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lfunc_lfunctions • Show schema
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{'Lhash': '81395351754252284931618982686', 'a10': [16.717379621456338, 14.850226213499791], 'a2': [0, -2.0], 'a3': [0, 3.0], 'a4': [-4.0, 0], 'a5': [-7.425113106749896, 8.358689810728169], 'a6': [6.0, 0], 'a7': [0, 7.6290377654858945], 'a8': [0, 8.0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.8717763053388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.0]]], [3, [[1.0, 0], [0, -3.0]]], [5, [[1.0, 0], [7.425113106749896, -8.358689810728169]]], [31, [[1.0, 0], [31.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.559', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '2452499817786348209162980549652', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [7.425113106749896, -8.358689810728169]], [[1.0, 0], [0, -7.6290377654858945], [-343.0, 0]], [[1.0, 0], [39.02651282299472, 0], [1331.0, 0]], [[1.0, 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0.7440846389107086], 'positive_zeros': ['0.06420961086564212873280481911343', '0.817083235342279949668562308919611', '2.59089722846465147503059140784678', '3.84552692065898479758309884631655', '5.00358414477942514049432211756549', '5.51517526513273479995292873204575', '6.82699063117106560457065176688557', '7.47640032911909948494567259474874', '8.247970331089338396832498226230790', '8.693524106351262593718275105473680'], 'prelabel': '2-930-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.40754860296838, 'root_angle': 0.7311945904436611, 'root_number': '-0.66412230589269680027311925524872679035995689961542447674 + 0.7476239447849214392336085870079085932143234930637380589*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36559729522183054', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06420961086564212873280481911', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.817083235342279949668562308920', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.59089722846465147503059140785', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.8717763053388, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/4/d/c/559/3'], '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': '2-930-5.4-c3-0-4', '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': '2-930-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.40754860296838, 'root_angle': 0.36559729522183054, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06420961086564212873280481911', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '81395351754252284931618982686', 'Lhash_array': ['81395351754252284931618982686'], 'label': '2-930-5.4-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/4/d/c/559/3'}