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lfunc_lfunctions • Show schema
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{'A10': 6, 'A2': 2, 'A3': -1, 'A4': 2, 'A5': 3, 'A6': -2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '449500763575691970', 'a10': [1.8973665961010275, 0], 'a2': [1.414213562373095, 0], 'a3': [-0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [1.3416407864998738, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, 1], [1, -3, 5], [1], [1, -2, 11], [1, 1], [1, 1], [1, 1, 19], [1, -3, 23], [1, -7, 29], [1, -5, 31], [1, -6, 37], [1, 6, 41], [1, -11, 43], [1, 5, 47], [1, -1, 53], [1, -4, 59], [1, 6, 61], [1, -8, 67], [1, -2, 71], [1, 5, 73], [1, -1, 79], [1, -3, 83], [1, 1, 89], [1, -15, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-32487-1.1-c1-0-6', 'leading_term': '5.87185076478', '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': 0, 'origin': 'EllipticCurve/Q/32487/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.871850764782819, 5.11289210987067, 2.976227473743903, 0.08991885417308292, -2.296790457381303, -2.896123645236452, -1.427601156552461, 0.8892682732436289, 2.160951957379415, 1.487702240510024, -0.1123952792007905, -0.6818191137313697, 0.5793880259472235, 2.351429731261366, 2.625609147108165, 1.031377648907484, -0.7237881013795245, -0.9406384790135576, 0.0491222653997401, 0.5564675469784968, -0.04467860974376895, -0.5760972001264771, -0.04226901712858781, 0.727329455930805, 0.4674347485374648, -0.2640549251174475, 0.01147320311143765, 0.5579375856061533, -1.405588944358231, -5.917612106603969, -7.816352058547698, -2.342724514388027, 7.246979639494439, 11.58907047348179, 6.3545624574614, -1.866218811600434, -3.918906655365908, 0.222605694373219, 2.73667254606645, -0.1012741299155442, -3.169045399446584, -1.38584960782887, 2.285287037436076, 2.032194261784467, -1.498680533739229, -2.789941502173221, -0.4965797948515065, 1.175589082235356, 0.03587362679520441, -1.043372287494858, 0.05722874503920179, 1.203180354006388, 0.5574938021459539, -0.1004374862335843, 0.6931178074218463, 1.159300515575545, 0.1789668137921317, -0.1637503550269543, 0.9602768102272281, 0.7286682182970957, -1.720898024823839, -2.409341363611775, 0.3756763977751468, 1.716934919836666, -1.623623127224735, -4.446029100256822, -1.616451296076057, 2.584163489981076, 1.943266044156139, -0.682791890530395, 0.3915857142239068, 2.20015371303545, -0.5836949290490975, -3.204923464859212, 1.782147698256104, 8.862732422172016, 6.524435767010117, -2.61009790217422, -4.802676437022245, 2.318241954053924, 6.758434285862852, 2.698276754467383, -1.973134949753985, -1.175333393432588, 0.9886471494173967, 0.5959388549237074, -0.04108733697188235, 0.520480932476518, 0.2475666408990603, -0.6316047648986668, -0.09037926004463138, 0.5407227571660197, -0.4866475319753811, -0.7719195011594452, 1.042857397045733, 1.396226620805667, -0.907246656988443, -1.596447590717887, 0.1533807425550203, -0.03645701113445624, -1.668497908553202, -0.2942072525711707, 0.8036724391335416, -4.313994581522011, -8.960023737912492, -2.786089669706432, 7.109109336025393, 6.094478332784373, -1.623750149044757, -0.9806659625589375, 5.529002390517609, 3.647435811199757, -4.773839036947698, -6.009705525589544, -0.05232812180558927, 2.236810026074748, 0.02150147446776928, -0.3246402778465017, 0.240599224893388, -1.510125957675311, -2.251300846167402], 'positive_zeros': ['0.7578248479287795', '1.651518763062426', '2.480291947926033', '2.916724474701606', '3.879717479635606', '4.488096559111814', '4.986716720151904', '5.511402088164677', '6.141163132151997', '6.496449185760815', '6.877579615587343', '7.812482243694367', '8.683471398869552', '9.238273299763628', '9.744014848869085', '10.33527529658437', '10.89696861768821', '11.54620844190860', '12.00503638530148', '12.49148614566179', '13.14800293621028', '13.31835253881075', '14.04317324423189', '14.30033080585966', '14.83601788946529', '15.47103734965091', '15.90609205194304', '16.58080281675356', '17.16135327266472', '17.46188247410568', '17.96617817642431', '18.44238333021513', '19.17501103303395', '19.68007503449033'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 449500763575691970, 'z1': {'__RealLiteral__': 0, 'data': '0.7578248479287795', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.651518763062426', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.480291947926033', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, 2, -1, 2, 3, -2, 0, 0, 1, 6, 2, -2, -1, 0, -3, -4, -1, 2, -1, 6, 0, 4, 3, 0, 4, -2, -1, 0, 7, -6, 5, -8, -2, -2, 0, 2, 6, -2, 1, 0, -6, 0, 11, 4, 3, 6, -5, 4, 0, 8, 1, -2, 1, -2, 6, 0, 1, 14, 4, -6, -6, 10, 0, -8, -3, -4, 8, -2, -3, 0, 2, 0, -5, 12, -4, -2, 0, 2, 1, -12, 1, -12, 3, 0, -3, 22, -7, 0, -1, 6, 0, 6, -5, -10, -3, 8, 15, 0, 2, 8], 'euler11': [1, -2, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 1, 19], 'euler2': [1, -2, 2], 'euler23': [1, -3, 23], 'euler29': [1, -7, 29], 'euler3': [1, 1, 0], 'euler31': [1, -5, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -11, 43], 'euler47': [1, 5, 47], 'euler5': [1, -3, 5], 'euler53': [1, -1, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, -2, 71], 'euler73': [1, 5, 73], 'euler79': [1, -1, 79], 'euler83': [1, -3, 83], 'euler89': [1, 1, 89], 'euler97': [1, -15, 97], 'euler_factors': [[1, -2, 2], [1, 1, 0], [1, -3, 5], [1, 0, 0], [1, -2, 11], [1, 1, 0], [1, 1, 0], [1, 1, 19], [1, -3, 23], [1, -7, 29], [1, -5, 31], [1, -6, 37], [1, 6, 41], [1, -11, 43], [1, 5, 47], [1, -1, 53], [1, -4, 59], [1, 6, 61], [1, -8, 67], [1, -2, 71], [1, 5, 73], [1, -1, 79], [1, -3, 83], [1, 1, 89], [1, -15, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/n'], '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': '2-32487-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 449500763575691970, 'z1': {'__RealLiteral__': 0, 'data': '0.7578248479287795', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '449500763575691970', 'Lhash_array': ['449500763575691970'], 'label': '2-32487-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/n'}