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lfunc_lfunctions • Show schema
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{'Lhash': '2646528224662477587022240728226,4313741479380107491255916163443', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2611645113532459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '64.1', 'coefficient_field': '1.1.1.1', 'conductor': 4096, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 14, 0, 49], [1, 0, 14, 0, 121], [1, 0, -26, 0, 169], [1, 12, 70, 204, 289], [1, 0, -34, 0, 361], [1, 0, 46, 0, 529], [1, 0, -58, 0, 841], [1, 0, 62, 0, 961], [1, 0, -74, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 62, 0, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 158, 0, 6241], [1, 0, 158, 0, 6889], [1, -36, 502, -3204, 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'6.66435165558541062030334206318524', '7.34996069932697346126672149292547', '8.351563371273259363456532004580327', '8.852476829446497820961864119357671', '9.334876857942576191292204419069575', '10.26762558111546507012807907342337', '10.65483692056500405743349122518082', '11.32208652688223242730440004647946', '11.74893177195257215025275776856790', '12.71928374289623567725367707514607', '13.01138251672671175392876917229383', '13.40416631353195959623048426493214', '14.11744779141590763691021382241214', '14.77666960937088281402227755552820', '15.24061031761495894594432737468641'], 'prelabel': '4-2e12-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7148724172439406, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 2256708071540773966, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08774265100019936984633203220', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2611645113532459, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 4096, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0], 'euler11': [1, 0, 14, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 0, -34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, -58, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, -74, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 14, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 0, -82, 0, 3481], 'euler61': [1, 0, -122, 0, 3721], 'euler67': [1, 0, 62, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 158, 0, 6889], 'euler89': [1, -36, 502, -3204, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 14, 0, 49], [1, 0, 14, 0, 121], [1, 0, -26, 0, 169], [1, 12, 70, 204, 289], [1, 0, -34, 0, 361], [1, 0, 46, 0, 529], [1, 0, -58, 0, 841], [1, 0, 62, 0, 961], [1, 0, -74, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 14, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, -82, 0, 3481], [1, 0, -122, 0, 3721], [1, 0, 62, 0, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 158, 0, 6241], [1, 0, 158, 0, 6889], [1, -36, 502, -3204, 7921], [1, -20, 294, -1940, 9409]], 'index': 1, 'instance_types': ['G2Q', 'ECNF', 'HMF', 'CMF'], 'instance_urls': ['Genus2Curve/Q/4096/b', 'EllipticCurve/2.2.8.1/64.1/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-64.1-a', 'ModularForm/GL2/Q/holomorphic/64/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-2e12-1.1-c1e2-0-1', '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': 0, 'prelabel': '4-2e12-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7148724172439406, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2256708071540773966, 'z1': {'__RealLiteral__': 0, 'data': '2.08774265100019936984633203220', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957714
{'Lhash': '2646528224662477587022240728226,4313741479380107491255916163443', 'Lhash_array': ['2646528224662477587022240728226', '4313741479380107491255916163443'], 'factors': ['2-2e6-8.5-c1-0-0', '2-2e6-8.5-c1-0-1'], 'label': '4-2e12-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/64/2/b/a'}
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id: 9566216
{'Lhash': '_2646528224662477587022240728226', 'Lhash_array': ['_2646528224662477587022240728226'], 'factors': ['4-2e12-1.1-c1e2-0-1'], 'label': '4-2e12-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-64.1-a'}
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id: 9566122
{'Lhash': '_2646528224662477587022240728226', 'Lhash_array': ['_2646528224662477587022240728226'], 'factors': ['4-2e12-1.1-c1e2-0-1'], 'label': '4-2e12-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/64.1/a'}
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id: 1223448
{'Lhash': '2256708071540773966', 'Lhash_array': ['2256708071540773966'], 'factors': ['4-2e12-1.1-c1e2-0-1'], 'label': '4-2e12-1.1-c1e2-0-1', 'type': 'G2Q', 'url': 'Genus2Curve/Q/4096/b'}