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lfunc_lfunctions • Show schema
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{'Lhash': '1504645233308014267597729338737', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [2.0, -1.0], 'a6': [0, 0], 'a7': [0, 4.0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.913325430639492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [-2.0, 1.0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '3120.1249', 'coefficient_field': 'CDF', 'conductor': 3120, 'conductor_radical': 390, 'conjugate': '1291300056340358657413795828656', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-2.0, 1.0]], [[1.0, 0], [0, -4.0], [-7.0, 0]], [[1.0, 0], [-6.0, 0], [11.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 4.0], [-17.0, 0]], [[1.0, 0], [-2.0, 0], [19.0, 0]], [[1.0, 0], [0, 6.0], [-23.0, 0]], [[1.0, 0], [-10.0, 0], [29.0, 0]], [[1.0, 0], [4.0, 0], 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2.5485605133455054, 2.083241128244175, 1.5420848010348196, 0.9500300373774869, 0.3347553326796973, -0.2747737341588225, -0.8498317399624792, -1.3634510868778147, -1.7918461793948086, -2.115664910367178, -2.3209975126371343, -2.400086141169951, -2.351695195362407, -2.181121453529389, -1.8998435004795982, -1.5248305210953759, -1.0775501181643024, -0.582732244194905, -0.06696057765029129, 0.44282714032615006, 0.9208428002523685, 1.3438682132537167], 'positive_zeros': ['1.18695580078384063840761271951814', '1.57864541294792856600228268624269', '3.05744024629474237944457919648668', '3.85582733959903566998354501762218', '4.65945338962121549324356948745827', '5.96078293697032060894740412649610', '6.42666367018735506774205082161865', '7.05381595381731855820387239896744', '7.66689760879511475984574926285052', '8.663198519662771624716587161982978'], 'prelabel': '2-3120-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.991325017531867, 'root_angle': -0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18695580078384063840761271952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.57864541294792856600228268624', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05744024629474237944457919649', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.913325430639492, 'bad_primes': [2, 3, 5, 13], 'central_character': '5.4', 'conductor': 3120, 'conductor_radical': 390, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3120/2/l/i/1249/2'], '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': '2-3120-5.4-c1-0-51', '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': '2-3120-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.991325017531867, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18695580078384063840761271952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1504645233308014267597729338737', 'Lhash_array': ['1504645233308014267597729338737'], 'label': '2-3120-5.4-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3120/2/l/i/1249/2'}