Properties

Label 432.2.be.b.95.3
Level $432$
Weight $2$
Character 432.95
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(47,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 95.3
Character \(\chi\) \(=\) 432.95
Dual form 432.2.be.b.191.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.249148 + 1.71404i) q^{3} +(-1.47612 + 1.75917i) q^{5} +(0.590654 - 1.62281i) q^{7} +(-2.87585 + 0.854099i) q^{9} +O(q^{10})\) \(q+(0.249148 + 1.71404i) q^{3} +(-1.47612 + 1.75917i) q^{5} +(0.590654 - 1.62281i) q^{7} +(-2.87585 + 0.854099i) q^{9} +(-0.867802 + 0.728172i) q^{11} +(-1.22373 + 6.94010i) q^{13} +(-3.38306 - 2.09183i) q^{15} +(-1.48526 - 0.857517i) q^{17} +(3.94280 - 2.27638i) q^{19} +(2.92872 + 0.608084i) q^{21} +(-6.51976 + 2.37300i) q^{23} +(-0.0475130 - 0.269460i) q^{25} +(-2.18047 - 4.71652i) q^{27} +(-6.35318 + 1.12024i) q^{29} +(-1.56666 - 4.30438i) q^{31} +(-1.46433 - 1.30602i) q^{33} +(1.98292 + 3.43452i) q^{35} +(1.47273 - 2.55085i) q^{37} +(-12.2005 - 0.368401i) q^{39} +(7.14576 + 1.25999i) q^{41} +(0.337693 + 0.402447i) q^{43} +(2.74260 - 6.31987i) q^{45} +(8.97326 + 3.26600i) q^{47} +(3.07767 + 2.58248i) q^{49} +(1.09977 - 2.75945i) q^{51} +8.57289i q^{53} -2.60148i q^{55} +(4.88414 + 6.19096i) q^{57} +(11.0297 + 9.25501i) q^{59} +(-0.269170 - 0.0979697i) q^{61} +(-0.312594 + 5.17143i) q^{63} +(-10.4025 - 12.3972i) q^{65} +(5.85364 + 1.03215i) q^{67} +(-5.69179 - 10.5839i) q^{69} +(-1.36269 + 2.36024i) q^{71} +(-1.58277 - 2.74144i) q^{73} +(0.450026 - 0.148574i) q^{75} +(0.669113 + 1.83837i) q^{77} +(9.41150 - 1.65950i) q^{79} +(7.54103 - 4.91252i) q^{81} +(-0.731691 - 4.14963i) q^{83} +(3.70095 - 1.34704i) q^{85} +(-3.50301 - 10.6105i) q^{87} +(-5.83560 + 3.36919i) q^{89} +(10.5397 + 6.08507i) q^{91} +(6.98753 - 3.75775i) q^{93} +(-1.81551 + 10.2963i) q^{95} +(-3.21229 + 2.69543i) q^{97} +(1.87374 - 2.83530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.249148 + 1.71404i 0.143846 + 0.989600i
\(4\) 0 0
\(5\) −1.47612 + 1.75917i −0.660141 + 0.786726i −0.987406 0.158207i \(-0.949429\pi\)
0.327265 + 0.944933i \(0.393873\pi\)
\(6\) 0 0
\(7\) 0.590654 1.62281i 0.223246 0.613364i −0.776616 0.629975i \(-0.783065\pi\)
0.999862 + 0.0166105i \(0.00528752\pi\)
\(8\) 0 0
\(9\) −2.87585 + 0.854099i −0.958617 + 0.284700i
\(10\) 0 0
\(11\) −0.867802 + 0.728172i −0.261652 + 0.219552i −0.764170 0.645014i \(-0.776851\pi\)
0.502518 + 0.864567i \(0.332407\pi\)
\(12\) 0 0
\(13\) −1.22373 + 6.94010i −0.339401 + 1.92484i 0.0391000 + 0.999235i \(0.487551\pi\)
−0.378501 + 0.925601i \(0.623560\pi\)
\(14\) 0 0
\(15\) −3.38306 2.09183i −0.873502 0.540109i
\(16\) 0 0
\(17\) −1.48526 0.857517i −0.360229 0.207979i 0.308952 0.951078i \(-0.400022\pi\)
−0.669181 + 0.743099i \(0.733355\pi\)
\(18\) 0 0
\(19\) 3.94280 2.27638i 0.904541 0.522237i 0.0258702 0.999665i \(-0.491764\pi\)
0.878671 + 0.477428i \(0.158431\pi\)
\(20\) 0 0
\(21\) 2.92872 + 0.608084i 0.639098 + 0.132695i
\(22\) 0 0
\(23\) −6.51976 + 2.37300i −1.35946 + 0.494804i −0.915889 0.401433i \(-0.868512\pi\)
−0.443575 + 0.896237i \(0.646290\pi\)
\(24\) 0 0
\(25\) −0.0475130 0.269460i −0.00950260 0.0538919i
\(26\) 0 0
\(27\) −2.18047 4.71652i −0.419632 0.907694i
\(28\) 0 0
\(29\) −6.35318 + 1.12024i −1.17976 + 0.208023i −0.728930 0.684589i \(-0.759982\pi\)
−0.450827 + 0.892612i \(0.648871\pi\)
\(30\) 0 0
\(31\) −1.56666 4.30438i −0.281381 0.773089i −0.997198 0.0748009i \(-0.976168\pi\)
0.715817 0.698288i \(-0.246054\pi\)
\(32\) 0 0
\(33\) −1.46433 1.30602i −0.254906 0.227349i
\(34\) 0 0
\(35\) 1.98292 + 3.43452i 0.335175 + 0.580540i
\(36\) 0 0
\(37\) 1.47273 2.55085i 0.242116 0.419357i −0.719201 0.694802i \(-0.755492\pi\)
0.961317 + 0.275445i \(0.0888253\pi\)
\(38\) 0 0
\(39\) −12.2005 0.368401i −1.95364 0.0589913i
\(40\) 0 0
\(41\) 7.14576 + 1.25999i 1.11598 + 0.196778i 0.701076 0.713087i \(-0.252704\pi\)
0.414905 + 0.909865i \(0.363815\pi\)
\(42\) 0 0
\(43\) 0.337693 + 0.402447i 0.0514978 + 0.0613727i 0.791178 0.611585i \(-0.209468\pi\)
−0.739681 + 0.672958i \(0.765023\pi\)
\(44\) 0 0
\(45\) 2.74260 6.31987i 0.408842 0.942110i
\(46\) 0 0
\(47\) 8.97326 + 3.26600i 1.30888 + 0.476395i 0.899880 0.436138i \(-0.143654\pi\)
0.409004 + 0.912533i \(0.365876\pi\)
\(48\) 0 0
\(49\) 3.07767 + 2.58248i 0.439668 + 0.368925i
\(50\) 0 0
\(51\) 1.09977 2.75945i 0.153998 0.386400i
\(52\) 0 0
\(53\) 8.57289i 1.17758i 0.808287 + 0.588788i \(0.200395\pi\)
−0.808287 + 0.588788i \(0.799605\pi\)
\(54\) 0 0
\(55\) 2.60148i 0.350784i
\(56\) 0 0
\(57\) 4.88414 + 6.19096i 0.646920 + 0.820012i
\(58\) 0 0
\(59\) 11.0297 + 9.25501i 1.43594 + 1.20490i 0.942093 + 0.335352i \(0.108855\pi\)
0.493850 + 0.869547i \(0.335589\pi\)
\(60\) 0 0
\(61\) −0.269170 0.0979697i −0.0344636 0.0125437i 0.324731 0.945806i \(-0.394726\pi\)
−0.359194 + 0.933263i \(0.616949\pi\)
\(62\) 0 0
\(63\) −0.312594 + 5.17143i −0.0393832 + 0.651539i
\(64\) 0 0
\(65\) −10.4025 12.3972i −1.29027 1.53768i
\(66\) 0 0
\(67\) 5.85364 + 1.03215i 0.715135 + 0.126098i 0.519365 0.854552i \(-0.326168\pi\)
0.195770 + 0.980650i \(0.437279\pi\)
\(68\) 0 0
\(69\) −5.69179 10.5839i −0.685212 1.27415i
\(70\) 0 0
\(71\) −1.36269 + 2.36024i −0.161721 + 0.280109i −0.935486 0.353364i \(-0.885038\pi\)
0.773765 + 0.633473i \(0.218371\pi\)
\(72\) 0 0
\(73\) −1.58277 2.74144i −0.185249 0.320861i 0.758411 0.651776i \(-0.225976\pi\)
−0.943660 + 0.330915i \(0.892643\pi\)
\(74\) 0 0
\(75\) 0.450026 0.148574i 0.0519645 0.0171559i
\(76\) 0 0
\(77\) 0.669113 + 1.83837i 0.0762525 + 0.209502i
\(78\) 0 0
\(79\) 9.41150 1.65950i 1.05888 0.186709i 0.383019 0.923741i \(-0.374884\pi\)
0.675858 + 0.737032i \(0.263773\pi\)
\(80\) 0 0
\(81\) 7.54103 4.91252i 0.837892 0.545836i
\(82\) 0 0
\(83\) −0.731691 4.14963i −0.0803135 0.455481i −0.998270 0.0587991i \(-0.981273\pi\)
0.917956 0.396681i \(-0.129838\pi\)
\(84\) 0 0
\(85\) 3.70095 1.34704i 0.401424 0.146106i
\(86\) 0 0
\(87\) −3.50301 10.6105i −0.375562 1.13756i
\(88\) 0 0
\(89\) −5.83560 + 3.36919i −0.618573 + 0.357133i −0.776313 0.630348i \(-0.782912\pi\)
0.157740 + 0.987481i \(0.449579\pi\)
\(90\) 0 0
\(91\) 10.5397 + 6.08507i 1.10486 + 0.637889i
\(92\) 0 0
\(93\) 6.98753 3.75775i 0.724573 0.389660i
\(94\) 0 0
\(95\) −1.81551 + 10.2963i −0.186267 + 1.05638i
\(96\) 0 0
\(97\) −3.21229 + 2.69543i −0.326159 + 0.273680i −0.791133 0.611645i \(-0.790508\pi\)
0.464974 + 0.885324i \(0.346064\pi\)
\(98\) 0 0
\(99\) 1.87374 2.83530i 0.188318 0.284959i
\(100\) 0 0
\(101\) 1.01338 2.78424i 0.100835 0.277042i −0.879009 0.476805i \(-0.841795\pi\)
0.979844 + 0.199763i \(0.0640171\pi\)
\(102\) 0 0
\(103\) −8.21708 + 9.79274i −0.809653 + 0.964907i −0.999858 0.0168372i \(-0.994640\pi\)
0.190205 + 0.981744i \(0.439085\pi\)
\(104\) 0 0
\(105\) −5.39286 + 4.25451i −0.526289 + 0.415198i
\(106\) 0 0
\(107\) −11.4207 −1.10408 −0.552038 0.833819i \(-0.686150\pi\)
−0.552038 + 0.833819i \(0.686150\pi\)
\(108\) 0 0
\(109\) 18.0047 1.72454 0.862269 0.506451i \(-0.169043\pi\)
0.862269 + 0.506451i \(0.169043\pi\)
\(110\) 0 0
\(111\) 4.73918 + 1.88878i 0.449823 + 0.179275i
\(112\) 0 0
\(113\) 7.65099 9.11809i 0.719745 0.857758i −0.274861 0.961484i \(-0.588632\pi\)
0.994606 + 0.103726i \(0.0330764\pi\)
\(114\) 0 0
\(115\) 5.44944 14.9722i 0.508163 1.39617i
\(116\) 0 0
\(117\) −2.40827 21.0039i −0.222645 1.94181i
\(118\) 0 0
\(119\) −2.26886 + 1.90380i −0.207986 + 0.174521i
\(120\) 0 0
\(121\) −1.68728 + 9.56907i −0.153390 + 0.869915i
\(122\) 0 0
\(123\) −0.379318 + 12.5620i −0.0342020 + 1.13268i
\(124\) 0 0
\(125\) −9.39970 5.42692i −0.840734 0.485398i
\(126\) 0 0
\(127\) 0.853895 0.492997i 0.0757710 0.0437464i −0.461636 0.887070i \(-0.652737\pi\)
0.537407 + 0.843323i \(0.319404\pi\)
\(128\) 0 0
\(129\) −0.605674 + 0.679088i −0.0533267 + 0.0597904i
\(130\) 0 0
\(131\) 8.93676 3.25271i 0.780808 0.284191i 0.0792985 0.996851i \(-0.474732\pi\)
0.701510 + 0.712660i \(0.252510\pi\)
\(132\) 0 0
\(133\) −1.36529 7.74297i −0.118386 0.671400i
\(134\) 0 0
\(135\) 11.5158 + 3.12633i 0.991122 + 0.269072i
\(136\) 0 0
\(137\) 21.5074 3.79234i 1.83750 0.324001i 0.856225 0.516603i \(-0.172804\pi\)
0.981277 + 0.192601i \(0.0616924\pi\)
\(138\) 0 0
\(139\) −6.57836 18.0739i −0.557969 1.53301i −0.822578 0.568652i \(-0.807465\pi\)
0.264609 0.964356i \(-0.414757\pi\)
\(140\) 0 0
\(141\) −3.36237 + 16.1942i −0.283163 + 1.36380i
\(142\) 0 0
\(143\) −3.99163 6.91371i −0.333797 0.578153i
\(144\) 0 0
\(145\) 7.40737 12.8299i 0.615149 1.06547i
\(146\) 0 0
\(147\) −3.65966 + 5.91867i −0.301844 + 0.488164i
\(148\) 0 0
\(149\) 2.02217 + 0.356564i 0.165663 + 0.0292108i 0.255864 0.966713i \(-0.417640\pi\)
−0.0902014 + 0.995924i \(0.528751\pi\)
\(150\) 0 0
\(151\) −6.39929 7.62638i −0.520767 0.620626i 0.439995 0.898000i \(-0.354980\pi\)
−0.960762 + 0.277374i \(0.910536\pi\)
\(152\) 0 0
\(153\) 5.00380 + 1.19753i 0.404533 + 0.0968146i
\(154\) 0 0
\(155\) 9.88472 + 3.59774i 0.793960 + 0.288978i
\(156\) 0 0
\(157\) 7.86613 + 6.60047i 0.627785 + 0.526775i 0.900240 0.435394i \(-0.143391\pi\)
−0.272455 + 0.962169i \(0.587835\pi\)
\(158\) 0 0
\(159\) −14.6943 + 2.13592i −1.16533 + 0.169389i
\(160\) 0 0
\(161\) 11.9819i 0.944310i
\(162\) 0 0
\(163\) 22.6034i 1.77044i 0.465176 + 0.885218i \(0.345991\pi\)
−0.465176 + 0.885218i \(0.654009\pi\)
\(164\) 0 0
\(165\) 4.45904 0.648154i 0.347136 0.0504587i
\(166\) 0 0
\(167\) −15.1820 12.7392i −1.17482 0.985787i −0.999999 0.00118593i \(-0.999623\pi\)
−0.174816 0.984601i \(-0.555933\pi\)
\(168\) 0 0
\(169\) −34.4514 12.5393i −2.65011 0.964561i
\(170\) 0 0
\(171\) −9.39466 + 9.91406i −0.718427 + 0.758147i
\(172\) 0 0
\(173\) −6.13700 7.31379i −0.466587 0.556057i 0.480516 0.876986i \(-0.340449\pi\)
−0.947103 + 0.320929i \(0.896005\pi\)
\(174\) 0 0
\(175\) −0.465345 0.0820529i −0.0351768 0.00620262i
\(176\) 0 0
\(177\) −13.1154 + 21.2112i −0.985814 + 1.59433i
\(178\) 0 0
\(179\) 2.34317 4.05850i 0.175137 0.303346i −0.765072 0.643945i \(-0.777296\pi\)
0.940209 + 0.340599i \(0.110630\pi\)
\(180\) 0 0
\(181\) 5.90627 + 10.2300i 0.439009 + 0.760387i 0.997613 0.0690479i \(-0.0219961\pi\)
−0.558604 + 0.829435i \(0.688663\pi\)
\(182\) 0 0
\(183\) 0.100861 0.485776i 0.00745584 0.0359096i
\(184\) 0 0
\(185\) 2.31345 + 6.35615i 0.170088 + 0.467313i
\(186\) 0 0
\(187\) 1.91333 0.337372i 0.139917 0.0246711i
\(188\) 0 0
\(189\) −8.94191 + 0.752655i −0.650428 + 0.0547476i
\(190\) 0 0
\(191\) −2.84710 16.1467i −0.206009 1.16833i −0.895844 0.444368i \(-0.853428\pi\)
0.689835 0.723966i \(-0.257683\pi\)
\(192\) 0 0
\(193\) −1.21489 + 0.442183i −0.0874495 + 0.0318290i −0.385374 0.922760i \(-0.625928\pi\)
0.297925 + 0.954589i \(0.403705\pi\)
\(194\) 0 0
\(195\) 18.6575 20.9189i 1.33609 1.49804i
\(196\) 0 0
\(197\) −17.7961 + 10.2746i −1.26792 + 0.732035i −0.974594 0.223977i \(-0.928096\pi\)
−0.293327 + 0.956012i \(0.594763\pi\)
\(198\) 0 0
\(199\) −6.12484 3.53618i −0.434179 0.250673i 0.266947 0.963711i \(-0.413985\pi\)
−0.701125 + 0.713038i \(0.747319\pi\)
\(200\) 0 0
\(201\) −0.310728 + 10.2905i −0.0219171 + 0.725837i
\(202\) 0 0
\(203\) −1.93460 + 10.9717i −0.135782 + 0.770060i
\(204\) 0 0
\(205\) −12.7645 + 10.7107i −0.891515 + 0.748070i
\(206\) 0 0
\(207\) 16.7231 12.3929i 1.16233 0.861367i
\(208\) 0 0
\(209\) −1.76398 + 4.84648i −0.122017 + 0.335238i
\(210\) 0 0
\(211\) −8.31514 + 9.90960i −0.572438 + 0.682205i −0.972129 0.234445i \(-0.924673\pi\)
0.399692 + 0.916650i \(0.369117\pi\)
\(212\) 0 0
\(213\) −4.38506 1.74765i −0.300459 0.119747i
\(214\) 0 0
\(215\) −1.20645 −0.0822792
\(216\) 0 0
\(217\) −7.91054 −0.537002
\(218\) 0 0
\(219\) 4.30458 3.39595i 0.290877 0.229477i
\(220\) 0 0
\(221\) 7.76881 9.25851i 0.522587 0.622795i
\(222\) 0 0
\(223\) −3.39317 + 9.32266i −0.227224 + 0.624292i −0.999945 0.0104532i \(-0.996673\pi\)
0.772722 + 0.634745i \(0.218895\pi\)
\(224\) 0 0
\(225\) 0.366785 + 0.734345i 0.0244523 + 0.0489563i
\(226\) 0 0
\(227\) −6.37742 + 5.35129i −0.423284 + 0.355178i −0.829411 0.558639i \(-0.811324\pi\)
0.406127 + 0.913817i \(0.366879\pi\)
\(228\) 0 0
\(229\) −2.18404 + 12.3863i −0.144325 + 0.818508i 0.823581 + 0.567198i \(0.191973\pi\)
−0.967907 + 0.251310i \(0.919139\pi\)
\(230\) 0 0
\(231\) −2.98433 + 1.60491i −0.196355 + 0.105596i
\(232\) 0 0
\(233\) 17.7507 + 10.2484i 1.16289 + 0.671393i 0.951994 0.306116i \(-0.0990296\pi\)
0.210893 + 0.977509i \(0.432363\pi\)
\(234\) 0 0
\(235\) −18.9911 + 10.9645i −1.23884 + 0.715245i
\(236\) 0 0
\(237\) 5.18931 + 15.7182i 0.337082 + 1.02101i
\(238\) 0 0
\(239\) 9.90855 3.60642i 0.640931 0.233280i −0.00105129 0.999999i \(-0.500335\pi\)
0.641982 + 0.766720i \(0.278112\pi\)
\(240\) 0 0
\(241\) −0.569580 3.23025i −0.0366898 0.208078i 0.960952 0.276716i \(-0.0892460\pi\)
−0.997642 + 0.0686372i \(0.978135\pi\)
\(242\) 0 0
\(243\) 10.2991 + 11.7017i 0.660686 + 0.750662i
\(244\) 0 0
\(245\) −9.08604 + 1.60211i −0.580486 + 0.102355i
\(246\) 0 0
\(247\) 10.9734 + 30.1491i 0.698219 + 1.91834i
\(248\) 0 0
\(249\) 6.93031 2.28802i 0.439191 0.144997i
\(250\) 0 0
\(251\) −13.5827 23.5259i −0.857333 1.48494i −0.874464 0.485091i \(-0.838786\pi\)
0.0171305 0.999853i \(-0.494547\pi\)
\(252\) 0 0
\(253\) 3.92991 6.80680i 0.247071 0.427940i
\(254\) 0 0
\(255\) 3.23095 + 6.00795i 0.202330 + 0.376233i
\(256\) 0 0
\(257\) 17.8463 + 3.14678i 1.11322 + 0.196291i 0.699862 0.714278i \(-0.253245\pi\)
0.413358 + 0.910569i \(0.364356\pi\)
\(258\) 0 0
\(259\) −3.26966 3.89663i −0.203167 0.242125i
\(260\) 0 0
\(261\) 17.3140 8.64788i 1.07171 0.535290i
\(262\) 0 0
\(263\) 22.9414 + 8.34997i 1.41463 + 0.514881i 0.932484 0.361212i \(-0.117637\pi\)
0.482141 + 0.876093i \(0.339859\pi\)
\(264\) 0 0
\(265\) −15.0812 12.6546i −0.926430 0.777367i
\(266\) 0 0
\(267\) −7.22884 9.16302i −0.442398 0.560767i
\(268\) 0 0
\(269\) 17.9539i 1.09467i 0.836913 + 0.547336i \(0.184358\pi\)
−0.836913 + 0.547336i \(0.815642\pi\)
\(270\) 0 0
\(271\) 12.9608i 0.787315i −0.919257 0.393658i \(-0.871210\pi\)
0.919257 0.393658i \(-0.128790\pi\)
\(272\) 0 0
\(273\) −7.80411 + 19.5814i −0.472326 + 1.18512i
\(274\) 0 0
\(275\) 0.237445 + 0.199240i 0.0143185 + 0.0120146i
\(276\) 0 0
\(277\) 12.5757 + 4.57718i 0.755600 + 0.275016i 0.690960 0.722893i \(-0.257188\pi\)
0.0646398 + 0.997909i \(0.479410\pi\)
\(278\) 0 0
\(279\) 8.18185 + 11.0407i 0.489835 + 0.660987i
\(280\) 0 0
\(281\) −12.6425 15.0667i −0.754188 0.898806i 0.243278 0.969957i \(-0.421777\pi\)
−0.997466 + 0.0711505i \(0.977333\pi\)
\(282\) 0 0
\(283\) −32.5889 5.74630i −1.93721 0.341582i −0.937234 0.348700i \(-0.886623\pi\)
−0.999975 + 0.00711797i \(0.997734\pi\)
\(284\) 0 0
\(285\) −18.1005 0.546557i −1.07218 0.0323752i
\(286\) 0 0
\(287\) 6.26540 10.8520i 0.369835 0.640573i
\(288\) 0 0
\(289\) −7.02933 12.1752i −0.413490 0.716185i
\(290\) 0 0
\(291\) −5.42041 4.83443i −0.317750 0.283399i
\(292\) 0 0
\(293\) 2.70081 + 7.42041i 0.157783 + 0.433505i 0.993244 0.116045i \(-0.0370216\pi\)
−0.835461 + 0.549550i \(0.814799\pi\)
\(294\) 0 0
\(295\) −32.5623 + 5.74161i −1.89585 + 0.334289i
\(296\) 0 0
\(297\) 5.32665 + 2.50525i 0.309084 + 0.145369i
\(298\) 0 0
\(299\) −8.49044 48.1517i −0.491015 2.78468i
\(300\) 0 0
\(301\) 0.852555 0.310305i 0.0491405 0.0178857i
\(302\) 0 0
\(303\) 5.02477 + 1.04328i 0.288665 + 0.0599351i
\(304\) 0 0
\(305\) 0.569672 0.328901i 0.0326193 0.0188328i
\(306\) 0 0
\(307\) 4.34321 + 2.50755i 0.247880 + 0.143114i 0.618793 0.785554i \(-0.287622\pi\)
−0.370913 + 0.928668i \(0.620955\pi\)
\(308\) 0 0
\(309\) −18.8324 11.6445i −1.07134 0.662435i
\(310\) 0 0
\(311\) 1.21509 6.89111i 0.0689014 0.390759i −0.930781 0.365576i \(-0.880872\pi\)
0.999683 0.0251831i \(-0.00801689\pi\)
\(312\) 0 0
\(313\) 7.39378 6.20412i 0.417921 0.350678i −0.409450 0.912332i \(-0.634280\pi\)
0.827372 + 0.561655i \(0.189835\pi\)
\(314\) 0 0
\(315\) −8.63601 8.18356i −0.486584 0.461092i
\(316\) 0 0
\(317\) 0.807269 2.21795i 0.0453408 0.124573i −0.914956 0.403554i \(-0.867775\pi\)
0.960296 + 0.278982i \(0.0899969\pi\)
\(318\) 0 0
\(319\) 4.69758 5.59835i 0.263014 0.313448i
\(320\) 0 0
\(321\) −2.84544 19.5754i −0.158817 1.09259i
\(322\) 0 0
\(323\) −7.80813 −0.434456
\(324\) 0 0
\(325\) 1.92822 0.106958
\(326\) 0 0
\(327\) 4.48584 + 30.8607i 0.248067 + 1.70660i
\(328\) 0 0
\(329\) 10.6002 12.6328i 0.584407 0.696469i
\(330\) 0 0
\(331\) −2.95113 + 8.10818i −0.162209 + 0.445666i −0.993994 0.109432i \(-0.965097\pi\)
0.831785 + 0.555098i \(0.187319\pi\)
\(332\) 0 0
\(333\) −2.05668 + 8.59371i −0.112706 + 0.470933i
\(334\) 0 0
\(335\) −10.4564 + 8.77397i −0.571294 + 0.479373i
\(336\) 0 0
\(337\) 0.218162 1.23726i 0.0118840 0.0673977i −0.978289 0.207245i \(-0.933550\pi\)
0.990173 + 0.139848i \(0.0446613\pi\)
\(338\) 0 0
\(339\) 17.5350 + 10.8423i 0.952370 + 0.588874i
\(340\) 0 0
\(341\) 4.49388 + 2.59454i 0.243357 + 0.140502i
\(342\) 0 0
\(343\) 16.4778 9.51348i 0.889719 0.513680i
\(344\) 0 0
\(345\) 27.0206 + 5.61024i 1.45474 + 0.302045i
\(346\) 0 0
\(347\) −19.5931 + 7.13131i −1.05181 + 0.382829i −0.809347 0.587331i \(-0.800179\pi\)
−0.242466 + 0.970160i \(0.577956\pi\)
\(348\) 0 0
\(349\) −3.21404 18.2277i −0.172043 0.975707i −0.941501 0.337009i \(-0.890585\pi\)
0.769458 0.638698i \(-0.220526\pi\)
\(350\) 0 0
\(351\) 35.4014 9.36094i 1.88959 0.499650i
\(352\) 0 0
\(353\) 10.6452 1.87704i 0.566588 0.0999048i 0.116986 0.993134i \(-0.462677\pi\)
0.449602 + 0.893229i \(0.351566\pi\)
\(354\) 0 0
\(355\) −2.14058 5.88120i −0.113610 0.312142i
\(356\) 0 0
\(357\) −3.82847 3.41459i −0.202624 0.180719i
\(358\) 0 0
\(359\) 0.479687 + 0.830842i 0.0253169 + 0.0438502i 0.878406 0.477915i \(-0.158607\pi\)
−0.853089 + 0.521765i \(0.825274\pi\)
\(360\) 0 0
\(361\) 0.863791 1.49613i 0.0454627 0.0787437i
\(362\) 0 0
\(363\) −16.8221 0.507954i −0.882933 0.0266607i
\(364\) 0 0
\(365\) 7.15902 + 1.26233i 0.374720 + 0.0660733i
\(366\) 0 0
\(367\) 12.8294 + 15.2895i 0.669688 + 0.798103i 0.988741 0.149634i \(-0.0478095\pi\)
−0.319054 + 0.947737i \(0.603365\pi\)
\(368\) 0 0
\(369\) −21.6263 + 2.47964i −1.12582 + 0.129085i
\(370\) 0 0
\(371\) 13.9122 + 5.06361i 0.722283 + 0.262890i
\(372\) 0 0
\(373\) 18.8836 + 15.8452i 0.977754 + 0.820433i 0.983749 0.179549i \(-0.0574638\pi\)
−0.00599498 + 0.999982i \(0.501908\pi\)
\(374\) 0 0
\(375\) 6.96002 17.4635i 0.359414 0.901813i
\(376\) 0 0
\(377\) 45.4626i 2.34144i
\(378\) 0 0
\(379\) 8.36788i 0.429829i 0.976633 + 0.214915i \(0.0689473\pi\)
−0.976633 + 0.214915i \(0.931053\pi\)
\(380\) 0 0
\(381\) 1.05776 + 1.34078i 0.0541908 + 0.0686902i
\(382\) 0 0
\(383\) 0.716215 + 0.600976i 0.0365969 + 0.0307084i 0.660903 0.750472i \(-0.270174\pi\)
−0.624306 + 0.781180i \(0.714618\pi\)
\(384\) 0 0
\(385\) −4.22171 1.53658i −0.215158 0.0783112i
\(386\) 0 0
\(387\) −1.31489 0.868955i −0.0668394 0.0441715i
\(388\) 0 0
\(389\) −8.06355 9.60976i −0.408838 0.487234i 0.521855 0.853034i \(-0.325240\pi\)
−0.930694 + 0.365800i \(0.880796\pi\)
\(390\) 0 0
\(391\) 11.7185 + 2.06628i 0.592627 + 0.104496i
\(392\) 0 0
\(393\) 7.80185 + 14.5075i 0.393551 + 0.731808i
\(394\) 0 0
\(395\) −10.9732 + 19.0061i −0.552120 + 0.956299i
\(396\) 0 0
\(397\) −10.5305 18.2393i −0.528509 0.915404i −0.999447 0.0332380i \(-0.989418\pi\)
0.470939 0.882166i \(-0.343915\pi\)
\(398\) 0 0
\(399\) 12.9316 4.26931i 0.647388 0.213733i
\(400\) 0 0
\(401\) −1.15588 3.17576i −0.0577220 0.158590i 0.907480 0.420095i \(-0.138003\pi\)
−0.965202 + 0.261505i \(0.915781\pi\)
\(402\) 0 0
\(403\) 31.7899 5.60543i 1.58357 0.279226i
\(404\) 0 0
\(405\) −2.48950 + 20.5174i −0.123704 + 1.01952i
\(406\) 0 0
\(407\) 0.579416 + 3.28603i 0.0287206 + 0.162883i
\(408\) 0 0
\(409\) −24.3709 + 8.87029i −1.20506 + 0.438607i −0.864989 0.501791i \(-0.832675\pi\)
−0.340075 + 0.940398i \(0.610452\pi\)
\(410\) 0 0
\(411\) 11.8587 + 35.9197i 0.584949 + 1.77179i
\(412\) 0 0
\(413\) 21.5338 12.4326i 1.05961 0.611767i
\(414\) 0 0
\(415\) 8.37997 + 4.83818i 0.411356 + 0.237497i
\(416\) 0 0
\(417\) 29.3404 15.7786i 1.43680 0.772683i
\(418\) 0 0
\(419\) 5.30706 30.0979i 0.259267 1.47038i −0.525610 0.850725i \(-0.676163\pi\)
0.784877 0.619651i \(-0.212726\pi\)
\(420\) 0 0
\(421\) 3.65610 3.06783i 0.178187 0.149517i −0.549332 0.835604i \(-0.685118\pi\)
0.727519 + 0.686087i \(0.240673\pi\)
\(422\) 0 0
\(423\) −28.5952 1.72848i −1.39035 0.0840414i
\(424\) 0 0
\(425\) −0.160497 + 0.440962i −0.00778524 + 0.0213898i
\(426\) 0 0
\(427\) −0.317972 + 0.378945i −0.0153878 + 0.0183384i
\(428\) 0 0
\(429\) 10.8559 8.56435i 0.524125 0.413491i
\(430\) 0 0
\(431\) 32.3238 1.55698 0.778491 0.627656i \(-0.215985\pi\)
0.778491 + 0.627656i \(0.215985\pi\)
\(432\) 0 0
\(433\) 14.6596 0.704497 0.352249 0.935907i \(-0.385417\pi\)
0.352249 + 0.935907i \(0.385417\pi\)
\(434\) 0 0
\(435\) 23.8365 + 9.49996i 1.14287 + 0.455488i
\(436\) 0 0
\(437\) −20.3043 + 24.1977i −0.971285 + 1.15753i
\(438\) 0 0
\(439\) 2.75846 7.57882i 0.131654 0.361717i −0.856297 0.516484i \(-0.827240\pi\)
0.987951 + 0.154767i \(0.0494627\pi\)
\(440\) 0 0
\(441\) −11.0566 4.79818i −0.526506 0.228485i
\(442\) 0 0
\(443\) −17.3346 + 14.5455i −0.823593 + 0.691076i −0.953810 0.300409i \(-0.902877\pi\)
0.130218 + 0.991485i \(0.458432\pi\)
\(444\) 0 0
\(445\) 2.68707 15.2392i 0.127380 0.722405i
\(446\) 0 0
\(447\) −0.107343 + 3.55492i −0.00507715 + 0.168142i
\(448\) 0 0
\(449\) 5.54560 + 3.20175i 0.261713 + 0.151100i 0.625116 0.780532i \(-0.285052\pi\)
−0.363403 + 0.931632i \(0.618385\pi\)
\(450\) 0 0
\(451\) −7.11860 + 4.10992i −0.335202 + 0.193529i
\(452\) 0 0
\(453\) 11.4775 12.8687i 0.539261 0.604625i
\(454\) 0 0
\(455\) −26.2625 + 9.55876i −1.23120 + 0.448122i
\(456\) 0 0
\(457\) 1.41804 + 8.04210i 0.0663331 + 0.376194i 0.999844 + 0.0176455i \(0.00561702\pi\)
−0.933511 + 0.358548i \(0.883272\pi\)
\(458\) 0 0
\(459\) −0.805924 + 8.87507i −0.0376173 + 0.414253i
\(460\) 0 0
\(461\) 21.5599 3.80159i 1.00414 0.177058i 0.352686 0.935742i \(-0.385269\pi\)
0.651459 + 0.758684i \(0.274157\pi\)
\(462\) 0 0
\(463\) −2.20720 6.06423i −0.102577 0.281829i 0.877778 0.479067i \(-0.159025\pi\)
−0.980356 + 0.197238i \(0.936803\pi\)
\(464\) 0 0
\(465\) −3.70391 + 17.8392i −0.171765 + 0.827271i
\(466\) 0 0
\(467\) 12.0625 + 20.8929i 0.558188 + 0.966810i 0.997648 + 0.0685478i \(0.0218366\pi\)
−0.439460 + 0.898262i \(0.644830\pi\)
\(468\) 0 0
\(469\) 5.13246 8.88969i 0.236995 0.410488i
\(470\) 0 0
\(471\) −9.35362 + 15.1273i −0.430992 + 0.697031i
\(472\) 0 0
\(473\) −0.586102 0.103346i −0.0269490 0.00475183i
\(474\) 0 0
\(475\) −0.800726 0.954268i −0.0367398 0.0437848i
\(476\) 0 0
\(477\) −7.32209 24.6543i −0.335256 1.12884i
\(478\) 0 0
\(479\) 20.6931 + 7.53168i 0.945493 + 0.344131i 0.768333 0.640051i \(-0.221087\pi\)
0.177160 + 0.984182i \(0.443309\pi\)
\(480\) 0 0
\(481\) 15.9009 + 13.3424i 0.725019 + 0.608363i
\(482\) 0 0
\(483\) −20.5375 + 2.98528i −0.934489 + 0.135835i
\(484\) 0 0
\(485\) 9.62976i 0.437265i
\(486\) 0 0
\(487\) 2.57215i 0.116555i −0.998300 0.0582777i \(-0.981439\pi\)
0.998300 0.0582777i \(-0.0185609\pi\)
\(488\) 0 0
\(489\) −38.7431 + 5.63160i −1.75202 + 0.254670i
\(490\) 0 0
\(491\) 24.4783 + 20.5398i 1.10469 + 0.926946i 0.997732 0.0673168i \(-0.0214438\pi\)
0.106960 + 0.994263i \(0.465888\pi\)
\(492\) 0 0
\(493\) 10.3968 + 3.78412i 0.468247 + 0.170428i
\(494\) 0 0
\(495\) 2.22192 + 7.48147i 0.0998680 + 0.336267i
\(496\) 0 0
\(497\) 3.02535 + 3.60547i 0.135705 + 0.161727i
\(498\) 0 0
\(499\) −25.8045 4.55003i −1.15517 0.203687i −0.436937 0.899492i \(-0.643937\pi\)
−0.718231 + 0.695805i \(0.755048\pi\)
\(500\) 0 0
\(501\) 18.0529 29.1964i 0.806543 1.30440i
\(502\) 0 0
\(503\) 13.4076 23.2226i 0.597814 1.03544i −0.395329 0.918540i \(-0.629369\pi\)
0.993143 0.116905i \(-0.0372972\pi\)
\(504\) 0 0
\(505\) 3.40208 + 5.89258i 0.151391 + 0.262216i
\(506\) 0 0
\(507\) 12.9093 62.1752i 0.573323 2.76130i
\(508\) 0 0
\(509\) −3.39845 9.33715i −0.150633 0.413862i 0.841308 0.540555i \(-0.181786\pi\)
−0.991942 + 0.126693i \(0.959564\pi\)
\(510\) 0 0
\(511\) −5.38370 + 0.949292i −0.238161 + 0.0419942i
\(512\) 0 0
\(513\) −19.3337 13.6327i −0.853605 0.601900i
\(514\) 0 0
\(515\) −5.09771 28.9105i −0.224632 1.27395i
\(516\) 0 0
\(517\) −10.1652 + 3.69984i −0.447066 + 0.162719i
\(518\) 0 0
\(519\) 11.0071 12.3413i 0.483158 0.541721i
\(520\) 0 0
\(521\) −9.45901 + 5.46116i −0.414407 + 0.239258i −0.692681 0.721244i \(-0.743571\pi\)
0.278275 + 0.960502i \(0.410237\pi\)
\(522\) 0 0
\(523\) −5.09476 2.94146i −0.222778 0.128621i 0.384458 0.923143i \(-0.374388\pi\)
−0.607236 + 0.794521i \(0.707722\pi\)
\(524\) 0 0
\(525\) 0.0247019 0.818062i 0.00107808 0.0357032i
\(526\) 0 0
\(527\) −1.36417 + 7.73657i −0.0594240 + 0.337010i
\(528\) 0 0
\(529\) 19.2571 16.1586i 0.837266 0.702550i
\(530\) 0 0
\(531\) −39.6244 17.1956i −1.71955 0.746224i
\(532\) 0 0
\(533\) −17.4889 + 48.0504i −0.757529 + 2.08129i
\(534\) 0 0
\(535\) 16.8583 20.0909i 0.728846 0.868605i
\(536\) 0 0
\(537\) 7.54021 + 3.00512i 0.325384 + 0.129681i
\(538\) 0 0
\(539\) −4.55130 −0.196038
\(540\) 0 0
\(541\) −31.3090 −1.34608 −0.673039 0.739607i \(-0.735011\pi\)
−0.673039 + 0.739607i \(0.735011\pi\)
\(542\) 0 0
\(543\) −16.0630 + 12.6723i −0.689329 + 0.543822i
\(544\) 0 0
\(545\) −26.5771 + 31.6734i −1.13844 + 1.35674i
\(546\) 0 0
\(547\) 1.77952 4.88920i 0.0760870 0.209047i −0.895818 0.444421i \(-0.853409\pi\)
0.971905 + 0.235374i \(0.0756315\pi\)
\(548\) 0 0
\(549\) 0.857767 + 0.0518489i 0.0366086 + 0.00221286i
\(550\) 0 0
\(551\) −22.4993 + 18.8791i −0.958500 + 0.804277i
\(552\) 0 0
\(553\) 2.86589 16.2533i 0.121870 0.691159i
\(554\) 0 0
\(555\) −10.3183 + 5.54896i −0.437987 + 0.235540i
\(556\) 0 0
\(557\) −24.3579 14.0631i −1.03208 0.595871i −0.114499 0.993423i \(-0.536526\pi\)
−0.917580 + 0.397552i \(0.869860\pi\)
\(558\) 0 0
\(559\) −3.20627 + 1.85114i −0.135611 + 0.0782949i
\(560\) 0 0
\(561\) 1.05497 + 3.19547i 0.0445410 + 0.134913i
\(562\) 0 0
\(563\) 25.1504 9.15398i 1.05996 0.385794i 0.247547 0.968876i \(-0.420375\pi\)
0.812414 + 0.583081i \(0.198153\pi\)
\(564\) 0 0
\(565\) 4.74651 + 26.9188i 0.199687 + 1.13248i
\(566\) 0 0
\(567\) −3.51794 15.1393i −0.147740 0.635789i
\(568\) 0 0
\(569\) 2.77648 0.489568i 0.116396 0.0205238i −0.115147 0.993348i \(-0.536734\pi\)
0.231543 + 0.972825i \(0.425623\pi\)
\(570\) 0 0
\(571\) 9.98909 + 27.4448i 0.418031 + 1.14853i 0.952818 + 0.303543i \(0.0981695\pi\)
−0.534787 + 0.844987i \(0.679608\pi\)
\(572\) 0 0
\(573\) 26.9667 8.90296i 1.12655 0.371926i
\(574\) 0 0
\(575\) 0.949200 + 1.64406i 0.0395844 + 0.0685622i
\(576\) 0 0
\(577\) −19.3591 + 33.5310i −0.805930 + 1.39591i 0.109731 + 0.993961i \(0.465001\pi\)
−0.915661 + 0.401951i \(0.868332\pi\)
\(578\) 0 0
\(579\) −1.06060 1.97219i −0.0440772 0.0819616i
\(580\) 0 0
\(581\) −7.16622 1.26360i −0.297305 0.0524229i
\(582\) 0 0
\(583\) −6.24254 7.43957i −0.258539 0.308115i
\(584\) 0 0
\(585\) 40.5043 + 26.7677i 1.67465 + 1.10671i
\(586\) 0 0
\(587\) −10.2093 3.71586i −0.421381 0.153370i 0.122622 0.992453i \(-0.460870\pi\)
−0.544003 + 0.839083i \(0.683092\pi\)
\(588\) 0 0
\(589\) −15.9754 13.4050i −0.658256 0.552343i
\(590\) 0 0
\(591\) −22.0449 27.9433i −0.906807 1.14944i
\(592\) 0 0
\(593\) 10.1060i 0.415003i 0.978235 + 0.207501i \(0.0665332\pi\)
−0.978235 + 0.207501i \(0.933467\pi\)
\(594\) 0 0
\(595\) 6.80156i 0.278837i
\(596\) 0 0
\(597\) 4.53515 11.3792i 0.185611 0.465722i
\(598\) 0 0
\(599\) −0.142727 0.119762i −0.00583168 0.00489336i 0.639867 0.768486i \(-0.278989\pi\)
−0.645699 + 0.763592i \(0.723434\pi\)
\(600\) 0 0
\(601\) 28.1284 + 10.2379i 1.14738 + 0.417612i 0.844573 0.535440i \(-0.179854\pi\)
0.302806 + 0.953052i \(0.402076\pi\)
\(602\) 0 0
\(603\) −17.7157 + 2.03126i −0.721441 + 0.0827194i
\(604\) 0 0
\(605\) −14.3430 17.0933i −0.583126 0.694942i
\(606\) 0 0
\(607\) 16.7567 + 2.95465i 0.680132 + 0.119926i 0.503033 0.864267i \(-0.332217\pi\)
0.177099 + 0.984193i \(0.443329\pi\)
\(608\) 0 0
\(609\) −19.2879 0.582409i −0.781584 0.0236004i
\(610\) 0 0
\(611\) −33.6472 + 58.2786i −1.36122 + 2.35770i
\(612\) 0 0
\(613\) 14.6554 + 25.3840i 0.591928 + 1.02525i 0.993973 + 0.109629i \(0.0349662\pi\)
−0.402045 + 0.915620i \(0.631700\pi\)
\(614\) 0 0
\(615\) −21.5389 19.2104i −0.868530 0.774636i
\(616\) 0 0
\(617\) −6.62643 18.2060i −0.266770 0.732945i −0.998671 0.0515338i \(-0.983589\pi\)
0.731901 0.681411i \(-0.238633\pi\)
\(618\) 0 0
\(619\) −0.171532 + 0.0302457i −0.00689445 + 0.00121568i −0.177094 0.984194i \(-0.556670\pi\)
0.170200 + 0.985410i \(0.445559\pi\)
\(620\) 0 0
\(621\) 25.4084 + 25.5763i 1.01961 + 1.02634i
\(622\) 0 0
\(623\) 2.02072 + 11.4601i 0.0809586 + 0.459139i
\(624\) 0 0
\(625\) 24.7075 8.99281i 0.988302 0.359712i
\(626\) 0 0
\(627\) −8.74654 1.81603i −0.349303 0.0725252i
\(628\) 0 0
\(629\) −4.37479 + 2.52579i −0.174434 + 0.100710i
\(630\) 0 0
\(631\) −19.9875 11.5398i −0.795691 0.459392i 0.0462714 0.998929i \(-0.485266\pi\)
−0.841962 + 0.539537i \(0.818599\pi\)
\(632\) 0 0
\(633\) −19.0571 11.7835i −0.757453 0.468352i
\(634\) 0 0
\(635\) −0.393186 + 2.22987i −0.0156031 + 0.0884897i
\(636\) 0 0
\(637\) −21.6889 + 18.1991i −0.859344 + 0.721075i
\(638\) 0 0
\(639\) 1.90300 7.95157i 0.0752816 0.314559i
\(640\) 0 0
\(641\) −10.1866 + 27.9876i −0.402348 + 1.10544i 0.558775 + 0.829320i \(0.311272\pi\)
−0.961123 + 0.276122i \(0.910951\pi\)
\(642\) 0 0
\(643\) 27.1310 32.3334i 1.06994 1.27511i 0.110294 0.993899i \(-0.464821\pi\)
0.959647 0.281207i \(-0.0907348\pi\)
\(644\) 0 0
\(645\) −0.300585 2.06790i −0.0118355 0.0814235i
\(646\) 0 0
\(647\) −22.3033 −0.876834 −0.438417 0.898772i \(-0.644461\pi\)
−0.438417 + 0.898772i \(0.644461\pi\)
\(648\) 0 0
\(649\) −16.3108 −0.640256
\(650\) 0 0
\(651\) −1.97090 13.5590i −0.0772455 0.531417i
\(652\) 0 0
\(653\) 12.2527 14.6022i 0.479487 0.571430i −0.471025 0.882120i \(-0.656116\pi\)
0.950511 + 0.310690i \(0.100560\pi\)
\(654\) 0 0
\(655\) −7.46965 + 20.5227i −0.291863 + 0.801888i
\(656\) 0 0
\(657\) 6.89327 + 6.53212i 0.268932 + 0.254842i
\(658\) 0 0
\(659\) 1.06327 0.892192i 0.0414193 0.0347549i −0.621843 0.783142i \(-0.713616\pi\)
0.663262 + 0.748387i \(0.269171\pi\)
\(660\) 0 0
\(661\) 6.42078 36.4141i 0.249739 1.41634i −0.559484 0.828841i \(-0.689000\pi\)
0.809223 0.587502i \(-0.199888\pi\)
\(662\) 0 0
\(663\) 17.8050 + 11.0093i 0.691489 + 0.427565i
\(664\) 0 0
\(665\) 15.6365 + 9.02776i 0.606359 + 0.350082i
\(666\) 0 0
\(667\) 38.7629 22.3798i 1.50091 0.866548i
\(668\) 0 0
\(669\) −16.8248 3.49330i −0.650484 0.135059i
\(670\) 0 0
\(671\) 0.304925 0.110984i 0.0117715 0.00428447i
\(672\) 0 0
\(673\) 4.93462 + 27.9856i 0.190215 + 1.07877i 0.919069 + 0.394096i \(0.128942\pi\)
−0.728854 + 0.684669i \(0.759947\pi\)
\(674\) 0 0
\(675\) −1.16731 + 0.811644i −0.0449298 + 0.0312402i
\(676\) 0 0
\(677\) 34.8917 6.15234i 1.34100 0.236454i 0.543313 0.839530i \(-0.317170\pi\)
0.797683 + 0.603077i \(0.206059\pi\)
\(678\) 0 0
\(679\) 2.47682 + 6.80500i 0.0950516 + 0.261152i
\(680\) 0 0
\(681\) −10.7612 9.59787i −0.412371 0.367791i
\(682\) 0 0
\(683\) 17.7063 + 30.6681i 0.677511 + 1.17348i 0.975728 + 0.218986i \(0.0702749\pi\)
−0.298217 + 0.954498i \(0.596392\pi\)
\(684\) 0 0
\(685\) −25.0762 + 43.4332i −0.958111 + 1.65950i
\(686\) 0 0
\(687\) −21.7747 0.657500i −0.830756 0.0250852i
\(688\) 0 0
\(689\) −59.4967 10.4909i −2.26664 0.399670i
\(690\) 0 0
\(691\) 3.47685 + 4.14355i 0.132266 + 0.157628i 0.828112 0.560563i \(-0.189415\pi\)
−0.695847 + 0.718191i \(0.744971\pi\)
\(692\) 0 0
\(693\) −3.49442 4.71540i −0.132742 0.179123i
\(694\) 0 0
\(695\) 41.5056 + 15.1068i 1.57440 + 0.573033i
\(696\) 0 0
\(697\) −9.53288 7.99904i −0.361084 0.302985i
\(698\) 0 0
\(699\) −13.1435 + 32.9787i −0.497134 + 1.24737i
\(700\) 0 0
\(701\) 35.4485i 1.33887i 0.742870 + 0.669436i \(0.233464\pi\)
−0.742870 + 0.669436i \(0.766536\pi\)
\(702\) 0 0
\(703\) 13.4100i 0.505767i
\(704\) 0 0
\(705\) −23.5251 29.8196i −0.886008 1.12307i
\(706\) 0 0
\(707\) −3.91973 3.28904i −0.147417 0.123697i
\(708\) 0 0
\(709\) 17.5781 + 6.39792i 0.660161 + 0.240279i 0.650306 0.759672i \(-0.274641\pi\)
0.00985524 + 0.999951i \(0.496863\pi\)
\(710\) 0 0
\(711\) −25.6487 + 12.8108i −0.961901 + 0.480444i
\(712\) 0 0
\(713\) 20.4286 + 24.3458i 0.765055 + 0.911757i
\(714\) 0 0
\(715\) 18.0545 + 3.18350i 0.675201 + 0.119056i
\(716\) 0 0
\(717\) 8.65023 + 16.0851i 0.323049 + 0.600709i
\(718\) 0 0
\(719\) 17.9949 31.1681i 0.671097 1.16237i −0.306496 0.951872i \(-0.599157\pi\)
0.977593 0.210503i \(-0.0675101\pi\)
\(720\) 0 0
\(721\) 11.0383 + 19.1189i 0.411087 + 0.712024i
\(722\) 0 0
\(723\) 5.39485 1.78109i 0.200637 0.0662395i
\(724\) 0 0
\(725\) 0.603717 + 1.65870i 0.0224215 + 0.0616026i
\(726\) 0 0
\(727\) −7.82609 + 1.37995i −0.290254 + 0.0511796i −0.316879 0.948466i \(-0.602635\pi\)
0.0266254 + 0.999645i \(0.491524\pi\)
\(728\) 0 0
\(729\) −17.4911 + 20.5685i −0.647819 + 0.761795i
\(730\) 0 0
\(731\) −0.156458 0.887319i −0.00578682 0.0328187i
\(732\) 0 0
\(733\) 8.97374 3.26618i 0.331453 0.120639i −0.170933 0.985283i \(-0.554678\pi\)
0.502385 + 0.864644i \(0.332456\pi\)
\(734\) 0 0
\(735\) −5.00985 15.1746i −0.184791 0.559725i
\(736\) 0 0
\(737\) −5.83138 + 3.36675i −0.214802 + 0.124016i
\(738\) 0 0
\(739\) −23.3163 13.4617i −0.857704 0.495195i 0.00553893 0.999985i \(-0.498237\pi\)
−0.863243 + 0.504789i \(0.831570\pi\)
\(740\) 0 0
\(741\) −48.9427 + 26.3204i −1.79795 + 0.966903i
\(742\) 0 0
\(743\) −2.09650 + 11.8899i −0.0769132 + 0.436196i 0.921897 + 0.387434i \(0.126639\pi\)
−0.998810 + 0.0487619i \(0.984472\pi\)
\(744\) 0 0
\(745\) −3.61223 + 3.03102i −0.132342 + 0.111048i
\(746\) 0 0
\(747\) 5.64842 + 11.3088i 0.206665 + 0.413766i
\(748\) 0 0
\(749\) −6.74566 + 18.5335i −0.246481 + 0.677201i
\(750\) 0 0
\(751\) 25.0832 29.8929i 0.915297 1.09081i −0.0802713 0.996773i \(-0.525579\pi\)
0.995569 0.0940360i \(-0.0299769\pi\)
\(752\) 0 0
\(753\) 36.9402 29.1427i 1.34618 1.06202i
\(754\) 0 0
\(755\) 22.8622 0.832042
\(756\) 0 0
\(757\) 14.8793 0.540797 0.270398 0.962749i \(-0.412845\pi\)
0.270398 + 0.962749i \(0.412845\pi\)
\(758\) 0 0
\(759\) 12.6462 + 5.04011i 0.459029 + 0.182944i
\(760\) 0 0
\(761\) 9.15327 10.9084i 0.331806 0.395431i −0.574187 0.818724i \(-0.694682\pi\)
0.905993 + 0.423294i \(0.139126\pi\)
\(762\) 0 0
\(763\) 10.6346 29.2182i 0.384997 1.05777i
\(764\) 0 0
\(765\) −9.49287 + 7.03485i −0.343216 + 0.254345i
\(766\) 0 0
\(767\) −77.7280 + 65.2215i −2.80659 + 2.35501i
\(768\) 0 0
\(769\) −0.349200 + 1.98041i −0.0125925 + 0.0714154i −0.990456 0.137826i \(-0.955988\pi\)
0.977864 + 0.209242i \(0.0670995\pi\)
\(770\) 0 0
\(771\) −0.947333 + 31.3732i −0.0341174 + 1.12988i
\(772\) 0 0
\(773\) −21.2389 12.2623i −0.763910 0.441044i 0.0667878 0.997767i \(-0.478725\pi\)
−0.830698 + 0.556724i \(0.812058\pi\)
\(774\) 0 0
\(775\) −1.08542 + 0.626666i −0.0389894 + 0.0225105i
\(776\) 0 0
\(777\) 5.86434 6.57516i 0.210382 0.235883i
\(778\) 0 0
\(779\) 31.0425 11.2986i 1.11221 0.404813i
\(780\) 0 0
\(781\) −0.536121 3.04049i −0.0191839 0.108797i
\(782\) 0 0
\(783\) 19.1365 + 27.5223i 0.683884 + 0.983565i
\(784\) 0 0
\(785\) −23.2227 + 4.09479i −0.828854 + 0.146149i
\(786\) 0 0
\(787\) −3.81446 10.4801i −0.135971 0.373577i 0.852956 0.521984i \(-0.174808\pi\)
−0.988926 + 0.148407i \(0.952586\pi\)
\(788\) 0 0
\(789\) −8.59637 + 41.4027i −0.306039 + 1.47398i
\(790\) 0 0
\(791\) −10.2778 17.8017i −0.365438 0.632957i
\(792\) 0 0
\(793\) 1.00931 1.74818i 0.0358416 0.0620795i
\(794\) 0 0
\(795\) 17.9330 29.0026i 0.636019 1.02862i
\(796\) 0 0
\(797\) −31.9401 5.63191i −1.13138 0.199492i −0.423547 0.905874i \(-0.639215\pi\)
−0.707831 + 0.706382i \(0.750326\pi\)
\(798\) 0 0
\(799\) −10.5270 12.5456i −0.372419 0.443831i
\(800\) 0 0
\(801\) 13.9047 14.6735i 0.491298 0.518461i
\(802\) 0 0
\(803\) 3.36977 + 1.22650i 0.118917 + 0.0432821i
\(804\) 0 0
\(805\) −21.0783 17.6868i −0.742912 0.623378i
\(806\) 0 0
\(807\) −30.7737 + 4.47319i −1.08329 + 0.157464i
\(808\) 0 0
\(809\) 50.2942i 1.76825i −0.467250 0.884125i \(-0.654755\pi\)
0.467250 0.884125i \(-0.345245\pi\)
\(810\) 0 0
\(811\) 29.1337i 1.02302i −0.859276 0.511512i \(-0.829086\pi\)
0.859276 0.511512i \(-0.170914\pi\)
\(812\) 0 0
\(813\) 22.2154 3.22917i 0.779127 0.113252i
\(814\) 0 0
\(815\) −39.7633 33.3654i −1.39285 1.16874i
\(816\) 0 0
\(817\) 2.24758 + 0.818053i 0.0786329 + 0.0286200i
\(818\) 0 0
\(819\) −35.5077 8.49785i −1.24074 0.296939i
\(820\) 0 0
\(821\) 7.24195 + 8.63062i 0.252746 + 0.301211i 0.877467 0.479637i \(-0.159232\pi\)
−0.624721 + 0.780848i \(0.714787\pi\)
\(822\) 0 0
\(823\) 36.2233 + 6.38715i 1.26267 + 0.222642i 0.764605 0.644499i \(-0.222934\pi\)
0.498062 + 0.867142i \(0.334045\pi\)
\(824\) 0 0
\(825\) −0.282346 + 0.456629i −0.00983001 + 0.0158978i
\(826\) 0 0
\(827\) 11.8729 20.5645i 0.412862 0.715097i −0.582340 0.812946i \(-0.697863\pi\)
0.995201 + 0.0978483i \(0.0311960\pi\)
\(828\) 0 0
\(829\) −6.19006 10.7215i −0.214990 0.372373i 0.738280 0.674495i \(-0.235638\pi\)
−0.953269 + 0.302122i \(0.902305\pi\)
\(830\) 0 0
\(831\) −4.71224 + 22.6956i −0.163466 + 0.787302i
\(832\) 0 0
\(833\) −2.35664 6.47482i −0.0816528 0.224339i
\(834\) 0 0
\(835\) 44.8208 7.90312i 1.55109 0.273499i
\(836\) 0 0
\(837\) −16.8856 + 16.7748i −0.583652 + 0.579821i
\(838\) 0 0
\(839\) 4.34934 + 24.6663i 0.150156 + 0.851576i 0.963082 + 0.269209i \(0.0867622\pi\)
−0.812926 + 0.582367i \(0.802127\pi\)
\(840\) 0 0
\(841\) 11.8569 4.31556i 0.408859 0.148812i
\(842\) 0 0
\(843\) 22.6751 25.4236i 0.780972 0.875634i
\(844\) 0 0
\(845\) 72.9132 42.0965i 2.50829 1.44816i
\(846\) 0 0
\(847\) 14.5322 + 8.39015i 0.499331 + 0.288289i
\(848\) 0 0
\(849\) 1.72992 57.2903i 0.0593705 1.96620i
\(850\) 0 0
\(851\) −3.54870 + 20.1257i −0.121648 + 0.689900i
\(852\) 0 0
\(853\) 24.5488 20.5989i 0.840534 0.705292i −0.117150 0.993114i \(-0.537376\pi\)
0.957684 + 0.287823i \(0.0929314\pi\)
\(854\) 0 0
\(855\) −3.57290 31.1612i −0.122190 1.06569i
\(856\) 0 0
\(857\) 2.97196 8.16540i 0.101520 0.278925i −0.878526 0.477695i \(-0.841472\pi\)
0.980046 + 0.198770i \(0.0636947\pi\)
\(858\) 0 0
\(859\) −22.4663 + 26.7742i −0.766539 + 0.913525i −0.998243 0.0592610i \(-0.981126\pi\)
0.231704 + 0.972786i \(0.425570\pi\)
\(860\) 0 0
\(861\) 20.1617 + 8.03538i 0.687110 + 0.273845i
\(862\) 0 0
\(863\) 16.7973 0.571787 0.285894 0.958261i \(-0.407710\pi\)
0.285894 + 0.958261i \(0.407710\pi\)
\(864\) 0 0
\(865\) 21.9252 0.745478
\(866\) 0 0
\(867\) 19.1173 15.0819i 0.649258 0.512210i
\(868\) 0 0
\(869\) −6.95891 + 8.29331i −0.236065 + 0.281331i
\(870\) 0 0
\(871\) −14.3265 + 39.3617i −0.485435 + 1.33372i
\(872\) 0 0
\(873\) 6.93591 10.4953i 0.234745 0.355211i
\(874\) 0 0
\(875\) −14.3588 + 12.0485i −0.485417 + 0.407313i
\(876\) 0 0
\(877\) −3.16969 + 17.9762i −0.107033 + 0.607014i 0.883356 + 0.468703i \(0.155278\pi\)
−0.990389 + 0.138311i \(0.955833\pi\)
\(878\) 0 0
\(879\) −12.0460 + 6.47807i −0.406300 + 0.218500i
\(880\) 0 0
\(881\) −13.0580 7.53906i −0.439937 0.253997i 0.263634 0.964623i \(-0.415079\pi\)
−0.703571 + 0.710625i \(0.748412\pi\)
\(882\) 0 0
\(883\) −50.9799 + 29.4332i −1.71561 + 0.990508i −0.789076 + 0.614295i \(0.789440\pi\)
−0.926534 + 0.376212i \(0.877226\pi\)
\(884\) 0 0
\(885\) −17.9542 54.3825i −0.603523 1.82805i
\(886\) 0 0
\(887\) 4.26584 1.55264i 0.143233 0.0521325i −0.269409 0.963026i \(-0.586828\pi\)
0.412642 + 0.910893i \(0.364606\pi\)
\(888\) 0 0
\(889\) −0.295683 1.67690i −0.00991688 0.0562414i
\(890\) 0 0
\(891\) −2.96696 + 9.75426i −0.0993969 + 0.326780i
\(892\) 0 0
\(893\) 42.8144 7.54934i 1.43273 0.252629i
\(894\) 0 0
\(895\) 3.68079 + 10.1129i 0.123035 + 0.338036i
\(896\) 0 0
\(897\) 80.4184 26.5498i 2.68509 0.886473i
\(898\) 0 0
\(899\) 14.7752 + 25.5914i 0.492781 + 0.853522i
\(900\) 0 0
\(901\) 7.35140 12.7330i 0.244911 0.424198i
\(902\) 0 0
\(903\) 0.744287 + 1.38400i 0.0247683 + 0.0460566i
\(904\) 0 0
\(905\) −26.7146 4.71051i −0.888024 0.156583i
\(906\) 0 0
\(907\) 28.1038 + 33.4928i 0.933170 + 1.11211i 0.993489 + 0.113930i \(0.0363439\pi\)
−0.0603187 + 0.998179i \(0.519212\pi\)
\(908\) 0 0
\(909\) −0.536315 + 8.87258i −0.0177884 + 0.294285i
\(910\) 0 0
\(911\) −19.4906 7.09401i −0.645753 0.235035i −0.00167985 0.999999i \(-0.500535\pi\)
−0.644074 + 0.764964i \(0.722757\pi\)
\(912\) 0 0
\(913\) 3.65660 + 3.06825i 0.121016 + 0.101544i
\(914\) 0 0
\(915\) 0.705681 + 0.894495i 0.0233291 + 0.0295711i
\(916\) 0 0
\(917\) 16.4239i 0.542364i
\(918\) 0 0
\(919\) 37.4910i 1.23671i −0.785897 0.618357i \(-0.787798\pi\)
0.785897 0.618357i \(-0.212202\pi\)
\(920\) 0 0
\(921\) −3.21594 + 8.06918i −0.105969 + 0.265888i
\(922\) 0 0
\(923\) −14.7128 12.3455i −0.484276 0.406356i
\(924\) 0 0
\(925\) −0.757324 0.275643i −0.0249007 0.00906310i
\(926\) 0 0
\(927\) 15.2671 35.1807i 0.501439 1.15548i
\(928\) 0 0
\(929\) 29.3763 + 35.0093i 0.963805 + 1.14862i 0.988848 + 0.148931i \(0.0475833\pi\)
−0.0250429 + 0.999686i \(0.507972\pi\)
\(930\) 0 0
\(931\) 18.0134 + 3.17624i 0.590364 + 0.104097i
\(932\) 0 0
\(933\) 12.1144 + 0.365801i 0.396607 + 0.0119758i
\(934\) 0 0
\(935\) −2.23082 + 3.86389i −0.0729555 + 0.126363i
\(936\) 0 0
\(937\) 8.33351 + 14.4341i 0.272244 + 0.471540i 0.969436 0.245344i \(-0.0789009\pi\)
−0.697192 + 0.716884i \(0.745568\pi\)
\(938\) 0 0
\(939\) 12.4762 + 11.1275i 0.407147 + 0.363132i
\(940\) 0 0
\(941\) −0.201193 0.552774i −0.00655871 0.0180199i 0.936370 0.351014i \(-0.114163\pi\)
−0.942929 + 0.332994i \(0.891941\pi\)
\(942\) 0 0
\(943\) −49.5786 + 8.74205i −1.61450 + 0.284680i
\(944\) 0 0
\(945\) 11.8753 16.8414i 0.386303 0.547850i
\(946\) 0 0
\(947\) −4.71530 26.7418i −0.153227 0.868991i −0.960389 0.278662i \(-0.910109\pi\)
0.807163 0.590329i \(-0.201002\pi\)
\(948\) 0 0
\(949\) 20.9627 7.62981i 0.680479 0.247674i
\(950\) 0 0
\(951\) 4.00279 + 0.831091i 0.129799 + 0.0269500i
\(952\) 0 0
\(953\) −10.9811 + 6.33992i −0.355711 + 0.205370i −0.667198 0.744880i \(-0.732506\pi\)
0.311486 + 0.950251i \(0.399173\pi\)
\(954\) 0 0
\(955\) 32.6075 + 18.8259i 1.05515 + 0.609193i
\(956\) 0 0
\(957\) 10.7662 + 6.65700i 0.348021 + 0.215190i
\(958\) 0 0
\(959\) 6.54920 37.1424i 0.211485 1.19939i
\(960\) 0 0
\(961\) 7.67417 6.43939i 0.247554 0.207722i
\(962\) 0 0
\(963\) 32.8441 9.75437i 1.05839 0.314330i
\(964\) 0 0
\(965\) 1.01544 2.78991i 0.0326883 0.0898104i
\(966\) 0 0
\(967\) −15.6644 + 18.6681i −0.503733 + 0.600326i −0.956655 0.291224i \(-0.905937\pi\)
0.452921 + 0.891550i \(0.350382\pi\)
\(968\) 0 0
\(969\) −1.94538 13.3834i −0.0624947 0.429938i
\(970\) 0 0
\(971\) 0.678594 0.0217771 0.0108886 0.999941i \(-0.496534\pi\)
0.0108886 + 0.999941i \(0.496534\pi\)
\(972\) 0 0
\(973\) −33.2160 −1.06486
\(974\) 0 0
\(975\) 0.480412 + 3.30504i 0.0153855 + 0.105846i
\(976\) 0 0
\(977\) −13.2188 + 15.7535i −0.422907 + 0.504000i −0.934862 0.355012i \(-0.884477\pi\)
0.511955 + 0.859012i \(0.328921\pi\)
\(978\) 0 0
\(979\) 2.61080 7.17311i 0.0834415 0.229254i
\(980\) 0 0
\(981\) −51.7788 + 15.3778i −1.65317 + 0.490975i
\(982\) 0 0
\(983\) 34.4879 28.9388i 1.09999 0.923005i 0.102570 0.994726i \(-0.467294\pi\)
0.997425 + 0.0717208i \(0.0228491\pi\)
\(984\) 0 0
\(985\) 8.19444 46.4730i 0.261097 1.48075i
\(986\) 0 0
\(987\) 24.2941 + 15.0217i 0.773290 + 0.478145i
\(988\) 0 0
\(989\) −3.15669 1.82251i −0.100377 0.0579526i
\(990\) 0 0
\(991\) 9.54334 5.50985i 0.303154 0.175026i −0.340705 0.940170i \(-0.610666\pi\)
0.643859 + 0.765144i \(0.277332\pi\)
\(992\) 0 0
\(993\) −14.6330 3.03822i −0.464364 0.0964150i
\(994\) 0 0
\(995\) 15.2618 5.55483i 0.483830 0.176100i
\(996\) 0 0
\(997\) −4.69470 26.6250i −0.148683 0.843222i −0.964336 0.264681i \(-0.914733\pi\)
0.815653 0.578541i \(-0.196378\pi\)
\(998\) 0 0
\(999\) −15.2424 1.38412i −0.482247 0.0437918i
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 432.2.be.b.95.3 36
4.3 odd 2 432.2.be.c.95.4 yes 36
27.2 odd 18 432.2.be.c.191.4 yes 36
108.83 even 18 inner 432.2.be.b.191.3 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.be.b.95.3 36 1.1 even 1 trivial
432.2.be.b.191.3 yes 36 108.83 even 18 inner
432.2.be.c.95.4 yes 36 4.3 odd 2
432.2.be.c.191.4 yes 36 27.2 odd 18