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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 2, 'A4': -2, 'A5': 0, 'A6': -2, 'A7': 5, 'A8': 3, 'A9': 0, 'Lhash': '2285133324391899457', 'a10': [0.0, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [-0.020618556701030927, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.020618556701030927, 0.0], 'a7': [0.05154639175257732, 0.0], 'a8': [0.030927835051546393, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 8.307977213089988, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1, -2, 4, -3]], [13, [1, -1, 13]], [257, [1, -26, 230, 257]]], 'bad_primes': [3, 13, 257], 'central_character': '130299.1', 'coefficient_field': '1.1.1.1', 'conductor': 130299, 'conductor_radical': 10023, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [1, -2, 4, -3], [1, 0, 6, 0, 25], [1, -5, 18, -35, 49], [1, 4, 5, 44, 121], [1, -1, 13], [1, -2, 15, -34, 289], [1, 3, 38, 57, 361], [1, 2, 15, 46, 529], [1, 12, 89, 348, 841], [1, 7, 50, 217, 961], [1, 7, 62, 259, 1369], [1, 5, 76, 205, 1681], [1, 1, -30, 43, 1849], [1, -14, 102, -658, 2209], [1, 4, 46, 212, 2809], [1, -10, 111, -590, 3481], [1, 3, 32, 183, 3721], [1, 1, 34, 67, 4489], [1, 5, 52, 355, 5041], [1, 1, 88, 73, 5329], [1, 13, 154, 1027, 6241], [1, 0, -146, 0, 6889], [1, 4, 37, 356, 7921], [1, 13, 208, 1261, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 4, 'label': '4-130299-1.1-c1e2-0-4', 'leading_term': '2.34118921183', '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': 1, 'origin': 'Genus2Curve/Q/130299/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.4444121102478946, 0.9143441837672293, 1.401921712406095, 1.843455899092912, 2.121122160658416, 2.100622973110274, 1.704868367810763, 0.9992034202994015, 0.2365155994542172, 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2.127848053633614], 'positive_zeros': [1.762846381524991, 2.049118303451278, 3.133307229741639, 3.933668318428303, 4.240597352261383, 5.090155228814345, 5.505136356903574, 5.801501627380928, 7.129049317387494, 7.598237990756377, 7.840002830036809, 8.396147861868249, 8.520913111629888, 8.94700140863439, 9.509426463936105, 9.851184936801417, 10.53047961165574, 10.82197920239348, 11.33165258158485, 11.72655432045361, 12.36060461356738, 13.01914826357037, 13.21227697628471, 13.81293596035944, 13.94508814420422, 14.40513366993676, 14.85496425086557, 15.00426762864684, 15.57419081375891, 15.98805447105946, 16.73925268264047, 17.0254496881571, 17.37434765136651, 17.8750756556028, 17.96417063622359, 18.58630895224629, 18.70444464004129, 19.08020856946389, 19.48596549621637], 'prelabel': '4-130299-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.697750332417715, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 2285133324391899457, 'z1': {'__RealLiteral__': 0, 'data': '1.76284638152', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.04911830345', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.13330722974', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.307977213089988, 'bad_primes': [3, 13, 257], 'central_character': '1.1', 'conductor': 130299, 'conductor_radical': 10023, 'degree': 4, 'dirichlet_coefficients': [1, -1, 2, -2, 0, -2, 5, 3, 0, 0, -4, -4, 1, -5, 0, 1, 2, 0, -3, 0, 10, 4, -2, 6, -6, -1, -5, -10, -12, 0, -7, -2, -8, -2, 0, 0, -7, 3, 2, 0, -5, -10, -1, 8, 0, 2, 14, 2, 7, 6, 4, -2, -4, 5, 0, 15, -6, 12, 10, 0, -3, 7, 0, 1, 0, 8, -1, -4, -4, 0, -5, 0, -1, 7, -12, 6, -20, -2, -13, 0, -4, 5, 0, -20, 0, 1, -24, -12, -4, 0, 5, 4, -14, -14, 0, -4, -13, -7, 0, 12], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, -1, 13, 0, 0], 'euler17': [1, -2, 15, -34, 289], 'euler19': [1, 3, 38, 57, 361], 'euler2': [1, 1, 3, 2, 4], 'euler23': [1, 2, 15, 46, 529], 'euler29': [1, 12, 89, 348, 841], 'euler3': [1, -2, 4, -3, 0], 'euler31': [1, 7, 50, 217, 961], 'euler37': [1, 7, 62, 259, 1369], 'euler41': [1, 5, 76, 205, 1681], 'euler43': [1, 1, -30, 43, 1849], 'euler47': [1, -14, 102, -658, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 4, 46, 212, 2809], 'euler59': [1, -10, 111, -590, 3481], 'euler61': [1, 3, 32, 183, 3721], 'euler67': [1, 1, 34, 67, 4489], 'euler7': [1, -5, 18, -35, 49], 'euler71': [1, 5, 52, 355, 5041], 'euler73': [1, 1, 88, 73, 5329], 'euler79': [1, 13, 154, 1027, 6241], 'euler83': [1, 0, -146, 0, 6889], 'euler89': [1, 4, 37, 356, 7921], 'euler97': [1, 13, 208, 1261, 9409], 'euler_factors': [[1, 1, 3, 2, 4], [1, -2, 4, -3, 0], [1, 0, 6, 0, 25], [1, -5, 18, -35, 49], [1, 4, 5, 44, 121], [1, -1, 13, 0, 0], [1, -2, 15, -34, 289], [1, 3, 38, 57, 361], [1, 2, 15, 46, 529], [1, 12, 89, 348, 841], [1, 7, 50, 217, 961], [1, 7, 62, 259, 1369], [1, 5, 76, 205, 1681], [1, 1, -30, 43, 1849], [1, -14, 102, -658, 2209], [1, 4, 46, 212, 2809], [1, -10, 111, -590, 3481], [1, 3, 32, 183, 3721], [1, 1, 34, 67, 4489], [1, 5, 52, 355, 5041], [1, 1, 88, 73, 5329], [1, 13, 154, 1027, 6241], [1, 0, -146, 0, 6889], [1, 4, 37, 356, 7921], [1, 13, 208, 1261, 9409]], 'index': 4, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/130299/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': '4-130299-1.1-c1e2-0-4', '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': 1, 'prelabel': '4-130299-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.697750332417715, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2285133324391899457, 'z1': {'__RealLiteral__': 0, 'data': '1.76284638152', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '2285133324391899457', 'Lhash_array': ['2285133324391899457'], 'label': '4-130299-1.1-c1e2-0-4', 'type': 'G2Q', 'url': 'Genus2Curve/Q/130299/a'}