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lfunc_lfunctions • Show schema
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{'Lhash': '1718901464840777556655611687795', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.7274573365655503], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -11.862596977318455], 'a8': [0, 0], 'a9': [13.106061804083653, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 135.7043930132035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 23.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '2300.1749', 'coefficient_field': 'CDF', 'conductor': 2300, 'conductor_radical': 230, 'conjugate': '621241260856724182298691262303', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.7274573365655503], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 11.862596977318455], [-343.0, 0]], [[1.0, 0], [-64.00852695868743, 0], [1331.0, 0]], [[1.0, 0], [0, 77.55490801636402], [-2197.0, 0]], [[1.0, 0], [0, 25.633827286020324], [-4913.0, 0]], [[1.0, 0], 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'2.08285276257850498832819048693413', '3.57538025633753915597389087541639', '4.13387697914081521124419218495913', '4.78307977366567560683432303496802', '5.96042837184958976218713982777159', '6.60997339055340627759755384327852', '7.27949649299263692400550842519693', '8.542472562055336487857188308961865', '9.160014579712816931644760474040567'], 'prelabel': '2-2300-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.649222850182046, 'root_angle': 0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35597416554001898031635972874', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08285276257850498832819048693', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57538025633753915597389087542', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 135.7043930132035, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 2300, 'conductor_radical': 230, 'degree': 2, 'index': 92, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2300/4/c/d/1749/4'], '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': '2-2300-5.4-c3-0-92', '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': '2-2300-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.649222850182046, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35597416554001898031635972874', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1718901464840777556655611687795', 'Lhash_array': ['1718901464840777556655611687795'], 'label': '2-2300-5.4-c3-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2300/4/c/d/1749/4'}