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: \( 7.4314578005 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.842490650\) \(a_{3}=+1.840592203\) \(a_{4}=-0.290209504\) \(a_{5}=+0.516254794\)
\(a_{6}=+1.550681722\) \(a_{7}=+0.377964473\) \(a_{8}=-1.086989444\) \(a_{9}=+2.387779657\) \(a_{10}=+0.434939837\)
\(a_{11}=+0.427295442\) \(a_{12}=-0.534157351\) \(a_{13}=-0.076844863\) \(a_{14}=+0.318431535\) \(a_{15}=+0.950214549\)
\(a_{16}=-0.625568939\) \(a_{17}=-1.477936641\) \(a_{18}=+2.011682036\) \(a_{19}=-0.331697381\) \(a_{20}=-0.149822048\)
\(a_{21}=+0.695678462\) \(a_{22}=+0.359992415\) \(a_{23}=-0.105530697\) \(a_{24}=-2.000704295\) \(a_{25}=-0.733480987\)
\(a_{26}=-0.064741078\) \(a_{27}=+2.554336416\) \(a_{28}=-0.109688882\) \(a_{29}=-0.275701942\) \(a_{30}=+0.800546873\)
\(a_{31}=-1.279805206\) \(a_{32}=+0.559953462\) \(a_{33}=+0.786476658\) \(a_{34}=-1.245147802\) \(a_{35}=+0.195125971\)
\(a_{36}=-0.692956350\) \(a_{37}=+0.114904033\) \(a_{38}=-0.279451942\) \(a_{39}=-0.141440055\) \(a_{40}=-0.561163512\)
\(a_{41}=+1.276168523\) \(a_{42}=+0.586102600\) \(a_{43}=-0.179968085\) \(a_{44}=-0.124005198\) \(a_{45}=+1.232702696\)
\(a_{46}=-0.088908625\) \(a_{47}=+0.411813032\) \(a_{48}=-1.151417312\) \(a_{49}=+0.142857143\) \(a_{50}=-0.617950874\)
\(a_{51}=-2.720278658\) \(a_{52}=+0.022301110\) \(a_{53}=+1.340402993\) \(a_{54}=+2.152004548\) \(a_{55}=+0.220593320\)
\(a_{56}=-0.410843392\) \(a_{57}=-0.610519613\) \(a_{58}=-0.232276308\) \(a_{59}=+0.103541617\) \(a_{60}=-0.275761293\)
\(a_{61}=+0.183472033\) \(a_{62}=-1.078223920\) \(a_{63}=+0.902495880\) \(a_{64}=+1.097324495\) \(a_{65}=-0.039671529\)
\(a_{66}=+0.662599231\) \(a_{67}=-0.354573519\) \(a_{68}=+0.428911260\) \(a_{69}=-0.194238978\) \(a_{70}=+0.164391806\)
\(a_{71}=-1.184415745\) \(a_{72}=-2.595491282\) \(a_{73}=+1.538389363\) \(a_{74}=+0.096805573\) \(a_{75}=-1.350039386\)
\(a_{76}=+0.096261732\) \(a_{77}=+0.161502496\) \(a_{78}=-0.119161924\) \(a_{79}=+1.720134401\) \(a_{80}=-0.322952964\)
\(a_{81}=+2.313712033\) \(a_{82}=+1.075160049\) \(a_{83}=-0.961375945\) \(a_{84}=-0.201892502\) \(a_{85}=-0.762991877\)
\(a_{86}=-0.151621429\) \(a_{87}=-0.507454844\) \(a_{88}=-0.464465635\) \(a_{89}=-0.083646356\) \(a_{90}=+1.038540496\)
\(a_{91}=-0.029044628\) \(a_{92}=+0.030626011\) \(a_{93}=-2.355599484\) \(a_{94}=+0.346948629\) \(a_{95}=-0.171240363\)
\(a_{96}=+1.030645975\) \(a_{97}=-0.826034559\) \(a_{98}=+0.120355807\) \(a_{99}=+1.020287363\) \(a_{100}=+0.212863154\)

Showing 100 of 1228 available coefficients

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