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lfunc_lfunctions • Show schema
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{'Lhash': '3697551440839585937322020877386', 'a10': [-6.242640687119285, 0.0], 'a2': [1.4142135623730951, 0.0], 'a3': [1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.414213562373095, 0.0], 'a6': [2.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.8284271247461903, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '3697551440839585937322020877386', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0], [2.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [4.414213562373095, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.242640687119285, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [17.0, 0]], 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[109.0, 0]], [[1.0, 0], [20.31370849898476, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-637-1.1-c1-0-40', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/a/g/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.7283066764526232e-120, 0.36753553876360684, 0.7450576630590943, 1.1402048871741353, 1.5563991030040463, 1.9917228176889161, 2.438557463880986, 2.8838631207467698, 3.309972789386203, 3.6958200384573576, 4.018550894796686, 4.255465112760519, 4.386193826066855, 4.3949660362661325, 4.272761927988528, 4.019110746513593, 3.6432762757519153, 3.164592104559552, 2.6117663449226494, 2.0210709085183587, 1.4334577766858458, 0.8907917599701314, 0.43153831412440025, 0.08637429381885263, -0.12572416525481747, 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'7.77990722361272211819462870737935', '8.247083166332149019636656831159121', '8.908967220311914474610397015751658', '10.30645035020357371713520906536168'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.91685377672197224188381781902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37369432541033221291342542597', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41651203737942914312023578712', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/g/1/2'], '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': '2-637-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.91685377672197224188381781902', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3697551440839585937322020877386', 'Lhash_array': ['3697551440839585937322020877386'], 'label': '2-637-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/g/1/2'}