-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1355799926117008495641678559159', 'a10': 2, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': -1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.67781535470485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [7, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '7098.1', 'coefficient_field': '1.1.1.1', 'conductor': 7098, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -2, 5], [1, 1], [1, 0, 11], [1], [1, -2, 17], [1, -4, 19], [1, -6, 23], [1, 0, 29], [1, 0, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, 8, 47], [1, -4, 53], [1, -6, 59], [1, -12, 61], [1, 2, 67], [1, 0, 71], [1, -14, 73], [1, 0, 79], [1, 14, 83], [1, 4, 89], [1, 2, 97], [1, 2, 101], [1, 14, 103], [1, 12, 107], [1, 6, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, 1], 1]], [[[1, 0, 11], 1]], [1], [[[1, -2, 17], 1]], [[[1, -4, 19], 1]], [[[1, -6, 23], 1]], [[[1, 0, 29], 1]], [[[1, 0, 31], 1]], [[[1, -2, 37], 1]], [[[1, 0, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -4, 53], 1]], [[[1, -6, 59], 1]], [[[1, -12, 61], 1]], [[[1, 2, 67], 1]], [[[1, 0, 71], 1]], [[[1, -14, 73], 1]], [[[1, 0, 79], 1]], [[[1, 14, 83], 1]], [[[1, 4, 89], 1]], [[[1, 2, 97], 1]], [[[1, 2, 101], 1]], [[[1, 14, 103], 1]], [[[1, 12, 107], 1]], [[[1, 6, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 81, 'label': '2-7098-1.1-c1-0-81', 'leading_term': '5.17747627061621358076169875249000000000000000000000000000000000000000000000000000000000000', '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/7098/2/a/bc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [5.177476270616213, 5.167170550862346, 5.1361684701536205, 5.084224001761032, 5.010955677281054, 4.915887582950799, 4.798503204740173, 4.6583089733787215, 4.494903957062892, 4.308052005953175, 4.09775273644951, 3.8643080035642106, 3.60838088934659, 3.3310446815856434, 3.0338197884352245, 2.718697003430885, 2.3881459868713426, 2.0451082592155454, 1.692974412113873, 1.335545638198921, 0.9769800673606841, 0.6217247788064552, 0.27443473583272593, -0.06011973826635983, -0.3771549647374452, -0.6719830756162504, -0.9401257126469916, -1.1774293613618374, -1.3801792086800675, -1.5452082650575492, -1.6699984233552019, -1.7527701463885872, -1.7925575916496623, -1.7892662003703048, -1.7437101012012508, -1.6576271050730231, -1.5336695922766526, -1.3753702065303672, -1.1870819609525574, -0.973893110845104, -0.7415179379400546, -0.49616539719117386, -0.2443883747881928, 0.00708293237133935, 0.2515193080496532, 0.48237766573519925, 0.6934877556702349, 0.8792347869628339, 1.034732143587109, 1.1559783766561438, 1.2399928526884496, 1.2849248344898396, 1.2901313668442829, 1.2562201253980334, 1.185054348503757, 1.0797180856067559, 0.9444412322392693, 0.7844851446867356, 0.6059909952613234, 0.4157943959148836, 0.22121113481751947, 0.029800087449890746, -0.15088956880180718, -0.31357883664290126, -0.45151844579914446, -0.558738476951685, -0.630279022208757, -0.6623931113702533, -0.6527137327794192, -0.6003777024726945, -0.5061003686558271, -0.37219665061863444, -0.20254566014645442, -0.00249808600704112, 0.22127242507994316, 0.46097055581183255, 0.707927865253292, 0.9528912214401086, 1.1863419692480701, 1.398835172613784, 1.581347096516339, 1.7256183187224903, 1.8244795331267956, 1.8721472594401394, 1.8644773245668775, 1.7991651269457183, 1.675883314287337, 1.4963495554299682, 1.2643195070458308, 0.985502786431272, 0.6674026678449301, 0.319083214618095, -0.04912947333809394, -0.4260023972090995, -0.7997951303922094, -1.1586894009539939, -1.491232879084648, -1.7867801539701234, -2.0359134195276836, -2.2308256134585505, -2.3656496882188596, -2.436719326309574, -2.4427487066460665, -2.384921815251957, -2.266885175874329, -2.0946416330639073, -1.876346809522598, -1.622013922920008, -1.3431366169095196, -1.0522431656547124, -0.762398683890249, -0.48667466002130677, -0.2376070914334494, -0.026665628002975998, 0.13624365778211361, 0.24322000087882217, 0.28873400696125234, 0.26990051103031587, 0.18664416543780887, 0.04174788626012665, -0.15922095164168143, -0.40810653996074026, -0.6944775433695498, -1.0060462984510457, -1.3291787594921864, -1.6494752096860552, -1.9523980563354444, -2.2239202545103556, -2.451166211057208, -2.6230165230946865, -2.7306486659917697, -2.767987774920668, -2.7320449142323486, -2.6231245960604093, -2.4448886353079553, -2.204269504857765, -1.9112329331619702, -1.5783962851710922, -1.2205159855561831, -0.8538635719918629, -0.4955156043898148, -0.16258732291142736, 0.12855660237979227, 0.36307885253710026, 0.5283979140343813, 0.614833497325263, 0.616136987128046, 0.5298793211728544, 0.3576744261441417, 0.10522325394417298, -0.2178287246110502, -0.5982193321683206, -1.0195729936848537, -1.4630613582726273, -1.9081952723638025, -2.333715341307314, -2.7185428399181264, -3.0427488768929742, -3.288497712671877, -3.4409201243687177, -3.4888747639972197, -3.4255595308785565, -3.248940942293307, -2.961977110826679, -2.572618909281797, -2.0935838377844, -1.5419075587920352, -0.9382885524996152, -0.30625137033973127, 0.32883696142611313, 0.940855170148267, 1.5040725244890156, 1.9942983911713554, 2.389983422867297, 2.673220385409474, 2.83059627905913, 2.853853441182258, 2.7403255031210865, 2.4931240682971247, 2.121063340717757, 1.638322144260653, 1.0638552601088063, 0.42057817160679895, -0.26563945695645685, -0.9671264970758154, -1.655656455296482, -2.3037288229143433, -2.885824959754165, -3.379578129582454, -3.7668005994085085, -4.034316866775644, -4.174560839896334, -4.185905781258353, -4.07270853268737, -3.84506336835347, -3.5182751024569896, -3.1120751042305512, -2.649616936598094, -2.156299762617263, -1.658476851130514, -1.1821129567774002, -0.751457675974021, -0.3878018672431072, -0.10838081492079495, 0.07451887431203125, 0.15420133646227235, 0.1299174044685692, 0.006913577939983048, -0.20383139724169005, -0.48617178160444086, -0.81963572393445, -1.1805010538203395, -1.5430526485137834, -1.8809579997540706, -2.1686907083732003, -2.3829282831090413, -2.503851043328215, -2.516273158154802, -2.410544732919535, -2.183175020246755, -1.8371407514672145, -1.3818595651211762, -0.8328257443463026, -0.21092307644887445, 0.4585533045435153, 1.147118643185675, 1.8245031187499745, 2.460168239518788, 3.024857440352019, 3.492100617150386, 3.839593900200652, 4.050381704291083, 4.113777741490832, 4.02597477446536, 3.7903087654293475, 3.417160921815488, 2.923500022092504, 2.33208632455318, 1.6703763052984997, 0.9691834672568121, 0.2611636327397569, -0.4207972557026457, -1.0452092953774976, -1.5835341440554236, -2.011588758730082, -2.3107240411313006, -2.4687168868797698, -2.4803293037282277, -2.3475059862916696, -2.079201056032351, -1.6908445463496091, -1.2034785454856962, -0.6426106386725817, -0.03684743137685954, 0.5836173588172043, 1.1885781432507745, 1.7493708564395114], 'positive_zeros': ['1.06953755701524424721279135111003', '2.01429250183908316404630683990937', '2.86686881991954095044885621744631', '3.42242408032929244291327889097477', '4.30634018946787709247788061956186', '5.30363454067779583882706909957103', '5.58896491836355001037497914219611', '6.63455642689407620522674667299532', '7.00071836734694839256778717960965', '7.897513703206257946329977259510773'], 'prelabel': '2-7098-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.528466998978268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 908481420297379413, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06953755701524424721279135111', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01429250183908316404630683991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86686881991954095044885621745', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 56.67781535470485, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 7098, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 2, 1, -1, 1, 1, 2, 0, 1, 0, -1, 2, 1, 2, 1, 4, 2, -1, 0, 6, 1, -1, 0, 1, -1, 0, 2, 0, 1, 0, 2, -2, 1, 2, 4, 0, 2, 0, -1, -4, 0, 2, 6, -8, 1, 1, -1, 2, 0, 4, 1, 0, -1, 4, 0, 6, 2, 12, 0, -1, 1, 0, 0, -2, 2, 6, -2, 0, 1, 14, 2, -1, 4, 0, 0, 0, 2, 1, 0, -14, -1, 4, -4, 0, 0, -4, 2, 0, 6, 0, -8, 8, 1, -2, 1, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -4, 53], 'euler59': [1, -6, 59], 'euler61': [1, -12, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 14, 83], 'euler89': [1, 4, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -2, 5], [1, 1, 0], [1, 0, 11], [1, 0, 0], [1, -2, 17], [1, -4, 19], [1, -6, 23], [1, 0, 29], [1, 0, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, 8, 47], [1, -4, 53], [1, -6, 59], [1, -12, 61], [1, 2, 67], [1, 0, 71], [1, -14, 73], [1, 0, 79], [1, 14, 83], [1, 4, 89], [1, 2, 97]], 'index': 81, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7098/bc', 'ModularForm/GL2/Q/holomorphic/7098/2/a/bc/1/1', 'ModularForm/GL2/Q/holomorphic/7098/2/a/bc'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-7098-1.1-c1-0-81', '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': '2-7098-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.528466998978268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 908481420297379413, 'z1': {'__RealLiteral__': 0, 'data': '1.06953755701524424721279135111', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21945340
{'Lhash': '1355799926117008495641678559159', 'Lhash_array': ['1355799926117008495641678559159'], 'label': '2-7098-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7098/2/a/bc'}
-
id: 24578148
{'Lhash': '1355799926117008495641678559159', 'Lhash_array': ['1355799926117008495641678559159'], 'label': '2-7098-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7098/2/a/bc/1/1'}
-
id: 33483
{'Lhash': '908481420297379413', 'Lhash_array': ['908481420297379413'], 'label': '2-7098-1.1-c1-0-81', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7098/bc'}