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lfunc_lfunctions • Show schema
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{'Lhash': '194154857694295382585101441360', 'a10': [0.0, 0.0], 'a2': [0.1781969793463003, 1.4029418507378895], 'a3': [0.0, 0.0], 'a4': [-1.9364916731037085, 0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0465478920452886, -2.6276867221294786], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.186536181915238, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.1781969793463003, -1.4029418507378895]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.343', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '2614490950205876634379949974209', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.1781969793463003, -1.4029418507378895]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 7.0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 0], [0, 13.0]], [[1.0, 0], [4.898979485566356, 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'6.02552247219850327584622659926952', '6.91414499323989511749952096451150', '8.328293266930894643507258380121696', '8.770344855222277239902622117430683', '9.763267522244841967459107795931888'], 'prelabel': '2-30e2-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.680771564664777, 'root_angle': 0.7433611855700504, 'root_number': '-0.6922063255165484 + 0.7216996625431373*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.371680592785', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15316117679377858447187782426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95006146493499595497982547531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85366723689828712933563529376', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.186536181915238, 'bad_primes': [2, 3, 5], 'central_character': '20.3', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/2/k/i/343/3'], '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': '2-30e2-20.3-c1-0-1', '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': '2-30e2-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.680771564664777, 'root_angle': 0.3716805927850252, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15316117679377858447187782426', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '194154857694295382585101441360', 'Lhash_array': ['194154857694295382585101441360'], 'label': '2-30e2-20.3-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/2/k/i/343/3'}