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lfunc_lfunctions • Show schema
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{'Lhash': '822183870290451903371183674094', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [6.824521654812797, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 104.07936925012649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.881', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '1073821908835189692714965728823', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.824521654812797, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 58.34736660995538], [-1331.0, 0]], [[1.0, 0], [0, 38.55351694886368], [-2197.0, 0]], [[1.0, 0], [-32.25191319251306, 0], [4913.0, 0]], [[1.0, 0], [0, -124.52993433266691], [-6859.0, 0]], [[1.0, 0], [0, -201.16835063606754], 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['0.64858871217544084290565973881010', '2.08597388767891249591130773469361', '2.53200490429256944000220852957867', '4.23041653863103412888984034503611', '4.58615440964772486299296112078360', '5.75016330444033999581809696123453', '6.55551632383087180764252525455317', '7.24914866937132367257509257372194', '8.049714135739986820187663890792246', '9.252428968278209040033262385804795'], 'prelabel': '2-42e2-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': -0.07690119815619134, 'root_number': '0.97095826429683353190130193259074594682080821794629164972 - 0.2392489268391404138298613148218196208704586221366353599*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.03845059907809567', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64858871217544084290565973881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08597388767891249591130773469', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53200490429256944000220852958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 104.07936925012649, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/4/f/a/881/9'], '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': '2-42e2-21.20-c3-0-19', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-42e2-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.201929682669181, 'root_angle': -0.03845059907809567, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64858871217544084290565973881', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '822183870290451903371183674094', 'Lhash_array': ['822183870290451903371183674094'], 'label': '2-42e2-21.20-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/4/f/a/881/9'}