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lfunc_lfunctions • Show schema
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{'Lhash': '969138377107791296325108891578', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6474070280928874, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': 'CDF', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6474070280928874, 0], [7.0, 0]], [[1.0, 0], [-0.5024671643906877, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.73073833245951, 0], [17.0, 0]], [[1.0, 0], [6.580864139975936, 0], [19.0, 0]], [[1.0, 0], [-2.850125807516425, 0], [23.0, 0]], [[1.0, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-7800-1.1-c1-0-32', 'leading_term': '2.53057989082115875198174122304', '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/7800/2/a/bx/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.530579890821159, 2.520662634265895, 2.4908833813455407, 2.4411666338601314, 2.3714092666858155, 2.281512996547542, 2.1714268120259828, 2.041196666652993, 1.8910193746557284, 1.7212975043866214, 1.5326921146886796, 1.3261703858984253, 1.1030455157872423, 0.8650066400546677, 0.6141369635584978, 0.35291872894978793, 0.08422409008628998, -0.1887086075815123, -0.46231320978748336, -0.7327484481100847, -0.995964179202986, -1.2477799913044894, -1.4839745998803364, -1.7003840682915845, -1.8930065266396807, 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'5.95669268582009978377571815773843', '6.47963741119584403173043300632723', '7.18532473576192883868776550605842', '7.981211741652367171201571364612065'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76451537744967454698853416196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98638976906454830002208137368', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54208834624490875512241101630', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bx/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': '2-7800-1.1-c1-0-32', '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': '2-7800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76451537744967454698853416196', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '969138377107791296325108891578', 'Lhash_array': ['969138377107791296325108891578'], 'label': '2-7800-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bx/1/2'}