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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': 2, 'A8': 0, 'A9': 0, 'Lhash': '1262263457132198102', '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': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2283.018814270833, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 11, 19], 'central_character': '285912.1', 'coefficient_field': '1.1.1.1', 'conductor': 285912, 'conductor_radical': 1254, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, -2, 7], [1, 1], [1, -5, 13], [1, 2, 17], [1], [1, -8, 23], [1, -5, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 11, 43], [1, 9, 47], [1, -2, 53], [1, -14, 59], [1, -7, 61], [1, -2, 67], [1, 3, 71], [1, 4, 73], [1, 0, 79], [1, -17, 83], [1, -7, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-285912-1.1-c1-0-17', 'leading_term': '3.38555976905', '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/285912/ba', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.385559769054615, 2.427197475378429, 0.242034845275842, -1.40736330246665, -1.060974650112053, 0.6319906852136583, 1.254422441148754, -0.2924147223603738, -1.820739458743287, -0.6049575238247697, 2.288289502258545, 2.923618975421349, 0.3681716903594493, -1.448910866266089, 0.2298453843307501, 2.337204001836864, 0.9995853876787835, -1.697197102490617, -1.201899153922543, 1.413940939349468, 1.503980858855448, -0.3198935618463504, 0.688453937368433, 3.846373041847121, 3.631250607433704, 0.234604710677144, -0.4733657830041093, 1.644128109137892, 0.7102878846628397, -3.039326279954535, -3.05233762198811, 0.7247001204825865, 1.80339654914303, -0.08538580597242149, 0.1313670973979598, 1.024772747180145, -1.787747252932143, -4.292583533530497, -1.278873368472792, 1.865784646112234, -0.692926011384417, -3.280521310673322, -0.5903324665607466, 1.794573007484489, 0.1460442336158658, -0.4291730678228549, 0.8357259443209182, -0.97452349314665, -2.668747977825695, 1.749324991489199, 6.309176322010403, 3.75330498168967, 0.006288405453107717, 0.6393481302742459, 0.3429803440048723, -1.969458694084005, 0.06474873728536529, 3.731760570464229, 1.771264442991267, -1.296233215384496, 0.09620854056810343, 0.1182260995276698, -3.100575391115575, -2.274710398012138, 1.037466602185469, -0.0764651806743215, -0.6690665980889688, 3.898970607261129, 5.140196319133005, 0.3856301063274395, -1.145912425632421, 0.8502114830873108, 0.2024155024494085, 0.7301819898368155, 4.381835120844046, 3.363476301605023, -0.897890459819571, -0.2343923325024271, 0.2506681505779425, -4.700402037753139, -5.797864326612272, -0.5701361296886907, 1.0091628637329, -0.5575625437480278, 0.7467427354039423, 0.369053324062159, -2.328017790806427, -0.7528496183696423, -0.08916695669232334, -5.872150860833306, -7.530037119560541, -1.412202750766298, 1.165733007003599, -0.3069871819170962, 0.4646606789993419, -1.281926989917733, -5.374423522361212, -3.23838720234793, 0.2930032964831925, -1.849071255427522, -2.093956251174195, 0.8403306732702801, -0.8153147824336926, -1.870454908699223, 2.090656238338711, 1.399502881786398, -3.038422084513199, -1.322670698353034, 1.250449771022726, -0.1575634795903627, 1.696853504391777, 3.878621657473186, 0.1358120752247977, -1.363760558391262, 0.8809226970694808, -1.385824080439311, -2.894002991971498, 0.2294349843861614, -1.818250227512168, -5.958952264116704, -2.248562038431032], 'positive_zeros': ['0.5272634057800945', '1.158657297381917', '1.715196605999622', '2.303732683565207', '3.031147296661547', '3.479136526250693', '4.082074988307346', '4.610943065679271', '5.191914282047039', '5.430261921715843', '6.271266187974615', '6.562197193492925', '7.049524490501907', '7.700396590716248', '8.235736171838056', '8.477626567875344', '8.879678812698532', '9.569696190481849', '9.958205314950929', '10.53804978503363', '11.01781848154754', '11.32525181545711', '11.66773599448276', '12.17930707650623', '13.00114583820283', '13.13479140080169', '13.53553631648491', '13.99630928143682', '14.60853165316389', '14.98876979077088', '15.26131670305803', '15.89864332672103', '16.24254741455982', '16.55250898560369', '17.27209813511066', '17.63269484843954', '18.04270575273374', '18.16293297647257', '18.93005815862978', '19.27394472972837', '19.52032864659306'], 'prelabel': '2-285912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.780946142482705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1262263457132198102, 'z1': {'__RealLiteral__': 0, 'data': '0.5272634057800945', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.158657297381917', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.715196605999622', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2283.018814270833, 'bad_primes': [2, 3, 11, 19], 'central_character': '1.1', 'conductor': 285912, 'conductor_radical': 1254, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -11, 0, 0, 0, -9, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 14, 0, 7, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 7, 0, 10, 0, 0, 0, 0, 0, -7, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -5, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 11, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, -14, 59], 'euler61': [1, -7, 61], 'euler67': [1, -2, 67], 'euler7': [1, -2, 7], 'euler71': [1, 3, 71], 'euler73': [1, 4, 73], 'euler79': [1, 0, 79], 'euler83': [1, -17, 83], 'euler89': [1, -7, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, -2, 7], [1, 1, 0], [1, -5, 13], [1, 2, 17], [1, 0, 0], [1, -8, 23], [1, -5, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 11, 43], [1, 9, 47], [1, -2, 53], [1, -14, 59], [1, -7, 61], [1, -2, 67], [1, 3, 71], [1, 4, 73], [1, 0, 79], [1, -17, 83], [1, -7, 89], [1, 7, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/285912/ba'], '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': '2-285912-1.1-c1-0-17', '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': '2-285912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.780946142482705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1262263457132198102, 'z1': {'__RealLiteral__': 0, 'data': '0.5272634057800945', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1262263457132198102', 'Lhash_array': ['1262263457132198102'], 'label': '2-285912-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/285912/ba'}