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lfunc_lfunctions • Show schema
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{'Lhash': '2647234966580983579120550170575', 'a10': [500.0, 866.0254037844386], 'a2': [-4.0, 6.928203230275509], 'a3': [-15.0, -25.98076211353316], 'a4': [-32.0, -55.42562584220407], 'a5': [62.5, -108.25317547305482], 'a6': [240.0, 0], 'a7': [-686.0, -594.0934269961249], 'a8': [512.0, 0], 'a9': [643.5, -1114.5746946705726], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.86695178388853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, -6.928203230275509]]], [5, [[1.0, 0], [-62.5, 108.25317547305482]]], [7, [[1.0, 0], [686.0, 594.0934269961249]]]], 'bad_primes': [2, 5, 7], 'central_character': '70.51', 'coefficient_field': 'CDF', 'conductor': 70, 'conductor_radical': 70, 'conjugate': '113594541112937908348998956985', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, -6.928203230275509]], [[1.0, 0], [15.0, 25.98076211353316], [-1093.5, 1893.9975580765674]], [[1.0, 0], [-62.5, 108.25317547305482]], [[1.0, 0], 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'12.57841888908371114608834281706200', '13.60236286053991764314744351284533'], 'prelabel': '2-70-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.676211263821228, 'root_angle': -0.4798270469460539, 'root_number': '-0.9919779164085226 - 0.12641128651274008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4798270469460539', 'prec': 64}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08830017206978964132829642591130', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.55018079325339840572283280199627', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.16633478467232399279743579450966', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.86695178388853, 'bad_primes': [2, 5, 7], 'central_character': '7.2', 'conductor': 70, 'conductor_radical': 70, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/70/8/e/a/51/1'], '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': '2-70-7.2-c7-0-16', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-70-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.676211263821228, 'root_angle': -0.4798270469460539, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08830017206978964132829642591130', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2647234966580983579120550170575', 'Lhash_array': ['2647234966580983579120550170575'], 'factors': ['2-70-7.2-c7-0-16'], 'label': '2-70-7.2-c7-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/8/e/a/51/1'}