Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 26.444565745 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.695997263\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.199251166\) \(a_{7}=-1.491320378\) \(a_{8}=+0.353553391\) \(a_{9}=+1.876406717\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.429384934\) \(a_{12}=+0.847998632\) \(a_{13}=-1.156128634\) \(a_{14}=-1.054522752\) \(a_{15}=-0.758473034\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.120542295\) \(a_{18}=+1.326819914\) \(a_{19}=+1.529822569\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.529275279\) \(a_{22}=-0.303620998\) \(a_{23}=+1.120053866\) \(a_{24}=+0.599625583\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.817506397\) \(a_{27}=+1.486383394\) \(a_{28}=-0.745660189\) \(a_{29}=-0.387824780\) \(a_{30}=-0.536321426\)
\(a_{31}=+0.600095807\) \(a_{32}=+0.176776695\) \(a_{33}=-0.728235672\) \(a_{34}=+0.792343055\) \(a_{35}=+0.666938748\)
\(a_{36}=+0.938203359\) \(a_{37}=-1.298177502\) \(a_{38}=+1.081747912\) \(a_{39}=-1.960790999\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.961916645\) \(a_{42}=-1.788467701\) \(a_{43}=+0.015678006\) \(a_{44}=-0.214692467\) \(a_{45}=-0.839154595\)
\(a_{46}=+0.791997684\) \(a_{47}=-0.100488502\) \(a_{48}=+0.423999316\) \(a_{49}=+1.224036469\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.900436665\) \(a_{52}=-0.578064317\) \(a_{53}=+1.802395100\) \(a_{54}=+1.051031778\) \(a_{55}=+0.192026780\)
\(a_{56}=-0.527261376\) \(a_{57}=+2.594574890\) \(a_{58}=-0.274233532\) \(a_{59}=-0.085643100\) \(a_{60}=-0.379236517\)
\(a_{61}=+1.231120043\) \(a_{62}=+0.424331815\) \(a_{63}=-2.798323574\) \(a_{64}=+0.125000000\) \(a_{65}=+0.517036443\)
\(a_{66}=-0.514940382\) \(a_{67}=-0.361147052\) \(a_{68}=+0.560271147\) \(a_{69}=+1.899608292\) \(a_{70}=+0.471596911\)
\(a_{71}=+0.751194184\) \(a_{72}=+0.663409957\) \(a_{73}=+0.228379287\) \(a_{74}=-0.917950115\) \(a_{75}=+0.339199453\)
\(a_{76}=+0.764911284\) \(a_{77}=+0.640350501\) \(a_{78}=-1.386488612\) \(a_{79}=+0.344625849\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.644495452\) \(a_{82}=+1.387284564\) \(a_{83}=+1.568270770\) \(a_{84}=-1.264637640\) \(a_{85}=-0.501121749\)
\(a_{86}=+0.011086025\) \(a_{87}=-0.657749766\) \(a_{88}=-0.151810499\) \(a_{89}=-0.388381304\) \(a_{90}=-0.593371904\)
\(a_{91}=+1.724158191\) \(a_{92}=+0.560026933\) \(a_{93}=+1.017760847\) \(a_{94}=-0.071056101\) \(a_{95}=-0.684157451\)
\(a_{96}=+0.299812791\) \(a_{97}=-0.724160252\) \(a_{98}=+0.865524487\) \(a_{99}=-0.805700774\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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