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lfunc_lfunctions • Show schema
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{'Lhash': '2484954624787831335128970076654', 'a10': [1.0876662333953473, -1.8838931779178103], 'a2': [0.8312509723876683, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.3090218209045559, 0.0], 'a5': [1.308469126082532, -2.2663350065101926], 'a6': [0.0, 0.0], 'a7': [1.7827996346350068, -1.9548978138883082], 'a8': [-2.750627606278925, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.7827996346350068, 1.9548978138883082]]], [13, [[1.0, 0], [-2.745064788990014, 2.3376525199967615]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.289', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '870007297198681804821918638489', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8312509723876683, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.308469126082532, 2.2663350065101926], [-2.5, 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'GL2', 'index': 38, 'label': '2-819-91.16-c1-0-38', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/819/2/s/e/289/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.650057157673431, 1.8981984880839469, 2.141416431979319, 2.377081717875486, 2.5970994333374198, 2.7885087724499393, 2.93485904861028, 3.018078662438066, 3.020623235594418, 2.9277475082004774, 2.7297527836588737, 2.4240303062680466, 2.0166804969863783, 1.5234643664638372, 0.9698537100097969, 0.38999952221445777, -0.1754653327540904, -0.6827387655900319, -1.0890679091124795, -1.3574997542037952, -1.4616458751248602, -1.389845081641948, -1.1480812858292155, -0.7610776709874254, -0.271150439302836, 0.2653404594018375, 0.7837830795128083, 1.2188339264997898, 1.5128213764007172, 1.6239332480528452, 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'9.539506510268919448959758993935610', '10.68878982760480954764332312765331'], 'prelabel': '2-819-91.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.5719336802837002, 'root_number': '-0.22406771386376254 + 0.9745735783427883*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.285966840142', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96028355474326836800778077426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06361239233489320521787942277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18098005851627096319991007531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.16', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/s/e/289/6'], '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': '2-819-91.16-c1-0-38', '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': '2-819-91.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.2859668401418501, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96028355474326836800778077426', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2484954624787831335128970076654', 'Lhash_array': ['2484954624787831335128970076654'], 'label': '2-819-91.16-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/s/e/289/6'}