Properties

Label 1008.2.r.h.673.1
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
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] = [1008,2,Mod(337,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("1008.337");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.h.337.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70574 - 0.300767i) q^{3} +(-1.26604 - 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\) \(q+(-1.70574 - 0.300767i) q^{3} +(-1.26604 - 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.81908 + 1.02606i) q^{9} +(0.233956 - 0.405223i) q^{11} +(-2.91147 - 5.04282i) q^{13} +(1.50000 + 4.12122i) q^{15} +3.87939 q^{17} +2.18479 q^{19} +(-1.11334 + 1.32683i) q^{21} +(-0.0530334 - 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(-3.84002 - 6.65111i) q^{31} +(-0.520945 + 0.620838i) q^{33} -2.53209 q^{35} -7.68004 q^{37} +(3.44949 + 9.47740i) q^{39} +(1.11334 + 1.92836i) q^{41} +(0.613341 - 1.06234i) q^{43} +(-1.31908 - 7.48086i) q^{45} +(-2.66637 + 4.61830i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-6.61721 - 1.16679i) q^{51} -0.716881 q^{53} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +(0.368241 + 0.637812i) q^{59} +(-0.479055 + 0.829748i) q^{61} +(2.29813 - 1.92836i) q^{63} +(-7.37211 + 12.7689i) q^{65} +(-4.81908 - 8.34689i) q^{67} +(0.0628336 + 0.172634i) q^{69} -13.2344 q^{71} -10.2686 q^{73} +(1.57145 - 1.87278i) q^{75} +(-0.233956 - 0.405223i) q^{77} +(-6.31908 + 10.9450i) q^{79} +(6.89440 + 5.78509i) q^{81} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +(9.77631 - 11.6510i) q^{87} -8.11381 q^{89} -5.82295 q^{91} +(4.54963 + 12.5000i) q^{93} +(-2.76604 - 4.79093i) q^{95} +(6.80200 - 11.7814i) q^{97} +(1.07532 - 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{5} + 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{5} + 3 q^{7} + 6 q^{11} + 3 q^{13} + 9 q^{15} + 12 q^{17} + 6 q^{19} + 12 q^{23} + 6 q^{25} - 27 q^{27} - 9 q^{29} - 3 q^{31} - 6 q^{35} - 6 q^{37} + 18 q^{39} - 3 q^{43} + 9 q^{45} + 3 q^{47} - 3 q^{49} - 9 q^{51} + 12 q^{53} - 9 q^{57} - 3 q^{59} - 6 q^{61} - 15 q^{65} - 12 q^{67} - 9 q^{69} - 18 q^{71} - 42 q^{73} + 9 q^{75} - 6 q^{77} - 21 q^{79} - 18 q^{83} - 9 q^{85} - 9 q^{87} + 24 q^{89} + 6 q^{91} - 27 q^{93} - 12 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.70574 0.300767i −0.984808 0.173648i
\(4\) 0 0
\(5\) −1.26604 2.19285i −0.566192 0.980674i −0.996938 0.0782003i \(-0.975083\pi\)
0.430745 0.902473i \(-0.358251\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) 2.81908 + 1.02606i 0.939693 + 0.342020i
\(10\) 0 0
\(11\) 0.233956 0.405223i 0.0705403 0.122179i −0.828598 0.559844i \(-0.810861\pi\)
0.899138 + 0.437665i \(0.144194\pi\)
\(12\) 0 0
\(13\) −2.91147 5.04282i −0.807498 1.39863i −0.914592 0.404378i \(-0.867488\pi\)
0.107094 0.994249i \(-0.465845\pi\)
\(14\) 0 0
\(15\) 1.50000 + 4.12122i 0.387298 + 1.06409i
\(16\) 0 0
\(17\) 3.87939 0.940889 0.470445 0.882430i \(-0.344094\pi\)
0.470445 + 0.882430i \(0.344094\pi\)
\(18\) 0 0
\(19\) 2.18479 0.501226 0.250613 0.968087i \(-0.419368\pi\)
0.250613 + 0.968087i \(0.419368\pi\)
\(20\) 0 0
\(21\) −1.11334 + 1.32683i −0.242951 + 0.289538i
\(22\) 0 0
\(23\) −0.0530334 0.0918566i −0.0110582 0.0191534i 0.860443 0.509546i \(-0.170187\pi\)
−0.871502 + 0.490393i \(0.836853\pi\)
\(24\) 0 0
\(25\) −0.705737 + 1.22237i −0.141147 + 0.244474i
\(26\) 0 0
\(27\) −4.50000 2.59808i −0.866025 0.500000i
\(28\) 0 0
\(29\) −4.39053 + 7.60462i −0.815301 + 1.41214i 0.0938108 + 0.995590i \(0.470095\pi\)
−0.909112 + 0.416552i \(0.863238\pi\)
\(30\) 0 0
\(31\) −3.84002 6.65111i −0.689688 1.19458i −0.971939 0.235235i \(-0.924414\pi\)
0.282250 0.959341i \(-0.408919\pi\)
\(32\) 0 0
\(33\) −0.520945 + 0.620838i −0.0906848 + 0.108074i
\(34\) 0 0
\(35\) −2.53209 −0.428001
\(36\) 0 0
\(37\) −7.68004 −1.26259 −0.631296 0.775542i \(-0.717477\pi\)
−0.631296 + 0.775542i \(0.717477\pi\)
\(38\) 0 0
\(39\) 3.44949 + 9.47740i 0.552361 + 1.51760i
\(40\) 0 0
\(41\) 1.11334 + 1.92836i 0.173875 + 0.301160i 0.939771 0.341804i \(-0.111038\pi\)
−0.765897 + 0.642964i \(0.777705\pi\)
\(42\) 0 0
\(43\) 0.613341 1.06234i 0.0935336 0.162005i −0.815462 0.578811i \(-0.803517\pi\)
0.908996 + 0.416806i \(0.136850\pi\)
\(44\) 0 0
\(45\) −1.31908 7.48086i −0.196637 1.11518i
\(46\) 0 0
\(47\) −2.66637 + 4.61830i −0.388931 + 0.673648i −0.992306 0.123810i \(-0.960489\pi\)
0.603375 + 0.797457i \(0.293822\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −6.61721 1.16679i −0.926595 0.163384i
\(52\) 0 0
\(53\) −0.716881 −0.0984712 −0.0492356 0.998787i \(-0.515679\pi\)
−0.0492356 + 0.998787i \(0.515679\pi\)
\(54\) 0 0
\(55\) −1.18479 −0.159757
\(56\) 0 0
\(57\) −3.72668 0.657115i −0.493611 0.0870369i
\(58\) 0 0
\(59\) 0.368241 + 0.637812i 0.0479409 + 0.0830360i 0.889000 0.457907i \(-0.151401\pi\)
−0.841059 + 0.540943i \(0.818067\pi\)
\(60\) 0 0
\(61\) −0.479055 + 0.829748i −0.0613368 + 0.106238i −0.895063 0.445939i \(-0.852870\pi\)
0.833726 + 0.552178i \(0.186203\pi\)
\(62\) 0 0
\(63\) 2.29813 1.92836i 0.289538 0.242951i
\(64\) 0 0
\(65\) −7.37211 + 12.7689i −0.914398 + 1.58378i
\(66\) 0 0
\(67\) −4.81908 8.34689i −0.588744 1.01973i −0.994397 0.105708i \(-0.966289\pi\)
0.405653 0.914027i \(-0.367044\pi\)
\(68\) 0 0
\(69\) 0.0628336 + 0.172634i 0.00756428 + 0.0207827i
\(70\) 0 0
\(71\) −13.2344 −1.57064 −0.785318 0.619092i \(-0.787501\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(72\) 0 0
\(73\) −10.2686 −1.20185 −0.600923 0.799307i \(-0.705200\pi\)
−0.600923 + 0.799307i \(0.705200\pi\)
\(74\) 0 0
\(75\) 1.57145 1.87278i 0.181456 0.216250i
\(76\) 0 0
\(77\) −0.233956 0.405223i −0.0266617 0.0461794i
\(78\) 0 0
\(79\) −6.31908 + 10.9450i −0.710952 + 1.23140i 0.253548 + 0.967323i \(0.418402\pi\)
−0.964500 + 0.264082i \(0.914931\pi\)
\(80\) 0 0
\(81\) 6.89440 + 5.78509i 0.766044 + 0.642788i
\(82\) 0 0
\(83\) −1.36571 + 2.36549i −0.149907 + 0.259646i −0.931193 0.364527i \(-0.881231\pi\)
0.781286 + 0.624173i \(0.214564\pi\)
\(84\) 0 0
\(85\) −4.91147 8.50692i −0.532724 0.922705i
\(86\) 0 0
\(87\) 9.77631 11.6510i 1.04813 1.24911i
\(88\) 0 0
\(89\) −8.11381 −0.860062 −0.430031 0.902814i \(-0.641497\pi\)
−0.430031 + 0.902814i \(0.641497\pi\)
\(90\) 0 0
\(91\) −5.82295 −0.610411
\(92\) 0 0
\(93\) 4.54963 + 12.5000i 0.471775 + 1.29619i
\(94\) 0 0
\(95\) −2.76604 4.79093i −0.283790 0.491539i
\(96\) 0 0
\(97\) 6.80200 11.7814i 0.690639 1.19622i −0.280990 0.959711i \(-0.590663\pi\)
0.971629 0.236511i \(-0.0760039\pi\)
\(98\) 0 0
\(99\) 1.07532 0.902302i 0.108074 0.0906848i
\(100\) 0 0
\(101\) 4.78699 8.29131i 0.476323 0.825016i −0.523309 0.852143i \(-0.675303\pi\)
0.999632 + 0.0271271i \(0.00863590\pi\)
\(102\) 0 0
\(103\) 1.52094 + 2.63435i 0.149863 + 0.259571i 0.931177 0.364568i \(-0.118783\pi\)
−0.781314 + 0.624139i \(0.785450\pi\)
\(104\) 0 0
\(105\) 4.31908 + 0.761570i 0.421499 + 0.0743216i
\(106\) 0 0
\(107\) 6.51754 0.630074 0.315037 0.949079i \(-0.397983\pi\)
0.315037 + 0.949079i \(0.397983\pi\)
\(108\) 0 0
\(109\) 10.6382 1.01895 0.509475 0.860485i \(-0.329840\pi\)
0.509475 + 0.860485i \(0.329840\pi\)
\(110\) 0 0
\(111\) 13.1001 + 2.30991i 1.24341 + 0.219247i
\(112\) 0 0
\(113\) −2.58853 4.48346i −0.243508 0.421768i 0.718203 0.695834i \(-0.244965\pi\)
−0.961711 + 0.274065i \(0.911632\pi\)
\(114\) 0 0
\(115\) −0.134285 + 0.232589i −0.0125222 + 0.0216890i
\(116\) 0 0
\(117\) −3.03343 17.2035i −0.280441 1.59046i
\(118\) 0 0
\(119\) 1.93969 3.35965i 0.177811 0.307978i
\(120\) 0 0
\(121\) 5.39053 + 9.33667i 0.490048 + 0.848788i
\(122\) 0 0
\(123\) −1.31908 3.62414i −0.118937 0.326777i
\(124\) 0 0
\(125\) −9.08647 −0.812718
\(126\) 0 0
\(127\) 8.88207 0.788157 0.394078 0.919077i \(-0.371064\pi\)
0.394078 + 0.919077i \(0.371064\pi\)
\(128\) 0 0
\(129\) −1.36571 + 1.62760i −0.120244 + 0.143302i
\(130\) 0 0
\(131\) 5.68139 + 9.84045i 0.496385 + 0.859764i 0.999991 0.00416893i \(-0.00132701\pi\)
−0.503606 + 0.863933i \(0.667994\pi\)
\(132\) 0 0
\(133\) 1.09240 1.89209i 0.0947228 0.164065i
\(134\) 0 0
\(135\) 13.1571i 1.13238i
\(136\) 0 0
\(137\) 2.86231 4.95767i 0.244544 0.423562i −0.717459 0.696600i \(-0.754695\pi\)
0.962003 + 0.273038i \(0.0880285\pi\)
\(138\) 0 0
\(139\) −0.461981 0.800175i −0.0391847 0.0678700i 0.845768 0.533551i \(-0.179143\pi\)
−0.884953 + 0.465681i \(0.845809\pi\)
\(140\) 0 0
\(141\) 5.93717 7.07564i 0.500000 0.595876i
\(142\) 0 0
\(143\) −2.72462 −0.227844
\(144\) 0 0
\(145\) 22.2344 1.84647
\(146\) 0 0
\(147\) 0.592396 + 1.62760i 0.0488600 + 0.134242i
\(148\) 0 0
\(149\) −4.36231 7.55574i −0.357374 0.618991i 0.630147 0.776476i \(-0.282995\pi\)
−0.987521 + 0.157485i \(0.949661\pi\)
\(150\) 0 0
\(151\) 9.21348 15.9582i 0.749782 1.29866i −0.198145 0.980173i \(-0.563492\pi\)
0.947927 0.318488i \(-0.103175\pi\)
\(152\) 0 0
\(153\) 10.9363 + 3.98048i 0.884147 + 0.321803i
\(154\) 0 0
\(155\) −9.72328 + 16.8412i −0.780992 + 1.35272i
\(156\) 0 0
\(157\) −2.46198 4.26428i −0.196488 0.340326i 0.750900 0.660416i \(-0.229620\pi\)
−0.947387 + 0.320090i \(0.896287\pi\)
\(158\) 0 0
\(159\) 1.22281 + 0.215615i 0.0969752 + 0.0170994i
\(160\) 0 0
\(161\) −0.106067 −0.00835924
\(162\) 0 0
\(163\) −7.63816 −0.598267 −0.299133 0.954211i \(-0.596698\pi\)
−0.299133 + 0.954211i \(0.596698\pi\)
\(164\) 0 0
\(165\) 2.02094 + 0.356347i 0.157330 + 0.0277416i
\(166\) 0 0
\(167\) −2.82770 4.89771i −0.218814 0.378996i 0.735632 0.677382i \(-0.236885\pi\)
−0.954446 + 0.298385i \(0.903552\pi\)
\(168\) 0 0
\(169\) −10.4534 + 18.1058i −0.804105 + 1.39275i
\(170\) 0 0
\(171\) 6.15910 + 2.24173i 0.470998 + 0.171429i
\(172\) 0 0
\(173\) −10.5346 + 18.2465i −0.800932 + 1.38725i 0.118071 + 0.993005i \(0.462329\pi\)
−0.919003 + 0.394250i \(0.871005\pi\)
\(174\) 0 0
\(175\) 0.705737 + 1.22237i 0.0533487 + 0.0924027i
\(176\) 0 0
\(177\) −0.436289 1.19869i −0.0327935 0.0900994i
\(178\) 0 0
\(179\) 5.12061 0.382733 0.191366 0.981519i \(-0.438708\pi\)
0.191366 + 0.981519i \(0.438708\pi\)
\(180\) 0 0
\(181\) −0.319955 −0.0237821 −0.0118910 0.999929i \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 0 0
\(183\) 1.06670 1.27125i 0.0788530 0.0939734i
\(184\) 0 0
\(185\) 9.72328 + 16.8412i 0.714870 + 1.23819i
\(186\) 0 0
\(187\) 0.907604 1.57202i 0.0663706 0.114957i
\(188\) 0 0
\(189\) −4.50000 + 2.59808i −0.327327 + 0.188982i
\(190\) 0 0
\(191\) −7.78359 + 13.4816i −0.563200 + 0.975492i 0.434014 + 0.900906i \(0.357097\pi\)
−0.997215 + 0.0745858i \(0.976237\pi\)
\(192\) 0 0
\(193\) −3.02094 5.23243i −0.217452 0.376639i 0.736576 0.676355i \(-0.236441\pi\)
−0.954028 + 0.299716i \(0.903108\pi\)
\(194\) 0 0
\(195\) 16.4153 19.5630i 1.17553 1.40094i
\(196\) 0 0
\(197\) 25.2344 1.79788 0.898939 0.438074i \(-0.144339\pi\)
0.898939 + 0.438074i \(0.144339\pi\)
\(198\) 0 0
\(199\) −3.04189 −0.215634 −0.107817 0.994171i \(-0.534386\pi\)
−0.107817 + 0.994171i \(0.534386\pi\)
\(200\) 0 0
\(201\) 5.70961 + 15.6870i 0.402725 + 1.10648i
\(202\) 0 0
\(203\) 4.39053 + 7.60462i 0.308155 + 0.533740i
\(204\) 0 0
\(205\) 2.81908 4.88279i 0.196893 0.341029i
\(206\) 0 0
\(207\) −0.0552549 0.313366i −0.00384048 0.0217805i
\(208\) 0 0
\(209\) 0.511144 0.885328i 0.0353566 0.0612394i
\(210\) 0 0
\(211\) −2.72668 4.72275i −0.187713 0.325128i 0.756775 0.653676i \(-0.226774\pi\)
−0.944487 + 0.328548i \(0.893441\pi\)
\(212\) 0 0
\(213\) 22.5744 + 3.98048i 1.54678 + 0.272738i
\(214\) 0 0
\(215\) −3.10607 −0.211832
\(216\) 0 0
\(217\) −7.68004 −0.521355
\(218\) 0 0
\(219\) 17.5155 + 3.08845i 1.18359 + 0.208698i
\(220\) 0 0
\(221\) −11.2947 19.5630i −0.759766 1.31595i
\(222\) 0 0
\(223\) 7.09627 12.2911i 0.475201 0.823073i −0.524395 0.851475i \(-0.675709\pi\)
0.999597 + 0.0284023i \(0.00904195\pi\)
\(224\) 0 0
\(225\) −3.24376 + 2.72183i −0.216250 + 0.181456i
\(226\) 0 0
\(227\) −1.44697 + 2.50622i −0.0960385 + 0.166344i −0.910042 0.414517i \(-0.863951\pi\)
0.814003 + 0.580861i \(0.197284\pi\)
\(228\) 0 0
\(229\) −4.58378 7.93934i −0.302905 0.524646i 0.673888 0.738834i \(-0.264623\pi\)
−0.976793 + 0.214187i \(0.931290\pi\)
\(230\) 0 0
\(231\) 0.277189 + 0.761570i 0.0182377 + 0.0501076i
\(232\) 0 0
\(233\) 13.2713 0.869429 0.434715 0.900568i \(-0.356849\pi\)
0.434715 + 0.900568i \(0.356849\pi\)
\(234\) 0 0
\(235\) 13.5030 0.880838
\(236\) 0 0
\(237\) 14.0706 16.7687i 0.913982 1.08924i
\(238\) 0 0
\(239\) 4.76857 + 8.25941i 0.308453 + 0.534257i 0.978024 0.208491i \(-0.0668553\pi\)
−0.669571 + 0.742748i \(0.733522\pi\)
\(240\) 0 0
\(241\) 4.47906 7.75795i 0.288521 0.499734i −0.684936 0.728604i \(-0.740170\pi\)
0.973457 + 0.228870i \(0.0735031\pi\)
\(242\) 0 0
\(243\) −10.0201 11.9415i −0.642788 0.766044i
\(244\) 0 0
\(245\) −1.26604 + 2.19285i −0.0808846 + 0.140096i
\(246\) 0 0
\(247\) −6.36097 11.0175i −0.404739 0.701028i
\(248\) 0 0
\(249\) 3.04101 3.62414i 0.192716 0.229670i
\(250\) 0 0
\(251\) 24.9982 1.57788 0.788938 0.614473i \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) 0 0
\(255\) 5.81908 + 15.9878i 0.364405 + 1.00119i
\(256\) 0 0
\(257\) −5.42602 9.39815i −0.338466 0.586240i 0.645678 0.763609i \(-0.276575\pi\)
−0.984144 + 0.177369i \(0.943241\pi\)
\(258\) 0 0
\(259\) −3.84002 + 6.65111i −0.238607 + 0.413280i
\(260\) 0 0
\(261\) −20.1800 + 16.9331i −1.24911 + 1.04813i
\(262\) 0 0
\(263\) 13.0437 22.5924i 0.804309 1.39310i −0.112448 0.993658i \(-0.535869\pi\)
0.916757 0.399446i \(-0.130798\pi\)
\(264\) 0 0
\(265\) 0.907604 + 1.57202i 0.0557537 + 0.0965682i
\(266\) 0 0
\(267\) 13.8400 + 2.44037i 0.846996 + 0.149348i
\(268\) 0 0
\(269\) −7.63310 −0.465399 −0.232699 0.972549i \(-0.574756\pi\)
−0.232699 + 0.972549i \(0.574756\pi\)
\(270\) 0 0
\(271\) −3.40373 −0.206762 −0.103381 0.994642i \(-0.532966\pi\)
−0.103381 + 0.994642i \(0.532966\pi\)
\(272\) 0 0
\(273\) 9.93242 + 1.75135i 0.601137 + 0.105997i
\(274\) 0 0
\(275\) 0.330222 + 0.571962i 0.0199131 + 0.0344906i
\(276\) 0 0
\(277\) 2.86097 4.95534i 0.171899 0.297738i −0.767185 0.641426i \(-0.778343\pi\)
0.939084 + 0.343689i \(0.111676\pi\)
\(278\) 0 0
\(279\) −4.00088 22.6901i −0.239526 1.35842i
\(280\) 0 0
\(281\) −14.1887 + 24.5755i −0.846425 + 1.46605i 0.0379535 + 0.999280i \(0.487916\pi\)
−0.884378 + 0.466771i \(0.845417\pi\)
\(282\) 0 0
\(283\) 2.28564 + 3.95885i 0.135867 + 0.235329i 0.925929 0.377699i \(-0.123285\pi\)
−0.790061 + 0.613028i \(0.789951\pi\)
\(284\) 0 0
\(285\) 3.27719 + 9.00400i 0.194124 + 0.533351i
\(286\) 0 0
\(287\) 2.22668 0.131437
\(288\) 0 0
\(289\) −1.95037 −0.114728
\(290\) 0 0
\(291\) −15.1459 + 18.0502i −0.887868 + 1.05812i
\(292\) 0 0
\(293\) −2.16385 3.74789i −0.126413 0.218954i 0.795871 0.605466i \(-0.207013\pi\)
−0.922285 + 0.386512i \(0.873680\pi\)
\(294\) 0 0
\(295\) 0.932419 1.61500i 0.0542875 0.0940287i
\(296\) 0 0
\(297\) −2.10560 + 1.21567i −0.122179 + 0.0705403i
\(298\) 0 0
\(299\) −0.308811 + 0.534876i −0.0178590 + 0.0309327i
\(300\) 0 0
\(301\) −0.613341 1.06234i −0.0353524 0.0612321i
\(302\) 0 0
\(303\) −10.6591 + 12.7030i −0.612349 + 0.729769i
\(304\) 0 0
\(305\) 2.42602 0.138914
\(306\) 0 0
\(307\) −12.3773 −0.706411 −0.353206 0.935546i \(-0.614908\pi\)
−0.353206 + 0.935546i \(0.614908\pi\)
\(308\) 0 0
\(309\) −1.80200 4.95096i −0.102512 0.281651i
\(310\) 0 0
\(311\) −10.9927 19.0400i −0.623340 1.07966i −0.988859 0.148853i \(-0.952442\pi\)
0.365519 0.930804i \(-0.380892\pi\)
\(312\) 0 0
\(313\) 6.94491 12.0289i 0.392549 0.679915i −0.600236 0.799823i \(-0.704927\pi\)
0.992785 + 0.119908i \(0.0382599\pi\)
\(314\) 0 0
\(315\) −7.13816 2.59808i −0.402190 0.146385i
\(316\) 0 0
\(317\) 3.09105 5.35386i 0.173611 0.300703i −0.766069 0.642759i \(-0.777790\pi\)
0.939680 + 0.342056i \(0.111123\pi\)
\(318\) 0 0
\(319\) 2.05438 + 3.55829i 0.115023 + 0.199226i
\(320\) 0 0
\(321\) −11.1172 1.96026i −0.620502 0.109411i
\(322\) 0 0
\(323\) 8.47565 0.471598
\(324\) 0 0
\(325\) 8.21894 0.455905
\(326\) 0 0
\(327\) −18.1459 3.19961i −1.00347 0.176939i
\(328\) 0 0
\(329\) 2.66637 + 4.61830i 0.147002 + 0.254615i
\(330\) 0 0
\(331\) 5.36571 9.29369i 0.294926 0.510827i −0.680041 0.733174i \(-0.738038\pi\)
0.974968 + 0.222346i \(0.0713715\pi\)
\(332\) 0 0
\(333\) −21.6506 7.88019i −1.18645 0.431832i
\(334\) 0 0
\(335\) −12.2023 + 21.1351i −0.666685 + 1.15473i
\(336\) 0 0
\(337\) 9.29726 + 16.1033i 0.506454 + 0.877204i 0.999972 + 0.00746831i \(0.00237726\pi\)
−0.493518 + 0.869735i \(0.664289\pi\)
\(338\) 0 0
\(339\) 3.06687 + 8.42615i 0.166569 + 0.457645i
\(340\) 0 0
\(341\) −3.59358 −0.194603
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.299011 0.356347i 0.0160982 0.0191851i
\(346\) 0 0
\(347\) −10.2062 17.6777i −0.547898 0.948987i −0.998418 0.0562207i \(-0.982095\pi\)
0.450521 0.892766i \(-0.351238\pi\)
\(348\) 0 0
\(349\) 1.78106 3.08489i 0.0953379 0.165130i −0.814412 0.580288i \(-0.802940\pi\)
0.909750 + 0.415157i \(0.136274\pi\)
\(350\) 0 0
\(351\) 30.2569i 1.61500i
\(352\) 0 0
\(353\) −5.01114 + 8.67956i −0.266716 + 0.461966i −0.968012 0.250904i \(-0.919272\pi\)
0.701296 + 0.712871i \(0.252605\pi\)
\(354\) 0 0
\(355\) 16.7554 + 29.0211i 0.889283 + 1.54028i
\(356\) 0 0
\(357\) −4.31908 + 5.14728i −0.228590 + 0.272423i
\(358\) 0 0
\(359\) −9.48070 −0.500372 −0.250186 0.968198i \(-0.580492\pi\)
−0.250186 + 0.968198i \(0.580492\pi\)
\(360\) 0 0
\(361\) −14.2267 −0.748773
\(362\) 0 0
\(363\) −6.38666 17.5472i −0.335213 0.920989i
\(364\) 0 0
\(365\) 13.0005 + 22.5175i 0.680476 + 1.17862i
\(366\) 0 0
\(367\) 8.06670 13.9719i 0.421079 0.729329i −0.574967 0.818177i \(-0.694985\pi\)
0.996045 + 0.0888474i \(0.0283183\pi\)
\(368\) 0 0
\(369\) 1.15998 + 6.57856i 0.0603860 + 0.342466i
\(370\) 0 0
\(371\) −0.358441 + 0.620838i −0.0186093 + 0.0322323i
\(372\) 0 0
\(373\) −7.02481 12.1673i −0.363731 0.630001i 0.624841 0.780752i \(-0.285164\pi\)
−0.988572 + 0.150752i \(0.951831\pi\)
\(374\) 0 0
\(375\) 15.4991 + 2.73291i 0.800371 + 0.141127i
\(376\) 0 0
\(377\) 51.1317 2.63341
\(378\) 0 0
\(379\) −16.0574 −0.824812 −0.412406 0.911000i \(-0.635311\pi\)
−0.412406 + 0.911000i \(0.635311\pi\)
\(380\) 0 0
\(381\) −15.1505 2.67144i −0.776183 0.136862i
\(382\) 0 0
\(383\) −16.0103 27.7306i −0.818086 1.41697i −0.907090 0.420936i \(-0.861702\pi\)
0.0890039 0.996031i \(-0.471632\pi\)
\(384\) 0 0
\(385\) −0.592396 + 1.02606i −0.0301913 + 0.0522929i
\(386\) 0 0
\(387\) 2.81908 2.36549i 0.143302 0.120244i
\(388\) 0 0
\(389\) 15.0214 26.0178i 0.761616 1.31916i −0.180402 0.983593i \(-0.557740\pi\)
0.942017 0.335564i \(-0.108927\pi\)
\(390\) 0 0
\(391\) −0.205737 0.356347i −0.0104046 0.0180212i
\(392\) 0 0
\(393\) −6.73127 18.4940i −0.339548 0.932899i
\(394\) 0 0
\(395\) 32.0009 1.61014
\(396\) 0 0
\(397\) −12.3200 −0.618321 −0.309160 0.951010i \(-0.600048\pi\)
−0.309160 + 0.951010i \(0.600048\pi\)
\(398\) 0 0
\(399\) −2.43242 + 2.89884i −0.121773 + 0.145124i
\(400\) 0 0
\(401\) −10.4880 18.1657i −0.523745 0.907152i −0.999618 0.0276385i \(-0.991201\pi\)
0.475873 0.879514i \(-0.342132\pi\)
\(402\) 0 0
\(403\) −22.3603 + 38.7291i −1.11384 + 1.92923i
\(404\) 0 0
\(405\) 3.95723 22.4426i 0.196637 1.11518i
\(406\) 0 0
\(407\) −1.79679 + 3.11213i −0.0890635 + 0.154263i
\(408\) 0 0
\(409\) −12.8307 22.2234i −0.634437 1.09888i −0.986634 0.162951i \(-0.947899\pi\)
0.352197 0.935926i \(-0.385435\pi\)
\(410\) 0 0
\(411\) −6.37346 + 7.59559i −0.314379 + 0.374663i
\(412\) 0 0
\(413\) 0.736482 0.0362399
\(414\) 0 0
\(415\) 6.91622 0.339504
\(416\) 0 0
\(417\) 0.547352 + 1.50384i 0.0268039 + 0.0736432i
\(418\) 0 0
\(419\) −0.739885 1.28152i −0.0361458 0.0626063i 0.847387 0.530976i \(-0.178175\pi\)
−0.883532 + 0.468370i \(0.844841\pi\)
\(420\) 0 0
\(421\) −6.55350 + 11.3510i −0.319398 + 0.553214i −0.980363 0.197203i \(-0.936814\pi\)
0.660965 + 0.750417i \(0.270147\pi\)
\(422\) 0 0
\(423\) −12.2554 + 10.2835i −0.595876 + 0.500000i
\(424\) 0 0
\(425\) −2.73783 + 4.74205i −0.132804 + 0.230023i
\(426\) 0 0
\(427\) 0.479055 + 0.829748i 0.0231831 + 0.0401543i
\(428\) 0 0
\(429\) 4.64749 + 0.819478i 0.224383 + 0.0395648i
\(430\) 0 0
\(431\) −17.7270 −0.853879 −0.426939 0.904280i \(-0.640408\pi\)
−0.426939 + 0.904280i \(0.640408\pi\)
\(432\) 0 0
\(433\) −5.83843 −0.280577 −0.140289 0.990111i \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) 0 0
\(435\) −37.9261 6.68739i −1.81842 0.320636i
\(436\) 0 0
\(437\) −0.115867 0.200688i −0.00554267 0.00960019i
\(438\) 0 0
\(439\) 14.9277 25.8555i 0.712459 1.23401i −0.251473 0.967864i \(-0.580915\pi\)
0.963931 0.266151i \(-0.0857518\pi\)
\(440\) 0 0
\(441\) −0.520945 2.95442i −0.0248069 0.140687i
\(442\) 0 0
\(443\) 5.33275 9.23659i 0.253367 0.438844i −0.711084 0.703107i \(-0.751795\pi\)
0.964451 + 0.264263i \(0.0851288\pi\)
\(444\) 0 0
\(445\) 10.2724 + 17.7924i 0.486960 + 0.843440i
\(446\) 0 0
\(447\) 5.16843 + 14.2002i 0.244459 + 0.671644i
\(448\) 0 0
\(449\) 3.55438 0.167741 0.0838707 0.996477i \(-0.473272\pi\)
0.0838707 + 0.996477i \(0.473272\pi\)
\(450\) 0 0
\(451\) 1.04189 0.0490606
\(452\) 0 0
\(453\) −20.5155 + 24.4494i −0.963901 + 1.14873i
\(454\) 0 0
\(455\) 7.37211 + 12.7689i 0.345610 + 0.598614i
\(456\) 0 0
\(457\) −2.51161 + 4.35024i −0.117488 + 0.203496i −0.918772 0.394789i \(-0.870818\pi\)
0.801283 + 0.598285i \(0.204151\pi\)
\(458\) 0 0
\(459\) −17.4572 10.0789i −0.814834 0.470445i
\(460\) 0 0
\(461\) −9.23055 + 15.9878i −0.429910 + 0.744625i −0.996865 0.0791233i \(-0.974788\pi\)
0.566955 + 0.823749i \(0.308121\pi\)
\(462\) 0 0
\(463\) −7.11721 12.3274i −0.330765 0.572902i 0.651897 0.758307i \(-0.273973\pi\)
−0.982662 + 0.185406i \(0.940640\pi\)
\(464\) 0 0
\(465\) 21.6506 25.8022i 1.00402 1.19655i
\(466\) 0 0
\(467\) 3.36865 0.155883 0.0779413 0.996958i \(-0.475165\pi\)
0.0779413 + 0.996958i \(0.475165\pi\)
\(468\) 0 0
\(469\) −9.63816 −0.445049
\(470\) 0 0
\(471\) 2.91694 + 8.01422i 0.134405 + 0.369276i
\(472\) 0 0
\(473\) −0.286989 0.497079i −0.0131958 0.0228557i
\(474\) 0 0
\(475\) −1.54189 + 2.67063i −0.0707467 + 0.122537i
\(476\) 0 0
\(477\) −2.02094 0.735564i −0.0925327 0.0336791i
\(478\) 0 0
\(479\) −18.3833 + 31.8407i −0.839952 + 1.45484i 0.0499812 + 0.998750i \(0.484084\pi\)
−0.889934 + 0.456090i \(0.849249\pi\)
\(480\) 0 0
\(481\) 22.3603 + 38.7291i 1.01954 + 1.76589i
\(482\) 0 0
\(483\) 0.180922 + 0.0319015i 0.00823224 + 0.00145157i
\(484\) 0 0
\(485\) −34.4466 −1.56414
\(486\) 0 0
\(487\) 37.4175 1.69555 0.847773 0.530358i \(-0.177943\pi\)
0.847773 + 0.530358i \(0.177943\pi\)
\(488\) 0 0
\(489\) 13.0287 + 2.29731i 0.589178 + 0.103888i
\(490\) 0 0
\(491\) −13.3353 23.0974i −0.601813 1.04237i −0.992547 0.121866i \(-0.961112\pi\)
0.390734 0.920504i \(-0.372221\pi\)
\(492\) 0 0
\(493\) −17.0326 + 29.5013i −0.767108 + 1.32867i
\(494\) 0 0
\(495\) −3.34002 1.21567i −0.150123 0.0546402i
\(496\) 0 0
\(497\) −6.61721 + 11.4613i −0.296822 + 0.514112i
\(498\) 0 0
\(499\) 16.8726 + 29.2242i 0.755320 + 1.30825i 0.945215 + 0.326449i \(0.105852\pi\)
−0.189895 + 0.981804i \(0.560815\pi\)
\(500\) 0 0
\(501\) 3.35023 + 9.20469i 0.149677 + 0.411235i
\(502\) 0 0
\(503\) 32.0401 1.42860 0.714299 0.699840i \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) 0 0
\(507\) 23.2763 27.7396i 1.03374 1.23196i
\(508\) 0 0
\(509\) 3.96926 + 6.87495i 0.175934 + 0.304727i 0.940484 0.339838i \(-0.110372\pi\)
−0.764550 + 0.644564i \(0.777039\pi\)
\(510\) 0 0
\(511\) −5.13429 + 8.89284i −0.227127 + 0.393396i
\(512\) 0 0
\(513\) −9.83157 5.67626i −0.434074 0.250613i
\(514\) 0 0
\(515\) 3.85117 6.67042i 0.169703 0.293934i
\(516\) 0 0
\(517\) 1.24763 + 2.16095i 0.0548705 + 0.0950386i
\(518\) 0 0
\(519\) 23.4572 27.9552i 1.02966 1.22710i
\(520\) 0 0
\(521\) −14.6750 −0.642923 −0.321462 0.946923i \(-0.604174\pi\)
−0.321462 + 0.946923i \(0.604174\pi\)
\(522\) 0 0
\(523\) −28.3432 −1.23936 −0.619680 0.784854i \(-0.712738\pi\)
−0.619680 + 0.784854i \(0.712738\pi\)
\(524\) 0 0
\(525\) −0.836152 2.29731i −0.0364927 0.100263i
\(526\) 0 0
\(527\) −14.8969 25.8022i −0.648920 1.12396i
\(528\) 0 0
\(529\) 11.4944 19.9088i 0.499755 0.865602i
\(530\) 0 0
\(531\) 0.383666 + 2.17588i 0.0166497 + 0.0944251i
\(532\) 0 0
\(533\) 6.48293 11.2288i 0.280807 0.486371i
\(534\) 0 0
\(535\) −8.25150 14.2920i −0.356743 0.617898i
\(536\) 0 0
\(537\) −8.73442 1.54011i −0.376918 0.0664608i
\(538\) 0 0
\(539\) −0.467911 −0.0201544
\(540\) 0 0
\(541\) 11.2858 0.485215 0.242607 0.970125i \(-0.421997\pi\)
0.242607 + 0.970125i \(0.421997\pi\)
\(542\) 0 0
\(543\) 0.545759 + 0.0962321i 0.0234208 + 0.00412972i
\(544\) 0 0
\(545\) −13.4684 23.3279i −0.576922 0.999258i
\(546\) 0 0
\(547\) −14.6202 + 25.3229i −0.625115 + 1.08273i 0.363404 + 0.931632i \(0.381615\pi\)
−0.988519 + 0.151099i \(0.951719\pi\)
\(548\) 0 0
\(549\) −2.20187 + 1.84759i −0.0939734 + 0.0788530i
\(550\) 0 0
\(551\) −9.59240 + 16.6145i −0.408650 + 0.707802i
\(552\) 0 0
\(553\) 6.31908 + 10.9450i 0.268715 + 0.465427i
\(554\) 0 0
\(555\) −11.5201 31.6511i −0.489000 1.34352i
\(556\) 0 0
\(557\) −0.775682 −0.0328667 −0.0164334 0.999865i \(-0.505231\pi\)
−0.0164334 + 0.999865i \(0.505231\pi\)
\(558\) 0 0
\(559\) −7.14290 −0.302113
\(560\) 0 0
\(561\) −2.02094 + 2.40847i −0.0853243 + 0.101686i
\(562\) 0 0
\(563\) 12.4761 + 21.6093i 0.525806 + 0.910722i 0.999548 + 0.0300588i \(0.00956944\pi\)
−0.473742 + 0.880663i \(0.657097\pi\)
\(564\) 0 0
\(565\) −6.55438 + 11.3525i −0.275745 + 0.477604i
\(566\) 0 0
\(567\) 8.45723 3.07818i 0.355170 0.129271i
\(568\) 0 0
\(569\) 12.4017 21.4803i 0.519905 0.900502i −0.479827 0.877363i \(-0.659301\pi\)
0.999732 0.0231391i \(-0.00736608\pi\)
\(570\) 0 0
\(571\) 4.39827 + 7.61803i 0.184062 + 0.318805i 0.943260 0.332055i \(-0.107742\pi\)
−0.759198 + 0.650860i \(0.774409\pi\)
\(572\) 0 0
\(573\) 17.3316 20.6550i 0.724037 0.862873i
\(574\) 0 0
\(575\) 0.149711 0.00624336
\(576\) 0 0
\(577\) −12.8743 −0.535965 −0.267983 0.963424i \(-0.586357\pi\)
−0.267983 + 0.963424i \(0.586357\pi\)
\(578\) 0 0
\(579\) 3.57919 + 9.83375i 0.148746 + 0.408677i
\(580\) 0 0
\(581\) 1.36571 + 2.36549i 0.0566594 + 0.0981369i
\(582\) 0 0
\(583\) −0.167718 + 0.290497i −0.00694619 + 0.0120311i
\(584\) 0 0
\(585\) −33.8842 + 28.4322i −1.40094 + 1.17553i
\(586\) 0 0
\(587\) 22.4315 38.8526i 0.925849 1.60362i 0.135658 0.990756i \(-0.456685\pi\)
0.790190 0.612861i \(-0.209982\pi\)
\(588\) 0 0
\(589\) −8.38965 14.5313i −0.345690 0.598752i
\(590\) 0 0
\(591\) −43.0433 7.58969i −1.77056 0.312198i
\(592\) 0 0
\(593\) 3.76053 0.154426 0.0772131 0.997015i \(-0.475398\pi\)
0.0772131 + 0.997015i \(0.475398\pi\)
\(594\) 0 0
\(595\) −9.82295 −0.402702
\(596\) 0 0
\(597\) 5.18866 + 0.914901i 0.212358 + 0.0374444i
\(598\) 0 0
\(599\) −1.84524 3.19604i −0.0753943 0.130587i 0.825863 0.563870i \(-0.190688\pi\)
−0.901258 + 0.433283i \(0.857355\pi\)
\(600\) 0 0
\(601\) 10.9285 18.9288i 0.445785 0.772122i −0.552322 0.833631i \(-0.686258\pi\)
0.998107 + 0.0615091i \(0.0195913\pi\)
\(602\) 0 0
\(603\) −5.02094 28.4752i −0.204469 1.15960i
\(604\) 0 0
\(605\) 13.6493 23.6413i 0.554923 0.961155i
\(606\) 0 0
\(607\) 12.1973 + 21.1263i 0.495072 + 0.857490i 0.999984 0.00568063i \(-0.00180821\pi\)
−0.504911 + 0.863171i \(0.668475\pi\)
\(608\) 0 0
\(609\) −5.20187 14.2920i −0.210790 0.579142i
\(610\) 0 0
\(611\) 31.0523 1.25624
\(612\) 0 0
\(613\) 42.0215 1.69723 0.848616 0.529010i \(-0.177437\pi\)
0.848616 + 0.529010i \(0.177437\pi\)
\(614\) 0 0
\(615\) −6.27719 + 7.48086i −0.253121 + 0.301657i
\(616\) 0 0
\(617\) −23.2049 40.1920i −0.934192 1.61807i −0.776068 0.630650i \(-0.782788\pi\)
−0.158125 0.987419i \(-0.550545\pi\)
\(618\) 0 0
\(619\) −13.6047 + 23.5641i −0.546820 + 0.947120i 0.451670 + 0.892185i \(0.350828\pi\)
−0.998490 + 0.0549349i \(0.982505\pi\)
\(620\) 0 0
\(621\) 0.551139i 0.0221165i
\(622\) 0 0
\(623\) −4.05690 + 7.02676i −0.162536 + 0.281521i
\(624\) 0 0
\(625\) 15.0326 + 26.0372i 0.601302 + 1.04149i
\(626\) 0 0
\(627\) −1.13816 + 1.35640i −0.0454536 + 0.0541694i
\(628\) 0 0
\(629\) −29.7939 −1.18796
\(630\) 0 0
\(631\) 29.6023 1.17845 0.589224 0.807970i \(-0.299434\pi\)
0.589224 + 0.807970i \(0.299434\pi\)
\(632\) 0 0
\(633\) 3.23055 + 8.87587i 0.128403 + 0.352784i
\(634\) 0 0
\(635\) −11.2451 19.4771i −0.446248 0.772925i
\(636\) 0 0
\(637\) −2.91147 + 5.04282i −0.115357 + 0.199804i
\(638\) 0 0
\(639\) −37.3089 13.5793i −1.47592 0.537189i
\(640\) 0 0
\(641\) 0.139500 0.241621i 0.00550991 0.00954345i −0.863257 0.504764i \(-0.831579\pi\)
0.868767 + 0.495221i \(0.164913\pi\)
\(642\) 0 0
\(643\) −9.12196 15.7997i −0.359735 0.623079i 0.628181 0.778067i \(-0.283800\pi\)
−0.987916 + 0.154988i \(0.950466\pi\)
\(644\) 0 0
\(645\) 5.29813 + 0.934204i 0.208614 + 0.0367842i
\(646\) 0 0
\(647\) −22.4570 −0.882875 −0.441438 0.897292i \(-0.645531\pi\)
−0.441438 + 0.897292i \(0.645531\pi\)
\(648\) 0 0
\(649\) 0.344608 0.0135270
\(650\) 0 0
\(651\) 13.1001 + 2.30991i 0.513435 + 0.0905324i
\(652\) 0 0
\(653\) 25.2656 + 43.7614i 0.988721 + 1.71251i 0.624066 + 0.781372i \(0.285480\pi\)
0.364655 + 0.931143i \(0.381187\pi\)
\(654\) 0 0
\(655\) 14.3858 24.9169i 0.562099 0.973584i
\(656\) 0 0
\(657\) −28.9479 10.5362i −1.12937 0.411055i
\(658\) 0 0
\(659\) −1.33631 + 2.31456i −0.0520554 + 0.0901626i −0.890879 0.454241i \(-0.849911\pi\)
0.838824 + 0.544403i \(0.183244\pi\)
\(660\) 0 0
\(661\) 17.3050 + 29.9731i 0.673086 + 1.16582i 0.977024 + 0.213128i \(0.0683651\pi\)
−0.303938 + 0.952692i \(0.598302\pi\)
\(662\) 0 0
\(663\) 13.3819 + 36.7665i 0.519710 + 1.42789i
\(664\) 0 0
\(665\) −5.53209 −0.214525
\(666\) 0 0
\(667\) 0.931379 0.0360631
\(668\) 0 0
\(669\) −15.8011 + 18.8310i −0.610907 + 0.728050i
\(670\) 0 0
\(671\) 0.224155 + 0.388249i 0.00865342 + 0.0149882i
\(672\) 0 0
\(673\) −8.25624 + 14.3002i −0.318255 + 0.551234i −0.980124 0.198386i \(-0.936430\pi\)
0.661869 + 0.749619i \(0.269763\pi\)
\(674\) 0 0
\(675\) 6.35163 3.66712i 0.244474 0.141147i
\(676\) 0 0
\(677\) 21.8790 37.8955i 0.840877 1.45644i −0.0482766 0.998834i \(-0.515373\pi\)
0.889154 0.457608i \(-0.151294\pi\)
\(678\) 0 0
\(679\) −6.80200 11.7814i −0.261037 0.452129i
\(680\) 0 0
\(681\) 3.22193 3.83975i 0.123465 0.147140i
\(682\) 0 0
\(683\) −28.2412 −1.08062 −0.540310 0.841466i \(-0.681693\pi\)
−0.540310 + 0.841466i \(0.681693\pi\)
\(684\) 0 0
\(685\) −14.4953 −0.553835
\(686\) 0 0
\(687\) 5.43083 + 14.9211i 0.207199 + 0.569274i
\(688\) 0 0
\(689\) 2.08718 + 3.61510i 0.0795153 + 0.137725i
\(690\) 0 0
\(691\) −14.5326 + 25.1711i −0.552844 + 0.957555i 0.445223 + 0.895420i \(0.353124\pi\)
−0.998068 + 0.0621351i \(0.980209\pi\)
\(692\) 0 0
\(693\) −0.243756 1.38241i −0.00925951 0.0525133i
\(694\) 0 0
\(695\) −1.16978 + 2.02611i −0.0443722 + 0.0768549i
\(696\) 0 0
\(697\) 4.31908 + 7.48086i 0.163597 + 0.283358i
\(698\) 0 0
\(699\) −22.6373 3.99156i −0.856221 0.150975i
\(700\) 0 0
\(701\) −1.10876 −0.0418771 −0.0209386 0.999781i \(-0.506665\pi\)
−0.0209386 + 0.999781i \(0.506665\pi\)
\(702\) 0 0
\(703\) −16.7793 −0.632843
\(704\) 0 0
\(705\) −23.0326 4.06126i −0.867456 0.152956i
\(706\) 0 0
\(707\) −4.78699 8.29131i −0.180033 0.311827i
\(708\) 0 0
\(709\) 9.23442 15.9945i 0.346806 0.600686i −0.638874 0.769311i \(-0.720600\pi\)
0.985680 + 0.168626i \(0.0539329\pi\)
\(710\) 0 0
\(711\) −29.0442 + 24.3709i −1.08924 + 0.913982i
\(712\) 0 0
\(713\) −0.407299 + 0.705463i −0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) 3.44949 + 5.97470i 0.129004 + 0.223441i
\(716\) 0 0
\(717\) −5.64977 15.5226i −0.210994 0.579702i
\(718\) 0 0
\(719\) 33.7769 1.25967 0.629834 0.776730i \(-0.283123\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(720\) 0 0
\(721\) 3.04189 0.113286
\(722\) 0 0
\(723\) −9.97343 + 11.8859i −0.370916 + 0.442040i
\(724\) 0 0
\(725\) −6.19712 10.7337i −0.230155 0.398641i
\(726\) 0 0
\(727\) 8.40214 14.5529i 0.311618 0.539738i −0.667095 0.744973i \(-0.732462\pi\)
0.978713 + 0.205234i \(0.0657957\pi\)
\(728\) 0 0
\(729\) 13.5000 + 23.3827i 0.500000 + 0.866025i
\(730\) 0 0
\(731\) 2.37939 4.12122i 0.0880047 0.152429i
\(732\) 0 0
\(733\) 6.81820 + 11.8095i 0.251836 + 0.436193i 0.964031 0.265789i \(-0.0856323\pi\)
−0.712195 + 0.701981i \(0.752299\pi\)
\(734\) 0 0
\(735\) 2.81908 3.35965i 0.103983 0.123922i
\(736\) 0 0
\(737\) −4.50980 −0.166121
\(738\) 0 0
\(739\) 32.0419 1.17868 0.589340 0.807885i \(-0.299388\pi\)
0.589340 + 0.807885i \(0.299388\pi\)
\(740\) 0 0
\(741\) 7.53643 + 20.7062i 0.276858 + 0.760660i
\(742\) 0 0
\(743\) 16.8764 + 29.2309i 0.619137 + 1.07238i 0.989644 + 0.143547i \(0.0458507\pi\)
−0.370507 + 0.928830i \(0.620816\pi\)
\(744\) 0 0
\(745\) −11.0458 + 19.1318i −0.404685 + 0.700936i
\(746\) 0 0
\(747\) −6.27719 + 5.26719i −0.229670 + 0.192716i
\(748\) 0 0
\(749\) 3.25877 5.64436i 0.119073 0.206240i
\(750\) 0 0
\(751\) 13.0582 + 22.6175i 0.476502 + 0.825326i 0.999637 0.0269236i \(-0.00857108\pi\)
−0.523135 + 0.852250i \(0.675238\pi\)
\(752\) 0 0
\(753\) −42.6404 7.51866i −1.55390 0.273995i
\(754\) 0 0
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) 0 0
\(759\) 0.0846555 + 0.0149270i 0.00307280 + 0.000541817i
\(760\) 0 0
\(761\) −20.3824 35.3033i −0.738861 1.27974i −0.953009 0.302943i \(-0.902031\pi\)
0.214148 0.976801i \(-0.431302\pi\)
\(762\) 0 0
\(763\) 5.31908 9.21291i 0.192564 0.333530i
\(764\) 0 0
\(765\) −5.11721 29.0211i −0.185013 1.04926i
\(766\) 0 0
\(767\) 2.14425 3.71395i 0.0774243 0.134103i
\(768\) 0 0
\(769\) −19.7135 34.1447i −0.710886 1.23129i −0.964525 0.263992i \(-0.914961\pi\)
0.253639 0.967299i \(-0.418373\pi\)
\(770\) 0 0
\(771\) 6.42871 + 17.6627i 0.231524 + 0.636108i
\(772\) 0 0
\(773\) 24.9026 0.895685 0.447842 0.894113i \(-0.352193\pi\)
0.447842 + 0.894113i \(0.352193\pi\)
\(774\) 0 0
\(775\) 10.8402 0.389391
\(776\) 0 0
\(777\) 8.55051 10.1901i 0.306748 0.365568i
\(778\) 0 0
\(779\) 2.43242 + 4.21307i 0.0871504 + 0.150949i
\(780\) 0 0
\(781\) −3.09627 + 5.36289i −0.110793 + 0.191899i
\(782\) 0 0
\(783\) 39.5148 22.8139i 1.41214 0.815301i
\(784\) 0 0
\(785\) −6.23396 + 10.7975i −0.222499 + 0.385380i
\(786\) 0 0
\(787\) −15.3525 26.5913i −0.547258 0.947879i −0.998461 0.0554572i \(-0.982338\pi\)
0.451203 0.892421i \(-0.350995\pi\)
\(788\) 0 0
\(789\) −29.0442 + 34.6135i −1.03400 + 1.23227i
\(790\) 0 0
\(791\) −5.17705 −0.184075
\(792\) 0 0
\(793\) 5.57903 0.198117
\(794\) 0 0
\(795\) −1.07532 2.95442i −0.0381377 0.104783i
\(796\) 0 0
\(797\) 5.50686 + 9.53817i 0.195063 + 0.337859i 0.946921 0.321466i \(-0.104175\pi\)
−0.751858 + 0.659325i \(0.770842\pi\)
\(798\) 0 0
\(799\) −10.3439 + 17.9161i −0.365941 + 0.633828i
\(800\) 0 0
\(801\) −22.8735 8.32526i −0.808194 0.294158i
\(802\) 0 0
\(803\) −2.40239 + 4.16106i −0.0847785 + 0.146841i
\(804\) 0 0
\(805\) 0.134285 + 0.232589i 0.00473294 + 0.00819769i
\(806\) 0 0
\(807\) 13.0201 + 2.29579i 0.458328 + 0.0808156i
\(808\) 0 0
\(809\) 16.9881 0.597271 0.298636 0.954367i \(-0.403468\pi\)
0.298636 + 0.954367i \(0.403468\pi\)
\(810\) 0 0
\(811\) −37.9796 −1.33364 −0.666822 0.745217i \(-0.732346\pi\)
−0.666822 + 0.745217i \(0.732346\pi\)
\(812\) 0 0
\(813\) 5.80587 + 1.02373i 0.203621 + 0.0359039i
\(814\) 0 0
\(815\) 9.67024 + 16.7494i 0.338734 + 0.586704i
\(816\) 0 0
\(817\) 1.34002 2.32099i 0.0468814 0.0812011i
\(818\) 0 0
\(819\) −16.4153 5.97470i −0.573599 0.208773i
\(820\) 0 0
\(821\) −4.13934 + 7.16954i −0.144464 + 0.250219i −0.929173 0.369646i \(-0.879479\pi\)
0.784709 + 0.619864i \(0.212812\pi\)
\(822\) 0 0
\(823\) 27.2763 + 47.2440i 0.950792 + 1.64682i 0.743716 + 0.668496i \(0.233062\pi\)
0.207077 + 0.978325i \(0.433605\pi\)
\(824\) 0 0
\(825\) −0.391245 1.07494i −0.0136214 0.0374245i
\(826\) 0 0
\(827\) 31.8708 1.10826 0.554129 0.832431i \(-0.313052\pi\)
0.554129 + 0.832431i \(0.313052\pi\)
\(828\) 0 0
\(829\) −0.352349 −0.0122376 −0.00611879 0.999981i \(-0.501948\pi\)
−0.00611879 + 0.999981i \(0.501948\pi\)
\(830\) 0 0
\(831\) −6.37046 + 7.59202i −0.220989 + 0.263364i
\(832\) 0 0
\(833\) −1.93969 3.35965i −0.0672064 0.116405i
\(834\) 0 0
\(835\) −7.15998 + 12.4014i −0.247781 + 0.429170i
\(836\) 0 0
\(837\) 39.9067i 1.37938i
\(838\) 0 0
\(839\) 12.5077 21.6640i 0.431815 0.747926i −0.565215 0.824944i \(-0.691207\pi\)
0.997030 + 0.0770182i \(0.0245399\pi\)
\(840\) 0 0
\(841\) −24.0535 41.6619i −0.829431 1.43662i
\(842\) 0 0
\(843\) 31.5936 37.6518i 1.08814 1.29680i
\(844\) 0 0
\(845\) 52.9377 1.82111
\(846\) 0 0
\(847\) 10.7811 0.370442
\(848\) 0 0
\(849\) −2.70801 7.44021i −0.0929388 0.255347i
\(850\) 0 0
\(851\) 0.407299 + 0.705463i 0.0139620 + 0.0241829i
\(852\) 0 0
\(853\) −19.5954 + 33.9402i −0.670933 + 1.16209i 0.306706 + 0.951804i \(0.400773\pi\)
−0.977640 + 0.210286i \(0.932560\pi\)
\(854\) 0 0
\(855\) −2.88191 16.3441i −0.0985593 0.558958i
\(856\) 0 0
\(857\) −8.20368 + 14.2092i −0.280232 + 0.485377i −0.971442 0.237278i \(-0.923745\pi\)
0.691210 + 0.722654i \(0.257078\pi\)
\(858\) 0 0
\(859\) −13.4162 23.2376i −0.457756 0.792856i 0.541086 0.840967i \(-0.318013\pi\)
−0.998842 + 0.0481111i \(0.984680\pi\)
\(860\) 0 0
\(861\) −3.79813 0.669713i −0.129440 0.0228238i
\(862\) 0 0
\(863\) −14.5057 −0.493779 −0.246890 0.969044i \(-0.579408\pi\)
−0.246890 + 0.969044i \(0.579408\pi\)
\(864\) 0 0
\(865\) 53.3492 1.81393
\(866\) 0 0
\(867\) 3.32682 + 0.586608i 0.112985 + 0.0199222i
\(868\) 0 0
\(869\) 2.95677 + 5.12127i 0.100301 + 0.173727i
\(870\) 0 0
\(871\) −28.0612 + 48.6035i −0.950819 + 1.64687i
\(872\) 0 0
\(873\) 31.2638 26.2335i 1.05812 0.887868i
\(874\) 0 0
\(875\) −4.54323 + 7.86911i −0.153589 + 0.266024i
\(876\) 0 0
\(877\) −9.45723 16.3804i −0.319348 0.553127i 0.661004 0.750382i \(-0.270131\pi\)
−0.980352 + 0.197255i \(0.936797\pi\)
\(878\) 0 0
\(879\) 2.56371 + 7.04374i 0.0864718 + 0.237579i
\(880\) 0 0
\(881\) 53.8976 1.81585 0.907927 0.419128i \(-0.137664\pi\)
0.907927 + 0.419128i \(0.137664\pi\)
\(882\) 0 0
\(883\) −43.4252 −1.46137 −0.730687 0.682712i \(-0.760800\pi\)
−0.730687 + 0.682712i \(0.760800\pi\)
\(884\) 0 0
\(885\) −2.07620 + 2.47432i −0.0697907 + 0.0831733i
\(886\) 0 0
\(887\) −19.4800 33.7403i −0.654074 1.13289i −0.982125 0.188229i \(-0.939725\pi\)
0.328051 0.944660i \(-0.393608\pi\)
\(888\) 0 0
\(889\) 4.44104 7.69210i 0.148948 0.257985i
\(890\) 0 0
\(891\) 3.95723 1.44032i 0.132572 0.0482524i
\(892\) 0 0
\(893\) −5.82547 + 10.0900i −0.194942 + 0.337650i
\(894\) 0 0
\(895\) −6.48293 11.2288i −0.216700 0.375336i
\(896\) 0 0
\(897\) 0.687623 0.819478i 0.0229591 0.0273616i
\(898\) 0 0
\(899\) 67.4389 2.24921
\(900\) 0 0
\(901\) −2.78106 −0.0926505
\(902\) 0 0
\(903\) 0.726682 + 1.99654i 0.0241824 + 0.0664407i
\(904\) 0 0
\(905\) 0.405078 + 0.701615i 0.0134652 + 0.0233225i
\(906\) 0 0
\(907\) 17.2638 29.9018i 0.573236 0.992874i −0.422995 0.906132i \(-0.639021\pi\)
0.996231 0.0867416i \(-0.0276454\pi\)
\(908\) 0 0
\(909\) 22.0023 18.4621i 0.729769 0.612349i
\(910\) 0 0
\(911\) 23.2631 40.2929i 0.770741 1.33496i −0.166416 0.986056i \(-0.553220\pi\)
0.937157 0.348907i \(-0.113447\pi\)
\(912\) 0 0
\(913\) 0.639033 + 1.10684i 0.0211489 + 0.0366310i
\(914\) 0 0
\(915\) −4.13816 0.729669i −0.136803 0.0241221i
\(916\) 0 0
\(917\) 11.3628 0.375232
\(918\) 0 0
\(919\) 9.95636 0.328430 0.164215 0.986425i \(-0.447491\pi\)
0.164215 + 0.986425i \(0.447491\pi\)
\(920\) 0 0
\(921\) 21.1125 + 3.72270i 0.695679 + 0.122667i
\(922\) 0 0
\(923\) 38.5317 + 66.7388i 1.26829 + 2.19674i
\(924\) 0 0
\(925\) 5.42009 9.38788i 0.178212 0.308671i
\(926\) 0 0
\(927\) 1.58466 + 8.98703i 0.0520469 + 0.295173i
\(928\) 0 0
\(929\) −4.52300 + 7.83407i −0.148395 + 0.257028i −0.930634 0.365950i \(-0.880744\pi\)
0.782239 + 0.622978i \(0.214077\pi\)
\(930\) 0 0
\(931\) −1.09240 1.89209i −0.0358018 0.0620106i
\(932\) 0 0
\(933\) 13.0241 + 35.7834i 0.426390 + 1.17150i
\(934\) 0 0
\(935\) −4.59627 −0.150314
\(936\) 0 0
\(937\) −24.3928 −0.796878 −0.398439 0.917195i \(-0.630448\pi\)
−0.398439 + 0.917195i \(0.630448\pi\)
\(938\) 0 0
\(939\) −15.4641 + 18.4294i −0.504652 + 0.601421i
\(940\) 0 0
\(941\) 29.7690 + 51.5615i 0.970443 + 1.68086i 0.694220 + 0.719763i \(0.255749\pi\)
0.276223 + 0.961094i \(0.410917\pi\)
\(942\) 0 0
\(943\) 0.118089 0.204535i 0.00384549 0.00666059i
\(944\) 0 0
\(945\) 11.3944 + 6.57856i 0.370660 + 0.214001i
\(946\) 0 0
\(947\) 4.32429 7.48989i 0.140521 0.243389i −0.787172 0.616733i \(-0.788456\pi\)
0.927693 + 0.373344i \(0.121789\pi\)
\(948\) 0 0
\(949\) 29.8967 + 51.7826i 0.970487 + 1.68093i
\(950\) 0 0
\(951\) −6.88279 + 8.20259i −0.223190 + 0.265987i
\(952\) 0 0
\(953\) 3.78249 0.122527 0.0612634 0.998122i \(-0.480487\pi\)
0.0612634 + 0.998122i \(0.480487\pi\)
\(954\) 0 0
\(955\) 39.4175 1.27552
\(956\) 0 0
\(957\) −2.43401 6.68739i −0.0786804 0.216173i
\(958\) 0 0
\(959\) −2.86231 4.95767i −0.0924288 0.160091i
\(960\) 0 0
\(961\) −13.9915 + 24.2341i −0.451340 + 0.781744i
\(962\) 0 0
\(963\) 18.3735 + 6.68739i 0.592076 + 0.215498i
\(964\) 0 0
\(965\) −7.64930 + 13.2490i −0.246240 + 0.426500i
\(966\) 0 0
\(967\) −16.4745 28.5346i −0.529783 0.917611i −0.999396 0.0347392i \(-0.988940\pi\)
0.469613 0.882872i \(-0.344393\pi\)
\(968\) 0 0
\(969\) −14.4572 2.54920i −0.464433 0.0818921i
\(970\) 0 0
\(971\) 55.4570 1.77970 0.889850 0.456254i \(-0.150809\pi\)
0.889850 + 0.456254i \(0.150809\pi\)
\(972\) 0 0
\(973\) −0.923963 −0.0296209
\(974\) 0 0
\(975\) −14.0194 2.47199i −0.448979 0.0791670i
\(976\) 0 0
\(977\) −28.2743 48.9724i −0.904573 1.56677i −0.821489 0.570225i \(-0.806856\pi\)
−0.0830847 0.996542i \(-0.526477\pi\)
\(978\) 0 0
\(979\) −1.89827 + 3.28790i −0.0606690 + 0.105082i
\(980\) 0 0
\(981\) 29.9898 + 10.9154i 0.957500 + 0.348502i
\(982\) 0 0
\(983\) 14.4987 25.1124i 0.462435 0.800961i −0.536646 0.843807i \(-0.680309\pi\)
0.999082 + 0.0428458i \(0.0136424\pi\)
\(984\) 0 0
\(985\) −31.9479 55.3354i −1.01794 1.76313i
\(986\) 0 0
\(987\) −3.15910 8.67956i −0.100555 0.276273i
\(988\) 0 0
\(989\) −0.130110 −0.00413726
\(990\) 0 0
\(991\) −6.80922 −0.216302 −0.108151 0.994134i \(-0.534493\pi\)
−0.108151 + 0.994134i \(0.534493\pi\)
\(992\) 0 0
\(993\) −11.9477 + 14.2388i −0.379150 + 0.451853i
\(994\) 0 0
\(995\) 3.85117 + 6.67042i 0.122090 + 0.211466i
\(996\) 0 0
\(997\) 19.4688 33.7210i 0.616585 1.06796i −0.373520 0.927622i \(-0.621849\pi\)
0.990104 0.140333i \(-0.0448175\pi\)
\(998\) 0 0
\(999\) 34.5602 + 19.9533i 1.09344 + 0.631296i
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 1008.2.r.h.673.1 6
3.2 odd 2 3024.2.r.k.2017.3 6
4.3 odd 2 63.2.f.a.43.2 yes 6
9.2 odd 6 9072.2.a.bs.1.1 3
9.4 even 3 inner 1008.2.r.h.337.1 6
9.5 odd 6 3024.2.r.k.1009.3 6
9.7 even 3 9072.2.a.ca.1.3 3
12.11 even 2 189.2.f.b.127.2 6
28.3 even 6 441.2.g.b.79.2 6
28.11 odd 6 441.2.g.c.79.2 6
28.19 even 6 441.2.h.e.214.2 6
28.23 odd 6 441.2.h.d.214.2 6
28.27 even 2 441.2.f.c.295.2 6
36.7 odd 6 567.2.a.h.1.2 3
36.11 even 6 567.2.a.c.1.2 3
36.23 even 6 189.2.f.b.64.2 6
36.31 odd 6 63.2.f.a.22.2 6
84.11 even 6 1323.2.g.d.667.2 6
84.23 even 6 1323.2.h.c.802.2 6
84.47 odd 6 1323.2.h.b.802.2 6
84.59 odd 6 1323.2.g.e.667.2 6
84.83 odd 2 1323.2.f.d.883.2 6
252.23 even 6 1323.2.g.d.361.2 6
252.31 even 6 441.2.h.e.373.2 6
252.59 odd 6 1323.2.h.b.226.2 6
252.67 odd 6 441.2.h.d.373.2 6
252.83 odd 6 3969.2.a.l.1.2 3
252.95 even 6 1323.2.h.c.226.2 6
252.103 even 6 441.2.g.b.67.2 6
252.131 odd 6 1323.2.g.e.361.2 6
252.139 even 6 441.2.f.c.148.2 6
252.167 odd 6 1323.2.f.d.442.2 6
252.223 even 6 3969.2.a.q.1.2 3
252.247 odd 6 441.2.g.c.67.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.a.22.2 6 36.31 odd 6
63.2.f.a.43.2 yes 6 4.3 odd 2
189.2.f.b.64.2 6 36.23 even 6
189.2.f.b.127.2 6 12.11 even 2
441.2.f.c.148.2 6 252.139 even 6
441.2.f.c.295.2 6 28.27 even 2
441.2.g.b.67.2 6 252.103 even 6
441.2.g.b.79.2 6 28.3 even 6
441.2.g.c.67.2 6 252.247 odd 6
441.2.g.c.79.2 6 28.11 odd 6
441.2.h.d.214.2 6 28.23 odd 6
441.2.h.d.373.2 6 252.67 odd 6
441.2.h.e.214.2 6 28.19 even 6
441.2.h.e.373.2 6 252.31 even 6
567.2.a.c.1.2 3 36.11 even 6
567.2.a.h.1.2 3 36.7 odd 6
1008.2.r.h.337.1 6 9.4 even 3 inner
1008.2.r.h.673.1 6 1.1 even 1 trivial
1323.2.f.d.442.2 6 252.167 odd 6
1323.2.f.d.883.2 6 84.83 odd 2
1323.2.g.d.361.2 6 252.23 even 6
1323.2.g.d.667.2 6 84.11 even 6
1323.2.g.e.361.2 6 252.131 odd 6
1323.2.g.e.667.2 6 84.59 odd 6
1323.2.h.b.226.2 6 252.59 odd 6
1323.2.h.b.802.2 6 84.47 odd 6
1323.2.h.c.226.2 6 252.95 even 6
1323.2.h.c.802.2 6 84.23 even 6
3024.2.r.k.1009.3 6 9.5 odd 6
3024.2.r.k.2017.3 6 3.2 odd 2
3969.2.a.l.1.2 3 252.83 odd 6
3969.2.a.q.1.2 3 252.223 even 6
9072.2.a.bs.1.1 3 9.2 odd 6
9072.2.a.ca.1.3 3 9.7 even 3