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lfunc_lfunctions • Show schema
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{'Lhash': '2082998589990713713237216709227', 'a10': [1.2371174545124184, 3.601187181627393], 'a2': [-1.0666588720198977, -0.9285681723714417], 'a3': [0.0, 0.0], 'a4': [0.2755222985175209, 1.9809309586705999], 'a5': [-2.3317650540987773, -1.3462451816708916], 'a6': [0.0, 0.0], 'a7': [1.1191467432469833, -2.397396622813937], 'a8': [1.5455411357337385, -2.36881881910687], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0666588720198977, 0.9285681723714417]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.1191467432469833, 2.397396622813937]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.451', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '565256591622444605984280955502', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0666588720198977, 0.9285681723714417]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'8.125763469979066774342972463825513', '8.902179184478142634028081159748916', '9.647242273505744613299627705158264', '10.76889661018918736878969540127670'], 'prelabel': '2-756-252.115-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.4545244858574517, 'root_number': '-0.9594558469798244 + 0.2818589677413648*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.454524485857', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64319615327416564046415384487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18605787172803650169670612345', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53258133885561283008472822501', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '252.115', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/bj/b/451/9'], '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': '2-756-252.115-c1-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-756-252.115-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.4545244858574517, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64319615327416564046415384487', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2082998589990713713237216709227', 'Lhash_array': ['2082998589990713713237216709227'], 'factors': ['2-756-252.115-c1-0-33'], 'label': '2-756-252.115-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/bj/b/451/9'}