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lfunc_lfunctions • Show schema
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{'Lhash': '468016105131531139549873925256,1166507496914571432005537655139', 'a10': 0, 'a2': 0, 'a3': -6, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -484, 'a8': 0, 'a9': -693, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1951.0228275672052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 6, 729]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 6, 729], [1, 0, -5330, 0, 244140625], [1, 484, 293862, 56942116, 13841287201], [1, 0, -406802, 0, 3138428376721], [1, 5236, 16507542, 25273171924, 23298085122481], [1, 0, 1905982, 0, 582622237229761], [1, -11572, 127569558, -544414934932, 2213314919066161], [1, 0, -208876898, 0, 21914624432020321], [1, 0, -1035966962, 0, 353814783205469041], [1, -40892, 2193046278, -36291800523452, 787662783788549761], [1, -93548, 7319259894, -240018574109132, 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{'algebraic': True, 'analytic_conductor': 1951.0228275672052, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -6, 0, 0, 0, -484, 0, -693, 0, 0, 0, -5236, 0, 0, 0, 0, 0, 11572, 0, 2904, 0, 0, 0, 5330, 0, 8532, 0, 0, 0, 40892, 0, 0, 0, 0, 0, 93548, 0, 31416, 0, 0, 0, 137236, 0, 0, 0, 0, 0, -59606, 0, 0, 0, 0, 0, 0, 0, -69432, 0, 0, 0, -49588, 0, 335412, 0, 0, 0, -168716, 0, 0, 0, 0, 0, -227612, 0, -31980, 0, 0, 0, 319484, 0, 454005, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2534224, 0, -245352, 0, 0, 0, 1799044, 0, 0, 0], 'euler11': [1, 0, -406802, 0, 3138428376721], 'euler13': [1, 5236, 16507542, 25273171924, 23298085122481], 'euler17': [1, 0, 1905982, 0, 582622237229761], 'euler19': [1, -11572, 127569558, -544414934932, 2213314919066161], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -208876898, 0, 21914624432020321], 'euler29': [1, 0, -1035966962, 0, 353814783205469041], 'euler3': [1, 6, 729, 0, 0], 'euler31': [1, -40892, 2193046278, -36291800523452, 787662783788549761], 'euler37': [1, -93548, 7319259894, -240018574109132, 6582952005840035281], 'euler41': [1, 0, -9487663202, 0, 22563490300366186081], 'euler43': [1, -137236, 17351156022, -867518579392564, 39959630797262576401], 'euler47': [1, 0, -21106800578, 0, 116191483108948578241], 'euler5': [1, 0, -5330, 0, 244140625], 'euler53': [1, 0, -14819087378, 0, 491258904256726154641], 'euler59': [1, 0, -61991044562, 0, 1779197418239532716881], 'euler61': [1, 49588, 103655491158, 2554792323813268, 2654348974297586158321], 'euler67': [1, 168716, 188033036502, 15261776406025004, 8182718904632857144561], 'euler7': [1, 484, 293862, 56942116, 13841287201], 'euler71': [1, 0, -151063967522, 0, 16409682740640811134241], 'euler73': [1, 227612, 315620258214, 34445485914091868, 22902048046490258711521], 'euler79': [1, -319484, 511692417606, -77662552639671164, 59091511031674153381441], 'euler83': [1, 0, -388294032818, 0, 106890007738661124410161], 'euler89': [1, 0, 583819025758, 0, 246990403565262140303521], 'euler97': [1, -1799044, 2475083838342, -1498553287635487876, 693842360995438000295041], 'euler_factors': [[1, 0, 0, 0, 0], [1, 6, 729, 0, 0], [1, 0, -5330, 0, 244140625], [1, 484, 293862, 56942116, 13841287201], [1, 0, -406802, 0, 3138428376721], [1, 5236, 16507542, 25273171924, 23298085122481], [1, 0, 1905982, 0, 582622237229761], [1, -11572, 127569558, -544414934932, 2213314919066161], [1, 0, -208876898, 0, 21914624432020321], [1, 0, -1035966962, 0, 353814783205469041], [1, -40892, 2193046278, -36291800523452, 787662783788549761], [1, -93548, 7319259894, -240018574109132, 6582952005840035281], [1, 0, -9487663202, 0, 22563490300366186081], [1, -137236, 17351156022, -867518579392564, 39959630797262576401], [1, 0, -21106800578, 0, 116191483108948578241], [1, 0, -14819087378, 0, 491258904256726154641], [1, 0, -61991044562, 0, 1779197418239532716881], [1, 49588, 103655491158, 2554792323813268, 2654348974297586158321], [1, 168716, 188033036502, 15261776406025004, 8182718904632857144561], [1, 0, -151063967522, 0, 16409682740640811134241], [1, 227612, 315620258214, 34445485914091868, 22902048046490258711521], [1, -319484, 511692417606, -77662552639671164, 59091511031674153381441], [1, 0, -388294032818, 0, 106890007738661124410161], [1, 0, 583819025758, 0, 246990403565262140303521], [1, -1799044, 2475083838342, -1498553287635487876, 693842360995438000295041]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/7/e/d'], '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': '4-192e2-1.1-c6e2-0-5', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6, 6], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c6e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.646080352735091, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6e2-0', 'trace_hash': 1848216652616723157, 'z1': {'__RealLiteral__': 0, 'data': '0.36919960835207188313787989637', 'prec': 103}}
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{'Lhash': '468016105131531139549873925256,1166507496914571432005537655139', 'Lhash_array': ['468016105131531139549873925256', '1166507496914571432005537655139'], 'label': '4-192e2-1.1-c6e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/7/e/d'}