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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 1, 'A6': -1, 'A7': 0, 'A8': 1, 'A9': 1, 'Lhash': '1758050801709352950', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2594.100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1, -1]], [7, [1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 13, 17], 'central_character': '324870.1', 'coefficient_field': '1.1.1.1', 'conductor': 324870, 'conductor_radical': 46410, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, -1], [1], [1, 1, 11], [1, -1], [1, -1], [1, 1, 19], [1, 0, 23], [1, 8, 29], [1, 5, 31], [1, 3, 37], [1, 4, 41], [1, 9, 43], [1, 6, 47], [1, -2, 53], [1, -14, 59], [1, -3, 61], [1, 4, 67], [1, 10, 71], [1, -4, 73], [1, -12, 79], [1, -3, 83], [1, -3, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-324870-1.1-c1-0-15', 'leading_term': '2.28320437953', '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/324870/ek', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.283204379526201, 1.058487180835871, -1.714235476206597, -3.718102425684472, -2.962206886642924, -0.1235992595087885, 1.709991046319899, 0.7611945181551655, -0.8123720253405657, 0.1892022353885629, 2.993291737296539, 3.513789352361222, 0.5708096526622756, -1.964399230765982, -1.202981958914188, 0.1628239218888002, -1.265594533576506, -3.483127156649723, -2.675258365730707, -0.09707989088176763, 0.4427639645818259, -0.4681111243361606, 0.1161200596662334, 1.051549132331653, -0.1625497897960907, -1.279025975909303, 0.2896954308665678, 1.221663422665861, -1.058298093805486, -1.737452039881285, 1.774834931213253, 2.459460025792839, -3.010652354475942, -5.279425341349006, 0.7717229857361533, 4.644347868490894, -0.5168815970258023, -4.499183953834963, 0.1693611366951909, 4.484931350237704, 1.914331413576091, -0.1249008297983624, 2.192736738922466, 2.227040757713059, -0.8264523586850655, -0.700656823366256, 1.130913833878952, -0.3026664671836499, -1.304135253264822, 1.409305733718263, 2.415903965854625, -0.02283901208789474, -0.5728982462528153, 0.2507907669727475, -1.121042234152281, -0.6991933460175341, 3.274585695868851, 3.76844148679124, 0.2731172349446487, 0.005835736260795655, 0.9644499681942708, -2.188922811229225, -3.604060122232477, 0.1963168695188462, 1.142853120289564, -1.732094504189335, -0.9866409253865872, 0.557919631544919, -1.689719945448329, -0.7236894302345515, 4.02395613785629, 2.556504971305455, -1.988735923180121, -0.5072972227429478, -0.2004813168582467, -5.674669004219074, -5.260510518646095, 0.4518367144683201, -2.318125521348015, -8.041781261709675, -3.881206136849025, 1.690453628904585, -0.07663879663058976, -0.8392609334890978, 1.442642444535806, 0.2114222886679986, -0.9247035817199619, 1.297846913741928, 1.099338747222224, -0.6716960588798792, 0.08419480049142766, -0.7535076961755457, -2.910375683424988, -1.021078558688301, 0.844182983813645, -0.3184740755398534, 0.6304281813912166, 0.999814229421191, -2.713342659418789, -2.341677376638582, 1.862497074699526, 0.835026309698281, 0.3579630127932917, 4.781157031614787, 2.853016360320677, -2.44644804435424, 0.8510504377849624, 1.642662008156028, -7.095365779170273, -7.546447741535197, 1.256184855902436, 1.890841821597623, -1.226729138735721, 1.225173754530731, 0.8308511888111608, -2.164511900002633, 0.1118386889147133, 1.462208558568301, -0.5639406618171778, 0.5428556224386298, 0.845398433394636], 'positive_zeros': ['0.3523556478233265', '1.260767374135582', '1.848356389649970', '2.230143782203189', '3.040577683247121', '3.681925959423324', '3.838822730886797', '4.762760141693671', '5.111927853958157', '5.477926829006351', '5.978613218349128', '6.466912826615296', '6.904822403755674', '7.388971373143921', '7.879524979838981', '8.474202853459403', '8.981761429146479', '9.493701032570117', '10.15957263886031', '10.27957464606218', '10.92491489905161', '11.32608177156449', '11.71880177629329', '12.14056183544489', '12.74749140394655', '13.12244114489101', '13.33243607121388', '13.80211041321337', '14.52763098417942', '14.74914263410153', '15.10825351703640', '15.73755777908533', '16.09925016277910', '16.59631700026546', '16.83946845438803', '17.28868882693779', '17.86740389768927', '18.29366035436053', '18.48535258824729', '19.21835106812584', '19.40310953650004'], 'prelabel': '2-324870-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.932308120340835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1758050801709352950, 'z1': {'__RealLiteral__': 0, 'data': '0.3523556478233265', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.260767374135582', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.848356389649970', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2594.100010465337, 'bad_primes': [2, 3, 5, 7, 13, 17], 'central_character': '1.1', 'conductor': 324870, 'conductor_radical': 46410, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, 0, 1, 1, 1, -1, -1, 1, 0, -1, 1, 1, 1, -1, 1, 0, -1, 0, -1, 1, 1, -1, 0, -8, -1, -5, 1, 1, 1, 0, 1, -3, -1, -1, 1, -4, 0, -9, -1, 1, 0, -6, -1, 0, 1, -1, 1, 2, -1, -1, 0, 1, -8, 14, -1, 3, -5, 0, 1, 1, 1, -4, 1, 0, 0, -10, 1, 4, -3, -1, -1, 0, -1, 12, 1, 1, -4, 3, 0, 1, -9, 8, -1, 3, 1, 0, 0, 5, -6, -1, -1, 2, 0, -1, 1], 'euler11': [1, 1, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, 1, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 5, 31], 'euler37': [1, 3, 37], 'euler41': [1, 4, 41], 'euler43': [1, 9, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -14, 59], 'euler61': [1, -3, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 10, 71], 'euler73': [1, -4, 73], 'euler79': [1, -12, 79], 'euler83': [1, -3, 83], 'euler89': [1, -3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 1, 11], [1, -1, 0], [1, -1, 0], [1, 1, 19], [1, 0, 23], [1, 8, 29], [1, 5, 31], [1, 3, 37], [1, 4, 41], [1, 9, 43], [1, 6, 47], [1, -2, 53], [1, -14, 59], [1, -3, 61], [1, 4, 67], [1, 10, 71], [1, -4, 73], [1, -12, 79], [1, -3, 83], [1, -3, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/324870/ek'], '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': '2-324870-1.1-c1-0-15', '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': '2-324870-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.932308120340835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1758050801709352950, 'z1': {'__RealLiteral__': 0, 'data': '0.3523556478233265', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1758050801709352950', 'Lhash_array': ['1758050801709352950'], 'label': '2-324870-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/324870/ek'}