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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '693328990289388607', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2929.807070643204, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '366912.1', 'coefficient_field': '1.1.1.1', 'conductor': 366912, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1], [1], [1, 3, 5], [1], [1, 3, 11], [1, -1], [1, 7, 17], [1, -1, 19], [1, 1, 23], [1, 2, 29], [1, -9, 31], [1, -3, 37], [1, 10, 41], [1, 4, 43], [1, 3, 47], [1, 1, 53], [1, 11, 59], [1, -1, 61], [1, -7, 67], [1, 8, 71], [1, 7, 73], [1, 11, 79], [1, 4, 83], [1, 1, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 138, 'label': '2-366912-1.1-c1-0-138', 'leading_term': '3.7066989837', '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/366912/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6563303099195223, -0.02744110122862372, -2.016771360262441, -3.349173056007581, -1.924366305013693, 1.471911698937654, 3.181569018544382, 1.105804192077561, -1.997803305817559, -1.958979151564457, 0.7487191092330219, 1.773650369012021, -0.07711828356483862, -0.9847695193663608, 1.041667271986294, 2.519961758954122, 0.9159679051016566, -0.6717453723905802, 0.09090461495329377, -0.4773337825265674, -4.697085427893086, -7.159511798772345, -3.580107025998894, 0.526955138875768, -0.8971940735697372, -3.667358132645198, -1.838103508127891, 1.086578077539096, 0.08050346941867435, -1.3541985316872, 0.5057689927005513, 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-0.3237462253418704, 2.405448219483241, 4.603192982331498, -0.9961922448178748, -4.014954162296423, 0.4152654901428852, 0.4531281630728809, -3.351647305424942, -1.267806006479365, 0.9836294904930581, -1.521005159712921, -1.418314704737469, 0.2395687209906145, -1.069846034725042, 0.1698184375415139, 2.490702531550617, -0.20917073083947, -0.6488557579472489, 2.28877398594639, -2.768550142029096, -9.354169291441718, -4.734354207170027, 1.05107121108228, -0.1799887871653433, -0.104119175345288, 0.6846214735296335, -1.653275005702658, -0.6076397707865497, 1.352389300379973, -1.921495523838383, -2.377960610340199, 1.161576748960299, 0.2238703333221265, -0.0737642593643455, 2.491971734272331, -1.408990696939266, -4.514371975326527, 2.350173219562962, 5.448581684184322], 'positive_zeros': ['0.4954316545192265', '1.394104768746960', '2.079087134667207', '2.682647864432714', '3.241120000984169', '3.647864311756290', '4.352805769909178', '4.728532676125892', '4.945256263339454', '5.943041203730555', '6.179423197520230', '6.878150954844761', '7.258563306653858', '7.700723756288172', '8.245660398282465', '8.555828435159155', '8.854533400481422', '9.665497323263322', '10.06765873930329', '10.54154742325340', '11.02229170568073', '11.53790731071722', '11.64464282051550', '12.17034010291879', '12.79743482747857', '13.23394916800388', '13.38005940201242', '14.08397694937966', '14.45080123823131', '15.28120383916165', '15.34375096744710', '15.70441011575633', '15.93267267277424', '16.63581498598233', '16.96096340392071', '17.49194246569668', '17.98677484274012', '18.43253767861122', '18.61215755626474', '19.29717187784319', '19.51516815571277', '19.98964390180080'], 'prelabel': '2-366912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.127692271546216, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 693328990289388607, 'z1': {'__RealLiteral__': 0, 'data': '0.4954316545192265', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.394104768746960', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.079087134667207', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2929.807070643204, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 366912, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, -7, 0, 1, 0, 0, 0, -1, 0, 4, 0, 0, 0, -2, 0, 9, 0, 0, 0, 0, 0, 3, 0, 0, 0, -10, 0, -4, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 9, 0, 0, 0, -11, 0, 1, 0, 0, 0, -3, 0, 7, 0, 0, 0, -8, 0, -7, 0, 0, 0, 0, 0, -11, 0, 0, 0, -4, 0, 21, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0], 'euler11': [1, 3, 11], 'euler13': [1, -1, 0], 'euler17': [1, 7, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -9, 31], 'euler37': [1, -3, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 3, 47], 'euler5': [1, 3, 5], 'euler53': [1, 1, 53], 'euler59': [1, 11, 59], 'euler61': [1, -1, 61], 'euler67': [1, -7, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 7, 73], 'euler79': [1, 11, 79], 'euler83': [1, 4, 83], 'euler89': [1, 1, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 3, 5], [1, 0, 0], [1, 3, 11], [1, -1, 0], [1, 7, 17], [1, -1, 19], [1, 1, 23], [1, 2, 29], [1, -9, 31], [1, -3, 37], [1, 10, 41], [1, 4, 43], [1, 3, 47], [1, 1, 53], [1, 11, 59], [1, -1, 61], [1, -7, 67], [1, 8, 71], [1, 7, 73], [1, 11, 79], [1, 4, 83], [1, 1, 89], [1, -2, 97]], 'index': 138, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/366912/bf'], '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': '2-366912-1.1-c1-0-138', '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': '2-366912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.127692271546216, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 693328990289388607, 'z1': {'__RealLiteral__': 0, 'data': '0.4954316545192265', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '693328990289388607', 'Lhash_array': ['693328990289388607'], 'factors': ['2-366912-1.1-c1-0-138'], 'label': '2-366912-1.1-c1-0-138', 'type': 'ECQ', 'url': 'EllipticCurve/Q/366912/bf'}