-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1742362638350773526235673764596', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, -1.4142135623730951], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.58204824255365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 1.4142135623730951]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1151', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '682407121207132921712246832069', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 1.4142135623730951]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [4.898979485566356, 0], [13.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-17.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-19.0, 0]], [[1.0, 0], [-6.0, 0], [23.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-29.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-31.0, 0]], [[1.0, 0], [4.898979485566356, 0], [37.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-41.0, 0]], [[1.0, 0], [0, 8.48528137423857], [-43.0, 0]], [[1.0, 0], [6.0, 0], [47.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-53.0, 0]], [[1.0, 0], [4.898979485566356, 0], [59.0, 0]], [[1.0, 0], [2.0, 0], [61.0, 0]], [[1.0, 0], [0, 8.48528137423857], [-67.0, 0]], [[1.0, 0], [9.797958971132712, 0], [71.0, 0]], [[1.0, 0], [9.797958971132712, 0], [73.0, 0]], [[1.0, 0], [0, 10.392304845413264], [-79.0, 0]], [[1.0, 0], [-6.0, 0], [83.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-89.0, 0]], [[1.0, 0], [0, 0], [97.0, 0]], [[1.0, 0], [0, 14.142135623730951], [-101.0, 0]], [[1.0, 0], [0, 0], [-103.0, 0]], [[1.0, 0], [-18.0, 0], [107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1200-12.11-c1-0-27', 'leading_term': '1.085411040153465000426599758909896854508957802308285738', '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/1200/2/h/j/1151/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.085411040153465, 1.1878510031249208, 1.285272506267214, 1.3772264762667652, 1.4629692461534163, 1.5414399740434335, 1.611259186301627, 1.670747665530137, 1.7179637742354914, 1.7507566602111604, 1.7668325651231838, 1.763831515224367, 1.7394118603099422, 1.69134032028734, 1.617585321534522, 1.516411427544637, 1.3864725956987727, 1.2269018517697807, 1.037394803509071, 0.8182842539318798, 0.5706030602876779, 0.2961323473750441, -0.002567751369864551, -0.32214746658753995, -0.6584792044063719, -1.0066936682312322, -1.3612415746014677, -1.7159815324116556, -2.0642938289167962, -2.3992189499746246, -2.713618683420728, -3.0003566464432043, -3.2524940782581924, -3.463495789973114, -3.6274403083512685, -3.739227534141317, -3.794776702544203, -3.7912071240416845, -3.7269941338316337, -3.6020929158611943, -3.418023411978067, -3.1779103859621394, -2.8864738814276705, -2.5499667733015556, -2.17605783191039, -1.7736606493887241, -1.3527108591658563, -0.9238962373449336, -0.49834642621240344, -0.08729107374390992, 0.2983029564777646, 0.6481030785101117, 0.952777761885226, 1.204344445733814, 1.3964842428827176, 1.5248094728185073, 1.587071060648654, 1.5832944552071775, 1.5158349304880634, 1.3893458890372663, 1.21065700323822, 0.9885626023844472, 0.7335245069462543, 0.4572973727098392, 0.1724883675786344, -0.10793351446246942, -0.3711601721833437, -0.6050784191757407, -0.7987929591319757, -0.9431152505704726, -1.03099548419615, -1.0578762369334884, -1.021948768107136, -0.9242963416015624, -0.7689132974531816, -0.5625937104312888, -0.314689167337104, -0.03674123313874075, 0.2579997098741793, 0.5551516661245036, 0.8398513037391606, 1.09744975385599, 1.314222879037375, 1.4780627684262533, 1.5791165264085925, 1.6103393503022643, 1.5679314883382445, 1.4516328979955437, 1.2648551677720226, 1.0146373196384417, 0.7114201924982717, 0.3686428671987891, 0.002173623670783949, -0.37040322447340923, -0.7306150549082915, -1.0600065329094075, -1.3410807822810755, -1.5582301114342971, -1.6986087290712601, -1.7529007070902225, -1.7159397189886145, -1.5871427533495681, -1.3707278972912158, -1.0756960997336558, -0.7155681363029754, -0.30788028187532274, 0.12654515079433062, 0.5645258817800379, 0.9816024117631276, 1.3532277191992468, 1.6560065946724853, 1.8689224341656505, 1.97448754909735, 1.9597546216246369, 1.8171318992560075, 1.5449529597144476, 1.147763075581954, 0.6362978810532042, 0.027145543603210098, -0.657899805176315, -1.392768892030359, -2.148291891728419, -2.8935619483601958, -3.59742095149197, -4.229992311020194, -4.764180755945866, -5.177058728225496, -5.45106292998364, -5.574932940347982, -5.544336223313834, -5.362139731662367, -5.038306883473031, -4.589418972055334, -4.037840957409812, -3.41057189331328, -2.737838777122683, -2.05150824076613, -1.3834022351499766, -0.7636108975083367, -0.21889758555848368, 0.2287126383063106, 0.5630789167756955, 0.7747569030024256, 0.8614279399705427, 0.8279173934821698, 0.6857983177763823, 0.45260123916923184, 0.15067468076421356, -0.19423735168541229, -0.55461672295735, -0.9028939909609641, -1.2131678972001219, -1.4628156260691034, -1.6338933879069937, -1.714238697607504, -1.6982033054359895, -1.5869681131587838, -1.388417269101036, -1.1165764149593322, -0.7906480244364748, -0.43370313945562133, -0.07111183922511555, 0.27118709471436736, 0.5684649174197937, 0.7989128379901338, 0.9451686564052559, 0.9955560138580617, 0.9449495863376574, 0.7952030835606159, 0.5551051280696994, 0.23985921673215388, -0.12988399896053435, -0.5293830597269968, -0.9314641170068361, -1.3083726170080998, -1.6336940779782587, -1.8842125204465119, -2.0415766392673453, -2.0936542532655205, -2.035474450401613, -1.869683091964704, -1.6064693431493031, -1.262956614527953, -0.8620883716775305, -0.43107518070905326, 0.0004984037243345548, 0.4027822617863637, 0.7478413360669676, 1.0117565576090453, 1.1764956981203862, 1.231415819708882, 1.1742809991520382, 1.0117097145995697, 0.7590037993933133, 0.4393527622841353, 0.08245074315207916, -0.2773945733193368, -0.6035441031836343, -0.8595530694510214, -1.011771726311496, -1.0318427121061313, -0.8989189790451986, -0.6014409247694624, -0.13833765924705835, 0.4804462667621741, 1.2341531671490766, 2.0921489993990345, 3.015549450113094, 3.959441523422576, 4.875563629787952, 5.71527257900129, 6.432602525030959, 6.98721068731641, 7.347008588085275, 7.490295618308722, 7.407242986106695, 7.1006185580221, 6.585693978246928, 5.889331284139836, 5.048303141851024, 4.106954762355793, 3.1143626195925607, 2.121181794689331, 1.1763973143049247, 0.32420334123791866, -0.3987733234075458, -0.9657119470615186, -1.3611424119788762, -1.581687962164667, -1.635955461391359, -1.5435835801115532, -1.3335201648875834, -1.0416561320973776, -0.7079903781472964, -0.37353482542079297, -0.07718812407219484, 0.1471908969755895, 0.273293552160515, 0.2842697947344957, 0.17389425992502977, -0.05309496003423466, -0.38150710464323034, -0.7870168513538959, -1.2381858318217684, -1.699029614037821, -2.1319300114504345, -2.50066558535553, -2.773323637232871, -2.9248657459311063, -2.9391454798081487, -2.8102193996907125, -2.542847690084431, -2.1521444993401877, -1.6624053957556533, -1.1052049700990192, -0.5169163148070546, 0.06414885577279957], 'positive_zeros': ['1.37448176811266162374016199869401', '3.07623460161938996424843183633586', '4.03814327840794976747259224921983', '4.82042653783507017369988367564004', '5.75036462864577452775225037478302', '6.60699832504716808653534874994019', '7.37759934495522948997820154766826', '8.716224184455137075058238657893498', '9.215472541076690350721456504951016', '10.07503704680591695131954225301132'], 'prelabel': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.6374200573180298, 'root_number': '-0.4184316465917346421462699718538703114610350620534105986 + 0.9082482904638630163662140124509818986609912467761116881*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3187100286590149', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37448176811266162374016199869', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07623460161938996424843183634', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03814327840794976747259224922', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.58204824255365, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/2/h/j/1151/2'], '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': '2-1200-12.11-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': '2-1200-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.095488368990207, 'root_angle': 0.3187100286590149, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37448176811266162374016199869', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1742362638350773526235673764596', 'Lhash_array': ['1742362638350773526235673764596'], 'label': '2-1200-12.11-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/2/h/j/1151/2'}