-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1039998036918380960588108662250', 'a10': [0, 0], 'a2': [-0.7071067811865476, -1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, 1.7320508075688772], 'a5': [0, 0], 'a6': [0, 0], 'a7': [3.4641016151377544, 0], 'a8': [2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.373072363830476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.899', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1551958261095713214932318177734', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-11.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [17.0, 0]], [[1.0, 0], [-4.0, 0], [19.0, 0]], [[1.0, 0], [0, -4.898979485566356], [-23.0, 0]], [[1.0, 0], [2.449489742783178, 0], [29.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-31.0, 0]], [[1.0, 0], [0, 0], [37.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-41.0, 0]], [[1.0, 0], [0, -8.0], [-43.0, 0]], [[1.0, 0], [0, -4.898979485566356], [-47.0, 0]], [[1.0, 0], [0, -7.3484692283495345], [-53.0, 0]], [[1.0, 0], [0, 11.313708498984761], [-59.0, 0]], [[1.0, 0], [0, -13.856406460551018], [-61.0, 0]], [[1.0, 0], [0, -4.0], [-67.0, 0]], [[1.0, 0], [14.696938456699069, 0], [71.0, 0]], [[1.0, 0], [0, 4.0], [-73.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-79.0, 0]], [[1.0, 0], [-14.142135623730951, 0], [83.0, 0]], [[1.0, 0], [0, 7.0710678118654755], [-89.0, 0]], [[1.0, 0], [0, 8.0], [-97.0, 0]], [[1.0, 0], [-2.449489742783178, 0], [101.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [103.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [107.0, 0]], [[1.0, 0], [0, -10.392304845413264], [-109.0, 0]], [[1.0, 0], [-18.384776310850235, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1800-120.59-c1-0-27', 'leading_term': '1.5411092259284847635903812073599163120387732836782458699', '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/1800/2/m/c/899/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5411092259284849, 1.510474518171683, 1.4725225589925286, 1.4269917877692235, 1.3735446874047499, 1.3117925955595446, 1.2413261992170483, 1.1617502588162492, 1.0727210084142187, 0.9739846929661118, 0.8654158027575592, 0.7470537131439969, 0.6191366028322702, 0.4821316819008553, 0.3367608975986394, 0.18402139710732457, 0.025200114519984825, -0.13811807862445086, -0.3040491547348988, -0.4704160715840924, -0.6347626243015492, -0.7943752647285954, -0.9463130309355994, -1.0874455935877878, -1.2144992675947626, -1.324110658762514, -1.412887419104842, -1.4774753754083414, -1.5146310789462123, -1.5212986060942282, -1.4946892268528764, -1.4323623582136946, -1.3323060394759352, -1.193015014625939, -1.0135643901736815, -0.7936767624385511, -0.5337806825907764, -0.23505835630434274, 0.1005194379445363, 0.4701730790549801, 0.8703101370981219, 1.2965390910502868, 1.7437017752981006, 2.2059252078118217, 2.6766930107447204, 3.1489361501858815, 3.615142206153046, 4.067481848772028, 4.49795065567394, 4.898523874000498, 5.261321224060432, 5.578778377198094, 5.843821334469368, 6.050039601485444, 6.191853813515621, 6.2646733273298985, 6.265039273907903, 6.190748668010744, 6.040955402554161, 5.816244320034364, 5.518675048347262, 5.151792908473912, 4.720604936679975, 4.2315198998329135, 3.6922521007989206, 3.1116897494411564, 2.4997296879205453, 1.867081278428837, 1.22504325672419, 0.5852582942388576, -0.04054913683385233, -0.640845268351107, -1.2045629993436722, -1.721373996058317, -2.1819493948091617, -2.578201575345813, -2.9034997003742498, -3.1528521758487282, -3.323049874427762, -3.412764871220942, -3.4226005491126137, -3.3550902154304523, -3.214642800261488, -3.007435740543756, -2.7412567488714905, -2.4252977730902563, -2.069906020644995, -1.686298397383785, -1.2862470416575202, -0.8817447709147441, -0.4846601535414697, -0.10639253337945814, 0.24246236419853207, 0.5524256507204077, 0.8154171075839561, 1.024996157730244, 1.176553573528909, 1.2674469076463037, 1.2970743034797463, 1.2668832453224843, 1.1803128887254963, 1.042670802801725, 0.8609471860178383, 0.6435718084919141, 0.40012100833572345, 0.14098394954432167, -0.12300103933191303, -0.3809279498458646, -0.6222094214260235, -0.8369544851199134, -1.01632431735674, -1.1528531016603447, -1.2407220800242111, -1.2759763185509547, -1.2566755752189833, -1.182972885311662, -1.057117000391906, -0.883377544324536, -0.6678945884127667, -0.418457193263049, -0.14421820966347734, 0.1446448331554731, 0.4373106993554811, 0.7227234084232793, 0.9900139885033815, 1.2289190482138888, 1.4301800203941808, 1.5859073821003715, 1.6898952304846897, 1.7378732690677903, 1.7276854836725057, 1.6593874886025624, 1.5352576066358885, 1.3597200977024304, 1.1391824428654735, 0.8817920847695423, 0.5971213809268784, 0.29579260118831335, -0.010942538308138074, -0.31165218636872527, -0.5951844061226891, -0.851119083299533, -1.0701928100514002, -1.244678645999773, -1.3687042208196707, -1.4384939381722783, -1.4525239919733859, -1.4115824053794632, -1.3187302163031445, -1.1791641046693238, -0.9999850140070508, -0.7898814823141992, -0.5587402818890526, -0.3172003988099797, -0.0761691980199556, 0.15367832060373018, 0.36239507770281204, 0.5412299360310531, 0.6830465769217194, 0.7826733321606547, 0.8371667135692866, 0.8459748639136306, 0.8109913429886356, 0.7364943955314337, 0.6289719271137127, 0.49683762270220744, 0.3500487497521817, 0.19964096027226996, 0.05719961860565397, -0.06570937393109251, -0.15812378953646417, -0.21025744465344195, -0.21403363678756732, -0.16355356834604753, -0.055475919875816446, 0.1107128613558101, 0.33255354529542586, 0.6046050457374769, 0.9185759874502208, 1.263595238431346, 1.6266132387650232, 1.992919639902375, 2.3467569232257763, 2.672004579624898, 2.952904362012549, 3.1747942912075673, 3.3248176732730497, 3.3925734843361126, 3.370676141297357, 3.2551958765535165, 3.0459555723650733, 2.746665816027534, 2.3648868761041486, 1.9118139823180325, 1.4018903827829612, 0.8522607876019137, 0.282085609130639, -0.28825649853683016, -0.83804426882595, -1.347129437236356, -1.7968511450934301, -2.1709067545345833, -2.456137457786054, -2.64318979195137, -2.727018798318819, -2.7072049335355004, -2.588064702893755, -2.378544019402597, -2.091893107107426, -1.7451319253932804, -1.3583251254250268, -0.9536949849382576, -0.5546091419699951, -0.18448683702528346, 0.13432759031047967, 0.3816723100494875, 0.5406045202253543, 0.5983155546611283, 0.5468785440083815, 0.3837891513482363, 0.11226848621597217, -0.2586924421108519, -0.7145558796836425, -1.2357250231221188, -1.7982808049105423, -2.374940351183423, -2.936198717127851, -3.451606060986653, -3.8911249900408693, -4.226507799829131, -4.432631024400589, -4.488725291239966, -4.379441966530222, -4.095704382755303, -3.6353003223057874, -3.003183520018173, -2.211464762887019, -1.2790871319294816, -0.2311944075615878, 0.9017840333530012, 2.085295047765806, 3.282021560353857, 4.453381840519008, 5.561102435287191, 6.568794741553354, 7.443464217295528, 8.156883587877372, 8.686767034186033, 9.01769102735549, 9.141718821275283, 9.058699114021925, 8.776224415031276, 8.309250495039802, 7.679394189903208, 6.913942004364715, 6.04461567074771, 5.106152377199947], 'positive_zeros': ['0.820413792831509259468289644955405', '1.91502674844665322562019872667417', '3.55134353859166349524417604376398', '4.63607026990518304485101258982800', '5.35913351615737614647606944363672', '6.11930714493494465697630371291088', '7.00599493579714642493072078442144', '7.83675991308938237292913454584235', '8.553611860552810907866831326171056', '8.854948075133559271354024203297024'], 'prelabel': '2-1800-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.04832965836487036, 'root_number': '0.98849563308738261028791073705322948599252104035008372741 + 0.1512494078242115090525888647704518588092264307068899408*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.02416482918243518', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.820413792831509259468289644955', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91502674844665322562019872667', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55134353859166349524417604376', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.373072363830476, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/2/m/c/899/2'], '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': '2-1800-120.59-c1-0-27', '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': '2-1800-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': 0.02416482918243518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.820413792831509259468289644955', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1039998036918380960588108662250', 'Lhash_array': ['1039998036918380960588108662250'], 'label': '2-1800-120.59-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/2/m/c/899/2'}