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lfunc_lfunctions • Show schema
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{'Lhash': '1741345698883746073700704787808', 'a10': [0.0, 0.0], 'a2': [1.5938090760594639, 0.5800990627889626], 'a3': [-0.13009950457737968, -0.7378309550509643], 'a4': [1.4376680051619113, 1.2063466928867357], 'a5': [0.0, 0.0], 'a6': [0.2206612743354821, -1.2514322734324956], 'a7': [-0.24192189559966773, 0.4190210146419981], 'a8': [0.7435196328887725, 1.2878137805883136], 'a9': [0.41222398364576995, -0.15003725989769806], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [0.9902680687415704, -0.13917310096006544]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '2211593904857329978327391437443', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[0.17364817766693036, -0.984807753012208]], [[1.0, 0], [1.765895185717854, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-2717-2717.1429-c0-0-4', 'leading_term': '2.9495311159279131422398000633937', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.949531115927913, 2.925941797850059, 2.929334261922395, 2.954943031909267, 2.996438661799811, 3.0466345581374177, 3.0981178873688062, 3.1437163301670226, 3.1767946918109518, 3.1914204856111477, 3.1824474004576744, 3.145556445236085, 3.0772803938913778, 2.975024835976172, 2.8370905649157026, 2.6626968422276813, 2.4520023006545406, 2.206119026092822, 1.9271150797219114, 1.6180010100476963, 1.2826965397928254, 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'4.21120377712706302969977888549167', '4.82142779517673540643808227862387', '5.55326740058384434515273035070351', '6.35487408531034979334260300346280', '7.06475335200958366692826510940048', '8.192042621748345247764649632940073', '9.128389549944718722830401925677003'], 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.19870561668638287, 'root_number': '0.81140048362857685702875069217411 - 0.58449059459268596498758538506152*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09935280834319143', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37367954432414737424597964922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80188806670403154914115405048', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41460510533341057161225696052', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/4'], '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': '2-2717-2717.1429-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.09935280834319143, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37367954432414737424597964922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1741345698883746073700704787808', 'Lhash_array': ['1741345698883746073700704787808'], 'label': '2-2717-2717.1429-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/4'}