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: \( 6.06885693385 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.055899966\) \(a_{3}=-0.938402764\) \(a_{4}=+0.114924739\) \(a_{5}=+0.732453443\)
\(a_{6}=+0.990859447\) \(a_{7}=-0.377964473\) \(a_{8}=+0.934550938\) \(a_{9}=-0.119400252\) \(a_{10}=-0.773397566\)
\(a_{11}=+0.707523953\) \(a_{12}=-0.107845693\) \(a_{13}=+1.052261616\) \(a_{14}=+0.399092674\) \(a_{15}=-0.687336336\)
\(a_{16}=-1.101717044\) \(a_{17}=-0.848894106\) \(a_{18}=+0.126074722\) \(a_{19}=+1.856224726\) \(a_{20}=+0.084177021\)
\(a_{21}=+0.354682906\) \(a_{22}=-0.747074518\) \(a_{23}=+0.975737598\) \(a_{24}=-0.876985184\) \(a_{25}=-0.463511954\)
\(a_{26}=-1.111083005\) \(a_{27}=+1.050448291\) \(a_{28}=-0.043437468\) \(a_{29}=-0.373038633\) \(a_{30}=+0.725758414\)
\(a_{31}=-0.001703684\) \(a_{32}=+0.228752051\) \(a_{33}=-0.663942433\) \(a_{34}=+0.896347258\) \(a_{35}=-0.276841380\)
\(a_{36}=-0.013722043\) \(a_{37}=+1.905934749\) \(a_{38}=-1.959987626\) \(a_{39}=-0.987445210\) \(a_{40}=+0.684515052\)
\(a_{41}=-0.427887750\) \(a_{42}=-0.374509669\) \(a_{43}=+0.958919221\) \(a_{44}=+0.081312006\) \(a_{45}=-0.087455126\)
\(a_{46}=-1.030281297\) \(a_{47}=-0.340367663\) \(a_{48}=+1.033854319\) \(a_{49}=+0.142857143\) \(a_{50}=+0.489422256\)
\(a_{51}=+0.796604576\) \(a_{52}=+0.120930892\) \(a_{53}=+0.665346144\) \(a_{54}=-1.109168315\) \(a_{55}=+0.518228355\)
\(a_{56}=-0.353227053\) \(a_{57}=-1.741886414\) \(a_{58}=+0.393891480\) \(a_{59}=-0.803457679\) \(a_{60}=-0.078991949\)
\(a_{61}=-0.544232925\) \(a_{62}=+0.001798920\) \(a_{63}=+0.045129053\) \(a_{64}=+0.860177760\) \(a_{65}=+0.770732644\)
\(a_{66}=+0.701056793\) \(a_{67}=+1.420745121\) \(a_{68}=-0.097558934\) \(a_{69}=-0.915634859\) \(a_{70}=+0.292316803\)
\(a_{71}=-0.017703755\) \(a_{72}=-0.111585617\) \(a_{73}=-0.385934033\) \(a_{74}=-2.012476438\) \(a_{75}=+0.434960899\)
\(a_{76}=+0.213326143\) \(a_{77}=-0.267418918\) \(a_{78}=+1.042643364\) \(a_{79}=+0.404965152\) \(a_{80}=-0.806956442\)
\(a_{81}=-0.866343328\) \(a_{82}=+0.451806661\) \(a_{83}=+0.877745295\) \(a_{84}=+0.040761841\) \(a_{85}=-0.621775411\)
\(a_{86}=-1.012522773\) \(a_{87}=+0.350060485\) \(a_{88}=+0.661217174\) \(a_{89}=+0.596428018\) \(a_{90}=+0.092343864\)
\(a_{91}=-0.397717507\) \(a_{92}=+0.112136389\) \(a_{93}=+0.001598742\) \(a_{94}=+0.359394204\) \(a_{95}=+1.359598192\)
\(a_{96}=-0.214661557\) \(a_{97}=-0.338933231\) \(a_{98}=-0.150842852\) \(a_{99}=-0.084478538\) \(a_{100}=-0.053268990\)

Showing 100 of 1228 available coefficients

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