Properties

Label 3150.2.bp.f.1349.3
Level $3150$
Weight $2$
Character 3150.1349
Analytic conductor $25.153$
Analytic rank $0$
Dimension $8$
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] = [3150,2,Mod(899,3150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3150.899");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.3
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 3150.1349
Dual form 3150.2.bp.f.899.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +(4.67303 - 2.69798i) q^{11} +2.51764 q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.89658 - 2.24969i) q^{17} +(2.48004 + 1.43185i) q^{19} -5.39595i q^{22} +(-0.133975 + 0.232051i) q^{23} +(1.25882 - 2.18034i) q^{26} +(-2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(4.18154 - 2.41421i) q^{31} +(0.500000 + 0.866025i) q^{32} -4.49938i q^{34} +(5.64444 + 3.25882i) q^{37} +(2.48004 - 1.43185i) q^{38} -0.760279 q^{41} +5.86370i q^{43} +(-4.67303 - 2.69798i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-6.92418 - 3.99768i) q^{47} +(-6.92820 - 1.00000i) q^{49} +(-1.25882 - 2.18034i) q^{52} +(-4.19918 - 7.27319i) q^{53} +(-0.189469 + 2.63896i) q^{56} +(7.70674 + 4.44949i) q^{58} +(6.33573 + 10.9738i) q^{59} +(-2.27035 - 1.31079i) q^{61} -4.82843i q^{62} +1.00000 q^{64} +(8.50643 - 4.91119i) q^{67} +(-3.89658 - 2.24969i) q^{68} -4.76268i q^{71} +(-5.82843 - 10.0951i) q^{73} +(5.64444 - 3.25882i) q^{74} -2.86370i q^{76} +(-6.23445 - 12.8431i) q^{77} +(4.29618 - 7.44120i) q^{79} +(-0.380139 + 0.658421i) q^{82} +9.45001i q^{83} +(5.07812 + 2.93185i) q^{86} +(-4.67303 + 2.69798i) q^{88} +(-3.98502 + 6.90226i) q^{89} +(0.477014 - 6.64394i) q^{91} +0.267949 q^{92} +(-6.92418 + 3.99768i) q^{94} -6.16353 q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 24 q^{11} + 16 q^{13} - 4 q^{16} + 24 q^{17} - 8 q^{23} + 8 q^{26} + 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{52} + 4 q^{53} + 24 q^{59} + 8 q^{64} + 48 q^{67} - 24 q^{68} - 24 q^{73} - 4 q^{77} + 24 q^{79} + 16 q^{82} - 24 q^{88} + 16 q^{89} - 20 q^{91} + 16 q^{92} + 12 q^{94} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.189469 2.63896i 0.0716124 0.997433i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 4.67303 2.69798i 1.40897 0.813471i 0.413683 0.910421i \(-0.364242\pi\)
0.995289 + 0.0969504i \(0.0309088\pi\)
\(12\) 0 0
\(13\) 2.51764 0.698267 0.349134 0.937073i \(-0.386476\pi\)
0.349134 + 0.937073i \(0.386476\pi\)
\(14\) −2.19067 1.48356i −0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.89658 2.24969i 0.945058 0.545630i 0.0535160 0.998567i \(-0.482957\pi\)
0.891542 + 0.452937i \(0.149624\pi\)
\(18\) 0 0
\(19\) 2.48004 + 1.43185i 0.568960 + 0.328489i 0.756734 0.653723i \(-0.226794\pi\)
−0.187774 + 0.982212i \(0.560127\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.39595i 1.15042i
\(23\) −0.133975 + 0.232051i −0.0279356 + 0.0483859i −0.879655 0.475612i \(-0.842227\pi\)
0.851720 + 0.523998i \(0.175560\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.25882 2.18034i 0.246875 0.427600i
\(27\) 0 0
\(28\) −2.38014 + 1.15539i −0.449804 + 0.218349i
\(29\) 8.89898i 1.65250i 0.563304 + 0.826250i \(0.309530\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(30\) 0 0
\(31\) 4.18154 2.41421i 0.751027 0.433606i −0.0750380 0.997181i \(-0.523908\pi\)
0.826065 + 0.563575i \(0.190574\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4.49938i 0.771637i
\(35\) 0 0
\(36\) 0 0
\(37\) 5.64444 + 3.25882i 0.927940 + 0.535747i 0.886160 0.463380i \(-0.153364\pi\)
0.0417807 + 0.999127i \(0.486697\pi\)
\(38\) 2.48004 1.43185i 0.402316 0.232277i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.760279 −0.118736 −0.0593678 0.998236i \(-0.518908\pi\)
−0.0593678 + 0.998236i \(0.518908\pi\)
\(42\) 0 0
\(43\) 5.86370i 0.894206i 0.894482 + 0.447103i \(0.147544\pi\)
−0.894482 + 0.447103i \(0.852456\pi\)
\(44\) −4.67303 2.69798i −0.704486 0.406735i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) −6.92418 3.99768i −1.01000 0.583121i −0.0988053 0.995107i \(-0.531502\pi\)
−0.911190 + 0.411986i \(0.864835\pi\)
\(48\) 0 0
\(49\) −6.92820 1.00000i −0.989743 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.25882 2.18034i −0.174567 0.302359i
\(53\) −4.19918 7.27319i −0.576802 0.999050i −0.995843 0.0910826i \(-0.970967\pi\)
0.419042 0.907967i \(-0.362366\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.189469 + 2.63896i −0.0253188 + 0.352646i
\(57\) 0 0
\(58\) 7.70674 + 4.44949i 1.01194 + 0.584247i
\(59\) 6.33573 + 10.9738i 0.824842 + 1.42867i 0.902040 + 0.431653i \(0.142069\pi\)
−0.0771977 + 0.997016i \(0.524597\pi\)
\(60\) 0 0
\(61\) −2.27035 1.31079i −0.290689 0.167829i 0.347564 0.937656i \(-0.387009\pi\)
−0.638253 + 0.769827i \(0.720342\pi\)
\(62\) 4.82843i 0.613211i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.50643 4.91119i 1.03923 0.599997i 0.119612 0.992821i \(-0.461835\pi\)
0.919614 + 0.392824i \(0.128502\pi\)
\(68\) −3.89658 2.24969i −0.472529 0.272815i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.76268i 0.565226i −0.959234 0.282613i \(-0.908799\pi\)
0.959234 0.282613i \(-0.0912013\pi\)
\(72\) 0 0
\(73\) −5.82843 10.0951i −0.682166 1.18155i −0.974319 0.225174i \(-0.927705\pi\)
0.292153 0.956372i \(-0.405628\pi\)
\(74\) 5.64444 3.25882i 0.656153 0.378830i
\(75\) 0 0
\(76\) 2.86370i 0.328489i
\(77\) −6.23445 12.8431i −0.710482 1.46361i
\(78\) 0 0
\(79\) 4.29618 7.44120i 0.483358 0.837200i −0.516460 0.856312i \(-0.672750\pi\)
0.999817 + 0.0191114i \(0.00608373\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.380139 + 0.658421i −0.0419794 + 0.0727104i
\(83\) 9.45001i 1.03727i 0.854995 + 0.518636i \(0.173560\pi\)
−0.854995 + 0.518636i \(0.826440\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.07812 + 2.93185i 0.547587 + 0.316150i
\(87\) 0 0
\(88\) −4.67303 + 2.69798i −0.498147 + 0.287605i
\(89\) −3.98502 + 6.90226i −0.422412 + 0.731638i −0.996175 0.0873828i \(-0.972150\pi\)
0.573763 + 0.819021i \(0.305483\pi\)
\(90\) 0 0
\(91\) 0.477014 6.64394i 0.0500046 0.696474i
\(92\) 0.267949 0.0279356
\(93\) 0 0
\(94\) −6.92418 + 3.99768i −0.714175 + 0.412329i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.16353 −0.625812 −0.312906 0.949784i \(-0.601302\pi\)
−0.312906 + 0.949784i \(0.601302\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) 7.02458 + 12.1669i 0.698972 + 1.21065i 0.968823 + 0.247753i \(0.0796920\pi\)
−0.269852 + 0.962902i \(0.586975\pi\)
\(102\) 0 0
\(103\) 7.08845 12.2776i 0.698446 1.20974i −0.270560 0.962703i \(-0.587209\pi\)
0.969005 0.247040i \(-0.0794579\pi\)
\(104\) −2.51764 −0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) −0.820863 + 1.42178i −0.0793559 + 0.137448i −0.902972 0.429699i \(-0.858620\pi\)
0.823616 + 0.567147i \(0.191953\pi\)
\(108\) 0 0
\(109\) −9.94887 17.2319i −0.952929 1.65052i −0.739039 0.673663i \(-0.764720\pi\)
−0.213890 0.976858i \(-0.568613\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.19067 + 1.48356i 0.206999 + 0.140184i
\(113\) 5.95867 0.560545 0.280272 0.959921i \(-0.409575\pi\)
0.280272 + 0.959921i \(0.409575\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.70674 4.44949i 0.715553 0.413125i
\(117\) 0 0
\(118\) 12.6715 1.16650
\(119\) −5.19856 10.7091i −0.476551 0.981706i
\(120\) 0 0
\(121\) 9.05816 15.6892i 0.823469 1.42629i
\(122\) −2.27035 + 1.31079i −0.205548 + 0.118673i
\(123\) 0 0
\(124\) −4.18154 2.41421i −0.375513 0.216803i
\(125\) 0 0
\(126\) 0 0
\(127\) 14.5103i 1.28758i −0.765200 0.643792i \(-0.777360\pi\)
0.765200 0.643792i \(-0.222640\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −7.73325 + 13.3944i −0.675657 + 1.17027i 0.300619 + 0.953744i \(0.402807\pi\)
−0.976276 + 0.216529i \(0.930527\pi\)
\(132\) 0 0
\(133\) 4.24849 6.27343i 0.368391 0.543975i
\(134\) 9.82237i 0.848524i
\(135\) 0 0
\(136\) −3.89658 + 2.24969i −0.334129 + 0.192909i
\(137\) −4.31079 7.46651i −0.368296 0.637907i 0.621004 0.783808i \(-0.286725\pi\)
−0.989299 + 0.145901i \(0.953392\pi\)
\(138\) 0 0
\(139\) 10.2512i 0.869495i −0.900552 0.434748i \(-0.856838\pi\)
0.900552 0.434748i \(-0.143162\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.12460 2.38134i −0.346129 0.199838i
\(143\) 11.7650 6.79253i 0.983839 0.568020i
\(144\) 0 0
\(145\) 0 0
\(146\) −11.6569 −0.964728
\(147\) 0 0
\(148\) 6.51764i 0.535747i
\(149\) −7.96640 4.59940i −0.652633 0.376798i 0.136831 0.990594i \(-0.456308\pi\)
−0.789464 + 0.613797i \(0.789641\pi\)
\(150\) 0 0
\(151\) 6.37429 + 11.0406i 0.518733 + 0.898471i 0.999763 + 0.0217674i \(0.00692931\pi\)
−0.481030 + 0.876704i \(0.659737\pi\)
\(152\) −2.48004 1.43185i −0.201158 0.116139i
\(153\) 0 0
\(154\) −14.2397 1.02236i −1.14747 0.0823845i
\(155\) 0 0
\(156\) 0 0
\(157\) 6.92236 + 11.9899i 0.552464 + 0.956896i 0.998096 + 0.0616798i \(0.0196457\pi\)
−0.445632 + 0.895216i \(0.647021\pi\)
\(158\) −4.29618 7.44120i −0.341786 0.591990i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.586988 + 0.397520i 0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) −17.8444 10.3025i −1.39768 0.806954i −0.403535 0.914964i \(-0.632219\pi\)
−0.994150 + 0.108010i \(0.965552\pi\)
\(164\) 0.380139 + 0.658421i 0.0296839 + 0.0514140i
\(165\) 0 0
\(166\) 8.18394 + 4.72500i 0.635197 + 0.366731i
\(167\) 6.84961i 0.530038i −0.964243 0.265019i \(-0.914622\pi\)
0.964243 0.265019i \(-0.0853783\pi\)
\(168\) 0 0
\(169\) −6.66150 −0.512423
\(170\) 0 0
\(171\) 0 0
\(172\) 5.07812 2.93185i 0.387203 0.223552i
\(173\) −11.0488 6.37902i −0.840024 0.484988i 0.0172486 0.999851i \(-0.494509\pi\)
−0.857272 + 0.514863i \(0.827843\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.39595i 0.406735i
\(177\) 0 0
\(178\) 3.98502 + 6.90226i 0.298690 + 0.517347i
\(179\) −16.3390 + 9.43331i −1.22123 + 0.705079i −0.965181 0.261584i \(-0.915755\pi\)
−0.256052 + 0.966663i \(0.582422\pi\)
\(180\) 0 0
\(181\) 25.5498i 1.89910i 0.313615 + 0.949550i \(0.398460\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(182\) −5.51532 3.73508i −0.408822 0.276862i
\(183\) 0 0
\(184\) 0.133975 0.232051i 0.00987674 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) 12.1392 21.0257i 0.887707 1.53755i
\(188\) 7.99536i 0.583121i
\(189\) 0 0
\(190\) 0 0
\(191\) 7.00657 + 4.04524i 0.506977 + 0.292704i 0.731590 0.681745i \(-0.238778\pi\)
−0.224613 + 0.974448i \(0.572112\pi\)
\(192\) 0 0
\(193\) 12.2343 7.06350i 0.880648 0.508442i 0.00977575 0.999952i \(-0.496888\pi\)
0.870872 + 0.491510i \(0.163555\pi\)
\(194\) −3.08176 + 5.33777i −0.221258 + 0.383230i
\(195\) 0 0
\(196\) 2.59808 + 6.50000i 0.185577 + 0.464286i
\(197\) 14.2738 1.01697 0.508483 0.861072i \(-0.330207\pi\)
0.508483 + 0.861072i \(0.330207\pi\)
\(198\) 0 0
\(199\) −3.06742 + 1.77098i −0.217444 + 0.125541i −0.604766 0.796403i \(-0.706733\pi\)
0.387322 + 0.921944i \(0.373400\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 14.0492 0.988495
\(203\) 23.4840 + 1.68608i 1.64826 + 0.118339i
\(204\) 0 0
\(205\) 0 0
\(206\) −7.08845 12.2776i −0.493876 0.855418i
\(207\) 0 0
\(208\) −1.25882 + 2.18034i −0.0872834 + 0.151179i
\(209\) 15.4524 1.06887
\(210\) 0 0
\(211\) −3.92340 −0.270098 −0.135049 0.990839i \(-0.543119\pi\)
−0.135049 + 0.990839i \(0.543119\pi\)
\(212\) −4.19918 + 7.27319i −0.288401 + 0.499525i
\(213\) 0 0
\(214\) 0.820863 + 1.42178i 0.0561131 + 0.0971907i
\(215\) 0 0
\(216\) 0 0
\(217\) −5.57874 11.4923i −0.378709 0.780150i
\(218\) −19.8977 −1.34764
\(219\) 0 0
\(220\) 0 0
\(221\) 9.81017 5.66390i 0.659903 0.380995i
\(222\) 0 0
\(223\) 14.6904 0.983740 0.491870 0.870669i \(-0.336314\pi\)
0.491870 + 0.870669i \(0.336314\pi\)
\(224\) 2.38014 1.15539i 0.159030 0.0771980i
\(225\) 0 0
\(226\) 2.97934 5.16036i 0.198182 0.343262i
\(227\) −19.7303 + 11.3913i −1.30955 + 0.756068i −0.982021 0.188774i \(-0.939549\pi\)
−0.327527 + 0.944842i \(0.606215\pi\)
\(228\) 0 0
\(229\) 17.5089 + 10.1087i 1.15702 + 0.668005i 0.950588 0.310456i \(-0.100482\pi\)
0.206431 + 0.978461i \(0.433815\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898i 0.584247i
\(233\) −1.31543 + 2.27840i −0.0861769 + 0.149263i −0.905892 0.423509i \(-0.860798\pi\)
0.819715 + 0.572771i \(0.194132\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.33573 10.9738i 0.412421 0.714334i
\(237\) 0 0
\(238\) −11.8737 0.852491i −0.769656 0.0552588i
\(239\) 16.8766i 1.09165i 0.837898 + 0.545827i \(0.183784\pi\)
−0.837898 + 0.545827i \(0.816216\pi\)
\(240\) 0 0
\(241\) −12.5793 + 7.26268i −0.810306 + 0.467831i −0.847062 0.531494i \(-0.821631\pi\)
0.0367560 + 0.999324i \(0.488298\pi\)
\(242\) −9.05816 15.6892i −0.582280 1.00854i
\(243\) 0 0
\(244\) 2.62158i 0.167829i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.24384 + 3.60488i 0.397286 + 0.229373i
\(248\) −4.18154 + 2.41421i −0.265528 + 0.153303i
\(249\) 0 0
\(250\) 0 0
\(251\) −15.7243 −0.992507 −0.496254 0.868178i \(-0.665291\pi\)
−0.496254 + 0.868178i \(0.665291\pi\)
\(252\) 0 0
\(253\) 1.44584i 0.0908993i
\(254\) −12.5663 7.25517i −0.788481 0.455230i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.0275 9.83083i −1.06215 0.613230i −0.136121 0.990692i \(-0.543464\pi\)
−0.926025 + 0.377462i \(0.876797\pi\)
\(258\) 0 0
\(259\) 9.66933 14.2780i 0.600823 0.887192i
\(260\) 0 0
\(261\) 0 0
\(262\) 7.73325 + 13.3944i 0.477762 + 0.827508i
\(263\) −2.16088 3.74275i −0.133245 0.230788i 0.791680 0.610935i \(-0.209206\pi\)
−0.924926 + 0.380148i \(0.875873\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.30871 6.81601i −0.202870 0.417917i
\(267\) 0 0
\(268\) −8.50643 4.91119i −0.519613 0.299999i
\(269\) 8.79895 + 15.2402i 0.536482 + 0.929214i 0.999090 + 0.0426509i \(0.0135803\pi\)
−0.462608 + 0.886563i \(0.653086\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) 4.49938i 0.272815i
\(273\) 0 0
\(274\) −8.62158 −0.520849
\(275\) 0 0
\(276\) 0 0
\(277\) 2.61489 1.50971i 0.157114 0.0907097i −0.419382 0.907810i \(-0.637753\pi\)
0.576496 + 0.817100i \(0.304420\pi\)
\(278\) −8.87780 5.12560i −0.532455 0.307413i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.6880i 0.637591i −0.947824 0.318795i \(-0.896722\pi\)
0.947824 0.318795i \(-0.103278\pi\)
\(282\) 0 0
\(283\) 8.78434 + 15.2149i 0.522175 + 0.904434i 0.999667 + 0.0257976i \(0.00821255\pi\)
−0.477492 + 0.878636i \(0.658454\pi\)
\(284\) −4.12460 + 2.38134i −0.244750 + 0.141307i
\(285\) 0 0
\(286\) 13.5851i 0.803301i
\(287\) −0.144049 + 2.00634i −0.00850295 + 0.118431i
\(288\) 0 0
\(289\) 1.62220 2.80973i 0.0954235 0.165278i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.82843 + 10.0951i −0.341083 + 0.590773i
\(293\) 14.6710i 0.857086i −0.903521 0.428543i \(-0.859027\pi\)
0.903521 0.428543i \(-0.140973\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −5.64444 3.25882i −0.328076 0.189415i
\(297\) 0 0
\(298\) −7.96640 + 4.59940i −0.461481 + 0.266436i
\(299\) −0.337300 + 0.584220i −0.0195065 + 0.0337863i
\(300\) 0 0
\(301\) 15.4741 + 1.11099i 0.891911 + 0.0640363i
\(302\) 12.7486 0.733599
\(303\) 0 0
\(304\) −2.48004 + 1.43185i −0.142240 + 0.0821223i
\(305\) 0 0
\(306\) 0 0
\(307\) 21.2772 1.21435 0.607177 0.794567i \(-0.292302\pi\)
0.607177 + 0.794567i \(0.292302\pi\)
\(308\) −8.00524 + 11.8208i −0.456141 + 0.673550i
\(309\) 0 0
\(310\) 0 0
\(311\) 5.91724 + 10.2490i 0.335536 + 0.581165i 0.983588 0.180431i \(-0.0577493\pi\)
−0.648052 + 0.761596i \(0.724416\pi\)
\(312\) 0 0
\(313\) −2.25485 + 3.90551i −0.127452 + 0.220753i −0.922689 0.385546i \(-0.874013\pi\)
0.795237 + 0.606299i \(0.207346\pi\)
\(314\) 13.8447 0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) −9.19151 + 15.9202i −0.516247 + 0.894165i 0.483576 + 0.875303i \(0.339338\pi\)
−0.999822 + 0.0188626i \(0.993995\pi\)
\(318\) 0 0
\(319\) 24.0092 + 41.5852i 1.34426 + 2.32833i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.637756 0.309587i 0.0355408 0.0172526i
\(323\) 12.8849 0.716934
\(324\) 0 0
\(325\) 0 0
\(326\) −17.8444 + 10.3025i −0.988313 + 0.570603i
\(327\) 0 0
\(328\) 0.760279 0.0419794
\(329\) −11.8616 + 17.5152i −0.653952 + 0.965644i
\(330\) 0 0
\(331\) −3.98066 + 6.89471i −0.218797 + 0.378967i −0.954440 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(332\) 8.18394 4.72500i 0.449152 0.259318i
\(333\) 0 0
\(334\) −5.93193 3.42480i −0.324581 0.187397i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.89417i 0.375549i −0.982212 0.187775i \(-0.939873\pi\)
0.982212 0.187775i \(-0.0601275\pi\)
\(338\) −3.33075 + 5.76903i −0.181169 + 0.313794i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.0270 22.5634i 0.705451 1.22188i
\(342\) 0 0
\(343\) −3.95164 + 18.0938i −0.213368 + 0.976972i
\(344\) 5.86370i 0.316150i
\(345\) 0 0
\(346\) −11.0488 + 6.37902i −0.593986 + 0.342938i
\(347\) 8.17789 + 14.1645i 0.439012 + 0.760392i 0.997614 0.0690448i \(-0.0219951\pi\)
−0.558601 + 0.829436i \(0.688662\pi\)
\(348\) 0 0
\(349\) 24.5851i 1.31601i −0.753014 0.658004i \(-0.771401\pi\)
0.753014 0.658004i \(-0.228599\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.67303 + 2.69798i 0.249073 + 0.143803i
\(353\) −11.8802 + 6.85906i −0.632321 + 0.365071i −0.781651 0.623717i \(-0.785622\pi\)
0.149329 + 0.988788i \(0.452289\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.97005 0.422412
\(357\) 0 0
\(358\) 18.8666i 0.997132i
\(359\) −10.3059 5.95011i −0.543924 0.314035i 0.202744 0.979232i \(-0.435014\pi\)
−0.746668 + 0.665197i \(0.768348\pi\)
\(360\) 0 0
\(361\) −5.39960 9.35238i −0.284190 0.492231i
\(362\) 22.1268 + 12.7749i 1.16296 + 0.671433i
\(363\) 0 0
\(364\) −5.99233 + 2.90887i −0.314083 + 0.152466i
\(365\) 0 0
\(366\) 0 0
\(367\) −6.29461 10.9026i −0.328576 0.569110i 0.653654 0.756794i \(-0.273235\pi\)
−0.982230 + 0.187684i \(0.939902\pi\)
\(368\) −0.133975 0.232051i −0.00698391 0.0120965i
\(369\) 0 0
\(370\) 0 0
\(371\) −19.9893 + 9.70342i −1.03779 + 0.503776i
\(372\) 0 0
\(373\) −23.5331 13.5868i −1.21850 0.703499i −0.253900 0.967230i \(-0.581714\pi\)
−0.964596 + 0.263731i \(0.915047\pi\)
\(374\) −12.1392 21.0257i −0.627704 1.08722i
\(375\) 0 0
\(376\) 6.92418 + 3.99768i 0.357087 + 0.206164i
\(377\) 22.4044i 1.15389i
\(378\) 0 0
\(379\) −15.7335 −0.808174 −0.404087 0.914721i \(-0.632411\pi\)
−0.404087 + 0.914721i \(0.632411\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.00657 4.04524i 0.358487 0.206973i
\(383\) −13.6669 7.89060i −0.698347 0.403191i 0.108384 0.994109i \(-0.465432\pi\)
−0.806732 + 0.590918i \(0.798766\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.1270i 0.719046i
\(387\) 0 0
\(388\) 3.08176 + 5.33777i 0.156453 + 0.270984i
\(389\) −13.7556 + 7.94182i −0.697438 + 0.402666i −0.806393 0.591381i \(-0.798583\pi\)
0.108954 + 0.994047i \(0.465250\pi\)
\(390\) 0 0
\(391\) 1.20560i 0.0609700i
\(392\) 6.92820 + 1.00000i 0.349927 + 0.0505076i
\(393\) 0 0
\(394\) 7.13689 12.3615i 0.359552 0.622762i
\(395\) 0 0
\(396\) 0 0
\(397\) −18.6806 + 32.3557i −0.937550 + 1.62388i −0.167528 + 0.985867i \(0.553578\pi\)
−0.770022 + 0.638017i \(0.779755\pi\)
\(398\) 3.54195i 0.177542i
\(399\) 0 0
\(400\) 0 0
\(401\) −24.4856 14.1368i −1.22275 0.705957i −0.257249 0.966345i \(-0.582816\pi\)
−0.965504 + 0.260389i \(0.916149\pi\)
\(402\) 0 0
\(403\) 10.5276 6.07812i 0.524417 0.302773i
\(404\) 7.02458 12.1669i 0.349486 0.605327i
\(405\) 0 0
\(406\) 13.2022 19.4947i 0.655214 0.967507i
\(407\) 35.1689 1.74326
\(408\) 0 0
\(409\) −13.8647 + 8.00481i −0.685567 + 0.395812i −0.801949 0.597392i \(-0.796204\pi\)
0.116382 + 0.993204i \(0.462870\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −14.1769 −0.698446
\(413\) 30.1599 14.6405i 1.48407 0.720414i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.25882 + 2.18034i 0.0617187 + 0.106900i
\(417\) 0 0
\(418\) 7.72620 13.3822i 0.377901 0.654544i
\(419\) 29.5137 1.44184 0.720919 0.693020i \(-0.243720\pi\)
0.720919 + 0.693020i \(0.243720\pi\)
\(420\) 0 0
\(421\) 0.309114 0.0150653 0.00753265 0.999972i \(-0.497602\pi\)
0.00753265 + 0.999972i \(0.497602\pi\)
\(422\) −1.96170 + 3.39776i −0.0954939 + 0.165400i
\(423\) 0 0
\(424\) 4.19918 + 7.27319i 0.203930 + 0.353217i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.88928 + 5.74301i −0.188215 + 0.277924i
\(428\) 1.64173 0.0793559
\(429\) 0 0
\(430\) 0 0
\(431\) −7.63843 + 4.41005i −0.367930 + 0.212425i −0.672554 0.740048i \(-0.734803\pi\)
0.304624 + 0.952473i \(0.401469\pi\)
\(432\) 0 0
\(433\) −9.56388 −0.459611 −0.229805 0.973237i \(-0.573809\pi\)
−0.229805 + 0.973237i \(0.573809\pi\)
\(434\) −12.7420 0.914836i −0.611636 0.0439135i
\(435\) 0 0
\(436\) −9.94887 + 17.2319i −0.476464 + 0.825260i
\(437\) −0.664525 + 0.383663i −0.0317885 + 0.0183531i
\(438\) 0 0
\(439\) 31.3336 + 18.0905i 1.49547 + 0.863412i 0.999986 0.00520362i \(-0.00165637\pi\)
0.495487 + 0.868615i \(0.334990\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 11.3278i 0.538809i
\(443\) 2.04284 3.53830i 0.0970582 0.168110i −0.813408 0.581694i \(-0.802390\pi\)
0.910466 + 0.413584i \(0.135723\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 7.34519 12.7222i 0.347805 0.602415i
\(447\) 0 0
\(448\) 0.189469 2.63896i 0.00895155 0.124679i
\(449\) 19.9377i 0.940918i −0.882422 0.470459i \(-0.844088\pi\)
0.882422 0.470459i \(-0.155912\pi\)
\(450\) 0 0
\(451\) −3.55281 + 2.05121i −0.167295 + 0.0965879i
\(452\) −2.97934 5.16036i −0.140136 0.242723i
\(453\) 0 0
\(454\) 22.7826i 1.06924i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.4283 + 10.0623i 0.815264 + 0.470693i 0.848780 0.528745i \(-0.177337\pi\)
−0.0335168 + 0.999438i \(0.510671\pi\)
\(458\) 17.5089 10.1087i 0.818136 0.472351i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.909299 0.0423503 0.0211751 0.999776i \(-0.493259\pi\)
0.0211751 + 0.999776i \(0.493259\pi\)
\(462\) 0 0
\(463\) 21.4280i 0.995843i −0.867222 0.497922i \(-0.834097\pi\)
0.867222 0.497922i \(-0.165903\pi\)
\(464\) −7.70674 4.44949i −0.357777 0.206562i
\(465\) 0 0
\(466\) 1.31543 + 2.27840i 0.0609363 + 0.105545i
\(467\) 10.9917 + 6.34607i 0.508636 + 0.293661i 0.732273 0.681012i \(-0.238460\pi\)
−0.223637 + 0.974672i \(0.571793\pi\)
\(468\) 0 0
\(469\) −11.3487 23.3786i −0.524035 1.07952i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.33573 10.9738i −0.291626 0.505111i
\(473\) 15.8201 + 27.4013i 0.727411 + 1.25991i
\(474\) 0 0
\(475\) 0 0
\(476\) −6.67511 + 9.85666i −0.305953 + 0.451779i
\(477\) 0 0
\(478\) 14.6155 + 8.43828i 0.668499 + 0.385958i
\(479\) 6.43828 + 11.1514i 0.294172 + 0.509522i 0.974792 0.223115i \(-0.0716227\pi\)
−0.680620 + 0.732637i \(0.738289\pi\)
\(480\) 0 0
\(481\) 14.2107 + 8.20453i 0.647950 + 0.374094i
\(482\) 14.5254i 0.661612i
\(483\) 0 0
\(484\) −18.1163 −0.823469
\(485\) 0 0
\(486\) 0 0
\(487\) −18.0301 + 10.4097i −0.817022 + 0.471708i −0.849388 0.527768i \(-0.823029\pi\)
0.0323665 + 0.999476i \(0.489696\pi\)
\(488\) 2.27035 + 1.31079i 0.102774 + 0.0593366i
\(489\) 0 0
\(490\) 0 0
\(491\) 27.3271i 1.23325i 0.787256 + 0.616627i \(0.211501\pi\)
−0.787256 + 0.616627i \(0.788499\pi\)
\(492\) 0 0
\(493\) 20.0199 + 34.6755i 0.901653 + 1.56171i
\(494\) 6.24384 3.60488i 0.280924 0.162191i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) −12.5685 0.902379i −0.563775 0.0404772i
\(498\) 0 0
\(499\) 16.6802 28.8909i 0.746708 1.29334i −0.202685 0.979244i \(-0.564967\pi\)
0.949393 0.314092i \(-0.101700\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −7.86214 + 13.6176i −0.350904 + 0.607784i
\(503\) 16.2936i 0.726494i −0.931693 0.363247i \(-0.881668\pi\)
0.931693 0.363247i \(-0.118332\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1.25214 + 0.722921i 0.0556642 + 0.0321377i
\(507\) 0 0
\(508\) −12.5663 + 7.25517i −0.557540 + 0.321896i
\(509\) 12.3400 21.3735i 0.546961 0.947365i −0.451519 0.892261i \(-0.649118\pi\)
0.998481 0.0551036i \(-0.0175489\pi\)
\(510\) 0 0
\(511\) −27.7449 + 13.4683i −1.22736 + 0.595801i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −17.0275 + 9.83083i −0.751051 + 0.433619i
\(515\) 0 0
\(516\) 0 0
\(517\) −43.1426 −1.89741
\(518\) −7.53044 15.5129i −0.330869 0.681597i
\(519\) 0 0
\(520\) 0 0
\(521\) −0.141663 0.245367i −0.00620635 0.0107497i 0.862906 0.505365i \(-0.168642\pi\)
−0.869112 + 0.494616i \(0.835309\pi\)
\(522\) 0 0
\(523\) −5.64083 + 9.77021i −0.246656 + 0.427222i −0.962596 0.270941i \(-0.912665\pi\)
0.715940 + 0.698162i \(0.245999\pi\)
\(524\) 15.4665 0.675657
\(525\) 0 0
\(526\) −4.32175 −0.188437
\(527\) 10.8625 18.8143i 0.473176 0.819565i
\(528\) 0 0
\(529\) 11.4641 + 19.8564i 0.498439 + 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) −7.55719 0.542582i −0.327646 0.0235239i
\(533\) −1.91411 −0.0829092
\(534\) 0 0
\(535\) 0 0
\(536\) −8.50643 + 4.91119i −0.367422 + 0.212131i
\(537\) 0 0
\(538\) 17.5979 0.758700
\(539\) −35.0737 + 14.0191i −1.51073 + 0.603845i
\(540\) 0 0
\(541\) 17.4125 30.1593i 0.748621 1.29665i −0.199862 0.979824i \(-0.564049\pi\)
0.948484 0.316826i \(-0.102617\pi\)
\(542\) −9.12436 + 5.26795i −0.391925 + 0.226278i
\(543\) 0 0
\(544\) 3.89658 + 2.24969i 0.167064 + 0.0964546i
\(545\) 0 0
\(546\) 0 0
\(547\) 35.4261i 1.51471i 0.653002 + 0.757356i \(0.273509\pi\)
−0.653002 + 0.757356i \(0.726491\pi\)
\(548\) −4.31079 + 7.46651i −0.184148 + 0.318953i
\(549\) 0 0
\(550\) 0 0
\(551\) −12.7420 + 22.0698i −0.542828 + 0.940206i
\(552\) 0 0
\(553\) −18.8230 12.7473i −0.800436 0.542071i
\(554\) 3.01942i 0.128283i
\(555\) 0 0
\(556\) −8.87780 + 5.12560i −0.376503 + 0.217374i
\(557\) −4.07093 7.05105i −0.172491 0.298763i 0.766799 0.641887i \(-0.221848\pi\)
−0.939290 + 0.343124i \(0.888515\pi\)
\(558\) 0 0
\(559\) 14.7627i 0.624395i
\(560\) 0 0
\(561\) 0 0
\(562\) −9.25605 5.34398i −0.390443 0.225422i
\(563\) −17.6821 + 10.2088i −0.745212 + 0.430248i −0.823961 0.566646i \(-0.808241\pi\)
0.0787491 + 0.996894i \(0.474907\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 17.5687 0.738467
\(567\) 0 0
\(568\) 4.76268i 0.199838i
\(569\) 22.5542 + 13.0217i 0.945520 + 0.545896i 0.891686 0.452654i \(-0.149523\pi\)
0.0538334 + 0.998550i \(0.482856\pi\)
\(570\) 0 0
\(571\) 6.18811 + 10.7181i 0.258964 + 0.448539i 0.965965 0.258674i \(-0.0832855\pi\)
−0.707000 + 0.707213i \(0.749952\pi\)
\(572\) −11.7650 6.79253i −0.491920 0.284010i
\(573\) 0 0
\(574\) 1.66552 + 1.12792i 0.0695175 + 0.0470786i
\(575\) 0 0
\(576\) 0 0
\(577\) 13.4753 + 23.3399i 0.560985 + 0.971654i 0.997411 + 0.0719139i \(0.0229107\pi\)
−0.436426 + 0.899740i \(0.643756\pi\)
\(578\) −1.62220 2.80973i −0.0674746 0.116869i
\(579\) 0 0
\(580\) 0 0
\(581\) 24.9382 + 1.79048i 1.03461 + 0.0742816i
\(582\) 0 0
\(583\) −39.2458 22.6586i −1.62539 0.938422i
\(584\) 5.82843 + 10.0951i 0.241182 + 0.417740i
\(585\) 0 0
\(586\) −12.7054 7.33548i −0.524856 0.303026i
\(587\) 35.3511i 1.45910i 0.683930 + 0.729548i \(0.260269\pi\)
−0.683930 + 0.729548i \(0.739731\pi\)
\(588\) 0 0
\(589\) 13.8272 0.569739
\(590\) 0 0
\(591\) 0 0
\(592\) −5.64444 + 3.25882i −0.231985 + 0.133937i
\(593\) 25.4711 + 14.7057i 1.04597 + 0.603893i 0.921519 0.388333i \(-0.126949\pi\)
0.124454 + 0.992225i \(0.460282\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.19881i 0.376798i
\(597\) 0 0
\(598\) 0.337300 + 0.584220i 0.0137932 + 0.0238905i
\(599\) 26.5494 15.3283i 1.08478 0.626298i 0.152598 0.988288i \(-0.451236\pi\)
0.932182 + 0.361990i \(0.117903\pi\)
\(600\) 0 0
\(601\) 34.3407i 1.40078i −0.713758 0.700392i \(-0.753008\pi\)
0.713758 0.700392i \(-0.246992\pi\)
\(602\) 8.69918 12.8454i 0.354552 0.523541i
\(603\) 0 0
\(604\) 6.37429 11.0406i 0.259366 0.449236i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.3087 + 28.2475i −0.661950 + 1.14653i 0.318153 + 0.948040i \(0.396938\pi\)
−0.980103 + 0.198492i \(0.936396\pi\)
\(608\) 2.86370i 0.116139i
\(609\) 0 0
\(610\) 0 0
\(611\) −17.4326 10.0647i −0.705247 0.407174i
\(612\) 0 0
\(613\) 13.8537 7.99843i 0.559545 0.323054i −0.193418 0.981117i \(-0.561957\pi\)
0.752963 + 0.658063i \(0.228624\pi\)
\(614\) 10.6386 18.4266i 0.429339 0.743636i
\(615\) 0 0
\(616\) 6.23445 + 12.8431i 0.251193 + 0.517464i
\(617\) −25.1429 −1.01221 −0.506107 0.862471i \(-0.668916\pi\)
−0.506107 + 0.862471i \(0.668916\pi\)
\(618\) 0 0
\(619\) −32.3379 + 18.6703i −1.29977 + 0.750423i −0.980364 0.197195i \(-0.936817\pi\)
−0.319406 + 0.947618i \(0.603483\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.8345 0.474519
\(623\) 17.4597 + 11.8241i 0.699510 + 0.473722i
\(624\) 0 0
\(625\) 0 0
\(626\) 2.25485 + 3.90551i 0.0901219 + 0.156096i
\(627\) 0 0
\(628\) 6.92236 11.9899i 0.276232 0.478448i
\(629\) 29.3253 1.16928
\(630\) 0 0
\(631\) 49.5015 1.97062 0.985311 0.170767i \(-0.0546245\pi\)
0.985311 + 0.170767i \(0.0546245\pi\)
\(632\) −4.29618 + 7.44120i −0.170893 + 0.295995i
\(633\) 0 0
\(634\) 9.19151 + 15.9202i 0.365041 + 0.632270i
\(635\) 0 0
\(636\) 0 0
\(637\) −17.4427 2.51764i −0.691105 0.0997525i
\(638\) 48.0185 1.90107
\(639\) 0 0
\(640\) 0 0
\(641\) 31.4439 18.1542i 1.24196 0.717046i 0.272467 0.962165i \(-0.412160\pi\)
0.969493 + 0.245119i \(0.0788271\pi\)
\(642\) 0 0
\(643\) −10.2653 −0.404824 −0.202412 0.979300i \(-0.564878\pi\)
−0.202412 + 0.979300i \(0.564878\pi\)
\(644\) 0.0507680 0.707107i 0.00200054 0.0278639i
\(645\) 0 0
\(646\) 6.44244 11.1586i 0.253474 0.439031i
\(647\) −18.8980 + 10.9108i −0.742956 + 0.428946i −0.823143 0.567834i \(-0.807782\pi\)
0.0801869 + 0.996780i \(0.474448\pi\)
\(648\) 0 0
\(649\) 59.2142 + 34.1873i 2.32436 + 1.34197i
\(650\) 0 0
\(651\) 0 0
\(652\) 20.6050i 0.806954i
\(653\) −23.6457 + 40.9556i −0.925329 + 1.60272i −0.134297 + 0.990941i \(0.542878\pi\)
−0.791032 + 0.611775i \(0.790456\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.380139 0.658421i 0.0148419 0.0257070i
\(657\) 0 0
\(658\) 9.23779 + 19.0301i 0.360127 + 0.741869i
\(659\) 3.58255i 0.139556i −0.997563 0.0697782i \(-0.977771\pi\)
0.997563 0.0697782i \(-0.0222291\pi\)
\(660\) 0 0
\(661\) −1.41761 + 0.818459i −0.0551388 + 0.0318344i −0.527316 0.849669i \(-0.676802\pi\)
0.472177 + 0.881504i \(0.343468\pi\)
\(662\) 3.98066 + 6.89471i 0.154713 + 0.267970i
\(663\) 0 0
\(664\) 9.45001i 0.366731i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.06502 1.19224i −0.0799577 0.0461636i
\(668\) −5.93193 + 3.42480i −0.229513 + 0.132510i
\(669\) 0 0
\(670\) 0 0
\(671\) −14.1459 −0.546097
\(672\) 0 0
\(673\) 2.02242i 0.0779587i 0.999240 + 0.0389794i \(0.0124107\pi\)
−0.999240 + 0.0389794i \(0.987589\pi\)
\(674\) −5.97053 3.44709i −0.229976 0.132777i
\(675\) 0 0
\(676\) 3.33075 + 5.76903i 0.128106 + 0.221886i
\(677\) −19.8169 11.4413i −0.761626 0.439725i 0.0682532 0.997668i \(-0.478257\pi\)
−0.829879 + 0.557943i \(0.811591\pi\)
\(678\) 0 0
\(679\) −1.16780 + 16.2653i −0.0448159 + 0.624205i
\(680\) 0 0
\(681\) 0 0
\(682\) −13.0270 22.5634i −0.498829 0.863997i
\(683\) 15.7026 + 27.1977i 0.600844 + 1.04069i 0.992694 + 0.120663i \(0.0385020\pi\)
−0.391850 + 0.920029i \(0.628165\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 13.6938 + 12.4691i 0.522834 + 0.476073i
\(687\) 0 0
\(688\) −5.07812 2.93185i −0.193601 0.111776i
\(689\) −10.5720 18.3113i −0.402762 0.697604i
\(690\) 0 0
\(691\) 29.3677 + 16.9554i 1.11720 + 0.645015i 0.940684 0.339283i \(-0.110184\pi\)
0.176515 + 0.984298i \(0.443518\pi\)
\(692\) 12.7580i 0.484988i
\(693\) 0 0
\(694\) 16.3558 0.620857
\(695\) 0 0
\(696\) 0 0
\(697\) −2.96248 + 1.71039i −0.112212 + 0.0647857i
\(698\) −21.2913 12.2925i −0.805887 0.465279i
\(699\) 0 0
\(700\) 0 0
\(701\) 10.5296i 0.397699i −0.980030 0.198849i \(-0.936280\pi\)
0.980030 0.198849i \(-0.0637205\pi\)
\(702\) 0 0
\(703\) 9.33229 + 16.1640i 0.351974 + 0.609637i
\(704\) 4.67303 2.69798i 0.176122 0.101684i
\(705\) 0 0
\(706\) 13.7181i 0.516288i
\(707\) 33.4390 16.2323i 1.25760 0.610479i
\(708\) 0 0
\(709\) 7.52572 13.0349i 0.282634 0.489537i −0.689398 0.724382i \(-0.742125\pi\)
0.972033 + 0.234845i \(0.0754584\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.98502 6.90226i 0.149345 0.258673i
\(713\) 1.29377i 0.0484522i
\(714\) 0 0
\(715\) 0 0
\(716\) 16.3390 + 9.43331i 0.610616 + 0.352539i
\(717\) 0 0
\(718\) −10.3059 + 5.95011i −0.384613 + 0.222056i
\(719\) 12.2137 21.1547i 0.455494 0.788938i −0.543223 0.839589i \(-0.682796\pi\)
0.998716 + 0.0506506i \(0.0161295\pi\)
\(720\) 0 0
\(721\) −31.0569 21.0323i −1.15662 0.783285i
\(722\) −10.7992 −0.401905
\(723\) 0 0
\(724\) 22.1268 12.7749i 0.822335 0.474775i
\(725\) 0 0
\(726\) 0 0
\(727\) 43.7349 1.62204 0.811019 0.585020i \(-0.198913\pi\)
0.811019 + 0.585020i \(0.198913\pi\)
\(728\) −0.477014 + 6.64394i −0.0176793 + 0.246241i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.1915 + 22.8484i 0.487906 + 0.845077i
\(732\) 0 0
\(733\) 22.3596 38.7280i 0.825872 1.43045i −0.0753789 0.997155i \(-0.524017\pi\)
0.901251 0.433297i \(-0.142650\pi\)
\(734\) −12.5892 −0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) 26.5005 45.9003i 0.976160 1.69076i
\(738\) 0 0
\(739\) −10.7360 18.5954i −0.394932 0.684042i 0.598161 0.801376i \(-0.295898\pi\)
−0.993092 + 0.117334i \(0.962565\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.59123 + 22.1629i −0.0584157 + 0.813626i
\(743\) −29.5637 −1.08459 −0.542293 0.840190i \(-0.682444\pi\)
−0.542293 + 0.840190i \(0.682444\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −23.5331 + 13.5868i −0.861607 + 0.497449i
\(747\) 0 0
\(748\) −24.2784 −0.887707
\(749\) 3.59648 + 2.43561i 0.131413 + 0.0889951i
\(750\) 0 0
\(751\) −0.596750 + 1.03360i −0.0217757 + 0.0377166i −0.876708 0.481023i \(-0.840265\pi\)
0.854932 + 0.518740i \(0.173599\pi\)
\(752\) 6.92418 3.99768i 0.252499 0.145780i
\(753\) 0 0
\(754\) 19.4028 + 11.2022i 0.706608 + 0.407960i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.8915i 0.977386i −0.872456 0.488693i \(-0.837474\pi\)
0.872456 0.488693i \(-0.162526\pi\)
\(758\) −7.86673 + 13.6256i −0.285732 + 0.494903i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.939574 1.62739i 0.0340595 0.0589928i −0.848493 0.529206i \(-0.822490\pi\)
0.882553 + 0.470213i \(0.155823\pi\)
\(762\) 0 0
\(763\) −47.3594 + 22.9897i −1.71452 + 0.832284i
\(764\) 8.09049i 0.292704i
\(765\) 0 0
\(766\) −13.6669 + 7.89060i −0.493806 + 0.285099i
\(767\) 15.9511 + 27.6281i 0.575960 + 0.997592i
\(768\) 0 0
\(769\) 50.6544i 1.82664i 0.407239 + 0.913322i \(0.366492\pi\)
−0.407239 + 0.913322i \(0.633508\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.2343 7.06350i −0.440324 0.254221i
\(773\) 42.1499 24.3353i 1.51603 0.875279i 0.516204 0.856466i \(-0.327345\pi\)
0.999823 0.0188128i \(-0.00598865\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.16353 0.221258
\(777\) 0 0
\(778\) 15.8836i 0.569456i
\(779\) −1.88552 1.08861i −0.0675558 0.0390034i
\(780\) 0 0
\(781\) −12.8496 22.2562i −0.459795 0.796388i
\(782\) 1.04408 + 0.602802i 0.0373364 + 0.0215562i
\(783\) 0 0
\(784\) 4.33013 5.50000i 0.154647 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.47307 12.9437i −0.266386 0.461395i 0.701540 0.712630i \(-0.252496\pi\)
−0.967926 + 0.251236i \(0.919163\pi\)
\(788\) −7.13689 12.3615i −0.254241 0.440359i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.12898 15.7247i 0.0401420 0.559105i
\(792\) 0 0
\(793\) −5.71593 3.30009i −0.202979 0.117190i
\(794\) 18.6806 + 32.3557i 0.662948 + 1.14826i
\(795\) 0 0
\(796\) 3.06742 + 1.77098i 0.108722 + 0.0627706i
\(797\) 15.0557i 0.533301i 0.963793 + 0.266650i \(0.0859169\pi\)
−0.963793 + 0.266650i \(0.914083\pi\)
\(798\) 0 0
\(799\) −35.9741 −1.27267
\(800\) 0 0
\(801\) 0 0
\(802\) −24.4856 + 14.1368i −0.864617 + 0.499187i
\(803\) −54.4729 31.4499i −1.92231 1.10984i
\(804\) 0 0
\(805\) 0 0
\(806\) 12.1562i 0.428185i
\(807\) 0 0
\(808\) −7.02458 12.1669i −0.247124 0.428031i
\(809\) 30.7426 17.7493i 1.08085 0.624031i 0.149727 0.988727i \(-0.452160\pi\)
0.931127 + 0.364696i \(0.118827\pi\)
\(810\) 0 0
\(811\) 24.5935i 0.863594i 0.901971 + 0.431797i \(0.142120\pi\)
−0.901971 + 0.431797i \(0.857880\pi\)
\(812\) −10.2818 21.1808i −0.360822 0.743301i
\(813\) 0 0
\(814\) 17.5844 30.4571i 0.616334 1.06752i
\(815\) 0 0
\(816\) 0 0
\(817\) −8.39595 + 14.5422i −0.293737 + 0.508768i
\(818\) 16.0096i 0.559763i
\(819\) 0 0
\(820\) 0 0
\(821\) 12.3035 + 7.10342i 0.429395 + 0.247911i 0.699089 0.715035i \(-0.253589\pi\)
−0.269694 + 0.962946i \(0.586923\pi\)
\(822\) 0 0
\(823\) −1.63780 + 0.945584i −0.0570901 + 0.0329610i −0.528273 0.849074i \(-0.677160\pi\)
0.471183 + 0.882035i \(0.343827\pi\)
\(824\) −7.08845 + 12.2776i −0.246938 + 0.427709i
\(825\) 0 0
\(826\) 2.40085 33.4395i 0.0835361 1.16351i
\(827\) 31.9280 1.11024 0.555122 0.831769i \(-0.312671\pi\)
0.555122 + 0.831769i \(0.312671\pi\)
\(828\) 0 0
\(829\) −3.38864 + 1.95643i −0.117692 + 0.0679497i −0.557691 0.830049i \(-0.688312\pi\)
0.439998 + 0.897999i \(0.354979\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 2.51764 0.0872834
\(833\) −29.2460 + 11.6897i −1.01331 + 0.405025i
\(834\) 0 0
\(835\) 0 0
\(836\) −7.72620 13.3822i −0.267216 0.462832i
\(837\) 0 0
\(838\) 14.7568 25.5596i 0.509766 0.882941i
\(839\) −15.3513 −0.529984 −0.264992 0.964251i \(-0.585369\pi\)
−0.264992 + 0.964251i \(0.585369\pi\)
\(840\) 0 0
\(841\) −50.1918 −1.73075
\(842\) 0.154557 0.267701i 0.00532639 0.00922557i
\(843\) 0 0
\(844\) 1.96170 + 3.39776i 0.0675244 + 0.116956i
\(845\) 0 0
\(846\) 0 0
\(847\) −39.6869 26.8767i −1.36366 0.923495i
\(848\) 8.39836 0.288401
\(849\) 0 0
\(850\) 0 0
\(851\) −1.51242 + 0.873198i −0.0518452 + 0.0299328i
\(852\) 0 0
\(853\) 22.2302 0.761148 0.380574 0.924750i \(-0.375726\pi\)
0.380574 + 0.924750i \(0.375726\pi\)
\(854\) 3.02896 + 6.23972i 0.103649 + 0.213519i
\(855\) 0 0
\(856\) 0.820863 1.42178i 0.0280565 0.0485953i
\(857\) 45.7432 26.4098i 1.56256 0.902143i 0.565560 0.824707i \(-0.308660\pi\)
0.996997 0.0774356i \(-0.0246732\pi\)
\(858\) 0 0
\(859\) 15.2916 + 8.82859i 0.521742 + 0.301228i 0.737647 0.675187i \(-0.235937\pi\)
−0.215905 + 0.976414i \(0.569270\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 8.82010i 0.300414i
\(863\) 8.22446 14.2452i 0.279964 0.484912i −0.691412 0.722461i \(-0.743011\pi\)
0.971375 + 0.237549i \(0.0763441\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −4.78194 + 8.28256i −0.162497 + 0.281453i
\(867\) 0 0
\(868\) −7.16328 + 10.5775i −0.243138 + 0.359024i
\(869\) 46.3639i 1.57279i
\(870\) 0 0
\(871\) 21.4161 12.3646i 0.725657 0.418958i
\(872\) 9.94887 + 17.2319i 0.336911 + 0.583547i
\(873\) 0 0
\(874\) 0.767327i 0.0259552i
\(875\) 0 0
\(876\) 0 0
\(877\) −46.9521 27.1078i −1.58546 0.915366i −0.994042 0.109001i \(-0.965235\pi\)
−0.591418 0.806365i \(-0.701432\pi\)
\(878\) 31.3336 18.0905i 1.05746 0.610524i
\(879\) 0 0
\(880\) 0 0
\(881\) 50.1647 1.69009 0.845046 0.534694i \(-0.179573\pi\)
0.845046 + 0.534694i \(0.179573\pi\)
\(882\) 0 0
\(883\) 0.841563i 0.0283208i 0.999900 + 0.0141604i \(0.00450755\pi\)
−0.999900 + 0.0141604i \(0.995492\pi\)
\(884\) −9.81017 5.66390i −0.329952 0.190498i
\(885\) 0 0
\(886\) −2.04284 3.53830i −0.0686305 0.118872i
\(887\) 34.7262 + 20.0492i 1.16599 + 0.673185i 0.952732 0.303811i \(-0.0982591\pi\)
0.213258 + 0.976996i \(0.431592\pi\)
\(888\) 0 0
\(889\) −38.2922 2.74926i −1.28428 0.0922071i
\(890\) 0 0
\(891\) 0 0
\(892\) −7.34519 12.7222i −0.245935 0.425972i
\(893\) −11.4482 19.8288i −0.383098 0.663546i
\(894\) 0 0
\(895\) 0 0
\(896\) −2.19067 1.48356i −0.0731852 0.0495624i
\(897\) 0 0
\(898\) −17.2665 9.96885i −0.576192 0.332665i
\(899\) 21.4840 + 37.2114i 0.716533 + 1.24107i
\(900\) 0 0
\(901\) −32.7248 18.8937i −1.09022 0.629440i
\(902\) 4.10243i 0.136596i
\(903\) 0 0
\(904\) −5.95867 −0.198182
\(905\) 0 0
\(906\) 0 0
\(907\) −39.1348 + 22.5945i −1.29945 + 0.750238i −0.980309 0.197469i \(-0.936728\pi\)
−0.319142 + 0.947707i \(0.603395\pi\)
\(908\) 19.7303 + 11.3913i 0.654774 + 0.378034i
\(909\) 0 0
\(910\) 0 0
\(911\) 58.2281i 1.92918i 0.263746 + 0.964592i \(0.415042\pi\)
−0.263746 + 0.964592i \(0.584958\pi\)
\(912\) 0 0
\(913\) 25.4959 + 44.1602i 0.843791 + 1.46149i
\(914\) 17.4283 10.0623i 0.576478 0.332830i
\(915\) 0 0
\(916\) 20.2175i 0.668005i
\(917\) 33.8820 + 22.9455i 1.11888 + 0.757729i
\(918\) 0 0
\(919\) 6.61745 11.4618i 0.218290 0.378089i −0.735996 0.676986i \(-0.763286\pi\)
0.954285 + 0.298898i \(0.0966190\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.454649 0.787476i 0.0149731 0.0259341i
\(923\) 11.9907i 0.394679i
\(924\) 0 0
\(925\) 0 0
\(926\) −18.5572 10.7140i −0.609827 0.352084i
\(927\) 0 0
\(928\) −7.70674 + 4.44949i −0.252986 + 0.146062i
\(929\) 10.4434 18.0885i 0.342637 0.593464i −0.642285 0.766466i \(-0.722013\pi\)
0.984921 + 0.173002i \(0.0553467\pi\)
\(930\) 0 0
\(931\) −15.7504 12.4002i −0.516197 0.406400i
\(932\) 2.63087 0.0861769
\(933\) 0 0
\(934\) 10.9917 6.34607i 0.359660 0.207650i
\(935\) 0 0
\(936\) 0 0
\(937\) −23.2465 −0.759430 −0.379715 0.925103i \(-0.623978\pi\)
−0.379715 + 0.925103i \(0.623978\pi\)
\(938\) −25.9208 1.86103i −0.846345 0.0607649i
\(939\) 0 0
\(940\) 0 0
\(941\) −0.752551 1.30346i −0.0245325 0.0424915i 0.853499 0.521095i \(-0.174476\pi\)
−0.878031 + 0.478604i \(0.841143\pi\)
\(942\) 0 0
\(943\) 0.101858 0.176423i 0.00331695 0.00574513i
\(944\) −12.6715 −0.412421
\(945\) 0 0
\(946\) 31.6403 1.02871
\(947\) −12.1314 + 21.0122i −0.394218 + 0.682805i −0.993001 0.118106i \(-0.962318\pi\)
0.598783 + 0.800911i \(0.295651\pi\)
\(948\) 0 0
\(949\) −14.6739 25.4159i −0.476334 0.825035i
\(950\) 0 0
\(951\) 0 0
\(952\) 5.19856 + 10.7091i 0.168486 + 0.347085i
\(953\) 56.7061 1.83689 0.918446 0.395547i \(-0.129445\pi\)
0.918446 + 0.395547i \(0.129445\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 14.6155 8.43828i 0.472700 0.272913i
\(957\) 0 0
\(958\) 12.8766 0.416023
\(959\) −20.5206 + 9.96132i −0.662643 + 0.321668i
\(960\) 0 0
\(961\) −3.84315 + 6.65652i −0.123972 + 0.214727i
\(962\) 14.2107 8.20453i 0.458170 0.264525i
\(963\) 0 0
\(964\) 12.5793 + 7.26268i 0.405153 + 0.233915i
\(965\) 0 0
\(966\) 0 0
\(967\) 7.23556i 0.232680i 0.993209 + 0.116340i \(0.0371162\pi\)
−0.993209 + 0.116340i \(0.962884\pi\)
\(968\) −9.05816 + 15.6892i −0.291140 + 0.504270i
\(969\) 0 0
\(970\) 0 0
\(971\) 19.3560 33.5256i 0.621163 1.07589i −0.368106 0.929784i \(-0.619994\pi\)
0.989269 0.146103i \(-0.0466730\pi\)
\(972\) 0 0
\(973\) −27.0525 1.94228i −0.867263 0.0622667i
\(974\) 20.8194i 0.667096i
\(975\) 0 0
\(976\) 2.27035 1.31079i 0.0726722 0.0419573i
\(977\) −9.08052 15.7279i −0.290512 0.503181i 0.683419 0.730026i \(-0.260492\pi\)
−0.973931 + 0.226845i \(0.927159\pi\)
\(978\) 0 0
\(979\) 43.0060i 1.37448i
\(980\) 0 0
\(981\) 0 0
\(982\) 23.6659 + 13.6635i 0.755211 + 0.436021i
\(983\) −14.2026 + 8.19988i −0.452993 + 0.261536i −0.709093 0.705115i \(-0.750896\pi\)
0.256100 + 0.966650i \(0.417562\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 40.0399 1.27513
\(987\) 0 0
\(988\) 7.20977i 0.229373i
\(989\) −1.36068 0.785587i −0.0432670 0.0249802i
\(990\) 0 0
\(991\) 5.44584 + 9.43247i 0.172993 + 0.299632i 0.939465 0.342645i \(-0.111323\pi\)
−0.766472 + 0.642278i \(0.777990\pi\)
\(992\) 4.18154 + 2.41421i 0.132764 + 0.0766514i
\(993\) 0 0
\(994\) −7.06574 + 10.4335i −0.224112 + 0.330930i
\(995\) 0 0
\(996\) 0 0
\(997\) 17.7740 + 30.7856i 0.562910 + 0.974988i 0.997241 + 0.0742349i \(0.0236515\pi\)
−0.434331 + 0.900753i \(0.643015\pi\)
\(998\) −16.6802 28.8909i −0.528002 0.914527i
\(999\) 0 0
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 3150.2.bp.f.1349.3 8
3.2 odd 2 3150.2.bp.a.1349.3 8
5.2 odd 4 3150.2.bf.c.1601.4 8
5.3 odd 4 630.2.be.b.341.1 yes 8
5.4 even 2 3150.2.bp.c.1349.2 8
7.3 odd 6 3150.2.bp.d.899.2 8
15.2 even 4 3150.2.bf.b.1601.2 8
15.8 even 4 630.2.be.a.341.3 8
15.14 odd 2 3150.2.bp.d.1349.2 8
21.17 even 6 3150.2.bp.c.899.2 8
35.3 even 12 630.2.be.a.521.3 yes 8
35.17 even 12 3150.2.bf.b.1151.2 8
35.23 odd 12 4410.2.b.b.881.8 8
35.24 odd 6 3150.2.bp.a.899.3 8
35.33 even 12 4410.2.b.e.881.8 8
105.17 odd 12 3150.2.bf.c.1151.4 8
105.23 even 12 4410.2.b.e.881.1 8
105.38 odd 12 630.2.be.b.521.1 yes 8
105.59 even 6 inner 3150.2.bp.f.899.3 8
105.68 odd 12 4410.2.b.b.881.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.be.a.341.3 8 15.8 even 4
630.2.be.a.521.3 yes 8 35.3 even 12
630.2.be.b.341.1 yes 8 5.3 odd 4
630.2.be.b.521.1 yes 8 105.38 odd 12
3150.2.bf.b.1151.2 8 35.17 even 12
3150.2.bf.b.1601.2 8 15.2 even 4
3150.2.bf.c.1151.4 8 105.17 odd 12
3150.2.bf.c.1601.4 8 5.2 odd 4
3150.2.bp.a.899.3 8 35.24 odd 6
3150.2.bp.a.1349.3 8 3.2 odd 2
3150.2.bp.c.899.2 8 21.17 even 6
3150.2.bp.c.1349.2 8 5.4 even 2
3150.2.bp.d.899.2 8 7.3 odd 6
3150.2.bp.d.1349.2 8 15.14 odd 2
3150.2.bp.f.899.3 8 105.59 even 6 inner
3150.2.bp.f.1349.3 8 1.1 even 1 trivial
4410.2.b.b.881.1 8 105.68 odd 12
4410.2.b.b.881.8 8 35.23 odd 12
4410.2.b.e.881.1 8 105.23 even 12
4410.2.b.e.881.8 8 35.33 even 12