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: \( 10.2763012571 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.072976639\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.051602276\) \(a_{7}=+0.223535808\) \(a_{8}=-0.353553391\) \(a_{9}=-0.994674410\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.793114431\) \(a_{12}=-0.036488320\) \(a_{13}=+0.998220851\) \(a_{14}=-0.158063686\) \(a_{15}=+0.032636145\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.043940513\) \(a_{18}=+0.703341020\) \(a_{19}=-0.906611330\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.016312892\) \(a_{22}=-1.267923374\) \(a_{23}=-1.699421614\) \(a_{24}=+0.025801138\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.705848733\) \(a_{27}=+0.145564635\) \(a_{28}=+0.111767904\) \(a_{29}=-0.010392689\) \(a_{30}=-0.023077240\)
\(a_{31}=-0.925532349\) \(a_{32}=-0.176776695\) \(a_{33}=-0.130855465\) \(a_{34}=+0.031070635\) \(a_{35}=-0.099968252\)
\(a_{36}=-0.497337205\) \(a_{37}=-0.663585882\) \(a_{38}=+0.641071019\) \(a_{39}=-0.072846803\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.351693018\) \(a_{42}=+0.011534957\) \(a_{43}=-1.463691162\) \(a_{44}=+0.896557216\) \(a_{45}=+0.444831919\)
\(a_{46}=+1.201672547\) \(a_{47}=-0.490899420\) \(a_{48}=-0.018244160\) \(a_{49}=-0.950031742\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.003206631\) \(a_{52}=+0.499110426\) \(a_{53}=-0.562264721\) \(a_{54}=-0.102929740\) \(a_{55}=-0.801905152\)
\(a_{56}=-0.079031843\) \(a_{57}=+0.066161448\) \(a_{58}=+0.007348741\) \(a_{59}=+0.752724199\) \(a_{60}=+0.016318073\)
\(a_{61}=+0.571787049\) \(a_{62}=+0.654450200\) \(a_{63}=-0.222345348\) \(a_{64}=+0.125000000\) \(a_{65}=-0.446417936\)
\(a_{66}=+0.092528787\) \(a_{67}=+0.744312754\) \(a_{68}=-0.021970257\) \(a_{69}=+0.124018078\) \(a_{70}=+0.070688229\)
\(a_{71}=-1.474046058\) \(a_{72}=+0.351670510\) \(a_{73}=-1.946976426\) \(a_{74}=+0.469226077\) \(a_{75}=-0.014595328\)
\(a_{76}=-0.453305665\) \(a_{77}=+0.400825287\) \(a_{78}=+0.051510468\) \(a_{79}=+0.245073053\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.984051598\) \(a_{82}=-0.248684518\) \(a_{83}=+1.249826340\) \(a_{84}=-0.008156446\) \(a_{85}=+0.019650795\)
\(a_{86}=+1.034985946\) \(a_{87}=+0.000758409\) \(a_{88}=-0.633961687\) \(a_{89}=-0.712987161\) \(a_{90}=-0.314543667\)
\(a_{91}=+0.223138095\) \(a_{92}=-0.849710807\) \(a_{93}=+0.067542159\) \(a_{94}=+0.347118309\) \(a_{95}=+0.405448912\)
\(a_{96}=+0.012900569\) \(a_{97}=-1.034909589\) \(a_{98}=+0.671773887\) \(a_{99}=-1.783565138\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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