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: \( 19.7360025488 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.150835840\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.813763827\) \(a_{7}=+0.750037516\) \(a_{8}=-0.353553391\) \(a_{9}=+0.324423131\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.981569086\) \(a_{12}=-0.575417920\) \(a_{13}=-0.809284270\) \(a_{14}=-0.530356614\) \(a_{15}=-0.514669434\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.239940931\) \(a_{18}=-0.229401796\) \(a_{19}=-1.435269981\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.863170055\) \(a_{22}=-0.694074157\) \(a_{23}=-1.062618135\) \(a_{24}=+0.406881913\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.572250395\) \(a_{27}=+0.777478073\) \(a_{28}=+0.375018758\) \(a_{29}=+0.681670356\) \(a_{30}=+0.363926247\)
\(a_{31}=-0.202675107\) \(a_{32}=-0.176776695\) \(a_{33}=-1.129624884\) \(a_{34}=-0.169663859\) \(a_{35}=+0.335426974\)
\(a_{36}=+0.162211566\) \(a_{37}=+1.670286986\) \(a_{38}=+1.014889136\) \(a_{39}=+0.931353342\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.593003704\) \(a_{42}=+0.610353400\) \(a_{43}=+1.121690507\) \(a_{44}=+0.490784543\) \(a_{45}=+0.145086435\)
\(a_{46}=+0.751384489\) \(a_{47}=+0.344576611\) \(a_{48}=-0.287708960\) \(a_{49}=-0.437443724\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.276132622\) \(a_{52}=-0.404642135\) \(a_{53}=+0.464485753\) \(a_{54}=-0.549760018\) \(a_{55}=+0.438971040\)
\(a_{56}=-0.265178307\) \(a_{57}=+1.651760134\) \(a_{58}=-0.482013731\) \(a_{59}=+0.251990962\) \(a_{60}=-0.257334717\)
\(a_{61}=+1.410227489\) \(a_{62}=+0.143312943\) \(a_{63}=+0.243329520\) \(a_{64}=+0.125000000\) \(a_{65}=-0.361922928\)
\(a_{66}=+0.798765416\) \(a_{67}=+0.559984891\) \(a_{68}=+0.119970465\) \(a_{69}=+1.222899034\) \(a_{70}=-0.237182688\)
\(a_{71}=-0.679322421\) \(a_{72}=-0.114700898\) \(a_{73}=-0.450614248\) \(a_{74}=-1.181071254\) \(a_{75}=-0.230167168\)
\(a_{76}=-0.717634990\) \(a_{77}=+0.736213640\) \(a_{78}=-0.658566264\) \(a_{79}=+1.062682980\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.219172763\) \(a_{82}=+1.126423721\) \(a_{83}=-1.113360146\) \(a_{84}=-0.431585028\) \(a_{85}=+0.107304846\)
\(a_{86}=-0.793154964\) \(a_{87}=-0.784490677\) \(a_{88}=-0.347037079\) \(a_{89}=-1.850476856\) \(a_{90}=-0.102591602\)
\(a_{91}=-0.606993564\) \(a_{92}=-0.531309067\) \(a_{93}=+0.233245777\) \(a_{94}=-0.243652458\) \(a_{95}=-0.641872249\)
\(a_{96}=+0.203440957\) \(a_{97}=-1.210736368\) \(a_{98}=+0.309319424\) \(a_{99}=+0.318443716\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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