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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '297106212790630923', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 258.4597812624805, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [17, [1]]], 'bad_primes': [2, 7, 17], 'central_character': '32368.1', 'coefficient_field': '1.1.1.1', 'conductor': 32368, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 2, 5], [1, -1], [1, 2, 11], [1, 2, 13], [1], [1, 4, 19], [1, 4, 23], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, -12, 47], [1, 14, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, 12, 71], [1, -4, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-32368-1.1-c1-0-1', 'leading_term': '1.20080003509', '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/32368/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.200800035090066, 0.6032448863637755, -1.024369201140052, -3.068758225478795, -4.472370911947752, -4.29844415029467, -2.566588936680881, -0.494454870373851, 0.3868666742026483, -0.3564219306284199, -1.556724945551409, -1.625880203029934, -0.3509952673773652, 0.7815670593045573, 0.3799651400201024, -0.965874249304383, -1.274591262136525, 0.1171120918509027, 1.217203885918008, -0.2700731668621633, -3.475566655558167, -4.663221054729349, -1.815368769768183, 2.138303608867821, 2.320437351823614, -1.997278269855327, -6.149417075545339, -5.744464742488028, -1.915319948577856, 0.7896192904855013, 0.5726702339904369, -0.1847403951000245, 0.4409537742270037, 1.007070893431673, -0.06836168836217987, -1.140439200467038, -0.06524452262959861, 1.4920401792995, 0.2393452987706118, -2.83671372801123, -3.078550095606736, 0.4928659573565169, 2.938209151775065, 0.8985801412938317, -1.89383468140918, -0.5862423072131577, 2.755905966078433, 2.557275698121421, -0.8703663965718706, -1.854558921842299, 0.9979456467440923, 2.605002615408115, 0.3574839332119372, -1.506048213727568, 0.4247583938020173, 2.874433551290571, 2.009287613431041, -0.02403257738489846, 0.2333739439418876, 1.193384812371025, 0.1471963871347616, -0.9545042935622545, 0.2140784042854573, 0.7130679941239713, -2.153212647292614, -4.138788694706611, -0.8162937456042901, 3.250046633114803, 1.33450132045532, -3.203524692137359, -2.035599237344725, 3.583273430789561, 4.893820166224559, 0.6811327511436587, -1.667644725316597, 0.3284342319187688, 1.476801388357963, -0.1027891265312382, -0.5325199802370923, 0.8530189394617365, 0.645448505439117, -0.7349257461343, -0.2673452502048534, 0.1243497394552014, -2.682444610459561, -4.896483522877123, -2.097881547449648, 1.068859794592318, -0.981477312737196, -3.078224287085683, 1.56962080979609, 7.548691270559572, 6.169234723475117, 0.7633618516473504, -0.6485904490818964, 0.2076283176306686, -1.773099163714329, -3.287729699576655, -0.1485275421275116, 2.911022792181121, 1.400381832975376, -0.2863852700425018, 1.315431702913786, 1.942874612372177, -0.2775355166524201, -0.6993376844589562, 1.278777897566134, 1.035987811003287, -0.5030599239725305, 0.9405891970224901, 2.333571513206768, -0.4954197122154329, -2.193766635158083, 1.642211679372999, 3.38773774093385, -2.166551262941074, -5.750126240662499, -0.6450827032424586, 4.219672090169759, 1.522701537532558, -1.792042405111589], 'positive_zeros': ['0.3584623519317678', '1.836015796499907', '2.173187230716611', '3.058857926708224', '3.573477965951280', '4.233201187751698', '4.725267974285974', '5.603929069100757', '6.152463052868837', '7.142635020808768', '7.645313697720401', '7.881998018660280', '8.489160750297061', '9.008377126875359', '9.520518339694775', '10.21993841805036', '10.81364072917071', '11.29223304010648', '11.93626879518887', '12.42565494775902', '13.02960563004189', '13.46548439813770', '14.24471242844370', '14.44907830473147', '15.02123693296786', '15.46832666857015', '15.83939715534293', '16.53929188586111', '17.06627811703091', '17.59314493116599', '18.28941393036248', '18.71850008818270', '19.23509638795534', '19.60163638848093'], 'prelabel': '2-32368-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.076684398920086, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 297106212790630923, 'z1': {'__RealLiteral__': 0, 'data': '0.3584623519317678', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.836015796499907', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.173187230716611', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 258.4597812624805, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 32368, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 1, 0, 1, 0, -2, 0, -2, 0, -4, 0, 0, 0, -4, 0, 2, 0, -4, 0, -1, 0, -4, 0, -2, 0, -8, 0, -4, 0, -2, 0, 2, 0, -4, 0, 0, 0, -4, 0, -2, 0, 12, 0, 1, 0, 0, 0, -14, 0, 4, 0, -8, 0, -12, 0, 10, 0, 1, 0, 4, 0, -4, 0, -8, 0, -12, 0, 4, 0, -2, 0, -2, 0, -4, 0, -11, 0, 12, 0, 0, 0, -4, 0, 6, 0, -2, 0, -16, 0, 8, 0, 0, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 14, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 2, 5], [1, -1, 0], [1, 2, 11], [1, 2, 13], [1, 0, 0], [1, 4, 19], [1, 4, 23], [1, 2, 29], [1, 8, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, -12, 47], [1, 14, 53], [1, 12, 59], [1, -10, 61], [1, 4, 67], [1, 12, 71], [1, -4, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, 0, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32368/bd'], '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': '2-32368-1.1-c1-0-1', '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': '2-32368-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.076684398920086, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 297106212790630923, 'z1': {'__RealLiteral__': 0, 'data': '0.3584623519317678', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '297106212790630923', 'Lhash_array': ['297106212790630923'], 'label': '2-32368-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32368/bd'}