-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1228843187635303387772103578161', 'a10': [1.0, -3.111507638930571e-61], 'a2': [0.5, -0.8660254037844386], 'a3': [0.0, 1.7320508075688772], 'a4': [0.5, 0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [1.5, 0.8660254037844386], 'a7': [-1.0, 1.7320508075688772], 'a8': [3.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.7320508075688772]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.196', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2810799049892263197918517543006', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.0, -1.7320508075688772], [-3.5, -6.06217782649107]], [[1.0, 0], [-0.5, 0.8660254037844386], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [3.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-11.5, 19.91858428704209]], [[1.0, 0], [2.5, -4.330127018922194], [-14.5, -25.11473670974872]], [[1.0, 0], [-0.5, -0.8660254037844386], [-15.5, 26.846787517317598]], [[1.0, 0], [5.0, 0], [37.0, 0]], [[1.0, 0], [0, 0], [-20.5, 35.50704155516198]], [[1.0, 0], [-4.0, 6.928203230275509], [-21.5, -37.239092362730865]], [[1.0, 0], [-1.0, 1.7320508075688772], [-23.5, -40.703193977868615]], [[1.0, 0], [-14.0, 0], [53.0, 0]], [[1.0, 0], [-4.5, -7.794228634059948], [-29.5, 51.09549882328188]], [[1.0, 0], [-0.5, 0.8660254037844386], [-30.5, -52.827549630850754]], [[1.0, 0], [7.0, 12.12435565298214], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [-6.0, 0], [73.0, 0]], [[1.0, 0], [-6.0, 10.392304845413264], [-39.5, -68.41600689897065]], [[1.0, 0], [-5.0, 8.660254037844387], [-41.5, -71.88010851410841]], [[1.0, 0], [-2.0, 0], [89.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-48.5, -84.00446416709055]], [[1.0, 0], [1.5, -2.598076211353316], [-50.5, -87.4685657822283]], [[1.0, 0], [-0.5, -0.8660254037844386], [-51.5, 89.20061658979718]], [[1.0, 0], [-19.0, 0], [107.0, 0]], [[1.0, 0], [14.0, 0], [109.0, 0]], [[1.0, 0], [5.0, 8.660254037844387], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-585-9.7-c1-0-17', '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/585/2/i/b/196/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8610504102288488, 1.676470878385579, 1.487218687871637, 1.2854719787184588, 1.0635580413726606, 0.8158447165057526, 0.5402698560024005, 0.23940321231752176, -0.0789699329025832, -0.4017400959772762, -0.7108576197807227, -0.9842415017147065, -1.197233473063129, -1.3245779607221744, -1.3428468597431444, -1.2331542640990072, -0.9839318646996288, -0.5934729154030974, -0.07191386141907477, 0.557680834306255, 1.2594249293388777, 1.9861139893702016, 2.6821989313085677, 3.2881319756025262, 3.7457974052668144, 4.00455254746168, 4.027247699352967, 3.795495421479433, 3.313444516339142, 2.609399027656728, 1.7348125876464562, 0.7604730958949337, -0.22995462615968332, -1.1484816192552212, -1.9125439431116285, -2.4547802529068536, -2.73153748831565, -2.728847908494434, -2.4648572098709813, -1.9881013243759762, -1.3715859242447759, -0.7032461638197113, -0.07396245722282363, 0.43521923363901033, 0.7647592793664878, 0.8853150337977969, 0.8019179943159703, 0.5527333691030059, 0.2023358833718103, -0.1696400097789729, -0.4827597701440626, -0.6706105246088714, -0.6935668708661208, -0.5470594077279648, -0.26354112162698634, 0.09262831786205188, 0.4368985882770509, 0.6810776072500148, 0.7518765353131808, 0.6079862058209208, 0.252197966350553, -0.2642701277527607, -0.8468212703430339, -1.3717946312275553, -1.7081125824704733, -1.7427038866429971, -1.4050681468827273, -0.6860786635714584, 0.35320611094528775, 1.5853820334666737, 2.8336097919346988, 3.8994929065871267, 4.597490066539892, 4.789777058963148, 4.414890404995866, 3.504178306130708, 2.182020759255314, 0.6486689385088138, -0.8521159229775749, -2.075314103039319, -2.8192012973855554, -2.9637154200781812, -2.494900394548976, -1.5100528802992839, -0.20178212159178532, 1.1766684064955941, 2.3586240487662162, 3.1147233640976357, 3.297183247761779, 2.8685637162063418, 1.9089316338260574, 0.5996274942227356, -0.8133348180224153, -2.0688773672451855, -2.9432452867734575, -3.2941997908419594, -3.0876710114784385, -2.401231134078347, -1.4037707606378054, -0.31600832440436183, 0.639248335325056, 1.2858407170274075, 1.5309670287590975, 1.3815959142968741, 0.9370569898871828, 0.35990096363230817, -0.16768553887705231, -0.4911202555664703, -0.5226006471074935, -0.2624272392314995, 0.20292322367590873, 0.725555743551344, 1.1374988791556502, 1.2980118161071428, 1.1344746405888073, 0.6658540476852922, 0.001997257377341673, -0.6818475027468119, -1.18938036098256, -1.3553789339837308, -1.0920523695147235, -0.41707269258744534, 0.544912245633742, 1.5887945011947642, 2.4777108143879003, 3.001998824377862, 3.033289120999628, 2.5593248338527483, 1.6896662294733722, 0.6298043067402196, -0.3704785863652415, -1.0815897767862257, -1.3546549877598986, -1.1617837690039101, -0.6046556503108899, 0.11182795636068342, 0.7347354838321133, 1.0330119646938487, 0.8634828766624859, 0.21476170145375126, -0.7837177235913649, -1.8912097432494328, -2.8169222922541177, -3.2972965052779126, -3.1686200749139535, -2.4148941191101647, -1.1770508224839231, 0.28013801693593154, 1.6355187118093204, 2.5956651922437866, 2.9727854595627288, 2.7346668627389157, 2.0121456567994844, 1.0611477433116943, 0.18910737433540595, -0.33404682838936994, -0.3551771055433298, 0.11562493651179738, 0.9058424289597824, 1.7298326660362546, 2.2739158272513804, 2.293743388262297, 1.6959980382174955, 0.5799018694708492, -0.775407773466984, -1.9766203585882451, -2.618904593143329, -2.398169611398315, -1.2019342349621858, 0.8472291264426647, 3.4092557404767003, 6.002153663066565, 8.11648628443137, 9.33867745950892, 9.450321684437439, 8.477123079269607, 6.674941890298589, 4.4577852321673195, 2.288482329036378, 0.5626707756953895, -0.4822319570219571, -0.8094209449524521, -0.5674634844138575, -0.0253182062145019, 0.5204082176130505, 0.8368645308199896, 0.817769811733526, 0.5004780999939211, 0.035177472021742553, -0.3806717179949874, -0.5789619561976355, -0.48226516792390145, -0.12951156403119307, 0.34169261892448766, 0.7487731140307926, 0.9341408238296359, 0.8259575188418745, 0.46739274661569297, 0.0029857487596228714, -0.37411345556045433, -0.4959824939275838, -0.28839257348544833, 0.1919712660458172, 0.7676579132893876, 1.1981071559952652, 1.2679466144557563, 0.876823381933554, 0.09868172303490226, -0.813749608077732, -1.4867946017361124, -1.533041851593949, -0.6773312139402979, 1.1378576352343706, 3.7034455460267033, 6.571626951590474, 9.158012922364069, 10.891996058809248, 11.372808053778805, 10.484860953168111, 8.436456341100206, 5.708036061328014, 2.9232409619192423, 0.6797335304802121, -0.6105364866659496, -0.8244392611421881, -0.14415473202261275, 1.0162868458803556, 2.1499813374740295, 2.8171722421606766, 2.7759734052412224, 2.043665004641023, 0.8714484771462199, -0.35612778063934947, -1.2614845863582023, -1.606059043691841, -1.3696767728939099, -0.7512415762692136, -0.09174670453400373, 0.25285174794928056, 0.04426288587084658, -0.7464882645604012, -1.9207877907610291, -3.114687353485957, -3.9210042342056575, -4.029706442609427, -3.338315029193938, -1.9939239694831736, -0.3515996355428027, 1.137513312996415, 2.0709011096971377, 2.2233516587870623, 1.6161337834121834, 0.5036143765211125, -0.7174018537987141, -1.6438211257877104, -2.0006823176003152, -1.7276804436529503], 'positive_zeros': ['0.969386349372659091894649488478561', '2.26531065152294420070403497531106', '3.97057079452193291999780406947573', '5.26612833496443986194770641291531', '6.06711973469745507013148682859241', '6.84334040578923709037252472115872', '7.56466385163742694478419648571805', '8.460876341539892122819138262146952', '9.677481595227111620669874779138528', '10.51811195697517297734044584970496'], 'prelabel': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.4444444444444444, 'root_number': '0.17364817766693041 - 0.984807753012208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.222222222222', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.969386349372659091894649488479', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26531065152294420070403497531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97057079452193291999780406948', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.7', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/b/196/1'], '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': '2-585-9.7-c1-0-17', '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': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.2222222222222222, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.969386349372659091894649488479', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1228843187635303387772103578161', 'Lhash_array': ['1228843187635303387772103578161'], 'label': '2-585-9.7-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/b/196/1'}