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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': -1, 'A4': -1, 'A5': 2, 'A6': 1, 'A7': -4, 'A8': 3, 'A9': -2, 'Lhash': '1467175788107318733', 'a10': [-0.020618556701030927, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.020618556701030927, 0.0], 'a6': [0.010309278350515464, 0.0], 'a7': [-0.041237113402061855, 0.0], 'a8': [0.030927835051546393, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.03825652021776063, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1, 2]], [3, [1, 1, 3, 3]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '600.1', 'coefficient_field': '1.1.1.1', 'conductor': 600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 1, 3, 3], [1, -2, 1], [1, 4, 14, 28, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, -4, 38, -68, 289], [1, -8, 54, -152, 361], [1, -4, 46, -92, 529], [1, 4, 62, 116, 841], [1, 8, 62, 248, 961], [1, 4, 14, 148, 1369], [1, -4, 22, -164, 1681], [1, 4, 54, 172, 1849], [1, -12, 126, -564, 2209], [1, 4, 46, 212, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, -20, 230, -1340, 4489], [1, 8, 142, 568, 5041], [1, -4, 86, -292, 5329], [1, 0, 158, 0, 6241], [1, 4, -26, 332, 6889], [1, 12, 214, 1068, 7921], [1, 12, 166, 1164, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-600-1.1-c1e2-0-0', 'leading_term': '0.259884078294', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'Genus2Curve/Q/600/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.2598840782939822, 0.2711324852552622, 0.3056374783139254, 0.3655680473838022, 0.4541489290858705, 0.5750029204926635, 0.731109276054755, 0.9233148734615312, 1.148401602295901, 1.396841989904833, 1.65056535518417, 1.881287399782967, 2.050175259130605, 2.109741747279666, 2.008775313845761, 1.700705119394009, 1.155008957959202, 0.3701360966118276, -0.6148621635368103, -1.713842564333067, -2.796353472950993, -3.702831570858504, -4.27277622476879, -4.382477891029351, -3.984308088648807, -3.135923095939536, -2.006838399150161, -0.8532577774834615, 0.03976956404071904, 0.4382464193378912, 0.2391238169180397, -0.4783664190166277, -1.455548828983419, -2.32250934454612, -2.719514656522017, -2.434716622842895, -1.505739958366942, -0.2363833817851625, 0.8939229581437594, 1.407397616969684, 1.028403274586682, -0.1786330360634278, -1.805275841906141, -3.248431928040203, -3.961039246446851, -3.694786965808523, -2.615249484810202, -1.221006454681197, -0.09404920824327181, 0.3968245987377268, 0.2791182941443435, -0.0655031194076555, -0.1586668450709802, 0.2443182251293851, 0.956180936754574, 1.438120051182202, 1.143178902654075, 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-1.872446436916422, 0.4540865788862178, 2.895437440859024, 2.816144948515568, -0.6851108437991807, -5.707937885988713, -8.94394567336401, -8.389323600484436, -4.928992195832574, -1.352830930940818, 0.2059756427751017, -0.06573155818436498, -0.4070798195451635, 0.3244874725261176, 1.430435295857724, 1.427349951048871, 0.1524999736488877, -0.5673693621194531, 1.307643044143072, 5.543082861754365, 9.204796909634785, 9.104467828708028, 4.873390076565474, -0.4623790409898442, -3.139835361621356, -1.995565538347967, 0.7944197511082164, 2.174210464350437, 1.203480603919596, -0.4643008465368763, -0.8280087462168683, 0.1979007385870028, 0.9999602357392824, 0.4739889168514128, -0.5437448003490221, -0.3540179641882181, 1.366846411686393, 2.955503321621457, 2.622776964736791, 0.6128762177410209, -0.9584725614526489, -0.4702944213415577, 1.405370930831223, 2.580582501371374, 1.988533509667791, 0.617136659707261, -0.001185948827726947, 0.2410333569813747, 0.2041460282750466, -0.4899585782636076, -0.5480421813311929, 1.16502694740011, 3.23795857891278, 2.314294744636785], 'positive_zeros': [3.261805874080346, 5.239203926245921, 5.700938888668087, 6.972385443911387, 7.664880134417454, 9.022035638415746, 9.523451675812284, 9.85184018389279, 10.67892245123374, 11.52426214006865, 12.64617876135106, 12.70951559228551, 13.90086992520561, 14.00692585049802, 14.95092089654112, 15.95902603015141, 16.54367915654916, 17.00801034817492, 17.23595347746433, 18.10585375705648, 18.49630413944425, 19.11046245900218, 19.64206670343833], 'prelabel': '4-600-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.44225868076075064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 1467175788107318733, 'z1': {'__RealLiteral__': 0, 'data': '3.26180587408', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.23920392625', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.70093888867', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.03825652021776063, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, -1, 2, 1, -4, 3, -2, -2, 0, 1, -4, 4, -2, -1, 4, 2, 8, -2, 4, 0, 4, -3, 3, 4, 2, 4, -4, 2, -8, -5, 0, -4, -8, 2, -4, -8, 4, 6, 4, -4, -4, 0, -4, -4, 12, 1, 2, -3, -4, 4, -4, -2, 0, -12, -8, 4, -8, 2, -4, 8, 8, 7, -8, 0, 20, -4, -4, 8, -8, -6, 4, 4, -3, -8, 0, -4, 0, -2, 7, -4, -4, -4, 8, 4, 4, 0, -12, 4, 16, -4, 8, -12, 16, 5, -12, -2, 0, -3], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, -4, 46, -92, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 1, 3, 3, 0], 'euler31': [1, 8, 62, 248, 961], 'euler37': [1, 4, 14, 148, 1369], 'euler41': [1, -4, 22, -164, 1681], 'euler43': [1, 4, 54, 172, 1849], 'euler47': [1, -12, 126, -564, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 4, 46, 212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, -20, 230, -1340, 4489], 'euler7': [1, 4, 14, 28, 49], 'euler71': [1, 8, 142, 568, 5041], 'euler73': [1, -4, 86, -292, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 4, -26, 332, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 12, 166, 1164, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 1, 3, 3, 0], [1, -2, 1, 0, 0], [1, 4, 14, 28, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, -4, 38, -68, 289], [1, -8, 54, -152, 361], [1, -4, 46, -92, 529], [1, 4, 62, 116, 841], [1, 8, 62, 248, 961], [1, 4, 14, 148, 1369], [1, -4, 22, -164, 1681], [1, 4, 54, 172, 1849], [1, -12, 126, -564, 2209], [1, 4, 46, 212, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, -20, 230, -1340, 4489], [1, 8, 142, 568, 5041], [1, -4, 86, -292, 5329], [1, 0, 158, 0, 6241], [1, 4, -26, 332, 6889], [1, 12, 214, 1068, 7921], [1, 12, 166, 1164, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/600/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-600-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-600-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.44225868076075064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1467175788107318733, 'z1': {'__RealLiteral__': 0, 'data': '3.26180587408', 'prec': 44}}
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lfunc_instances • Show schema
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id: 9954329
{'Lhash': '1467175788107318733', 'Lhash_array': ['1467175788107318733'], 'label': '4-600-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/15/a|EllipticCurve/Q/40/a'}
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id: 9953150
{'Lhash': '1467175788107318733', 'Lhash_array': ['1467175788107318733'], 'label': '4-600-1.1-c1e2-0-0', 'type': 'ECQP', 'url': 'EllipticCurve/Q/15/a|EllipticCurve/Q/40/a'}
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id: 1223145
{'Lhash': '1467175788107318733', 'Lhash_array': ['1467175788107318733'], 'label': '4-600-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/600/b'}