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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '1624874030218871202', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 527.5396659937912, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1, 1]], [11, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 7, 11, 13], 'central_character': '66066.1', 'coefficient_field': '1.1.1.1', 'conductor': 66066, 'conductor_radical': 6006, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 0, 5], [1, 1], [1], [1, -1], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, -10, 29], [1, -2, 31], [1, -8, 37], [1, -6, 41], [1, 2, 43], [1, 4, 47], [1, 6, 53], [1, 10, 59], [1, -6, 61], [1, 2, 67], [1, -6, 71], [1, 6, 73], [1, 0, 79], [1, 4, 83], [1, -6, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 47, 'label': '2-66066-1.1-c1-0-47', 'leading_term': '3.45250397028', '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/66066/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7552192849207033, 0.9134799044939272, 0.2086948507437079, -0.8879838910488203, -1.26521581932213, -0.1752571403970168, 1.654756370629475, 2.317718755055604, 0.7381963160620442, -1.62125752886851, -1.865991461546243, 0.9103860915397312, 3.892881488295559, 3.419228574984082, -0.3500613552108983, -3.089750525046887, -1.6125833625261, 1.731312661744642, 1.908114949690256, -1.968633822267556, -5.266972173489178, -4.170734226296142, -0.7429013803096682, 0.6264889440274903, -0.2345474835065985, 0.09171016174467984, 2.224957355705451, 2.696510803520266, 0.05272797623230665, -2.158086591026761, -1.062487854157671, 0.739076113001145, -0.2037015749045823, -2.001273243931749, -0.7309178723298432, 2.371289278858819, 2.743183079225813, 0.2903524796010827, -0.8249738239826121, 0.1899632299785105, -0.06480486452089662, -1.998945705651624, -2.05562243230809, -0.04829223954264157, -0.0903847229198371, -2.520613769336814, -2.778965628667948, -0.3834236093815794, -0.2702832859128886, -2.67118942721424, -1.660307222270721, 2.837067343212515, 2.928832564703354, -2.722186936975148, -4.691536436785046, 0.7664711956419334, 4.229755969849893, -0.291417711051969, -4.680620258295876, -1.594814585196658, 3.081888824968252, 2.243391918041627, -0.4633343881850203, 0.011050554626937, 0.7111542171571062, -1.089713189496661, -1.7193047911701, 0.3391163386009565, 0.9670908278655994, -0.5232598054916613, -0.2496424546103847, 1.143370153596794, -0.0235590140480654, -1.575327380034875, 0.1664232419980111, 1.850314273455579, 0.1152651587633031, -0.8694930526658111, 0.9981118767238129, 0.1698700070423219, -3.893080170624689, -3.359817177019867, 2.03334094426116, 3.232395609466208, -0.3066857895525699, -0.7025656651977916, 0.6905815217340565, -2.980078839178813, -6.980575544253715, -3.371253181322956, 1.93487821535164, 0.7512896094270435, -1.712228598279178, -0.1075039580512787, -0.315843628980139, -4.023347934250421, -2.965987496965267, 2.80345971898893, 3.693263254513157, 0.004604871775561464, -0.3506587818115359, 0.814964234407235, -1.691768710045003, -3.296744091080561, -0.520818913607325, 0.446089638179487, -2.230907921160659, -2.181739805250432, 0.4958291477293764, 0.3892717266674618, -0.5126627257529595, 1.143997306782946, 1.510211646331031, -0.4766507104057939, -0.09832932304283022, 1.313222131375559, -0.2354609245408828, -0.6879191077124273, 2.0804012181791, 1.718243740990297], 'positive_zeros': ['0.7978887691945390', '1.524833864243290', '2.323202826519019', '2.934941004520474', '3.728910802138176', '4.363812768570230', '4.890897136691111', '5.823966435261240', '6.188502657750104', '6.484953629747495', '7.254069914758283', '7.868871189236362', '8.225489460910975', '8.808170157941690', '9.531357281838475', '9.955290944368863', '10.23915180411900', '11.00756573592493', '11.23691726702358', '12.05703860132792', '12.20791707603471', '12.84462772270512', '13.38896388138846', '13.97103552047473', '14.48881492926551', '15.06949365707272', '15.68556920335392', '15.99818719522202', '16.37342669932226', '16.96147258768426', '17.41050117096891', '17.78819137019529', '18.24740081614594', '18.73486111416969', '19.26217403629362', '19.62814125561862'], 'prelabel': '2-66066-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.968231668846236, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1624874030218871202, 'z1': {'__RealLiteral__': 0, 'data': '0.7978887691945390', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.524833864243290', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.323202826519019', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 527.5396659937912, 'bad_primes': [2, 3, 7, 11, 13], 'central_character': '1.1', 'conductor': 66066, 'conductor_radical': 6006, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 0, -1, 1, 1, 0, 1, 2, -1, -4, 0, 1, 0, -4, 1, -5, -1, -1, -1, 10, 0, 2, -1, 0, -2, 0, 1, 8, 4, -1, 0, 6, -1, -2, 0, 0, 4, -4, -1, 1, 5, -2, 1, -6, 1, 0, 1, 4, -10, -10, 0, 6, -2, -1, 1, 0, 0, -2, 2, 4, 0, 6, -1, -6, -8, 5, -4, 0, 1, 0, 0, 1, -6, -4, 1, 0, 2, -10, 0, 6, 0, -1, -4, -2, 4, 0, 1, -8, -1, 0, -5], 'euler11': [1, 0, 0], 'euler13': [1, -1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -8, 37], 'euler41': [1, -6, 41], 'euler43': [1, 2, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 10, 59], 'euler61': [1, -6, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -6, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 5], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, -10, 29], [1, -2, 31], [1, -8, 37], [1, -6, 41], [1, 2, 43], [1, 4, 47], [1, 6, 53], [1, 10, 59], [1, -6, 61], [1, 2, 67], [1, -6, 71], [1, 6, 73], [1, 0, 79], [1, 4, 83], [1, -6, 89], [1, 8, 97]], 'index': 47, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/66066/l'], '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': '2-66066-1.1-c1-0-47', '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': '2-66066-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.968231668846236, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1624874030218871202, 'z1': {'__RealLiteral__': 0, 'data': '0.7978887691945390', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1624874030218871202', 'Lhash_array': ['1624874030218871202'], 'factors': ['2-66066-1.1-c1-0-47'], 'label': '2-66066-1.1-c1-0-47', 'type': 'ECQ', 'url': 'EllipticCurve/Q/66066/l'}