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- 2025-07-30T00:26:19.678400+00:00
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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1272751679870710314395192071574', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.55976426717146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, 2, 3]], [5, [1, 0, 1]], [37, [1, 0, -1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '1232100.1', 'coefficient_field': '1.1.1.1', 'conductor': 1232100, 'conductor_radical': 1110, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 2, 3], [1, 0, 1], [1, 4, 17, 28, 49], [1, 0, -7, 0, 121], [1, -6, 31, -78, 169], [1, 0, -9, 0, 289], [1, -4, 33, -76, 361], [1, 0, 29, 0, 529], [1, 0, 2, 0, 841], [1, -8, 74, -248, 961], [1, 0, -1], [1, 0, 10, 0, 1681], [1, 8, 102, 344, 1849], [1, 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0.32736151857787427, 0.5584859852610567, 0.6949849387445735, 0.6860419760384362, 0.5039017728015353, 0.1502630518675428], 'positive_zeros': ['1.00402404230437196821566182156171', '1.59651631208303436278229670137739', '2.68985241690590522148729296525686', '3.19110399319157223137105548531949', '3.42665838600910385696912032165715', '4.16198853833206437749890734961454', '4.71491570384763710121902296679514', '5.26638380188506621374707060833925', '5.81156544978872936451623421425815', '6.10065510704317972095508908800285', '6.40818821278537747508017147952154', '6.70040122798654550620733112587479', '7.16152902049794544132675437201839', '7.74151171551449502330125125699350'], 'prelabel': '4-1110e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2048426544941964497, 'z1': {'__RealLiteral__': 0, 'data': '1.00402404230437196821566182156171', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.59651631208303436278229670137739', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.68985241690590522148729296525686', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.55976426717146, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 1232100, 'conductor_radical': 1110, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, 0, 0, -4, 0, 1, 0, 0, -2, 6, 0, 0, 1, 0, 0, 4, 0, 8, 0, 0, 0, -1, 0, 4, -4, 0, 0, 8, 0, 0, 0, 0, 1, 0, 0, -12, 0, 0, 0, -8, 0, 0, 0, 0, -2, -1, 0, 0, 6, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -4, 1, 0, 0, -8, 0, 0, 0, 0, 0, -10, 0, 2, 4, 0, 0, -2, 0, -11, 0, 0, 8, 0, 0, 0, 0, 0, 0, -24, 0, -16, 0, 0, 0, 10, 0, 0, -1], 'euler11': [1, 0, -7, 0, 121], 'euler13': [1, -6, 31, -78, 169], 'euler17': [1, 0, -9, 0, 289], 'euler19': [1, -4, 33, -76, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 29, 0, 529], 'euler29': [1, 0, 2, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, -8, 74, -248, 961], 'euler37': [1, 0, -1, 0, 0], 'euler41': [1, 0, 10, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -62, 0, 2209], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 0, 51, 0, 2809], 'euler59': [1, 0, 2, 0, 3481], 'euler61': [1, 8, 134, 488, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 4, 17, 28, 49], 'euler71': [1, 0, 42, 0, 5041], 'euler73': [1, 10, 135, 730, 5329], 'euler79': [1, 2, -10, 158, 6241], 'euler83': [1, 0, -7, 0, 6889], 'euler89': [1, 0, 15, 0, 7921], 'euler97': [1, -10, 218, -970, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 2, 3, 0, 0], [1, 0, 1, 0, 0], [1, 4, 17, 28, 49], [1, 0, -7, 0, 121], [1, -6, 31, -78, 169], [1, 0, -9, 0, 289], [1, -4, 33, -76, 361], [1, 0, 29, 0, 529], [1, 0, 2, 0, 841], [1, -8, 74, -248, 961], [1, 0, -1, 0, 0], [1, 0, 10, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -62, 0, 2209], [1, 0, 51, 0, 2809], [1, 0, 2, 0, 3481], [1, 8, 134, 488, 3721], [1, 8, 150, 536, 4489], [1, 0, 42, 0, 5041], [1, 10, 135, 730, 5329], [1, 2, -10, 158, 6241], [1, 0, -7, 0, 6889], [1, 0, 15, 0, 7921], [1, -10, 218, -970, 9409]], 'index': 19, 'instance_types': ['BMF', 'ECNF', 'BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/136900.2/b', 'EllipticCurve/2.0.3.1/136900.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/136900.2/a', 'EllipticCurve/2.0.3.1/136900.2/b'], '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': '4-1110e2-1.1-c1e2-0-19', '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': '4-1110e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2048426544941964497, 'z1': {'__RealLiteral__': 0, 'data': '1.00402404230437196821566182156171', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9719128
{'Lhash': '1272751679870710314395192071574', 'Lhash_array': ['1272751679870710314395192071574'], 'factors': ['4-1110e2-1.1-c1e2-0-19'], 'label': '4-1110e2-1.1-c1e2-0-19', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/136900.2/b'}
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id: 9718813
{'Lhash': '1272751679870710314395192071574', 'Lhash_array': ['1272751679870710314395192071574'], 'factors': ['4-1110e2-1.1-c1e2-0-19'], 'label': '4-1110e2-1.1-c1e2-0-19', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/136900.2/a'}
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id: 9718811
{'Lhash': '1272751679870710314395192071574', 'Lhash_array': ['1272751679870710314395192071574'], 'factors': ['4-1110e2-1.1-c1e2-0-19'], 'label': '4-1110e2-1.1-c1e2-0-19', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/136900.2/a'}
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id: 9718632
{'Lhash': '1272751679870710314395192071574', 'Lhash_array': ['1272751679870710314395192071574'], 'factors': ['4-1110e2-1.1-c1e2-0-19'], 'label': '4-1110e2-1.1-c1e2-0-19', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/136900.2/b'}