-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3174821112291654333590926070214', 'a10': [12.0, 0.0], 'a2': [0.0, 1.4142135623730951], 'a3': [-1.0, -2.8284271247461903], 'a4': [-2.0, 0.0], 'a5': [0.0, -8.48528137423857], 'a6': [4.0, -1.4142135623730951], 'a7': [0.0, 0.0], 'a8': [0.0, -2.8284271247461903], 'a9': [-7.0, 5.656854249492381], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.01091977219273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [1.0, 2.8284271247461903]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '294.197', 'coefficient_field': 'CDF', 'conductor': 294, 'conductor_radical': 42, 'conjugate': '381101709222330428770486015416', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [1.0, 2.8284271247461903]], [[1.0, 0], [0, 8.48528137423857], [-25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-121.0, 0]], [[1.0, 0], [1.0, 0], [169.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-289.0, 0]], [[1.0, 0], [31.0, 0], [361.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-529.0, 0]], [[1.0, 0], [0, 16.97056274847714], [-841.0, 0]], [[1.0, 0], [7.0, 0], [961.0, 0]], [[1.0, 0], [1.0, 0], [1369.0, 0]], [[1.0, 0], [0, 33.94112549695428], [-1681.0, 0]], [[1.0, 0], [31.0, 0], [1849.0, 0]], [[1.0, 0], [0, 42.42640687119285], [-2209.0, 0]], [[1.0, 0], [0, 25.45584412271571], [-2809.0, 0]], [[1.0, 0], [0, -8.48528137423857], [-3481.0, 0]], [[1.0, 0], [-50.0, 0], [3721.0, 0]], [[1.0, 0], [-65.0, 0], [4489.0, 0]], [[1.0, 0], [0, -59.39696961966999], [-5041.0, 0]], [[1.0, 0], [97.0, 0], [5329.0, 0]], [[1.0, 0], [103.0, 0], [6241.0, 0]], [[1.0, 0], [0, 42.42640687119285], [-6889.0, 0]], [[1.0, 0], [0, 118.79393923933998], [-7921.0, 0]], [[1.0, 0], [166.0, 0], [9409.0, 0]], [[1.0, 0], [0, 135.7645019878171], [-10201.0, 0]], [[1.0, 0], [-65.0, 0], [10609.0, 0]], [[1.0, 0], [0, -161.22034611053283], [-11449.0, 0]], [[1.0, 0], [-167.0, 0], [11881.0, 0]], [[1.0, 0], [0, 161.22034611053283], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-294-3.2-c2-0-26', '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/294/3/b/b/197/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6053368411183346, 0.8631052102427906, 1.1212690181871423, 1.3770821478977118, 1.626703919566884, 1.8648817675523832, 2.0848497250402227, 2.27845911546138, 2.436537555482437, 2.5494565459034875, 2.6078745739451414, 2.603609466746092, 2.5305795958265755, 2.3857389619062173, 2.1699181024166263, 1.8884738943038495, 1.5516496280044725, 1.1745548463817972, 0.7766942353753176, 0.38100699631261853, 0.01242178651270247, -0.3040150744681323, -0.5453231968449139, -0.692912628279419, -0.7348308333055739, -0.6676821136658184, -0.49796101297614687, -0.24256172094141462, 0.07172193532192195, 0.4098069541092806, 0.7310314484990329, 0.9928241256660225, 1.1550570700341691, 1.1846817336500919, 1.0601527173817602, 0.7750947693397312, 0.34067963119389594, -0.21374048120697847, -0.8420461019172062, -1.4849027456582293, -2.075290557984962, -2.5455802136725496, -2.835472264859881, -2.899919904428509, -2.716046733288716, -2.288078850470301, -1.6494494025172046, -0.8615023090406142, -0.008600351247121812, 0.810107065463327, 1.4915330070400856, 1.940972574631048, 2.0844337308957717, 1.8793745157448405, 1.322302920948456, 0.4519777361523875, -0.6525651906402553, -1.8792955694897067, -3.0951955219214695, -4.1617068698920034, -4.951760318252736, -5.366174107068315, -5.347148978077969, -4.886852960781568, -4.02967040379209, -2.8675216654218527, -1.5286348818659061, -0.16112943942485244, 1.0863996920381767, 2.0845670242762724, 2.740274227461518, 3.008598636567803, 2.897627486014529, 2.4654196006698306, 1.8095003224861268, 1.0505036315417773, 0.31256454970668557, -0.2963438355138827, -0.7008624585121198, -0.8687070536413657, -0.8133434872101426, -0.5884205030653412, -0.274968817228343, 0.03628763778459818, 0.2642050455327779, 0.3543915923050163, 0.29088423158231247, 0.09988416985537608, -0.1554371224225757, -0.38833181550406304, -0.507678378673569, -0.43932137846122754, -0.14524930865103572, 0.36350114016155183, 1.023310464212368, 1.7252130509105261, 2.332226519203884, 2.7040176750017864, 2.7244889537285184, 2.326984878762487, 1.5119366175960782, 0.35292511861361753, -1.0108167779132666, -2.3948796368323255, -3.5999429596238297, -4.446522083032189, -4.807705234666455, -4.633441467820278, -3.9612876668977757, -2.9109657913106273, -1.6631833923332542, -0.426333553466647, 0.6027297693146216, 1.276208604238847, 1.5235982769217766, 1.3646922750708088, 0.9043175305334157, 0.30942892098932706, -0.2271246910355787, -0.5289226075088843, -0.47562122017577274, -0.0314377572293383, 0.7439429923191414, 1.7049267279026459, 2.648645971654609, 3.357150870929368, 3.6445273080654466, 3.398957899299708, 2.610493045535261, 1.378077286653047, -0.1063487167659058, -1.593957984131998, -2.828187320650185, -3.5967260792145463, -3.7752565012314583, -3.3533831329673864, -2.4368604019491746, -1.2252934029636005, 0.030143683621147194, 1.0799490106683267, 1.7289154572885588, 1.8765460130297256, 1.5362755094473286, 0.8291915999379836, -0.04631867207681354, -0.862077729178722, -1.413883207111668, -1.569117764275382, -1.2971403606075926, -0.6753476245823824, 0.1305367078986589, 0.9073084398020265, 1.4465793184600046, 1.596035453595668, 1.2973257936872338, 0.6013720661107468, -0.3427252265719106, -1.3226387002331461, -2.113256492013286, -2.530410574175692, -2.474806536938804, -1.9554082150518368, -1.086551424833644, -0.059550210064389805, 0.9040899016347428, 1.6061258963056566, 1.9182927296848038, 1.810592989629774, 1.3541968133958355, 0.698540776594391, 0.028923289490579304, -0.48399067838493176, -0.7291926995345276, -0.6827577449779391, -0.4102675081721527, -0.04362618493209128, 0.2612294831526213, 0.3737362787410816, 0.2309151977656215, -0.14033473142530778, -0.6283671138132706, -1.0692993971185798, -1.2989504198369632, -1.2101478934613525, -0.7988318408152858, -0.18433430058286646, 0.40464284242102094, 0.6779376696375099, 0.35592542039032427, -0.7515666133758541, -2.6798480092159838, -5.2759057409817425, -8.208374135030517, -11.022014547247437, -13.22651175400135, -14.400145632054164, -14.284168499312802, -12.844923719359748, -10.28779591408391, -7.018374323963249, -3.5589700777885422, -0.43962524431639527, 1.9108670400290177, 3.248360892855764, 3.5519791595778822, 3.009982773274706, 1.9581068632672811, 0.7873330526213341, -0.1546863795409509, -0.643475499743373, -0.6194829640480808, -0.1830598060940068, 0.45323724816527067, 1.0395607281131798, 1.3685778814989735, 1.3372903856065312, 0.9738408458340675, 0.42281255734652123, -0.10527608170464106, -0.40421246097133895, -0.34041576794282397, 0.10150454860145465, 0.8098832283216613, 1.5767206708096766, 2.158981087910682, 2.3521857694576864, 2.054142266956785, 1.2993625556532853, 0.25328580980336585, -0.83264943618999, -1.6922618444483963, -2.1212909630835775, -2.036607482026648, -1.500012997102446, -0.6990608714015107, 0.10982637015780718, 0.6791959956605526, 0.8460046625188156, 0.5816531422020889, 0.0009563768434991084, -0.673350775292176, -1.1804166776742102, -1.3044780076239022, -0.9459574424252091, -0.15804777239447826, 0.8635676145764426, 1.8360930720012127, 2.4743707031764894, 2.57974463237963, 2.105727054223162, 1.179415777003249, 0.07051394456057442, -0.8844149628193358, -1.380905503072291, -1.239466040751128, -0.46404631326931756, 0.7525981224477979], 'positive_zeros': ['2.50449225655717400743056059183345', '3.47280463764752374706074937286890', '4.57936349551115430058826044094716', '6.00126048529382743648643433039006', '6.92873019094949383832012862066324', '8.390217434238413612560123698454715', '9.559721191266592519689023540102694', '10.35917386067993420639895914538845', '10.92546721175649204149241301385025', '11.54099593810411389838942966422064'], 'prelabel': '2-294-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.830356827714967, 'root_angle': 0.8918265520306073, 'root_number': '-0.9428090415820634 + 0.3333333333333333*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.445913276015', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50449225655717400743056059183', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47280463764752374706074937287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57936349551115430058826044095', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.01091977219273, 'bad_primes': [2, 3, 7], 'central_character': '3.2', 'conductor': 294, 'conductor_radical': 42, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/294/3/b/b/197/2'], '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': '2-294-3.2-c2-0-26', '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': '2-294-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.830356827714967, 'root_angle': 0.4459132760153037, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50449225655717400743056059183', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3174821112291654333590926070214', 'Lhash_array': ['3174821112291654333590926070214'], 'label': '2-294-3.2-c2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/294/3/b/b/197/2'}