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lfunc_lfunctions • Show schema
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{'Lhash': '547286115764034326856668686505', 'a10': [0, -2.7661203788279543], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, 2.7661203788279543], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.8774472402820013, -3.9338520383915685]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1709', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'conjugate': '2120146649982464841169619627863', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.7661203788279543], [-5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -4.928267923055738], [-11.0, 0]], [[1.0, 0], [0, -2.9394361537273994], [-13.0, 0]], [[1.0, 0], [0, -4.928267923055738], 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'2.74200825224158117946595404335688', '3.44722028829542747549029361081941', '4.88360351899177413825221251013858', '5.37322446627425756852745324236591', '6.34300223773880358276545956783185', '7.16814783415401064868657588481346', '8.203962363300017330207425952143246', '8.532604553892064498836789363972274'], 'prelabel': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.9458256342482748, 'root_number': '-0.98555196264745171093996800506847671621581121600963087057 - 0.16937334182732519830867195038532776416283565603472634540*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4729128171241374', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43173262069650757805699897322', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.12575221377167456691436763035', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74200825224158117946595404336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '57.56', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/b/i/1709/6'], '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': '2-2394-57.56-c1-0-4', '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': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.4729128171241374, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43173262069650757805699897322', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '547286115764034326856668686505', 'Lhash_array': ['547286115764034326856668686505'], 'label': '2-2394-57.56-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/b/i/1709/6'}