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lfunc_lfunctions • Show schema
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{'Lhash': '1833512583575729367843452833315', 'a10': [2.4248657107091125, 0.0], 'a2': [-1.7474684539079484, 0.0], 'a3': [0.82478794234553, 0.0], 'a4': [1.0536459974034353, 0.0], 'a5': [-1.387644913009026, 0.0], 'a6': [-1.4412909104124614, 0.0], 'a7': [2.707369763170453, 0.0], 'a8': [1.6537237657670174, 0.0], 'a9': [-2.3197248501614265, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7474684539079484, 0], [2.0, 0]], [[1.0, 0], [-0.82478794234553, 0], [3.0, 0]], [[1.0, 0], [1.387644913009026, 0], [5.0, 0]], [[1.0, 0], [-2.707369763170453, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.270226733833949, 0], [17.0, 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[107.0, 0]], [[1.0, 0], [18.111983105143153, 0], [109.0, 0]], [[1.0, 0], [12.435312607120212, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 78, 'label': '2-1859-1.1-c1-0-78', '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/1859/2/a/i/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.094781591905313e-61, 0.09159943133097881, 0.18289845565858634, 0.2735693637366787, 0.3632314770197922, 0.45142862458265925, 0.53761104032461, 0.6211226534476355, 0.7011944124284799, 0.7769439588259959, 0.8473816806728727, 0.9114229412302219, 0.9679061003813898, 1.0156158163870774, 1.0533110233645295, 1.0797569115658234, 1.0937601816583986, 1.0942067921725693, 1.0801013661023178, 1.0506073667545486, 1.0050870955520501, 0.9431405088481133, 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'5.63688763857098562136013659720336', '6.82830499267195184148072480679763', '7.85564074524551390795347385618155', '8.205176484521623443775112209293302', '8.492709652736321053807243822565980'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, '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': '1.44638639641366593149325890766', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51057805756129295628014911480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75021814745422503667749609494', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/i/1/2'], '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': '2-1859-1.1-c1-0-78', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44638639641366593149325890766', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1833512583575729367843452833315', 'Lhash_array': ['1833512583575729367843452833315'], 'label': '2-1859-1.1-c1-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/i/1/2'}