-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2265286958877637932079338322371', 'a10': [-0.42089216504135707, 0.7290066143592957], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.3690266650833442, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.42089216504135707, 0.7290066143592957], 'a6': [-0.1845133325416721, -0.31958646663602797], 'a7': [-1.0352906465444773, -1.793176000415867], 'a8': [-1.0, 0.0], 'a9': [-2.8638193204574653, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.435942402915202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [3.50364213869336, 0.8511708195023002]]], [31, [[1.0, 0], [1.8185959810587866, -5.262386213275954]]]], 'bad_primes': [2, 13, 31], 'central_character': '806.315', 'coefficient_field': 'CDF', 'conductor': 806, 'conductor_radical': 806, 'conjugate': '508578576783049213488731044635', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.3690266650833442, 0], [3.0, 0]], [[1.0, 0], [-0.42089216504135707, -0.7290066143592957], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0352906465444773, 1.793176000415867], [-3.5, 6.06217782649107]], [[1.0, 0], [-2.761204805649429, 4.782547013488159], [-5.5, -9.526279441628825]], [[1.0, 0], [3.50364213869336, 0.8511708195023002]], [[1.0, 0], [3.1996004892023895, 5.541870611220774], [-8.5, 14.722431864335457]], [[1.0, 0], [0.16628399010673128, 0.28801231935013916], [-9.5, 16.454482671904334]], [[1.0, 0], [-0.14775308958021646, -0.2559158581282106], [-11.5, 19.91858428704209]], [[1.0, 0], [-4.323367974804014, -7.488292992176714], [-14.5, 25.11473670974872]], [[1.0, 0], [1.8185959810587866, -5.262386213275954]], [[1.0, 0], [8.275065161968083, 0], [37.0, 0]], [[1.0, 0], [-3.4312166760136424, 5.943041614633229], [-20.5, -35.50704155516198]], [[1.0, 0], [5.012082721229079, 8.681181924906841], [-21.5, 37.239092362730865]], [[1.0, 0], [-3.37265194494992, 0], [47.0, 0]], [[1.0, 0], [4.526386356013899, 7.83993114330262], [-26.5, 45.89934640057525]], [[1.0, 0], [-4.475396522777982, -7.751614161468549], [-29.5, 51.09549882328188]], [[1.0, 0], [0.9774271289067779, -1.6929534479627137], [-30.5, -52.827549630850754]], [[1.0, 0], [-3.752130112002141, 6.49887999059681], [-33.5, -58.023702053557386]], [[1.0, 0], [11.559286891415372, 0], [71.0, 0]], [[1.0, 0], [-6.545089663757414, -11.336427837721741], [-36.5, 63.21985447626402]], [[1.0, 0], [4.580760624428825, -7.93411013882166], [-39.5, -68.41600689897065]], [[1.0, 0], [2.621484128589936, 4.540543701953193], [-41.5, 71.88010851410841]], [[1.0, 0], [1.5271710543667079, 2.6451378580116702], [-44.5, 77.07626093681505]], [[1.0, 0], [-6.040103194696261, 10.461765616173015], [-48.5, -84.00446416709055]], [[1.0, 0], [7.969911920904873, 13.804292378856108], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.2877005704250073, -5.694464428049293], [-51.5, 89.20061658979718]], [[1.0, 0], [9.32301648285546, 0], [107.0, 0]], [[1.0, 0], [8.912475701827333, 0], [109.0, 0]], [[1.0, 0], [-12.565222975413679, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-806-403.315-c1-0-30', '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/806/2/h/b/315/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9257313724275451, 1.150028154969051, 1.35317596865395, 1.5345798377590911, 1.6890526132905093, 1.8076230744536863, 1.8790229989501934, 1.8915518024848368, 1.8350826077650058, 1.7030318716463566, 1.4941310546689057, 1.2138255860412226, 0.8751104318623459, 0.4986154255770508, 0.11179037575934597, -0.2528857366277836, -0.5606385842814353, -0.7779096131221032, -0.876337732730385, -0.8367766154503196, -0.6528205964497872, -0.3332790821039885, 0.09691656776917554, 0.5977590077071628, 1.117334413684702, 1.5970048800167378, 1.9781769369299518, 2.20992279317672, 2.2564753259259445, 2.103484655612876, 1.761945488300488, 1.268903959355985, 0.6844279235086302, 0.08484219233930457, -0.44717377263149033, -0.834442372440668, -1.0174414463279524, -0.9648349706619088, -0.6804867705241787, -0.2054160556453899, 0.386180643471645, 0.9968108839270207, 1.520422669507426, 1.8599835568889955, 1.9451617681812978, 1.74703850740322, 1.2869610940705463, 0.6373695410195531, -0.08637040979680888, -0.7425806365667125, -1.1861992355264717, -1.2945271933463893, -0.9914293349612732, -0.2654779818650499, 0.8217944867093263, 2.139905590519691, 3.5060176111402948, 4.712138136228187, 5.558811848127714, 5.889649650634282, 5.620451872951051, 4.757242847314625, 3.399233363700357, 1.7253242493324972, -0.03418519462231661, -1.6360899884187827, -2.8661668819842157, -3.576652300834261, -3.712009932386914, -3.317685777687274, -2.529724547336689, -1.546886407675795, -0.5905044962952641, 0.14000565440456422, 0.5069490689348091, 0.46117106328211566, 0.050134155174577755, -0.5946424148239264, -1.2882674048543619, -1.8347724437697253, -2.0718164630394122, -1.9078836383907485, -1.3435544584031855, -0.4718804913688046, 0.5424205118632739, 1.500352772057977, 2.214078334528179, 2.549829127187089, 2.458142407228637, 1.9841258840257607, 1.2551527589747928, 0.4488364021936153, -0.2509722618742254, -0.6993152007605948, -0.8250555942274205, -0.6466359000005701, -0.26440916968019235, 0.16876410088495952, 0.49125559945411484, 0.5793707678244774, 0.3844980978239518, -0.04968981146157153, -0.595415780095609, -1.0731645850420717, -1.3004382947615092, -1.1442843001190073, -0.5633307627435129, 0.3728089487204536, 1.4933729717913087, 2.564521660077, 3.34687954300292, 3.657990289478514, 3.422976491284544, 2.69898153006346, 1.6653176957860558, 0.5801488592647177, -0.28629215518679746, -0.7250052161561635, -0.6484016276291511, -0.12024529922329451, 0.6544162098853635, 1.3787006737670167, 1.74131869576886, 1.5023750570682362, 0.5646871817261229, -0.9893982591909942, -2.9072682574105366, -4.820977954075577, -6.335056861202379, -7.124983551855035, -7.020427092442435, -6.050607715744146, -4.438700331144431, -2.5456702909293316, -0.7776893835436386, 0.5184832380404709, 1.1440138753465583, 1.0962160064648359, 0.5630617159161392, -0.13471838115958262, -0.638036412350035, -0.6540713193961172, -0.041742475051254196, 1.1461439739955122, 2.676108553900456, 4.198889609640156, 5.347525141982582, 5.84054341049846, 5.56065101311743, 4.586381731106297, 3.1678611978535063, 1.654178043285985, 0.394017071971812, -0.3610263131533653, -0.5220333879284205, -0.178354205849898, 0.44048338279500493, 1.0439292704162773, 1.375585637062674, 1.2946454297707697, 0.8183432067785457, 0.11253464166404298, -0.5660646698080898, -0.9571206960868196, -0.8851481457552793, -0.320522415993878, 0.6068840763445513, 1.646128933041104, 2.503506265814053, 2.935475222054918, 2.825974644581141, 2.2227436863761207, 1.3205181777277497, 0.3963970197810771, -0.2814082541641051, -0.5411200834833579, -0.3617894389635376, 0.12413322980743893, 0.6814263742156274, 1.0591464233717545, 1.0844173582230971, 0.7301578156836911, 0.1319657306804359, -0.4538111785256001, -0.7386199074787767, -0.5078927538514634, 0.2915876867618232, 1.5149109976619493, 2.8487772682246626, 3.901639812150556, 4.327129862989261, 3.940854316890191, 2.790810054884623, 1.1552813333579297, -0.5348269622813167, -1.8270968017979956, -2.39116156797735, -2.1278083461349135, -1.2062154149560378, -0.014318202303711369, 0.9644327273094603, 1.3097549522286926, 0.8074036600455567, -0.47152049920436023, -2.183090576818522, -3.8136986531738035, -4.842692813725943, -4.91291803372025, -3.9536477134650183, -2.21469481218016, -0.19866903305370517, 1.488682003939056, 2.3231995148511557, 2.023420204865894, 0.6366999539532174, -1.476793276639992, -3.756220259738528, -5.611286763702784, -6.596857962051444, -6.53529344987612, -5.549310762794752, -3.998738571131438, -2.346633459482306, -1.00293118723122, -0.19944545875151595, 0.06303606298136619, -0.018320899498950927, -0.15035073816747616, -0.07360306978273659, 0.3298990383180466, 0.9908876574786518, 1.6848829457888943, 2.128134431895712, 2.0993601394160013, 1.5394175199468871, 0.5893658433032666, -0.4492908154441804, -1.2187397880405133, -1.4350710433684957, -0.9956028825941355, -0.022106575727190745, 1.1778102620971356, 2.2183283573027106, 2.7729860575851912, 2.6912316114379435, 2.050175134764507, 1.121622364847914, 0.26626828280417, -0.2052789477356167, -0.15183431624177823, 0.34467175116728405, 1.01260223229136, 1.4993195993644433, 1.513982761684092, 0.9490817884751344, -0.06770421174869416, -1.2138390128248122], 'positive_zeros': ['1.78699632096556640391962624382459', '2.72397657942225009855783619904788', '4.14346936910066283610645595350871', '4.92024399288704079610749953290427', '5.98497154563602532710208411722765', '6.65914659445318995399985739937631', '7.997518177337864966421699108195230', '9.096159483442544647216103449806989', '9.511074274894699315374332831233302', '10.43388087882503209885565785150944'], 'prelabel': '2-806-403.315-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5369159235014473, 'root_angle': 0.3907475184445381, 'root_number': '0.3365274252680294 + 0.9416736653652744*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.195373759222', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78699632096556640391962624382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72397657942225009855783619905', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14346936910066283610645595351', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.435942402915202, 'bad_primes': [2, 13, 31], 'central_character': '403.315', 'conductor': 806, 'conductor_radical': 806, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/806/2/h/b/315/9'], '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': '2-806-403.315-c1-0-30', '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': '2-806-403.315-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5369159235014473, 'root_angle': 0.19537375922226904, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78699632096556640391962624382', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2265286958877637932079338322371', 'Lhash_array': ['2265286958877637932079338322371'], 'label': '2-806-403.315-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/806/2/h/b/315/9'}