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: \( 10.1994943801 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.888171681\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.628032219\) \(a_{7}=-0.602337361\) \(a_{8}=+0.353553391\) \(a_{9}=-0.211151064\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.758502643\) \(a_{12}=-0.444085841\) \(a_{13}=-0.155517678\) \(a_{14}=-0.425916833\) \(a_{15}=-0.397202451\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.279807518\) \(a_{18}=-0.149306349\) \(a_{19}=+0.782621316\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.534978987\) \(a_{22}=+0.536342362\) \(a_{23}=+0.851050520\) \(a_{24}=-0.314016109\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.109967605\) \(a_{27}=+1.075710077\) \(a_{28}=-0.301168681\) \(a_{29}=+1.908360074\) \(a_{30}=-0.280864547\)
\(a_{31}=+0.250511898\) \(a_{32}=+0.176776695\) \(a_{33}=-0.673680567\) \(a_{34}=+0.904960575\) \(a_{35}=-0.269373457\)
\(a_{36}=-0.105575532\) \(a_{37}=-1.826729714\) \(a_{38}=+0.553396840\) \(a_{39}=+0.138126398\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.732431648\) \(a_{42}=+0.378287269\) \(a_{43}=+0.870803592\) \(a_{44}=+0.379251321\) \(a_{45}=-0.094429627\)
\(a_{46}=+0.601783594\) \(a_{47}=-1.261143854\) \(a_{48}=-0.222042920\) \(a_{49}=-0.637189703\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.136688795\) \(a_{52}=-0.077758839\) \(a_{53}=+0.199128115\) \(a_{54}=+0.760641890\) \(a_{55}=+0.339212694\)
\(a_{56}=-0.212958416\) \(a_{57}=-0.695102090\) \(a_{58}=+1.349414349\) \(a_{59}=+1.170153095\) \(a_{60}=-0.198601226\)
\(a_{61}=-1.644834146\) \(a_{62}=+0.177138662\) \(a_{63}=+0.127184175\) \(a_{64}=+0.125000000\) \(a_{65}=-0.069549620\)
\(a_{66}=-0.476364098\) \(a_{67}=+1.347094645\) \(a_{68}=+0.639903759\) \(a_{69}=-0.755878972\) \(a_{70}=-0.190475798\)
\(a_{71}=-0.394700591\) \(a_{72}=-0.074653175\) \(a_{73}=+0.065870495\) \(a_{74}=-1.291692968\) \(a_{75}=-0.177634336\)
\(a_{76}=+0.391310658\) \(a_{77}=-0.456874485\) \(a_{78}=+0.097670113\) \(a_{79}=+1.054783887\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.744264167\) \(a_{82}=+0.517907385\) \(a_{83}=+0.367418121\) \(a_{84}=+0.267489493\) \(a_{85}=+0.572347322\)
\(a_{86}=+0.615751125\) \(a_{87}=-1.694951399\) \(a_{88}=+0.268171181\) \(a_{89}=+0.839111258\) \(a_{90}=-0.066771829\)
\(a_{91}=+0.093674077\) \(a_{92}=+0.425525260\) \(a_{93}=-0.222497550\) \(a_{94}=-0.891763371\) \(a_{95}=+0.349998893\)
\(a_{96}=-0.157008055\) \(a_{97}=-1.020490530\) \(a_{98}=-0.450561160\) \(a_{99}=-0.160159167\) \(a_{100}=+0.099975586\)

Showing 100 of 148 available coefficients

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