-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1190079623629554984467070219530', 'a10': -1, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': -1, 'a6': 1, 'a7': 2, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.06620206734282, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1, 1]], [11, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 19], 'central_character': '6270.1', 'coefficient_field': '1.1.1.1', 'conductor': 6270, 'conductor_radical': 6270, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 1], [1, -2, 7], [1, 1], [1, 2, 13], [1, 0, 17], [1, -1], [1, 4, 23], [1, -2, 29], [1, -10, 31], [1, 2, 37], [1, -12, 41], [1, 0, 43], [1, -4, 47], [1, -10, 53], [1, -2, 59], [1, 6, 61], [1, -4, 67], [1, -12, 71], [1, -2, 73], [1, 2, 79], [1, -6, 83], [1, -12, 89], [1, 18, 97], [1, -14, 101], [1, 12, 103], [1, 8, 107], [1, -16, 109], [1, 2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -2, 7], 1]], [[[1, 1], 1]], [[[1, 2, 13], 1]], [[[1, 0, 17], 1]], [[[1, -1], 1]], [[[1, 4, 23], 1]], [[[1, -2, 29], 1]], [[[1, -10, 31], 1]], [[[1, 2, 37], 1]], [[[1, -12, 41], 1]], [[[1, 0, 43], 1]], [[[1, -4, 47], 1]], [[[1, -10, 53], 1]], [[[1, -2, 59], 1]], [[[1, 6, 61], 1]], [[[1, -4, 67], 1]], [[[1, -12, 71], 1]], [[[1, -2, 73], 1]], [[[1, 2, 79], 1]], [[[1, -6, 83], 1]], [[[1, -12, 89], 1]], [[[1, 18, 97], 1]], [[[1, -14, 101], 1]], [[[1, 12, 103], 1]], [[[1, 8, 107], 1]], [[[1, -16, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-6270-1.1-c1-0-53', 'leading_term': '4.07861883548250876530394586712000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/6270/2/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.078618835482509, 4.068561476874576, 4.03831444476161, 3.9876607033126046, 3.9162641552563664, 3.8237064492709223, 3.709535399338471, 3.573322253192158, 3.4147246884131754, 3.233552281551543, 3.029831259705974, 2.8038655608565755, 2.5562915492114455, 2.2881241091911626, 2.0007922405365406, 1.6961626735586866, 1.3765504053642146, 1.0447154215938248, 0.7038452162775918, 0.35752306010521756, 0.009682300313541092, -0.3354526923557262, -0.6734379809115084, -0.999692641824675, -1.30959085674399, -1.5985615881219692, -1.8621936128521015, -2.096343420341846, -2.2972432550491546, -2.461606409776826, -2.5867267659383235, -2.670569540584109, -2.7118502456726734, -2.710098999306521, -2.6657075553664082, -2.579956738247589, -2.4550223811677943, -2.2939583643829566, -2.1006559248011234, -1.8797790487311505, -1.6366764494167387, -1.3772713522213331, -1.1079310419479274, -0.8353188459076561, -0.5662319087553448, -0.30742873595736675, -0.06545101745213405, 0.1535553318642827, 0.3440146841745348, 0.5010863881496832, 0.6208142802509066, 0.7002558562715405, 0.7375863141214322, 0.7321732291036156, 0.6846183432746952, 0.5967638269661064, 0.47166138282502945, 0.31350368435207454, 0.12751883983532672, -0.08017018801598515, -0.3027180371452109, -0.5327569102968072, -0.762618574081609, -0.9845719416274153, -1.1910689834290578, -1.374991118093114, -1.5298878855037636, -1.650199625174668, -1.7314560895002844, -1.7704434230597135, -1.765332732435809, -1.7157645426304655, -1.6228847614311408, -1.4893293165373696, -1.3191563462927662, -1.117726658911863, -0.8915350651482931, -0.6479970679572473, -0.39519718920794705, -0.14160685660477276, 0.1042188055363105, 0.3339548044640739, 0.539819458987294, 0.7148752641708312, 0.8533057972499117, 0.9506574874885304, 1.0040359841869593, 1.0122481992513623, 0.975882841547794, 0.8973243503012948, 0.7806975085091333, 0.6317425947404272, 0.4576236208559567, 0.2666749032800043, 0.06809382038893518, -0.1284099890149494, -0.31299663564246627, -0.4760951558341867, -0.6088046088854526, -0.7032812062862112, -0.7530955476675729, -0.7535446383302419, -0.7019046022605968, -0.5976118595158652, -0.4423629585296455, -0.24012616754058752, 0.0029387632988803155, 0.2786526753861858, 0.5770771953871322, 0.886855620099173, 1.1956235105626856, 1.4904747748866636, 1.7584662413765908, 1.9871415400239338, 2.1650536355815557, 2.2822646786972203, 2.330802022443767, 2.305050315904038, 2.202061523801551, 2.021767483673786, 1.7670831149622763, 1.4438925179405862, 1.0609147936843966, 0.629451302334034, 0.1630210592523751, -0.32310416090286703, -0.8124488951747122, -1.2879471034279366, -1.732595886439413, -2.1301239659879494, -2.465647691051967, -2.726287059314351, -2.901715134299037, -2.984616296581172, -2.971031942571908, -2.8605764355725145, -2.65651117208423, -2.365670359274763, -1.998238278056053, -1.5673841737767662, -1.0887671992158832, -0.5799297529329183, -0.05960283738791649, 0.4530485478495872, 0.9392086840965737, 1.381189802729469, 1.7631722986390879, 2.0718735612815715, 2.297114906611923, 2.4322599283014243, 2.4745027155936508, 2.4249906136823793, 2.2887732801354717, 2.074577420582553, 1.7944144370814163, 1.4630359413766731, 1.0972593159959363, 0.7151919037155555, 0.33538765327020736, -0.024026127191717886, -0.3462120731849384, -0.616435888954628, -0.8227905138126572, -0.956795838315202, -1.0138435001914674, -0.9934628557721368, -0.8993920675624587, -0.7394470393199194, -0.525190279157532, -0.27141125397701643, 0.004561028324767225, 0.28368405014443965, 0.5461300168736076, 0.7722741688637214, 0.9436971951488672, 1.044154002534645, 1.060461549890785, 0.9832611749968497, 0.8076157490611374, 0.5334089141802552, 0.16552231230357484, -0.2862232692635298, -0.8073659765475264, -1.3793319819069403, -1.9801761491266876, -2.5855042571804883, -3.1695373840923327, -3.706271334228957, -4.170678353714563, -4.539895141385093, -4.794340540086866, -4.918708376588606, -4.9027856698273995, -4.742053677610943, -4.438038706253292, -3.9983908563242005, -3.43668141385974, -2.7719228384618333, -2.02782861838707, -1.2318430108711558, -0.4139822302453605, 0.3944616009117809, 1.1622949733260213, 1.8598124848078756, 2.460136065944068, 2.94044009499713, 3.283003082862956, 3.4760340916057464, 3.514232174837822, 3.399049440564376, 3.13864226518213, 2.747510068214426, 2.2458361687925366, 1.658559840464351, 1.0142220274141158, 0.34363859995388285, -0.32153608633601655, -0.9502866837180858, -1.513684214702202, -1.986233092826469, -2.3470520683368967, -2.5808311644101387, -2.678517434911158, -2.6376955945362854, -2.4626446024509816, -2.164067375852301, -1.7585071606894138, -1.267479860223078, -0.716366004998714, -0.13311828918792576, 0.45314995055904755, 1.0136237876862235, 1.5212192598320669, 1.9519166950478062, 2.2859271464063515, 2.5086328651617458, 2.611254439879016, 2.5912114370650277, 2.4521593669822166, 2.203702734641168, 1.8608009306702489, 1.4428998690719599, 0.972836725155198, 0.4755770874832778, -0.023147340343228927, -0.4982271582107344, -0.9265152100267715, -1.2880461928998503, -1.5670707108180102, -1.7528487210197599, -1.8401604999451773, -1.8295087357304827, -1.7270022994971377, -1.5439297355171135, -1.2960475815671868, -1.0026243424596912, -0.6852944174799862], 'positive_zeros': ['0.938807289181491775996032330550074', '2.16970081935074665585588571067596', '2.74801024334518992786568969276656', '3.72984217375553538303485753938561', '4.42231900043726605021999191647626', '4.96822164670189356884257822170166', '5.82835451590808052320601497422452', '6.66163117079340794372788881734334', '7.44985818622744180059220043792247', '7.967988589004075164769783940151096'], 'prelabel': '2-6270-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.075747456441816, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1234820813666824771, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.938807289181491775996032330550', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.16970081935074665585588571068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74801024334518992786568969277', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 50.06620206734282, 'bad_primes': [2, 3, 5, 11, 19], 'central_character': '1.1', 'conductor': 6270, 'conductor_radical': 6270, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -1, 1, 2, 1, 1, -1, -1, 1, -2, 2, -1, 1, 0, 1, 1, -1, 2, -1, -4, 1, 1, -2, 1, 2, 2, -1, 10, 1, -1, 0, -2, 1, -2, 1, -2, -1, 12, 2, 0, -1, -1, -4, 4, 1, -3, 1, 0, -2, 10, 1, 1, 2, 1, 2, 2, -1, -6, 10, 2, 1, 2, -1, 4, 0, -4, -2, 12, 1, 2, -2, 1, 1, -2, -2, -2, -1, 1, 12, 6, 2, 0, 0, 2, -1, 12, -1, -4, -4, 10, 4, -1, 1, -18, -3, -1, 1], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, -1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -12, 41], 'euler43': [1, 0, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -2, 59], 'euler61': [1, 6, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, -12, 71], 'euler73': [1, -2, 73], 'euler79': [1, 2, 79], 'euler83': [1, -6, 83], 'euler89': [1, -12, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -2, 7], [1, 1, 0], [1, 2, 13], [1, 0, 17], [1, -1, 0], [1, 4, 23], [1, -2, 29], [1, -10, 31], [1, 2, 37], [1, -12, 41], [1, 0, 43], [1, -4, 47], [1, -10, 53], [1, -2, 59], [1, 6, 61], [1, -4, 67], [1, -12, 71], [1, -2, 73], [1, 2, 79], [1, -6, 83], [1, -12, 89], [1, 18, 97]], 'index': 53, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6270/q', 'ModularForm/GL2/Q/holomorphic/6270/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/6270/2/a/q'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-6270-1.1-c1-0-53', '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': '2-6270-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.075747456441816, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1234820813666824771, 'z1': {'__RealLiteral__': 0, 'data': '0.938807289181491775996032330550', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21669989
{'Lhash': '1190079623629554984467070219530', 'Lhash_array': ['1190079623629554984467070219530'], 'label': '2-6270-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6270/2/a/q'}
-
id: 24574221
{'Lhash': '1190079623629554984467070219530', 'Lhash_array': ['1190079623629554984467070219530'], 'label': '2-6270-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6270/2/a/q/1/1'}
-
id: 23130
{'Lhash': '1234820813666824771', 'Lhash_array': ['1234820813666824771'], 'label': '2-6270-1.1-c1-0-53', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6270/q'}