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lfunc_lfunctions • Show schema
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{'Lhash': '1443452573076796143173735780752,1772916247768006885043831169529', 'a10': 0, 'a2': -2, 'a3': -2, 'a4': -1, 'a5': 0, 'a6': 4, 'a7': 0, 'a8': 8, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 224.1592981509412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': '1.1.1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 2, 5, 4, 4], [1, 2, 1], [1], [1, 0, -6, 0, 49], [1, -2, 18, -22, 121], [1, 9, 45, 117, 169], [1, 1, 23, 17, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, -11, 87, -319, 841], [1, -10, 82, -310, 961], [1, 5, 49, 185, 1369], [1, 5, 87, 205, 1681], [1, 2, 42, 86, 1849], [1, -6, 98, -282, 2209], [1, 5, 111, 265, 2809], [1, 8, 134, 472, 3481], [1, -1, 121, -61, 3721], [1, 6, 138, 402, 4489], [1, 6, 146, 426, 5041], [1, -5, 121, -365, 5329], [1, 0, 158, 0, 6241], [1, 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'4.82239830035640573639637618657104', '5.28833856937473056467156442621544', '5.72969960009539445483473881836397', '6.62479377385035413489690622074108', '6.67003064948681231442910331723044', '7.08906283646487937755354944775376', '7.57759296941742729926394613198831', '8.048192055739203630957445198756058', '8.189373589478111696146722531932697', '8.730264778061087714549711535863056', '9.139631341288759573391165811585497'], 'prelabel': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, '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': 62375452211912308, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13868330344096009920645055642', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39858431609530956214490230704', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.41606283400103252543369505909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 224.1592981509412, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 3515625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, -2, -2, -1, 0, 4, 0, 8, 3, 0, 2, 2, -9, 0, 0, -7, -1, -6, -2, 0, 0, -4, 0, -16, 0, 18, -4, 0, 11, 0, 10, -14, -4, 2, 0, -3, -5, 4, 18, 0, -5, 0, -2, -2, 0, 0, 6, 14, 6, 0, 2, 9, -5, 8, 0, 0, 4, -22, -8, 0, 1, -20, 0, 35, 0, 8, -6, 1, 0, 0, -6, 24, 5, 10, 0, 2, 0, -36, 0, 0, 5, 10, -16, 0, 0, 4, -22, 16, 13, 0, 0, 0, -20, -12, 0, 28, -11, -12, 6, 0], 'euler11': [1, -2, 18, -22, 121], 'euler13': [1, 9, 45, 117, 169], 'euler17': [1, 1, 23, 17, 289], 'euler19': [1, 2, 34, 38, 361], 'euler2': [1, 2, 5, 4, 4], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, -11, 87, -319, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -10, 82, -310, 961], 'euler37': [1, 5, 49, 185, 1369], 'euler41': [1, 5, 87, 205, 1681], 'euler43': [1, 2, 42, 86, 1849], 'euler47': [1, -6, 98, -282, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 5, 111, 265, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -1, 121, -61, 3721], 'euler67': [1, 6, 138, 402, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 6, 146, 426, 5041], 'euler73': [1, -5, 121, -365, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 16, 210, 1328, 6889], 'euler89': [1, -13, 219, -1157, 7921], 'euler97': [1, 11, 213, 1067, 9409], 'euler_factors': [[1, 2, 5, 4, 4], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 49], [1, -2, 18, -22, 121], [1, 9, 45, 117, 169], [1, 1, 23, 17, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, -11, 87, -319, 841], [1, -10, 82, -310, 961], [1, 5, 49, 185, 1369], [1, 5, 87, 205, 1681], [1, 2, 42, 86, 1849], [1, -6, 98, -282, 2209], [1, 5, 111, 265, 2809], [1, 8, 134, 472, 3481], [1, -1, 121, -61, 3721], [1, 6, 138, 402, 4489], [1, 6, 146, 426, 5041], [1, -5, 121, -365, 5329], [1, 0, 158, 0, 6241], [1, 16, 210, 1328, 6889], [1, -13, 219, -1157, 7921], [1, 11, 213, 1067, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/a'], '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': '4-1875e2-1.1-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': 2, 'prelabel': '4-1875e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 62375452211912308, 'z1': {'__RealLiteral__': 0, 'data': '1.13868330344096009920645055642', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1443452573076796143173735780752,1772916247768006885043831169529', 'Lhash_array': ['1443452573076796143173735780752', '1772916247768006885043831169529'], 'label': '4-1875e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/a'}