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lfunc_lfunctions • Show schema
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{'Lhash': '450285644177526076626236203836', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.449489742783178, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.4142135623730951, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.449489742783178, 0], [5.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [7.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [11.0, 0]], [[1.0, 0], [4.898979485566356, 0], [13.0, 0]], [[1.0, 0], [-4.0, 0], [17.0, 0]], [[1.0, 0], [6.928203230275509, 0], [19.0, 0]], [[1.0, 0], [5.656854249492381, 0], [23.0, 0]], [[1.0, 0], 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'2-4608-1.1-c1-0-3', 'leading_term': '0.47229816581683099599811642446325', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4608/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.472298165816831, 0.4627012349184335, 0.433885961980839, 0.3857862919331059, 0.3183162382787294, 0.23140429818893954, 0.12503833355527638, -0.00068198625998263, -0.14548843291916605, -0.308886520487551, -0.49010012859177327, -0.6880214751504781, -0.9011691308742062, -1.127656382433727, -1.3651718470602732, -1.6109738349871594, -1.8618995526341318, -2.114389836323653, -2.3645296977292465, -2.6081045422619185, -2.8406714865655576, -3.0576447512194487, -3.254393643806508, -3.4263511839694574, -3.5691309678497634, -3.678649439222723, -3.751250345633829, -3.783827828012914, 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'6.07701350004751985649604477033614', '7.14664586315026700853661347026046', '7.56968261334377706744850402480531', '8.179241106968710109652229542484283'], 'prelabel': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35521274087390964463913027938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13011582929890769845634910224', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88199546820798744855326852443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/a/z/1/1'], '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': '2-4608-1.1-c1-0-3', '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': '2-4608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35521274087390964463913027938', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '450285644177526076626236203836', 'Lhash_array': ['450285644177526076626236203836'], 'label': '2-4608-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/a/z/1/1'}