Properties

Label 88.2.i.b.81.2
Level $88$
Weight $2$
Character 88.81
Analytic conductor $0.703$
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] = [88,2,Mod(9,88)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(88, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("88.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 88 = 2^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 88.i (of order \(5\), degree \(4\), 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: \(0.702683537787\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.682515625.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.2
Root \(0.581882 - 1.79085i\) of defining polynomial
Character \(\chi\) \(=\) 88.81
Dual form 88.2.i.b.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.941506 - 2.89766i) q^{3} +(-1.44151 + 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +(-5.08293 - 3.69296i) q^{9} +O(q^{10})\) \(q+(0.941506 - 2.89766i) q^{3} +(-1.44151 + 1.04732i) q^{5} +(0.109101 + 0.335777i) q^{7} +(-5.08293 - 3.69296i) q^{9} +(2.91429 + 1.58333i) q^{11} +(4.48828 + 3.26093i) q^{13} +(1.67757 + 5.16304i) q^{15} +(-3.08462 + 2.24111i) q^{17} +(1.42705 - 4.39201i) q^{19} +1.07569 q^{21} -7.00209 q^{23} +(-0.564016 + 1.73586i) q^{25} +(-8.09186 + 5.87908i) q^{27} +(0.654831 + 2.01536i) q^{29} +(-2.79456 - 2.03037i) q^{31} +(7.33176 - 6.95389i) q^{33} +(-0.508933 - 0.369762i) q^{35} +(-0.537843 - 1.65531i) q^{37} +(13.6748 - 9.93532i) q^{39} +(-0.458327 + 1.41059i) q^{41} -3.92979 q^{43} +11.1948 q^{45} +(-0.374078 + 1.15129i) q^{47} +(5.56228 - 4.04123i) q^{49} +(3.58977 + 11.0482i) q^{51} +(-6.41260 - 4.65902i) q^{53} +(-5.85921 + 0.769801i) q^{55} +(-11.3830 - 8.27021i) q^{57} +(-0.954915 - 2.93893i) q^{59} +(6.15309 - 4.47048i) q^{61} +(0.685462 - 2.10963i) q^{63} -9.88510 q^{65} +1.17352 q^{67} +(-6.59251 + 20.2896i) q^{69} +(1.91702 - 1.39280i) q^{71} +(1.20648 + 3.71317i) q^{73} +(4.49891 + 3.26865i) q^{75} +(-0.213695 + 1.15129i) q^{77} +(-3.32452 - 2.41540i) q^{79} +(3.59251 + 11.0566i) q^{81} +(-0.662074 + 0.481025i) q^{83} +(2.09935 - 6.46114i) q^{85} +6.45636 q^{87} -1.92979 q^{89} +(-0.605270 + 1.86283i) q^{91} +(-8.51441 + 6.18608i) q^{93} +(2.54272 + 7.82568i) q^{95} +(7.66755 + 5.57080i) q^{97} +(-8.96594 - 18.8103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9} + 7 q^{11} + 7 q^{13} - 13 q^{15} + q^{17} - 2 q^{19} - 2 q^{21} - 4 q^{23} - 33 q^{25} - 22 q^{27} + 17 q^{29} - 13 q^{31} + 16 q^{33} + 11 q^{35} + q^{37} + 39 q^{39} + 9 q^{41} + 6 q^{43} + 44 q^{45} - q^{47} + 3 q^{49} + 38 q^{51} - 33 q^{53} + 13 q^{55} - 6 q^{57} - 30 q^{59} - 9 q^{61} - 10 q^{63} - 10 q^{65} - 10 q^{67} - 38 q^{69} - 25 q^{71} - 7 q^{73} - 6 q^{75} - 7 q^{77} - q^{79} + 14 q^{81} + 39 q^{85} - 6 q^{87} + 22 q^{89} + 7 q^{91} - 5 q^{93} + 7 q^{95} + 8 q^{97} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/88\mathbb{Z}\right)^\times\).

\(n\) \(23\) \(45\) \(57\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.941506 2.89766i 0.543578 1.67296i −0.180767 0.983526i \(-0.557858\pi\)
0.724346 0.689437i \(-0.242142\pi\)
\(4\) 0 0
\(5\) −1.44151 + 1.04732i −0.644661 + 0.468374i −0.861448 0.507845i \(-0.830442\pi\)
0.216787 + 0.976219i \(0.430442\pi\)
\(6\) 0 0
\(7\) 0.109101 + 0.335777i 0.0412361 + 0.126912i 0.969555 0.244873i \(-0.0787461\pi\)
−0.928319 + 0.371784i \(0.878746\pi\)
\(8\) 0 0
\(9\) −5.08293 3.69296i −1.69431 1.23099i
\(10\) 0 0
\(11\) 2.91429 + 1.58333i 0.878691 + 0.477391i
\(12\) 0 0
\(13\) 4.48828 + 3.26093i 1.24483 + 0.904419i 0.997910 0.0646185i \(-0.0205831\pi\)
0.246915 + 0.969037i \(0.420583\pi\)
\(14\) 0 0
\(15\) 1.67757 + 5.16304i 0.433148 + 1.33309i
\(16\) 0 0
\(17\) −3.08462 + 2.24111i −0.748130 + 0.543548i −0.895247 0.445571i \(-0.853001\pi\)
0.147117 + 0.989119i \(0.453001\pi\)
\(18\) 0 0
\(19\) 1.42705 4.39201i 0.327388 1.00760i −0.642963 0.765897i \(-0.722295\pi\)
0.970351 0.241699i \(-0.0777048\pi\)
\(20\) 0 0
\(21\) 1.07569 0.234734
\(22\) 0 0
\(23\) −7.00209 −1.46004 −0.730018 0.683428i \(-0.760489\pi\)
−0.730018 + 0.683428i \(0.760489\pi\)
\(24\) 0 0
\(25\) −0.564016 + 1.73586i −0.112803 + 0.347172i
\(26\) 0 0
\(27\) −8.09186 + 5.87908i −1.55728 + 1.13143i
\(28\) 0 0
\(29\) 0.654831 + 2.01536i 0.121599 + 0.374244i 0.993266 0.115855i \(-0.0369608\pi\)
−0.871667 + 0.490099i \(0.836961\pi\)
\(30\) 0 0
\(31\) −2.79456 2.03037i −0.501918 0.364665i 0.307831 0.951441i \(-0.400397\pi\)
−0.809749 + 0.586776i \(0.800397\pi\)
\(32\) 0 0
\(33\) 7.33176 6.95389i 1.27630 1.21052i
\(34\) 0 0
\(35\) −0.508933 0.369762i −0.0860254 0.0625011i
\(36\) 0 0
\(37\) −0.537843 1.65531i −0.0884208 0.272131i 0.897063 0.441904i \(-0.145697\pi\)
−0.985483 + 0.169773i \(0.945697\pi\)
\(38\) 0 0
\(39\) 13.6748 9.93532i 2.18972 1.59092i
\(40\) 0 0
\(41\) −0.458327 + 1.41059i −0.0715787 + 0.220297i −0.980446 0.196789i \(-0.936949\pi\)
0.908867 + 0.417086i \(0.136949\pi\)
\(42\) 0 0
\(43\) −3.92979 −0.599287 −0.299643 0.954051i \(-0.596868\pi\)
−0.299643 + 0.954051i \(0.596868\pi\)
\(44\) 0 0
\(45\) 11.1948 1.66882
\(46\) 0 0
\(47\) −0.374078 + 1.15129i −0.0545648 + 0.167933i −0.974625 0.223844i \(-0.928140\pi\)
0.920060 + 0.391777i \(0.128140\pi\)
\(48\) 0 0
\(49\) 5.56228 4.04123i 0.794611 0.577319i
\(50\) 0 0
\(51\) 3.58977 + 11.0482i 0.502668 + 1.54705i
\(52\) 0 0
\(53\) −6.41260 4.65902i −0.880838 0.639966i 0.0526352 0.998614i \(-0.483238\pi\)
−0.933473 + 0.358648i \(0.883238\pi\)
\(54\) 0 0
\(55\) −5.85921 + 0.769801i −0.790055 + 0.103800i
\(56\) 0 0
\(57\) −11.3830 8.27021i −1.50771 1.09542i
\(58\) 0 0
\(59\) −0.954915 2.93893i −0.124319 0.382616i 0.869457 0.494008i \(-0.164469\pi\)
−0.993776 + 0.111393i \(0.964469\pi\)
\(60\) 0 0
\(61\) 6.15309 4.47048i 0.787823 0.572387i −0.119494 0.992835i \(-0.538127\pi\)
0.907317 + 0.420448i \(0.138127\pi\)
\(62\) 0 0
\(63\) 0.685462 2.10963i 0.0863601 0.265789i
\(64\) 0 0
\(65\) −9.88510 −1.22610
\(66\) 0 0
\(67\) 1.17352 0.143368 0.0716839 0.997427i \(-0.477163\pi\)
0.0716839 + 0.997427i \(0.477163\pi\)
\(68\) 0 0
\(69\) −6.59251 + 20.2896i −0.793645 + 2.44259i
\(70\) 0 0
\(71\) 1.91702 1.39280i 0.227509 0.165295i −0.468191 0.883627i \(-0.655094\pi\)
0.695700 + 0.718332i \(0.255094\pi\)
\(72\) 0 0
\(73\) 1.20648 + 3.71317i 0.141208 + 0.434594i 0.996504 0.0835461i \(-0.0266246\pi\)
−0.855296 + 0.518140i \(0.826625\pi\)
\(74\) 0 0
\(75\) 4.49891 + 3.26865i 0.519489 + 0.377431i
\(76\) 0 0
\(77\) −0.213695 + 1.15129i −0.0243528 + 0.131202i
\(78\) 0 0
\(79\) −3.32452 2.41540i −0.374037 0.271754i 0.384846 0.922981i \(-0.374255\pi\)
−0.758883 + 0.651227i \(0.774255\pi\)
\(80\) 0 0
\(81\) 3.59251 + 11.0566i 0.399167 + 1.22851i
\(82\) 0 0
\(83\) −0.662074 + 0.481025i −0.0726720 + 0.0527993i −0.623528 0.781801i \(-0.714301\pi\)
0.550856 + 0.834600i \(0.314301\pi\)
\(84\) 0 0
\(85\) 2.09935 6.46114i 0.227706 0.700809i
\(86\) 0 0
\(87\) 6.45636 0.692194
\(88\) 0 0
\(89\) −1.92979 −0.204557 −0.102279 0.994756i \(-0.532613\pi\)
−0.102279 + 0.994756i \(0.532613\pi\)
\(90\) 0 0
\(91\) −0.605270 + 1.86283i −0.0634496 + 0.195278i
\(92\) 0 0
\(93\) −8.51441 + 6.18608i −0.882903 + 0.641466i
\(94\) 0 0
\(95\) 2.54272 + 7.82568i 0.260877 + 0.802898i
\(96\) 0 0
\(97\) 7.66755 + 5.57080i 0.778521 + 0.565629i 0.904535 0.426400i \(-0.140218\pi\)
−0.126014 + 0.992029i \(0.540218\pi\)
\(98\) 0 0
\(99\) −8.96594 18.8103i −0.901111 1.89051i
\(100\) 0 0
\(101\) 11.6541 + 8.46723i 1.15963 + 0.842520i 0.989731 0.142941i \(-0.0456559\pi\)
0.169899 + 0.985462i \(0.445656\pi\)
\(102\) 0 0
\(103\) 2.48002 + 7.63273i 0.244364 + 0.752075i 0.995740 + 0.0922013i \(0.0293903\pi\)
−0.751376 + 0.659874i \(0.770610\pi\)
\(104\) 0 0
\(105\) −1.55061 + 1.12658i −0.151324 + 0.109943i
\(106\) 0 0
\(107\) 1.41364 4.35074i 0.136662 0.420602i −0.859183 0.511669i \(-0.829028\pi\)
0.995845 + 0.0910665i \(0.0290276\pi\)
\(108\) 0 0
\(109\) −20.6592 −1.97880 −0.989398 0.145228i \(-0.953608\pi\)
−0.989398 + 0.145228i \(0.953608\pi\)
\(110\) 0 0
\(111\) −5.30290 −0.503329
\(112\) 0 0
\(113\) 2.72094 8.37418i 0.255964 0.787777i −0.737674 0.675157i \(-0.764076\pi\)
0.993638 0.112620i \(-0.0359242\pi\)
\(114\) 0 0
\(115\) 10.0936 7.33339i 0.941229 0.683843i
\(116\) 0 0
\(117\) −10.7711 33.1501i −0.995791 3.06473i
\(118\) 0 0
\(119\) −1.08905 0.791238i −0.0998327 0.0725327i
\(120\) 0 0
\(121\) 5.98614 + 9.22855i 0.544195 + 0.838959i
\(122\) 0 0
\(123\) 3.65588 + 2.65615i 0.329639 + 0.239497i
\(124\) 0 0
\(125\) −3.75799 11.5659i −0.336125 1.03449i
\(126\) 0 0
\(127\) −14.3946 + 10.4583i −1.27732 + 0.928025i −0.999468 0.0325998i \(-0.989621\pi\)
−0.277849 + 0.960625i \(0.589621\pi\)
\(128\) 0 0
\(129\) −3.69992 + 11.3872i −0.325759 + 1.00258i
\(130\) 0 0
\(131\) 18.3585 1.60399 0.801996 0.597329i \(-0.203771\pi\)
0.801996 + 0.597329i \(0.203771\pi\)
\(132\) 0 0
\(133\) 1.63043 0.141376
\(134\) 0 0
\(135\) 5.50721 16.9495i 0.473985 1.45878i
\(136\) 0 0
\(137\) 10.9036 7.92194i 0.931559 0.676817i −0.0148153 0.999890i \(-0.504716\pi\)
0.946374 + 0.323073i \(0.104716\pi\)
\(138\) 0 0
\(139\) 4.40981 + 13.5720i 0.374035 + 1.15116i 0.944127 + 0.329581i \(0.106908\pi\)
−0.570092 + 0.821581i \(0.693092\pi\)
\(140\) 0 0
\(141\) 2.98385 + 2.16790i 0.251286 + 0.182570i
\(142\) 0 0
\(143\) 7.91702 + 16.6097i 0.662055 + 1.38897i
\(144\) 0 0
\(145\) −3.05466 2.21934i −0.253676 0.184306i
\(146\) 0 0
\(147\) −6.47318 19.9224i −0.533899 1.64317i
\(148\) 0 0
\(149\) 8.25430 5.99710i 0.676219 0.491302i −0.195882 0.980627i \(-0.562757\pi\)
0.872101 + 0.489326i \(0.162757\pi\)
\(150\) 0 0
\(151\) 1.35621 4.17399i 0.110367 0.339674i −0.880586 0.473887i \(-0.842851\pi\)
0.990953 + 0.134213i \(0.0428505\pi\)
\(152\) 0 0
\(153\) 23.9552 1.93666
\(154\) 0 0
\(155\) 6.15481 0.494366
\(156\) 0 0
\(157\) 6.85433 21.0955i 0.547035 1.68360i −0.169066 0.985605i \(-0.554075\pi\)
0.716101 0.697996i \(-0.245925\pi\)
\(158\) 0 0
\(159\) −19.5377 + 14.1950i −1.54944 + 1.12574i
\(160\) 0 0
\(161\) −0.763932 2.35114i −0.0602063 0.185296i
\(162\) 0 0
\(163\) −15.9621 11.5971i −1.25025 0.908356i −0.252009 0.967725i \(-0.581091\pi\)
−0.998236 + 0.0593688i \(0.981091\pi\)
\(164\) 0 0
\(165\) −3.28586 + 17.7027i −0.255804 + 1.37816i
\(166\) 0 0
\(167\) 0.800035 + 0.581259i 0.0619085 + 0.0449792i 0.618309 0.785935i \(-0.287818\pi\)
−0.556401 + 0.830914i \(0.687818\pi\)
\(168\) 0 0
\(169\) 5.49380 + 16.9082i 0.422600 + 1.30063i
\(170\) 0 0
\(171\) −23.4731 + 17.0542i −1.79504 + 1.30417i
\(172\) 0 0
\(173\) −5.40772 + 16.6433i −0.411141 + 1.26536i 0.504516 + 0.863403i \(0.331671\pi\)
−0.915657 + 0.401961i \(0.868329\pi\)
\(174\) 0 0
\(175\) −0.644397 −0.0487118
\(176\) 0 0
\(177\) −9.41506 −0.707679
\(178\) 0 0
\(179\) −0.881320 + 2.71242i −0.0658730 + 0.202736i −0.978575 0.205889i \(-0.933992\pi\)
0.912702 + 0.408625i \(0.133992\pi\)
\(180\) 0 0
\(181\) 1.70101 1.23586i 0.126435 0.0918605i −0.522770 0.852474i \(-0.675102\pi\)
0.649206 + 0.760613i \(0.275102\pi\)
\(182\) 0 0
\(183\) −7.16075 22.0385i −0.529338 1.62913i
\(184\) 0 0
\(185\) 2.50893 + 1.82285i 0.184460 + 0.134018i
\(186\) 0 0
\(187\) −12.5379 + 1.64726i −0.916860 + 0.120460i
\(188\) 0 0
\(189\) −2.85689 2.07565i −0.207808 0.150981i
\(190\) 0 0
\(191\) −5.29073 16.2832i −0.382824 1.17821i −0.938047 0.346509i \(-0.887367\pi\)
0.555223 0.831702i \(-0.312633\pi\)
\(192\) 0 0
\(193\) −16.2846 + 11.8314i −1.17219 + 0.851645i −0.991269 0.131853i \(-0.957907\pi\)
−0.180919 + 0.983498i \(0.557907\pi\)
\(194\) 0 0
\(195\) −9.30688 + 28.6436i −0.666479 + 2.05121i
\(196\) 0 0
\(197\) 12.5589 0.894786 0.447393 0.894337i \(-0.352352\pi\)
0.447393 + 0.894337i \(0.352352\pi\)
\(198\) 0 0
\(199\) −3.32962 −0.236031 −0.118015 0.993012i \(-0.537653\pi\)
−0.118015 + 0.993012i \(0.537653\pi\)
\(200\) 0 0
\(201\) 1.10487 3.40044i 0.0779316 0.239849i
\(202\) 0 0
\(203\) −0.605270 + 0.439755i −0.0424817 + 0.0308647i
\(204\) 0 0
\(205\) −0.816647 2.51338i −0.0570371 0.175542i
\(206\) 0 0
\(207\) 35.5911 + 25.8585i 2.47375 + 1.79729i
\(208\) 0 0
\(209\) 11.1128 10.5401i 0.768691 0.729073i
\(210\) 0 0
\(211\) 19.4927 + 14.1623i 1.34194 + 0.974973i 0.999370 + 0.0354791i \(0.0112957\pi\)
0.342565 + 0.939494i \(0.388704\pi\)
\(212\) 0 0
\(213\) −2.23096 6.86620i −0.152863 0.470464i
\(214\) 0 0
\(215\) 5.66481 4.11573i 0.386337 0.280690i
\(216\) 0 0
\(217\) 0.376863 1.15986i 0.0255831 0.0787367i
\(218\) 0 0
\(219\) 11.8954 0.803817
\(220\) 0 0
\(221\) −21.1527 −1.42289
\(222\) 0 0
\(223\) 0.163537 0.503315i 0.0109512 0.0337044i −0.945432 0.325821i \(-0.894359\pi\)
0.956383 + 0.292116i \(0.0943594\pi\)
\(224\) 0 0
\(225\) 9.27732 6.74037i 0.618488 0.449358i
\(226\) 0 0
\(227\) −3.91835 12.0594i −0.260070 0.800412i −0.992788 0.119881i \(-0.961749\pi\)
0.732719 0.680532i \(-0.238251\pi\)
\(228\) 0 0
\(229\) 4.93708 + 3.58700i 0.326251 + 0.237035i 0.738838 0.673883i \(-0.235375\pi\)
−0.412587 + 0.910918i \(0.635375\pi\)
\(230\) 0 0
\(231\) 3.13486 + 1.70316i 0.206258 + 0.112060i
\(232\) 0 0
\(233\) 2.01513 + 1.46408i 0.132016 + 0.0959149i 0.651833 0.758362i \(-0.274000\pi\)
−0.519818 + 0.854277i \(0.674000\pi\)
\(234\) 0 0
\(235\) −0.666531 2.05137i −0.0434797 0.133817i
\(236\) 0 0
\(237\) −10.1291 + 7.35919i −0.657953 + 0.478031i
\(238\) 0 0
\(239\) 6.91215 21.2734i 0.447110 1.37606i −0.433044 0.901373i \(-0.642560\pi\)
0.880153 0.474689i \(-0.157440\pi\)
\(240\) 0 0
\(241\) −24.1025 −1.55258 −0.776288 0.630378i \(-0.782900\pi\)
−0.776288 + 0.630378i \(0.782900\pi\)
\(242\) 0 0
\(243\) 5.41432 0.347329
\(244\) 0 0
\(245\) −3.78561 + 11.6509i −0.241854 + 0.744349i
\(246\) 0 0
\(247\) 20.7270 15.0591i 1.31883 0.958186i
\(248\) 0 0
\(249\) 0.770498 + 2.37135i 0.0488283 + 0.150278i
\(250\) 0 0
\(251\) 5.60736 + 4.07399i 0.353933 + 0.257148i 0.750517 0.660851i \(-0.229804\pi\)
−0.396584 + 0.917999i \(0.629804\pi\)
\(252\) 0 0
\(253\) −20.4061 11.0866i −1.28292 0.697009i
\(254\) 0 0
\(255\) −16.7456 12.1664i −1.04865 0.761889i
\(256\) 0 0
\(257\) −4.52799 13.9357i −0.282448 0.869286i −0.987152 0.159784i \(-0.948920\pi\)
0.704704 0.709501i \(-0.251080\pi\)
\(258\) 0 0
\(259\) 0.497136 0.361190i 0.0308905 0.0224433i
\(260\) 0 0
\(261\) 4.11420 12.6622i 0.254663 0.783772i
\(262\) 0 0
\(263\) −22.9868 −1.41742 −0.708712 0.705497i \(-0.750724\pi\)
−0.708712 + 0.705497i \(0.750724\pi\)
\(264\) 0 0
\(265\) 14.1233 0.867585
\(266\) 0 0
\(267\) −1.81691 + 5.59186i −0.111193 + 0.342216i
\(268\) 0 0
\(269\) 4.48828 3.26093i 0.273655 0.198822i −0.442490 0.896773i \(-0.645905\pi\)
0.716145 + 0.697951i \(0.245905\pi\)
\(270\) 0 0
\(271\) −4.18270 12.8730i −0.254081 0.781980i −0.994009 0.109295i \(-0.965141\pi\)
0.739929 0.672685i \(-0.234859\pi\)
\(272\) 0 0
\(273\) 4.82798 + 3.50773i 0.292203 + 0.212298i
\(274\) 0 0
\(275\) −4.39214 + 4.16578i −0.264856 + 0.251206i
\(276\) 0 0
\(277\) 2.39473 + 1.73987i 0.143885 + 0.104539i 0.657399 0.753542i \(-0.271657\pi\)
−0.513514 + 0.858081i \(0.671657\pi\)
\(278\) 0 0
\(279\) 6.70648 + 20.6404i 0.401507 + 1.23571i
\(280\) 0 0
\(281\) 7.25120 5.26830i 0.432570 0.314281i −0.350106 0.936710i \(-0.613854\pi\)
0.782676 + 0.622430i \(0.213854\pi\)
\(282\) 0 0
\(283\) 5.57487 17.1577i 0.331392 1.01992i −0.637081 0.770797i \(-0.719858\pi\)
0.968472 0.249121i \(-0.0801417\pi\)
\(284\) 0 0
\(285\) 25.0701 1.48503
\(286\) 0 0
\(287\) −0.523646 −0.0309099
\(288\) 0 0
\(289\) −0.760976 + 2.34204i −0.0447633 + 0.137767i
\(290\) 0 0
\(291\) 23.3613 16.9730i 1.36946 0.994973i
\(292\) 0 0
\(293\) 8.54122 + 26.2872i 0.498984 + 1.53571i 0.810655 + 0.585524i \(0.199111\pi\)
−0.311671 + 0.950190i \(0.600889\pi\)
\(294\) 0 0
\(295\) 4.45450 + 3.23638i 0.259351 + 0.188429i
\(296\) 0 0
\(297\) −32.8905 + 4.32126i −1.90850 + 0.250745i
\(298\) 0 0
\(299\) −31.4274 22.8333i −1.81749 1.32048i
\(300\) 0 0
\(301\) −0.428742 1.31953i −0.0247123 0.0760566i
\(302\) 0 0
\(303\) 35.5075 25.7977i 2.03986 1.48204i
\(304\) 0 0
\(305\) −4.18771 + 12.8885i −0.239788 + 0.737991i
\(306\) 0 0
\(307\) 0.662166 0.0377918 0.0188959 0.999821i \(-0.493985\pi\)
0.0188959 + 0.999821i \(0.493985\pi\)
\(308\) 0 0
\(309\) 24.4520 1.39102
\(310\) 0 0
\(311\) −4.03889 + 12.4304i −0.229024 + 0.704864i 0.768834 + 0.639449i \(0.220837\pi\)
−0.997858 + 0.0654157i \(0.979163\pi\)
\(312\) 0 0
\(313\) −16.0289 + 11.6457i −0.906006 + 0.658252i −0.940002 0.341170i \(-0.889177\pi\)
0.0339952 + 0.999422i \(0.489177\pi\)
\(314\) 0 0
\(315\) 1.22136 + 3.75894i 0.0688156 + 0.211793i
\(316\) 0 0
\(317\) 15.9693 + 11.6024i 0.896924 + 0.651653i 0.937674 0.347516i \(-0.112975\pi\)
−0.0407503 + 0.999169i \(0.512975\pi\)
\(318\) 0 0
\(319\) −1.28262 + 6.91016i −0.0718127 + 0.386895i
\(320\) 0 0
\(321\) −11.2760 8.19249i −0.629365 0.457260i
\(322\) 0 0
\(323\) 5.44106 + 16.7459i 0.302749 + 0.931764i
\(324\) 0 0
\(325\) −8.19198 + 5.95182i −0.454409 + 0.330148i
\(326\) 0 0
\(327\) −19.4508 + 59.8634i −1.07563 + 3.31045i
\(328\) 0 0
\(329\) −0.427390 −0.0235628
\(330\) 0 0
\(331\) 21.0860 1.15899 0.579494 0.814976i \(-0.303250\pi\)
0.579494 + 0.814976i \(0.303250\pi\)
\(332\) 0 0
\(333\) −3.37918 + 10.4000i −0.185178 + 0.569919i
\(334\) 0 0
\(335\) −1.69163 + 1.22904i −0.0924236 + 0.0671496i
\(336\) 0 0
\(337\) −0.428343 1.31830i −0.0233333 0.0718126i 0.938712 0.344703i \(-0.112020\pi\)
−0.962045 + 0.272890i \(0.912020\pi\)
\(338\) 0 0
\(339\) −21.7037 15.7687i −1.17878 0.856437i
\(340\) 0 0
\(341\) −4.92942 10.3418i −0.266943 0.560039i
\(342\) 0 0
\(343\) 3.96320 + 2.87944i 0.213993 + 0.155475i
\(344\) 0 0
\(345\) −11.7465 36.1521i −0.632411 1.94636i
\(346\) 0 0
\(347\) −15.4653 + 11.2362i −0.830220 + 0.603190i −0.919622 0.392805i \(-0.871505\pi\)
0.0894013 + 0.995996i \(0.471505\pi\)
\(348\) 0 0
\(349\) 6.40170 19.7024i 0.342675 1.05464i −0.620142 0.784490i \(-0.712925\pi\)
0.962817 0.270155i \(-0.0870750\pi\)
\(350\) 0 0
\(351\) −55.4898 −2.96183
\(352\) 0 0
\(353\) 5.09091 0.270962 0.135481 0.990780i \(-0.456742\pi\)
0.135481 + 0.990780i \(0.456742\pi\)
\(354\) 0 0
\(355\) −1.30470 + 4.01546i −0.0692463 + 0.213118i
\(356\) 0 0
\(357\) −3.31808 + 2.41073i −0.175611 + 0.127589i
\(358\) 0 0
\(359\) −1.27450 3.92251i −0.0672655 0.207022i 0.911774 0.410692i \(-0.134713\pi\)
−0.979040 + 0.203670i \(0.934713\pi\)
\(360\) 0 0
\(361\) −1.88197 1.36733i −0.0990508 0.0719646i
\(362\) 0 0
\(363\) 32.3771 8.65705i 1.69936 0.454377i
\(364\) 0 0
\(365\) −5.62801 4.08899i −0.294584 0.214028i
\(366\) 0 0
\(367\) 11.2797 + 34.7153i 0.588795 + 1.81212i 0.583464 + 0.812139i \(0.301697\pi\)
0.00533096 + 0.999986i \(0.498303\pi\)
\(368\) 0 0
\(369\) 7.53889 5.47732i 0.392459 0.285138i
\(370\) 0 0
\(371\) 0.864775 2.66150i 0.0448969 0.138178i
\(372\) 0 0
\(373\) −5.01741 −0.259792 −0.129896 0.991528i \(-0.541464\pi\)
−0.129896 + 0.991528i \(0.541464\pi\)
\(374\) 0 0
\(375\) −37.0522 −1.91337
\(376\) 0 0
\(377\) −3.63289 + 11.1809i −0.187103 + 0.575845i
\(378\) 0 0
\(379\) −16.3812 + 11.9017i −0.841447 + 0.611347i −0.922774 0.385340i \(-0.874084\pi\)
0.0813276 + 0.996687i \(0.474084\pi\)
\(380\) 0 0
\(381\) 16.7520 + 51.5573i 0.858229 + 2.64136i
\(382\) 0 0
\(383\) 7.60736 + 5.52707i 0.388718 + 0.282420i 0.764930 0.644113i \(-0.222774\pi\)
−0.376212 + 0.926534i \(0.622774\pi\)
\(384\) 0 0
\(385\) −0.897724 1.88340i −0.0457522 0.0959870i
\(386\) 0 0
\(387\) 19.9748 + 14.5126i 1.01538 + 0.737715i
\(388\) 0 0
\(389\) 2.09040 + 6.43358i 0.105987 + 0.326196i 0.989961 0.141341i \(-0.0451415\pi\)
−0.883974 + 0.467537i \(0.845141\pi\)
\(390\) 0 0
\(391\) 21.5988 15.6924i 1.09230 0.793600i
\(392\) 0 0
\(393\) 17.2847 53.1967i 0.871896 2.68342i
\(394\) 0 0
\(395\) 7.32200 0.368410
\(396\) 0 0
\(397\) −5.18919 −0.260438 −0.130219 0.991485i \(-0.541568\pi\)
−0.130219 + 0.991485i \(0.541568\pi\)
\(398\) 0 0
\(399\) 1.53506 4.72442i 0.0768490 0.236517i
\(400\) 0 0
\(401\) −4.76448 + 3.46160i −0.237927 + 0.172864i −0.700359 0.713791i \(-0.746977\pi\)
0.462432 + 0.886655i \(0.346977\pi\)
\(402\) 0 0
\(403\) −5.92190 18.2257i −0.294991 0.907888i
\(404\) 0 0
\(405\) −16.7584 12.1757i −0.832730 0.605014i
\(406\) 0 0
\(407\) 1.05347 5.67563i 0.0522186 0.281330i
\(408\) 0 0
\(409\) 27.9425 + 20.3014i 1.38167 + 1.00384i 0.996722 + 0.0808983i \(0.0257789\pi\)
0.384943 + 0.922940i \(0.374221\pi\)
\(410\) 0 0
\(411\) −12.6892 39.0535i −0.625914 1.92637i
\(412\) 0 0
\(413\) 0.882642 0.641277i 0.0434320 0.0315552i
\(414\) 0 0
\(415\) 0.450599 1.38680i 0.0221190 0.0680753i
\(416\) 0 0
\(417\) 43.4789 2.12917
\(418\) 0 0
\(419\) −7.32141 −0.357674 −0.178837 0.983879i \(-0.557233\pi\)
−0.178837 + 0.983879i \(0.557233\pi\)
\(420\) 0 0
\(421\) 10.1601 31.2694i 0.495171 1.52398i −0.321519 0.946903i \(-0.604194\pi\)
0.816690 0.577076i \(-0.195806\pi\)
\(422\) 0 0
\(423\) 6.15309 4.47048i 0.299174 0.217362i
\(424\) 0 0
\(425\) −2.15048 6.61849i −0.104313 0.321044i
\(426\) 0 0
\(427\) 2.17239 + 1.57833i 0.105129 + 0.0763810i
\(428\) 0 0
\(429\) 55.5831 7.30268i 2.68358 0.352577i
\(430\) 0 0
\(431\) 4.21992 + 3.06595i 0.203267 + 0.147682i 0.684762 0.728767i \(-0.259906\pi\)
−0.481495 + 0.876449i \(0.659906\pi\)
\(432\) 0 0
\(433\) 3.40789 + 10.4884i 0.163773 + 0.504041i 0.998944 0.0459495i \(-0.0146313\pi\)
−0.835171 + 0.549990i \(0.814631\pi\)
\(434\) 0 0
\(435\) −9.30688 + 6.76184i −0.446231 + 0.324206i
\(436\) 0 0
\(437\) −9.99234 + 30.7533i −0.477998 + 1.47113i
\(438\) 0 0
\(439\) 22.5808 1.07772 0.538862 0.842394i \(-0.318855\pi\)
0.538862 + 0.842394i \(0.318855\pi\)
\(440\) 0 0
\(441\) −43.1968 −2.05699
\(442\) 0 0
\(443\) −10.9139 + 33.5895i −0.518534 + 1.59589i 0.258223 + 0.966085i \(0.416863\pi\)
−0.776758 + 0.629800i \(0.783137\pi\)
\(444\) 0 0
\(445\) 2.78180 2.02110i 0.131870 0.0958091i
\(446\) 0 0
\(447\) −9.60607 29.5644i −0.454351 1.39835i
\(448\) 0 0
\(449\) −29.9820 21.7832i −1.41494 1.02801i −0.992581 0.121584i \(-0.961203\pi\)
−0.422358 0.906429i \(-0.638797\pi\)
\(450\) 0 0
\(451\) −3.56912 + 3.38517i −0.168063 + 0.159401i
\(452\) 0 0
\(453\) −10.8179 7.85967i −0.508269 0.369279i
\(454\) 0 0
\(455\) −1.07847 3.31919i −0.0505595 0.155606i
\(456\) 0 0
\(457\) −0.285580 + 0.207486i −0.0133589 + 0.00970579i −0.594445 0.804137i \(-0.702628\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(458\) 0 0
\(459\) 11.7847 36.2694i 0.550061 1.69291i
\(460\) 0 0
\(461\) 12.2449 0.570303 0.285151 0.958482i \(-0.407956\pi\)
0.285151 + 0.958482i \(0.407956\pi\)
\(462\) 0 0
\(463\) 20.9578 0.973992 0.486996 0.873404i \(-0.338093\pi\)
0.486996 + 0.873404i \(0.338093\pi\)
\(464\) 0 0
\(465\) 5.79479 17.8345i 0.268727 0.827057i
\(466\) 0 0
\(467\) −23.9281 + 17.3848i −1.10726 + 0.804473i −0.982230 0.187680i \(-0.939903\pi\)
−0.125031 + 0.992153i \(0.539903\pi\)
\(468\) 0 0
\(469\) 0.128031 + 0.394039i 0.00591193 + 0.0181951i
\(470\) 0 0
\(471\) −54.6740 39.7230i −2.51924 1.83034i
\(472\) 0 0
\(473\) −11.4525 6.22214i −0.526588 0.286094i
\(474\) 0 0
\(475\) 6.81904 + 4.95433i 0.312879 + 0.227320i
\(476\) 0 0
\(477\) 15.3892 + 47.3630i 0.704621 + 2.16860i
\(478\) 0 0
\(479\) 4.71340 3.42449i 0.215361 0.156469i −0.474875 0.880053i \(-0.657507\pi\)
0.690236 + 0.723584i \(0.257507\pi\)
\(480\) 0 0
\(481\) 2.98385 9.18336i 0.136052 0.418725i
\(482\) 0 0
\(483\) −7.53204 −0.342720
\(484\) 0 0
\(485\) −16.8872 −0.766808
\(486\) 0 0
\(487\) 9.56462 29.4369i 0.433414 1.33391i −0.461288 0.887250i \(-0.652613\pi\)
0.894703 0.446662i \(-0.147387\pi\)
\(488\) 0 0
\(489\) −48.6328 + 35.3338i −2.19925 + 1.59785i
\(490\) 0 0
\(491\) 3.30431 + 10.1696i 0.149122 + 0.458949i 0.997518 0.0704125i \(-0.0224316\pi\)
−0.848396 + 0.529361i \(0.822432\pi\)
\(492\) 0 0
\(493\) −6.53655 4.74908i −0.294391 0.213888i
\(494\) 0 0
\(495\) 32.6248 + 17.7250i 1.46637 + 0.796679i
\(496\) 0 0
\(497\) 0.676818 + 0.491737i 0.0303595 + 0.0220574i
\(498\) 0 0
\(499\) 7.93548 + 24.4229i 0.355241 + 1.09332i 0.955870 + 0.293791i \(0.0949169\pi\)
−0.600629 + 0.799528i \(0.705083\pi\)
\(500\) 0 0
\(501\) 2.43753 1.77097i 0.108901 0.0791210i
\(502\) 0 0
\(503\) −5.33277 + 16.4126i −0.237777 + 0.731801i 0.758964 + 0.651132i \(0.225706\pi\)
−0.996741 + 0.0806690i \(0.974294\pi\)
\(504\) 0 0
\(505\) −25.6674 −1.14218
\(506\) 0 0
\(507\) 54.1666 2.40562
\(508\) 0 0
\(509\) 10.7918 33.2137i 0.478337 1.47217i −0.363067 0.931763i \(-0.618270\pi\)
0.841404 0.540407i \(-0.181730\pi\)
\(510\) 0 0
\(511\) −1.11517 + 0.810218i −0.0493322 + 0.0358419i
\(512\) 0 0
\(513\) 14.2735 + 43.9293i 0.630190 + 1.93953i
\(514\) 0 0
\(515\) −11.5688 8.40526i −0.509784 0.370380i
\(516\) 0 0
\(517\) −2.91304 + 2.76291i −0.128116 + 0.121513i
\(518\) 0 0
\(519\) 43.1350 + 31.3394i 1.89342 + 1.37565i
\(520\) 0 0
\(521\) −2.46282 7.57979i −0.107898 0.332076i 0.882502 0.470310i \(-0.155858\pi\)
−0.990400 + 0.138233i \(0.955858\pi\)
\(522\) 0 0
\(523\) −18.4741 + 13.4223i −0.807818 + 0.586914i −0.913197 0.407518i \(-0.866394\pi\)
0.105379 + 0.994432i \(0.466394\pi\)
\(524\) 0 0
\(525\) −0.606703 + 1.86724i −0.0264787 + 0.0814931i
\(526\) 0 0
\(527\) 13.1704 0.573713
\(528\) 0 0
\(529\) 26.0293 1.13171
\(530\) 0 0
\(531\) −5.99958 + 18.4648i −0.260360 + 0.801305i
\(532\) 0 0
\(533\) −6.65692 + 4.83654i −0.288343 + 0.209494i
\(534\) 0 0
\(535\) 2.51882 + 7.75215i 0.108898 + 0.335154i
\(536\) 0 0
\(537\) 7.02991 + 5.10753i 0.303363 + 0.220406i
\(538\) 0 0
\(539\) 22.6087 2.97040i 0.973824 0.127944i
\(540\) 0 0
\(541\) −32.3265 23.4866i −1.38983 1.00977i −0.995885 0.0906312i \(-0.971112\pi\)
−0.393941 0.919136i \(-0.628888\pi\)
\(542\) 0 0
\(543\) −1.97958 6.09251i −0.0849517 0.261455i
\(544\) 0 0
\(545\) 29.7804 21.6367i 1.27565 0.926816i
\(546\) 0 0
\(547\) −5.14156 + 15.8241i −0.219837 + 0.676590i 0.778937 + 0.627102i \(0.215759\pi\)
−0.998775 + 0.0494881i \(0.984241\pi\)
\(548\) 0 0
\(549\) −47.7850 −2.03942
\(550\) 0 0
\(551\) 9.78598 0.416897
\(552\) 0 0
\(553\) 0.448330 1.37982i 0.0190649 0.0586758i
\(554\) 0 0
\(555\) 7.64416 5.55381i 0.324476 0.235746i
\(556\) 0 0
\(557\) −6.10617 18.7929i −0.258727 0.796280i −0.993072 0.117504i \(-0.962511\pi\)
0.734346 0.678776i \(-0.237489\pi\)
\(558\) 0 0
\(559\) −17.6380 12.8148i −0.746008 0.542006i
\(560\) 0 0
\(561\) −7.03127 + 37.8814i −0.296860 + 1.59935i
\(562\) 0 0
\(563\) −19.6319 14.2634i −0.827385 0.601130i 0.0914334 0.995811i \(-0.470855\pi\)
−0.918818 + 0.394681i \(0.870855\pi\)
\(564\) 0 0
\(565\) 4.84816 + 14.9211i 0.203964 + 0.627736i
\(566\) 0 0
\(567\) −3.32061 + 2.41256i −0.139452 + 0.101318i
\(568\) 0 0
\(569\) −8.79195 + 27.0588i −0.368578 + 1.13437i 0.579133 + 0.815233i \(0.303391\pi\)
−0.947710 + 0.319132i \(0.896609\pi\)
\(570\) 0 0
\(571\) −26.9485 −1.12776 −0.563879 0.825858i \(-0.690692\pi\)
−0.563879 + 0.825858i \(0.690692\pi\)
\(572\) 0 0
\(573\) −52.1644 −2.17920
\(574\) 0 0
\(575\) 3.94929 12.1547i 0.164697 0.506884i
\(576\) 0 0
\(577\) −8.80048 + 6.39392i −0.366369 + 0.266183i −0.755704 0.654914i \(-0.772705\pi\)
0.389335 + 0.921096i \(0.372705\pi\)
\(578\) 0 0
\(579\) 18.9514 + 58.3264i 0.787594 + 2.42396i
\(580\) 0 0
\(581\) −0.233750 0.169829i −0.00969757 0.00704570i
\(582\) 0 0
\(583\) −11.3114 23.7310i −0.468470 0.982837i
\(584\) 0 0
\(585\) 50.2453 + 36.5053i 2.07739 + 1.50931i
\(586\) 0 0
\(587\) −8.35893 25.7261i −0.345010 1.06183i −0.961579 0.274530i \(-0.911478\pi\)
0.616569 0.787301i \(-0.288522\pi\)
\(588\) 0 0
\(589\) −12.9054 + 9.37631i −0.531757 + 0.386344i
\(590\) 0 0
\(591\) 11.8243 36.3914i 0.486387 1.49694i
\(592\) 0 0
\(593\) 6.72088 0.275993 0.137997 0.990433i \(-0.455934\pi\)
0.137997 + 0.990433i \(0.455934\pi\)
\(594\) 0 0
\(595\) 2.39854 0.0983306
\(596\) 0 0
\(597\) −3.13486 + 9.64809i −0.128301 + 0.394870i
\(598\) 0 0
\(599\) −22.6797 + 16.4777i −0.926666 + 0.673262i −0.945174 0.326566i \(-0.894108\pi\)
0.0185083 + 0.999829i \(0.494108\pi\)
\(600\) 0 0
\(601\) −5.29192 16.2868i −0.215862 0.664354i −0.999091 0.0426217i \(-0.986429\pi\)
0.783229 0.621733i \(-0.213571\pi\)
\(602\) 0 0
\(603\) −5.96489 4.33375i −0.242909 0.176484i
\(604\) 0 0
\(605\) −18.2943 7.03363i −0.743767 0.285958i
\(606\) 0 0
\(607\) −30.3423 22.0450i −1.23156 0.894777i −0.234550 0.972104i \(-0.575362\pi\)
−0.997006 + 0.0773268i \(0.975362\pi\)
\(608\) 0 0
\(609\) 0.704392 + 2.16790i 0.0285434 + 0.0878476i
\(610\) 0 0
\(611\) −5.43325 + 3.94749i −0.219806 + 0.159698i
\(612\) 0 0
\(613\) 8.22609 25.3173i 0.332249 1.02256i −0.635813 0.771843i \(-0.719335\pi\)
0.968061 0.250713i \(-0.0806650\pi\)
\(614\) 0 0
\(615\) −8.05179 −0.324680
\(616\) 0 0
\(617\) 13.8616 0.558047 0.279024 0.960284i \(-0.409989\pi\)
0.279024 + 0.960284i \(0.409989\pi\)
\(618\) 0 0
\(619\) 2.53801 7.81120i 0.102011 0.313959i −0.887006 0.461758i \(-0.847219\pi\)
0.989017 + 0.147799i \(0.0472189\pi\)
\(620\) 0 0
\(621\) 56.6599 41.1659i 2.27369 1.65193i
\(622\) 0 0
\(623\) −0.210541 0.647978i −0.00843514 0.0259607i
\(624\) 0 0
\(625\) 10.1473 + 7.37242i 0.405891 + 0.294897i
\(626\) 0 0
\(627\) −20.0788 42.1247i −0.801869 1.68230i
\(628\) 0 0
\(629\) 5.36876 + 3.90064i 0.214067 + 0.155529i
\(630\) 0 0
\(631\) 12.1950 + 37.5323i 0.485475 + 1.49414i 0.831292 + 0.555836i \(0.187602\pi\)
−0.345817 + 0.938302i \(0.612398\pi\)
\(632\) 0 0
\(633\) 59.3900 43.1494i 2.36054 1.71503i
\(634\) 0 0
\(635\) 9.79679 30.1514i 0.388774 1.19652i
\(636\) 0 0
\(637\) 38.1432 1.51129
\(638\) 0 0
\(639\) −14.8876 −0.588946
\(640\) 0 0
\(641\) −11.1686 + 34.3735i −0.441134 + 1.35767i 0.445534 + 0.895265i \(0.353014\pi\)
−0.886668 + 0.462406i \(0.846986\pi\)
\(642\) 0 0
\(643\) 19.4047 14.0983i 0.765245 0.555983i −0.135270 0.990809i \(-0.543190\pi\)
0.900515 + 0.434826i \(0.143190\pi\)
\(644\) 0 0
\(645\) −6.59251 20.2896i −0.259580 0.798904i
\(646\) 0 0
\(647\) 33.6307 + 24.4341i 1.32216 + 0.960605i 0.999903 + 0.0139526i \(0.00444138\pi\)
0.322257 + 0.946652i \(0.395559\pi\)
\(648\) 0 0
\(649\) 1.87039 10.0768i 0.0734192 0.395550i
\(650\) 0 0
\(651\) −3.00607 2.18404i −0.117817 0.0855992i
\(652\) 0 0
\(653\) 9.28600 + 28.5794i 0.363389 + 1.11840i 0.950984 + 0.309241i \(0.100075\pi\)
−0.587594 + 0.809156i \(0.699925\pi\)
\(654\) 0 0
\(655\) −26.4639 + 19.2272i −1.03403 + 0.751267i
\(656\) 0 0
\(657\) 7.58014 23.3293i 0.295730 0.910162i
\(658\) 0 0
\(659\) 25.2450 0.983405 0.491702 0.870763i \(-0.336375\pi\)
0.491702 + 0.870763i \(0.336375\pi\)
\(660\) 0 0
\(661\) 9.51852 0.370227 0.185114 0.982717i \(-0.440735\pi\)
0.185114 + 0.982717i \(0.440735\pi\)
\(662\) 0 0
\(663\) −19.9154 + 61.2933i −0.773450 + 2.38044i
\(664\) 0 0
\(665\) −2.35027 + 1.70757i −0.0911396 + 0.0662168i
\(666\) 0 0
\(667\) −4.58519 14.1118i −0.177539 0.546410i
\(668\) 0 0
\(669\) −1.30446 0.947747i −0.0504334 0.0366420i
\(670\) 0 0
\(671\) 25.0101 3.28591i 0.965505 0.126851i
\(672\) 0 0
\(673\) −9.13567 6.63745i −0.352154 0.255855i 0.397618 0.917551i \(-0.369837\pi\)
−0.749772 + 0.661696i \(0.769837\pi\)
\(674\) 0 0
\(675\) −5.64133 17.3622i −0.217135 0.668273i
\(676\) 0 0
\(677\) 28.7064 20.8564i 1.10328 0.801577i 0.121684 0.992569i \(-0.461170\pi\)
0.981592 + 0.190992i \(0.0611704\pi\)
\(678\) 0 0
\(679\) −1.03401 + 3.18236i −0.0396818 + 0.122128i
\(680\) 0 0
\(681\) −38.6332 −1.48043
\(682\) 0 0
\(683\) 24.8947 0.952569 0.476284 0.879291i \(-0.341983\pi\)
0.476284 + 0.879291i \(0.341983\pi\)
\(684\) 0 0
\(685\) −7.42085 + 22.8390i −0.283536 + 0.872635i
\(686\) 0 0
\(687\) 15.0422 10.9288i 0.573895 0.416959i
\(688\) 0 0
\(689\) −13.5888 41.8220i −0.517692 1.59329i
\(690\) 0 0
\(691\) 0.513361 + 0.372978i 0.0195292 + 0.0141888i 0.597507 0.801864i \(-0.296158\pi\)
−0.577978 + 0.816052i \(0.696158\pi\)
\(692\) 0 0
\(693\) 5.33788 5.06277i 0.202769 0.192319i
\(694\) 0 0
\(695\) −20.5709 14.9457i −0.780300 0.566921i
\(696\) 0 0
\(697\) −1.74751 5.37828i −0.0661916 0.203717i
\(698\) 0 0
\(699\) 6.13965 4.46072i 0.232223 0.168720i
\(700\) 0 0
\(701\) 5.39612 16.6076i 0.203809 0.627259i −0.795951 0.605361i \(-0.793029\pi\)
0.999760 0.0218985i \(-0.00697107\pi\)
\(702\) 0 0
\(703\) −8.03767 −0.303146
\(704\) 0 0
\(705\) −6.57171 −0.247505
\(706\) 0 0
\(707\) −1.57163 + 4.83697i −0.0591071 + 0.181913i
\(708\) 0 0
\(709\) −26.3781 + 19.1648i −0.990651 + 0.719750i −0.960064 0.279782i \(-0.909738\pi\)
−0.0305874 + 0.999532i \(0.509738\pi\)
\(710\) 0 0
\(711\) 7.97828 + 24.5546i 0.299209 + 0.920871i
\(712\) 0 0
\(713\) 19.5678 + 14.2168i 0.732819 + 0.532424i
\(714\) 0 0
\(715\) −28.8080 15.6514i −1.07736 0.585328i
\(716\) 0 0
\(717\) −55.1352 40.0581i −2.05906 1.49600i
\(718\) 0 0
\(719\) −10.8109 33.2726i −0.403180 1.24086i −0.922405 0.386223i \(-0.873780\pi\)
0.519226 0.854637i \(-0.326220\pi\)
\(720\) 0 0
\(721\) −2.29232 + 1.66547i −0.0853706 + 0.0620254i
\(722\) 0 0
\(723\) −22.6926 + 69.8407i −0.843947 + 2.59740i
\(724\) 0 0
\(725\) −3.86773 −0.143644
\(726\) 0 0
\(727\) −16.2644 −0.603214 −0.301607 0.953432i \(-0.597523\pi\)
−0.301607 + 0.953432i \(0.597523\pi\)
\(728\) 0 0
\(729\) −5.67991 + 17.4810i −0.210367 + 0.647443i
\(730\) 0 0
\(731\) 12.1219 8.80707i 0.448344 0.325741i
\(732\) 0 0
\(733\) 13.9308 + 42.8746i 0.514546 + 1.58361i 0.784106 + 0.620627i \(0.213122\pi\)
−0.269560 + 0.962984i \(0.586878\pi\)
\(734\) 0 0
\(735\) 30.1962 + 21.9388i 1.11380 + 0.809225i
\(736\) 0 0
\(737\) 3.41996 + 1.85806i 0.125976 + 0.0684425i
\(738\) 0 0
\(739\) 11.8506 + 8.60999i 0.435933 + 0.316724i 0.784017 0.620740i \(-0.213168\pi\)
−0.348084 + 0.937463i \(0.613168\pi\)
\(740\) 0 0
\(741\) −24.1214 74.2380i −0.886122 2.72720i
\(742\) 0 0
\(743\) −3.42499 + 2.48840i −0.125651 + 0.0912906i −0.648836 0.760929i \(-0.724744\pi\)
0.523185 + 0.852219i \(0.324744\pi\)
\(744\) 0 0
\(745\) −5.61777 + 17.2897i −0.205819 + 0.633446i
\(746\) 0 0
\(747\) 5.14168 0.188124
\(748\) 0 0
\(749\) 1.61511 0.0590148
\(750\) 0 0
\(751\) −7.05755 + 21.7209i −0.257534 + 0.792607i 0.735786 + 0.677214i \(0.236813\pi\)
−0.993320 + 0.115393i \(0.963187\pi\)
\(752\) 0 0
\(753\) 17.0844 12.4125i 0.622589 0.452337i
\(754\) 0 0
\(755\) 2.41649 + 7.43721i 0.0879453 + 0.270668i
\(756\) 0 0
\(757\) 25.0773 + 18.2197i 0.911450 + 0.662207i 0.941381 0.337345i \(-0.109529\pi\)
−0.0299310 + 0.999552i \(0.509529\pi\)
\(758\) 0 0
\(759\) −51.3376 + 48.6918i −1.86344 + 1.76740i
\(760\) 0 0
\(761\) 23.3917 + 16.9951i 0.847948 + 0.616071i 0.924580 0.380989i \(-0.124416\pi\)
−0.0766312 + 0.997060i \(0.524416\pi\)
\(762\) 0 0
\(763\) −2.25393 6.93690i −0.0815979 0.251133i
\(764\) 0 0
\(765\) −34.5316 + 25.0887i −1.24849 + 0.907082i
\(766\) 0 0
\(767\) 5.29770 16.3046i 0.191289 0.588726i
\(768\) 0 0
\(769\) 5.37741 0.193914 0.0969571 0.995289i \(-0.469089\pi\)
0.0969571 + 0.995289i \(0.469089\pi\)
\(770\) 0 0
\(771\) −44.6440 −1.60782
\(772\) 0 0
\(773\) 13.7820 42.4167i 0.495705 1.52562i −0.320150 0.947367i \(-0.603733\pi\)
0.815855 0.578256i \(-0.196267\pi\)
\(774\) 0 0
\(775\) 5.10062 3.70581i 0.183220 0.133117i
\(776\) 0 0
\(777\) −0.578549 1.78059i −0.0207553 0.0638784i
\(778\) 0 0
\(779\) 5.54125 + 4.02596i 0.198536 + 0.144245i
\(780\) 0 0
\(781\) 7.79202 1.02374i 0.278820 0.0366323i
\(782\) 0 0
\(783\) −17.1473 12.4582i −0.612794 0.445221i
\(784\) 0 0
\(785\) 12.2130 + 37.5879i 0.435902 + 1.34157i
\(786\) 0 0
\(787\) 33.6779 24.4684i 1.20049 0.872206i 0.206156 0.978519i \(-0.433905\pi\)
0.994333 + 0.106313i \(0.0339047\pi\)
\(788\) 0 0
\(789\) −21.6422 + 66.6078i −0.770482 + 2.37130i
\(790\) 0 0
\(791\) 3.10871 0.110533
\(792\) 0 0
\(793\) 42.1947 1.49838
\(794\) 0 0
\(795\) 13.2971 40.9244i 0.471601 1.45144i
\(796\) 0 0
\(797\) 4.07959 2.96400i 0.144507 0.104990i −0.513183 0.858279i \(-0.671534\pi\)
0.657690 + 0.753289i \(0.271534\pi\)
\(798\) 0 0
\(799\) −1.42628 4.38965i −0.0504583 0.155295i
\(800\) 0 0
\(801\) 9.80897 + 7.12663i 0.346583 + 0.251807i
\(802\) 0 0
\(803\) −2.36313 + 12.7315i −0.0833932 + 0.449285i
\(804\) 0 0
\(805\) 3.56360 + 2.58911i 0.125600 + 0.0912540i
\(806\) 0 0
\(807\) −5.22330 16.0757i −0.183869 0.565891i
\(808\) 0 0
\(809\) −22.6592 + 16.4628i −0.796654 + 0.578803i −0.909931 0.414761i \(-0.863865\pi\)
0.113277 + 0.993563i \(0.463865\pi\)
\(810\) 0 0
\(811\) −10.3208 + 31.7642i −0.362413 + 1.11539i 0.589172 + 0.808008i \(0.299454\pi\)
−0.951585 + 0.307386i \(0.900546\pi\)
\(812\) 0 0
\(813\) −41.2396 −1.44634
\(814\) 0 0
\(815\) 35.1552 1.23143
\(816\) 0 0
\(817\) −5.60801 + 17.2597i −0.196199 + 0.603839i
\(818\) 0 0
\(819\) 9.95591 7.23339i 0.347888 0.252755i
\(820\) 0 0
\(821\) 9.37955 + 28.8673i 0.327349 + 1.00748i 0.970369 + 0.241627i \(0.0776809\pi\)
−0.643021 + 0.765849i \(0.722319\pi\)
\(822\) 0 0
\(823\) −5.46823 3.97290i −0.190610 0.138487i 0.488387 0.872627i \(-0.337585\pi\)
−0.678998 + 0.734140i \(0.737585\pi\)
\(824\) 0 0
\(825\) 7.93576 + 16.6490i 0.276288 + 0.579645i
\(826\) 0 0
\(827\) 26.5609 + 19.2976i 0.923614 + 0.671045i 0.944421 0.328739i \(-0.106623\pi\)
−0.0208068 + 0.999784i \(0.506623\pi\)
\(828\) 0 0
\(829\) 4.77520 + 14.6966i 0.165850 + 0.510433i 0.999098 0.0424663i \(-0.0135215\pi\)
−0.833248 + 0.552899i \(0.813522\pi\)
\(830\) 0 0
\(831\) 7.29620 5.30100i 0.253103 0.183890i
\(832\) 0 0
\(833\) −8.10067 + 24.9313i −0.280672 + 0.863819i
\(834\) 0 0
\(835\) −1.76202 −0.0609771
\(836\) 0 0
\(837\) 34.5499 1.19422
\(838\) 0 0
\(839\) 8.63951 26.5897i 0.298269 0.917978i −0.683835 0.729637i \(-0.739689\pi\)
0.982104 0.188341i \(-0.0603109\pi\)
\(840\) 0 0
\(841\) 19.8286 14.4063i 0.683745 0.496770i
\(842\) 0 0
\(843\) −8.43869 25.9716i −0.290644 0.894510i
\(844\) 0 0
\(845\) −25.6275 18.6195i −0.881614 0.640530i
\(846\) 0 0
\(847\) −2.44564 + 3.01685i −0.0840333 + 0.103660i
\(848\) 0 0
\(849\) −44.4683 32.3081i −1.52615 1.10881i
\(850\) 0 0
\(851\) 3.76602 + 11.5906i 0.129098 + 0.397321i
\(852\) 0 0
\(853\) −11.3899 + 8.27524i −0.389983 + 0.283339i −0.765448 0.643497i \(-0.777483\pi\)
0.375466 + 0.926836i \(0.377483\pi\)
\(854\) 0 0
\(855\) 15.9755 49.1675i 0.546351 1.68149i
\(856\) 0 0
\(857\) 26.4776 0.904457 0.452228 0.891902i \(-0.350629\pi\)
0.452228 + 0.891902i \(0.350629\pi\)
\(858\) 0 0
\(859\) −47.5614 −1.62277 −0.811387 0.584510i \(-0.801287\pi\)
−0.811387 + 0.584510i \(0.801287\pi\)
\(860\) 0 0
\(861\) −0.493016 + 1.51735i −0.0168019 + 0.0517110i
\(862\) 0 0
\(863\) −35.1250 + 25.5198i −1.19567 + 0.868704i −0.993852 0.110720i \(-0.964684\pi\)
−0.201817 + 0.979423i \(0.564684\pi\)
\(864\) 0 0
\(865\) −9.63547 29.6549i −0.327616 1.00830i
\(866\) 0 0
\(867\) 6.06997 + 4.41009i 0.206147 + 0.149775i
\(868\) 0 0
\(869\) −5.86422 12.3030i −0.198930 0.417350i
\(870\) 0 0
\(871\) 5.26707 + 3.82675i 0.178468 + 0.129664i
\(872\) 0 0
\(873\) −18.4008 56.6319i −0.622774 1.91670i
\(874\) 0 0
\(875\) 3.47357 2.52370i 0.117428 0.0853165i
\(876\) 0 0
\(877\) 4.05884 12.4918i 0.137057 0.421819i −0.858847 0.512232i \(-0.828819\pi\)
0.995904 + 0.0904129i \(0.0288187\pi\)
\(878\) 0 0
\(879\) 84.2128 2.84043
\(880\) 0 0
\(881\) −36.3388 −1.22429 −0.612143 0.790747i \(-0.709692\pi\)
−0.612143 + 0.790747i \(0.709692\pi\)
\(882\) 0 0
\(883\) 10.3944 31.9907i 0.349800 1.07657i −0.609163 0.793045i \(-0.708495\pi\)
0.958964 0.283529i \(-0.0915054\pi\)
\(884\) 0 0
\(885\) 13.5719 9.86053i 0.456213 0.331458i
\(886\) 0 0
\(887\) −10.8199 33.3001i −0.363295 1.11811i −0.951042 0.309062i \(-0.899985\pi\)
0.587747 0.809045i \(-0.300015\pi\)
\(888\) 0 0
\(889\) −5.08212 3.69238i −0.170449 0.123838i
\(890\) 0 0
\(891\) −7.03663 + 37.9102i −0.235736 + 1.27004i
\(892\) 0 0
\(893\) 4.52266 + 3.28591i 0.151345 + 0.109959i
\(894\) 0 0
\(895\) −1.57034 4.83299i −0.0524905 0.161549i
\(896\) 0 0
\(897\) −95.7521 + 69.5680i −3.19707 + 2.32281i
\(898\) 0 0
\(899\) 2.26196 6.96161i 0.0754407 0.232183i
\(900\) 0 0
\(901\) 30.2218 1.00683
\(902\) 0 0
\(903\) −4.22721 −0.140673
\(904\) 0 0
\(905\) −1.15768 + 3.56299i −0.0384827 + 0.118438i
\(906\) 0 0
\(907\) −41.9407 + 30.4717i −1.39262 + 1.01180i −0.397046 + 0.917799i \(0.629965\pi\)
−0.995572 + 0.0939979i \(0.970035\pi\)
\(908\) 0 0
\(909\) −27.9680 86.0766i −0.927639 2.85498i
\(910\) 0 0
\(911\) 23.9715 + 17.4163i 0.794212 + 0.577029i 0.909210 0.416337i \(-0.136686\pi\)
−0.114998 + 0.993366i \(0.536686\pi\)
\(912\) 0 0
\(913\) −2.69109 + 0.353564i −0.0890622 + 0.0117013i
\(914\) 0 0
\(915\) 33.4035 + 24.2691i 1.10429 + 0.802312i
\(916\) 0 0
\(917\) 2.00293 + 6.16437i 0.0661424 + 0.203566i
\(918\) 0 0
\(919\) 24.3567 17.6962i 0.803454 0.583743i −0.108472 0.994100i \(-0.534596\pi\)
0.911925 + 0.410356i \(0.134596\pi\)
\(920\) 0 0
\(921\) 0.623433 1.91873i 0.0205428 0.0632243i
\(922\) 0 0
\(923\) 13.1460 0.432704
\(924\) 0 0
\(925\) 3.17674 0.104451
\(926\) 0 0
\(927\) 15.5816 47.9553i 0.511767 1.57506i
\(928\) 0 0
\(929\) 41.3186 30.0197i 1.35562 0.984914i 0.356908 0.934140i \(-0.383831\pi\)
0.998710 0.0507745i \(-0.0161690\pi\)
\(930\) 0 0
\(931\) −9.81148 30.1966i −0.321558 0.989654i
\(932\) 0 0
\(933\) 32.2164 + 23.4066i 1.05472 + 0.766298i
\(934\) 0 0
\(935\) 16.3482 15.5056i 0.534644 0.507089i
\(936\) 0 0
\(937\) 6.75635 + 4.90878i 0.220720 + 0.160363i 0.692651 0.721273i \(-0.256443\pi\)
−0.471931 + 0.881636i \(0.656443\pi\)
\(938\) 0 0
\(939\) 18.6539 + 57.4107i 0.608746 + 1.87353i
\(940\) 0 0
\(941\) −43.1964 + 31.3840i −1.40816 + 1.02309i −0.414576 + 0.910015i \(0.636070\pi\)
−0.993586 + 0.113075i \(0.963930\pi\)
\(942\) 0 0
\(943\) 3.20925 9.87705i 0.104508 0.321641i
\(944\) 0 0
\(945\) 6.29208 0.204681
\(946\) 0 0
\(947\) −19.2532 −0.625646 −0.312823 0.949811i \(-0.601275\pi\)
−0.312823 + 0.949811i \(0.601275\pi\)
\(948\) 0 0
\(949\) −6.69335 + 20.6000i −0.217275 + 0.668705i
\(950\) 0 0
\(951\) 48.6548 35.3498i 1.57774 1.14630i
\(952\) 0 0
\(953\) −11.3253 34.8556i −0.366862 1.12908i −0.948807 0.315857i \(-0.897708\pi\)
0.581945 0.813228i \(-0.302292\pi\)
\(954\) 0 0
\(955\) 24.6803 + 17.9313i 0.798634 + 0.580242i
\(956\) 0 0
\(957\) 18.8157 + 10.2225i 0.608225 + 0.330448i
\(958\) 0 0
\(959\) 3.84960 + 2.79689i 0.124310 + 0.0903164i
\(960\) 0 0
\(961\) −5.89234 18.1348i −0.190076 0.584993i
\(962\) 0 0
\(963\) −23.2526 + 16.8940i −0.749303 + 0.544401i
\(964\) 0 0
\(965\) 11.0831 34.1101i 0.356776 1.09804i
\(966\) 0 0
\(967\) −45.6501 −1.46801 −0.734004 0.679146i \(-0.762351\pi\)
−0.734004 + 0.679146i \(0.762351\pi\)
\(968\) 0 0
\(969\) 53.6465 1.72337
\(970\) 0 0
\(971\) 14.2715 43.9232i 0.457995 1.40956i −0.409588 0.912270i \(-0.634328\pi\)
0.867583 0.497292i \(-0.165672\pi\)
\(972\) 0 0
\(973\) −4.07605 + 2.96143i −0.130672 + 0.0949390i
\(974\) 0 0
\(975\) 9.53354 + 29.3412i 0.305318 + 0.939671i
\(976\) 0 0
\(977\) −43.1572 31.3555i −1.38072 1.00315i −0.996812 0.0797806i \(-0.974578\pi\)
−0.383908 0.923371i \(-0.625422\pi\)
\(978\) 0 0
\(979\) −5.62395 3.05549i −0.179742 0.0976538i
\(980\) 0 0
\(981\) 105.009 + 76.2938i 3.35269 + 2.43587i
\(982\) 0 0
\(983\) 3.73470 + 11.4942i 0.119118 + 0.366609i 0.992784 0.119919i \(-0.0382634\pi\)
−0.873665 + 0.486527i \(0.838263\pi\)
\(984\) 0 0
\(985\) −18.1038 + 13.1532i −0.576834 + 0.419094i
\(986\) 0 0
\(987\) −0.402390 + 1.23843i −0.0128082 + 0.0394196i
\(988\) 0 0
\(989\) 27.5167 0.874981
\(990\) 0 0
\(991\) −36.0620 −1.14555 −0.572774 0.819714i \(-0.694133\pi\)
−0.572774 + 0.819714i \(0.694133\pi\)
\(992\) 0 0
\(993\) 19.8525 61.0998i 0.630001 1.93894i
\(994\) 0 0
\(995\) 4.79967 3.48716i 0.152160 0.110550i
\(996\) 0 0
\(997\) −2.88069 8.86586i −0.0912325 0.280785i 0.895021 0.446024i \(-0.147160\pi\)
−0.986254 + 0.165239i \(0.947160\pi\)
\(998\) 0 0
\(999\) 14.0838 + 10.2325i 0.445593 + 0.323742i
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 88.2.i.b.81.2 yes 8
3.2 odd 2 792.2.r.g.433.2 8
4.3 odd 2 176.2.m.d.81.1 8
8.3 odd 2 704.2.m.i.257.2 8
8.5 even 2 704.2.m.l.257.1 8
11.2 odd 10 968.2.i.t.753.1 8
11.3 even 5 inner 88.2.i.b.25.2 8
11.4 even 5 968.2.i.s.9.1 8
11.5 even 5 968.2.a.n.1.4 4
11.6 odd 10 968.2.a.m.1.4 4
11.7 odd 10 968.2.i.t.9.1 8
11.8 odd 10 968.2.i.p.729.2 8
11.9 even 5 968.2.i.s.753.1 8
11.10 odd 2 968.2.i.p.81.2 8
33.5 odd 10 8712.2.a.ce.1.2 4
33.14 odd 10 792.2.r.g.289.2 8
33.17 even 10 8712.2.a.cd.1.2 4
44.3 odd 10 176.2.m.d.113.1 8
44.27 odd 10 1936.2.a.bb.1.1 4
44.39 even 10 1936.2.a.bc.1.1 4
88.3 odd 10 704.2.m.i.641.2 8
88.5 even 10 7744.2.a.di.1.1 4
88.27 odd 10 7744.2.a.dr.1.4 4
88.61 odd 10 7744.2.a.dh.1.1 4
88.69 even 10 704.2.m.l.641.1 8
88.83 even 10 7744.2.a.ds.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.i.b.25.2 8 11.3 even 5 inner
88.2.i.b.81.2 yes 8 1.1 even 1 trivial
176.2.m.d.81.1 8 4.3 odd 2
176.2.m.d.113.1 8 44.3 odd 10
704.2.m.i.257.2 8 8.3 odd 2
704.2.m.i.641.2 8 88.3 odd 10
704.2.m.l.257.1 8 8.5 even 2
704.2.m.l.641.1 8 88.69 even 10
792.2.r.g.289.2 8 33.14 odd 10
792.2.r.g.433.2 8 3.2 odd 2
968.2.a.m.1.4 4 11.6 odd 10
968.2.a.n.1.4 4 11.5 even 5
968.2.i.p.81.2 8 11.10 odd 2
968.2.i.p.729.2 8 11.8 odd 10
968.2.i.s.9.1 8 11.4 even 5
968.2.i.s.753.1 8 11.9 even 5
968.2.i.t.9.1 8 11.7 odd 10
968.2.i.t.753.1 8 11.2 odd 10
1936.2.a.bb.1.1 4 44.27 odd 10
1936.2.a.bc.1.1 4 44.39 even 10
7744.2.a.dh.1.1 4 88.61 odd 10
7744.2.a.di.1.1 4 88.5 even 10
7744.2.a.dr.1.4 4 88.27 odd 10
7744.2.a.ds.1.4 4 88.83 even 10
8712.2.a.cd.1.2 4 33.17 even 10
8712.2.a.ce.1.2 4 33.5 odd 10