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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': -1, 'A3': -2, 'A4': 1, 'A5': -4, 'A6': 2, 'A7': 1, 'A8': 1, 'A9': 2, 'Lhash': '1445475659822937675', 'a10': [0.041237113402061855, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.041237113402061855, 0.0], 'a6': [0.020618556701030927, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [0.010309278350515464, 0.0], 'a9': [0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.025121781609662816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1, 0, -2]], [197, [1, -19, 215, -197]]], 'bad_primes': [2, 197], 'central_character': '394.1', 'coefficient_field': '1.1.1.1', 'conductor': 394, 'conductor_radical': 394, 'degree': 4, 'euler_factors': [[1, 1, 0, -2], [1, 2, 2, 6, 9], [1, 4, 10, 20, 25], [1, -1, -2, -7, 49], [1, -2, 2, -22, 121], [1, 2, 22, 26, 169], [1, 2, -6, 34, 289], [1, -1, -22, -19, 361], [1, -5, 30, -115, 529], [1, 3, 28, 87, 841], [1, -6, 30, -186, 961], [1, 7, 44, 259, 1369], [1, -3, 44, -123, 1681], [1, -1, -6, -43, 1849], [1, 7, 94, 329, 2209], [1, 0, 70, 0, 2809], [1, -12, 118, -708, 3481], [1, 1, 16, 61, 3721], [1, 2, 14, 134, 4489], [1, -2, 102, -142, 5041], [1, -2, -62, -146, 5329], [1, 0, -42, 0, 6241], [1, -9, 66, -747, 6889], [1, 8, 158, 712, 7921], [1, 4, 198, 388, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-394-1.1-c1e2-0-0', 'leading_term': '0.200782743639', 'load_key': 'G2Q', '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, 'origin': 'Genus2Curve/Q/394/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.2007827436393816, 0.209904930222546, 0.2380945288004872, 0.2877911163268665, 0.3629434710718886, 0.4687701016287933, 0.6113040185536707, 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-1.920525100806041, -0.9922343696783478, 1.756580468212573, 3.487297551530436], 'positive_zeros': [4.061981033678487, 5.094100499501989, 6.651354334563617, 7.360370069829906, 8.0378184376724, 9.019033231731973, 10.09722232422138, 10.99793646281934, 11.48064672388995, 11.74830153827534, 12.54893036511147, 13.50787100859696, 14.56473296897452, 15.4443043074416, 15.60045769535683, 16.52316749398574, 16.84878657059589, 17.51762566771649, 17.99472965592394, 19.02483565276616, 19.30594698237417, 19.62957155046993], 'prelabel': '4-394-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.39811872905085893, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1445475659822937675, 'z1': {'__RealLiteral__': 0, 'data': '4.06198103368', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.0941004995', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '6.65135433456', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.025121781609662816, 'bad_primes': [2, 197], 'central_character': '1.1', 'conductor': 394, 'conductor_radical': 394, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 1, -4, 2, 1, 1, 2, 4, 2, -2, -2, -1, 8, -3, -2, -2, 1, -4, -2, -2, 5, -2, 6, 2, -6, 1, -3, -8, 6, 5, -4, 2, -4, 2, -7, -1, 4, -4, 3, 2, 1, 2, -8, -5, -7, 6, 3, -6, 4, -2, 0, 6, -8, 1, -2, 3, 12, 8, -1, -6, 2, -3, 8, 4, -2, -2, -10, 4, 2, 2, 2, 7, -12, 1, 2, -4, 0, 12, 11, -3, 9, -2, 8, -1, 6, 2, -8, 8, -2, 5, -12, 7, -4, -10, -4, -3, 4, 6], 'euler11': [1, -2, 2, -22, 121], 'euler13': [1, 2, 22, 26, 169], 'euler17': [1, 2, -6, 34, 289], 'euler19': [1, -1, -22, -19, 361], 'euler2': [1, 1, 0, -2, 0], 'euler23': [1, -5, 30, -115, 529], 'euler29': [1, 3, 28, 87, 841], 'euler3': [1, 2, 2, 6, 9], 'euler31': [1, -6, 30, -186, 961], 'euler37': [1, 7, 44, 259, 1369], 'euler41': [1, -3, 44, -123, 1681], 'euler43': [1, -1, -6, -43, 1849], 'euler47': [1, 7, 94, 329, 2209], 'euler5': [1, 4, 10, 20, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, -12, 118, -708, 3481], 'euler61': [1, 1, 16, 61, 3721], 'euler67': [1, 2, 14, 134, 4489], 'euler7': [1, -1, -2, -7, 49], 'euler71': [1, -2, 102, -142, 5041], 'euler73': [1, -2, -62, -146, 5329], 'euler79': [1, 0, -42, 0, 6241], 'euler83': [1, -9, 66, -747, 6889], 'euler89': [1, 8, 158, 712, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 1, 0, -2, 0], [1, 2, 2, 6, 9], [1, 4, 10, 20, 25], [1, -1, -2, -7, 49], [1, -2, 2, -22, 121], [1, 2, 22, 26, 169], [1, 2, -6, 34, 289], [1, -1, -22, -19, 361], [1, -5, 30, -115, 529], [1, 3, 28, 87, 841], [1, -6, 30, -186, 961], [1, 7, 44, 259, 1369], [1, -3, 44, -123, 1681], [1, -1, -6, -43, 1849], [1, 7, 94, 329, 2209], [1, 0, 70, 0, 2809], [1, -12, 118, -708, 3481], [1, 1, 16, 61, 3721], [1, 2, 14, 134, 4489], [1, -2, 102, -142, 5041], [1, -2, -62, -146, 5329], [1, 0, -42, 0, 6241], [1, -9, 66, -747, 6889], [1, 8, 158, 712, 7921], [1, 4, 198, 388, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/394/a'], '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': '4-394-1.1-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': '4-394-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.39811872905085893, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1445475659822937675, 'z1': {'__RealLiteral__': 0, 'data': '4.06198103368', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1445475659822937675', 'Lhash_array': ['1445475659822937675'], 'label': '4-394-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/394/a'}