-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1776900712187368663223759518479', 'a10': [2.0, 1.0], 'a2': [0.0, -1.0], 'a3': [0.0, 1.0], 'a4': [-1.0, 0.0], 'a5': [-1.0, 2.0], 'a6': [1.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 1.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [1.0, -2.0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.559', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '460661357261875326592360539866', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [1.0, -2.0]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [5.0, 0], [11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [-5.0, 0], [19.0, 0]], [[1.0, 0], [0, 9.0], [-23.0, 0]], [[1.0, 0], [-2.0, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 8.0], [-37.0, 0]], [[1.0, 0], [-6.0, 0], [41.0, 0]], [[1.0, 0], [0, -1.0], [-43.0, 0]], [[1.0, 0], [0, -12.0], [-47.0, 0]], [[1.0, 0], [0, 13.0], [-53.0, 0]], [[1.0, 0], [10.0, 0], [59.0, 0]], [[1.0, 0], [14.0, 0], [61.0, 0]], [[1.0, 0], [0, 14.0], [-67.0, 0]], [[1.0, 0], [9.0, 0], [71.0, 0]], [[1.0, 0], [0, 9.0], [-73.0, 0]], [[1.0, 0], [5.0, 0], [79.0, 0]], [[1.0, 0], [0, -6.0], [-83.0, 0]], [[1.0, 0], [3.0, 0], [89.0, 0]], [[1.0, 0], [0, -18.0], [-97.0, 0]], [[1.0, 0], [7.0, 0], [101.0, 0]], [[1.0, 0], [0, -8.0], [-103.0, 0]], [[1.0, 0], [0, 11.0], [-107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, -13.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-930-5.4-c1-0-18', '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/930/2/d/b/559/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7393943458342666, 0.9446629759805228, 1.1272029727269164, 1.2829941860700238, 1.4032706762294271, 1.475137043546981, 1.4830383075398192, 1.410820312009744, 1.244145487197721, 0.9730583831381063, 0.5944874359936515, 0.11443255035352783, -0.4504505456944178, -1.0721724206211183, -1.7119131818935753, -2.3219006002326434, -2.8487232186183573, -3.2379608810248808, -3.4398114137400033, -3.4151886929370576, -3.14159615062472, -2.617974960747835, -1.8677184521102028, -0.9391552075317924, 0.09696064048127934, 1.1530650154575384, 2.1331917868828842, 2.943408030332968, 3.5031039666592845, 3.7556740202383545, 3.6770182815115136, 3.280417422890075, 2.6167044607982892, 1.7692494092253719, 0.8440210810173074, -0.044210275953046885, -0.7877443188329531, -1.3016014940471226, -1.536477661042682, -1.4867457918082019, -1.1918775015392211, -0.7306328257959799, -0.20855242136764982, 0.25951000325552515, 0.5690747074461315, 0.6446075626047898, 0.4536079382706297, 0.013434000853812036, -0.6107528327151096, -1.3169806931998032, -1.9847577615534904, -2.4975126528364067, -2.7650331539964883, -2.741498866935064, -2.4353178163610347, -1.9084076120834972, -1.264581652262769, -0.628937778288703, -0.1221471227819861, 0.16514093238468175, 0.19226571337589177, -0.02174247656267274, -0.4014080187552669, -0.8309952794994209, -1.1807305265737902, -1.3376889952221551, -1.2345247961337855, -0.8692034410183478, -0.3104392897175768, 0.31357416067125266, 0.8418699561599094, 1.1178761244300706, 1.0292067774287095, 0.5409412575934224, -0.28602797651122713, -1.2972652983530288, -2.269079523412832, -2.9512559497636204, -3.120103267399323, -2.630644052256249, -1.4560822573253402, 0.2953222231503346, 2.391416346260294, 4.514802147257577, 6.322145354108588, 7.512222378245477, 7.888136806952155, 7.399714419027077, 6.155941448896773, 4.403714169585516, 2.476732231791617, 0.7253481450480088, -0.5571169153062645, -1.1948940924935902, -1.1631818216900538, -0.5866871548040108, 0.2962667369565708, 1.1953402055359474, 1.840442558674952, 2.0469137446818833, 1.7575523488162919, 1.0511778281455082, 0.11588434141346188, -0.8057882080580322, -1.4852102538553424, -1.7713545414895993, -1.6327355098153224, -1.1661680096916385, -0.5697328221088778, -0.08701463193601265, 0.062376024730376345, -0.25302520049078014, -1.0355728434043476, -2.1525866395601283, -3.367820442545179, -4.402342915616613, -5.0085054255326105, -5.0367101931747, -4.4763345346167265, -3.4590934951763237, -2.2235033232949557, -1.0500738211217806, -0.18528867855331171, 0.22415273892658463, 0.1680660832729542, -0.2300913685045783, -0.7548600623151643, -1.1669730384358858, -1.2779167873983759, -1.008528702259836, -0.41378478669162494, 0.3341332031694079, 0.9998566783167248, 1.359864927793473, 1.2756434433316832, 0.7420842078280152, -0.10470132934875076, -1.0238317886660986, -1.740365330128075, -2.029244698121678, -1.7866033889016861, -1.0656166219841168, -0.06439197724630259, 0.9319847393693212, 1.638613862983332, 1.8606679469003369, 1.5576143464031527, 0.8603814424101841, 0.034129688878676755, -0.6037306771330753, -0.7859695690767706, -0.386508234954928, 0.5297863632710538, 1.7164747365355648, 2.8140937592354596, 3.4590670990508894, 3.400428817734639, 2.5877482968388734, 1.2009745675902446, -0.39016990778685834, -1.7280474175699376, -2.401401700614324, -2.1718862592112624, -1.0533666951097589, 0.6823322295052832, 2.5777238235124083, 4.120489848619123, 4.8946334223677335, 4.70637582949059, 3.6458205918207667, 2.06428272575211, 0.4727092129814268, -0.6090601459537593, -0.8069741747521628, -0.004559789869939086, 1.6220900383700636, 3.656490175033659, 5.564631172031929, 6.850427820118497, 7.196036970072864, 6.544812671373326, 5.103404786180521, 3.2653964878083266, 1.4834981592244056, 0.13270063098940796, -0.5919480981044846, -0.7123224705670013, -0.4311007405171397, -0.03937950119691352, 0.19691554920223736, 0.13107699516510296, -0.22202916443028645, -0.7078089313492434, -1.1068728527526406, -1.2327759753247949, -1.0144083566347382, -0.5310913712208014, 0.013526316234635776, 0.36937691698049424, 0.34027228287940636, -0.1320865163406443, -0.9339364115215129, -1.810715496772931, -2.454950941781105, -2.6200068130925827, -2.2177075001232716, -1.3619386626087073, -0.33878234495846604, 0.4897216799040891, 0.8159926020480357, 0.5049890606713856, -0.34434659784484056, -1.4199418524055019, -2.296494400969689, -2.582150959481673, -2.0611886547745644, -0.7811161880378111, 0.949492480614641, 2.655307751452674, 3.850560261506633, 4.203920923856862, 3.653704476521053, 2.431230099152175, 0.9819674899554041, -0.1894319927887388, -0.6960714675808899, -0.4043779065148597, 0.5214726039478337, 1.6840470525171172, 2.6045362152872014, 2.9080225231618546, 2.4745170412534634, 1.498852784627222, 0.4342773527564979, -0.16364752403096258, 0.1605734291376282, 1.5854551144005686, 3.9256163244814095, 6.6687175234239735, 9.126648286510672, 10.65064013237736, 10.83676466212264, 9.65115324233072, 7.43241694207194, 4.772103387187209, 2.316924846029048, 0.5633535833507812, -0.2837190004513597, -0.3414678919339347, 0.036482078145124566, 0.42435147346601465, 0.5018376698151166, 0.1768530683916774, -0.39190460351926326, -0.8780022165610272, -0.9400574536181859, -0.38141092799802817], 'positive_zeros': ['1.40172750430398820767725177858809', '2.98857294562736104201925937534846', '4.36839168767893088398497180252564', '5.30221655571935217398086244201502', '5.87805932560752718461395752671106', '7.29121855227043982553249199145844', '7.61616000176016779642244096715314', '8.561884869855235754382523425159994', '9.211098191991994807640338601732712', '10.10600486064744863422335040362771'], 'prelabel': '2-930-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.323791808825', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40172750430398820767725177859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98857294562736104201925937535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36839168767893088398497180253', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/d/b/559/1'], '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': '2-930-5.4-c1-0-18', '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': '2-930-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40172750430398820767725177859', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1776900712187368663223759518479', 'Lhash_array': ['1776900712187368663223759518479'], 'label': '2-930-5.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/d/b/559/1'}