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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '492434641612099950', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2612.577393493061, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1]], [13, [1]]], 'bad_primes': [2, 11, 13], 'central_character': '327184.1', 'coefficient_field': '1.1.1.1', 'conductor': 327184, 'conductor_radical': 286, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 1, 5], [1, -3, 7], [1], [1], [1, -6, 17], [1, 0, 19], [1, 1, 23], [1, -3, 29], [1, -10, 31], [1, 2, 37], [1, -7, 41], [1, 1, 43], [1, 4, 47], [1, -6, 53], [1, 5, 59], [1, -11, 61], [1, 1, 67], [1, -16, 71], [1, 7, 73], [1, -4, 79], [1, 4, 83], [1, 12, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 104, 'label': '2-572e2-1.1-c1-0-104', 'leading_term': '6.2698153216', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/327184/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.340330458335564, 1.536516741488599, 0.523928589852994, -0.2459910054973733, 0.7119617160592219, 2.501487094517184, 2.168399006311167, -1.249632086517394, -4.190672061396387, -2.612783988025217, 1.785904195375356, 2.922917036207665, -1.064928262274352, -4.664512971939373, -3.112344557700648, 0.5309806433194141, 0.8695397051049945, -1.140976812137877, -1.065380879496388, 0.6484668249490422, 0.4518635982520018, -0.7483958690318392, 0.1667241586602022, 1.271133033400149, -0.7415894270883828, -2.769912725033841, -0.701256399181604, 1.594596832722096, -0.8664207927569822, -3.959129225757546, 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4.239515470443994, 4.882740411949973, -0.8393855177686178, -1.170848505979839, 0.7707069414789602, -0.4733504137901135, 1.656787394432359, 5.397507868122553, 2.312275116387641, -1.823232573723974, -0.6817996417610221, 0.05813767764413895, -0.180961594433197, 1.725764751641261, 1.242380295565626, -0.7277021326671694, 0.738564111072645, -0.4462552617859274, -4.678057586829906, -1.468907716470643, 3.017055041655924, -1.700505202980335, -2.87686242408095, 5.318173298266875, 5.807706752490349, -1.613186026105547, -1.625861403822807, 1.263195511171233, -1.049828311575793, -1.657496987488557, 0.1235087687907196, -0.09530110332571243, 1.115005798107332, 1.465939691550066, -2.491236820599689, -2.570159883002672, 1.053138362049647, -0.4086515199600618, -1.689573636109515, 0.5852424797686524], 'positive_zeros': ['0.8706000642604717', '1.125369086681763', '1.922468407648957', '2.646234923904665', '3.197040529224166', '3.953619328644403', '4.357639704720495', '4.895828860646336', '5.327695419169873', '5.726448674251658', '6.187351026118108', '6.801424621813864', '7.195434852219513', '7.959443196176491', '8.174382694378943', '8.376680414761283', '9.330227329498338', '9.734604234337026', '10.30072960803895', '10.58964540125998', '11.19387761628992', '11.49077177484391', '11.94252214785768', '12.13317759536728', '12.56675615888937', '13.24920527400328', '13.82973884189721', '14.14850634313356', '14.61588421636720', '14.96013963230925', '15.66013660927261', '15.88071996519587', '16.35664015731133', '16.86753312533155', '17.19805346667978', '17.61494249496711', '17.87374430520637', '18.31836850309665', '18.89149923586307', '19.17455997328363', '19.71441681579431'], 'prelabel': '2-572e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.11337783294175, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 492434641612099950, 'z1': {'__RealLiteral__': 0, 'data': '0.8706000642604717', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.125369086681763', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.922468407648957', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2612.577393493061, 'bad_primes': [2, 11, 13], 'central_character': '1.1', 'conductor': 327184, 'conductor_radical': 286, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, 3, 0, 1, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, -6, 0, -1, 0, -4, 0, 4, 0, 3, 0, 10, 0, 0, 0, -3, 0, -2, 0, 0, 0, 7, 0, -1, 0, -1, 0, -4, 0, 2, 0, -12, 0, 6, 0, 0, 0, 0, 0, -5, 0, 11, 0, 3, 0, 0, 0, -1, 0, 2, 0, 16, 0, -7, 0, 8, 0, 0, 0, 4, 0, -11, 0, -4, 0, -6, 0, -6, 0, -12, 0, 0, 0, -20, 0, 0, 0, 16, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -3, 29], 'euler3': [1, 2, 3], 'euler31': [1, -10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -7, 41], 'euler43': [1, 1, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 5], 'euler53': [1, -6, 53], 'euler59': [1, 5, 59], 'euler61': [1, -11, 61], 'euler67': [1, 1, 67], 'euler7': [1, -3, 7], 'euler71': [1, -16, 71], 'euler73': [1, 7, 73], 'euler79': [1, -4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 12, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 1, 5], [1, -3, 7], [1, 0, 0], [1, 0, 0], [1, -6, 17], [1, 0, 19], [1, 1, 23], [1, -3, 29], [1, -10, 31], [1, 2, 37], [1, -7, 41], [1, 1, 43], [1, 4, 47], [1, -6, 53], [1, 5, 59], [1, -11, 61], [1, 1, 67], [1, -16, 71], [1, 7, 73], [1, -4, 79], [1, 4, 83], [1, 12, 89], [1, -16, 97]], 'index': 104, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/327184/s'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-572e2-1.1-c1-0-104', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-572e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.11337783294175, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 492434641612099950, 'z1': {'__RealLiteral__': 0, 'data': '0.8706000642604717', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '492434641612099950', 'Lhash_array': ['492434641612099950'], 'factors': ['2-572e2-1.1-c1-0-104'], 'label': '2-572e2-1.1-c1-0-104', 'type': 'ECQ', 'url': 'EllipticCurve/Q/327184/s'}