Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 8.45261564535 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.271088354\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.191688413\) \(a_{7}=+0.673628224\) \(a_{8}=+0.353553391\) \(a_{9}=-0.926511105\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.398373200\) \(a_{12}=+0.135544177\) \(a_{13}=+1.654677485\) \(a_{14}=+0.476327085\) \(a_{15}=+0.121234397\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.863960267\) \(a_{18}=-0.655142285\) \(a_{19}=+0.947785757\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.182612766\) \(a_{22}=+0.281692391\) \(a_{23}=-0.038459254\) \(a_{24}=+0.095844207\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.170033670\) \(a_{27}=-0.522254724\) \(a_{28}=+0.336814112\) \(a_{29}=-0.887427571\) \(a_{30}=+0.085725664\)
\(a_{31}=-1.115168568\) \(a_{32}=+0.176776695\) \(a_{33}=+0.107994335\) \(a_{34}=+0.610912163\) \(a_{35}=+0.301255700\)
\(a_{36}=-0.463255552\) \(a_{37}=+0.827010203\) \(a_{38}=+0.670185736\) \(a_{39}=+0.448563795\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.822146034\) \(a_{42}=+0.129126725\) \(a_{43}=+0.308511525\) \(a_{44}=+0.199186600\) \(a_{45}=-0.414348362\)
\(a_{46}=-0.027194799\) \(a_{47}=-1.099820495\) \(a_{48}=+0.067772088\) \(a_{49}=-0.546225016\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.234209566\) \(a_{52}=+0.827338742\) \(a_{53}=+1.551575033\) \(a_{54}=-0.369289857\) \(a_{55}=+0.178157911\)
\(a_{56}=+0.238163543\) \(a_{57}=+0.256933681\) \(a_{58}=-0.627506053\) \(a_{59}=-0.443946703\) \(a_{60}=+0.060617199\)
\(a_{61}=+0.303210777\) \(a_{62}=-0.788543256\) \(a_{63}=-0.624124030\) \(a_{64}=+0.125000000\) \(a_{65}=+0.739994267\)
\(a_{66}=+0.076363527\) \(a_{67}=-1.916311188\) \(a_{68}=+0.431980133\) \(a_{69}=-0.010425856\) \(a_{70}=+0.213019948\)
\(a_{71}=+1.545393675\) \(a_{72}=-0.327571142\) \(a_{73}=-1.033714670\) \(a_{74}=+0.584784523\) \(a_{75}=+0.054217671\)
\(a_{76}=+0.473892879\) \(a_{77}=+0.268355431\) \(a_{78}=+0.317182501\) \(a_{79}=-0.718510960\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.784933931\) \(a_{82}=-1.288451817\) \(a_{83}=+0.651158680\) \(a_{84}=+0.091306383\) \(a_{85}=+0.386374777\)
\(a_{86}=+0.218150591\) \(a_{87}=-0.240571279\) \(a_{88}=+0.140846196\) \(a_{89}=-1.671277900\) \(a_{90}=-0.292988537\)
\(a_{91}=+1.114637455\) \(a_{92}=-0.019229627\) \(a_{93}=-0.302309211\) \(a_{94}=-0.777690530\) \(a_{95}=+0.423862676\)
\(a_{96}=+0.047922103\) \(a_{97}=-0.478436200\) \(a_{98}=-0.386239413\) \(a_{99}=-0.369097193\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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