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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '150254463348015843', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 114.9845789106438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '14400.1', 'coefficient_field': '1.1.1.1', 'conductor': 14400, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1, -4, 11], [1, -4, 13], [1, -6, 17], [1, 4, 19], [1, 4, 23], [1, 4, 29], [1, 0, 31], [1, -4, 37], [1, 8, 41], [1, 0, 43], [1, 12, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, 8, 67], [1, -8, 71], [1, -16, 73], [1, -8, 79], [1, -8, 83], [1, 0, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 97, 'label': '2-120e2-1.1-c1-0-97', 'leading_term': '4.55985208358', '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/14400/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.080964400286556, 1.789937103017254, 1.747622212814647, 0.8009780582890526, -0.6645554769897302, -1.729080533443223, -1.464743963477294, 0.2873088844305824, 2.55491925620441, 3.802217612926821, 3.163325314861487, 1.287770208643362, -0.1600380824962071, -0.1026993909438044, 0.7713475049592216, 0.6483876029068866, -1.350323532321852, -3.843395667975924, -4.318878083955215, -1.821382482557476, 1.74272241286307, 3.418041129399025, 2.315259301416835, 0.4153638592407418, -0.01396375577003775, 0.7344300842408187, 0.3806879137612868, -1.95174713302347, -4.044619266814317, -3.20364834605212, -0.01178553301262935, 1.95610663325519, 0.5335094910880546, -2.214122603114217, -2.704507045090113, -0.5633031466964283, 1.144283278758055, 0.4781200220401444, -0.6422722625145298, 0.3949962086057574, 2.552427517197303, 2.414350684943513, -0.4820086102948461, -2.368361817693884, -0.4724732318998229, 2.798872558720177, 3.210041011350628, 0.7882456998445115, -0.5382526817805391, 0.850702907797832, 1.947325557133318, 0.2883793037374576, -1.838236572710404, -1.165360179404813, 0.9021058596553118, 0.324430376601595, -2.80326682636987, -3.98385733309057, -1.49373252561186, 0.6128475764489167, -1.091993942519837, -3.888629513220597, -3.367391486828014, -0.4565664759860184, 0.6096261576746661, -0.4593663259563916, -0.2158981644836525, 1.463263593383382, 0.4759475276380984, -3.934979262879297, -6.466744222889314, -3.664303305548358, 0.4433642546475156, 0.7600728871821641, -1.110842616026154, -0.6794224068597411, 1.373067685473713, 1.210945234445119, -0.4186903532129082, 0.4949022959700604, 3.131839083702591, 2.496307304019204, -1.449680493591754, -2.856965062727519, 0.1630787428772237, 2.250909487672406, 0.1615844141273724, -1.914255961432307, -0.3270986902945726, 1.737227111188984, 0.8882141035291906, -0.1274518285791384, 1.472699957371143, 2.271403282680492, -0.7699600324387053, -3.216336137371871, -0.2216582151497052, 4.333263277882394, 3.909564394647587, 0.116166593000926, -1.045581688521317, 0.3232133620265488, 0.2495482169733661, -0.1599327971704799, 2.40911585875091, 4.914762354155234, 2.270668981979432, -2.512795545170361, -2.586211561218765, 0.9453215894045097, 1.752022290908215, 0.06402766359187294, 0.9064995347213252, 3.148725059746825, 1.613119723238977, -2.093519164975325, -2.114300416677904, 0.5470210188195761, 0.5143647702957505, -1.203574147034541], 'positive_zeros': ['1.138975776607557', '1.967542702135946', '3.205073973628076', '3.532652904237496', '4.106245630737826', '5.123194238908634', '6.104997042216896', '6.257204333242348', '6.805396225745496', '7.750913280924547', '8.296877066396202', '9.058151252710508', '9.580882031426038', '9.949846600800077', '10.71272636833609', '11.28412785484713', '12.08841149464404', '12.38574315425292', '13.02748211362506', '13.62833067042053', '14.03132632014166', '14.88138829688207', '15.15054241606149', '16.04951347676580', '16.40145334237691', '16.78401873566803', '17.28426452878397', '18.21221407662809', '18.59748502860870', '19.07967059323756', '19.66821764781239', '19.94482366857830'], 'prelabel': '2-120e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.723086258659109, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 150254463348015843, 'z1': {'__RealLiteral__': 0, 'data': '1.138975776607557', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.967542702135946', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.205073973628076', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 114.9845789106438, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 14400, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 6, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, -12, 0, 9, 0, 0, 0, -2, 0, 0, 0, 0, 0, -12, 0, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 16, 0, 0, 0, -16, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -4, 37], 'euler41': [1, 8, 41], 'euler43': [1, 0, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -16, 73], 'euler79': [1, -8, 79], 'euler83': [1, -8, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, -4, 11], [1, -4, 13], [1, -6, 17], [1, 4, 19], [1, 4, 23], [1, 4, 29], [1, 0, 31], [1, -4, 37], [1, 8, 41], [1, 0, 43], [1, 12, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, 8, 67], [1, -8, 71], [1, -16, 73], [1, -8, 79], [1, -8, 83], [1, 0, 89], [1, -8, 97]], 'index': 97, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/14400/s'], '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': '2-120e2-1.1-c1-0-97', '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': '2-120e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.723086258659109, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 150254463348015843, 'z1': {'__RealLiteral__': 0, 'data': '1.138975776607557', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '150254463348015843', 'Lhash_array': ['150254463348015843'], 'label': '2-120e2-1.1-c1-0-97', 'type': 'ECQ', 'url': 'EllipticCurve/Q/14400/s'}