Properties

Label 882.4.g.k.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
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] = [882,4,Mod(361,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), 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: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.k.667.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.00000 + 12.1244i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.00000 + 12.1244i) q^{5} +8.00000 q^{8} +(14.0000 - 24.2487i) q^{10} +(-14.0000 + 24.2487i) q^{11} -18.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-37.0000 + 64.0859i) q^{17} +(40.0000 + 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(-56.0000 - 96.9948i) q^{23} +(-35.5000 + 61.4878i) q^{25} +(18.0000 + 31.1769i) q^{26} -190.000 q^{29} +(36.0000 - 62.3538i) q^{31} +(-16.0000 + 27.7128i) q^{32} +148.000 q^{34} +(173.000 + 299.645i) q^{37} +(80.0000 - 138.564i) q^{38} +(56.0000 + 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(-56.0000 - 96.9948i) q^{44} +(-112.000 + 193.990i) q^{46} +(-12.0000 - 20.7846i) q^{47} +142.000 q^{50} +(36.0000 - 62.3538i) q^{52} +(159.000 - 275.396i) q^{53} -392.000 q^{55} +(190.000 + 329.090i) q^{58} +(100.000 - 173.205i) q^{59} +(-99.0000 - 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-126.000 - 218.238i) q^{65} +(358.000 - 620.074i) q^{67} +(-148.000 - 256.344i) q^{68} -392.000 q^{71} +(269.000 - 465.922i) q^{73} +(346.000 - 599.290i) q^{74} -320.000 q^{76} +(-120.000 - 207.846i) q^{79} +(112.000 - 193.990i) q^{80} +(-162.000 - 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(412.000 + 713.605i) q^{86} +(-112.000 + 193.990i) q^{88} +(-405.000 - 701.481i) q^{89} +448.000 q^{92} +(-24.0000 + 41.5692i) q^{94} +(-560.000 + 969.948i) q^{95} -1354.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} + 14 q^{5} + 16 q^{8} + 28 q^{10} - 28 q^{11} - 36 q^{13} - 16 q^{16} - 74 q^{17} + 80 q^{19} - 112 q^{20} + 112 q^{22} - 112 q^{23} - 71 q^{25} + 36 q^{26} - 380 q^{29} + 72 q^{31} - 32 q^{32} + 296 q^{34} + 346 q^{37} + 160 q^{38} + 112 q^{40} + 324 q^{41} - 824 q^{43} - 112 q^{44} - 224 q^{46} - 24 q^{47} + 284 q^{50} + 72 q^{52} + 318 q^{53} - 784 q^{55} + 380 q^{58} + 200 q^{59} - 198 q^{61} - 288 q^{62} + 128 q^{64} - 252 q^{65} + 716 q^{67} - 296 q^{68} - 784 q^{71} + 538 q^{73} + 692 q^{74} - 640 q^{76} - 240 q^{79} + 224 q^{80} - 324 q^{82} - 2144 q^{83} - 2072 q^{85} + 824 q^{86} - 224 q^{88} - 810 q^{89} + 896 q^{92} - 48 q^{94} - 1120 q^{95} - 2708 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 7.00000 + 12.1244i 0.626099 + 1.08444i 0.988327 + 0.152346i \(0.0486828\pi\)
−0.362228 + 0.932089i \(0.617984\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 14.0000 24.2487i 0.442719 0.766812i
\(11\) −14.0000 + 24.2487i −0.383742 + 0.664660i −0.991594 0.129390i \(-0.958698\pi\)
0.607852 + 0.794050i \(0.292031\pi\)
\(12\) 0 0
\(13\) −18.0000 −0.384023 −0.192012 0.981393i \(-0.561501\pi\)
−0.192012 + 0.981393i \(0.561501\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −37.0000 + 64.0859i −0.527872 + 0.914301i 0.471600 + 0.881812i \(0.343676\pi\)
−0.999472 + 0.0324882i \(0.989657\pi\)
\(18\) 0 0
\(19\) 40.0000 + 69.2820i 0.482980 + 0.836547i 0.999809 0.0195422i \(-0.00622087\pi\)
−0.516829 + 0.856089i \(0.672888\pi\)
\(20\) −56.0000 −0.626099
\(21\) 0 0
\(22\) 56.0000 0.542693
\(23\) −56.0000 96.9948i −0.507687 0.879340i −0.999960 0.00889936i \(-0.997167\pi\)
0.492273 0.870441i \(-0.336166\pi\)
\(24\) 0 0
\(25\) −35.5000 + 61.4878i −0.284000 + 0.491902i
\(26\) 18.0000 + 31.1769i 0.135773 + 0.235165i
\(27\) 0 0
\(28\) 0 0
\(29\) −190.000 −1.21662 −0.608312 0.793698i \(-0.708153\pi\)
−0.608312 + 0.793698i \(0.708153\pi\)
\(30\) 0 0
\(31\) 36.0000 62.3538i 0.208574 0.361261i −0.742692 0.669634i \(-0.766451\pi\)
0.951266 + 0.308373i \(0.0997845\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 148.000 0.746523
\(35\) 0 0
\(36\) 0 0
\(37\) 173.000 + 299.645i 0.768676 + 1.33139i 0.938281 + 0.345874i \(0.112418\pi\)
−0.169605 + 0.985512i \(0.554249\pi\)
\(38\) 80.0000 138.564i 0.341519 0.591528i
\(39\) 0 0
\(40\) 56.0000 + 96.9948i 0.221359 + 0.383406i
\(41\) 162.000 0.617077 0.308538 0.951212i \(-0.400160\pi\)
0.308538 + 0.951212i \(0.400160\pi\)
\(42\) 0 0
\(43\) −412.000 −1.46115 −0.730575 0.682833i \(-0.760748\pi\)
−0.730575 + 0.682833i \(0.760748\pi\)
\(44\) −56.0000 96.9948i −0.191871 0.332330i
\(45\) 0 0
\(46\) −112.000 + 193.990i −0.358989 + 0.621787i
\(47\) −12.0000 20.7846i −0.0372421 0.0645053i 0.846804 0.531906i \(-0.178524\pi\)
−0.884046 + 0.467401i \(0.845191\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 142.000 0.401637
\(51\) 0 0
\(52\) 36.0000 62.3538i 0.0960058 0.166287i
\(53\) 159.000 275.396i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) −392.000 −0.961041
\(56\) 0 0
\(57\) 0 0
\(58\) 190.000 + 329.090i 0.430142 + 0.745027i
\(59\) 100.000 173.205i 0.220659 0.382193i −0.734349 0.678772i \(-0.762512\pi\)
0.955008 + 0.296579i \(0.0958458\pi\)
\(60\) 0 0
\(61\) −99.0000 171.473i −0.207798 0.359916i 0.743223 0.669044i \(-0.233296\pi\)
−0.951020 + 0.309128i \(0.899963\pi\)
\(62\) −144.000 −0.294968
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −126.000 218.238i −0.240437 0.416448i
\(66\) 0 0
\(67\) 358.000 620.074i 0.652786 1.13066i −0.329658 0.944100i \(-0.606933\pi\)
0.982444 0.186558i \(-0.0597332\pi\)
\(68\) −148.000 256.344i −0.263936 0.457150i
\(69\) 0 0
\(70\) 0 0
\(71\) −392.000 −0.655237 −0.327619 0.944810i \(-0.606246\pi\)
−0.327619 + 0.944810i \(0.606246\pi\)
\(72\) 0 0
\(73\) 269.000 465.922i 0.431289 0.747014i −0.565696 0.824614i \(-0.691392\pi\)
0.996985 + 0.0776001i \(0.0247257\pi\)
\(74\) 346.000 599.290i 0.543536 0.941432i
\(75\) 0 0
\(76\) −320.000 −0.482980
\(77\) 0 0
\(78\) 0 0
\(79\) −120.000 207.846i −0.170899 0.296006i 0.767835 0.640647i \(-0.221334\pi\)
−0.938735 + 0.344641i \(0.888001\pi\)
\(80\) 112.000 193.990i 0.156525 0.271109i
\(81\) 0 0
\(82\) −162.000 280.592i −0.218170 0.377881i
\(83\) −1072.00 −1.41768 −0.708839 0.705370i \(-0.750781\pi\)
−0.708839 + 0.705370i \(0.750781\pi\)
\(84\) 0 0
\(85\) −1036.00 −1.32200
\(86\) 412.000 + 713.605i 0.516594 + 0.894767i
\(87\) 0 0
\(88\) −112.000 + 193.990i −0.135673 + 0.234993i
\(89\) −405.000 701.481i −0.482359 0.835470i 0.517436 0.855722i \(-0.326886\pi\)
−0.999795 + 0.0202521i \(0.993553\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 448.000 0.507687
\(93\) 0 0
\(94\) −24.0000 + 41.5692i −0.0263342 + 0.0456121i
\(95\) −560.000 + 969.948i −0.604787 + 1.04752i
\(96\) 0 0
\(97\) −1354.00 −1.41730 −0.708649 0.705561i \(-0.750695\pi\)
−0.708649 + 0.705561i \(0.750695\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −142.000 245.951i −0.142000 0.245951i
\(101\) 679.000 1176.06i 0.668941 1.15864i −0.309260 0.950978i \(-0.600081\pi\)
0.978201 0.207662i \(-0.0665854\pi\)
\(102\) 0 0
\(103\) −416.000 720.533i −0.397958 0.689284i 0.595516 0.803344i \(-0.296948\pi\)
−0.993474 + 0.114060i \(0.963614\pi\)
\(104\) −144.000 −0.135773
\(105\) 0 0
\(106\) −636.000 −0.582772
\(107\) 222.000 + 384.515i 0.200575 + 0.347406i 0.948714 0.316136i \(-0.102386\pi\)
−0.748139 + 0.663542i \(0.769052\pi\)
\(108\) 0 0
\(109\) −935.000 + 1619.47i −0.821622 + 1.42309i 0.0828525 + 0.996562i \(0.473597\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(110\) 392.000 + 678.964i 0.339779 + 0.588515i
\(111\) 0 0
\(112\) 0 0
\(113\) −1378.00 −1.14718 −0.573590 0.819143i \(-0.694450\pi\)
−0.573590 + 0.819143i \(0.694450\pi\)
\(114\) 0 0
\(115\) 784.000 1357.93i 0.635725 1.10111i
\(116\) 380.000 658.179i 0.304156 0.526814i
\(117\) 0 0
\(118\) −400.000 −0.312059
\(119\) 0 0
\(120\) 0 0
\(121\) 273.500 + 473.716i 0.205485 + 0.355910i
\(122\) −198.000 + 342.946i −0.146935 + 0.254499i
\(123\) 0 0
\(124\) 144.000 + 249.415i 0.104287 + 0.180630i
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) 1944.00 1.35828 0.679142 0.734007i \(-0.262352\pi\)
0.679142 + 0.734007i \(0.262352\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −252.000 + 436.477i −0.170014 + 0.294473i
\(131\) 424.000 + 734.390i 0.282787 + 0.489801i 0.972070 0.234691i \(-0.0754078\pi\)
−0.689283 + 0.724492i \(0.742074\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1432.00 −0.923179
\(135\) 0 0
\(136\) −296.000 + 512.687i −0.186631 + 0.323254i
\(137\) −1483.00 + 2568.63i −0.924827 + 1.60185i −0.132987 + 0.991118i \(0.542457\pi\)
−0.791840 + 0.610729i \(0.790877\pi\)
\(138\) 0 0
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 392.000 + 678.964i 0.231661 + 0.401249i
\(143\) 252.000 436.477i 0.147366 0.255245i
\(144\) 0 0
\(145\) −1330.00 2303.63i −0.761728 1.31935i
\(146\) −1076.00 −0.609934
\(147\) 0 0
\(148\) −1384.00 −0.768676
\(149\) 255.000 + 441.673i 0.140204 + 0.242841i 0.927573 0.373641i \(-0.121891\pi\)
−0.787369 + 0.616482i \(0.788557\pi\)
\(150\) 0 0
\(151\) −296.000 + 512.687i −0.159524 + 0.276304i −0.934697 0.355445i \(-0.884329\pi\)
0.775173 + 0.631749i \(0.217663\pi\)
\(152\) 320.000 + 554.256i 0.170759 + 0.295764i
\(153\) 0 0
\(154\) 0 0
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) −1343.00 + 2326.14i −0.682695 + 1.18246i 0.291461 + 0.956583i \(0.405859\pi\)
−0.974155 + 0.225879i \(0.927475\pi\)
\(158\) −240.000 + 415.692i −0.120844 + 0.209308i
\(159\) 0 0
\(160\) −448.000 −0.221359
\(161\) 0 0
\(162\) 0 0
\(163\) 506.000 + 876.418i 0.243147 + 0.421143i 0.961609 0.274423i \(-0.0884869\pi\)
−0.718462 + 0.695566i \(0.755154\pi\)
\(164\) −324.000 + 561.184i −0.154269 + 0.267202i
\(165\) 0 0
\(166\) 1072.00 + 1856.76i 0.501225 + 0.868147i
\(167\) 544.000 0.252072 0.126036 0.992026i \(-0.459775\pi\)
0.126036 + 0.992026i \(0.459775\pi\)
\(168\) 0 0
\(169\) −1873.00 −0.852526
\(170\) 1036.00 + 1794.40i 0.467397 + 0.809556i
\(171\) 0 0
\(172\) 824.000 1427.21i 0.365287 0.632696i
\(173\) −929.000 1609.08i −0.408269 0.707143i 0.586427 0.810002i \(-0.300534\pi\)
−0.994696 + 0.102859i \(0.967201\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 448.000 0.191871
\(177\) 0 0
\(178\) −810.000 + 1402.96i −0.341079 + 0.590766i
\(179\) −150.000 + 259.808i −0.0626342 + 0.108486i −0.895642 0.444775i \(-0.853283\pi\)
0.833008 + 0.553261i \(0.186617\pi\)
\(180\) 0 0
\(181\) 2358.00 0.968336 0.484168 0.874975i \(-0.339122\pi\)
0.484168 + 0.874975i \(0.339122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −448.000 775.959i −0.179495 0.310894i
\(185\) −2422.00 + 4195.03i −0.962535 + 1.66716i
\(186\) 0 0
\(187\) −1036.00 1794.40i −0.405133 0.701710i
\(188\) 96.0000 0.0372421
\(189\) 0 0
\(190\) 2240.00 0.855298
\(191\) 696.000 + 1205.51i 0.263669 + 0.456688i 0.967214 0.253962i \(-0.0817340\pi\)
−0.703545 + 0.710651i \(0.748401\pi\)
\(192\) 0 0
\(193\) −889.000 + 1539.79i −0.331563 + 0.574284i −0.982818 0.184575i \(-0.940909\pi\)
0.651256 + 0.758858i \(0.274243\pi\)
\(194\) 1354.00 + 2345.20i 0.501090 + 0.867914i
\(195\) 0 0
\(196\) 0 0
\(197\) −1214.00 −0.439055 −0.219528 0.975606i \(-0.570452\pi\)
−0.219528 + 0.975606i \(0.570452\pi\)
\(198\) 0 0
\(199\) 520.000 900.666i 0.185235 0.320837i −0.758420 0.651766i \(-0.774029\pi\)
0.943656 + 0.330929i \(0.107362\pi\)
\(200\) −284.000 + 491.902i −0.100409 + 0.173914i
\(201\) 0 0
\(202\) −2716.00 −0.946025
\(203\) 0 0
\(204\) 0 0
\(205\) 1134.00 + 1964.15i 0.386351 + 0.669180i
\(206\) −832.000 + 1441.07i −0.281399 + 0.487397i
\(207\) 0 0
\(208\) 144.000 + 249.415i 0.0480029 + 0.0831435i
\(209\) −2240.00 −0.741359
\(210\) 0 0
\(211\) −3868.00 −1.26201 −0.631005 0.775779i \(-0.717357\pi\)
−0.631005 + 0.775779i \(0.717357\pi\)
\(212\) 636.000 + 1101.58i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 444.000 769.031i 0.141828 0.245653i
\(215\) −2884.00 4995.23i −0.914824 1.58452i
\(216\) 0 0
\(217\) 0 0
\(218\) 3740.00 1.16195
\(219\) 0 0
\(220\) 784.000 1357.93i 0.240260 0.416143i
\(221\) 666.000 1153.55i 0.202715 0.351113i
\(222\) 0 0
\(223\) −3968.00 −1.19156 −0.595778 0.803149i \(-0.703156\pi\)
−0.595778 + 0.803149i \(0.703156\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1378.00 + 2386.77i 0.405589 + 0.702501i
\(227\) 1968.00 3408.68i 0.575422 0.996660i −0.420574 0.907258i \(-0.638171\pi\)
0.995996 0.0894015i \(-0.0284954\pi\)
\(228\) 0 0
\(229\) 2405.00 + 4165.58i 0.694004 + 1.20205i 0.970515 + 0.241039i \(0.0774883\pi\)
−0.276512 + 0.961011i \(0.589178\pi\)
\(230\) −3136.00 −0.899051
\(231\) 0 0
\(232\) −1520.00 −0.430142
\(233\) −1091.00 1889.67i −0.306754 0.531314i 0.670896 0.741551i \(-0.265910\pi\)
−0.977650 + 0.210237i \(0.932576\pi\)
\(234\) 0 0
\(235\) 168.000 290.985i 0.0466345 0.0807734i
\(236\) 400.000 + 692.820i 0.110330 + 0.191096i
\(237\) 0 0
\(238\) 0 0
\(239\) 3000.00 0.811941 0.405970 0.913886i \(-0.366934\pi\)
0.405970 + 0.913886i \(0.366934\pi\)
\(240\) 0 0
\(241\) 1021.00 1768.42i 0.272898 0.472673i −0.696705 0.717358i \(-0.745351\pi\)
0.969603 + 0.244685i \(0.0786845\pi\)
\(242\) 547.000 947.432i 0.145300 0.251666i
\(243\) 0 0
\(244\) 792.000 0.207798
\(245\) 0 0
\(246\) 0 0
\(247\) −720.000 1247.08i −0.185476 0.321253i
\(248\) 288.000 498.831i 0.0737420 0.127725i
\(249\) 0 0
\(250\) −756.000 1309.43i −0.191255 0.331263i
\(251\) −528.000 −0.132777 −0.0663886 0.997794i \(-0.521148\pi\)
−0.0663886 + 0.997794i \(0.521148\pi\)
\(252\) 0 0
\(253\) 3136.00 0.779283
\(254\) −1944.00 3367.11i −0.480226 0.831776i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2817.00 4879.19i −0.683734 1.18426i −0.973833 0.227265i \(-0.927022\pi\)
0.290099 0.956997i \(-0.406312\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1008.00 0.240437
\(261\) 0 0
\(262\) 848.000 1468.78i 0.199960 0.346342i
\(263\) 84.0000 145.492i 0.0196945 0.0341119i −0.856010 0.516959i \(-0.827064\pi\)
0.875705 + 0.482847i \(0.160397\pi\)
\(264\) 0 0
\(265\) 4452.00 1.03202
\(266\) 0 0
\(267\) 0 0
\(268\) 1432.00 + 2480.30i 0.326393 + 0.565329i
\(269\) 655.000 1134.49i 0.148461 0.257142i −0.782198 0.623030i \(-0.785901\pi\)
0.930659 + 0.365888i \(0.119235\pi\)
\(270\) 0 0
\(271\) −1104.00 1912.18i −0.247466 0.428623i 0.715356 0.698760i \(-0.246264\pi\)
−0.962822 + 0.270137i \(0.912931\pi\)
\(272\) 1184.00 0.263936
\(273\) 0 0
\(274\) 5932.00 1.30790
\(275\) −994.000 1721.66i −0.217965 0.377527i
\(276\) 0 0
\(277\) −2647.00 + 4584.74i −0.574162 + 0.994477i 0.421970 + 0.906610i \(0.361339\pi\)
−0.996132 + 0.0878678i \(0.971995\pi\)
\(278\) 2800.00 + 4849.74i 0.604075 + 1.04629i
\(279\) 0 0
\(280\) 0 0
\(281\) −3242.00 −0.688262 −0.344131 0.938922i \(-0.611826\pi\)
−0.344131 + 0.938922i \(0.611826\pi\)
\(282\) 0 0
\(283\) −796.000 + 1378.71i −0.167199 + 0.289597i −0.937434 0.348163i \(-0.886806\pi\)
0.770235 + 0.637760i \(0.220139\pi\)
\(284\) 784.000 1357.93i 0.163809 0.283726i
\(285\) 0 0
\(286\) −1008.00 −0.208407
\(287\) 0 0
\(288\) 0 0
\(289\) −281.500 487.572i −0.0572970 0.0992413i
\(290\) −2660.00 + 4607.26i −0.538623 + 0.932922i
\(291\) 0 0
\(292\) 1076.00 + 1863.69i 0.215644 + 0.373507i
\(293\) −5022.00 −1.00133 −0.500663 0.865642i \(-0.666910\pi\)
−0.500663 + 0.865642i \(0.666910\pi\)
\(294\) 0 0
\(295\) 2800.00 0.552618
\(296\) 1384.00 + 2397.16i 0.271768 + 0.470716i
\(297\) 0 0
\(298\) 510.000 883.346i 0.0991393 0.171714i
\(299\) 1008.00 + 1745.91i 0.194964 + 0.337687i
\(300\) 0 0
\(301\) 0 0
\(302\) 1184.00 0.225601
\(303\) 0 0
\(304\) 640.000 1108.51i 0.120745 0.209137i
\(305\) 1386.00 2400.62i 0.260204 0.450686i
\(306\) 0 0
\(307\) 9536.00 1.77280 0.886398 0.462924i \(-0.153200\pi\)
0.886398 + 0.462924i \(0.153200\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1008.00 1745.91i −0.184679 0.319874i
\(311\) 484.000 838.313i 0.0882480 0.152850i −0.818523 0.574474i \(-0.805207\pi\)
0.906771 + 0.421624i \(0.138540\pi\)
\(312\) 0 0
\(313\) 1529.00 + 2648.31i 0.276116 + 0.478246i 0.970416 0.241439i \(-0.0776194\pi\)
−0.694300 + 0.719685i \(0.744286\pi\)
\(314\) 5372.00 0.965476
\(315\) 0 0
\(316\) 960.000 0.170899
\(317\) −2493.00 4318.00i −0.441706 0.765057i 0.556110 0.831109i \(-0.312293\pi\)
−0.997816 + 0.0660512i \(0.978960\pi\)
\(318\) 0 0
\(319\) 2660.00 4607.26i 0.466870 0.808642i
\(320\) 448.000 + 775.959i 0.0782624 + 0.135554i
\(321\) 0 0
\(322\) 0 0
\(323\) −5920.00 −1.01981
\(324\) 0 0
\(325\) 639.000 1106.78i 0.109063 0.188902i
\(326\) 1012.00 1752.84i 0.171931 0.297793i
\(327\) 0 0
\(328\) 1296.00 0.218170
\(329\) 0 0
\(330\) 0 0
\(331\) −4306.00 7458.21i −0.715043 1.23849i −0.962943 0.269705i \(-0.913074\pi\)
0.247900 0.968786i \(-0.420259\pi\)
\(332\) 2144.00 3713.52i 0.354420 0.613873i
\(333\) 0 0
\(334\) −544.000 942.236i −0.0891208 0.154362i
\(335\) 10024.0 1.63483
\(336\) 0 0
\(337\) −10206.0 −1.64972 −0.824861 0.565336i \(-0.808747\pi\)
−0.824861 + 0.565336i \(0.808747\pi\)
\(338\) 1873.00 + 3244.13i 0.301414 + 0.522064i
\(339\) 0 0
\(340\) 2072.00 3588.81i 0.330500 0.572443i
\(341\) 1008.00 + 1745.91i 0.160077 + 0.277262i
\(342\) 0 0
\(343\) 0 0
\(344\) −3296.00 −0.516594
\(345\) 0 0
\(346\) −1858.00 + 3218.15i −0.288690 + 0.500026i
\(347\) 1002.00 1735.51i 0.155015 0.268494i −0.778050 0.628203i \(-0.783791\pi\)
0.933064 + 0.359709i \(0.117124\pi\)
\(348\) 0 0
\(349\) −1330.00 −0.203992 −0.101996 0.994785i \(-0.532523\pi\)
−0.101996 + 0.994785i \(0.532523\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −448.000 775.959i −0.0678366 0.117496i
\(353\) −489.000 + 846.973i −0.0737304 + 0.127705i −0.900533 0.434787i \(-0.856824\pi\)
0.826803 + 0.562492i \(0.190157\pi\)
\(354\) 0 0
\(355\) −2744.00 4752.75i −0.410243 0.710562i
\(356\) 3240.00 0.482359
\(357\) 0 0
\(358\) 600.000 0.0885782
\(359\) −4840.00 8383.13i −0.711547 1.23244i −0.964276 0.264899i \(-0.914661\pi\)
0.252729 0.967537i \(-0.418672\pi\)
\(360\) 0 0
\(361\) 229.500 397.506i 0.0334597 0.0579539i
\(362\) −2358.00 4084.18i −0.342358 0.592982i
\(363\) 0 0
\(364\) 0 0
\(365\) 7532.00 1.08012
\(366\) 0 0
\(367\) −4328.00 + 7496.32i −0.615585 + 1.06622i 0.374696 + 0.927148i \(0.377747\pi\)
−0.990282 + 0.139077i \(0.955586\pi\)
\(368\) −896.000 + 1551.92i −0.126922 + 0.219835i
\(369\) 0 0
\(370\) 9688.00 1.36123
\(371\) 0 0
\(372\) 0 0
\(373\) −2639.00 4570.88i −0.366333 0.634508i 0.622656 0.782496i \(-0.286054\pi\)
−0.988989 + 0.147988i \(0.952720\pi\)
\(374\) −2072.00 + 3588.81i −0.286472 + 0.496184i
\(375\) 0 0
\(376\) −96.0000 166.277i −0.0131671 0.0228061i
\(377\) 3420.00 0.467212
\(378\) 0 0
\(379\) 6340.00 0.859272 0.429636 0.903002i \(-0.358642\pi\)
0.429636 + 0.903002i \(0.358642\pi\)
\(380\) −2240.00 3879.79i −0.302394 0.523761i
\(381\) 0 0
\(382\) 1392.00 2411.01i 0.186442 0.322927i
\(383\) 3116.00 + 5397.07i 0.415718 + 0.720045i 0.995504 0.0947240i \(-0.0301968\pi\)
−0.579785 + 0.814769i \(0.696864\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3556.00 0.468901
\(387\) 0 0
\(388\) 2708.00 4690.39i 0.354324 0.613708i
\(389\) −7405.00 + 12825.8i −0.965163 + 1.67171i −0.255986 + 0.966680i \(0.582400\pi\)
−0.709177 + 0.705031i \(0.750933\pi\)
\(390\) 0 0
\(391\) 8288.00 1.07197
\(392\) 0 0
\(393\) 0 0
\(394\) 1214.00 + 2102.71i 0.155230 + 0.268865i
\(395\) 1680.00 2909.85i 0.214000 0.370659i
\(396\) 0 0
\(397\) 2577.00 + 4463.49i 0.325783 + 0.564273i 0.981671 0.190586i \(-0.0610387\pi\)
−0.655887 + 0.754859i \(0.727705\pi\)
\(398\) −2080.00 −0.261962
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) 1641.00 + 2842.30i 0.204358 + 0.353959i 0.949928 0.312469i \(-0.101156\pi\)
−0.745570 + 0.666427i \(0.767823\pi\)
\(402\) 0 0
\(403\) −648.000 + 1122.37i −0.0800972 + 0.138732i
\(404\) 2716.00 + 4704.25i 0.334470 + 0.579320i
\(405\) 0 0
\(406\) 0 0
\(407\) −9688.00 −1.17989
\(408\) 0 0
\(409\) 2905.00 5031.61i 0.351205 0.608306i −0.635256 0.772302i \(-0.719105\pi\)
0.986461 + 0.163996i \(0.0524386\pi\)
\(410\) 2268.00 3928.29i 0.273192 0.473182i
\(411\) 0 0
\(412\) 3328.00 0.397958
\(413\) 0 0
\(414\) 0 0
\(415\) −7504.00 12997.3i −0.887607 1.53738i
\(416\) 288.000 498.831i 0.0339432 0.0587913i
\(417\) 0 0
\(418\) 2240.00 + 3879.79i 0.262110 + 0.453988i
\(419\) 13560.0 1.58102 0.790512 0.612446i \(-0.209814\pi\)
0.790512 + 0.612446i \(0.209814\pi\)
\(420\) 0 0
\(421\) −738.000 −0.0854345 −0.0427172 0.999087i \(-0.513601\pi\)
−0.0427172 + 0.999087i \(0.513601\pi\)
\(422\) 3868.00 + 6699.57i 0.446188 + 0.772820i
\(423\) 0 0
\(424\) 1272.00 2203.17i 0.145693 0.252347i
\(425\) −2627.00 4550.10i −0.299831 0.519323i
\(426\) 0 0
\(427\) 0 0
\(428\) −1776.00 −0.200575
\(429\) 0 0
\(430\) −5768.00 + 9990.47i −0.646878 + 1.12043i
\(431\) 636.000 1101.58i 0.0710790 0.123112i −0.828295 0.560292i \(-0.810689\pi\)
0.899374 + 0.437179i \(0.144022\pi\)
\(432\) 0 0
\(433\) 5062.00 0.561811 0.280906 0.959735i \(-0.409365\pi\)
0.280906 + 0.959735i \(0.409365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3740.00 6477.87i −0.410811 0.711545i
\(437\) 4480.00 7759.59i 0.490406 0.849408i
\(438\) 0 0
\(439\) 2820.00 + 4884.38i 0.306586 + 0.531023i 0.977613 0.210410i \(-0.0674800\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(440\) −3136.00 −0.339779
\(441\) 0 0
\(442\) −2664.00 −0.286682
\(443\) 6694.00 + 11594.3i 0.717927 + 1.24349i 0.961820 + 0.273683i \(0.0882421\pi\)
−0.243893 + 0.969802i \(0.578425\pi\)
\(444\) 0 0
\(445\) 5670.00 9820.73i 0.604008 1.04617i
\(446\) 3968.00 + 6872.78i 0.421279 + 0.729676i
\(447\) 0 0
\(448\) 0 0
\(449\) 3230.00 0.339495 0.169747 0.985488i \(-0.445705\pi\)
0.169747 + 0.985488i \(0.445705\pi\)
\(450\) 0 0
\(451\) −2268.00 + 3928.29i −0.236798 + 0.410146i
\(452\) 2756.00 4773.53i 0.286795 0.496743i
\(453\) 0 0
\(454\) −7872.00 −0.813769
\(455\) 0 0
\(456\) 0 0
\(457\) 5323.00 + 9219.71i 0.544857 + 0.943719i 0.998616 + 0.0525950i \(0.0167492\pi\)
−0.453759 + 0.891124i \(0.649917\pi\)
\(458\) 4810.00 8331.16i 0.490735 0.849978i
\(459\) 0 0
\(460\) 3136.00 + 5431.71i 0.317863 + 0.550554i
\(461\) 7282.00 0.735698 0.367849 0.929886i \(-0.380094\pi\)
0.367849 + 0.929886i \(0.380094\pi\)
\(462\) 0 0
\(463\) 12688.0 1.27357 0.636783 0.771043i \(-0.280265\pi\)
0.636783 + 0.771043i \(0.280265\pi\)
\(464\) 1520.00 + 2632.72i 0.152078 + 0.263407i
\(465\) 0 0
\(466\) −2182.00 + 3779.33i −0.216908 + 0.375696i
\(467\) 1408.00 + 2438.73i 0.139517 + 0.241651i 0.927314 0.374285i \(-0.122112\pi\)
−0.787797 + 0.615935i \(0.788778\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −672.000 −0.0659512
\(471\) 0 0
\(472\) 800.000 1385.64i 0.0780148 0.135126i
\(473\) 5768.00 9990.47i 0.560704 0.971168i
\(474\) 0 0
\(475\) −5680.00 −0.548666
\(476\) 0 0
\(477\) 0 0
\(478\) −3000.00 5196.15i −0.287064 0.497210i
\(479\) 1580.00 2736.64i 0.150714 0.261044i −0.780776 0.624811i \(-0.785176\pi\)
0.931490 + 0.363766i \(0.118509\pi\)
\(480\) 0 0
\(481\) −3114.00 5393.61i −0.295190 0.511283i
\(482\) −4084.00 −0.385936
\(483\) 0 0
\(484\) −2188.00 −0.205485
\(485\) −9478.00 16416.4i −0.887369 1.53697i
\(486\) 0 0
\(487\) 7088.00 12276.8i 0.659523 1.14233i −0.321216 0.947006i \(-0.604091\pi\)
0.980739 0.195322i \(-0.0625752\pi\)
\(488\) −792.000 1371.78i −0.0734675 0.127249i
\(489\) 0 0
\(490\) 0 0
\(491\) 11268.0 1.03568 0.517839 0.855478i \(-0.326737\pi\)
0.517839 + 0.855478i \(0.326737\pi\)
\(492\) 0 0
\(493\) 7030.00 12176.3i 0.642222 1.11236i
\(494\) −1440.00 + 2494.15i −0.131151 + 0.227160i
\(495\) 0 0
\(496\) −1152.00 −0.104287
\(497\) 0 0
\(498\) 0 0
\(499\) 2230.00 + 3862.47i 0.200057 + 0.346509i 0.948547 0.316638i \(-0.102554\pi\)
−0.748489 + 0.663147i \(0.769221\pi\)
\(500\) −1512.00 + 2618.86i −0.135237 + 0.234238i
\(501\) 0 0
\(502\) 528.000 + 914.523i 0.0469438 + 0.0813091i
\(503\) −1512.00 −0.134029 −0.0670147 0.997752i \(-0.521347\pi\)
−0.0670147 + 0.997752i \(0.521347\pi\)
\(504\) 0 0
\(505\) 19012.0 1.67529
\(506\) −3136.00 5431.71i −0.275518 0.477212i
\(507\) 0 0
\(508\) −3888.00 + 6734.21i −0.339571 + 0.588154i
\(509\) 5895.00 + 10210.4i 0.513342 + 0.889135i 0.999880 + 0.0154756i \(0.00492624\pi\)
−0.486538 + 0.873660i \(0.661740\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −5634.00 + 9758.37i −0.483473 + 0.837400i
\(515\) 5824.00 10087.5i 0.498323 0.863120i
\(516\) 0 0
\(517\) 672.000 0.0571654
\(518\) 0 0
\(519\) 0 0
\(520\) −1008.00 1745.91i −0.0850072 0.147237i
\(521\) −681.000 + 1179.53i −0.0572652 + 0.0991862i −0.893237 0.449586i \(-0.851571\pi\)
0.835972 + 0.548773i \(0.184905\pi\)
\(522\) 0 0
\(523\) 3484.00 + 6034.47i 0.291290 + 0.504529i 0.974115 0.226053i \(-0.0725822\pi\)
−0.682825 + 0.730582i \(0.739249\pi\)
\(524\) −3392.00 −0.282787
\(525\) 0 0
\(526\) −336.000 −0.0278523
\(527\) 2664.00 + 4614.18i 0.220200 + 0.381398i
\(528\) 0 0
\(529\) −188.500 + 326.492i −0.0154927 + 0.0268342i
\(530\) −4452.00 7711.09i −0.364873 0.631978i
\(531\) 0 0
\(532\) 0 0
\(533\) −2916.00 −0.236972
\(534\) 0 0
\(535\) −3108.00 + 5383.21i −0.251160 + 0.435022i
\(536\) 2864.00 4960.59i 0.230795 0.399748i
\(537\) 0 0
\(538\) −2620.00 −0.209956
\(539\) 0 0
\(540\) 0 0
\(541\) −3531.00 6115.87i −0.280609 0.486029i 0.690926 0.722926i \(-0.257203\pi\)
−0.971535 + 0.236896i \(0.923870\pi\)
\(542\) −2208.00 + 3824.37i −0.174985 + 0.303082i
\(543\) 0 0
\(544\) −1184.00 2050.75i −0.0933154 0.161627i
\(545\) −26180.0 −2.05767
\(546\) 0 0
\(547\) −8196.00 −0.640650 −0.320325 0.947308i \(-0.603792\pi\)
−0.320325 + 0.947308i \(0.603792\pi\)
\(548\) −5932.00 10274.5i −0.462413 0.800923i
\(549\) 0 0
\(550\) −1988.00 + 3443.32i −0.154125 + 0.266952i
\(551\) −7600.00 13163.6i −0.587606 1.01776i
\(552\) 0 0
\(553\) 0 0
\(554\) 10588.0 0.811987
\(555\) 0 0
\(556\) 5600.00 9699.48i 0.427146 0.739838i
\(557\) −3733.00 + 6465.75i −0.283972 + 0.491854i −0.972359 0.233490i \(-0.924986\pi\)
0.688388 + 0.725343i \(0.258319\pi\)
\(558\) 0 0
\(559\) 7416.00 0.561115
\(560\) 0 0
\(561\) 0 0
\(562\) 3242.00 + 5615.31i 0.243337 + 0.421472i
\(563\) −12484.0 + 21622.9i −0.934526 + 1.61865i −0.159048 + 0.987271i \(0.550842\pi\)
−0.775478 + 0.631375i \(0.782491\pi\)
\(564\) 0 0
\(565\) −9646.00 16707.4i −0.718248 1.24404i
\(566\) 3184.00 0.236455
\(567\) 0 0
\(568\) −3136.00 −0.231661
\(569\) 7125.00 + 12340.9i 0.524948 + 0.909237i 0.999578 + 0.0290514i \(0.00924865\pi\)
−0.474630 + 0.880186i \(0.657418\pi\)
\(570\) 0 0
\(571\) −3186.00 + 5518.31i −0.233503 + 0.404438i −0.958836 0.283959i \(-0.908352\pi\)
0.725334 + 0.688397i \(0.241685\pi\)
\(572\) 1008.00 + 1745.91i 0.0736829 + 0.127622i
\(573\) 0 0
\(574\) 0 0
\(575\) 7952.00 0.576733
\(576\) 0 0
\(577\) −4183.00 + 7245.17i −0.301803 + 0.522739i −0.976545 0.215316i \(-0.930922\pi\)
0.674741 + 0.738055i \(0.264255\pi\)
\(578\) −563.000 + 975.145i −0.0405151 + 0.0701742i
\(579\) 0 0
\(580\) 10640.0 0.761728
\(581\) 0 0
\(582\) 0 0
\(583\) 4452.00 + 7711.09i 0.316266 + 0.547789i
\(584\) 2152.00 3727.37i 0.152484 0.264109i
\(585\) 0 0
\(586\) 5022.00 + 8698.36i 0.354022 + 0.613184i
\(587\) 20384.0 1.43328 0.716642 0.697441i \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(588\) 0 0
\(589\) 5760.00 0.402948
\(590\) −2800.00 4849.74i −0.195380 0.338408i
\(591\) 0 0
\(592\) 2768.00 4794.32i 0.192169 0.332847i
\(593\) −4689.00 8121.59i −0.324712 0.562417i 0.656742 0.754115i \(-0.271934\pi\)
−0.981454 + 0.191698i \(0.938601\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2040.00 −0.140204
\(597\) 0 0
\(598\) 2016.00 3491.81i 0.137860 0.238781i
\(599\) −4500.00 + 7794.23i −0.306953 + 0.531659i −0.977694 0.210033i \(-0.932643\pi\)
0.670741 + 0.741692i \(0.265976\pi\)
\(600\) 0 0
\(601\) −7562.00 −0.513245 −0.256623 0.966512i \(-0.582610\pi\)
−0.256623 + 0.966512i \(0.582610\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1184.00 2050.75i −0.0797620 0.138152i
\(605\) −3829.00 + 6632.02i −0.257307 + 0.445670i
\(606\) 0 0
\(607\) −1488.00 2577.29i −0.0994993 0.172338i 0.811978 0.583688i \(-0.198391\pi\)
−0.911478 + 0.411350i \(0.865057\pi\)
\(608\) −2560.00 −0.170759
\(609\) 0 0
\(610\) −5544.00 −0.367984
\(611\) 216.000 + 374.123i 0.0143018 + 0.0247715i
\(612\) 0 0
\(613\) −2139.00 + 3704.86i −0.140935 + 0.244107i −0.927849 0.372956i \(-0.878344\pi\)
0.786914 + 0.617063i \(0.211678\pi\)
\(614\) −9536.00 16516.8i −0.626778 1.08561i
\(615\) 0 0
\(616\) 0 0
\(617\) −18794.0 −1.22629 −0.613143 0.789972i \(-0.710095\pi\)
−0.613143 + 0.789972i \(0.710095\pi\)
\(618\) 0 0
\(619\) 9020.00 15623.1i 0.585694 1.01445i −0.409095 0.912492i \(-0.634155\pi\)
0.994789 0.101959i \(-0.0325112\pi\)
\(620\) −2016.00 + 3491.81i −0.130588 + 0.226185i
\(621\) 0 0
\(622\) −1936.00 −0.124801
\(623\) 0 0
\(624\) 0 0
\(625\) 9729.50 + 16852.0i 0.622688 + 1.07853i
\(626\) 3058.00 5296.61i 0.195243 0.338171i
\(627\) 0 0
\(628\) −5372.00 9304.58i −0.341347 0.591231i
\(629\) −25604.0 −1.62305
\(630\) 0 0
\(631\) −21688.0 −1.36828 −0.684141 0.729350i \(-0.739823\pi\)
−0.684141 + 0.729350i \(0.739823\pi\)
\(632\) −960.000 1662.77i −0.0604221 0.104654i
\(633\) 0 0
\(634\) −4986.00 + 8636.01i −0.312333 + 0.540977i
\(635\) 13608.0 + 23569.7i 0.850420 + 1.47297i
\(636\) 0 0
\(637\) 0 0
\(638\) −10640.0 −0.660253
\(639\) 0 0
\(640\) 896.000 1551.92i 0.0553399 0.0958514i
\(641\) −5279.00 + 9143.50i −0.325285 + 0.563411i −0.981570 0.191102i \(-0.938794\pi\)
0.656285 + 0.754513i \(0.272127\pi\)
\(642\) 0 0
\(643\) 26152.0 1.60394 0.801971 0.597363i \(-0.203785\pi\)
0.801971 + 0.597363i \(0.203785\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5920.00 + 10253.7i 0.360556 + 0.624502i
\(647\) −12792.0 + 22156.4i −0.777288 + 1.34630i 0.156211 + 0.987724i \(0.450072\pi\)
−0.933499 + 0.358579i \(0.883261\pi\)
\(648\) 0 0
\(649\) 2800.00 + 4849.74i 0.169352 + 0.293327i
\(650\) −2556.00 −0.154238
\(651\) 0 0
\(652\) −4048.00 −0.243147
\(653\) 7599.00 + 13161.9i 0.455393 + 0.788764i 0.998711 0.0507630i \(-0.0161653\pi\)
−0.543317 + 0.839527i \(0.682832\pi\)
\(654\) 0 0
\(655\) −5936.00 + 10281.5i −0.354105 + 0.613328i
\(656\) −1296.00 2244.74i −0.0771346 0.133601i
\(657\) 0 0
\(658\) 0 0
\(659\) 6100.00 0.360580 0.180290 0.983613i \(-0.442296\pi\)
0.180290 + 0.983613i \(0.442296\pi\)
\(660\) 0 0
\(661\) −1159.00 + 2007.45i −0.0681995 + 0.118125i −0.898109 0.439773i \(-0.855059\pi\)
0.829909 + 0.557898i \(0.188392\pi\)
\(662\) −8612.00 + 14916.4i −0.505612 + 0.875745i
\(663\) 0 0
\(664\) −8576.00 −0.501225
\(665\) 0 0
\(666\) 0 0
\(667\) 10640.0 + 18429.0i 0.617665 + 1.06983i
\(668\) −1088.00 + 1884.47i −0.0630179 + 0.109150i
\(669\) 0 0
\(670\) −10024.0 17362.1i −0.578001 1.00113i
\(671\) 5544.00 0.318962
\(672\) 0 0
\(673\) −10222.0 −0.585482 −0.292741 0.956192i \(-0.594567\pi\)
−0.292741 + 0.956192i \(0.594567\pi\)
\(674\) 10206.0 + 17677.3i 0.583265 + 1.01024i
\(675\) 0 0
\(676\) 3746.00 6488.26i 0.213132 0.369155i
\(677\) −12717.0 22026.5i −0.721941 1.25044i −0.960221 0.279242i \(-0.909917\pi\)
0.238280 0.971197i \(-0.423416\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −8288.00 −0.467397
\(681\) 0 0
\(682\) 2016.00 3491.81i 0.113192 0.196053i
\(683\) −4266.00 + 7388.93i −0.238996 + 0.413952i −0.960426 0.278534i \(-0.910151\pi\)
0.721431 + 0.692487i \(0.243485\pi\)
\(684\) 0 0
\(685\) −41524.0 −2.31613
\(686\) 0 0
\(687\) 0 0
\(688\) 3296.00 + 5708.84i 0.182644 + 0.316348i
\(689\) −2862.00 + 4957.13i −0.158249 + 0.274095i
\(690\) 0 0
\(691\) 10336.0 + 17902.5i 0.569030 + 0.985589i 0.996662 + 0.0816365i \(0.0260146\pi\)
−0.427632 + 0.903953i \(0.640652\pi\)
\(692\) 7432.00 0.408269
\(693\) 0 0
\(694\) −4008.00 −0.219224
\(695\) −19600.0 33948.2i −1.06974 1.85285i
\(696\) 0 0
\(697\) −5994.00 + 10381.9i −0.325737 + 0.564194i
\(698\) 1330.00 + 2303.63i 0.0721221 + 0.124919i
\(699\) 0 0
\(700\) 0 0
\(701\) 21458.0 1.15614 0.578072 0.815985i \(-0.303805\pi\)
0.578072 + 0.815985i \(0.303805\pi\)
\(702\) 0 0
\(703\) −13840.0 + 23971.6i −0.742511 + 1.28607i
\(704\) −896.000 + 1551.92i −0.0479677 + 0.0830825i
\(705\) 0 0
\(706\) 1956.00 0.104271
\(707\) 0 0
\(708\) 0 0
\(709\) 4925.00 + 8530.35i 0.260878 + 0.451853i 0.966475 0.256759i \(-0.0826547\pi\)
−0.705598 + 0.708613i \(0.749321\pi\)
\(710\) −5488.00 + 9505.49i −0.290086 + 0.502443i
\(711\) 0 0
\(712\) −3240.00 5611.84i −0.170540 0.295383i
\(713\) −8064.00 −0.423561
\(714\) 0 0
\(715\) 7056.00 0.369062
\(716\) −600.000 1039.23i −0.0313171 0.0542428i
\(717\) 0 0
\(718\) −9680.00 + 16766.3i −0.503140 + 0.871464i
\(719\) 9420.00 + 16315.9i 0.488605 + 0.846288i 0.999914 0.0131086i \(-0.00417273\pi\)
−0.511309 + 0.859397i \(0.670839\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −918.000 −0.0473191
\(723\) 0 0
\(724\) −4716.00 + 8168.35i −0.242084 + 0.419302i
\(725\) 6745.00 11682.7i 0.345521 0.598461i
\(726\) 0 0
\(727\) −37504.0 −1.91327 −0.956634 0.291291i \(-0.905915\pi\)
−0.956634 + 0.291291i \(0.905915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7532.00 13045.8i −0.381879 0.661434i
\(731\) 15244.0 26403.4i 0.771299 1.33593i
\(732\) 0 0
\(733\) 6669.00 + 11551.0i 0.336051 + 0.582057i 0.983686 0.179894i \(-0.0575753\pi\)
−0.647635 + 0.761950i \(0.724242\pi\)
\(734\) 17312.0 0.870569
\(735\) 0 0
\(736\) 3584.00 0.179495
\(737\) 10024.0 + 17362.1i 0.501002 + 0.867762i
\(738\) 0 0
\(739\) −8550.00 + 14809.0i −0.425598 + 0.737157i −0.996476 0.0838776i \(-0.973270\pi\)
0.570878 + 0.821035i \(0.306603\pi\)
\(740\) −9688.00 16780.1i −0.481268 0.833580i
\(741\) 0 0
\(742\) 0 0
\(743\) 19632.0 0.969352 0.484676 0.874694i \(-0.338938\pi\)
0.484676 + 0.874694i \(0.338938\pi\)
\(744\) 0 0
\(745\) −3570.00 + 6183.42i −0.175563 + 0.304085i
\(746\) −5278.00 + 9141.76i −0.259037 + 0.448665i
\(747\) 0 0
\(748\) 8288.00 0.405133
\(749\) 0 0
\(750\) 0 0
\(751\) −16956.0 29368.7i −0.823879 1.42700i −0.902773 0.430117i \(-0.858472\pi\)
0.0788938 0.996883i \(-0.474861\pi\)
\(752\) −192.000 + 332.554i −0.00931053 + 0.0161263i
\(753\) 0 0
\(754\) −3420.00 5923.61i −0.165184 0.286108i
\(755\) −8288.00 −0.399512
\(756\) 0 0
\(757\) −31386.0 −1.50693 −0.753463 0.657490i \(-0.771618\pi\)
−0.753463 + 0.657490i \(0.771618\pi\)
\(758\) −6340.00 10981.2i −0.303798 0.526194i
\(759\) 0 0
\(760\) −4480.00 + 7759.59i −0.213825 + 0.370355i
\(761\) 17279.0 + 29928.1i 0.823079 + 1.42561i 0.903378 + 0.428844i \(0.141079\pi\)
−0.0802993 + 0.996771i \(0.525588\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5568.00 −0.263669
\(765\) 0 0
\(766\) 6232.00 10794.1i 0.293957 0.509149i
\(767\) −1800.00 + 3117.69i −0.0847382 + 0.146771i
\(768\) 0 0
\(769\) −39130.0 −1.83493 −0.917467 0.397812i \(-0.869769\pi\)
−0.917467 + 0.397812i \(0.869769\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3556.00 6159.17i −0.165781 0.287142i
\(773\) 12991.0 22501.1i 0.604468 1.04697i −0.387667 0.921799i \(-0.626719\pi\)
0.992135 0.125170i \(-0.0399476\pi\)
\(774\) 0 0
\(775\) 2556.00 + 4427.12i 0.118470 + 0.205196i
\(776\) −10832.0 −0.501090
\(777\) 0 0
\(778\) 29620.0 1.36495
\(779\) 6480.00 + 11223.7i 0.298036 + 0.516214i
\(780\) 0 0
\(781\) 5488.00 9505.49i 0.251442 0.435510i
\(782\) −8288.00 14355.2i −0.379000 0.656448i
\(783\) 0 0
\(784\) 0 0
\(785\) −37604.0 −1.70974
\(786\) 0 0
\(787\) 17712.0 30678.1i 0.802242 1.38952i −0.115895 0.993261i \(-0.536974\pi\)
0.918137 0.396263i \(-0.129693\pi\)
\(788\) 2428.00 4205.42i 0.109764 0.190117i
\(789\) 0 0
\(790\) −6720.00 −0.302642
\(791\) 0 0
\(792\) 0 0
\(793\) 1782.00 + 3086.51i 0.0797991 + 0.138216i
\(794\) 5154.00 8926.99i 0.230363 0.399001i
\(795\) 0 0
\(796\) 2080.00 + 3602.67i 0.0926176 + 0.160418i
\(797\) −30606.0 −1.36025 −0.680126 0.733096i \(-0.738075\pi\)
−0.680126 + 0.733096i \(0.738075\pi\)
\(798\) 0 0
\(799\) 1776.00 0.0786362
\(800\) −1136.00 1967.61i −0.0502046 0.0869569i
\(801\) 0 0
\(802\) 3282.00 5684.59i 0.144503 0.250287i
\(803\) 7532.00 + 13045.8i 0.331007 + 0.573321i
\(804\) 0 0
\(805\) 0 0
\(806\) 2592.00 0.113275
\(807\) 0 0
\(808\) 5432.00 9408.50i 0.236506 0.409641i
\(809\) 8405.00 14557.9i 0.365271 0.632668i −0.623549 0.781784i \(-0.714310\pi\)
0.988820 + 0.149117i \(0.0476431\pi\)
\(810\) 0 0
\(811\) 9368.00 0.405616 0.202808 0.979218i \(-0.434993\pi\)
0.202808 + 0.979218i \(0.434993\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 9688.00 + 16780.1i 0.417155 + 0.722534i
\(815\) −7084.00 + 12269.8i −0.304468 + 0.527355i
\(816\) 0 0
\(817\) −16480.0 28544.2i −0.705707 1.22232i
\(818\) −11620.0 −0.496679
\(819\) 0 0
\(820\) −9072.00 −0.386351
\(821\) 17191.0 + 29775.7i 0.730780 + 1.26575i 0.956550 + 0.291567i \(0.0941766\pi\)
−0.225771 + 0.974180i \(0.572490\pi\)
\(822\) 0 0
\(823\) 2236.00 3872.87i 0.0947048 0.164034i −0.814781 0.579769i \(-0.803143\pi\)
0.909485 + 0.415736i \(0.136476\pi\)
\(824\) −3328.00 5764.27i −0.140699 0.243699i
\(825\) 0 0
\(826\) 0 0
\(827\) 1716.00 0.0721538 0.0360769 0.999349i \(-0.488514\pi\)
0.0360769 + 0.999349i \(0.488514\pi\)
\(828\) 0 0
\(829\) −3955.00 + 6850.26i −0.165697 + 0.286996i −0.936903 0.349591i \(-0.886321\pi\)
0.771206 + 0.636586i \(0.219654\pi\)
\(830\) −15008.0 + 25994.6i −0.627633 + 1.08709i
\(831\) 0 0
\(832\) −1152.00 −0.0480029
\(833\) 0 0
\(834\) 0 0
\(835\) 3808.00 + 6595.65i 0.157822 + 0.273356i
\(836\) 4480.00 7759.59i 0.185340 0.321018i
\(837\) 0 0
\(838\) −13560.0 23486.6i −0.558977 0.968176i
\(839\) −19360.0 −0.796641 −0.398320 0.917246i \(-0.630407\pi\)
−0.398320 + 0.917246i \(0.630407\pi\)
\(840\) 0 0
\(841\) 11711.0 0.480175
\(842\) 738.000 + 1278.25i 0.0302057 + 0.0523177i
\(843\) 0 0
\(844\) 7736.00 13399.1i 0.315502 0.546466i
\(845\) −13111.0 22708.9i −0.533766 0.924510i
\(846\) 0 0
\(847\) 0 0
\(848\) −5088.00 −0.206041
\(849\) 0 0
\(850\) −5254.00 + 9100.19i −0.212013 + 0.367217i
\(851\) 19376.0 33560.2i 0.780494 1.35186i
\(852\) 0 0
\(853\) −698.000 −0.0280177 −0.0140088 0.999902i \(-0.504459\pi\)
−0.0140088 + 0.999902i \(0.504459\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1776.00 + 3076.12i 0.0709141 + 0.122827i
\(857\) 11703.0 20270.2i 0.466472 0.807954i −0.532794 0.846245i \(-0.678858\pi\)
0.999267 + 0.0382909i \(0.0121914\pi\)
\(858\) 0 0
\(859\) 3640.00 + 6304.66i 0.144581 + 0.250422i 0.929217 0.369536i \(-0.120483\pi\)
−0.784635 + 0.619957i \(0.787150\pi\)
\(860\) 23072.0 0.914824
\(861\) 0 0
\(862\) −2544.00 −0.100521
\(863\) 4904.00 + 8493.98i 0.193435 + 0.335039i 0.946386 0.323037i \(-0.104704\pi\)
−0.752952 + 0.658076i \(0.771371\pi\)
\(864\) 0 0
\(865\) 13006.0 22527.1i 0.511234 0.885483i
\(866\) −5062.00 8767.64i −0.198630 0.344038i
\(867\) 0 0
\(868\) 0 0
\(869\) 6720.00 0.262325
\(870\) 0 0
\(871\) −6444.00 + 11161.3i −0.250685 + 0.434199i
\(872\) −7480.00 + 12955.7i −0.290487 + 0.503138i
\(873\) 0 0
\(874\) −17920.0 −0.693539
\(875\) 0 0
\(876\) 0 0
\(877\) 4033.00 + 6985.36i 0.155285 + 0.268961i 0.933163 0.359454i \(-0.117037\pi\)
−0.777878 + 0.628415i \(0.783704\pi\)
\(878\) 5640.00 9768.77i 0.216789 0.375490i
\(879\) 0 0
\(880\) 3136.00 + 5431.71i 0.120130 + 0.208072i
\(881\) 25842.0 0.988240 0.494120 0.869394i \(-0.335490\pi\)
0.494120 + 0.869394i \(0.335490\pi\)
\(882\) 0 0
\(883\) −5692.00 −0.216932 −0.108466 0.994100i \(-0.534594\pi\)
−0.108466 + 0.994100i \(0.534594\pi\)
\(884\) 2664.00 + 4614.18i 0.101357 + 0.175556i
\(885\) 0 0
\(886\) 13388.0 23188.7i 0.507651 0.879277i
\(887\) 6768.00 + 11722.5i 0.256198 + 0.443747i 0.965220 0.261439i \(-0.0841969\pi\)
−0.709023 + 0.705186i \(0.750864\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −22680.0 −0.854197
\(891\) 0 0
\(892\) 7936.00 13745.6i 0.297889 0.515959i
\(893\) 960.000 1662.77i 0.0359744 0.0623096i
\(894\) 0 0
\(895\) −4200.00 −0.156861
\(896\) 0 0
\(897\) 0 0
\(898\) −3230.00 5594.52i −0.120030 0.207897i
\(899\) −6840.00 + 11847.2i −0.253756 + 0.439519i
\(900\) 0 0
\(901\) 11766.0 + 20379.3i 0.435052 + 0.753533i
\(902\) 9072.00 0.334883
\(903\) 0 0
\(904\) −11024.0 −0.405589
\(905\) 16506.0 + 28589.2i 0.606274 + 1.05010i
\(906\) 0 0
\(907\) −8502.00 + 14725.9i −0.311251 + 0.539102i −0.978633 0.205613i \(-0.934081\pi\)
0.667383 + 0.744715i \(0.267415\pi\)
\(908\) 7872.00 + 13634.7i 0.287711 + 0.498330i
\(909\) 0 0
\(910\) 0 0
\(911\) 14568.0 0.529813 0.264906 0.964274i \(-0.414659\pi\)
0.264906 + 0.964274i \(0.414659\pi\)
\(912\) 0 0
\(913\) 15008.0 25994.6i 0.544022 0.942274i
\(914\) 10646.0 18439.4i 0.385272 0.667310i
\(915\) 0 0
\(916\) −19240.0 −0.694004
\(917\) 0 0
\(918\) 0 0
\(919\) 700.000 + 1212.44i 0.0251261 + 0.0435197i 0.878315 0.478082i \(-0.158668\pi\)
−0.853189 + 0.521602i \(0.825335\pi\)
\(920\) 6272.00 10863.4i 0.224763 0.389300i
\(921\) 0 0
\(922\) −7282.00 12612.8i −0.260108 0.450521i
\(923\) 7056.00 0.251626
\(924\) 0 0
\(925\) −24566.0 −0.873216
\(926\) −12688.0 21976.3i −0.450274 0.779897i
\(927\) 0 0
\(928\) 3040.00 5265.43i 0.107535 0.186257i
\(929\) 6915.00 + 11977.1i 0.244213 + 0.422989i 0.961910 0.273366i \(-0.0881371\pi\)
−0.717697 + 0.696355i \(0.754804\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 8728.00 0.306754
\(933\) 0 0
\(934\) 2816.00 4877.46i 0.0986535 0.170873i
\(935\) 14504.0 25121.7i 0.507306 0.878681i
\(936\) 0 0
\(937\) 24166.0 0.842549 0.421275 0.906933i \(-0.361583\pi\)
0.421275 + 0.906933i \(0.361583\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 672.000 + 1163.94i 0.0233173 + 0.0403867i
\(941\) 5419.00 9385.98i 0.187730 0.325159i −0.756763 0.653690i \(-0.773220\pi\)
0.944493 + 0.328531i \(0.106554\pi\)
\(942\) 0 0
\(943\) −9072.00 15713.2i −0.313282 0.542620i
\(944\) −3200.00 −0.110330
\(945\) 0 0
\(946\) −23072.0 −0.792955
\(947\) −20458.0 35434.3i −0.702002 1.21590i −0.967763 0.251864i \(-0.918957\pi\)
0.265761 0.964039i \(-0.414377\pi\)
\(948\) 0 0
\(949\) −4842.00 + 8386.59i −0.165625 + 0.286871i
\(950\) 5680.00 + 9838.05i 0.193983 + 0.335988i
\(951\) 0 0
\(952\) 0 0
\(953\) −56618.0 −1.92449 −0.962244 0.272189i \(-0.912253\pi\)
−0.962244 + 0.272189i \(0.912253\pi\)
\(954\) 0 0
\(955\) −9744.00 + 16877.1i −0.330166 + 0.571864i
\(956\) −6000.00 + 10392.3i −0.202985 + 0.351581i
\(957\) 0 0
\(958\) −6320.00 −0.213142
\(959\) 0 0
\(960\) 0 0
\(961\) 12303.5 + 21310.3i 0.412994 + 0.715326i
\(962\) −6228.00 + 10787.2i −0.208731 + 0.361532i
\(963\) 0 0
\(964\) 4084.00 + 7073.70i 0.136449 + 0.236337i
\(965\) −24892.0 −0.830365
\(966\) 0 0
\(967\) 17504.0 0.582100 0.291050 0.956708i \(-0.405995\pi\)
0.291050 + 0.956708i \(0.405995\pi\)
\(968\) 2188.00 + 3789.73i 0.0726498 + 0.125833i
\(969\) 0 0
\(970\) −18956.0 + 32832.8i −0.627464 + 1.08680i
\(971\) −11556.0 20015.6i −0.381926 0.661514i 0.609412 0.792854i \(-0.291406\pi\)
−0.991337 + 0.131339i \(0.958072\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −28352.0 −0.932707
\(975\) 0 0
\(976\) −1584.00 + 2743.57i −0.0519494 + 0.0899790i
\(977\) 11937.0 20675.5i 0.390889 0.677039i −0.601678 0.798739i \(-0.705501\pi\)
0.992567 + 0.121699i \(0.0388343\pi\)
\(978\) 0 0
\(979\) 22680.0 0.740404
\(980\) 0 0
\(981\) 0 0
\(982\) −11268.0 19516.7i −0.366167 0.634220i
\(983\) 7656.00 13260.6i 0.248411 0.430261i −0.714674 0.699458i \(-0.753425\pi\)
0.963085 + 0.269197i \(0.0867582\pi\)
\(984\) 0 0
\(985\) −8498.00 14719.0i −0.274892 0.476127i
\(986\) −28120.0 −0.908239
\(987\) 0 0
\(988\) 5760.00 0.185476
\(989\) 23072.0 + 39961.9i 0.741807 + 1.28485i
\(990\) 0 0
\(991\) 8264.00 14313.7i 0.264899 0.458818i −0.702638 0.711547i \(-0.747995\pi\)
0.967537 + 0.252729i \(0.0813281\pi\)
\(992\) 1152.00 + 1995.32i 0.0368710 + 0.0638625i
\(993\) 0 0
\(994\) 0 0
\(995\) 14560.0 0.463903
\(996\) 0 0
\(997\) −14303.0 + 24773.5i −0.454344 + 0.786946i −0.998650 0.0519402i \(-0.983459\pi\)
0.544307 + 0.838886i \(0.316793\pi\)
\(998\) 4460.00 7724.95i 0.141462 0.245019i
\(999\) 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 882.4.g.k.361.1 2
3.2 odd 2 98.4.c.f.67.1 2
7.2 even 3 inner 882.4.g.k.667.1 2
7.3 odd 6 126.4.a.h.1.1 1
7.4 even 3 882.4.a.i.1.1 1
7.5 odd 6 882.4.g.b.667.1 2
7.6 odd 2 882.4.g.b.361.1 2
21.2 odd 6 98.4.c.f.79.1 2
21.5 even 6 98.4.c.d.79.1 2
21.11 odd 6 98.4.a.a.1.1 1
21.17 even 6 14.4.a.a.1.1 1
21.20 even 2 98.4.c.d.67.1 2
28.3 even 6 1008.4.a.s.1.1 1
84.11 even 6 784.4.a.s.1.1 1
84.59 odd 6 112.4.a.a.1.1 1
105.17 odd 12 350.4.c.b.99.1 2
105.38 odd 12 350.4.c.b.99.2 2
105.59 even 6 350.4.a.l.1.1 1
105.74 odd 6 2450.4.a.bo.1.1 1
168.59 odd 6 448.4.a.o.1.1 1
168.101 even 6 448.4.a.b.1.1 1
231.164 odd 6 1694.4.a.g.1.1 1
273.38 even 6 2366.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.a.a.1.1 1 21.17 even 6
98.4.a.a.1.1 1 21.11 odd 6
98.4.c.d.67.1 2 21.20 even 2
98.4.c.d.79.1 2 21.5 even 6
98.4.c.f.67.1 2 3.2 odd 2
98.4.c.f.79.1 2 21.2 odd 6
112.4.a.a.1.1 1 84.59 odd 6
126.4.a.h.1.1 1 7.3 odd 6
350.4.a.l.1.1 1 105.59 even 6
350.4.c.b.99.1 2 105.17 odd 12
350.4.c.b.99.2 2 105.38 odd 12
448.4.a.b.1.1 1 168.101 even 6
448.4.a.o.1.1 1 168.59 odd 6
784.4.a.s.1.1 1 84.11 even 6
882.4.a.i.1.1 1 7.4 even 3
882.4.g.b.361.1 2 7.6 odd 2
882.4.g.b.667.1 2 7.5 odd 6
882.4.g.k.361.1 2 1.1 even 1 trivial
882.4.g.k.667.1 2 7.2 even 3 inner
1008.4.a.s.1.1 1 28.3 even 6
1694.4.a.g.1.1 1 231.164 odd 6
2366.4.a.h.1.1 1 273.38 even 6
2450.4.a.bo.1.1 1 105.74 odd 6