-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3250310074730666662805683404270', 'a10': [-0.3009441430851283, 0.5212505460637202], 'a2': [-0.14568344511778392, -0.2523311287656738], 'a3': [1.216049478359583, -2.1062594810364277], 'a4': [0.9575526676372272, -1.6585298712707923], 'a5': [-1.0328700795132122, -1.7889834553345898], 'a6': [-0.7086331097644322, 8.456678435898259e-61], 'a7': [0.0, 0.0], 'a8': [-1.140732066483598, 0.0], 'a9': [-1.4575526676372272, -2.524555275055231], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.434072428181207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [7, 19], 'central_character': '931.704', 'coefficient_field': 'CDF', 'conductor': 931, 'conductor_radical': 133, 'conjugate': '1078954670914192230384857186939', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.14568344511778392, 0.2523311287656738], [-1.0, 1.7320508075688772]], [[1.0, 0], [-1.216049478359583, 2.1062594810364277], [-1.5, -2.598076211353316]], [[1.0, 0], [1.0328700795132122, 1.7889834553345898], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.4745462890819385, 4.28603989837094], [-5.5, -9.526279441628825]], [[1.0, 0], [1.6237384450388868, 0], [13.0, 0]], [[1.0, 0], [3.495048621365814, -6.05360178712915], [-8.5, -14.722431864335457]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-3.7064722255100224, -6.419798211426248], [-11.5, 19.91858428704209]], [[1.0, 0], [-3.8833524191374527, 0], [29.0, 0]], [[1.0, 0], [-0.4041802558401395, 0.700060738531309], [-15.5, -26.846787517317598]], [[1.0, 0], [2.053372411797088, 3.556545344092799], [-18.5, 32.04293994002423]], [[1.0, 0], [-8.50709086417634, 0], [41.0, 0]], [[1.0, 0], [-7.315451375856618, 0], [43.0, 0]], [[1.0, 0], [2.709750273140642, 4.693425148903235], [-23.5, 40.703193977868615]], [[1.0, 0], [-0.9950486213658141, 1.7234747682069562], [-26.5, -45.89934640057525]], [[1.0, 0], [2.877609381545868, -4.984165653174298], [-29.5, -51.09549882328188]], [[1.0, 0], [5.690595767441521, 9.856400994545123], [-30.5, 52.827549630850754]], [[1.0, 0], [6.997513611326779, -12.120049101472759], [-33.5, -58.023702053557386]], [[1.0, 0], [-6.519689274614221, 0], [71.0, 0]], [[1.0, 0], [1.0449123223237375, -1.8098412317195005], [-36.5, -63.21985447626402]], [[1.0, 0], [-1.159886572182719, -2.008982474037375], [-39.5, 68.41600689897065]], [[1.0, 0], [5.017528390359811, 0], [83.0, 0]], [[1.0, 0], [-3.3472042919936205, -5.797527897045562], [-44.5, 77.07626093681505]], [[1.0, 0], [14.066348370439535, 0], [97.0, 0]], [[1.0, 0], [-0.8970679929515437, 1.5537673416359132], [-50.5, -87.4685657822283]], [[1.0, 0], [8.450440404748631, 14.636592127357538], [-51.5, 89.20061658979718]], [[1.0, 0], [4.504625874215375, 7.802240883230399], [-53.5, 92.66471820493493]], [[1.0, 0], [3.5046258742153746, -6.070190075661522], [-54.5, -94.39676901250381]], [[1.0, 0], [0.261701415854965, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-931-7.4-c1-0-57', '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/931/2/f/n/704/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8487504752128974, 2.176659150333724, 2.529393546199514, 2.906064804855861, 3.2999256383004223, 3.6979573564960697, 4.081377779719516, 4.426890949028267, 4.708523382397825, 4.899930066367466, 4.977048941237204, 4.9209324848375156, 4.720512595840778, 4.374988042104921, 3.8954856914756846, 3.3056548090133417, 2.6409182894572707, 1.9462283014321788, 1.272349754119278, 0.6709065860221717, 0.18864693234469518, -0.1384197896519085, -0.29022483560243395, -0.2663517637458576, -0.08750970695625292, 0.2057659512873735, 0.5573830223580374, 0.9027024761234456, 1.177596225589797, 1.3284321133400891, 1.3215511229069787, 1.150673993521901, 0.8407863647203093, 0.44742359044496405, 0.05088599521473885, -0.25430606072591017, -0.3735706615074993, -0.22813232887874588, 0.22983617771265372, 1.0054129339494382, 2.054826442337408, 3.2867131829523637, 4.571309026952707, 5.75683750084075, 6.691024930227392, 7.24456248051097, 7.332680018245232, 6.93097083924883, 6.0822845607056335, 4.892835872541209, 3.5174749106409418, 2.1360343338974697, 0.9244464528641265, 0.02554814704212987, -0.47512799734546823, -0.5638905007796767, -0.30063738762438086, 0.19300838449173333, 0.7573909128192213, 1.226132762005631, 1.4591340605945813, 1.370710526502829, 0.9470194768905822, 0.24888049786968627, -0.6010149354697126, -1.4442497270779884, -2.1209747703046613, -2.505159835316034, -2.5331003237915546, -2.218643826559467, -1.651286691989711, -0.9769863904119243, -0.36546203669549543, 0.028973118139653434, 0.10418338499391208, -0.16413273572405288, -0.7144234587377981, -1.4115666632091493, -2.0774130053549644, -2.5330637577687436, -2.643188335746716, -2.3516790460160792, -1.699476335031003, -0.819262975175906, 0.09287927079328757, 0.8230625236003263, 1.192041510795164, 1.1018191783497628, 0.5644256651272729, -0.29536312331394304, -1.2655631328373251, -2.096016205803699, -2.55997921916102, -2.5135248239173342, -1.93769286927665, -0.9517893156674584, 0.20718936344470132, 1.2358105534868173, 1.835081250192839, 1.784398630384891, 1.000433698686854, -0.43429044235415976, -2.2814831730050833, -4.194904656313635, -5.795565571773742, -6.75680486838145, -6.8787866327054035, -6.134107470126601, -4.673073022723392, -2.787145903052623, -0.8395804924414632, 0.8193946403831919, 1.9315501705748728, 2.3840862873172055, 2.2246150348308538, 1.635028846559076, 0.8725424726490146, 0.19487887350608288, -0.2094318431302017, -0.26651218786479297, -0.02644104687979882, 0.3649270386779418, 0.7220008621899058, 0.8855723563910993, 0.7783166740971399, 0.4322246213889357, -0.020905933595873435, -0.39335746681590383, -0.5062907955428856, -0.25494864575182236, 0.34712435504096795, 1.1604687812932017, 1.9534254478554287, 2.469007673284682, 2.5057764032134555, 1.9879780372216678, 1.002014299908293, -0.21465902290850114, -1.3322649077779531, -2.0204724412060857, -2.047580596534603, -1.3576760715346305, -0.10123165734620353, 1.392801359772781, 2.6985334846907705, 3.4072765154791758, 3.242656457138266, 2.143474106776534, 0.28931204407620226, -1.940182946676865, -4.062310429600628, -5.617961091929547, -6.292153650877307, -5.994096357630177, -4.874035949542609, -3.2726990827512235, -1.6190504608214595, -0.3073257204640573, 0.40986885401832907, 0.4810276950208209, 0.05149169424178316, -0.6008013116257955, -1.167134541836721, -1.4135403814969438, -1.2556823117158584, -0.7793539147724722, -0.2011753182790372, 0.21588969525809112, 0.26241724146739714, -0.13715103934510856, -0.8920559364054259, -1.7725700761546581, -2.488343011436914, -2.7908457878564747, -2.5638368898576362, -1.8689000854985094, -0.9278421270550362, -0.04538650203636156, 0.5030706584263479, 0.5802497323027667, 0.2530330471710713, -0.21082110824544498, -0.41933553321114, 0.014744754601519494, 1.333068345081482, 3.5257649517627425, 6.29852123169612, 9.128613448085606, 11.397504826054806, 12.562146236889637, 12.31308996658923, 10.66993475610938, 7.983128476515317, 4.840061638509811, 1.9034103196869636, -0.268989179429425, -1.3679009142245002, -1.3973748126982075, -0.6434646234822254, 0.43897564248486365, 1.3816115921122962, 1.8482111663256044, 1.7241403827488793, 1.1243025907649178, 0.3228685226149232, -0.3652146198540457, -0.7057223212853713, -0.6257534614018946, -0.22654233294670928, 0.27213447562873105, 0.6308004866933872, 0.6914688118048732, 0.4403585549955031, 0.007145176974523817, -0.3986716066465325, -0.5881209101142488, -0.4879995284786322, -0.18972475040036957, 0.07239283187413775, 0.010114235334480023, -0.5935682357150548, -1.7712110945096329, -3.3170731030986396, -4.820856399044398, -5.785794383323102, -5.795383860840873, -4.671771062282074, -2.5673002288654407, 0.04930589785496362, 2.5154331398078753, 4.170630311051778, 4.56335699786476, 3.5988869491085627, 1.5764875527026048, -0.8995077863003403, -3.107238844936877, -4.431808283223442, -4.551923739637324, -3.526780751059292, -1.7558950892195138, 0.17123140517626897, 1.6807464407515031, 2.4023523939624583, 2.2745818417736112, 1.5338900054852538, 0.5969812023221807, -0.11547096035517015, -0.34529261139161355, -0.09062690311569913, 0.40665922820190725, 0.7723006245997418, 0.6640111544686836, -0.07687784163212354, -1.3469018598074955, -2.806675592963006, -4.002416966587914, -4.535977315607624], 'positive_zeros': ['2.56404254780100823263837628122897', '3.04164859741554940473563858518866', '4.26765084662865382797752367773208', '4.69801086378788115108981327640272', '6.62955590709864897954700713180070', '7.08040143274198047427008755975257', '7.912953944415630876335071971775216', '9.111266988124839011101481000046650', '9.317493656335545016196775990389200', '10.48658106745232365544385851476745'], 'prelabel': '2-931-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': 0.9596540938921078, 'root_number': '-0.9919779164085226 + 0.12641128651274008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.479827046946', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.56404254780100823263837628123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04164859741554940473563858519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26765084662865382797752367773', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.434072428181207, 'bad_primes': [7, 19], 'central_character': '7.4', 'conductor': 931, 'conductor_radical': 133, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/931/2/f/n/704/2'], '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': '2-931-7.4-c1-0-57', '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': '2-931-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': 0.4798270469460539, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.56404254780100823263837628123', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3250310074730666662805683404270', 'Lhash_array': ['3250310074730666662805683404270'], 'label': '2-931-7.4-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/931/2/f/n/704/2'}