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lfunc_lfunctions • Show schema
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{'Lhash': '714984317827460631884977393715', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.735489498215868, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': 'CDF', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.735489498215868, 0], [7.0, 0]], [[1.0, 0], [4.844685644748453, 0], [11.0, 0]], [[1.0, 0], [2.8446856447484534, 0], [13.0, 0]], [[1.0, 0], [-0.8908038534674149, 0], [17.0, 0]], [[1.0, 0], [6.844685644748453, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-5520-1.1-c1-0-7', 'leading_term': '1.115420533873147666010237314219', '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/5520/2/a/bv/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1154205338731478, 1.1062918931361632, 1.0788870954696945, 1.0331574801444476, 0.969047903249397, 0.8865336556387301, 0.7856683290618591, 0.6666392747025625, 0.5298269035419327, 0.3758639660003239, 0.2056910753679381, 0.02060504470504945, -0.1777029719863496, -0.38712205850827497, -0.6051108468319067, -0.8287030512384113, -1.0545301993235592, -1.2788620136664957, -1.4976643742014393, -1.706674259102088, -1.9014905201752235, -2.0776788005644224, -2.2308883559866133, -2.356978008337522, -2.4521479587654547, 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'5.39615097898362078985309661355162', '5.64636316829900980952359678357128', '6.93146970404755496431654384596702', '7.49545686675649568097929187760295', '8.057962229421811608305950691485440'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56402317618019820284477534291', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96437124743490682258231862530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56927071739488823782904089074', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/bv/1/3'], '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': '2-5520-1.1-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': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56402317618019820284477534291', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '714984317827460631884977393715', 'Lhash_array': ['714984317827460631884977393715'], 'label': '2-5520-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/bv/1/3'}