-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2830460370761810246067857730179', 'a10': [0.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [-0.5, -0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [-1.0, 3.9689140359382235e-80], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1051', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1249539521792257103525163874424', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 1.7320508075688772], [-0.5, -0.8660254037844386]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-0.5, 0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1800-72.43-c0-0-4', 'leading_term': '1.5478931548974913714753146919935', '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/1800/1/bk/d/1051/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5478931548974915, 1.6553054248194987, 1.7851519245659544, 1.939176280722526, 2.1178466632010373, 2.3204844340564375, 2.5454658518876547, 2.790423212074378, 3.0524055010593805, 3.327989783744979, 3.6133523224186965, 3.9043142872884142, 4.196376114204263, 4.484751324491006, 4.764407168617428, 5.030116593574077, 5.276523872496245, 5.498224640480912, 5.689859882800612, 5.846222485269786, 5.962374191964516, 6.033770171920677, 6.056387850334343, 6.026856205635269, 5.942581377122301, 5.801864180343701, 5.604005003522521, 5.349391572729258, 5.039565239121526, 4.6772617680397195, 4.266423102133037, 3.8121772284537014, 3.3207840956714203, 2.7995464883818575, 2.2566858499121065, 1.7011842249737616, 1.142594734201362, 0.5908242533126087, 0.05589320474185802, -0.45232146992130334, -0.9243530533107771, -1.351413549078337, -1.7256553349243555, -2.040417007752118, -2.290444394428897, -2.472077971326593, -2.5833985540197646, -2.624324088792729, -2.5966516893140805, -2.5040406893333644, -2.351934384663446, -2.147420259352137, -1.8990307624630314, -1.6164890420947724, -1.3104063616982795, -0.9919401238259027, -0.6724234092197102, -0.3629786074711771, -0.07412897845364419, 0.18457723879502627, 0.40491532602794506, 0.5802907199535204, 0.705990294046287, 0.7793664057901757, 0.7999440176938144, 0.7694439190575871, 0.6917182366226038, 0.5725979147762137, 0.41965553653623305, 0.2418905939854859, 0.04934793811567842, -0.1473165251162792, -0.3373059393207021, -0.510169169444188, -0.6562832710730983, -0.7673103066279093, -0.836607310902523, -0.8595694352758978, -0.833888496973433, -0.7597122774121288, -0.6396938558180972, -0.4789248899915222, -0.2847518834946076, -0.0664798912771513, 0.16502642867224054, 0.39782927000182006, 0.6194717292488022, 0.817575513590844, 0.9804552985647557, 1.0977208241648786, 1.160837225132656, 1.1636149053895417, 1.102602516922106, 0.9773602494329017, 0.7905955661519587, 0.548149550409653, 0.25882890892079674, -0.06591389275134035, -0.4124422568779597, -0.7655212813423417, -1.1090033325876996, -1.4265829498705758, -1.7025859930509994, -1.922754854397025, -2.074990276202521, -2.1500109984807603, -2.1418951576724807, -2.048472018516452, -1.871539091858983, -1.6168877134987587, -1.2941293813288512, -0.9163251381158286, -0.4994305523460886, -0.061578859251055405, 0.37776596281220015, 0.7987465122650124, 1.182093914903764, 1.510104739005782, 1.767561804627008, 1.942549086801754, 2.0271148965713195, 2.0177441158021234, 1.9156092078181965, 1.7265806319146642, 1.4609896368668454, 1.1331495758200942, 0.7606551798045662, 0.3634919205539363, -0.03700104082747105, -0.4192614668112164, -0.7626686173567083, -1.0486785200558248, -1.2618664135906552, -1.3908161317947252, -1.4288029813493175, -1.3742266936847354, -1.230763852203766, -1.0072241830099935, -0.7171114751464595, -0.37790677829250857, -0.010107960994974718, 0.3639252619746275, 0.7212590278308948, 1.0397343965146137, 1.2993007112981125, 1.483254727682612, 1.57931008103387, 1.5804292704442386, 1.4853621767476772, 1.2988506648443212, 1.0314772643601884, 0.6991562960228743, 0.3222869799733099, -0.07539119794860953, -0.46818152077155817, -0.829975937483529, -1.135876022629039, -1.3637937449572042, -1.4959347645251346, -1.5200706930517853, -1.43051619389259, -1.2287416049784456, -0.9235712437583258, -0.5309406943318508, -0.07321192279257728, 0.42192843421467346, 0.9229363719462376, 1.3961684730614887, 1.8078355685745926, 2.1260421727007857, 2.3227928766154133, 2.3758448449205276, 2.2702907109357926, 1.9997684385943664, 1.567213599732433, 0.9850940764155619, 0.27509613246347414, -0.5327375087075266, -1.401384326519123, -2.2886685620502223, -3.149444211253417, -3.9380171686359704, -4.610671795976592, -5.1281573689591315, -5.457988459814762, -5.5764206579745155, -5.469978895891172, -5.136439285109553, -4.585195530387578, -3.8369759937080015, -2.922915299646897, -1.883022758420062, -0.7641264931722713, 0.3825952910227637, 1.5043580519892217, 2.549633309739712, 3.4709640114835936, 4.227567775987476, 4.787573604364268, 5.129757898854727, 5.244674364854702, 5.13510792791845, 4.815823060086863, 4.3126194279848225, 3.6607499146708533, 2.902795176628064, 2.0861224779325758, 1.2600824139175568, 0.47311357866396786, -0.23006889058763225, -0.8110301123041533, -1.2397627700225713, -1.496295899631508, -1.5716701841617686, -1.4682249634479274, -1.1991858920613325, -0.7875866293518942, -0.26460022416459095, 0.3326068124807463, 0.9633548402827979, 1.586102419771307, 2.1610955193018238, 2.652843220505938, 3.0322616367051065, 3.27835133252215, 3.3793060019547796, 3.3329893277780145, 3.146760140992774, 2.836670271095134, 2.426101786542153, 1.9439477551752182, 1.422470620974057, 0.8949927235982178, 0.3935829703745788, -0.05309843675603979, -0.421648839630747, -0.6953410999634166, -0.865018933233254, -0.9294168018087127, -0.8948940587984274, -0.7746159456385062, -0.5872542519763438, -0.3553150058189572, -0.10322693871311205, 0.14465927843723775, 0.3660061106284947, 0.5422103981611437, 0.6597805738193171, 0.7112674754630836, 0.6956819253163745, 0.6183728586210786, 0.4903823602842081, 0.3273352438929263, 0.14795759244775103, -0.0276518982701759, -0.17985420618266615, -0.29125390524701533], 'positive_zeros': ['2.23283953027136232683978123553475', '3.41446386523052970658644001782868', '4.11625409633618176365314735333383', '4.88032251321097002335431450116329', '5.67209306781243868914257604543266', '6.62925789129856628560630353917013', '7.49452179579131963571774420118111', '8.204705140434863655409862636269170', '8.953797535661373239910293335311095', '9.618235159545732777315043180133243'], 'prelabel': '2-1800-72.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': 0.8888888888888888, 'root_number': '-0.93969262078590838405410927732446 + 0.34202014332566873304409961468239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4444444444444444', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23283953027136232683978123553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41446386523052970658644001783', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11625409633618176365314735333', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'bad_primes': [2, 3, 5], 'central_character': '72.43', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/1/bk/d/1051/1', 'ArtinRepresentation/2.1800.12t18.a.a'], 'is_instance_Artin': True, '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': '2-1800-72.43-c0-0-4', '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': '2-1800-72.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': 0.4444444444444444, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23283953027136232683978123553', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24605254
{'Lhash': '2830460370761810246067857730179', 'Lhash_array': ['2830460370761810246067857730179'], 'label': '2-1800-72.43-c0-0-4', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1800.12t18.a.a'}
-
id: 19837849
{'Lhash': '2830460370761810246067857730179', 'Lhash_array': ['2830460370761810246067857730179'], 'label': '2-1800-72.43-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/1/bk/d/1051/1'}