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lfunc_lfunctions • Show schema
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{'Lhash': '1855572965554286755965353044690', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.307773698387228, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2280.1', 'coefficient_field': 'CDF', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.307773698387228, 0], [7.0, 0]], [[1.0, 0], [-2.2491405381295495, 0], [11.0, 0]], [[1.0, 0], [3.1905073778718704, 0], [13.0, 0]], [[1.0, 0], [-3.5569142365167776, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5569142365167774, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-2280-1.1-c1-0-24', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2280/2/a/s/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.264942165909329e-61, 0.13518754446514006, 0.26997898889980965, 0.4039384363192756, 0.5365527264742488, 0.6671984481097498, 0.7951152417356432, 0.9193867667210068, 1.038930226288206, 1.1524948772792016, 1.2586695396538237, 1.355898785908149, 1.4425072372464254, 1.5167312121171679, 1.5767568467685626, 1.6207637179261716, 1.646972927777842, 1.6536985487993938, 1.6394012633615727, 1.6027429681557488, 1.5426410478302293, 1.4583209602325986, 1.3493657234466494, 1.21576085936227, 1.0579333368839143, 0.8767830766661319, 0.6737056341865992, 0.45060477357415496, 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'6.92140919991834372947016840675699', '7.66073330845500757154470076045055', '8.899944735596474152475211232322672'], 'prelabel': '2-2280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46378896931079200813069068779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79622383721541992509548105205', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64574304128244307403457979507', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.205891660851936, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2280/2/a/s/1/1'], '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': '2-2280-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46378896931079200813069068779', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1855572965554286755965353044690', 'Lhash_array': ['1855572965554286755965353044690'], 'label': '2-2280-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2280/2/a/s/1/1'}