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lfunc_lfunctions • Show schema
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{'Lhash': '1326558103781680286550490193355', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [3.8442065059629646, 0], 'a8': [0, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-2.9520877676878063, 3.207051264303086]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2280.961', 'coefficient_field': 'CDF', 'conductor': 2280, 'conductor_radical': 570, 'conjugate': '1565638573584322545452554219452', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-3.8442065059629646, 0], [7.0, 0]], [[1.0, 0], [-3.959473172475158, 0], 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'2.5268205220846968181095284823707534097827130214566262169', '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/2280/2/bg/v/961/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.5268205220846967, 2.509445127109232, 2.4831603108519067, 2.4476685103539118, 2.402543434995481, 2.3472586246084313, 2.281224143366924, 2.2038294309038426, 2.1144901601345767, 2.0126969499316525, 1.8980639107976505, 1.7703752141843458, 1.6296281244029867, 1.4760711796273502, 1.3102364324171245, 1.1329648508749834, 0.945424139894792, 0.7491183756607154, 0.545888966573012, 0.3379065715204721, 0.12765373189179008, -0.08210188553604537, -0.28834357699418994, -0.4878507810913909, -0.6772529054028575, -0.8530911352005829, -1.011887325028045, -1.1502188332262957, -1.2647979202396706, 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'8.321133088263074344577200150554983', '8.869790236405460170745616804386027'], 'prelabel': '2-2280-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.002410819675286858, 'root_number': '0.9999713188125376109247015367245565735304432904320704005537 + 0.00757374097221867615494377270321077779267673322736127363*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.001205409837643429', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04646982657748523476922737302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05221532524949253626131727493', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49576889904763115460974590446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.205891660851936, 'bad_primes': [2, 3, 5, 19], 'central_character': '19.11', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2280/2/bg/v/961/4'], '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': '2-2280-19.11-c1-0-22', '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': '2-2280-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.001205409837643429, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04646982657748523476922737302', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1326558103781680286550490193355', 'Lhash_array': ['1326558103781680286550490193355'], 'label': '2-2280-19.11-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2280/2/bg/v/961/4'}