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lfunc_lfunctions • Show schema
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{'Lhash': '337319781028344573054426941776', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.3546091220107779, -0.6142010161500583], 'a4': [0, 0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [-3.110788174114542, 0], 'a8': [0, 0], 'a9': [1.2485047411734904, 2.1624736452031166], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [4.351618604357759, 0.2518243876343803]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.961', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '2070423315989086271864001217971', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3546091220107779, 0.6142010161500583], [-1.5, -2.598076211353316]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [3.110788174114542, 0], [7.0, 0]], [[1.0, 0], 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'0.7202629017902635035778483967077348069511288000145519371', '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/1520/2/q/m/961/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7202629017902635, 0.5691148705420972, 0.41384013026391114, 0.2543196765087119, 0.09048673986460813, -0.07759908493491312, -0.24968360265464543, -0.42525933231256563, -0.6035190652239739, -0.7833233784264183, -0.9631829586747007, -1.141255929065729, -1.315359908741958, -1.4829982400064974, -1.6413996300239722, -1.7875703183839826, -1.9183577503926388, -2.030524578231174, -2.120831613335689, -2.186128112237161, -2.223447503370554, -2.230106369374283, -2.2038042074054767, -2.142721220043761, -2.0456111627685636, -1.9118861112297214, -1.7416899312976415, -1.53595725339751, -1.2964548829726354, 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'8.706603105679073087078924635152087', '9.224128536525669568464742311815915'], 'prelabel': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.7160201591774041, 'root_number': '-0.6277406615468891653073099061860294272828426496956644447 - 0.7784225471045105502593386522704563342970830664027215870*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35801007958870207', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26609838781097338435771723128', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88605308473779344674031651835', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44226504253301436005943124126', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.11', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/m/961/3'], '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': '2-1520-19.11-c1-0-2', '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': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': -0.35801007958870207, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26609838781097338435771723128', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '337319781028344573054426941776', 'Lhash_array': ['337319781028344573054426941776'], 'label': '2-1520-19.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/m/961/3'}