-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '176374809872909966063695717850', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.7320508075688772], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-3.4641016151377544, 0], 'a8': [0, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.58204824255365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1199', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1719148133158942249665940546065', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-19.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-23.0, 0]], [[1.0, 0], [0, -6.0], [-29.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-31.0, 0]], [[1.0, 0], [0, 4.0], [-37.0, 0]], [[1.0, 0], [0, -12.0], [-41.0, 0]], [[1.0, 0], [6.928203230275509, 0], [43.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-47.0, 0]], [[1.0, 0], [6.0, 0], [53.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [59.0, 0]], [[1.0, 0], [10.0, 0], [61.0, 0]], [[1.0, 0], [-6.928203230275509, 0], [67.0, 0]], [[1.0, 0], [13.856406460551018, 0], [71.0, 0]], [[1.0, 0], [0, -2.0], [-73.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-79.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-83.0, 0]], [[1.0, 0], [0, 0], [-89.0, 0]], [[1.0, 0], [0, -10.0], [-97.0, 0]], [[1.0, 0], [0, -6.0], [-101.0, 0]], [[1.0, 0], [10.392304845413264, 0], [103.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-107.0, 0]], [[1.0, 0], [10.0, 0], [109.0, 0]], [[1.0, 0], [-6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1200-60.59-c1-0-2', 'leading_term': '0.3227412984428312272181157097041837598375485828341616174', '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/1200/2/o/b/1199/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.3227412984428312, 0.19268061596481595, 0.054157871039227444, -0.09328407142188434, -0.2501050514895706, -0.416701988770449, -0.5933442423262189, -0.7801131132817378, -0.9768480029718151, -1.1831010416064505, -1.3981013707466141, -1.6207297676566494, -1.849503960048438, -2.082574776236032, -2.317733167310907, -2.55242807814626, -2.7837950916260428, -3.0086956948697723, -3.2237668986244716, -3.4254807732963246, -3.6102132476170663, -3.7743212551596326, -3.9142270205176377, -4.026507964346991, -4.107990389681891, -4.155844806896209, -4.167680477578241, -4.141636524397657, -4.07646678006049, -3.9716154478080683, -3.8272806311095793, -3.6444628715613594, -3.424996019209201, -3.171558053062791, -2.887659872373863, -2.5776105882120564, -2.2464584526360833, -1.8999072575408562, -1.544208800855133, -1.1860328336995116, -0.8323167440099702, -0.4900980722351951, -0.1663337626338642, 0.1322892026894874, 0.39954649333568026, 0.6298666328245476, 0.8185125449130403, 0.9617481045263275, 1.0569833920346645, 1.1028926134982628, 1.0994991484022496, 1.0482229214595027, 0.9518862584155818, 0.8146755600840899, 0.6420574870379007, 0.44064985299610004, 0.21804903267362147, -0.017382653366753865, -0.2567644678567705, -0.4909730185737146, -0.7109381389809079, -0.9079495474084169, -1.0739639861229966, -1.2019019084357296, -1.285922521999314, -1.3216661463979418, -1.3064534259821252, -1.2394319617589662, -1.121662378744324, -0.9561376989433309, -0.7477320979626148, -0.5030776201414483, -0.23037013143768173, 0.06089139479934672, 0.3602253438316427, 0.6565380522815459, 0.9385324214647663, 1.1951403090155548, 1.4159627751013173, 1.591701130613149, 1.7145612390866165, 1.7786137208449153, 1.780093630305247, 1.7176248299308359, 1.5923566402232698, 1.408003345701939, 1.1707806917382844, 0.8892374965113184, 0.5739847801049266, 0.23732921132858517, -0.1071779906604945, -0.4452614794127662, -0.7624926690595896, -1.0448892144377662, -1.279518990074559, -1.4550831851516965, -1.562452879183411, -1.5951343131443378, -1.5496400425787826, -1.4257462227859132, -1.2266203505521842, -0.9588087410130068, -0.6320786740608653, -0.2591162829285488, 0.14491237465453471, 0.5629233013869223, 0.9765798542668963, 1.3670362371156217, 1.7157296139853104, 2.0051879389766807, 2.219818616094355, 2.3466426169527486, 2.3759397830109275, 2.3017737411129806, 2.122369110540163, 1.8403193451695175, 1.4626104314285486, 1.0004534806863925, 0.46892768593904754, -0.11355621405627978, -0.7259533034994474, -1.3454160800078185, -1.9482266678743079, -2.510790399508172, -3.010647506250166, -3.427457559192189, -3.743911273323908, -3.9465264094035852, -4.0262887502774785, -3.9791053595960055, -3.8060453156309655, -3.51335252035238, -3.1122256005003344, -2.618370864276588, -2.051345232044813, -1.4337164807758809, -0.7900774965629919, -0.1459590194890718, 0.47330884510760163, 1.0437326338972581, 1.5437344843205603, 1.9551213306424422, 2.2638961612766044, 2.4608702264920375, 2.54204438362519, 2.5087388787243423, 2.367463262716088, 2.129531217006195, 1.8104381543668846, 1.429031882062343, 1.0065176968221266, 0.5653484085133189, 0.12805643065618694, -0.28391118140965865, -0.6512932885765024, -0.9579920636254947, -1.1918743675794077, -1.3453531110834973, -1.4157160131343212, -1.405182560643676, -1.3206846586804741, -1.1733816645331416, -0.9779353908666183, -0.7515844107920518, -0.5130688082827864, -0.28146568545184897, -0.07500168720199553, 0.09008887737551158, 0.2005932659822563, 0.247175216680275, 0.22500289431051218, 0.13410945220557066, -0.020539386263784206, -0.22927969755724287, -0.47827713730495985, -0.7503221746399723, -1.0258505264440325, -1.2841323227601498, -1.5045622888986556, -1.667975684884246, -1.757911436434271, -1.7617451285388408, -1.6716203602951665, -1.4851171571883264, -1.2056102205522323, -0.8422870369073002, -0.4098153386460553, 0.07232998951221195, 0.5808499164729127, 1.089864269566328, 1.5723480074713692, 2.0016807341639176, 2.353220537832144, 2.605809405890944, 2.7431190555836156, 2.7547530802833595, 2.6370335694464537, 2.3934172210587334, 2.034506542608778, 1.5776448958084375, 1.0461085609782426, 0.4679332470724388, -0.1255649075547045, -0.7014942110649005, -1.2272232368254004, -1.6722426637612402, -2.0099442769161366, -2.219210758090641, -2.2857188234618535, -2.2028732407347085, -1.9723095177466008, -1.603927491887382, -1.1154452778211421, -0.5314914587588316, 0.11771866799570462, 0.7980512679879841, 1.4733731602621671, 2.1076119695697813, 2.6668369107581045, 3.12123672092134, 3.4468755546025283, 3.6271192902981775, 3.653643084415097, 3.526955142296529, 3.256400168120368, 2.8596371206632525, 2.3616178549143645, 1.7931239999355437, 1.1889470780322975, 0.5858196360943246, 0.02022153923375289, -0.4738055521017255, -0.8667018045784398, -1.1351648575603461, -1.2635470273083542, -1.2447863109771666, -1.0808118874842272, -0.7823972864757466, -0.36846887313201543, 0.13508839949415133, 0.6970540837320521, 1.2828227984266625, 1.8565596518067728, 2.3834243917794375, 2.831723278887377, 3.1748518708579807, 3.392904985262327, 3.4738513036863474, 3.4141980890395875, 3.2191045336542556, 2.9019382106702896, 2.4833056162375886, 1.9896224499927169, 1.4513197643059874, 0.9008063475261743, 0.3703240146575688, -0.11016030549437979], 'positive_zeros': ['0.13913519217452760597168849125100', '2.49288223119239946990374059844567', '3.33557797184952633163442298521305', '4.26529821317504420513894404820465', '5.25520674165005389280692451914259', '6.07309799562132128577814309948548', '6.96153231702213991202372303888636', '8.040859998437126273922459313722516', '8.923950932926339665345100251167071', '9.751097024153991486737584027478170'], 'prelabel': '2-1200-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.5190830490162334, 'root_number': '-0.0599152608792162507639081937680152860048315013931460622 - 0.9982034669914623466767704468296075457106461770194707378*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2595415245081167', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13913519217452760597168849125', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49288223119239946990374059845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33557797184952633163442298521', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.58204824255365, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/o/b/1199/1'], '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': '2-1200-60.59-c1-0-2', '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': '2-1200-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': -0.2595415245081167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13913519217452760597168849125', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '176374809872909966063695717850', 'Lhash_array': ['176374809872909966063695717850'], 'label': '2-1200-60.59-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/o/b/1199/1'}