-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1575806458205172629202819150026', 'a10': [-1.307007203691177, 1.8143131398684653], 'a2': [0.5, 0.8660254037844386], 'a3': [0.7588190451025207, 2.831951230073507], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.9177376677004119, 2.0390580112600545], 'a6': [-2.0731321849709863, 2.0731321849709863], 'a7': [-0.49086985267139804, -1.831951230073507], 'a8': [-1.0, 0.0], 'a9': [-4.846065214951231, 2.797877056362575], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [-0.9177376677004119, -2.0390580112600545]]], [37, [[1.0, 0], [5.726204603613395, 2.0519699894386276]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '3971530146590094859132963938010', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.7588190451025207, -2.831951230073507], [-2.598076211353316, 1.5]], [[1.0, 0], [-0.9177376677004119, -2.0390580112600545]], [[1.0, 0], [0.49086985267139804, 1.831951230073507], [-6.06217782649107, 3.5]], [[1.0, 0], [0, 0.0963763171773128], [-11.0, 0]], [[1.0, 0], [-1.5907702751760278, 2.755294939775204], [-6.5, -11.258330249197702]], [[1.0, 0], [-3.7393567437461654, 2.158918622597891], [8.5, -14.722431864335457]], [[1.0, 0], [-4.712090618735671, 1.2626008759524923], [16.454482671904334, -9.5]], [[1.0, 0], [-1.9671278329882196, 0], [23.0, 0]], [[1.0, 0], [3.5073059361772883, -3.5073059361772883], [0, -29.0]], [[1.0, 0], [3.0498880527646595, 3.0498880527646595], [0, 31.0]], [[1.0, 0], [5.726204603613395, 2.0519699894386276]], [[1.0, 0], [-7.684824493725175, -4.436835490127259], [20.5, 35.50704155516198]], [[1.0, 0], [7.577493818067946, 0], [43.0, 0]], [[1.0, 0], [9.56288194571337, -9.56288194571337], [0, -47.0]], [[1.0, 0], [0.38838960601594835, -1.449489742783178], [-45.89934640057525, -26.5]], [[1.0, 0], [-2.9817397053427963, 11.12800407528477], [-51.09549882328188, -29.5]], [[1.0, 0], [-9.90774515396545, 2.654772312818412], [52.827549630850754, -30.5]], [[1.0, 0], [6.8886473315386025, -1.845807489428577], [58.023702053557386, -33.5]], [[1.0, 0], [0.9586198901117801, -1.660378354819697], [-35.5, -61.48780366869514]], [[1.0, 0], [-4.628626279736931, 4.628626279736931], [0, -73.0]], [[1.0, 0], [2.893291528794934, -0.775255128608411], [68.41600689897065, -39.5]], [[1.0, 0], [-3.3237653639214018, 12.40446121059233], [-71.88010851410841, -41.5]], [[1.0, 0], [-4.694452528530629, -1.257874763926024], [77.07626093681505, 44.5]], [[1.0, 0], [0, -17.672874360291555], [-97.0, 0]], [[1.0, 0], [0, -7.179136536953752], [-101.0, 0]], [[1.0, 0], [0, 8.901898950009969], [-103.0, 0]], [[1.0, 0], [3.190412972158003, 11.906783309220497], [-92.66471820493493, 53.5]], [[1.0, 0], [-1.4465878419080236, 5.398739323612159], [-94.39676901250381, -54.5]], [[1.0, 0], [-13.67663862757307, 7.896210993238546], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-370-185.103-c1-0-7', '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/370/2/q/c/103/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8510388006297227, 1.651184277696962, 1.4675398633227887, 1.2919040458253654, 1.1169497329116576, 0.9373767641268327, 0.7506637458908737, 0.5574273684978344, 0.36145484783145776, 0.16946710756524175, -0.00935971227245321, -0.16410782972811783, -0.28306128815792736, -0.3548575970344952, -0.3697973019903343, -0.3212272429484842, -0.20687997568792407, -0.030025090580518363, 0.1997265867429061, 0.46612290273382845, 0.7466090085785315, 1.0133949196061627, 1.235276576178109, 1.3801519879952635, 1.4180807200842749, 1.324641307934988, 1.0842593724141192, 0.6931224325043861, 0.161278210646838, -0.48645847570794565, -1.211083967406525, -1.961629737489234, -2.6790158334127985, -3.301313021385076, -3.769983504168899, -4.036483536132456, -4.068476865661043, -3.854852701126518, -3.408786086090872, -2.768231510516529, -1.9934973949277779, -1.1618890025505424, -0.35979421938332234, 0.3270280520469129, 0.8238689519885426, 1.0768963055157805, 1.061025483480573, 0.7846028533271443, 0.28999151383453814, -0.35036232762053543, -1.0422010359926632, -1.6812442442156907, -2.1670898448174656, -2.4173904313083194, -2.380270853886485, -2.0430454102816156, -1.4356922581745473, -0.6282164724110322, 0.2780974607978386, 1.164597576107432, 1.9125179743752965, 2.4210915370215282, 2.6237243553515066, 2.499546963636397, 2.0782169817336347, 1.4368002070884152, 0.6887767683703367, -0.03347730151587781, -0.6002087737164141, -0.9064483495091318, -0.8911329797660852, -0.5497902665156564, 0.06172958481346826, 0.8336112663245588, 1.6179935196217763, 2.252242963695117, 2.5859783336588817, 2.50739290965257, 1.9643115968230975, 0.9761108064901379, -0.3659520835920589, -1.9105222495665994, -3.4684472950224685, -4.842067939099235, -5.856601426199791, -6.388186071132478, -6.383600582995135, -5.868056352093923, -4.939562851516986, -3.7508137534832198, -2.4818767143969476, -1.3087356531902492, -0.37356487911067215, 0.23768609477747202, 0.50622653932279, 0.47797386185166135, 0.248505330052823, -0.06122806115534273, -0.3331497220863623, -0.47815558607417796, -0.45440560646694816, -0.27384276374829686, 0.004426175261407859, 0.29228350835781847, 0.4979873946299449, 0.552688997094857, 0.43151101818950416, 0.16366162633225273, -0.17155341713343616, -0.4627008801593705, -0.5946327356547618, -0.48100326256005016, -0.09306743718068801, 0.5228001744431189, 1.2443575798340714, 1.8914877123668858, 2.2606381239301356, 2.169347559963099, 1.5015800600845444, 0.243573511253922, -1.4988278914127693, -3.5069747481687434, -5.481027636860851, -7.091622520947562, -8.042068670642275, -8.128613813215003, -7.2859425291123845, -5.607515838519291, -3.335219169374941, -0.8190997361821346, 1.545598605398356, 3.391785851229392, 4.449349315528005, 4.5951308788339595, 3.873494783693004, 2.483092753565873, 0.7326908307692718, -1.0243492067718973, -2.4626813621486643, -3.348935909883545, -3.5833486054356687, -3.210560449368618, -2.3982118528399354, -1.3893600786564513, -0.4406884359601132, 0.23846971814225124, 0.5318386070122381, 0.43624378068752473, 0.05215009173842198, -0.45171865781555326, -0.8896395975270818, -1.112143911599613, -1.0471161309245842, -0.7179962555082646, -0.23454563208946577, 0.24095884887506291, 0.542572268994909, 0.5508890458770332, 0.2304329766697719, -0.35659182111435594, -1.0646350304268806, -1.7039295892268727, -2.094101044645034, -2.1175610117600985, -1.7575293887254329, -1.1092412491539192, -0.35989945333286516, 0.2585713613232569, 0.5322033234480158, 0.3265449783513101, -0.3698897099550146, -1.4330847485206502, -2.626848057739925, -3.6574412316688565, -4.2463178580003484, -4.202393121621993, -3.4747170560532252, -2.1710167482960427, -0.5362258851013131, 1.104394615064813, 2.423421563261776, 3.1706593195675956, 3.233046098828044, 2.65931000914174, 1.6429058288264986, 0.46795005851999505, -0.5671022234166714, -1.2272255210497949, -1.3988630107371678, -1.1125992840134347, -0.5247953558265627, 0.13584404621955698, 0.640773351445959, 0.8316685202179641, 0.6672098305714038, 0.2325274861749053, -0.29170416388079806, -0.6913714884847773, -0.7933408792512995, -0.5289626717940092, 0.03406188860444815, 0.7033112745400052, 1.2158104942876153, 1.3206407494499854, 0.8663447153976243, -0.1335014242534015, -1.4783995167088329, -2.813073505696445, -3.7088184824169645, -3.7746236085059546, -2.768865123798697, -0.6804548673890489, 2.2448390964050793, 5.5432113935851435, 8.629680495877793, 10.929852723086746, 12.013328466947943, 11.694277406093837, 10.072930345685293, 7.507247158625666, 4.522577902824978, 1.6835755758175261, -0.5376614206686035, -1.8629566633509804, -2.253852879751518, -1.892715568267571, -1.108127708359529, -0.2686051803311615, 0.3236282647309055, 0.5087683183764057, 0.29580315506951904, -0.1647589848173089, -0.6494062337804102, -0.9470969806200881, -0.9334359608926627, -0.6102630274785743, -0.0994961251706373, 0.40461965767751146, 0.7071552153480807, 0.6828697316405865, 0.3211166282716345, -0.2699138425847628, -0.9007957962457076, -1.367121675769042, -1.5212952964620519, -1.3246462940980812, -0.8611687234689827, -0.3072635101618743, 0.13281423667507275, 0.3037085871945423, 0.16068500429252575, -0.20677945146501994, -0.6002916752248405, -0.7807861733323925, -0.5582449250075199, 0.12759973414825995, 1.1651662434771863], 'positive_zeros': ['1.24309210907284898626155213855772', '2.14293626902417542608089902027171', '3.53303574467963588425094559024541', '5.31194307648342477875989713906884', '6.05910322922075029269085134556050', '7.21212918310928966767547015998790', '8.368741733978146588616650062733358', '8.989078764551651665062326914223867', '9.968335795322151899410382494809473', '11.56759631507770612517027457490388'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.8591086055489979, 'root_number': '-0.9036311545089774 - 0.42831149482680564*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.429554302774', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24309210907284898626155213856', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14293626902417542608089902027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53303574467963588425094559025', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/c/103/2'], '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': '2-370-185.103-c1-0-7', '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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.42955430277449896, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24309210907284898626155213856', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1575806458205172629202819150026', 'Lhash_array': ['1575806458205172629202819150026'], 'label': '2-370-185.103-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/c/103/2'}