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lfunc_lfunctions • Show schema
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{'Lhash': '1925146381402721246796449290513', 'a10': [2.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [2.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5615528128088303, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '1925146381402721246796449290513', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [1.5615528128088303, 0], [7.0, 0]], [[1.0, 0], [1.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [-6.68465843842649, 0], [13.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [17.0, 0]], [[1.0, 0], [3.5615528128088303, 0], [19.0, 0]], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-666-1.1-c1-0-7', '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/666/2/a/k/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.6234940856595137, 2.6203837146081077, 2.608284559455175, 2.5794444385387685, 2.5226047546110486, 2.424991715151107, 2.274413295967062, 2.061202744844268, 1.7798883159987937, 1.430527411578426, 1.0196371646372036, 0.560626546669029, 0.07362094928809908, -0.4154151088954022, -0.876304527076489, -1.2770054469173704, -1.5865571861866483, -1.7783981205590822, -1.8337333895784942, -1.7445577613188956, -1.5159060213988143, -1.166923387879076, -0.730429974877366, -0.25079680234303625, 0.2198526586954293, 0.6268709769137739, 0.9192647514898507, 1.0561345965448325, 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'7.79780882030356989594681079952820', '8.921140041973633294089213449529291', '9.666111955655835904257090591883585', '10.82492279477294017339874254147864'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51867271711630592964624695034', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94038964370464569084863133877', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84507218104634077762312831185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/a/k/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': '2-666-1.1-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': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51867271711630592964624695034', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1925146381402721246796449290513', 'Lhash_array': ['1925146381402721246796449290513'], 'label': '2-666-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/k/1/1'}