-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1353195530351594429859181458876', 'a10': [0.0, 0.0], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [-0.09903113209758087, 0.4338837391175581], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.0, 0.0], 'a6': [-0.09903113209758087, -0.4338837391175581], 'a7': [0.2225209339563144, -0.9749279121818236], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [0.7225209339563144, 0.3479477433504717], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9009688679024191, -0.4338837391175581]]], [7, [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]]], [17, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1186895268661799880594303422233', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.09903113209758087, -0.4338837391175581], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [1.6234898018587336, -0.7818314824680298], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [-1.6234898018587336, 0.7818314824680298], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.1234898018587336, 1.4088116512993818], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0.2774790660436856, -0.3479477433504717], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.2774790660436856, 0.3479477433504717], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [-1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [-0.40096886790241915, -0.1930964297137938], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.40096886790241915, 1.7567593946498534], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-1.1234898018587336, -0.5410441730642654], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3332-3332.1835-c0-0-1', 'leading_term': '0.88324513087135754296131920918474', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/be/a/1835/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.8832451308713576, 0.8861650150804549, 0.892142795306327, 0.9004169022185555, 0.9097640570968096, 0.9186350576375962, 0.9252984570008839, 0.927970961352372, 0.9249241262568515, 0.9145660135501179, 0.8955016062963952, 0.8665773741323808, 0.8269148494070618, 0.7759366936301166, 0.713387277150003, 0.6393486006772227, 0.554251536914185, 0.45888183243594405, 0.35438001967179933, 0.2422342845198627, 0.1242653682572629, 0.0026027179502994733, -0.1203486872357299, -0.2419511335910271, -0.3593865756879882, -0.4697182742536561, -0.5699609256099406, -0.6571581561760934, -0.728465875119643, -0.7812396134980247, -0.8131236427422532, -0.8221393729725216, -0.8067702961988505, -0.7660405742104921, -0.6995842881167379, -0.6077023767066035, -0.49140440254877665, -0.3524325038905662, -0.19326521960728532, -0.017099312784015244, 0.17219173886300015, 0.370123279588484, 0.5716890130981969, 0.7714737300683927, 0.9637875868237932, 1.1428194497741393, 1.3028059830476337, 1.4382123590061353, 1.543919744349158, 1.6154140899590708, 1.6489702612917512, 1.6418252166761982, 1.5923337987206525, 1.5001007699269029, 1.3660830126362757, 1.1926563338085094, 0.9836420674021563, 0.7442896434331624, 0.4812124764885303, 0.20227589200294607, -0.08356267828803086, -0.36645938200256295, -0.6359319892289137, -0.8811450953691293, -1.09122567148016, -1.2556006570944063, -1.3643469817340528, -1.4085433367555802, -1.3806122543532153, -1.2746406340491274, -1.086666827925526, -0.8149227817328858, -0.4600205438699667, -0.025073697105580803, 0.4842540782008392, 1.0597790692289446, 1.6909096249983138, 2.3648410594425653, 3.0668313389988104, 3.78055263548125, 4.488510939680114, 5.172523162132722, 5.81423860370717, 6.3956894669452415, 6.899853300231337, 7.311209010945217, 7.6162674262517225, 7.8040573779373865, 7.866548975655213, 7.798997121422067, 7.600190391128069, 7.272593122744063, 6.822371835285002, 6.259300860979287, 5.596546185641378, 4.850330819157506, 4.0394894040893625, 3.1849240505227647, 2.3089773904402153, 1.43474240886624, 0.585331575266313, -0.21686997288733537, -0.9509410688899003, -1.598124421847289, -2.1424637985967276, -2.571354073583838, -2.8759823084205833, -3.051641519035781, -3.0979031052397388, -3.0186389127191107, -2.8218893951897313, -2.5195801414753936, -2.1270949053934833, -1.6627189907399365, -1.1469721625131164, -0.6018549497859981, -0.0500360642020165, 0.4859885026114793, 0.9847324663957396, 1.4265196821926283, 1.7942162985308958, 2.073865149305073, 2.2551963983112873, 2.3319930987472377, 2.3022959583897746, 2.168437996530817, 1.9369066874098269, 1.618038323434522, 1.2255563983607682, 0.7759724988555874, 0.28787420366494565, -0.21887045412986697, -0.7239585467648698, -1.20751195091652, -1.6509143667024468, -2.03758950315252, -2.3536865489123264, -2.5886428551268135, -2.735598960172957, -2.7916474746336477, -2.757904651782998, -2.6394013774897145, -2.4447984722875042, -2.1859392361744376, -1.8772597094584866, -1.5350838113893301, -1.1768360252678325, -0.8202083455767113, -0.4823205738552259, -0.17891360497120654, 0.07638597277695734, 0.27269480001881014, 0.40236490773142486, 0.46131522865457264, 0.44918619369570606, 0.3693096520298963, 0.22849533664789834, 0.036644127397809347, -0.1937930022139836, -0.44848366289918973, -0.7119770848161325, -0.9685232442135575, -1.2029066700324942, -1.401252415269058, -1.5517627057810717, -1.645345922803973, -1.676104711332032, -1.64165690755723, -1.5432713229244241, -1.3858098077991765, -1.1774769802813483, -0.9293890420584832, -0.6549826958447393, -0.3692938225531247, -0.0881428042764956, 0.17273121129087612, 0.3985415344027516, 0.5762841449862811, 0.6954819017798374, 0.7488016715219938, 0.7325094571509629, 0.6467367196693923, 0.49554076987938317, 0.28675286838281955, 0.03161896181890957, -0.25575079310550686, -0.5590970113542033, -0.8608545543713564, -1.1430809530428436, -1.3884209169714974, -1.5810552978876284, -1.7075828519412402, -1.7577859258874682, -1.7252366807019202, -1.6077084182443677, -1.4073666076449816, -1.1307258113126057, -0.7883712816598801, -0.39445686804340113, 0.03399666298538365, 0.47796742753320054, 0.9174172643524499, 1.3323432393103187, 1.7038389123952336, 2.015107016266888, 2.2523669668981166, 2.405605585819852, 2.4691273477092754, 2.441870992917209, 2.3274719242161415, 2.1340637750624505, 1.873827134146702, 1.5623078262683245, 1.2175405626935047, 0.8590254032228241, 0.5066136186175277, 0.17936563233540886, -0.10555365786593618, -0.33387794909547863, -0.4950815459907702, -0.5830091684306364, -0.5962538207782143, -0.5382569307771934, -0.41712068555632054, -0.24513911958875326, -0.03807110173367971, 0.18580603847113839, 0.40680984115911273, 0.6050697050338723, 0.7617768134332966, 0.8603928398481887, 0.8877441227471731, 0.8349331854991462, 0.6980088039444361, 0.47834884694260327, 0.1827261613225448, -0.17695402531806229, -0.5842373691813313, -1.018997157113984, -1.4585590929131644, -1.8790126418315931, -2.2566346387863367, -2.5693421211121983, -2.798087297382707, -2.928108577241305, -2.949957742600583, -2.8602344164865543, -2.6619744647108092, -2.3646580561815127, -1.9838247840194725, -1.540306304930528, -1.0591100669791293, -0.568009504435854, -0.09591526019959085, 0.3288826531031219, 0.6805013352116678, 0.9371747972481482], 'positive_zeros': ['1.06748305101418593736976033203801', '1.98518704187982317773688742128989', '3.03205587319924430838075138901793', '3.70971037076037997130686393963997', '5.11479966696119749304116492927451', '5.89527135838287467227718524356397', '6.63050906769722321567733556697865', '7.60080360299507606931143394430651', '7.981246875049074950077669674279813', '8.852515983537283689492893576032485'], 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.06122448979591837, 'root_number': '0.92691675734602176302483849969967 - 0.37526700487937413388755922567427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.061224489795918366', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06748305101418593736976033204', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98518704187982317773688742129', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03205587319924430838075138902', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/a/1835/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-3332-3332.1835-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.06122448979591837, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06748305101418593736976033204', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1353195530351594429859181458876', 'Lhash_array': ['1353195530351594429859181458876'], 'factors': ['2-3332-3332.1835-c0-0-1'], 'label': '2-3332-3332.1835-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/a/1835/1'}