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lfunc_lfunctions • Show schema
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{'Lhash': '2910334385436087167762909782376', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7078461369316704, -0.4086751577023366], 'a4': [0.0, 0.0], 'a5': [2.5097345402881803, -4.3469877372896475], 'a6': [0.0, 0.0], 'a7': [7.916246188044541, 0.0], 'a8': [0.0, 0.0], 'a9': [-4.165969230953941, -7.215670370780868], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [18.52975753504574, 4.200962472150351]]]], 'bad_primes': [2, 19], 'central_character': '76.65', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '1957193137558413258515621072765', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7078461369316704, 0.4086751577023366], [4.5, 7.794228634059948]], [[1.0, 0], [-2.5097345402881803, 4.3469877372896475], [-12.5, -21.650635094610966]], [[1.0, 0], [-7.916246188044541, 0], [49.0, 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'2-76-19.8-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/76/3/h/a/65/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3304454556774057, 1.3741515077447544, 1.4165062553841183, 1.457077769648746, 1.4946588340649627, 1.5273162269474951, 1.5524747172218767, 1.5670287459921017, 1.5674768972868527, 1.5500769827038008, 1.5110215394684163, 1.4466340736013568, 1.3535853941138132, 1.2291271793878704, 1.0713369267096169, 0.8793650909608662, 0.6536719021830408, 0.39623840539101923, 0.11073400611025787, -0.19737846677796897, -0.5208191702477389, -0.8505666001685126, -1.17604613750672, -1.485441015709948, -1.7661281469896064, -2.005232867627105, -2.1902870510661576, -2.3099647257019456, -2.3548590273169974, -2.3182548654245347, -2.1968440396769906, 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'14.54239991846361307201219527447968'], 'prelabel': '2-76-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4390448252706574, 'root_angle': 0.2064723686995483, 'root_number': '0.7968988199726873 + 0.6041127963601983*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10323618435', 'prec': 44}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.29584901779094879969739897445', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.51076751117253871137929725877', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95819999960680972104565533837', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'bad_primes': [2, 19], 'central_character': '19.8', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/3/h/a/65/2'], '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': '2-76-19.8-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-76-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4390448252706574, 'root_angle': 0.10323618434977415, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.29584901779094879969739897445', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2910334385436087167762909782376', 'Lhash_array': ['2910334385436087167762909782376'], 'label': '2-76-19.8-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/3/h/a/65/2'}