{'Lhash': '1713562394916394256008645100097', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 25, 'a6': 0, 'a7': -49, 'a8': 0, 'a9': -242, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.81493909526917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -25]], [7, [1, 49]]], 'bad_primes': [2, 5, 7], 'central_character': '560.1', 'coefficient_field': '1.1.1.1', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 1, 243], [1, -25], [1, 49], [1, -453, 161051], [1, 969, 371293], [1, -1637, 1419857], [1, -1550, 2476099], [1, -1654, 6436343], [1, 4985, 20511149], [1, 1192, 28629151], [1, 11018, 69343957], [1, 1728, 115856201], [1, -10814, 147008443], [1, 26237, 229345007], [1, -25936, 418195493], [1, -4580, 714924299], [1, 12488, 844596301], [1, -15848, 1350125107], [1, 51792, 1804229351], [1, -4846, 2073071593], [1, 62765, 3077056399], [1, -23644, 3939040643], [1, 147300, 5584059449], [1, 8343, 8587340257], [1, 11878, 10510100501], [1, -132439, 11592740743], [1, 136842, 14025517307], [1, -109485, 15386239549], [1, 200934, 18424351793]], 'euler_factors_factorization': [[1], [[[1, 1, 243], 1]], [[[1, -25], 1]], [[[1, 49], 1]], [[[1, -453, 161051], 1]], [[[1, 969, 371293], 1]], [[[1, -1637, 1419857], 1]], [[[1, -1550, 2476099], 1]], [[[1, -1654, 6436343], 1]], [[[1, 4985, 20511149], 1]], [[[1, 1192, 28629151], 1]], [[[1, 11018, 69343957], 1]], [[[1, 1728, 115856201], 1]], [[[1, -10814, 147008443], 1]], [[[1, 26237, 229345007], 1]], [[[1, -25936, 418195493], 1]], [[[1, -4580, 714924299], 1]], [[[1, 12488, 844596301], 1]], [[[1, -15848, 1350125107], 1]], [[[1, 51792, 1804229351], 1]], [[[1, -4846, 2073071593], 1]], [[[1, 62765, 3077056399], 1]], [[[1, -23644, 3939040643], 1]], [[[1, 147300, 5584059449], 1]], [[[1, 8343, 8587340257], 1]], [[[1, 11878, 10510100501], 1]], [[[1, -132439, 11592740743], 1]], [[[1, 136842, 14025517307], 1]], [[[1, -109485, 15386239549], 1]], [[[1, 200934, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20489215, 'index': 46, 'label': '2-560-1.1-c5-0-46', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/560/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.6481267024960367e-60, 0.25999614969123647, 0.5154880344174808, 0.7620395560817947, 0.9953502743727101, 1.211321538576934, 1.4061205634252167, 1.5762417332673455, 1.7185643968863211, 1.8304063926635799, 1.9095725235710885, 1.9543971868913959, 1.9637803581437971, 1.9372161359610056, 1.8748130780487144, 1.7773056010439443, 1.646055781829949, 1.483044986872047, 1.2908548709252305, 1.0726374277352417, 0.8320739429033187, 0.5733228917156862, 0.3009570402169745, 0.019890242835125863, -0.26470531990474344, -0.5474904599654721, -0.823057589436718, -1.086035089891161, -1.331195667337995, -1.5535666874237264, -1.748540284365622, -1.911980872537, -2.0403275699441976, -2.1306889758015912, -2.180927736959406, -2.18973239588585, -2.1566741406591308, -2.0822462777156843, -1.967884521735148, -1.8159665426988907, -1.629789624231387, -1.4135257638343408, -1.1721540761521931, -0.9113709341975897, -0.6374788875095562, -0.3572560154792722, -0.07780799179000852, 0.19359426604120977, 0.44968792867459306, 0.683398633864749, 0.8880235535405955, 1.0574124616968732, 1.1861418993905062, 1.2696774436045966, 1.3045191357688157, 1.2883253215848025, 1.2200105007747883, 1.0998132832667966, 0.9293311921603743, 0.7115198335761483, 0.4506548540999808, 0.1522561079452885, -0.17702546653897613, -0.529556636703008, -0.8969035680479674, -1.2700425365852213, -1.6395947167174267, -1.9960791333609182, -2.330177031749398, -2.633000249589162, -2.8963557055979163, -3.1129978729874077, -3.276861107342686, -3.3832639598364342, -3.429078135087708, -3.4128555458347902, -3.3349079623636917, -3.1973350323589744, -3.003997926310223, -2.7604375058209105, -2.4737376701706544, -2.1523363565282327, -1.8057884922546297, -1.444486961218326, -1.079349285943666, -0.7214791804569086, -0.38181333471023315, -0.07076469575422532, 0.20212593350025448, 0.42851798694853444, 0.6015671687706226, 0.7161783394091275, 0.7692052466519966, 0.75958857516009, 0.6884256338831398, 0.5589671625929065, 0.37653915232126955, 0.14839016331985463, -0.1165326986364448, -0.4078733157425508, -0.714213203730363, -1.023464511014386, -1.3232965542752964, -1.6015814070949221, -1.8468428640694707, -2.048692446111533, -2.1982360412894795, -2.2884353171397662, -2.3144092001217746, -2.273662477241408, -2.16623089115182, -1.9947349068751414, -1.7643375371066328, -1.4826051155417412, -1.1592735791140505, -0.8059265235987213, -0.43559488864303125, -0.06229146209763718, 0.2995036722325574, 0.6353882163846035, 0.9315929868937975, 1.1755261938680601, 1.3562851706862362, 1.4651146999587468, 1.4957925809424344, 1.4449254078859823, 1.312140613380683, 1.1001645774177116, 0.8147808819958922, 0.46466744613412775, 0.06111612866197672, -0.3823567572759142, -0.8504959144893757, -1.3268711510659146, -1.7944990493758086, -2.2364982637577344, -2.6367524938775735, -2.9805542027357417, -3.2552022691490374, -3.450528014848183, -3.5593264093592953, -3.577672666353408, -3.505108790421379, -3.34468975611791, -3.1028847052489694, -2.7893346052969816, -2.4164739699056192, -1.9990302368237045, -1.5534199632497707, -1.0970658767848496, -0.6476627776873258, -0.22242312343618587, 0.1626653183170096, 0.49353719357218695, 0.7586713727778364, 0.9496082422591503, 1.0613378921352257, 1.0925398348837285, 1.0456611018507256, 0.9268265202828782, 0.7455823765699601, 0.5144821985242449, 0.24853070132017918, -0.035491301602192764, -0.3197923442555375, -0.586392728039881, -0.817967250580924, -0.9986699056453472, -1.114902274077701, -1.155989156371787, -1.1147285619090983, -0.9877883464137642, -0.7759283767747057, -0.4840348277437696, -0.12096174323309698, 0.3008160564096461, 0.7657256837905614, 1.255772934827566, 1.751343800443149, 2.2320949786557627, 2.6778927075820493, 3.0697561581545036, 3.3907605733101334, 3.6268564177720597, 3.767564008430127, 3.8065083252803373, 3.7417657510161404, 3.5760030535249543, 3.3163986273812114, 2.9743463999100936, 2.564953391096099, 2.106352178875929, 1.618858949299538, 1.1240159201554734, 0.6435632857633338, 0.19839008493364993, -0.19248471497429823, -0.5128502441062507, -0.7501133461321301, -0.8959378498751216, -0.946679352767966, -0.9035910235381857, -0.7727869967397627, -0.5649618820511491, -0.2948771601766942, 0.01936283078129854, 0.3572116132067079, 0.6967147964584122, 1.015627153303673, 1.2925568760141022, 1.5080790890457993, 1.6457613732576664, 1.6930476897369637, 1.6419535510696546, 1.4895342961259228, 1.2380994640343475, 0.8951589964364352, 0.4731006916078465, -0.011387707350102265, -0.5381249112953891, -1.0844317743593057, -1.6262666097270189, -2.139442437280076, -2.6008633456283663, -2.9897152620848506, -3.2885479301213083, -3.4841897782531475, -3.568445429782219, -3.5385364776372774, -3.397259302561012, -3.152848482534, -2.818549962395726, -2.411923799345315, -1.953911128404632, -1.4677131852516256, -0.9775410375966276, -0.5073024804443845, -0.07929686651155277, 0.2870108269923683, 0.5760687466264347, 0.7771088982894886, 0.8847596080239034, 0.8993629371326144, 0.8269760066919739, 0.6790523199021339, 0.4718167900647423, 0.22536532122610434, -0.037464510350496256, -0.29239175913119353, -0.5150892343628589, -0.682602775795435, -0.7747136750423648, -0.7751672711911379, -0.6726971155790354, -0.4617845150265218, -0.1431072087341558, 0.27635231351738837], 'positive_zeros': ['1.35176238200643169071789916647990', '2.71186632685840340404323915357516', '3.60191736160286866933116757354690', '5.11201887030831891432761688710777', '5.71726696045434833088435956042457', '6.86536183999845443653507492507991', '7.62554005630913192388611599452930', '8.880602516006217601798289818687784', '9.543538046471764630152849894926010'], 'prelabel': '2-560-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.477074395364276, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 451905880001945683, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35176238200643169071789916648', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71186632685840340404323915358', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60191736160286866933116757355', 'prec': 103}}
