-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2233790090133323090891862579811', 'a10': [1.6002062903825311, -0.9238795325112867], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.9238795325112867, -1.6002062903825311], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.215', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '1959467625046862160735871282054', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9238795325112867, 1.6002062903825311], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -0.7653668647301796], [-1.0, 0]], [[1.0, 0], [0.3826834323650898, 0.6628271480711836], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.7071067811865476, -1.224744871391589], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.7653668647301796, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.224744871391589, 0.7071067811865476], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.6002062903825311, 0.9238795325112867], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.6002062903825311, -0.9238795325112867], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.9238795325112867, -1.6002062903825311], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.8477590650225735], [-1.0, 0]], [[1.0, 0], [0.9238795325112867, 1.6002062903825311], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.7071067811865476, -1.224744871391589], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-42e2-84.47-c0-0-9', 'leading_term': '2.12654161759079566709839496351', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1764/1/q/b/215/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.126541617590796, 2.1400430019275203, 2.1751468582445774, 2.229531987418964, 2.2996350963224086, 2.3810998701523034, 2.4691987020523967, 2.559157021222264, 2.6463670290810026, 2.7265119710740153, 2.7956322396947892, 2.85016065667797, 2.886945698919513, 2.9032733323767874, 2.8968921693090297, 2.8660428473058603, 2.8094903032171734, 2.7265564368153097, 2.6171501281979843, 2.4817914352389194, 2.321626904125534, 2.1384331951710447, 1.9346066139664602, 1.7131366209892078, 1.4775619566173486, 1.2319086515464268, 0.9806098826043949, 0.7284083661033908, 0.48024273700479936, 0.2411201206698091, 0.015977840017825058, -0.19046211279438996, -0.3738416034331047, -0.5303131448514118, -0.656679849801297, -0.750523246937465, -0.8103136465718576, -0.8354979309079449, -0.8265600468444894, -0.785050100831364, -0.7135787898589242, -0.6157749362837408, -0.4962051030523406, -0.3602556166480237, -0.21397877536160345, -0.06390651977039082, 0.08316366660778726, 0.22040443769807336, 0.3412083716011259, 0.439443302665997, 0.5097038129726486, 0.5475489897525299, 0.5497164122525493, 0.5143025884410912, 0.4409007397992886, 0.33068793569703575, 0.18645509375572553, 0.012575256194926132, -0.1850922278555223, -0.39936150865751574, -0.6219412823829772, -0.8437116212495327, -1.0550484704821623, -1.246185202984076, -1.4075984196582458, -1.5304033874700511, -1.6067432267344541, -1.6301552865765767, -1.5958981550383424, -1.5012234840523777, -1.345578285677324, -1.1307255577731683, -0.8607739731617902, -0.5421108298533037, -0.18323639132870725, 0.20549800478618713, 0.6122412991801068, 1.0240724128229037, 1.4274931011283116, 1.8089651388698929, 2.1554700496935544, 2.4550674682612605, 2.6974270872697903, 2.8743091092367017, 2.9799692616400995, 3.0114667591067903, 2.968857066715219, 2.855255834694631, 2.676765780212895, 2.442264376671513, 2.16305671880334, 1.8524045702134473, 1.5249490518913824, 1.1960503688227553, 0.8810730762019338, 0.5946493584000411, 0.34995537321231973, 0.15803669594574818, 0.027218145859060645, -0.0373692659626204, -0.034115833094646976, 0.03490739416935448, 0.163972315195705, 0.34390724962873565, 0.5624975069455033, 0.8050607859703294, 1.0551756705161703, 1.2955326516458705, 1.5088693855072586, 1.6789457422664105, 1.7915100138912432, 1.8352057435804432, 1.8023692331512053, 1.6896709739132285, 1.4985599986226004, 1.2354782987622697, 0.9118226905096535, 0.5436434171405172, 0.1510818090171747, -0.2424371379179638, -0.6112280385046812, -0.92854253627886, -1.1678882352680482, -1.3044078198334426, -1.3162511124250262, -1.1858701060014751, -0.9011677935734947, -0.45643601715573245, 0.14697449909508964, 0.9002975447521232, 1.7873398091392627, 2.7848295566519345, 3.863123183431208, 4.9872489697301585, 6.1182494354362085, 7.2147671302420795, 8.234804372002088, 9.137576228997466, 9.885368631714439, 10.445310426030698, 10.790969756122871, 10.903691464970287, 10.773603042085462, 10.40023159754231, 9.792692725123668, 8.96943305194577, 7.957530705261227, 6.79158069168364, 5.5122140579343855, 4.164319475943193, 2.7950524401589973, 1.4517295997686066, 0.17971309893490303, -0.9796083525602549, -1.9906388297759188, -2.825101618711218, -3.463194090909097, -3.8943116141291654, -4.117303806662522, -4.140251454877651, -3.9797783465142764, -3.6599376728458424, -3.210736068466142, -2.6663784211550543, -2.063332097175085, -1.4383192333868635, -0.8263495957521684, -0.25890389382446705, 0.23763155112857787, 0.643192804355711, 0.9448630282725776, 1.1372519496784605, 1.2224147042760372, 1.2093222632907952, 1.1129225822513582, 0.9528562567896087, 0.7519112988680081, 0.5343173457411426, 0.323989167706513, 0.14283210055739798, 0.009217760078528241, -0.06327269898226336, -0.06675780419059889, 0.00044006286464402447, 0.13372684600828666, 0.32260827138244447, 0.5514747820082538, 0.8007469174690747, 1.0483041413931666, 1.271101011508844, 1.4468616330160335, 1.555737451295158, 1.5818150917874796, 1.514370123551872, 1.3487787943928258, 1.0870219758309905, 0.7377423686529649, 0.31584572928171406, -0.15833246081407806, -0.6602438845097168, -1.1626503470553895, -1.6373537271951664, -2.0570186886621538, -2.396966302889548, -2.6368172785566353, -2.761872276930034, -2.764133332600019, -2.642893679592023, -2.404851808506724, -2.0637374732946063, -1.6394704865716996, -1.1569052304638836, -0.6442426402091099, -0.13121495302339978, 0.35283494878262645, 0.7808494795302908, 1.1297981006224964, 1.3821450646459794, 1.5269414649715083, 1.5604653415898055, 1.4863646568976117, 1.315292528982872, 1.0640597972172556, 0.754364278395375, 0.41118649074622315, 0.06096595056980869, -0.27031144828768533, -0.5589772725938524, -0.7853605870132028, -0.9351616772366349, -1.000418517470503, -0.9799942497164811, -0.8795487764254759, -0.71099556674096, -0.491483199427394, -0.24197718679381502, 0.014451463366329905, 0.25450107325239296, 0.4565335948167388, 0.6023410416383502, 0.6786443622553155, 0.678203454692838, 0.6004450021256227, 0.4515504881473625, 0.24398761460313498, -0.004488567251628065, -0.2722963946439983, -0.5358438704424189, -0.7715634162689902, -0.9580070086580965, -1.0778341451624025, -1.1195282443742778, -1.0786929869595059, -0.9588079278197997, -0.7713607054455723, -0.535318779418921, -0.2759536276219179], 'positive_zeros': ['1.76214967257629880486954558776503', '2.66187345004498787139801367263420', '3.34377010565217061031362112948508', '4.36401294119883361986638010686654', '5.76032570795371438607034991161815', '5.89476955870057440798421982459235', '6.93637303082961526894799416395246', '7.48702428855222534343240557189540', '8.914926578966166700924130948379424', '9.814495354905709674096300764599147'], 'prelabel': '2-42e2-84.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9382700476326719, 'root_angle': -0.036040917197787535, 'root_number': '0.97446918273604469734984581370095 - 0.22452129497610049009779535861726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.036040917197787535', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76214967257629880486954558777', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66187345004498787139801367263', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34377010565217061031362112949', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'bad_primes': [2, 3, 7], 'central_character': '84.47', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/1/q/b/215/8'], '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': '2-42e2-84.47-c0-0-9', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-42e2-84.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9382700476326719, 'root_angle': -0.036040917197787535, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76214967257629880486954558777', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2233790090133323090891862579811', 'Lhash_array': ['2233790090133323090891862579811'], 'factors': ['2-42e2-84.47-c0-0-9'], 'label': '2-42e2-84.47-c0-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/1/q/b/215/8'}