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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': 1, 'A9': 1, 'Lhash': '1791777021084258993', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1819.3914100548745, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1]], [7, [1]], [31, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 31], 'central_character': '227850.1', 'coefficient_field': '1.1.1.1', 'conductor': 227850, 'conductor_radical': 6510, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1], [1], [1, 4, 11], [1, 4, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, -4, 29], [1, 1], [1, 4, 37], [1, -6, 41], [1, -8, 43], [1, 12, 47], [1, -2, 53], [1, 6, 59], [1, 10, 61], [1, -10, 67], [1, 14, 71], [1, -4, 73], [1, 8, 79], [1, 4, 83], [1, -8, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 105, 'label': '2-227850-1.1-c1-0-105', 'leading_term': '6.92258519839', '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/227850/fc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.418278185964578, 1.16975143156101, -1.2552791674643, -4.272473897700794, -5.113553942304436, -2.734009078703845, 0.5059630949837886, 1.291637424641027, -0.4741844115449119, -1.56032954639615, -0.1799360473959309, 1.127797481431506, -0.6150851775371062, -3.735509016494018, -3.99148997266107, -1.073285036311501, 1.005795653747728, 0.3872325004550675, -0.3104494336294103, 0.4804789741777818, 0.4520565082912371, -1.403558008209212, -2.094589487606974, -0.4659055986737987, -0.08637644829285376, -2.333424944309808, -3.023613535078308, -0.5232308146292367, 0.4702187050124514, -1.436388113292996, -0.3803127576103349, 4.648723771671578, 5.24670559575352, -0.8774436694339811, -3.155091649499422, 3.491574656503656, 8.394169941758841, 3.973356304118557, -1.205031740840153, 0.6044370778898382, 3.209473963235946, 0.977167361304673, -0.9018513395083305, 0.5576469935974941, 0.2649802425488196, -2.264050619167335, -1.581515077844275, 1.127283733812375, 0.6330741780024651, -0.8896129572074983, 0.2567204859835525, 0.741152805249598, -0.7986846355759688, 0.3817120108147882, 3.22917159494404, 1.830983899824194, -0.7592054338269608, 1.524917590428362, 3.921392646338069, 1.211025868077933, -0.8586552393706481, 0.9462310372353315, 1.061910375039725, -0.11651538626884, 2.368071123568199, 3.72488832951814, -0.5137457763644343, -2.410037552869715, 1.168453399415286, 1.353884664317429, -1.748457728969028, -0.1452808769602953, 0.9486899244885525, -4.986112975725971, -7.290583824954545, -0.2469611511937612, 3.294218363006667, -0.2948241591145279, 0.2434280813667184, 3.423857465499228, 0.01441088294889262, -3.797663999403251, -1.01630845300441, 0.6840526111713249, -1.733428857033361, -1.466338192709709, 0.1073607272091481, -1.327904609734958, -1.365652952659102, 0.8508308930205426, 0.4219159339467454, -0.07561922872871524, 2.001273183574939, 1.546345726205454, -0.611670051766859, 0.6599483066023655, 1.387010914199211, -0.4658958401564524, -0.000151989399608776, -1.929307601162209, -10.41468837303721, -12.45615336683584, -3.692788578801854, 0.8291477897113494, -0.0399082467934156, 4.10296071159939, 5.471045066108301, -1.985348187704418, -4.204853256444935, 0.1282126710313092, -2.700900315960359, -6.962279992419836, -1.995647119574311, 2.384900414645236, 0.4410314602154421, 0.1442313525247696, 0.6960826393755153, -0.4166690588049145, 2.168720922193274, 4.146742306137718], 'positive_zeros': ['0.6427696588379394', '1.702347792048421', '2.193390830401888', '2.772235242089721', '3.197592279624541', '4.091738662478755', '4.582930916893987', '4.878267960554994', '5.325136365604348', '6.083471776557163', '6.231435797886091', '7.053796004694905', '7.326421441480684', '7.772909892056431', '8.466670973427074', '8.892915269685332', '9.657813052068305', '9.960729507183488', '10.57884131693311', '10.92121698451834', '11.27798089461650', '11.88077279847546', '12.32604255691775', '12.71303446434439', '13.11889268451424', '13.46716738756175', '14.13693777767284', '14.39250451792419', '15.08746696944772', '15.39228366909468', '15.91563308876564', '16.03667466027923', '16.72422203224949', '17.17423217711695', '17.59721429606011', '18.01069438228567', '18.31090451241500', '19.00799686589688', '19.47800083412656', '19.73337464787501'], 'prelabel': '2-227850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.65432463484652, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1791777021084258993, 'z1': {'__RealLiteral__': 0, 'data': '0.6427696588379394', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.702347792048421', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.193390830401888', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1819.3914100548745, 'bad_primes': [2, 3, 5, 7, 31], 'central_character': '1.1', 'conductor': 227850, 'conductor_radical': 6510, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 0, 1, 1, 0, -4, -1, -4, 0, 0, 1, -6, 1, 0, 0, 0, -4, 0, -1, 0, -4, -1, 0, 4, 0, -1, 1, 4, -6, 0, 1, -4, 0, 4, 0, 6, 0, 8, -4, 0, 0, -12, -1, 0, 0, 6, -4, 2, -1, 0, 0, 0, 4, -6, 0, -10, -1, 0, 1, 0, 4, 10, -6, 0, 0, -14, 1, 4, -4, 0, 0, 0, 4, -8, 0, 1, 6, -4, 0, 0, 8, -4, -4, 8, 0, 0, 0, 1, -12, 0, -1, -2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 1, 0], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, -10, 67], 'euler7': [1, 0, 0], 'euler71': [1, 14, 71], 'euler73': [1, -4, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -8, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 4, 11], [1, 4, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, -4, 29], [1, 1, 0], [1, 4, 37], [1, -6, 41], [1, -8, 43], [1, 12, 47], [1, -2, 53], [1, 6, 59], [1, 10, 61], [1, -10, 67], [1, 14, 71], [1, -4, 73], [1, 8, 79], [1, 4, 83], [1, -8, 89], [1, 2, 97]], 'index': 105, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/227850/fc'], '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': '2-227850-1.1-c1-0-105', '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': '2-227850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.65432463484652, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1791777021084258993, 'z1': {'__RealLiteral__': 0, 'data': '0.6427696588379394', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1791777021084258993', 'Lhash_array': ['1791777021084258993'], 'label': '2-227850-1.1-c1-0-105', 'type': 'ECQ', 'url': 'EllipticCurve/Q/227850/fc'}