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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': -3, 'A8': 1, 'A9': 1, 'Lhash': '1594806734516261999', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 445.3256920726809, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1, -1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '55770.1', 'coefficient_field': '1.1.1.1', 'conductor': 55770, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, 3, 7], [1, -1], [1], [1, -2, 17], [1, 2, 19], [1, -3, 23], [1, -1, 29], [1, 7, 31], [1, -2, 37], [1, 5, 41], [1, -11, 43], [1, 11, 47], [1, -11, 53], [1, -6, 59], [1, 14, 61], [1, 14, 67], [1, 6, 71], [1, 11, 73], [1, 8, 79], [1, 8, 83], [1, -6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 77, 'label': '2-55770-1.1-c1-0-77', 'leading_term': '11.7881587875', '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/55770/cx', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.771997593102425, 4.49119125696157, 4.296266017802166, 2.192641733682598, -0.4903402551134996, -1.824761229792598, -0.9267966842563653, 1.084651119795028, 2.1152953606521, 1.303129816705725, -0.07245038027382306, -0.2564782112573224, 0.6736582640947357, 0.9513270165340079, -0.2487739713225595, -1.328714280172062, -0.4170145234764038, 1.592718586307245, 1.795906463678288, -0.6289267797556578, -2.85035646516766, -2.186654182018932, -0.01342095134675044, 0.3275776600165922, -1.262327863555253, -1.549096689082319, 0.5340762325194499, 1.803611407536933, 0.2316163206166692, -0.8700923543397695, 2.21450230956973, 6.764440611093872, 6.761984401760733, 2.161013738069312, -0.731962356403256, 0.9401526400885167, 2.525416301765489, 0.3033121442234517, -2.161171278446505, -0.8277181022172871, 1.131977702712366, -0.970769913014202, -4.182111229255186, -2.402373022475377, 2.597635761904407, 3.419905549798448, -0.7424268687297351, -3.140046133135376, -0.9774751634834008, 1.098148956927619, 0.272967438290854, -0.4648670433937328, 0.4142680238153635, 0.1753166929654126, -1.570847695672529, -1.518753758781652, 0.3050858507288438, 0.2296965773592955, -1.396317999223775, -0.8304668457815803, 0.7228228848546276, -1.04757641543568, -4.119585723767067, -3.111380174696223, 0.004467639337474084, -0.120617956372117, -0.5340633495967201, 4.250866069397294, 8.88061970019692, 5.0404120088605, -1.791007424630769, -0.440048253153049, 5.934512944768361, 5.791556250753773, -0.07576934590978476, -2.005604493893472, 0.09100909790854084, -0.461970731101551, -2.308513028600847, -0.5353422671711436, 1.605236355006546, -0.2482353307473773, -1.96225752369591, 0.04262656622830989, 1.308864574617063, -0.4303033042370416, -0.5359731342117242, 1.588868368052133, 1.096319423922933, -1.02035879795152, -0.05951344896665269, 1.396883461809555, -0.6867068049039377, -1.751069107821754, 1.793093628298148, 3.753124760327449, 0.6864504394868545, -0.9659190300091592, 1.207148162169369, 1.301080546434395, -1.141092394000377, -0.9901767858177334, 0.2964506887292794, -0.2047943705669672, 2.107477836509254, 7.434870804284603, 6.137334764663646, -1.758779624867905, -3.500568330412054, 1.19590086764432, -0.8598312840007108, -8.470688616601262, -7.734914191562745, -0.03557136446416536, 2.044304738770374, -0.5742582121454781, 0.1129039750456203, 1.341215753176239, -0.5868801806425827, -0.4861178789310912], 'positive_zeros': ['1.199615423258650', '1.866310912672305', '2.732254231274159', '3.082746897729389', '3.709851891431660', '4.301985511752405', '4.946937837186412', '5.752004378905931', '6.063848665012141', '6.695042398331414', '7.276397289917524', '7.613577411331547', '8.635496457768491', '8.909590637770564', '9.522426981530344', '10.07601225886175', '10.43131240625813', '11.11695944853134', '11.70983278559033', '12.33315444089458', '12.79862906809239', '13.14780837598524', '13.52888063884677', '14.20187591650269', '14.53614314628493', '15.10524007045581', '15.41315784309372', '16.24941671238532', '16.47996048954898', '16.80092521655565', '17.66557544378855', '18.01815788735250', '18.74634019392936', '19.23585689609002', '19.44238797662992'], 'prelabel': '2-55770-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.10274134023068, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1594806734516261999, 'z1': {'__RealLiteral__': 0, 'data': '1.199615423258650', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.866310912672305', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.732254231274159', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 445.3256920726809, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 55770, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, -3, 1, 1, 1, 1, 1, 0, -3, 1, 1, 2, 1, -2, 1, -3, 1, 3, 1, 1, 0, 1, -3, 1, 1, -7, 1, 1, 2, -3, 1, 2, -2, 0, 1, -5, -3, 11, 1, 1, 3, -11, 1, 2, 1, 2, 0, 11, 1, 1, -3, -2, 1, 6, 1, -14, -7, -3, 1, 0, 1, -14, 2, 3, -3, -6, 1, -11, 2, 1, -2, -3, 0, -8, 1, 1, -5, -8, -3, 2, 11, 1, 1, 6, 1, 0, 3, -7, -11, -2, 1, 2, 2, 1, 1], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -1, 29], 'euler3': [1, -1, 0], 'euler31': [1, 7, 31], 'euler37': [1, -2, 37], 'euler41': [1, 5, 41], 'euler43': [1, -11, 43], 'euler47': [1, 11, 47], 'euler5': [1, -1, 0], 'euler53': [1, -11, 53], 'euler59': [1, -6, 59], 'euler61': [1, 14, 61], 'euler67': [1, 14, 67], 'euler7': [1, 3, 7], 'euler71': [1, 6, 71], 'euler73': [1, 11, 73], 'euler79': [1, 8, 79], 'euler83': [1, 8, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 3, 7], [1, -1, 0], [1, 0, 0], [1, -2, 17], [1, 2, 19], [1, -3, 23], [1, -1, 29], [1, 7, 31], [1, -2, 37], [1, 5, 41], [1, -11, 43], [1, 11, 47], [1, -11, 53], [1, -6, 59], [1, 14, 61], [1, 14, 67], [1, 6, 71], [1, 11, 73], [1, 8, 79], [1, 8, 83], [1, -6, 89], [1, -2, 97]], 'index': 77, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/55770/cx'], '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': '2-55770-1.1-c1-0-77', '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': '2-55770-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.10274134023068, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1594806734516261999, 'z1': {'__RealLiteral__': 0, 'data': '1.199615423258650', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1594806734516261999', 'Lhash_array': ['1594806734516261999'], 'factors': ['2-55770-1.1-c1-0-77'], 'label': '2-55770-1.1-c1-0-77', 'type': 'ECQ', 'url': 'EllipticCurve/Q/55770/cx'}