Table lfunc_lfunctions
L-functions
{'Lhash': '1588584542674111237592541246272', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.695518130045147, 0], 'a6': [0, 0], 'a7': [0, -3.414213562373095], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.2303', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1151166544954120888794667269835', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.695518130045147, 0], [5.0, 0]], [[1.0, 0], [0, 3.414213562373095], [-7.0, 0]], [[1.0, 0], [0, 2.164784400584788], [-11.0, 0]], [[1.0, 0], [0, 2.164784400584788], [-13.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-17.0, 0]], [[1.0, 0], [-7.391036260090294, 0], [19.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [23.0, 0]], [[1.0, 0], [6.756985588965865, 0], [29.0, 0]], [[1.0, 0], [0, -2.242640687119285], [-31.0, 0]], [[1.0, 0], [0, -7.391036260090294], [-37.0, 0]], [[1.0, 0], [0, -12.242640687119286], [-41.0, 0]], [[1.0, 0], [-10.452503719011013, 0], [43.0, 0]], [[1.0, 0], [3.1715728752538097, 0], [47.0, 0]], [[1.0, 0], [-6.756985588965865, 0], [53.0, 0]], [[1.0, 0], [0, 10.452503719011013], [-59.0, 0]], [[1.0, 0], [0, 3.0614674589207183], [-61.0, 0]], [[1.0, 0], [11.72060506125987, 0], [67.0, 0]], [[1.0, 0], [-6.48528137423857, 0], [71.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [73.0, 0]], [[1.0, 0], [0, 17.071067811865476], [-79.0, 0]], [[1.0, 0], [0, -8.287719318426225], [-83.0, 0]], [[1.0, 0], [0, 7.0710678118654755], [-89.0, 0]], [[1.0, 0], [11.313708498984761, 0], [97.0, 0]], [[1.0, 0], [8.025086931214723, 0], [101.0, 0]], [[1.0, 0], [0, 11.414213562373096], [-103.0, 0]], [[1.0, 0], [0, -4.329568801169576], [-107.0, 0]], [[1.0, 0], [0, 8.287719318426225], [-109.0, 0]], [[1.0, 0], [0, 9.414213562373096], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23388630, 'index': 49, 'label': '2-4608-24.11-c1-0-49', 'leading_term': '2.976616938283830053941799256543850682699779595650938894', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.97661693828383, 3.0580128101183943, 3.1263894286170126, 3.1810508855481308, 3.2211462907160846, 3.24568573950071, 3.253572233881811, 3.2436475971829153, 3.214749686515236, 3.1657777412431805, 3.095762495950117, 3.0039376870987042, 2.8898097350878276, 2.753222630463882, 2.594415348917314, 2.414069434451253, 2.21334470923569, 1.993901389830674, 1.7579072181616389, 1.5080285609027235, 1.24740480191451, 0.9796057559067798, 0.7085722705822494, 0.43854065772737455, 0.1739520950471761, -0.08065134029476108, -0.3207418225071302, -0.5419294187729605, -0.7400910509714357, -0.911501183156963, -1.0529602912409224, -1.1619169173374742, -1.2365789716946358, -1.2760099368617832, -1.280205765237689, -1.2501485516973692, -1.1878335119481882, -1.096266403354179, -0.9794292808584875, -0.842213372644335, -0.690318868220814, -0.5301225094126811, -0.3685150302401609, -0.21271166784886372, -0.07004012242698107, 0.05228856440817285, 0.1474197610959575, 0.20909834781012343, 0.23190725743010684, 0.21149314915352252, 0.14477078062165635, 0.030097810422473975, -0.13258776175840203, -0.34167451993368864, -0.5938348256701949, -0.884036797044527, -1.2056139424392498, -1.5503934580962102, -1.9088821782450545, -2.2705070527164066, -2.623904893055952, -2.9572540541187684, -3.2586387870255256, -3.5164352944088906, -3.719707120037239, -3.8585964854272876, -3.9246976090340318, -3.91139795867385, -3.814173828230001, -3.6308276097627905, -3.3616556455128737, -3.0095375627035974, -2.579940467152297, -2.080834227654649, -1.522517230210736, -0.9173553104151703, -0.27943996090532325, 0.37582477371811374, 1.032194196542534, 1.6730983750362562, 2.28218351288573, 2.8438600225363335, 3.3438370415626757, 3.7696228983776883, 4.110971606568335, 4.360256867179454, 4.512757265283274, 4.56683930670963, 4.52402856365657, 4.388963362083979, 4.169229998155634, 3.8750832402588857, 3.519060664325964, 3.115503980226264, 2.6800047311576636, 2.228795388833091, 1.7781097439130478, 1.3435384480253885, 0.939406478876267, 0.5781990921300278, 0.27006145799324327, 0.02239467198387476, -0.16043275477065175, -0.2772433619401134, -0.3300699319042101, -0.3240320902636773, -0.2670732496201549, -0.16956715021615473, -0.0438093531635539, 0.09658535843045606, 0.23735389231006634, 0.3642944990330216, 0.46398302927118823, 0.5244625040868665, 0.535873051144326, 0.49099114625702533, 0.3856504935017694, 0.21902167229415098, -0.006266300049011191, -0.2841723378082399, -0.6054597453614635, -0.9580768854246698, -1.3276881664149578, -1.6983338549082432, -2.05319040145007, -2.3753972898222164, -2.6489121931003052, -2.859353697409824, -2.99479021561956, -3.046435052557367, -3.0092109018833946, -2.8821522570249223, -2.668621113450245, -2.376319646142926, -2.0170929043231602, -1.6065245508700168, -1.1633388166290097, -0.7086316461986033, -0.264962988291497, 0.14465013844663918, 0.4977942138359585, 0.7737239349755878, 0.9543800297394558, 1.0253100063139242, 0.9764450744439834, 0.802692269040417, 0.5043087819188403, 0.08703532526533332, -0.43802342996609256, -1.0547712013324575, -1.7427327009824105, -2.477881912062498, -3.23365032954442, -3.9820698738294187, -4.694997656832024, -5.345364742810257, -5.908388817548167, -6.362691440567137, -6.69126433673121, -6.882235860746667, -6.929398061482135, -6.832466259917792, -6.59705618661298, -6.234377853679148, -5.7606597458661675, -5.196330856933003, -4.56500082934089, -3.8922892826038105, -3.204563728718625, -2.527650782566197, -1.8855873413410944, -1.2994768621875525, -0.7865108289825969, -0.3592071744911448, -0.02490620250202707, 0.21444900836725495, 0.36223594640219686, 0.4267840357597225, 0.42073435052332137, 0.36016312808425716, 0.26351792217046077, 0.1504260998650789, 0.040443080773937275, -0.048188245298692936, -0.09969539486930977, -0.10178386740842178, -0.04643463805291846, 0.06955689935926854, 0.24433475253176593, 0.4710466943185074, 0.738219227207991, 1.030425179224173, 1.3292086536463272, 1.6142164699456285, 1.8644722990066525, 2.0597202078871444, 2.1817589034272897, 2.215686995185248, 2.150983233599707, 1.9823538036860684, 1.7102909907336177, 1.3413032588802922, 0.8877951566777046, 0.36759547416657723, -0.1968474055204333, -0.779564173911265, -1.3524005006042732, -1.8865183246759565, -2.35397949661945, -2.729322152173626, -2.991038707491836, -3.1228681552090674, -3.114824300121215, -2.9638952824396423, -2.6743674888467517, -2.2577477869708864, -1.7322807758897942, -1.1220811250068778, -0.4559237139358945, 0.23424515917186484, 0.9149950136972914, 1.5532035719107904, 2.117853438380619, 2.5817304463732293, 2.9229252672017445, 3.126049949733841, 3.1830964786818186, 3.0938843851507922, 2.866067799045026, 2.514697764046129, 2.061361657793741, 1.532946627295199, 0.9600965482841884, 0.3754507564868358, -0.18823350213623852, -0.6999651911294654, -1.1322991830801097, -1.462905919154135, -1.6758371915503012, -1.7624117752628772, -1.721666985660475, -1.5603480733680877, -1.292435153185472, -0.9382354225586708, -0.5230950397612047, -0.07580854940414876, 0.3731773216754522, 0.7936555434269444, 1.157529932201461, 1.4405498738858202, 1.62380082247095, 1.6948574529368048, 1.6485269585467102, 1.4871353007995276, 1.2203377058306326, 0.8644645944675553, 0.44144356279001423], 'positive_zeros': ['1.25317224035400644878349259476069', '2.26221791983709642465466451752929', '2.60046963557257122331755587858243', '3.88112313368845467249860424301222', '5.13426364389626945820546834854291', '5.50055186617722065451823616164842', '5.99092587327837417667523369999601', '7.03999216868491185876425931921359', '7.47399211406665416370861623269044', '8.840414601286037516285881866185349'], 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.1520433619923482, 'root_number': '0.57735026918962576450914878050195745564760175127012687602 + 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1520433619923482', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25317224035400644878349259476', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.26221791983709642465466451753', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.60046963557257122331755587858', 'prec': 100}}