.923605i) q^{79} +(7.87827 + 4.35119i) q^{81} +(-0.517786 - 1.42261i) q^{83} +(-2.09842 - 2.50080i) q^{85} +(-9.40778 + 2.13256i) q^{87} +(-5.93630 - 3.42732i) q^{89} +(-1.15312 - 1.99727i) q^{91} +(0.746255 + 1.15920i) q^{93} +(-4.90566 - 1.78551i) q^{95} +(-1.47950 + 8.39068i) q^{97} +(13.2523 + 6.02715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{18}\right)\) \(-1\)

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
\(3\) −1.71829 0.217923i −0.992053 0.125818i
\(4\) 0 0
\(5\) −0.693543 3.93328i −0.310162 1.75901i −0.598153 0.801382i \(-0.704099\pi\)
0.287992 0.957633i \(-0.407012\pi\)
\(6\) 0 0
\(7\) 2.05979 2.45476i 0.778528 0.927814i −0.220338 0.975424i \(-0.570716\pi\)
0.998866 + 0.0476099i \(0.0151604\pi\)
\(8\) 0 0
\(9\) 2.90502 + 0.748909i 0.968340 + 0.249636i
\(10\) 0 0
\(11\) 4.77912 + 0.842688i 1.44096 + 0.254080i 0.838862 0.544343i \(-0.183221\pi\)
0.602096 + 0.798423i \(0.294332\pi\)
\(12\) 0 0
\(13\) 0.246151 0.676295i 0.0682700 0.187570i −0.900866 0.434098i \(-0.857067\pi\)
0.969136 + 0.246527i \(0.0792895\pi\)
\(14\) 0 0
\(15\) 0.334553 + 6.90964i 0.0863813 + 1.78406i
\(16\) 0 0
\(17\) 0.707869 0.408688i 0.171683 0.0991214i −0.411696 0.911321i \(-0.635063\pi\)
0.583379 + 0.812200i \(0.301730\pi\)
\(18\) 0 0
\(19\) 0.653550 1.13198i 0.149935 0.259694i −0.781268 0.624195i \(-0.785427\pi\)
0.931203 + 0.364501i \(0.118760\pi\)
\(20\) 0 0
\(21\) −4.07426 + 3.76911i −0.889077 + 0.822488i
\(22\) 0 0
\(23\) 2.96174 2.48519i 0.617565 0.518198i −0.279472 0.960154i \(-0.590160\pi\)
0.897037 + 0.441955i \(0.145715\pi\)
\(24\) 0 0
\(25\) −10.2912 + 3.74569i −2.05824 + 0.749138i
\(26\) 0 0
\(27\) −4.82845 1.91991i −0.929236 0.369487i
\(28\) 0 0
\(29\) 5.23351 1.90484i 0.971838 0.353720i 0.193177 0.981164i \(-0.438121\pi\)
0.778662 + 0.627444i \(0.215899\pi\)
\(30\) 0 0
\(31\) −0.511632 0.609740i −0.0918919 0.109512i 0.718139 0.695900i \(-0.244994\pi\)
−0.810031 + 0.586387i \(0.800550\pi\)
\(32\) 0 0
\(33\) −8.02826 2.48946i −1.39754 0.433359i
\(34\) 0 0
\(35\) −11.0838 6.39925i −1.87351 1.08167i
\(36\) 0 0
\(37\) −2.71792 + 1.56919i −0.446823 + 0.257974i −0.706488 0.707725i \(-0.749721\pi\)
0.259664 + 0.965699i \(0.416388\pi\)
\(38\) 0 0
\(39\) −0.570338 + 1.10843i −0.0913272 + 0.177490i
\(40\) 0 0
\(41\) 3.40768 9.36253i 0.532191 1.46218i −0.324268 0.945965i \(-0.605118\pi\)
0.856458 0.516216i \(-0.172660\pi\)
\(42\) 0 0
\(43\) −2.01090 + 11.4044i −0.306660 + 1.73915i 0.308927 + 0.951086i \(0.400030\pi\)
−0.615587 + 0.788069i \(0.711081\pi\)
\(44\) 0 0
\(45\) 0.930912 11.9456i 0.138772 1.78075i
\(46\) 0 0
\(47\) −3.89967 3.27222i −0.568826 0.477302i 0.312430 0.949941i \(-0.398857\pi\)
−0.881256 + 0.472639i \(0.843301\pi\)
\(48\) 0 0
\(49\) −0.567588 3.21895i −0.0810840 0.459850i
\(50\) 0 0
\(51\) −1.30538 + 0.547982i −0.182790 + 0.0767329i
\(52\) 0 0
\(53\) −0.181698 −0.0249581 −0.0124790 0.999922i \(-0.503972\pi\)
−0.0124790 + 0.999922i \(0.503972\pi\)
\(54\) 0 0
\(55\) 19.3820i 2.61347i
\(56\) 0 0
\(57\) −1.36967 + 1.80265i −0.181417 + 0.238766i
\(58\) 0 0
\(59\) −0.908057 + 0.160115i −0.118219 + 0.0208452i −0.232445 0.972610i \(-0.574672\pi\)
0.114226 + 0.993455i \(0.463561\pi\)
\(60\) 0 0
\(61\) −0.975724 + 1.16282i −0.124929 + 0.148884i −0.824883 0.565303i \(-0.808759\pi\)
0.699954 + 0.714187i \(0.253204\pi\)
\(62\) 0 0
\(63\) 7.82213 5.58854i 0.985496 0.704090i
\(64\) 0 0
\(65\) −2.83077 0.499141i −0.351114 0.0619108i
\(66\) 0 0
\(67\) −5.95586 2.16776i −0.727624 0.264834i −0.0484653 0.998825i \(-0.515433\pi\)
−0.679159 + 0.733991i \(0.737655\pi\)
\(68\) 0 0
\(69\) −5.63069 + 3.62484i −0.677856 + 0.436380i
\(70\) 0 0
\(71\) 4.91251 + 8.50871i 0.583008 + 1.00980i 0.995121 + 0.0986659i \(0.0314575\pi\)
−0.412113 + 0.911133i \(0.635209\pi\)
\(72\) 0 0
\(73\) −0.606035 + 1.04968i −0.0709311 + 0.122856i −0.899310 0.437313i \(-0.855930\pi\)
0.828379 + 0.560169i \(0.189264\pi\)
\(74\) 0 0
\(75\) 18.4995 4.19348i 2.13614 0.484221i
\(76\) 0 0
\(77\) 11.9126 9.99585i 1.35757 1.13913i
\(78\) 0 0
\(79\) −0.336165 0.923605i −0.0378215 0.103914i 0.919344 0.393454i \(-0.128720\pi\)
−0.957166 + 0.289540i \(0.906498\pi\)
\(80\) 0 0
\(81\) 7.87827 + 4.35119i 0.875363 + 0.483466i
\(82\) 0 0
\(83\) −0.517786 1.42261i −0.0568344 0.156151i 0.908026 0.418913i \(-0.137589\pi\)
−0.964861 + 0.262762i \(0.915367\pi\)
\(84\) 0 0
\(85\) −2.09842 2.50080i −0.227606 0.271250i
\(86\) 0 0
\(87\) −9.40778 + 2.13256i −1.00862 + 0.228635i
\(88\) 0 0
\(89\) −5.93630 3.42732i −0.629246 0.363296i 0.151214 0.988501i \(-0.451682\pi\)
−0.780460 + 0.625206i \(0.785015\pi\)
\(90\) 0 0
\(91\) −1.15312 1.99727i −0.120880 0.209371i
\(92\) 0 0
\(93\) 0.746255 + 1.15920i 0.0773830 + 0.120204i
\(94\) 0 0
\(95\) −4.90566 1.78551i −0.503310 0.183190i
\(96\) 0 0
\(97\) −1.47950 + 8.39068i −0.150221 + 0.851945i 0.812805 + 0.582536i \(0.197939\pi\)
−0.963026 + 0.269409i \(0.913172\pi\)
\(98\) 0 0
\(99\) 13.2523 + 6.02715i 1.33191 + 0.605751i
\(100\) 0 0
\(101\) 13.0625 + 10.9607i 1.29976 + 1.09063i 0.990186 + 0.139756i \(0.0446317\pi\)
0.309577 + 0.950875i \(0.399813\pi\)
\(102\) 0 0
\(103\) −11.4111 + 2.01208i −1.12437 + 0.198256i −0.704757 0.709448i \(-0.748944\pi\)
−0.419610 + 0.907705i \(0.637833\pi\)
\(104\) 0 0
\(105\) 17.6506 + 13.4112i 1.72253 + 1.30880i
\(106\) 0 0
\(107\) 6.92250i 0.669223i −0.942356 0.334612i \(-0.891395\pi\)
0.942356 0.334612i \(-0.108605\pi\)
\(108\) 0 0
\(109\) 3.45030i 0.330479i −0.986253 0.165239i \(-0.947160\pi\)
0.986253 0.165239i \(-0.0528397\pi\)
\(110\) 0 0
\(111\) 5.01213 2.10402i 0.475730 0.199705i
\(112\) 0 0
\(113\) −14.4711 + 2.55165i −1.36133 + 0.240039i −0.806160 0.591698i \(-0.798458\pi\)
−0.555170 + 0.831737i \(0.687347\pi\)
\(114\) 0 0
\(115\) −11.8290 9.92574i −1.10306 0.925580i
\(116\) 0 0
\(117\) 1.22156 1.78030i 0.112933 0.164589i
\(118\) 0 0
\(119\) 0.454829 2.57946i 0.0416941 0.236459i
\(120\) 0 0
\(121\) 11.7932 + 4.29239i 1.07211 + 0.390217i
\(122\) 0 0
\(123\) −7.89569 + 15.3449i −0.711930 + 1.38360i
\(124\) 0 0
\(125\) 11.8853 + 20.5860i 1.06306 + 1.84127i
\(126\) 0 0
\(127\) −1.53630 0.886983i −0.136325 0.0787070i 0.430287 0.902692i \(-0.358412\pi\)
−0.566611 + 0.823985i \(0.691746\pi\)
\(128\) 0 0
\(129\) 5.94059 19.1578i 0.523040 1.68675i
\(130\) 0 0
\(131\) 1.60193 + 1.90910i 0.139961 + 0.166799i 0.831472 0.555567i \(-0.187499\pi\)
−0.691510 + 0.722366i \(0.743054\pi\)
\(132\) 0 0
\(133\) −1.43257 3.93596i −0.124220 0.341291i
\(134\) 0 0
\(135\) −4.20281 + 20.3232i −0.361720 + 1.74914i
\(136\) 0 0
\(137\) 5.54495 + 15.2346i 0.473737 + 1.30158i 0.914728 + 0.404069i \(0.132405\pi\)
−0.440992 + 0.897511i \(0.645373\pi\)
\(138\) 0 0
\(139\) 0.802121 0.673059i 0.0680350 0.0570881i −0.608136 0.793833i \(-0.708082\pi\)
0.676171 + 0.736745i \(0.263638\pi\)
\(140\) 0 0
\(141\) 5.98767 + 6.47243i 0.504253 + 0.545077i
\(142\) 0 0
\(143\) 1.74629 3.02466i 0.146032 0.252935i
\(144\) 0 0
\(145\) −11.1219 19.2638i −0.923626 1.59977i
\(146\) 0 0
\(147\) 0.273795 + 5.65477i 0.0225822 + 0.466398i
\(148\) 0 0
\(149\) −20.8730 7.59715i −1.70998 0.622383i −0.713085 0.701078i \(-0.752703\pi\)
−0.996899 + 0.0786947i \(0.974925\pi\)
\(150\) 0 0
\(151\) −5.72685 1.00980i −0.466045 0.0821762i −0.0643052 0.997930i \(-0.520483\pi\)
−0.401739 + 0.915754i \(0.631594\pi\)
\(152\) 0 0
\(153\) 2.36244 0.657118i 0.190992 0.0531248i
\(154\) 0 0
\(155\) −2.04344 + 2.43527i −0.164133 + 0.195606i
\(156\) 0 0
\(157\) −10.1064 + 1.78204i −0.806582 + 0.142222i −0.561711 0.827334i \(-0.689857\pi\)
−0.244871 + 0.969556i \(0.578746\pi\)
\(158\) 0 0
\(159\) 0.312209 + 0.0395961i 0.0247598 + 0.00314018i
\(160\) 0 0
\(161\) 12.3893i 0.976417i
\(162\) 0 0
\(163\) 11.7405 0.919590 0.459795 0.888025i \(-0.347923\pi\)
0.459795 + 0.888025i \(0.347923\pi\)
\(164\) 0 0
\(165\) −4.22380 + 33.3039i −0.328822 + 2.59271i
\(166\) 0 0
\(167\) 2.71920 + 15.4214i 0.210418 + 1.19334i 0.888683 + 0.458523i \(0.151621\pi\)
−0.678265 + 0.734818i \(0.737268\pi\)
\(168\) 0 0
\(169\) 9.56179 + 8.02330i 0.735523 + 0.617177i
\(170\) 0 0
\(171\) 2.74633 2.79898i 0.210017 0.214043i
\(172\) 0 0
\(173\) −1.41091 + 8.00169i −0.107270 + 0.608357i 0.883020 + 0.469336i \(0.155507\pi\)
−0.990289 + 0.139021i \(0.955604\pi\)
\(174\) 0 0
\(175\) −12.0029 + 32.9778i −0.907337 + 2.49289i
\(176\) 0 0
\(177\) 1.59519 0.0772367i 0.119902 0.00580547i
\(178\) 0 0
\(179\) 13.3490 7.70708i 0.997755 0.576054i 0.0901716 0.995926i \(-0.471258\pi\)
0.907583 + 0.419872i \(0.137925\pi\)
\(180\) 0 0
\(181\) 12.4342 + 7.17888i 0.924226 + 0.533602i 0.884981 0.465628i \(-0.154171\pi\)
0.0392449 + 0.999230i \(0.487505\pi\)
\(182\) 0 0
\(183\) 1.92998 1.78543i 0.142668 0.131983i
\(184\) 0 0
\(185\) 8.05706 + 9.60203i 0.592367 + 0.705955i
\(186\) 0 0
\(187\) 3.72739 1.35666i 0.272573 0.0992086i
\(188\) 0 0
\(189\) −14.6585 + 7.89809i −1.06625 + 0.574502i
\(190\) 0 0
\(191\) −10.3786 + 3.77752i −0.750972 + 0.273332i −0.689015 0.724747i \(-0.741957\pi\)
−0.0619574 + 0.998079i \(0.519734\pi\)
\(192\) 0 0
\(193\) −4.41602 + 3.70548i −0.317872 + 0.266726i −0.787737 0.616012i \(-0.788747\pi\)
0.469865 + 0.882738i \(0.344303\pi\)
\(194\) 0 0
\(195\) 4.75530 + 1.47456i 0.340534 + 0.105595i
\(196\) 0 0
\(197\) 9.38881 16.2619i 0.668925 1.15861i −0.309280 0.950971i \(-0.600088\pi\)
0.978205 0.207641i \(-0.0665785\pi\)
\(198\) 0 0
\(199\) 10.5780 6.10722i 0.749856 0.432930i −0.0757858 0.997124i \(-0.524147\pi\)
0.825642 + 0.564194i \(0.190813\pi\)
\(200\) 0 0
\(201\) 9.76147 + 5.02275i 0.688521 + 0.354277i
\(202\) 0 0
\(203\) 6.10400 16.7706i 0.428417 1.17707i
\(204\) 0 0
\(205\) −39.1888 6.91004i −2.73706 0.482618i
\(206\) 0 0
\(207\) 10.4651 5.00146i 0.727373 0.347625i
\(208\) 0 0
\(209\) 4.07730 4.85914i 0.282033 0.336113i
\(210\) 0 0
\(211\) 3.21591 + 18.2383i 0.221393 + 1.25558i 0.869463 + 0.493999i \(0.164465\pi\)
−0.648070 + 0.761581i \(0.724424\pi\)
\(212\) 0 0
\(213\) −6.58685 15.6910i −0.451324 1.07513i
\(214\) 0 0
\(215\) 46.2513 3.15431
\(216\) 0 0
\(217\) −2.55062 −0.173148
\(218\) 0 0
\(219\) 1.27009 1.67159i 0.0858249 0.112956i
\(220\) 0 0
\(221\) −0.102151 0.579327i −0.00687142 0.0389697i
\(222\) 0 0
\(223\) 7.23856 8.62658i 0.484730 0.577679i −0.467139 0.884184i \(-0.654715\pi\)
0.951869 + 0.306505i \(0.0991597\pi\)
\(224\) 0 0
\(225\) −32.7013 + 3.17413i −2.18009 + 0.211609i
\(226\) 0 0
\(227\) 8.98787 + 1.58480i 0.596546 + 0.105187i 0.463765 0.885958i \(-0.346498\pi\)
0.132781 + 0.991145i \(0.457609\pi\)
\(228\) 0 0
\(229\) 6.36470 17.4869i 0.420591 1.15557i −0.530777 0.847511i \(-0.678100\pi\)
0.951369 0.308054i \(-0.0996778\pi\)
\(230\) 0 0
\(231\) −22.6476 + 14.5797i −1.49010 + 0.959274i
\(232\) 0 0
\(233\) 19.2286 11.1016i 1.25971 0.727291i 0.286688 0.958024i \(-0.407446\pi\)
0.973017 + 0.230732i \(0.0741122\pi\)
\(234\) 0 0
\(235\) −10.1659 + 17.6079i −0.663153 + 1.14861i
\(236\) 0 0
\(237\) 0.376352 + 1.66028i 0.0244467 + 0.107847i
\(238\) 0 0
\(239\) 13.4989 11.3269i 0.873169 0.732676i −0.0915939 0.995796i \(-0.529196\pi\)
0.964763 + 0.263121i \(0.0847517\pi\)
\(240\) 0 0
\(241\) 8.85508 3.22299i 0.570406 0.207611i −0.0406839 0.999172i \(-0.512954\pi\)
0.611090 + 0.791561i \(0.290731\pi\)
\(242\) 0 0
\(243\) −12.5889 9.19345i −0.807578 0.589760i
\(244\) 0 0
\(245\) −12.2674 + 4.46496i −0.783734 + 0.285256i
\(246\) 0 0
\(247\) −0.604681 0.720631i −0.0384749 0.0458526i
\(248\) 0 0
\(249\) 0.579686 + 2.55728i 0.0367361 + 0.162061i
\(250\) 0 0
\(251\) 26.8008 + 15.4735i 1.69165 + 0.976676i 0.953185 + 0.302388i \(0.0977840\pi\)
0.738468 + 0.674288i \(0.235549\pi\)
\(252\) 0 0
\(253\) 16.2487 9.38121i 1.02155 0.589792i
\(254\) 0 0
\(255\) 3.06071 + 4.75439i 0.191669 + 0.297731i
\(256\) 0 0
\(257\) 3.14184 8.63213i 0.195982 0.538457i −0.802308 0.596911i \(-0.796395\pi\)
0.998290 + 0.0584533i \(0.0186169\pi\)
\(258\) 0 0
\(259\) −1.74635 + 9.90406i −0.108513 + 0.615408i
\(260\) 0 0
\(261\) 16.6300 1.61418i 1.02937 0.0999151i
\(262\) 0 0
\(263\) −3.59765 3.01879i −0.221841 0.186147i 0.525093 0.851045i \(-0.324030\pi\)
−0.746934 + 0.664898i \(0.768475\pi\)
\(264\) 0 0
\(265\) 0.126015 + 0.714667i 0.00774104 + 0.0439016i
\(266\) 0 0
\(267\) 9.45337 + 7.18278i 0.578537 + 0.439579i
\(268\) 0 0
\(269\) −28.2139 −1.72023 −0.860115 0.510100i \(-0.829608\pi\)
−0.860115 + 0.510100i \(0.829608\pi\)
\(270\) 0 0
\(271\) 15.1576i 0.920757i 0.887723 + 0.460378i \(0.152286\pi\)
−0.887723 + 0.460378i \(0.847714\pi\)
\(272\) 0 0
\(273\) 1.54615 + 3.68317i 0.0935770 + 0.222916i
\(274\) 0 0
\(275\) −52.3393 + 9.22883i −3.15618 + 0.556520i
\(276\) 0 0
\(277\) 9.43735 11.2470i 0.567035 0.675766i −0.403984 0.914766i \(-0.632375\pi\)
0.971020 + 0.239000i \(0.0768195\pi\)
\(278\) 0 0
\(279\) −1.02966 2.15447i −0.0616443 0.128985i
\(280\) 0 0
\(281\) 3.57405 + 0.630201i 0.213210 + 0.0375946i 0.279233 0.960223i \(-0.409920\pi\)
−0.0660229 + 0.997818i \(0.521031\pi\)
\(282\) 0 0
\(283\) 6.78947 + 2.47116i 0.403592 + 0.146895i 0.535837 0.844322i \(-0.319996\pi\)
−0.132245 + 0.991217i \(0.542218\pi\)
\(284\) 0 0
\(285\) 8.04023 + 4.13708i 0.476262 + 0.245060i
\(286\) 0 0
\(287\) −15.9637 27.6499i −0.942307 1.63212i
\(288\) 0 0
\(289\) −8.16595 + 14.1438i −0.480350 + 0.831990i
\(290\) 0 0
\(291\) 4.37074 14.0952i 0.256217 0.826274i
\(292\) 0 0
\(293\) 6.40067 5.37080i 0.373931 0.313765i −0.436383 0.899761i \(-0.643741\pi\)
0.810314 + 0.585996i \(0.199296\pi\)
\(294\) 0 0
\(295\) 1.25955 + 3.46059i 0.0733340 + 0.201483i
\(296\) 0 0
\(297\) −21.4579 13.2444i −1.24511 0.768516i
\(298\) 0 0
\(299\) −0.951687 2.61474i −0.0550375 0.151214i
\(300\) 0 0
\(301\) 23.8531 + 28.4270i 1.37487 + 1.63850i
\(302\) 0 0
\(303\) −20.0564 21.6802i −1.15221 1.24550i
\(304\) 0 0
\(305\) 5.25041 + 3.03133i 0.300638 + 0.173573i
\(306\) 0 0
\(307\) −14.2168 24.6242i −0.811393 1.40537i −0.911889 0.410437i \(-0.865376\pi\)
0.100495 0.994938i \(-0.467957\pi\)
\(308\) 0 0
\(309\) 20.0460 0.970593i 1.14038 0.0552151i
\(310\) 0 0
\(311\) −10.5053 3.82361i −0.595701 0.216817i 0.0265343 0.999648i \(-0.491553\pi\)
−0.622235 + 0.782831i \(0.713775\pi\)
\(312\) 0 0
\(313\) −1.64149 + 9.30937i −0.0927827 + 0.526197i 0.902622 + 0.430435i \(0.141640\pi\)
−0.995404 + 0.0957617i \(0.969471\pi\)
\(314\) 0 0
\(315\) −27.4063 26.8907i −1.54417 1.51512i
\(316\) 0 0
\(317\) −16.2563 13.6406i −0.913043 0.766134i 0.0596524 0.998219i \(-0.481001\pi\)
−0.972695 + 0.232085i \(0.925445\pi\)
\(318\) 0 0
\(319\) 26.6168 4.69325i 1.49025 0.262772i
\(320\) 0 0
\(321\) −1.50857 + 11.8948i −0.0842003 + 0.663905i
\(322\) 0 0
\(323\) 1.06839i 0.0594469i
\(324\) 0 0
\(325\) 7.88189i 0.437208i
\(326\) 0 0
\(327\) −0.751900 + 5.92860i −0.0415802 + 0.327853i
\(328\) 0 0
\(329\) −16.0650 + 2.83270i −0.885694 + 0.156172i
\(330\) 0 0
\(331\) 7.45482 + 6.25534i 0.409754 + 0.343825i 0.824249 0.566227i \(-0.191597\pi\)
−0.414495 + 0.910051i \(0.636042\pi\)
\(332\) 0 0
\(333\) −9.07079 + 2.52306i −0.497076 + 0.138263i
\(334\) 0 0
\(335\) −4.39574 + 24.9295i −0.240165 + 1.36204i
\(336\) 0 0
\(337\) 17.8549 + 6.49864i 0.972617 + 0.354004i 0.778966 0.627067i \(-0.215745\pi\)
0.193652 + 0.981070i \(0.437967\pi\)
\(338\) 0 0
\(339\) 25.4216 1.23087i 1.38071 0.0668518i
\(340\) 0 0
\(341\) −1.93133 3.34517i −0.104588 0.181151i
\(342\) 0 0
\(343\) 10.3552 + 5.97856i 0.559126 + 0.322812i
\(344\) 0 0
\(345\) 18.1626 + 19.6331i 0.977843 + 1.05701i
\(346\) 0 0
\(347\) 7.03596 + 8.38513i 0.377710 + 0.450137i 0.921090 0.389350i \(-0.127300\pi\)
−0.543380 + 0.839487i \(0.682856\pi\)
\(348\) 0 0
\(349\) −8.70795 23.9249i −0.466126 1.28067i −0.920808 0.390017i \(-0.872469\pi\)
0.454682 0.890654i \(-0.349753\pi\)
\(350\) 0 0
\(351\) −2.48695 + 2.79287i −0.132744 + 0.149072i
\(352\) 0 0
\(353\) −3.42693 9.41540i −0.182397 0.501131i 0.814472 0.580203i \(-0.197027\pi\)
−0.996869 + 0.0790715i \(0.974804\pi\)
\(354\) 0 0
\(355\) 30.0601 25.2234i 1.59542 1.33872i
\(356\) 0 0
\(357\) −1.34365 + 4.33314i −0.0711136 + 0.229334i
\(358\) 0 0
\(359\) −2.79690 + 4.84437i −0.147615 + 0.255676i −0.930345 0.366685i \(-0.880493\pi\)
0.782731 + 0.622360i \(0.213826\pi\)
\(360\) 0 0
\(361\) 8.64575 + 14.9749i 0.455039 + 0.788151i
\(362\) 0 0
\(363\) −19.3288 9.94558i −1.01450 0.522007i
\(364\) 0 0
\(365\) 4.54901 + 1.65570i 0.238106 + 0.0866635i
\(366\) 0 0
\(367\) −30.7502 5.42209i −1.60515 0.283031i −0.701940 0.712236i \(-0.747683\pi\)
−0.903207 + 0.429205i \(0.858794\pi\)
\(368\) 0 0
\(369\) 16.9111 24.6463i 0.880355 1.28303i
\(370\) 0 0
\(371\) −0.374259 + 0.446025i −0.0194306 + 0.0231565i
\(372\) 0 0
\(373\) 13.5451 2.38837i 0.701340 0.123665i 0.188403 0.982092i \(-0.439669\pi\)
0.512936 + 0.858427i \(0.328558\pi\)
\(374\) 0 0
\(375\) −15.9362 37.9627i −0.822944 1.96039i
\(376\) 0 0
\(377\) 4.00827i 0.206437i
\(378\) 0 0
\(379\) −31.9660 −1.64199 −0.820993 0.570939i \(-0.806579\pi\)
−0.820993 + 0.570939i \(0.806579\pi\)
\(380\) 0 0
\(381\) 2.44651 + 1.85889i 0.125338 + 0.0952337i
\(382\) 0 0
\(383\) −1.30024 7.37403i −0.0664392 0.376795i −0.999839 0.0179566i \(-0.994284\pi\)
0.933400 0.358839i \(-0.116827\pi\)
\(384\) 0 0
\(385\) −47.5783 39.9230i −2.42482 2.03466i
\(386\) 0 0
\(387\) −14.3826 + 31.6240i −0.731107 + 1.60754i
\(388\) 0 0
\(389\) −4.61608 + 26.1791i −0.234044 + 1.32733i 0.610572 + 0.791960i \(0.290939\pi\)
−0.844617 + 0.535371i \(0.820172\pi\)
\(390\) 0 0
\(391\) 1.08085 2.96962i 0.0546610 0.150180i
\(392\) 0 0
\(393\) −2.33654 3.62949i −0.117863 0.183083i
\(394\) 0 0
\(395\) −3.39965 + 1.96279i −0.171055 + 0.0987586i
\(396\) 0 0
\(397\) 25.7004 + 14.8381i 1.28986 + 0.744704i 0.978630 0.205629i \(-0.0659241\pi\)
0.311235 + 0.950333i \(0.399257\pi\)
\(398\) 0 0
\(399\) 1.60383 + 7.07529i 0.0802920 + 0.354208i
\(400\) 0 0
\(401\) −15.5172 18.4927i −0.774891 0.923480i 0.223799 0.974635i \(-0.428154\pi\)
−0.998691 + 0.0511557i \(0.983710\pi\)
\(402\) 0 0
\(403\) −0.538303 + 0.195926i −0.0268148 + 0.00975977i
\(404\) 0 0
\(405\) 11.6505 34.0052i 0.578919 1.68973i
\(406\) 0 0
\(407\) −14.3116 + 5.20900i −0.709400 + 0.258200i
\(408\) 0 0
\(409\) −7.17989 + 6.02464i −0.355023 + 0.297899i −0.802803 0.596244i \(-0.796659\pi\)
0.447781 + 0.894143i \(0.352215\pi\)
\(410\) 0 0
\(411\) −6.20783 27.3858i −0.306210 1.35084i
\(412\) 0 0
\(413\) −1.47736 + 2.55887i −0.0726963 + 0.125914i
\(414\) 0 0
\(415\) −5.23640 + 3.02323i −0.257045 + 0.148405i
\(416\) 0 0
\(417\) −1.52495 + 0.981708i −0.0746771 + 0.0480745i
\(418\) 0 0
\(419\) −6.17961 + 16.9783i −0.301894 + 0.829446i 0.692277 + 0.721631i \(0.256607\pi\)
−0.994171 + 0.107814i \(0.965615\pi\)
\(420\) 0 0
\(421\) −10.9086 1.92348i −0.531653 0.0937447i −0.0986239 0.995125i \(-0.531444\pi\)
−0.433029 + 0.901380i \(0.642555\pi\)
\(422\) 0 0
\(423\) −8.87804 12.4264i −0.431665 0.604190i
\(424\) 0 0
\(425\) −5.75400 + 6.85735i −0.279110 + 0.332630i
\(426\) 0 0
\(427\) 0.844667 + 4.79035i 0.0408763 + 0.231821i
\(428\) 0 0
\(429\) −3.65977 + 4.81668i −0.176695 + 0.232552i
\(430\) 0 0
\(431\) 24.5183 1.18101 0.590503 0.807036i \(-0.298930\pi\)
0.590503 + 0.807036i \(0.298930\pi\)
\(432\) 0 0
\(433\) −8.35856 −0.401687 −0.200843 0.979623i \(-0.564368\pi\)
−0.200843 + 0.979623i \(0.564368\pi\)
\(434\) 0 0
\(435\) 14.9127 + 35.5244i 0.715007 + 1.70326i
\(436\) 0 0
\(437\) −0.877549 4.97683i −0.0419789 0.238074i
\(438\) 0 0
\(439\) 6.95815 8.29240i 0.332094 0.395775i −0.573997 0.818858i \(-0.694608\pi\)
0.906091 + 0.423083i \(0.139052\pi\)
\(440\) 0 0
\(441\) 0.761848 9.77619i 0.0362785 0.465533i
\(442\) 0 0
\(443\) 0.0932147 + 0.0164363i 0.00442876 + 0.000780910i 0.175862 0.984415i \(-0.443729\pi\)
−0.171433 + 0.985196i \(0.554840\pi\)
\(444\) 0 0
\(445\) −9.36353 + 25.7261i −0.443874 + 1.21953i
\(446\) 0 0
\(447\) 34.2102 + 17.6028i 1.61809 + 0.832584i
\(448\) 0 0
\(449\) −22.5438 + 13.0157i −1.06391 + 0.614247i −0.926511 0.376269i \(-0.877207\pi\)
−0.137397 + 0.990516i \(0.543874\pi\)
\(450\) 0 0
\(451\) 24.1754 41.8730i 1.13838 1.97172i
\(452\) 0 0
\(453\) 9.62032 + 2.98314i 0.452002 + 0.140160i
\(454\) 0 0
\(455\) −7.05607 + 5.92075i −0.330794 + 0.277569i
\(456\) 0 0
\(457\) 29.3356 10.6773i 1.37226 0.499463i 0.452439 0.891795i \(-0.350554\pi\)
0.919823 + 0.392333i \(0.128332\pi\)
\(458\) 0 0
\(459\) −4.20255 + 0.614285i −0.196158 + 0.0286724i
\(460\) 0 0
\(461\) −29.8177 + 10.8528i −1.38875 + 0.505464i −0.924819 0.380407i \(-0.875784\pi\)
−0.463931 + 0.885871i \(0.653562\pi\)
\(462\) 0 0
\(463\) 4.54519 + 5.41674i 0.211233 + 0.251737i 0.861249 0.508183i \(-0.169683\pi\)
−0.650017 + 0.759920i \(0.725238\pi\)
\(464\) 0 0
\(465\) 4.04191 3.73918i 0.187439 0.173400i
\(466\) 0 0
\(467\) −22.4420 12.9569i −1.03849 0.599572i −0.119085 0.992884i \(-0.537996\pi\)
−0.919405 + 0.393312i \(0.871329\pi\)
\(468\) 0 0
\(469\) −17.5892 + 10.1551i −0.812192 + 0.468919i
\(470\) 0 0
\(471\) 17.7541 0.859624i 0.818066 0.0396094i
\(472\) 0 0
\(473\) −19.2207 + 52.8084i −0.883768 + 2.42813i
\(474\) 0 0
\(475\) −2.48576 + 14.0974i −0.114054 + 0.646835i
\(476\) 0 0
\(477\) −0.527835 0.136075i −0.0241679 0.00623045i
\(478\) 0 0
\(479\) −0.164361 0.137915i −0.00750983 0.00630150i 0.639025 0.769186i \(-0.279338\pi\)
−0.646535 + 0.762884i \(0.723782\pi\)
\(480\) 0 0
\(481\) 0.392217 + 2.22437i 0.0178836 + 0.101423i
\(482\) 0 0
\(483\) −2.69992 + 21.2884i −0.122851 + 0.968658i
\(484\) 0 0
\(485\) 34.0290 1.54518
\(486\) 0 0
\(487\) 0.392983i 0.0178078i −0.999960 0.00890388i \(-0.997166\pi\)
0.999960 0.00890388i \(-0.00283423\pi\)
\(488\) 0 0
\(489\) −20.1736 2.55854i −0.912282 0.115701i
\(490\) 0 0
\(491\) 13.4296 2.36800i 0.606070 0.106866i 0.137812 0.990458i \(-0.455993\pi\)
0.468258 + 0.883592i \(0.344882\pi\)
\(492\) 0 0
\(493\) 2.92615 3.48725i 0.131787 0.157058i
\(494\) 0 0
\(495\) 14.5154 56.3052i 0.652418 2.53073i
\(496\) 0 0
\(497\) 31.0056 + 5.46713i 1.39079 + 0.245234i
\(498\) 0 0
\(499\) 24.6543 + 8.97345i 1.10368 + 0.401707i 0.828672 0.559735i \(-0.189097\pi\)
0.275008 + 0.961442i \(0.411319\pi\)
\(500\) 0 0
\(501\) −1.31170 27.0909i −0.0586023 1.21033i
\(502\) 0 0
\(503\) −8.03410 13.9155i −0.358223 0.620460i 0.629441 0.777048i \(-0.283284\pi\)
−0.987664 + 0.156588i \(0.949950\pi\)
\(504\) 0 0
\(505\) 34.0521 58.9799i 1.51530 2.62457i
\(506\) 0 0
\(507\) −14.6814 15.8701i −0.652026 0.704814i
\(508\) 0 0
\(509\) 14.1393 11.8643i 0.626714 0.525875i −0.273192 0.961959i \(-0.588079\pi\)
0.899906 + 0.436084i \(0.143635\pi\)
\(510\) 0 0
\(511\) 1.32842 + 3.64980i 0.0587658 + 0.161458i
\(512\) 0 0
\(513\) −5.32894 + 4.21096i −0.235278 + 0.185918i
\(514\) 0 0
\(515\) 15.8281 + 43.4875i 0.697471 + 1.91629i
\(516\) 0 0
\(517\) −15.8796 18.9245i −0.698382 0.832299i
\(518\) 0 0
\(519\) 4.16811 13.4417i 0.182960 0.590026i
\(520\) 0 0
\(521\) 22.1275 + 12.7753i 0.969421 + 0.559696i 0.899060 0.437826i \(-0.144251\pi\)
0.0703617 + 0.997522i \(0.477585\pi\)
\(522\) 0 0
\(523\) −1.67576 2.90250i −0.0732759 0.126918i 0.827059 0.562115i \(-0.190012\pi\)
−0.900335 + 0.435197i \(0.856679\pi\)
\(524\) 0 0
\(525\) 27.8111 54.0496i 1.21378 2.35892i
\(526\) 0 0
\(527\) −0.611362 0.222518i −0.0266313 0.00969302i
\(528\) 0 0
\(529\) −1.39821 + 7.92962i −0.0607915 + 0.344766i
\(530\) 0 0
\(531\) −2.75783 0.214915i −0.119680 0.00932652i
\(532\) 0 0
\(533\) −5.49302 4.60919i −0.237929 0.199646i
\(534\) 0 0
\(535\) −27.2281 + 4.80105i −1.17717 + 0.207567i
\(536\) 0 0
\(537\) −24.6170 + 10.3339i −1.06230 + 0.445941i
\(538\) 0 0
\(539\) 15.8621i 0.683227i
\(540\) 0 0
\(541\) 25.0374i 1.07644i −0.842804 0.538221i \(-0.819097\pi\)
0.842804 0.538221i \(-0.180903\pi\)
\(542\) 0 0
\(543\) −19.8010 15.0451i −0.849744 0.645646i
\(544\) 0 0
\(545\) −13.5710 + 2.39293i −0.581317 + 0.102502i
\(546\) 0 0
\(547\) −2.10713 1.76810i −0.0900946 0.0755983i 0.596628 0.802518i \(-0.296507\pi\)
−0.686723 + 0.726920i \(0.740951\pi\)
\(548\) 0 0
\(549\) −3.70535 + 2.64729i −0.158140 + 0.112984i
\(550\) 0 0
\(551\) 1.26411 7.16914i 0.0538531 0.305416i
\(552\) 0 0
\(553\) −2.95966 1.07723i −0.125858 0.0458084i
\(554\) 0 0
\(555\) −11.7518 18.2549i −0.498838 0.774876i
\(556\) 0 0
\(557\) 16.8751 + 29.2285i 0.715019 + 1.23845i 0.962952 + 0.269673i \(0.0869155\pi\)
−0.247933 + 0.968777i \(0.579751\pi\)
\(558\) 0 0
\(559\) 7.21775 + 4.16717i 0.305278 + 0.176252i
\(560\) 0 0
\(561\) −6.70036 + 1.51884i −0.282890 + 0.0641256i
\(562\) 0 0
\(563\) −5.43652 6.47899i −0.229122 0.273057i 0.639219 0.769025i \(-0.279258\pi\)
−0.868341 + 0.495968i \(0.834813\pi\)
\(564\) 0 0
\(565\) 20.0727 + 55.1493i 0.844465 + 2.32015i
\(566\) 0 0
\(567\) 26.9087 10.3768i 1.13006 0.435783i
\(568\) 0 0
\(569\) −1.75562 4.82354i −0.0735996 0.202213i 0.897438 0.441141i \(-0.145426\pi\)
−0.971037 + 0.238928i \(0.923204\pi\)
\(570\) 0 0
\(571\) −2.13892 + 1.79477i −0.0895112 + 0.0751088i −0.686445 0.727182i \(-0.740830\pi\)
0.596934 + 0.802290i \(0.296385\pi\)
\(572\) 0 0
\(573\) 18.6567 4.22911i 0.779395 0.176674i
\(574\) 0 0
\(575\) −21.1711 + 36.6693i −0.882894 + 1.52922i
\(576\) 0 0
\(577\) −4.57149 7.91805i −0.190314 0.329633i 0.755041 0.655678i \(-0.227617\pi\)
−0.945354 + 0.326045i \(0.894284\pi\)
\(578\) 0 0
\(579\) 8.39549 5.40472i 0.348905 0.224613i
\(580\) 0 0
\(581\) −4.55869 1.65923i −0.189127 0.0688364i
\(582\) 0 0
\(583\) −0.868355 0.153114i −0.0359636 0.00634135i
\(584\) 0 0
\(585\) −7.84963 3.57000i −0.324542 0.147601i
\(586\) 0 0
\(587\) 1.90264 2.26748i 0.0785303 0.0935887i −0.725349 0.688382i \(-0.758321\pi\)
0.803879 + 0.594793i \(0.202766\pi\)
\(588\) 0 0
\(589\) −1.02459 + 0.180663i −0.0422175 + 0.00744409i
\(590\) 0 0
\(591\) −19.6765 + 25.8966i −0.809383 + 1.06524i
\(592\) 0 0
\(593\) 1.86981i 0.0767837i −0.999263 0.0383919i \(-0.987776\pi\)
0.999263 0.0383919i \(-0.0122235\pi\)
\(594\) 0 0
\(595\) −10.4612 −0.428867
\(596\) 0 0
\(597\) −19.5070 + 8.18877i −0.798368 + 0.335144i
\(598\) 0 0
\(599\) −5.09545 28.8978i −0.208195 1.18073i −0.892333 0.451378i \(-0.850933\pi\)
0.684138 0.729352i \(-0.260179\pi\)
\(600\) 0 0
\(601\) 3.02633 + 2.53939i 0.123447 + 0.103584i 0.702421 0.711762i \(-0.252102\pi\)
−0.578974 + 0.815346i \(0.696547\pi\)
\(602\) 0 0
\(603\) −15.6784 10.7578i −0.638475 0.438090i
\(604\) 0 0
\(605\) 8.70404 49.3630i 0.353869 2.00689i
\(606\) 0 0
\(607\) 7.61399 20.9193i 0.309042 0.849087i −0.683802 0.729668i \(-0.739675\pi\)
0.992844 0.119419i \(-0.0381031\pi\)
\(608\) 0 0
\(609\) −14.1431 + 27.4865i −0.573109 + 1.11381i
\(610\) 0 0
\(611\) −3.17289 + 1.83187i −0.128361 + 0.0741095i
\(612\) 0 0
\(613\) −32.5675 18.8029i −1.31539 0.759441i −0.332407 0.943136i \(-0.607861\pi\)
−0.982983 + 0.183695i \(0.941194\pi\)
\(614\) 0 0
\(615\) 65.8317 + 20.4136i 2.65459 + 0.823155i
\(616\) 0 0
\(617\) 18.4585 + 21.9980i 0.743111 + 0.885605i 0.996655 0.0817186i \(-0.0260409\pi\)
−0.253544 + 0.967324i \(0.581596\pi\)
\(618\) 0 0
\(619\) −24.3178 + 8.85094i −0.977413 + 0.355749i −0.780834 0.624738i \(-0.785206\pi\)
−0.196579 + 0.980488i \(0.562983\pi\)
\(620\) 0 0
\(621\) −19.0719 + 6.31335i −0.765331 + 0.253346i
\(622\) 0 0
\(623\) −20.6408 + 7.51264i −0.826956 + 0.300988i
\(624\) 0 0
\(625\) 30.7801 25.8276i 1.23121 1.03310i
\(626\) 0 0
\(627\) −8.06489 + 7.46085i −0.322081 + 0.297958i
\(628\) 0 0
\(629\) −1.28262 + 2.22156i −0.0511414 + 0.0885795i
\(630\) 0 0
\(631\) 12.0456 6.95454i 0.479528 0.276856i −0.240692 0.970602i \(-0.577374\pi\)
0.720220 + 0.693746i \(0.244041\pi\)
\(632\) 0 0
\(633\) −1.55130 32.0395i −0.0616587 1.27346i
\(634\) 0 0
\(635\) −2.42326 + 6.65785i −0.0961642 + 0.264209i
\(636\) 0 0
\(637\) −2.31667 0.408492i −0.0917899 0.0161850i
\(638\) 0 0
\(639\) 7.89868 + 28.3970i 0.312467 + 1.12337i
\(640\) 0 0
\(641\) 1.21478 1.44771i 0.0479808 0.0571813i −0.741520 0.670930i \(-0.765895\pi\)
0.789501 + 0.613749i \(0.210339\pi\)
\(642\) 0 0
\(643\) −2.69381 15.2774i −0.106234 0.602480i −0.990720 0.135915i \(-0.956602\pi\)
0.884487 0.466565i \(-0.154509\pi\)
\(644\) 0 0
\(645\) −79.4730 10.0792i −3.12925 0.396869i
\(646\) 0 0
\(647\) −29.1611 −1.14644 −0.573221 0.819401i \(-0.694306\pi\)
−0.573221 + 0.819401i \(0.694306\pi\)
\(648\) 0 0
\(649\) −4.47464 −0.175645
\(650\) 0 0
\(651\) 4.38270 + 0.555840i 0.171772 + 0.0217851i
\(652\) 0 0
\(653\) −1.67688 9.51004i −0.0656212 0.372157i −0.999879 0.0155580i \(-0.995048\pi\)
0.934258 0.356599i \(-0.116064\pi\)
\(654\) 0 0
\(655\) 6.39803 7.62488i 0.249992 0.297929i
\(656\) 0 0
\(657\) −2.54666 + 2.59549i −0.0993547 + 0.101260i
\(658\) 0 0
\(659\) −40.5315 7.14680i −1.57888 0.278400i −0.685629 0.727951i \(-0.740473\pi\)
−0.893254 + 0.449551i \(0.851584\pi\)
\(660\) 0 0
\(661\) −12.8126 + 35.2022i −0.498351 + 1.36921i 0.394516 + 0.918889i \(0.370912\pi\)
−0.892868 + 0.450319i \(0.851310\pi\)
\(662\) 0 0
\(663\) 0.0492759 + 1.01771i 0.00191372 + 0.0395246i
\(664\) 0 0
\(665\) −14.4877 + 8.36445i −0.561807 + 0.324360i
\(666\) 0 0
\(667\) 10.7664 18.6479i 0.416876 0.722050i
\(668\) 0 0
\(669\) −14.3179 + 13.2455i −0.553560 + 0.512100i
\(670\) 0 0
\(671\) −5.64300 + 4.73504i −0.217846 + 0.182794i
\(672\) 0 0
\(673\) 11.9812 4.36081i 0.461842 0.168097i −0.100611 0.994926i \(-0.532080\pi\)
0.562453 + 0.826829i \(0.309858\pi\)
\(674\) 0 0
\(675\) 56.8819 + 1.67231i 2.18939 + 0.0643673i
\(676\) 0 0
\(677\) 20.8147 7.57594i 0.799974 0.291167i 0.0904985 0.995897i \(-0.471154\pi\)
0.709476 + 0.704730i \(0.248932\pi\)
\(678\) 0 0
\(679\) 17.5497 + 20.9149i 0.673495 + 0.802640i
\(680\) 0 0
\(681\) −15.0984 4.68181i −0.578571 0.179408i
\(682\) 0 0
\(683\) 9.46338 + 5.46368i 0.362106 + 0.209062i 0.670004 0.742357i \(-0.266292\pi\)
−0.307898 + 0.951419i \(0.599626\pi\)
\(684\) 0 0
\(685\) 56.0763 32.3757i 2.14256 1.23701i
\(686\) 0 0
\(687\) −14.7472 + 28.6605i −0.562640 + 1.09346i
\(688\) 0 0
\(689\) −0.0447251 + 0.122881i −0.00170389 + 0.00468140i
\(690\) 0 0
\(691\) 3.31599 18.8059i 0.126146 0.715410i −0.854474 0.519494i \(-0.826121\pi\)
0.980621 0.195917i \(-0.0627683\pi\)
\(692\) 0 0
\(693\) 42.0923 20.1167i 1.59895 0.764170i
\(694\) 0 0
\(695\) −3.20363 2.68817i −0.121521 0.101968i
\(696\) 0 0
\(697\) −1.41416 8.02012i −0.0535653 0.303784i
\(698\) 0 0
\(699\) −35.4595 + 14.8854i −1.34120 + 0.563018i
\(700\) 0 0
\(701\) −23.5901 −0.890985 −0.445493 0.895286i \(-0.646971\pi\)
−0.445493 + 0.895286i \(0.646971\pi\)
\(702\) 0 0
\(703\) 4.10218i 0.154717i
\(704\) 0 0
\(705\) 21.3052 28.0401i 0.802399 1.05605i
\(706\) 0 0
\(707\) 53.8119 9.48848i 2.02380 0.356851i
\(708\) 0 0
\(709\) 12.3497 14.7178i 0.463804 0.552740i −0.482551 0.875868i \(-0.660290\pi\)
0.946355 + 0.323128i \(0.104734\pi\)
\(710\) 0 0
\(711\) −0.284869 2.93485i −0.0106834 0.110065i
\(712\) 0 0
\(713\) −3.03064 0.534384i −0.113498 0.0200128i
\(714\) 0 0
\(715\) −13.1080 4.77091i −0.490210 0.178422i
\(716\) 0 0
\(717\) −25.6633 + 16.5211i −0.958414 + 0.616993i
\(718\) 0 0
\(719\) 14.2201 + 24.6300i 0.530321 + 0.918542i 0.999374 + 0.0353726i \(0.0112618\pi\)
−0.469054 + 0.883170i \(0.655405\pi\)
\(720\) 0 0
\(721\) −18.5653 + 32.1560i −0.691406 + 1.19755i
\(722\) 0 0
\(723\) −15.9179 + 3.60829i −0.591994 + 0.134194i
\(724\) 0 0
\(725\) −46.7241 + 39.2062i −1.73529 + 1.45608i
\(726\) 0 0
\(727\) 17.4790 + 48.0230i 0.648259 + 1.78108i 0.624070 + 0.781369i \(0.285478\pi\)
0.0241888 + 0.999707i \(0.492300\pi\)
\(728\) 0 0
\(729\) 19.6279 + 18.5404i 0.726958 + 0.686681i
\(730\) 0 0
\(731\) 3.23739 + 8.89465i 0.119739 + 0.328980i
\(732\) 0 0
\(733\) 23.4532 + 27.9504i 0.866264 + 1.03237i 0.999149 + 0.0412414i \(0.0131313\pi\)
−0.132886 + 0.991131i \(0.542424\pi\)
\(734\) 0 0
\(735\) 22.0519 4.99874i 0.813397 0.184381i
\(736\) 0 0
\(737\) −26.6370 15.3789i −0.981187 0.566489i
\(738\) 0 0
\(739\) 14.3403 + 24.8381i 0.527516 + 0.913684i 0.999486 + 0.0320692i \(0.0102097\pi\)
−0.471970 + 0.881615i \(0.656457\pi\)
\(740\) 0 0
\(741\) 0.881973 + 1.37002i 0.0324001 + 0.0503291i
\(742\) 0 0
\(743\) −34.8288 12.6767i −1.27775 0.465061i −0.388060 0.921634i \(-0.626855\pi\)
−0.889686 + 0.456573i \(0.849077\pi\)
\(744\) 0 0
\(745\) −15.4054 + 87.3683i −0.564410 + 3.20093i
\(746\) 0 0
\(747\) −0.438776 4.52047i −0.0160540 0.165395i
\(748\) 0 0
\(749\) −16.9931 14.2589i −0.620914 0.521009i
\(750\) 0 0
\(751\) 35.3512 6.23338i 1.28998 0.227459i 0.513770 0.857928i \(-0.328248\pi\)
0.776215 + 0.630469i \(0.217137\pi\)
\(752\) 0 0
\(753\) −42.6795 32.4284i −1.55533 1.18176i
\(754\) 0 0
\(755\) 23.2256i 0.845267i
\(756\) 0 0
\(757\) 40.0043i 1.45398i 0.686647 + 0.726991i \(0.259082\pi\)
−0.686647 + 0.726991i \(0.740918\pi\)
\(758\) 0 0
\(759\) −29.9644 + 12.5786i −1.08764 + 0.456575i
\(760\) 0 0
\(761\) 49.8212 8.78482i 1.80602 0.318449i 0.833718 0.552191i \(-0.186208\pi\)
0.972299 + 0.233741i \(0.0750969\pi\)
\(762\) 0 0
\(763\) −8.46967 7.10690i −0.306623 0.257287i
\(764\) 0 0
\(765\) −4.22308 8.83640i −0.152686 0.319481i
\(766\) 0 0
\(767\) −0.115234 + 0.653526i −0.00416087 + 0.0235975i
\(768\) 0 0
\(769\) 22.5878 + 8.22128i 0.814536 + 0.296467i 0.715496 0.698616i \(-0.246201\pi\)
0.0990400 + 0.995083i \(0.468423\pi\)
\(770\) 0 0
\(771\) −7.27972 + 14.1478i −0.262173 + 0.509520i
\(772\) 0 0
\(773\) −2.65158 4.59267i −0.0953707 0.165187i 0.814393 0.580314i \(-0.197070\pi\)
−0.909763 + 0.415127i \(0.863737\pi\)
\(774\) 0 0
\(775\) 7.54921 + 4.35854i 0.271175 + 0.156563i
\(776\) 0 0
\(777\) 5.15906 16.6374i 0.185080 0.596865i
\(778\) 0 0
\(779\) −8.37112 9.97631i −0.299927 0.357439i
\(780\) 0 0
\(781\) 16.3073 + 44.8039i 0.583520 + 1.60321i
\(782\) 0 0
\(783\) −28.9269 0.850441i −1.03376 0.0303923i
\(784\) 0 0
\(785\) 14.0185 + 38.5155i 0.500341 + 1.37468i
\(786\) 0 0
\(787\) −21.0660 + 17.6764i −0.750921 + 0.630097i −0.935746 0.352674i \(-0.885272\pi\)
0.184826 + 0.982771i \(0.440828\pi\)
\(788\) 0 0
\(789\) 5.52394 + 5.97116i 0.196657 + 0.212579i
\(790\) 0 0
\(791\) −23.5438 + 40.7791i −0.837122 + 1.44994i
\(792\) 0 0
\(793\) 0.546235 + 0.946107i 0.0193974 + 0.0335973i
\(794\) 0 0
\(795\) −0.0607875 1.25546i −0.00215591 0.0445267i
\(796\) 0 0
\(797\) 26.4946 + 9.64326i 0.938488 + 0.341582i 0.765569 0.643354i \(-0.222458\pi\)
0.172919 + 0.984936i \(0.444680\pi\)
\(798\) 0 0
\(799\) −4.09777 0.722548i −0.144969 0.0255619i
\(800\) 0 0
\(801\) −14.6783 14.4022i −0.518632 0.508876i
\(802\) 0 0
\(803\) −3.78087 + 4.50587i −0.133424 + 0.159009i
\(804\) 0 0
\(805\) −48.7307 + 8.59254i −1.71753 + 0.302847i
\(806\) 0 0
\(807\) 48.4795 + 6.14846i 1.70656 + 0.216436i
\(808\) 0 0
\(809\) 53.0126i 1.86382i −0.362683 0.931912i \(-0.618139\pi\)
0.362683 0.931912i \(-0.381861\pi\)
\(810\) 0 0
\(811\) 54.1169 1.90030 0.950150 0.311792i \(-0.100929\pi\)
0.950150 + 0.311792i \(0.100929\pi\)
\(812\) 0 0
\(813\) 3.30319 26.0451i 0.115848 0.913440i
\(814\) 0 0
\(815\) −8.14256 46.1788i −0.285222 1.61757i
\(816\) 0 0
\(817\) 11.5953 + 9.72965i 0.405670 + 0.340397i
\(818\) 0 0
\(819\) −1.85407 6.66569i −0.0647866 0.232918i
\(820\) 0 0
\(821\) −7.33356 + 41.5907i −0.255943 + 1.45152i 0.537697 + 0.843138i \(0.319294\pi\)
−0.793640 + 0.608387i \(0.791817\pi\)
\(822\) 0 0
\(823\) 3.41874 9.39291i 0.119170 0.327416i −0.865738 0.500498i \(-0.833150\pi\)
0.984907 + 0.173082i \(0.0553725\pi\)
\(824\) 0 0
\(825\) 91.9451 4.45183i 3.20112 0.154993i
\(826\) 0 0
\(827\) 24.9490 14.4043i 0.867561 0.500886i 0.00102385 0.999999i \(-0.499674\pi\)
0.866537 + 0.499113i \(0.166341\pi\)
\(828\) 0 0
\(829\) −25.8979 14.9522i −0.899473 0.519311i −0.0224435 0.999748i \(-0.507145\pi\)
−0.877029 + 0.480437i \(0.840478\pi\)
\(830\) 0 0
\(831\) −18.6670 + 17.2689i −0.647553 + 0.599053i
\(832\) 0 0
\(833\) −1.71733 2.04663i −0.0595018 0.0709115i
\(834\) 0 0
\(835\) 58.7706 21.3907i 2.03384 0.740257i
\(836\) 0 0
\(837\) 1.29975 + 3.92639i 0.0449258 + 0.135716i
\(838\) 0 0
\(839\) 25.4014 9.24535i 0.876954 0.319185i 0.135974 0.990712i \(-0.456584\pi\)
0.740980 + 0.671527i \(0.234361\pi\)
\(840\) 0 0
\(841\) 1.54592 1.29718i 0.0533074 0.0447302i
\(842\) 0 0
\(843\) −6.00390 1.86173i −0.206785 0.0641215i
\(844\) 0 0
\(845\) 24.9263 43.1737i 0.857492 1.48522i
\(846\) 0 0
\(847\) 34.8284 20.1082i 1.19672 0.690926i
\(848\) 0 0
\(849\) −11.1277 5.72575i −0.381903 0.196507i
\(850\) 0 0
\(851\) −4.15002 + 11.4021i −0.142261 + 0.390858i
\(852\) 0 0
\(853\) 39.4657 + 6.95887i 1.35128 + 0.238267i 0.801977 0.597355i \(-0.203782\pi\)
0.549304 + 0.835623i \(0.314893\pi\)
\(854\) 0 0
\(855\) −12.9138 8.86085i −0.441644 0.303035i
\(856\) 0 0
\(857\) −21.1106 + 25.1586i −0.721123 + 0.859401i −0.994739 0.102438i \(-0.967336\pi\)
0.273616 + 0.961839i \(0.411780\pi\)
\(858\) 0 0
\(859\) 5.44881 + 30.9017i 0.185911 + 1.05435i 0.924779 + 0.380504i \(0.124249\pi\)
−0.738868 + 0.673850i \(0.764640\pi\)
\(860\) 0 0
\(861\) 21.4046 + 50.9894i 0.729468 + 1.73771i
\(862\) 0 0
\(863\) −23.6646 −0.805553 −0.402777 0.915298i \(-0.631955\pi\)
−0.402777 + 0.915298i \(0.631955\pi\)
\(864\) 0 0
\(865\) 32.4514 1.10338
\(866\) 0 0
\(867\) 17.1137 22.5236i 0.581212 0.764942i
\(868\) 0 0
\(869\) −0.828261 4.69730i −0.0280968 0.159345i
\(870\) 0 0
\(871\) −2.93208 + 3.49432i −0.0993498 + 0.118401i
\(872\) 0 0
\(873\) −10.5818 + 23.2671i −0.358141 + 0.787471i
\(874\) 0 0
\(875\) 75.0151 + 13.2272i 2.53597 + 0.447161i
\(876\) 0 0
\(877\) −7.18418 + 19.7384i −0.242592 + 0.666517i 0.757317 + 0.653048i \(0.226510\pi\)
−0.999909 + 0.0134696i \(0.995712\pi\)
\(878\) 0 0
\(879\) −12.1686 + 7.83372i −0.410437 + 0.264225i
\(880\) 0 0
\(881\) 22.9740 13.2641i 0.774014 0.446877i −0.0602904 0.998181i \(-0.519203\pi\)
0.834305 + 0.551303i \(0.185869\pi\)
\(882\) 0 0
\(883\) −10.5094 + 18.2028i −0.353669 + 0.612573i −0.986889 0.161399i \(-0.948399\pi\)
0.633220 + 0.773972i \(0.281733\pi\)
\(884\) 0 0
\(885\) −1.41013 6.22078i −0.0474010 0.209109i
\(886\) 0 0
\(887\) −20.1742 + 16.9281i −0.677382 + 0.568391i −0.915240 0.402909i \(-0.867999\pi\)
0.237858 + 0.971300i \(0.423555\pi\)
\(888\) 0 0
\(889\) −5.34179 + 1.94425i −0.179158 + 0.0652082i
\(890\) 0 0
\(891\) 33.9845 + 27.4338i 1.13852 + 0.919066i
\(892\) 0 0
\(893\) −6.25272 + 2.27580i −0.209239 + 0.0761569i
\(894\) 0 0
\(895\) −39.5722 47.1603i −1.32275 1.57640i
\(896\) 0 0
\(897\) 1.06546 + 4.70027i 0.0355746 + 0.156937i
\(898\) 0 0
\(899\) −3.83909 2.21650i −0.128041 0.0739244i
\(900\) 0 0
\(901\) −0.128618 + 0.0742576i −0.00428489 + 0.00247388i
\(902\) 0 0
\(903\) −34.7915 54.0438i −1.15779 1.79847i
\(904\) 0 0
\(905\) 19.6129 53.8859i 0.651954 1.79123i
\(906\) 0 0
\(907\) −9.92172 + 56.2689i −0.329445 + 1.86838i 0.146948 + 0.989144i \(0.453055\pi\)
−0.476393 + 0.879233i \(0.658056\pi\)
\(908\) 0 0
\(909\) 29.7381 + 41.6236i 0.986351 + 1.38057i
\(910\) 0 0
\(911\) 42.5909 + 35.7380i 1.41110 + 1.18405i 0.955911 + 0.293658i \(0.0948726\pi\)
0.455189 + 0.890395i \(0.349572\pi\)
\(912\) 0 0
\(913\) −1.27575 7.23514i −0.0422212 0.239448i
\(914\) 0 0
\(915\) −8.36111 6.35287i −0.276410 0.210020i
\(916\) 0 0
\(917\) 7.98604 0.263722
\(918\) 0 0
\(919\) 44.1041i 1.45486i 0.686182 + 0.727430i \(0.259285\pi\)
−0.686182 + 0.727430i \(0.740715\pi\)
\(920\) 0 0
\(921\) 19.0623 + 45.4095i 0.628124 + 1.49629i
\(922\) 0 0
\(923\) 6.96362 1.22787i 0.229210 0.0404160i
\(924\) 0 0
\(925\) 22.0929 26.3294i 0.726412 0.865704i
\(926\) 0 0
\(927\) −34.6563 2.70073i −1.13826 0.0887035i
\(928\) 0 0
\(929\) 30.7854 + 5.42829i 1.01004 + 0.178096i 0.654095 0.756412i \(-0.273050\pi\)
0.355940 + 0.934509i \(0.384161\pi\)
\(930\) 0 0
\(931\) −4.01474 1.46125i −0.131578 0.0478904i
\(932\) 0 0
\(933\) 17.2179 + 8.85941i 0.563687 + 0.290044i
\(934\) 0 0
\(935\) −7.92121 13.7199i −0.259051 0.448690i
\(936\) 0 0
\(937\) 10.1116 17.5138i 0.330332 0.572152i −0.652245 0.758008i \(-0.726173\pi\)
0.982577 + 0.185856i \(0.0595059\pi\)
\(938\) 0 0
\(939\) 4.84928 15.6384i 0.158250 0.510341i
\(940\) 0 0
\(941\) −17.1063 + 14.3539i −0.557650 + 0.467924i −0.877522 0.479537i \(-0.840805\pi\)
0.319872 + 0.947461i \(0.396360\pi\)
\(942\) 0 0
\(943\) −13.1750 36.1981i −0.429038 1.17877i
\(944\) 0 0
\(945\) 41.2317 + 52.1784i 1.34127 + 1.69736i
\(946\) 0 0
\(947\) −9.78332 26.8794i −0.317915 0.873465i −0.990995 0.133895i \(-0.957251\pi\)
0.673080 0.739569i \(-0.264971\pi\)
\(948\) 0 0
\(949\) 0.560719 + 0.668239i 0.0182017 + 0.0216920i
\(950\) 0 0
\(951\) 24.9603 + 26.9811i 0.809394 + 0.874923i
\(952\) 0 0
\(953\) −11.8170 6.82255i −0.382790 0.221004i 0.296241 0.955113i \(-0.404267\pi\)
−0.679032 + 0.734109i \(0.737600\pi\)
\(954\) 0 0
\(955\) 22.0561 + 38.2022i 0.713717 + 1.23619i
\(956\) 0 0
\(957\) −46.7580 + 2.26394i −1.51147 + 0.0731829i
\(958\) 0 0
\(959\) 48.8188 + 17.7686i 1.57644 + 0.573778i
\(960\) 0 0
\(961\) 5.27308 29.9051i 0.170099 0.964681i
\(962\) 0 0
\(963\) 5.18432 20.1100i 0.167062 0.648035i
\(964\) 0 0
\(965\) 17.6374 + 14.7995i 0.567767 + 0.476413i
\(966\) 0 0
\(967\) −35.2023 + 6.20712i −1.13203 + 0.199607i −0.708117 0.706095i \(-0.750455\pi\)
−0.423913 + 0.905703i \(0.639344\pi\)
\(968\) 0 0
\(969\) −0.232827 + 1.83580i −0.00747949 + 0.0589745i
\(970\) 0 0
\(971\) 2.58655i 0.0830062i −0.999138 0.0415031i \(-0.986785\pi\)
0.999138 0.0415031i \(-0.0132146\pi\)
\(972\) 0 0
\(973\) 3.35538i 0.107569i
\(974\) 0 0
\(975\) 1.71765 13.5433i 0.0550087 0.433734i
\(976\) 0 0
\(977\) 6.01215 1.06011i 0.192346 0.0339158i −0.0766452 0.997058i \(-0.524421\pi\)
0.268991 + 0.963143i \(0.413310\pi\)
\(978\) 0 0
\(979\) −25.4821 21.3820i −0.814412 0.683373i
\(980\) 0 0
\(981\) 2.58396 10.0232i 0.0824995 0.320016i
\(982\) 0 0
\(983\) −1.84783 + 10.4796i −0.0589367 + 0.334247i −0.999992 0.00400613i \(-0.998725\pi\)
0.941055 + 0.338253i \(0.109836\pi\)
\(984\) 0 0
\(985\) −70.4740 25.6505i −2.24549 0.817291i
\(986\) 0 0
\(987\) 28.2217 1.36645i 0.898305 0.0434944i
\(988\) 0 0
\(989\) 22.3864 + 38.7743i 0.711845 + 1.23295i
\(990\) 0 0
\(991\) −27.4598 15.8539i −0.872288 0.503616i −0.00418044 0.999991i \(-0.501331\pi\)
−0.868108 + 0.496375i \(0.834664\pi\)
\(992\) 0 0
\(993\) −11.4463 12.3730i −0.363239 0.392647i
\(994\) 0 0
\(995\) −31.3577 37.3707i −0.994106 1.18473i
\(996\) 0 0
\(997\) 3.77204 + 10.3636i 0.119462 + 0.328218i 0.984982 0.172655i \(-0.0552345\pi\)
−0.865521 + 0.500873i \(0.833012\pi\)
\(998\) 0 0
\(999\) 16.1361 2.35860i 0.510522 0.0746228i
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 864.2.bh.b.47.1 192
4.3 odd 2 216.2.v.b.155.30 yes 192
8.3 odd 2 inner 864.2.bh.b.47.2 192
8.5 even 2 216.2.v.b.155.12 yes 192
12.11 even 2 648.2.v.b.467.3 192
24.5 odd 2 648.2.v.b.467.21 192
27.23 odd 18 inner 864.2.bh.b.239.2 192
108.23 even 18 216.2.v.b.131.12 192
108.31 odd 18 648.2.v.b.179.21 192
216.77 odd 18 216.2.v.b.131.30 yes 192
216.85 even 18 648.2.v.b.179.3 192
216.131 even 18 inner 864.2.bh.b.239.1 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.131.12 192 108.23 even 18
216.2.v.b.131.30 yes 192 216.77 odd 18
216.2.v.b.155.12 yes 192 8.5 even 2
216.2.v.b.155.30 yes 192 4.3 odd 2
648.2.v.b.179.3 192 216.85 even 18
648.2.v.b.179.21 192 108.31 odd 18
648.2.v.b.467.3 192 12.11 even 2
648.2.v.b.467.21 192 24.5 odd 2
864.2.bh.b.47.1 192 1.1 even 1 trivial
864.2.bh.b.47.2 192 8.3 odd 2 inner
864.2.bh.b.239.1 192 216.131 even 18 inner
864.2.bh.b.239.2 192 27.23 odd 18 inner