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lfunc_lfunctions • Show schema
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{'Lhash': '1141840077746015417008646510749', 'a10': [1.5, 2.598076211353316], 'a2': [-1.6275953626987474, 0.5923962654520477], 'a3': [0.0, 0.0], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [-0.3007674663608706, -1.7057370639048863], 'a6': [0.0, 0.0], 'a7': [1.532088886237956, 1.2855752193730787], 'a8': [0.8660254037844386, -1.5], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.163', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1194890529790750040982784275707', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6275953626987474, -0.5923962654520477], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3007674663608706, 1.7057370639048863], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], 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['0.900752997348352219079508655158209', '2.30922252866518167977126876976366', '3.54481088504721843867996240705935', '4.83393439557923513683416203368632', '6.06446580540033435691991764915108', '7.11671535361540543328282503485057', '8.006004257064976461115722214285532', '8.623606804774169742589535000896028', '9.459719122780327452256448405723961', '10.63994363549316905181273609461599'], 'prelabel': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.14814814814814817, 'root_number': '0.8936326403234123 - 0.4487991802004622*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0740740740741', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.900752997348352219079508655158', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.30922252866518167977126876976', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54481088504721843867996240706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/o/163/1'], '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': '2-3e6-27.7-c1-0-11', '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': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.07407407407407408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.900752997348352219079508655158', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1141840077746015417008646510749', 'Lhash_array': ['1141840077746015417008646510749'], 'label': '2-3e6-27.7-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/o/163/1'}