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: \( 31.9875849983 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.072200766\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.758160432\) \(a_{7}=-0.181080411\) \(a_{8}=+0.353553391\) \(a_{9}=+0.149614482\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.728992676\) \(a_{12}=+0.536100383\) \(a_{13}=-0.145308459\) \(a_{14}=-0.128043187\) \(a_{15}=-0.479502759\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.196406341\) \(a_{18}=+0.105793415\) \(a_{19}=+0.456782629\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.194154555\) \(a_{22}=-1.222582446\) \(a_{23}=-1.320479048\) \(a_{24}=+0.379080216\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.102748597\) \(a_{27}=-0.911784004\) \(a_{28}=-0.090540206\) \(a_{29}=+1.502252390\) \(a_{30}=-0.339059653\)
\(a_{31}=+0.271183049\) \(a_{32}=+0.176776695\) \(a_{33}=-1.853827271\) \(a_{34}=-0.138880256\) \(a_{35}=+0.080981622\)
\(a_{36}=+0.074807241\) \(a_{37}=+1.875246569\) \(a_{38}=+0.322994095\) \(a_{39}=-0.155799841\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.071639722\) \(a_{42}=-0.137288003\) \(a_{43}=+0.606860290\) \(a_{44}=-0.864496338\) \(a_{45}=-0.066909630\)
\(a_{46}=-0.933719689\) \(a_{47}=+0.690982965\) \(a_{48}=+0.268050191\) \(a_{49}=-0.967209885\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.210587029\) \(a_{52}=-0.072654230\) \(a_{53}=+0.504557627\) \(a_{54}=-0.644728652\) \(a_{55}=+0.773229031\)
\(a_{56}=-0.064021593\) \(a_{57}=+0.489762685\) \(a_{58}=+1.062252852\) \(a_{59}=-0.541190959\) \(a_{60}=-0.239751380\)
\(a_{61}=+0.015369023\) \(a_{62}=+0.191755373\) \(a_{63}=-0.027092252\) \(a_{64}=+0.125000000\) \(a_{65}=+0.064983919\)
\(a_{66}=-1.310853834\) \(a_{67}=-0.354533685\) \(a_{68}=-0.098203170\) \(a_{69}=-1.415818646\) \(a_{70}=+0.057262654\)
\(a_{71}=+1.792708781\) \(a_{72}=+0.052896707\) \(a_{73}=+1.393938037\) \(a_{74}=+1.325999565\) \(a_{75}=+0.214440153\)
\(a_{76}=+0.228391315\) \(a_{77}=+0.313086704\) \(a_{78}=-0.110167124\) \(a_{79}=+0.823550262\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.127229989\) \(a_{82}=+0.757763714\) \(a_{83}=+1.459145905\) \(a_{84}=-0.097077278\) \(a_{85}=+0.087835586\)
\(a_{86}=+0.429115026\) \(a_{87}=+1.610716163\) \(a_{88}=-0.611291223\) \(a_{89}=+0.245439998\) \(a_{90}=-0.047312253\)
\(a_{91}=+0.026312516\) \(a_{92}=-0.660239524\) \(a_{93}=+0.290762672\) \(a_{94}=+0.488598740\) \(a_{95}=-0.204279402\)
\(a_{96}=+0.189540108\) \(a_{97}=+0.075779878\) \(a_{98}=-0.683920668\) \(a_{99}=-0.258682343\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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