Formats: - HTML - YAML - JSON - 2026-09-22T23:37:20.869152
  • lfunc_lfunctions • Show schema
    {'Lhash': '2219283491051625911777630008075', 'a10': 0, 'a2': -6, 'a3': 27, 'a4': -92, 'a5': 0, 'a6': -162, 'a7': 64, 'a8': 1320, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.428876911309143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[3, [1, -27]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': '1.1.1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, 6, 128], [1, -27], [1], [1, -64, 823543], [1, 948, 19487171], [1, -5098, 62748517], [1, 28386, 410338673], [1, 8620, 893871739], [1, -15288, 3404825447], [1, -36510, 17249876309], [1, 276808, 27512614111], [1, 268526, 94931877133], [1, 629718, 194754273881], [1, 685772, 271818611107], [1, 583296, 506623120463], [1, -428058, 1174711139837], [1, -1306380, 2488651484819], [1, -300662, 3142742836021], [1, -507244, 6060711605323], [1, -5560632, 9095120158391], [1, 1369082, 11047398519097], [1, 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27136050989627], 1]], [[[1, 8528310, 44231334895529], 1]], [[[1, -8826814, 80798284478113], 1]], [[[1, -11986422, 107213535210701], 1]], [[[1, 7209392, 122987386542487], 1]], [[[1, 11426076, 160578147647843], 1]], [[[1, -4020950, 182803912081669], 1]], [[[1, -17706318, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-75-1.1-c7-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/75/8/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 24}, 'plot_values': [-9.46822051065201e-61, 0.19326773025209468, 0.38355983976282054, 0.5679354502862562, 0.7435230131520717, 0.9075545783812944, 1.0573995693003742, 1.190597865826638, 1.30489197382356, 1.3982580277277314, 1.4689353403199215, 1.5154541785384141, 1.5366614092702406, 1.5317436258935615, 1.5002473368627547, 1.442095773754724, 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['1.75070598369303286956411496559841', '3.66033208967544635713432022352151', '4.99887208551786807683805672884460', '6.87122362662039265666322735214680', '8.288927942706428154565646572768530', '8.929231150691246109000272832027781', '10.08900940400237195845216841165750', '11.18709112718531932496653723204549', '12.90899629170101606814239506455146'], 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c7-0', 'trace_hash': 1781576519116339598, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75070598369303286956411496560', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.66033208967544635713432022352', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.99887208551786807683805672884', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.428876911309143, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, -6, 27, -92, 0, -162, 64, 1320, 729, 0, -948, -2484, 5098, -384, 0, 3856, -28386, -4374, -8620, 0, 1728, 5688, 15288, 35640, 0, -30588, 19683, -5888, 36510, 0, -276808, -192096, -25596, 170316, 0, -67068, -268526, 51720, 137646, 0, -629718, -10368, -685772, 87216, 0, -91728, -583296, 104112, -819447, 0, -766422, -469016, 428058, -118098, 0, 84480, -232740, -219060, 1306380, 0, 300662, 1660848, 46656, 659008, 0, 153576, 507244, 2611512, 412776, 0, 5560632, 962280, -1369082, 1611156, 0, 793040, -60672, -825876, -6913720, 0, 531441, 3778308, 4376748, -158976, 0, 4114632, 985770, -1251360, -8528310, 0, 326272, -1406496, -7473816, 3499776, 0, -5186592, 8826814, 4916682, -691092, 0], 'euler11': [1, 948, 19487171], 'euler13': [1, -5098, 62748517], 'euler17': [1, 28386, 410338673], 'euler19': [1, 8620, 893871739], 'euler2': [1, 6, 128], 'euler23': [1, -15288, 3404825447], 'euler29': [1, -36510, 17249876309], 'euler3': [1, -27, 0], 'euler31': [1, 276808, 27512614111], 'euler37': [1, 268526, 94931877133], 'euler41': [1, 629718, 194754273881], 'euler43': [1, 685772, 271818611107], 'euler47': [1, 583296, 506623120463], 'euler5': [1, 0, 0], 'euler53': [1, -428058, 1174711139837], 'euler59': [1, -1306380, 2488651484819], 'euler61': [1, -300662, 3142742836021], 'euler67': [1, -507244, 6060711605323], 'euler7': [1, -64, 823543], 'euler71': [1, -5560632, 9095120158391], 'euler73': [1, 1369082, 11047398519097], 'euler79': [1, 6913720, 19203908986159], 'euler83': [1, -4376748, 27136050989627], 'euler89': [1, 8528310, 44231334895529], 'euler97': [1, -8826814, 80798284478113], 'euler_factors': [[1, 6, 128], [1, -27, 0], [1, 0, 0], [1, -64, 823543], [1, 948, 19487171], [1, -5098, 62748517], [1, 28386, 410338673], [1, 8620, 893871739], [1, -15288, 3404825447], [1, -36510, 17249876309], [1, 276808, 27512614111], [1, 268526, 94931877133], [1, 629718, 194754273881], [1, 685772, 271818611107], [1, 583296, 506623120463], [1, -428058, 1174711139837], [1, -1306380, 2488651484819], [1, -300662, 3142742836021], [1, -507244, 6060711605323], [1, -5560632, 9095120158391], [1, 1369082, 11047398519097], [1, 6913720, 19203908986159], [1, -4376748, 27136050989627], [1, 8528310, 44231334895529], [1, -8826814, 80798284478113]], 'index': 17, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/8/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/75/8/a/a'], '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': '2-75-1.1-c7-0-17', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1781576519116339598, 'z1': {'__RealLiteral__': 0, 'data': '1.75070598369303286956411496560', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 20734850
      {'Lhash': '2219283491051625911777630008075', 'Lhash_array': ['2219283491051625911777630008075'], 'factors': ['2-75-1.1-c7-0-17'], 'label': '2-75-1.1-c7-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/a/a'}
    • id: 24559427
      {'Lhash': '2219283491051625911777630008075', 'Lhash_array': ['2219283491051625911777630008075'], 'factors': ['2-75-1.1-c7-0-17'], 'label': '2-75-1.1-c7-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/a/a/1/1'}