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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '299025842416991723', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 105.40253066809017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '13200.1', 'coefficient_field': '1.1.1.1', 'conductor': 13200, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 0, 7], [1, -1], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, -12, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 0, 79], [1, -4, 83], [1, 6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 29, 'label': '2-13200-1.1-c1-0-29', 'leading_term': '2.2535923986', '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/13200/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.253592398604086, 1.976350690392091, 1.200627850633772, 0.1848855331541218, -0.5308212595094359, -0.3414092285397028, 0.9359702648551136, 2.685153190872136, 3.682396640490273, 2.938376563179773, 0.630495851163206, -1.763023271758337, -2.517876718948456, -1.187151383250029, 0.8302358544205539, 1.456450193073869, -0.06502877849245697, -2.323367406490399, -3.111499936736566, -1.754326271429572, 0.1305334048697321, 0.4435593088067441, -0.9586646789987626, -2.102316169639103, -1.367089825740035, 0.3715786617872261, 0.7623160541769581, -0.9003498845600095, -2.475689439823361, -1.584566430135573, 1.114445667858961, 2.459777766550391, 0.8620580988343131, -1.345692909557703, -0.7551033766201009, 2.507225440876267, 4.650047042063981, 3.073497647803353, -0.2213386691321093, -1.410726725839268, -0.02404715082205159, 0.7501481933727044, -1.01152828346106, -3.063973290769104, -2.40724167826295, 0.1502273181956478, 1.25044384501571, 0.1305011530283889, -0.4097459995126637, 1.185212516446802, 2.368569036750321, 0.5235332663600148, -2.326243196450767, -2.070579270043994, 1.107885518603635, 2.690750534954722, 0.7346822934775933, -1.021979490938292, 0.8785275920557366, 3.839513346985678, 3.048756758540318, -0.9246367807854305, -2.916344190424402, -1.090143280230344, 0.7602715592201555, -0.09764135147190026, -1.087752719125745, 0.576601568939107, 2.646159083372138, 1.697193622385443, -0.7549037517524185, -0.8645558251573885, 0.6913642747435145, -0.04178222855152184, -2.889656352876084, -3.377571019520155, -0.6609096685753139, 0.5760899779507669, -1.650373088772388, -2.592106717238301, 1.222239501007825, 5.431373371071419, 4.538180480657077, 0.6959992733872716, -0.4660790431853674, 0.6250274395016346, -0.671555511230265, -3.956043845747598, -4.205252517011245, -0.8833133016690283, 1.129469692196066, 0.2382273635838994, 0.1377468235802779, 1.862478692938521, 1.605215630448787, -1.345732863064493, -2.270010168139216, 0.3498767961706573, 1.575727758175467, -0.8583157421771145, -2.024270902909242, 0.9270218142870633, 2.914913946827126, 0.151512726742637, -2.499781782076452, -0.2591495864376528, 2.725021117375319, 1.018383064482852, -2.256511748019213, -1.597132606995748, 0.87056041563905, 0.2666149314228229, -1.680580695347578, -0.9765648841990919, 0.182900465942059, -1.834248351267757, -4.045069981202037, -2.369747219788574, 0.1185898512805677, -0.7992805059057178, -2.057996915623239], 'positive_zeros': ['0.7990863200188872', '1.338528014430990', '2.559158806498639', '3.390037660664842', '3.992801458045159', '4.977088542828107', '5.351228117004448', '6.191103447786898', '6.639648623816088', '7.399543407923355', '8.083019212052405', '8.568854295944422', '9.480411825581867', '10.00355036625704', '10.39183616679602', '11.23422359554211', '11.77413910581588', '12.09389449698874', '12.79139627814599', '13.41815109441764', '14.06932161665215', '14.42858132138331', '15.19286087946564', '15.85994025484203', '16.23515356776139', '16.69249402773045', '17.41162550586544', '17.87990570796540', '18.24557497071657', '19.06401764631365', '19.34354162611033', '19.94016526411191'], 'prelabel': '2-13200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.266573462849724, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 299025842416991723, 'z1': {'__RealLiteral__': 0, 'data': '0.7990863200188872', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.338528014430990', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.559158806498639', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 105.40253066809017, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 13200, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 6, 0, 8, 0, -1, 0, 0, 0, -6, 0, -2, 0, 10, 0, -4, 0, 0, 0, -8, 0, -7, 0, -6, 0, 10, 0, 0, 0, -4, 0, 12, 0, 6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, -6, 0, -6, 0, 0, 0, -8, 0, 0, 0, 14, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -12, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 7], [1, -1, 0], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, 4, 43], [1, 8, 47], [1, -10, 53], [1, -12, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 0, 79], [1, -4, 83], [1, 6, 89], [1, -14, 97]], 'index': 29, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/13200/t'], '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': '2-13200-1.1-c1-0-29', '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': '2-13200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.266573462849724, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 299025842416991723, 'z1': {'__RealLiteral__': 0, 'data': '0.7990863200188872', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '299025842416991723', 'Lhash_array': ['299025842416991723'], 'label': '2-13200-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/13200/t'}