Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.10146081193 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.623813551\) \(a_{3}=-1.581126254\) \(a_{4}=-0.610856654\) \(a_{5}=+0.694965679\)
\(a_{6}=-0.986327982\) \(a_{7}=-0.377964473\) \(a_{8}=-1.004874209\) \(a_{9}=+1.499960230\) \(a_{10}=+0.433529008\)
\(a_{11}=-1.409091786\) \(a_{12}=+0.965841493\) \(a_{13}=+0.048781475\) \(a_{14}=-0.235779360\) \(a_{15}=-1.098828481\)
\(a_{16}=-0.015997494\) \(a_{17}=+0.192364225\) \(a_{18}=+0.935695517\) \(a_{19}=+0.550397187\) \(a_{20}=-0.424524409\)
\(a_{21}=+0.597609551\) \(a_{22}=-0.879010551\) \(a_{23}=-1.161971264\) \(a_{24}=+1.588832994\) \(a_{25}=-0.517022705\)
\(a_{26}=+0.030430545\) \(a_{27}=-0.790500246\) \(a_{28}=+0.230882113\) \(a_{29}=+0.373249306\) \(a_{30}=-0.685464096\)
\(a_{31}=-0.445257274\) \(a_{32}=+0.994894755\) \(a_{33}=+2.227952017\) \(a_{34}=+0.119999410\) \(a_{35}=-0.262672337\)
\(a_{36}=-0.916260687\) \(a_{37}=-1.831500023\) \(a_{38}=+0.343345224\) \(a_{39}=-0.077129672\) \(a_{40}=-0.698353087\)
\(a_{41}=-0.207479469\) \(a_{42}=+0.372796936\) \(a_{43}=+0.625133676\) \(a_{44}=+0.860753094\) \(a_{45}=+1.042420880\)
\(a_{46}=-0.724853420\) \(a_{47}=-0.180722220\) \(a_{48}=+0.025294058\) \(a_{49}=+0.142857143\) \(a_{50}=-0.322525769\)
\(a_{51}=-0.304152127\) \(a_{52}=-0.029798489\) \(a_{53}=+1.280438892\) \(a_{54}=-0.493124765\) \(a_{55}=-0.979270430\)
\(a_{56}=+0.379806751\) \(a_{57}=-0.870247443\) \(a_{58}=+0.232837975\) \(a_{59}=-1.050517223\) \(a_{60}=+0.671226689\)
\(a_{61}=+0.721884579\) \(a_{62}=-0.277757521\) \(a_{63}=-0.566931678\) \(a_{64}=+0.636626324\) \(a_{65}=+0.033901451\)
\(a_{66}=+1.389826659\) \(a_{67}=-0.838654912\) \(a_{68}=-0.117506967\) \(a_{69}=+1.837223271\) \(a_{70}=-0.163858563\)
\(a_{71}=+0.298503296\) \(a_{72}=-1.507271350\) \(a_{73}=-0.584408616\) \(a_{74}=-1.142514532\) \(a_{75}=+0.817478172\)
\(a_{76}=-0.336213784\) \(a_{77}=+0.532586634\) \(a_{78}=-0.048114534\) \(a_{79}=+0.212474145\) \(a_{80}=-0.011117710\)
\(a_{81}=-0.250079538\) \(a_{82}=-0.129428504\) \(a_{83}=-0.855408263\) \(a_{84}=-0.365053771\) \(a_{85}=+0.133686534\)
\(a_{86}=+0.389966858\) \(a_{87}=-0.590154277\) \(a_{88}=+1.415959994\) \(a_{89}=+0.898195407\) \(a_{90}=+0.650276271\)
\(a_{91}=-0.018437665\) \(a_{92}=+0.709797878\) \(a_{93}=+0.704007966\) \(a_{94}=-0.112736969\) \(a_{95}=+0.382507155\)
\(a_{96}=-1.573054217\) \(a_{97}=-1.699837957\) \(a_{98}=+0.089116222\) \(a_{99}=-2.113581640\) \(a_{100}=+0.315826759\)

Showing 100 of 1228 available coefficients

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