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- 2025-07-19T20:52:47.770541+00:00
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lfunc_lfunctions • Show schema
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{'Lhash': '1861010488971328872644974708507', 'a10': [5.372281323269014, 1.7320508075688772], 'a2': [0.0, 2.5243377989621387], 'a3': [0.0, 0.7922869913932613], 'a4': [-4.372281323269014, 0.0], 'a5': [0.6861406616345072, -2.128194303265508], 'a6': [-2.0, 0.0], 'a7': [0.0, -3.4641016151377544], 'a8': [0.0, -5.9884394140998936], 'a9': [2.3722813232690143, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.6861406616345072, 2.128194303265508]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.364', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '1176822416137696133395758986107', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.5243377989621387], [-2.0, 0]], [[1.0, 0], [0, -0.7922869913932613], [-3.0, 0]], [[1.0, 0], [-0.6861406616345072, 2.128194303265508]], [[1.0, 0], [0, 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'2.48924736349072704104789548393188', '3.24076928710729858462834979967574', '4.57078960261336057308232382301326', '5.76747495233482591773060691657509', '6.86155895943070410537506426621923', '8.135813054304680301963330940785553', '9.101436849108355547396581663096510', '9.950783526445393507902468497506337', '10.43514543590271844527785654901592'], 'prelabel': '2-605-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.20036226322601836, 'root_number': '0.30685143230828793 - 0.9517574262858957*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.200362263226', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46807841895572030158506165825', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48924736349072704104789548393', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24076928710729858462834979968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/b/c/364/4'], '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': '2-605-5.4-c1-0-24', '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': '2-605-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': -0.20036226322601836, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46807841895572030158506165825', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1861010488971328872644974708507', 'Lhash_array': ['1861010488971328872644974708507'], 'factors': ['2-605-5.4-c1-0-24'], 'label': '2-605-5.4-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/b/c/364/4'}