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: \( 4.11900929292 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.021172946\) \(a_{3}=-0.017722795\) \(a_{4}=+0.042794186\) \(a_{5}=-0.723502780\)
\(a_{6}=+0.018098039\) \(a_{7}=-0.377964473\) \(a_{8}=+0.977472681\) \(a_{9}=-0.999685903\) \(a_{10}=+0.738821466\)
\(a_{11}=+0.416257170\) \(a_{12}=-0.000758433\) \(a_{13}=-1.410426444\) \(a_{14}=+0.385967094\) \(a_{15}=+0.012822492\)
\(a_{16}=-1.040962844\) \(a_{17}=+1.280497897\) \(a_{18}=+1.020852198\) \(a_{19}=-0.027788684\) \(a_{20}=-0.030961713\)
\(a_{21}=+0.006698587\) \(a_{22}=-0.425070560\) \(a_{23}=-1.527251946\) \(a_{24}=-0.017323548\) \(a_{25}=-0.476543727\)
\(a_{26}=+1.440289327\) \(a_{27}=+0.035440024\) \(a_{28}=-0.016174682\) \(a_{29}=+0.673031987\) \(a_{30}=-0.013093982\)
\(a_{31}=+0.210801252\) \(a_{32}=+0.085530413\) \(a_{33}=-0.007377241\) \(a_{34}=-1.307609811\) \(a_{35}=+0.273458347\)
\(a_{36}=-0.042780745\) \(a_{37}=+0.033243094\) \(a_{38}=+0.028377053\) \(a_{39}=+0.024996699\) \(a_{40}=-0.707204202\)
\(a_{41}=+0.943139441\) \(a_{42}=-0.006840416\) \(a_{43}=-1.230192100\) \(a_{44}=+0.017813387\) \(a_{45}=+0.723275530\)
\(a_{46}=+1.559588369\) \(a_{47}=-0.595206974\) \(a_{48}=+0.018448771\) \(a_{49}=+0.142857143\) \(a_{50}=+0.486633562\)
\(a_{51}=-0.022694002\) \(a_{52}=-0.060358052\) \(a_{53}=-1.173262670\) \(a_{54}=-0.036190394\) \(a_{55}=-0.301163220\)
\(a_{56}=-0.369449947\) \(a_{57}=+0.000492493\) \(a_{58}=-0.687282057\) \(a_{59}=-0.635884617\) \(a_{60}=+0.000548728\)
\(a_{61}=+1.833530892\) \(a_{62}=-0.215264535\) \(a_{63}=+0.377845755\) \(a_{64}=+0.953621500\) \(a_{65}=+1.020447454\)
\(a_{66}=+0.007533439\) \(a_{67}=-0.836030095\) \(a_{68}=+0.054797865\) \(a_{69}=+0.027067174\) \(a_{70}=-0.279248266\)
\(a_{71}=-0.191431698\) \(a_{72}=-0.977165659\) \(a_{73}=-0.384240379\) \(a_{74}=-0.033946948\) \(a_{75}=+0.008445687\)
\(a_{76}=-0.001189194\) \(a_{77}=-0.157330422\) \(a_{78}=-0.025525953\) \(a_{79}=-0.636762657\) \(a_{80}=+0.753139511\)
\(a_{81}=+0.999057806\) \(a_{82}=-0.963108482\) \(a_{83}=+1.134556772\) \(a_{84}=+0.000286661\) \(a_{85}=-0.926443789\)
\(a_{86}=+1.256238891\) \(a_{87}=-0.011928008\) \(a_{88}=+0.406880012\) \(a_{89}=-0.681969649\) \(a_{90}=-0.738589404\)
\(a_{91}=+0.533091088\) \(a_{92}=-0.065357504\) \(a_{93}=-0.003735987\) \(a_{94}=+0.607809259\) \(a_{95}=+0.020105190\)
\(a_{96}=-0.001515838\) \(a_{97}=+0.147786829\) \(a_{98}=-0.145881849\) \(a_{99}=-0.416126424\) \(a_{100}=-0.020393301\)

Showing 100 of 1228 available coefficients

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