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: \( 25.4802073427 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.278477174\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.904019879\) \(a_{7}=-0.453209243\) \(a_{8}=-0.353553391\) \(a_{9}=+0.634503884\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.050357782\) \(a_{12}=-0.639238587\) \(a_{13}=-1.133591124\) \(a_{14}=+0.320467329\) \(a_{15}=+0.571752374\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.727231078\) \(a_{18}=-0.448661999\) \(a_{19}=-0.903974379\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.579417672\) \(a_{22}=-0.035608329\) \(a_{23}=-0.398819364\) \(a_{24}=+0.452009940\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.801569971\) \(a_{27}=+0.467278441\) \(a_{28}=-0.226604621\) \(a_{29}=-0.262169196\) \(a_{30}=-0.404289981\)
\(a_{31}=-0.791243983\) \(a_{32}=-0.176776695\) \(a_{33}=-0.064381274\) \(a_{34}=-0.514230027\) \(a_{35}=+0.202681335\)
\(a_{36}=+0.317251942\) \(a_{37}=+1.776237488\) \(a_{38}=+0.639206413\) \(a_{39}=+1.449270376\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.454917000\) \(a_{42}=-0.409710165\) \(a_{43}=-1.569433839\) \(a_{44}=+0.025178891\) \(a_{45}=-0.283758763\)
\(a_{46}=+0.282007877\) \(a_{47}=+0.353544321\) \(a_{48}=-0.319619293\) \(a_{49}=-0.794601382\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.929748334\) \(a_{52}=-0.566795562\) \(a_{53}=-0.959414143\) \(a_{54}=-0.330415755\) \(a_{55}=-0.022520685\)
\(a_{56}=+0.160233664\) \(a_{57}=+1.155710609\) \(a_{58}=+0.185381616\) \(a_{59}=-1.599706991\) \(a_{60}=+0.285876187\)
\(a_{61}=-0.933136160\) \(a_{62}=+0.559493986\) \(a_{63}=-0.287563025\) \(a_{64}=+0.125000000\) \(a_{65}=+0.506957362\)
\(a_{66}=+0.045524436\) \(a_{67}=-0.969500917\) \(a_{68}=+0.363615539\) \(a_{69}=+0.509881453\) \(a_{70}=-0.143317346\)
\(a_{71}=-0.615850778\) \(a_{72}=-0.224331000\) \(a_{73}=+0.150239323\) \(a_{74}=-1.255989573\) \(a_{75}=-0.255695435\)
\(a_{76}=-0.451987189\) \(a_{77}=-0.022822612\) \(a_{78}=-1.024788911\) \(a_{79}=-1.318827631\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.231908705\) \(a_{82}=+0.321674895\) \(a_{83}=+0.158064495\) \(a_{84}=+0.289708836\) \(a_{85}=-0.325227625\)
\(a_{86}=+1.109757310\) \(a_{87}=+0.335177333\) \(a_{88}=-0.017804164\) \(a_{89}=-0.869985623\) \(a_{90}=+0.200647746\)
\(a_{91}=+0.513753975\) \(a_{92}=-0.199409682\) \(a_{93}=+1.011587371\) \(a_{94}=-0.249993587\) \(a_{95}=+0.404269632\)
\(a_{96}=+0.226004970\) \(a_{97}=-1.441930911\) \(a_{98}=+0.561868026\) \(a_{99}=+0.031952208\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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