-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1265341800411837250751554498843', 'a10': [3.2232399678686128, 0.0], 'a2': [-0.6446479935737226, 0.0], 'a3': [0.0, 0.0], 'a4': [-7.584428964381374, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [10.046470862880659, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 130.09921156265813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': 'CDF', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6446479935737226, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-47.70132089019757, 0], [1331.0, 0]], [[1.0, 0], [57.225606049653365, 0], [2197.0, 0]], [[1.0, 0], [36.9685718364845, 0], [4913.0, 0]], [[1.0, 0], [30.765923068992876, 0], [6859.0, 0]], [[1.0, 0], [53.12817938371485, 0], [12167.0, 0]], [[1.0, 0], [-195.6626747074976, 0], [24389.0, 0]], [[1.0, 0], [257.8701868793332, 0], [29791.0, 0]], [[1.0, 0], [-346.42314179297136, 0], [50653.0, 0]], [[1.0, 0], [-267.0495827777011, 0], [68921.0, 0]], [[1.0, 0], [176.8591189473204, 0], [79507.0, 0]], [[1.0, 0], [311.59830986778815, 0], [103823.0, 0]], [[1.0, 0], [-492.2701520494797, 0], [148877.0, 0]], [[1.0, 0], [-98.7653235048425, 0], [205379.0, 0]], [[1.0, 0], [82.16815240605791, 0], [226981.0, 0]], [[1.0, 0], [-654.6681797716002, 0], [300763.0, 0]], [[1.0, 0], [779.6575053746692, 0], [357911.0, 0]], [[1.0, 0], [-829.6728293658197, 0], [389017.0, 0]], [[1.0, 0], [769.426157873387, 0], [493039.0, 0]], [[1.0, 0], [-613.2032342312918, 0], [571787.0, 0]], [[1.0, 0], [457.66606027183957, 0], [704969.0, 0]], [[1.0, 0], [-1412.1121211423617, 0], [912673.0, 0]], [[1.0, 0], [-1823.7900552644753, 0], [1030301.0, 0]], [[1.0, 0], [407.77489170744934, 0], [1092727.0, 0]], [[1.0, 0], [-370.1087972037802, 0], [1225043.0, 0]], [[1.0, 0], [-975.5704448908585, 0], [1295029.0, 0]], [[1.0, 0], [1978.8511097986184, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 111, 'label': '2-2205-1.1-c3-0-111', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2205/4/a/bz/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.0695807508823837e-61, 0.16250153177850435, 0.32167800025340304, 0.4742465175157962, 0.6170086076057291, 0.7468925364190092, 0.8609957106656776, 0.9566270403698133, 1.0313490575333726, 1.0830194661855452, 1.109831672071081, 1.1103537102579526, 1.0835648628585326, 1.0288891438151968, 0.9462247300637603, 0.8359683446861078, 0.6990335535760869, 0.5368619275082586, 0.35142605015076506, 0.1452234221942446, -0.078739576177816, -0.3169743476629942, -0.5655478523932712, -0.8201317475792174, -1.076062876261848, -1.3284147913081839, -1.5720796807213457, -1.801859726103988, -2.012566586808566, -2.1991273679190853, -2.356695111402217, -2.480761557623123, -2.567269670145608, -2.6127232113226464, -2.614290510067157, -2.569899485879834, -2.4783209929011893, -2.3392376309736704, -2.1532953419443808, -1.922135370860861, -1.6484045228436575, -1.3357420839608545, -0.9887422921124954, -0.6128918324657113, -0.21448247909387705, 0.19950030493834817, 0.6215112804204018, 1.0435996068718891, 1.4575803220260943, 1.855219500553122, 2.228428860639392, 2.5694650660988607, 2.871128557981642, 3.1269564635246963, 3.3314039894959766, 3.480008725845243, 3.5695324742678993, 3.5980755801829543, 3.565159285747143, 3.4717723301570897, 3.3203788899441564, 3.114885958551606, 2.860569387676881, 2.5639590236944514, 2.232684637142391, 1.875285623942455, 1.5009887129269703, 1.1194591027840082, 0.7405315296972546, 0.37392869278154417, 0.028975198503941448, -0.28568430764355235, -0.5623539035446581, -0.7945331571432742, -0.9771333301553322, -1.1066550727818585, -1.1813205783081706, -1.2011543595393497, -1.168008254112918, -1.0855279264063942, -0.9590599639567838, -0.7955006114285763, -0.6030891835322388, -0.3911511829806689, -0.16979805052606414, 0.05040777945795087, 0.258812321503299, 0.4450425485838874, 0.5993796484747729, 0.7131202113107828, 0.7789124670643246, 0.7910550780752759, 0.7457468371278099, 0.6412769162682341, 0.4781470289815757, 0.25911896498744663, -0.010816626858539784, -0.3245516706080219, -0.6730509535456115, -1.045617037142005, -1.4302227124617173, -1.8139012347285763, -2.1831821381652907, -2.524558355430805, -2.824968738218494, -3.072278976077712, -3.2557434018189273, -3.366430296599073, -3.3975940861206824, -3.344979247181791, -3.2070427917120434, -2.9850848088335247, -2.683279645608988, -2.3086037930516903, -1.8706602956144383, -1.381403384511878, -0.8547709021706564, -0.3062357860801826, 0.24770873469032756, 0.7901126512610173, 1.3041614797629968, 1.7737758091449343, 2.1841956962707156, 2.522527515627133, 2.7782317500798985, 2.943531957472731, 3.013727723203934, 2.987397733977715, 2.8664830723007633, 2.6562452947264052, 2.3650986539472694, 2.0043207710143025, 1.5876509624192796, 1.1307900762964183, 0.6508198951978453, 0.16556373467285018, -0.3070873573687906, -0.7498565522334573, -1.146744285352242, -1.4836456226305517, -1.7488965738116309, -1.9337264577523572, -2.0325969089739075, -2.043412482660929, -1.9675929033750827, -1.8100026125162214, -1.5787391743523265, -1.2847880545302783, -0.941557033730573, -0.5643088098523473, -0.1695149352431528, 0.22584208446435866, 0.6049891175247318, 0.9520743930195702, 1.2528403463399822, 1.4952278365714504, 1.6698848847454688, 1.7705569503030862, 1.794340718572405, 1.741789216357783, 1.6168625625680797, 1.426725517567546, 1.181399916396655, 0.8932867444921513, 0.576578730911789, 0.24658960208789896, -0.08096970066138842, -0.3907346990280441, -0.6684164540926179, -0.9014817638120538, -1.0797520225927117, -1.1958916502310313, -1.24576178728577, -1.2286209729133226, -1.1471615125041086, -1.0073778971246563, -0.8182716068978811, -0.5914045446795976, -0.34032082691637566, -0.07986333901227304, 0.1745829942649361, 0.4078851578250783, 0.6059546920614203, 0.7564998688803429, 0.8496994727858166, 0.8787633710633659, 0.8403499259184118, 0.7348167335445683, 0.5662888933899302, 0.3425376687029045, 0.07467159567627651, -0.22334860421101288, -0.535351008929368, -0.8437209322095901, -1.1302614385399714, -1.3771052244618456, -1.5676337025884848, -1.687357776566488, -1.7247156660127367, -1.6717462393549793, -1.5246015383135723, -1.283869321244433, -0.9546852040116697, -0.5466239391426245, -0.07337007937003585, 0.44782079554179544, 0.9968484892430126, 1.5516506658455873, 2.089201408406855, 2.5865792673916403, 3.0220537809362114, 3.3761374721207402, 3.6325509554515496, 3.779052041184418, 3.808085505675136, 3.7172182623413943, 3.509334663654717, 3.1925781265831876, 2.780037654009675, 2.289190515939977, 1.7411247206450329, 1.1595763137417678, 0.5698263942613211, -0.0024895006828101716, -0.5326017530566275, -0.9977964759395272, -1.3785151134522269, -1.65930782433364, -1.8295912196990123, -1.8841702288551299, -1.8234952740673445, -1.6536389985637, -1.3859908679425237, -1.0366823445491746, -0.6257692788615745, -0.17621094153677425, 0.2873039485141766, 0.7396253601882969, 1.1564398558029645, 1.5155315844619255, 1.7979408341760736, 1.9889592012358421, 2.0789082711933746, 2.0636594289845953, 1.9448655061640137, 1.7298897764624193, 1.4314335702438539, 1.0668796734678687, 0.6573838657989165, 0.2267606173260015, -0.19977964653520885, -0.5969758282168944, -0.9408730427413047, -1.2101188264848315, -1.387128917835317, -1.4590591583150863, -1.4185298523478775], 'positive_zeros': ['0.998178678086866782112530470344852', '2.26086568436114719232449294985555', '3.55914854678792437858934322194725', '4.30462885022467551900177280185744', '4.87312129884779533239193993492121', '5.96944177626039225073422574190234', '6.87300748463116316141211816636154', '7.63884260737345136390926414218492', '8.416967073773433515706622400378652'], 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.998178678086866782112530470345', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26086568436114719232449294986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55914854678792437858934322195', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 130.09921156265813, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'index': 111, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/bz/1/3'], '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': '2-2205-1.1-c3-0-111', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.998178678086866782112530470345', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1265341800411837250751554498843', 'Lhash_array': ['1265341800411837250751554498843'], 'label': '2-2205-1.1-c3-0-111', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/bz/1/3'}