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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '1211387632488554247', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '286650.1', 'coefficient_field': '1.1.1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1], [1, 0, 11], [1, -1], [1, 0, 17], [1, 5, 19], [1, 0, 23], [1, 3, 29], [1, -4, 31], [1, -7, 37], [1, -3, 41], [1, 2, 43], [1, 9, 47], [1, -9, 53], [1, -6, 59], [1, 8, 61], [1, 5, 67], [1, -3, 71], [1, 4, 73], [1, -11, 79], [1, -6, 83], [1, -6, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 97, 'label': '2-286650-1.1-c1-0-97', 'leading_term': '1.641663192', '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/286650/ei', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.641663191999355, 1.0150379000068, -0.2907853886821616, -0.8937400072468032, 0.131919454971968, 1.858929896839943, 2.169250987906524, 0.5475570675111119, -0.7121558894157028, 0.4411911308893967, 2.285139441455021, 1.37364851097327, -1.752145991987636, -2.42097270650918, 0.898434027949514, 3.190502869575674, 0.467576633429744, -3.097470290169279, -1.513269723736668, 2.554504214787746, 1.642499501253408, -3.654190740028391, -5.240714222214712, -1.197204973060664, 1.605880136533912, 0.2563219675554543, -0.02732313823594268, 2.730237075802775, 3.345668626026547, 0.3805467877366445, -0.7522212847225147, 1.272969066624418, 1.502627089482205, -0.6123529889153276, -0.579453918091565, 0.9401333600316312, -0.172118849913333, -1.82164178322084, -0.1605578283878952, 1.457558192740161, -0.318358343692406, -1.255822742380792, 0.798420349444886, 0.836123445687236, -1.547670451503903, -0.8119622730389792, 1.240577327603583, -0.9801990351510981, -2.892542980977225, 0.9593439776637585, 3.296102607137632, -0.9479007664094172, -2.999918271000106, 0.1073223606962783, -1.63721209624728, -7.68549000409668, -5.884828380765886, 1.273154864144496, 1.343230366989563, -2.549962173684478, -1.319383094013709, 0.0561696587275582, -2.953322260456542, -2.861901428971045, 1.428070713325792, 1.802111177046326, -0.421395163018348, 0.4612170885451763, 0.5123246844459316, -2.260773535864226, -1.784078446399085, 0.935300932801355, 0.3533105851178899, 0.07149777703959306, 2.657466245626581, 2.36401073676039, -0.01931415530203933, 1.088928235411798, 1.872302456348056, -0.1956073389208684, 1.046984817648895, 3.526803918915847, 0.4045323795932686, -2.223645671758363, 0.2107926380841486, -0.2385734930689735, -2.259475981755124, 2.013003936527299, 3.850003970605654, -3.00914642991707, -4.570408161264099, 1.953545417677451, 1.976908351589035, -1.79888088522096, 1.533914251401085, 3.551041933127639, -0.9036646432550148, -0.7666250755802566, 2.882942710090064, 0.7581717716179412, -1.17034468326023, 1.29062566934771, 0.4755451401560179, -1.890107482842638, -0.2179381593832732, 0.06950708173899035, -1.386228343092421, 1.150374315028873, 2.539634223011442, -0.3925294247696563, -0.5634702536626646, 0.7394415865928909, -0.8353718767941499, -0.009552568782716986, 2.080370879803418, -0.3151465021970253, -0.8325950699658147, 2.309413127989467, 0.7141130429598239, -1.354147820979282, 1.409371121797776], 'positive_zeros': ['0.4429779539889366', '0.9802278959181047', '1.823560019466532', '2.194406629478461', '2.861992059838521', '3.443882326922550', '4.026151695719317', '4.585018557851692', '5.083318311087110', '5.818344961126768', '6.286948269698491', '6.503898743727588', '7.283528611141105', '7.609484041613832', '8.173151483246972', '8.582207924648481', '8.981158375110071', '9.514952001405982', '9.967388302324030', '10.41208653366560', '10.83646471319504', '11.32416022470260', '11.68088463116978', '12.20291953317871', '12.70465443164665', '13.23904027818373', '13.40809359356983', '14.19503980061582', '14.57577811418959', '15.13116927359988', '15.25965642018563', '15.91272198140148', '16.42841578443454', '16.68207252992959', '17.05280524499415', '17.64424625548764', '18.05856455409746', '18.23896393947611', '18.99508867163953', '19.10197545200930', '19.71922708750613', '19.90695540740811'], 'prelabel': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1211387632488554247, 'z1': {'__RealLiteral__': 0, 'data': '0.4429779539889366', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9802278959181047', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.823560019466532', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -5, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, 4, -1, 0, 0, 0, 0, 7, 5, 0, 0, 3, 0, -2, 0, 0, 0, -9, 0, 0, 0, 0, 1, 9, 0, 0, 0, 0, 3, 6, 0, -8, -4, 0, 1, 0, 0, -5, 0, 0, 0, 3, 0, -4, -7, 0, -5, 0, 0, 11, 0, 0, -3, 6, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 9, 0, 0, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 0, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -7, 37], 'euler41': [1, -3, 41], 'euler43': [1, 2, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -6, 59], 'euler61': [1, 8, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 0], 'euler71': [1, -3, 71], 'euler73': [1, 4, 73], 'euler79': [1, -11, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, -1, 0], [1, 0, 17], [1, 5, 19], [1, 0, 23], [1, 3, 29], [1, -4, 31], [1, -7, 37], [1, -3, 41], [1, 2, 43], [1, 9, 47], [1, -9, 53], [1, -6, 59], [1, 8, 61], [1, 5, 67], [1, -3, 71], [1, 4, 73], [1, -11, 79], [1, -6, 83], [1, -6, 89], [1, -8, 97]], 'index': 97, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/286650/ei'], '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': '2-286650-1.1-c1-0-97', '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': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1211387632488554247, 'z1': {'__RealLiteral__': 0, 'data': '0.4429779539889366', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1211387632488554247', 'Lhash_array': ['1211387632488554247'], 'label': '2-286650-1.1-c1-0-97', 'type': 'ECQ', 'url': 'EllipticCurve/Q/286650/ei'}