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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': '1822614267360690938', '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': 1648.1122977192279, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [43, [1, 1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '206400.1', 'coefficient_field': '1.1.1.1', 'conductor': 206400, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, -4, 19], [1, 8, 23], [1, 6, 29], [1, 0, 31], [1, 10, 37], [1, 6, 41], [1, 1], [1, 8, 47], [1, 2, 53], [1, 4, 59], [1, -14, 61], [1, -4, 67], [1, 16, 71], [1, 10, 73], [1, -8, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 276, 'label': '2-206400-1.1-c1-0-276', 'leading_term': '16.2388905133', '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': 2, 'origin': 'EllipticCurve/Q/206400/ht', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.9596588818330057, -3.178838229197445, -4.887404048994758, -4.357770997255282, -1.747278885700157, 0.6005026985579272, 0.6265573520270104, -0.8108681383971521, -0.9710167191839617, 0.8537738005826019, 2.111042656053316, 0.85102135536598, -0.9375414349240869, -0.2946138043685087, 1.629836955197215, 1.116915511648521, -1.636501574665625, -2.17124627396164, 0.7552355016905066, 2.497637380249491, 0.3411396192888278, -1.385905516942809, 1.172315091734391, 4.002701965386433, 1.949977809741828, -1.849838747606667, -1.357162294631728, 1.590608937832585, 1.100689009327309, -1.714602028147458, -1.525864243850664, 0.6879396106097919, 0.3982091752078386, -0.8242271408735826, 0.8098869870550961, 2.31536203614307, -0.2237219127883359, -2.731958520563952, -0.9478169809798576, 0.7054399242326682, -1.398598988523327, -2.054600722437284, 1.332027706938654, 2.191904077648482, -1.411703417265966, -1.941220752605881, 1.611233876044547, 0.8562850122774068, -4.27715720090472, -4.684232400524791, -0.3268565821355582, 0.8137971739006421, -0.8148014899463897, -0.1234332509724645, 0.1609175170536449, -2.472423081140973, -2.546092063334865, 0.7725567617760125, 0.3684947446336713, -3.136442547757307, -2.462132695129779, 0.4337415485526569, -0.007363500644684949, -0.4042897833277937, 0.7111820587321829, -3.151284084551933, -9.247762885720295, -6.525344302164212, 1.566295164637551, 2.803050544145752, -0.2268539338781983, 0.706633178820979, 1.530114958392036, -0.9052365683979657, -0.177074168372203, 2.78181850992607, 0.756428077541287, -2.057342207043659, 0.557527490361529, 2.586803526291417, 0.4962198213961266, -0.04462202195131047, 0.10151313851161, -2.729569711495179, -2.503202559194607, 2.206814519040597, 2.177024687218186, -1.555687432857556, -0.6209632129209343, -0.08907896709196582, -4.860137585020259, -4.974105838946661, 1.348634624950924, 2.184268183373768, -1.5595636586591, -0.6472471821449379, 0.9698564696852626, -0.2668376015713756, 2.064285837550563, 5.116500955963346, 1.3217469719354, -2.554029944849101, -0.6065128891984078, 0.4422809238750359, -0.3306078671928721, 1.076554814106998, 0.236755112091933, -1.892608343806022, 2.611569596348699, 7.054926917114757, 2.601881277257592, -1.308954413330782, 0.2087185724582848, -1.80293778841213, -4.433831084443796, -0.4200496681830743, 1.609247348293335, -1.297249540680589, 0.7643363320343909, 3.998051840100072], 'positive_zeros': ['1.414481156402592', '1.862315301987673', '2.399544626190368', '3.098433231701626', '3.536942410914320', '4.105574238831314', '4.694492292954042', '5.278516260026130', '5.670919308645741', '6.362738762704853', '6.856720598760746', '7.343200170043675', '7.909266472261080', '8.308670776779834', '8.668483179800299', '9.235014542254089', '9.836338856022358', '10.11905271706910', '10.66185360249121', '11.15879167697824', '11.63645260097013', '12.04567640136834', '12.77303585012310', '13.11516774979905', '13.52084115349458', '13.77301020401182', '14.43593551127997', '14.77724379214142', '15.44429811396884', '15.74876002135212', '16.07170367277810', '16.34995691973593', '17.19253062022942', '17.71890219517941', '17.91847532655554', '18.40887060240983', '18.76349802532947', '19.29541239391913', '19.71453030574110'], 'prelabel': '2-206400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.596949364690296, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1822614267360690938, 'z1': {'__RealLiteral__': 0, 'data': '1.414481156402592', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.862315301987673', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.399544626190368', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1648.1122977192279, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 206400, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 2, 0, 0, 0, -6, 0, 4, 0, 0, 0, -8, 0, 0, 0, 1, 0, -6, 0, 0, 0, -4, 0, 0, 0, -10, 0, 2, 0, -6, 0, -1, 0, 0, 0, -8, 0, -7, 0, -6, 0, -2, 0, 0, 0, 4, 0, -4, 0, 14, 0, 0, 0, 0, 0, 4, 0, -8, 0, -16, 0, -10, 0, 0, 0, 0, 0, 8, 0, 1, 0, -16, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 1, 0], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -14, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 16, 71], 'euler73': [1, 10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 16, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, -4, 19], [1, 8, 23], [1, 6, 29], [1, 0, 31], [1, 10, 37], [1, 6, 41], [1, 1, 0], [1, 8, 47], [1, 2, 53], [1, 4, 59], [1, -14, 61], [1, -4, 67], [1, 16, 71], [1, 10, 73], [1, -8, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'index': 276, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/206400/ht'], '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': '2-206400-1.1-c1-0-276', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-206400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.596949364690296, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1822614267360690938, 'z1': {'__RealLiteral__': 0, 'data': '1.414481156402592', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1822614267360690938', 'Lhash_array': ['1822614267360690938'], 'label': '2-206400-1.1-c1-0-276', 'type': 'ECQ', 'url': 'EllipticCurve/Q/206400/ht'}