-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1137250165868101090308424582214', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.158105378588505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '960.449', 'coefficient_field': '1.1.1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, 3], [1, -5], [1, 0, -49], [1, 0, -121], [1, 0, -169], [1, -14, 289], [1, -22, 361], [1, 34, 529], [1, 0, -841], [1, -2, 961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, -14, 2209], [1, 86, 2809], [1, 0, -3481], [1, -118, 3721], [1, 0, -4489], [1, 0, -5041], [1, 0, -5329], [1, -98, 6241], [1, -154, 6889], [1, 0, -7921], [1, 0, -9409], [1, 0, -10201], [1, 0, -10609], [1, -106, 11449], [1, -22, 11881], [1, -206, 12769]], 'euler_factors_factorization': [[1], [[[1, 3], 1]], [[[1, -5], 1]], [[[1, -7], 1], [[1, 7], 1]], [[[1, -11], 1], [[1, 11], 1]], [[[1, -13], 1], [[1, 13], 1]], [[[1, -14, 289], 1]], [[[1, -22, 361], 1]], [[[1, 34, 529], 1]], [[[1, -29], 1], [[1, 29], 1]], [[[1, -2, 961], 1]], [[[1, -37], 1], [[1, 37], 1]], [[[1, -41], 1], [[1, 41], 1]], [[[1, -43], 1], [[1, 43], 1]], [[[1, -14, 2209], 1]], [[[1, 86, 2809], 1]], [[[1, -59], 1], [[1, 59], 1]], [[[1, -118, 3721], 1]], [[[1, -67], 1], [[1, 67], 1]], [[[1, -71], 1], [[1, 71], 1]], [[[1, -73], 1], [[1, 73], 1]], [[[1, -98, 6241], 1]], [[[1, -154, 6889], 1]], [[[1, -89], 1], [[1, 89], 1]], [[[1, -97], 1], [[1, 97], 1]], [[[1, -101], 1], [[1, 101], 1]], [[[1, -103], 1], [[1, 103], 1]], [[[1, -106, 11449], 1]], [[[1, -22, 11881], 1]], [[[1, -206, 12769], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-960-15.14-c2-0-45', 'leading_term': '1.710789635910569243491526641741980353712036791229800614000000000000000000000000000000000000', '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/960/3/c/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.7107896359105692, 1.7025680090195148, 1.6779318451426093, 1.6369703275791412, 1.5798420398256223, 1.5067893140532016, 1.4181572137555596, 1.3144161161717252, 1.196186657597814, 1.0642656594125475, 0.9196515661056417, 0.763567896801857, 0.5974832342751961, 0.4231263445905439, 0.2424951304742561, 0.0578582670601045, -0.12825145450413641, -0.31305284527159305, -0.4935416379348989, -0.6665256933528799, -0.8286701055290691, -0.9765519237900034, -1.1067239039535117, -1.2157863839415177, -1.300466059875374, -1.3577001238429476, -1.3847239231478772, -1.3791600228968426, -1.3391063099659355, -1.2632205778242527, -1.1507988894670755, -1.0018449404152105, -0.8171276449792885, -0.5982242548894618, -0.3475464960938576, -0.06834748072985859, 0.23529248219622004, 0.5585025944051013, 0.8956816646318975, 1.240581839863198, 1.586415529209003, 1.9259843418532234, 2.251828096692932, 2.5563911928566125, 2.8322028826700603, 3.072067288881368, 3.2692583839790483, 3.4177146290568565, 3.512227579576549, 3.5486185300049757, 3.5238972097556562, 3.436396675805167, 3.2858788839678836, 3.073605965901328, 2.802372990145809, 2.4764989328649847, 2.1017737094652973, 1.6853603959673968, 1.2356531652385305, 0.7620929372801545, 0.2749442479239199, -0.21496167505151723, -0.6965112299930871, -1.15861247729127, -1.5905101257068404, -1.982101849969965, -2.3242457555601512, -2.6090485682885025, -2.8301242450460906, -2.982813196734581, -3.064353190750839, -3.07399424996024, -3.013051464365168, -2.8848915419983876, -2.694851093582936, -2.450087004224913, -2.1593617159892333, -1.8327687392751038, -1.4814061334842965, -1.1170079504027035, -0.7515456194435693, -0.396812879525231, -0.06400904375089081, 0.23666395107378332, 0.49637516238256973, 0.7079938887855334, 0.866360633681822, 0.9684876036379748, 1.0136788559788346, 1.0035630083736657, 0.9420346350038017, 0.8351039883740916, 0.6906583732618514, 0.5181422154522036, 0.32816645936217764, 0.13206123885035434, -0.05861135866386759, -0.23256531600487532, -0.379298783461974, -0.489580744223876, -0.555894829922627, -0.5728198715714534, -0.5373286914728393, -0.4489894394609052, -0.3100573722272739, -0.12544924840087654, 0.09740269053749849, 0.3488150485667274, 0.6172285457648723, 0.8896817017969118, 1.1523655727987219, 1.3912379146194331, 1.5926716558866476, 1.7441100440211688, 1.834699432595957, 1.8558705221958842, 1.8018400111303878, 1.670007062561159, 1.4612226969881994, 1.1799150598789785, 0.8340593222928838, 0.43498752406285374, -0.0029593035762980027, -0.46292719812821087, -0.9261769200198339, -1.3728200419163847, -1.7826345476214225, -2.135926351152115, -2.4143998458294114, -2.601998862955926, -2.6856794020111914, -2.6560772565043957, -2.508037187495571, -2.2409754918441194, -1.8590544927941404, -1.3711553868980741, -0.7906446851164005, -0.13493880311140358, 0.5751192371779869, 1.3160479794406919, 2.0626493072185976, 2.789025511723125, 3.469647902665294, 4.080429678748088, 4.599754382172597, 5.009412144553333, 5.295399118011007, 5.448540890632032, 5.464908113450422, 5.346001713615467, 5.098695537290822, 4.734935579375122, 4.271206581341693, 3.7277881470787486, 3.127833068597974, 2.4963097220854538, 1.8588576961084073, 1.2406108339066781, 0.6650443004410975, 0.15290193525469334, -0.27874302596515055, -0.6172466913796136, -0.8549339558888975, -0.9893904246523947, -1.0234907636853783, -0.9651606338442186, -0.8268829542528146, -0.6249725122271592, -0.3786551889198567, -0.10899863875018465, 0.16225044623014123, 0.4138618252153288, 0.6262868724340096, 0.7827312292075691, 0.8700769789421682, 0.8796037733380511, 0.8074685715410524, 0.6549162327144582, 0.4282074925223225, 0.13826611253075247, -0.19993759513361165, -0.5682349391384784, -0.9462935722577162, -1.312782678682364, -1.6466045175437247, -1.928123624773042, -2.140324141564286, -2.2698287842891482, -2.307719807271623, -2.2501126305793324, -2.098446100348704, -1.8594689291755577, -1.5449188928091524, -1.1709088985125022, -0.7570511002250061, -0.32536583006033526, 0.10096468095995255, 0.4989278181912512, 0.8470212052071476, 1.1265244342455143, 1.322626526780207, 1.4253407995915424, 1.4301499874320176, 1.3383392109258516, 1.1569918962799444, 0.8986430888055863, 0.580604662403415, 0.2239965502084589, -0.1474638568702913, -0.5088466753505891, -0.8354897338512113, -1.104487675451481, -1.2961013654575673, -1.3950019757482943, -1.3912722374156772, -1.2811002659261996, -1.0671184078903557, -0.7583598134077945, -0.36982776620561325, 0.07830408296506434, 0.5618199026404147, 1.0538570245850913, 1.5264898255848658, 1.952410514410888, 2.3066074056745967, 2.5679392922676794, 2.7205086246829664, 2.754746258908384, 2.668136071741404, 2.4655279467875446, 2.15901138733213, 1.7673479534464596, 1.3149873254116322, 0.8307174638095551, 0.3460224891323983, -0.10675892095464823, -0.49636787175266117, -0.7945378251551151, -0.9777699334836933, -1.028861679446701, -0.9380921505758314, -0.7039861769888597, -0.3336035452368898, 0.1576728003527362, 0.7468458693163279, 1.4044772592643813, 2.096260969197467, 2.7849108145481822, 3.432253561697596, 4.001405858557134, 4.458906230967902, 4.7766743807933985, 4.9336788251908255, 4.917210134869015, 4.7236797694243675, 4.358892454743898, 3.8377715381552178], 'positive_zeros': ['0.897132195309456049095487338101600', '2.06435819921759419808522984176975', '3.54846471045103199402469838026208', '4.81659415479777361561111306117325', '5.60659555763739050823007864988999', '6.18640057988757255764426764158808', '7.14805377170756364569631604980284', '8.038772993624185170257372302307845', '9.335852816491659953378042539387333', '9.925668948784454626557899350944764'], 'prelabel': '2-960-15.14-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2-0', 'trace_hash': 767997500290096095, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.897132195309456049095487338102', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06435819921759419808522984177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54846471045103199402469838026', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 26.158105378588505, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, -15, 0, 14, 0, 22, 0, 0, 0, -34, 0, 25, 0, -27, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 14, 0, 49, 0, -42, 0, -86, 0, 0, 0, -66, 0, 0, 0, 118, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, -75, 0, 0, 0, 98, 0, 81, 0, 154, 0, 70, 0, 0, 0, 0, 0, 0, 0, -6, 0, 110, 0, 0, 0, 0, 0], 'euler11': [1, 0, -121], 'euler13': [1, 0, -169], 'euler17': [1, -14, 289], 'euler19': [1, -22, 361], 'euler2': [1, 0, 0], 'euler23': [1, 34, 529], 'euler29': [1, 0, -841], 'euler3': [1, 3, 0], 'euler31': [1, -2, 961], 'euler37': [1, 0, -1369], 'euler41': [1, 0, -1681], 'euler43': [1, 0, -1849], 'euler47': [1, -14, 2209], 'euler5': [1, -5, 0], 'euler53': [1, 86, 2809], 'euler59': [1, 0, -3481], 'euler61': [1, -118, 3721], 'euler67': [1, 0, -4489], 'euler7': [1, 0, -49], 'euler71': [1, 0, -5041], 'euler73': [1, 0, -5329], 'euler79': [1, -98, 6241], 'euler83': [1, -154, 6889], 'euler89': [1, 0, -7921], 'euler97': [1, 0, -9409], 'euler_factors': [[1, 0, 0], [1, 3, 0], [1, -5, 0], [1, 0, -49], [1, 0, -121], [1, 0, -169], [1, -14, 289], [1, -22, 361], [1, 34, 529], [1, 0, -841], [1, -2, 961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, -14, 2209], [1, 86, 2809], [1, 0, -3481], [1, -118, 3721], [1, 0, -4489], [1, 0, -5041], [1, 0, -5329], [1, -98, 6241], [1, -154, 6889], [1, 0, -7921], [1, 0, -9409]], 'index': 45, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/3/c/b', 'ModularForm/GL2/Q/holomorphic/960/3/c/b/449/1'], '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': '2-960-15.14-c2-0-45', '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': '2-960-15.14-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2-0', 'trace_hash': 767997500290096095, 'z1': {'__RealLiteral__': 0, 'data': '0.897132195309456049095487338102', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24560866
{'Lhash': '1137250165868101090308424582214', 'Lhash_array': ['1137250165868101090308424582214'], 'label': '2-960-15.14-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/3/c/b/449/1'}
-
id: 24374119
{'Lhash': '1137250165868101090308424582214', 'Lhash_array': ['1137250165868101090308424582214'], 'label': '2-960-15.14-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/3/c/b'}