-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2459250633492878934553960438144', 'a10': [0.0, 0.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.7071067811865476, 0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5769191546037508, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 17], 'central_character': '1156.179', 'coefficient_field': 'CDF', 'conductor': 1156, 'conductor_radical': 34, 'conjugate': '1611297000223361924149097834629', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.4142135623730951, -1.4142135623730951], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-34e2-68.43-c0-0-2', 'leading_term': '1.5187522816774512186344161868666', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1156/1/g/a/179/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.5187522816774512, 1.5779182485922114, 1.6580515354043006, 1.7589299887412302, 1.8789778974801676, 2.0155916081370204, 2.1654776912976583, 2.3249225030587435, 2.489971095199312, 2.656530683556457, 2.8204260730918644, 2.9774320282231184, 3.123300340743553, 3.2537923424140978, 3.3647223962267003, 3.4520144443694636, 3.511771508706214, 3.5403566661150063, 3.534483128440933, 3.4913104456922293, 3.408543412774549, 3.2845299426457637, 3.1183539535104985, 2.909919203882387, 2.6600200052730845, 2.3703948594778237, 2.043759317219715, 1.6838147459619617, 1.2952302313804893, 0.8835955182090297, 0.45534371451023986, 0.01764342464888228, -0.42173898092079676, -0.8546051346599864, -1.2725155002304214, -1.6670011268328582, -2.0297910887863297, -2.3530493558115113, -2.6296139685874005, -2.853230714270389, -3.0187730529962384, -3.1224398788363867, -3.161922839559536, -3.1365354113604287, -3.047296738163919, -2.896964397437835, -2.6900117282213394, -2.4325471195236443, -2.1321746602298317, -1.7977977323360617, -1.4393694116331013, -1.0675958366918015, -0.6936009228317435, -0.3285628327267935, 0.01666563100948148, 0.33193916988583716, 0.6081902180620785, 0.8377724315431063, 1.0147628375999984, 1.1352088958339919, 1.1973082104398436, 1.2015107372421303, 1.1505359990000237, 1.0493009787209033, 0.9047578954767622, 0.725644847297779, 0.5221561769128702, 0.3055432088999368, 0.08765954331789146, -0.11953180720933401, -0.3044696529007558, -0.4565027116105996, -0.5663721664181008, -0.6266464452747424, -0.6320871300739753, -0.5799270994625011, -0.4700452021600361, -0.305025850849942, -0.0900967760688182, 0.16705640614828357, 0.45659441080647506, 0.7669370622361809, 1.0852688008523748, 1.3981159721274017, 1.6919706170837152, 1.953932185949812, 2.172336556697224, 2.3373411278891147, 2.441435677378065, 2.4798511689419773, 2.4508427029340982, 2.355828217806738, 2.199371150293533, 1.989002772438998, 1.7348879992544302, 1.4493467081208011, 1.1462506056559902, 0.8403229849885119, 0.5463749142924612, 0.27851610035715124, 0.04938155253709837, -0.13058401311681553, -0.2537434894621417, -0.3157495219625985, -0.31586039964025164, -0.2570663761668517, -0.14601249264104432, 0.007285447848551396, 0.1899238592787457, 0.38677408892503257, 0.5812948790264781, 0.7564549794729973, 0.8957184802515089, 0.9840398862394462, 1.0088131246304934, 0.9607188485909814, 0.8344177163079897, 0.6290437476758044, 0.34846117812634914, 0.0012600512078192485, -0.39952043388898634, -0.8369367687611209, -1.2909346293631565, -1.7393563794807914, -2.1591141478017244, -2.527468390047468, -2.8233431157902102, -3.0286037903778484, -3.12922278251399, -3.1162603723539752, -2.9865967808759044, -2.743362195751944, -2.3960268698018843, -1.9601313401347251, -1.4566567418240506, -0.9110559941863716, -0.35198714353844346, 0.19019085986006937, 0.6850833709075288, 1.103997128885731, 1.4216522201545658, 1.6177693953481271, 1.6784363742282633, 1.5971656913668761, 1.3755710269375931, 1.0236082041721912, 0.5593501781822278, 0.008291177194733696, -0.5977977367004377, -1.2224126016318662, -1.8261859702649288, -2.3689863022207445, -2.8121351913168615, -3.1206196564617974, -3.265172958491743, -3.2241009651079446, -2.9847420111848932, -2.5444660860903103, -1.911143180783643, -1.1030395020565575, -0.14813242736653723, 0.9171313038018507, 2.049576570823408, 3.2014518800343876, 4.322878163667761, 5.364460209410182, 6.279914179898453, 7.028560794511376, 7.577538804014077, 7.903607301504099, 7.99442753749431, 7.8492440712108005, 7.478919653033846, 6.905316174349078, 6.160053059789948, 5.282712209072281, 4.318592645000094, 3.316146194824493, 2.3242459540202853, 1.3894505392325605, 0.5534283720283241, -0.14930278581742928, -0.6931846792586385, -1.0628670463184835, -1.2538217417490056, -1.2722882110656537, -1.134558214031699, -0.8656496472825154, -0.4974582971229942, -0.06650978530046996, 0.38854039895907894, 0.829494824408669, 1.2211207022811474, 1.5334116613056967, 1.7434579533355248, 1.8368048856999573, 1.8082139682440903, 1.6617818044343005, 1.410415433248894, 1.0747066806994645, 0.681289098738921, 0.2607964080110239, -0.15443146592572551, -0.532731610021858, -0.8454217475262081, -1.0688615697153045, -1.1861267138754255, -1.1881782780713024, -1.0744471127713178, -0.8527943381982843, -0.538854619082416, -0.15481346088360026, 0.27228906096073785, 0.7126011751367797, 1.1356965361660367, 1.512838930834436, 1.8191058194086336, 2.0352123450006805, 2.148899631601463, 2.1557836345643246, 2.0596011788795776, 1.8718351736670364, 1.6107479703506207, 1.2998969172056605, 0.9662459319523317, 0.6380183008369035, 0.3424564448922221, 0.10366239005514252, -0.059312612844062244, -0.13397919575074493, -0.11540168701043367, -0.006590308479844744, 0.181740219448706, 0.43203015544601153, 0.7212879724050161, 1.0229486955656182, 1.3090323755226858, 1.5524323942082785, 1.7291511033721922, 1.8203023953920852, 1.8137172664641465, 1.7050181839661598, 1.498068976214764, 1.2047559648654949, 0.8441093984587686, 0.4408277426593938, 0.023316764776981646, -0.37860341611999143, -0.7361405238461813, -1.0239233841151727, -1.2221484341039581, -1.3182980926237637, -1.3082810997751138, -1.196889292119584, -0.9975191920726683, -0.7311661079964336, -0.4247584789082651], 'positive_zeros': ['1.94000668090253920983587136553953', '3.37186842420301803839305182207116', '4.27584797284342223247705736724605', '4.89797416652445988361001569565747', '6.26544091862923101944558774157502', '6.68481664619663487812150277936674', '7.43770911518328827387415129516410', '8.540129327357044549807926270714656', '9.188386244521097214075755138820071', '10.00903543783694252362392919977105'], 'prelabel': '2-34e2-68.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7595519433216867, 'root_angle': 0.47582148590088835, 'root_number': '0.075886018893623272943884011291181 + 0.99711649877859139336171925323720*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23791074295044418', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94000668090253920983587136554', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37186842420301803839305182207', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27584797284342223247705736725', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5769191546037508, 'bad_primes': [2, 17], 'central_character': '68.43', 'conductor': 1156, 'conductor_radical': 34, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1156/1/g/a/179/1'], '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': '2-34e2-68.43-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-34e2-68.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7595519433216867, 'root_angle': 0.23791074295044418, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94000668090253920983587136554', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2459250633492878934553960438144', 'Lhash_array': ['2459250633492878934553960438144'], 'label': '2-34e2-68.43-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1156/1/g/a/179/1'}