Table lfunc_lfunctions
L-functions
{'Lhash': '318912376491701537667979273909,660290265166598155996998987627,1139366788252989985549761369300,2154458898410256452634912658392,2155899747951236760336249843499,2448091110773809299147688799377', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 327991.5671351532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [5, [1, 0, 3, 0, 3, 0, 1]], [13, [1, 0, -9, -16, -117, 0, 2197]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.1', 'coefficient_field': '1.1.1.1', 'conductor': 1265319018496000000, 'conductor_radical': 130, 'degree': 12, 'euler_factors': [[1], [1, 0, 6, 4, 27, 12, 112, 36, 243, 108, 486, 0, 729], [1, 0, 3, 0, 3, 0, 1], [1, 0, -18, 0, 207, 0, -1676, 0, 10143, 0, -43218, 0, 117649], [1, 0, -30, 0, 447, 0, -4912, 0, 54087, 0, -439230, 0, 1771561], [1, 0, -9, -16, -117, 0, 2197], [1, 0, 102, 0, 4335, 0, 98260, 0, 1252815, 0, 8519142, 0, 24137569], [1, 0, -18, 0, 423, 0, -3800, 0, 152703, 0, -2345778, 0, 47045881], [1, -12, 114, -672, 4539, -25068, 142792, -576564, 2401131, -8176224, 31901874, -77236116, 148035889], [1, 12, 186, 1428, 13143, 75792, 505276, 2197968, 11053263, 34827492, 131554266, 246133788, 594823321], [1, 0, -126, 0, 7911, 0, -303536, 0, 7602471, 0, -116363646, 0, 887503681], [1, 0, -78, 0, 5271, 0, -214292, 0, 7215999, 0, -146184558, 0, 2565726409], [1, 0, -138, 0, 9663, 0, -461068, 0, 16243503, 0, -389955018, 0, 4750104241], [1, 12, 210, 1984, 20691, 148860, 1163976, 6400980, 38257659, 157741888, 717948210, 1764101316, 6321363049], [1, 0, -66, 0, 5055, 0, -172204, 0, 11166495, 0, -322058946, 0, 10779215329], [1, 12, 186, 2220, 21495, 180408, 1531852, 9561624, 60379455, 330506940, 1467629466, 5018345916, 22164361129], [1, 0, -138, 0, 13767, 0, -903112, 0, 47922927, 0, -1672195818, 0, 42180533641], [1, 12, 210, 1444, 20583, 143136, 1685292, 8731296, 76589343, 327760564, 2907626610, 10135155612, 51520374361], [1, 0, -162, 0, 19431, 0, -1405100, 0, 87225759, 0, -3264481602, 0, 90458382169], [1, 0, 6, 0, -417, 0, -224296, 0, -2102097, 0, 152470086, 0, 128100283921], [1, 0, -150, 0, 4479, 0, 230236, 0, 23868591, 0, -4259736150, 0, 151334226289], [1, -24, 330, -2632, 28143, -363312, 4190028, -28701648, 175640463, -1297678648, 12853526730, -73849353576, 243087455521], [1, 0, -354, 0, 61575, 0, -6424108, 0, 424190175, 0, -16800245634, 0, 326940373369], [1, 0, 42, 0, 10527, 0, 115148, 0, 83384367, 0, 2635174122, 0, 496981290961], [1, 0, -378, 0, 64719, 0, -7267052, 0, 608941071, 0, -33464068218, 0, 832972004929], [1, -12, 474, -5100, 107031, -929208, 14010892, -93850008, 1091823231, -5254535100, 49324630074, -126121206012, 1061520150601], [1, 24, 726, 11524, 199107, 2295108, 27838032, 236396124, 2112326163, 12592585948, 81711939606, 278225777832, 1194052296529], [1, 60, 2058, 48936, 885027, 12623604, 145181464, 1350725628, 10132674123, 59948704248, 269761818858, 841531038420, 1500730351849], [1, 0, -162, 0, 24039, 0, -3883772, 0, 285607359, 0, -22867622082, 0, 1677100110841], [1, -48, 1446, -31920, 552495, -7774752, 90830932, -878546976, 7054808655, -46057272240, 235766484006, -884368886064, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, 0, 3, 2, 9, 0, 27], 2]], [[[1, 0, 1], 3]], [[[1, 0, -18, 0, 207, 0, -1676, 0, 10143, 0, -43218, 0, 117649], 1]], [[[1, 0, -30, 0, 447, 0, -4912, 0, 54087, 0, -439230, 0, 1771561], 1]], [[[1, 0, -9, -16, -117, 0, 2197], 1]], [[[1, 0, 17], 6]], [[[1, 0, -18, 0, 423, 0, -3800, 0, 152703, 0, -2345778, 0, 47045881], 1]], [[[1, -6, 39, -102, 897, -3174, 12167], 2]], [[[1, 6, 75, 264, 2175, 5046, 24389], 2]], [[[1, 0, -126, 0, 7911, 0, -303536, 0, 7602471, 0, -116363646, 0, 887503681], 1]], [[[1, 0, -78, 0, 5271, 0, -214292, 0, 7215999, 0, -146184558, 0, 2565726409], 1]], [[[1, 0, -138, 0, 9663, 0, -461068, 0, 16243503, 0, -389955018, 0, 4750104241], 1]], [[[1, 6, 87, 470, 3741, 11094, 79507], 2]], [[[1, 0, -66, 0, 5055, 0, -172204, 0, 11166495, 0, -322058946, 0, 10779215329], 1]], [[[1, 6, 75, 660, 3975, 16854, 148877], 2]], [[[1, 0, -138, 0, 13767, 0, -903112, 0, 47922927, 0, -1672195818, 0, 42180533641], 1]], [[[1, 6, 87, 200, 5307, 22326, 226981], 2]], [[[1, 0, -162, 0, 19431, 0, -1405100, 0, 87225759, 0, -3264481602, 0, 90458382169], 1]], [[[1, 0, 6, 0, -417, 0, -224296, 0, -2102097, 0, 152470086, 0, 128100283921], 1]], [[[1, 0, -150, 0, 4479, 0, 230236, 0, 23868591, 0, -4259736150, 0, 151334226289], 1]], [[[1, -12, 93, -200, 7347, -74892, 493039], 2]], [[[1, 0, -354, 0, 61575, 0, -6424108, 0, 424190175, 0, -16800245634, 0, 326940373369], 1]], [[[1, 0, 42, 0, 10527, 0, 115148, 0, 83384367, 0, 2635174122, 0, 496981290961], 1]], [[[1, 0, -378, 0, 64719, 0, -7267052, 0, 608941071, 0, -33464068218, 0, 832972004929], 1]], [[[1, -6, 219, -1236, 22119, -61206, 1030301], 2]], [[[1, 12, 291, 2270, 29973, 127308, 1092727], 2]], [[[1, 30, 579, 7098, 61953, 343470, 1225043], 2]], [[[1, 0, -162, 0, 24039, 0, -3883772, 0, 285607359, 0, -22867622082, 0, 1677100110841], 1]], [[[1, -24, 435, -5520, 49155, -306456, 1442897], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'id': 23257133, 'index': 1, 'label': '12-1040e6-1.1-c1e6-0-1', 'leading_term': '1.3579905548325812682498747812628858926166886338767890945488174531436773454625530476832418', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1040/2/k/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.010416666666666666', 'prec': 57}, 'plot_values': [1.3579905548325815, 1.3549026109028073, 1.345892783872797, 1.3309790829560684, 1.3102068019919986, 1.2836514051459238, 1.2514217046956497, 1.2136746319652165, 1.1706027727576094, 1.1224230745629549, 1.0693791255249816, 1.0117400285795635, 0.949798865418874, 0.8838709372888677, 0.8143000717210929, 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