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lfunc_lfunctions • Show schema
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{'Lhash': '2650634001437487278433066276094', 'a10': [1.700491853955282, 0], 'a2': [0, -2.568058186279691], 'a3': [0, 0], 'a4': [-2.594922848118136, 0], 'a5': [0, 0.6621702977917179], 'a6': [0, 0], 'a7': [-12.817667004818869, 0], 'a8': [0, -3.608319882244773], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.14449421638194, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [127, [[1.0, 0], [-11.269427669584644, 0]]]], 'bad_primes': [3, 127], 'central_character': '1143.890', 'coefficient_field': 'CDF', 'conductor': 1143, 'conductor_radical': 381, 'conjugate': '37053686457483882715568691208', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.568058186279691], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.6621702977917179], [-25.0, 0]], [[1.0, 0], [12.817667004818869, 0], [49.0, 0]], [[1.0, 0], [0, 20.539126798589102], [-121.0, 0]], [[1.0, 0], [-4.921720964369195, 0], [169.0, 0]], [[1.0, 0], 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['2.09098153778356892153410903705715', '3.34933565860313476736507233023728', '4.53784898959342419201306212492516', '5.40242392517966454751643637890808', '6.55527190591980874194344799322548', '6.74507802591025629704142349842055', '7.53206402319084476250491297183338', '8.669223431082526222283316598925659', '9.281007610666203777204344828514072', '10.08131703897920622016581936272694'], 'prelabel': '2-1143-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.580725241075925, 'root_angle': -0.3040867239846964, 'root_number': '0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09098153778356892153410903706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34933565860313476736507233024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53784898959342419201306212493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.14449421638194, 'bad_primes': [3, 127], 'central_character': '3.2', 'conductor': 1143, 'conductor_radical': 381, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1143/3/b/a/890/17'], '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': '2-1143-3.2-c2-0-80', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1143-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.580725241075925, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09098153778356892153410903706', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2650634001437487278433066276094', 'Lhash_array': ['2650634001437487278433066276094'], 'label': '2-1143-3.2-c2-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1143/3/b/a/890/17'}