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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 3, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '788645642350050161', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1825.9551131010237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [397, [1, -1]]], 'bad_primes': [2, 3, 397], 'central_character': '228672.1', 'coefficient_field': '1.1.1.1', 'conductor': 228672, 'conductor_radical': 2382, 'degree': 2, 'euler_factors': [[1], [1], [1, -3, 5], [1, 1, 7], [1, 1, 11], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 3, 23], [1, 4, 29], [1, 10, 31], [1, 7, 37], [1, 5, 41], [1, 4, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, 0, 61], [1, 10, 67], [1, -10, 71], [1, -9, 73], [1, 6, 79], [1, 9, 83], [1, 2, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-228672-1.1-c1-0-13', 'leading_term': '1.85085182741', '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/228672/dg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.850851827411411, 0.8793348416049088, -1.380394159506657, -3.18276487478225, -2.865991086931444, -0.6517162341492764, 1.22089342462043, 1.054901674465971, 0.0139222191917479, 0.5405689475068806, 2.46231955614321, 2.71867417879334, 0.05781465967691183, -2.28575949031363, -1.160603551026879, 1.095418635641056, -0.1871319654969563, -4.215248973347998, -5.232719384369485, -1.551131798005816, 1.663764248067611, 0.8621090199013391, -0.715106071731133, 0.08189336579381166, 0.6349014174407629, -1.28834689570999, -2.24635249054507, -0.04668854007517671, 0.9019799858860911, -1.895506712600059, -2.749543135740649, 1.977702739355415, 5.737552401138286, 2.856052949292101, -1.333959618335294, -0.80721119374638, 0.7266077864157902, -0.9384211928505563, -1.953362483652871, 0.2230884764515025, 1.086902104169212, -0.4697360898617386, 0.4001599987806478, 2.699299399804581, 0.7839635365858943, -2.158309407300723, 0.7360481727438021, 4.626413387976997, 1.34649732261751, -3.965878202856616, -3.004650658380946, 0.00599515692053034, -0.8965847365381066, -1.746532680619016, -0.1278374696700157, -0.5115650923266191, -1.88509828900412, 0.3440698001847955, 1.714382998225668, -2.136311523309634, -3.786970552094599, 0.604486909623832, 2.18435660759821, -1.233625450060976, -0.6511105076460089, 3.43496170027397, 2.643432807479167, -0.2237886559439467, 0.8641860009262291, 0.9406856967033042, -2.577620891698065, -2.931754988653892, -0.2852258323736823, -0.3613820030945501, 0.1389367595474745, 3.202609667812551, 0.962048023153589, -5.366079699255382, -4.731698139069056, -0.140049929738292, -1.702931239504435, -4.227186843709636, -1.084299349497091, 0.8034742973695735, -0.7087408950037668, 1.041601292680032, 3.248031699603455, 0.8820785521956116, -0.484486960672166, 0.2178945318317493, -2.587606014688077, -3.778490658038786, 1.132896748798654, 2.036875137211708, -3.170952463700028, -2.828292178469687, 1.496943415856041, 0.4298798707488516, -0.3740957364708971, 3.649582413727085, 3.839644572515571, -0.02968496148609345, -0.402251894118248, 0.0354470770656366, -0.4176556897697742, 2.813241341599157, 4.332047860364807, 0.1600463593334164, 0.9424921767268197, 6.754322094823655, 4.507983691006027, -1.311959446284881, 0.4824984522908341, 2.428042677167496, -0.7453257850057112, -1.031657235145529, 0.5685589626357969, -0.5326120698557169, 0.812637886214788, 3.056089830297489, 0.5998103121217417], 'positive_zeros': ['0.3555162438490880', '1.317893207178183', '2.006515980805008', '2.126695609336077', '3.004400035041652', '3.608792531778598', '3.986010248216734', '4.840779719909611', '5.354278779829855', '5.735694511076270', '6.109204439788463', '6.754522746775306', '7.104652875014231', '7.665347336585805', '8.395266264763234', '8.839635378544816', '9.149696068100410', '9.727678564866889', '10.16922267510930', '10.45828247739465', '11.04921767225992', '11.46387949216110', '12.05280579453252', '12.74873210686165', '12.86935317493503', '13.52774207149450', '13.66388439851727', '14.22376071480063', '14.63581473614085', '15.21917609227730', '15.66108740550307', '16.03959181266620', '16.71021632278788', '16.88800429068413', '17.32661663697357', '18.06105856781286', '18.14879346535854', '18.48590589127462', '19.03749483473100', '19.76857361456087', '19.86243496436288'], 'prelabel': '2-228672-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.7311960176757, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 788645642350050161, 'z1': {'__RealLiteral__': 0, 'data': '0.3555162438490880', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.317893207178183', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.006515980805008', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1825.9551131010237, 'bad_primes': [2, 3, 397], 'central_character': '1.1', 'conductor': 228672, 'conductor_radical': 2382, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 4, 0, 0, 0, -4, 0, -10, 0, 0, 0, -3, 0, -7, 0, 0, 0, -5, 0, -4, 0, 0, 0, 9, 0, -6, 0, 0, 0, 9, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, -10, 0, 0, 0, 10, 0, 9, 0, 0, 0, 1, 0, -6, 0, 0, 0, -9, 0, -6, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 1, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 7, 37], 'euler41': [1, 5, 41], 'euler43': [1, 4, 43], 'euler47': [1, -9, 47], 'euler5': [1, -3, 5], 'euler53': [1, -9, 53], 'euler59': [1, -6, 59], 'euler61': [1, 0, 61], 'euler67': [1, 10, 67], 'euler7': [1, 1, 7], 'euler71': [1, -10, 71], 'euler73': [1, -9, 73], 'euler79': [1, 6, 79], 'euler83': [1, 9, 83], 'euler89': [1, 2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -3, 5], [1, 1, 7], [1, 1, 11], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 3, 23], [1, 4, 29], [1, 10, 31], [1, 7, 37], [1, 5, 41], [1, 4, 43], [1, -9, 47], [1, -9, 53], [1, -6, 59], [1, 0, 61], [1, 10, 67], [1, -10, 71], [1, -9, 73], [1, 6, 79], [1, 9, 83], [1, 2, 89], [1, -2, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/228672/dg'], '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': '2-228672-1.1-c1-0-13', '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': '2-228672-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.7311960176757, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 788645642350050161, 'z1': {'__RealLiteral__': 0, 'data': '0.3555162438490880', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '788645642350050161', 'Lhash_array': ['788645642350050161'], 'factors': ['2-228672-1.1-c1-0-13'], 'label': '2-228672-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/228672/dg'}