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lfunc_lfunctions • Show schema
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{'Lhash': '1556798764013605698889072926365', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.414213562373095, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8284271247461901, 0.0], 'a8': [0.0, 0.0], 'a9': [8.65685424949238, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.549044428938494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '6080.1', 'coefficient_field': 'CDF', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.414213562373095, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-6.242640687119285, 0], [13.0, 0]], [[1.0, 0], [-0.8284271247461901, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [6.0, 0], [23.0, 0]], [[1.0, 0], 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[0]], 'group': 'GL2', 'index': 100, 'label': '2-6080-1.1-c1-0-100', 'leading_term': '5.03341538743089950092374161015', '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/6080/2/a/bl/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [5.0334153874309, 5.0240582116935375, 4.9958734401789675, 4.9485333768962665, 4.881531111902375, 4.7942364426387725, 4.685968601417321, 4.556080959867256, 4.404052386231109, 4.2295798679922605, 4.03266730115148, 3.8137058830149697, 3.573542222291591, 3.3135310122571213, 3.0355698411067604, 2.742114407581826, 2.436173060966126, 2.121280198346994, 1.8014486408695516, 1.4811016870934672, 1.16498611410462, 0.8580679682367532, 0.5654135528163696, 0.2920585695386312, 0.0428688868253602, -0.17760312724312907, -0.3652623805479729, 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'6.79376646119022485963412203909283', '7.72626455796562468528070299048260', '8.178714704335085695066612810442576'], 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22809768222672532943618612491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85293454380981843244540192559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94786755752464223868595662193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.549044428938494, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'index': 100, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6080/2/a/bl/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': '2-6080-1.1-c1-0-100', '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': '2-6080-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22809768222672532943618612491', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1556798764013605698889072926365', 'Lhash_array': ['1556798764013605698889072926365'], 'label': '2-6080-1.1-c1-0-100', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/bl/1/2'}