-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '777746823699161360375568335874', 'a10': [-2.0646747130008554, -0.8585559559486127], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [-0.6917973546894448, 1.9006976108476896], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [1.6465161610235157, 1.5129390375981393], 'a6': [-5.3124389709239086e-61, -2.0226801496621825], 'a7': [-2.3020625538856563, 0.4059157395286757], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.8359344985698682, -0.701432329438341], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [5, [[1.0, 0], [-1.6465161610235157, -1.5129390375981393]]], [37, [[1.0, 0], [5.969511016248582, -1.1683057078037509]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.289', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2903570413896063722716132798482', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0.6917973546894448, -1.9006976108476896], [-2.298133329356934, -1.928362829059618]], [[1.0, 0], [-1.6465161610235157, -1.5129390375981393]], [[1.0, 0], [2.3020625538856563, -0.4059157395286757], [6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [2.8202350356439703, -4.88479037102118], [-5.5, -9.526279441628825]], [[1.0, 0], [-3.98903410976681, 3.3471970502589197], [2.2574263096700946, -12.802500789158705]], [[1.0, 0], [0.9260949373821799, 0.7770859203925333], [2.952019020337816, 16.741731801207536]], [[1.0, 0], [1.3436277207854086, -3.6915868230111903], [-14.554844419260583, -12.212964584044247]], [[1.0, 0], [0.9580882652752918, 1.6594575535923337], [-11.5, 19.91858428704209]], [[1.0, 0], [0.4556227467540588, 0.2630539154873725], [14.5, 25.11473670974872]], [[1.0, 0], [0, 9.666056998658982], [-31.0, 0]], [[1.0, 0], [5.969511016248582, -1.1683057078037509]], [[1.0, 0], [7.683927117314568, -6.447580410131754], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [-0.37566830754359015, 0], [43.0, 0]], [[1.0, 0], [-0.3774806583936419, 0.21793855973744633], [23.5, -40.703193977868615]], [[1.0, 0], [-12.102034367031099, -2.133915180368673], [49.803708901653145, 18.127067596260442]], [[1.0, 0], [-14.510431323624212, -2.5585805440721923], [55.44186462636859, 20.179188456214455]], [[1.0, 0], [2.2178607523775526, 2.6431435195196458], [-10.592538837682751, 60.07327293374469]], [[1.0, 0], [-9.613856384335332, 1.6951822692146488], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [-3.3788961837071714, -1.2298176355450763], [54.38915546144744, 45.63792028774429]], [[1.0, 0], [0, -13.485691859012123], [-73.0, 0]], [[1.0, 0], [-7.0136887098405, 1.2367025538352245], [74.23571704208676, -27.01959132272783]], [[1.0, 0], [5.255782007023047, -6.263597088761723], [-14.412798746355218, -81.73904350001327]], [[1.0, 0], [-5.4535447436107045, -0.9616070787993952], [83.63264324994584, 30.439792755984517]], [[1.0, 0], [0.9291933474407315, 1.6094100878223474], [-48.5, 84.00446416709055]], [[1.0, 0], [-6.89066856004542, -11.934988044116142], [-50.5, 87.4685657822283]], [[1.0, 0], [1.1634712656519526, -2.0151913452556482], [-51.5, -89.20061658979718]], [[1.0, 0], [-3.4279961183393732, -4.085326689429955], [-18.580355010361547, 105.37442957230627]], [[1.0, 0], [-1.173057620023983, -3.222949322735074], [-83.49884429996861, 70.06384945583278]], [[1.0, 0], [-10.61986751430562, 3.865315667057849], [86.56302207244451, -72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-370-185.104-c1-0-4', '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/v/a/289/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7166771845674181, 0.5675993099877301, 0.42304325407870835, 0.27924298407743725, 0.13379922524081891, -0.013554606244240491, -0.16052595952214346, -0.302156718110109, -0.4309939752616378, -0.5375089738550208, -0.6107539716683099, -0.6392523767853724, -0.6121061120419193, -0.5202793859346998, -0.35798558251548607, -0.12406970660936521, 0.17675158902871757, 0.5329514278953426, 0.9257212103645895, 1.3291196236585163, 1.7109617334482004, 2.03451144137027, 2.2609638595322306, 2.3526120937539132, 2.276493844924414, 2.008218218775764, 1.5355951490996376, 0.8616423610397483, 0.006540036104528401, -0.9918497498300055, -2.0791793807321, -3.1876535890756723, -4.240838037543909, -5.159947798128323, -5.871106537991549, -6.312879508675484, -6.443256299547765, -6.2452192450848285, -5.730099010798181, -4.938096966107944, -3.9356363563426813, -2.8095667915237845, -1.658649897885993, -0.583147304224348, 0.32634104693150695, 0.9994344740386831, 1.3945304042746134, 1.5041192332976092, 1.3559494391461495, 1.00963818965816, 0.5489285579400967, 0.07042589383429158, -0.3297894883703677, -0.5698707315085542, -0.5942627666527365, -0.38225606085188035, 0.04840843773038872, 0.6436615543369869, 1.3208955541336609, 1.9814704001562813, 2.526181693150773, 2.871356934213423, 2.9630079238784277, 2.7866351998958794, 2.3708597685058406, 1.7839824284704786, 1.1237108549614812, 0.5014698426366506, 0.02371976937000557, -0.22663624129914178, -0.2055163286502812, 0.08324434302120239, 0.586875297958621, 1.211308655155803, 1.8365333374094661, 2.3372822219020497, 2.605570160565827, 2.5710730006556033, 2.2155174146330907, 1.5781523502921517, 0.7508738544212161, -0.1365682392558923, -0.9389703225160723, -1.5218190483984921, -1.7864159665182586, -1.6891834461731294, -1.2512415017868048, -0.5560411191238509, 0.26494238328410014, 1.0561201778525717, 1.6669797151890247, 1.980999421124413, 1.9385569478065903, 1.5490696398342947, 0.8895906525671983, 0.0897343291397475, -0.6943887043450303, -1.3121558071115589, -1.649812980723028, -1.65457313598298, -1.3460007747157063, -0.8117197371296153, -0.187714880339857, 0.37314671754712575, 0.737986433191768, 0.828246744065883, 0.6436427436100859, 0.26968474360364875, -0.13405632783613172, -0.3637362409343411, -0.21385225129519578, 0.4756752866524651, 1.777831761820248, 3.6515983701471555, 5.936580876783851, 8.371777322398831, 10.63612143657787, 12.403722326490765, 13.403285257351513, 13.46984743045671, 12.578082394788703, 10.849878048208494, 8.534018255598292, 5.961543444545087, 3.485500388425888, 1.4171764408554652, -0.02823919328974817, -0.7655605511799364, -0.8464175610679937, -0.4381526285522117, 0.2199829016523059, 0.8732296568555042, 1.3076010943177132, 1.3935994171126553, 1.1080356864587815, 0.5298674081905069, -0.18788233892360534, -0.8624574251973572, -1.3305725588537365, -1.4901847750506914, -1.3246268543589592, -0.9035084701670671, -0.3607780049732923, 0.1437963788458811, 0.4692125410731779, 0.531832415314198, 0.32754085152774554, -0.068611544851485, -0.5253118934172615, -0.8943094457796085, -1.0554028546754195, -0.9544994446830259, -0.6236964593703456, -0.17694320823580265, 0.21861611652352367, 0.38874325632721657, 0.20359115286330923, -0.3796012849283641, -1.2951150765473762, -2.375997136545167, -3.389842184939396, -4.095195068528532, -4.3045748432570985, -3.9374998962851504, -3.0486180699441707, -1.8218765249106208, -0.530245914201579, 0.5303203547988417, 1.1166843846756669, 1.1046353002442706, 0.52742854764695, -0.4247568916487835, -1.446235464967421, -2.189270972283549, -2.3519795788237485, -1.758599064967639, -0.41117748145416544, 1.501599898420485, 3.6420979329857777, 5.599674489634214, 6.986536063115987, 7.529625668187026, 7.135254323796739, 5.909894690178415, 4.131724615692163, 2.1802490876750023, 0.4422659312644108, -0.7813811287594666, -1.344117698321477, -1.2796413806662417, -0.7796816068160601, -0.13063838269333086, 0.3726904461235005, 0.5120252998064322, 0.20557005722232422, -0.473318924486277, -1.323283398137861, -2.0793739213454154, -2.495520826185512, -2.420717061171288, -1.8464221510015526, -0.9110822943610808, 0.13978953615169218, 1.026418299590871, 1.5190420450632371, 1.5085610396105298, 1.0421270326416407, 0.31228426480130483, -0.39814744471505786, -0.8000820071321448, -0.6868197261157704, -0.001196698120987099, 1.139143743062201, 2.4668577106522025, 3.634304579784218, 4.308132029624178, 4.262301867000339, 3.4429231664558326, 1.98616021831354, 0.1839274888088004, -1.5928529728799288, -2.9914232955556463, -3.7670238109375487, -3.840071084498948, -3.3052933912414892, -2.3918633613016387, -1.3881211953014485, -0.5547376199727316, -0.0529984132673198, 0.09054553986448868, -0.02619060573337038, -0.2311998328472182, -0.3504844076018969, -0.2766600949797167, -0.01025736171670744, 0.34078224080128666, 0.6036551687540712, 0.6109119694361039, 0.2738130176826808, -0.36787801536371595, -1.139560282926666, -1.7749374679537109, -1.9979886048620294, -1.6190631591801372, -0.6137132231341105, 0.843842168150739, 2.408004121298764, 3.6466601200496047, 4.1617288547835125, 3.710576681274944, 2.2908399870714957, 0.16015497262469516, -2.219348078808799, -4.299481479154277, -5.595330962759863, -5.822661044806733, -4.982424793992631], 'positive_zeros': ['0.61353406337608710814589099044467', '1.92976233429560614597919957011400', '3.50087433063965841211337485490361', '5.45175049133930683988445343237526', '6.39464990183819979775737179156398', '6.98829064919784396370182656474282', '8.508066426799152610336479072599539', '8.847945544498735953076468915820632', '10.10549539426860329241722491638656', '10.96032350336228225131380943922778'], 'prelabel': '2-370-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.9334445490881876, 'root_number': '-0.9782201842495875 - 0.2075699186459908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.466722274544', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61353406337608710814589099044', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92976233429560614597919957011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50087433063965841211337485490', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.104', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/v/a/289/3'], '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': '2-370-185.104-c1-0-4', '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': '2-370-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.4667222745440938, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61353406337608710814589099044', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '777746823699161360375568335874', 'Lhash_array': ['777746823699161360375568335874'], 'label': '2-370-185.104-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/v/a/289/3'}