-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2197345536374245251951832927947', 'a10': [-0.9510565162951535, 0.30901699437494745], 'a2': [-0.4539904997395468, -0.8910065241883679], 'a3': [0.0, 0.0], 'a4': [-0.5877852522924731, 0.8090169943749475], 'a5': [0.15643446504023087, -0.9876883405951378], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.9876883405951378, 0.15643446504023087], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.4539904997395468, 0.8910065241883679]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.15643446504023087, 0.9876883405951378]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.647', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '1227681179526397213305522808773', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4539904997395468, 0.8910065241883679]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.15643446504023087, 0.9876883405951378]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.2787682579175257, -0.14203952192020614], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.2975560346993159, 1.8786948647835056], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-0.734572059148137, -0.5336978408555909], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.8090169943749475, 1.5877852522924731], [-0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [1.8786948647835056, -0.6104249647797777], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0.18389974300182033, 1.1610972809260942], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.36327126400268045, 1.118033988749895], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.8968022466674206, -1.760073510670101], [-0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0.5506723161463166, -1.6947951217816852], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.14203952192020614, -0.8968022466674206], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, -1.7820130483767358], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.118033988749895, 0.36327126400268045], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.2805815594085902, -0.5506723161463166], [-0.5877852522924731, -0.8090169943749475]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-30e2-300.47-c0-0-1', 'leading_term': '0.76278114876883842800258169972572', '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/900/1/bh/a/647/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.7627811487688384, 0.8055552795349428, 0.858926851291725, 0.9231840606223233, 0.9977963674229425, 1.081558830370299, 1.1727600266800178, 1.2693255024812085, 1.3689192355795556, 1.46900703870712, 1.5668944483001959, 1.6597519553410063, 1.7446374669128961, 1.8185225177506568, 1.8783260343538626, 1.920957525973483, 1.9433702639065638, 1.94262410415263, 1.9159569487241885, 1.8608633256092826, 1.77517813904609, 1.657163272747591, 1.5055944100223937, 1.3198451685559651, 1.099965442495768, 0.8467507122454337, 0.5617990360042027, 0.24755248920427353, -0.09268002036544062, -0.4547213543613141, -0.8335485526695583, -1.2233409129075095, -1.6175549582472333, -2.009026754399547, -2.390101183814856, -2.7527868564884015, -3.0889343576470147, -3.39043453337638, -3.649432530459785, -3.858552374143527, -4.011126027104121, -4.101420165130871, -4.124853369608908, -4.078196110817134, -3.9597458119388724, -3.769469467884987, -3.509106763952797, -3.182227405857796, -2.7942374327851645, -2.3523306249578213, -1.8653827104967782, -1.343787884178389, -0.7992391220398094, -0.24445584844829035, 0.3071353855723585, 0.8417595015484454, 1.3456811405141629, 1.805611228976947, 2.209119139759159, 2.545036710199322, 2.803839817882156, 2.9779931587790234, 3.062244363752636, 3.053854646448889, 2.952754796141296, 2.761617486743891, 2.485839517002757, 2.1334306515424, 1.7148090998115844, 1.2425072315418282, 0.7307947479617931, 0.19523006067651458, -0.34784607842177906, -0.8818577556601582, -1.390562585053169, -1.8586209265212887, -2.2721437488175997, -2.61919721740898, -2.890242967898869, -3.0784948341147107, -3.1801755079907026, -3.1946601449020653, -3.1244981805128442, -2.9753094417311283, -2.755555828768667, -2.4761952034055192, -2.1502294066518477, -1.7921633036996976, -1.4173961733201963, -1.041570393618925, -0.6799050219940109, -0.3465433559770179, -0.053943771395059584, 0.18765800212742648, 0.37068949673355567, 0.4905631226229032, 0.5458618439158969, 0.538377902057014, 0.4730002384880807, 0.3574533734069165, 0.20189771455191366, 0.018408248599817524, -0.17964504720488375, -0.3782862860877, -0.5636592549888686, -0.722753813987425, -0.8440964348727539, -0.9183690337842771, -0.9389229376510777, -0.9021592972389622, -0.8077533605302641, -0.6587074963548244, -0.4612263737421793, -0.22441685183224888, 0.040175538610638835, 0.3191726244674931, 0.5980830170824153, 0.8620988786134978, 1.0969287180235978, 1.289621696864331, 1.4293380104831839, 1.5080214307885975, 1.5209340648929004, 1.4670196788481271, 1.349070303113086, 1.1736808968009422, 0.9509881115111947, 0.6942010850934028, 0.4189440737990257, 0.1424419340708605, -0.11741066169132539, -0.3430474551661779, -0.5182419830965, -0.6290752080156925, -0.66480302085801, -0.6185709849678934, -0.4879305765909478, -0.2751209314999704, 0.012907714365549727, 0.36473870423109145, 0.7649964900457431, 1.1950964013581011, 1.6342013220257785, 2.060336722238262, 2.4516046003832885, 2.787429051821397, 3.049761978726803, 3.2241772769492525, 3.3007858522488713, 3.2749119591994336, 3.14748330517704, 2.9251025644762816, 2.6197856333247285, 2.24837117576861, 1.8316256830893918, 1.3930872441258866, 0.9577083435166625, 0.5503721757926775, 0.19436722358521238, -0.09008956868585899, -0.28719030548108043, -0.38664864634169915, -0.38451197906728485, -0.283613204650013, -0.09362153636673737, 0.1693256529843531, 0.48340333818731535, 0.8222600176706526, 1.1565037551202149, 1.455435628205807, 1.6889353349479914, 1.8293910008378163, 1.853558562634868, 1.7442361026448563, 1.4916454122725498, 1.0944267056483612, 0.5601721958157382, -0.09455079659349437, -0.8447077436477012, -1.6578253567303807, -2.4954987045636488, -3.315305201268834, -4.073027089149261, -4.725062542296671, -5.230890561238793, -5.555447527864159, -5.671274320007961, -5.5603024303575275, -5.2151652592897095, -4.639945805564983, -3.850303034468735, -2.87295452287416, -1.7445305151577846, -0.5098520302211746, 0.7802791623208272, 2.071660244328893, 3.309494173685632, 4.441265130767283, 5.419517457889891, 6.204376249885167, 6.765660947338889, 7.08446575091916, 7.154111184942403, 6.9804079269883825, 6.58121489181292, 5.98531601504478, 5.230681581684468, 4.362217663746445, 3.42913883912996, 2.4821227812623445, 1.5704189522373913, 0.7390865244131016, 0.0265285024057922, -0.537529761457526, -0.9334977520000847, -1.1527288106530182, -1.1976386331025761, -1.0811351947218948, -0.8254062688721143, -0.4601519156780801, -0.020384785788731426, 0.4560515808154745, 0.9310789393530811, 1.3689213450620856, 1.7384148326987432, 2.0149384716705727, 2.181842567687697, 2.231285259542211, 2.1644302362704035, 1.991002932907673, 1.7282472683300054, 1.399366653214158, 1.0315686954132715, 0.6538602358032827, 0.2947561109430768, -0.019929865247211357, -0.2690501855927011, -0.4377022816343426, -0.518306514696648, -0.5111067566881126, -0.4240596440750302, -0.27212398715212816, -0.07600646163423096, 0.13953967377583298, 0.34773251201142186, 0.5219417452558196, 0.6378642730169274, 0.6755280285911444, 0.6209692263141033, 0.46745229100453545, 0.21613580371601496, -0.12387058331948271, -0.5360672057599786, -0.9977052079213773, -1.4814242597715819, -1.9572655627911912, -2.3949087115600385], 'positive_zeros': ['1.73339998890753683225415096371753', '3.34006237433020444579974751398769', '4.45996800367113574001194358651550', '5.76280529887054441818396383951712', '6.31843822283589925636486984091095', '7.11580315275210090739241463722705', '8.095988553510903370117928663791768', '8.622485955073829276506194713862019', '9.915679063825848240511083519134735', '10.27404933109684301280784186878378'], 'prelabel': '2-30e2-300.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': 0.6159132760153037, 'root_number': '-0.35615730622874792966254977261576 + 0.93442601270506263190754295780000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.30795663800765183', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73339998890753683225415096372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34006237433020444579974751399', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45996800367113574001194358652', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'bad_primes': [2, 3, 5], 'central_character': '300.47', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/1/bh/a/647/1'], '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': '2-30e2-300.47-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': '2-30e2-300.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': 0.30795663800765183, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73339998890753683225415096372', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2197345536374245251951832927947', 'Lhash_array': ['2197345536374245251951832927947'], 'label': '2-30e2-300.47-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/1/bh/a/647/1'}