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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': -2, 'Lhash': '662291292879567945,1489687595124662811', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.48564968900904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [7, [1, 0, -1]]], 'bad_primes': [2, 5, 7], 'central_character': '980000.1', 'coefficient_field': '1.1.1.1', 'conductor': 980000, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 2, 0, 9], [1], [1, 0, -1], [1, 0, 22, 0, 121], [1, -8, 42, -104, 169], [1, 12, 70, 204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, 46, 0, 961], [1, 4, 78, 148, 1369], [1, -12, 118, -492, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, 12, 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5.10810305104954, 6.76408731727888, 8.428664629402714, 9.965044521096933], 'positive_zeros': ['1.31920416816215806650160602271280', '2.07204529193989626181377807358534', '2.50419401332512614244886579025520', '3.28327332646103144207952017477711', '3.83664653997120963252560991499378', '4.11500666640753372808858013263498', '4.58557293909771964767836479941646', '5.38990980084792703269563412867196', '5.59857578974307577358363282054972', '6.19185902002877876721827038865020', '6.60348506563741211247253098955864', '6.66965130292041403123447657278242', '7.60707532453471338039224955289125', '7.71895664384636679391588711626644'], 'prelabel': '4-980000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8115452165954427, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2151978888004230756, 'z1': {'__RealLiteral__': 0, 'data': '1.31920416816215806650160602271280', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.07204529193989626181377807358534', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.50419401332512614244886579025520', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.48564968900904, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 980000, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, 8, 0, 0, 1, -12, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -12, 0, 0, 1, 0, -12, 0, -2, -4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 8, -12, 0, 0, 0, 0, -12, 0, 0, 16, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 0, 0, -5, 12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 20, 1, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 82, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 22, 0, 121], [1, -8, 42, -104, 169], [1, 12, 70, 204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, 46, 0, 961], [1, 4, 78, 148, 1369], [1, -12, 118, -492, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 82, 0, 3481], [1, -16, 186, -976, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 94, 0, 6241], [1, 0, 130, 0, 6889], [1, 12, 214, 1068, 7921], [1, -20, 294, -1940, 9409]], 'index': 7, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/61250.3/e', 'EllipticCurve/2.0.4.1/61250.3/e'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-980000-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-980000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8115452165954427, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2151978888004230756, 'z1': {'__RealLiteral__': 0, 'data': '1.31920416816215806650160602271280', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9715838
{'Lhash': '662291292879567945,1489687595124662811', 'Lhash_array': ['662291292879567945', '1489687595124662811'], 'label': '4-980000-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/61250.3/e'}
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id: 9716647
{'Lhash': '662291292879567945,1489687595124662811', 'Lhash_array': ['662291292879567945', '1489687595124662811'], 'label': '4-980000-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/61250.3/e'}