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: \( 10.5312060637 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.928677526\) \(a_{3}=-0.529403419\) \(a_{4}=+2.719796998\) \(a_{5}=+0.153165864\)
\(a_{6}=+1.021048476\) \(a_{7}=+0.377964473\) \(a_{8}=-3.316933819\) \(a_{9}=-0.719732020\) \(a_{10}=-0.295407560\)
\(a_{11}=-0.598309769\) \(a_{12}=-1.439869830\) \(a_{13}=+1.129024601\) \(a_{14}=-0.728971585\) \(a_{15}=-0.081086532\)
\(a_{16}=+3.677498713\) \(a_{17}=-1.338549674\) \(a_{18}=+1.388130972\) \(a_{19}=-0.908978393\) \(a_{20}=+0.416580058\)
\(a_{21}=-0.200095684\) \(a_{22}=+1.153946605\) \(a_{23}=+0.228912429\) \(a_{24}=+1.755996104\) \(a_{25}=-0.976540218\)
\(a_{26}=-2.177524374\) \(a_{27}=+0.910432011\) \(a_{28}=+1.027986639\) \(a_{29}=+1.153114056\) \(a_{30}=+0.156389772\)
\(a_{31}=+0.178228490\) \(a_{32}=-3.775775299\) \(a_{33}=+0.316747237\) \(a_{34}=+2.581630672\) \(a_{35}=+0.057891255\)
\(a_{36}=-1.957524988\) \(a_{37}=+0.888116568\) \(a_{38}=+1.753126197\) \(a_{39}=-0.597709484\) \(a_{40}=-0.508041035\)
\(a_{41}=+0.113141349\) \(a_{42}=+0.385920049\) \(a_{43}=+0.798466583\) \(a_{44}=-1.627281114\) \(a_{45}=-0.110238377\)
\(a_{46}=-0.441498257\) \(a_{47}=-0.136449091\) \(a_{48}=-1.946880392\) \(a_{49}=+0.142857143\) \(a_{50}=+1.883431171\)
\(a_{51}=+0.708632774\) \(a_{52}=+3.070717721\) \(a_{53}=+0.355738936\) \(a_{54}=-1.755929758\) \(a_{55}=-0.091640633\)
\(a_{56}=-1.253683143\) \(a_{57}=+0.481216269\) \(a_{58}=-2.223985164\) \(a_{59}=-0.171547722\) \(a_{60}=-0.220538907\)
\(a_{61}=+0.468256911\) \(a_{62}=-0.343745282\) \(a_{63}=-0.272033134\) \(a_{64}=+3.604754249\) \(a_{65}=+0.172928029\)
\(a_{66}=-0.610903278\) \(a_{67}=+1.404913910\) \(a_{68}=-3.640583384\) \(a_{69}=-0.121187022\) \(a_{70}=-0.111653563\)
\(a_{71}=+0.184731712\) \(a_{72}=+2.387303478\) \(a_{73}=+1.305252332\) \(a_{74}=-1.712890465\) \(a_{75}=+0.516983730\)
\(a_{76}=-2.472236704\) \(a_{77}=-0.226139837\) \(a_{78}=+1.152788849\) \(a_{79}=-0.530647095\) \(a_{80}=+0.563267269\)
\(a_{81}=+0.237746201\) \(a_{82}=-0.218213176\) \(a_{83}=+1.213666401\) \(a_{84}=-0.544219641\) \(a_{85}=-0.205020118\)
\(a_{86}=-1.539984555\) \(a_{87}=-0.610462523\) \(a_{88}=+1.984553908\) \(a_{89}=-1.518741561\) \(a_{90}=+0.212614280\)
\(a_{91}=+0.426731188\) \(a_{92}=+0.622595337\) \(a_{93}=-0.094354772\) \(a_{94}=+0.263166294\) \(a_{95}=-0.139224461\)
\(a_{96}=+1.998908353\) \(a_{97}=+1.180504466\) \(a_{98}=-0.275525361\) \(a_{99}=+0.430622699\) \(a_{100}=-2.655991154\)

Showing 100 of 1228 available coefficients

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