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  • lfunc_lfunctions • Show schema
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'9.131126785841765477617157557679301', '9.179278558063589002750104557368398', '10.10753785302168163968277595759855', '10.72665792889003534743245662326835', '10.87340721492894986045430752164811', '11.26615596369562402083065683203878', '11.76637313414445777803365983016376', '11.96700065379150229602644614103589', '12.57742948317407991377594083787963', '12.96371228446560967973435590436129', '12.99788698840615984940876288346161', '13.62064953262927678806666962453713', '13.84607403568569026553937743450832', '14.10805208349481581765795652614701'], 'prelabel': '6-85e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.239455815703439, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e3-0', 'trace_hash': 339429590117236220, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844794642058816184049789383884', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.88011937806202983031938187515', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.62531486020739504467690275918', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 126.14062822545836, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 614125, 'conductor_radical': 85, 'degree': 6, 'dirichlet_coefficients': [1, 3, 9, -8, -15, 27, 34, -28, 30, -45, 52, -72, 19, 102, -135, 57, -51, 90, -153, 120, 306, 156, 162, -252, 150, 57, 43, -272, 45, -405, -67, 55, 468, -153, -510, -240, -308, -459, 171, 420, 498, 918, -246, -416, -450, 486, 101, 513, 77, 450, -459, -152, 893, 129, -780, -952, -1377, 135, 355, 1080, 1019, -201, 1020, -968, -285, 1404, 334, 408, 1458, -1530, 313, -840, 639, -924, 1350, 1224, 1768, 513, -92, -855, -432, 1494, 2736, -2448, 765, -738, 405, -1456, 1623, -1350, 646, -1296, -603, 303, 2295, 495, -475, 231, 1560, -1200], 'euler11': [1, -52, 4255, -131640, 5663405, -92121172, 2357947691], 'euler13': [1, -19, 3503, -63078, 7696091, -91709371, 10604499373], 'euler17': [1, 51, 867, 4913, 0, 0, 0], 'euler19': [1, 153, 24705, 2055742, 169451595, 7198019793, 322687697779], 'euler2': [1, -3, 17, -47, 136, -192, 512], 'euler23': [1, -162, 33959, -3354848, 413179153, -23981814018, 1801152661463], 'euler29': [1, -45, 41855, -3758830, 1020801595, -26767049445, 14507145975869], 'euler3': [1, -9, 51, -232, 1377, -6561, 19683], 'euler31': [1, 67, 90455, 3992628, 2694744905, 59462746627, 26439622160671], 'euler37': [1, 308, 167747, 30322920, 8496888791, 790243733972, 129961739795077], 'euler41': [1, -498, 254751, -67696460, 17557693671, -2365551912018, 327381934393961], 'euler43': [1, 246, 181205, 31053676, 14407065935, 1555055310054, 502592611936843], 'euler47': [1, -101, 57549, -58547970, 5974909827, -1088700748229, 1119130473102767], 'euler5': [1, 15, 75, 125, 0, 0, 0], 'euler53': [1, -893, 701847, -288997110, 104488875819, -19792774488197, 3299763591802133], 'euler59': [1, -355, 550657, -122030058, 113093384003, -14974089442555, 8662995818654939], 'euler61': [1, -1019, 1002319, -494848778, 227507368939, -52499261473859, 11694146092834141], 'euler67': [1, -334, 908949, 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[1, 153, 24705, 2055742, 169451595, 7198019793, 322687697779], [1, -162, 33959, -3354848, 413179153, -23981814018, 1801152661463], [1, -45, 41855, -3758830, 1020801595, -26767049445, 14507145975869], [1, 67, 90455, 3992628, 2694744905, 59462746627, 26439622160671], [1, 308, 167747, 30322920, 8496888791, 790243733972, 129961739795077], [1, -498, 254751, -67696460, 17557693671, -2365551912018, 327381934393961], [1, 246, 181205, 31053676, 14407065935, 1555055310054, 502592611936843], [1, -101, 57549, -58547970, 5974909827, -1088700748229, 1119130473102767], [1, -893, 701847, -288997110, 104488875819, -19792774488197, 3299763591802133], [1, -355, 550657, -122030058, 113093384003, -14974089442555, 8662995818654939], [1, -1019, 1002319, -494848778, 227507368939, -52499261473859, 11694146092834141], [1, -334, 908949, -198667084, 273378228087, -30213099644446, 27206534396294947], [1, -313, 220279, -328713084, 78840277169, -40095388867273, 45848500718449031], [1, -639, 561171, -520727922, 218305058907, -96702570598671, 58871586708267913], [1, 92, 473747, 401620008, 233575747133, 22364045907932, 119851595982618319], [1, -2736, 4202357, -3879938416, 2402853101959, -894508861537584, 186940255267540403], [1, -1623, 2707547, -2262712862, 1908736701043, -806600635229703, 350356403707485209], [1, 475, 1815539, 393329682, 1656993425747, 395661702341275, 760231058654565217]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/4/a/f'], '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': '6-85e3-1.1-c3e3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '6-85e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.239455815703439, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 339429590117236220, 'z1': {'__RealLiteral__': 0, 'data': '0.844794642058816184049789383884', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1070904435075450546545131173404,2383334458101057472019713556257,3327981958329994492107237401816', 'Lhash_array': ['1070904435075450546545131173404', '2383334458101057472019713556257', '3327981958329994492107237401816'], 'factors': ['2-85-1.1-c3-0-0', '2-85-1.1-c3-0-5', '2-85-1.1-c3-0-9'], 'label': '6-85e3-1.1-c3e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/4/a/f'}