Properties

Label 756.2.ca.a.173.16
Level $756$
Weight $2$
Character 756.173
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
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] = [756,2,Mod(173,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 13, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.173");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ca (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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 173.16
Character \(\chi\) \(=\) 756.173
Dual form 756.2.ca.a.437.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.785443 - 1.54372i) q^{3} +(1.98604 - 1.66648i) q^{5} +(2.56407 - 0.652322i) q^{7} +(-1.76616 - 2.42501i) q^{9} +O(q^{10})\) \(q+(0.785443 - 1.54372i) q^{3} +(1.98604 - 1.66648i) q^{5} +(2.56407 - 0.652322i) q^{7} +(-1.76616 - 2.42501i) q^{9} +(1.39489 - 1.66236i) q^{11} +(3.09514 + 3.68865i) q^{13} +(-1.01267 - 4.37482i) q^{15} +(0.112229 - 0.194386i) q^{17} +(-3.55570 + 2.05288i) q^{19} +(1.00693 - 4.47058i) q^{21} +(-1.54617 + 4.24806i) q^{23} +(0.298938 - 1.69536i) q^{25} +(-5.13076 + 0.821750i) q^{27} +(2.32377 - 2.76937i) q^{29} +(0.136553 + 0.162737i) q^{31} +(-1.47062 - 3.45901i) q^{33} +(4.00526 - 5.56852i) q^{35} -0.566309 q^{37} +(8.12531 - 1.88082i) q^{39} +(-5.59066 + 4.69112i) q^{41} +(-8.59473 + 3.12823i) q^{43} +(-7.54890 - 1.87289i) q^{45} +(3.19402 + 2.68010i) q^{47} +(6.14895 - 3.34520i) q^{49} +(-0.211929 - 0.325929i) q^{51} +(-1.97080 + 1.13784i) q^{53} -5.62606i q^{55} +(0.376284 + 7.10144i) q^{57} +(-2.17119 - 12.3135i) q^{59} +(-4.30785 + 5.13389i) q^{61} +(-6.11045 - 5.06581i) q^{63} +(12.2941 + 2.16779i) q^{65} +(-0.302537 - 0.110114i) q^{67} +(5.34340 + 5.72346i) q^{69} +(9.64073 - 5.56608i) q^{71} -5.54969i q^{73} +(-2.38237 - 1.79309i) q^{75} +(2.49220 - 5.17233i) q^{77} +(-6.43798 + 2.34323i) q^{79} +(-2.76137 + 8.56591i) q^{81} +(-12.5514 - 10.5319i) q^{83} +(-0.101050 - 0.573085i) q^{85} +(-2.44994 - 5.76244i) q^{87} +(-1.19114 - 2.06312i) q^{89} +(10.3424 + 7.43894i) q^{91} +(0.358476 - 0.0829788i) q^{93} +(-3.64066 + 10.0026i) q^{95} +(5.73931 + 15.7686i) q^{97} +(-6.49483 - 0.446623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 0.785443 1.54372i 0.453476 0.891269i
\(4\) 0 0
\(5\) 1.98604 1.66648i 0.888183 0.745274i −0.0796617 0.996822i \(-0.525384\pi\)
0.967845 + 0.251548i \(0.0809396\pi\)
\(6\) 0 0
\(7\) 2.56407 0.652322i 0.969129 0.246555i
\(8\) 0 0
\(9\) −1.76616 2.42501i −0.588720 0.808337i
\(10\) 0 0
\(11\) 1.39489 1.66236i 0.420574 0.501220i −0.513604 0.858027i \(-0.671690\pi\)
0.934178 + 0.356807i \(0.116135\pi\)
\(12\) 0 0
\(13\) 3.09514 + 3.68865i 0.858438 + 1.02305i 0.999454 + 0.0330397i \(0.0105188\pi\)
−0.141016 + 0.990007i \(0.545037\pi\)
\(14\) 0 0
\(15\) −1.01267 4.37482i −0.261470 1.12957i
\(16\) 0 0
\(17\) 0.112229 0.194386i 0.0272195 0.0471455i −0.852095 0.523387i \(-0.824668\pi\)
0.879314 + 0.476242i \(0.158001\pi\)
\(18\) 0 0
\(19\) −3.55570 + 2.05288i −0.815733 + 0.470964i −0.848943 0.528485i \(-0.822760\pi\)
0.0332096 + 0.999448i \(0.489427\pi\)
\(20\) 0 0
\(21\) 1.00693 4.47058i 0.219730 0.975561i
\(22\) 0 0
\(23\) −1.54617 + 4.24806i −0.322398 + 0.885781i 0.667577 + 0.744541i \(0.267331\pi\)
−0.989975 + 0.141241i \(0.954891\pi\)
\(24\) 0 0
\(25\) 0.298938 1.69536i 0.0597876 0.339072i
\(26\) 0 0
\(27\) −5.13076 + 0.821750i −0.987416 + 0.158146i
\(28\) 0 0
\(29\) 2.32377 2.76937i 0.431514 0.514258i −0.505844 0.862625i \(-0.668819\pi\)
0.937358 + 0.348366i \(0.113263\pi\)
\(30\) 0 0
\(31\) 0.136553 + 0.162737i 0.0245256 + 0.0292285i 0.778168 0.628056i \(-0.216149\pi\)
−0.753642 + 0.657285i \(0.771705\pi\)
\(32\) 0 0
\(33\) −1.47062 3.45901i −0.256002 0.602136i
\(34\) 0 0
\(35\) 4.00526 5.56852i 0.677013 0.941252i
\(36\) 0 0
\(37\) −0.566309 −0.0931007 −0.0465503 0.998916i \(-0.514823\pi\)
−0.0465503 + 0.998916i \(0.514823\pi\)
\(38\) 0 0
\(39\) 8.12531 1.88082i 1.30109 0.301172i
\(40\) 0 0
\(41\) −5.59066 + 4.69112i −0.873114 + 0.732630i −0.964752 0.263163i \(-0.915234\pi\)
0.0916371 + 0.995792i \(0.470790\pi\)
\(42\) 0 0
\(43\) −8.59473 + 3.12823i −1.31068 + 0.477050i −0.900462 0.434936i \(-0.856771\pi\)
−0.410222 + 0.911986i \(0.634549\pi\)
\(44\) 0 0
\(45\) −7.54890 1.87289i −1.12532 0.279194i
\(46\) 0 0
\(47\) 3.19402 + 2.68010i 0.465896 + 0.390933i 0.845295 0.534300i \(-0.179425\pi\)
−0.379399 + 0.925233i \(0.623869\pi\)
\(48\) 0 0
\(49\) 6.14895 3.34520i 0.878422 0.477886i
\(50\) 0 0
\(51\) −0.211929 0.325929i −0.0296759 0.0456392i
\(52\) 0 0
\(53\) −1.97080 + 1.13784i −0.270711 + 0.156295i −0.629211 0.777235i \(-0.716622\pi\)
0.358500 + 0.933530i \(0.383288\pi\)
\(54\) 0 0
\(55\) 5.62606i 0.758618i
\(56\) 0 0
\(57\) 0.376284 + 7.10144i 0.0498401 + 0.940608i
\(58\) 0 0
\(59\) −2.17119 12.3135i −0.282665 1.60308i −0.713507 0.700648i \(-0.752894\pi\)
0.430842 0.902428i \(-0.358217\pi\)
\(60\) 0 0
\(61\) −4.30785 + 5.13389i −0.551563 + 0.657327i −0.967738 0.251957i \(-0.918926\pi\)
0.416175 + 0.909284i \(0.363370\pi\)
\(62\) 0 0
\(63\) −6.11045 5.06581i −0.769844 0.638232i
\(64\) 0 0
\(65\) 12.2941 + 2.16779i 1.52490 + 0.268881i
\(66\) 0 0
\(67\) −0.302537 0.110114i −0.0369607 0.0134526i 0.323474 0.946237i \(-0.395149\pi\)
−0.360434 + 0.932785i \(0.617372\pi\)
\(68\) 0 0
\(69\) 5.34340 + 5.72346i 0.643269 + 0.689023i
\(70\) 0 0
\(71\) 9.64073 5.56608i 1.14414 0.660572i 0.196691 0.980466i \(-0.436980\pi\)
0.947453 + 0.319894i \(0.103647\pi\)
\(72\) 0 0
\(73\) 5.54969i 0.649542i −0.945793 0.324771i \(-0.894713\pi\)
0.945793 0.324771i \(-0.105287\pi\)
\(74\) 0 0
\(75\) −2.38237 1.79309i −0.275092 0.207048i
\(76\) 0 0
\(77\) 2.49220 5.17233i 0.284012 0.589442i
\(78\) 0 0
\(79\) −6.43798 + 2.34323i −0.724330 + 0.263634i −0.677763 0.735281i \(-0.737050\pi\)
−0.0465669 + 0.998915i \(0.514828\pi\)
\(80\) 0 0
\(81\) −2.76137 + 8.56591i −0.306819 + 0.951768i
\(82\) 0 0
\(83\) −12.5514 10.5319i −1.37770 1.15602i −0.970056 0.242882i \(-0.921907\pi\)
−0.407641 0.913142i \(-0.633648\pi\)
\(84\) 0 0
\(85\) −0.101050 0.573085i −0.0109604 0.0621598i
\(86\) 0 0
\(87\) −2.44994 5.76244i −0.262661 0.617799i
\(88\) 0 0
\(89\) −1.19114 2.06312i −0.126261 0.218690i 0.795964 0.605344i \(-0.206964\pi\)
−0.922225 + 0.386653i \(0.873631\pi\)
\(90\) 0 0
\(91\) 10.3424 + 7.43894i 1.08417 + 0.779813i
\(92\) 0 0
\(93\) 0.358476 0.0829788i 0.0371722 0.00860450i
\(94\) 0 0
\(95\) −3.64066 + 10.0026i −0.373523 + 1.02625i
\(96\) 0 0
\(97\) 5.73931 + 15.7686i 0.582738 + 1.60106i 0.783481 + 0.621416i \(0.213442\pi\)
−0.200742 + 0.979644i \(0.564335\pi\)
\(98\) 0 0
\(99\) −6.49483 0.446623i −0.652755 0.0448873i
\(100\) 0 0
\(101\) 13.9107 5.06308i 1.38417 0.503795i 0.460727 0.887542i \(-0.347589\pi\)
0.923438 + 0.383747i \(0.125366\pi\)
\(102\) 0 0
\(103\) −10.3220 12.3012i −1.01705 1.21208i −0.977079 0.212877i \(-0.931717\pi\)
−0.0399744 0.999201i \(-0.512728\pi\)
\(104\) 0 0
\(105\) −5.45035 10.5568i −0.531900 1.03024i
\(106\) 0 0
\(107\) 10.3758 + 5.99046i 1.00307 + 0.579120i 0.909154 0.416461i \(-0.136730\pi\)
0.0939113 + 0.995581i \(0.470063\pi\)
\(108\) 0 0
\(109\) 5.70820 + 9.88689i 0.546746 + 0.946992i 0.998495 + 0.0548467i \(0.0174670\pi\)
−0.451749 + 0.892145i \(0.649200\pi\)
\(110\) 0 0
\(111\) −0.444804 + 0.874224i −0.0422189 + 0.0829777i
\(112\) 0 0
\(113\) −0.0403812 + 0.110946i −0.00379874 + 0.0104370i −0.941578 0.336796i \(-0.890657\pi\)
0.937779 + 0.347233i \(0.112879\pi\)
\(114\) 0 0
\(115\) 4.00857 + 11.0135i 0.373801 + 1.02701i
\(116\) 0 0
\(117\) 3.47850 14.0205i 0.321588 1.29620i
\(118\) 0 0
\(119\) 0.160961 0.571629i 0.0147552 0.0524011i
\(120\) 0 0
\(121\) 1.09240 + 6.19528i 0.0993087 + 0.563207i
\(122\) 0 0
\(123\) 2.85064 + 12.3150i 0.257034 + 1.11041i
\(124\) 0 0
\(125\) 4.24988 + 7.36101i 0.380121 + 0.658389i
\(126\) 0 0
\(127\) −9.92811 + 17.1960i −0.880978 + 1.52590i −0.0307219 + 0.999528i \(0.509781\pi\)
−0.850256 + 0.526370i \(0.823553\pi\)
\(128\) 0 0
\(129\) −1.92156 + 15.7249i −0.169184 + 1.38450i
\(130\) 0 0
\(131\) 2.54115 + 0.924904i 0.222021 + 0.0808092i 0.450636 0.892708i \(-0.351197\pi\)
−0.228614 + 0.973517i \(0.573420\pi\)
\(132\) 0 0
\(133\) −7.77793 + 7.58321i −0.674432 + 0.657548i
\(134\) 0 0
\(135\) −8.82046 + 10.1824i −0.759144 + 0.876358i
\(136\) 0 0
\(137\) 14.0805 + 2.48277i 1.20298 + 0.212118i 0.738985 0.673721i \(-0.235305\pi\)
0.463993 + 0.885839i \(0.346416\pi\)
\(138\) 0 0
\(139\) −12.3851 + 2.18382i −1.05049 + 0.185230i −0.672133 0.740430i \(-0.734622\pi\)
−0.378356 + 0.925660i \(0.623511\pi\)
\(140\) 0 0
\(141\) 6.64605 2.82561i 0.559699 0.237960i
\(142\) 0 0
\(143\) 10.4492 0.873809
\(144\) 0 0
\(145\) 9.37260i 0.778352i
\(146\) 0 0
\(147\) −0.334416 12.1197i −0.0275822 0.999620i
\(148\) 0 0
\(149\) 0.127833 0.0225403i 0.0104724 0.00184658i −0.168409 0.985717i \(-0.553863\pi\)
0.178882 + 0.983871i \(0.442752\pi\)
\(150\) 0 0
\(151\) −6.80289 5.70830i −0.553611 0.464535i 0.322550 0.946552i \(-0.395460\pi\)
−0.876162 + 0.482017i \(0.839904\pi\)
\(152\) 0 0
\(153\) −0.669602 + 0.0711602i −0.0541341 + 0.00575296i
\(154\) 0 0
\(155\) 0.542398 + 0.0956394i 0.0435665 + 0.00768194i
\(156\) 0 0
\(157\) 6.61613 1.16660i 0.528025 0.0931050i 0.0967204 0.995312i \(-0.469165\pi\)
0.431304 + 0.902207i \(0.358054\pi\)
\(158\) 0 0
\(159\) 0.208562 + 3.93609i 0.0165400 + 0.312152i
\(160\) 0 0
\(161\) −1.19338 + 11.9009i −0.0940518 + 0.937925i
\(162\) 0 0
\(163\) 7.06404 12.2353i 0.553298 0.958341i −0.444735 0.895662i \(-0.646702\pi\)
0.998034 0.0626788i \(-0.0199644\pi\)
\(164\) 0 0
\(165\) −8.68508 4.41895i −0.676133 0.344015i
\(166\) 0 0
\(167\) −6.43143 2.34085i −0.497679 0.181140i 0.0809706 0.996716i \(-0.474198\pi\)
−0.578650 + 0.815576i \(0.696420\pi\)
\(168\) 0 0
\(169\) −1.76879 + 10.0313i −0.136061 + 0.771638i
\(170\) 0 0
\(171\) 11.2582 + 4.99690i 0.860936 + 0.382122i
\(172\) 0 0
\(173\) −1.19428 + 6.77307i −0.0907991 + 0.514947i 0.905155 + 0.425082i \(0.139755\pi\)
−0.995954 + 0.0898652i \(0.971356\pi\)
\(174\) 0 0
\(175\) −0.339422 4.54203i −0.0256579 0.343345i
\(176\) 0 0
\(177\) −20.7139 6.31980i −1.55695 0.475025i
\(178\) 0 0
\(179\) −1.23847 0.715030i −0.0925675 0.0534439i 0.453002 0.891510i \(-0.350353\pi\)
−0.545569 + 0.838066i \(0.683686\pi\)
\(180\) 0 0
\(181\) −1.39468 0.805221i −0.103666 0.0598516i 0.447271 0.894399i \(-0.352396\pi\)
−0.550937 + 0.834547i \(0.685729\pi\)
\(182\) 0 0
\(183\) 4.54173 + 10.6825i 0.335735 + 0.789673i
\(184\) 0 0
\(185\) −1.12471 + 0.943745i −0.0826904 + 0.0693855i
\(186\) 0 0
\(187\) −0.166593 0.457711i −0.0121825 0.0334711i
\(188\) 0 0
\(189\) −12.6196 + 5.45394i −0.917942 + 0.396716i
\(190\) 0 0
\(191\) −6.06721 16.6695i −0.439008 1.20616i −0.940139 0.340792i \(-0.889305\pi\)
0.501131 0.865372i \(-0.332918\pi\)
\(192\) 0 0
\(193\) −16.6268 + 13.9515i −1.19682 + 1.00425i −0.197105 + 0.980382i \(0.563154\pi\)
−0.999715 + 0.0238686i \(0.992402\pi\)
\(194\) 0 0
\(195\) 13.0028 17.2761i 0.931151 1.23717i
\(196\) 0 0
\(197\) −10.7354 6.19810i −0.764867 0.441596i 0.0661732 0.997808i \(-0.478921\pi\)
−0.831041 + 0.556212i \(0.812254\pi\)
\(198\) 0 0
\(199\) 20.2325 + 11.6812i 1.43424 + 0.828059i 0.997441 0.0714995i \(-0.0227784\pi\)
0.436800 + 0.899559i \(0.356112\pi\)
\(200\) 0 0
\(201\) −0.407611 + 0.380544i −0.0287507 + 0.0268415i
\(202\) 0 0
\(203\) 4.15181 8.61671i 0.291400 0.604775i
\(204\) 0 0
\(205\) −3.28559 + 18.6335i −0.229475 + 1.30142i
\(206\) 0 0
\(207\) 13.0324 3.75327i 0.905812 0.260870i
\(208\) 0 0
\(209\) −1.54716 + 8.77439i −0.107019 + 0.606937i
\(210\) 0 0
\(211\) −6.53452 2.37837i −0.449855 0.163734i 0.107150 0.994243i \(-0.465827\pi\)
−0.557005 + 0.830509i \(0.688050\pi\)
\(212\) 0 0
\(213\) −1.02024 19.2545i −0.0699055 1.31929i
\(214\) 0 0
\(215\) −11.8563 + 20.5357i −0.808594 + 1.40053i
\(216\) 0 0
\(217\) 0.456289 + 0.328194i 0.0309749 + 0.0222793i
\(218\) 0 0
\(219\) −8.56718 4.35896i −0.578916 0.294551i
\(220\) 0 0
\(221\) 1.06439 0.187680i 0.0715983 0.0126247i
\(222\) 0 0
\(223\) 5.93704 + 1.04686i 0.397573 + 0.0701029i 0.368860 0.929485i \(-0.379748\pi\)
0.0287129 + 0.999588i \(0.490859\pi\)
\(224\) 0 0
\(225\) −4.63924 + 2.26935i −0.309283 + 0.151290i
\(226\) 0 0
\(227\) 17.8453 + 14.9740i 1.18444 + 0.993861i 0.999939 + 0.0110282i \(0.00351046\pi\)
0.184498 + 0.982833i \(0.440934\pi\)
\(228\) 0 0
\(229\) 5.61842 0.990679i 0.371276 0.0654659i 0.0151026 0.999886i \(-0.495193\pi\)
0.356173 + 0.934420i \(0.384081\pi\)
\(230\) 0 0
\(231\) −6.02716 7.90983i −0.396558 0.520429i
\(232\) 0 0
\(233\) 26.2537i 1.71994i 0.510345 + 0.859970i \(0.329518\pi\)
−0.510345 + 0.859970i \(0.670482\pi\)
\(234\) 0 0
\(235\) 10.8098 0.705153
\(236\) 0 0
\(237\) −1.43936 + 11.7789i −0.0934968 + 0.765124i
\(238\) 0 0
\(239\) −10.5819 + 1.86587i −0.684484 + 0.120693i −0.505067 0.863080i \(-0.668532\pi\)
−0.179417 + 0.983773i \(0.557421\pi\)
\(240\) 0 0
\(241\) 27.9936 + 4.93603i 1.80323 + 0.317957i 0.971466 0.237178i \(-0.0762224\pi\)
0.831760 + 0.555135i \(0.187334\pi\)
\(242\) 0 0
\(243\) 11.0545 + 10.9908i 0.709146 + 0.705061i
\(244\) 0 0
\(245\) 6.63732 16.8908i 0.424043 1.07912i
\(246\) 0 0
\(247\) −18.5778 6.76175i −1.18208 0.430240i
\(248\) 0 0
\(249\) −26.1167 + 11.1037i −1.65508 + 0.703669i
\(250\) 0 0
\(251\) −2.47277 + 4.28296i −0.156080 + 0.270338i −0.933452 0.358703i \(-0.883219\pi\)
0.777372 + 0.629041i \(0.216552\pi\)
\(252\) 0 0
\(253\) 4.90508 + 8.49584i 0.308379 + 0.534129i
\(254\) 0 0
\(255\) −0.964054 0.294132i −0.0603714 0.0184193i
\(256\) 0 0
\(257\) −3.66570 20.7892i −0.228660 1.29679i −0.855564 0.517698i \(-0.826789\pi\)
0.626904 0.779097i \(-0.284322\pi\)
\(258\) 0 0
\(259\) −1.45206 + 0.369416i −0.0902265 + 0.0229544i
\(260\) 0 0
\(261\) −10.8199 0.744041i −0.669735 0.0460550i
\(262\) 0 0
\(263\) 1.90652 + 5.23812i 0.117561 + 0.322996i 0.984491 0.175433i \(-0.0561326\pi\)
−0.866930 + 0.498429i \(0.833910\pi\)
\(264\) 0 0
\(265\) −2.01789 + 5.54411i −0.123958 + 0.340572i
\(266\) 0 0
\(267\) −4.12046 + 0.218331i −0.252168 + 0.0133616i
\(268\) 0 0
\(269\) −4.08518 7.07574i −0.249078 0.431415i 0.714192 0.699949i \(-0.246794\pi\)
−0.963270 + 0.268534i \(0.913461\pi\)
\(270\) 0 0
\(271\) −14.2833 8.24647i −0.867649 0.500937i −0.00108263 0.999999i \(-0.500345\pi\)
−0.866566 + 0.499062i \(0.833678\pi\)
\(272\) 0 0
\(273\) 19.6070 10.1229i 1.18667 0.612665i
\(274\) 0 0
\(275\) −2.40132 2.86178i −0.144805 0.172572i
\(276\) 0 0
\(277\) 15.4208 5.61271i 0.926546 0.337235i 0.165707 0.986175i \(-0.447010\pi\)
0.760840 + 0.648940i \(0.224787\pi\)
\(278\) 0 0
\(279\) 0.153466 0.618562i 0.00918777 0.0370323i
\(280\) 0 0
\(281\) −5.91472 16.2506i −0.352843 0.969427i −0.981452 0.191706i \(-0.938598\pi\)
0.628610 0.777721i \(-0.283624\pi\)
\(282\) 0 0
\(283\) 9.47841 26.0417i 0.563433 1.54802i −0.251135 0.967952i \(-0.580804\pi\)
0.814568 0.580068i \(-0.196974\pi\)
\(284\) 0 0
\(285\) 12.5817 + 13.4767i 0.745278 + 0.798288i
\(286\) 0 0
\(287\) −11.2747 + 15.6753i −0.665527 + 0.925283i
\(288\) 0 0
\(289\) 8.47481 + 14.6788i 0.498518 + 0.863459i
\(290\) 0 0
\(291\) 28.8503 + 3.52545i 1.69123 + 0.206666i
\(292\) 0 0
\(293\) −2.48057 14.0680i −0.144916 0.821862i −0.967434 0.253123i \(-0.918542\pi\)
0.822518 0.568740i \(-0.192569\pi\)
\(294\) 0 0
\(295\) −24.8322 20.8367i −1.44579 1.21316i
\(296\) 0 0
\(297\) −5.79078 + 9.67542i −0.336015 + 0.561425i
\(298\) 0 0
\(299\) −20.4552 + 7.44508i −1.18295 + 0.430560i
\(300\) 0 0
\(301\) −19.9969 + 13.6275i −1.15260 + 0.785478i
\(302\) 0 0
\(303\) 3.11007 25.4510i 0.178669 1.46212i
\(304\) 0 0
\(305\) 17.3751i 0.994893i
\(306\) 0 0
\(307\) 26.2164 15.1360i 1.49625 0.863860i 0.496258 0.868175i \(-0.334707\pi\)
0.999991 + 0.00431530i \(0.00137361\pi\)
\(308\) 0 0
\(309\) −27.0970 + 6.27233i −1.54150 + 0.356820i
\(310\) 0 0
\(311\) −27.6217 10.0535i −1.56628 0.570080i −0.594118 0.804378i \(-0.702499\pi\)
−0.972165 + 0.234298i \(0.924721\pi\)
\(312\) 0 0
\(313\) −12.2416 2.15853i −0.691936 0.122007i −0.183388 0.983041i \(-0.558707\pi\)
−0.508548 + 0.861033i \(0.669818\pi\)
\(314\) 0 0
\(315\) −20.5777 + 0.122083i −1.15942 + 0.00687857i
\(316\) 0 0
\(317\) 7.99306 9.52575i 0.448935 0.535020i −0.493351 0.869831i \(-0.664228\pi\)
0.942285 + 0.334811i \(0.108672\pi\)
\(318\) 0 0
\(319\) −1.36228 7.72590i −0.0762733 0.432567i
\(320\) 0 0
\(321\) 17.3972 11.3122i 0.971017 0.631384i
\(322\) 0 0
\(323\) 0.921570i 0.0512775i
\(324\) 0 0
\(325\) 7.17885 4.14471i 0.398211 0.229907i
\(326\) 0 0
\(327\) 19.7461 1.04629i 1.09196 0.0578598i
\(328\) 0 0
\(329\) 9.93800 + 4.78845i 0.547899 + 0.263996i
\(330\) 0 0
\(331\) −9.05881 7.60124i −0.497917 0.417802i 0.358936 0.933362i \(-0.383139\pi\)
−0.856853 + 0.515560i \(0.827584\pi\)
\(332\) 0 0
\(333\) 1.00019 + 1.37331i 0.0548102 + 0.0752567i
\(334\) 0 0
\(335\) −0.784353 + 0.285481i −0.0428538 + 0.0155975i
\(336\) 0 0
\(337\) 12.7768 10.7210i 0.695999 0.584012i −0.224633 0.974443i \(-0.572118\pi\)
0.920632 + 0.390431i \(0.127674\pi\)
\(338\) 0 0
\(339\) 0.139553 + 0.149479i 0.00757950 + 0.00811861i
\(340\) 0 0
\(341\) 0.461003 0.0249647
\(342\) 0 0
\(343\) 13.5842 12.5884i 0.733479 0.679712i
\(344\) 0 0
\(345\) 20.1502 + 2.46232i 1.08485 + 0.132567i
\(346\) 0 0
\(347\) 13.5004 + 16.0891i 0.724738 + 0.863710i 0.995082 0.0990543i \(-0.0315817\pi\)
−0.270344 + 0.962764i \(0.587137\pi\)
\(348\) 0 0
\(349\) 1.30780 1.55858i 0.0700052 0.0834289i −0.729905 0.683548i \(-0.760436\pi\)
0.799910 + 0.600119i \(0.204880\pi\)
\(350\) 0 0
\(351\) −18.9116 16.3821i −1.00943 0.874414i
\(352\) 0 0
\(353\) 5.97307 33.8749i 0.317914 1.80298i −0.237478 0.971393i \(-0.576321\pi\)
0.555393 0.831588i \(-0.312568\pi\)
\(354\) 0 0
\(355\) 9.87108 27.1206i 0.523902 1.43941i
\(356\) 0 0
\(357\) −0.756011 0.697460i −0.0400124 0.0369135i
\(358\) 0 0
\(359\) −15.8073 + 9.12635i −0.834278 + 0.481670i −0.855315 0.518108i \(-0.826636\pi\)
0.0210374 + 0.999779i \(0.493303\pi\)
\(360\) 0 0
\(361\) −1.07133 + 1.85561i −0.0563860 + 0.0976635i
\(362\) 0 0
\(363\) 10.4218 + 3.17968i 0.547003 + 0.166890i
\(364\) 0 0
\(365\) −9.24846 11.0219i −0.484087 0.576912i
\(366\) 0 0
\(367\) 7.63485 9.09886i 0.398536 0.474956i −0.529037 0.848599i \(-0.677447\pi\)
0.927573 + 0.373642i \(0.121891\pi\)
\(368\) 0 0
\(369\) 21.2500 + 5.27215i 1.10623 + 0.274457i
\(370\) 0 0
\(371\) −4.31105 + 4.20312i −0.223818 + 0.218215i
\(372\) 0 0
\(373\) −3.97831 + 3.33820i −0.205989 + 0.172845i −0.739946 0.672666i \(-0.765149\pi\)
0.533957 + 0.845512i \(0.320704\pi\)
\(374\) 0 0
\(375\) 14.7014 0.778984i 0.759177 0.0402266i
\(376\) 0 0
\(377\) 17.4076 0.896539
\(378\) 0 0
\(379\) 17.0605 0.876340 0.438170 0.898892i \(-0.355627\pi\)
0.438170 + 0.898892i \(0.355627\pi\)
\(380\) 0 0
\(381\) 18.7479 + 28.8327i 0.960483 + 1.47715i
\(382\) 0 0
\(383\) −19.0730 + 16.0042i −0.974587 + 0.817775i −0.983264 0.182187i \(-0.941682\pi\)
0.00867707 + 0.999962i \(0.497238\pi\)
\(384\) 0 0
\(385\) −3.67001 14.4256i −0.187041 0.735199i
\(386\) 0 0
\(387\) 22.7656 + 15.3174i 1.15724 + 0.778626i
\(388\) 0 0
\(389\) 10.1394 12.0836i 0.514086 0.612663i −0.445086 0.895488i \(-0.646827\pi\)
0.959172 + 0.282824i \(0.0912714\pi\)
\(390\) 0 0
\(391\) 0.652238 + 0.777307i 0.0329851 + 0.0393101i
\(392\) 0 0
\(393\) 3.42372 3.19637i 0.172704 0.161236i
\(394\) 0 0
\(395\) −8.88111 + 15.3825i −0.446857 + 0.773980i
\(396\) 0 0
\(397\) 14.2110 8.20473i 0.713230 0.411783i −0.0990260 0.995085i \(-0.531573\pi\)
0.812256 + 0.583301i \(0.198239\pi\)
\(398\) 0 0
\(399\) 5.59724 + 17.9632i 0.280213 + 0.899282i
\(400\) 0 0
\(401\) −4.47100 + 12.2840i −0.223271 + 0.613432i −0.999863 0.0165720i \(-0.994725\pi\)
0.776592 + 0.630004i \(0.216947\pi\)
\(402\) 0 0
\(403\) −0.177630 + 1.00739i −0.00884839 + 0.0501817i
\(404\) 0 0
\(405\) 8.79077 + 21.6140i 0.436817 + 1.07401i
\(406\) 0 0
\(407\) −0.789937 + 0.941410i −0.0391557 + 0.0466640i
\(408\) 0 0
\(409\) −21.5577 25.6914i −1.06596 1.27036i −0.961198 0.275861i \(-0.911037\pi\)
−0.104760 0.994498i \(-0.533407\pi\)
\(410\) 0 0
\(411\) 14.8921 19.7863i 0.734575 0.975987i
\(412\) 0 0
\(413\) −13.5994 30.1563i −0.669185 1.48389i
\(414\) 0 0
\(415\) −42.4788 −2.08520
\(416\) 0 0
\(417\) −6.35656 + 20.8344i −0.311282 + 1.02027i
\(418\) 0 0
\(419\) 2.19492 1.84175i 0.107229 0.0899756i −0.587597 0.809154i \(-0.699926\pi\)
0.694826 + 0.719178i \(0.255481\pi\)
\(420\) 0 0
\(421\) −1.37714 + 0.501238i −0.0671177 + 0.0244288i −0.375361 0.926879i \(-0.622481\pi\)
0.308243 + 0.951308i \(0.400259\pi\)
\(422\) 0 0
\(423\) 0.858132 12.4790i 0.0417238 0.606751i
\(424\) 0 0
\(425\) −0.296005 0.248377i −0.0143583 0.0120481i
\(426\) 0 0
\(427\) −7.69668 + 15.9738i −0.372469 + 0.773025i
\(428\) 0 0
\(429\) 8.20728 16.1307i 0.396251 0.778798i
\(430\) 0 0
\(431\) 27.6179 15.9452i 1.33031 0.768053i 0.344960 0.938617i \(-0.387892\pi\)
0.985347 + 0.170564i \(0.0545591\pi\)
\(432\) 0 0
\(433\) 25.7093i 1.23551i −0.786370 0.617756i \(-0.788042\pi\)
0.786370 0.617756i \(-0.211958\pi\)
\(434\) 0 0
\(435\) −14.4687 7.36164i −0.693721 0.352964i
\(436\) 0 0
\(437\) −3.22307 18.2789i −0.154180 0.874399i
\(438\) 0 0
\(439\) 7.42622 8.85022i 0.354434 0.422398i −0.559138 0.829074i \(-0.688868\pi\)
0.913572 + 0.406676i \(0.133312\pi\)
\(440\) 0 0
\(441\) −18.9722 9.00312i −0.903437 0.428720i
\(442\) 0 0
\(443\) 33.5393 + 5.91388i 1.59350 + 0.280977i 0.898812 0.438334i \(-0.144431\pi\)
0.694688 + 0.719311i \(0.255542\pi\)
\(444\) 0 0
\(445\) −5.80381 2.11242i −0.275127 0.100138i
\(446\) 0 0
\(447\) 0.0656091 0.215042i 0.00310321 0.0101711i
\(448\) 0 0
\(449\) 0.130210 0.0751766i 0.00614498 0.00354780i −0.496924 0.867794i \(-0.665537\pi\)
0.503069 + 0.864246i \(0.332204\pi\)
\(450\) 0 0
\(451\) 15.8373i 0.745748i
\(452\) 0 0
\(453\) −14.1553 + 6.01823i −0.665075 + 0.282761i
\(454\) 0 0
\(455\) 32.9372 2.46137i 1.54412 0.115391i
\(456\) 0 0
\(457\) −23.0320 + 8.38297i −1.07739 + 0.392139i −0.818936 0.573884i \(-0.805436\pi\)
−0.258456 + 0.966023i \(0.583214\pi\)
\(458\) 0 0
\(459\) −0.416082 + 1.08957i −0.0194211 + 0.0508569i
\(460\) 0 0
\(461\) −31.0542 26.0575i −1.44634 1.21362i −0.935200 0.354121i \(-0.884780\pi\)
−0.511137 0.859499i \(-0.670776\pi\)
\(462\) 0 0
\(463\) −7.18093 40.7251i −0.333726 1.89265i −0.439464 0.898260i \(-0.644831\pi\)
0.105738 0.994394i \(-0.466280\pi\)
\(464\) 0 0
\(465\) 0.573663 0.762193i 0.0266030 0.0353458i
\(466\) 0 0
\(467\) 6.77643 + 11.7371i 0.313576 + 0.543129i 0.979134 0.203217i \(-0.0651397\pi\)
−0.665558 + 0.746346i \(0.731806\pi\)
\(468\) 0 0
\(469\) −0.847556 0.0849900i −0.0391365 0.00392447i
\(470\) 0 0
\(471\) 3.39568 11.1298i 0.156465 0.512833i
\(472\) 0 0
\(473\) −6.78843 + 18.6511i −0.312132 + 0.857576i
\(474\) 0 0
\(475\) 2.41745 + 6.64188i 0.110920 + 0.304750i
\(476\) 0 0
\(477\) 6.24004 + 2.76961i 0.285712 + 0.126812i
\(478\) 0 0
\(479\) −11.3785 + 4.14144i −0.519897 + 0.189227i −0.588622 0.808409i \(-0.700329\pi\)
0.0687246 + 0.997636i \(0.478107\pi\)
\(480\) 0 0
\(481\) −1.75281 2.08892i −0.0799212 0.0952464i
\(482\) 0 0
\(483\) 17.4344 + 11.1898i 0.793293 + 0.509152i
\(484\) 0 0
\(485\) 37.6766 + 21.7526i 1.71081 + 0.987735i
\(486\) 0 0
\(487\) 15.7532 + 27.2853i 0.713844 + 1.23641i 0.963404 + 0.268055i \(0.0863809\pi\)
−0.249559 + 0.968360i \(0.580286\pi\)
\(488\) 0 0
\(489\) −13.3395 20.5150i −0.603232 0.927722i
\(490\) 0 0
\(491\) 1.81876 4.99699i 0.0820793 0.225511i −0.891864 0.452304i \(-0.850602\pi\)
0.973943 + 0.226794i \(0.0728243\pi\)
\(492\) 0 0
\(493\) −0.277531 0.762511i −0.0124994 0.0343418i
\(494\) 0 0
\(495\) −13.6433 + 9.93652i −0.613220 + 0.446613i
\(496\) 0 0
\(497\) 21.0887 20.5607i 0.945956 0.922273i
\(498\) 0 0
\(499\) −0.0815778 0.462650i −0.00365192 0.0207111i 0.982927 0.183994i \(-0.0589027\pi\)
−0.986579 + 0.163283i \(0.947792\pi\)
\(500\) 0 0
\(501\) −8.66515 + 8.08975i −0.387130 + 0.361423i
\(502\) 0 0
\(503\) −4.34578 7.52712i −0.193769 0.335618i 0.752727 0.658332i \(-0.228738\pi\)
−0.946496 + 0.322715i \(0.895405\pi\)
\(504\) 0 0
\(505\) 19.1896 33.2374i 0.853927 1.47905i
\(506\) 0 0
\(507\) 14.0963 + 10.6095i 0.626037 + 0.471186i
\(508\) 0 0
\(509\) −13.5820 4.94345i −0.602012 0.219114i 0.0229925 0.999736i \(-0.492681\pi\)
−0.625004 + 0.780621i \(0.714903\pi\)
\(510\) 0 0
\(511\) −3.62018 14.2298i −0.160147 0.629490i
\(512\) 0 0
\(513\) 16.5565 13.4548i 0.730987 0.594042i
\(514\) 0 0
\(515\) −40.9996 7.22934i −1.80666 0.318563i
\(516\) 0 0
\(517\) 8.91059 1.57118i 0.391887 0.0691003i
\(518\) 0 0
\(519\) 9.51771 + 7.16349i 0.417781 + 0.314442i
\(520\) 0 0
\(521\) 13.3084 0.583050 0.291525 0.956563i \(-0.405837\pi\)
0.291525 + 0.956563i \(0.405837\pi\)
\(522\) 0 0
\(523\) 22.1919i 0.970384i 0.874408 + 0.485192i \(0.161250\pi\)
−0.874408 + 0.485192i \(0.838750\pi\)
\(524\) 0 0
\(525\) −7.27824 3.04353i −0.317648 0.132831i
\(526\) 0 0
\(527\) 0.0469590 0.00828013i 0.00204556 0.000360688i
\(528\) 0 0
\(529\) 1.96366 + 1.64771i 0.0853766 + 0.0716395i
\(530\) 0 0
\(531\) −26.0256 + 27.0127i −1.12942 + 1.17225i
\(532\) 0 0
\(533\) −34.6078 6.10229i −1.49903 0.264319i
\(534\) 0 0
\(535\) 30.5897 5.39379i 1.32251 0.233194i
\(536\) 0 0
\(537\) −2.07655 + 1.35024i −0.0896099 + 0.0582670i
\(538\) 0 0
\(539\) 3.01615 14.8879i 0.129915 0.641269i
\(540\) 0 0
\(541\) 1.27017 2.19999i 0.0546087 0.0945851i −0.837429 0.546546i \(-0.815942\pi\)
0.892038 + 0.451961i \(0.149276\pi\)
\(542\) 0 0
\(543\) −2.33848 + 1.52055i −0.100354 + 0.0652531i
\(544\) 0 0
\(545\) 27.8130 + 10.1231i 1.19138 + 0.433627i
\(546\) 0 0
\(547\) −5.70930 + 32.3791i −0.244112 + 1.38443i 0.578433 + 0.815730i \(0.303664\pi\)
−0.822546 + 0.568699i \(0.807447\pi\)
\(548\) 0 0
\(549\) 20.0581 + 1.37931i 0.856058 + 0.0588676i
\(550\) 0 0
\(551\) −2.57746 + 14.6175i −0.109803 + 0.622725i
\(552\) 0 0
\(553\) −14.9789 + 10.2079i −0.636968 + 0.434082i
\(554\) 0 0
\(555\) 0.573484 + 2.47750i 0.0243430 + 0.105164i
\(556\) 0 0
\(557\) −38.4235 22.1838i −1.62805 0.939958i −0.984673 0.174412i \(-0.944197\pi\)
−0.643382 0.765545i \(-0.722469\pi\)
\(558\) 0 0
\(559\) −38.1408 22.0206i −1.61319 0.931373i
\(560\) 0 0
\(561\) −0.837427 0.102332i −0.0353562 0.00432047i
\(562\) 0 0
\(563\) −30.4568 + 25.5563i −1.28360 + 1.07707i −0.290863 + 0.956765i \(0.593943\pi\)
−0.992737 + 0.120304i \(0.961613\pi\)
\(564\) 0 0
\(565\) 0.104692 + 0.287638i 0.00440442 + 0.0121010i
\(566\) 0 0
\(567\) −1.49262 + 23.7649i −0.0626840 + 0.998033i
\(568\) 0 0
\(569\) 4.39306 + 12.0698i 0.184167 + 0.505994i 0.997078 0.0763942i \(-0.0243407\pi\)
−0.812911 + 0.582388i \(0.802119\pi\)
\(570\) 0 0
\(571\) 15.4769 12.9866i 0.647686 0.543473i −0.258682 0.965963i \(-0.583288\pi\)
0.906368 + 0.422489i \(0.138844\pi\)
\(572\) 0 0
\(573\) −30.4986 3.72687i −1.27410 0.155692i
\(574\) 0 0
\(575\) 6.73978 + 3.89121i 0.281068 + 0.162275i
\(576\) 0 0
\(577\) −3.59744 2.07698i −0.149763 0.0864660i 0.423246 0.906015i \(-0.360891\pi\)
−0.573009 + 0.819549i \(0.694224\pi\)
\(578\) 0 0
\(579\) 8.47788 + 36.6252i 0.352329 + 1.52209i
\(580\) 0 0
\(581\) −39.0529 18.8170i −1.62019 0.780660i
\(582\) 0 0
\(583\) −0.857539 + 4.86335i −0.0355157 + 0.201419i
\(584\) 0 0
\(585\) −16.4565 33.6421i −0.680392 1.39093i
\(586\) 0 0
\(587\) −7.14533 + 40.5232i −0.294920 + 1.67257i 0.372610 + 0.927988i \(0.378463\pi\)
−0.667529 + 0.744584i \(0.732648\pi\)
\(588\) 0 0
\(589\) −0.819621 0.298318i −0.0337719 0.0122920i
\(590\) 0 0
\(591\) −18.0002 + 11.7043i −0.740430 + 0.481449i
\(592\) 0 0
\(593\) 2.89650 5.01689i 0.118945 0.206019i −0.800405 0.599460i \(-0.795382\pi\)
0.919350 + 0.393441i \(0.128715\pi\)
\(594\) 0 0
\(595\) −0.632937 1.40352i −0.0259479 0.0575385i
\(596\) 0 0
\(597\) 33.9240 22.0584i 1.38842 0.902789i
\(598\) 0 0
\(599\) −47.0439 + 8.29511i −1.92216 + 0.338929i −0.998968 0.0454091i \(-0.985541\pi\)
−0.923192 + 0.384338i \(0.874430\pi\)
\(600\) 0 0
\(601\) −8.96343 1.58049i −0.365626 0.0644697i −0.0121829 0.999926i \(-0.503878\pi\)
−0.353443 + 0.935456i \(0.614989\pi\)
\(602\) 0 0
\(603\) 0.267299 + 0.928134i 0.0108853 + 0.0377966i
\(604\) 0 0
\(605\) 12.4939 + 10.4836i 0.507948 + 0.426219i
\(606\) 0 0
\(607\) 9.80730 1.72929i 0.398066 0.0701898i 0.0289682 0.999580i \(-0.490778\pi\)
0.369098 + 0.929391i \(0.379667\pi\)
\(608\) 0 0
\(609\) −10.0408 13.1772i −0.406874 0.533966i
\(610\) 0 0
\(611\) 20.0769i 0.812225i
\(612\) 0 0
\(613\) −14.6234 −0.590635 −0.295317 0.955399i \(-0.595425\pi\)
−0.295317 + 0.955399i \(0.595425\pi\)
\(614\) 0 0
\(615\) 26.1843 + 19.7076i 1.05585 + 0.794686i
\(616\) 0 0
\(617\) −39.1155 + 6.89711i −1.57473 + 0.277667i −0.891667 0.452692i \(-0.850464\pi\)
−0.683063 + 0.730360i \(0.739353\pi\)
\(618\) 0 0
\(619\) −16.7016 2.94495i −0.671296 0.118368i −0.172397 0.985028i \(-0.555151\pi\)
−0.498899 + 0.866660i \(0.666262\pi\)
\(620\) 0 0
\(621\) 4.44217 23.0663i 0.178258 0.925620i
\(622\) 0 0
\(623\) −4.40000 4.51299i −0.176282 0.180809i
\(624\) 0 0
\(625\) 28.7959 + 10.4809i 1.15184 + 0.419234i
\(626\) 0 0
\(627\) 12.3300 + 9.28017i 0.492413 + 0.370614i
\(628\) 0 0
\(629\) −0.0635562 + 0.110083i −0.00253415 + 0.00438928i
\(630\) 0 0
\(631\) 10.1926 + 17.6541i 0.405761 + 0.702799i 0.994410 0.105590i \(-0.0336731\pi\)
−0.588648 + 0.808389i \(0.700340\pi\)
\(632\) 0 0
\(633\) −8.80404 + 8.21941i −0.349929 + 0.326692i
\(634\) 0 0
\(635\) 8.93924 + 50.6969i 0.354743 + 2.01185i
\(636\) 0 0
\(637\) 31.3712 + 12.3274i 1.24297 + 0.488431i
\(638\) 0 0
\(639\) −30.5249 13.5483i −1.20755 0.535963i
\(640\) 0 0
\(641\) 9.88726 + 27.1650i 0.390523 + 1.07295i 0.966763 + 0.255673i \(0.0822971\pi\)
−0.576240 + 0.817281i \(0.695481\pi\)
\(642\) 0 0
\(643\) 3.06889 8.43171i 0.121025 0.332514i −0.864355 0.502882i \(-0.832273\pi\)
0.985381 + 0.170367i \(0.0544954\pi\)
\(644\) 0 0
\(645\) 22.3890 + 34.4325i 0.881567 + 1.35578i
\(646\) 0 0
\(647\) −24.4220 42.3001i −0.960128 1.66299i −0.722171 0.691715i \(-0.756856\pi\)
−0.237957 0.971276i \(-0.576478\pi\)
\(648\) 0 0
\(649\) −23.4980 13.5666i −0.922376 0.532534i
\(650\) 0 0
\(651\) 0.865029 0.446605i 0.0339032 0.0175038i
\(652\) 0 0
\(653\) −6.36517 7.58571i −0.249088 0.296852i 0.626984 0.779033i \(-0.284289\pi\)
−0.876072 + 0.482181i \(0.839845\pi\)
\(654\) 0 0
\(655\) 6.58816 2.39789i 0.257421 0.0936935i
\(656\) 0 0
\(657\) −13.4581 + 9.80163i −0.525049 + 0.382398i
\(658\) 0 0
\(659\) 6.97443 + 19.1621i 0.271685 + 0.746449i 0.998238 + 0.0593380i \(0.0188990\pi\)
−0.726553 + 0.687111i \(0.758879\pi\)
\(660\) 0 0
\(661\) 2.41286 6.62928i 0.0938494 0.257849i −0.883882 0.467710i \(-0.845079\pi\)
0.977731 + 0.209861i \(0.0673013\pi\)
\(662\) 0 0
\(663\) 0.546288 1.79053i 0.0212161 0.0695383i
\(664\) 0 0
\(665\) −2.80998 + 28.0223i −0.108966 + 1.08666i
\(666\) 0 0
\(667\) 8.17149 + 14.1534i 0.316401 + 0.548023i
\(668\) 0 0
\(669\) 6.27927 8.34289i 0.242770 0.322555i
\(670\) 0 0
\(671\) 2.52542 + 14.3224i 0.0974928 + 0.552909i
\(672\) 0 0
\(673\) 31.3859 + 26.3359i 1.20984 + 1.01517i 0.999293 + 0.0375895i \(0.0119679\pi\)
0.210544 + 0.977584i \(0.432477\pi\)
\(674\) 0 0
\(675\) −0.140616 + 8.94415i −0.00541232 + 0.344260i
\(676\) 0 0
\(677\) 2.23162 0.812242i 0.0857680 0.0312170i −0.298780 0.954322i \(-0.596580\pi\)
0.384548 + 0.923105i \(0.374357\pi\)
\(678\) 0 0
\(679\) 25.0022 + 36.6880i 0.959497 + 1.40796i
\(680\) 0 0
\(681\) 37.1322 15.7870i 1.42291 0.604960i
\(682\) 0 0
\(683\) 1.35064i 0.0516808i −0.999666 0.0258404i \(-0.991774\pi\)
0.999666 0.0258404i \(-0.00822617\pi\)
\(684\) 0 0
\(685\) 32.1019 18.5340i 1.22655 0.708149i
\(686\) 0 0
\(687\) 2.88361 9.45140i 0.110017 0.360593i
\(688\) 0 0
\(689\) −10.2970 3.74781i −0.392286 0.142780i
\(690\) 0 0
\(691\) −33.3633 5.88285i −1.26920 0.223794i −0.501812 0.864977i \(-0.667333\pi\)
−0.767388 + 0.641182i \(0.778444\pi\)
\(692\) 0 0
\(693\) −16.9446 + 3.09155i −0.643671 + 0.117438i
\(694\) 0 0
\(695\) −20.9579 + 24.9767i −0.794980 + 0.947420i
\(696\) 0 0
\(697\) 0.284455 + 1.61322i 0.0107745 + 0.0611052i
\(698\) 0 0
\(699\) 40.5285 + 20.6208i 1.53293 + 0.779951i
\(700\) 0 0
\(701\) 41.0135i 1.54906i 0.632538 + 0.774530i \(0.282013\pi\)
−0.632538 + 0.774530i \(0.717987\pi\)
\(702\) 0 0
\(703\) 2.01363 1.16257i 0.0759453 0.0438471i
\(704\) 0 0
\(705\) 8.49048 16.6873i 0.319770 0.628481i
\(706\) 0 0
\(707\) 32.3653 22.0564i 1.21722 0.829515i
\(708\) 0 0
\(709\) −19.7567 16.5778i −0.741979 0.622594i 0.191389 0.981514i \(-0.438701\pi\)
−0.933368 + 0.358920i \(0.883145\pi\)
\(710\) 0 0
\(711\) 17.0529 + 11.4737i 0.639532 + 0.430296i
\(712\) 0 0
\(713\) −0.902451 + 0.328465i −0.0337970 + 0.0123011i
\(714\) 0 0
\(715\) 20.7526 17.4135i 0.776102 0.651227i
\(716\) 0 0
\(717\) −5.43107 + 17.8010i −0.202827 + 0.664791i
\(718\) 0 0
\(719\) −16.5418 −0.616904 −0.308452 0.951240i \(-0.599811\pi\)
−0.308452 + 0.951240i \(0.599811\pi\)
\(720\) 0 0
\(721\) −34.4907 24.8080i −1.28450 0.923900i
\(722\) 0 0
\(723\) 29.6072 39.3374i 1.10110 1.46297i
\(724\) 0 0
\(725\) −4.00041 4.76750i −0.148572 0.177061i
\(726\) 0 0
\(727\) −4.20390 + 5.01002i −0.155914 + 0.185811i −0.838347 0.545137i \(-0.816478\pi\)
0.682433 + 0.730948i \(0.260922\pi\)
\(728\) 0 0
\(729\) 25.6495 8.43241i 0.949980 0.312311i
\(730\) 0 0
\(731\) −0.356493 + 2.02177i −0.0131854 + 0.0747779i
\(732\) 0 0
\(733\) 0.0154721 0.0425092i 0.000571474 0.00157011i −0.939407 0.342805i \(-0.888623\pi\)
0.939978 + 0.341235i \(0.110845\pi\)
\(734\) 0 0
\(735\) −20.8615 23.5130i −0.769489 0.867289i
\(736\) 0 0
\(737\) −0.605054 + 0.349328i −0.0222874 + 0.0128677i
\(738\) 0 0
\(739\) 12.8012 22.1723i 0.470898 0.815620i −0.528548 0.848904i \(-0.677263\pi\)
0.999446 + 0.0332840i \(0.0105966\pi\)
\(740\) 0 0
\(741\) −25.0301 + 23.3679i −0.919502 + 0.858443i
\(742\) 0 0
\(743\) 14.2738 + 17.0109i 0.523655 + 0.624068i 0.961441 0.275012i \(-0.0886817\pi\)
−0.437786 + 0.899079i \(0.644237\pi\)
\(744\) 0 0
\(745\) 0.216317 0.257797i 0.00792525 0.00944494i
\(746\) 0 0
\(747\) −3.37216 + 49.0383i −0.123381 + 1.79422i
\(748\) 0 0
\(749\) 30.5120 + 8.59164i 1.11488 + 0.313932i
\(750\) 0 0
\(751\) −27.8913 + 23.4036i −1.01777 + 0.854010i −0.989346 0.145586i \(-0.953493\pi\)
−0.0284237 + 0.999596i \(0.509049\pi\)
\(752\) 0 0
\(753\) 4.66948 + 7.18128i 0.170165 + 0.261701i
\(754\) 0 0
\(755\) −23.0236 −0.837914
\(756\) 0 0
\(757\) 31.4588 1.14339 0.571695 0.820466i \(-0.306286\pi\)
0.571695 + 0.820466i \(0.306286\pi\)
\(758\) 0 0
\(759\) 16.9679 0.899078i 0.615895 0.0326345i
\(760\) 0 0
\(761\) −11.8922 + 9.97872i −0.431091 + 0.361728i −0.832363 0.554230i \(-0.813013\pi\)
0.401272 + 0.915959i \(0.368568\pi\)
\(762\) 0 0
\(763\) 21.0857 + 21.6271i 0.763353 + 0.782954i
\(764\) 0 0
\(765\) −1.21127 + 1.25721i −0.0437935 + 0.0454544i
\(766\) 0 0
\(767\) 38.6999 46.1207i 1.39737 1.66532i
\(768\) 0 0
\(769\) −32.7371 39.0146i −1.18053 1.40690i −0.893549 0.448966i \(-0.851792\pi\)
−0.286982 0.957936i \(-0.592652\pi\)
\(770\) 0 0
\(771\) −34.9720 10.6699i −1.25948 0.384267i
\(772\) 0 0
\(773\) 12.0041 20.7916i 0.431756 0.747824i −0.565269 0.824907i \(-0.691227\pi\)
0.997025 + 0.0770834i \(0.0245608\pi\)
\(774\) 0 0
\(775\) 0.316719 0.182858i 0.0113769 0.00656845i
\(776\) 0 0
\(777\) −0.570234 + 2.53173i −0.0204570 + 0.0908254i
\(778\) 0 0
\(779\) 10.2484 28.1572i 0.367186 1.00884i
\(780\) 0 0
\(781\) 4.19489 23.7904i 0.150105 0.851288i
\(782\) 0 0
\(783\) −9.64701 + 16.1185i −0.344756 + 0.576029i
\(784\) 0 0
\(785\) 11.1958 13.3426i 0.399594 0.476217i
\(786\) 0 0
\(787\) 23.3903 + 27.8755i 0.833774 + 0.993654i 0.999971 + 0.00756100i \(0.00240676\pi\)
−0.166197 + 0.986093i \(0.553149\pi\)
\(788\) 0 0
\(789\) 9.58366 + 1.17111i 0.341187 + 0.0416925i
\(790\) 0 0
\(791\) −0.0311676 + 0.310816i −0.00110819 + 0.0110514i
\(792\) 0 0
\(793\) −32.2705 −1.14596
\(794\) 0 0
\(795\) 6.97363 + 7.46965i 0.247329 + 0.264921i
\(796\) 0 0
\(797\) 18.5769 15.5879i 0.658028 0.552151i −0.251467 0.967866i \(-0.580913\pi\)
0.909495 + 0.415715i \(0.136469\pi\)
\(798\) 0 0
\(799\) 0.879435 0.320088i 0.0311122 0.0113239i
\(800\) 0 0
\(801\) −2.89935 + 6.53234i −0.102443 + 0.230809i
\(802\) 0 0
\(803\) −9.22558 7.74118i −0.325563 0.273180i
\(804\) 0 0
\(805\) 17.4626 + 25.6245i 0.615476 + 0.903143i
\(806\) 0 0
\(807\) −14.1317 + 0.748795i −0.497458 + 0.0263588i
\(808\) 0 0
\(809\) −29.3442 + 16.9419i −1.03169 + 0.595646i −0.917468 0.397810i \(-0.869770\pi\)
−0.114220 + 0.993455i \(0.536437\pi\)
\(810\) 0 0
\(811\) 31.8441i 1.11820i −0.829101 0.559098i \(-0.811147\pi\)
0.829101 0.559098i \(-0.188853\pi\)
\(812\) 0 0
\(813\) −23.9490 + 15.5723i −0.839927 + 0.546145i
\(814\) 0 0
\(815\) −6.36044 36.0718i −0.222796 1.26354i
\(816\) 0 0
\(817\) 24.1384 28.7670i 0.844495 1.00643i
\(818\) 0 0
\(819\) −0.226743 38.2187i −0.00792303 1.33547i
\(820\) 0 0
\(821\) 40.6295 + 7.16407i 1.41798 + 0.250028i 0.829509 0.558493i \(-0.188620\pi\)
0.588468 + 0.808520i \(0.299731\pi\)
\(822\) 0 0
\(823\) −15.3129 5.57346i −0.533776 0.194279i 0.0610476 0.998135i \(-0.480556\pi\)
−0.594824 + 0.803856i \(0.702778\pi\)
\(824\) 0 0
\(825\) −6.30389 + 1.45920i −0.219473 + 0.0508029i
\(826\) 0 0
\(827\) 16.9881 9.80811i 0.590736 0.341061i −0.174653 0.984630i \(-0.555880\pi\)
0.765388 + 0.643569i \(0.222547\pi\)
\(828\) 0 0
\(829\) 38.6506i 1.34239i 0.741281 + 0.671195i \(0.234219\pi\)
−0.741281 + 0.671195i \(0.765781\pi\)
\(830\) 0 0
\(831\) 3.44769 28.2139i 0.119599 0.978730i
\(832\) 0 0
\(833\) 0.0398286 1.57070i 0.00137998 0.0544214i
\(834\) 0 0
\(835\) −16.6741 + 6.06886i −0.577030 + 0.210022i
\(836\) 0 0
\(837\) −0.834349 0.722754i −0.0288393 0.0249820i
\(838\) 0 0
\(839\) 24.0568 + 20.1861i 0.830534 + 0.696901i 0.955413 0.295271i \(-0.0954100\pi\)
−0.124880 + 0.992172i \(0.539854\pi\)
\(840\) 0 0
\(841\) 2.76633 + 15.6887i 0.0953908 + 0.540988i
\(842\) 0 0
\(843\) −29.7320 3.63320i −1.02403 0.125134i
\(844\) 0 0
\(845\) 13.2041 + 22.8702i 0.454235 + 0.786758i
\(846\) 0 0
\(847\) 6.84230 + 15.1726i 0.235104 + 0.521336i
\(848\) 0 0
\(849\) −32.7564 35.0863i −1.12420 1.20416i
\(850\) 0 0
\(851\) 0.875608 2.40571i 0.0300155 0.0824668i
\(852\) 0 0
\(853\) 13.2053 + 36.2813i 0.452141 + 1.24225i 0.931214 + 0.364472i \(0.118751\pi\)
−0.479073 + 0.877775i \(0.659027\pi\)
\(854\) 0 0
\(855\) 30.6865 8.83758i 1.04945 0.302239i
\(856\) 0 0
\(857\) −35.0639 + 12.7622i −1.19776 + 0.435948i −0.862441 0.506157i \(-0.831066\pi\)
−0.335317 + 0.942105i \(0.608843\pi\)
\(858\) 0 0
\(859\) 4.40030 + 5.24407i 0.150136 + 0.178925i 0.835871 0.548927i \(-0.184963\pi\)
−0.685734 + 0.727852i \(0.740519\pi\)
\(860\) 0 0
\(861\) 15.3426 + 29.7171i 0.522876 + 1.01276i
\(862\) 0 0
\(863\) −2.04515 1.18077i −0.0696178 0.0401938i 0.464787 0.885422i \(-0.346131\pi\)
−0.534405 + 0.845229i \(0.679464\pi\)
\(864\) 0 0
\(865\) 8.91534 + 15.4418i 0.303131 + 0.525038i
\(866\) 0 0
\(867\) 29.3165 1.55339i 0.995640 0.0527560i
\(868\) 0 0
\(869\) −5.08495 + 13.9708i −0.172495 + 0.473926i
\(870\) 0 0
\(871\) −0.530221 1.45677i −0.0179659 0.0493608i
\(872\) 0 0
\(873\) 28.1026 41.7678i 0.951127 1.41362i
\(874\) 0 0
\(875\) 15.6988 + 16.1019i 0.530715 + 0.544343i
\(876\) 0 0
\(877\) 2.02348 + 11.4757i 0.0683279 + 0.387507i 0.999724 + 0.0234992i \(0.00748072\pi\)
−0.931396 + 0.364008i \(0.881408\pi\)
\(878\) 0 0
\(879\) −23.6655 7.22031i −0.798216 0.243535i
\(880\) 0 0
\(881\) −25.9854 45.0079i −0.875469 1.51636i −0.856263 0.516541i \(-0.827219\pi\)
−0.0192061 0.999816i \(-0.506114\pi\)
\(882\) 0 0
\(883\) 1.83460 3.17763i 0.0617393 0.106936i −0.833504 0.552514i \(-0.813669\pi\)
0.895243 + 0.445578i \(0.147002\pi\)
\(884\) 0 0
\(885\) −51.6704 + 21.9680i −1.73688 + 0.738448i
\(886\) 0 0
\(887\) −28.8253 10.4915i −0.967858 0.352271i −0.190750 0.981639i \(-0.561092\pi\)
−0.777108 + 0.629367i \(0.783314\pi\)
\(888\) 0 0
\(889\) −14.2391 + 50.5681i −0.477564 + 1.69600i
\(890\) 0 0
\(891\) 10.3878 + 16.5389i 0.348006 + 0.554072i
\(892\) 0 0
\(893\) −16.8589 2.97268i −0.564162 0.0994770i
\(894\) 0 0
\(895\) −3.65123 + 0.643811i −0.122047 + 0.0215202i
\(896\) 0 0
\(897\) −4.57325 + 37.4248i −0.152696 + 1.24958i
\(898\) 0 0
\(899\) 0.767997 0.0256141
\(900\) 0 0
\(901\) 0.510795i 0.0170171i
\(902\) 0 0
\(903\) 5.33070 + 41.5733i 0.177394 + 1.38347i
\(904\) 0 0
\(905\) −4.11178 + 0.725019i −0.136680 + 0.0241004i
\(906\) 0 0
\(907\) −2.48432 2.08459i −0.0824904 0.0692176i 0.600610 0.799542i \(-0.294924\pi\)
−0.683100 + 0.730324i \(0.739369\pi\)
\(908\) 0 0
\(909\) −36.8465 24.7914i −1.22212 0.822279i
\(910\) 0 0
\(911\) 20.3632 + 3.59058i 0.674662 + 0.118961i 0.500474 0.865751i \(-0.333159\pi\)
0.174188 + 0.984712i \(0.444270\pi\)
\(912\) 0 0
\(913\) −35.0156 + 6.17419i −1.15885 + 0.204336i
\(914\) 0 0
\(915\) 26.8223 + 13.6471i 0.886717 + 0.451160i
\(916\) 0 0
\(917\) 7.11904 + 0.713872i 0.235091 + 0.0235741i
\(918\) 0 0
\(919\) −22.0932 + 38.2666i −0.728788 + 1.26230i 0.228608 + 0.973519i \(0.426583\pi\)
−0.957396 + 0.288779i \(0.906751\pi\)
\(920\) 0 0
\(921\) −2.77437 52.3593i −0.0914185 1.72530i
\(922\) 0 0
\(923\) 50.3708 + 18.3335i 1.65797 + 0.603453i
\(924\) 0 0
\(925\) −0.169291 + 0.960098i −0.00556626 + 0.0315678i
\(926\) 0 0
\(927\) −11.6004 + 46.7568i −0.381008 + 1.53570i
\(928\) 0 0
\(929\) 0.564009 3.19865i 0.0185045 0.104944i −0.974157 0.225874i \(-0.927476\pi\)
0.992661 + 0.120929i \(0.0385874\pi\)
\(930\) 0 0
\(931\) −14.9965 + 24.5176i −0.491491 + 0.803533i
\(932\) 0 0
\(933\) −37.2150 + 34.7438i −1.21837 + 1.13746i
\(934\) 0 0
\(935\) −1.09363 0.631406i −0.0357654 0.0206492i
\(936\) 0 0
\(937\) 24.3329 + 14.0486i 0.794920 + 0.458947i 0.841692 0.539958i \(-0.181560\pi\)
−0.0467718 + 0.998906i \(0.514893\pi\)
\(938\) 0 0
\(939\) −12.9472 + 17.2022i −0.422517 + 0.561374i
\(940\) 0 0
\(941\) 3.23631 2.71558i 0.105501 0.0885255i −0.588512 0.808489i \(-0.700286\pi\)
0.694012 + 0.719963i \(0.255841\pi\)
\(942\) 0 0
\(943\) −11.2841 31.0027i −0.367460 1.00959i
\(944\) 0 0
\(945\) −15.9741 + 31.8621i −0.519638 + 1.03647i
\(946\) 0 0
\(947\) −13.8020 37.9208i −0.448506 1.23226i −0.933764 0.357890i \(-0.883496\pi\)
0.485258 0.874371i \(-0.338726\pi\)
\(948\) 0 0
\(949\) 20.4708 17.1771i 0.664512 0.557591i
\(950\) 0 0
\(951\) −8.42703 19.8210i −0.273265 0.642740i
\(952\) 0 0
\(953\) 16.4227 + 9.48165i 0.531983 + 0.307141i 0.741824 0.670595i \(-0.233961\pi\)
−0.209840 + 0.977736i \(0.567294\pi\)
\(954\) 0 0
\(955\) −39.8292 22.9954i −1.28884 0.744113i
\(956\) 0 0
\(957\) −12.9966 3.96526i −0.420122 0.128179i
\(958\) 0 0
\(959\) 37.7230 2.81901i 1.21814 0.0910306i
\(960\) 0 0
\(961\) 5.37526 30.4846i 0.173395 0.983374i
\(962\) 0 0
\(963\) −3.79834 35.7415i −0.122400 1.15175i
\(964\) 0 0
\(965\) −9.77141 + 55.4164i −0.314553 + 1.78392i
\(966\) 0 0
\(967\) 4.72573 + 1.72002i 0.151969 + 0.0553122i 0.416885 0.908959i \(-0.363122\pi\)
−0.264916 + 0.964272i \(0.585344\pi\)
\(968\) 0 0
\(969\) 1.42265 + 0.723841i 0.0457021 + 0.0232531i
\(970\) 0 0
\(971\) 8.48615 14.6984i 0.272333 0.471695i −0.697125 0.716949i \(-0.745538\pi\)
0.969459 + 0.245254i \(0.0788713\pi\)
\(972\) 0 0
\(973\) −30.3317 + 13.6786i −0.972390 + 0.438514i
\(974\) 0 0
\(975\) −0.759706 14.3376i −0.0243301 0.459170i
\(976\) 0 0
\(977\) 10.1582 1.79116i 0.324989 0.0573043i −0.00877375 0.999962i \(-0.502793\pi\)
0.333762 + 0.942657i \(0.391682\pi\)
\(978\) 0 0
\(979\) −5.09116 0.897709i −0.162714 0.0286909i
\(980\) 0 0
\(981\) 13.8942 31.3043i 0.443609 0.999468i
\(982\) 0 0
\(983\) −10.1715 8.53491i −0.324421 0.272221i 0.466001 0.884784i \(-0.345694\pi\)
−0.790422 + 0.612563i \(0.790139\pi\)
\(984\) 0 0
\(985\) −31.6500 + 5.58075i −1.00845 + 0.177817i
\(986\) 0 0
\(987\) 15.1978 11.5805i 0.483750 0.368610i
\(988\) 0 0
\(989\) 41.3477i 1.31478i
\(990\) 0 0
\(991\) −37.2285 −1.18260 −0.591300 0.806451i \(-0.701385\pi\)
−0.591300 + 0.806451i \(0.701385\pi\)
\(992\) 0 0
\(993\) −18.8494 + 8.01394i −0.598167 + 0.254315i
\(994\) 0 0
\(995\) 59.6490 10.5177i 1.89100 0.333434i
\(996\) 0 0
\(997\) 38.8916 + 6.85765i 1.23171 + 0.217184i 0.751360 0.659893i \(-0.229398\pi\)
0.480351 + 0.877076i \(0.340509\pi\)
\(998\) 0 0
\(999\) 2.90560 0.465365i 0.0919291 0.0147235i
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 756.2.ca.a.173.16 144
7.3 odd 6 756.2.ck.a.605.23 yes 144
27.5 odd 18 756.2.ck.a.5.23 yes 144
189.59 even 18 inner 756.2.ca.a.437.16 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.ca.a.173.16 144 1.1 even 1 trivial
756.2.ca.a.437.16 yes 144 189.59 even 18 inner
756.2.ck.a.5.23 yes 144 27.5 odd 18
756.2.ck.a.605.23 yes 144 7.3 odd 6