Properties

Label 864.2.bh.b.47.15
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 47.15
Character \(\chi\) \(=\) 864.47
Dual form 864.2.bh.b.239.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0100749 - 1.73202i) q^{3} +(-0.710827 - 4.03130i) q^{5} +(-0.183548 + 0.218744i) q^{7} +(-2.99980 - 0.0348998i) q^{9} +O(q^{10})\) \(q+(0.0100749 - 1.73202i) q^{3} +(-0.710827 - 4.03130i) q^{5} +(-0.183548 + 0.218744i) q^{7} +(-2.99980 - 0.0348998i) q^{9} +(-1.72450 - 0.304076i) q^{11} +(1.16532 - 3.20170i) q^{13} +(-6.98946 + 1.19055i) q^{15} +(4.91624 - 2.83839i) q^{17} +(-3.46260 + 5.99739i) q^{19} +(0.377021 + 0.320113i) q^{21} +(3.02493 - 2.53822i) q^{23} +(-11.0476 + 4.02101i) q^{25} +(-0.0906699 + 5.19536i) q^{27} +(-1.90156 + 0.692110i) q^{29} +(-2.53206 - 3.01760i) q^{31} +(-0.544040 + 2.98381i) q^{33} +(1.01229 + 0.584449i) q^{35} +(5.14294 - 2.96928i) q^{37} +(-5.53368 - 2.05062i) q^{39} +(-0.535228 + 1.47053i) q^{41} +(-0.0461253 + 0.261589i) q^{43} +(1.99164 + 12.1179i) q^{45} +(4.77762 + 4.00890i) q^{47} +(1.20138 + 6.81335i) q^{49} +(-4.86662 - 8.54363i) q^{51} -5.82891 q^{53} +7.16812i q^{55} +(10.3527 + 6.05771i) q^{57} +(4.26158 - 0.751431i) q^{59} +(-4.79887 + 5.71906i) q^{61} +(0.558242 - 0.649783i) q^{63} +(-13.7354 - 2.42191i) q^{65} +(0.743215 + 0.270508i) q^{67} +(-4.36577 - 5.26482i) q^{69} +(-5.39967 - 9.35250i) q^{71} +(-0.194878 + 0.337539i) q^{73} +(6.85317 + 19.1753i) q^{75} +(0.383044 - 0.321412i) q^{77} +(-4.44109 - 12.2018i) q^{79} +(8.99756 + 0.209385i) q^{81} +(-0.720133 - 1.97855i) q^{83} +(-14.9370 - 17.8012i) q^{85} +(1.17959 + 3.30051i) q^{87} +(-1.61708 - 0.933622i) q^{89} +(0.486461 + 0.842575i) q^{91} +(-5.25205 + 4.35519i) q^{93} +(26.6386 + 9.69565i) q^{95} +(2.86855 - 16.2684i) q^{97} +(5.16254 + 0.972351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 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
\(3\) 0.0100749 1.73202i 0.00581674 0.999983i
\(4\) 0 0
\(5\) −0.710827 4.03130i −0.317891 1.80285i −0.555528 0.831498i \(-0.687484\pi\)
0.237637 0.971354i \(-0.423627\pi\)
\(6\) 0 0
\(7\) −0.183548 + 0.218744i −0.0693747 + 0.0826776i −0.799616 0.600512i \(-0.794963\pi\)
0.730241 + 0.683190i \(0.239408\pi\)
\(8\) 0 0
\(9\) −2.99980 0.0348998i −0.999932 0.0116333i
\(10\) 0 0
\(11\) −1.72450 0.304076i −0.519957 0.0916824i −0.0924901 0.995714i \(-0.529483\pi\)
−0.427466 + 0.904031i \(0.640594\pi\)
\(12\) 0 0
\(13\) 1.16532 3.20170i 0.323203 0.887992i −0.666583 0.745431i \(-0.732244\pi\)
0.989786 0.142562i \(-0.0455339\pi\)
\(14\) 0 0
\(15\) −6.98946 + 1.19055i −1.80467 + 0.307399i
\(16\) 0 0
\(17\) 4.91624 2.83839i 1.19236 0.688411i 0.233521 0.972352i \(-0.424975\pi\)
0.958842 + 0.283941i \(0.0916419\pi\)
\(18\) 0 0
\(19\) −3.46260 + 5.99739i −0.794374 + 1.37590i 0.128862 + 0.991663i \(0.458868\pi\)
−0.923236 + 0.384234i \(0.874466\pi\)
\(20\) 0 0
\(21\) 0.377021 + 0.320113i 0.0822727 + 0.0698545i
\(22\) 0 0
\(23\) 3.02493 2.53822i 0.630742 0.529255i −0.270417 0.962743i \(-0.587162\pi\)
0.901159 + 0.433488i \(0.142717\pi\)
\(24\) 0 0
\(25\) −11.0476 + 4.02101i −2.20953 + 0.804202i
\(26\) 0 0
\(27\) −0.0906699 + 5.19536i −0.0174494 + 0.999848i
\(28\) 0 0
\(29\) −1.90156 + 0.692110i −0.353110 + 0.128522i −0.512484 0.858697i \(-0.671275\pi\)
0.159374 + 0.987218i \(0.449052\pi\)
\(30\) 0 0
\(31\) −2.53206 3.01760i −0.454772 0.541976i 0.489126 0.872213i \(-0.337316\pi\)
−0.943898 + 0.330237i \(0.892871\pi\)
\(32\) 0 0
\(33\) −0.544040 + 2.98381i −0.0947053 + 0.519414i
\(34\) 0 0
\(35\) 1.01229 + 0.584449i 0.171109 + 0.0987899i
\(36\) 0 0
\(37\) 5.14294 2.96928i 0.845494 0.488146i −0.0136340 0.999907i \(-0.504340\pi\)
0.859128 + 0.511761i \(0.171007\pi\)
\(38\) 0 0
\(39\) −5.53368 2.05062i −0.886097 0.328363i
\(40\) 0 0
\(41\) −0.535228 + 1.47053i −0.0835886 + 0.229658i −0.974445 0.224628i \(-0.927883\pi\)
0.890856 + 0.454286i \(0.150106\pi\)
\(42\) 0 0
\(43\) −0.0461253 + 0.261589i −0.00703404 + 0.0398920i −0.988123 0.153667i \(-0.950892\pi\)
0.981089 + 0.193559i \(0.0620029\pi\)
\(44\) 0 0
\(45\) 1.99164 + 12.1179i 0.296897 + 1.80643i
\(46\) 0 0
\(47\) 4.77762 + 4.00890i 0.696888 + 0.584759i 0.920886 0.389831i \(-0.127467\pi\)
−0.223998 + 0.974590i \(0.571911\pi\)
\(48\) 0 0
\(49\) 1.20138 + 6.81335i 0.171625 + 0.973336i
\(50\) 0 0
\(51\) −4.86662 8.54363i −0.681464 1.19635i
\(52\) 0 0
\(53\) −5.82891 −0.800662 −0.400331 0.916371i \(-0.631105\pi\)
−0.400331 + 0.916371i \(0.631105\pi\)
\(54\) 0 0
\(55\) 7.16812i 0.966550i
\(56\) 0 0
\(57\) 10.3527 + 6.05771i 1.37125 + 0.802364i
\(58\) 0 0
\(59\) 4.26158 0.751431i 0.554810 0.0978280i 0.110788 0.993844i \(-0.464662\pi\)
0.444022 + 0.896016i \(0.353551\pi\)
\(60\) 0 0
\(61\) −4.79887 + 5.71906i −0.614432 + 0.732251i −0.980102 0.198493i \(-0.936395\pi\)
0.365671 + 0.930744i \(0.380840\pi\)
\(62\) 0 0
\(63\) 0.558242 0.649783i 0.0703318 0.0818649i
\(64\) 0 0
\(65\) −13.7354 2.42191i −1.70366 0.300402i
\(66\) 0 0
\(67\) 0.743215 + 0.270508i 0.0907981 + 0.0330478i 0.387020 0.922071i \(-0.373504\pi\)
−0.296222 + 0.955119i \(0.595727\pi\)
\(68\) 0 0
\(69\) −4.36577 5.26482i −0.525578 0.633810i
\(70\) 0 0
\(71\) −5.39967 9.35250i −0.640823 1.10994i −0.985249 0.171124i \(-0.945260\pi\)
0.344427 0.938813i \(-0.388073\pi\)
\(72\) 0 0
\(73\) −0.194878 + 0.337539i −0.0228088 + 0.0395060i −0.877205 0.480117i \(-0.840594\pi\)
0.854396 + 0.519623i \(0.173928\pi\)
\(74\) 0 0
\(75\) 6.85317 + 19.1753i 0.791336 + 2.21417i
\(76\) 0 0
\(77\) 0.383044 0.321412i 0.0436519 0.0366283i
\(78\) 0 0
\(79\) −4.44109 12.2018i −0.499661 1.37281i −0.891603 0.452818i \(-0.850419\pi\)
0.391942 0.919990i \(-0.371804\pi\)
\(80\) 0 0
\(81\) 8.99756 + 0.209385i 0.999729 + 0.0232650i
\(82\) 0 0
\(83\) −0.720133 1.97855i −0.0790448 0.217174i 0.893875 0.448316i \(-0.147976\pi\)
−0.972920 + 0.231142i \(0.925754\pi\)
\(84\) 0 0
\(85\) −14.9370 17.8012i −1.62015 1.93081i
\(86\) 0 0
\(87\) 1.17959 + 3.30051i 0.126465 + 0.353852i
\(88\) 0 0
\(89\) −1.61708 0.933622i −0.171410 0.0989637i 0.411840 0.911256i \(-0.364886\pi\)
−0.583251 + 0.812292i \(0.698219\pi\)
\(90\) 0 0
\(91\) 0.486461 + 0.842575i 0.0509950 + 0.0883258i
\(92\) 0 0
\(93\) −5.25205 + 4.35519i −0.544612 + 0.451612i
\(94\) 0 0
\(95\) 26.6386 + 9.69565i 2.73306 + 0.994753i
\(96\) 0 0
\(97\) 2.86855 16.2684i 0.291257 1.65180i −0.390780 0.920484i \(-0.627795\pi\)
0.682037 0.731318i \(-0.261094\pi\)
\(98\) 0 0
\(99\) 5.16254 + 0.972351i 0.518855 + 0.0977250i
\(100\) 0 0
\(101\) −0.0683785 0.0573764i −0.00680391 0.00570916i 0.639379 0.768891i \(-0.279191\pi\)
−0.646183 + 0.763182i \(0.723636\pi\)
\(102\) 0 0
\(103\) −11.0453 + 1.94759i −1.08833 + 0.191901i −0.688895 0.724861i \(-0.741904\pi\)
−0.399432 + 0.916763i \(0.630793\pi\)
\(104\) 0 0
\(105\) 1.02248 1.74743i 0.0997835 0.170532i
\(106\) 0 0
\(107\) 10.2098i 0.987019i −0.869740 0.493510i \(-0.835714\pi\)
0.869740 0.493510i \(-0.164286\pi\)
\(108\) 0 0
\(109\) 8.75424i 0.838504i −0.907870 0.419252i \(-0.862292\pi\)
0.907870 0.419252i \(-0.137708\pi\)
\(110\) 0 0
\(111\) −5.09104 8.93760i −0.483220 0.848319i
\(112\) 0 0
\(113\) 16.0414 2.82854i 1.50905 0.266086i 0.642931 0.765924i \(-0.277718\pi\)
0.866119 + 0.499837i \(0.166607\pi\)
\(114\) 0 0
\(115\) −12.3825 10.3902i −1.15468 0.968889i
\(116\) 0 0
\(117\) −3.60747 + 9.56379i −0.333511 + 0.884172i
\(118\) 0 0
\(119\) −0.281485 + 1.59638i −0.0258037 + 0.146340i
\(120\) 0 0
\(121\) −7.45518 2.71346i −0.677743 0.246678i
\(122\) 0 0
\(123\) 2.54159 + 0.941842i 0.229168 + 0.0849231i
\(124\) 0 0
\(125\) 13.8291 + 23.9528i 1.23692 + 2.14240i
\(126\) 0 0
\(127\) 0.766625 + 0.442611i 0.0680270 + 0.0392754i 0.533628 0.845719i \(-0.320828\pi\)
−0.465601 + 0.884995i \(0.654162\pi\)
\(128\) 0 0
\(129\) 0.452614 + 0.0825254i 0.0398504 + 0.00726596i
\(130\) 0 0
\(131\) −12.7169 15.1554i −1.11108 1.32414i −0.940885 0.338726i \(-0.890004\pi\)
−0.170197 0.985410i \(-0.554440\pi\)
\(132\) 0 0
\(133\) −0.676342 1.85823i −0.0586463 0.161129i
\(134\) 0 0
\(135\) 21.0085 3.32748i 1.80812 0.286384i
\(136\) 0 0
\(137\) 0.0756258 + 0.207780i 0.00646115 + 0.0177519i 0.942881 0.333129i \(-0.108104\pi\)
−0.936420 + 0.350881i \(0.885882\pi\)
\(138\) 0 0
\(139\) −5.07052 + 4.25467i −0.430076 + 0.360876i −0.831980 0.554805i \(-0.812793\pi\)
0.401905 + 0.915682i \(0.368348\pi\)
\(140\) 0 0
\(141\) 6.99164 8.23456i 0.588802 0.693475i
\(142\) 0 0
\(143\) −2.98316 + 5.16699i −0.249465 + 0.432085i
\(144\) 0 0
\(145\) 4.14178 + 7.17377i 0.343956 + 0.595749i
\(146\) 0 0
\(147\) 11.8130 2.01217i 0.974318 0.165961i
\(148\) 0 0
\(149\) 16.6006 + 6.04213i 1.35998 + 0.494991i 0.916047 0.401071i \(-0.131362\pi\)
0.443929 + 0.896062i \(0.353584\pi\)
\(150\) 0 0
\(151\) 9.59083 + 1.69112i 0.780491 + 0.137622i 0.549678 0.835377i \(-0.314750\pi\)
0.230813 + 0.972998i \(0.425862\pi\)
\(152\) 0 0
\(153\) −14.8468 + 8.34302i −1.20029 + 0.674493i
\(154\) 0 0
\(155\) −10.3650 + 12.3525i −0.832535 + 0.992176i
\(156\) 0 0
\(157\) 3.00447 0.529770i 0.239783 0.0422802i −0.0524650 0.998623i \(-0.516708\pi\)
0.292248 + 0.956343i \(0.405597\pi\)
\(158\) 0 0
\(159\) −0.0587256 + 10.0958i −0.00465724 + 0.800649i
\(160\) 0 0
\(161\) 1.12757i 0.0888652i
\(162\) 0 0
\(163\) 2.38504 0.186811 0.0934053 0.995628i \(-0.470225\pi\)
0.0934053 + 0.995628i \(0.470225\pi\)
\(164\) 0 0
\(165\) 12.4153 + 0.0722180i 0.966533 + 0.00562217i
\(166\) 0 0
\(167\) −1.11048 6.29787i −0.0859319 0.487344i −0.997152 0.0754233i \(-0.975969\pi\)
0.911220 0.411921i \(-0.135142\pi\)
\(168\) 0 0
\(169\) 1.06566 + 0.894199i 0.0819742 + 0.0687845i
\(170\) 0 0
\(171\) 10.5964 17.8701i 0.810326 1.36656i
\(172\) 0 0
\(173\) 1.92057 10.8921i 0.146018 0.828110i −0.820526 0.571609i \(-0.806319\pi\)
0.966544 0.256501i \(-0.0825695\pi\)
\(174\) 0 0
\(175\) 1.14820 3.15466i 0.0867959 0.238470i
\(176\) 0 0
\(177\) −1.25856 7.38871i −0.0945991 0.555370i
\(178\) 0 0
\(179\) 20.8325 12.0276i 1.55709 0.898987i 0.559558 0.828791i \(-0.310971\pi\)
0.997533 0.0701962i \(-0.0223625\pi\)
\(180\) 0 0
\(181\) 16.0634 + 9.27419i 1.19398 + 0.689345i 0.959207 0.282705i \(-0.0912316\pi\)
0.234774 + 0.972050i \(0.424565\pi\)
\(182\) 0 0
\(183\) 9.85720 + 8.36936i 0.728665 + 0.618681i
\(184\) 0 0
\(185\) −15.6258 18.6221i −1.14883 1.36912i
\(186\) 0 0
\(187\) −9.34114 + 3.39990i −0.683092 + 0.248625i
\(188\) 0 0
\(189\) −1.11981 0.973433i −0.0814544 0.0708068i
\(190\) 0 0
\(191\) −6.74802 + 2.45608i −0.488270 + 0.177716i −0.574411 0.818567i \(-0.694769\pi\)
0.0861410 + 0.996283i \(0.472546\pi\)
\(192\) 0 0
\(193\) −2.83658 + 2.38017i −0.204182 + 0.171329i −0.739145 0.673547i \(-0.764770\pi\)
0.534963 + 0.844875i \(0.320326\pi\)
\(194\) 0 0
\(195\) −4.33319 + 23.7655i −0.310306 + 1.70189i
\(196\) 0 0
\(197\) −0.837761 + 1.45104i −0.0596880 + 0.103383i −0.894325 0.447417i \(-0.852344\pi\)
0.834637 + 0.550800i \(0.185677\pi\)
\(198\) 0 0
\(199\) −13.6618 + 7.88767i −0.968462 + 0.559142i −0.898767 0.438426i \(-0.855536\pi\)
−0.0696952 + 0.997568i \(0.522203\pi\)
\(200\) 0 0
\(201\) 0.476014 1.28454i 0.0335754 0.0906044i
\(202\) 0 0
\(203\) 0.197632 0.542990i 0.0138711 0.0381104i
\(204\) 0 0
\(205\) 6.30859 + 1.11237i 0.440611 + 0.0776916i
\(206\) 0 0
\(207\) −9.16277 + 7.50857i −0.636856 + 0.521882i
\(208\) 0 0
\(209\) 7.79491 9.28962i 0.539185 0.642576i
\(210\) 0 0
\(211\) 0.579130 + 3.28441i 0.0398690 + 0.226108i 0.998232 0.0594461i \(-0.0189335\pi\)
−0.958363 + 0.285554i \(0.907822\pi\)
\(212\) 0 0
\(213\) −16.2531 + 9.25812i −1.11365 + 0.634356i
\(214\) 0 0
\(215\) 1.08733 0.0741554
\(216\) 0 0
\(217\) 1.12484 0.0763590
\(218\) 0 0
\(219\) 0.582662 + 0.340934i 0.0393727 + 0.0230382i
\(220\) 0 0
\(221\) −3.35867 19.0480i −0.225929 1.28131i
\(222\) 0 0
\(223\) 17.2863 20.6010i 1.15757 1.37954i 0.245562 0.969381i \(-0.421027\pi\)
0.912012 0.410163i \(-0.134528\pi\)
\(224\) 0 0
\(225\) 33.2810 11.6767i 2.21873 0.778444i
\(226\) 0 0
\(227\) 7.12707 + 1.25669i 0.473040 + 0.0834098i 0.405086 0.914279i \(-0.367242\pi\)
0.0679544 + 0.997688i \(0.478353\pi\)
\(228\) 0 0
\(229\) −4.81653 + 13.2333i −0.318286 + 0.874482i 0.672628 + 0.739981i \(0.265166\pi\)
−0.990913 + 0.134501i \(0.957057\pi\)
\(230\) 0 0
\(231\) −0.552834 0.666679i −0.0363738 0.0438642i
\(232\) 0 0
\(233\) −3.43407 + 1.98266i −0.224974 + 0.129889i −0.608251 0.793745i \(-0.708129\pi\)
0.383278 + 0.923633i \(0.374795\pi\)
\(234\) 0 0
\(235\) 12.7650 22.1097i 0.832698 1.44228i
\(236\) 0 0
\(237\) −21.1785 + 7.56913i −1.37569 + 0.491668i
\(238\) 0 0
\(239\) −6.58643 + 5.52667i −0.426041 + 0.357491i −0.830456 0.557085i \(-0.811920\pi\)
0.404415 + 0.914576i \(0.367475\pi\)
\(240\) 0 0
\(241\) −6.35562 + 2.31326i −0.409401 + 0.149010i −0.538507 0.842621i \(-0.681012\pi\)
0.129106 + 0.991631i \(0.458789\pi\)
\(242\) 0 0
\(243\) 0.453309 15.5819i 0.0290798 0.999577i
\(244\) 0 0
\(245\) 26.6127 9.68623i 1.70022 0.618831i
\(246\) 0 0
\(247\) 15.1668 + 18.0751i 0.965041 + 1.15009i
\(248\) 0 0
\(249\) −3.43414 + 1.22735i −0.217630 + 0.0777803i
\(250\) 0 0
\(251\) 9.52905 + 5.50160i 0.601469 + 0.347258i 0.769619 0.638503i \(-0.220446\pi\)
−0.168151 + 0.985761i \(0.553779\pi\)
\(252\) 0 0
\(253\) −5.98831 + 3.45735i −0.376482 + 0.217362i
\(254\) 0 0
\(255\) −30.9826 + 25.6919i −1.94020 + 1.60889i
\(256\) 0 0
\(257\) 2.14513 5.89371i 0.133810 0.367640i −0.854633 0.519232i \(-0.826218\pi\)
0.988443 + 0.151593i \(0.0484402\pi\)
\(258\) 0 0
\(259\) −0.294465 + 1.66999i −0.0182972 + 0.103768i
\(260\) 0 0
\(261\) 5.72844 2.00982i 0.354581 0.124405i
\(262\) 0 0
\(263\) −18.7660 15.7466i −1.15716 0.970975i −0.157301 0.987551i \(-0.550279\pi\)
−0.999863 + 0.0165753i \(0.994724\pi\)
\(264\) 0 0
\(265\) 4.14335 + 23.4981i 0.254524 + 1.44348i
\(266\) 0 0
\(267\) −1.63335 + 2.79141i −0.0999591 + 0.170832i
\(268\) 0 0
\(269\) 11.2760 0.687508 0.343754 0.939060i \(-0.388301\pi\)
0.343754 + 0.939060i \(0.388301\pi\)
\(270\) 0 0
\(271\) 8.04477i 0.488685i −0.969689 0.244343i \(-0.921428\pi\)
0.969689 0.244343i \(-0.0785721\pi\)
\(272\) 0 0
\(273\) 1.46426 0.834072i 0.0886210 0.0504803i
\(274\) 0 0
\(275\) 20.2744 3.57492i 1.22259 0.215575i
\(276\) 0 0
\(277\) 6.95949 8.29400i 0.418155 0.498338i −0.515311 0.857003i \(-0.672324\pi\)
0.933466 + 0.358665i \(0.116768\pi\)
\(278\) 0 0
\(279\) 7.49036 + 9.14054i 0.448436 + 0.547230i
\(280\) 0 0
\(281\) 10.2657 + 1.81011i 0.612399 + 0.107982i 0.471241 0.882005i \(-0.343806\pi\)
0.141158 + 0.989987i \(0.454917\pi\)
\(282\) 0 0
\(283\) 5.61267 + 2.04285i 0.333639 + 0.121435i 0.503407 0.864049i \(-0.332080\pi\)
−0.169768 + 0.985484i \(0.554302\pi\)
\(284\) 0 0
\(285\) 17.0615 46.0409i 1.01063 2.72723i
\(286\) 0 0
\(287\) −0.223429 0.386991i −0.0131886 0.0228434i
\(288\) 0 0
\(289\) 7.61293 13.1860i 0.447819 0.775646i
\(290\) 0 0
\(291\) −28.1482 5.13229i −1.65008 0.300860i
\(292\) 0 0
\(293\) −20.4054 + 17.1222i −1.19210 + 1.00029i −0.192275 + 0.981341i \(0.561587\pi\)
−0.999821 + 0.0189459i \(0.993969\pi\)
\(294\) 0 0
\(295\) −6.05849 16.6456i −0.352739 0.969142i
\(296\) 0 0
\(297\) 1.73615 8.93183i 0.100741 0.518278i
\(298\) 0 0
\(299\) −4.60160 12.6428i −0.266117 0.731151i
\(300\) 0 0
\(301\) −0.0487550 0.0581039i −0.00281019 0.00334905i
\(302\) 0 0
\(303\) −0.100066 + 0.117855i −0.00574864 + 0.00677059i
\(304\) 0 0
\(305\) 26.4664 + 15.2804i 1.51546 + 0.874953i
\(306\) 0 0
\(307\) 5.60040 + 9.70017i 0.319632 + 0.553618i 0.980411 0.196962i \(-0.0631075\pi\)
−0.660780 + 0.750580i \(0.729774\pi\)
\(308\) 0 0
\(309\) 3.26198 + 19.1503i 0.185568 + 1.08943i
\(310\) 0 0
\(311\) 7.17205 + 2.61041i 0.406690 + 0.148023i 0.537261 0.843416i \(-0.319459\pi\)
−0.130571 + 0.991439i \(0.541681\pi\)
\(312\) 0 0
\(313\) −0.157445 + 0.892917i −0.00889933 + 0.0504706i −0.988934 0.148356i \(-0.952602\pi\)
0.980035 + 0.198826i \(0.0637130\pi\)
\(314\) 0 0
\(315\) −3.01628 1.78856i −0.169948 0.100774i
\(316\) 0 0
\(317\) −20.1111 16.8752i −1.12955 0.947806i −0.130504 0.991448i \(-0.541659\pi\)
−0.999047 + 0.0436420i \(0.986104\pi\)
\(318\) 0 0
\(319\) 3.48969 0.615326i 0.195385 0.0344516i
\(320\) 0 0
\(321\) −17.6836 0.102863i −0.987003 0.00574123i
\(322\) 0 0
\(323\) 39.3128i 2.18742i
\(324\) 0 0
\(325\) 40.0570i 2.22196i
\(326\) 0 0
\(327\) −15.1625 0.0881980i −0.838490 0.00487736i
\(328\) 0 0
\(329\) −1.75385 + 0.309251i −0.0966929 + 0.0170496i
\(330\) 0 0
\(331\) 16.2372 + 13.6246i 0.892477 + 0.748877i 0.968705 0.248213i \(-0.0798434\pi\)
−0.0762285 + 0.997090i \(0.524288\pi\)
\(332\) 0 0
\(333\) −15.5314 + 8.72774i −0.851115 + 0.478277i
\(334\) 0 0
\(335\) 0.562202 3.18841i 0.0307164 0.174201i
\(336\) 0 0
\(337\) −2.22733 0.810682i −0.121330 0.0441606i 0.280641 0.959813i \(-0.409453\pi\)
−0.401972 + 0.915652i \(0.631675\pi\)
\(338\) 0 0
\(339\) −4.73747 27.8126i −0.257304 1.51057i
\(340\) 0 0
\(341\) 3.44897 + 5.97379i 0.186772 + 0.323499i
\(342\) 0 0
\(343\) −3.44195 1.98721i −0.185848 0.107299i
\(344\) 0 0
\(345\) −18.1208 + 21.3421i −0.975589 + 1.14902i
\(346\) 0 0
\(347\) −13.7753 16.4167i −0.739496 0.881297i 0.256873 0.966445i \(-0.417308\pi\)
−0.996368 + 0.0851487i \(0.972863\pi\)
\(348\) 0 0
\(349\) −0.388725 1.06801i −0.0208080 0.0571694i 0.928854 0.370447i \(-0.120795\pi\)
−0.949662 + 0.313277i \(0.898573\pi\)
\(350\) 0 0
\(351\) 16.5283 + 6.34458i 0.882217 + 0.338649i
\(352\) 0 0
\(353\) 3.26744 + 8.97721i 0.173908 + 0.477809i 0.995770 0.0918778i \(-0.0292869\pi\)
−0.821862 + 0.569686i \(0.807065\pi\)
\(354\) 0 0
\(355\) −33.8645 + 28.4157i −1.79734 + 1.50815i
\(356\) 0 0
\(357\) 2.76213 + 0.503622i 0.146187 + 0.0266545i
\(358\) 0 0
\(359\) −14.6607 + 25.3930i −0.773760 + 1.34019i 0.161729 + 0.986835i \(0.448293\pi\)
−0.935489 + 0.353356i \(0.885040\pi\)
\(360\) 0 0
\(361\) −14.4791 25.0786i −0.762060 1.31993i
\(362\) 0 0
\(363\) −4.77489 + 12.8852i −0.250617 + 0.676297i
\(364\) 0 0
\(365\) 1.49925 + 0.545681i 0.0784742 + 0.0285623i
\(366\) 0 0
\(367\) 18.4024 + 3.24484i 0.960599 + 0.169379i 0.631895 0.775054i \(-0.282277\pi\)
0.328703 + 0.944433i \(0.393388\pi\)
\(368\) 0 0
\(369\) 1.65690 4.39260i 0.0862546 0.228670i
\(370\) 0 0
\(371\) 1.06989 1.27504i 0.0555457 0.0661968i
\(372\) 0 0
\(373\) −31.6158 + 5.57471i −1.63700 + 0.288648i −0.915063 0.403310i \(-0.867860\pi\)
−0.721938 + 0.691958i \(0.756748\pi\)
\(374\) 0 0
\(375\) 41.6260 23.7110i 2.14956 1.22443i
\(376\) 0 0
\(377\) 6.89475i 0.355097i
\(378\) 0 0
\(379\) 22.2516 1.14299 0.571494 0.820606i \(-0.306364\pi\)
0.571494 + 0.820606i \(0.306364\pi\)
\(380\) 0 0
\(381\) 0.774336 1.32335i 0.0396704 0.0677974i
\(382\) 0 0
\(383\) −2.21165 12.5429i −0.113010 0.640911i −0.987716 0.156258i \(-0.950057\pi\)
0.874706 0.484653i \(-0.161054\pi\)
\(384\) 0 0
\(385\) −1.56799 1.31570i −0.0799120 0.0670541i
\(386\) 0 0
\(387\) 0.147496 0.783105i 0.00749763 0.0398075i
\(388\) 0 0
\(389\) 4.88879 27.7257i 0.247872 1.40575i −0.565856 0.824504i \(-0.691454\pi\)
0.813728 0.581246i \(-0.197435\pi\)
\(390\) 0 0
\(391\) 7.66683 21.0644i 0.387728 1.06527i
\(392\) 0 0
\(393\) −26.3777 + 21.8733i −1.33058 + 1.10336i
\(394\) 0 0
\(395\) −46.0322 + 26.5767i −2.31613 + 1.33722i
\(396\) 0 0
\(397\) −18.6821 10.7861i −0.937626 0.541339i −0.0484110 0.998828i \(-0.515416\pi\)
−0.889215 + 0.457489i \(0.848749\pi\)
\(398\) 0 0
\(399\) −3.22532 + 1.15272i −0.161468 + 0.0577080i
\(400\) 0 0
\(401\) −16.6424 19.8336i −0.831079 0.990442i −0.999988 0.00481031i \(-0.998469\pi\)
0.168909 0.985632i \(-0.445976\pi\)
\(402\) 0 0
\(403\) −12.6121 + 4.59043i −0.628254 + 0.228666i
\(404\) 0 0
\(405\) −5.55162 36.4207i −0.275862 1.80976i
\(406\) 0 0
\(407\) −9.77189 + 3.55668i −0.484374 + 0.176298i
\(408\) 0 0
\(409\) −19.7032 + 16.5330i −0.974262 + 0.817502i −0.983214 0.182457i \(-0.941595\pi\)
0.00895224 + 0.999960i \(0.497150\pi\)
\(410\) 0 0
\(411\) 0.360642 0.128892i 0.0177891 0.00635778i
\(412\) 0 0
\(413\) −0.617834 + 1.07012i −0.0304016 + 0.0526571i
\(414\) 0 0
\(415\) −7.46423 + 4.30948i −0.366405 + 0.211544i
\(416\) 0 0
\(417\) 7.31809 + 8.82511i 0.358369 + 0.432168i
\(418\) 0 0
\(419\) 1.71802 4.72021i 0.0839305 0.230597i −0.890627 0.454734i \(-0.849734\pi\)
0.974558 + 0.224137i \(0.0719564\pi\)
\(420\) 0 0
\(421\) 29.5017 + 5.20195i 1.43783 + 0.253528i 0.837592 0.546296i \(-0.183963\pi\)
0.600235 + 0.799824i \(0.295074\pi\)
\(422\) 0 0
\(423\) −14.1920 12.1926i −0.690038 0.592826i
\(424\) 0 0
\(425\) −42.8996 + 51.1258i −2.08094 + 2.47996i
\(426\) 0 0
\(427\) −0.370190 2.09945i −0.0179147 0.101599i
\(428\) 0 0
\(429\) 8.91928 + 5.21896i 0.430627 + 0.251974i
\(430\) 0 0
\(431\) 28.3440 1.36528 0.682640 0.730754i \(-0.260832\pi\)
0.682640 + 0.730754i \(0.260832\pi\)
\(432\) 0 0
\(433\) 37.9757 1.82499 0.912497 0.409083i \(-0.134151\pi\)
0.912497 + 0.409083i \(0.134151\pi\)
\(434\) 0 0
\(435\) 12.4669 7.10137i 0.597740 0.340485i
\(436\) 0 0
\(437\) 4.74858 + 26.9305i 0.227155 + 1.28826i
\(438\) 0 0
\(439\) −7.33133 + 8.73714i −0.349905 + 0.417001i −0.912077 0.410020i \(-0.865522\pi\)
0.562171 + 0.827021i \(0.309966\pi\)
\(440\) 0 0
\(441\) −3.36611 20.4806i −0.160291 0.975267i
\(442\) 0 0
\(443\) −19.1408 3.37504i −0.909406 0.160353i −0.300672 0.953728i \(-0.597211\pi\)
−0.608734 + 0.793375i \(0.708322\pi\)
\(444\) 0 0
\(445\) −2.61425 + 7.18258i −0.123927 + 0.340487i
\(446\) 0 0
\(447\) 10.6324 28.6918i 0.502893 1.35707i
\(448\) 0 0
\(449\) 15.4365 8.91229i 0.728495 0.420597i −0.0893764 0.995998i \(-0.528487\pi\)
0.817871 + 0.575401i \(0.195154\pi\)
\(450\) 0 0
\(451\) 1.37015 2.37318i 0.0645180 0.111748i
\(452\) 0 0
\(453\) 3.02569 16.5945i 0.142159 0.779677i
\(454\) 0 0
\(455\) 3.05088 2.55999i 0.143028 0.120014i
\(456\) 0 0
\(457\) 14.7281 5.36059i 0.688952 0.250758i 0.0262653 0.999655i \(-0.491639\pi\)
0.662686 + 0.748897i \(0.269416\pi\)
\(458\) 0 0
\(459\) 14.3007 + 25.7990i 0.667500 + 1.20419i
\(460\) 0 0
\(461\) −26.7308 + 9.72920i −1.24498 + 0.453134i −0.878701 0.477373i \(-0.841589\pi\)
−0.366274 + 0.930507i \(0.619367\pi\)
\(462\) 0 0
\(463\) −4.52477 5.39241i −0.210284 0.250606i 0.650585 0.759433i \(-0.274524\pi\)
−0.860869 + 0.508827i \(0.830079\pi\)
\(464\) 0 0
\(465\) 21.2904 + 18.0768i 0.987317 + 0.838292i
\(466\) 0 0
\(467\) 9.49779 + 5.48355i 0.439505 + 0.253749i 0.703388 0.710806i \(-0.251670\pi\)
−0.263882 + 0.964555i \(0.585003\pi\)
\(468\) 0 0
\(469\) −0.195588 + 0.112923i −0.00903141 + 0.00521429i
\(470\) 0 0
\(471\) −0.887303 5.20915i −0.0408847 0.240025i
\(472\) 0 0
\(473\) 0.159086 0.437085i 0.00731479 0.0200972i
\(474\) 0 0
\(475\) 14.1379 80.1801i 0.648692 3.67892i
\(476\) 0 0
\(477\) 17.4855 + 0.203428i 0.800608 + 0.00931433i
\(478\) 0 0
\(479\) −18.9431 15.8951i −0.865530 0.726266i 0.0976217 0.995224i \(-0.468876\pi\)
−0.963152 + 0.268957i \(0.913321\pi\)
\(480\) 0 0
\(481\) −3.51355 19.9263i −0.160204 0.908562i
\(482\) 0 0
\(483\) 1.95298 + 0.0113602i 0.0888637 + 0.000516905i
\(484\) 0 0
\(485\) −67.6217 −3.07054
\(486\) 0 0
\(487\) 20.8260i 0.943714i 0.881675 + 0.471857i \(0.156416\pi\)
−0.881675 + 0.471857i \(0.843584\pi\)
\(488\) 0 0
\(489\) 0.0240290 4.13094i 0.00108663 0.186808i
\(490\) 0 0
\(491\) −17.3028 + 3.05095i −0.780865 + 0.137687i −0.549851 0.835263i \(-0.685315\pi\)
−0.231014 + 0.972950i \(0.574204\pi\)
\(492\) 0 0
\(493\) −7.38402 + 8.79993i −0.332560 + 0.396329i
\(494\) 0 0
\(495\) 0.250166 21.5029i 0.0112441 0.966484i
\(496\) 0 0
\(497\) 3.03691 + 0.535489i 0.136224 + 0.0240199i
\(498\) 0 0
\(499\) 8.48450 + 3.08810i 0.379818 + 0.138243i 0.524872 0.851181i \(-0.324113\pi\)
−0.145054 + 0.989424i \(0.546335\pi\)
\(500\) 0 0
\(501\) −10.9192 + 1.85993i −0.487835 + 0.0830957i
\(502\) 0 0
\(503\) −4.43613 7.68360i −0.197797 0.342595i 0.750017 0.661419i \(-0.230045\pi\)
−0.947814 + 0.318824i \(0.896712\pi\)
\(504\) 0 0
\(505\) −0.182696 + 0.316439i −0.00812987 + 0.0140813i
\(506\) 0 0
\(507\) 1.55951 1.83674i 0.0692602 0.0815727i
\(508\) 0 0
\(509\) 15.9153 13.3546i 0.705435 0.591930i −0.217879 0.975976i \(-0.569914\pi\)
0.923314 + 0.384046i \(0.125469\pi\)
\(510\) 0 0
\(511\) −0.0380652 0.104583i −0.00168391 0.00462649i
\(512\) 0 0
\(513\) −30.8447 18.5332i −1.36183 0.818262i
\(514\) 0 0
\(515\) 15.7026 + 43.1426i 0.691940 + 1.90109i
\(516\) 0 0
\(517\) −7.02001 8.36612i −0.308740 0.367941i
\(518\) 0 0
\(519\) −18.8460 3.43620i −0.827246 0.150833i
\(520\) 0 0
\(521\) −10.0938 5.82764i −0.442216 0.255314i 0.262321 0.964981i \(-0.415512\pi\)
−0.704537 + 0.709667i \(0.748845\pi\)
\(522\) 0 0
\(523\) −12.0754 20.9151i −0.528019 0.914555i −0.999466 0.0326613i \(-0.989602\pi\)
0.471448 0.881894i \(-0.343732\pi\)
\(524\) 0 0
\(525\) −5.45237 2.02049i −0.237961 0.0881815i
\(526\) 0 0
\(527\) −21.0133 7.64823i −0.915356 0.333162i
\(528\) 0 0
\(529\) −1.28625 + 7.29469i −0.0559240 + 0.317161i
\(530\) 0 0
\(531\) −12.8101 + 2.10541i −0.555910 + 0.0913671i
\(532\) 0 0
\(533\) 4.08448 + 3.42728i 0.176918 + 0.148452i
\(534\) 0 0
\(535\) −41.1588 + 7.25740i −1.77945 + 0.313765i
\(536\) 0 0
\(537\) −20.6222 36.2035i −0.889915 1.56229i
\(538\) 0 0
\(539\) 12.1149i 0.521828i
\(540\) 0 0
\(541\) 1.65438i 0.0711274i −0.999367 0.0355637i \(-0.988677\pi\)
0.999367 0.0355637i \(-0.0113227\pi\)
\(542\) 0 0
\(543\) 16.2249 27.7287i 0.696279 1.18995i
\(544\) 0 0
\(545\) −35.2910 + 6.22275i −1.51170 + 0.266553i
\(546\) 0 0
\(547\) 21.7235 + 18.2281i 0.928828 + 0.779379i 0.975607 0.219526i \(-0.0704511\pi\)
−0.0467786 + 0.998905i \(0.514896\pi\)
\(548\) 0 0
\(549\) 14.5952 16.9886i 0.622909 0.725054i
\(550\) 0 0
\(551\) 2.43347 13.8009i 0.103669 0.587937i
\(552\) 0 0
\(553\) 3.48423 + 1.26815i 0.148164 + 0.0539274i
\(554\) 0 0
\(555\) −32.4113 + 26.8766i −1.37578 + 1.14085i
\(556\) 0 0
\(557\) 9.50566 + 16.4643i 0.402768 + 0.697614i 0.994059 0.108844i \(-0.0347149\pi\)
−0.591291 + 0.806458i \(0.701382\pi\)
\(558\) 0 0
\(559\) 0.783780 + 0.452516i 0.0331504 + 0.0191394i
\(560\) 0 0
\(561\) 5.79459 + 16.2133i 0.244648 + 0.684527i
\(562\) 0 0
\(563\) 22.8594 + 27.2427i 0.963408 + 1.14814i 0.988917 + 0.148470i \(0.0474349\pi\)
−0.0255091 + 0.999675i \(0.508121\pi\)
\(564\) 0 0
\(565\) −22.8054 62.6572i −0.959429 2.63601i
\(566\) 0 0
\(567\) −1.69729 + 1.92973i −0.0712794 + 0.0810412i
\(568\) 0 0
\(569\) 0.493250 + 1.35519i 0.0206781 + 0.0568127i 0.949602 0.313457i \(-0.101487\pi\)
−0.928924 + 0.370270i \(0.879265\pi\)
\(570\) 0 0
\(571\) 21.1309 17.7309i 0.884300 0.742016i −0.0827583 0.996570i \(-0.526373\pi\)
0.967059 + 0.254554i \(0.0819285\pi\)
\(572\) 0 0
\(573\) 4.18599 + 11.7125i 0.174872 + 0.489295i
\(574\) 0 0
\(575\) −23.2121 + 40.2046i −0.968013 + 1.67665i
\(576\) 0 0
\(577\) 16.6302 + 28.8044i 0.692325 + 1.19914i 0.971074 + 0.238778i \(0.0767468\pi\)
−0.278749 + 0.960364i \(0.589920\pi\)
\(578\) 0 0
\(579\) 4.09393 + 4.93700i 0.170138 + 0.205175i
\(580\) 0 0
\(581\) 0.564975 + 0.205634i 0.0234391 + 0.00853115i
\(582\) 0 0
\(583\) 10.0520 + 1.77243i 0.416310 + 0.0734066i
\(584\) 0 0
\(585\) 41.1188 + 7.74461i 1.70005 + 0.320200i
\(586\) 0 0
\(587\) 2.57594 3.06988i 0.106320 0.126708i −0.710260 0.703939i \(-0.751423\pi\)
0.816580 + 0.577232i \(0.195867\pi\)
\(588\) 0 0
\(589\) 26.8652 4.73706i 1.10696 0.195187i
\(590\) 0 0
\(591\) 2.50480 + 1.46564i 0.103034 + 0.0602883i
\(592\) 0 0
\(593\) 21.2442i 0.872395i 0.899851 + 0.436198i \(0.143675\pi\)
−0.899851 + 0.436198i \(0.856325\pi\)
\(594\) 0 0
\(595\) 6.63558 0.272032
\(596\) 0 0
\(597\) 13.5240 + 23.7421i 0.553499 + 0.971698i
\(598\) 0 0
\(599\) 2.69240 + 15.2693i 0.110008 + 0.623888i 0.989101 + 0.147238i \(0.0470382\pi\)
−0.879093 + 0.476651i \(0.841851\pi\)
\(600\) 0 0
\(601\) 8.35047 + 7.00688i 0.340623 + 0.285817i 0.797012 0.603964i \(-0.206413\pi\)
−0.456389 + 0.889781i \(0.650857\pi\)
\(602\) 0 0
\(603\) −2.22005 0.837407i −0.0904075 0.0341019i
\(604\) 0 0
\(605\) −5.63944 + 31.9829i −0.229276 + 1.30029i
\(606\) 0 0
\(607\) −15.2605 + 41.9279i −0.619405 + 1.70180i 0.0890338 + 0.996029i \(0.471622\pi\)
−0.708439 + 0.705772i \(0.750600\pi\)
\(608\) 0 0
\(609\) −0.938479 0.347774i −0.0380291 0.0140925i
\(610\) 0 0
\(611\) 18.4028 10.6249i 0.744497 0.429836i
\(612\) 0 0
\(613\) 31.4233 + 18.1422i 1.26918 + 0.732759i 0.974832 0.222941i \(-0.0715658\pi\)
0.294343 + 0.955700i \(0.404899\pi\)
\(614\) 0 0
\(615\) 1.99022 10.9154i 0.0802532 0.440152i
\(616\) 0 0
\(617\) 29.1074 + 34.6889i 1.17182 + 1.39652i 0.900959 + 0.433904i \(0.142864\pi\)
0.270862 + 0.962618i \(0.412691\pi\)
\(618\) 0 0
\(619\) −41.0905 + 14.9557i −1.65157 + 0.601121i −0.989005 0.147885i \(-0.952753\pi\)
−0.662563 + 0.749006i \(0.730531\pi\)
\(620\) 0 0
\(621\) 12.9127 + 15.9458i 0.518169 + 0.639881i
\(622\) 0 0
\(623\) 0.501037 0.182363i 0.0200736 0.00730620i
\(624\) 0 0
\(625\) 41.7001 34.9905i 1.66800 1.39962i
\(626\) 0 0
\(627\) −16.0113 13.5945i −0.639429 0.542914i
\(628\) 0 0
\(629\) 16.8559 29.1953i 0.672090 1.16409i
\(630\) 0 0
\(631\) 31.6964 18.2999i 1.26181 0.728509i 0.288389 0.957513i \(-0.406880\pi\)
0.973425 + 0.229004i \(0.0735470\pi\)
\(632\) 0 0
\(633\) 5.69450 0.969975i 0.226336 0.0385531i
\(634\) 0 0
\(635\) 1.23936 3.40512i 0.0491825 0.135128i
\(636\) 0 0
\(637\) 23.2143 + 4.09331i 0.919785 + 0.162183i
\(638\) 0 0
\(639\) 15.8715 + 28.2440i 0.627867 + 1.11732i
\(640\) 0 0
\(641\) 16.5704 19.7478i 0.654490 0.779990i −0.332094 0.943246i \(-0.607755\pi\)
0.986584 + 0.163256i \(0.0521996\pi\)
\(642\) 0 0
\(643\) 5.30668 + 30.0957i 0.209275 + 1.18686i 0.890569 + 0.454848i \(0.150306\pi\)
−0.681294 + 0.732010i \(0.738583\pi\)
\(644\) 0 0
\(645\) 0.0109547 1.88328i 0.000431343 0.0741542i
\(646\) 0 0
\(647\) 20.9596 0.824008 0.412004 0.911182i \(-0.364829\pi\)
0.412004 + 0.911182i \(0.364829\pi\)
\(648\) 0 0
\(649\) −7.57758 −0.297446
\(650\) 0 0
\(651\) 0.0113326 1.94824i 0.000444160 0.0763577i
\(652\) 0 0
\(653\) −1.21883 6.91233i −0.0476965 0.270500i 0.951628 0.307253i \(-0.0994098\pi\)
−0.999324 + 0.0367525i \(0.988299\pi\)
\(654\) 0 0
\(655\) −52.0566 + 62.0386i −2.03402 + 2.42405i
\(656\) 0 0
\(657\) 0.596376 1.00575i 0.0232668 0.0392380i
\(658\) 0 0
\(659\) −24.6203 4.34123i −0.959072 0.169110i −0.327865 0.944725i \(-0.606329\pi\)
−0.631207 + 0.775614i \(0.717440\pi\)
\(660\) 0 0
\(661\) −2.17476 + 5.97510i −0.0845883 + 0.232404i −0.974774 0.223193i \(-0.928352\pi\)
0.890186 + 0.455597i \(0.150574\pi\)
\(662\) 0 0
\(663\) −33.0253 + 5.62539i −1.28260 + 0.218472i
\(664\) 0 0
\(665\) −7.01034 + 4.04742i −0.271849 + 0.156952i
\(666\) 0 0
\(667\) −3.99535 + 6.92015i −0.154701 + 0.267949i
\(668\) 0 0
\(669\) −35.5072 30.1478i −1.37279 1.16558i
\(670\) 0 0
\(671\) 10.0147 8.40331i 0.386612 0.324406i
\(672\) 0 0
\(673\) −31.0990 + 11.3191i −1.19878 + 0.436320i −0.862798 0.505549i \(-0.831290\pi\)
−0.335981 + 0.941869i \(0.609068\pi\)
\(674\) 0 0
\(675\) −19.8889 57.7611i −0.765525 2.22322i
\(676\) 0 0
\(677\) −21.7565 + 7.91874i −0.836172 + 0.304342i −0.724389 0.689391i \(-0.757878\pi\)
−0.111783 + 0.993733i \(0.535656\pi\)
\(678\) 0 0
\(679\) 3.03209 + 3.61351i 0.116361 + 0.138674i
\(680\) 0 0
\(681\) 2.24843 12.3316i 0.0861599 0.472547i
\(682\) 0 0
\(683\) 21.4976 + 12.4116i 0.822583 + 0.474918i 0.851306 0.524669i \(-0.175811\pi\)
−0.0287236 + 0.999587i \(0.509144\pi\)
\(684\) 0 0
\(685\) 0.783867 0.452566i 0.0299500 0.0172917i
\(686\) 0 0
\(687\) 22.8719 + 8.47567i 0.872616 + 0.323367i
\(688\) 0 0
\(689\) −6.79257 + 18.6624i −0.258776 + 0.710982i
\(690\) 0 0
\(691\) −0.875636 + 4.96598i −0.0333108 + 0.188915i −0.996923 0.0783902i \(-0.975022\pi\)
0.963612 + 0.267305i \(0.0861331\pi\)
\(692\) 0 0
\(693\) −1.16027 + 0.950803i −0.0440751 + 0.0361180i
\(694\) 0 0
\(695\) 20.7561 + 17.4164i 0.787324 + 0.660643i
\(696\) 0 0
\(697\) 1.54262 + 8.74865i 0.0584310 + 0.331379i
\(698\) 0 0
\(699\) 3.39942 + 5.96786i 0.128578 + 0.225725i
\(700\) 0 0
\(701\) −23.1723 −0.875207 −0.437604 0.899168i \(-0.644173\pi\)
−0.437604 + 0.899168i \(0.644173\pi\)
\(702\) 0 0
\(703\) 41.1256i 1.55108i
\(704\) 0 0
\(705\) −38.1658 22.3320i −1.43741 0.841074i
\(706\) 0 0
\(707\) 0.0251015 0.00442607i 0.000944039 0.000166460i
\(708\) 0 0
\(709\) 10.0337 11.9577i 0.376823 0.449081i −0.543986 0.839095i \(-0.683085\pi\)
0.920809 + 0.390014i \(0.127530\pi\)
\(710\) 0 0
\(711\) 12.8965 + 36.7579i 0.483657 + 1.37853i
\(712\) 0 0
\(713\) −15.3186 2.70109i −0.573688 0.101157i
\(714\) 0 0
\(715\) 22.9502 + 8.35319i 0.858289 + 0.312392i
\(716\) 0 0
\(717\) 9.50596 + 11.4635i 0.355007 + 0.428113i
\(718\) 0 0
\(719\) −18.4776 32.0041i −0.689096 1.19355i −0.972131 0.234440i \(-0.924674\pi\)
0.283034 0.959110i \(-0.408659\pi\)
\(720\) 0 0
\(721\) 1.60132 2.77358i 0.0596365 0.103293i
\(722\) 0 0
\(723\) 3.94258 + 11.0314i 0.146626 + 0.410261i
\(724\) 0 0
\(725\) 18.2247 15.2924i 0.676849 0.567944i
\(726\) 0 0
\(727\) 4.03567 + 11.0879i 0.149675 + 0.411228i 0.991759 0.128118i \(-0.0408937\pi\)
−0.842084 + 0.539346i \(0.818671\pi\)
\(728\) 0 0
\(729\) −26.9836 0.942126i −0.999391 0.0348935i
\(730\) 0 0
\(731\) 0.515730 + 1.41696i 0.0190750 + 0.0524080i
\(732\) 0 0
\(733\) 22.2989 + 26.5748i 0.823629 + 0.981562i 0.999996 0.00276204i \(-0.000879186\pi\)
−0.176368 + 0.984324i \(0.556435\pi\)
\(734\) 0 0
\(735\) −16.5086 46.1914i −0.608930 1.70379i
\(736\) 0 0
\(737\) −1.19942 0.692485i −0.0441812 0.0255080i
\(738\) 0 0
\(739\) 9.86442 + 17.0857i 0.362868 + 0.628507i 0.988432 0.151667i \(-0.0484641\pi\)
−0.625563 + 0.780173i \(0.715131\pi\)
\(740\) 0 0
\(741\) 31.4593 26.0871i 1.15569 0.958335i
\(742\) 0 0
\(743\) −13.0759 4.75924i −0.479709 0.174600i 0.0908366 0.995866i \(-0.471046\pi\)
−0.570545 + 0.821266i \(0.693268\pi\)
\(744\) 0 0
\(745\) 12.5575 71.2170i 0.460070 2.60919i
\(746\) 0 0
\(747\) 2.09120 + 5.96038i 0.0765131 + 0.218079i
\(748\) 0 0
\(749\) 2.23334 + 1.87399i 0.0816044 + 0.0684742i
\(750\) 0 0
\(751\) 37.4163 6.59750i 1.36534 0.240746i 0.557514 0.830168i \(-0.311755\pi\)
0.807826 + 0.589421i \(0.200644\pi\)
\(752\) 0 0
\(753\) 9.62490 16.4491i 0.350751 0.599438i
\(754\) 0 0
\(755\) 39.8656i 1.45086i
\(756\) 0 0
\(757\) 13.2372i 0.481113i −0.970635 0.240556i \(-0.922670\pi\)
0.970635 0.240556i \(-0.0773299\pi\)
\(758\) 0 0
\(759\) 5.92788 + 10.4067i 0.215168 + 0.377740i
\(760\) 0 0
\(761\) 46.5700 8.21155i 1.68816 0.297668i 0.754626 0.656155i \(-0.227818\pi\)
0.933535 + 0.358486i \(0.116707\pi\)
\(762\) 0 0
\(763\) 1.91494 + 1.60683i 0.0693255 + 0.0581710i
\(764\) 0 0
\(765\) 44.1867 + 53.9214i 1.59757 + 1.94953i
\(766\) 0 0
\(767\) 2.56026 14.5200i 0.0924456 0.524285i
\(768\) 0 0
\(769\) 13.2190 + 4.81132i 0.476689 + 0.173501i 0.569180 0.822213i \(-0.307261\pi\)
−0.0924911 + 0.995714i \(0.529483\pi\)
\(770\) 0 0
\(771\) −10.1864 3.77480i −0.366855 0.135946i
\(772\) 0 0
\(773\) −17.6365 30.5473i −0.634341 1.09871i −0.986654 0.162829i \(-0.947938\pi\)
0.352313 0.935882i \(-0.385395\pi\)
\(774\) 0 0
\(775\) 40.1071 + 23.1558i 1.44069 + 0.831783i
\(776\) 0 0
\(777\) 2.88950 + 0.526845i 0.103660 + 0.0189005i
\(778\) 0 0
\(779\) −6.96605 8.30182i −0.249585 0.297443i
\(780\) 0 0
\(781\) 6.46786 + 17.7703i 0.231438 + 0.635871i
\(782\) 0 0
\(783\) −3.42335 9.94202i −0.122340 0.355299i
\(784\) 0 0
\(785\) −4.27132 11.7354i −0.152450 0.418853i
\(786\) 0 0
\(787\) 22.1892 18.6190i 0.790961 0.663695i −0.155022 0.987911i \(-0.549545\pi\)
0.945983 + 0.324216i \(0.105100\pi\)
\(788\) 0 0
\(789\) −27.4625 + 32.3445i −0.977690 + 1.15150i
\(790\) 0 0
\(791\) −2.32565 + 4.02814i −0.0826906 + 0.143224i
\(792\) 0 0
\(793\) 12.7185 + 22.0291i 0.451647 + 0.782276i
\(794\) 0 0
\(795\) 40.7409 6.93962i 1.44493 0.246123i
\(796\) 0 0
\(797\) −8.52330 3.10223i −0.301911 0.109887i 0.186623 0.982432i \(-0.440246\pi\)
−0.488534 + 0.872545i \(0.662468\pi\)
\(798\) 0 0
\(799\) 34.8668 + 6.14795i 1.23350 + 0.217499i
\(800\) 0 0
\(801\) 4.81833 + 2.85711i 0.170247 + 0.100951i
\(802\) 0 0
\(803\) 0.438706 0.522829i 0.0154816 0.0184502i
\(804\) 0 0
\(805\) 4.54558 0.801509i 0.160211 0.0282495i
\(806\) 0 0
\(807\) 0.113604 19.5302i 0.00399906 0.687497i
\(808\) 0 0
\(809\) 9.61585i 0.338075i −0.985610 0.169038i \(-0.945934\pi\)
0.985610 0.169038i \(-0.0540660\pi\)
\(810\) 0 0
\(811\) 13.5031 0.474156 0.237078 0.971491i \(-0.423810\pi\)
0.237078 + 0.971491i \(0.423810\pi\)
\(812\) 0 0
\(813\) −13.9337 0.0810502i −0.488677 0.00284255i
\(814\) 0 0
\(815\) −1.69535 9.61481i −0.0593855 0.336792i
\(816\) 0 0
\(817\) −1.40914 1.18241i −0.0492996 0.0413673i
\(818\) 0 0
\(819\) −1.42988 2.54453i −0.0499640 0.0889131i
\(820\) 0 0
\(821\) −1.09003 + 6.18187i −0.0380423 + 0.215749i −0.997903 0.0647288i \(-0.979382\pi\)
0.959861 + 0.280478i \(0.0904929\pi\)
\(822\) 0 0
\(823\) 14.0239 38.5302i 0.488841 1.34308i −0.412890 0.910781i \(-0.635480\pi\)
0.901731 0.432298i \(-0.142297\pi\)
\(824\) 0 0
\(825\) −5.98757 35.1516i −0.208460 1.22382i
\(826\) 0 0
\(827\) 36.5263 21.0885i 1.27014 0.733318i 0.295129 0.955457i \(-0.404637\pi\)
0.975015 + 0.222139i \(0.0713040\pi\)
\(828\) 0 0
\(829\) 3.97893 + 2.29724i 0.138194 + 0.0797864i 0.567503 0.823371i \(-0.307910\pi\)
−0.429309 + 0.903158i \(0.641243\pi\)
\(830\) 0 0
\(831\) −14.2953 12.1375i −0.495897 0.421047i
\(832\) 0 0
\(833\) 25.2452 + 30.0861i 0.874695 + 1.04242i
\(834\) 0 0
\(835\) −24.5992 + 8.95339i −0.851292 + 0.309845i
\(836\) 0 0
\(837\) 15.9071 12.8814i 0.549829 0.445246i
\(838\) 0 0
\(839\) 29.1595 10.6132i 1.00670 0.366408i 0.214533 0.976717i \(-0.431177\pi\)
0.792163 + 0.610309i \(0.208955\pi\)
\(840\) 0 0
\(841\) −19.0784 + 16.0087i −0.657876 + 0.552023i
\(842\) 0 0
\(843\) 3.23858 17.7621i 0.111543 0.611760i
\(844\) 0 0
\(845\) 2.84728 4.93163i 0.0979494 0.169653i
\(846\) 0 0
\(847\) 1.96194 1.13273i 0.0674130 0.0389209i
\(848\) 0 0
\(849\) 3.59480 9.70069i 0.123373 0.332927i
\(850\) 0 0
\(851\) 8.02036 22.0358i 0.274935 0.755376i
\(852\) 0 0
\(853\) 28.5512 + 5.03434i 0.977573 + 0.172373i 0.639537 0.768761i \(-0.279126\pi\)
0.338036 + 0.941133i \(0.390237\pi\)
\(854\) 0 0
\(855\) −79.5720 30.0147i −2.72130 1.02648i
\(856\) 0 0
\(857\) 4.00052 4.76763i 0.136655 0.162859i −0.693377 0.720575i \(-0.743878\pi\)
0.830032 + 0.557716i \(0.188322\pi\)
\(858\) 0 0
\(859\) −4.56731 25.9025i −0.155835 0.883782i −0.958019 0.286705i \(-0.907440\pi\)
0.802184 0.597076i \(-0.203671\pi\)
\(860\) 0 0
\(861\) −0.672528 + 0.383086i −0.0229197 + 0.0130555i
\(862\) 0 0
\(863\) −21.6556 −0.737166 −0.368583 0.929595i \(-0.620157\pi\)
−0.368583 + 0.929595i \(0.620157\pi\)
\(864\) 0 0
\(865\) −45.2744 −1.53938
\(866\) 0 0
\(867\) −22.7617 13.3186i −0.773028 0.452324i
\(868\) 0 0
\(869\) 3.94839 + 22.3924i 0.133940 + 0.759611i
\(870\) 0 0
\(871\) 1.73217 2.06432i 0.0586924 0.0699469i
\(872\) 0 0
\(873\) −9.17283 + 48.7017i −0.310453 + 1.64830i
\(874\) 0 0
\(875\) −7.77785 1.37144i −0.262939 0.0463633i
\(876\) 0 0
\(877\) 16.3125 44.8181i 0.550833 1.51340i −0.281744 0.959490i \(-0.590913\pi\)
0.832576 0.553910i \(-0.186865\pi\)
\(878\) 0 0
\(879\) 29.4504 + 35.5151i 0.993336 + 1.19789i
\(880\) 0 0
\(881\) 10.2022 5.89026i 0.343722 0.198448i −0.318195 0.948025i \(-0.603077\pi\)
0.661917 + 0.749578i \(0.269743\pi\)
\(882\) 0 0
\(883\) 4.94659 8.56774i 0.166466 0.288327i −0.770709 0.637187i \(-0.780098\pi\)
0.937175 + 0.348860i \(0.113431\pi\)
\(884\) 0 0
\(885\) −28.8915 + 10.3257i −0.971177 + 0.347095i
\(886\) 0 0
\(887\) 28.2674 23.7192i 0.949127 0.796412i −0.0300236 0.999549i \(-0.509558\pi\)
0.979150 + 0.203137i \(0.0651138\pi\)
\(888\) 0 0
\(889\) −0.237531 + 0.0864544i −0.00796655 + 0.00289959i
\(890\) 0 0
\(891\) −15.4526 3.09703i −0.517683 0.103754i
\(892\) 0 0
\(893\) −40.5859 + 14.7721i −1.35816 + 0.494329i
\(894\) 0 0
\(895\) −63.2952 75.4323i −2.11573 2.52143i
\(896\) 0 0
\(897\) −21.9439 + 7.84269i −0.732686 + 0.261860i
\(898\) 0 0
\(899\) 6.90337 + 3.98566i 0.230240 + 0.132929i
\(900\) 0 0
\(901\) −28.6563 + 16.5447i −0.954680 + 0.551185i
\(902\) 0 0
\(903\) −0.101128 + 0.0838593i −0.00336534 + 0.00279066i
\(904\) 0 0
\(905\) 25.9688 71.3486i 0.863231 2.37171i
\(906\) 0 0
\(907\) 2.93067 16.6207i 0.0973113 0.551880i −0.896703 0.442632i \(-0.854045\pi\)
0.994015 0.109248i \(-0.0348441\pi\)
\(908\) 0 0
\(909\) 0.203119 + 0.174504i 0.00673704 + 0.00578793i
\(910\) 0 0
\(911\) 15.2762 + 12.8182i 0.506122 + 0.424687i 0.859762 0.510695i \(-0.170612\pi\)
−0.353640 + 0.935382i \(0.615056\pi\)
\(912\) 0 0
\(913\) 0.640240 + 3.63098i 0.0211889 + 0.120168i
\(914\) 0 0
\(915\) 26.7326 45.6865i 0.883753 1.51035i
\(916\) 0 0
\(917\) 5.64933 0.186557
\(918\) 0 0
\(919\) 52.4126i 1.72893i −0.502690 0.864467i \(-0.667656\pi\)
0.502690 0.864467i \(-0.332344\pi\)
\(920\) 0 0
\(921\) 16.8573 9.60228i 0.555468 0.316406i
\(922\) 0 0
\(923\) −36.2363 + 6.38943i −1.19273 + 0.210311i
\(924\) 0 0
\(925\) −44.8778 + 53.4833i −1.47557 + 1.75852i
\(926\) 0 0
\(927\) 33.2017 5.45689i 1.09049 0.179228i
\(928\) 0 0
\(929\) −16.3482 2.88262i −0.536366 0.0945757i −0.101097 0.994877i \(-0.532235\pi\)
−0.435268 + 0.900301i \(0.643346\pi\)
\(930\) 0 0
\(931\) −45.0222 16.3868i −1.47554 0.537054i
\(932\) 0 0
\(933\) 4.59355 12.3958i 0.150386 0.405822i
\(934\) 0 0
\(935\) 20.3459 + 35.2402i 0.665383 + 1.15248i
\(936\) 0 0
\(937\) 2.11716 3.66703i 0.0691647 0.119797i −0.829369 0.558701i \(-0.811300\pi\)
0.898534 + 0.438904i \(0.144633\pi\)
\(938\) 0 0
\(939\) 1.54496 + 0.281695i 0.0504180 + 0.00919276i
\(940\) 0 0
\(941\) 46.5192 39.0342i 1.51648 1.27248i 0.666727 0.745302i \(-0.267695\pi\)
0.849755 0.527178i \(-0.176750\pi\)
\(942\) 0 0
\(943\) 2.11349 + 5.80677i 0.0688248 + 0.189095i
\(944\) 0 0
\(945\) −3.12821 + 5.20625i −0.101761 + 0.169359i
\(946\) 0 0
\(947\) −2.60051 7.14483i −0.0845051 0.232176i 0.890242 0.455488i \(-0.150535\pi\)
−0.974747 + 0.223312i \(0.928313\pi\)
\(948\) 0 0
\(949\) 0.853604 + 1.01729i 0.0277092 + 0.0330225i
\(950\) 0 0
\(951\) −29.4308 + 34.6628i −0.954360 + 1.12402i
\(952\) 0 0
\(953\) −5.40608 3.12120i −0.175120 0.101106i 0.409878 0.912140i \(-0.365571\pi\)
−0.584998 + 0.811035i \(0.698905\pi\)
\(954\) 0 0
\(955\) 14.6979 + 25.4574i 0.475612 + 0.823783i
\(956\) 0 0
\(957\) −1.03060 6.05041i −0.0333146 0.195582i
\(958\) 0 0
\(959\) −0.0593317 0.0215950i −0.00191592 0.000697338i
\(960\) 0 0
\(961\) 2.68856 15.2476i 0.0867276 0.491857i
\(962\) 0 0
\(963\) −0.356321 + 30.6273i −0.0114823 + 0.986952i
\(964\) 0 0
\(965\) 11.6115 + 9.74321i 0.373788 + 0.313645i
\(966\) 0 0
\(967\) −8.55187 + 1.50792i −0.275009 + 0.0484916i −0.309452 0.950915i \(-0.600146\pi\)
0.0344424 + 0.999407i \(0.489034\pi\)
\(968\) 0 0
\(969\) 68.0906 + 0.396072i 2.18739 + 0.0127237i
\(970\) 0 0
\(971\) 28.6838i 0.920507i 0.887787 + 0.460254i \(0.152242\pi\)
−0.887787 + 0.460254i \(0.847758\pi\)
\(972\) 0 0
\(973\) 1.89008i 0.0605933i
\(974\) 0 0
\(975\) 69.3796 + 0.403570i 2.22193 + 0.0129246i
\(976\) 0 0
\(977\) −24.0242 + 4.23611i −0.768601 + 0.135525i −0.544182 0.838967i \(-0.683160\pi\)
−0.224420 + 0.974493i \(0.572049\pi\)
\(978\) 0 0
\(979\) 2.50476 + 2.10175i 0.0800526 + 0.0671721i
\(980\) 0 0
\(981\) −0.305522 + 26.2609i −0.00975456 + 0.838448i
\(982\) 0 0
\(983\) −1.90983 + 10.8312i −0.0609141 + 0.345461i 0.939084 + 0.343687i \(0.111676\pi\)
−0.999998 + 0.00177427i \(0.999435\pi\)
\(984\) 0 0
\(985\) 6.44509 + 2.34582i 0.205358 + 0.0747441i
\(986\) 0 0
\(987\) 0.517960 + 3.04082i 0.0164868 + 0.0967904i
\(988\) 0 0
\(989\) 0.524445 + 0.908366i 0.0166764 + 0.0288844i
\(990\) 0 0
\(991\) 32.0529 + 18.5057i 1.01819 + 0.587854i 0.913580 0.406659i \(-0.133306\pi\)
0.104613 + 0.994513i \(0.466640\pi\)
\(992\) 0 0
\(993\) 23.7617 27.9859i 0.754056 0.888106i
\(994\) 0 0
\(995\) 41.5088 + 49.4682i 1.31592 + 1.56825i
\(996\) 0 0
\(997\) 4.24777 + 11.6706i 0.134528 + 0.369613i 0.988605 0.150534i \(-0.0480993\pi\)
−0.854077 + 0.520147i \(0.825877\pi\)
\(998\) 0 0
\(999\) 14.9602 + 26.9886i 0.473318 + 0.853883i
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.47.15 192
4.3 odd 2 216.2.v.b.155.6 yes 192
8.3 odd 2 inner 864.2.bh.b.47.16 192
8.5 even 2 216.2.v.b.155.20 yes 192
12.11 even 2 648.2.v.b.467.27 192
24.5 odd 2 648.2.v.b.467.13 192
27.23 odd 18 inner 864.2.bh.b.239.16 192
108.23 even 18 216.2.v.b.131.20 yes 192
108.31 odd 18 648.2.v.b.179.13 192
216.77 odd 18 216.2.v.b.131.6 192
216.85 even 18 648.2.v.b.179.27 192
216.131 even 18 inner 864.2.bh.b.239.15 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.131.6 192 216.77 odd 18
216.2.v.b.131.20 yes 192 108.23 even 18
216.2.v.b.155.6 yes 192 4.3 odd 2
216.2.v.b.155.20 yes 192 8.5 even 2
648.2.v.b.179.13 192 108.31 odd 18
648.2.v.b.179.27 192 216.85 even 18
648.2.v.b.467.13 192 24.5 odd 2
648.2.v.b.467.27 192 12.11 even 2
864.2.bh.b.47.15 192 1.1 even 1 trivial
864.2.bh.b.47.16 192 8.3 odd 2 inner
864.2.bh.b.239.15 192 216.131 even 18 inner
864.2.bh.b.239.16 192 27.23 odd 18 inner