Properties

Label 7.10.a.b.1.3
Level $7$
Weight $10$
Character 7.1
Self dual yes
Analytic conductor $3.605$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.60525085315\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \( x^{3} - x^{2} - 426x + 2016 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(4.96128\) of defining polynomial
Character \(\chi\) \(=\) 7.1

$q$-expansion

\(f(q)\) \(=\) \(q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} +O(q^{10})\) \(q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} -74904.4 q^{10} +17401.5 q^{11} +287.032 q^{12} -122541. q^{13} +100366. q^{14} -416.326 q^{15} +631550. q^{16} +331933. q^{17} -822785. q^{18} +761707. q^{19} -2.21370e6 q^{20} +557.846 q^{21} +727418. q^{22} +1.23249e6 q^{23} +7025.85 q^{24} +1.25774e6 q^{25} -5.12246e6 q^{26} -9146.25 q^{27} +2.96620e6 q^{28} +634604. q^{29} -17403.2 q^{30} -5.38069e6 q^{31} +1.09173e7 q^{32} +4043.06 q^{33} +1.38754e7 q^{34} -4.30232e6 q^{35} -2.43164e7 q^{36} -3.03611e6 q^{37} +3.18408e7 q^{38} -28471.1 q^{39} -5.41861e7 q^{40} -7.37009e6 q^{41} +23319.1 q^{42} -2.06990e7 q^{43} +2.14979e7 q^{44} +3.52696e7 q^{45} +5.15203e7 q^{46} +2.03632e7 q^{47} +146734. q^{48} +5.76480e6 q^{49} +5.25760e7 q^{50} +77120.9 q^{51} -1.51388e8 q^{52} -5.97380e7 q^{53} -382331. q^{54} -3.11816e7 q^{55} +7.26054e7 q^{56} +176974. q^{57} +2.65277e7 q^{58} +6.03461e7 q^{59} -514330. q^{60} -9.44357e6 q^{61} -2.24923e8 q^{62} -4.72588e7 q^{63} +1.33012e8 q^{64} +2.19580e8 q^{65} +169008. q^{66} -2.19187e8 q^{67} +4.10071e8 q^{68} +286355. q^{69} -1.79846e8 q^{70} -5.58741e7 q^{71} -5.95205e8 q^{72} +4.54332e8 q^{73} -1.26915e8 q^{74} +292222. q^{75} +9.41015e8 q^{76} +4.17811e7 q^{77} -1.19015e6 q^{78} +4.51057e7 q^{79} -1.13167e9 q^{80} +3.87417e8 q^{81} -3.08084e8 q^{82} -3.34665e8 q^{83} +689165. q^{84} -5.94786e8 q^{85} -8.65259e8 q^{86} +147443. q^{87} +5.26216e8 q^{88} +6.51886e8 q^{89} +1.47434e9 q^{90} -2.94221e8 q^{91} +1.52262e9 q^{92} -1.25014e6 q^{93} +8.51220e8 q^{94} -1.36489e9 q^{95} +2.53652e6 q^{96} -1.42804e9 q^{97} +2.40980e8 q^{98} -3.42514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.8019 1.84740 0.923701 0.383114i \(-0.125148\pi\)
0.923701 + 0.383114i \(0.125148\pi\)
\(3\) 0.232339 0.00165606 0.000828031 1.00000i \(-0.499736\pi\)
0.000828031 1.00000i \(0.499736\pi\)
\(4\) 1235.40 2.41290
\(5\) −1791.89 −1.28217 −0.641086 0.767469i \(-0.721516\pi\)
−0.641086 + 0.767469i \(0.721516\pi\)
\(6\) 9.71222 0.00305941
\(7\) 2401.00 0.377964
\(8\) 30239.6 2.61019
\(9\) −19682.9 −0.999997
\(10\) −74904.4 −2.36869
\(11\) 17401.5 0.358361 0.179180 0.983816i \(-0.442655\pi\)
0.179180 + 0.983816i \(0.442655\pi\)
\(12\) 287.032 0.00399591
\(13\) −122541. −1.18997 −0.594986 0.803736i \(-0.702842\pi\)
−0.594986 + 0.803736i \(0.702842\pi\)
\(14\) 100366. 0.698253
\(15\) −416.326 −0.00212335
\(16\) 631550. 2.40917
\(17\) 331933. 0.963895 0.481948 0.876200i \(-0.339930\pi\)
0.481948 + 0.876200i \(0.339930\pi\)
\(18\) −822785. −1.84740
\(19\) 761707. 1.34090 0.670450 0.741954i \(-0.266101\pi\)
0.670450 + 0.741954i \(0.266101\pi\)
\(20\) −2.21370e6 −3.09375
\(21\) 557.846 0.000625933 0
\(22\) 727418. 0.662037
\(23\) 1.23249e6 0.918347 0.459173 0.888347i \(-0.348146\pi\)
0.459173 + 0.888347i \(0.348146\pi\)
\(24\) 7025.85 0.00432263
\(25\) 1.25774e6 0.643963
\(26\) −5.12246e6 −2.19836
\(27\) −9146.25 −0.00331212
\(28\) 2.96620e6 0.911989
\(29\) 634604. 0.166614 0.0833071 0.996524i \(-0.473452\pi\)
0.0833071 + 0.996524i \(0.473452\pi\)
\(30\) −17403.2 −0.00392269
\(31\) −5.38069e6 −1.04643 −0.523215 0.852201i \(-0.675268\pi\)
−0.523215 + 0.852201i \(0.675268\pi\)
\(32\) 1.09173e7 1.84052
\(33\) 4043.06 0.000593468 0
\(34\) 1.38754e7 1.78070
\(35\) −4.30232e6 −0.484615
\(36\) −2.43164e7 −2.41289
\(37\) −3.03611e6 −0.266324 −0.133162 0.991094i \(-0.542513\pi\)
−0.133162 + 0.991094i \(0.542513\pi\)
\(38\) 3.18408e7 2.47718
\(39\) −28471.1 −0.00197067
\(40\) −5.41861e7 −3.34671
\(41\) −7.37009e6 −0.407329 −0.203665 0.979041i \(-0.565285\pi\)
−0.203665 + 0.979041i \(0.565285\pi\)
\(42\) 23319.1 0.00115635
\(43\) −2.06990e7 −0.923297 −0.461649 0.887063i \(-0.652742\pi\)
−0.461649 + 0.887063i \(0.652742\pi\)
\(44\) 2.14979e7 0.864687
\(45\) 3.52696e7 1.28217
\(46\) 5.15203e7 1.69656
\(47\) 2.03632e7 0.608702 0.304351 0.952560i \(-0.401560\pi\)
0.304351 + 0.952560i \(0.401560\pi\)
\(48\) 146734. 0.00398974
\(49\) 5.76480e6 0.142857
\(50\) 5.25760e7 1.18966
\(51\) 77120.9 0.00159627
\(52\) −1.51388e8 −2.87128
\(53\) −5.97380e7 −1.03994 −0.519971 0.854184i \(-0.674057\pi\)
−0.519971 + 0.854184i \(0.674057\pi\)
\(54\) −382331. −0.00611882
\(55\) −3.11816e7 −0.459480
\(56\) 7.26054e7 0.986558
\(57\) 176974. 0.00222061
\(58\) 2.65277e7 0.307803
\(59\) 6.03461e7 0.648358 0.324179 0.945996i \(-0.394912\pi\)
0.324179 + 0.945996i \(0.394912\pi\)
\(60\) −514330. −0.00512343
\(61\) −9.44357e6 −0.0873277 −0.0436639 0.999046i \(-0.513903\pi\)
−0.0436639 + 0.999046i \(0.513903\pi\)
\(62\) −2.24923e8 −1.93318
\(63\) −4.72588e7 −0.377963
\(64\) 1.33012e8 0.991013
\(65\) 2.19580e8 1.52575
\(66\) 169008. 0.00109637
\(67\) −2.19187e8 −1.32885 −0.664427 0.747353i \(-0.731324\pi\)
−0.664427 + 0.747353i \(0.731324\pi\)
\(68\) 4.10071e8 2.32578
\(69\) 286355. 0.00152084
\(70\) −1.79846e8 −0.895279
\(71\) −5.58741e7 −0.260944 −0.130472 0.991452i \(-0.541649\pi\)
−0.130472 + 0.991452i \(0.541649\pi\)
\(72\) −5.95205e8 −2.61018
\(73\) 4.54332e8 1.87250 0.936248 0.351340i \(-0.114274\pi\)
0.936248 + 0.351340i \(0.114274\pi\)
\(74\) −1.26915e8 −0.492007
\(75\) 292222. 0.00106644
\(76\) 9.41015e8 3.23545
\(77\) 4.17811e7 0.135448
\(78\) −1.19015e6 −0.00364062
\(79\) 4.51057e7 0.130289 0.0651447 0.997876i \(-0.479249\pi\)
0.0651447 + 0.997876i \(0.479249\pi\)
\(80\) −1.13167e9 −3.08897
\(81\) 3.87417e8 0.999992
\(82\) −3.08084e8 −0.752501
\(83\) −3.34665e8 −0.774031 −0.387016 0.922073i \(-0.626494\pi\)
−0.387016 + 0.922073i \(0.626494\pi\)
\(84\) 689165. 0.00151031
\(85\) −5.94786e8 −1.23588
\(86\) −8.65259e8 −1.70570
\(87\) 147443. 0.000275923 0
\(88\) 5.26216e8 0.935389
\(89\) 6.51886e8 1.10133 0.550664 0.834727i \(-0.314375\pi\)
0.550664 + 0.834727i \(0.314375\pi\)
\(90\) 1.47434e9 2.36868
\(91\) −2.94221e8 −0.449767
\(92\) 1.52262e9 2.21588
\(93\) −1.25014e6 −0.00173295
\(94\) 8.51220e8 1.12452
\(95\) −1.36489e9 −1.71926
\(96\) 2.53652e6 0.00304802
\(97\) −1.42804e9 −1.63783 −0.818914 0.573916i \(-0.805424\pi\)
−0.818914 + 0.573916i \(0.805424\pi\)
\(98\) 2.40980e8 0.263915
\(99\) −3.42514e8 −0.358360
\(100\) 1.55382e9 1.55382
\(101\) 8.91532e8 0.852493 0.426247 0.904607i \(-0.359836\pi\)
0.426247 + 0.904607i \(0.359836\pi\)
\(102\) 3.22380e6 0.00294895
\(103\) −7.12000e8 −0.623322 −0.311661 0.950193i \(-0.600885\pi\)
−0.311661 + 0.950193i \(0.600885\pi\)
\(104\) −3.70560e9 −3.10605
\(105\) −999598. −0.000802553 0
\(106\) −2.49716e9 −1.92119
\(107\) 2.48598e9 1.83346 0.916729 0.399510i \(-0.130820\pi\)
0.916729 + 0.399510i \(0.130820\pi\)
\(108\) −1.12993e7 −0.00799180
\(109\) 3.83455e8 0.260193 0.130096 0.991501i \(-0.458471\pi\)
0.130096 + 0.991501i \(0.458471\pi\)
\(110\) −1.30345e9 −0.848844
\(111\) −705407. −0.000441048 0
\(112\) 1.51635e9 0.910581
\(113\) 2.39582e9 1.38230 0.691148 0.722713i \(-0.257105\pi\)
0.691148 + 0.722713i \(0.257105\pi\)
\(114\) 7.39787e6 0.00410237
\(115\) −2.20848e9 −1.17748
\(116\) 7.83991e8 0.402023
\(117\) 2.41197e9 1.18997
\(118\) 2.52258e9 1.19778
\(119\) 7.96970e8 0.364318
\(120\) −1.25895e7 −0.00554235
\(121\) −2.05513e9 −0.871578
\(122\) −3.94760e8 −0.161329
\(123\) −1.71236e6 −0.000674562 0
\(124\) −6.64732e9 −2.52493
\(125\) 1.24605e9 0.456501
\(126\) −1.97551e9 −0.698251
\(127\) 1.88261e9 0.642161 0.321080 0.947052i \(-0.395954\pi\)
0.321080 + 0.947052i \(0.395954\pi\)
\(128\) −2.95237e7 −0.00972134
\(129\) −4.80919e6 −0.00152904
\(130\) 9.17888e9 2.81867
\(131\) −1.49241e9 −0.442760 −0.221380 0.975188i \(-0.571056\pi\)
−0.221380 + 0.975188i \(0.571056\pi\)
\(132\) 4.99480e6 0.00143198
\(133\) 1.82886e9 0.506813
\(134\) −9.16242e9 −2.45493
\(135\) 1.63891e7 0.00424670
\(136\) 1.00375e10 2.51595
\(137\) −3.21118e9 −0.778792 −0.389396 0.921070i \(-0.627316\pi\)
−0.389396 + 0.921070i \(0.627316\pi\)
\(138\) 1.19702e7 0.00280960
\(139\) −3.03934e9 −0.690577 −0.345289 0.938497i \(-0.612219\pi\)
−0.345289 + 0.938497i \(0.612219\pi\)
\(140\) −5.31510e9 −1.16933
\(141\) 4.73116e6 0.00100805
\(142\) −2.33565e9 −0.482070
\(143\) −2.13240e9 −0.426439
\(144\) −1.24308e10 −2.40917
\(145\) −1.13714e9 −0.213628
\(146\) 1.89920e10 3.45925
\(147\) 1.33939e6 0.000236580 0
\(148\) −3.75082e9 −0.642611
\(149\) −3.64286e9 −0.605487 −0.302743 0.953072i \(-0.597902\pi\)
−0.302743 + 0.953072i \(0.597902\pi\)
\(150\) 1.22155e7 0.00197015
\(151\) 5.05862e9 0.791837 0.395919 0.918286i \(-0.370426\pi\)
0.395919 + 0.918286i \(0.370426\pi\)
\(152\) 2.30337e10 3.50000
\(153\) −6.53341e9 −0.963893
\(154\) 1.74653e9 0.250226
\(155\) 9.64159e9 1.34170
\(156\) −3.51733e7 −0.00475502
\(157\) −1.19687e10 −1.57216 −0.786082 0.618122i \(-0.787894\pi\)
−0.786082 + 0.618122i \(0.787894\pi\)
\(158\) 1.88551e9 0.240697
\(159\) −1.38795e7 −0.00172221
\(160\) −1.95626e10 −2.35986
\(161\) 2.95920e9 0.347102
\(162\) 1.61948e10 1.84739
\(163\) 1.40960e10 1.56405 0.782027 0.623245i \(-0.214186\pi\)
0.782027 + 0.623245i \(0.214186\pi\)
\(164\) −9.10503e9 −0.982843
\(165\) −7.24471e6 −0.000760927 0
\(166\) −1.39896e10 −1.42995
\(167\) 3.56028e9 0.354210 0.177105 0.984192i \(-0.443327\pi\)
0.177105 + 0.984192i \(0.443327\pi\)
\(168\) 1.68691e7 0.00163380
\(169\) 4.41184e9 0.416034
\(170\) −2.48632e10 −2.28317
\(171\) −1.49926e10 −1.34090
\(172\) −2.55716e10 −2.22782
\(173\) 2.64068e9 0.224134 0.112067 0.993701i \(-0.464253\pi\)
0.112067 + 0.993701i \(0.464253\pi\)
\(174\) 6.16342e6 0.000509741 0
\(175\) 3.01983e9 0.243395
\(176\) 1.09899e10 0.863353
\(177\) 1.40208e7 0.00107372
\(178\) 2.72501e10 2.03459
\(179\) 1.26973e9 0.0924430 0.0462215 0.998931i \(-0.485282\pi\)
0.0462215 + 0.998931i \(0.485282\pi\)
\(180\) 4.35722e10 3.09374
\(181\) −2.17242e10 −1.50449 −0.752247 0.658881i \(-0.771030\pi\)
−0.752247 + 0.658881i \(0.771030\pi\)
\(182\) −1.22990e10 −0.830901
\(183\) −2.19411e6 −0.000144620 0
\(184\) 3.72699e10 2.39706
\(185\) 5.44037e9 0.341473
\(186\) −5.22584e7 −0.00320146
\(187\) 5.77614e9 0.345422
\(188\) 2.51567e10 1.46874
\(189\) −2.19601e7 −0.00125186
\(190\) −5.70552e10 −3.17617
\(191\) −1.07035e10 −0.581937 −0.290968 0.956733i \(-0.593977\pi\)
−0.290968 + 0.956733i \(0.593977\pi\)
\(192\) 3.09038e7 0.00164118
\(193\) 7.66063e9 0.397426 0.198713 0.980058i \(-0.436324\pi\)
0.198713 + 0.980058i \(0.436324\pi\)
\(194\) −5.96950e10 −3.02573
\(195\) 5.10170e7 0.00252673
\(196\) 7.12185e9 0.344699
\(197\) −4.26160e9 −0.201592 −0.100796 0.994907i \(-0.532139\pi\)
−0.100796 + 0.994907i \(0.532139\pi\)
\(198\) −1.43177e10 −0.662035
\(199\) 3.16291e10 1.42971 0.714856 0.699272i \(-0.246492\pi\)
0.714856 + 0.699272i \(0.246492\pi\)
\(200\) 3.80336e10 1.68086
\(201\) −5.09256e7 −0.00220066
\(202\) 3.72678e10 1.57490
\(203\) 1.52368e9 0.0629742
\(204\) 9.52754e7 0.00385163
\(205\) 1.32064e10 0.522266
\(206\) −2.97630e10 −1.15153
\(207\) −2.42590e10 −0.918344
\(208\) −7.73909e10 −2.86685
\(209\) 1.32549e10 0.480526
\(210\) −4.17851e7 −0.00148264
\(211\) 1.76561e10 0.613229 0.306615 0.951834i \(-0.400804\pi\)
0.306615 + 0.951834i \(0.400804\pi\)
\(212\) −7.38005e10 −2.50927
\(213\) −1.29817e7 −0.000432140 0
\(214\) 1.03919e11 3.38713
\(215\) 3.70903e10 1.18383
\(216\) −2.76579e8 −0.00864525
\(217\) −1.29190e10 −0.395513
\(218\) 1.60292e10 0.480681
\(219\) 1.05559e8 0.00310097
\(220\) −3.85219e10 −1.10868
\(221\) −4.06754e10 −1.14701
\(222\) −2.94874e7 −0.000814794 0
\(223\) −1.04686e10 −0.283476 −0.141738 0.989904i \(-0.545269\pi\)
−0.141738 + 0.989904i \(0.545269\pi\)
\(224\) 2.62125e10 0.695652
\(225\) −2.47560e10 −0.643961
\(226\) 1.00150e11 2.55366
\(227\) 1.95043e10 0.487543 0.243772 0.969833i \(-0.421615\pi\)
0.243772 + 0.969833i \(0.421615\pi\)
\(228\) 2.18634e8 0.00535811
\(229\) −5.96135e10 −1.43247 −0.716234 0.697860i \(-0.754136\pi\)
−0.716234 + 0.697860i \(0.754136\pi\)
\(230\) −9.23187e10 −2.17528
\(231\) 9.70738e6 0.000224310 0
\(232\) 1.91902e10 0.434894
\(233\) 8.42619e10 1.87296 0.936482 0.350716i \(-0.114062\pi\)
0.936482 + 0.350716i \(0.114062\pi\)
\(234\) 1.00825e11 2.19835
\(235\) −3.64885e10 −0.780460
\(236\) 7.45517e10 1.56442
\(237\) 1.04798e7 0.000215767 0
\(238\) 3.33149e10 0.673042
\(239\) −7.28353e10 −1.44395 −0.721974 0.691920i \(-0.756765\pi\)
−0.721974 + 0.691920i \(0.756765\pi\)
\(240\) −2.62930e8 −0.00511553
\(241\) 4.45555e10 0.850795 0.425397 0.905007i \(-0.360134\pi\)
0.425397 + 0.905007i \(0.360134\pi\)
\(242\) −8.59086e10 −1.61015
\(243\) 2.70038e8 0.00496817
\(244\) −1.16666e10 −0.210713
\(245\) −1.03299e10 −0.183167
\(246\) −7.15800e7 −0.00124619
\(247\) −9.33404e10 −1.59564
\(248\) −1.62710e11 −2.73138
\(249\) −7.77557e7 −0.00128184
\(250\) 5.20874e10 0.843340
\(251\) −9.55068e10 −1.51881 −0.759404 0.650620i \(-0.774509\pi\)
−0.759404 + 0.650620i \(0.774509\pi\)
\(252\) −5.83836e10 −0.911987
\(253\) 2.14472e10 0.329100
\(254\) 7.86968e10 1.18633
\(255\) −1.38192e8 −0.00204669
\(256\) −6.93361e10 −1.00897
\(257\) 9.12794e10 1.30519 0.652595 0.757707i \(-0.273680\pi\)
0.652595 + 0.757707i \(0.273680\pi\)
\(258\) −2.01033e8 −0.00282475
\(259\) −7.28970e9 −0.100661
\(260\) 2.71270e11 3.68147
\(261\) −1.24909e10 −0.166614
\(262\) −6.23858e10 −0.817956
\(263\) 1.50976e11 1.94584 0.972921 0.231138i \(-0.0742449\pi\)
0.972921 + 0.231138i \(0.0742449\pi\)
\(264\) 1.22261e8 0.00154906
\(265\) 1.07044e11 1.33338
\(266\) 7.64498e10 0.936287
\(267\) 1.51458e8 0.00182387
\(268\) −2.70784e11 −3.20639
\(269\) 2.39622e10 0.279024 0.139512 0.990220i \(-0.455447\pi\)
0.139512 + 0.990220i \(0.455447\pi\)
\(270\) 6.85094e8 0.00784537
\(271\) −5.51248e10 −0.620848 −0.310424 0.950598i \(-0.600471\pi\)
−0.310424 + 0.950598i \(0.600471\pi\)
\(272\) 2.09632e11 2.32219
\(273\) −6.83591e7 −0.000744842 0
\(274\) −1.34233e11 −1.43874
\(275\) 2.18866e10 0.230771
\(276\) 3.53763e8 0.00366963
\(277\) 2.19632e10 0.224149 0.112074 0.993700i \(-0.464251\pi\)
0.112074 + 0.993700i \(0.464251\pi\)
\(278\) −1.27050e11 −1.27577
\(279\) 1.05908e11 1.04643
\(280\) −1.30101e11 −1.26494
\(281\) −1.62670e10 −0.155643 −0.0778213 0.996967i \(-0.524796\pi\)
−0.0778213 + 0.996967i \(0.524796\pi\)
\(282\) 1.97772e8 0.00186227
\(283\) 1.35590e10 0.125657 0.0628287 0.998024i \(-0.479988\pi\)
0.0628287 + 0.998024i \(0.479988\pi\)
\(284\) −6.90270e10 −0.629632
\(285\) −3.17118e8 −0.00284721
\(286\) −8.91387e10 −0.787805
\(287\) −1.76956e10 −0.153956
\(288\) −2.14885e11 −1.84052
\(289\) −8.40858e9 −0.0709059
\(290\) −4.75346e10 −0.394657
\(291\) −3.31790e8 −0.00271235
\(292\) 5.61284e11 4.51814
\(293\) 5.41900e10 0.429551 0.214776 0.976663i \(-0.431098\pi\)
0.214776 + 0.976663i \(0.431098\pi\)
\(294\) 5.59890e7 0.000437059 0
\(295\) −1.08133e11 −0.831306
\(296\) −9.18109e10 −0.695155
\(297\) −1.59159e8 −0.00118693
\(298\) −1.52279e11 −1.11858
\(299\) −1.51030e11 −1.09281
\(300\) 3.61012e8 0.00257321
\(301\) −4.96983e10 −0.348974
\(302\) 2.11460e11 1.46284
\(303\) 2.07138e8 0.00141178
\(304\) 4.81056e11 3.23046
\(305\) 1.69218e10 0.111969
\(306\) −2.73109e11 −1.78070
\(307\) 7.32498e10 0.470634 0.235317 0.971919i \(-0.424387\pi\)
0.235317 + 0.971919i \(0.424387\pi\)
\(308\) 5.16165e10 0.326821
\(309\) −1.65425e8 −0.00103226
\(310\) 4.03037e11 2.47866
\(311\) −2.44502e11 −1.48204 −0.741021 0.671482i \(-0.765658\pi\)
−0.741021 + 0.671482i \(0.765658\pi\)
\(312\) −8.60956e8 −0.00514381
\(313\) −4.39895e10 −0.259060 −0.129530 0.991576i \(-0.541347\pi\)
−0.129530 + 0.991576i \(0.541347\pi\)
\(314\) −5.00314e11 −2.90442
\(315\) 8.46824e10 0.484614
\(316\) 5.57237e10 0.314375
\(317\) −2.17653e11 −1.21059 −0.605297 0.795999i \(-0.706946\pi\)
−0.605297 + 0.795999i \(0.706946\pi\)
\(318\) −5.80189e8 −0.00318161
\(319\) 1.10431e10 0.0597080
\(320\) −2.38342e11 −1.27065
\(321\) 5.77591e8 0.00303632
\(322\) 1.23700e11 0.641238
\(323\) 2.52835e11 1.29249
\(324\) 4.78616e11 2.41288
\(325\) −1.54125e11 −0.766298
\(326\) 5.89240e11 2.88944
\(327\) 8.90917e7 0.000430896 0
\(328\) −2.22869e11 −1.06321
\(329\) 4.88920e10 0.230068
\(330\) −3.02843e8 −0.00140574
\(331\) −3.66945e11 −1.68026 −0.840128 0.542389i \(-0.817520\pi\)
−0.840128 + 0.542389i \(0.817520\pi\)
\(332\) −4.13446e11 −1.86766
\(333\) 5.97596e10 0.266323
\(334\) 1.48827e11 0.654368
\(335\) 3.92758e11 1.70382
\(336\) 3.52308e8 0.00150798
\(337\) 1.99451e11 0.842367 0.421183 0.906976i \(-0.361615\pi\)
0.421183 + 0.906976i \(0.361615\pi\)
\(338\) 1.84423e11 0.768583
\(339\) 5.56642e8 0.00228917
\(340\) −7.34801e11 −2.98205
\(341\) −9.36322e10 −0.374999
\(342\) −6.26721e11 −2.47718
\(343\) 1.38413e10 0.0539949
\(344\) −6.25931e11 −2.40998
\(345\) −5.13116e8 −0.00194998
\(346\) 1.10385e11 0.414066
\(347\) 6.63180e10 0.245555 0.122777 0.992434i \(-0.460820\pi\)
0.122777 + 0.992434i \(0.460820\pi\)
\(348\) 1.82152e8 0.000665774 0
\(349\) −1.20301e11 −0.434065 −0.217033 0.976164i \(-0.569638\pi\)
−0.217033 + 0.976164i \(0.569638\pi\)
\(350\) 1.26235e11 0.449649
\(351\) 1.12079e9 0.00394133
\(352\) 1.89978e11 0.659571
\(353\) 2.43060e11 0.833159 0.416580 0.909099i \(-0.363229\pi\)
0.416580 + 0.909099i \(0.363229\pi\)
\(354\) 5.86095e8 0.00198360
\(355\) 1.00120e11 0.334575
\(356\) 8.05341e11 2.65739
\(357\) 1.85167e8 0.000603333 0
\(358\) 5.30773e10 0.170779
\(359\) 2.81654e11 0.894933 0.447466 0.894301i \(-0.352326\pi\)
0.447466 + 0.894301i \(0.352326\pi\)
\(360\) 1.06654e12 3.34670
\(361\) 2.57510e11 0.798015
\(362\) −9.08115e11 −2.77941
\(363\) −4.77488e8 −0.00144339
\(364\) −3.63482e11 −1.08524
\(365\) −8.14113e11 −2.40086
\(366\) −9.17181e7 −0.000267172 0
\(367\) −2.41000e11 −0.693458 −0.346729 0.937965i \(-0.612708\pi\)
−0.346729 + 0.937965i \(0.612708\pi\)
\(368\) 7.78376e11 2.21246
\(369\) 1.45065e11 0.407328
\(370\) 2.27418e11 0.630837
\(371\) −1.43431e11 −0.393061
\(372\) −1.54443e9 −0.00418143
\(373\) −1.33921e11 −0.358227 −0.179114 0.983828i \(-0.557323\pi\)
−0.179114 + 0.983828i \(0.557323\pi\)
\(374\) 2.41454e11 0.638134
\(375\) 2.89507e8 0.000755993 0
\(376\) 6.15775e11 1.58883
\(377\) −7.77651e10 −0.198266
\(378\) −9.17976e8 −0.00231270
\(379\) 5.67201e11 1.41208 0.706042 0.708170i \(-0.250479\pi\)
0.706042 + 0.708170i \(0.250479\pi\)
\(380\) −1.68619e12 −4.14841
\(381\) 4.37404e8 0.00106346
\(382\) −4.47427e11 −1.07507
\(383\) −1.03509e11 −0.245800 −0.122900 0.992419i \(-0.539219\pi\)
−0.122900 + 0.992419i \(0.539219\pi\)
\(384\) −6.85951e6 −1.60991e−5 0
\(385\) −7.48671e10 −0.173667
\(386\) 3.20229e11 0.734206
\(387\) 4.07417e11 0.923295
\(388\) −1.76421e12 −3.95191
\(389\) −5.83600e11 −1.29224 −0.646119 0.763237i \(-0.723609\pi\)
−0.646119 + 0.763237i \(0.723609\pi\)
\(390\) 2.13261e9 0.00466789
\(391\) 4.09102e11 0.885190
\(392\) 1.74326e11 0.372884
\(393\) −3.46746e8 −0.000733238 0
\(394\) −1.78143e11 −0.372422
\(395\) −8.08243e10 −0.167053
\(396\) −4.23142e11 −0.864685
\(397\) −6.54542e10 −0.132245 −0.0661226 0.997812i \(-0.521063\pi\)
−0.0661226 + 0.997812i \(0.521063\pi\)
\(398\) 1.32216e12 2.64125
\(399\) 4.24915e8 0.000839313 0
\(400\) 7.94326e11 1.55142
\(401\) 4.06647e10 0.0785359 0.0392679 0.999229i \(-0.487497\pi\)
0.0392679 + 0.999229i \(0.487497\pi\)
\(402\) −2.12879e9 −0.00406551
\(403\) 6.59356e11 1.24522
\(404\) 1.10140e12 2.05698
\(405\) −6.94209e11 −1.28216
\(406\) 6.36930e10 0.116339
\(407\) −5.28330e10 −0.0954400
\(408\) 2.33211e9 0.00416657
\(409\) 1.06163e12 1.87594 0.937970 0.346716i \(-0.112703\pi\)
0.937970 + 0.346716i \(0.112703\pi\)
\(410\) 5.52052e11 0.964835
\(411\) −7.46081e8 −0.00128973
\(412\) −8.79607e11 −1.50401
\(413\) 1.44891e11 0.245056
\(414\) −1.01407e12 −1.69655
\(415\) 5.99682e11 0.992441
\(416\) −1.33782e12 −2.19017
\(417\) −7.06157e8 −0.00114364
\(418\) 5.54079e11 0.887726
\(419\) −1.19335e12 −1.89149 −0.945744 0.324912i \(-0.894665\pi\)
−0.945744 + 0.324912i \(0.894665\pi\)
\(420\) −1.23491e9 −0.00193648
\(421\) −5.88397e11 −0.912853 −0.456427 0.889761i \(-0.650871\pi\)
−0.456427 + 0.889761i \(0.650871\pi\)
\(422\) 7.38058e11 1.13288
\(423\) −4.00807e11 −0.608701
\(424\) −1.80646e12 −2.71444
\(425\) 4.17485e11 0.620713
\(426\) −5.42662e8 −0.000798337 0
\(427\) −2.26740e10 −0.0330068
\(428\) 3.07119e12 4.42394
\(429\) −4.95441e8 −0.000706210 0
\(430\) 1.55045e12 2.18700
\(431\) −1.22932e12 −1.71599 −0.857997 0.513655i \(-0.828291\pi\)
−0.857997 + 0.513655i \(0.828291\pi\)
\(432\) −5.77631e9 −0.00797946
\(433\) −4.73819e10 −0.0647764 −0.0323882 0.999475i \(-0.510311\pi\)
−0.0323882 + 0.999475i \(0.510311\pi\)
\(434\) −5.40041e11 −0.730672
\(435\) −2.64202e8 −0.000353781 0
\(436\) 4.73722e11 0.627819
\(437\) 9.38793e11 1.23141
\(438\) 4.41258e9 0.00572874
\(439\) 6.14236e11 0.789305 0.394652 0.918830i \(-0.370865\pi\)
0.394652 + 0.918830i \(0.370865\pi\)
\(440\) −9.42921e11 −1.19933
\(441\) −1.13468e11 −0.142857
\(442\) −1.70031e12 −2.11899
\(443\) −8.19199e11 −1.01058 −0.505292 0.862948i \(-0.668615\pi\)
−0.505292 + 0.862948i \(0.668615\pi\)
\(444\) −8.71462e8 −0.00106420
\(445\) −1.16811e12 −1.41209
\(446\) −4.37607e11 −0.523694
\(447\) −8.46379e8 −0.00100272
\(448\) 3.19361e11 0.374568
\(449\) 4.81029e11 0.558551 0.279276 0.960211i \(-0.409906\pi\)
0.279276 + 0.960211i \(0.409906\pi\)
\(450\) −1.03485e12 −1.18966
\(451\) −1.28251e11 −0.145971
\(452\) 2.95980e12 3.33534
\(453\) 1.17532e9 0.00131133
\(454\) 8.15316e11 0.900689
\(455\) 5.27212e11 0.576679
\(456\) 5.35164e9 0.00579622
\(457\) 1.15328e12 1.23684 0.618419 0.785849i \(-0.287774\pi\)
0.618419 + 0.785849i \(0.287774\pi\)
\(458\) −2.49196e12 −2.64635
\(459\) −3.03594e9 −0.00319254
\(460\) −2.72836e12 −2.84113
\(461\) −6.06986e11 −0.625928 −0.312964 0.949765i \(-0.601322\pi\)
−0.312964 + 0.949765i \(0.601322\pi\)
\(462\) 4.05787e8 0.000414390 0
\(463\) −8.87758e11 −0.897801 −0.448900 0.893582i \(-0.648184\pi\)
−0.448900 + 0.893582i \(0.648184\pi\)
\(464\) 4.00784e11 0.401402
\(465\) 2.24012e9 0.00222194
\(466\) 3.52231e12 3.46012
\(467\) −1.09779e12 −1.06806 −0.534029 0.845466i \(-0.679323\pi\)
−0.534029 + 0.845466i \(0.679323\pi\)
\(468\) 2.97976e12 2.87127
\(469\) −5.26267e11 −0.502260
\(470\) −1.52529e12 −1.44182
\(471\) −2.78079e9 −0.00260360
\(472\) 1.82484e12 1.69234
\(473\) −3.60195e11 −0.330874
\(474\) 4.38076e8 0.000398609 0
\(475\) 9.58029e11 0.863490
\(476\) 9.84579e11 0.879062
\(477\) 1.17582e12 1.03994
\(478\) −3.04466e12 −2.66755
\(479\) −3.12229e11 −0.270996 −0.135498 0.990778i \(-0.543263\pi\)
−0.135498 + 0.990778i \(0.543263\pi\)
\(480\) −4.54516e9 −0.00390808
\(481\) 3.72048e11 0.316918
\(482\) 1.86251e12 1.57176
\(483\) 6.87537e8 0.000574823 0
\(484\) −2.53892e12 −2.10303
\(485\) 2.55889e12 2.09998
\(486\) 1.12881e10 0.00917820
\(487\) 1.08377e12 0.873088 0.436544 0.899683i \(-0.356202\pi\)
0.436544 + 0.899683i \(0.356202\pi\)
\(488\) −2.85570e11 −0.227942
\(489\) 3.27505e9 0.00259017
\(490\) −4.31809e11 −0.338384
\(491\) 2.14702e12 1.66713 0.833567 0.552419i \(-0.186295\pi\)
0.833567 + 0.552419i \(0.186295\pi\)
\(492\) −2.11545e9 −0.00162765
\(493\) 2.10646e11 0.160599
\(494\) −3.90181e12 −2.94778
\(495\) 6.13746e11 0.459479
\(496\) −3.39817e12 −2.52103
\(497\) −1.34154e11 −0.0986277
\(498\) −3.25034e9 −0.00236808
\(499\) −1.85705e12 −1.34082 −0.670411 0.741990i \(-0.733882\pi\)
−0.670411 + 0.741990i \(0.733882\pi\)
\(500\) 1.53938e12 1.10149
\(501\) 8.27193e8 0.000586593 0
\(502\) −3.99237e12 −2.80585
\(503\) −1.59040e12 −1.10777 −0.553885 0.832593i \(-0.686855\pi\)
−0.553885 + 0.832593i \(0.686855\pi\)
\(504\) −1.42909e12 −0.986556
\(505\) −1.59753e12 −1.09304
\(506\) 8.96533e11 0.607979
\(507\) 1.02504e9 0.000688979 0
\(508\) 2.32578e12 1.54947
\(509\) 2.32864e12 1.53771 0.768853 0.639426i \(-0.220828\pi\)
0.768853 + 0.639426i \(0.220828\pi\)
\(510\) −5.77670e9 −0.00378106
\(511\) 1.09085e12 0.707737
\(512\) −2.88327e12 −1.85426
\(513\) −6.96676e9 −0.00444122
\(514\) 3.81566e12 2.41121
\(515\) 1.27582e12 0.799205
\(516\) −5.94128e9 −0.00368941
\(517\) 3.54350e11 0.218135
\(518\) −3.04724e11 −0.185961
\(519\) 6.13532e8 0.000371180 0
\(520\) 6.64003e12 3.98249
\(521\) −1.48366e12 −0.882197 −0.441099 0.897459i \(-0.645411\pi\)
−0.441099 + 0.897459i \(0.645411\pi\)
\(522\) −5.22143e11 −0.307802
\(523\) −1.95584e12 −1.14308 −0.571540 0.820574i \(-0.693654\pi\)
−0.571540 + 0.820574i \(0.693654\pi\)
\(524\) −1.84373e12 −1.06833
\(525\) 7.01625e8 0.000403077 0
\(526\) 6.31110e12 3.59475
\(527\) −1.78603e12 −1.00865
\(528\) 2.55339e9 0.00142977
\(529\) −2.82131e11 −0.156639
\(530\) 4.47464e12 2.46330
\(531\) −1.18779e12 −0.648357
\(532\) 2.25938e12 1.22289
\(533\) 9.03139e11 0.484710
\(534\) 6.33126e9 0.00336941
\(535\) −4.45460e12 −2.35081
\(536\) −6.62812e12 −3.46856
\(537\) 2.95009e8 0.000153091 0
\(538\) 1.00167e12 0.515470
\(539\) 1.00316e11 0.0511944
\(540\) 2.02471e10 0.0102469
\(541\) −1.34802e12 −0.676563 −0.338281 0.941045i \(-0.609846\pi\)
−0.338281 + 0.941045i \(0.609846\pi\)
\(542\) −2.30433e12 −1.14696
\(543\) −5.04738e9 −0.00249154
\(544\) 3.62381e12 1.77407
\(545\) −6.87109e11 −0.333612
\(546\) −2.85754e9 −0.00137602
\(547\) 1.02503e12 0.489548 0.244774 0.969580i \(-0.421286\pi\)
0.244774 + 0.969580i \(0.421286\pi\)
\(548\) −3.96710e12 −1.87914
\(549\) 1.85877e11 0.0873275
\(550\) 9.14903e11 0.426327
\(551\) 4.83382e11 0.223413
\(552\) 8.65926e9 0.00396968
\(553\) 1.08299e11 0.0492448
\(554\) 9.18103e11 0.414093
\(555\) 1.26401e9 0.000565500 0
\(556\) −3.75481e12 −1.66629
\(557\) 1.75343e12 0.771864 0.385932 0.922527i \(-0.373880\pi\)
0.385932 + 0.922527i \(0.373880\pi\)
\(558\) 4.42715e12 1.93317
\(559\) 2.53648e12 1.09870
\(560\) −2.71713e12 −1.16752
\(561\) 1.34202e9 0.000572041 0
\(562\) −6.79991e11 −0.287535
\(563\) −2.17456e12 −0.912185 −0.456092 0.889932i \(-0.650751\pi\)
−0.456092 + 0.889932i \(0.650751\pi\)
\(564\) 5.84489e9 0.00243232
\(565\) −4.29304e12 −1.77234
\(566\) 5.66792e11 0.232140
\(567\) 9.30189e11 0.377961
\(568\) −1.68961e12 −0.681114
\(569\) 3.13812e12 1.25506 0.627531 0.778592i \(-0.284066\pi\)
0.627531 + 0.778592i \(0.284066\pi\)
\(570\) −1.32562e10 −0.00525994
\(571\) 2.05979e12 0.810887 0.405444 0.914120i \(-0.367117\pi\)
0.405444 + 0.914120i \(0.367117\pi\)
\(572\) −2.63438e12 −1.02895
\(573\) −2.48684e9 −0.000963723 0
\(574\) −7.39710e11 −0.284419
\(575\) 1.55015e12 0.591381
\(576\) −2.61806e12 −0.991011
\(577\) 3.94380e12 1.48123 0.740617 0.671927i \(-0.234533\pi\)
0.740617 + 0.671927i \(0.234533\pi\)
\(578\) −3.51495e11 −0.130992
\(579\) 1.77986e9 0.000658162 0
\(580\) −1.40483e12 −0.515462
\(581\) −8.03530e11 −0.292556
\(582\) −1.38695e10 −0.00501079
\(583\) −1.03953e12 −0.372675
\(584\) 1.37389e13 4.88757
\(585\) −4.32198e12 −1.52574
\(586\) 2.26525e12 0.793555
\(587\) 3.68239e12 1.28014 0.640071 0.768315i \(-0.278905\pi\)
0.640071 + 0.768315i \(0.278905\pi\)
\(588\) 1.65468e9 0.000570844 0
\(589\) −4.09851e12 −1.40316
\(590\) −4.52019e12 −1.53576
\(591\) −9.90135e8 −0.000333850 0
\(592\) −1.91746e12 −0.641620
\(593\) −1.17114e12 −0.388921 −0.194460 0.980910i \(-0.562296\pi\)
−0.194460 + 0.980910i \(0.562296\pi\)
\(594\) −6.65315e9 −0.00219274
\(595\) −1.42808e12 −0.467118
\(596\) −4.50040e12 −1.46098
\(597\) 7.34868e9 0.00236769
\(598\) −6.31336e12 −2.01886
\(599\) 2.83757e12 0.900586 0.450293 0.892881i \(-0.351319\pi\)
0.450293 + 0.892881i \(0.351319\pi\)
\(600\) 8.83669e9 0.00278361
\(601\) 2.37066e12 0.741198 0.370599 0.928793i \(-0.379152\pi\)
0.370599 + 0.928793i \(0.379152\pi\)
\(602\) −2.07749e12 −0.644695
\(603\) 4.31424e12 1.32885
\(604\) 6.24943e12 1.91062
\(605\) 3.68257e12 1.11751
\(606\) 8.65876e9 0.00260813
\(607\) 4.40080e12 1.31578 0.657889 0.753115i \(-0.271450\pi\)
0.657889 + 0.753115i \(0.271450\pi\)
\(608\) 8.31580e12 2.46796
\(609\) 3.54011e8 0.000104289 0
\(610\) 7.07366e11 0.206852
\(611\) −2.49533e12 −0.724339
\(612\) −8.07140e12 −2.32577
\(613\) −1.87570e12 −0.536527 −0.268264 0.963346i \(-0.586450\pi\)
−0.268264 + 0.963346i \(0.586450\pi\)
\(614\) 3.06198e12 0.869451
\(615\) 3.06836e9 0.000864904 0
\(616\) 1.26345e12 0.353544
\(617\) −3.18170e12 −0.883845 −0.441922 0.897053i \(-0.645703\pi\)
−0.441922 + 0.897053i \(0.645703\pi\)
\(618\) −6.91510e9 −0.00190700
\(619\) −1.16476e11 −0.0318880 −0.0159440 0.999873i \(-0.505075\pi\)
−0.0159440 + 0.999873i \(0.505075\pi\)
\(620\) 1.19113e13 3.23739
\(621\) −1.12726e10 −0.00304167
\(622\) −1.02207e13 −2.73793
\(623\) 1.56518e12 0.416263
\(624\) −1.79809e10 −0.00474768
\(625\) −4.68931e12 −1.22927
\(626\) −1.83885e12 −0.478587
\(627\) 3.07962e9 0.000795781 0
\(628\) −1.47861e13 −3.79347
\(629\) −1.00778e12 −0.256708
\(630\) 3.53989e12 0.895277
\(631\) −3.71283e12 −0.932338 −0.466169 0.884696i \(-0.654366\pi\)
−0.466169 + 0.884696i \(0.654366\pi\)
\(632\) 1.36398e12 0.340080
\(633\) 4.10219e9 0.00101555
\(634\) −9.09834e12 −2.23646
\(635\) −3.37343e12 −0.823360
\(636\) −1.71467e10 −0.00415551
\(637\) −7.06425e11 −0.169996
\(638\) 4.61622e11 0.110305
\(639\) 1.09977e12 0.260944
\(640\) 5.29032e10 0.0124644
\(641\) 2.93764e11 0.0687285 0.0343642 0.999409i \(-0.489059\pi\)
0.0343642 + 0.999409i \(0.489059\pi\)
\(642\) 2.41444e10 0.00560930
\(643\) 5.27980e12 1.21806 0.609029 0.793148i \(-0.291559\pi\)
0.609029 + 0.793148i \(0.291559\pi\)
\(644\) 3.65580e12 0.837522
\(645\) 8.61753e9 0.00196049
\(646\) 1.05690e13 2.38775
\(647\) −2.62000e12 −0.587804 −0.293902 0.955836i \(-0.594954\pi\)
−0.293902 + 0.955836i \(0.594954\pi\)
\(648\) 1.17154e13 2.61017
\(649\) 1.05011e12 0.232346
\(650\) −6.44272e12 −1.41566
\(651\) −3.00160e9 −0.000654995 0
\(652\) 1.74142e13 3.77390
\(653\) 3.15918e12 0.679931 0.339965 0.940438i \(-0.389585\pi\)
0.339965 + 0.940438i \(0.389585\pi\)
\(654\) 3.72420e9 0.000796038 0
\(655\) 2.67424e12 0.567694
\(656\) −4.65458e12 −0.981326
\(657\) −8.94260e12 −1.87249
\(658\) 2.04378e12 0.425028
\(659\) 8.77292e11 0.181201 0.0906004 0.995887i \(-0.471121\pi\)
0.0906004 + 0.995887i \(0.471121\pi\)
\(660\) −8.95013e9 −0.00183604
\(661\) 8.22108e12 1.67503 0.837514 0.546416i \(-0.184008\pi\)
0.837514 + 0.546416i \(0.184008\pi\)
\(662\) −1.53390e13 −3.10411
\(663\) −9.45049e9 −0.00189952
\(664\) −1.01201e13 −2.02037
\(665\) −3.27711e12 −0.649821
\(666\) 2.49807e12 0.492006
\(667\) 7.82140e11 0.153010
\(668\) 4.39838e12 0.854671
\(669\) −2.43226e9 −0.000469454 0
\(670\) 1.64180e13 3.14764
\(671\) −1.64333e11 −0.0312948
\(672\) 6.09018e9 0.00115204
\(673\) −7.47304e12 −1.40420 −0.702101 0.712077i \(-0.747754\pi\)
−0.702101 + 0.712077i \(0.747754\pi\)
\(674\) 8.33743e12 1.55619
\(675\) −1.15036e10 −0.00213288
\(676\) 5.45039e12 1.00385
\(677\) 8.71309e12 1.59413 0.797064 0.603895i \(-0.206386\pi\)
0.797064 + 0.603895i \(0.206386\pi\)
\(678\) 2.32687e10 0.00422901
\(679\) −3.42873e12 −0.619041
\(680\) −1.79861e13 −3.22588
\(681\) 4.53160e9 0.000807402 0
\(682\) −3.91401e12 −0.692775
\(683\) −3.73903e12 −0.657455 −0.328727 0.944425i \(-0.606620\pi\)
−0.328727 + 0.944425i \(0.606620\pi\)
\(684\) −1.85219e13 −3.23545
\(685\) 5.75407e12 0.998545
\(686\) 5.78593e11 0.0997504
\(687\) −1.38505e10 −0.00237226
\(688\) −1.30725e13 −2.22438
\(689\) 7.32036e12 1.23750
\(690\) −2.14492e10 −0.00360239
\(691\) −6.26971e12 −1.04616 −0.523078 0.852285i \(-0.675216\pi\)
−0.523078 + 0.852285i \(0.675216\pi\)
\(692\) 3.26230e12 0.540812
\(693\) −8.22375e11 −0.135447
\(694\) 2.77222e12 0.453639
\(695\) 5.44616e12 0.885439
\(696\) 4.45863e9 0.000720212 0
\(697\) −2.44637e12 −0.392623
\(698\) −5.02882e12 −0.801893
\(699\) 1.95773e10 0.00310174
\(700\) 3.73071e12 0.587287
\(701\) −5.13904e12 −0.803805 −0.401903 0.915682i \(-0.631651\pi\)
−0.401903 + 0.915682i \(0.631651\pi\)
\(702\) 4.68513e10 0.00728122
\(703\) −2.31263e12 −0.357114
\(704\) 2.31461e12 0.355140
\(705\) −8.47771e9 −0.00129249
\(706\) 1.01604e13 1.53918
\(707\) 2.14057e12 0.322212
\(708\) 1.73213e10 0.00259078
\(709\) −2.95438e12 −0.439094 −0.219547 0.975602i \(-0.570458\pi\)
−0.219547 + 0.975602i \(0.570458\pi\)
\(710\) 4.18522e12 0.618096
\(711\) −8.87813e11 −0.130289
\(712\) 1.97128e13 2.87467
\(713\) −6.63162e12 −0.960986
\(714\) 7.74035e9 0.00111460
\(715\) 3.82103e12 0.546768
\(716\) 1.56863e12 0.223055
\(717\) −1.69225e10 −0.00239127
\(718\) 1.17737e13 1.65330
\(719\) −1.21819e13 −1.69994 −0.849971 0.526829i \(-0.823381\pi\)
−0.849971 + 0.526829i \(0.823381\pi\)
\(720\) 2.22745e13 3.08896
\(721\) −1.70951e12 −0.235594
\(722\) 1.07644e13 1.47426
\(723\) 1.03520e10 0.00140897
\(724\) −2.68382e13 −3.63019
\(725\) 7.98167e11 0.107293
\(726\) −1.99599e10 −0.00266652
\(727\) 1.26291e13 1.67675 0.838376 0.545093i \(-0.183506\pi\)
0.838376 + 0.545093i \(0.183506\pi\)
\(728\) −8.89715e12 −1.17398
\(729\) −7.62547e12 −0.999984
\(730\) −3.40315e13 −4.43536
\(731\) −6.87068e12 −0.889962
\(732\) −2.71061e9 −0.000348953 0
\(733\) 9.16594e12 1.17276 0.586380 0.810036i \(-0.300553\pi\)
0.586380 + 0.810036i \(0.300553\pi\)
\(734\) −1.00743e13 −1.28110
\(735\) −2.40003e9 −0.000303336 0
\(736\) 1.34554e13 1.69024
\(737\) −3.81418e12 −0.476209
\(738\) 6.06400e12 0.752499
\(739\) 1.10658e13 1.36484 0.682420 0.730960i \(-0.260927\pi\)
0.682420 + 0.730960i \(0.260927\pi\)
\(740\) 6.72105e12 0.823938
\(741\) −2.16866e10 −0.00264247
\(742\) −5.99569e12 −0.726142
\(743\) 1.84642e12 0.222270 0.111135 0.993805i \(-0.464551\pi\)
0.111135 + 0.993805i \(0.464551\pi\)
\(744\) −3.78039e10 −0.00452333
\(745\) 6.52760e12 0.776337
\(746\) −5.59816e12 −0.661790
\(747\) 6.58719e12 0.774029
\(748\) 7.13586e12 0.833468
\(749\) 5.96884e12 0.692982
\(750\) 1.21019e10 0.00139662
\(751\) −9.19672e12 −1.05500 −0.527501 0.849555i \(-0.676871\pi\)
−0.527501 + 0.849555i \(0.676871\pi\)
\(752\) 1.28604e13 1.46647
\(753\) −2.21900e10 −0.00251524
\(754\) −3.25073e12 −0.366277
\(755\) −9.06449e12 −1.01527
\(756\) −2.71296e10 −0.00302062
\(757\) 8.81778e12 0.975950 0.487975 0.872858i \(-0.337736\pi\)
0.487975 + 0.872858i \(0.337736\pi\)
\(758\) 2.37101e13 2.60869
\(759\) 4.98301e9 0.000545009 0
\(760\) −4.12739e13 −4.48760
\(761\) −2.42043e12 −0.261614 −0.130807 0.991408i \(-0.541757\pi\)
−0.130807 + 0.991408i \(0.541757\pi\)
\(762\) 1.82843e10 0.00196464
\(763\) 9.20676e11 0.0983437
\(764\) −1.32231e13 −1.40415
\(765\) 1.17071e13 1.23588
\(766\) −4.32686e12 −0.454092
\(767\) −7.39488e12 −0.771528
\(768\) −1.61095e10 −0.00167092
\(769\) 7.67945e12 0.791885 0.395942 0.918275i \(-0.370418\pi\)
0.395942 + 0.918275i \(0.370418\pi\)
\(770\) −3.12959e12 −0.320833
\(771\) 2.12078e10 0.00216148
\(772\) 9.46396e12 0.958948
\(773\) 1.04693e13 1.05466 0.527328 0.849662i \(-0.323194\pi\)
0.527328 + 0.849662i \(0.323194\pi\)
\(774\) 1.70308e13 1.70570
\(775\) −6.76751e12 −0.673862
\(776\) −4.31835e13 −4.27504
\(777\) −1.69368e9 −0.000166701 0
\(778\) −2.43956e13 −2.38728
\(779\) −5.61385e12 −0.546188
\(780\) 6.30266e10 0.00609675
\(781\) −9.72296e11 −0.0935123
\(782\) 1.71013e13 1.63530
\(783\) −5.80424e9 −0.000551846 0
\(784\) 3.64076e12 0.344167
\(785\) 2.14465e13 2.01578
\(786\) −1.44947e10 −0.00135459
\(787\) −1.26490e13 −1.17535 −0.587677 0.809095i \(-0.699958\pi\)
−0.587677 + 0.809095i \(0.699958\pi\)
\(788\) −5.26479e12 −0.486422
\(789\) 3.50777e10 0.00322243
\(790\) −3.37862e12 −0.308615
\(791\) 5.75236e12 0.522459
\(792\) −1.03575e13 −0.935387
\(793\) 1.15723e12 0.103918
\(794\) −2.73611e12 −0.244310
\(795\) 2.48705e10 0.00220817
\(796\) 3.90747e13 3.44975
\(797\) −6.02337e11 −0.0528782 −0.0264391 0.999650i \(-0.508417\pi\)
−0.0264391 + 0.999650i \(0.508417\pi\)
\(798\) 1.77623e10 0.00155055
\(799\) 6.75920e12 0.586725
\(800\) 1.37311e13 1.18523
\(801\) −1.28310e13 −1.10132
\(802\) 1.69986e12 0.145087
\(803\) 7.90608e12 0.671029
\(804\) −6.29136e10 −0.00530997
\(805\) −5.30256e12 −0.445045
\(806\) 2.75624e13 2.30043
\(807\) 5.56736e9 0.000462081 0
\(808\) 2.69596e13 2.22517
\(809\) −7.72967e12 −0.634443 −0.317222 0.948351i \(-0.602750\pi\)
−0.317222 + 0.948351i \(0.602750\pi\)
\(810\) −2.90193e13 −2.36867
\(811\) −1.20157e13 −0.975335 −0.487668 0.873029i \(-0.662152\pi\)
−0.487668 + 0.873029i \(0.662152\pi\)
\(812\) 1.88236e12 0.151950
\(813\) −1.28077e10 −0.00102816
\(814\) −2.20852e12 −0.176316
\(815\) −2.52585e13 −2.00538
\(816\) 4.87057e10 0.00384569
\(817\) −1.57666e13 −1.23805
\(818\) 4.43783e13 3.46562
\(819\) 5.79114e12 0.449766
\(820\) 1.63152e13 1.26017
\(821\) 1.39952e13 1.07507 0.537533 0.843243i \(-0.319356\pi\)
0.537533 + 0.843243i \(0.319356\pi\)
\(822\) −3.11877e10 −0.00238265
\(823\) 1.61982e13 1.23074 0.615371 0.788238i \(-0.289006\pi\)
0.615371 + 0.788238i \(0.289006\pi\)
\(824\) −2.15306e13 −1.62699
\(825\) 5.08511e9 0.000382171 0
\(826\) 6.05672e12 0.452718
\(827\) −1.30127e13 −0.967374 −0.483687 0.875241i \(-0.660703\pi\)
−0.483687 + 0.875241i \(0.660703\pi\)
\(828\) −2.99696e13 −2.21587
\(829\) −1.31364e13 −0.966007 −0.483004 0.875618i \(-0.660454\pi\)
−0.483004 + 0.875618i \(0.660454\pi\)
\(830\) 2.50679e13 1.83344
\(831\) 5.10290e9 0.000371204 0
\(832\) −1.62994e13 −1.17928
\(833\) 1.91353e12 0.137699
\(834\) −2.95187e10 −0.00211276
\(835\) −6.37963e12 −0.454157
\(836\) 1.63751e13 1.15946
\(837\) 4.92131e10 0.00346590
\(838\) −4.98842e13 −3.49434
\(839\) −5.22420e12 −0.363991 −0.181996 0.983299i \(-0.558256\pi\)
−0.181996 + 0.983299i \(0.558256\pi\)
\(840\) −3.02275e10 −0.00209481
\(841\) −1.41044e13 −0.972240
\(842\) −2.45961e13 −1.68641
\(843\) −3.77945e9 −0.000257754 0
\(844\) 2.18124e13 1.47966
\(845\) −7.90552e12 −0.533427
\(846\) −1.67545e13 −1.12452
\(847\) −4.93438e12 −0.329425
\(848\) −3.77275e13 −2.50540
\(849\) 3.15028e9 0.000208096 0
\(850\) 1.74517e13 1.14671
\(851\) −3.74196e12 −0.244578
\(852\) −1.60377e10 −0.00104271
\(853\) −5.65076e12 −0.365457 −0.182728 0.983163i \(-0.558493\pi\)
−0.182728 + 0.983163i \(0.558493\pi\)
\(854\) −9.47818e11 −0.0609768
\(855\) 2.68651e13 1.71926
\(856\) 7.51752e13 4.78567
\(857\) 1.42516e12 0.0902503 0.0451251 0.998981i \(-0.485631\pi\)
0.0451251 + 0.998981i \(0.485631\pi\)
\(858\) −2.07104e10 −0.00130465
\(859\) 2.77961e13 1.74186 0.870932 0.491404i \(-0.163516\pi\)
0.870932 + 0.491404i \(0.163516\pi\)
\(860\) 4.58215e13 2.85645
\(861\) −4.11137e9 −0.000254960 0
\(862\) −5.13878e13 −3.17013
\(863\) −1.14117e13 −0.700326 −0.350163 0.936689i \(-0.613874\pi\)
−0.350163 + 0.936689i \(0.613874\pi\)
\(864\) −9.98525e10 −0.00609603
\(865\) −4.73180e12 −0.287378
\(866\) −1.98066e12 −0.119668
\(867\) −1.95364e9 −0.000117425 0
\(868\) −1.59602e13 −0.954333
\(869\) 7.84908e11 0.0466906
\(870\) −1.10442e10 −0.000653576 0
\(871\) 2.68594e13 1.58130
\(872\) 1.15956e13 0.679153
\(873\) 2.81081e13 1.63782
\(874\) 3.92434e13 2.27491
\(875\) 2.99177e12 0.172541
\(876\) 1.30408e11 0.00748232
\(877\) −1.21188e13 −0.691769 −0.345884 0.938277i \(-0.612421\pi\)
−0.345884 + 0.938277i \(0.612421\pi\)
\(878\) 2.56763e13 1.45816
\(879\) 1.25905e10 0.000711364 0
\(880\) −1.96927e13 −1.10697
\(881\) −4.60741e12 −0.257671 −0.128836 0.991666i \(-0.541124\pi\)
−0.128836 + 0.991666i \(0.541124\pi\)
\(882\) −4.74319e12 −0.263914
\(883\) 1.04709e13 0.579642 0.289821 0.957081i \(-0.406404\pi\)
0.289821 + 0.957081i \(0.406404\pi\)
\(884\) −5.02505e13 −2.76761
\(885\) −2.51236e10 −0.00137669
\(886\) −3.42441e13 −1.86696
\(887\) −3.68711e12 −0.200000 −0.0999999 0.994987i \(-0.531884\pi\)
−0.0999999 + 0.994987i \(0.531884\pi\)
\(888\) −2.13313e10 −0.00115122
\(889\) 4.52015e12 0.242714
\(890\) −4.88291e13 −2.60870
\(891\) 6.74166e12 0.358358
\(892\) −1.29329e13 −0.683998
\(893\) 1.55108e13 0.816209
\(894\) −3.53803e10 −0.00185243
\(895\) −2.27522e12 −0.118528
\(896\) −7.08864e10 −0.00367432
\(897\) −3.50902e10 −0.00180976
\(898\) 2.01080e13 1.03187
\(899\) −3.41461e12 −0.174350
\(900\) −3.05837e13 −1.55381
\(901\) −1.98290e13 −1.00240
\(902\) −5.36114e12 −0.269667
\(903\) −1.15469e10 −0.000577922 0
\(904\) 7.24487e13 3.60805
\(905\) 3.89274e13 1.92902
\(906\) 4.91305e10 0.00242256
\(907\) −6.05209e11 −0.0296943 −0.0148471 0.999890i \(-0.504726\pi\)
−0.0148471 + 0.999890i \(0.504726\pi\)
\(908\) 2.40956e13 1.17639
\(909\) −1.75480e13 −0.852491
\(910\) 2.20385e13 1.06536
\(911\) −3.27450e12 −0.157512 −0.0787559 0.996894i \(-0.525095\pi\)
−0.0787559 + 0.996894i \(0.525095\pi\)
\(912\) 1.11768e11 0.00534984
\(913\) −5.82368e12 −0.277383
\(914\) 4.82094e13 2.28494
\(915\) 3.93160e9 0.000185428 0
\(916\) −7.36467e13 −3.45640
\(917\) −3.58329e12 −0.167348
\(918\) −1.26908e11 −0.00589790
\(919\) 2.21117e11 0.0102259 0.00511295 0.999987i \(-0.498372\pi\)
0.00511295 + 0.999987i \(0.498372\pi\)
\(920\) −6.67836e13 −3.07344
\(921\) 1.70188e10 0.000779400 0
\(922\) −2.53732e13 −1.15634
\(923\) 6.84688e12 0.310517
\(924\) 1.19925e10 0.000541236 0
\(925\) −3.81864e12 −0.171503
\(926\) −3.71100e13 −1.65860
\(927\) 1.40143e13 0.623320
\(928\) 6.92817e12 0.306657
\(929\) −4.00147e12 −0.176258 −0.0881290 0.996109i \(-0.528089\pi\)
−0.0881290 + 0.996109i \(0.528089\pi\)
\(930\) 9.36413e10 0.00410482
\(931\) 4.39109e12 0.191557
\(932\) 1.04097e14 4.51927
\(933\) −5.68073e10 −0.00245435
\(934\) −4.58899e13 −1.97313
\(935\) −1.03502e13 −0.442890
\(936\) 7.29372e13 3.10604
\(937\) −3.76138e10 −0.00159411 −0.000797056 1.00000i \(-0.500254\pi\)
−0.000797056 1.00000i \(0.500254\pi\)
\(938\) −2.19990e13 −0.927876
\(939\) −1.02205e10 −0.000429019 0
\(940\) −4.50780e13 −1.88317
\(941\) −2.21494e12 −0.0920894 −0.0460447 0.998939i \(-0.514662\pi\)
−0.0460447 + 0.998939i \(0.514662\pi\)
\(942\) −1.16242e11 −0.00480990
\(943\) −9.08353e12 −0.374069
\(944\) 3.81116e13 1.56201
\(945\) 3.93501e10 0.00160510
\(946\) −1.50568e13 −0.611257
\(947\) 2.36266e13 0.954610 0.477305 0.878738i \(-0.341614\pi\)
0.477305 + 0.878738i \(0.341614\pi\)
\(948\) 1.29468e10 0.000520624 0
\(949\) −5.56744e13 −2.22822
\(950\) 4.00475e13 1.59521
\(951\) −5.05694e10 −0.00200482
\(952\) 2.41001e13 0.950939
\(953\) −1.15037e13 −0.451771 −0.225885 0.974154i \(-0.572527\pi\)
−0.225885 + 0.974154i \(0.572527\pi\)
\(954\) 4.91516e13 1.92119
\(955\) 1.91795e13 0.746142
\(956\) −8.99810e13 −3.48410
\(957\) 2.56574e9 9.88801e−5 0
\(958\) −1.30518e13 −0.500639
\(959\) −7.71003e12 −0.294356
\(960\) −5.53761e10 −0.00210427
\(961\) 2.51218e12 0.0950156
\(962\) 1.55524e13 0.585475
\(963\) −4.89314e13 −1.83345
\(964\) 5.50440e13 2.05288
\(965\) −1.37270e13 −0.509568
\(966\) 2.87404e10 0.00106193
\(967\) −1.36863e13 −0.503346 −0.251673 0.967812i \(-0.580981\pi\)
−0.251673 + 0.967812i \(0.580981\pi\)
\(968\) −6.21465e13 −2.27498
\(969\) 5.87435e10 0.00214044
\(970\) 1.06967e14 3.87950
\(971\) 9.95259e12 0.359294 0.179647 0.983731i \(-0.442504\pi\)
0.179647 + 0.983731i \(0.442504\pi\)
\(972\) 3.33605e11 0.0119877
\(973\) −7.29745e12 −0.261014
\(974\) 4.53038e13 1.61295
\(975\) −3.58092e10 −0.00126904
\(976\) −5.96409e12 −0.210387
\(977\) 1.51387e13 0.531575 0.265787 0.964032i \(-0.414368\pi\)
0.265787 + 0.964032i \(0.414368\pi\)
\(978\) 1.36903e11 0.00478508
\(979\) 1.13438e13 0.394673
\(980\) −1.27616e13 −0.441964
\(981\) −7.54753e12 −0.260192
\(982\) 8.97498e13 3.07987
\(983\) 5.47141e13 1.86899 0.934497 0.355970i \(-0.115849\pi\)
0.934497 + 0.355970i \(0.115849\pi\)
\(984\) −5.17811e10 −0.00176073
\(985\) 7.63631e12 0.258476
\(986\) 8.80540e12 0.296690
\(987\) 1.13595e10 0.000381007 0
\(988\) −1.15313e14 −3.85010
\(989\) −2.55112e13 −0.847907
\(990\) 2.56558e13 0.848842
\(991\) 4.86384e13 1.60195 0.800974 0.598699i \(-0.204316\pi\)
0.800974 + 0.598699i \(0.204316\pi\)
\(992\) −5.87427e13 −1.92598
\(993\) −8.52557e10 −0.00278261
\(994\) −5.60789e12 −0.182205
\(995\) −5.66759e13 −1.83314
\(996\) −9.60596e10 −0.00309296
\(997\) 2.77758e13 0.890304 0.445152 0.895455i \(-0.353150\pi\)
0.445152 + 0.895455i \(0.353150\pi\)
\(998\) −7.76283e13 −2.47704
\(999\) 2.77690e10 0.000882096 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 7.10.a.b.1.3 3
3.2 odd 2 63.10.a.e.1.1 3
4.3 odd 2 112.10.a.h.1.2 3
5.2 odd 4 175.10.b.d.99.6 6
5.3 odd 4 175.10.b.d.99.1 6
5.4 even 2 175.10.a.d.1.1 3
7.2 even 3 49.10.c.d.18.1 6
7.3 odd 6 49.10.c.e.30.1 6
7.4 even 3 49.10.c.d.30.1 6
7.5 odd 6 49.10.c.e.18.1 6
7.6 odd 2 49.10.a.c.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.10.a.b.1.3 3 1.1 even 1 trivial
49.10.a.c.1.3 3 7.6 odd 2
49.10.c.d.18.1 6 7.2 even 3
49.10.c.d.30.1 6 7.4 even 3
49.10.c.e.18.1 6 7.5 odd 6
49.10.c.e.30.1 6 7.3 odd 6
63.10.a.e.1.1 3 3.2 odd 2
112.10.a.h.1.2 3 4.3 odd 2
175.10.a.d.1.1 3 5.4 even 2
175.10.b.d.99.1 6 5.3 odd 4
175.10.b.d.99.6 6 5.2 odd 4