Properties

Label 1323.2.f.h.883.1
Level $1323$
Weight $2$
Character 1323.883
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(442,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.442");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.f (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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 883.1
Character \(\chi\) \(=\) 1323.883
Dual form 1323.2.f.h.442.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})\) \(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +9.15528 q^{8} -4.30727 q^{10} +(-0.674376 + 1.16805i) q^{11} +(-1.58916 - 2.75251i) q^{13} +(-7.05696 + 12.2230i) q^{16} +2.80054 q^{17} -0.625693 q^{19} +(4.26101 - 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 - 0.246702i) q^{23} +(1.24168 - 2.15065i) q^{25} +8.62957 q^{26} +(-2.27396 + 3.93861i) q^{29} +(3.71502 + 6.43461i) q^{31} +(-10.0053 - 17.3297i) q^{32} +(-3.80191 + 6.58511i) q^{34} +8.02252 q^{37} +(0.849420 - 1.47124i) q^{38} +(7.26194 + 12.5780i) q^{40} +(5.01329 + 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +7.24542 q^{44} +0.773452 q^{46} +(-5.57383 + 9.65415i) q^{47} +(3.37132 + 5.83930i) q^{50} +(-8.53689 + 14.7863i) q^{52} -2.78698 q^{53} -2.13965 q^{55} +(-6.17410 - 10.6939i) q^{58} +(-2.28734 - 3.96180i) q^{59} +(-0.192507 + 0.333432i) q^{61} -20.1736 q^{62} +26.1036 q^{64} +(2.52104 - 4.36656i) q^{65} +(1.26958 + 2.19898i) q^{67} +(-7.52217 - 13.0288i) q^{68} +1.45208 q^{71} +0.468134 q^{73} +(-10.8911 + 18.8639i) q^{74} +(1.68059 + 2.91087i) q^{76} +(7.85620 - 13.6073i) q^{79} -22.3902 q^{80} -27.2235 q^{82} +(-6.99338 + 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 - 14.7166i) q^{86} +(-6.17410 + 10.6939i) q^{88} -2.58706 q^{89} +(-0.765146 + 1.32527i) q^{92} +(-15.1337 - 26.2123i) q^{94} +(-0.496297 - 0.859612i) q^{95} +(-7.22962 + 12.5221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35757 + 2.35137i −0.959944 + 1.66267i −0.237320 + 0.971432i \(0.576269\pi\)
−0.722624 + 0.691241i \(0.757064\pi\)
\(3\) 0 0
\(4\) −2.68597 4.65224i −1.34299 2.32612i
\(5\) 0.793197 + 1.37386i 0.354728 + 0.614407i 0.987071 0.160281i \(-0.0512400\pi\)
−0.632343 + 0.774688i \(0.717907\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 9.15528 3.23688
\(9\) 0 0
\(10\) −4.30727 −1.36208
\(11\) −0.674376 + 1.16805i −0.203332 + 0.352181i −0.949600 0.313464i \(-0.898510\pi\)
0.746268 + 0.665646i \(0.231844\pi\)
\(12\) 0 0
\(13\) −1.58916 2.75251i −0.440754 0.763409i 0.556991 0.830518i \(-0.311956\pi\)
−0.997746 + 0.0671096i \(0.978622\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −7.05696 + 12.2230i −1.76424 + 3.05575i
\(17\) 2.80054 0.679230 0.339615 0.940565i \(-0.389703\pi\)
0.339615 + 0.940565i \(0.389703\pi\)
\(18\) 0 0
\(19\) −0.625693 −0.143544 −0.0717719 0.997421i \(-0.522865\pi\)
−0.0717719 + 0.997421i \(0.522865\pi\)
\(20\) 4.26101 7.38028i 0.952791 1.65028i
\(21\) 0 0
\(22\) −1.83102 3.17142i −0.390375 0.676149i
\(23\) −0.142434 0.246702i −0.0296995 0.0514410i 0.850794 0.525500i \(-0.176122\pi\)
−0.880493 + 0.474059i \(0.842788\pi\)
\(24\) 0 0
\(25\) 1.24168 2.15065i 0.248336 0.430130i
\(26\) 8.62957 1.69240
\(27\) 0 0
\(28\) 0 0
\(29\) −2.27396 + 3.93861i −0.422264 + 0.731382i −0.996161 0.0875454i \(-0.972098\pi\)
0.573897 + 0.818928i \(0.305431\pi\)
\(30\) 0 0
\(31\) 3.71502 + 6.43461i 0.667238 + 1.15569i 0.978673 + 0.205423i \(0.0658569\pi\)
−0.311435 + 0.950267i \(0.600810\pi\)
\(32\) −10.0053 17.3297i −1.76870 3.06348i
\(33\) 0 0
\(34\) −3.80191 + 6.58511i −0.652023 + 1.12934i
\(35\) 0 0
\(36\) 0 0
\(37\) 8.02252 1.31889 0.659447 0.751751i \(-0.270791\pi\)
0.659447 + 0.751751i \(0.270791\pi\)
\(38\) 0.849420 1.47124i 0.137794 0.238666i
\(39\) 0 0
\(40\) 7.26194 + 12.5780i 1.14821 + 1.98876i
\(41\) 5.01329 + 8.68327i 0.782944 + 1.35610i 0.930219 + 0.367004i \(0.119616\pi\)
−0.147275 + 0.989096i \(0.547050\pi\)
\(42\) 0 0
\(43\) −3.12937 + 5.42022i −0.477224 + 0.826576i −0.999659 0.0261027i \(-0.991690\pi\)
0.522435 + 0.852679i \(0.325024\pi\)
\(44\) 7.24542 1.09229
\(45\) 0 0
\(46\) 0.773452 0.114039
\(47\) −5.57383 + 9.65415i −0.813026 + 1.40820i 0.0977106 + 0.995215i \(0.468848\pi\)
−0.910737 + 0.412988i \(0.864485\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.37132 + 5.83930i 0.476777 + 0.825802i
\(51\) 0 0
\(52\) −8.53689 + 14.7863i −1.18385 + 2.05049i
\(53\) −2.78698 −0.382821 −0.191410 0.981510i \(-0.561306\pi\)
−0.191410 + 0.981510i \(0.561306\pi\)
\(54\) 0 0
\(55\) −2.13965 −0.288510
\(56\) 0 0
\(57\) 0 0
\(58\) −6.17410 10.6939i −0.810699 1.40417i
\(59\) −2.28734 3.96180i −0.297787 0.515782i 0.677842 0.735207i \(-0.262915\pi\)
−0.975629 + 0.219425i \(0.929582\pi\)
\(60\) 0 0
\(61\) −0.192507 + 0.333432i −0.0246480 + 0.0426916i −0.878086 0.478502i \(-0.841180\pi\)
0.853438 + 0.521194i \(0.174513\pi\)
\(62\) −20.1736 −2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) 2.52104 4.36656i 0.312696 0.541605i
\(66\) 0 0
\(67\) 1.26958 + 2.19898i 0.155104 + 0.268648i 0.933097 0.359625i \(-0.117095\pi\)
−0.777993 + 0.628273i \(0.783762\pi\)
\(68\) −7.52217 13.0288i −0.912197 1.57997i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.45208 0.172330 0.0861651 0.996281i \(-0.472539\pi\)
0.0861651 + 0.996281i \(0.472539\pi\)
\(72\) 0 0
\(73\) 0.468134 0.0547909 0.0273955 0.999625i \(-0.491279\pi\)
0.0273955 + 0.999625i \(0.491279\pi\)
\(74\) −10.8911 + 18.8639i −1.26606 + 2.19289i
\(75\) 0 0
\(76\) 1.68059 + 2.91087i 0.192777 + 0.333900i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.85620 13.6073i 0.883892 1.53095i 0.0369135 0.999318i \(-0.488247\pi\)
0.846978 0.531627i \(-0.178419\pi\)
\(80\) −22.3902 −2.50330
\(81\) 0 0
\(82\) −27.2235 −3.00633
\(83\) −6.99338 + 12.1129i −0.767623 + 1.32956i 0.171225 + 0.985232i \(0.445228\pi\)
−0.938848 + 0.344331i \(0.888106\pi\)
\(84\) 0 0
\(85\) 2.22138 + 3.84754i 0.240942 + 0.417324i
\(86\) −8.49665 14.7166i −0.916217 1.58693i
\(87\) 0 0
\(88\) −6.17410 + 10.6939i −0.658162 + 1.13997i
\(89\) −2.58706 −0.274228 −0.137114 0.990555i \(-0.543783\pi\)
−0.137114 + 0.990555i \(0.543783\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.765146 + 1.32527i −0.0797719 + 0.138169i
\(93\) 0 0
\(94\) −15.1337 26.2123i −1.56092 2.70359i
\(95\) −0.496297 0.859612i −0.0509190 0.0881944i
\(96\) 0 0
\(97\) −7.22962 + 12.5221i −0.734057 + 1.27142i 0.221079 + 0.975256i \(0.429042\pi\)
−0.955136 + 0.296168i \(0.904291\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −13.3405 −1.33405
\(101\) −4.91888 + 8.51975i −0.489447 + 0.847747i −0.999926 0.0121430i \(-0.996135\pi\)
0.510479 + 0.859890i \(0.329468\pi\)
\(102\) 0 0
\(103\) 5.52897 + 9.57646i 0.544786 + 0.943597i 0.998620 + 0.0525110i \(0.0167225\pi\)
−0.453834 + 0.891086i \(0.649944\pi\)
\(104\) −14.5492 25.2000i −1.42667 2.47106i
\(105\) 0 0
\(106\) 3.78350 6.55322i 0.367486 0.636505i
\(107\) 1.92431 0.186030 0.0930149 0.995665i \(-0.470350\pi\)
0.0930149 + 0.995665i \(0.470350\pi\)
\(108\) 0 0
\(109\) −18.6068 −1.78221 −0.891105 0.453797i \(-0.850069\pi\)
−0.891105 + 0.453797i \(0.850069\pi\)
\(110\) 2.90472 5.03112i 0.276954 0.479698i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.59338 2.75982i −0.149893 0.259622i 0.781295 0.624162i \(-0.214560\pi\)
−0.931188 + 0.364540i \(0.881226\pi\)
\(114\) 0 0
\(115\) 0.225956 0.391367i 0.0210705 0.0364951i
\(116\) 24.4312 2.26838
\(117\) 0 0
\(118\) 12.4209 1.14344
\(119\) 0 0
\(120\) 0 0
\(121\) 4.59043 + 7.95086i 0.417312 + 0.722806i
\(122\) −0.522682 0.905312i −0.0473214 0.0819631i
\(123\) 0 0
\(124\) 19.9569 34.5664i 1.79218 3.10415i
\(125\) 11.8715 1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) −15.4267 + 26.7199i −1.36354 + 2.36173i
\(129\) 0 0
\(130\) 6.84495 + 11.8558i 0.600341 + 1.03982i
\(131\) 5.98629 + 10.3686i 0.523024 + 0.905905i 0.999641 + 0.0267937i \(0.00852971\pi\)
−0.476616 + 0.879111i \(0.658137\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.89415 −0.595564
\(135\) 0 0
\(136\) 25.6397 2.19859
\(137\) 8.27525 14.3332i 0.707003 1.22456i −0.258961 0.965888i \(-0.583380\pi\)
0.965964 0.258677i \(-0.0832865\pi\)
\(138\) 0 0
\(139\) −3.95119 6.84367i −0.335136 0.580472i 0.648375 0.761321i \(-0.275449\pi\)
−0.983511 + 0.180849i \(0.942116\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.97130 + 3.41438i −0.165427 + 0.286529i
\(143\) 4.28677 0.358478
\(144\) 0 0
\(145\) −7.21479 −0.599156
\(146\) −0.635523 + 1.10076i −0.0525962 + 0.0910994i
\(147\) 0 0
\(148\) −21.5483 37.3227i −1.77126 3.06791i
\(149\) −6.83427 11.8373i −0.559885 0.969749i −0.997505 0.0705895i \(-0.977512\pi\)
0.437620 0.899160i \(-0.355821\pi\)
\(150\) 0 0
\(151\) −1.94982 + 3.37718i −0.158674 + 0.274831i −0.934391 0.356250i \(-0.884055\pi\)
0.775717 + 0.631081i \(0.217389\pi\)
\(152\) −5.72839 −0.464634
\(153\) 0 0
\(154\) 0 0
\(155\) −5.89349 + 10.2078i −0.473376 + 0.819912i
\(156\) 0 0
\(157\) −0.147176 0.254917i −0.0117459 0.0203446i 0.860093 0.510138i \(-0.170406\pi\)
−0.871839 + 0.489793i \(0.837072\pi\)
\(158\) 21.3306 + 36.9457i 1.69697 + 2.93925i
\(159\) 0 0
\(160\) 15.8723 27.4917i 1.25482 2.17341i
\(161\) 0 0
\(162\) 0 0
\(163\) 10.7091 0.838802 0.419401 0.907801i \(-0.362240\pi\)
0.419401 + 0.907801i \(0.362240\pi\)
\(164\) 26.9311 46.6461i 2.10297 3.64245i
\(165\) 0 0
\(166\) −18.9880 32.8881i −1.47375 2.55261i
\(167\) 1.59872 + 2.76907i 0.123713 + 0.214277i 0.921229 0.389020i \(-0.127186\pi\)
−0.797516 + 0.603298i \(0.793853\pi\)
\(168\) 0 0
\(169\) 1.44913 2.50997i 0.111472 0.193074i
\(170\) −12.0627 −0.925164
\(171\) 0 0
\(172\) 33.6216 2.56362
\(173\) 5.71875 9.90517i 0.434789 0.753076i −0.562490 0.826804i \(-0.690156\pi\)
0.997278 + 0.0737284i \(0.0234898\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −9.51809 16.4858i −0.717453 1.24266i
\(177\) 0 0
\(178\) 3.51210 6.08314i 0.263243 0.455951i
\(179\) −1.09855 −0.0821095 −0.0410547 0.999157i \(-0.513072\pi\)
−0.0410547 + 0.999157i \(0.513072\pi\)
\(180\) 0 0
\(181\) −3.19013 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.30402 2.25863i −0.0961336 0.166508i
\(185\) 6.36343 + 11.0218i 0.467849 + 0.810338i
\(186\) 0 0
\(187\) −1.88861 + 3.27118i −0.138109 + 0.239212i
\(188\) 59.8846 4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) 1.93407 3.34992i 0.139945 0.242391i −0.787531 0.616275i \(-0.788641\pi\)
0.927475 + 0.373884i \(0.121974\pi\)
\(192\) 0 0
\(193\) 2.06793 + 3.58175i 0.148853 + 0.257820i 0.930804 0.365520i \(-0.119109\pi\)
−0.781951 + 0.623340i \(0.785775\pi\)
\(194\) −19.6294 33.9991i −1.40931 2.44099i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.889267 0.0633576 0.0316788 0.999498i \(-0.489915\pi\)
0.0316788 + 0.999498i \(0.489915\pi\)
\(198\) 0 0
\(199\) −6.32386 −0.448287 −0.224143 0.974556i \(-0.571958\pi\)
−0.224143 + 0.974556i \(0.571958\pi\)
\(200\) 11.3679 19.6898i 0.803833 1.39228i
\(201\) 0 0
\(202\) −13.3554 23.1323i −0.939684 1.62758i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.95305 + 13.7751i −0.555465 + 0.962093i
\(206\) −30.0238 −2.09186
\(207\) 0 0
\(208\) 44.8586 3.11038
\(209\) 0.421952 0.730843i 0.0291870 0.0505535i
\(210\) 0 0
\(211\) 5.71291 + 9.89505i 0.393293 + 0.681204i 0.992882 0.119105i \(-0.0380025\pi\)
−0.599589 + 0.800308i \(0.704669\pi\)
\(212\) 7.48574 + 12.9657i 0.514123 + 0.890487i
\(213\) 0 0
\(214\) −2.61237 + 4.52476i −0.178578 + 0.309307i
\(215\) −9.92881 −0.677139
\(216\) 0 0
\(217\) 0 0
\(218\) 25.2600 43.7516i 1.71082 2.96323i
\(219\) 0 0
\(220\) 5.74705 + 9.95417i 0.387466 + 0.671110i
\(221\) −4.45051 7.70850i −0.299373 0.518530i
\(222\) 0 0
\(223\) −8.35953 + 14.4791i −0.559796 + 0.969595i 0.437717 + 0.899113i \(0.355787\pi\)
−0.997513 + 0.0704822i \(0.977546\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 8.65250 0.575555
\(227\) −8.53501 + 14.7831i −0.566489 + 0.981187i 0.430421 + 0.902628i \(0.358365\pi\)
−0.996909 + 0.0785588i \(0.974968\pi\)
\(228\) 0 0
\(229\) 9.89471 + 17.1381i 0.653861 + 1.13252i 0.982178 + 0.187953i \(0.0601851\pi\)
−0.328317 + 0.944567i \(0.606482\pi\)
\(230\) 0.613500 + 1.06261i 0.0404530 + 0.0700666i
\(231\) 0 0
\(232\) −20.8187 + 36.0591i −1.36682 + 2.36740i
\(233\) −5.93159 −0.388591 −0.194296 0.980943i \(-0.562242\pi\)
−0.194296 + 0.980943i \(0.562242\pi\)
\(234\) 0 0
\(235\) −17.6846 −1.15361
\(236\) −12.2875 + 21.2826i −0.799847 + 1.38538i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0277 + 17.3685i 0.648637 + 1.12347i 0.983449 + 0.181187i \(0.0579939\pi\)
−0.334812 + 0.942285i \(0.608673\pi\)
\(240\) 0 0
\(241\) 14.6444 25.3648i 0.943326 1.63389i 0.184256 0.982878i \(-0.441012\pi\)
0.759069 0.651010i \(-0.225654\pi\)
\(242\) −24.9273 −1.60239
\(243\) 0 0
\(244\) 2.06827 0.132408
\(245\) 0 0
\(246\) 0 0
\(247\) 0.994327 + 1.72223i 0.0632675 + 0.109583i
\(248\) 34.0121 + 58.9107i 2.15977 + 3.74083i
\(249\) 0 0
\(250\) −16.1164 + 27.9144i −1.01929 + 1.76546i
\(251\) −22.7856 −1.43821 −0.719106 0.694901i \(-0.755448\pi\)
−0.719106 + 0.694901i \(0.755448\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) 11.3681 19.6901i 0.713297 1.23547i
\(255\) 0 0
\(256\) −15.7821 27.3354i −0.986381 1.70846i
\(257\) 12.1444 + 21.0348i 0.757550 + 1.31211i 0.944097 + 0.329668i \(0.106937\pi\)
−0.186547 + 0.982446i \(0.559730\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −27.0857 −1.67979
\(261\) 0 0
\(262\) −32.5071 −2.00830
\(263\) −4.30578 + 7.45782i −0.265506 + 0.459869i −0.967696 0.252120i \(-0.918872\pi\)
0.702190 + 0.711989i \(0.252206\pi\)
\(264\) 0 0
\(265\) −2.21062 3.82890i −0.135797 0.235208i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.82011 11.8128i 0.416605 0.721581i
\(269\) −15.2312 −0.928664 −0.464332 0.885661i \(-0.653706\pi\)
−0.464332 + 0.885661i \(0.653706\pi\)
\(270\) 0 0
\(271\) 4.67820 0.284181 0.142090 0.989854i \(-0.454618\pi\)
0.142090 + 0.989854i \(0.454618\pi\)
\(272\) −19.7633 + 34.2310i −1.19832 + 2.07556i
\(273\) 0 0
\(274\) 22.4684 + 38.9164i 1.35737 + 2.35103i
\(275\) 1.67472 + 2.90069i 0.100989 + 0.174918i
\(276\) 0 0
\(277\) 8.19537 14.1948i 0.492412 0.852883i −0.507550 0.861622i \(-0.669449\pi\)
0.999962 + 0.00873986i \(0.00278202\pi\)
\(278\) 21.4560 1.28685
\(279\) 0 0
\(280\) 0 0
\(281\) −1.75702 + 3.04325i −0.104815 + 0.181545i −0.913663 0.406473i \(-0.866758\pi\)
0.808848 + 0.588018i \(0.200092\pi\)
\(282\) 0 0
\(283\) 13.0354 + 22.5780i 0.774874 + 1.34212i 0.934865 + 0.355002i \(0.115520\pi\)
−0.159992 + 0.987118i \(0.551147\pi\)
\(284\) −3.90025 6.75543i −0.231437 0.400861i
\(285\) 0 0
\(286\) −5.81958 + 10.0798i −0.344119 + 0.596031i
\(287\) 0 0
\(288\) 0 0
\(289\) −9.15699 −0.538647
\(290\) 9.79455 16.9647i 0.575156 0.996199i
\(291\) 0 0
\(292\) −1.25740 2.17787i −0.0735835 0.127450i
\(293\) −9.44192 16.3539i −0.551603 0.955404i −0.998159 0.0606487i \(-0.980683\pi\)
0.446556 0.894756i \(-0.352650\pi\)
\(294\) 0 0
\(295\) 3.62863 6.28497i 0.211267 0.365925i
\(296\) 73.4484 4.26910
\(297\) 0 0
\(298\) 37.1119 2.14983
\(299\) −0.452700 + 0.784099i −0.0261803 + 0.0453456i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.29401 9.16950i −0.304636 0.527645i
\(303\) 0 0
\(304\) 4.41549 7.64785i 0.253246 0.438634i
\(305\) −0.610783 −0.0349734
\(306\) 0 0
\(307\) 21.6407 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −16.0016 27.7156i −0.908830 1.57414i
\(311\) −2.24724 3.89234i −0.127429 0.220714i 0.795251 0.606281i \(-0.207339\pi\)
−0.922680 + 0.385567i \(0.874006\pi\)
\(312\) 0 0
\(313\) 4.30102 7.44958i 0.243108 0.421075i −0.718490 0.695537i \(-0.755166\pi\)
0.961598 + 0.274462i \(0.0884997\pi\)
\(314\) 0.799206 0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) −4.03128 + 6.98237i −0.226419 + 0.392169i −0.956744 0.290930i \(-0.906035\pi\)
0.730325 + 0.683100i \(0.239369\pi\)
\(318\) 0 0
\(319\) −3.06701 5.31221i −0.171719 0.297427i
\(320\) 20.7053 + 35.8626i 1.15746 + 2.00478i
\(321\) 0 0
\(322\) 0 0
\(323\) −1.75228 −0.0974992
\(324\) 0 0
\(325\) −7.89291 −0.437820
\(326\) −14.5383 + 25.1811i −0.805203 + 1.39465i
\(327\) 0 0
\(328\) 45.8981 + 79.4978i 2.53430 + 4.38953i
\(329\) 0 0
\(330\) 0 0
\(331\) 11.4513 19.8342i 0.629419 1.09019i −0.358249 0.933626i \(-0.616626\pi\)
0.987668 0.156560i \(-0.0500405\pi\)
\(332\) 75.1361 4.12363
\(333\) 0 0
\(334\) −8.68150 −0.475030
\(335\) −2.01405 + 3.48844i −0.110039 + 0.190594i
\(336\) 0 0
\(337\) −6.81891 11.8107i −0.371450 0.643369i 0.618339 0.785911i \(-0.287806\pi\)
−0.989789 + 0.142542i \(0.954472\pi\)
\(338\) 3.93458 + 6.81489i 0.214013 + 0.370681i
\(339\) 0 0
\(340\) 11.9331 20.6688i 0.647164 1.12092i
\(341\) −10.0213 −0.542683
\(342\) 0 0
\(343\) 0 0
\(344\) −28.6502 + 49.6237i −1.54472 + 2.67553i
\(345\) 0 0
\(346\) 15.5272 + 26.8938i 0.834746 + 1.44582i
\(347\) −1.41282 2.44707i −0.0758440 0.131366i 0.825609 0.564243i \(-0.190832\pi\)
−0.901453 + 0.432877i \(0.857498\pi\)
\(348\) 0 0
\(349\) 1.81202 3.13851i 0.0969951 0.168000i −0.813444 0.581643i \(-0.802410\pi\)
0.910440 + 0.413642i \(0.135744\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 26.9893 1.43854
\(353\) 1.37701 2.38504i 0.0732907 0.126943i −0.827051 0.562127i \(-0.809983\pi\)
0.900342 + 0.435184i \(0.143317\pi\)
\(354\) 0 0
\(355\) 1.15179 + 1.99495i 0.0611304 + 0.105881i
\(356\) 6.94877 + 12.0356i 0.368284 + 0.637887i
\(357\) 0 0
\(358\) 1.49135 2.58310i 0.0788205 0.136521i
\(359\) 16.8015 0.886750 0.443375 0.896336i \(-0.353781\pi\)
0.443375 + 0.896336i \(0.353781\pi\)
\(360\) 0 0
\(361\) −18.6085 −0.979395
\(362\) 4.33081 7.50119i 0.227622 0.394254i
\(363\) 0 0
\(364\) 0 0
\(365\) 0.371322 + 0.643149i 0.0194359 + 0.0336640i
\(366\) 0 0
\(367\) −11.9670 + 20.7274i −0.624670 + 1.08196i 0.363934 + 0.931425i \(0.381433\pi\)
−0.988605 + 0.150536i \(0.951900\pi\)
\(368\) 4.02059 0.209588
\(369\) 0 0
\(370\) −34.5551 −1.79644
\(371\) 0 0
\(372\) 0 0
\(373\) 9.58030 + 16.5936i 0.496049 + 0.859182i 0.999990 0.00455622i \(-0.00145030\pi\)
−0.503941 + 0.863738i \(0.668117\pi\)
\(374\) −5.12784 8.88168i −0.265154 0.459261i
\(375\) 0 0
\(376\) −51.0299 + 88.3865i −2.63167 + 4.55818i
\(377\) 14.4548 0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) −2.66608 + 4.61779i −0.136767 + 0.236888i
\(381\) 0 0
\(382\) 5.25127 + 9.09546i 0.268678 + 0.465364i
\(383\) 10.0718 + 17.4448i 0.514643 + 0.891388i 0.999856 + 0.0169915i \(0.00540883\pi\)
−0.485213 + 0.874396i \(0.661258\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −11.2294 −0.571561
\(387\) 0 0
\(388\) 77.6743 3.94332
\(389\) 6.69736 11.6002i 0.339570 0.588152i −0.644782 0.764366i \(-0.723052\pi\)
0.984352 + 0.176215i \(0.0563853\pi\)
\(390\) 0 0
\(391\) −0.398891 0.690899i −0.0201728 0.0349402i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.20724 + 2.09100i −0.0608198 + 0.105343i
\(395\) 24.9261 1.25417
\(396\) 0 0
\(397\) 18.0133 0.904061 0.452031 0.892002i \(-0.350700\pi\)
0.452031 + 0.892002i \(0.350700\pi\)
\(398\) 8.58506 14.8698i 0.430330 0.745354i
\(399\) 0 0
\(400\) 17.5249 + 30.3541i 0.876247 + 1.51770i
\(401\) 14.4337 + 25.0000i 0.720787 + 1.24844i 0.960685 + 0.277642i \(0.0895528\pi\)
−0.239898 + 0.970798i \(0.577114\pi\)
\(402\) 0 0
\(403\) 11.8075 20.4513i 0.588176 1.01875i
\(404\) 52.8479 2.62928
\(405\) 0 0
\(406\) 0 0
\(407\) −5.41019 + 9.37073i −0.268173 + 0.464490i
\(408\) 0 0
\(409\) −5.42937 9.40395i −0.268465 0.464995i 0.700000 0.714142i \(-0.253183\pi\)
−0.968466 + 0.249147i \(0.919850\pi\)
\(410\) −21.5936 37.4012i −1.06643 1.84711i
\(411\) 0 0
\(412\) 29.7014 51.4443i 1.46328 2.53448i
\(413\) 0 0
\(414\) 0 0
\(415\) −22.1885 −1.08919
\(416\) −31.8001 + 55.0793i −1.55913 + 2.70049i
\(417\) 0 0
\(418\) 1.14566 + 1.98434i 0.0560359 + 0.0970570i
\(419\) −0.247572 0.428807i −0.0120947 0.0209486i 0.859915 0.510438i \(-0.170517\pi\)
−0.872009 + 0.489489i \(0.837183\pi\)
\(420\) 0 0
\(421\) 9.50320 16.4600i 0.463158 0.802212i −0.535959 0.844244i \(-0.680050\pi\)
0.999116 + 0.0420318i \(0.0133831\pi\)
\(422\) −31.0226 −1.51016
\(423\) 0 0
\(424\) −25.5155 −1.23914
\(425\) 3.47737 6.02298i 0.168677 0.292157i
\(426\) 0 0
\(427\) 0 0
\(428\) −5.16864 8.95234i −0.249835 0.432728i
\(429\) 0 0
\(430\) 13.4790 23.3464i 0.650016 1.12586i
\(431\) 16.9215 0.815078 0.407539 0.913188i \(-0.366387\pi\)
0.407539 + 0.913188i \(0.366387\pi\)
\(432\) 0 0
\(433\) 33.4740 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 49.9774 + 86.5634i 2.39348 + 4.14564i
\(437\) 0.0891197 + 0.154360i 0.00426317 + 0.00738403i
\(438\) 0 0
\(439\) 10.4657 18.1272i 0.499502 0.865163i −0.500498 0.865738i \(-0.666850\pi\)
1.00000 0.000574559i \(0.000182888\pi\)
\(440\) −19.5891 −0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) −15.4290 + 26.7238i −0.733054 + 1.26969i 0.222517 + 0.974929i \(0.428573\pi\)
−0.955572 + 0.294759i \(0.904761\pi\)
\(444\) 0 0
\(445\) −2.05205 3.55425i −0.0972763 0.168487i
\(446\) −22.6972 39.3128i −1.07475 1.86151i
\(447\) 0 0
\(448\) 0 0
\(449\) 33.2789 1.57053 0.785263 0.619162i \(-0.212528\pi\)
0.785263 + 0.619162i \(0.212528\pi\)
\(450\) 0 0
\(451\) −13.5234 −0.636791
\(452\) −8.55957 + 14.8256i −0.402608 + 0.697338i
\(453\) 0 0
\(454\) −23.1737 40.1380i −1.08760 1.88377i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.8952 + 20.6031i −0.556434 + 0.963772i 0.441356 + 0.897332i \(0.354498\pi\)
−0.997790 + 0.0664402i \(0.978836\pi\)
\(458\) −53.7309 −2.51068
\(459\) 0 0
\(460\) −2.42764 −0.113189
\(461\) 8.53122 14.7765i 0.397339 0.688211i −0.596058 0.802941i \(-0.703267\pi\)
0.993397 + 0.114731i \(0.0366005\pi\)
\(462\) 0 0
\(463\) 18.1243 + 31.3922i 0.842306 + 1.45892i 0.887940 + 0.459959i \(0.152136\pi\)
−0.0456338 + 0.998958i \(0.514531\pi\)
\(464\) −32.0945 55.5893i −1.48995 2.58067i
\(465\) 0 0
\(466\) 8.05253 13.9474i 0.373026 0.646100i
\(467\) −8.19160 −0.379062 −0.189531 0.981875i \(-0.560697\pi\)
−0.189531 + 0.981875i \(0.560697\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0080 41.5830i 1.10740 1.91808i
\(471\) 0 0
\(472\) −20.9413 36.2714i −0.963900 1.66952i
\(473\) −4.22074 7.31054i −0.194070 0.336139i
\(474\) 0 0
\(475\) −0.776909 + 1.34565i −0.0356470 + 0.0617425i
\(476\) 0 0
\(477\) 0 0
\(478\) −54.4530 −2.49062
\(479\) 12.7775 22.1312i 0.583817 1.01120i −0.411205 0.911543i \(-0.634892\pi\)
0.995022 0.0996574i \(-0.0317747\pi\)
\(480\) 0 0
\(481\) −12.7491 22.0820i −0.581308 1.00685i
\(482\) 39.7614 + 68.8687i 1.81108 + 3.13688i
\(483\) 0 0
\(484\) 24.6596 42.7116i 1.12089 1.94144i
\(485\) −22.9381 −1.04156
\(486\) 0 0
\(487\) −6.92281 −0.313702 −0.156851 0.987622i \(-0.550134\pi\)
−0.156851 + 0.987622i \(0.550134\pi\)
\(488\) −1.76246 + 3.05266i −0.0797826 + 0.138188i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.7262 32.4348i −0.845103 1.46376i −0.885532 0.464578i \(-0.846206\pi\)
0.0404294 0.999182i \(-0.487127\pi\)
\(492\) 0 0
\(493\) −6.36831 + 11.0302i −0.286814 + 0.496777i
\(494\) −5.39946 −0.242933
\(495\) 0 0
\(496\) −104.867 −4.70867
\(497\) 0 0
\(498\) 0 0
\(499\) −12.8125 22.1919i −0.573566 0.993446i −0.996196 0.0871432i \(-0.972226\pi\)
0.422630 0.906302i \(-0.361107\pi\)
\(500\) −31.8867 55.2293i −1.42601 2.46993i
\(501\) 0 0
\(502\) 30.9329 53.5774i 1.38060 2.39127i
\(503\) −5.79692 −0.258472 −0.129236 0.991614i \(-0.541252\pi\)
−0.129236 + 0.991614i \(0.541252\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) −0.521598 + 0.903434i −0.0231878 + 0.0401625i
\(507\) 0 0
\(508\) 22.4920 + 38.9573i 0.997921 + 1.72845i
\(509\) −12.5697 21.7714i −0.557144 0.965002i −0.997733 0.0672931i \(-0.978564\pi\)
0.440589 0.897709i \(-0.354770\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 23.9940 1.06039
\(513\) 0 0
\(514\) −65.9475 −2.90882
\(515\) −8.77113 + 15.1920i −0.386502 + 0.669441i
\(516\) 0 0
\(517\) −7.51771 13.0211i −0.330629 0.572665i
\(518\) 0 0
\(519\) 0 0
\(520\) 23.0808 39.9771i 1.01216 1.75311i
\(521\) 7.29656 0.319668 0.159834 0.987144i \(-0.448904\pi\)
0.159834 + 0.987144i \(0.448904\pi\)
\(522\) 0 0
\(523\) −16.7727 −0.733421 −0.366710 0.930335i \(-0.619516\pi\)
−0.366710 + 0.930335i \(0.619516\pi\)
\(524\) 32.1580 55.6993i 1.40483 2.43324i
\(525\) 0 0
\(526\) −11.6908 20.2490i −0.509741 0.882898i
\(527\) 10.4041 + 18.0204i 0.453208 + 0.784979i
\(528\) 0 0
\(529\) 11.4594 19.8483i 0.498236 0.862970i
\(530\) 12.0042 0.521431
\(531\) 0 0
\(532\) 0 0
\(533\) 15.9339 27.5982i 0.690172 1.19541i
\(534\) 0 0
\(535\) 1.52635 + 2.64372i 0.0659900 + 0.114298i
\(536\) 11.6234 + 20.1322i 0.502053 + 0.869581i
\(537\) 0 0
\(538\) 20.6774 35.8143i 0.891466 1.54406i
\(539\) 0 0
\(540\) 0 0
\(541\) −5.29816 −0.227786 −0.113893 0.993493i \(-0.536332\pi\)
−0.113893 + 0.993493i \(0.536332\pi\)
\(542\) −6.35097 + 11.0002i −0.272798 + 0.472499i
\(543\) 0 0
\(544\) −28.0202 48.5324i −1.20136 2.08081i
\(545\) −14.7589 25.5631i −0.632200 1.09500i
\(546\) 0 0
\(547\) 16.4325 28.4619i 0.702603 1.21694i −0.264947 0.964263i \(-0.585354\pi\)
0.967550 0.252681i \(-0.0813123\pi\)
\(548\) −88.9084 −3.79798
\(549\) 0 0
\(550\) −9.09416 −0.387776
\(551\) 1.42280 2.46436i 0.0606133 0.104985i
\(552\) 0 0
\(553\) 0 0
\(554\) 22.2515 + 38.5408i 0.945376 + 1.63744i
\(555\) 0 0
\(556\) −21.2256 + 36.7638i −0.900166 + 1.55913i
\(557\) 18.8160 0.797258 0.398629 0.917112i \(-0.369486\pi\)
0.398629 + 0.917112i \(0.369486\pi\)
\(558\) 0 0
\(559\) 19.8923 0.841354
\(560\) 0 0
\(561\) 0 0
\(562\) −4.77054 8.26282i −0.201233 0.348546i
\(563\) −13.8325 23.9586i −0.582970 1.00973i −0.995125 0.0986197i \(-0.968557\pi\)
0.412155 0.911114i \(-0.364776\pi\)
\(564\) 0 0
\(565\) 2.52773 4.37816i 0.106343 0.184191i
\(566\) −70.7856 −2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) −20.0916 + 34.7996i −0.842282 + 1.45888i 0.0456782 + 0.998956i \(0.485455\pi\)
−0.887961 + 0.459920i \(0.847878\pi\)
\(570\) 0 0
\(571\) 3.40565 + 5.89875i 0.142522 + 0.246855i 0.928446 0.371468i \(-0.121146\pi\)
−0.785924 + 0.618323i \(0.787812\pi\)
\(572\) −11.5142 19.9431i −0.481431 0.833863i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.707427 −0.0295017
\(576\) 0 0
\(577\) 36.4222 1.51628 0.758138 0.652094i \(-0.226109\pi\)
0.758138 + 0.652094i \(0.226109\pi\)
\(578\) 12.4312 21.5315i 0.517071 0.895593i
\(579\) 0 0
\(580\) 19.3787 + 33.5649i 0.804658 + 1.39371i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.87947 3.25534i 0.0778397 0.134822i
\(584\) 4.28590 0.177352
\(585\) 0 0
\(586\) 51.2721 2.11803
\(587\) 5.57943 9.66385i 0.230288 0.398870i −0.727605 0.685996i \(-0.759367\pi\)
0.957893 + 0.287126i \(0.0927000\pi\)
\(588\) 0 0
\(589\) −2.32446 4.02609i −0.0957779 0.165892i
\(590\) 9.85220 + 17.0645i 0.405609 + 0.702535i
\(591\) 0 0
\(592\) −56.6145 + 98.0593i −2.32684 + 4.03021i
\(593\) 19.8085 0.813439 0.406720 0.913553i \(-0.366673\pi\)
0.406720 + 0.913553i \(0.366673\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36.7133 + 63.5893i −1.50384 + 2.60472i
\(597\) 0 0
\(598\) −1.22914 2.12893i −0.0502633 0.0870586i
\(599\) −9.06600 15.7028i −0.370427 0.641598i 0.619204 0.785230i \(-0.287455\pi\)
−0.989631 + 0.143632i \(0.954122\pi\)
\(600\) 0 0
\(601\) 12.3285 21.3536i 0.502889 0.871030i −0.497105 0.867690i \(-0.665604\pi\)
0.999994 0.00333942i \(-0.00106297\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 20.9486 0.852387
\(605\) −7.28223 + 12.6132i −0.296065 + 0.512799i
\(606\) 0 0
\(607\) 8.63876 + 14.9628i 0.350637 + 0.607320i 0.986361 0.164596i \(-0.0526319\pi\)
−0.635725 + 0.771916i \(0.719299\pi\)
\(608\) 6.26024 + 10.8431i 0.253886 + 0.439744i
\(609\) 0 0
\(610\) 0.829179 1.43618i 0.0335725 0.0581492i
\(611\) 35.4308 1.43338
\(612\) 0 0
\(613\) 19.5566 0.789882 0.394941 0.918707i \(-0.370765\pi\)
0.394941 + 0.918707i \(0.370765\pi\)
\(614\) −29.3787 + 50.8855i −1.18563 + 2.05357i
\(615\) 0 0
\(616\) 0 0
\(617\) −10.8723 18.8314i −0.437702 0.758122i 0.559810 0.828621i \(-0.310874\pi\)
−0.997512 + 0.0704988i \(0.977541\pi\)
\(618\) 0 0
\(619\) 16.9024 29.2758i 0.679366 1.17670i −0.295807 0.955248i \(-0.595588\pi\)
0.975172 0.221448i \(-0.0710782\pi\)
\(620\) 63.3190 2.54295
\(621\) 0 0
\(622\) 12.2031 0.489300
\(623\) 0 0
\(624\) 0 0
\(625\) 3.20808 + 5.55655i 0.128323 + 0.222262i
\(626\) 11.6778 + 20.2266i 0.466740 + 0.808418i
\(627\) 0 0
\(628\) −0.790623 + 1.36940i −0.0315493 + 0.0546450i
\(629\) 22.4674 0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) 71.9258 124.579i 2.86105 4.95549i
\(633\) 0 0
\(634\) −10.9454 18.9581i −0.434699 0.752921i
\(635\) −6.64213 11.5045i −0.263585 0.456542i
\(636\) 0 0
\(637\) 0 0
\(638\) 16.6547 0.659365
\(639\) 0 0
\(640\) −48.9458 −1.93475
\(641\) 7.95901 13.7854i 0.314362 0.544491i −0.664940 0.746897i \(-0.731543\pi\)
0.979302 + 0.202406i \(0.0648760\pi\)
\(642\) 0 0
\(643\) 13.2527 + 22.9544i 0.522636 + 0.905231i 0.999653 + 0.0263376i \(0.00838450\pi\)
−0.477017 + 0.878894i \(0.658282\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.37883 4.12026i 0.0935938 0.162109i
\(647\) 0.0160392 0.000630565 0.000315282 1.00000i \(-0.499900\pi\)
0.000315282 1.00000i \(0.499900\pi\)
\(648\) 0 0
\(649\) 6.17012 0.242198
\(650\) 10.7152 18.5592i 0.420283 0.727951i
\(651\) 0 0
\(652\) −28.7644 49.8214i −1.12650 1.95115i
\(653\) −16.6440 28.8282i −0.651328 1.12813i −0.982801 0.184669i \(-0.940879\pi\)
0.331473 0.943465i \(-0.392455\pi\)
\(654\) 0 0
\(655\) −9.49661 + 16.4486i −0.371063 + 0.642700i
\(656\) −141.514 −5.52520
\(657\) 0 0
\(658\) 0 0
\(659\) −19.4156 + 33.6288i −0.756324 + 1.30999i 0.188389 + 0.982094i \(0.439673\pi\)
−0.944713 + 0.327897i \(0.893660\pi\)
\(660\) 0 0
\(661\) 2.65322 + 4.59551i 0.103198 + 0.178745i 0.913001 0.407958i \(-0.133759\pi\)
−0.809802 + 0.586703i \(0.800426\pi\)
\(662\) 31.0917 + 53.8525i 1.20842 + 2.09304i
\(663\) 0 0
\(664\) −64.0264 + 110.897i −2.48471 + 4.30364i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.29555 0.0501640
\(668\) 8.58826 14.8753i 0.332290 0.575543i
\(669\) 0 0
\(670\) −5.46842 9.47158i −0.211263 0.365919i
\(671\) −0.259644 0.449717i −0.0100235 0.0173611i
\(672\) 0 0
\(673\) −3.03565 + 5.25789i −0.117016 + 0.202677i −0.918584 0.395227i \(-0.870666\pi\)
0.801568 + 0.597903i \(0.203999\pi\)
\(674\) 37.0285 1.42628
\(675\) 0 0
\(676\) −15.5693 −0.598819
\(677\) 17.3925 30.1247i 0.668449 1.15779i −0.309889 0.950773i \(-0.600292\pi\)
0.978338 0.207014i \(-0.0663747\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 20.3373 + 35.2253i 0.779901 + 1.35083i
\(681\) 0 0
\(682\) 13.6046 23.5638i 0.520946 0.902305i
\(683\) −19.4241 −0.743243 −0.371622 0.928384i \(-0.621198\pi\)
−0.371622 + 0.928384i \(0.621198\pi\)
\(684\) 0 0
\(685\) 26.2556 1.00318
\(686\) 0 0
\(687\) 0 0
\(688\) −44.1676 76.5006i −1.68387 2.91656i
\(689\) 4.42895 + 7.67117i 0.168730 + 0.292248i
\(690\) 0 0
\(691\) −3.31837 + 5.74759i −0.126237 + 0.218649i −0.922216 0.386676i \(-0.873623\pi\)
0.795979 + 0.605324i \(0.206957\pi\)
\(692\) −61.4416 −2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) 6.26814 10.8567i 0.237764 0.411820i
\(696\) 0 0
\(697\) 14.0399 + 24.3178i 0.531799 + 0.921103i
\(698\) 4.91987 + 8.52147i 0.186220 + 0.322542i
\(699\) 0 0
\(700\) 0 0
\(701\) 13.9153 0.525574 0.262787 0.964854i \(-0.415358\pi\)
0.262787 + 0.964854i \(0.415358\pi\)
\(702\) 0 0
\(703\) −5.01963 −0.189319
\(704\) −17.6036 + 30.4904i −0.663462 + 1.14915i
\(705\) 0 0
\(706\) 3.73876 + 6.47571i 0.140710 + 0.243717i
\(707\) 0 0
\(708\) 0 0
\(709\) −17.0778 + 29.5796i −0.641370 + 1.11089i 0.343757 + 0.939059i \(0.388300\pi\)
−0.985127 + 0.171827i \(0.945033\pi\)
\(710\) −6.25450 −0.234727
\(711\) 0 0
\(712\) −23.6852 −0.887642
\(713\) 1.05829 1.83301i 0.0396332 0.0686467i
\(714\) 0 0
\(715\) 3.40025 + 5.88941i 0.127162 + 0.220251i
\(716\) 2.95068 + 5.11072i 0.110272 + 0.190997i
\(717\) 0 0
\(718\) −22.8092 + 39.5066i −0.851231 + 1.47437i
\(719\) −44.2900 −1.65174 −0.825870 0.563861i \(-0.809316\pi\)
−0.825870 + 0.563861i \(0.809316\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 25.2623 43.7556i 0.940165 1.62841i
\(723\) 0 0
\(724\) 8.56860 + 14.8413i 0.318450 + 0.551571i
\(725\) 5.64705 + 9.78099i 0.209726 + 0.363257i
\(726\) 0 0
\(727\) −14.1247 + 24.4647i −0.523857 + 0.907346i 0.475758 + 0.879576i \(0.342174\pi\)
−0.999614 + 0.0277700i \(0.991159\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.01638 −0.0746295
\(731\) −8.76391 + 15.1795i −0.324145 + 0.561435i
\(732\) 0 0
\(733\) −12.5084 21.6653i −0.462010 0.800225i 0.537051 0.843550i \(-0.319538\pi\)
−0.999061 + 0.0433249i \(0.986205\pi\)
\(734\) −32.4919 56.2776i −1.19930 2.07724i
\(735\) 0 0
\(736\) −2.85018 + 4.93666i −0.105059 + 0.181968i
\(737\) −3.42470 −0.126150
\(738\) 0 0
\(739\) 32.0230 1.17798 0.588992 0.808139i \(-0.299525\pi\)
0.588992 + 0.808139i \(0.299525\pi\)
\(740\) 34.1840 59.2084i 1.25663 2.17655i
\(741\) 0 0
\(742\) 0 0
\(743\) −19.4031 33.6072i −0.711833 1.23293i −0.964169 0.265290i \(-0.914532\pi\)
0.252336 0.967640i \(-0.418801\pi\)
\(744\) 0 0
\(745\) 10.8418 18.7786i 0.397214 0.687995i
\(746\) −52.0236 −1.90472
\(747\) 0 0
\(748\) 20.2911 0.741915
\(749\) 0 0
\(750\) 0 0
\(751\) −10.8495 18.7920i −0.395905 0.685728i 0.597311 0.802010i \(-0.296236\pi\)
−0.993216 + 0.116282i \(0.962903\pi\)
\(752\) −78.6685 136.258i −2.86874 4.96881i
\(753\) 0 0
\(754\) −19.6233 + 33.9885i −0.714638 + 1.23779i
\(755\) −6.18635 −0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) −13.6802 + 23.6949i −0.496889 + 0.860637i
\(759\) 0 0
\(760\) −4.54374 7.86999i −0.164819 0.285475i
\(761\) 6.66048 + 11.5363i 0.241442 + 0.418190i 0.961125 0.276113i \(-0.0890462\pi\)
−0.719683 + 0.694303i \(0.755713\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.7795 −0.751775
\(765\) 0 0
\(766\) −54.6923 −1.97611
\(767\) −7.26992 + 12.5919i −0.262502 + 0.454666i
\(768\) 0 0
\(769\) −27.3568 47.3833i −0.986510 1.70869i −0.635022 0.772494i \(-0.719009\pi\)
−0.351488 0.936192i \(-0.614324\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.1088 19.2410i 0.399814 0.692498i
\(773\) 2.36042 0.0848983 0.0424491 0.999099i \(-0.486484\pi\)
0.0424491 + 0.999099i \(0.486484\pi\)
\(774\) 0 0
\(775\) 18.4515 0.662796
\(776\) −66.1892 + 114.643i −2.37606 + 4.11545i
\(777\) 0 0
\(778\) 18.1842 + 31.4960i 0.651936 + 1.12919i
\(779\) −3.13678 5.43306i −0.112387 0.194660i
\(780\) 0 0
\(781\) −0.979248 + 1.69611i −0.0350403 + 0.0606915i
\(782\) 2.16608 0.0774589
\(783\) 0 0
\(784\) 0 0
\(785\) 0.233479 0.404398i 0.00833323 0.0144336i
\(786\) 0 0
\(787\) −0.833971 1.44448i −0.0297278 0.0514901i 0.850779 0.525524i \(-0.176131\pi\)
−0.880507 + 0.474034i \(0.842797\pi\)
\(788\) −2.38855 4.13708i −0.0850884 0.147377i
\(789\) 0 0
\(790\) −33.8388 + 58.6105i −1.20393 + 2.08527i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.22370 0.0434548
\(794\) −24.4542 + 42.3560i −0.867848 + 1.50316i
\(795\) 0 0
\(796\) 16.9857 + 29.4201i 0.602043 + 1.04277i
\(797\) −14.3148 24.7939i −0.507055 0.878244i −0.999967 0.00816511i \(-0.997401\pi\)
0.492912 0.870079i \(-0.335932\pi\)
\(798\) 0 0
\(799\) −15.6097 + 27.0368i −0.552232 + 0.956493i
\(800\) −49.6934 −1.75693
\(801\) 0 0
\(802\) −78.3791 −2.76766
\(803\) −0.315698 + 0.546805i −0.0111408 + 0.0192963i
\(804\) 0 0
\(805\) 0 0
\(806\) 32.0591 + 55.5279i 1.12923 + 1.95589i
\(807\) 0 0
\(808\) −45.0337 + 78.0007i −1.58428 + 2.74406i
\(809\) 2.85691 0.100444 0.0502219 0.998738i \(-0.484007\pi\)
0.0502219 + 0.998738i \(0.484007\pi\)
\(810\) 0 0
\(811\) −26.2917 −0.923225 −0.461613 0.887082i \(-0.652729\pi\)
−0.461613 + 0.887082i \(0.652729\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −14.6894 25.4428i −0.514863 0.891769i
\(815\) 8.49443 + 14.7128i 0.297547 + 0.515366i
\(816\) 0 0
\(817\) 1.95802 3.39139i 0.0685025 0.118650i
\(818\) 29.4829 1.03085
\(819\) 0 0
\(820\) 85.4467 2.98393
\(821\) −1.32925 + 2.30232i −0.0463910 + 0.0803517i −0.888289 0.459286i \(-0.848105\pi\)
0.841897 + 0.539638i \(0.181439\pi\)
\(822\) 0 0
\(823\) 6.10769 + 10.5788i 0.212901 + 0.368755i 0.952621 0.304160i \(-0.0983756\pi\)
−0.739721 + 0.672914i \(0.765042\pi\)
\(824\) 50.6193 + 87.6752i 1.76341 + 3.05431i
\(825\) 0 0
\(826\) 0 0
\(827\) −9.15812 −0.318459 −0.159230 0.987242i \(-0.550901\pi\)
−0.159230 + 0.987242i \(0.550901\pi\)
\(828\) 0 0
\(829\) −18.3431 −0.637083 −0.318541 0.947909i \(-0.603193\pi\)
−0.318541 + 0.947909i \(0.603193\pi\)
\(830\) 30.1224 52.1735i 1.04556 1.81097i
\(831\) 0 0
\(832\) −41.4828 71.8503i −1.43816 2.49096i
\(833\) 0 0
\(834\) 0 0
\(835\) −2.53620 + 4.39284i −0.0877690 + 0.152020i
\(836\) −4.53341 −0.156791
\(837\) 0 0
\(838\) 1.34438 0.0464409
\(839\) −9.47055 + 16.4035i −0.326960 + 0.566311i −0.981907 0.189364i \(-0.939357\pi\)
0.654947 + 0.755675i \(0.272691\pi\)
\(840\) 0 0
\(841\) 4.15821 + 7.20224i 0.143387 + 0.248353i
\(842\) 25.8024 + 44.6911i 0.889211 + 1.54016i
\(843\) 0 0
\(844\) 30.6895 53.1557i 1.05637 1.82969i
\(845\) 4.59778 0.158168
\(846\) 0 0
\(847\) 0 0
\(848\) 19.6676 34.0652i 0.675387 1.16980i
\(849\) 0 0
\(850\) 9.44151 + 16.3532i 0.323841 + 0.560909i
\(851\) −1.14268 1.97917i −0.0391704 0.0678452i
\(852\) 0 0
\(853\) 9.97922 17.2845i 0.341682 0.591811i −0.643063 0.765813i \(-0.722337\pi\)
0.984745 + 0.174002i \(0.0556701\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 17.6176 0.602156
\(857\) 8.20001 14.2028i 0.280107 0.485159i −0.691304 0.722564i \(-0.742963\pi\)
0.971411 + 0.237405i \(0.0762967\pi\)
\(858\) 0 0
\(859\) 16.8575 + 29.1981i 0.575172 + 0.996226i 0.996023 + 0.0890968i \(0.0283980\pi\)
−0.420851 + 0.907130i \(0.638269\pi\)
\(860\) 26.6685 + 46.1912i 0.909389 + 1.57511i
\(861\) 0 0
\(862\) −22.9720 + 39.7887i −0.782429 + 1.35521i
\(863\) 28.6831 0.976383 0.488191 0.872737i \(-0.337657\pi\)
0.488191 + 0.872737i \(0.337657\pi\)
\(864\) 0 0
\(865\) 18.1444 0.616927
\(866\) −45.4432 + 78.7100i −1.54422 + 2.67467i
\(867\) 0 0
\(868\) 0 0
\(869\) 10.5961 + 18.3529i 0.359447 + 0.622581i
\(870\) 0 0
\(871\) 4.03513 6.98906i 0.136725 0.236815i
\(872\) −170.351 −5.76880
\(873\) 0 0
\(874\) −0.483944 −0.0163696
\(875\) 0 0
\(876\) 0 0
\(877\) 14.7621 + 25.5688i 0.498482 + 0.863396i 0.999998 0.00175202i \(-0.000557684\pi\)
−0.501517 + 0.865148i \(0.667224\pi\)
\(878\) 28.4159 + 49.2177i 0.958989 + 1.66102i
\(879\) 0 0
\(880\) 15.0994 26.1530i 0.509001 0.881616i
\(881\) 57.5032 1.93733 0.968666 0.248366i \(-0.0798934\pi\)
0.968666 + 0.248366i \(0.0798934\pi\)
\(882\) 0 0
\(883\) 19.8715 0.668730 0.334365 0.942444i \(-0.391478\pi\)
0.334365 + 0.942444i \(0.391478\pi\)
\(884\) −23.9079 + 41.4097i −0.804109 + 1.39276i
\(885\) 0 0
\(886\) −41.8918 72.5587i −1.40738 2.43766i
\(887\) −18.5475 32.1253i −0.622766 1.07866i −0.988968 0.148127i \(-0.952676\pi\)
0.366203 0.930535i \(-0.380658\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 11.1432 0.373519
\(891\) 0 0
\(892\) 89.8139 3.00719
\(893\) 3.48750 6.04053i 0.116705 0.202139i
\(894\) 0 0
\(895\) −0.871366 1.50925i −0.0291266 0.0504487i
\(896\) 0 0
\(897\) 0 0
\(898\) −45.1783 + 78.2511i −1.50762 + 2.61127i
\(899\) −33.7913 −1.12700
\(900\) 0 0
\(901\) −7.80503 −0.260023
\(902\) 18.3589 31.7985i 0.611284 1.05877i
\(903\) 0 0
\(904\) −14.5879 25.2669i −0.485185 0.840366i
\(905\) −2.53040 4.38278i −0.0841133 0.145689i
\(906\) 0 0
\(907\) −12.2044 + 21.1386i −0.405240 + 0.701896i −0.994349 0.106157i \(-0.966145\pi\)
0.589110 + 0.808053i \(0.299479\pi\)
\(908\) 91.6993 3.04315
\(909\) 0 0
\(910\) 0 0
\(911\) 12.5493 21.7360i 0.415776 0.720146i −0.579733 0.814806i \(-0.696843\pi\)
0.995510 + 0.0946604i \(0.0301765\pi\)
\(912\) 0 0
\(913\) −9.43234 16.3373i −0.312165 0.540685i
\(914\) −32.2971 55.9401i −1.06829 1.85034i
\(915\) 0 0
\(916\) 53.1538 92.0652i 1.75625 3.04192i
\(917\) 0 0
\(918\) 0 0
\(919\) −28.5976 −0.943348 −0.471674 0.881773i \(-0.656350\pi\)
−0.471674 + 0.881773i \(0.656350\pi\)
\(920\) 2.06869 3.58307i 0.0682026 0.118130i
\(921\) 0 0
\(922\) 23.1634 + 40.1202i 0.762846 + 1.32129i
\(923\) −2.30759 3.99686i −0.0759553 0.131558i
\(924\) 0 0
\(925\) 9.96139 17.2536i 0.327528 0.567296i
\(926\) −98.4196 −3.23427
\(927\) 0 0
\(928\) 91.0065 2.98744
\(929\) 22.7285 39.3669i 0.745698 1.29159i −0.204170 0.978935i \(-0.565450\pi\)
0.949868 0.312651i \(-0.101217\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 15.9321 + 27.5952i 0.521873 + 0.903910i
\(933\) 0 0
\(934\) 11.1206 19.2615i 0.363878 0.630256i
\(935\) −5.99217 −0.195965
\(936\) 0 0
\(937\) −27.0083 −0.882322 −0.441161 0.897428i \(-0.645433\pi\)
−0.441161 + 0.897428i \(0.645433\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 47.5002 + 82.2728i 1.54929 + 2.68344i
\(941\) −6.35657 11.0099i −0.207218 0.358912i 0.743619 0.668604i \(-0.233108\pi\)
−0.950837 + 0.309691i \(0.899774\pi\)
\(942\) 0 0
\(943\) 1.42812 2.47358i 0.0465060 0.0805508i
\(944\) 64.5667 2.10147
\(945\) 0 0
\(946\) 22.9197 0.745185
\(947\) 23.7724 41.1749i 0.772498 1.33801i −0.163692 0.986511i \(-0.552340\pi\)
0.936190 0.351494i \(-0.114326\pi\)
\(948\) 0 0
\(949\) −0.743940 1.28854i −0.0241493 0.0418279i
\(950\) −2.10941 3.65361i −0.0684384 0.118539i
\(951\) 0 0
\(952\) 0 0
\(953\) −38.2355 −1.23857 −0.619285 0.785166i \(-0.712577\pi\)
−0.619285 + 0.785166i \(0.712577\pi\)
\(954\) 0 0
\(955\) 6.13640 0.198569
\(956\) 53.8682 93.3024i 1.74222 3.01762i
\(957\) 0 0
\(958\) 34.6925 + 60.0891i 1.12086 + 1.94139i
\(959\) 0 0
\(960\) 0 0
\(961\) −12.1028 + 20.9627i −0.390413 + 0.676215i
\(962\) 69.2309 2.23209
\(963\) 0 0
\(964\) −157.337 −5.06749
\(965\) −3.28054 + 5.68207i −0.105604 + 0.182912i
\(966\) 0 0
\(967\) −20.4093 35.3499i −0.656317 1.13678i −0.981562 0.191145i \(-0.938780\pi\)
0.325244 0.945630i \(-0.394553\pi\)
\(968\) 42.0267 + 72.7924i 1.35079 + 2.33964i
\(969\) 0 0
\(970\) 31.1399 53.9359i 0.999843 1.73178i
\(971\) 44.9471 1.44242 0.721210 0.692717i \(-0.243586\pi\)
0.721210 + 0.692717i \(0.243586\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 9.39817 16.2781i 0.301137 0.521584i
\(975\) 0 0
\(976\) −2.71703 4.70603i −0.0869699 0.150636i
\(977\) 26.7552 + 46.3414i 0.855974 + 1.48259i 0.875738 + 0.482787i \(0.160375\pi\)
−0.0197635 + 0.999805i \(0.506291\pi\)
\(978\) 0 0
\(979\) 1.74465 3.02182i 0.0557593 0.0965779i
\(980\) 0 0
\(981\) 0 0
\(982\) 101.688 3.24501
\(983\) −5.80278 + 10.0507i −0.185080 + 0.320568i −0.943603 0.331078i \(-0.892588\pi\)
0.758524 + 0.651646i \(0.225921\pi\)
\(984\) 0 0
\(985\) 0.705363 + 1.22172i 0.0224747 + 0.0389274i
\(986\) −17.2908 29.9485i −0.550651 0.953756i
\(987\) 0 0
\(988\) 5.34147 9.25170i 0.169935 0.294336i
\(989\) 1.78291 0.0566932
\(990\) 0 0
\(991\) 26.0091 0.826208 0.413104 0.910684i \(-0.364445\pi\)
0.413104 + 0.910684i \(0.364445\pi\)
\(992\) 74.3398 128.760i 2.36029 4.08814i
\(993\) 0 0
\(994\) 0 0
\(995\) −5.01607 8.68808i −0.159020 0.275431i
\(996\) 0 0
\(997\) −23.4499 + 40.6164i −0.742666 + 1.28633i 0.208612 + 0.977999i \(0.433105\pi\)
−0.951277 + 0.308336i \(0.900228\pi\)
\(998\) 69.5753 2.20237
\(999\) 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 1323.2.f.h.883.1 24
3.2 odd 2 441.2.f.h.295.11 yes 24
7.2 even 3 1323.2.h.h.802.11 24
7.3 odd 6 1323.2.g.h.667.1 24
7.4 even 3 1323.2.g.h.667.2 24
7.5 odd 6 1323.2.h.h.802.12 24
7.6 odd 2 inner 1323.2.f.h.883.2 24
9.2 odd 6 3969.2.a.bh.1.2 12
9.4 even 3 inner 1323.2.f.h.442.1 24
9.5 odd 6 441.2.f.h.148.11 24
9.7 even 3 3969.2.a.bi.1.11 12
21.2 odd 6 441.2.h.h.214.1 24
21.5 even 6 441.2.h.h.214.2 24
21.11 odd 6 441.2.g.h.79.12 24
21.17 even 6 441.2.g.h.79.11 24
21.20 even 2 441.2.f.h.295.12 yes 24
63.4 even 3 1323.2.h.h.226.11 24
63.5 even 6 441.2.g.h.67.11 24
63.13 odd 6 inner 1323.2.f.h.442.2 24
63.20 even 6 3969.2.a.bh.1.1 12
63.23 odd 6 441.2.g.h.67.12 24
63.31 odd 6 1323.2.h.h.226.12 24
63.32 odd 6 441.2.h.h.373.1 24
63.34 odd 6 3969.2.a.bi.1.12 12
63.40 odd 6 1323.2.g.h.361.1 24
63.41 even 6 441.2.f.h.148.12 yes 24
63.58 even 3 1323.2.g.h.361.2 24
63.59 even 6 441.2.h.h.373.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.h.148.11 24 9.5 odd 6
441.2.f.h.148.12 yes 24 63.41 even 6
441.2.f.h.295.11 yes 24 3.2 odd 2
441.2.f.h.295.12 yes 24 21.20 even 2
441.2.g.h.67.11 24 63.5 even 6
441.2.g.h.67.12 24 63.23 odd 6
441.2.g.h.79.11 24 21.17 even 6
441.2.g.h.79.12 24 21.11 odd 6
441.2.h.h.214.1 24 21.2 odd 6
441.2.h.h.214.2 24 21.5 even 6
441.2.h.h.373.1 24 63.32 odd 6
441.2.h.h.373.2 24 63.59 even 6
1323.2.f.h.442.1 24 9.4 even 3 inner
1323.2.f.h.442.2 24 63.13 odd 6 inner
1323.2.f.h.883.1 24 1.1 even 1 trivial
1323.2.f.h.883.2 24 7.6 odd 2 inner
1323.2.g.h.361.1 24 63.40 odd 6
1323.2.g.h.361.2 24 63.58 even 3
1323.2.g.h.667.1 24 7.3 odd 6
1323.2.g.h.667.2 24 7.4 even 3
1323.2.h.h.226.11 24 63.4 even 3
1323.2.h.h.226.12 24 63.31 odd 6
1323.2.h.h.802.11 24 7.2 even 3
1323.2.h.h.802.12 24 7.5 odd 6
3969.2.a.bh.1.1 12 63.20 even 6
3969.2.a.bh.1.2 12 9.2 odd 6
3969.2.a.bi.1.11 12 9.7 even 3
3969.2.a.bi.1.12 12 63.34 odd 6