Properties

Label 864.2.bh.b.239.9
Level $864$
Weight $2$
Character 864.239
Analytic conductor $6.899$
Analytic rank $0$
Dimension $192$
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 239.9
Character \(\chi\) \(=\) 864.239
Dual form 864.2.bh.b.47.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.967099 - 1.43691i) q^{3} +(-0.586059 + 3.32370i) q^{5} +(1.89356 + 2.25666i) q^{7} +(-1.12944 + 2.77927i) q^{9} +O(q^{10})\) \(q+(-0.967099 - 1.43691i) q^{3} +(-0.586059 + 3.32370i) q^{5} +(1.89356 + 2.25666i) q^{7} +(-1.12944 + 2.77927i) q^{9} +(-3.51297 + 0.619431i) q^{11} +(-0.204490 - 0.561832i) q^{13} +(5.34265 - 2.37223i) q^{15} +(-1.97627 - 1.14100i) q^{17} +(-2.72623 - 4.72197i) q^{19} +(1.41136 - 4.90330i) q^{21} +(-6.69233 - 5.61553i) q^{23} +(-6.00508 - 2.18567i) q^{25} +(5.08586 - 1.06492i) q^{27} +(-4.86478 - 1.77064i) q^{29} +(0.468156 - 0.557926i) q^{31} +(4.28745 + 4.44878i) q^{33} +(-8.61021 + 4.97111i) q^{35} +(-0.422340 - 0.243838i) q^{37} +(-0.609542 + 0.837181i) q^{39} +(0.645850 + 1.77446i) q^{41} +(1.01523 + 5.75766i) q^{43} +(-8.57557 - 5.38274i) q^{45} +(-3.87524 + 3.25171i) q^{47} +(-0.291398 + 1.65260i) q^{49} +(0.271731 + 3.94320i) q^{51} +13.0806 q^{53} -12.0391i q^{55} +(-4.14853 + 8.48397i) q^{57} +(-7.04866 - 1.24287i) q^{59} +(5.74555 + 6.84728i) q^{61} +(-8.41054 + 2.71397i) q^{63} +(1.98721 - 0.350398i) q^{65} +(-2.79254 + 1.01640i) q^{67} +(-1.59689 + 15.0471i) q^{69} +(1.67775 - 2.90596i) q^{71} +(-5.59255 - 9.68658i) q^{73} +(2.66689 + 10.7425i) q^{75} +(-8.04987 - 6.75464i) q^{77} +(-5.79167 + 15.9125i) q^{79} +(-6.44873 - 6.27805i) q^{81} +(-2.75916 + 7.58072i) q^{83} +(4.95057 - 5.89986i) q^{85} +(2.16047 + 8.70265i) q^{87} +(-13.3509 + 7.70815i) q^{89} +(0.880649 - 1.52533i) q^{91} +(-1.25444 - 0.133129i) q^{93} +(17.2922 - 6.29383i) q^{95} +(-1.67485 - 9.49852i) q^{97} +(2.24612 - 10.4631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(-1\)

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
\(3\) −0.967099 1.43691i −0.558355 0.829602i
\(4\) 0 0
\(5\) −0.586059 + 3.32370i −0.262093 + 1.48641i 0.515092 + 0.857135i \(0.327758\pi\)
−0.777186 + 0.629271i \(0.783354\pi\)
\(6\) 0 0
\(7\) 1.89356 + 2.25666i 0.715700 + 0.852937i 0.994205 0.107497i \(-0.0342836\pi\)
−0.278506 + 0.960435i \(0.589839\pi\)
\(8\) 0 0
\(9\) −1.12944 + 2.77927i −0.376480 + 0.926425i
\(10\) 0 0
\(11\) −3.51297 + 0.619431i −1.05920 + 0.186765i −0.676001 0.736901i \(-0.736289\pi\)
−0.383198 + 0.923666i \(0.625177\pi\)
\(12\) 0 0
\(13\) −0.204490 0.561832i −0.0567153 0.155824i 0.908099 0.418755i \(-0.137533\pi\)
−0.964815 + 0.262930i \(0.915311\pi\)
\(14\) 0 0
\(15\) 5.34265 2.37223i 1.37947 0.612508i
\(16\) 0 0
\(17\) −1.97627 1.14100i −0.479317 0.276734i 0.240815 0.970571i \(-0.422585\pi\)
−0.720132 + 0.693837i \(0.755919\pi\)
\(18\) 0 0
\(19\) −2.72623 4.72197i −0.625440 1.08329i −0.988456 0.151511i \(-0.951586\pi\)
0.363016 0.931783i \(-0.381747\pi\)
\(20\) 0 0
\(21\) 1.41136 4.90330i 0.307985 1.06999i
\(22\) 0 0
\(23\) −6.69233 5.61553i −1.39545 1.17092i −0.963078 0.269222i \(-0.913234\pi\)
−0.432368 0.901697i \(-0.642322\pi\)
\(24\) 0 0
\(25\) −6.00508 2.18567i −1.20102 0.437134i
\(26\) 0 0
\(27\) 5.08586 1.06492i 0.978774 0.204945i
\(28\) 0 0
\(29\) −4.86478 1.77064i −0.903368 0.328799i −0.151766 0.988416i \(-0.548496\pi\)
−0.751601 + 0.659618i \(0.770718\pi\)
\(30\) 0 0
\(31\) 0.468156 0.557926i 0.0840832 0.100206i −0.722363 0.691515i \(-0.756944\pi\)
0.806446 + 0.591308i \(0.201388\pi\)
\(32\) 0 0
\(33\) 4.28745 + 4.44878i 0.746350 + 0.774433i
\(34\) 0 0
\(35\) −8.61021 + 4.97111i −1.45539 + 0.840271i
\(36\) 0 0
\(37\) −0.422340 0.243838i −0.0694322 0.0400867i 0.464882 0.885373i \(-0.346097\pi\)
−0.534314 + 0.845286i \(0.679430\pi\)
\(38\) 0 0
\(39\) −0.609542 + 0.837181i −0.0976048 + 0.134056i
\(40\) 0 0
\(41\) 0.645850 + 1.77446i 0.100865 + 0.277124i 0.979853 0.199720i \(-0.0640031\pi\)
−0.878988 + 0.476843i \(0.841781\pi\)
\(42\) 0 0
\(43\) 1.01523 + 5.75766i 0.154821 + 0.878035i 0.958949 + 0.283578i \(0.0915216\pi\)
−0.804128 + 0.594456i \(0.797367\pi\)
\(44\) 0 0
\(45\) −8.57557 5.38274i −1.27837 0.802412i
\(46\) 0 0
\(47\) −3.87524 + 3.25171i −0.565262 + 0.474311i −0.880070 0.474844i \(-0.842504\pi\)
0.314808 + 0.949155i \(0.398060\pi\)
\(48\) 0 0
\(49\) −0.291398 + 1.65260i −0.0416284 + 0.236086i
\(50\) 0 0
\(51\) 0.271731 + 3.94320i 0.0380499 + 0.552158i
\(52\) 0 0
\(53\) 13.0806 1.79676 0.898380 0.439220i \(-0.144745\pi\)
0.898380 + 0.439220i \(0.144745\pi\)
\(54\) 0 0
\(55\) 12.0391i 1.62335i
\(56\) 0 0
\(57\) −4.14853 + 8.48397i −0.549486 + 1.12373i
\(58\) 0 0
\(59\) −7.04866 1.24287i −0.917658 0.161808i −0.305179 0.952295i \(-0.598716\pi\)
−0.612479 + 0.790487i \(0.709827\pi\)
\(60\) 0 0
\(61\) 5.74555 + 6.84728i 0.735642 + 0.876705i 0.996050 0.0887943i \(-0.0283014\pi\)
−0.260408 + 0.965499i \(0.583857\pi\)
\(62\) 0 0
\(63\) −8.41054 + 2.71397i −1.05963 + 0.341928i
\(64\) 0 0
\(65\) 1.98721 0.350398i 0.246483 0.0434615i
\(66\) 0 0
\(67\) −2.79254 + 1.01640i −0.341163 + 0.124173i −0.506919 0.861994i \(-0.669216\pi\)
0.165756 + 0.986167i \(0.446994\pi\)
\(68\) 0 0
\(69\) −1.59689 + 15.0471i −0.192243 + 1.81145i
\(70\) 0 0
\(71\) 1.67775 2.90596i 0.199113 0.344873i −0.749128 0.662425i \(-0.769527\pi\)
0.948241 + 0.317552i \(0.102861\pi\)
\(72\) 0 0
\(73\) −5.59255 9.68658i −0.654558 1.13373i −0.982004 0.188858i \(-0.939521\pi\)
0.327446 0.944870i \(-0.393812\pi\)
\(74\) 0 0
\(75\) 2.66689 + 10.7425i 0.307946 + 1.24044i
\(76\) 0 0
\(77\) −8.04987 6.75464i −0.917368 0.769763i
\(78\) 0 0
\(79\) −5.79167 + 15.9125i −0.651614 + 1.79030i −0.0399179 + 0.999203i \(0.512710\pi\)
−0.611696 + 0.791093i \(0.709513\pi\)
\(80\) 0 0
\(81\) −6.44873 6.27805i −0.716526 0.697561i
\(82\) 0 0
\(83\) −2.75916 + 7.58072i −0.302857 + 0.832092i 0.691144 + 0.722717i \(0.257107\pi\)
−0.994001 + 0.109375i \(0.965115\pi\)
\(84\) 0 0
\(85\) 4.95057 5.89986i 0.536965 0.639929i
\(86\) 0 0
\(87\) 2.16047 + 8.70265i 0.231627 + 0.933022i
\(88\) 0 0
\(89\) −13.3509 + 7.70815i −1.41519 + 0.817063i −0.995871 0.0907747i \(-0.971066\pi\)
−0.419323 + 0.907837i \(0.637732\pi\)
\(90\) 0 0
\(91\) 0.880649 1.52533i 0.0923171 0.159898i
\(92\) 0 0
\(93\) −1.25444 0.133129i −0.130080 0.0138049i
\(94\) 0 0
\(95\) 17.2922 6.29383i 1.77414 0.645733i
\(96\) 0 0
\(97\) −1.67485 9.49852i −0.170055 0.964429i −0.943698 0.330807i \(-0.892679\pi\)
0.773643 0.633621i \(-0.218432\pi\)
\(98\) 0 0
\(99\) 2.24612 10.4631i 0.225743 1.05158i
\(100\) 0 0
\(101\) −1.58712 + 1.33175i −0.157924 + 0.132514i −0.718326 0.695707i \(-0.755091\pi\)
0.560402 + 0.828221i \(0.310647\pi\)
\(102\) 0 0
\(103\) 5.47205 + 0.964870i 0.539177 + 0.0950715i 0.436604 0.899654i \(-0.356181\pi\)
0.102573 + 0.994725i \(0.467292\pi\)
\(104\) 0 0
\(105\) 15.4700 + 7.56458i 1.50972 + 0.738227i
\(106\) 0 0
\(107\) 11.8518i 1.14576i 0.819640 + 0.572879i \(0.194174\pi\)
−0.819640 + 0.572879i \(0.805826\pi\)
\(108\) 0 0
\(109\) 5.60849i 0.537196i −0.963252 0.268598i \(-0.913440\pi\)
0.963252 0.268598i \(-0.0865603\pi\)
\(110\) 0 0
\(111\) 0.0580702 + 0.842681i 0.00551178 + 0.0799837i
\(112\) 0 0
\(113\) 1.25678 + 0.221604i 0.118228 + 0.0208467i 0.232449 0.972609i \(-0.425326\pi\)
−0.114221 + 0.993455i \(0.536437\pi\)
\(114\) 0 0
\(115\) 22.5865 18.9523i 2.10620 1.76731i
\(116\) 0 0
\(117\) 1.79244 + 0.0662214i 0.165712 + 0.00612217i
\(118\) 0 0
\(119\) −1.16734 6.62034i −0.107010 0.606886i
\(120\) 0 0
\(121\) 1.62062 0.589859i 0.147329 0.0536235i
\(122\) 0 0
\(123\) 1.92514 2.64411i 0.173584 0.238411i
\(124\) 0 0
\(125\) 2.34641 4.06411i 0.209870 0.363505i
\(126\) 0 0
\(127\) −5.76339 + 3.32750i −0.511419 + 0.295268i −0.733417 0.679779i \(-0.762075\pi\)
0.221998 + 0.975047i \(0.428742\pi\)
\(128\) 0 0
\(129\) 7.29143 7.02702i 0.641975 0.618695i
\(130\) 0 0
\(131\) 10.6613 12.7057i 0.931486 1.11010i −0.0622173 0.998063i \(-0.519817\pi\)
0.993704 0.112040i \(-0.0357384\pi\)
\(132\) 0 0
\(133\) 5.49359 15.0935i 0.476355 1.30877i
\(134\) 0 0
\(135\) 0.558885 + 17.5280i 0.0481012 + 1.50857i
\(136\) 0 0
\(137\) −6.41579 + 17.6272i −0.548138 + 1.50600i 0.288085 + 0.957605i \(0.406982\pi\)
−0.836222 + 0.548391i \(0.815241\pi\)
\(138\) 0 0
\(139\) 0.589031 + 0.494256i 0.0499610 + 0.0419223i 0.667426 0.744676i \(-0.267396\pi\)
−0.617465 + 0.786598i \(0.711840\pi\)
\(140\) 0 0
\(141\) 8.42017 + 2.42366i 0.709106 + 0.204109i
\(142\) 0 0
\(143\) 1.06638 + 1.84703i 0.0891754 + 0.154456i
\(144\) 0 0
\(145\) 8.73612 15.1314i 0.725495 1.25659i
\(146\) 0 0
\(147\) 2.65646 1.17952i 0.219101 0.0972848i
\(148\) 0 0
\(149\) 2.83808 1.03298i 0.232504 0.0846246i −0.223141 0.974786i \(-0.571631\pi\)
0.455645 + 0.890162i \(0.349409\pi\)
\(150\) 0 0
\(151\) 2.11341 0.372652i 0.171987 0.0303260i −0.0869913 0.996209i \(-0.527725\pi\)
0.258978 + 0.965883i \(0.416614\pi\)
\(152\) 0 0
\(153\) 5.40324 4.20391i 0.436826 0.339866i
\(154\) 0 0
\(155\) 1.58001 + 1.88299i 0.126910 + 0.151245i
\(156\) 0 0
\(157\) −7.69184 1.35628i −0.613876 0.108243i −0.141939 0.989875i \(-0.545334\pi\)
−0.471936 + 0.881633i \(0.656445\pi\)
\(158\) 0 0
\(159\) −12.6502 18.7957i −1.00323 1.49060i
\(160\) 0 0
\(161\) 25.7357i 2.02825i
\(162\) 0 0
\(163\) −12.9106 −1.01124 −0.505620 0.862756i \(-0.668736\pi\)
−0.505620 + 0.862756i \(0.668736\pi\)
\(164\) 0 0
\(165\) −17.2991 + 11.6430i −1.34674 + 0.906405i
\(166\) 0 0
\(167\) −2.62966 + 14.9135i −0.203489 + 1.15404i 0.696310 + 0.717741i \(0.254824\pi\)
−0.899800 + 0.436304i \(0.856287\pi\)
\(168\) 0 0
\(169\) 9.68474 8.12646i 0.744980 0.625112i
\(170\) 0 0
\(171\) 16.2028 2.24376i 1.23906 0.171585i
\(172\) 0 0
\(173\) 3.13725 + 17.7922i 0.238521 + 1.35272i 0.835071 + 0.550142i \(0.185426\pi\)
−0.596551 + 0.802576i \(0.703462\pi\)
\(174\) 0 0
\(175\) −6.43868 17.6901i −0.486719 1.33725i
\(176\) 0 0
\(177\) 5.03086 + 11.3303i 0.378142 + 0.851637i
\(178\) 0 0
\(179\) −5.86858 3.38823i −0.438638 0.253248i 0.264381 0.964418i \(-0.414832\pi\)
−0.703020 + 0.711170i \(0.748166\pi\)
\(180\) 0 0
\(181\) −8.33722 + 4.81350i −0.619701 + 0.357784i −0.776753 0.629806i \(-0.783134\pi\)
0.157052 + 0.987590i \(0.449801\pi\)
\(182\) 0 0
\(183\) 4.28243 14.8779i 0.316567 1.09980i
\(184\) 0 0
\(185\) 1.05796 1.26083i 0.0777828 0.0926980i
\(186\) 0 0
\(187\) 7.64936 + 2.78414i 0.559377 + 0.203596i
\(188\) 0 0
\(189\) 12.0336 + 9.46055i 0.875313 + 0.688154i
\(190\) 0 0
\(191\) 0.938669 + 0.341648i 0.0679197 + 0.0247208i 0.375757 0.926718i \(-0.377383\pi\)
−0.307837 + 0.951439i \(0.599605\pi\)
\(192\) 0 0
\(193\) −0.369507 0.310054i −0.0265977 0.0223181i 0.629392 0.777088i \(-0.283304\pi\)
−0.655990 + 0.754770i \(0.727748\pi\)
\(194\) 0 0
\(195\) −2.42532 2.51657i −0.173681 0.180216i
\(196\) 0 0
\(197\) −6.10771 10.5789i −0.435157 0.753713i 0.562152 0.827034i \(-0.309974\pi\)
−0.997308 + 0.0733207i \(0.976640\pi\)
\(198\) 0 0
\(199\) 11.7431 + 6.77986i 0.832444 + 0.480612i 0.854689 0.519141i \(-0.173748\pi\)
−0.0222449 + 0.999753i \(0.507081\pi\)
\(200\) 0 0
\(201\) 4.16114 + 3.02968i 0.293504 + 0.213697i
\(202\) 0 0
\(203\) −5.21605 14.3310i −0.366095 1.00584i
\(204\) 0 0
\(205\) −6.27628 + 1.10668i −0.438355 + 0.0772937i
\(206\) 0 0
\(207\) 23.1657 12.2574i 1.61013 0.851949i
\(208\) 0 0
\(209\) 12.5021 + 14.8994i 0.864788 + 1.03061i
\(210\) 0 0
\(211\) 2.37424 13.4650i 0.163449 0.926968i −0.787199 0.616699i \(-0.788470\pi\)
0.950649 0.310269i \(-0.100419\pi\)
\(212\) 0 0
\(213\) −5.79816 + 0.399558i −0.397283 + 0.0273773i
\(214\) 0 0
\(215\) −19.7317 −1.34569
\(216\) 0 0
\(217\) 2.14553 0.145648
\(218\) 0 0
\(219\) −8.51023 + 17.4039i −0.575068 + 1.17605i
\(220\) 0 0
\(221\) −0.236923 + 1.34366i −0.0159372 + 0.0903842i
\(222\) 0 0
\(223\) 3.52036 + 4.19541i 0.235741 + 0.280945i 0.870925 0.491415i \(-0.163520\pi\)
−0.635184 + 0.772361i \(0.719076\pi\)
\(224\) 0 0
\(225\) 12.8570 14.2212i 0.857131 0.948079i
\(226\) 0 0
\(227\) −10.8215 + 1.90812i −0.718247 + 0.126646i −0.520814 0.853670i \(-0.674372\pi\)
−0.197433 + 0.980316i \(0.563261\pi\)
\(228\) 0 0
\(229\) 9.00757 + 24.7481i 0.595237 + 1.63540i 0.760640 + 0.649174i \(0.224885\pi\)
−0.165403 + 0.986226i \(0.552892\pi\)
\(230\) 0 0
\(231\) −1.92082 + 18.0994i −0.126381 + 1.19085i
\(232\) 0 0
\(233\) −8.32478 4.80631i −0.545374 0.314872i 0.201880 0.979410i \(-0.435295\pi\)
−0.747254 + 0.664538i \(0.768628\pi\)
\(234\) 0 0
\(235\) −8.53661 14.7858i −0.556867 0.964522i
\(236\) 0 0
\(237\) 28.4660 7.06682i 1.84907 0.459039i
\(238\) 0 0
\(239\) 11.0157 + 9.24328i 0.712547 + 0.597898i 0.925313 0.379205i \(-0.123803\pi\)
−0.212765 + 0.977103i \(0.568247\pi\)
\(240\) 0 0
\(241\) 12.6743 + 4.61308i 0.816426 + 0.297155i 0.716276 0.697818i \(-0.245845\pi\)
0.100150 + 0.994972i \(0.468068\pi\)
\(242\) 0 0
\(243\) −2.78445 + 15.3378i −0.178623 + 0.983918i
\(244\) 0 0
\(245\) −5.32199 1.93704i −0.340009 0.123753i
\(246\) 0 0
\(247\) −2.09547 + 2.49728i −0.133331 + 0.158898i
\(248\) 0 0
\(249\) 13.5612 3.36664i 0.859407 0.213352i
\(250\) 0 0
\(251\) 12.4670 7.19782i 0.786910 0.454323i −0.0519636 0.998649i \(-0.516548\pi\)
0.838874 + 0.544326i \(0.183215\pi\)
\(252\) 0 0
\(253\) 26.9884 + 15.5817i 1.69674 + 0.979615i
\(254\) 0 0
\(255\) −13.2653 1.40779i −0.830704 0.0881594i
\(256\) 0 0
\(257\) 1.76587 + 4.85170i 0.110152 + 0.302641i 0.982505 0.186236i \(-0.0596289\pi\)
−0.872353 + 0.488877i \(0.837407\pi\)
\(258\) 0 0
\(259\) −0.249467 1.41480i −0.0155011 0.0879113i
\(260\) 0 0
\(261\) 10.4156 11.5207i 0.644707 0.713116i
\(262\) 0 0
\(263\) 0.180828 0.151733i 0.0111503 0.00935624i −0.637195 0.770702i \(-0.719906\pi\)
0.648346 + 0.761346i \(0.275461\pi\)
\(264\) 0 0
\(265\) −7.66600 + 43.4761i −0.470919 + 2.67071i
\(266\) 0 0
\(267\) 23.9876 + 11.7296i 1.46802 + 0.717837i
\(268\) 0 0
\(269\) −18.1431 −1.10620 −0.553102 0.833114i \(-0.686556\pi\)
−0.553102 + 0.833114i \(0.686556\pi\)
\(270\) 0 0
\(271\) 7.29313i 0.443026i 0.975157 + 0.221513i \(0.0710995\pi\)
−0.975157 + 0.221513i \(0.928900\pi\)
\(272\) 0 0
\(273\) −3.04344 + 0.209727i −0.184197 + 0.0126933i
\(274\) 0 0
\(275\) 22.4495 + 3.95846i 1.35376 + 0.238704i
\(276\) 0 0
\(277\) −8.65619 10.3160i −0.520100 0.619831i 0.440505 0.897750i \(-0.354800\pi\)
−0.960604 + 0.277920i \(0.910355\pi\)
\(278\) 0 0
\(279\) 1.02188 + 1.93128i 0.0611781 + 0.115623i
\(280\) 0 0
\(281\) 8.48774 1.49662i 0.506336 0.0892807i 0.0853558 0.996351i \(-0.472797\pi\)
0.420980 + 0.907070i \(0.361686\pi\)
\(282\) 0 0
\(283\) −25.0099 + 9.10286i −1.48668 + 0.541109i −0.952574 0.304306i \(-0.901575\pi\)
−0.534110 + 0.845415i \(0.679353\pi\)
\(284\) 0 0
\(285\) −25.7669 18.7606i −1.52630 1.11128i
\(286\) 0 0
\(287\) −2.78139 + 4.81751i −0.164180 + 0.284369i
\(288\) 0 0
\(289\) −5.89623 10.2126i −0.346837 0.600739i
\(290\) 0 0
\(291\) −12.0288 + 11.5926i −0.705141 + 0.679571i
\(292\) 0 0
\(293\) −5.26423 4.41721i −0.307540 0.258056i 0.475935 0.879481i \(-0.342110\pi\)
−0.783474 + 0.621424i \(0.786554\pi\)
\(294\) 0 0
\(295\) 8.26186 22.6993i 0.481024 1.32160i
\(296\) 0 0
\(297\) −17.2068 + 6.89138i −0.998440 + 0.399879i
\(298\) 0 0
\(299\) −1.78647 + 4.90828i −0.103314 + 0.283853i
\(300\) 0 0
\(301\) −11.0707 + 13.1935i −0.638103 + 0.760462i
\(302\) 0 0
\(303\) 3.44851 + 0.992616i 0.198111 + 0.0570243i
\(304\) 0 0
\(305\) −26.1256 + 15.0836i −1.49595 + 0.863685i
\(306\) 0 0
\(307\) −2.12558 + 3.68162i −0.121314 + 0.210121i −0.920286 0.391247i \(-0.872044\pi\)
0.798972 + 0.601368i \(0.205377\pi\)
\(308\) 0 0
\(309\) −3.90558 8.79598i −0.222181 0.500386i
\(310\) 0 0
\(311\) −1.79911 + 0.654823i −0.102018 + 0.0371316i −0.392525 0.919741i \(-0.628398\pi\)
0.290507 + 0.956873i \(0.406176\pi\)
\(312\) 0 0
\(313\) 3.78761 + 21.4806i 0.214088 + 1.21415i 0.882482 + 0.470347i \(0.155871\pi\)
−0.668393 + 0.743808i \(0.733018\pi\)
\(314\) 0 0
\(315\) −4.09135 29.5447i −0.230522 1.66466i
\(316\) 0 0
\(317\) −0.457251 + 0.383679i −0.0256818 + 0.0215496i −0.655538 0.755162i \(-0.727558\pi\)
0.629856 + 0.776712i \(0.283114\pi\)
\(318\) 0 0
\(319\) 18.1866 + 3.20679i 1.01825 + 0.179546i
\(320\) 0 0
\(321\) 17.0300 11.4619i 0.950524 0.639740i
\(322\) 0 0
\(323\) 12.4425i 0.692322i
\(324\) 0 0
\(325\) 3.82080i 0.211940i
\(326\) 0 0
\(327\) −8.05892 + 5.42397i −0.445659 + 0.299946i
\(328\) 0 0
\(329\) −14.6760 2.58778i −0.809115 0.142669i
\(330\) 0 0
\(331\) 3.25579 2.73193i 0.178954 0.150161i −0.548911 0.835881i \(-0.684957\pi\)
0.727865 + 0.685721i \(0.240513\pi\)
\(332\) 0 0
\(333\) 1.15470 0.898397i 0.0632771 0.0492319i
\(334\) 0 0
\(335\) −1.74163 9.87725i −0.0951552 0.539652i
\(336\) 0 0
\(337\) 4.55155 1.65663i 0.247939 0.0902424i −0.215061 0.976601i \(-0.568995\pi\)
0.463000 + 0.886358i \(0.346773\pi\)
\(338\) 0 0
\(339\) −0.897003 2.02019i −0.0487185 0.109722i
\(340\) 0 0
\(341\) −1.29902 + 2.24997i −0.0703458 + 0.121842i
\(342\) 0 0
\(343\) 13.5772 7.83879i 0.733099 0.423255i
\(344\) 0 0
\(345\) −49.0761 14.1260i −2.64217 0.760521i
\(346\) 0 0
\(347\) 13.5458 16.1432i 0.727176 0.866615i −0.268131 0.963382i \(-0.586406\pi\)
0.995307 + 0.0967678i \(0.0308504\pi\)
\(348\) 0 0
\(349\) −6.80166 + 18.6874i −0.364084 + 1.00031i 0.613486 + 0.789705i \(0.289767\pi\)
−0.977571 + 0.210608i \(0.932456\pi\)
\(350\) 0 0
\(351\) −1.63832 2.63963i −0.0874468 0.140893i
\(352\) 0 0
\(353\) 7.96814 21.8923i 0.424101 1.16521i −0.525238 0.850955i \(-0.676024\pi\)
0.949339 0.314253i \(-0.101754\pi\)
\(354\) 0 0
\(355\) 8.67527 + 7.27942i 0.460436 + 0.386351i
\(356\) 0 0
\(357\) −8.38392 + 8.07990i −0.443724 + 0.427633i
\(358\) 0 0
\(359\) −5.84236 10.1193i −0.308348 0.534075i 0.669653 0.742674i \(-0.266443\pi\)
−0.978001 + 0.208599i \(0.933110\pi\)
\(360\) 0 0
\(361\) −5.36466 + 9.29186i −0.282351 + 0.489045i
\(362\) 0 0
\(363\) −2.41488 1.75824i −0.126748 0.0922839i
\(364\) 0 0
\(365\) 35.4729 12.9111i 1.85674 0.675797i
\(366\) 0 0
\(367\) −3.28119 + 0.578562i −0.171277 + 0.0302007i −0.258629 0.965977i \(-0.583271\pi\)
0.0873521 + 0.996178i \(0.472159\pi\)
\(368\) 0 0
\(369\) −5.66116 0.209150i −0.294708 0.0108879i
\(370\) 0 0
\(371\) 24.7689 + 29.5185i 1.28594 + 1.53252i
\(372\) 0 0
\(373\) −34.7339 6.12453i −1.79845 0.317116i −0.828425 0.560101i \(-0.810762\pi\)
−0.970030 + 0.242985i \(0.921874\pi\)
\(374\) 0 0
\(375\) −8.10898 + 0.558800i −0.418746 + 0.0288563i
\(376\) 0 0
\(377\) 3.09527i 0.159414i
\(378\) 0 0
\(379\) −15.7785 −0.810486 −0.405243 0.914209i \(-0.632813\pi\)
−0.405243 + 0.914209i \(0.632813\pi\)
\(380\) 0 0
\(381\) 10.3551 + 5.06348i 0.530508 + 0.259410i
\(382\) 0 0
\(383\) −1.89462 + 10.7449i −0.0968106 + 0.549040i 0.897367 + 0.441285i \(0.145477\pi\)
−0.994177 + 0.107755i \(0.965634\pi\)
\(384\) 0 0
\(385\) 27.1681 22.7968i 1.38462 1.16183i
\(386\) 0 0
\(387\) −17.1488 3.68133i −0.871720 0.187132i
\(388\) 0 0
\(389\) −4.60469 26.1145i −0.233467 1.32406i −0.845818 0.533471i \(-0.820887\pi\)
0.612352 0.790586i \(-0.290224\pi\)
\(390\) 0 0
\(391\) 6.81854 + 18.7338i 0.344828 + 0.947408i
\(392\) 0 0
\(393\) −28.5676 3.03177i −1.44104 0.152932i
\(394\) 0 0
\(395\) −49.4942 28.5755i −2.49032 1.43779i
\(396\) 0 0
\(397\) 21.7835 12.5767i 1.09328 0.631208i 0.158835 0.987305i \(-0.449226\pi\)
0.934449 + 0.356098i \(0.115893\pi\)
\(398\) 0 0
\(399\) −27.0009 + 6.70311i −1.35174 + 0.335575i
\(400\) 0 0
\(401\) 13.8988 16.5639i 0.694071 0.827162i −0.297770 0.954638i \(-0.596243\pi\)
0.991842 + 0.127475i \(0.0406874\pi\)
\(402\) 0 0
\(403\) −0.409194 0.148934i −0.0203834 0.00741895i
\(404\) 0 0
\(405\) 24.6457 17.7544i 1.22466 0.882222i
\(406\) 0 0
\(407\) 1.63471 + 0.594984i 0.0810293 + 0.0294923i
\(408\) 0 0
\(409\) 11.4354 + 9.59540i 0.565442 + 0.474462i 0.880130 0.474733i \(-0.157455\pi\)
−0.314688 + 0.949195i \(0.601900\pi\)
\(410\) 0 0
\(411\) 31.5335 7.82834i 1.55543 0.386144i
\(412\) 0 0
\(413\) −10.5424 18.2599i −0.518755 0.898510i
\(414\) 0 0
\(415\) −23.5791 13.6134i −1.15745 0.668254i
\(416\) 0 0
\(417\) 0.140552 1.32438i 0.00688284 0.0648552i
\(418\) 0 0
\(419\) 5.14629 + 14.1393i 0.251413 + 0.690751i 0.999627 + 0.0272945i \(0.00868919\pi\)
−0.748214 + 0.663457i \(0.769089\pi\)
\(420\) 0 0
\(421\) 5.74293 1.01263i 0.279893 0.0493527i −0.0319393 0.999490i \(-0.510168\pi\)
0.311832 + 0.950137i \(0.399057\pi\)
\(422\) 0 0
\(423\) −4.66055 14.4430i −0.226604 0.702241i
\(424\) 0 0
\(425\) 9.37384 + 11.1713i 0.454698 + 0.541888i
\(426\) 0 0
\(427\) −4.57243 + 25.9315i −0.221275 + 1.25491i
\(428\) 0 0
\(429\) 1.62272 3.31856i 0.0783458 0.160222i
\(430\) 0 0
\(431\) −2.52134 −0.121449 −0.0607244 0.998155i \(-0.519341\pi\)
−0.0607244 + 0.998155i \(0.519341\pi\)
\(432\) 0 0
\(433\) −32.6249 −1.56785 −0.783927 0.620854i \(-0.786786\pi\)
−0.783927 + 0.620854i \(0.786786\pi\)
\(434\) 0 0
\(435\) −30.1912 + 2.08051i −1.44756 + 0.0997530i
\(436\) 0 0
\(437\) −8.27153 + 46.9102i −0.395681 + 2.24402i
\(438\) 0 0
\(439\) −6.25287 7.45188i −0.298433 0.355659i 0.595901 0.803058i \(-0.296795\pi\)
−0.894335 + 0.447399i \(0.852350\pi\)
\(440\) 0 0
\(441\) −4.26392 2.67639i −0.203044 0.127447i
\(442\) 0 0
\(443\) 17.6810 3.11764i 0.840050 0.148123i 0.262963 0.964806i \(-0.415300\pi\)
0.577087 + 0.816683i \(0.304189\pi\)
\(444\) 0 0
\(445\) −17.7952 48.8919i −0.843574 2.31770i
\(446\) 0 0
\(447\) −4.22900 3.07908i −0.200025 0.145635i
\(448\) 0 0
\(449\) −5.44960 3.14633i −0.257182 0.148484i 0.365866 0.930667i \(-0.380773\pi\)
−0.623049 + 0.782183i \(0.714106\pi\)
\(450\) 0 0
\(451\) −3.36801 5.83356i −0.158593 0.274691i
\(452\) 0 0
\(453\) −2.57935 2.67640i −0.121188 0.125748i
\(454\) 0 0
\(455\) 4.55363 + 3.82095i 0.213477 + 0.179129i
\(456\) 0 0
\(457\) −26.0970 9.49851i −1.22076 0.444322i −0.350339 0.936623i \(-0.613934\pi\)
−0.870425 + 0.492301i \(0.836156\pi\)
\(458\) 0 0
\(459\) −11.2661 3.69839i −0.525858 0.172626i
\(460\) 0 0
\(461\) 31.8699 + 11.5997i 1.48433 + 0.540251i 0.951950 0.306255i \(-0.0990759\pi\)
0.532379 + 0.846506i \(0.321298\pi\)
\(462\) 0 0
\(463\) −24.5141 + 29.2148i −1.13927 + 1.35773i −0.214712 + 0.976677i \(0.568881\pi\)
−0.924555 + 0.381049i \(0.875563\pi\)
\(464\) 0 0
\(465\) 1.17766 4.09138i 0.0546127 0.189733i
\(466\) 0 0
\(467\) 13.7803 7.95604i 0.637674 0.368161i −0.146044 0.989278i \(-0.546654\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(468\) 0 0
\(469\) −7.58152 4.37719i −0.350082 0.202120i
\(470\) 0 0
\(471\) 5.48991 + 12.3642i 0.252962 + 0.569711i
\(472\) 0 0
\(473\) −7.13294 19.5976i −0.327973 0.901099i
\(474\) 0 0
\(475\) 6.05057 + 34.3145i 0.277619 + 1.57446i
\(476\) 0 0
\(477\) −14.7738 + 36.3546i −0.676444 + 1.66456i
\(478\) 0 0
\(479\) 9.67464 8.11798i 0.442045 0.370920i −0.394429 0.918927i \(-0.629058\pi\)
0.836474 + 0.548006i \(0.184613\pi\)
\(480\) 0 0
\(481\) −0.0506316 + 0.287146i −0.00230860 + 0.0130927i
\(482\) 0 0
\(483\) −36.9799 + 24.8889i −1.68264 + 1.13249i
\(484\) 0 0
\(485\) 32.5518 1.47810
\(486\) 0 0
\(487\) 0.979490i 0.0443849i −0.999754 0.0221925i \(-0.992935\pi\)
0.999754 0.0221925i \(-0.00706466\pi\)
\(488\) 0 0
\(489\) 12.4859 + 18.5515i 0.564631 + 0.838927i
\(490\) 0 0
\(491\) 2.99103 + 0.527400i 0.134983 + 0.0238012i 0.240732 0.970592i \(-0.422613\pi\)
−0.105748 + 0.994393i \(0.533724\pi\)
\(492\) 0 0
\(493\) 7.59385 + 9.04999i 0.342010 + 0.407591i
\(494\) 0 0
\(495\) 33.4599 + 13.5974i 1.50391 + 0.611159i
\(496\) 0 0
\(497\) 9.73469 1.71649i 0.436660 0.0769950i
\(498\) 0 0
\(499\) 11.5067 4.18808i 0.515109 0.187484i −0.0713684 0.997450i \(-0.522737\pi\)
0.586477 + 0.809966i \(0.300514\pi\)
\(500\) 0 0
\(501\) 23.9726 10.6443i 1.07102 0.475551i
\(502\) 0 0
\(503\) 18.8493 32.6480i 0.840450 1.45570i −0.0490653 0.998796i \(-0.515624\pi\)
0.889515 0.456906i \(-0.151042\pi\)
\(504\) 0 0
\(505\) −3.49620 6.05559i −0.155579 0.269470i
\(506\) 0 0
\(507\) −21.0431 6.05704i −0.934558 0.269003i
\(508\) 0 0
\(509\) 5.48541 + 4.60281i 0.243137 + 0.204016i 0.756210 0.654329i \(-0.227049\pi\)
−0.513074 + 0.858345i \(0.671493\pi\)
\(510\) 0 0
\(511\) 11.2695 30.9626i 0.498532 1.36971i
\(512\) 0 0
\(513\) −18.8938 21.1120i −0.834180 0.932119i
\(514\) 0 0
\(515\) −6.41388 + 17.6220i −0.282630 + 0.776518i
\(516\) 0 0
\(517\) 11.5994 13.8236i 0.510140 0.607961i
\(518\) 0 0
\(519\) 22.5319 21.7148i 0.989038 0.953173i
\(520\) 0 0
\(521\) 11.2996 6.52385i 0.495046 0.285815i −0.231619 0.972806i \(-0.574402\pi\)
0.726665 + 0.686992i \(0.241069\pi\)
\(522\) 0 0
\(523\) −9.72356 + 16.8417i −0.425181 + 0.736436i −0.996437 0.0843361i \(-0.973123\pi\)
0.571256 + 0.820772i \(0.306456\pi\)
\(524\) 0 0
\(525\) −19.1924 + 26.3599i −0.837623 + 1.15044i
\(526\) 0 0
\(527\) −1.56180 + 0.568448i −0.0680330 + 0.0247620i
\(528\) 0 0
\(529\) 9.25917 + 52.5113i 0.402572 + 2.28310i
\(530\) 0 0
\(531\) 11.4153 18.1864i 0.495383 0.789223i
\(532\) 0 0
\(533\) 0.864878 0.725718i 0.0374620 0.0314344i
\(534\) 0 0
\(535\) −39.3919 6.94586i −1.70306 0.300296i
\(536\) 0 0
\(537\) 0.806909 + 11.7094i 0.0348207 + 0.505298i
\(538\) 0 0
\(539\) 5.98604i 0.257837i
\(540\) 0 0
\(541\) 8.91838i 0.383431i −0.981451 0.191716i \(-0.938595\pi\)
0.981451 0.191716i \(-0.0614051\pi\)
\(542\) 0 0
\(543\) 14.9795 + 7.32474i 0.642832 + 0.314335i
\(544\) 0 0
\(545\) 18.6410 + 3.28691i 0.798491 + 0.140796i
\(546\) 0 0
\(547\) 10.8502 9.10444i 0.463923 0.389278i −0.380649 0.924720i \(-0.624299\pi\)
0.844572 + 0.535442i \(0.179855\pi\)
\(548\) 0 0
\(549\) −25.5197 + 8.23487i −1.08916 + 0.351456i
\(550\) 0 0
\(551\) 4.90163 + 27.7985i 0.208816 + 1.18426i
\(552\) 0 0
\(553\) −46.8760 + 17.0615i −1.99337 + 0.725527i
\(554\) 0 0
\(555\) −2.83485 0.300852i −0.120333 0.0127705i
\(556\) 0 0
\(557\) −14.2671 + 24.7114i −0.604517 + 1.04705i 0.387611 + 0.921823i \(0.373300\pi\)
−0.992128 + 0.125231i \(0.960033\pi\)
\(558\) 0 0
\(559\) 3.02723 1.74777i 0.128038 0.0739229i
\(560\) 0 0
\(561\) −3.39712 13.6840i −0.143426 0.577739i
\(562\) 0 0
\(563\) −3.67507 + 4.37978i −0.154886 + 0.184586i −0.837907 0.545813i \(-0.816221\pi\)
0.683022 + 0.730398i \(0.260666\pi\)
\(564\) 0 0
\(565\) −1.47309 + 4.04728i −0.0619734 + 0.170271i
\(566\) 0 0
\(567\) 1.95634 26.4405i 0.0821588 1.11040i
\(568\) 0 0
\(569\) −11.0377 + 30.3258i −0.462723 + 1.27132i 0.460706 + 0.887553i \(0.347596\pi\)
−0.923429 + 0.383769i \(0.874626\pi\)
\(570\) 0 0
\(571\) 3.60436 + 3.02442i 0.150838 + 0.126568i 0.715084 0.699039i \(-0.246389\pi\)
−0.564246 + 0.825607i \(0.690833\pi\)
\(572\) 0 0
\(573\) −0.416868 1.67919i −0.0174149 0.0701493i
\(574\) 0 0
\(575\) 27.9143 + 48.3489i 1.16411 + 2.01629i
\(576\) 0 0
\(577\) −5.60346 + 9.70547i −0.233275 + 0.404044i −0.958770 0.284183i \(-0.908278\pi\)
0.725495 + 0.688227i \(0.241611\pi\)
\(578\) 0 0
\(579\) −0.0881699 + 0.830803i −0.00366422 + 0.0345270i
\(580\) 0 0
\(581\) −22.3318 + 8.12809i −0.926477 + 0.337210i
\(582\) 0 0
\(583\) −45.9517 + 8.10253i −1.90313 + 0.335573i
\(584\) 0 0
\(585\) −1.27058 + 5.91874i −0.0525319 + 0.244710i
\(586\) 0 0
\(587\) −24.7159 29.4553i −1.02013 1.21575i −0.976235 0.216713i \(-0.930466\pi\)
−0.0438990 0.999036i \(-0.513978\pi\)
\(588\) 0 0
\(589\) −3.91081 0.689581i −0.161142 0.0284137i
\(590\) 0 0
\(591\) −9.29416 + 19.0071i −0.382311 + 0.781846i
\(592\) 0 0
\(593\) 13.0127i 0.534370i 0.963645 + 0.267185i \(0.0860934\pi\)
−0.963645 + 0.267185i \(0.913907\pi\)
\(594\) 0 0
\(595\) 22.6882 0.930125
\(596\) 0 0
\(597\) −1.61463 23.4306i −0.0660824 0.958949i
\(598\) 0 0
\(599\) −1.26632 + 7.18164i −0.0517403 + 0.293434i −0.999688 0.0249933i \(-0.992044\pi\)
0.947947 + 0.318427i \(0.103155\pi\)
\(600\) 0 0
\(601\) 24.0699 20.1971i 0.981833 0.823856i −0.00253165 0.999997i \(-0.500806\pi\)
0.984365 + 0.176141i \(0.0563614\pi\)
\(602\) 0 0
\(603\) 0.329148 8.90920i 0.0134040 0.362811i
\(604\) 0 0
\(605\) 1.01074 + 5.73217i 0.0410923 + 0.233046i
\(606\) 0 0
\(607\) −9.22172 25.3365i −0.374298 1.02838i −0.973681 0.227913i \(-0.926810\pi\)
0.599383 0.800462i \(-0.295412\pi\)
\(608\) 0 0
\(609\) −15.5479 + 21.3545i −0.630034 + 0.865327i
\(610\) 0 0
\(611\) 2.61936 + 1.51229i 0.105968 + 0.0611807i
\(612\) 0 0
\(613\) 3.01282 1.73945i 0.121687 0.0702559i −0.437921 0.899013i \(-0.644285\pi\)
0.559608 + 0.828758i \(0.310952\pi\)
\(614\) 0 0
\(615\) 7.65999 + 7.94821i 0.308880 + 0.320503i
\(616\) 0 0
\(617\) 23.1805 27.6254i 0.933210 1.11216i −0.0602731 0.998182i \(-0.519197\pi\)
0.993484 0.113975i \(-0.0363584\pi\)
\(618\) 0 0
\(619\) −20.9325 7.61881i −0.841349 0.306226i −0.114841 0.993384i \(-0.536636\pi\)
−0.726508 + 0.687158i \(0.758858\pi\)
\(620\) 0 0
\(621\) −40.0163 21.4329i −1.60580 0.860075i
\(622\) 0 0
\(623\) −42.6755 15.5326i −1.70976 0.622301i
\(624\) 0 0
\(625\) −12.3442 10.3580i −0.493768 0.414320i
\(626\) 0 0
\(627\) 9.31841 32.3736i 0.372141 1.29288i
\(628\) 0 0
\(629\) 0.556439 + 0.963781i 0.0221867 + 0.0384285i
\(630\) 0 0
\(631\) 8.28573 + 4.78377i 0.329850 + 0.190439i 0.655774 0.754957i \(-0.272342\pi\)
−0.325925 + 0.945396i \(0.605676\pi\)
\(632\) 0 0
\(633\) −21.6441 + 9.61039i −0.860278 + 0.381979i
\(634\) 0 0
\(635\) −7.68193 21.1059i −0.304848 0.837563i
\(636\) 0 0
\(637\) 0.988073 0.174224i 0.0391489 0.00690300i
\(638\) 0 0
\(639\) 6.18152 + 7.94504i 0.244537 + 0.314301i
\(640\) 0 0
\(641\) 1.06709 + 1.27171i 0.0421477 + 0.0502297i 0.786706 0.617327i \(-0.211785\pi\)
−0.744559 + 0.667557i \(0.767340\pi\)
\(642\) 0 0
\(643\) −5.71286 + 32.3993i −0.225293 + 1.27770i 0.636830 + 0.771004i \(0.280245\pi\)
−0.862124 + 0.506698i \(0.830866\pi\)
\(644\) 0 0
\(645\) 19.0825 + 28.3528i 0.751374 + 1.11639i
\(646\) 0 0
\(647\) 25.6189 1.00718 0.503592 0.863942i \(-0.332012\pi\)
0.503592 + 0.863942i \(0.332012\pi\)
\(648\) 0 0
\(649\) 25.5316 1.00220
\(650\) 0 0
\(651\) −2.07494 3.08294i −0.0813233 0.120830i
\(652\) 0 0
\(653\) 7.68220 43.5679i 0.300628 1.70495i −0.342775 0.939417i \(-0.611367\pi\)
0.643403 0.765528i \(-0.277522\pi\)
\(654\) 0 0
\(655\) 35.9818 + 42.8815i 1.40593 + 1.67552i
\(656\) 0 0
\(657\) 33.2381 4.60282i 1.29674 0.179573i
\(658\) 0 0
\(659\) 28.0225 4.94113i 1.09160 0.192479i 0.401262 0.915963i \(-0.368572\pi\)
0.690341 + 0.723484i \(0.257461\pi\)
\(660\) 0 0
\(661\) 10.5767 + 29.0592i 0.411385 + 1.13027i 0.956455 + 0.291881i \(0.0942811\pi\)
−0.545069 + 0.838391i \(0.683497\pi\)
\(662\) 0 0
\(663\) 2.15985 0.959012i 0.0838815 0.0372449i
\(664\) 0 0
\(665\) 46.9468 + 27.1048i 1.82052 + 1.05108i
\(666\) 0 0
\(667\) 22.6137 + 39.1680i 0.875604 + 1.51659i
\(668\) 0 0
\(669\) 2.62390 9.11583i 0.101446 0.352438i
\(670\) 0 0
\(671\) −24.4253 20.4953i −0.942930 0.791212i
\(672\) 0 0
\(673\) −5.42191 1.97341i −0.208999 0.0760695i 0.235399 0.971899i \(-0.424360\pi\)
−0.444398 + 0.895829i \(0.646583\pi\)
\(674\) 0 0
\(675\) −32.8686 4.72105i −1.26511 0.181713i
\(676\) 0 0
\(677\) −38.0136 13.8358i −1.46098 0.531754i −0.515346 0.856982i \(-0.672336\pi\)
−0.945635 + 0.325229i \(0.894559\pi\)
\(678\) 0 0
\(679\) 18.2635 21.7656i 0.700889 0.835287i
\(680\) 0 0
\(681\) 13.2073 + 13.7042i 0.506103 + 0.525146i
\(682\) 0 0
\(683\) 6.34298 3.66212i 0.242707 0.140127i −0.373713 0.927544i \(-0.621916\pi\)
0.616420 + 0.787417i \(0.288582\pi\)
\(684\) 0 0
\(685\) −54.8277 31.6548i −2.09486 1.20947i
\(686\) 0 0
\(687\) 26.8497 36.8770i 1.02438 1.40694i
\(688\) 0 0
\(689\) −2.67485 7.34910i −0.101904 0.279978i
\(690\) 0 0
\(691\) 4.43476 + 25.1508i 0.168706 + 0.956781i 0.945160 + 0.326607i \(0.105905\pi\)
−0.776454 + 0.630174i \(0.782984\pi\)
\(692\) 0 0
\(693\) 27.8648 14.7438i 1.05850 0.560072i
\(694\) 0 0
\(695\) −1.98797 + 1.66810i −0.0754079 + 0.0632748i
\(696\) 0 0
\(697\) 0.748285 4.24373i 0.0283433 0.160743i
\(698\) 0 0
\(699\) 1.14463 + 16.6102i 0.0432938 + 0.628254i
\(700\) 0 0
\(701\) −19.0555 −0.719715 −0.359857 0.933007i \(-0.617175\pi\)
−0.359857 + 0.933007i \(0.617175\pi\)
\(702\) 0 0
\(703\) 2.65903i 0.100287i
\(704\) 0 0
\(705\) −12.9902 + 26.5657i −0.489240 + 1.00052i
\(706\) 0 0
\(707\) −6.01061 1.05983i −0.226052 0.0398591i
\(708\) 0 0
\(709\) 20.4893 + 24.4183i 0.769494 + 0.917047i 0.998408 0.0563997i \(-0.0179621\pi\)
−0.228915 + 0.973447i \(0.573518\pi\)
\(710\) 0 0
\(711\) −37.6838 34.0689i −1.41325 1.27768i
\(712\) 0 0
\(713\) −6.26610 + 1.10488i −0.234667 + 0.0413782i
\(714\) 0 0
\(715\) −6.76394 + 2.46187i −0.252957 + 0.0920689i
\(716\) 0 0
\(717\) 2.62851 24.7678i 0.0981636 0.924970i
\(718\) 0 0
\(719\) 16.9767 29.4045i 0.633124 1.09660i −0.353785 0.935327i \(-0.615106\pi\)
0.986909 0.161277i \(-0.0515611\pi\)
\(720\) 0 0
\(721\) 8.18429 + 14.1756i 0.304799 + 0.527927i
\(722\) 0 0
\(723\) −5.62874 22.6732i −0.209335 0.843227i
\(724\) 0 0
\(725\) 25.3434 + 21.2656i 0.941230 + 0.789786i
\(726\) 0 0
\(727\) −17.7280 + 48.7074i −0.657497 + 1.80646i −0.0695178 + 0.997581i \(0.522146\pi\)
−0.587979 + 0.808876i \(0.700076\pi\)
\(728\) 0 0
\(729\) 24.7319 10.8321i 0.915995 0.401189i
\(730\) 0 0
\(731\) 4.56313 12.5371i 0.168773 0.463701i
\(732\) 0 0
\(733\) 2.97953 3.55086i 0.110051 0.131154i −0.708207 0.706005i \(-0.750496\pi\)
0.818258 + 0.574851i \(0.194940\pi\)
\(734\) 0 0
\(735\) 2.36352 + 9.52055i 0.0871798 + 0.351171i
\(736\) 0 0
\(737\) 9.18051 5.30037i 0.338168 0.195242i
\(738\) 0 0
\(739\) 25.0295 43.3524i 0.920726 1.59474i 0.122430 0.992477i \(-0.460931\pi\)
0.798295 0.602266i \(-0.205736\pi\)
\(740\) 0 0
\(741\) 5.61490 + 0.595888i 0.206268 + 0.0218905i
\(742\) 0 0
\(743\) −11.2170 + 4.08266i −0.411512 + 0.149778i −0.539477 0.842000i \(-0.681378\pi\)
0.127964 + 0.991779i \(0.459156\pi\)
\(744\) 0 0
\(745\) 1.77002 + 10.0383i 0.0648487 + 0.367775i
\(746\) 0 0
\(747\) −17.9526 16.2304i −0.656851 0.593840i
\(748\) 0 0
\(749\) −26.7455 + 22.4422i −0.977260 + 0.820019i
\(750\) 0 0
\(751\) 19.4858 + 3.43587i 0.711046 + 0.125377i 0.517461 0.855707i \(-0.326877\pi\)
0.193585 + 0.981083i \(0.437988\pi\)
\(752\) 0 0
\(753\) −22.3995 10.9530i −0.816282 0.399149i
\(754\) 0 0
\(755\) 7.24276i 0.263591i
\(756\) 0 0
\(757\) 16.3318i 0.593590i 0.954941 + 0.296795i \(0.0959178\pi\)
−0.954941 + 0.296795i \(0.904082\pi\)
\(758\) 0 0
\(759\) −3.71080 53.8490i −0.134694 1.95460i
\(760\) 0 0
\(761\) 40.2204 + 7.09194i 1.45799 + 0.257082i 0.845745 0.533588i \(-0.179157\pi\)
0.612242 + 0.790670i \(0.290268\pi\)
\(762\) 0 0
\(763\) 12.6565 10.6200i 0.458195 0.384471i
\(764\) 0 0
\(765\) 10.8060 + 20.4225i 0.390690 + 0.738378i
\(766\) 0 0
\(767\) 0.743098 + 4.21432i 0.0268317 + 0.152170i
\(768\) 0 0
\(769\) 23.2382 8.45800i 0.837989 0.305003i 0.112856 0.993611i \(-0.464000\pi\)
0.725134 + 0.688608i \(0.241778\pi\)
\(770\) 0 0
\(771\) 5.26370 7.22948i 0.189567 0.260363i
\(772\) 0 0
\(773\) −9.22148 + 15.9721i −0.331674 + 0.574475i −0.982840 0.184459i \(-0.940947\pi\)
0.651167 + 0.758935i \(0.274280\pi\)
\(774\) 0 0
\(775\) −4.03076 + 2.32716i −0.144789 + 0.0835940i
\(776\) 0 0
\(777\) −1.79168 + 1.72671i −0.0642763 + 0.0619455i
\(778\) 0 0
\(779\) 6.61820 7.88727i 0.237122 0.282591i
\(780\) 0 0
\(781\) −4.09386 + 11.2478i −0.146490 + 0.402477i
\(782\) 0 0
\(783\) −26.6272 3.82457i −0.951578 0.136679i
\(784\) 0 0
\(785\) 9.01574 24.7705i 0.321786 0.884099i
\(786\) 0 0
\(787\) 25.2598 + 21.1955i 0.900415 + 0.755538i 0.970272 0.242019i \(-0.0778096\pi\)
−0.0698563 + 0.997557i \(0.522254\pi\)
\(788\) 0 0
\(789\) −0.392905 0.113094i −0.0139878 0.00402624i
\(790\) 0 0
\(791\) 1.87970 + 3.25574i 0.0668345 + 0.115761i
\(792\) 0 0
\(793\) 2.67211 4.62823i 0.0948895 0.164353i
\(794\) 0 0
\(795\) 69.8851 31.0303i 2.47857 1.10053i
\(796\) 0 0
\(797\) −24.1141 + 8.77682i −0.854166 + 0.310891i −0.731738 0.681586i \(-0.761290\pi\)
−0.122428 + 0.992477i \(0.539068\pi\)
\(798\) 0 0
\(799\) 11.3687 2.00462i 0.402197 0.0709182i
\(800\) 0 0
\(801\) −6.34402 45.8117i −0.224155 1.61868i
\(802\) 0 0
\(803\) 25.6466 + 30.5644i 0.905049 + 1.07860i
\(804\) 0 0
\(805\) 85.5378 + 15.0826i 3.01481 + 0.531592i
\(806\) 0 0
\(807\) 17.5462 + 26.0701i 0.617654 + 0.917709i
\(808\) 0 0
\(809\) 35.5723i 1.25066i −0.780362 0.625328i \(-0.784965\pi\)
0.780362 0.625328i \(-0.215035\pi\)
\(810\) 0 0
\(811\) −5.98290 −0.210088 −0.105044 0.994468i \(-0.533498\pi\)
−0.105044 + 0.994468i \(0.533498\pi\)
\(812\) 0 0
\(813\) 10.4796 7.05318i 0.367535 0.247366i
\(814\) 0 0
\(815\) 7.56640 42.9112i 0.265039 1.50311i
\(816\) 0 0
\(817\) 24.4197 20.4906i 0.854338 0.716875i
\(818\) 0 0
\(819\) 3.24467 + 4.17033i 0.113378 + 0.145723i
\(820\) 0 0
\(821\) 1.31505 + 7.45804i 0.0458957 + 0.260287i 0.999118 0.0419816i \(-0.0133671\pi\)
−0.953223 + 0.302269i \(0.902256\pi\)
\(822\) 0 0
\(823\) 8.60702 + 23.6476i 0.300022 + 0.824303i 0.994495 + 0.104784i \(0.0334152\pi\)
−0.694473 + 0.719519i \(0.744363\pi\)
\(824\) 0 0
\(825\) −16.0230 36.0863i −0.557848 1.25636i
\(826\) 0 0
\(827\) −2.17911 1.25811i −0.0757749 0.0437487i 0.461634 0.887071i \(-0.347263\pi\)
−0.537409 + 0.843322i \(0.680597\pi\)
\(828\) 0 0
\(829\) 23.0116 13.2858i 0.799227 0.461434i −0.0439737 0.999033i \(-0.514002\pi\)
0.843201 + 0.537599i \(0.180668\pi\)
\(830\) 0 0
\(831\) −6.45187 + 22.4148i −0.223813 + 0.777562i
\(832\) 0 0
\(833\) 2.46151 2.93351i 0.0852862 0.101640i
\(834\) 0 0
\(835\) −48.0271 17.4804i −1.66205 0.604935i
\(836\) 0 0
\(837\) 1.78682 3.33608i 0.0617616 0.115312i
\(838\) 0 0
\(839\) 20.0868 + 7.31100i 0.693473 + 0.252404i 0.664622 0.747180i \(-0.268593\pi\)
0.0288517 + 0.999584i \(0.490815\pi\)
\(840\) 0 0
\(841\) −1.68433 1.41332i −0.0580803 0.0487351i
\(842\) 0 0
\(843\) −10.3590 10.7488i −0.356783 0.370207i
\(844\) 0 0
\(845\) 21.3341 + 36.9518i 0.733916 + 1.27118i
\(846\) 0 0
\(847\) 4.39987 + 2.54026i 0.151181 + 0.0872845i
\(848\) 0 0
\(849\) 37.2671 + 27.1337i 1.27900 + 0.931226i
\(850\) 0 0
\(851\) 1.45716 + 4.00350i 0.0499507 + 0.137238i
\(852\) 0 0
\(853\) −10.2340 + 1.80454i −0.350407 + 0.0617861i −0.346081 0.938205i \(-0.612488\pi\)
−0.00432523 + 0.999991i \(0.501377\pi\)
\(854\) 0 0
\(855\) −2.03818 + 55.1682i −0.0697041 + 1.88671i
\(856\) 0 0
\(857\) −18.8893 22.5114i −0.645245 0.768973i 0.339944 0.940446i \(-0.389592\pi\)
−0.985189 + 0.171472i \(0.945148\pi\)
\(858\) 0 0
\(859\) −2.76131 + 15.6602i −0.0942148 + 0.534319i 0.900770 + 0.434296i \(0.143003\pi\)
−0.994985 + 0.100023i \(0.968108\pi\)
\(860\) 0 0
\(861\) 9.61223 0.662391i 0.327584 0.0225742i
\(862\) 0 0
\(863\) −25.8291 −0.879233 −0.439617 0.898185i \(-0.644886\pi\)
−0.439617 + 0.898185i \(0.644886\pi\)
\(864\) 0 0
\(865\) −60.9747 −2.07320
\(866\) 0 0
\(867\) −8.97234 + 18.3489i −0.304717 + 0.623162i
\(868\) 0 0
\(869\) 10.4893 59.4876i 0.355824 2.01798i
\(870\) 0 0
\(871\) 1.14209 + 1.36109i 0.0386984 + 0.0461189i
\(872\) 0 0
\(873\) 28.2906 + 6.07315i 0.957493 + 0.205545i
\(874\) 0 0
\(875\) 13.6144 2.40058i 0.460250 0.0811546i
\(876\) 0 0
\(877\) 4.98502 + 13.6962i 0.168332 + 0.462489i 0.994961 0.100258i \(-0.0319668\pi\)
−0.826629 + 0.562747i \(0.809745\pi\)
\(878\) 0 0
\(879\) −1.25612 + 11.8361i −0.0423680 + 0.399223i
\(880\) 0 0
\(881\) −10.8614 6.27081i −0.365929 0.211269i 0.305750 0.952112i \(-0.401093\pi\)
−0.671678 + 0.740843i \(0.734426\pi\)
\(882\) 0 0
\(883\) −14.5195 25.1485i −0.488620 0.846315i 0.511294 0.859406i \(-0.329166\pi\)
−0.999914 + 0.0130911i \(0.995833\pi\)
\(884\) 0 0
\(885\) −40.6069 + 10.0809i −1.36499 + 0.338865i
\(886\) 0 0
\(887\) 16.1110 + 13.5188i 0.540955 + 0.453915i 0.871864 0.489747i \(-0.162911\pi\)
−0.330909 + 0.943663i \(0.607355\pi\)
\(888\) 0 0
\(889\) −18.4224 6.70520i −0.617867 0.224885i
\(890\) 0 0
\(891\) 26.5430 + 18.0600i 0.889224 + 0.605034i
\(892\) 0 0
\(893\) 25.9193 + 9.43384i 0.867355 + 0.315692i
\(894\) 0 0
\(895\) 14.7008 17.5197i 0.491394 0.585620i
\(896\) 0 0
\(897\) 8.78047 2.17979i 0.293171 0.0727812i
\(898\) 0 0
\(899\) −3.26536 + 1.88526i −0.108906 + 0.0628768i
\(900\) 0 0
\(901\) −25.8509 14.9250i −0.861217 0.497224i
\(902\) 0 0
\(903\) 29.6644 + 3.14817i 0.987169 + 0.104765i
\(904\) 0 0
\(905\) −11.1125 30.5315i −0.369393 1.01490i
\(906\) 0 0
\(907\) 1.09570 + 6.21403i 0.0363822 + 0.206333i 0.997580 0.0695260i \(-0.0221487\pi\)
−0.961198 + 0.275859i \(0.911038\pi\)
\(908\) 0 0
\(909\) −1.90874 5.91516i −0.0633090 0.196194i
\(910\) 0 0
\(911\) −30.4836 + 25.5788i −1.00997 + 0.847463i −0.988334 0.152303i \(-0.951331\pi\)
−0.0216332 + 0.999766i \(0.506887\pi\)
\(912\) 0 0
\(913\) 4.99710 28.3399i 0.165380 0.937915i
\(914\) 0 0
\(915\) 46.9398 + 22.9528i 1.55178 + 0.758798i
\(916\) 0 0
\(917\) 48.8604 1.61351
\(918\) 0 0
\(919\) 43.2414i 1.42640i 0.700960 + 0.713201i \(0.252755\pi\)
−0.700960 + 0.713201i \(0.747245\pi\)
\(920\) 0 0
\(921\) 7.34582 0.506210i 0.242053 0.0166802i
\(922\) 0 0
\(923\) −1.97574 0.348377i −0.0650324 0.0114670i
\(924\) 0 0
\(925\) 2.00323 + 2.38736i 0.0658659 + 0.0784960i
\(926\) 0 0
\(927\) −8.86199 + 14.1186i −0.291066 + 0.463714i
\(928\) 0 0
\(929\) −4.34064 + 0.765372i −0.142412 + 0.0251111i −0.244400 0.969675i \(-0.578591\pi\)
0.101988 + 0.994786i \(0.467480\pi\)
\(930\) 0 0
\(931\) 8.59796 3.12940i 0.281787 0.102562i
\(932\) 0 0
\(933\) 2.68084 + 1.95189i 0.0877668 + 0.0639020i
\(934\) 0 0
\(935\) −13.7366 + 23.7925i −0.449236 + 0.778099i
\(936\) 0 0
\(937\) 0.581707 + 1.00755i 0.0190035 + 0.0329151i 0.875371 0.483452i \(-0.160617\pi\)
−0.856367 + 0.516367i \(0.827284\pi\)
\(938\) 0 0
\(939\) 27.2028 26.2163i 0.887728 0.855537i
\(940\) 0 0
\(941\) 24.6581 + 20.6906i 0.803833 + 0.674496i 0.949127 0.314893i \(-0.101969\pi\)
−0.145295 + 0.989388i \(0.546413\pi\)
\(942\) 0 0
\(943\) 5.64228 15.5021i 0.183738 0.504816i
\(944\) 0 0
\(945\) −38.4964 + 34.4516i −1.25229 + 1.12071i
\(946\) 0 0
\(947\) 9.21146 25.3083i 0.299332 0.822408i −0.695280 0.718739i \(-0.744719\pi\)
0.994612 0.103669i \(-0.0330583\pi\)
\(948\) 0 0
\(949\) −4.29861 + 5.12288i −0.139539 + 0.166296i
\(950\) 0 0
\(951\) 0.993520 + 0.285974i 0.0322171 + 0.00927335i
\(952\) 0 0
\(953\) −24.2787 + 14.0173i −0.786465 + 0.454066i −0.838717 0.544568i \(-0.816694\pi\)
0.0522513 + 0.998634i \(0.483360\pi\)
\(954\) 0 0
\(955\) −1.68565 + 2.91963i −0.0545464 + 0.0944771i
\(956\) 0 0
\(957\) −12.9804 29.2339i −0.419596 0.944997i
\(958\) 0 0
\(959\) −51.9274 + 18.9000i −1.67682 + 0.610313i
\(960\) 0 0
\(961\) 5.29098 + 30.0066i 0.170677 + 0.967956i
\(962\) 0 0
\(963\) −32.9395 13.3859i −1.06146 0.431355i
\(964\) 0 0
\(965\) 1.24708 1.04642i 0.0401449 0.0336856i
\(966\) 0 0
\(967\) −46.5149 8.20184i −1.49582 0.263753i −0.634940 0.772562i \(-0.718975\pi\)
−0.860880 + 0.508809i \(0.830086\pi\)
\(968\) 0 0
\(969\) 17.8789 12.0332i 0.574352 0.386561i
\(970\) 0 0
\(971\) 3.24802i 0.104234i −0.998641 0.0521170i \(-0.983403\pi\)
0.998641 0.0521170i \(-0.0165969\pi\)
\(972\) 0 0
\(973\) 2.26515i 0.0726173i
\(974\) 0 0
\(975\) 5.49015 3.69509i 0.175826 0.118337i
\(976\) 0 0
\(977\) 25.4482 + 4.48720i 0.814160 + 0.143558i 0.565198 0.824955i \(-0.308800\pi\)
0.248962 + 0.968513i \(0.419911\pi\)
\(978\) 0 0
\(979\) 42.1267 35.3485i 1.34637 1.12974i
\(980\) 0 0
\(981\) 15.5875 + 6.33446i 0.497672 + 0.202244i
\(982\) 0 0
\(983\) 5.64306 + 32.0034i 0.179986 + 1.02075i 0.932230 + 0.361866i \(0.117860\pi\)
−0.752244 + 0.658884i \(0.771029\pi\)
\(984\) 0 0
\(985\) 38.7405 14.1004i 1.23438 0.449276i
\(986\) 0 0
\(987\) 10.4747 + 23.5908i 0.333415 + 0.750904i
\(988\) 0 0
\(989\) 25.5381 44.2332i 0.812063 1.40653i
\(990\) 0 0
\(991\) 4.42071 2.55230i 0.140429 0.0810765i −0.428140 0.903713i \(-0.640831\pi\)
0.568568 + 0.822636i \(0.307498\pi\)
\(992\) 0 0
\(993\) −7.07422 2.03624i −0.224494 0.0646181i
\(994\) 0 0
\(995\) −29.4164 + 35.0571i −0.932562 + 1.11138i
\(996\) 0 0
\(997\) 11.4461 31.4478i 0.362501 0.995963i −0.615641 0.788026i \(-0.711103\pi\)
0.978142 0.207937i \(-0.0666748\pi\)
\(998\) 0 0
\(999\) −2.40763 0.790364i −0.0761740 0.0250060i
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.239.9 192
4.3 odd 2 216.2.v.b.131.17 yes 192
8.3 odd 2 inner 864.2.bh.b.239.10 192
8.5 even 2 216.2.v.b.131.10 192
12.11 even 2 648.2.v.b.179.16 192
24.5 odd 2 648.2.v.b.179.23 192
27.20 odd 18 inner 864.2.bh.b.47.10 192
108.7 odd 18 648.2.v.b.467.23 192
108.47 even 18 216.2.v.b.155.10 yes 192
216.61 even 18 648.2.v.b.467.16 192
216.101 odd 18 216.2.v.b.155.17 yes 192
216.155 even 18 inner 864.2.bh.b.47.9 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.131.10 192 8.5 even 2
216.2.v.b.131.17 yes 192 4.3 odd 2
216.2.v.b.155.10 yes 192 108.47 even 18
216.2.v.b.155.17 yes 192 216.101 odd 18
648.2.v.b.179.16 192 12.11 even 2
648.2.v.b.179.23 192 24.5 odd 2
648.2.v.b.467.16 192 216.61 even 18
648.2.v.b.467.23 192 108.7 odd 18
864.2.bh.b.47.9 192 216.155 even 18 inner
864.2.bh.b.47.10 192 27.20 odd 18 inner
864.2.bh.b.239.9 192 1.1 even 1 trivial
864.2.bh.b.239.10 192 8.3 odd 2 inner