-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1249615780196689583950991440567', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.5615528128088303, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.36998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '4680.1', 'coefficient_field': 'CDF', 'conductor': 4680, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [7.0, 0]], [[1.0, 0], [-5.56155281280883, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-6.68465843842649, 0], [17.0, 0]], [[1.0, 0], [-3.1231056256176606, 0], [19.0, 0]], [[1.0, 0], [-5.56155281280883, 0], [23.0, 0]], [[1.0, 0], [-2.0, 0], [29.0, 0]], [[1.0, 0], [7.123105625617661, 0], [31.0, 0]], [[1.0, 0], [-9.807764064044152, 0], [37.0, 0]], [[1.0, 0], [2.684658438426491, 0], [41.0, 0]], [[1.0, 0], [10.246211251235321, 0], [43.0, 0]], [[1.0, 0], [7.123105625617661, 0], [47.0, 0]], [[1.0, 0], [3.5615528128088303, 0], [53.0, 0]], [[1.0, 0], [-8.0, 0], [59.0, 0]], [[1.0, 0], [10.68465843842649, 0], [61.0, 0]], [[1.0, 0], [14.246211251235321, 0], [67.0, 0]], [[1.0, 0], [4.68465843842649, 0], [71.0, 0]], [[1.0, 0], [-16.24621125123532, 0], [73.0, 0]], [[1.0, 0], [-11.807764064044152, 0], [79.0, 0]], [[1.0, 0], [-8.0, 0], [83.0, 0]], [[1.0, 0], [-14.68465843842649, 0], [89.0, 0]], [[1.0, 0], [17.80776406404415, 0], [97.0, 0]], [[1.0, 0], [1.1231056256176606, 0], [101.0, 0]], [[1.0, 0], [-14.246211251235321, 0], [103.0, 0]], [[1.0, 0], [-15.807764064044152, 0], [107.0, 0]], [[1.0, 0], [13.12310562561766, 0], [109.0, 0]], [[1.0, 0], [2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-4680-1.1-c1-0-27', 'leading_term': '2.48636044310176798019176539634', '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/4680/2/a/y/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.486360443101768, 2.479182592542122, 2.4576000049907605, 2.421473708242628, 2.3705986189720436, 2.3047413797517904, 2.223689614583755, 2.12730935615563, 2.01560703828388, 1.8887923662401165, 1.7473385268040147, 1.5920365130198415, 1.4240407497521494, 1.2449036610869972, 1.0565972827696575, 0.8615204732227008, 0.6624907104405349, 0.46271988354396476, 0.26577390548625746, 0.075516395922178, -0.10396288347961172, -0.26843371323851484, -0.41362363648951855, -0.5353266752450253, -0.629520054818487, -0.6924860261779413, -0.720935495330986, -0.712129848503564, -0.6639971205443728, -0.5752385095906545, -0.44542120977077737, -0.27505362915112147, -0.06563929232021212, 0.18029389825368924, 0.45919184975016675, 0.7665020658978733, 1.0967323978298533, 1.4435412249173667, 1.7998585422684856, 2.1580363787776955, 2.510025885558594, 2.847577355567444, 3.1624584005435024, 3.4466845621317086, 3.6927558116123524, 3.8938917371680244, 4.044257766246228, 4.139174555840271, 4.175302731589761, 4.1507954857753075, 4.065412163552833, 3.920586874747035, 3.7194473526166663, 3.4667807170379574, 3.168944451789792, 2.8337227272808314, 2.470130134307959, 2.088166875907202, 1.698531421108936, 1.3122984803184816, 0.940571839571268, 0.5941230141287401, 0.2830277796624831, 0.016313348537773494, -0.19837077243934242, -0.3550454157984248, -0.44964576040413917, -0.4802058039539946, -0.4469740881511731, -0.35245360474954357, -0.2013613391240777, -0.0005057458335643754, 0.2414164976812124, 0.5140999576355915, 0.8059784906913905, 1.1046312372227711, 1.3972332070209996, 1.6710347818262747, 1.91385265197998, 2.114553512824437, 2.263511351141429, 2.353019409115571, 2.3776389506624995, 2.3344687686712082, 2.223321924881803, 2.046799436469294, 1.8102544124050974, 1.5216443662007901, 1.1912739321045567, 0.8314348116314771, 0.4559542855862708, 0.07966784699247313, -0.2821647511560246, -0.6144776649134521, -0.9030267283763463, -1.1350009172519013, -1.2995913706009141, -1.388492716751715, -1.3963134542910944, -1.320875226179848, -1.1633849041110815, -0.928468332547445, -0.6240601843332166, -0.2611504310549931, 0.146605819831034, 0.5834021937606614, 1.0318998739532235, 1.473927438397915, 1.891233456922542, 2.26626040302839, 2.5829065431964833, 2.8272420101105795, 2.988146319267675, 3.0578371574117442, 3.0322642926811643, 2.91134779675118, 2.6990462282689864, 2.40324774414525, 2.0354849702169258, 1.6104825274034493, 1.1455540033425557, 0.6598725066744244, 0.17364537799097454, -0.29277117539558195, -0.7197780901089303, -1.0894187605624344, -1.3862023005780508, -1.5978253420529078, -1.7157568295949488, -1.7356559371198461, -1.6576004776768687, -1.4861116977131468, -1.2299707656583905, -0.9018321497766923, -0.5176489623832081, -0.09593474252995597, 0.34310541839706393, 0.7785344767829799, 1.1896885962418313, 1.5571795661794061, 1.8638453597414049, 2.0956013100053013, 2.242148384868555, 2.2975013088333816, 2.260307558064237, 2.1339381782988665, 1.926342483520685, 1.6496704529220234, 1.3196784719904682, 0.9549453576722672, 0.5759357749710432, 0.20395664189333532, -0.1399415484118892, -0.43606276632550284, -0.6671061285094128, -0.8190944324314483, -0.8821405653007754, -0.8510093344638462, -0.7254421717679977, -0.5102239880986835, -0.214984619649785, 0.14625884855096832, 0.5557987904487535, 0.9931396524498689, 1.4360617960411952, 1.8617924763986662, 2.2482231350677955, 2.5751085672971925, 2.8251832852420256, 2.9851336284768717, 3.046370779258727, 3.0055595426775623, 2.864870096979095, 2.631934297552686, 2.319503793938476, 1.9448233682091518, 1.5287486545057396, 1.0946518831222467, 0.6671716865988785, 0.270872583225489, -0.07111407351541785, -0.33839353730007726, -0.5144830394292056, -0.5877923289034764, -0.5523521257288975, -0.408246083780756, -0.16171741931769412, 0.17506118144115906, 0.5845473414452144, 1.0446930491839874, 1.53007028218453, 2.013200252669799, 2.4660160577863843, 2.861379954900826, 3.174572185812927, 3.3846685668117678, 3.475729014855031, 3.4377286005410266, 3.267176153979526, 2.9673822095086275, 2.548357264504102, 2.026341894045549, 1.422991054670926, 0.7642547390160623, 0.07901485342244866, -0.6024472725175424, -1.2500678633705422, -1.8356115458737652, -2.334184861917389, -2.7255659141351836, -2.995273358738178, -3.1353122915555094, -3.144552721606887, -3.0287172863487917, -2.799977444810831, -2.4761802831098514, -2.07974993357834, -1.6363271339295151, -1.173226442963631, -0.7178020808221948, -0.2958195250667278, 0.07006957704805286, 0.361657034383851, 0.5662311485726476, 0.6772880749765742, 0.6948565895889496, 0.6254144794787169, 0.48139951881844717, 0.2803428652885017, 0.04367619954968589, -0.2047154209865434, -0.4401065195577807, -0.6386102105086334, -0.7788182137058484, -0.8432979434982717, -0.8198503040904042, -0.7024454606274237, -0.49177282217393814, -0.19536468016875014, 0.17272097633642364, 0.5926455710547809, 1.039923083519242, 1.4868764023587524, 1.9043307880904095, 2.263442103076088, 2.5375473563199487, 2.7039218634957964, 2.7453312525173943, 2.65127752282017, 2.4188558192535017, 2.0531615202124773, 1.5672143143648467, 0.9813955184576135, 0.3224251529200311, -0.37806564824530986, -1.0852853071024084, -1.763252688289154], 'positive_zeros': ['0.985773035544421462851908715761758', '1.63928801998691322522002884309926', '3.20266951605659161800882819319922', '3.60558390242330559636734911977115', '4.63202992754454959423379687597851', '5.26350848774820290129026635031273', '6.21385289254595971035196991561691', '6.86665299028155737679554142139346', '7.69738746027565250462421092568530', '8.156172213138674823885627091359527'], 'prelabel': '2-4680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.985773035544421462851908715762', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.63928801998691322522002884310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20266951605659161800882819320', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 37.36998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 4680, 'conductor_radical': 390, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4680/2/a/y/1/2'], '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': '2-4680-1.1-c1-0-27', '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': '2-4680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.985773035544421462851908715762', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1249615780196689583950991440567', 'Lhash_array': ['1249615780196689583950991440567'], 'label': '2-4680-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4680/2/a/y/1/2'}