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lfunc_lfunctions • Show schema
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{'Lhash': '2446775822339985798954252055523', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.696558951756152, 0.34883767459388204], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-1.0821350889012482, -2.4143288196450556], 'a8': [0.0, 0.0], 'a9': [2.7566245535678657, 1.1836473590841003], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.696558951756152, -0.34883767459388204]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.0821350889012482, 2.4143288196450556]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.341', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '1753654804092884651178353263801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.696558951756152, -0.34883767459388204]], [[1.0, 0], [-0.5, 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'GL2', 'index': 6, 'label': '2-420-21.5-c1-0-6', '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/420/2/bh/b/341/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9473213202051056, 2.0043730540735805, 2.063515578823267, 2.120829157972083, 2.169198892081791, 2.1993497167853593, 2.2010389973580686, 2.16425007297309, 2.0803245258849175, 1.9430162408205094, 1.749447073803606, 1.500916797201131, 1.2034910831844836, 0.8682733547120078, 0.511265017432019, 0.15273570909207945, -0.183939557676415, -0.47396820193810674, -0.693281319097367, -0.8209874468897146, -0.8419304441881748, -0.7490869130899127, -0.5455037386684602, -0.2454720561112812, 0.1253325900882204, 0.5309394978562838, 0.9274827972134417, 1.2668469862108898, 1.5013275149453509, 1.5889106462838376, 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'9.878708520269529664795046724641647', '11.57049967683239618473218476085703'], 'prelabel': '2-420-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.13743676953290737, 'root_number': '0.9082263203072424 + 0.41847933174909174*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0687183847665', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93016579008400675698332641412', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95967889714600831243729318901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14408008463203194631867713191', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.5', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/bh/b/341/5'], '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': '2-420-21.5-c1-0-6', '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': '2-420-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.06871838476645369, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93016579008400675698332641412', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2446775822339985798954252055523', 'Lhash_array': ['2446775822339985798954252055523'], 'label': '2-420-21.5-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/bh/b/341/5'}