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lfunc_lfunctions • Show schema
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{'Lhash': '1255202806305416213392124460497', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [5.2219863816702095, 3.0149152431618553], 'a6': [0, 0], 'a7': [2.272386330583451, 6.62089573732871], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.599507985638446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.272386330583451, -6.62089573732871]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.485', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '1830099762658793814878600857947', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.2219863816702095, -3.0149152431618553], [12.5, 21.650635094610966]], [[1.0, 0], [-2.272386330583451, -6.62089573732871]], [[1.0, 0], [-8.172570886548092, 4.71843600131984], [60.5, -104.78907385791707]], [[1.0, 0], 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[-2244.5, 3887.5880375883453]], [[1.0, 0], [0, -11.288988079244435], [-5041.0, 0]], [[1.0, 0], [-10.268973169233224, -17.78638327067354], [-2664.5, 4615.049376767273]], [[1.0, 0], [-57.590736689617245, 99.75008199173811], [-3120.5, -5404.864545018681]], [[1.0, 0], [0, -35.038526729215434], [-6889.0, 0]], [[1.0, 0], [-45.24042021246101, -26.11956878791615], [3960.5, 6859.787223376538]], [[1.0, 0], [-182.13239769880303, 0], [9409.0, 0]], [[1.0, 0], [6.603872286622349, -3.8127474423753225], [5100.5, -8834.325144005059]], [[1.0, 0], [33.76065923075464, -58.475177084686244], [-5304.5, -9187.66350874911]], [[1.0, 0], [-127.39897591320538, -73.55383303797177], [5724.5, 9915.124847928038]], [[1.0, 0], [9.724483846935463, 16.843300100275073], [-5940.5, 10289.247822362915]], [[1.0, 0], [0, -208.36764944926148], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-756-21.2-c2-0-8', 'leading_term': '2.5181630050709227945239584585411562265480524655626025067', 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'10.03359507296862758215601270263675'], 'prelabel': '2-756-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.53866808498247, 'root_angle': -0.14603913023240742, 'root_number': '0.60773506685693205294873039103251784494082643561312954994 - 0.79413984191224175587033551050297666618089769145563227985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1460391302324074', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.990180422018044978877612690957', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.93099855349301778703553506385', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60197725221195807950600611655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.599507985638446, 'bad_primes': [2, 3, 7], 'central_character': '21.2', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/3/bk/g/485/7'], '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': '2-756-21.2-c2-0-8', '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': '2-756-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.53866808498247, 'root_angle': -0.14603913023240742, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.990180422018044978877612690957', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1255202806305416213392124460497', 'Lhash_array': ['1255202806305416213392124460497'], 'factors': ['2-756-21.2-c2-0-8'], 'label': '2-756-21.2-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/3/bk/g/485/7'}