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: \( 25.1274344211 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.719674160\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.215993260\) \(a_{7}=+1.820848222\) \(a_{8}=+0.353553391\) \(a_{9}=+1.957279216\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.202573479\) \(a_{12}=+0.859837080\) \(a_{13}=-1.701367804\) \(a_{14}=+1.287534126\) \(a_{15}=+0.769061664\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.187030193\) \(a_{18}=+1.384005406\) \(a_{19}=-0.368523454\) \(a_{20}=+0.223606798\)
\(a_{21}=+3.131265637\) \(a_{22}=-0.143241081\) \(a_{23}=+1.486428856\) \(a_{24}=+0.607996630\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.203048711\) \(a_{27}=+1.646208331\) \(a_{28}=+0.910424111\) \(a_{29}=+0.379048760\) \(a_{30}=+0.543808718\)
\(a_{31}=+0.598835226\) \(a_{32}=+0.176776695\) \(a_{33}=-0.348360378\) \(a_{34}=+0.132250318\) \(a_{35}=+0.814308080\)
\(a_{36}=+0.978639608\) \(a_{37}=-1.194455660\) \(a_{38}=-0.260585433\) \(a_{39}=-2.925798248\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.945143126\) \(a_{42}=+2.214139166\) \(a_{43}=+0.416096689\) \(a_{44}=-0.101286740\) \(a_{45}=+0.875321875\)
\(a_{46}=+1.051063924\) \(a_{47}=+0.600857516\) \(a_{48}=+0.429918540\) \(a_{49}=+2.315488249\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.321630990\) \(a_{52}=-0.850683902\) \(a_{53}=-0.774480328\) \(a_{54}=+1.164045074\) \(a_{55}=-0.090593614\)
\(a_{56}=+0.643767063\) \(a_{57}=-0.633740261\) \(a_{58}=+0.268027949\) \(a_{59}=+0.171218087\) \(a_{60}=+0.384530832\)
\(a_{61}=-1.121458781\) \(a_{62}=+0.423440449\) \(a_{63}=+3.563908380\) \(a_{64}=+0.125000000\) \(a_{65}=-0.760874813\)
\(a_{66}=-0.246327986\) \(a_{67}=-1.505202894\) \(a_{68}=+0.093515096\) \(a_{69}=+2.556173295\) \(a_{70}=+0.575802766\)
\(a_{71}=+0.598355625\) \(a_{72}=+0.692002703\) \(a_{73}=-0.706260807\) \(a_{74}=-0.844607697\) \(a_{75}=+0.343934832\)
\(a_{76}=-0.184261727\) \(a_{77}=-0.368855560\) \(a_{78}=-2.068851782\) \(a_{79}=+1.518295083\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.873662712\) \(a_{82}=+0.668317114\) \(a_{83}=-0.587666822\) \(a_{84}=+1.565632818\) \(a_{85}=+0.083642445\)
\(a_{86}=+0.294224790\) \(a_{87}=+0.651840359\) \(a_{88}=-0.071620540\) \(a_{89}=+1.562422915\) \(a_{90}=+0.618946034\)
\(a_{91}=-3.097932541\) \(a_{92}=+0.743214428\) \(a_{93}=+1.029801464\) \(a_{94}=+0.424870424\) \(a_{95}=-0.164808699\)
\(a_{96}=+0.303998315\) \(a_{97}=-1.110675839\) \(a_{98}=+1.637297443\) \(a_{99}=-0.396492861\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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