-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1316942207729960791434069922599', 'a10': [0.0, 0.0], 'a2': [-1.9559424774475482, 0.0], 'a3': [-0.2968417846343463, 0.0], 'a4': [1.8257109750836524, 0.0], 'a5': [0.0, 0.0], 'a6': [0.5806054556476549, 0.0], 'a7': [3.5633069050624013, 0.0], 'a8': [0.3408993071867981, 0.0], 'a9': [-2.9118849548950965, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1316942207729960791434069922599', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9559424774475482, 0], [2.0, 0]], [[1.0, 0], [0.2968417846343463, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.5633069050624013, 0], [7.0, 0]], [[1.0, 0], [-5.563306905062402, 0], [11.0, 0]], [[1.0, 0], [5.266465120428055, 0], [13.0, 0]], [[1.0, 0], [1.4063164307313074, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-6.969623335793709, 0], [23.0, 0]], [[1.0, 0], [-1.4063164307313074, 0], [29.0, 0]], [[1.0, 0], [-1.7548944805640023, 0], [31.0, 0]], [[1.0, 0], [3.61504317026075, 0], [37.0, 0]], [[1.0, 0], [-4.348578049832695, 0], [41.0, 0]], [[1.0, 0], [-3.5633069050624013, 0], [43.0, 0]], [[1.0, 0], [-8.260463004727791, 0], [47.0, 0]], [[1.0, 0], [-7.61504317026075, 0], [53.0, 0]], [[1.0, 0], [-9.475191859957498, 0], [59.0, 0]], [[1.0, 0], [-9.214728855229707, 0], [61.0, 0]], [[1.0, 0], [-4.760896596264266, 0], [67.0, 0]], [[1.0, 0], [14.06887542922619, 0], [71.0, 0]], [[1.0, 0], [6.593683569268693, 0], [73.0, 0]], [[1.0, 0], [-5.475191859957498, 0], [79.0, 0]], [[1.0, 0], [-4.156990474331094, 0], [83.0, 0]], [[1.0, 0], [9.2300863405215, 0], [89.0, 0]], [[1.0, 0], [11.511570639864052, 0], [97.0, 0]], [[1.0, 0], [11.851131626482514, 0], [101.0, 0]], [[1.0, 0], [1.3545801655329588, 0], [103.0, 0]], [[1.0, 0], [-7.062873313525927, 0], [107.0, 0]], [[1.0, 0], [-10.184352191023414, 0], [109.0, 0]], [[1.0, 0], [1.8601486896967476, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-475-1.1-c1-0-5', '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/475/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.734631389950068, 0.7278804107908037, 0.7064913515917173, 0.6673221045763416, 0.6059479359994493, 0.517665184672052, 0.39859420835506165, 0.2467551287199008, 0.06304094884707728, -0.14796929281825058, -0.37742317376769946, -0.611915585751052, -0.8336087030046204, -1.0208355559965328, -1.1492455537854038, -1.1935053457167206, -1.1295072155336188, -0.9369648863255811, -0.6022006824648124, -0.12085802931449806, 0.499779754441498, 1.239208284231657, 2.0631892275040884, 2.9245780847819844, 3.7656594283855522, 4.522007460103697, 5.127708361631842, 5.5215848993065775, 5.653876746012587, 5.492679185799278, 5.029355711805426, 4.282140176997178, 3.297247208867129, 2.1470191922628645, 0.924943132038264, -0.2622558022252803, -1.304836765047227, -2.101599282975593, -2.571497411216962, -2.663879373426065, -2.3659401236015136, -1.7061925193765297, -0.7531732735145014, 0.39083339247572874, 1.6006130561913683, 2.7422750589045424, 3.6892700548558013, 4.338119607544787, 4.621695678420305, 4.518089094239628, 4.053618292971481, 3.2993018170105053, 2.361051639590139, 1.3648046103716218, 0.43864364773047604, -0.30547714127652115, -0.787612125138496, -0.9707840366810998, -0.8651974854050148, -0.5249203722220586, -0.03747574809684355, 0.4919988510438211, 0.9593813940240766, 1.2797736160437319, 1.4020552260872785, 1.3171143906433378, 1.0581630597352754, 0.6929694619151106, 0.30936158024149835, -0.0033096453407158916, -0.17317880893091778, -0.16155184554873234, 0.02801259689854963, 0.3493131795731816, 0.7222142966552499, 1.0490041206727205, 1.2352895999481102, 1.2111992100744702, 0.9483638480989055, 0.4687810328297735, -0.15683030104796322, -0.8214635858582972, -1.40300670438019, -1.7900880929261072, -1.9071947158276756, -1.7334374490090292, -1.3103173662723524, -0.7359181267719777, -0.14575123951780744, 0.31654069275039054, 0.532900353904828, 0.4418031578355402, 0.05924110429095534, -0.5158750377871744, -1.1145690108448132, -1.5278029390043348, -1.5486744351750985, -1.0187617511983307, 0.13101412770857965, 1.8542606058673954, 3.984552083952089, 6.255193901864323, 8.341099997531243, 9.915729365916029, 10.712372054374443, 10.577483084105548, 9.504708394301089, 7.641677353234212, 5.266946917422285, 2.7406182594407107, 0.43781192920341877, -1.3218772236440521, -2.334557365163302, -2.5492515905606568, -2.0741181833053086, -1.1500953884066774, -0.09733471350024936, 0.7542891380713347, 1.1357524894448832, 0.8953759948662783, 0.029112095371178315, -1.3217194903477087, -2.9043503020805193, -4.412168847628202, -5.552784122046687, -6.111097320339022, -5.99329103459689, -5.2422773470585184, -4.021959376368935, -2.575026702239894, -1.1651475614631468, -0.017850271714173062, 0.7257264608003988, 1.031642638792246, 0.9681326310766213, 0.6755255420037404, 0.32021291718942846, 0.045615975771843585, -0.06651311283379119, -0.014293697967392447, 0.1308666796029761, 0.25294184852632606, 0.2331393630262308, -0.007674686195324959, -0.4787465854107603, -1.1106894126233948, -1.771312316151015, -2.3019086670211033, -2.5637038845646027, -2.4808093614600946, -2.0665612020153503, -1.4245256917973959, -0.7226008662076875, -0.1465728146029185, 0.1540774229724434, 0.11232376155435161, -0.23259852011923826, -0.7422457831188627, -1.216767526472612, -1.4542274558007484, -1.315231091181704, -0.7739553676690913, 0.060678013704037526, 0.9623917016798048, 1.6416230955247468, 1.8236274279218556, 1.3300969918001753, 0.14124716578955657, -1.5808189910468138, -3.5170997909387256, -5.261776527467341, -6.421334872194467, -6.717587130861199, -6.06683275458876, -4.612319183831252, -2.6986611133367338, -0.7920772618732592, 0.6348287856265692, 1.224611445634686, 0.8308355684312017, -0.4380428938802865, -2.239966032726417, -4.081850370086001, -5.443064734754288, -5.9080510159475, -5.273338726978493, -3.6005970979381976, -1.2015542721470391, 1.4412022339938995, 3.7963213013493604, 5.415997549931454, 6.0433137243671355, 5.666621369027059, 4.507827492309366, 2.949804732463472, 1.4247913719202776, 0.29589466542944487, -0.23519689374729336, -0.1696229154786896, 0.30748242445648355, 0.8977990209611759, 1.2895604100912808, 1.2555489058272777, 0.7203076952819654, -0.22223263944210483, -1.3439241310908419, -2.357453696410869, -3.006625922143569, -3.1433869192403425, -2.7681900342458654, -2.022562463687268, -1.13817533173233, -0.3604062044004384, 0.1280214866044637, 0.2585794903227568, 0.08780288495709632, -0.23443135783718938, -0.5267875669128729, -0.6461046559171808, -0.5400745300700335, -0.26443562543020666, 0.041266297299556824, 0.21055884829636035, 0.11892579535635053, -0.2607461552129784, -0.8375044066474394, -1.4259861919594208, -1.8082568289998033, -1.8134988168509985, -1.3875324927871817, -0.6259681005355479, 0.2440308876329589, 0.9312325797586944, 1.177397995755092, 0.852382050925548, 0.013966056583102831, -1.0913295107292045, -2.091863526692732, -2.602878750174951, -2.3533178874851965, -1.2864076762299568, 0.401322143255208, 2.3001227184110986, 3.899035230829995, 4.738746190641613, 4.558999823883126, 3.393194986033468, 1.5769285579565442, -0.3372091829181098, -1.7370128690809366, -2.1348674522326347, -1.322987344048858, 0.5493777210395224, 3.0034560241520314, 5.358409508885918, 6.923076705571738, 7.195793639300697], 'positive_zeros': ['1.03888422211361464049850295981780', '2.40159277881274627052346039447171', '4.34645696729541782834819138730569', '5.33379504728974060162794953732411', '6.81889230570599300259343450749678', '7.50887323311184825290869264057387', '8.623357474022990250994013914136506', '8.986479645325782915771213959966576', '9.970257018727239853744647533508957', '11.03440528866184541543097749094929'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03888422211361464049850295982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40159277881274627052346039447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34645696729541782834819138731', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/i/1/1'], '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': '2-475-1.1-c1-0-5', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03888422211361464049850295982', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1316942207729960791434069922599', 'Lhash_array': ['1316942207729960791434069922599'], 'label': '2-475-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/i/1/1'}