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: \( 24.5253828384 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.938990146\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.663966299\) \(a_{7}=+1.646675024\) \(a_{8}=+0.353553391\) \(a_{9}=-0.118297506\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.130279290\) \(a_{12}=-0.469495073\) \(a_{13}=+0.032489875\) \(a_{14}=+1.164375076\) \(a_{15}=+0.419929159\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.159908552\) \(a_{18}=-0.083648969\) \(a_{19}=-0.486099358\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.546211621\) \(a_{22}=-0.092121369\) \(a_{23}=+0.327812621\) \(a_{24}=-0.331983150\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.022973811\) \(a_{27}=+1.050070338\) \(a_{28}=+0.823337512\) \(a_{29}=+0.460311486\) \(a_{30}=+0.296934756\)
\(a_{31}=-1.569126205\) \(a_{32}=+0.176776695\) \(a_{33}=+0.122330969\) \(a_{34}=-0.820179202\) \(a_{35}=-0.736415458\)
\(a_{36}=-0.059148753\) \(a_{37}=+1.317333551\) \(a_{38}=-0.343724152\) \(a_{39}=-0.030507673\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.290083231\) \(a_{42}=-1.093336722\) \(a_{43}=-0.053984627\) \(a_{44}=-0.065139645\) \(a_{45}=+0.052904253\)
\(a_{46}=+0.231798528\) \(a_{47}=+1.625124716\) \(a_{48}=-0.234747536\) \(a_{49}=+1.711538635\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.089142700\) \(a_{52}=+0.016244938\) \(a_{53}=-1.012786029\) \(a_{54}=+0.742511857\) \(a_{55}=+0.058262670\)
\(a_{56}=+0.582187538\) \(a_{57}=+0.456442507\) \(a_{58}=+0.325489373\) \(a_{59}=-0.247766396\) \(a_{60}=+0.209964580\)
\(a_{61}=-1.534065437\) \(a_{62}=-1.109539780\) \(a_{63}=-0.194797549\) \(a_{64}=+0.125000000\) \(a_{65}=-0.014529914\)
\(a_{66}=+0.086501058\) \(a_{67}=+0.717611681\) \(a_{68}=-0.579954276\) \(a_{69}=-0.307812821\) \(a_{70}=-0.520724364\)
\(a_{71}=+1.094730914\) \(a_{72}=-0.041824484\) \(a_{73}=-1.063066368\) \(a_{74}=+0.931495487\) \(a_{75}=-0.187798029\)
\(a_{76}=-0.243049679\) \(a_{77}=-0.214527653\) \(a_{78}=-0.021572182\) \(a_{79}=-0.897492113\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.867708194\) \(a_{82}=+0.205119820\) \(a_{83}=-0.874191771\) \(a_{84}=-0.773105810\) \(a_{85}=+0.518726874\)
\(a_{86}=-0.038172896\) \(a_{87}=-0.432227949\) \(a_{88}=-0.046060685\) \(a_{89}=-1.728378175\) \(a_{90}=+0.037408956\)
\(a_{91}=+0.053500266\) \(a_{92}=+0.163906311\) \(a_{93}=+1.473394043\) \(a_{94}=+1.149136707\) \(a_{95}=+0.217390242\)
\(a_{96}=-0.165991575\) \(a_{97}=-1.650984766\) \(a_{98}=+1.210240575\) \(a_{99}=+0.015411715\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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