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lfunc_lfunctions • Show schema
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{'Lhash': '362095720819073529792771632731', 'a10': [140.38475772933683, 0], 'a2': [-4.898979485566356, -2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, 27.712812921102035], 'a5': [-21.4919390063195, 12.408376770705582], 'a6': [0, 0], 'a7': [3.098076211353316, -5.366025403784438], 'a8': [0, -181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.898979485566356, 2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1549234161601962269986078174904', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.898979485566356, 2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [21.4919390063195, -12.408376770705582], [7812.5, -13531.646934131853]], [[1.0, 0], [-3.098076211353316, 5.366025403784438], 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'3.49994927874634060274780474356433', '5.10355810501637904239282027490496', '6.23942387072235382087698766631820', '7.45344881985822656989678836236627', '8.329036149511503889962366369332195', '9.377939370628444094898333494097214', '10.37553193020612015712668944461789', '11.32165804649126235109827056074189'], 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.5277777777777778, 'root_number': '-0.087155742747658173558064270837473551377701156149702673 - 0.996194698091745532295010402473888046183562672645850975*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2638888888888889', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28564315810198911496395496353', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78233249484582640718848110531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49994927874634060274780474356', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/f/107/2'], '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': '2-162-9.2-c6-0-4', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.2638888888888889, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28564315810198911496395496353', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '362095720819073529792771632731', 'Lhash_array': ['362095720819073529792771632731'], 'label': '2-162-9.2-c6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/f/107/2'}