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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1733315270175919912', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.7320508075688774, 0], 'a4': [0.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 1057.985886621157, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [13, [1]]], 'bad_primes': [2, 7, 13], 'central_character': '132496.1', 'coefficient_field': '1.1.1.1', 'conductor': 132496, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1, 3, 5], [1], [1, 5, 11], [1], [1, -1, 17], [1, -7, 19], [1, -1, 23], [1, 2, 29], [1, -5, 31], [1, -11, 37], [1, 6, 41], [1, -12, 43], [1, -7, 47], [1, -11, 53], [1, 3, 59], [1, -5, 61], [1, 1, 67], [1, 0, 71], [1, 11, 73], [1, -5, 79], [1, 4, 83], [1, -5, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 68, 'label': '2-364e2-1.1-c1-0-68', 'leading_term': '2.92294028212', '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/132496/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6100351645635471, 0.6175051545999664, 0.05478700317888004, -0.02249862784679869, 1.725383576131206, 5.087584936685653, 7.429372063188126, 5.804161887502416, 0.6207724253420087, -3.690896453111482, -3.101332170193391, 1.10760440142062, 3.560598786299266, 1.42060589868181, -2.156954287995614, -2.679743264985203, -0.4881256553573672, 0.5508202411874602, -0.6304361746184693, -1.200623456612405, 0.1145139071994439, 0.877349296235978, -0.08927303131755618, -0.008056157964983063, 2.602662952645795, 4.231304417355617, 2.020936670190048, -0.9077953738061039, -0.812530665070158, 0.1222063104190301, -1.143660616939651, 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-1.198813523651281, 2.575662120491802, -0.6943683764491358, -5.065117482208729, -2.030698423483769, 1.33320079229268, -0.9096439398453668, -2.190994896417963, -0.0297704278832765, 0.4353735610866187, -0.202021610497035, 0.7501320344469058, 0.7300482980149681, -0.05040811898038257, 0.5829591075397209, -1.066444996071246, -4.025377078079257, -0.1606734715259376, 4.534333290531427, -3.870017058684527, -15.53093228523418, -10.76003227455038, 2.090315815099786, 3.991505861099353, -0.0522239038880327, 1.020493294944155, 1.969566213107478, -0.4665691650211396, -0.3482252371310821, 0.7674939290592978, -1.166331273852714, -1.772996818885159, -0.03024398579148818, -0.08500802132326699, 0.2996670733393351, 1.743630527106719, -1.132737919614135, -3.979556476391504, 0.3883740683564427], 'positive_zeros': ['0.7751149281360981', '1.007956022344481', '2.277702484922133', '2.937667701739510', '3.590728259506125', '4.310975174085230', '4.643389713110555', '5.231911137569394', '5.729650798303675', '6.001290211678413', '6.900585946123381', '7.414415308813100', '7.562421837459509', '8.100427911917014', '8.791141192857409', '9.537530777511888', '10.10331165895932', '10.39792795964453', '11.11264999751832', '11.20938083976643', '11.92287042321430', '11.96884131176762', '12.60374167035248', '13.04968510843745', '13.51362804826923', '14.10290369712453', '14.91761901180425', '15.33150223533914', '15.73116208347008', '16.05066583794740', '16.40061792984269', '16.81187194407912', '17.46348485820419', '17.82290109667753', '18.38600831097033', '18.53593699845929', '19.02799970139684', '19.54564571478569'], 'prelabel': '2-364e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.526694984599295, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1733315270175919912, 'z1': {'__RealLiteral__': 0, 'data': '0.7751149281360981', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.007956022344481', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.277702484922133', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1057.985886621157, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 132496, 'conductor_radical': 182, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, -3, 0, 0, 0, 6, 0, -5, 0, 0, 0, 9, 0, 1, 0, 7, 0, 0, 0, 1, 0, 4, 0, -9, 0, -2, 0, 5, 0, 15, 0, 0, 0, 11, 0, 0, 0, -6, 0, 12, 0, -18, 0, 7, 0, 0, 0, -3, 0, 11, 0, 15, 0, -21, 0, -3, 0, 5, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, -11, 0, -12, 0, 0, 0, 5, 0, 9, 0, -4, 0, -3, 0, 6, 0, 5, 0, 0, 0, -15, 0, -21, 0, 2, 0, -30, 0], 'euler11': [1, 5, 11], 'euler13': [1, 0, 0], 'euler17': [1, -1, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, 2, 29], 'euler3': [1, 3, 3], 'euler31': [1, -5, 31], 'euler37': [1, -11, 37], 'euler41': [1, 6, 41], 'euler43': [1, -12, 43], 'euler47': [1, -7, 47], 'euler5': [1, 3, 5], 'euler53': [1, -11, 53], 'euler59': [1, 3, 59], 'euler61': [1, -5, 61], 'euler67': [1, 1, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 11, 73], 'euler79': [1, -5, 79], 'euler83': [1, 4, 83], 'euler89': [1, -5, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 3, 5], [1, 0, 0], [1, 5, 11], [1, 0, 0], [1, -1, 17], [1, -7, 19], [1, -1, 23], [1, 2, 29], [1, -5, 31], [1, -11, 37], [1, 6, 41], [1, -12, 43], [1, -7, 47], [1, -11, 53], [1, 3, 59], [1, -5, 61], [1, 1, 67], [1, 0, 71], [1, 11, 73], [1, -5, 79], [1, 4, 83], [1, -5, 89], [1, -2, 97]], 'index': 68, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/132496/b'], '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': '2-364e2-1.1-c1-0-68', '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': '2-364e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.526694984599295, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1733315270175919912, 'z1': {'__RealLiteral__': 0, 'data': '0.7751149281360981', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1733315270175919912', 'Lhash_array': ['1733315270175919912'], 'factors': ['2-364e2-1.1-c1-0-68'], 'label': '2-364e2-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/132496/b'}