-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3257932538752045491375012119287', 'a10': [0.24290431929882841, -0.4207226224035042], 'a2': [0.15659795699115286, 0.09041187262338754], 'a3': [0.9130064415994333, -1.5813735444878856], 'a4': [-0.9836513865774646, -1.7037341784877436], 'a5': [0.0, -2.68664183420524], 'a6': [0.2859498869484672, -0.16509324420444058], 'a7': [0.0, 0.0], 'a8': [0.0, -0.7173825459697912], 'a9': [-0.16716152480411908, -0.28953225403141936], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.9215308905402626, 3.0508554598177122]]]], 'bad_primes': [7, 13], 'central_character': '637.589', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1018680019161347733170289004606', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.15659795699115286, -0.09041187262338754], [1.0, 1.7320508075688772]], [[1.0, 0], [-0.9130064415994333, 1.5813735444878856], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 2.68664183420524], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.333282503220793, 1.3471212813299687], [5.5, 9.526279441628825]], [[1.0, 0], [-1.9215308905402626, 3.0508554598177122]], [[1.0, 0], [-2.382466466774555, -4.126552967782637], [-8.5, 14.722431864335457]], [[1.0, 0], [0.1631803809201881, -0.09421223685073628], [9.5, -16.454482671904334]], [[1.0, 0], [-2.1996435246407917, 3.8098943432177346], [-11.5, -19.91858428704209]], [[1.0, 0], [3.5428023995816598, -6.1363137572523705], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -3.6993058896987874], [-31.0, 0]], [[1.0, 0], [6.888480313400638, 3.977065963249296], [18.5, 32.04293994002423]], [[1.0, 0], [-4.702154612597422, -2.7147902313543617], [20.5, 35.50704155516198]], [[1.0, 0], [4.005326650533192, 6.937429259633162], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 1.8488890889411587], [-47.0, 0]], [[1.0, 0], [7.072439951305249, 0], [53.0, 0]], [[1.0, 0], [-6.572162760255997, 3.7944399387918337], [29.5, -51.09549882328188]], [[1.0, 0], [-0.20578192054491473, -0.3564247416628941], [-30.5, 52.827549630850754]], [[1.0, 0], [-9.87357977214075, -5.7005139393107065], [33.5, 58.023702053557386]], [[1.0, 0], [-2.896753491918417, 1.6724414083350865], [35.5, -61.48780366869514]], [[1.0, 0], [0, 14.215801222196559], [-73.0, 0]], [[1.0, 0], [-9.110589808080375, 0], [79.0, 0]], [[1.0, 0], [0, 16.58658466842761], [-83.0, 0]], [[1.0, 0], [-5.1023151994437725, -2.9458230538891814], [44.5, 77.07626093681505]], [[1.0, 0], [-0.39065850003587105, 0.22554679015692558], [48.5, -84.00446416709055]], [[1.0, 0], [3.828398936235573, -6.630981469202655], [-50.5, -87.4685657822283]], [[1.0, 0], [5.157395820952503, 0], [103.0, 0]], [[1.0, 0], [4.016444762805938, -6.956686394973812], [-53.5, -92.66471820493493]], [[1.0, 0], [0, 1.3335615220103427], [-109.0, 0]], [[1.0, 0], [-9.96917393872745, -17.267115771367482], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-637-13.4-c1-0-40', '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/637/2/q/g/589/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5344050696127358, 1.7974784226525413, 2.0796853508188886, 2.3816309547590113, 2.6993198278609785, 3.0238839688893453, 3.3419429405347545, 3.6364398099406356, 3.8878413701753805, 4.075641839831066, 4.180121937421636, 4.184288606816183, 4.0758718007869, 3.849202410078074, 3.5067548546536367, 3.0601204270776923, 2.5301912770584996, 1.9463845365057366, 1.3448218335794588, 0.7654965385025911, 0.24859910832486032, -0.16968596606749534, -0.46146992583287777, -0.6110034705476003, -0.6175089581014974, -0.4964778663553915, -0.279036044966334, -0.009185587879277101, 0.2609971635673895, 0.4778224875793776, 0.5934225285022572, 0.5732304912657173, 0.4024286871907972, 0.0902869363365995, -0.328525187263271, -0.7962401514434294, -1.2380268100430802, -1.571319150826923, -1.7174340738345295, -1.6139857489496758, -1.226288657373383, -0.5558741643136643, 0.3555276423951235, 1.4276654994901214, 2.5494560733158034, 3.592112844614913, 4.426204496116367, 4.940337211598683, 5.05865641529697, 4.754281651480353, 4.056185367889871, 3.0478865003359914, 1.8575524675661932, 0.6405112272237277, -0.4434622013069091, -1.2546503839397334, -1.695697919240766, -1.727828617035818, -1.3778945400628861, -0.7345976214924707, 0.06594896268291148, 0.8632278740692598, 1.500131861274837, 1.8507450481734387, 1.8430131727468306, 1.4719351261668119, 0.800497208872264, -0.052209884313433624, -0.933797350978136, -1.6881962975136895, -2.186454660930956, -2.3526074589438926, -2.179253514379605, -1.7293463122654695, -1.1233994127235711, -0.5143064171255319, -0.05467005875715189, 0.13666456472204858, 0.0017093109126154605, -0.4420537594934308, -1.1032410515122095, -1.8346572743440632, -2.464633780940477, -2.835254978892544, -2.839263164222586, -2.4473064582974082, -1.718923019848033, -0.7939594960841369, 0.13464868714333098, 0.8615552949781284, 1.2146481923053476, 1.0956071892276076, 0.5059627031415193, -0.4479348143951154, -1.5731519541406969, -2.6285524741280364, -3.375529307339122, -3.6301422730481163, -3.3049450421492566, -2.430693762283049, -1.1523950606065456, 0.3001242448664593, 1.6610476297750587, 2.686044826530304, 3.2053431785230693, 3.160070705417093, 2.613232369728561, 1.7325395892468418, 0.7489958966876007, -0.09895703888918747, -0.6222847827006065, -0.7253335064104616, -0.4260832339107385, 0.15237448203038562, 0.8169987138250663, 1.3576604522674334, 1.6040944771822274, 1.472067464436349, 0.9864557693377475, 0.2747782448548576, -0.46756282975258084, -1.0314859118171993, -1.253568065250364, -1.0643986375728192, -0.512297604545241, 0.2450151233074807, 0.9797399880387924, 1.4547398345060742, 1.4898945990676653, 1.0160714037496676, 0.10134015762317956, -1.059007425819497, -2.187558637660227, -2.9943044641068397, -3.252797877589215, -2.862631500717185, -1.8808447981813305, -0.5126608905528626, 0.9373376896112285, 2.1416868929319026, 2.834346657317953, 2.8802572926699903, 2.3109320423192723, 1.315629679028495, 0.1895631943273586, -0.7475352234316756, -1.2406566753649255, -1.1720371112849688, -0.5964870146329577, 0.27107437374613075, 1.1134098037043505, 1.5989133496170824, 1.47581523159387, 0.6465201659973924, -0.7989673404945435, -2.600486845708123, -4.391910412478398, -5.794828178907531, -6.516075035589198, -6.422222693830052, -5.570575688363652, -4.188499297718597, -2.607576809543, -1.1719018165162176, -0.14700622496549304, 0.34463704238711435, 0.3437844689543891, 0.025917745622389306, -0.3656606365125146, -0.6034299796147443, -0.5495093447117182, -0.19676344606331644, 0.33524813400801573, 0.8473579016430726, 1.134867791875877, 1.0636635364898763, 0.6224500287348763, -0.0673491600600162, -0.7887958832858134, -1.302839635362381, -1.434370324268972, -1.1419772223976765, -0.5463585349912755, 0.09536425874107976, 0.46504753257123255, 0.2876231714358108, -0.5679028183653578, -2.023521122219619, -3.787057438416849, -5.413192503725532, -6.416858339561472, -6.408262940811779, -5.210561296921529, -2.924570318768206, 0.08070326742023042, 3.2516610584178887, 5.985911211195156, 7.782597645524634, 8.364917876786544, 7.740489573442187, 6.1835915446651, 4.146459158995309, 2.127628696393937, 0.5373539979345989, -0.40034398972545454, -0.6821445030594238, -0.49037006992005827, -0.10452981881122769, 0.20805688274749978, 0.28478249295465774, 0.11301533669565662, -0.1848643167393485, -0.4180962981642022, -0.41901862527584266, -0.12386573140474802, 0.3887133253891929, 0.9177052171800549, 1.213150439573937, 1.077523451178114, 0.45794384621129314, -0.5067234168833405, -1.5056545165595179, -2.1418356757138097, -2.0593065272762066, -1.0710419981872783, 0.7564156992503744, 3.0935826079807933, 5.422515747533099, 7.176295364278736, 7.902273638838462, 7.398287457235285, 5.777914044609334, 3.442385888185682, 0.9662008321297868, -1.0688230915073742, -2.2395114175978117, -2.395643951737316, -1.6876844368347959, -0.5011834304230043, 0.6786120786621044, 1.4261472644972624, 1.5063564176464617, 0.9351648801069258, -0.047255229802573545, -1.077374823984303, -1.8052679775449283, -2.0182615554660885, -1.7080592319441201, -1.0594264187260678, -0.3672883945272804, 0.08498857331176347, 0.13959022125921086, -0.1726994697445799, -0.6444047354021945, -0.9740876330604007, -0.888989655438906, -0.2611283659414602], 'positive_zeros': ['2.57005561166892772922646766626610', '3.37911443448704959944585074797673', '4.15426876262368627613650930173099', '5.20447613017797282366227963316548', '6.69585880446788713677718688332923', '7.49002357827674346702837875529075', '8.367691431820097209261299480781367', '9.521563759395299399857943315860191', '9.750713001596074537146434336883135', '10.98077883448616842789174709204724'], 'prelabel': '2-637-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.8414964132431015, 'root_number': '-0.878561770537832 + 0.4776287421726522*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.420748206622', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.57005561166892772922646766627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37911443448704959944585074798', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15426876262368627613650930173', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/g/589/4'], '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': '2-637-13.4-c1-0-40', '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': '2-637-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.42074820662155077, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.57005561166892772922646766627', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3257932538752045491375012119287', 'Lhash_array': ['3257932538752045491375012119287'], 'label': '2-637-13.4-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/g/589/4'}