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              lfunc_lfunctions •   Show schema
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{'Lhash': '1051443025653340969243910711657', 'a10': [0.4680044487798611, 0.2702024944849952], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.2702024944849952, -0.4680044487798611], 'a6': [-1.0, 0], 'a7': [1.409981241248707, 2.238739131593218], 'a8': [0, 1.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.725778966191955, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [-1.409981241248707, -2.238739131593218]]], [29, [[1.0, 0], [2.7697852631706454, 4.618256120650166]]]], 'bad_primes': [2, 3, 7, 29], 'central_character': '1218.1159', 'coefficient_field': 'CDF', 'conductor': 1218, 'conductor_radical': 1218, 'conjugate': '1880269469458919288094930437934', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 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[0, -2.8825751602558154], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1218-203.144-c1-0-7', 'leading_term': '1.540626025411826385804493490325491867683262949075634590', '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/1218/2/p/b/1159/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5406260254118265, 1.4629599206947765, 1.3809833306107127, 1.2945131989878351, 1.2032828288678368, 1.106998948545267, 1.0054008064688669, 0.8983178224755681, 0.7857228038617415, 0.6677783761812831, 0.5448749460441117, 0.41765910688948016, 0.2870518667137249, 0.15425641080928465, 0.020755334786819832, -0.11170256968469884, -0.24112578302136173, -0.365313478691722, -0.4818984682632345, -0.588399080832338, -0.6822791885845886, -0.7610153567739865, 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'5.24316602572160403899284282111413', '6.54871657278822315409640539221170', '7.31794944870113338972231034651519', '7.82371055191634577885359389296190', '8.899554806152276514372385615060018', '9.314101539748038835551069602255585'], 'prelabel': '2-1218-203.144-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1186181180439445, 'root_angle': -0.2486808791932365, 'root_number': '0.0082881855770534534883763638781306383753607685073233129 - 0.9999656524000413500963806668447971470655313172625785151*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2486808791932365', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.829442297005214094658543890059', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91966457448185698330416743388', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31921390189128423391038044347', 'prec': 103}}
           
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              lfunc_search •   Show schema
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{'algebraic': True, 'analytic_conductor': 9.725778966191955, 'bad_primes': [2, 3, 7, 29], 'central_character': '203.144', 'conductor': 1218, 'conductor_radical': 1218, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1218/2/p/b/1159/9'], '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': '2-1218-203.144-c1-0-7', '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': '2-1218-203.144-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1186181180439445, 'root_angle': -0.2486808791932365, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829442297005214094658543890059', 'prec': 107}}
           
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              lfunc_instances •   Show schema
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{'Lhash': '1051443025653340969243910711657', 'Lhash_array': ['1051443025653340969243910711657'], 'factors': ['2-1218-203.144-c1-0-7'], 'label': '2-1218-203.144-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1218/2/p/b/1159/9'}