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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 3, 'Lhash': '1560038282679592288,2249195285544657104', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.381007527240165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, 0, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '460800.1', 'coefficient_field': '1.1.1.1', 'conductor': 460800, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 0, -1], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, 0, 22, 0, 169], [1, 4, 38, 68, 289], [1, 16, 102, 304, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 0, 62, 0, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 8, 102, 344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 24, 262, 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-4.413017515275214, -3.2568150142364365, -2.0680335897074555, -0.9509574379972708], 'positive_zeros': ['1.90410956588849953091073290915852', '2.15654793577695836540091578775035', '3.01325599841700254495812174326707', '3.76484405045814108002996889467251', '4.59744237493557402533707286051552', '4.78210199118180492802537017049885', '5.10335741728591181213017059039250', '5.86487938441035862983502527783786', '6.25812475404630879226037514190479', '6.76366111244607068879792174830511', '6.84594392053537268258202260884291', '7.888892617242428206551037061143644', '7.985644465490789105614221217605191'], 'prelabel': '4-460800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3281806270075056, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1503390559010555441, 'z1': {'__RealLiteral__': 0, 'data': '1.90410956588849953091073290915852', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.15654793577695836540091578775035', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.01325599841700254495812174326707', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.381007527240165, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 460800, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, -8, 0, 0, 0, 0, 0, -4, 0, -16, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -12, 0, -8, 0, 0, 0, 0, 0, -14, 0, 8, 0, 0, 0, 0, 0, 32, 0, -24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 5, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -28, 0, -24, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 16, 102, 304, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, -24, 278, -1608, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, 28, 390, 2716, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, -1, 0, 0], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, 0, 22, 0, 169], [1, 4, 38, 68, 289], [1, 16, 102, 304, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, 0, 62, 0, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 8, 102, 344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 24, 262, 1416, 3481], [1, 0, -74, 0, 3721], [1, -24, 278, -1608, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 94, 0, 6241], [1, -8, 182, -664, 6889], [1, -4, 182, -356, 7921], [1, 28, 390, 2716, 9409]], 'index': 68, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/7200.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/7200.2/a'], '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': '4-460800-1.1-c1e2-0-68', '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': 2, 'prelabel': '4-460800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3281806270075056, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1503390559010555441, 'z1': {'__RealLiteral__': 0, 'data': '1.90410956588849953091073290915852', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9883853
{'Lhash': '1560038282679592288,2249195285544657104', 'Lhash_array': ['1560038282679592288', '2249195285544657104'], 'label': '4-460800-1.1-c1e2-0-68', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/7200.2/a'}
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id: 9883851
{'Lhash': '1560038282679592288,2249195285544657104', 'Lhash_array': ['1560038282679592288', '2249195285544657104'], 'label': '4-460800-1.1-c1e2-0-68', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/7200.2/a'}