Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.35463469751 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.200609854\) \(a_{3}=-0.926533346\) \(a_{4}=-0.959755686\) \(a_{5}=-0.168179353\)
\(a_{6}=-0.185871720\) \(a_{7}=-0.377964473\) \(a_{8}=-0.393146303\) \(a_{9}=-0.141535959\) \(a_{10}=-0.033738435\)
\(a_{11}=+1.492938860\) \(a_{12}=+0.889245647\) \(a_{13}=+0.149216740\) \(a_{14}=-0.075823398\) \(a_{15}=+0.155823778\)
\(a_{16}=+0.880886664\) \(a_{17}=+0.974296390\) \(a_{18}=-0.028393508\) \(a_{19}=-0.090254745\) \(a_{20}=+0.161411090\)
\(a_{21}=+0.350196688\) \(a_{22}=+0.299498247\) \(a_{23}=-0.865665648\) \(a_{24}=+0.364263159\) \(a_{25}=-0.971715705\)
\(a_{26}=+0.029934348\) \(a_{27}=+1.057671131\) \(a_{28}=+0.362753552\) \(a_{29}=+1.078873513\) \(a_{30}=+0.031259785\)
\(a_{31}=-1.553582280\) \(a_{32}=+0.569860848\) \(a_{33}=-1.383257637\) \(a_{34}=+0.195453457\) \(a_{35}=+0.063565820\)
\(a_{36}=+0.135839941\) \(a_{37}=+0.484518475\) \(a_{38}=-0.018105991\) \(a_{39}=-0.138254285\) \(a_{40}=+0.066119091\)
\(a_{41}=+0.611594022\) \(a_{42}=+0.070252907\) \(a_{43}=+0.976974029\) \(a_{44}=-1.432856560\) \(a_{45}=+0.023803426\)
\(a_{46}=-0.173661060\) \(a_{47}=+0.581869447\) \(a_{48}=-0.816170868\) \(a_{49}=+0.142857143\) \(a_{50}=-0.194935746\)
\(a_{51}=-0.902718094\) \(a_{52}=-0.143211614\) \(a_{53}=+1.246108212\) \(a_{54}=+0.212179252\) \(a_{55}=-0.251081491\)
\(a_{56}=+0.148595335\) \(a_{57}=+0.083624030\) \(a_{58}=+0.216432658\) \(a_{59}=+1.275143659\) \(a_{60}=-0.149552757\)
\(a_{61}=-0.537500815\) \(a_{62}=-0.311663915\) \(a_{63}=+0.053495564\) \(a_{64}=-0.766566962\) \(a_{65}=-0.025095175\)
\(a_{66}=-0.277495113\) \(a_{67}=-0.344856593\) \(a_{68}=-0.935086500\) \(a_{69}=+0.802068089\) \(a_{70}=+0.012751930\)
\(a_{71}=+1.467182532\) \(a_{72}=+0.055644339\) \(a_{73}=-1.311670677\) \(a_{74}=+0.097199181\) \(a_{75}=+0.900327004\)
\(a_{76}=+0.086622504\) \(a_{77}=-0.564277849\) \(a_{78}=-0.027735172\) \(a_{79}=+1.795600063\) \(a_{80}=-0.148146949\)
\(a_{81}=-0.838431614\) \(a_{82}=+0.122691788\) \(a_{83}=+0.467057591\) \(a_{84}=-0.336103262\) \(a_{85}=-0.163856536\)
\(a_{86}=+0.195990618\) \(a_{87}=-0.999612286\) \(a_{88}=-0.586943393\) \(a_{89}=-1.595262186\) \(a_{90}=+0.004775202\)
\(a_{91}=-0.056398626\) \(a_{92}=+0.830827528\) \(a_{93}=+1.439445788\) \(a_{94}=+0.116728745\) \(a_{95}=+0.015178984\)
\(a_{96}=-0.527995078\) \(a_{97}=+1.526022847\) \(a_{98}=+0.028658551\) \(a_{99}=-0.211304533\) \(a_{100}=+0.932609674\)

Showing 100 of 1228 available coefficients

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