-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '507306095723996926280150207929', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 4.47213595499958], 'a4': [-3.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 4.47213595499958], 'a7': [-7.0, 0.0], 'a8': [-7.0, 0.0], 'a9': [-11.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.7684046263051965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '175.76', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '4316014242761350254072366227563', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0], [4.0, 0]], [[1.0, 0], [0, -4.47213595499958], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [121.0, 0]], [[1.0, 0], [0, 13.416407864998739], [-169.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-289.0, 0]], [[1.0, 0], [0, -13.416407864998739], [-361.0, 0]], [[1.0, 0], [26.0, 0], [529.0, 0]], [[1.0, 0], [22.0, 0], [841.0, 0]], [[1.0, 0], [0, -53.665631459994955], [-961.0, 0]], [[1.0, 0], [14.0, 0], [1369.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-1681.0, 0]], [[1.0, 0], [-34.0, 0], [1849.0, 0]], [[1.0, 0], [0, 26.832815729997478], [-2209.0, 0]], [[1.0, 0], [-34.0, 0], [2809.0, 0]], [[1.0, 0], [0, -40.24922359499622], [-3481.0, 0]], [[1.0, 0], [0, 93.91485505499116], [-3721.0, 0]], [[1.0, 0], [14.0, 0], [4489.0, 0]], [[1.0, 0], [-62.0, 0], [5041.0, 0]], [[1.0, 0], [0, 53.665631459994955], [-5329.0, 0]], [[1.0, 0], [-38.0, 0], [6241.0, 0]], [[1.0, 0], [0, -40.24922359499622], [-6889.0, 0]], [[1.0, 0], [0, -26.832815729997478], [-7921.0, 0]], [[1.0, 0], [0, 26.832815729997478], [-9409.0, 0]], [[1.0, 0], [0, 67.08203932499369], [-10201.0, 0]], [[1.0, 0], [0, -160.99689437998487], [-10609.0, 0]], [[1.0, 0], [-106.0, 0], [11449.0, 0]], [[1.0, 0], [142.0, 0], [11881.0, 0]], [[1.0, 0], [-34.0, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-175-7.6-c2-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/175/3/d/f/76/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7833035690482433, 0.5337050465803022, 0.2890715633531792, 0.048162547045236495, -0.18946608517308972, -0.4231087187092294, -0.6506660094709751, -0.8685262475792377, -1.0715791689762186, -1.2533636850105268, -1.4063477260916022, -1.5223353401069748, -1.5929915980699298, -1.6104688718711342, -1.5681087162370346, -1.4611826813597246, -1.2876241547552965, -1.0486933097846163, -0.7495100703077531, -0.3993873010546113, -0.011899627271128916, 0.3953665611851273, 0.801418735210229, 1.1828313740137253, 1.5150673479233592, 1.7740927537653504, 1.9381934398886398, 1.9898665823605508, 1.9176319992720037, 1.7175896527637073, 1.3945459013075117, 0.9625445944208142, 0.44467173823078043, -0.1279459549518482, -0.7179601330494881, -1.2843688710494583, -1.7856799564783383, -2.1834340577529794, -2.4457842224121418, -2.5507830663937887, -2.489015742441389, -2.265241626488287, -1.8987733964686992, -1.422427076070573, -0.8800139520593154, -0.3225033601556995, 0.19685179126053365, 0.6279861054007447, 0.9295338698210068, 1.0737642356596537, 1.0503254105888986, 0.8682624789907035, 0.5559260105166698, 0.15860497394037104, -0.2660220453151661, -0.6542466446111994, -0.9438714144876963, -1.082095206923496, -1.0327853018070348, -0.7821687557739857, -0.3420893753573944, 0.24978647645777094, 0.9330911527744575, 1.6310697529152263, 2.2595211032881926, 2.7374034252774684, 2.9978384766958492, 2.9980871980394754, 2.7270882744384966, 2.2093629905446956, 1.5044838915743883, 0.7018427011348657, -0.08892786782128316, -0.7509034315867814, -1.174679580947498, -1.2731728488592364, -0.994409260114972, -0.3304426368362891, 0.6790382484490973, 1.9492045032915921, 3.358669103526884, 4.76328679532077, 6.013521753402935, 6.973145707680943, 7.536735538963811, 7.643501014763941, 7.285402157453774, 6.508267693102709, 5.405604177036242, 4.105851445981602, 2.754833543953173, 1.4959168059665755, 0.45078773552467394, -0.2962771182599144, -0.7082715519122849, -0.7979603923681058, -0.6226829376682479, -0.2723596998908311, 0.14727557130797694, 0.5333844163798557, 0.8034850096989307, 0.9086615796421929, 0.8402255914845299, 0.6286628838762159, 0.33507087900868426, 0.03666522994604944, -0.19093091738198434, -0.29122527181732705, -0.24075723531844345, -0.05646394849634282, 0.20524858066984467, 0.4579658211766226, 0.6018478246960524, 0.5444617288648573, 0.2219921466755768, -0.3833587097186038, -1.2335050211351515, -2.2346660332978323, -3.2483718389304936, -4.112035954327613, -4.665943538405848, -4.782082373992832, -4.389599083840021, -3.491963185271744, -2.172164059736181, -0.5842685556798616, 1.0679076826367075, 2.5618507216607607, 3.6920165004854955, 4.303935585400263, 4.320605113826322, 3.7562035189831873, 2.7143267666591604, 1.3707139760004876, -0.05670065593944389, -1.34515105416108, -2.305067623117019, -2.811779912697972, -2.82499943983335, -2.392449299872423, -1.637021691135088, -0.7300378539784146, 0.14407300291317532, 0.8246288500920586, 1.2056925860865415, 1.2549666594694606, 1.0167780673240243, 0.5986111984982148, 0.14408085289444586, -0.20186638439967527, -0.32799732943135373, -0.18437764245709842, 0.20375239819502777, 0.739229524187235, 1.2731188397831656, 1.6378334650013893, 1.686321831564446, 1.3288502275970013, 0.5591192258704623, -0.5365387115773362, -1.7896995571446597, -2.9787802742737712, -3.8709980140029296, -4.2689900521256625, -4.052430670048366, -3.2057209901034267, -1.825507846370545, -0.10588470909533985, 1.6962069950524967, 3.3086214779387344, 4.4950660873778965, 5.099082430329118, 5.07184819069744, 4.478069800584448, 3.4788886291128405, 2.2956498808172334, 1.162497641075863, 0.2781370026438526, -0.23280483073645875, -0.34062394618630126, -0.10947602129541605, 0.32470674827688567, 0.7916381560349315, 1.130293302506228, 1.228243479401568, 1.0473783812896749, 0.6300432053739952, 0.08441792394877655, -0.44692995224367493, -0.8272088061051523, -0.9639485431566821, -0.8359038264279479, -0.5011063193605025, -0.08353895312869729, 0.25866421126893274, 0.37574273488422866, 0.1687766736995518, -0.3790871686494182, -1.1914076645003895, -2.1112327356639318, -2.935940017646326, -3.466442768407363, -3.5590068655032514, -3.1666291747726, -2.3588453773132043, -1.3136328405906805, -0.28168798203764744, 0.4697715347429627, 0.7210908707519893, 0.35695972153130995, -0.5982934998039043, -1.9765657573357858, -3.4956067076173927, -4.817020353736907, -5.6202421432044884, -5.67580627144353, -4.900788960678894, -3.3829701742640443, -1.367236488215446, 0.7935435423426984, 2.7125630811347237, 4.051415884750598, 4.591952324551448, 4.281168594033531, 3.2388966980024976, 1.7268031895168166, 0.08633300418970047, -1.339470704559497, -2.2816706968037064, -2.60092822386462, -2.3102333889376423, -1.5605346594877039, -0.5941112088692186, 0.32162144585557667, 0.9626404769762007, 1.2018389024686482, 1.034518121539829, 0.5704160462202215, -0.004293984674278593, -0.48377963161459764, -0.702129374401179, -0.5793764371099697, -0.14162966890299283, 0.4896954541465229, 1.1359092981936398, 1.6151110292493625, 1.7965881851513166, 1.6397812317001428, 1.2064013708673393, 0.6419168556532854, 0.131423773268325, -0.15756324308775788, -0.12877085427613333, 0.20878852368020245, 0.7372754250596346, 1.259417870540642, 1.553835238621161], 'positive_zeros': ['0.40019394589696948159491333000609', '2.50371016408415745461142317958535', '4.09769343200612127736577170691422', '5.70072161390158234500649530094084', '6.67164245295287379208520995704850', '7.57536351186365520859072305526360', '8.985239900909979527651130182767712', '9.670426737687766323550471917526655', '11.56866256009431629392314537404803', '12.20647871316742965032368694329243'], 'prelabel': '2-175-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.183667700522494, 'root_angle': -1.0, 'root_number': '-1.0 - 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.5', 'prec': 14}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40019394589696948159491333001', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50371016408415745461142317959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09769343200612127736577170691', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.7684046263051965, 'bad_primes': [5, 7], 'central_character': '7.6', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/3/d/f/76/2'], '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': '2-175-7.6-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-175-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.183667700522494, 'root_angle': -0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40019394589696948159491333001', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '507306095723996926280150207929', 'Lhash_array': ['507306095723996926280150207929'], 'label': '2-175-7.6-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/3/d/f/76/2'}