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lfunc_lfunctions • Show schema
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{'Lhash': '1654082797928101414587002887315,2580860163830432304220454759947', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.974827012133067, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '216.1', 'coefficient_field': '1.1.1.1', 'conductor': 46656, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, -4, 5, 25], [1, -3, 2, -21, 49], [1, -5, 14, -55, 121], [1, -5, 12, -65, 169], [1, -4, 38, -68, 289], [1, 8, 54, 152, 361], [1, 1, -22, 23, 529], [1, 9, 52, 261, 841], [1, -1, -30, -31, 961], [1, 12, 110, 444, 1369], [1, -3, -32, -123, 1681], [1, 1, -42, 43, 1849], [1, 3, -38, 141, 2209], [1, 4, 110, 212, 2809], [1, -11, 62, -649, 3481], [1, 7, -12, 427, 3721], [1, -1, -66, -67, 4489], [1, 8, 158, 568, 5041], [1, 4, 150, 292, 5329], [1, 1, -78, 79, 6241], [1, -1, -82, 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['1.30484125328406603231345639003572', '2.03593968508812365837195667137882', '3.62592093821060769785626162041032', '3.67068864511486347733686858898642', '4.55642019763593254059847043673713', '5.10502125316642197607072094461185', '6.08959875774201484024840710971527', '6.21757808552297405855662949323437', '7.12232559630798562910267941349736', '7.47582765709396604650330576332712', '8.421991505255167162476740288671326', '8.428057998910143146019568767755243', '8.999481552695027050128102820440163', '9.482776687426013354812159507705761', '10.52469225284218391935921330480745', '10.54941577732228680779928163284871', '11.19138873605400697127518679357400', '11.54674992129962279971637330725532', '12.08951976212825155123198909488261', '12.33301225841225625353032989755805'], 'prelabel': '4-6e6-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3133044900782367, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 582998737114334983, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30484125328406603231345639004', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03593968508812365837195667138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62592093821060769785626162041', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.974827012133067, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 46656, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 5, 0, 5, 0, 0, 0, 4, 0, -8, 0, 0, 0, -1, 0, 5, 0, 0, 0, -9, 0, 1, 0, 0, 0, -3, 0, -12, 0, 0, 0, 3, 0, -1, 0, 0, 0, -3, 0, 7, 0, 0, 0, -4, 0, -5, 0, 0, 0, 11, 0, -7, 0, 0, 0, -5, 0, 1, 0, 0, 0, -8, 0, -4, 0, 0, 0, 15, 0, -1, 0, 0, 0, 1, 0, -4, 0, 0, 0, 36, 0, 15, 0, 0, 0, 8, 0, 13, 0, 0, 0], 'euler11': [1, -5, 14, -55, 121], 'euler13': [1, -5, 12, -65, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 1, -22, 23, 529], 'euler29': [1, 9, 52, 261, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -1, -30, -31, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, -3, -32, -123, 1681], 'euler43': [1, 1, -42, 43, 1849], 'euler47': [1, 3, -38, 141, 2209], 'euler5': [1, 1, -4, 5, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, -11, 62, -649, 3481], 'euler61': [1, 7, -12, 427, 3721], 'euler67': [1, -1, -66, -67, 4489], 'euler7': [1, -3, 2, -21, 49], 'euler71': [1, 8, 158, 568, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 1, -78, 79, 6241], 'euler83': [1, -1, -82, -83, 6889], 'euler89': [1, -36, 502, -3204, 7921], 'euler97': [1, -13, 72, -1261, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, -4, 5, 25], [1, -3, 2, -21, 49], [1, -5, 14, -55, 121], [1, -5, 12, -65, 169], [1, -4, 38, -68, 289], [1, 8, 54, 152, 361], [1, 1, -22, 23, 529], [1, 9, 52, 261, 841], [1, -1, -30, -31, 961], [1, 12, 110, 444, 1369], [1, -3, -32, -123, 1681], [1, 1, -42, 43, 1849], [1, 3, -38, 141, 2209], [1, 4, 110, 212, 2809], [1, -11, 62, -649, 3481], [1, 7, -12, 427, 3721], [1, -1, -66, -67, 4489], [1, 8, 158, 568, 5041], [1, 4, 150, 292, 5329], [1, 1, -78, 79, 6241], [1, -1, -82, -83, 6889], [1, -36, 502, -3204, 7921], [1, -13, 72, -1261, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/216/2/i/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': '4-6e6-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-6e6-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3133044900782367, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 582998737114334983, 'z1': {'__RealLiteral__': 0, 'data': '1.30484125328406603231345639004', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1654082797928101414587002887315,2580860163830432304220454759947', 'Lhash_array': ['1654082797928101414587002887315', '2580860163830432304220454759947'], 'label': '4-6e6-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/216/2/i/a'}