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lfunc_lfunctions • Show schema
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{'Lhash': '560805036595632847101845538545', 'a10': [0, 0], 'a2': [0, 0], 'a3': [5.193861488894165, 0.154281671568869], 'a4': [0, 0], 'a5': [0, 12.376240721376051], 'a6': [0, 0], 'a7': [0, -15.875286502595271], 'a8': [0, 0], 'a9': [26.95239433163583, 1.602635264807533], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.81719184358216, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-5.193861488894165, -0.154281671568869]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.287', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '2077641752745566007226070378564', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-5.193861488894165, -0.154281671568869]], [[1.0, 0], [0, -12.376240721376051], [-125.0, 0]], [[1.0, 0], [0, 15.875286502595271], [-343.0, 0]], [[1.0, 0], [66.2636811718761, 0], [1331.0, 0]], [[1.0, 0], 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-1.314055736700742, -0.8220662980759984, -0.38801552605719813], 'positive_zeros': ['0.44239716882133358043447982248297', '2.12516459292911421249307574303412', '2.86132418714154310838690055824617', '4.40752745672804156793830950927944', '5.11929279312321229036702847470757', '6.23361253521308517678279246117150', '7.78084783130135844728394300319726', '8.091843607046658012198608299008964', '9.081232513101728934918854741793776', '9.567842748505651146826251755885736'], 'prelabel': '2-624-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.0677171855304985, 'root_angle': -0.6572141726133811, 'root_number': '-0.4740659428629679680314529781927059324405342457563519661 - 0.8804893422509128758034505154955334920381178837401690509*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32860708630669055', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44239716882133358043447982248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12516459292911421249307574303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86132418714154310838690055825', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.81719184358216, 'bad_primes': [2, 3, 13], 'central_character': '12.11', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/4/d/d/287/24'], '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': '2-624-12.11-c3-0-12', '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': '2-624-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.0677171855304985, 'root_angle': -0.32860708630669055, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44239716882133358043447982248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '560805036595632847101845538545', 'Lhash_array': ['560805036595632847101845538545'], 'label': '2-624-12.11-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/4/d/d/287/24'}