Properties

Label 3150.2.bp.d.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.d.899.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.189469 - 2.63896i) q^{7} -1.00000 q^{8} +(-1.32697 + 0.766125i) q^{11} -1.48236 q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.10342 - 1.21441i) q^{17} +(-4.21209 - 2.43185i) q^{19} +1.53225i q^{22} +(-0.133975 + 0.232051i) q^{23} +(-0.741181 + 1.28376i) q^{26} +(-2.38014 + 1.15539i) q^{28} +0.898979i q^{29} +(-0.717439 + 0.414214i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.42883i q^{34} +(-4.74786 - 2.74118i) q^{37} +(-4.21209 + 2.43185i) q^{38} -8.76028 q^{41} +1.86370i q^{43} +(1.32697 + 0.766125i) q^{44} +(0.133975 + 0.232051i) q^{46} +(6.46008 + 3.72973i) q^{47} +(-6.92820 - 1.00000i) q^{49} +(0.741181 + 1.28376i) q^{52} +(1.73508 + 3.00524i) q^{53} +(-0.189469 + 2.63896i) q^{56} +(0.778539 + 0.449490i) q^{58} +(-3.12837 - 5.41849i) q^{59} +(5.73445 + 3.31079i) q^{61} +0.828427i q^{62} +1.00000 q^{64} +(-13.8859 + 8.01702i) q^{67} +(-2.10342 - 1.21441i) q^{68} -12.7627i q^{71} +(0.171573 + 0.297173i) q^{73} +(-4.74786 + 2.74118i) q^{74} +4.86370i q^{76} +(1.77035 + 3.64697i) q^{77} +(-5.22438 + 9.04889i) q^{79} +(-4.38014 + 7.58662i) q^{82} -5.45001i q^{83} +(1.61401 + 0.931852i) q^{86} +(1.32697 - 0.766125i) q^{88} +(-7.98502 + 13.8305i) q^{89} +(-0.280861 + 3.91189i) q^{91} +0.267949 q^{92} +(6.46008 - 3.72973i) q^{94} -14.9481 q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 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
\(11\) −1.32697 + 0.766125i −0.400096 + 0.230995i −0.686525 0.727106i \(-0.740865\pi\)
0.286430 + 0.958101i \(0.407532\pi\)
\(12\) 0 0
\(13\) −1.48236 −0.411133 −0.205567 0.978643i \(-0.565904\pi\)
−0.205567 + 0.978643i \(0.565904\pi\)
\(14\) −2.19067 1.48356i −0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.10342 1.21441i 0.510155 0.294538i −0.222742 0.974877i \(-0.571501\pi\)
0.732898 + 0.680339i \(0.238167\pi\)
\(18\) 0 0
\(19\) −4.21209 2.43185i −0.966320 0.557905i −0.0682075 0.997671i \(-0.521728\pi\)
−0.898112 + 0.439766i \(0.855061\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.53225i 0.326677i
\(23\) −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
\(26\) −0.741181 + 1.28376i −0.145358 + 0.251767i
\(27\) 0 0
\(28\) −2.38014 + 1.15539i −0.449804 + 0.218349i
\(29\) 0.898979i 0.166936i 0.996510 + 0.0834681i \(0.0265997\pi\)
−0.996510 + 0.0834681i \(0.973400\pi\)
\(30\) 0 0
\(31\) −0.717439 + 0.414214i −0.128856 + 0.0743950i −0.563042 0.826428i \(-0.690369\pi\)
0.434187 + 0.900823i \(0.357036\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 2.42883i 0.416540i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.74786 2.74118i −0.780544 0.450647i 0.0560790 0.998426i \(-0.482140\pi\)
−0.836623 + 0.547779i \(0.815473\pi\)
\(38\) −4.21209 + 2.43185i −0.683291 + 0.394498i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.76028 −1.36813 −0.684063 0.729423i \(-0.739789\pi\)
−0.684063 + 0.729423i \(0.739789\pi\)
\(42\) 0 0
\(43\) 1.86370i 0.284212i 0.989851 + 0.142106i \(0.0453874\pi\)
−0.989851 + 0.142106i \(0.954613\pi\)
\(44\) 1.32697 + 0.766125i 0.200048 + 0.115498i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) 6.46008 + 3.72973i 0.942299 + 0.544037i 0.890680 0.454630i \(-0.150229\pi\)
0.0516191 + 0.998667i \(0.483562\pi\)
\(48\) 0 0
\(49\) −6.92820 1.00000i −0.989743 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.741181 + 1.28376i 0.102783 + 0.178026i
\(53\) 1.73508 + 3.00524i 0.238331 + 0.412802i 0.960236 0.279191i \(-0.0900663\pi\)
−0.721904 + 0.691993i \(0.756733\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.189469 + 2.63896i −0.0253188 + 0.352646i
\(57\) 0 0
\(58\) 0.778539 + 0.449490i 0.102227 + 0.0590209i
\(59\) −3.12837 5.41849i −0.407279 0.705428i 0.587305 0.809366i \(-0.300189\pi\)
−0.994584 + 0.103938i \(0.966856\pi\)
\(60\) 0 0
\(61\) 5.73445 + 3.31079i 0.734222 + 0.423903i 0.819965 0.572414i \(-0.193993\pi\)
−0.0857429 + 0.996317i \(0.527326\pi\)
\(62\) 0.828427i 0.105210i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −13.8859 + 8.01702i −1.69643 + 0.979434i −0.747334 + 0.664449i \(0.768666\pi\)
−0.949097 + 0.314985i \(0.898000\pi\)
\(68\) −2.10342 1.21441i −0.255078 0.147269i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7627i 1.51465i −0.653037 0.757326i \(-0.726505\pi\)
0.653037 0.757326i \(-0.273495\pi\)
\(72\) 0 0
\(73\) 0.171573 + 0.297173i 0.0200811 + 0.0347815i 0.875891 0.482508i \(-0.160274\pi\)
−0.855810 + 0.517290i \(0.826941\pi\)
\(74\) −4.74786 + 2.74118i −0.551928 + 0.318656i
\(75\) 0 0
\(76\) 4.86370i 0.557905i
\(77\) 1.77035 + 3.64697i 0.201750 + 0.415611i
\(78\) 0 0
\(79\) −5.22438 + 9.04889i −0.587789 + 1.01808i 0.406733 + 0.913547i \(0.366668\pi\)
−0.994521 + 0.104533i \(0.966665\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.38014 + 7.58662i −0.483705 + 0.837802i
\(83\) 5.45001i 0.598216i −0.954219 0.299108i \(-0.903311\pi\)
0.954219 0.299108i \(-0.0966891\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.61401 + 0.931852i 0.174044 + 0.100484i
\(87\) 0 0
\(88\) 1.32697 0.766125i 0.141455 0.0816692i
\(89\) −7.98502 + 13.8305i −0.846411 + 1.46603i 0.0379795 + 0.999279i \(0.487908\pi\)
−0.884390 + 0.466748i \(0.845426\pi\)
\(90\) 0 0
\(91\) −0.280861 + 3.91189i −0.0294423 + 0.410078i
\(92\) 0.267949 0.0279356
\(93\) 0 0
\(94\) 6.46008 3.72973i 0.666306 0.384692i
\(95\) 0 0
\(96\) 0 0
\(97\) −14.9481 −1.51775 −0.758877 0.651234i \(-0.774252\pi\)
−0.758877 + 0.651234i \(0.774252\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.36773 2.36897i −0.136094 0.235721i 0.789921 0.613209i \(-0.210122\pi\)
−0.926015 + 0.377487i \(0.876788\pi\)
\(102\) 0 0
\(103\) 3.08845 5.34935i 0.304314 0.527087i −0.672794 0.739829i \(-0.734906\pi\)
0.977108 + 0.212742i \(0.0682395\pi\)
\(104\) 1.48236 0.145358
\(105\) 0 0
\(106\) 3.47015 0.337051
\(107\) 2.28497 3.95768i 0.220896 0.382603i −0.734184 0.678950i \(-0.762435\pi\)
0.955080 + 0.296347i \(0.0957686\pi\)
\(108\) 0 0
\(109\) −2.97934 5.16036i −0.285369 0.494273i 0.687330 0.726345i \(-0.258783\pi\)
−0.972699 + 0.232072i \(0.925449\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.19067 + 1.48356i 0.206999 + 0.140184i
\(113\) 19.8977 1.87182 0.935911 0.352237i \(-0.114579\pi\)
0.935911 + 0.352237i \(0.114579\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.778539 0.449490i 0.0722855 0.0417341i
\(117\) 0 0
\(118\) −6.25674 −0.575979
\(119\) −2.80625 5.78094i −0.257249 0.529938i
\(120\) 0 0
\(121\) −4.32611 + 7.49303i −0.393282 + 0.681185i
\(122\) 5.73445 3.31079i 0.519173 0.299745i
\(123\) 0 0
\(124\) 0.717439 + 0.414214i 0.0644279 + 0.0371975i
\(125\) 0 0
\(126\) 0 0
\(127\) 21.2025i 1.88142i 0.339219 + 0.940708i \(0.389837\pi\)
−0.339219 + 0.940708i \(0.610163\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.73085 6.46202i 0.325966 0.564589i −0.655742 0.754985i \(-0.727644\pi\)
0.981707 + 0.190396i \(0.0609772\pi\)
\(132\) 0 0
\(133\) −7.21561 + 10.6548i −0.625673 + 0.923886i
\(134\) 16.0340i 1.38513i
\(135\) 0 0
\(136\) −2.10342 + 1.21441i −0.180367 + 0.104135i
\(137\) 0.310789 + 0.538302i 0.0265525 + 0.0459903i 0.878996 0.476829i \(-0.158214\pi\)
−0.852444 + 0.522819i \(0.824880\pi\)
\(138\) 0 0
\(139\) 18.5334i 1.57198i −0.618237 0.785992i \(-0.712153\pi\)
0.618237 0.785992i \(-0.287847\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −11.0528 6.38134i −0.927531 0.535510i
\(143\) 1.96705 1.13567i 0.164493 0.0949699i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.343146 0.0283989
\(147\) 0 0
\(148\) 5.48236i 0.450647i
\(149\) −12.1100 6.99171i −0.992089 0.572783i −0.0861911 0.996279i \(-0.527470\pi\)
−0.905898 + 0.423496i \(0.860803\pi\)
\(150\) 0 0
\(151\) −9.83839 17.0406i −0.800637 1.38674i −0.919197 0.393797i \(-0.871161\pi\)
0.118560 0.992947i \(-0.462172\pi\)
\(152\) 4.21209 + 2.43185i 0.341646 + 0.197249i
\(153\) 0 0
\(154\) 4.04354 + 0.290313i 0.325838 + 0.0233941i
\(155\) 0 0
\(156\) 0 0
\(157\) 4.53005 + 7.84628i 0.361538 + 0.626201i 0.988214 0.153078i \(-0.0489186\pi\)
−0.626677 + 0.779279i \(0.715585\pi\)
\(158\) 5.22438 + 9.04889i 0.415629 + 0.719891i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.586988 + 0.397520i 0.0462612 + 0.0313289i
\(162\) 0 0
\(163\) −10.2368 5.91019i −0.801804 0.462922i 0.0422974 0.999105i \(-0.486532\pi\)
−0.844102 + 0.536183i \(0.819866\pi\)
\(164\) 4.38014 + 7.58662i 0.342031 + 0.592416i
\(165\) 0 0
\(166\) −4.71984 2.72500i −0.366331 0.211501i
\(167\) 15.7778i 1.22092i 0.792046 + 0.610462i \(0.209016\pi\)
−0.792046 + 0.610462i \(0.790984\pi\)
\(168\) 0 0
\(169\) −10.8026 −0.830969
\(170\) 0 0
\(171\) 0 0
\(172\) 1.61401 0.931852i 0.123067 0.0710530i
\(173\) 17.5129 + 10.1111i 1.33148 + 0.768730i 0.985527 0.169521i \(-0.0542221\pi\)
0.345954 + 0.938252i \(0.387555\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.53225i 0.115498i
\(177\) 0 0
\(178\) 7.98502 + 13.8305i 0.598503 + 1.03664i
\(179\) −5.94667 + 3.43331i −0.444475 + 0.256618i −0.705494 0.708716i \(-0.749275\pi\)
0.261019 + 0.965334i \(0.415941\pi\)
\(180\) 0 0
\(181\) 16.3066i 1.21206i 0.795441 + 0.606031i \(0.207239\pi\)
−0.795441 + 0.606031i \(0.792761\pi\)
\(182\) 3.24737 + 2.19918i 0.240711 + 0.163014i
\(183\) 0 0
\(184\) 0.133975 0.232051i 0.00987674 0.0171070i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.86078 + 3.22297i −0.136074 + 0.235687i
\(188\) 7.45946i 0.544037i
\(189\) 0 0
\(190\) 0 0
\(191\) 14.8630 + 8.58114i 1.07545 + 0.620910i 0.929665 0.368407i \(-0.120097\pi\)
0.145782 + 0.989317i \(0.453430\pi\)
\(192\) 0 0
\(193\) 7.84204 4.52761i 0.564483 0.325904i −0.190460 0.981695i \(-0.560998\pi\)
0.754943 + 0.655791i \(0.227665\pi\)
\(194\) −7.47407 + 12.9455i −0.536607 + 0.929430i
\(195\) 0 0
\(196\) 2.59808 + 6.50000i 0.185577 + 0.464286i
\(197\) −21.7379 −1.54876 −0.774380 0.632720i \(-0.781938\pi\)
−0.774380 + 0.632720i \(0.781938\pi\)
\(198\) 0 0
\(199\) 7.21101 4.16328i 0.511175 0.295127i −0.222141 0.975014i \(-0.571305\pi\)
0.733317 + 0.679887i \(0.237971\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.73545 −0.192466
\(203\) 2.37237 + 0.170328i 0.166508 + 0.0119547i
\(204\) 0 0
\(205\) 0 0
\(206\) −3.08845 5.34935i −0.215182 0.372707i
\(207\) 0 0
\(208\) 0.741181 1.28376i 0.0513917 0.0890130i
\(209\) 7.45241 0.515494
\(210\) 0 0
\(211\) −19.9330 −1.37225 −0.686123 0.727486i \(-0.740689\pi\)
−0.686123 + 0.727486i \(0.740689\pi\)
\(212\) 1.73508 3.00524i 0.119166 0.206401i
\(213\) 0 0
\(214\) −2.28497 3.95768i −0.156197 0.270541i
\(215\) 0 0
\(216\) 0 0
\(217\) 0.957160 + 1.97177i 0.0649763 + 0.133853i
\(218\) −5.95867 −0.403572
\(219\) 0 0
\(220\) 0 0
\(221\) −3.11804 + 1.80020i −0.209742 + 0.121094i
\(222\) 0 0
\(223\) −7.16604 −0.479873 −0.239937 0.970789i \(-0.577127\pi\)
−0.239937 + 0.970789i \(0.577127\pi\)
\(224\) 2.38014 1.15539i 0.159030 0.0771980i
\(225\) 0 0
\(226\) 9.94887 17.2319i 0.661789 1.14625i
\(227\) 13.7303 7.92721i 0.911314 0.526147i 0.0304601 0.999536i \(-0.490303\pi\)
0.880854 + 0.473389i \(0.156969\pi\)
\(228\) 0 0
\(229\) −24.4371 14.1087i −1.61485 0.932332i −0.988225 0.153009i \(-0.951104\pi\)
−0.626622 0.779323i \(-0.715563\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.898979i 0.0590209i
\(233\) −12.1487 + 21.0421i −0.795886 + 1.37851i 0.126390 + 0.991981i \(0.459661\pi\)
−0.922275 + 0.386534i \(0.873672\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.12837 + 5.41849i −0.203639 + 0.352714i
\(237\) 0 0
\(238\) −6.40957 0.460186i −0.415471 0.0298295i
\(239\) 19.9081i 1.28774i −0.765133 0.643872i \(-0.777327\pi\)
0.765133 0.643872i \(-0.222673\pi\)
\(240\) 0 0
\(241\) 17.7755 10.2627i 1.14502 0.661078i 0.197351 0.980333i \(-0.436766\pi\)
0.947669 + 0.319255i \(0.103433\pi\)
\(242\) 4.32611 + 7.49303i 0.278093 + 0.481670i
\(243\) 0 0
\(244\) 6.62158i 0.423903i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.24384 + 3.60488i 0.397286 + 0.229373i
\(248\) 0.717439 0.414214i 0.0455574 0.0263026i
\(249\) 0 0
\(250\) 0 0
\(251\) −5.86787 −0.370376 −0.185188 0.982703i \(-0.559289\pi\)
−0.185188 + 0.982703i \(0.559289\pi\)
\(252\) 0 0
\(253\) 0.410565i 0.0258120i
\(254\) 18.3619 + 10.6012i 1.15213 + 0.665181i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.63519 + 3.83083i 0.413892 + 0.238961i 0.692461 0.721456i \(-0.256527\pi\)
−0.278569 + 0.960416i \(0.589860\pi\)
\(258\) 0 0
\(259\) −8.13343 + 12.0100i −0.505387 + 0.746268i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.73085 6.46202i −0.230493 0.399225i
\(263\) −4.23143 7.32905i −0.260921 0.451929i 0.705566 0.708644i \(-0.250693\pi\)
−0.966487 + 0.256716i \(0.917360\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 5.61950 + 11.5763i 0.344553 + 0.709788i
\(267\) 0 0
\(268\) 13.8859 + 8.01702i 0.848215 + 0.489717i
\(269\) −8.52155 14.7598i −0.519568 0.899919i −0.999741 0.0227449i \(-0.992759\pi\)
0.480173 0.877174i \(-0.340574\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) 2.42883i 0.147269i
\(273\) 0 0
\(274\) 0.621578 0.0375509
\(275\) 0 0
\(276\) 0 0
\(277\) 7.00720 4.04561i 0.421022 0.243077i −0.274493 0.961589i \(-0.588510\pi\)
0.695514 + 0.718512i \(0.255177\pi\)
\(278\) −16.0504 9.26670i −0.962639 0.555780i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1684i 0.666253i 0.942882 + 0.333127i \(0.108104\pi\)
−0.942882 + 0.333127i \(0.891896\pi\)
\(282\) 0 0
\(283\) −3.60796 6.24917i −0.214471 0.371475i 0.738638 0.674103i \(-0.235469\pi\)
−0.953109 + 0.302628i \(0.902136\pi\)
\(284\) −11.0528 + 6.38134i −0.655863 + 0.378663i
\(285\) 0 0
\(286\) 2.27135i 0.134308i
\(287\) −1.65980 + 23.1180i −0.0979748 + 1.36461i
\(288\) 0 0
\(289\) −5.55040 + 9.61358i −0.326494 + 0.565505i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.171573 0.297173i 0.0100405 0.0173907i
\(293\) 18.2573i 1.06660i −0.845926 0.533300i \(-0.820952\pi\)
0.845926 0.533300i \(-0.179048\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.74786 + 2.74118i 0.275964 + 0.159328i
\(297\) 0 0
\(298\) −12.1100 + 6.99171i −0.701513 + 0.405019i
\(299\) 0.198599 0.343983i 0.0114853 0.0198931i
\(300\) 0 0
\(301\) 4.91824 + 0.353113i 0.283482 + 0.0203531i
\(302\) −19.6768 −1.13227
\(303\) 0 0
\(304\) 4.21209 2.43185i 0.241580 0.139476i
\(305\) 0 0
\(306\) 0 0
\(307\) 3.42078 0.195234 0.0976172 0.995224i \(-0.468878\pi\)
0.0976172 + 0.995224i \(0.468878\pi\)
\(308\) 2.27319 3.35666i 0.129527 0.191263i
\(309\) 0 0
\(310\) 0 0
\(311\) 2.84544 + 4.92845i 0.161350 + 0.279467i 0.935353 0.353715i \(-0.115082\pi\)
−0.774003 + 0.633182i \(0.781748\pi\)
\(312\) 0 0
\(313\) 6.67335 11.5586i 0.377200 0.653330i −0.613453 0.789731i \(-0.710220\pi\)
0.990654 + 0.136401i \(0.0435535\pi\)
\(314\) 9.06010 0.511291
\(315\) 0 0
\(316\) 10.4488 0.587789
\(317\) 6.26330 10.8484i 0.351782 0.609305i −0.634780 0.772693i \(-0.718909\pi\)
0.986562 + 0.163389i \(0.0522424\pi\)
\(318\) 0 0
\(319\) −0.688731 1.19292i −0.0385615 0.0667905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.637756 0.309587i 0.0355408 0.0172526i
\(323\) −11.8131 −0.657298
\(324\) 0 0
\(325\) 0 0
\(326\) −10.2368 + 5.91019i −0.566961 + 0.327335i
\(327\) 0 0
\(328\) 8.76028 0.483705
\(329\) 11.0666 16.3412i 0.610120 0.900920i
\(330\) 0 0
\(331\) 0.640916 1.11010i 0.0352279 0.0610166i −0.847874 0.530198i \(-0.822118\pi\)
0.883102 + 0.469181i \(0.155451\pi\)
\(332\) −4.71984 + 2.72500i −0.259035 + 0.149554i
\(333\) 0 0
\(334\) 13.6640 + 7.88891i 0.747660 + 0.431662i
\(335\) 0 0
\(336\) 0 0
\(337\) 13.1058i 0.713920i 0.934120 + 0.356960i \(0.116187\pi\)
−0.934120 + 0.356960i \(0.883813\pi\)
\(338\) −5.40130 + 9.35533i −0.293792 + 0.508863i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.634679 1.09930i 0.0343698 0.0595302i
\(342\) 0 0
\(343\) −3.95164 + 18.0938i −0.213368 + 0.976972i
\(344\) 1.86370i 0.100484i
\(345\) 0 0
\(346\) 17.5129 10.1111i 0.941499 0.543574i
\(347\) 7.14262 + 12.3714i 0.383436 + 0.664130i 0.991551 0.129719i \(-0.0414074\pi\)
−0.608115 + 0.793849i \(0.708074\pi\)
\(348\) 0 0
\(349\) 13.2713i 0.710399i −0.934791 0.355200i \(-0.884413\pi\)
0.934791 0.355200i \(-0.115587\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.32697 0.766125i −0.0707276 0.0408346i
\(353\) 28.2725 16.3232i 1.50480 0.868794i 0.504811 0.863230i \(-0.331562\pi\)
0.999985 0.00556437i \(-0.00177120\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 15.9700 0.846411
\(357\) 0 0
\(358\) 6.86662i 0.362912i
\(359\) 5.40692 + 3.12168i 0.285366 + 0.164756i 0.635850 0.771812i \(-0.280650\pi\)
−0.350484 + 0.936569i \(0.613983\pi\)
\(360\) 0 0
\(361\) 2.32780 + 4.03188i 0.122516 + 0.212204i
\(362\) 14.1220 + 8.15331i 0.742233 + 0.428529i
\(363\) 0 0
\(364\) 3.52823 1.71271i 0.184929 0.0897705i
\(365\) 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
\(371\) 8.25945 4.00940i 0.428809 0.208158i
\(372\) 0 0
\(373\) −31.1408 17.9791i −1.61241 0.930924i −0.988810 0.149179i \(-0.952337\pi\)
−0.623598 0.781745i \(-0.714330\pi\)
\(374\) 1.86078 + 3.22297i 0.0962188 + 0.166656i
\(375\) 0 0
\(376\) −6.46008 3.72973i −0.333153 0.192346i
\(377\) 1.33261i 0.0686331i
\(378\) 0 0
\(379\) 11.5899 0.595331 0.297666 0.954670i \(-0.403792\pi\)
0.297666 + 0.954670i \(0.403792\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 14.8630 8.58114i 0.760456 0.439049i
\(383\) −3.86897 2.23375i −0.197695 0.114139i 0.397885 0.917435i \(-0.369744\pi\)
−0.595580 + 0.803296i \(0.703078\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.05521i 0.460898i
\(387\) 0 0
\(388\) 7.47407 + 12.9455i 0.379438 + 0.657207i
\(389\) −11.2197 + 6.47772i −0.568863 + 0.328433i −0.756695 0.653768i \(-0.773187\pi\)
0.187832 + 0.982201i \(0.439854\pi\)
\(390\) 0 0
\(391\) 0.650802i 0.0329125i
\(392\) 6.92820 + 1.00000i 0.349927 + 0.0505076i
\(393\) 0 0
\(394\) −10.8689 + 18.8256i −0.547570 + 0.948418i
\(395\) 0 0
\(396\) 0 0
\(397\) 4.63995 8.03664i 0.232873 0.403347i −0.725780 0.687927i \(-0.758521\pi\)
0.958652 + 0.284580i \(0.0918541\pi\)
\(398\) 8.32656i 0.417373i
\(399\) 0 0
\(400\) 0 0
\(401\) 6.44260 + 3.71964i 0.321728 + 0.185750i 0.652163 0.758079i \(-0.273862\pi\)
−0.330434 + 0.943829i \(0.607195\pi\)
\(402\) 0 0
\(403\) 1.06350 0.614014i 0.0529769 0.0305862i
\(404\) −1.36773 + 2.36897i −0.0680469 + 0.117861i
\(405\) 0 0
\(406\) 1.33369 1.96937i 0.0661901 0.0977381i
\(407\) 8.40035 0.416390
\(408\) 0 0
\(409\) 13.8647 8.00481i 0.685567 0.395812i −0.116382 0.993204i \(-0.537130\pi\)
0.801949 + 0.597392i \(0.203796\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −6.17690 −0.304314
\(413\) −14.8919 + 7.22900i −0.732783 + 0.355716i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.741181 1.28376i −0.0363394 0.0629417i
\(417\) 0 0
\(418\) 3.72620 6.45398i 0.182255 0.315674i
\(419\) 28.4419 1.38948 0.694738 0.719263i \(-0.255520\pi\)
0.694738 + 0.719263i \(0.255520\pi\)
\(420\) 0 0
\(421\) 17.8345 0.869199 0.434600 0.900624i \(-0.356890\pi\)
0.434600 + 0.900624i \(0.356890\pi\)
\(422\) −9.96651 + 17.2625i −0.485162 + 0.840325i
\(423\) 0 0
\(424\) −1.73508 3.00524i −0.0842628 0.145947i
\(425\) 0 0
\(426\) 0 0
\(427\) 9.82353 14.5057i 0.475394 0.701980i
\(428\) −4.56993 −0.220896
\(429\) 0 0
\(430\) 0 0
\(431\) 26.7539 15.4464i 1.28869 0.744025i 0.310268 0.950649i \(-0.399581\pi\)
0.978420 + 0.206624i \(0.0662477\pi\)
\(432\) 0 0
\(433\) 15.2207 0.731462 0.365731 0.930721i \(-0.380819\pi\)
0.365731 + 0.930721i \(0.380819\pi\)
\(434\) 2.18618 + 0.156961i 0.104940 + 0.00753437i
\(435\) 0 0
\(436\) −2.97934 + 5.16036i −0.142684 + 0.247136i
\(437\) 1.12863 0.651613i 0.0539895 0.0311709i
\(438\) 0 0
\(439\) −12.4054 7.16228i −0.592079 0.341837i 0.173840 0.984774i \(-0.444382\pi\)
−0.765919 + 0.642937i \(0.777716\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.60040i 0.171253i
\(443\) −2.57874 + 4.46651i −0.122520 + 0.212210i −0.920761 0.390128i \(-0.872431\pi\)
0.798241 + 0.602338i \(0.205764\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.58302 + 6.20597i −0.169661 + 0.293861i
\(447\) 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
\(451\) 11.6246 6.71147i 0.547381 0.316031i
\(452\) −9.94887 17.2319i −0.467955 0.810522i
\(453\) 0 0
\(454\) 15.8544i 0.744085i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.82065 + 5.66995i 0.459391 + 0.265229i 0.711788 0.702394i \(-0.247886\pi\)
−0.252397 + 0.967624i \(0.581219\pi\)
\(458\) −24.4371 + 14.1087i −1.14187 + 0.659258i
\(459\) 0 0
\(460\) 0 0
\(461\) −2.01890 −0.0940298 −0.0470149 0.998894i \(-0.514971\pi\)
−0.0470149 + 0.998894i \(0.514971\pi\)
\(462\) 0 0
\(463\) 27.2844i 1.26801i −0.773327 0.634007i \(-0.781409\pi\)
0.773327 0.634007i \(-0.218591\pi\)
\(464\) −0.778539 0.449490i −0.0361428 0.0208670i
\(465\) 0 0
\(466\) 12.1487 + 21.0421i 0.562776 + 0.974757i
\(467\) −0.599403 0.346065i −0.0277370 0.0160140i 0.486067 0.873921i \(-0.338431\pi\)
−0.513804 + 0.857907i \(0.671764\pi\)
\(468\) 0 0
\(469\) 18.5256 + 38.1632i 0.855434 + 1.76221i
\(470\) 0 0
\(471\) 0 0
\(472\) 3.12837 + 5.41849i 0.143995 + 0.249406i
\(473\) −1.42783 2.47307i −0.0656517 0.113712i
\(474\) 0 0
\(475\) 0 0
\(476\) −3.60332 + 5.32076i −0.165158 + 0.243876i
\(477\) 0 0
\(478\) −17.2409 9.95403i −0.788580 0.455287i
\(479\) −7.95403 13.7768i −0.363429 0.629477i 0.625094 0.780550i \(-0.285061\pi\)
−0.988523 + 0.151072i \(0.951727\pi\)
\(480\) 0 0
\(481\) 7.03805 + 4.06342i 0.320908 + 0.185276i
\(482\) 20.5254i 0.934905i
\(483\) 0 0
\(484\) 8.65221 0.393282
\(485\) 0 0
\(486\) 0 0
\(487\) 24.8981 14.3749i 1.12824 0.651390i 0.184749 0.982786i \(-0.440853\pi\)
0.943492 + 0.331396i \(0.107520\pi\)
\(488\) −5.73445 3.31079i −0.259587 0.149872i
\(489\) 0 0
\(490\) 0 0
\(491\) 5.45753i 0.246295i −0.992388 0.123148i \(-0.960701\pi\)
0.992388 0.123148i \(-0.0392988\pi\)
\(492\) 0 0
\(493\) 1.09173 + 1.89094i 0.0491691 + 0.0851635i
\(494\) 6.24384 3.60488i 0.280924 0.162191i
\(495\) 0 0
\(496\) 0.828427i 0.0371975i
\(497\) −33.6802 2.41813i −1.51076 0.108468i
\(498\) 0 0
\(499\) −4.43148 + 7.67555i −0.198380 + 0.343605i −0.948003 0.318260i \(-0.896901\pi\)
0.749623 + 0.661865i \(0.230235\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −2.93393 + 5.08172i −0.130948 + 0.226808i
\(503\) 9.36536i 0.417581i 0.977960 + 0.208790i \(0.0669526\pi\)
−0.977960 + 0.208790i \(0.933047\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.355560 0.205283i −0.0158066 0.00912592i
\(507\) 0 0
\(508\) 18.3619 10.6012i 0.814677 0.470354i
\(509\) −17.5164 + 30.3393i −0.776400 + 1.34477i 0.157603 + 0.987502i \(0.449623\pi\)
−0.934004 + 0.357263i \(0.883710\pi\)
\(510\) 0 0
\(511\) 0.816735 0.396469i 0.0361302 0.0175387i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.63519 3.83083i 0.292666 0.168971i
\(515\) 0 0
\(516\) 0 0
\(517\) −11.4298 −0.502680
\(518\) 6.33429 + 13.0488i 0.278313 + 0.573331i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.99807 17.3172i −0.438023 0.758679i 0.559514 0.828821i \(-0.310988\pi\)
−0.997537 + 0.0701424i \(0.977655\pi\)
\(522\) 0 0
\(523\) 16.7515 29.0144i 0.732491 1.26871i −0.223325 0.974744i \(-0.571691\pi\)
0.955816 0.293967i \(-0.0949756\pi\)
\(524\) −7.46170 −0.325966
\(525\) 0 0
\(526\) −8.46286 −0.368998
\(527\) −1.00605 + 1.74253i −0.0438243 + 0.0759060i
\(528\) 0 0
\(529\) 11.4641 + 19.8564i 0.498439 + 0.863322i
\(530\) 0 0
\(531\) 0 0
\(532\) 12.8351 + 0.921519i 0.556473 + 0.0399529i
\(533\) 12.9859 0.562482
\(534\) 0 0
\(535\) 0 0
\(536\) 13.8859 8.01702i 0.599779 0.346282i
\(537\) 0 0
\(538\) −17.0431 −0.734781
\(539\) 9.95962 3.98090i 0.428991 0.171470i
\(540\) 0 0
\(541\) −18.8766 + 32.6952i −0.811568 + 1.40568i 0.100198 + 0.994967i \(0.468052\pi\)
−0.911766 + 0.410710i \(0.865281\pi\)
\(542\) −9.12436 + 5.26795i −0.391925 + 0.226278i
\(543\) 0 0
\(544\) 2.10342 + 1.21441i 0.0901836 + 0.0520675i
\(545\) 0 0
\(546\) 0 0
\(547\) 5.07130i 0.216833i −0.994106 0.108417i \(-0.965422\pi\)
0.994106 0.108417i \(-0.0345780\pi\)
\(548\) 0.310789 0.538302i 0.0132762 0.0229951i
\(549\) 0 0
\(550\) 0 0
\(551\) 2.18618 3.78658i 0.0931346 0.161314i
\(552\) 0 0
\(553\) 22.8898 + 15.5014i 0.973373 + 0.659187i
\(554\) 8.09122i 0.343763i
\(555\) 0 0
\(556\) −16.0504 + 9.26670i −0.680689 + 0.392996i
\(557\) −17.1778 29.7528i −0.727846 1.26067i −0.957792 0.287463i \(-0.907188\pi\)
0.229946 0.973203i \(-0.426145\pi\)
\(558\) 0 0
\(559\) 2.76268i 0.116849i
\(560\) 0 0
\(561\) 0 0
\(562\) 9.67215 + 5.58422i 0.407995 + 0.235556i
\(563\) 40.7539 23.5293i 1.71757 0.991641i 0.794272 0.607562i \(-0.207852\pi\)
0.923300 0.384079i \(-0.125481\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −7.21592 −0.303308
\(567\) 0 0
\(568\) 12.7627i 0.535510i
\(569\) 38.2670 + 22.0934i 1.60424 + 0.926206i 0.990627 + 0.136595i \(0.0436159\pi\)
0.613608 + 0.789611i \(0.289717\pi\)
\(570\) 0 0
\(571\) −20.5804 35.6463i −0.861263 1.49175i −0.870710 0.491797i \(-0.836340\pi\)
0.00944654 0.999955i \(-0.496993\pi\)
\(572\) −1.96705 1.13567i −0.0822463 0.0474849i
\(573\) 0 0
\(574\) 19.1909 + 12.9964i 0.801012 + 0.542461i
\(575\) 0 0
\(576\) 0 0
\(577\) −7.06058 12.2293i −0.293936 0.509112i 0.680801 0.732469i \(-0.261632\pi\)
−0.974737 + 0.223357i \(0.928299\pi\)
\(578\) 5.55040 + 9.61358i 0.230866 + 0.399872i
\(579\) 0 0
\(580\) 0 0
\(581\) −14.3823 1.03261i −0.596680 0.0428397i
\(582\) 0 0
\(583\) −4.60478 2.65857i −0.190711 0.110107i
\(584\) −0.171573 0.297173i −0.00709974 0.0122971i
\(585\) 0 0
\(586\) −15.8112 9.12863i −0.653156 0.377100i
\(587\) 37.7819i 1.55942i −0.626138 0.779712i \(-0.715365\pi\)
0.626138 0.779712i \(-0.284635\pi\)
\(588\) 0 0
\(589\) 4.02922 0.166021
\(590\) 0 0
\(591\) 0 0
\(592\) 4.74786 2.74118i 0.195136 0.112662i
\(593\) −22.6865 13.0981i −0.931623 0.537873i −0.0442982 0.999018i \(-0.514105\pi\)
−0.887324 + 0.461146i \(0.847438\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 13.9834i 0.572783i
\(597\) 0 0
\(598\) −0.198599 0.343983i −0.00812131 0.0140665i
\(599\) 4.15712 2.40012i 0.169856 0.0980661i −0.412662 0.910884i \(-0.635401\pi\)
0.582518 + 0.812818i \(0.302068\pi\)
\(600\) 0 0
\(601\) 37.3722i 1.52444i −0.647317 0.762221i \(-0.724109\pi\)
0.647317 0.762221i \(-0.275891\pi\)
\(602\) 2.76492 4.08276i 0.112690 0.166401i
\(603\) 0 0
\(604\) −9.83839 + 17.0406i −0.400319 + 0.693372i
\(605\) 0 0
\(606\) 0 0
\(607\) 18.6195 32.2499i 0.755742 1.30898i −0.189263 0.981927i \(-0.560610\pi\)
0.945005 0.327057i \(-0.106057\pi\)
\(608\) 4.86370i 0.197249i
\(609\) 0 0
\(610\) 0 0
\(611\) −9.57618 5.52881i −0.387411 0.223672i
\(612\) 0 0
\(613\) −8.53861 + 4.92977i −0.344871 + 0.199112i −0.662424 0.749129i \(-0.730472\pi\)
0.317553 + 0.948241i \(0.397139\pi\)
\(614\) 1.71039 2.96248i 0.0690258 0.119556i
\(615\) 0 0
\(616\) −1.77035 3.64697i −0.0713296 0.146941i
\(617\) −31.3545 −1.26229 −0.631143 0.775666i \(-0.717414\pi\)
−0.631143 + 0.775666i \(0.717414\pi\)
\(618\) 0 0
\(619\) 13.1943 7.61774i 0.530325 0.306183i −0.210824 0.977524i \(-0.567615\pi\)
0.741149 + 0.671341i \(0.234281\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 5.69089 0.228184
\(623\) 34.9851 + 23.6926i 1.40165 + 0.949223i
\(624\) 0 0
\(625\) 0 0
\(626\) −6.67335 11.5586i −0.266721 0.461974i
\(627\) 0 0
\(628\) 4.53005 7.84628i 0.180769 0.313101i
\(629\) −13.3157 −0.530932
\(630\) 0 0
\(631\) −1.00406 −0.0399710 −0.0199855 0.999800i \(-0.506362\pi\)
−0.0199855 + 0.999800i \(0.506362\pi\)
\(632\) 5.22438 9.04889i 0.207815 0.359946i
\(633\) 0 0
\(634\) −6.26330 10.8484i −0.248748 0.430844i
\(635\) 0 0
\(636\) 0 0
\(637\) 10.2701 + 1.48236i 0.406916 + 0.0587333i
\(638\) −1.37746 −0.0545342
\(639\) 0 0
\(640\) 0 0
\(641\) −20.2689 + 11.7023i −0.800574 + 0.462211i −0.843672 0.536860i \(-0.819611\pi\)
0.0430981 + 0.999071i \(0.486277\pi\)
\(642\) 0 0
\(643\) 33.4475 1.31904 0.659521 0.751686i \(-0.270759\pi\)
0.659521 + 0.751686i \(0.270759\pi\)
\(644\) 0.0507680 0.707107i 0.00200054 0.0278639i
\(645\) 0 0
\(646\) −5.90654 + 10.2304i −0.232390 + 0.402511i
\(647\) −14.3507 + 8.28540i −0.564185 + 0.325733i −0.754824 0.655928i \(-0.772278\pi\)
0.190638 + 0.981660i \(0.438944\pi\)
\(648\) 0 0
\(649\) 8.30249 + 4.79344i 0.325901 + 0.188159i
\(650\) 0 0
\(651\) 0 0
\(652\) 11.8204i 0.462922i
\(653\) −3.01453 + 5.22132i −0.117968 + 0.204326i −0.918962 0.394346i \(-0.870971\pi\)
0.800994 + 0.598672i \(0.204305\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.38014 7.58662i 0.171016 0.296208i
\(657\) 0 0
\(658\) −8.61862 17.7545i −0.335989 0.692144i
\(659\) 36.3672i 1.41666i −0.705880 0.708332i \(-0.749448\pi\)
0.705880 0.708332i \(-0.250552\pi\)
\(660\) 0 0
\(661\) −9.90289 + 5.71744i −0.385178 + 0.222383i −0.680069 0.733148i \(-0.738050\pi\)
0.294891 + 0.955531i \(0.404717\pi\)
\(662\) −0.640916 1.11010i −0.0249099 0.0431452i
\(663\) 0 0
\(664\) 5.45001i 0.211501i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.208609 0.120440i −0.00807737 0.00466347i
\(668\) 13.6640 7.88891i 0.528675 0.305231i
\(669\) 0 0
\(670\) 0 0
\(671\) −10.1459 −0.391679
\(672\) 0 0
\(673\) 10.8070i 0.416581i 0.978067 + 0.208290i \(0.0667899\pi\)
−0.978067 + 0.208290i \(0.933210\pi\)
\(674\) 11.3500 + 6.55291i 0.437185 + 0.252409i
\(675\) 0 0
\(676\) 5.40130 + 9.35533i 0.207742 + 0.359820i
\(677\) −12.1638 7.02280i −0.467494 0.269908i 0.247696 0.968838i \(-0.420327\pi\)
−0.715190 + 0.698930i \(0.753660\pi\)
\(678\) 0 0
\(679\) −2.83220 + 39.4475i −0.108690 + 1.51386i
\(680\) 0 0
\(681\) 0 0
\(682\) −0.634679 1.09930i −0.0243031 0.0420942i
\(683\) −18.2385 31.5900i −0.697877 1.20876i −0.969201 0.246271i \(-0.920795\pi\)
0.271324 0.962488i \(-0.412539\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 13.6938 + 12.4691i 0.522834 + 0.476073i
\(687\) 0 0
\(688\) −1.61401 0.931852i −0.0615337 0.0355265i
\(689\) −2.57201 4.45486i −0.0979859 0.169716i
\(690\) 0 0
\(691\) −20.5831 11.8836i −0.783017 0.452075i 0.0544816 0.998515i \(-0.482649\pi\)
−0.837498 + 0.546440i \(0.815983\pi\)
\(692\) 20.2221i 0.768730i
\(693\) 0 0
\(694\) 14.2852 0.542260
\(695\) 0 0
\(696\) 0 0
\(697\) −18.4266 + 10.6386i −0.697957 + 0.402965i
\(698\) −11.4933 6.63567i −0.435029 0.251164i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.74502i 0.0659086i −0.999457 0.0329543i \(-0.989508\pi\)
0.999457 0.0329543i \(-0.0104916\pi\)
\(702\) 0 0
\(703\) 13.3323 + 23.0922i 0.502837 + 0.870939i
\(704\) −1.32697 + 0.766125i −0.0500120 + 0.0288744i
\(705\) 0 0
\(706\) 32.6463i 1.22866i
\(707\) −6.51075 + 3.16052i −0.244862 + 0.118864i
\(708\) 0 0
\(709\) −6.06162 + 10.4990i −0.227649 + 0.394299i −0.957111 0.289722i \(-0.906437\pi\)
0.729462 + 0.684021i \(0.239770\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 7.98502 13.8305i 0.299251 0.518319i
\(713\) 0.221976i 0.00831308i
\(714\) 0 0
\(715\) 0 0
\(716\) 5.94667 + 3.43331i 0.222237 + 0.128309i
\(717\) 0 0
\(718\) 5.40692 3.12168i 0.201784 0.116500i
\(719\) 0.893176 1.54703i 0.0333098 0.0576943i −0.848890 0.528570i \(-0.822729\pi\)
0.882200 + 0.470875i \(0.156062\pi\)
\(720\) 0 0
\(721\) −13.5315 9.16382i −0.503941 0.341279i
\(722\) 4.65561 0.173264
\(723\) 0 0
\(724\) 14.1220 8.15331i 0.524838 0.303015i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.8785 1.10813 0.554066 0.832472i \(-0.313075\pi\)
0.554066 + 0.832472i \(0.313075\pi\)
\(728\) 0.280861 3.91189i 0.0104094 0.144984i
\(729\) 0 0
\(730\) 0 0
\(731\) 2.26330 + 3.92016i 0.0837114 + 0.144992i
\(732\) 0 0
\(733\) 6.89554 11.9434i 0.254692 0.441140i −0.710119 0.704081i \(-0.751359\pi\)
0.964812 + 0.262941i \(0.0846924\pi\)
\(734\) −12.5892 −0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) 12.2841 21.2766i 0.452490 0.783735i
\(738\) 0 0
\(739\) 3.68349 + 6.37999i 0.135499 + 0.234692i 0.925788 0.378043i \(-0.123403\pi\)
−0.790289 + 0.612735i \(0.790069\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.657486 9.15759i 0.0241371 0.336186i
\(743\) −11.0774 −0.406389 −0.203194 0.979138i \(-0.565132\pi\)
−0.203194 + 0.979138i \(0.565132\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −31.1408 + 17.9791i −1.14014 + 0.658263i
\(747\) 0 0
\(748\) 3.72157 0.136074
\(749\) −10.0112 6.77978i −0.365802 0.247728i
\(750\) 0 0
\(751\) −12.1879 + 21.1100i −0.444741 + 0.770315i −0.998034 0.0626722i \(-0.980038\pi\)
0.553293 + 0.832987i \(0.313371\pi\)
\(752\) −6.46008 + 3.72973i −0.235575 + 0.136009i
\(753\) 0 0
\(754\) −1.15408 0.666306i −0.0420290 0.0242655i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.6761i 0.715139i −0.933887 0.357569i \(-0.883606\pi\)
0.933887 0.357569i \(-0.116394\pi\)
\(758\) 5.79493 10.0371i 0.210481 0.364565i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.9168 + 43.1572i −0.903234 + 1.56445i −0.0799647 + 0.996798i \(0.525481\pi\)
−0.823270 + 0.567650i \(0.807853\pi\)
\(762\) 0 0
\(763\) −14.1825 + 6.88462i −0.513440 + 0.249240i
\(764\) 17.1623i 0.620910i
\(765\) 0 0
\(766\) −3.86897 + 2.23375i −0.139792 + 0.0807087i
\(767\) 4.63737 + 8.03217i 0.167446 + 0.290025i
\(768\) 0 0
\(769\) 31.0584i 1.12000i 0.828494 + 0.559998i \(0.189198\pi\)
−0.828494 + 0.559998i \(0.810802\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.84204 4.52761i −0.282241 0.162952i
\(773\) 3.43855 1.98525i 0.123676 0.0714043i −0.436886 0.899517i \(-0.643919\pi\)
0.560562 + 0.828113i \(0.310585\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 14.9481 0.536607
\(777\) 0 0
\(778\) 12.9554i 0.464475i
\(779\) 36.8991 + 21.3037i 1.32205 + 0.763284i
\(780\) 0 0
\(781\) 9.77781 + 16.9357i 0.349878 + 0.606006i
\(782\) 0.563611 + 0.325401i 0.0201547 + 0.0116363i
\(783\) 0 0
\(784\) 4.33013 5.50000i 0.154647 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −22.4013 38.8001i −0.798519 1.38308i −0.920580 0.390553i \(-0.872284\pi\)
0.122061 0.992523i \(-0.461050\pi\)
\(788\) 10.8689 + 18.8256i 0.387190 + 0.670633i
\(789\) 0 0
\(790\) 0 0
\(791\) 3.77000 52.5093i 0.134046 1.86702i
\(792\) 0 0
\(793\) −8.50054 4.90779i −0.301863 0.174281i
\(794\) −4.63995 8.03664i −0.164666 0.285210i
\(795\) 0 0
\(796\) −7.21101 4.16328i −0.255588 0.147564i
\(797\) 38.4813i 1.36308i −0.731781 0.681539i \(-0.761311\pi\)
0.731781 0.681539i \(-0.238689\pi\)
\(798\) 0 0
\(799\) 18.1177 0.640959
\(800\) 0 0
\(801\) 0 0
\(802\) 6.44260 3.71964i 0.227496 0.131345i
\(803\) −0.455343 0.262893i −0.0160687 0.00927728i
\(804\) 0 0
\(805\) 0 0
\(806\) 1.22803i 0.0432555i
\(807\) 0 0
\(808\) 1.36773 + 2.36897i 0.0481164 + 0.0833401i
\(809\) 15.0298 8.67748i 0.528421 0.305084i −0.211952 0.977280i \(-0.567982\pi\)
0.740373 + 0.672196i \(0.234649\pi\)
\(810\) 0 0
\(811\) 32.7270i 1.14920i 0.818434 + 0.574601i \(0.194843\pi\)
−0.818434 + 0.574601i \(0.805157\pi\)
\(812\) −1.03868 2.13970i −0.0364504 0.0750886i
\(813\) 0 0
\(814\) 4.20017 7.27492i 0.147216 0.254986i
\(815\) 0 0
\(816\) 0 0
\(817\) 4.53225 7.85009i 0.158563 0.274640i
\(818\) 16.0096i 0.559763i
\(819\) 0 0
\(820\) 0 0
\(821\) −15.4093 8.89658i −0.537789 0.310493i 0.206393 0.978469i \(-0.433827\pi\)
−0.744182 + 0.667976i \(0.767161\pi\)
\(822\) 0 0
\(823\) 8.50579 4.91082i 0.296493 0.171181i −0.344373 0.938833i \(-0.611909\pi\)
0.640867 + 0.767652i \(0.278575\pi\)
\(824\) −3.08845 + 5.34935i −0.107591 + 0.186353i
\(825\) 0 0
\(826\) −1.18546 + 16.5113i −0.0412473 + 0.574501i
\(827\) 7.78482 0.270705 0.135352 0.990798i \(-0.456783\pi\)
0.135352 + 0.990798i \(0.456783\pi\)
\(828\) 0 0
\(829\) 13.1015 7.56413i 0.455032 0.262713i −0.254921 0.966962i \(-0.582049\pi\)
0.709953 + 0.704249i \(0.248716\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.48236 −0.0513917
\(833\) −15.7874 + 6.31027i −0.547000 + 0.218638i
\(834\) 0 0
\(835\) 0 0
\(836\) −3.72620 6.45398i −0.128873 0.223215i
\(837\) 0 0
\(838\) 14.2209 24.6314i 0.491254 0.850877i
\(839\) −25.2077 −0.870265 −0.435133 0.900366i \(-0.643299\pi\)
−0.435133 + 0.900366i \(0.643299\pi\)
\(840\) 0 0
\(841\) 28.1918 0.972132
\(842\) 8.91724 15.4451i 0.307308 0.532274i
\(843\) 0 0
\(844\) 9.96651 + 17.2625i 0.343061 + 0.594200i
\(845\) 0 0
\(846\) 0 0
\(847\) 18.9541 + 12.8361i 0.651272 + 0.441054i
\(848\) −3.47015 −0.119166
\(849\) 0 0
\(850\) 0 0
\(851\) 1.27219 0.734497i 0.0436100 0.0251782i
\(852\) 0 0
\(853\) 23.3020 0.797846 0.398923 0.916984i \(-0.369384\pi\)
0.398923 + 0.916984i \(0.369384\pi\)
\(854\) −7.65053 15.7603i −0.261796 0.539306i
\(855\) 0 0
\(856\) −2.28497 + 3.95768i −0.0780985 + 0.135271i
\(857\) 23.0414 13.3030i 0.787080 0.454421i −0.0518534 0.998655i \(-0.516513\pi\)
0.838934 + 0.544234i \(0.183180\pi\)
\(858\) 0 0
\(859\) −49.0044 28.2927i −1.67201 0.965334i −0.966512 0.256620i \(-0.917391\pi\)
−0.705495 0.708714i \(-0.749275\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 30.8927i 1.05221i
\(863\) −17.0283 + 29.4939i −0.579650 + 1.00398i 0.415869 + 0.909425i \(0.363478\pi\)
−0.995519 + 0.0945593i \(0.969856\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 7.61037 13.1815i 0.258611 0.447927i
\(867\) 0 0
\(868\) 1.22902 1.81481i 0.0417158 0.0615987i
\(869\) 16.0101i 0.543106i
\(870\) 0 0
\(871\) 20.5839 11.8841i 0.697459 0.402678i
\(872\) 2.97934 + 5.16036i 0.100893 + 0.174752i
\(873\) 0 0
\(874\) 1.30323i 0.0440823i
\(875\) 0 0
\(876\) 0 0
\(877\) 20.9043 + 12.0691i 0.705888 + 0.407545i 0.809537 0.587069i \(-0.199718\pi\)
−0.103649 + 0.994614i \(0.533052\pi\)
\(878\) −12.4054 + 7.16228i −0.418663 + 0.241715i
\(879\) 0 0
\(880\) 0 0
\(881\) −37.2609 −1.25535 −0.627676 0.778475i \(-0.715994\pi\)
−0.627676 + 0.778475i \(0.715994\pi\)
\(882\) 0 0
\(883\) 48.5544i 1.63398i 0.576648 + 0.816992i \(0.304360\pi\)
−0.576648 + 0.816992i \(0.695640\pi\)
\(884\) 3.11804 + 1.80020i 0.104871 + 0.0605472i
\(885\) 0 0
\(886\) 2.57874 + 4.46651i 0.0866344 + 0.150055i
\(887\) 15.1302 + 8.73545i 0.508024 + 0.293308i 0.732021 0.681282i \(-0.238577\pi\)
−0.223997 + 0.974590i \(0.571911\pi\)
\(888\) 0 0
\(889\) 55.9524 + 4.01720i 1.87658 + 0.134733i
\(890\) 0 0
\(891\) 0 0
\(892\) 3.58302 + 6.20597i 0.119968 + 0.207791i
\(893\) −18.1403 31.4199i −0.607042 1.05143i
\(894\) 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
\(899\) −0.372369 0.644963i −0.0124192 0.0215107i
\(900\) 0 0
\(901\) 7.29921 + 4.21420i 0.243172 + 0.140395i
\(902\) 13.4229i 0.446935i
\(903\) 0 0
\(904\) −19.8977 −0.661789
\(905\) 0 0
\(906\) 0 0
\(907\) 18.5780 10.7260i 0.616872 0.356151i −0.158778 0.987314i \(-0.550756\pi\)
0.775650 + 0.631163i \(0.217422\pi\)
\(908\) −13.7303 7.92721i −0.455657 0.263074i
\(909\) 0 0
\(910\) 0 0
\(911\) 42.2281i 1.39908i 0.714593 + 0.699540i \(0.246612\pi\)
−0.714593 + 0.699540i \(0.753388\pi\)
\(912\) 0 0
\(913\) 4.17539 + 7.23198i 0.138185 + 0.239344i
\(914\) 9.82065 5.66995i 0.324838 0.187545i
\(915\) 0 0
\(916\) 28.2175i 0.932332i
\(917\) −16.3461 11.0699i −0.539797 0.365560i
\(918\) 0 0
\(919\) −28.0816 + 48.6387i −0.926325 + 1.60444i −0.136908 + 0.990584i \(0.543717\pi\)
−0.789416 + 0.613858i \(0.789617\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.00945 + 1.74842i −0.0332445 + 0.0575812i
\(923\) 18.9189i 0.622724i
\(924\) 0 0
\(925\) 0 0
\(926\) −23.6290 13.6422i −0.776497 0.448311i
\(927\) 0 0
\(928\) −0.778539 + 0.449490i −0.0255568 + 0.0147552i
\(929\) −9.26942 + 16.0551i −0.304120 + 0.526751i −0.977065 0.212941i \(-0.931696\pi\)
0.672945 + 0.739692i \(0.265029\pi\)
\(930\) 0 0
\(931\) 26.7504 + 21.0605i 0.876708 + 0.690228i
\(932\) 24.2973 0.795886
\(933\) 0 0
\(934\) −0.599403 + 0.346065i −0.0196131 + 0.0113236i
\(935\) 0 0
\(936\) 0 0
\(937\) −39.5337 −1.29151 −0.645755 0.763545i \(-0.723457\pi\)
−0.645755 + 0.763545i \(0.723457\pi\)
\(938\) 42.3131 + 3.03795i 1.38157 + 0.0991925i
\(939\) 0 0
\(940\) 0 0
\(941\) 25.2474 + 43.7299i 0.823043 + 1.42555i 0.903406 + 0.428787i \(0.141059\pi\)
−0.0803623 + 0.996766i \(0.525608\pi\)
\(942\) 0 0
\(943\) 1.17365 2.03283i 0.0382195 0.0661980i
\(944\) 6.25674 0.203639
\(945\) 0 0
\(946\) −2.85566 −0.0928455
\(947\) −19.5814 + 33.9160i −0.636310 + 1.10212i 0.349926 + 0.936777i \(0.386207\pi\)
−0.986236 + 0.165344i \(0.947126\pi\)
\(948\) 0 0
\(949\) −0.254333 0.440518i −0.00825600 0.0142998i
\(950\) 0 0
\(951\) 0 0
\(952\) 2.80625 + 5.78094i 0.0909511 + 0.187361i
\(953\) −52.9933 −1.71662 −0.858311 0.513130i \(-0.828486\pi\)
−0.858311 + 0.513130i \(0.828486\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −17.2409 + 9.95403i −0.557610 + 0.321936i
\(957\) 0 0
\(958\) −15.9081 −0.513966
\(959\) 1.47944 0.718168i 0.0477737 0.0231909i
\(960\) 0 0
\(961\) −15.1569 + 26.2524i −0.488931 + 0.846853i
\(962\) 7.03805 4.06342i 0.226916 0.131010i
\(963\) 0 0
\(964\) −17.7755 10.2627i −0.572510 0.330539i
\(965\) 0 0
\(966\) 0 0
\(967\) 30.6208i 0.984700i −0.870397 0.492350i \(-0.836138\pi\)
0.870397 0.492350i \(-0.163862\pi\)
\(968\) 4.32611 7.49303i 0.139046 0.240835i
\(969\) 0 0
\(970\) 0 0
\(971\) 6.03548 10.4538i 0.193688 0.335477i −0.752782 0.658270i \(-0.771288\pi\)
0.946470 + 0.322793i \(0.104622\pi\)
\(972\) 0 0
\(973\) −48.9089 3.51150i −1.56795 0.112574i
\(974\) 28.7498i 0.921205i
\(975\) 0 0
\(976\) −5.73445 + 3.31079i −0.183555 + 0.105976i
\(977\) 5.61642 + 9.72792i 0.179685 + 0.311224i 0.941773 0.336250i \(-0.109159\pi\)
−0.762088 + 0.647474i \(0.775825\pi\)
\(978\) 0 0
\(979\) 24.4701i 0.782068i
\(980\) 0 0
\(981\) 0 0
\(982\) −4.72636 2.72877i −0.150824 0.0870784i
\(983\) 19.7385 11.3960i 0.629561 0.363477i −0.151021 0.988531i \(-0.548256\pi\)
0.780582 + 0.625053i \(0.214923\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2.18346 0.0695357
\(987\) 0 0
\(988\) 7.20977i 0.229373i
\(989\) −0.432474 0.249689i −0.0137519 0.00793965i
\(990\) 0 0
\(991\) 4.41057 + 7.63932i 0.140106 + 0.242671i 0.927536 0.373733i \(-0.121922\pi\)
−0.787430 + 0.616404i \(0.788589\pi\)
\(992\) −0.717439 0.414214i −0.0227787 0.0131513i
\(993\) 0 0
\(994\) −18.9343 + 27.9588i −0.600558 + 0.886800i
\(995\) 0 0
\(996\) 0 0
\(997\) 23.2381 + 40.2497i 0.735960 + 1.27472i 0.954301 + 0.298847i \(0.0966020\pi\)
−0.218342 + 0.975872i \(0.570065\pi\)
\(998\) 4.43148 + 7.67555i 0.140276 + 0.242965i
\(999\) 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.d.1349.3 8
3.2 odd 2 3150.2.bp.c.1349.3 8
5.2 odd 4 630.2.be.a.341.4 8
5.3 odd 4 3150.2.bf.b.1601.1 8
5.4 even 2 3150.2.bp.a.1349.2 8
7.3 odd 6 3150.2.bp.f.899.2 8
15.2 even 4 630.2.be.b.341.2 yes 8
15.8 even 4 3150.2.bf.c.1601.3 8
15.14 odd 2 3150.2.bp.f.1349.2 8
21.17 even 6 3150.2.bp.a.899.2 8
35.2 odd 12 4410.2.b.e.881.2 8
35.3 even 12 3150.2.bf.c.1151.3 8
35.12 even 12 4410.2.b.b.881.2 8
35.17 even 12 630.2.be.b.521.2 yes 8
35.24 odd 6 3150.2.bp.c.899.3 8
105.2 even 12 4410.2.b.b.881.7 8
105.17 odd 12 630.2.be.a.521.4 yes 8
105.38 odd 12 3150.2.bf.b.1151.1 8
105.47 odd 12 4410.2.b.e.881.7 8
105.59 even 6 inner 3150.2.bp.d.899.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.be.a.341.4 8 5.2 odd 4
630.2.be.a.521.4 yes 8 105.17 odd 12
630.2.be.b.341.2 yes 8 15.2 even 4
630.2.be.b.521.2 yes 8 35.17 even 12
3150.2.bf.b.1151.1 8 105.38 odd 12
3150.2.bf.b.1601.1 8 5.3 odd 4
3150.2.bf.c.1151.3 8 35.3 even 12
3150.2.bf.c.1601.3 8 15.8 even 4
3150.2.bp.a.899.2 8 21.17 even 6
3150.2.bp.a.1349.2 8 5.4 even 2
3150.2.bp.c.899.3 8 35.24 odd 6
3150.2.bp.c.1349.3 8 3.2 odd 2
3150.2.bp.d.899.3 8 105.59 even 6 inner
3150.2.bp.d.1349.3 8 1.1 even 1 trivial
3150.2.bp.f.899.2 8 7.3 odd 6
3150.2.bp.f.1349.2 8 15.14 odd 2
4410.2.b.b.881.2 8 35.12 even 12
4410.2.b.b.881.7 8 105.2 even 12
4410.2.b.e.881.2 8 35.2 odd 12
4410.2.b.e.881.7 8 105.47 odd 12