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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -1, 'Lhash': '1610760359549582575', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.010309278350515464, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 0.9630441356150943, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [59, [1, 11, 47, -59]]], 'bad_primes': [2, 59], 'central_character': '15104.1', 'coefficient_field': '1.1.1.1', 'conductor': 15104, 'conductor_radical': 118, 'degree': 4, 'euler_factors': [[1], [1, -1, 2, -3, 9], [1, 1, 0, 5, 25], [1, -1, 6, -7, 49], [1, -2, 14, -22, 121], [1, -4, 14, -52, 169], [1, 0, -34, 0, 289], [1, 3, 2, 57, 361], [1, -4, 14, -92, 529], [1, -1, -12, -29, 841], [1, -2, 30, -62, 961], [1, 2, 26, 74, 1369], [1, 7, 72, 287, 1681], [1, 10, 62, 430, 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3.576794756913877, 4.357087215866445, 5.069976354562647, 5.959026635485109, 6.601308688087154, 7.127695012273319, 7.983392925819125, 8.425923915999551, 8.809935172654638, 9.250402812698448, 10.16351872790508, 10.57493378829188, 11.21210584519711, 11.6034643338867, 12.07529323607967, 12.73428321272052, 13.25000620799535, 13.75409231113716, 14.14356617226694, 14.67098902078356, 15.12583596436612, 15.49785131964158, 15.93739954356086, 16.70050283875215, 16.9645226508618, 17.31354372970834, 18.07318956337009, 18.48221351791206, 18.77587054845748, 19.32800930699308, 19.91726844271722, 19.99625021990932], 'prelabel': '4-15104-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9906301638463122, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1610760359549582575, 'z1': {'__RealLiteral__': 0, 'data': '1.5605345582', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.90071851112', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.57679475691', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9630441356150943, 'bad_primes': [2, 59], 'central_character': '1.1', 'conductor': 15104, 'conductor_radical': 118, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 2, 0, 4, 0, -1, 0, 0, 0, -3, 0, 1, 0, 4, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, -1, 0, -2, 0, 4, 0, -7, 0, -10, 0, 1, 0, 6, 0, -5, 0, 0, 0, 7, 0, -2, 0, -3, 0, -11, 0, -6, 0, -1, 0, -4, 0, -2, 0, 4, 0, 4, 0, 2, 0, 1, 0, 2, 0, -9, 0, -4, 0, -6, 0, 0, 0, 1, 0, -10, 0, 4, 0, 2, 0, 3, 0, 14, 0, -2, 0], 'euler11': [1, -2, 14, -22, 121], 'euler13': [1, -4, 14, -52, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 3, 2, 57, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 14, -92, 529], 'euler29': [1, -1, -12, -29, 841], 'euler3': [1, -1, 2, -3, 9], 'euler31': [1, -2, 30, -62, 961], 'euler37': [1, 2, 26, 74, 1369], 'euler41': [1, 7, 72, 287, 1681], 'euler43': [1, 10, 62, 430, 1849], 'euler47': [1, -6, 62, -282, 2209], 'euler5': [1, 1, 0, 5, 25], 'euler53': [1, -7, 32, -371, 2809], 'euler59': [1, 11, 47, -59, 0], 'euler61': [1, 6, 66, 366, 3721], 'euler67': [1, 2, 94, 134, 4489], 'euler7': [1, -1, 6, -7, 49], 'euler71': [1, -4, 46, -284, 5041], 'euler73': [1, -2, 66, -146, 5329], 'euler79': [1, 9, 78, 711, 6241], 'euler83': [1, 6, 46, 498, 6889], 'euler89': [1, 10, 138, 890, 7921], 'euler97': [1, -14, 154, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 2, -3, 9], [1, 1, 0, 5, 25], [1, -1, 6, -7, 49], [1, -2, 14, -22, 121], [1, -4, 14, -52, 169], [1, 0, -34, 0, 289], [1, 3, 2, 57, 361], [1, -4, 14, -92, 529], [1, -1, -12, -29, 841], [1, -2, 30, -62, 961], [1, 2, 26, 74, 1369], [1, 7, 72, 287, 1681], [1, 10, 62, 430, 1849], [1, -6, 62, -282, 2209], [1, -7, 32, -371, 2809], [1, 11, 47, -59, 0], [1, 6, 66, 366, 3721], [1, 2, 94, 134, 4489], [1, -4, 46, -284, 5041], [1, -2, 66, -146, 5329], [1, 9, 78, 711, 6241], [1, 6, 46, 498, 6889], [1, 10, 138, 890, 7921], [1, -14, 154, -1358, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/15104/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-15104-1.1-c1e2-0-0', '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': '4-15104-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9906301638463122, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1610760359549582575, 'z1': {'__RealLiteral__': 0, 'data': '1.5605345582', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': '1610760359549582575', 'Lhash_array': ['1610760359549582575'], 'label': '4-15104-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/15104/c'}