- 
              lfunc_lfunctions •   Show schema
  Hide schema
   
        
{'Lhash': '2563945269285502776847889192995', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [2.0, 0.0], 'a7': [-4.372281323269014, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.1', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2563945269285502776847889192995', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.372281323269014, 0], [7.0, 0]], [[1.0, 0], [-2.3722813232690143, 0], [11.0, 0]], [[1.0, 0], [-6.744562646538029, 0], [13.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [4.744562646538029, 0], [23.0, 0]], [[1.0, 0], [9.116843969807043, 0], [29.0, 0]], [[1.0, 0], [8.372281323269014, 0], [31.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.3722813232690143, 0], [41.0, 0]], [[1.0, 0], [-1.6277186767309857, 0], [43.0, 0]], [[1.0, 0], [-2.7445626465380286, 0], [47.0, 0]], [[1.0, 0], [4.372281323269014, 0], [53.0, 0]], [[1.0, 0], [-1.2554373534619714, 0], [59.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [61.0, 0]], [[1.0, 0], [6.744562646538029, 0], [67.0, 0]], [[1.0, 0], [-4.744562646538029, 0], [71.0, 0]], [[1.0, 0], [2.7445626465380286, 0], [73.0, 0]], [[1.0, 0], [-6.744562646538029, 0], [79.0, 0]], [[1.0, 0], [-10.744562646538029, 0], [83.0, 0]], [[1.0, 0], [-10.0, 0], [89.0, 0]], [[1.0, 0], [-17.116843969807043, 0], [97.0, 0]], [[1.0, 0], [-11.489125293076057, 0], [101.0, 0]], [[1.0, 0], [-13.489125293076057, 0], [103.0, 0]], [[1.0, 0], [-19.489125293076057, 0], [107.0, 0]], [[1.0, 0], [17.116843969807043, 0], [109.0, 0]], [[1.0, 0], [-11.627718676730986, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-370-1.1-c1-0-6', '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/370/2/a/f/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.710486559166393, 2.7183248431701634, 2.739604468457775, 2.767979703006883, 2.793945274082657, 2.8060866820076047, 2.7923597187202502, 2.7412582258984886, 2.6428445504617915, 2.489663672587604, 2.2775517877182363, 2.006316216927746, 1.68023057444228, 1.3082689354808155, 0.9039990804244189, 0.4850679640838122, 0.07224113015293131, -0.31200039903836885, -0.6452506402578281, -0.9072449779923414, -1.0820356381468477, -1.1600633757906487, -1.1398828156270373, -1.0292932228276788, -0.8456505107143256, -0.6151929562524012, -0.37130153413824313, -0.1517306193680193, 0.005024048701741414, 0.06392016523830471, -0.002291122873859085, -0.20908093205539754, -0.5570469002694375, -1.030205777395446, -1.5960696654391076, -2.2077277479322097, -2.807925615388338, -3.334871347344107, -3.7292330739288087, -3.941563979499221, -3.9392355794233076, -3.71191172316359, -3.2746766154677145, -2.6681468430614355, -1.9552372272521632, -1.2146801554442999, -0.5318663355478731, 0.011983003159260397, 0.3509561626198015, 0.4443607599070006, 0.28388251713120166, -0.10327609506769476, -0.656076692494337, -1.2863039903947742, -1.8896306487917671, -2.3597986878301533, -2.6040400577877705, -2.557506672780454, -2.19444475530097, -1.5341678248290618, -0.6405409880832357, 0.3853875865625714, 1.418909846205129, 2.3295983269475773, 3.0010851734078936, 3.349615925558982, 3.3382989463091723, 2.984469346819694, 2.3585568288346193, 1.5741635423586877, 0.7705225750345309, 0.08987820700909219, -0.3466408023043379, -0.46060104649506245, -0.23143555974643062, 0.2977724806791487, 1.0254040421430866, 1.8069949482848402, 2.479289164711265, 2.8888265298621003, 2.9202127416988133, 2.519011581928127, 1.7048985045686949, 0.5722489194954865, -0.7225293048866507, -1.9852330343476199, -3.0157979471211607, -3.642480737696639, -3.7522053330719976, -3.3114630112690757, -2.373704159355534, -1.0715355532391986, 0.40517845269596925, 1.8415409898520378, 3.034370610487408, 3.8266963655929143, 4.133544092719423, 3.9541515246781067, 3.3683403688099283, 2.517869859432861, 1.5765839500288745, 0.7154275096648389, 0.06945759485232136, -0.28643729892796793, -0.3482247352654771, -0.17782636587589337, 0.11601322149610081, 0.40661899776376953, 0.5814002974309364, 0.5696195826474064, 0.35946262957618896, 0.00036048862194209, -0.4100967210567593, -0.7516824960263222, -0.913479049390979, -0.824508462202261, -0.4753681169162162, 0.07491687739553934, 0.7092431181496538, 1.2782884495270201, 1.6362824598205434, 1.6783321589519513, 1.3700667013919936, 0.7616793068652336, -0.018234833147761434, -0.7889989342905147, -1.3593530721007496, -1.5750991476218739, -1.3617229120755832, -0.751233766743849, 0.11451598037298515, 1.0066977880238352, 1.6551838063241722, 1.8080294766331486, 1.291903865337304, 0.0595506538484189, -1.7874918376123878, -4.007663218512787, -6.259534686359059, -8.166048442598242, -9.38971648634888, -9.702604771861003, -9.035497518300618, -7.494830038739225, -5.342942876540727, -2.9453993423439266, -0.6966307814094371, 1.0597641548171428, 2.098394656897671, 2.352223513540602, 1.9168737775050535, 1.0188523686453266, -0.04410493742925873, -0.9758775590305541, -1.5503791492426338, -1.6593146487521004, -1.3283978009172035, -0.6991731381460496, 0.017736351128541057, 0.6049967694708819, 0.8998135657578706, 0.8379023834274463, 0.4687978711952583, -0.06112646497564069, -0.5528497678708956, -0.8136780429182155, -0.7145475847294999, -0.22961754140145707, 0.5530995040617113, 1.4533999378511677, 2.2472391325128074, 2.7286421992985397, 2.7680348103420314, 2.350522227307199, 1.582908489574241, 0.6667487604375169, -0.15582041724204929, -0.668933439665868, -0.7440679015707805, -0.3780179090220269, 0.303525846375227, 1.0787331616031302, 1.6905254214014078, 1.9192772629650938, 1.6472457552010193, 0.8964195345893833, -0.17155919546184287, -1.2944220169388443, -2.1774035598357315, -2.572260551070719, -2.345530714237307, -1.5169589747860737, -0.2570186437863179, 1.1562723485539517, 2.409632195307165, 3.2359918654126605, 3.4825211389101653, 3.1462518759902074, 2.3675330694779593, 1.3836694386143307, 0.45666860411813714, -0.20334671582170555, -0.4961398544258948, -0.45329126244170626, -0.2173569123087096, 0.015412693224364919, 0.07101952821730012, -0.13179168207106248, -0.5397939719367862, -0.9675682243975042, -1.1460474588452467, -0.8051893101513868, 0.23271606427341532, 1.977416937073433, 4.237588355520307, 6.643953860191378, 8.72654120464706, 10.02793451206797, 10.22284315612195, 9.210842153650317, 7.1550931640753985, 4.453860463143744, 1.6499237317344537, -0.6995779173479132, -2.1587967177246608, -2.518060415711443, -1.8397191218861608, -0.4327435342624005, 1.236496205033984, 2.67221290904639, 3.4803447593904706, 3.4668553092745897, 2.6770448537962954, 1.3669544211206395, -0.08251162388107441, -1.2819878573047918, -1.9458046539284422, -1.9674968057597022, -1.43815576118148, -0.6048284093721239, 0.21574197920157756, 0.7397583425545049, 0.8031282603033086, 0.4061235328621991, -0.29623911881941334, -1.0527912618897783, -1.6031047339808375, -1.7635905406979246, -1.4848284981712763, -0.862301904132955, -0.09848784555526262, 0.5695613413547287, 0.9517485296826818, 0.9675439306522133, 0.6684954343648134, 0.21347870862697316, -0.1939894002282513], 'positive_zeros': ['2.02259618606569259686588845235593', '3.49455304925544319783485761219059', '3.74786059982972828851228147626108', '5.87169576061093445842092703018419', '6.34714050316419728421997080073496', '7.57899665809056725753882985405373', '8.895229980931036036550921747096107', '9.312317635453180027617770363634573', '10.43111387338297534143893299369577', '11.46613437349725801106723157170568'], 'prelabel': '2-370-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02259618606569259686588845236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49455304925544319783485761219', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74786059982972828851228147626', 'prec': 103}}
           
      - 
              lfunc_search •   Show schema
  Hide schema
   
        
{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/a/f/1/1'], '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': '2-370-1.1-c1-0-6', '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': '2-370-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02259618606569259686588845236', 'prec': 103}}
           
      - 
              lfunc_instances •   Show schema
  Hide schema
   
        
{'Lhash': '2563945269285502776847889192995', 'Lhash_array': ['2563945269285502776847889192995'], 'factors': ['2-370-1.1-c1-0-6'], 'label': '2-370-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/a/f/1/1'}