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lfunc_lfunctions • Show schema
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{'Lhash': '1666203346572341396772283154403,2675436043684638178303464271354', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 235.04806021792132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]], [5, [1, 2, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '1920.1', 'coefficient_field': '1.1.1.1', 'conductor': 3686400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1, 2, 5], [1, 0, -14, 0, 49], [1, 4, 26, 44, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 8, 54, 152, 361], [1, 0, -46, 0, 529], [1, 4, 62, 116, 841], [1, -4, 66, -124, 961], [1, 0, -38, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, -22, 0, 1849], [1, 0, 50, 0, 2209], [1, 0, -42, 0, 2809], [1, 20, 218, 1180, 3481], [1, -20, 222, -1220, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, 20, 258, 1580, 6241], 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'positive_zeros': ['1.31440268025933649203576461662908', '2.11054689928198615821237636806637', '2.49032777584496753482590794624888', '3.06765707790770807966495293630759', '3.66755594390135529130877505856015', '3.93296243177478523102646233861780', '4.62217490875236822024850053425875', '4.76620266825936465418058900243705', '5.46422574694358174010560560398206', '5.72463504373034276653714353170653', '6.23721875831596843815286731298878', '6.69528160587130971565562916772980', '7.25565955360981304513100174161853', '7.27655235269514207531850519138492', '8.026118965324219905115704444601313', '8.278826299493909442646128934790767', '8.450007369571122748142489196569754', '8.862653069328900294902203271510018'], 'prelabel': '4-1920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2243262959747375123, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31440268025933649203576461663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11054689928198615821237636807', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.49032777584496753482590794625', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 235.04806021792132, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 3686400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 8, 0, 0, 0, -20, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 16, 0, 0, 0, 4, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 0, -38, 0, 1369], 'euler41': [1, 20, 182, 820, 1681], 'euler43': [1, 0, -22, 0, 1849], 'euler47': [1, 0, 50, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 0, -42, 0, 2809], 'euler59': [1, 20, 218, 1180, 3481], 'euler61': [1, -20, 222, -1220, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 2, 5, 0, 0], [1, 0, -14, 0, 49], [1, 4, 26, 44, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 8, 54, 152, 361], [1, 0, -46, 0, 529], [1, 4, 62, 116, 841], [1, -4, 66, -124, 961], [1, 0, -38, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, -22, 0, 1849], [1, 0, 50, 0, 2209], [1, 0, -42, 0, 2809], [1, 20, 218, 1180, 3481], [1, -20, 222, -1220, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, 20, 258, 1580, 6241], [1, 0, -150, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -130, 0, 9409]], 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1920/2/f/e'], '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': '4-1920e2-1.1-c1e2-0-31', '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': 2, 'prelabel': '4-1920e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2243262959747375123, 'z1': {'__RealLiteral__': 0, 'data': '1.31440268025933649203576461663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1666203346572341396772283154403,2675436043684638178303464271354', 'Lhash_array': ['1666203346572341396772283154403', '2675436043684638178303464271354'], 'label': '4-1920e2-1.1-c1e2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1920/2/f/e'}