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lfunc_lfunctions • Show schema
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{'Lhash': '2282062233552383688918639717802', 'a10': [17.95405358176029, -31.097333005422804], 'a2': [1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, 3.4641016151377544], 'a5': [-8.977026790880146, -15.548666502711402], 'a6': [0, 0], 'a7': [13.22781231792035, 12.962445034864166], 'a8': [-8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.302721982169963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-13.22781231792035, -12.962445034864166]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.109', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '76067660497738369273043026264', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [8.977026790880146, 15.548666502711402], [-62.5, 108.25317547305482]], [[1.0, 0], [-13.22781231792035, 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'7.67678419136027767063057006564810', '8.260182476995878583878485417208941', '9.889230674343010214946608532344811', '10.65732544635163499072494182676689', '11.33512341346874615712321666775785'], 'prelabel': '2-378-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.7669478553359796, 'root_number': '-0.74373563220757223891861721348959965230811795367452739 + 0.66847386589514689520437740819885547656244536664175098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3834739276679898', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80022967933081745604693068960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43835058544111494226552412324', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80220911749361987296092249267', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.302721982169963, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/4/g/e/109/1'], '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': '2-378-7.4-c3-0-29', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-378-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': 0.3834739276679898, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80022967933081745604693068960', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2282062233552383688918639717802', 'Lhash_array': ['2282062233552383688918639717802'], 'label': '2-378-7.4-c3-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/4/g/e/109/1'}