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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '490354577531461073', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, -1], [1, -4, 13], [1, -2, 17], [1, -4, 19], [1, 2, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, 6, 61], [1, 4, 67], [1, 0, 71], [1, -4, 73], [1, -14, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 99, 'label': '2-369600-1.1-c1-0-99', 'leading_term': '1.73706866613', '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/369600/fw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.737068666131774, 0.9196494592782677, -0.807087662847215, -1.733574494257015, -0.8079642200527596, 0.7150245344940099, 0.3926902184262466, -1.821423948972911, -2.547910885977475, 0.6021234020715232, 4.74013526085418, 4.895012108863886, 1.19917257717964, -1.187520803797216, -0.193091540678206, 0.1701956562635146, -2.558677729497561, -4.315882005738078, -1.704213630537587, 1.400730244319146, 0.5329760885796337, -1.437033278119208, -0.2111199903452956, 1.659333738972123, 0.4068631780583213, -1.148707020178781, 0.04942930737693381, 0.3572079418989902, -2.427354770253706, -2.971312872439804, 0.8186300248369492, 2.153852904346632, -1.20353191566619, -1.681666562278858, 2.598394176118348, 3.522798667024242, -0.1718567370071953, -0.4250425444170649, 2.870051866510467, 2.170716365877626, -1.111679121659453, -0.5029892260219014, 0.9248831005973625, -1.467221116375737, -2.586221765189763, 0.48478121755479, 1.527295717213908, -0.4580152179652351, 0.1527533414776397, 1.218550839427229, -1.609517539469147, -2.604364924675367, 1.358104671732815, 2.425057890969124, -0.5846908616282579, -0.06827157350991996, 1.274983914063064, -2.792372191917819, -4.547263194663666, 1.393166866885064, 4.270809109372704, -0.0993409056017865, -1.599734914570545, 0.8283609004254398, 0.09820000823688205, -0.6346849303298906, 1.89311705488479, 1.5906189694407, -0.67770166251239, 1.379871244557563, 2.758728873214855, -0.7900981725487751, -1.796752542599506, 0.3551891220611179, -0.978404908497498, -1.44890980158688, 2.280054166446913, 1.698969977159501, -1.865882942346472, 1.146101734625301, 4.17564536796772, -0.3594855008875945, -2.630459420793438, 0.2614020754086914, -1.018962928629036, -2.625425305852682, 1.968138162846485, 3.849756185696989, 0.389067604456558, 0.3511290963687087, 1.45023645691895, -0.7176962939322815, -0.2729067044805493, 1.383885649825891, -1.047337176247412, -1.216422253516278, 1.496087159535808, -0.922067249422653, -2.542379188742535, 2.20122243153464, 2.716475328127216, -1.170726978423315, 0.3969935880367445, 1.026519837374192, -3.491178785435692, -2.377879222355287, 1.632031572910996, -0.5433668059409182, -0.3981455599895433, 4.438816113288059, 3.080563938064782, -0.6200420733248972, 0.4604340014215405, -0.04713205079385453, -1.282352951743222, 1.35902484507186, 1.030898257023882, -1.162600533405346, 1.792365174117149, 2.548030710384912, -0.8298435794354606], 'positive_zeros': ['0.3850848401828601', '1.118550265683077', '1.553549185610789', '2.216163501813192', '3.084226726367865', '3.532222400021667', '3.777078937797023', '4.610629404673798', '5.053026218807198', '5.521022277236809', '6.043978615380578', '6.492789666152273', '6.795532406418576', '7.450514851914359', '7.919175433395191', '8.359039239444276', '8.987001792340950', '9.285586828786696', '9.898380884841526', '10.30313639263221', '10.63151265200419', '11.21413331581183', '11.68382657586658', '11.98085375567547', '12.38574977092651', '12.92253636027386', '13.44411936637890', '13.75666433808002', '14.11036281206015', '14.70000215126577', '15.24466563927578', '15.65455758980040', '16.01189333679688', '16.32767920100044', '16.89116587159577', '17.14149205835989', '17.70025002894436', '18.18860976107568', '18.39630478264698', '18.85552743606692', '19.34706789858669', '19.69595909133789'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 490354577531461073, 'z1': {'__RealLiteral__': 0, 'data': '0.3850848401828601', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.118550265683077', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.553549185610789', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 4, 0, 0, 0, 2, 0, 4, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, -8, 0, -4, 0, -6, 0, -4, 0, 0, 0, 0, 0, 1, 0, -2, 0, -6, 0, 0, 0, -4, 0, 4, 0, -6, 0, -1, 0, 0, 0, -4, 0, 2, 0, 0, 0, 4, 0, 0, 0, -1, 0, 14, 0, 1, 0, 6, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 10, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -4, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, -14, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -4, 13], [1, -2, 17], [1, -4, 19], [1, 2, 23], [1, 0, 29], [1, -2, 31], [1, 8, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, 6, 61], [1, 4, 67], [1, 0, 71], [1, -4, 73], [1, -14, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'index': 99, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/fw'], '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': '2-369600-1.1-c1-0-99', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 490354577531461073, 'z1': {'__RealLiteral__': 0, 'data': '0.3850848401828601', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '490354577531461073', 'Lhash_array': ['490354577531461073'], 'label': '2-369600-1.1-c1-0-99', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/fw'}