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lfunc_lfunctions • Show schema
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{'Lhash': '1043597207758009712082367444773', 'a10': -4100, 'a2': -10, 'a3': 0, 'a4': -28, 'a5': 410, 'a6': 0, 'a7': -1028, 'a8': 1560, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.926117522928067, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1, -1331]]], 'bad_primes': [3, 11], 'central_character': '99.1', 'coefficient_field': '1.1.1.1', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[1, 10, 128], [1], [1, -410, 78125], [1, 1028, 823543], [1, -1331], [1, -12958, 62748517], [1, 17062, 410338673], [1, 54168, 893871739], [1, -11488, 3404825447], [1, -186654, 17249876309], [1, 188672, 27512614111], [1, -395886, 94931877133], [1, -47546, 194754273881], [1, -602088, 271818611107], [1, -647200, 506623120463], [1, -1312722, 1174711139837], [1, -2681140, 2488651484819], [1, -551190, 3142742836021], [1, -459260, 6060711605323], [1, -18072, 9095120158391], [1, 426062, 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19203908986159], 1]], [[[1, 5684028, 27136050989627], 1]], [[[1, -6342966, 44231334895529], 1]], [[[1, -16651586, 80798284478113], 1]], [[[1, -2083270, 107213535210701], 1]], [[[1, 2390464, 122987386542487], 1]], [[[1, -14061468, 160578147647843], 1]], [[[1, 11132066, 182803912081669], 1]], [[[1, 5669034, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-99-1.1-c7-0-6', 'leading_term': '1.272065352183493205630924370840000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/99/8/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [1.2720653521834933, 1.256720124074019, 1.2110283739616443, 1.1360165513474554, 1.0333775736040907, 0.9054441235679153, 0.7551513680717211, 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'z3': {'__RealLiteral__': 0, 'data': '4.10809983599880512602002387262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.926117522928067, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'dirichlet_coefficients': [1, -10, 0, -28, 410, 0, -1028, 1560, 0, -4100, 1331, 0, 12958, 10280, 0, -12016, -17062, 0, -54168, -11480, 0, -13310, 11488, 0, 89975, -129580, 0, 28784, 186654, 0, -188672, -79520, 0, 170620, -421480, 0, 395886, 541680, 0, 639600, 47546, 0, 602088, -37268, 0, -114880, 647200, 0, 233241, -899750, 0, -362824, 1312722, 0, 545710, -1603680, 0, -1866540, 2681140, 0, 551190, 1886720, 0, 2333248, 5312780, 0, 459260, 477736, 0, 4214800, 18072, 0, -426062, -3958860, 0, 1516704, -1368268, 0, 297764, -4926560, 0, -475460, -5684028, 0, -6995420, -6020880, 0, 2076360, 6342966, 0, -13320824, -321664, 0, -6472000, -22208880, 0, 16651586, -2332410, 0, -2519300], 'euler11': [1, -1331, 0], 'euler13': [1, -12958, 62748517], 'euler17': [1, 17062, 410338673], 'euler19': [1, 54168, 893871739], 'euler2': [1, 10, 128], 'euler23': [1, -11488, 3404825447], 'euler29': [1, -186654, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 188672, 27512614111], 'euler37': [1, -395886, 94931877133], 'euler41': [1, -47546, 194754273881], 'euler43': [1, -602088, 271818611107], 'euler47': [1, -647200, 506623120463], 'euler5': [1, -410, 78125], 'euler53': [1, -1312722, 1174711139837], 'euler59': [1, -2681140, 2488651484819], 'euler61': [1, -551190, 3142742836021], 'euler67': [1, -459260, 6060711605323], 'euler7': [1, 1028, 823543], 'euler71': [1, -18072, 9095120158391], 'euler73': [1, 426062, 11047398519097], 'euler79': [1, -297764, 19203908986159], 'euler83': [1, 5684028, 27136050989627], 'euler89': [1, -6342966, 44231334895529], 'euler97': [1, -16651586, 80798284478113], 'euler_factors': [[1, 10, 128], [1, 0, 0], [1, -410, 78125], [1, 1028, 823543], [1, -1331, 0], [1, -12958, 62748517], [1, 17062, 410338673], [1, 54168, 893871739], [1, -11488, 3404825447], [1, -186654, 17249876309], [1, 188672, 27512614111], [1, -395886, 94931877133], [1, -47546, 194754273881], [1, -602088, 271818611107], [1, -647200, 506623120463], [1, -1312722, 1174711139837], [1, -2681140, 2488651484819], [1, -551190, 3142742836021], [1, -459260, 6060711605323], [1, -18072, 9095120158391], [1, 426062, 11047398519097], [1, -297764, 19203908986159], [1, 5684028, 27136050989627], [1, -6342966, 44231334895529], [1, -16651586, 80798284478113]], 'index': 6, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/8/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/99/8/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-99-1.1-c7-0-6', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-99-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.561125562593248, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 486907050352868752, 'z1': {'__RealLiteral__': 0, 'data': '0.823253037998103865481322327784', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20709021
{'Lhash': '1043597207758009712082367444773', 'Lhash_array': ['1043597207758009712082367444773'], 'label': '2-99-1.1-c7-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/8/a/a'}
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id: 24563452
{'Lhash': '1043597207758009712082367444773', 'Lhash_array': ['1043597207758009712082367444773'], 'label': '2-99-1.1-c7-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/8/a/a/1/1'}