-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '564868658760625027416037950204', 'a10': [3.0, -1.7320508075688772], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 3.4641016151377544], 'a6': [1.5, 0.8660254037844386], 'a7': [0.5, 2.598076211353316], 'a8': [1.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [-0.5, -2.598076211353316]]], [13, [[1.0, 0], [3.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.335', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2709129413090723750244998052385', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [0, -3.4641016151377544], [-5.0, 0]], [[1.0, 0], [-0.5, -2.598076211353316]], [[1.0, 0], [-1.5, -2.598076211353316], [-5.5, 9.526279441628825]], [[1.0, 0], [3.5, 0.8660254037844386]], [[1.0, 0], [1.5, -2.598076211353316], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.5, 6.06217782649107], [-9.5, -16.454482671904334]], [[1.0, 0], [6.0, -3.4641016151377544], [11.5, -19.91858428704209]], [[1.0, 0], [-1.5, 0.8660254037844386], [14.5, -25.11473670974872]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [6.0, -3.4641016151377544], [18.5, -32.04293994002423]], [[1.0, 0], [4.5, -2.598076211353316], [20.5, -35.50704155516198]], [[1.0, 0], [-4.0, 6.928203230275509], [-21.5, -37.239092362730865]], [[1.0, 0], [0, 8.660254037844387], [-47.0, 0]], [[1.0, 0], [0, -8.660254037844387], [-53.0, 0]], [[1.0, 0], [-9.0, -5.196152422706632], [29.5, 51.09549882328188]], [[1.0, 0], [4.5, 2.598076211353316], [30.5, 52.827549630850754]], [[1.0, 0], [0, 0], [33.5, -58.023702053557386]], [[1.0, 0], [3.0, -5.196152422706632], [-35.5, -61.48780366869514]], [[1.0, 0], [-4.0, 0], [73.0, 0]], [[1.0, 0], [11.0, 0], [79.0, 0]], [[1.0, 0], [0, 13.856406460551018], [-83.0, 0]], [[1.0, 0], [7.5, -4.330127018922194], [44.5, -77.07626093681505]], [[1.0, 0], [1.0, -1.7320508075688772], [-48.5, -84.00446416709055]], [[1.0, 0], [0, 0], [-50.5, 87.4685657822283]], [[1.0, 0], [0, -3.4641016151377544], [-103.0, 0]], [[1.0, 0], [-4.5, 2.598076211353316], [53.5, -92.66471820493493]], [[1.0, 0], [0, 3.4641016151377544], [-109.0, 0]], [[1.0, 0], [-12.0, -6.928203230275509], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-546-273.62-c1-0-6', '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/546/2/q/a/335/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5950255752393094, 0.42569361210632256, 0.2589036891159731, 0.09307952148527666, -0.07102735521844059, -0.22931220303099223, -0.3737747946835623, -0.49246161905601304, -0.5698615821295508, -0.5877330725269561, -0.5263502586770111, -0.36614600672173725, -0.08969490913128929, 0.31607070510388613, 0.8575763085738615, 1.5324704068374195, 2.3278970616900008, 3.219448964016232, 4.171058139317274, 5.136028083138611, 6.059319486812107, 6.881075624347152, 7.5412225970129745, 7.9848193182130505, 8.16768239176302, 8.061694629434307, 7.659145477999432, 6.975466106649884, 6.049823140690094, 4.943224320405853, 3.7340552511012843, 2.5112839714824604, 1.365902267137651, 0.3814739027494878, -0.3751182782720686, -0.8615364302389896, -1.0653310729640026, -1.0058591837825233, -0.7322577972876169, -0.3174596296117074, 0.1511986914243691, 0.5836827800722294, 0.8997545429321917, 1.0404843032606839, 0.9770185599477227, 0.7151259063416078, 0.29459017340322863, -0.2167338651834282, -0.7335438524552511, -1.1669255352806198, -1.4393007618604965, -1.498055237953997, -1.3254684342956755, -0.9430380417955112, -0.40913292539778773, 0.18999326768480757, 0.7546141734947421, 1.1890962528841447, 1.4196145827939024, 1.4087763105394173, 1.1642499721086133, 0.7394076961977996, 0.22534314828130464, -0.2647870978663164, -0.6166200448996283, -0.7369838020349301, -0.5736126895787503, -0.12816409951484237, 0.5404712066477227, 1.3238966688250324, 2.082235348220421, 2.669626115130537, 2.9626759562533755, 2.886436683727944, 2.432574794660931, 1.6655824066443699, 0.7149810979469852, -0.24585729965184033, -1.0309109699916632, -1.4771204942589435, -1.4775473591789183, -1.005277130908813, -0.12273259253482265, 1.0262764867761052, 2.2410589663070724, 3.3009553368740465, 4.007731894954362, 4.2250426541451755, 3.9067447178709003, 3.1077972702742636, 1.9748498246948303, 0.7177873274308686, -0.43240774913157537, -1.270985679626657, -1.662027032027978, -1.567046015982986, -1.0530590998141651, -0.27785486163934653, 0.5448445573965078, 1.1930850175162857, 1.4868876514134792, 1.3297055234444346, 0.7314912511701739, -0.19238580414464365, -1.2467885532889635, -2.2017973342613404, -2.847148777818617, -3.0437098210025493, -2.759827723515738, -2.0835054987295023, -1.206694477204982, -0.38440161789012667, 0.12269319826280678, 0.10926049621746597, -0.5241226789036721, -1.7429551697771675, -3.380450168104288, -5.1691707924138015, -6.795977571196759, -7.968011158973167, -8.474663683711618, -8.231280090173081, -7.294558393496534, -5.846313748407984, -4.149828210038215, -2.489567534690583, -1.1089616131503428, -0.1612058234107973, 0.31545167168300076, 0.3928543482869464, 0.22107994537124573, -0.02091860043116089, -0.17828184276311543, -0.162264103059108, 0.029982812676815015, 0.32279160950094515, 0.5937116781501597, 0.7197665878436813, 0.6241082124245441, 0.30861182915840774, -0.13819704531162447, -0.5614447549237259, -0.7836615065662423, -0.6599239632246394, -0.12825332431982242, 0.7604141808115544, 1.843298899654169, 2.880050242729701, 3.6127974451104237, 3.836549662710647, 3.4604772670401664, 2.5419192417477707, 1.281556902307273, -0.021510434408237297, -1.0447806104859243, -1.5283499895668333, -1.3485757624273176, -0.5581925153343175, 0.6201237877763865, 1.8474635130160157, 2.7572566317601637, 3.0559903952669454, 2.6088754237443745, 1.486154568270706, -0.044476309387317725, -1.5796461024767412, -2.6817193197739755, -2.9938671891277426, -2.3381912217587497, -0.7699470947566229, 1.427897855697579, 3.8097251400216035, 5.875734581638837, 7.195599926002167, 7.514650282520763, 6.814419426106329, 5.311708796671499, 3.397048926749818, 1.5299473026024681, 0.11992472022075762, -0.5742268346590221, -0.5002472944766139, 0.19025491249494494, 1.1996390272394026, 2.1783970667744232, 2.827047716360651, 2.9759945414927653, 2.6212434964815707, 1.9079435811707177, 1.0698528005232006, 0.34608709954673184, -0.09716747411249124, -0.21480470460023415, -0.08610930685626698, 0.1263954861069167, 0.24734467941000954, 0.16313320470447767, -0.12588895171829775, -0.4949577510647624, -0.7316165863194523, -0.6090111130117007, 0.02782983925645746, 1.1918604443073322, 2.725222876597635, 4.324537616958128, 5.615861939381076, 6.258456916303911, 6.046158853994801, 4.974472876155551, 3.251041879828512, 1.2441520064756137, -0.6168229054586193, -1.9597722460039324, -2.5712723812998766, -2.4500946301738424, -1.7964604604819425, -0.9407667936928428, -0.2346130799019899, 0.06106296453853716, -0.14492447191740238, -0.752669881751005, -1.5136707425574798, -2.122238566581848, -2.3247064216983864, -2.0093454744866817, -1.2463088079127533, -0.2637457628959541, 0.6320131334274152, 1.1648801146112977, 1.1882889867041637, 0.7399033496963147, 0.030963289796466727, -0.6282361085564254, -0.9427130400532485, -0.7479510767960342, -0.08465784241669742, 0.7960072332361269, 1.5032296793669868, 1.6338979354336718, 0.9164847493118478, -0.6765693699777521, -2.8881521663621377, -5.225946461857894, -7.09171434776065, -7.953374754016412, -7.5072753796705785, -5.779097807174346, -3.1296573717983267, -0.16109040421107454, 2.449714832406757, 4.140271075111354, 4.616509002696142, 3.924812233761394, 2.4211429982801214, 0.6489308481948214, -0.8339436179665862, -1.6233773110526313], 'positive_zeros': ['0.44560280148088547958625287159439', '1.53150468806062065916599278994246', '4.18281535533042208124895976524273', '4.95975274207266589749162577806255', '5.82342839953051674251294832004999', '6.83558620697021117082112387211027', '7.80493686535132373946583636312902', '8.401915404565964842425635768301006', '9.591764581077383762854464237297310', '10.26446171288301205093854652485259'], 'prelabel': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.8125598105544052, 'root_number': '-0.8315739894918478 - 0.555413989741537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406279905277', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44560280148088547958625287159', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53150468806062065916599278994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18281535533042208124895976524', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.62', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/a/335/1'], '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': '2-546-273.62-c1-0-6', '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': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4062799052772026, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44560280148088547958625287159', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '564868658760625027416037950204', 'Lhash_array': ['564868658760625027416037950204'], 'label': '2-546-273.62-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/a/335/1'}