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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': 0, 'A8': 0, 'A9': 0, 'Lhash': '756232890374787628', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 239.45538558141573, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '29988.1', 'coefficient_field': '1.1.1.1', 'conductor': 29988, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1], [1], [1, 3, 5], [1], [1, -4, 11], [1, 1, 13], [1, -1], [1, 0, 19], [1, -4, 23], [1, -1, 29], [1, -3, 31], [1, -2, 37], [1, -5, 41], [1, -6, 43], [1, 9, 47], [1, -2, 53], [1, 1, 59], [1, 12, 61], [1, -10, 67], [1, 0, 71], [1, -8, 73], [1, 0, 79], [1, -5, 83], [1, -6, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-29988-1.1-c1-0-12', 'leading_term': '1.78763087979', '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/29988/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.787630879790231, 1.39171180879017, 0.3602835020499759, -0.7631450751607533, -1.119084373885588, -0.08983471445053666, 1.96507262681672, 3.604218572894619, 3.297884850216894, 0.8881169181395325, -1.939291194106789, -2.999796276207277, -1.723741005164242, 0.2006302500203064, 0.6323618126872429, -0.6019533256091606, -1.585198260485958, -0.8724541092519701, 0.3987993938030163, -0.1429027005734209, -2.670356491965829, -4.263561587032583, -2.362366764392965, 1.599345467331477, 3.517597672165796, 1.701036236814656, -0.9862869895889463, -1.056878221549549, 0.9282812919116019, 1.571017934855229, -0.1102479000514428, -1.323008975522436, -0.1333631198526689, 1.232126156725286, -0.08262385016294561, -2.655965296748121, -2.736054786258498, -0.442135299463483, -0.06572841884559465, -3.223830363209872, -5.635722356714585, -3.330600410491624, 1.113516425842253, 2.37162350897508, 0.2881053696628453, -0.7165913287425529, 0.7691073726262316, 1.53656316825549, 0.2718397638979196, 0.009601265024904921, 1.919976788313175, 2.142505998482833, -1.449600070311762, -4.22776908253934, -1.643599947367194, 2.889215192661611, 3.060098806273829, -0.3813382739843671, -1.670628478943838, -0.04269669457931457, 0.02438476576609452, -2.159086736986288, -2.405835494247597, -0.1458004836362032, 0.2241323106921157, -2.025820708777791, -2.242677856735438, 0.5267942951214627, 1.290124729496105, -1.135223607123646, -1.075347595180185, 3.351942641249706, 5.666850097952715, 2.106136559828147, -1.658538181660729, -0.5785171916302738, 1.712372318844998, 0.9506672857210335, -0.3349698956787921, 0.3023323948418042, -0.2472809913441561, -2.988802022170986, -2.857275646507675, 1.400768362321953, 3.147565177243597, -0.2259030851123552, -1.861436580218937, 1.866899848252012, 4.493787768554637, 1.691159374464352, -1.285640912635253, -0.5512229874988218, -0.08497494631514398, -1.769755808705647, -1.197995936428464, 2.017432934401336, 2.289079043775133, -0.5310231414126103, -0.8003144413505935, 0.7455290488524576, -1.535531864025387, -5.216524106576359, -3.306644151068169, 1.351930325479426, 0.6531620445293485, -3.370314375046311, -3.058816114643744, 0.1693830518328633, 0.2982629705882949, -1.052373246430966, -0.1135476008499346, 0.3208829840968395, -1.178901492831693, 0.4588467057518596, 5.196982753927238, 5.205927524758948, 0.1685587711849474, -1.00626270528676, 2.493310916870893, 2.298468223607234, -1.85925593974342], 'positive_zeros': ['0.5743808226760613', '1.262939526443419', '2.322882840105712', '3.217342986380655', '3.648861089865249', '4.402278047976074', '4.729205921573479', '5.648414135331871', '6.391913820257550', '6.888226284864712', '7.486602661894247', '8.017339105936953', '8.491916333462923', '9.312621958378128', '9.489685624958141', '10.42968573263102', '11.03329771384316', '11.39440221388327', '12.05590430922745', '12.24785765184672', '12.91638272193689', '13.58233535452926', '14.22135295162351', '14.75695485800430', '15.00383546613591', '15.76861611584455', '16.03337246235439', '16.70375317234556', '17.14244030228768', '17.57604297948881', '18.35969844753770', '18.80034323410243', '19.39076780322136', '19.66652031574641', '19.96818130683078'], 'prelabel': '2-29988-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.47434604697128, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 756232890374787628, 'z1': {'__RealLiteral__': 0, 'data': '0.5743808226760613', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.262939526443419', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.322882840105712', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 239.45538558141573, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 29988, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 5, 0, 6, 0, 0, 0, -9, 0, 0, 0, 0, 0, 2, 0, -12, 0, 0, 0, -1, 0, -12, 0, 0, 0, 3, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 1, 13], 'euler17': [1, -1, 0], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -1, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, -2, 37], 'euler41': [1, -5, 41], 'euler43': [1, -6, 43], 'euler47': [1, 9, 47], 'euler5': [1, 3, 5], 'euler53': [1, -2, 53], 'euler59': [1, 1, 59], 'euler61': [1, 12, 61], 'euler67': [1, -10, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -8, 73], 'euler79': [1, 0, 79], 'euler83': [1, -5, 83], 'euler89': [1, -6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 3, 5], [1, 0, 0], [1, -4, 11], [1, 1, 13], [1, -1, 0], [1, 0, 19], [1, -4, 23], [1, -1, 29], [1, -3, 31], [1, -2, 37], [1, -5, 41], [1, -6, 43], [1, 9, 47], [1, -2, 53], [1, 1, 59], [1, 12, 61], [1, -10, 67], [1, 0, 71], [1, -8, 73], [1, 0, 79], [1, -5, 83], [1, -6, 89], [1, -12, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/29988/g'], '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': '2-29988-1.1-c1-0-12', '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': '2-29988-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.47434604697128, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 756232890374787628, 'z1': {'__RealLiteral__': 0, 'data': '0.5743808226760613', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '756232890374787628', 'Lhash_array': ['756232890374787628'], 'label': '2-29988-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/29988/g'}